LMFDB - Embedded newform 4021.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1078466528$
Analytic rank:	$0$
Dimension:	$182$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58653 q^{2} +3.00156 q^{3} +4.69012 q^{4} +3.01819 q^{5} -7.76362 q^{6} +1.43921 q^{7} -6.95807 q^{8} +6.00937 q^{9} +O(q^{10})$	\(q-2.58653 q^{2} +3.00156 q^{3} +4.69012 q^{4} +3.01819 q^{5} -7.76362 q^{6} +1.43921 q^{7} -6.95807 q^{8} +6.00937 q^{9} -7.80662 q^{10} +5.06689 q^{11} +14.0777 q^{12} -4.59337 q^{13} -3.72256 q^{14} +9.05927 q^{15} +8.61699 q^{16} -6.68326 q^{17} -15.5434 q^{18} +7.92577 q^{19} +14.1557 q^{20} +4.31989 q^{21} -13.1057 q^{22} +4.59880 q^{23} -20.8851 q^{24} +4.10944 q^{25} +11.8809 q^{26} +9.03282 q^{27} +6.75008 q^{28} -8.82195 q^{29} -23.4320 q^{30} -8.60760 q^{31} -8.37193 q^{32} +15.2086 q^{33} +17.2864 q^{34} +4.34381 q^{35} +28.1847 q^{36} +10.9620 q^{37} -20.5002 q^{38} -13.7873 q^{39} -21.0007 q^{40} +9.91870 q^{41} -11.1735 q^{42} -1.64947 q^{43} +23.7643 q^{44} +18.1374 q^{45} -11.8949 q^{46} -0.646357 q^{47} +25.8644 q^{48} -4.92867 q^{49} -10.6292 q^{50} -20.0602 q^{51} -21.5434 q^{52} +0.401339 q^{53} -23.3636 q^{54} +15.2928 q^{55} -10.0141 q^{56} +23.7897 q^{57} +22.8182 q^{58} -0.169090 q^{59} +42.4891 q^{60} -10.5852 q^{61} +22.2638 q^{62} +8.64877 q^{63} +4.42025 q^{64} -13.8636 q^{65} -39.3374 q^{66} +3.00365 q^{67} -31.3453 q^{68} +13.8036 q^{69} -11.2354 q^{70} +8.29203 q^{71} -41.8136 q^{72} +8.11030 q^{73} -28.3534 q^{74} +12.3348 q^{75} +37.1728 q^{76} +7.29234 q^{77} +35.6612 q^{78} -6.44433 q^{79} +26.0077 q^{80} +9.08444 q^{81} -25.6550 q^{82} -5.04354 q^{83} +20.2608 q^{84} -20.1713 q^{85} +4.26640 q^{86} -26.4796 q^{87} -35.2558 q^{88} -0.600222 q^{89} -46.9129 q^{90} -6.61083 q^{91} +21.5689 q^{92} -25.8362 q^{93} +1.67182 q^{94} +23.9214 q^{95} -25.1289 q^{96} -7.57527 q^{97} +12.7481 q^{98} +30.4489 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) $ 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.58653	−1.82895	−0.914475	−	0.404642i	$-0.867396\pi$
$2$	−2.58653	−1.82895	−0.914475	+	0.404642i	$0.867396\pi$
$3$	3.00156	1.73295	0.866476	−	0.499218i	$-0.166379\pi$
$3$	3.00156	1.73295	0.866476	+	0.499218i	$0.166379\pi$
$4$	4.69012	2.34506
$5$	3.01819	1.34977	0.674887	−	0.737921i	$-0.264192\pi$
$5$	3.01819	1.34977	0.674887	+	0.737921i	$0.264192\pi$
$6$	−7.76362	−3.16948
$7$	1.43921	0.543971	0.271986	−	0.962301i	$-0.412320\pi$
$7$	1.43921	0.543971	0.271986	+	0.962301i	$0.412320\pi$
$8$	−6.95807	−2.46005
$9$	6.00937	2.00312
$10$	−7.80662	−2.46867
$11$	5.06689	1.52773	0.763863	−	0.645378i	$-0.223300\pi$
$11$	5.06689	1.52773	0.763863	+	0.645378i	$0.223300\pi$
$12$	14.0777	4.06388
$13$	−4.59337	−1.27397	−0.636986	−	0.770876i	$-0.719819\pi$
$13$	−4.59337	−1.27397	−0.636986	+	0.770876i	$0.719819\pi$
$14$	−3.72256	−0.994897
$15$	9.05927	2.33909
$16$	8.61699	2.15425
$17$	−6.68326	−1.62093	−0.810464	−	0.585789i	$-0.800785\pi$
$17$	−6.68326	−1.62093	−0.810464	+	0.585789i	$0.800785\pi$
$18$	−15.5434	−3.66362
$19$	7.92577	1.81830	0.909148	−	0.416474i	$-0.136734\pi$
$19$	7.92577	1.81830	0.909148	+	0.416474i	$0.136734\pi$
$20$	14.1557	3.16530
$21$	4.31989	0.942676
$22$	−13.1057	−2.79414
$23$	4.59880	0.958916	0.479458	−	0.877565i	$-0.340833\pi$
$23$	4.59880	0.958916	0.479458	+	0.877565i	$0.340833\pi$
$24$	−20.8851	−4.26315
$25$	4.10944	0.821889
$26$	11.8809	2.33003
$27$	9.03282	1.73837
$28$	6.75008	1.27565
$29$	−8.82195	−1.63820	−0.819098	−	0.573654i	$-0.805525\pi$
$29$	−8.82195	−1.63820	−0.819098	+	0.573654i	$0.805525\pi$
$30$	−23.4320	−4.27809
$31$	−8.60760	−1.54597	−0.772986	−	0.634424i	$-0.781237\pi$
$31$	−8.60760	−1.54597	−0.772986	+	0.634424i	$0.781237\pi$
$32$	−8.37193	−1.47996
$33$	15.2086	2.64748
$34$	17.2864	2.96460
$35$	4.34381	0.734238
$36$	28.1847	4.69745
$37$	10.9620	1.80214	0.901068	−	0.433677i	$-0.142784\pi$
$37$	10.9620	1.80214	0.901068	+	0.433677i	$0.142784\pi$
$38$	−20.5002	−3.32557
$39$	−13.7873	−2.20773
$40$	−21.0007	−3.32051
$41$	9.91870	1.54904	0.774520	−	0.632549i	$-0.217991\pi$
$41$	9.91870	1.54904	0.774520	+	0.632549i	$0.217991\pi$
$42$	−11.1735	−1.72411
$43$	−1.64947	−0.251542	−0.125771	−	0.992059i	$-0.540140\pi$
$43$	−1.64947	−0.251542	−0.125771	+	0.992059i	$0.540140\pi$
$44$	23.7643	3.58261
$45$	18.1374	2.70376
$46$	−11.8949	−1.75381
$47$	−0.646357	−0.0942809	−0.0471404	−	0.998888i	$-0.515011\pi$
$47$	−0.646357	−0.0942809	−0.0471404	+	0.998888i	$0.515011\pi$
$48$	25.8644	3.73321
$49$	−4.92867	−0.704095
$50$	−10.6292	−1.50319
$51$	−20.0602	−2.80899
$52$	−21.5434	−2.98754
$53$	0.401339	0.0551281	0.0275641	−	0.999620i	$-0.491225\pi$
$53$	0.401339	0.0551281	0.0275641	+	0.999620i	$0.491225\pi$
$54$	−23.3636	−3.17939
$55$	15.2928	2.06208
$56$	−10.0141	−1.33820
$57$	23.7897	3.15102
$58$	22.8182	2.99618
$59$	−0.169090	−0.0220137	−0.0110068	−	0.999939i	$-0.503504\pi$
$59$	−0.169090	−0.0220137	−0.0110068	+	0.999939i	$0.503504\pi$
$60$	42.4891	5.48532
$61$	−10.5852	−1.35529	−0.677647	−	0.735387i	$-0.737000\pi$
$61$	−10.5852	−1.35529	−0.677647	+	0.735387i	$0.737000\pi$
$62$	22.2638	2.82750
$63$	8.64877	1.08964
$64$	4.42025	0.552531
$65$	−13.8636	−1.71957
$66$	−39.3374	−4.84210
$67$	3.00365	0.366954	0.183477	−	0.983024i	$-0.441265\pi$
$67$	3.00365	0.366954	0.183477	+	0.983024i	$0.441265\pi$
$68$	−31.3453	−3.80117
$69$	13.8036	1.66176
$70$	−11.2354	−1.34289
$71$	8.29203	0.984082	0.492041	−	0.870572i	$-0.336251\pi$
$71$	8.29203	0.984082	0.492041	+	0.870572i	$0.336251\pi$
$72$	−41.8136	−4.92778
$73$	8.11030	0.949239	0.474620	−	0.880191i	$-0.342586\pi$
$73$	8.11030	0.949239	0.474620	+	0.880191i	$0.342586\pi$
$74$	−28.3534	−3.29602
$75$	12.3348	1.42429
$76$	37.1728	4.26401
$77$	7.29234	0.831039
$78$	35.6612	4.03783
$79$	−6.44433	−0.725043	−0.362522	−	0.931975i	$-0.618084\pi$
$79$	−6.44433	−0.725043	−0.362522	+	0.931975i	$0.618084\pi$
$80$	26.0077	2.90775
$81$	9.08444	1.00938
$82$	−25.6550	−2.83312
$83$	−5.04354	−0.553601	−0.276800	−	0.960927i	$-0.589274\pi$
$83$	−5.04354	−0.553601	−0.276800	+	0.960927i	$0.589274\pi$
$84$	20.2608	2.21063
$85$	−20.1713	−2.18789
$86$	4.26640	0.460058
$87$	−26.4796	−2.83891
$88$	−35.2558	−3.75828
$89$	−0.600222	−0.0636234	−0.0318117	−	0.999494i	$-0.510128\pi$
$89$	−0.600222	−0.0636234	−0.0318117	+	0.999494i	$0.510128\pi$
$90$	−46.9129	−4.94505
$91$	−6.61083	−0.693004
$92$	21.5689	2.24871
$93$	−25.8362	−2.67909
$94$	1.67182	0.172435
$95$	23.9214	2.45429
$96$	−25.1289	−2.56470
$97$	−7.57527	−0.769152	−0.384576	−	0.923093i	$-0.625652\pi$
$97$	−7.57527	−0.769152	−0.384576	+	0.923093i	$0.625652\pi$
$98$	12.7481	1.28776
$99$	30.4489	3.06022
$100$	19.2738	1.92738
$101$	6.49299	0.646076	0.323038	−	0.946386i	$-0.395296\pi$
$101$	6.49299	0.646076	0.323038	+	0.946386i	$0.395296\pi$
$102$	51.8863	5.13750
$103$	2.15905	0.212737	0.106369	−	0.994327i	$-0.466078\pi$
$103$	2.15905	0.212737	0.106369	+	0.994327i	$0.466078\pi$
$104$	31.9610	3.13403
$105$	13.0382	1.27240
$106$	−1.03807	−0.100827
$107$	3.47781	0.336213	0.168106	−	0.985769i	$-0.446235\pi$
$107$	3.47781	0.336213	0.168106	+	0.985769i	$0.446235\pi$
$108$	42.3650	4.07657
$109$	20.2184	1.93657	0.968286	−	0.249845i	$-0.0803796\pi$
$109$	20.2184	1.93657	0.968286	+	0.249845i	$0.0803796\pi$
$110$	−39.5553	−3.77145
$111$	32.9030	3.12302
$112$	12.4017	1.17185
$113$	9.50949	0.894577	0.447289	−	0.894390i	$-0.352390\pi$
$113$	9.50949	0.894577	0.447289	+	0.894390i	$0.352390\pi$
$114$	−61.5326	−5.76306
$115$	13.8800	1.29432
$116$	−41.3760	−3.84167
$117$	−27.6033	−2.55192
$118$	0.437356	0.0402619
$119$	−9.61863	−0.881738
$120$	−63.0350	−5.75428
$121$	14.6734	1.33395
$122$	27.3789	2.47877
$123$	29.7716	2.68441
$124$	−40.3707	−3.62539
$125$	−2.68786	−0.240410
$126$	−22.3703	−1.99290
$127$	−3.82170	−0.339121	−0.169560	−	0.985520i	$-0.554235\pi$
$127$	−3.82170	−0.339121	−0.169560	+	0.985520i	$0.554235\pi$
$128$	5.31077	0.469410
$129$	−4.95099	−0.435910
$130$	35.8587	3.14501
$131$	0.250535	0.0218893	0.0109447	−	0.999940i	$-0.496516\pi$
$131$	0.250535	0.0218893	0.0109447	+	0.999940i	$0.496516\pi$
$132$	71.3301	6.20849
$133$	11.4069	0.989101
$134$	−7.76902	−0.671141
$135$	27.2627	2.34640
$136$	46.5025	3.98756
$137$	15.2138	1.29980	0.649902	−	0.760018i	$-0.274810\pi$
$137$	15.2138	1.29980	0.649902	+	0.760018i	$0.274810\pi$
$138$	−35.7033	−3.03927
$139$	12.2777	1.04138	0.520692	−	0.853745i	$-0.325674\pi$
$139$	12.2777	1.04138	0.520692	+	0.853745i	$0.325674\pi$
$140$	20.3730	1.72183
$141$	−1.94008	−0.163384
$142$	−21.4475	−1.79984
$143$	−23.2741	−1.94628
$144$	51.7827	4.31522
$145$	−26.6263	−2.21119
$146$	−20.9775	−1.73611
$147$	−14.7937	−1.22016
$148$	51.4130	4.22612
$149$	11.9793	0.981382	0.490691	−	0.871334i	$-0.336744\pi$
$149$	11.9793	0.981382	0.490691	+	0.871334i	$0.336744\pi$
$150$	−31.9042	−2.60496
$151$	−4.16430	−0.338886	−0.169443	−	0.985540i	$-0.554197\pi$
$151$	−4.16430	−0.338886	−0.169443	+	0.985540i	$0.554197\pi$
$152$	−55.1480	−4.47309
$153$	−40.1622	−3.24692
$154$	−18.8618	−1.51993
$155$	−25.9793	−2.08671
$156$	−64.6640	−5.17726
$157$	−15.6718	−1.25075	−0.625374	−	0.780325i	$-0.715054\pi$
$157$	−15.6718	−1.25075	−0.625374	+	0.780325i	$0.715054\pi$
$158$	16.6684	1.32607
$159$	1.20464	0.0955345
$160$	−25.2680	−1.99761
$161$	6.61865	0.521623
$162$	−23.4972	−1.84611
$163$	8.46999	0.663421	0.331710	−	0.943381i	$-0.392374\pi$
$163$	8.46999	0.663421	0.331710	+	0.943381i	$0.392374\pi$
$164$	46.5199	3.63259
$165$	45.9024	3.57349
$166$	13.0453	1.01251
$167$	−24.2823	−1.87902	−0.939510	−	0.342522i	$-0.888719\pi$
$167$	−24.2823	−1.87902	−0.939510	+	0.342522i	$0.888719\pi$
$168$	−30.0581	−2.31903
$169$	8.09903	0.623002
$170$	52.1736	4.00153
$171$	47.6289	3.64227
$172$	−7.73621	−0.589881
$173$	−3.18179	−0.241907	−0.120953	−	0.992658i	$-0.538595\pi$
$173$	−3.18179	−0.241907	−0.120953	+	0.992658i	$0.538595\pi$
$174$	68.4903	5.19223
$175$	5.91437	0.447084
$176$	43.6614	3.29110
$177$	−0.507535	−0.0381486
$178$	1.55249	0.116364
$179$	7.57342	0.566064	0.283032	−	0.959110i	$-0.408660\pi$
$179$	7.57342	0.566064	0.283032	+	0.959110i	$0.408660\pi$
$180$	85.0666	6.34049
$181$	−8.34578	−0.620337	−0.310169	−	0.950682i	$-0.600385\pi$
$181$	−8.34578	−0.620337	−0.310169	+	0.950682i	$0.600385\pi$
$182$	17.0991	1.26747
$183$	−31.7721	−2.34866
$184$	−31.9987	−2.35898
$185$	33.0853	2.43248
$186$	66.8261	4.89993
$187$	−33.8633	−2.47633
$188$	−3.03149	−0.221094
$189$	13.0001	0.945622
$190$	−61.8734	−4.48877
$191$	13.7570	0.995420	0.497710	−	0.867343i	$-0.334174\pi$
$191$	13.7570	0.995420	0.497710	+	0.867343i	$0.334174\pi$
$192$	13.2677	0.957511
$193$	−13.5171	−0.972982	−0.486491	−	0.873686i	$-0.661723\pi$
$193$	−13.5171	−0.972982	−0.486491	+	0.873686i	$0.661723\pi$
$194$	19.5936	1.40674
$195$	−41.6126	−2.97994
$196$	−23.1160	−1.65115
$197$	8.12820	0.579110	0.289555	−	0.957161i	$-0.406493\pi$
$197$	8.12820	0.579110	0.289555	+	0.957161i	$0.406493\pi$
$198$	−78.7568	−5.59700
$199$	5.48651	0.388928	0.194464	−	0.980910i	$-0.437703\pi$
$199$	5.48651	0.388928	0.194464	+	0.980910i	$0.437703\pi$
$200$	−28.5938	−2.02189
$201$	9.01564	0.635914
$202$	−16.7943	−1.18164
$203$	−12.6967	−0.891131
$204$	−94.0848	−6.58725
$205$	29.9365	2.09085
$206$	−5.58443	−0.389086
$207$	27.6359	1.92083
$208$	−39.5810	−2.74445
$209$	40.1590	2.77786
$210$	−33.7237	−2.32716
$211$	−11.4741	−0.789909	−0.394955	−	0.918701i	$-0.629240\pi$
$211$	−11.4741	−0.789909	−0.394955	+	0.918701i	$0.629240\pi$
$212$	1.88233	0.129279
$213$	24.8890	1.70537
$214$	−8.99545	−0.614916
$215$	−4.97841	−0.339525
$216$	−62.8510	−4.27647
$217$	−12.3882	−0.840964
$218$	−52.2954	−3.54189
$219$	24.3436	1.64499
$220$	71.7252	4.83571
$221$	30.6987	2.06501
$222$	−85.1046	−5.71184
$223$	−7.62397	−0.510539	−0.255270	−	0.966870i	$-0.582164\pi$
$223$	−7.62397	−0.510539	−0.255270	+	0.966870i	$0.582164\pi$
$224$	−12.0490	−0.805057
$225$	24.6952	1.64635
$226$	−24.5965	−1.63614
$227$	−2.60279	−0.172753	−0.0863767	−	0.996263i	$-0.527529\pi$
$227$	−2.60279	−0.172753	−0.0863767	+	0.996263i	$0.527529\pi$
$228$	111.576	7.38933
$229$	−4.20891	−0.278133	−0.139066	−	0.990283i	$-0.544410\pi$
$229$	−4.20891	−0.278133	−0.139066	+	0.990283i	$0.544410\pi$
$230$	−35.9011	−2.36725
$231$	21.8884	1.44015
$232$	61.3837	4.03004
$233$	−4.30047	−0.281733	−0.140866	−	0.990029i	$-0.544989\pi$
$233$	−4.30047	−0.281733	−0.140866	+	0.990029i	$0.544989\pi$
$234$	71.3966	4.66734
$235$	−1.95083	−0.127258
$236$	−0.793053	−0.0516234
$237$	−19.3430	−1.25647
$238$	24.8788	1.61266
$239$	7.15106	0.462564	0.231282	−	0.972887i	$-0.425708\pi$
$239$	7.15106	0.462564	0.231282	+	0.972887i	$0.425708\pi$
$240$	78.0636	5.03899
$241$	−3.98919	−0.256966	−0.128483	−	0.991712i	$-0.541011\pi$
$241$	−3.98919	−0.256966	−0.128483	+	0.991712i	$0.541011\pi$
$242$	−37.9532	−2.43972
$243$	0.169061	0.0108453
$244$	−49.6458	−3.17825
$245$	−14.8756	−0.950369
$246$	−77.0050	−4.90966
$247$	−36.4060	−2.31646
$248$	59.8923	3.80316
$249$	−15.1385	−0.959364
$250$	6.95222	0.439697
$251$	−3.87391	−0.244519	−0.122259	−	0.992498i	$-0.539014\pi$
$251$	−3.87391	−0.244519	−0.122259	+	0.992498i	$0.539014\pi$
$252$	40.5638	2.55528
$253$	23.3016	1.46496
$254$	9.88492	0.620235
$255$	−60.5454	−3.79150
$256$	−22.5769	−1.41106
$257$	−29.4265	−1.83557	−0.917786	−	0.397075i	$-0.870025\pi$
$257$	−29.4265	−1.83557	−0.917786	+	0.397075i	$0.870025\pi$
$258$	12.8059	0.797258
$259$	15.7766	0.980311
$260$	−65.0221	−4.03250
$261$	−53.0144	−3.28151
$262$	−0.648015	−0.0400345
$263$	−27.8368	−1.71649	−0.858246	−	0.513239i	$-0.828445\pi$
$263$	−27.8368	−1.71649	−0.858246	+	0.513239i	$0.828445\pi$
$264$	−105.822	−6.51292
$265$	1.21132	0.0744105
$266$	−29.5042	−1.80902
$267$	−1.80160	−0.110256
$268$	14.0875	0.860529
$269$	−7.05650	−0.430243	−0.215121	−	0.976587i	$-0.569015\pi$
$269$	−7.05650	−0.430243	−0.215121	+	0.976587i	$0.569015\pi$
$270$	−70.5158	−4.29145
$271$	−22.2925	−1.35418	−0.677088	−	0.735902i	$-0.736758\pi$
$271$	−22.2925	−1.35418	−0.677088	+	0.735902i	$0.736758\pi$
$272$	−57.5895	−3.49188
$273$	−19.8428	−1.20094
$274$	−39.3509	−2.37728
$275$	20.8221	1.25562
$276$	64.7404	3.89692
$277$	−11.9068	−0.715411	−0.357706	−	0.933834i	$-0.616441\pi$
$277$	−11.9068	−0.715411	−0.357706	+	0.933834i	$0.616441\pi$
$278$	−31.7567	−1.90464
$279$	−51.7263	−3.09677
$280$	−30.2245	−1.80626
$281$	5.80386	0.346229	0.173115	−	0.984902i	$-0.444617\pi$
$281$	5.80386	0.346229	0.173115	+	0.984902i	$0.444617\pi$
$282$	5.01807	0.298822
$283$	−30.6435	−1.82157	−0.910785	−	0.412882i	$-0.864522\pi$
$283$	−30.6435	−1.82157	−0.910785	+	0.412882i	$0.864522\pi$
$284$	38.8906	2.30773
$285$	71.8017	4.25316
$286$	60.1991	3.55965
$287$	14.2751	0.842633
$288$	−50.3101	−2.96455
$289$	27.6659	1.62741
$290$	68.8696	4.04416
$291$	−22.7376	−1.33290
$292$	38.0383	2.22602
$293$	−3.61225	−0.211030	−0.105515	−	0.994418i	$-0.533649\pi$
$293$	−3.61225	−0.211030	−0.105515	+	0.994418i	$0.533649\pi$
$294$	38.2643	2.23162
$295$	−0.510346	−0.0297135
$296$	−76.2741	−4.43334
$297$	45.7683	2.65575
$298$	−30.9848	−1.79490
$299$	−21.1240	−1.22163
$300$	57.8515	3.34006
$301$	−2.37394	−0.136832
$302$	10.7711	0.619806
$303$	19.4891	1.11962
$304$	68.2962	3.91706
$305$	−31.9481	−1.82934
$306$	103.881	5.93846
$307$	−7.33716	−0.418754	−0.209377	−	0.977835i	$-0.567144\pi$
$307$	−7.33716	−0.418754	−0.209377	+	0.977835i	$0.567144\pi$
$308$	34.2019	1.94884
$309$	6.48051	0.368663
$310$	67.1963	3.81649
$311$	−23.4992	−1.33252	−0.666258	−	0.745722i	$-0.732105\pi$
$311$	−23.4992	−1.33252	−0.666258	+	0.745722i	$0.732105\pi$
$312$	95.9328	5.43113
$313$	2.74304	0.155046	0.0775228	−	0.996991i	$-0.475299\pi$
$313$	2.74304	0.155046	0.0775228	+	0.996991i	$0.475299\pi$
$314$	40.5356	2.28756
$315$	26.1036	1.47077
$316$	−30.2247	−1.70027
$317$	−19.4667	−1.09336	−0.546678	−	0.837343i	$-0.684108\pi$
$317$	−19.4667	−1.09336	−0.546678	+	0.837343i	$0.684108\pi$
$318$	−3.11584	−0.174728
$319$	−44.6999	−2.50271
$320$	13.3411	0.745792
$321$	10.4389	0.582641
$322$	−17.1193	−0.954022
$323$	−52.9699	−2.94733
$324$	42.6071	2.36706
$325$	−18.8762	−1.04706
$326$	−21.9079	−1.21336
$327$	60.6868	3.35599
$328$	−69.0150	−3.81071
$329$	−0.930246	−0.0512861
$330$	−118.728	−6.53574
$331$	−32.7076	−1.79777	−0.898886	−	0.438183i	$-0.855622\pi$
$331$	−32.7076	−1.79777	−0.898886	+	0.438183i	$0.855622\pi$
$332$	−23.6548	−1.29823
$333$	65.8746	3.60990
$334$	62.8068	3.43663
$335$	9.06557	0.495305
$336$	37.2244	2.03076
$337$	4.09382	0.223005	0.111502	−	0.993764i	$-0.464434\pi$
$337$	4.09382	0.223005	0.111502	+	0.993764i	$0.464434\pi$
$338$	−20.9484	−1.13944
$339$	28.5433	1.55026
$340$	−94.6059	−5.13072
$341$	−43.6138	−2.36182
$342$	−123.193	−6.66153
$343$	−17.1679	−0.926979
$344$	11.4771	0.618805
$345$	41.6618	2.24299
$346$	8.22977	0.442435
$347$	20.4529	1.09797	0.548986	−	0.835832i	$-0.315014\pi$
$347$	20.4529	1.09797	0.548986	+	0.835832i	$0.315014\pi$
$348$	−124.193	−6.65743
$349$	17.7225	0.948661	0.474331	−	0.880347i	$-0.342690\pi$
$349$	17.7225	0.948661	0.474331	+	0.880347i	$0.342690\pi$
$350$	−15.2977	−0.817695
$351$	−41.4911	−2.21463
$352$	−42.4197	−2.26098
$353$	28.5481	1.51946	0.759730	−	0.650239i	$-0.225331\pi$
$353$	28.5481	1.51946	0.759730	+	0.650239i	$0.225331\pi$
$354$	1.31275	0.0697720
$355$	25.0269	1.32829
$356$	−2.81511	−0.149201
$357$	−28.8709	−1.52801
$358$	−19.5889	−1.03530
$359$	7.46012	0.393730	0.196865	−	0.980431i	$-0.436924\pi$
$359$	7.46012	0.393730	0.196865	+	0.980431i	$0.436924\pi$
$360$	−126.201	−6.65139
$361$	43.8178	2.30620
$362$	21.5866	1.13457
$363$	44.0432	2.31167
$364$	−31.0056	−1.62514
$365$	24.4784	1.28126
$366$	82.1794	4.29558
$367$	−13.6193	−0.710923	−0.355462	−	0.934691i	$-0.615676\pi$
$367$	−13.6193	−0.710923	−0.355462	+	0.934691i	$0.615676\pi$
$368$	39.6278	2.06574
$369$	59.6051	3.10292
$370$	−85.5759	−4.44888
$371$	0.577612	0.0299881
$372$	−121.175	−6.28264
$373$	−28.8187	−1.49218	−0.746089	−	0.665846i	$-0.768071\pi$
$373$	−28.8187	−1.49218	−0.746089	+	0.665846i	$0.768071\pi$
$374$	87.5885	4.52909
$375$	−8.06778	−0.416618
$376$	4.49740	0.231936
$377$	40.5225	2.08701
$378$	−33.6252	−1.72950
$379$	−2.63594	−0.135399	−0.0676996	−	0.997706i	$-0.521566\pi$
$379$	−2.63594	−0.135399	−0.0676996	+	0.997706i	$0.521566\pi$
$380$	112.194	5.75545
$381$	−11.4711	−0.587680
$382$	−35.5828	−1.82057
$383$	−26.7787	−1.36833	−0.684165	−	0.729327i	$-0.739833\pi$
$383$	−26.7787	−1.36833	−0.684165	+	0.729327i	$0.739833\pi$
$384$	15.9406	0.813465
$385$	22.0096	1.12171
$386$	34.9623	1.77954
$387$	−9.91228	−0.503870
$388$	−35.5289	−1.80371
$389$	37.9071	1.92197	0.960984	−	0.276605i	$-0.0892093\pi$
$389$	37.9071	1.92197	0.960984	+	0.276605i	$0.0892093\pi$
$390$	107.632	5.45016
$391$	−30.7349	−1.55433
$392$	34.2940	1.73211
$393$	0.751996	0.0379332
$394$	−21.0238	−1.05916
$395$	−19.4502	−0.978644
$396$	142.809	7.17641
$397$	−1.33203	−0.0668528	−0.0334264	−	0.999441i	$-0.510642\pi$
$397$	−1.33203	−0.0668528	−0.0334264	+	0.999441i	$0.510642\pi$
$398$	−14.1910	−0.711330
$399$	34.2384	1.71406
$400$	35.4110	1.77055
$401$	13.6183	0.680066	0.340033	−	0.940414i	$-0.389562\pi$
$401$	13.6183	0.680066	0.340033	+	0.940414i	$0.389562\pi$
$402$	−23.3192	−1.16306
$403$	39.5379	1.96952
$404$	30.4529	1.51509
$405$	27.4185	1.36244
$406$	32.8403	1.62984
$407$	55.5431	2.75317
$408$	139.580	6.91025
$409$	−6.80957	−0.336711	−0.168356	−	0.985726i	$-0.553846\pi$
$409$	−6.80957	−0.336711	−0.168356	+	0.985726i	$0.553846\pi$
$410$	−77.4315	−3.82407
$411$	45.6652	2.25250
$412$	10.1262	0.498881
$413$	−0.243357	−0.0119748
$414$	−71.4810	−3.51310
$415$	−15.2224	−0.747236
$416$	38.4554	1.88543
$417$	36.8524	1.80467
$418$	−103.872	−5.08056
$419$	−0.120549	−0.00588920	−0.00294460	−	0.999996i	$-0.500937\pi$
$419$	−0.120549	−0.00588920	−0.00294460	+	0.999996i	$0.500937\pi$
$420$	61.1508	2.98385
$421$	2.10659	0.102669	0.0513345	−	0.998682i	$-0.483653\pi$
$421$	2.10659	0.102669	0.0513345	+	0.998682i	$0.483653\pi$
$422$	29.6781	1.44471
$423$	−3.88420	−0.188856
$424$	−2.79254	−0.135618
$425$	−27.4645	−1.33222
$426$	−64.3761	−3.11903
$427$	−15.2343	−0.737241
$428$	16.3113	0.788439
$429$	−69.8587	−3.37281
$430$	12.8768	0.620974
$431$	8.17717	0.393880	0.196940	−	0.980416i	$-0.436900\pi$
$431$	8.17717	0.393880	0.196940	+	0.980416i	$0.436900\pi$
$432$	77.8357	3.74487
$433$	−23.1737	−1.11366	−0.556829	−	0.830627i	$-0.687982\pi$
$433$	−23.1737	−1.11366	−0.556829	+	0.830627i	$0.687982\pi$
$434$	32.0423	1.53808
$435$	−79.9204	−3.83189
$436$	94.8267	4.54138
$437$	36.4490	1.74359
$438$	−62.9653	−3.00860
$439$	−15.1756	−0.724293	−0.362146	−	0.932121i	$-0.617956\pi$
$439$	−15.1756	−0.724293	−0.362146	+	0.932121i	$0.617956\pi$
$440$	−106.409	−5.07283
$441$	−29.6182	−1.41039
$442$	−79.4029	−3.77681
$443$	15.0513	0.715107	0.357553	−	0.933893i	$-0.383611\pi$
$443$	15.0513	0.715107	0.357553	+	0.933893i	$0.383611\pi$
$444$	154.319	7.32366
$445$	−1.81158	−0.0858771
$446$	19.7196	0.933751
$447$	35.9566	1.70069
$448$	6.36168	0.300561
$449$	20.8411	0.983551	0.491776	−	0.870722i	$-0.336348\pi$
$449$	20.8411	0.983551	0.491776	+	0.870722i	$0.336348\pi$
$450$	−63.8748	−3.01108
$451$	50.2570	2.36651
$452$	44.6006	2.09784
$453$	−12.4994	−0.587273
$454$	6.73220	0.315958
$455$	−19.9527	−0.935398
$456$	−165.530	−7.75166
$457$	−38.9177	−1.82049	−0.910246	−	0.414067i	$-0.864108\pi$
$457$	−38.9177	−1.82049	−0.910246	+	0.414067i	$0.864108\pi$
$458$	10.8865	0.508691
$459$	−60.3686	−2.81777
$460$	65.0990	3.03526
$461$	20.3986	0.950058	0.475029	−	0.879970i	$-0.342438\pi$
$461$	20.3986	0.950058	0.475029	+	0.879970i	$0.342438\pi$
$462$	−56.6149	−2.63397
$463$	−5.96444	−0.277191	−0.138596	−	0.990349i	$-0.544259\pi$
$463$	−5.96444	−0.277191	−0.138596	+	0.990349i	$0.544259\pi$
$464$	−76.0186	−3.52908
$465$	−77.9786	−3.61617
$466$	11.1233	0.515276
$467$	17.8983	0.828236	0.414118	−	0.910223i	$-0.364090\pi$
$467$	17.8983	0.828236	0.414118	+	0.910223i	$0.364090\pi$
$468$	−129.463	−5.98441
$469$	4.32289	0.199613
$470$	5.04586	0.232748
$471$	−47.0400	−2.16749
$472$	1.17654	0.0541547
$473$	−8.35769	−0.384287
$474$	50.0313	2.29801
$475$	32.5705	1.49444
$476$	−45.1125	−2.06773
$477$	2.41180	0.110429
$478$	−18.4964	−0.846006
$479$	10.9787	0.501629	0.250814	−	0.968035i	$-0.419302\pi$
$479$	10.9787	0.501629	0.250814	+	0.968035i	$0.419302\pi$
$480$	−75.8436	−3.46177
$481$	−50.3524	−2.29587
$482$	10.3181	0.469979
$483$	19.8663	0.903947
$484$	68.8201	3.12818
$485$	−22.8636	−1.03818
$486$	−0.437281	−0.0198355
$487$	−27.6678	−1.25375	−0.626875	−	0.779120i	$-0.715666\pi$
$487$	−27.6678	−1.25375	−0.626875	+	0.779120i	$0.715666\pi$
$488$	73.6524	3.33409
$489$	25.4232	1.14968
$490$	38.4762	1.73818
$491$	37.5333	1.69385	0.846927	−	0.531710i	$-0.178450\pi$
$491$	37.5333	1.69385	0.846927	+	0.531710i	$0.178450\pi$
$492$	139.632	6.29511
$493$	58.9594	2.65540
$494$	94.1650	4.23668
$495$	91.9003	4.13061
$496$	−74.1716	−3.33040
$497$	11.9340	0.535313
$498$	39.1562	1.75463
$499$	20.5215	0.918667	0.459334	−	0.888264i	$-0.348088\pi$
$499$	20.5215	0.918667	0.459334	+	0.888264i	$0.348088\pi$
$500$	−12.6064	−0.563775
$501$	−72.8848	−3.25625
$502$	10.0200	0.447213
$503$	24.6662	1.09981	0.549905	−	0.835227i	$-0.314664\pi$
$503$	24.6662	1.09981	0.549905	+	0.835227i	$0.314664\pi$
$504$	−60.1787	−2.68057
$505$	19.5970	0.872057
$506$	−60.2703	−2.67934
$507$	24.3097	1.07963
$508$	−17.9242	−0.795258
$509$	−29.2023	−1.29437	−0.647185	−	0.762333i	$-0.724054\pi$
$509$	−29.2023	−1.29437	−0.647185	+	0.762333i	$0.724054\pi$
$510$	156.602	6.93447
$511$	11.6725	0.516359
$512$	47.7743	2.11135
$513$	71.5920	3.16086
$514$	76.1123	3.35717
$515$	6.51640	0.287147
$516$	−23.2207	−1.02224
$517$	−3.27502	−0.144035
$518$	−40.8066	−1.79294
$519$	−9.55033	−0.419213
$520$	96.4641	4.23023
$521$	5.19858	0.227754	0.113877	−	0.993495i	$-0.463673\pi$
$521$	5.19858	0.227754	0.113877	+	0.993495i	$0.463673\pi$
$522$	137.123	6.00172
$523$	−14.7532	−0.645112	−0.322556	−	0.946550i	$-0.604542\pi$
$523$	−14.7532	−0.645112	−0.322556	+	0.946550i	$0.604542\pi$
$524$	1.17504	0.0513318
$525$	17.7523	0.774775
$526$	72.0007	3.13938
$527$	57.5268	2.50591
$528$	131.052	5.70332
$529$	−1.85106	−0.0804807
$530$	−3.13310	−0.136093
$531$	−1.01613	−0.0440961
$532$	53.4996	2.31950
$533$	−45.5602	−1.97343
$534$	4.65989	0.201653
$535$	10.4967	0.453811
$536$	−20.8996	−0.902725
$537$	22.7321	0.980962
$538$	18.2518	0.786892
$539$	−24.9730	−1.07566
$540$	127.865	5.50245
$541$	28.1561	1.21052	0.605262	−	0.796026i	$-0.293068\pi$
$541$	28.1561	1.21052	0.605262	+	0.796026i	$0.293068\pi$
$542$	57.6603	2.47672
$543$	−25.0504	−1.07501
$544$	55.9518	2.39891
$545$	61.0229	2.61393
$546$	51.3240	2.19646
$547$	14.4197	0.616541	0.308271	−	0.951299i	$-0.400250\pi$
$547$	14.4197	0.616541	0.308271	+	0.951299i	$0.400250\pi$
$548$	71.3546	3.04812
$549$	−63.6103	−2.71482
$550$	−53.8570	−2.29647
$551$	−69.9207	−2.97872
$552$	−96.0462	−4.08800
$553$	−9.27476	−0.394403
$554$	30.7973	1.30845
$555$	99.3074	4.21537
$556$	57.5840	2.44211
$557$	9.93385	0.420911	0.210455	−	0.977603i	$-0.432505\pi$
$557$	9.93385	0.420911	0.210455	+	0.977603i	$0.432505\pi$
$558$	133.791	5.66384
$559$	7.57662	0.320457
$560$	37.4306	1.58173
$561$	−101.643	−4.29137
$562$	−15.0118	−0.633237
$563$	−0.493083	−0.0207810	−0.0103905	−	0.999946i	$-0.503307\pi$
$563$	−0.493083	−0.0207810	−0.0103905	+	0.999946i	$0.503307\pi$
$564$	−9.09921	−0.383146
$565$	28.7014	1.20748
$566$	79.2603	3.33156
$567$	13.0744	0.549075
$568$	−57.6965	−2.42089
$569$	−37.0689	−1.55401	−0.777005	−	0.629495i	$-0.783262\pi$
$569$	−37.0689	−1.55401	−0.777005	+	0.629495i	$0.783262\pi$
$570$	−185.717	−7.77883
$571$	−0.340246	−0.0142388	−0.00711942	−	0.999975i	$-0.502266\pi$
$571$	−0.340246	−0.0142388	−0.00711942	+	0.999975i	$0.502266\pi$
$572$	−109.158	−4.56414
$573$	41.2924	1.72502
$574$	−36.9230	−1.54113
$575$	18.8985	0.788122
$576$	26.5629	1.10679
$577$	−12.8747	−0.535982	−0.267991	−	0.963421i	$-0.586360\pi$
$577$	−12.8747	−0.535982	−0.267991	+	0.963421i	$0.586360\pi$
$578$	−71.5586	−2.97645
$579$	−40.5724	−1.68613
$580$	−124.880	−5.18538
$581$	−7.25873	−0.301143
$582$	58.8115	2.43782
$583$	2.03354	0.0842207
$584$	−56.4320	−2.33517
$585$	−83.3118	−3.44452
$586$	9.34319	0.385964
$587$	−26.7644	−1.10468	−0.552342	−	0.833617i	$-0.686266\pi$
$587$	−26.7644	−1.10468	−0.552342	+	0.833617i	$0.686266\pi$
$588$	−69.3842	−2.86136
$589$	−68.2218	−2.81103
$590$	1.32002	0.0543445
$591$	24.3973	1.00357
$592$	94.4591	3.88225
$593$	41.4229	1.70103	0.850517	−	0.525947i	$-0.176289\pi$
$593$	41.4229	1.70103	0.850517	+	0.525947i	$0.176289\pi$
$594$	−118.381	−4.85723
$595$	−29.0308	−1.19015
$596$	56.1843	2.30140
$597$	16.4681	0.673994
$598$	54.6377	2.23430
$599$	13.4559	0.549793	0.274897	−	0.961474i	$-0.411356\pi$
$599$	13.4559	0.549793	0.274897	+	0.961474i	$0.411356\pi$
$600$	−85.8260	−3.50383
$601$	2.05134	0.0836758	0.0418379	−	0.999124i	$-0.486679\pi$
$601$	2.05134	0.0836758	0.0418379	+	0.999124i	$0.486679\pi$
$602$	6.14026	0.250258
$603$	18.0500	0.735055
$604$	−19.5311	−0.794708
$605$	44.2871	1.80053
$606$	−50.4091	−2.04773
$607$	4.45875	0.180975	0.0904874	−	0.995898i	$-0.471158\pi$
$607$	4.45875	0.180975	0.0904874	+	0.995898i	$0.471158\pi$
$608$	−66.3540	−2.69101
$609$	−38.1098	−1.54429
$610$	82.6345	3.34577
$611$	2.96896	0.120111
$612$	−188.365	−7.61422
$613$	−21.0513	−0.850255	−0.425127	−	0.905134i	$-0.639771\pi$
$613$	−21.0513	−0.850255	−0.425127	+	0.905134i	$0.639771\pi$
$614$	18.9778	0.765880
$615$	89.8562	3.62335
$616$	−50.7406	−2.04440
$617$	3.10914	0.125169	0.0625846	−	0.998040i	$-0.480066\pi$
$617$	3.10914	0.125169	0.0625846	+	0.998040i	$0.480066\pi$
$618$	−16.7620	−0.674267
$619$	−34.0006	−1.36660	−0.683300	−	0.730138i	$-0.739456\pi$
$619$	−34.0006	−1.36660	−0.683300	+	0.730138i	$0.739456\pi$
$620$	−121.846	−4.89346
$621$	41.5401	1.66695
$622$	60.7812	2.43710
$623$	−0.863847	−0.0346093
$624$	−118.805	−4.75600
$625$	−28.6597	−1.14639
$626$	−7.09493	−0.283571
$627$	120.540	4.81389
$628$	−73.5028	−2.93308
$629$	−73.2616	−2.92113
$630$	−67.5176	−2.68997
$631$	32.4138	1.29037	0.645186	−	0.764026i	$-0.276780\pi$
$631$	32.4138	1.29037	0.645186	+	0.764026i	$0.276780\pi$
$632$	44.8401	1.78364
$633$	−34.4402	−1.36888
$634$	50.3510	1.99969
$635$	−11.5346	−0.457736
$636$	5.64992	0.224034
$637$	22.6392	0.896997
$638$	115.617	4.57734
$639$	49.8299	1.97124
$640$	16.0289	0.633597
$641$	−14.4692	−0.571498	−0.285749	−	0.958305i	$-0.592242\pi$
$641$	−14.4692	−0.571498	−0.285749	+	0.958305i	$0.592242\pi$
$642$	−27.0004	−1.06562
$643$	−45.3646	−1.78900	−0.894502	−	0.447065i	$-0.852469\pi$
$643$	−45.3646	−1.78900	−0.894502	+	0.447065i	$0.852469\pi$
$644$	31.0423	1.22324
$645$	−14.9430	−0.588380
$646$	137.008	5.39051
$647$	−15.0112	−0.590153	−0.295076	−	0.955474i	$-0.595345\pi$
$647$	−15.0112	−0.590153	−0.295076	+	0.955474i	$0.595345\pi$
$648$	−63.2102	−2.48313
$649$	−0.856762	−0.0336309
$650$	48.8238	1.91503
$651$	−37.1839	−1.45735
$652$	39.7253	1.55576
$653$	−35.3340	−1.38273	−0.691364	−	0.722507i	$-0.742990\pi$
$653$	−35.3340	−1.38273	−0.691364	+	0.722507i	$0.742990\pi$
$654$	−156.968	−6.13793
$655$	0.756161	0.0295456
$656$	85.4693	3.33701
$657$	48.7378	1.90144
$658$	2.40610	0.0937997
$659$	27.2928	1.06317	0.531587	−	0.847004i	$-0.321596\pi$
$659$	27.2928	1.06317	0.531587	+	0.847004i	$0.321596\pi$
$660$	215.288	8.38006
$661$	8.93200	0.347414	0.173707	−	0.984797i	$-0.444425\pi$
$661$	8.93200	0.347414	0.173707	+	0.984797i	$0.444425\pi$
$662$	84.5990	3.28804
$663$	92.1439	3.57857
$664$	35.0933	1.36189
$665$	34.4280	1.33506
$666$	−170.386	−6.60233
$667$	−40.5704	−1.57089
$668$	−113.887	−4.40641
$669$	−22.8838	−0.884740
$670$	−23.4483	−0.905888
$671$	−53.6340	−2.07052
$672$	−36.1658	−1.39513
$673$	10.5016	0.404806	0.202403	−	0.979302i	$-0.435125\pi$
$673$	10.5016	0.404806	0.202403	+	0.979302i	$0.435125\pi$
$674$	−10.5888	−0.407865
$675$	37.1199	1.42874
$676$	37.9854	1.46098
$677$	−3.33588	−0.128208	−0.0641042	−	0.997943i	$-0.520419\pi$
$677$	−3.33588	−0.128208	−0.0641042	+	0.997943i	$0.520419\pi$
$678$	−73.8280	−2.83535
$679$	−10.9024	−0.418397
$680$	140.353	5.38230
$681$	−7.81245	−0.299374
$682$	112.808	4.31965
$683$	−20.7789	−0.795081	−0.397541	−	0.917585i	$-0.630136\pi$
$683$	−20.7789	−0.795081	−0.397541	+	0.917585i	$0.630136\pi$
$684$	223.385	8.54135
$685$	45.9181	1.75444
$686$	44.4052	1.69540
$687$	−12.6333	−0.481991
$688$	−14.2135	−0.541883
$689$	−1.84350	−0.0702317
$690$	−107.759	−4.10232
$691$	20.6742	0.786482	0.393241	−	0.919435i	$-0.371354\pi$
$691$	20.6742	0.786482	0.393241	+	0.919435i	$0.371354\pi$
$692$	−14.9230	−0.567286
$693$	43.8224	1.66467
$694$	−52.9021	−2.00814
$695$	37.0565	1.40563
$696$	184.247	6.98387
$697$	−66.2892	−2.51088
$698$	−45.8396	−1.73505
$699$	−12.9081	−0.488230
$700$	27.7391	1.04844
$701$	21.8857	0.826611	0.413305	−	0.910592i	$-0.364374\pi$
$701$	21.8857	0.826611	0.413305	+	0.910592i	$0.364374\pi$
$702$	107.318	4.05045
$703$	86.8820	3.27682
$704$	22.3969	0.844117
$705$	−5.85552	−0.220532
$706$	−73.8403	−2.77902
$707$	9.34479	0.351447
$708$	−2.38040	−0.0894609
$709$	10.7132	0.402342	0.201171	−	0.979556i	$-0.435525\pi$
$709$	10.7132	0.402342	0.201171	+	0.979556i	$0.435525\pi$
$710$	−64.7327	−2.42937
$711$	−38.7264	−1.45235
$712$	4.17638	0.156517
$713$	−39.5846	−1.48246
$714$	74.6754	2.79466
$715$	−70.2456	−2.62704
$716$	35.5203	1.32745
$717$	21.4644	0.801601
$718$	−19.2958	−0.720113
$719$	5.11055	0.190591	0.0952956	−	0.995449i	$-0.469620\pi$
$719$	5.11055	0.190591	0.0952956	+	0.995449i	$0.469620\pi$
$720$	156.290	5.82458
$721$	3.10733	0.115723
$722$	−113.336	−4.21792
$723$	−11.9738	−0.445310
$724$	−39.1427	−1.45473
$725$	−36.2533	−1.34641
$726$	−113.919	−4.22792
$727$	43.8195	1.62517	0.812587	−	0.582840i	$-0.198058\pi$
$727$	43.8195	1.62517	0.812587	+	0.582840i	$0.198058\pi$
$728$	45.9986	1.70482
$729$	−26.7459	−0.990588
$730$	−63.3140	−2.34336
$731$	11.0238	0.407731
$732$	−149.015	−5.50775
$733$	−18.2235	−0.673099	−0.336549	−	0.941666i	$-0.609260\pi$
$733$	−18.2235	−0.673099	−0.336549	+	0.941666i	$0.609260\pi$
$734$	35.2268	1.30024
$735$	−44.6501	−1.64694
$736$	−38.5008	−1.41916
$737$	15.2192	0.560605
$738$	−154.170	−5.67509
$739$	−27.3061	−1.00447	−0.502235	−	0.864731i	$-0.667489\pi$
$739$	−27.3061	−1.00447	−0.502235	+	0.864731i	$0.667489\pi$
$740$	155.174	5.70430
$741$	−109.275	−4.01431
$742$	−1.49401	−0.0548468
$743$	−31.1645	−1.14332	−0.571658	−	0.820492i	$-0.693700\pi$
$743$	−31.1645	−1.14332	−0.571658	+	0.820492i	$0.693700\pi$
$744$	179.770	6.59070
$745$	36.1557	1.32464
$746$	74.5404	2.72912
$747$	−30.3085	−1.10893
$748$	−158.823	−5.80715
$749$	5.00531	0.182890
$750$	20.8675	0.761974
$751$	1.12502	0.0410526	0.0205263	−	0.999789i	$-0.493466\pi$
$751$	1.12502	0.0410526	0.0205263	+	0.999789i	$0.493466\pi$
$752$	−5.56965	−0.203104
$753$	−11.6278	−0.423739
$754$	−104.812	−3.81704
$755$	−12.5686	−0.457419
$756$	60.9723	2.21754
$757$	5.24182	0.190517	0.0952586	−	0.995453i	$-0.469632\pi$
$757$	5.24182	0.190517	0.0952586	+	0.995453i	$0.469632\pi$
$758$	6.81793	0.247638
$759$	69.9413	2.53871
$760$	−166.447	−6.03767
$761$	40.3101	1.46124	0.730620	−	0.682784i	$-0.239231\pi$
$761$	40.3101	1.46124	0.730620	+	0.682784i	$0.239231\pi$
$762$	29.6702	1.07484
$763$	29.0986	1.05344
$764$	64.5219	2.33432
$765$	−121.217	−4.38261
$766$	69.2639	2.50261
$767$	0.776694	0.0280448
$768$	−67.7661	−2.44530
$769$	48.6269	1.75353	0.876766	−	0.480917i	$-0.159696\pi$
$769$	48.6269	1.75353	0.876766	+	0.480917i	$0.159696\pi$
$770$	−56.9285	−2.05156
$771$	−88.3253	−3.18096
$772$	−63.3968	−2.28170
$773$	20.4908	0.737002	0.368501	−	0.929627i	$-0.379871\pi$
$773$	20.4908	0.737002	0.368501	+	0.929627i	$0.379871\pi$
$774$	25.6384	0.921553
$775$	−35.3725	−1.27062
$776$	52.7093	1.89215
$777$	47.3545	1.69883
$778$	−98.0478	−3.51518
$779$	78.6133	2.81661
$780$	−195.168	−6.98813
$781$	42.0148	1.50341
$782$	79.4968	2.84280
$783$	−79.6871	−2.84778
$784$	−42.4703	−1.51679
$785$	−47.3005	−1.68823
$786$	−1.94506	−0.0693779
$787$	1.07465	0.0383072	0.0191536	−	0.999817i	$-0.493903\pi$
$787$	1.07465	0.0383072	0.0191536	+	0.999817i	$0.493903\pi$
$788$	38.1222	1.35805
$789$	−83.5539	−2.97460
$790$	50.3084	1.78989
$791$	13.6862	0.486624
$792$	−211.865	−7.52830
$793$	48.6217	1.72661
$794$	3.44534	0.122270
$795$	3.63584	0.128950
$796$	25.7324	0.912060
$797$	−6.98723	−0.247500	−0.123750	−	0.992313i	$-0.539492\pi$
$797$	−6.98723	−0.247500	−0.123750	+	0.992313i	$0.539492\pi$
$798$	−88.5586	−3.13494
$799$	4.31977	0.152822
$800$	−34.4040	−1.21636
$801$	−3.60696	−0.127445
$802$	−35.2241	−1.24381
$803$	41.0940	1.45018
$804$	42.2844	1.49126
$805$	19.9763	0.704073
$806$	−102.266	−3.60216
$807$	−21.1805	−0.745590
$808$	−45.1787	−1.58938
$809$	−19.0492	−0.669733	−0.334867	−	0.942266i	$-0.608691\pi$
$809$	−19.0492	−0.669733	−0.334867	+	0.942266i	$0.608691\pi$
$810$	−70.9188	−2.49183
$811$	27.0772	0.950809	0.475404	−	0.879767i	$-0.342302\pi$
$811$	27.0772	0.950809	0.475404	+	0.879767i	$0.342302\pi$
$812$	−59.5489	−2.08976
$813$	−66.9124	−2.34672
$814$	−143.664	−5.03541
$815$	25.5640	0.895468
$816$	−172.859	−6.05126
$817$	−13.0733	−0.457377
$818$	17.6131	0.615829
$819$	−39.7270	−1.38817
$820$	140.406	4.90318
$821$	−51.7846	−1.80729	−0.903647	−	0.428278i	$-0.859120\pi$
$821$	−51.7846	−1.80729	−0.903647	+	0.428278i	$0.859120\pi$
$822$	−118.114	−4.11971
$823$	−36.7156	−1.27983	−0.639913	−	0.768447i	$-0.721030\pi$
$823$	−36.7156	−1.27983	−0.639913	+	0.768447i	$0.721030\pi$
$824$	−15.0228	−0.523343
$825$	62.4989	2.17593
$826$	0.629449	0.0219013
$827$	−4.21270	−0.146490	−0.0732450	−	0.997314i	$-0.523335\pi$
$827$	−4.21270	−0.146490	−0.0732450	+	0.997314i	$0.523335\pi$
$828$	129.616	4.50446
$829$	−45.0387	−1.56426	−0.782129	−	0.623117i	$-0.785866\pi$
$829$	−45.0387	−1.56426	−0.782129	+	0.623117i	$0.785866\pi$
$830$	39.3730	1.36666
$831$	−35.7390	−1.23977
$832$	−20.3038	−0.703909
$833$	32.9395	1.14129
$834$	−95.3196	−3.30065
$835$	−73.2885	−2.53625
$836$	188.351	6.51424
$837$	−77.7509	−2.68746
$838$	0.311803	0.0107711
$839$	32.6063	1.12569	0.562847	−	0.826561i	$-0.309706\pi$
$839$	32.6063	1.12569	0.562847	+	0.826561i	$0.309706\pi$
$840$	−90.7208	−3.13017
$841$	48.8268	1.68368
$842$	−5.44876	−0.187776
$843$	17.4207	0.599999
$844$	−53.8149	−1.85238
$845$	24.4444	0.840912
$846$	10.0466	0.345409
$847$	21.1182	0.725629
$848$	3.45833	0.118760
$849$	−91.9785	−3.15669
$850$	71.0376	2.43657
$851$	50.4119	1.72810
$852$	116.733	3.99919
$853$	−30.5799	−1.04704	−0.523518	−	0.852014i	$-0.675381\pi$
$853$	−30.5799	−1.04704	−0.523518	+	0.852014i	$0.675381\pi$
$854$	39.4040	1.34838
$855$	143.753	4.91624
$856$	−24.1988	−0.827099
$857$	−7.40421	−0.252923	−0.126462	−	0.991972i	$-0.540362\pi$
$857$	−7.40421	−0.252923	−0.126462	+	0.991972i	$0.540362\pi$
$858$	180.691	6.16870
$859$	−30.9220	−1.05505	−0.527523	−	0.849541i	$-0.676879\pi$
$859$	−30.9220	−1.05505	−0.527523	+	0.849541i	$0.676879\pi$
$860$	−23.3493	−0.796206
$861$	42.8476	1.46024
$862$	−21.1505	−0.720388
$863$	14.3145	0.487270	0.243635	−	0.969867i	$-0.421660\pi$
$863$	14.3145	0.487270	0.243635	+	0.969867i	$0.421660\pi$
$864$	−75.6221	−2.57272
$865$	−9.60322	−0.326519
$866$	59.9395	2.03683
$867$	83.0409	2.82022
$868$	−58.1020	−1.97211
$869$	−32.6527	−1.10767
$870$	206.716	7.00834
$871$	−13.7969	−0.467489
$872$	−140.681	−4.76406
$873$	−45.5226	−1.54071
$874$	−94.2763	−3.18894
$875$	−3.86840	−0.130776
$876$	114.174	3.85759
$877$	55.7540	1.88268	0.941339	−	0.337464i	$-0.109569\pi$
$877$	55.7540	1.88268	0.941339	+	0.337464i	$0.109569\pi$
$878$	39.2522	1.32470
$879$	−10.8424	−0.365705
$880$	131.778	4.44224
$881$	−3.64469	−0.122793	−0.0613963	−	0.998113i	$-0.519555\pi$
$881$	−3.64469	−0.122793	−0.0613963	+	0.998113i	$0.519555\pi$
$882$	76.6082	2.57953
$883$	−35.9463	−1.20969	−0.604844	−	0.796344i	$-0.706765\pi$
$883$	−35.9463	−1.20969	−0.604844	+	0.796344i	$0.706765\pi$
$884$	143.980	4.84258
$885$	−1.53183	−0.0514920
$886$	−38.9305	−1.30790
$887$	−35.8313	−1.20310	−0.601549	−	0.798836i	$-0.705450\pi$
$887$	−35.8313	−1.20310	−0.601549	+	0.798836i	$0.705450\pi$
$888$	−228.941	−7.68277
$889$	−5.50023	−0.184472
$890$	4.68570	0.157065
$891$	46.0299	1.54206
$892$	−35.7574	−1.19724
$893$	−5.12288	−0.171430
$894$	−93.0027	−3.11048
$895$	22.8580	0.764058
$896$	7.64332	0.255346
$897$	−63.4049	−2.11703
$898$	−53.9060	−1.79887
$899$	75.9359	2.53260
$900$	115.823	3.86078
$901$	−2.68225	−0.0893587
$902$	−129.991	−4.32823
$903$	−7.12552	−0.237123
$904$	−66.1677	−2.20070
$905$	−25.1891	−0.837315
$906$	32.3301	1.07409
$907$	41.6534	1.38308	0.691539	−	0.722339i	$-0.256933\pi$
$907$	41.6534	1.38308	0.691539	+	0.722339i	$0.256933\pi$
$908$	−12.2074	−0.405117
$909$	39.0188	1.29417
$910$	51.6083	1.71080
$911$	3.90926	0.129519	0.0647597	−	0.997901i	$-0.479372\pi$
$911$	3.90926	0.129519	0.0647597	+	0.997901i	$0.479372\pi$
$912$	204.995	6.78807
$913$	−25.5551	−0.845750
$914$	100.662	3.32959
$915$	−95.8941	−3.17016
$916$	−19.7403	−0.652238
$917$	0.360573	0.0119072
$918$	156.145	5.15356
$919$	9.20002	0.303481	0.151740	−	0.988420i	$-0.451512\pi$
$919$	9.20002	0.303481	0.151740	+	0.988420i	$0.451512\pi$
$920$	−96.5782	−3.18409
$921$	−22.0230	−0.725681
$922$	−52.7616	−1.73761
$923$	−38.0883	−1.25369
$924$	102.659	3.37724
$925$	45.0476	1.48116
$926$	15.4272	0.506969
$927$	12.9745	0.426139
$928$	73.8568	2.42447
$929$	−14.4433	−0.473869	−0.236934	−	0.971526i	$-0.576143\pi$
$929$	−14.4433	−0.473869	−0.236934	+	0.971526i	$0.576143\pi$
$930$	201.694	6.61380
$931$	−39.0635	−1.28025
$932$	−20.1697	−0.660681
$933$	−70.5342	−2.30919
$934$	−46.2945	−1.51480
$935$	−102.206	−3.34249
$936$	192.065	6.27785
$937$	21.1210	0.689994	0.344997	−	0.938604i	$-0.387880\pi$
$937$	21.1210	0.689994	0.344997	+	0.938604i	$0.387880\pi$
$938$	−11.1813	−0.365081
$939$	8.23339	0.268687
$940$	−9.14961	−0.298427
$941$	−48.9806	−1.59672	−0.798361	−	0.602179i	$-0.794299\pi$
$941$	−48.9806	−1.59672	−0.798361	+	0.602179i	$0.794299\pi$
$942$	121.670	3.96423
$943$	45.6141	1.48540
$944$	−1.45705	−0.0474229
$945$	39.2369	1.27638
$946$	21.6174	0.702842
$947$	5.93853	0.192976	0.0964882	−	0.995334i	$-0.469239\pi$
$947$	5.93853	0.192976	0.0964882	+	0.995334i	$0.469239\pi$
$948$	−90.7212	−2.94649
$949$	−37.2536	−1.20930
$950$	−84.2445	−2.73325
$951$	−58.4304	−1.89473
$952$	66.9271	2.16912
$953$	−42.7988	−1.38639	−0.693194	−	0.720751i	$-0.743797\pi$
$953$	−42.7988	−1.38639	−0.693194	+	0.720751i	$0.743797\pi$
$954$	−6.23817	−0.201968
$955$	41.5211	1.34359
$956$	33.5393	1.08474
$957$	−134.169	−4.33708
$958$	−28.3966	−0.917454
$959$	21.8959	0.707056
$960$	40.0443	1.29242
$961$	43.0908	1.39003
$962$	130.238	4.19903
$963$	20.8995	0.673476
$964$	−18.7098	−0.602601
$965$	−40.7971	−1.31331
$966$	−51.3847	−1.65327
$967$	27.1485	0.873037	0.436518	−	0.899695i	$-0.356211\pi$
$967$	27.1485	0.873037	0.436518	+	0.899695i	$0.356211\pi$
$968$	−102.099	−3.28157
$969$	−158.992	−5.10757
$970$	59.1372	1.89878
$971$	48.8676	1.56823	0.784117	−	0.620613i	$-0.213116\pi$
$971$	48.8676	1.56823	0.784117	+	0.620613i	$0.213116\pi$
$972$	0.792917	0.0254328
$973$	17.6703	0.566483
$974$	71.5636	2.29305
$975$	−56.6581	−1.81451
$976$	−91.2124	−2.91964
$977$	18.8278	0.602356	0.301178	−	0.953568i	$-0.402620\pi$
$977$	18.8278	0.602356	0.301178	+	0.953568i	$0.402620\pi$
$978$	−65.7578	−2.10270
$979$	−3.04126	−0.0971991
$980$	−69.7685	−2.22867
$981$	121.500	3.87919
$982$	−97.0808	−3.09797
$983$	45.9537	1.46569	0.732847	−	0.680393i	$-0.238191\pi$
$983$	45.9537	1.46569	0.732847	+	0.680393i	$0.238191\pi$
$984$	−207.153	−6.60379
$985$	24.5324	0.781668
$986$	−152.500	−4.85659
$987$	−2.79219	−0.0888764
$988$	−170.748	−5.43223
$989$	−7.58558	−0.241207
$990$	−237.703	−7.55468
$991$	0.129745	0.00412147	0.00206074	−	0.999998i	$-0.499344\pi$
$991$	0.129745	0.00412147	0.00206074	+	0.999998i	$0.499344\pi$
$992$	72.0623	2.28798
$993$	−98.1738	−3.11545
$994$	−30.8676	−0.979060
$995$	16.5593	0.524965
$996$	−71.0014	−2.24977
$997$	28.8185	0.912691	0.456345	−	0.889803i	$-0.349158\pi$
$997$	28.8185	0.912691	0.456345	+	0.889803i	$0.349158\pi$
$998$	−53.0793	−1.68020
$999$	99.0175	3.13277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.9	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.9	✓	182	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58653 q^{2} +3.00156 q^{3} +4.69012 q^{4} +3.01819 q^{5} -7.76362 q^{6} +1.43921 q^{7} -6.95807 q^{8} +6.00937 q^{9} +O(q^{10})\)	\(q-2.58653 q^{2} +3.00156 q^{3} +4.69012 q^{4} +3.01819 q^{5} -7.76362 q^{6} +1.43921 q^{7} -6.95807 q^{8} +6.00937 q^{9} -7.80662 q^{10} +5.06689 q^{11} +14.0777 q^{12} -4.59337 q^{13} -3.72256 q^{14} +9.05927 q^{15} +8.61699 q^{16} -6.68326 q^{17} -15.5434 q^{18} +7.92577 q^{19} +14.1557 q^{20} +4.31989 q^{21} -13.1057 q^{22} +4.59880 q^{23} -20.8851 q^{24} +4.10944 q^{25} +11.8809 q^{26} +9.03282 q^{27} +6.75008 q^{28} -8.82195 q^{29} -23.4320 q^{30} -8.60760 q^{31} -8.37193 q^{32} +15.2086 q^{33} +17.2864 q^{34} +4.34381 q^{35} +28.1847 q^{36} +10.9620 q^{37} -20.5002 q^{38} -13.7873 q^{39} -21.0007 q^{40} +9.91870 q^{41} -11.1735 q^{42} -1.64947 q^{43} +23.7643 q^{44} +18.1374 q^{45} -11.8949 q^{46} -0.646357 q^{47} +25.8644 q^{48} -4.92867 q^{49} -10.6292 q^{50} -20.0602 q^{51} -21.5434 q^{52} +0.401339 q^{53} -23.3636 q^{54} +15.2928 q^{55} -10.0141 q^{56} +23.7897 q^{57} +22.8182 q^{58} -0.169090 q^{59} +42.4891 q^{60} -10.5852 q^{61} +22.2638 q^{62} +8.64877 q^{63} +4.42025 q^{64} -13.8636 q^{65} -39.3374 q^{66} +3.00365 q^{67} -31.3453 q^{68} +13.8036 q^{69} -11.2354 q^{70} +8.29203 q^{71} -41.8136 q^{72} +8.11030 q^{73} -28.3534 q^{74} +12.3348 q^{75} +37.1728 q^{76} +7.29234 q^{77} +35.6612 q^{78} -6.44433 q^{79} +26.0077 q^{80} +9.08444 q^{81} -25.6550 q^{82} -5.04354 q^{83} +20.2608 q^{84} -20.1713 q^{85} +4.26640 q^{86} -26.4796 q^{87} -35.2558 q^{88} -0.600222 q^{89} -46.9129 q^{90} -6.61083 q^{91} +21.5689 q^{92} -25.8362 q^{93} +1.67182 q^{94} +23.9214 q^{95} -25.1289 q^{96} -7.57527 q^{97} +12.7481 q^{98} +30.4489 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * q^99

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