LMFDB - Embedded newform 4031.2.a.e.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$103$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41155 q^{2} +2.97695 q^{3} +3.81557 q^{4} +2.55399 q^{5} -7.17907 q^{6} +0.984137 q^{7} -4.37835 q^{8} +5.86223 q^{9} +O(q^{10})$	\(q-2.41155 q^{2} +2.97695 q^{3} +3.81557 q^{4} +2.55399 q^{5} -7.17907 q^{6} +0.984137 q^{7} -4.37835 q^{8} +5.86223 q^{9} -6.15908 q^{10} +6.58049 q^{11} +11.3588 q^{12} -5.60305 q^{13} -2.37329 q^{14} +7.60311 q^{15} +2.92746 q^{16} +1.70395 q^{17} -14.1371 q^{18} +3.31734 q^{19} +9.74494 q^{20} +2.92973 q^{21} -15.8692 q^{22} -6.07787 q^{23} -13.0341 q^{24} +1.52287 q^{25} +13.5120 q^{26} +8.52073 q^{27} +3.75505 q^{28} -1.00000 q^{29} -18.3353 q^{30} -3.27677 q^{31} +1.69699 q^{32} +19.5898 q^{33} -4.10916 q^{34} +2.51348 q^{35} +22.3678 q^{36} -5.27768 q^{37} -7.99993 q^{38} -16.6800 q^{39} -11.1823 q^{40} +9.08164 q^{41} -7.06518 q^{42} +6.42284 q^{43} +25.1084 q^{44} +14.9721 q^{45} +14.6571 q^{46} +9.30849 q^{47} +8.71489 q^{48} -6.03148 q^{49} -3.67248 q^{50} +5.07258 q^{51} -21.3788 q^{52} -2.92515 q^{53} -20.5482 q^{54} +16.8065 q^{55} -4.30889 q^{56} +9.87555 q^{57} +2.41155 q^{58} -4.18735 q^{59} +29.0102 q^{60} +13.0226 q^{61} +7.90211 q^{62} +5.76924 q^{63} -9.94728 q^{64} -14.3101 q^{65} -47.2418 q^{66} -8.87285 q^{67} +6.50155 q^{68} -18.0935 q^{69} -6.06137 q^{70} -8.36612 q^{71} -25.6669 q^{72} -6.29778 q^{73} +12.7274 q^{74} +4.53351 q^{75} +12.6575 q^{76} +6.47610 q^{77} +40.2246 q^{78} +8.05893 q^{79} +7.47670 q^{80} +7.77909 q^{81} -21.9008 q^{82} +14.7289 q^{83} +11.1786 q^{84} +4.35187 q^{85} -15.4890 q^{86} -2.97695 q^{87} -28.8117 q^{88} +18.1388 q^{89} -36.1060 q^{90} -5.51416 q^{91} -23.1906 q^{92} -9.75480 q^{93} -22.4479 q^{94} +8.47245 q^{95} +5.05184 q^{96} +13.8628 q^{97} +14.5452 q^{98} +38.5764 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) $ 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * 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 $

$2$	−2.41155	−1.70522	−0.852612	−	0.522545i	$-0.824983\pi$
$2$	−2.41155	−1.70522	−0.852612	+	0.522545i	$0.824983\pi$
$3$	2.97695	1.71874	0.859372	−	0.511352i	$-0.170855\pi$
$3$	2.97695	1.71874	0.859372	+	0.511352i	$0.170855\pi$
$4$	3.81557	1.90779
$5$	2.55399	1.14218	0.571090	−	0.820888i	$-0.306521\pi$
$5$	2.55399	1.14218	0.571090	+	0.820888i	$0.306521\pi$
$6$	−7.17907	−2.93084
$7$	0.984137	0.371969	0.185984	−	0.982553i	$-0.440453\pi$
$7$	0.984137	0.371969	0.185984	+	0.982553i	$0.440453\pi$
$8$	−4.37835	−1.54798
$9$	5.86223	1.95408
$10$	−6.15908	−1.94767
$11$	6.58049	1.98409	0.992046	−	0.125872i	$-0.0401728\pi$
$11$	6.58049	1.98409	0.992046	+	0.125872i	$0.0401728\pi$
$12$	11.3588	3.27900
$13$	−5.60305	−1.55401	−0.777003	−	0.629497i	$-0.783261\pi$
$13$	−5.60305	−1.55401	−0.777003	+	0.629497i	$0.783261\pi$
$14$	−2.37329	−0.634290
$15$	7.60311	1.96311
$16$	2.92746	0.731864
$17$	1.70395	0.413269	0.206634	−	0.978418i	$-0.433749\pi$
$17$	1.70395	0.413269	0.206634	+	0.978418i	$0.433749\pi$
$18$	−14.1371	−3.33214
$19$	3.31734	0.761050	0.380525	−	0.924771i	$-0.375743\pi$
$19$	3.31734	0.761050	0.380525	+	0.924771i	$0.375743\pi$
$20$	9.74494	2.17904
$21$	2.92973	0.639319
$22$	−15.8692	−3.38332
$23$	−6.07787	−1.26732	−0.633662	−	0.773610i	$-0.718449\pi$
$23$	−6.07787	−1.26732	−0.633662	+	0.773610i	$0.718449\pi$
$24$	−13.0341	−2.66058
$25$	1.52287	0.304574
$26$	13.5120	2.64993
$27$	8.52073	1.63982
$28$	3.75505	0.709637
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−18.3353	−3.34755
$31$	−3.27677	−0.588526	−0.294263	−	0.955724i	$-0.595074\pi$
$31$	−3.27677	−0.588526	−0.294263	+	0.955724i	$0.595074\pi$
$32$	1.69699	0.299988
$33$	19.5898	3.41015
$34$	−4.10916	−0.704715
$35$	2.51348	0.424855
$36$	22.3678	3.72796
$37$	−5.27768	−0.867645	−0.433822	−	0.900998i	$-0.642835\pi$
$37$	−5.27768	−0.867645	−0.433822	+	0.900998i	$0.642835\pi$
$38$	−7.99993	−1.29776
$39$	−16.6800	−2.67094
$40$	−11.1823	−1.76807
$41$	9.08164	1.41831	0.709157	−	0.705051i	$-0.249076\pi$
$41$	9.08164	1.41831	0.709157	+	0.705051i	$0.249076\pi$
$42$	−7.06518	−1.09018
$43$	6.42284	0.979474	0.489737	−	0.871870i	$-0.337093\pi$
$43$	6.42284	0.979474	0.489737	+	0.871870i	$0.337093\pi$
$44$	25.1084	3.78523
$45$	14.9721	2.23191
$46$	14.6571	2.16107
$47$	9.30849	1.35778	0.678891	−	0.734239i	$-0.262461\pi$
$47$	9.30849	1.35778	0.678891	+	0.734239i	$0.262461\pi$
$48$	8.71489	1.25789
$49$	−6.03148	−0.861639
$50$	−3.67248	−0.519367
$51$	5.07258	0.710303
$52$	−21.3788	−2.96471
$53$	−2.92515	−0.401800	−0.200900	−	0.979612i	$-0.564387\pi$
$53$	−2.92515	−0.401800	−0.200900	+	0.979612i	$0.564387\pi$
$54$	−20.5482	−2.79625
$55$	16.8065	2.26619
$56$	−4.30889	−0.575800
$57$	9.87555	1.30805
$58$	2.41155	0.316652
$59$	−4.18735	−0.545146	−0.272573	−	0.962135i	$-0.587875\pi$
$59$	−4.18735	−0.545146	−0.272573	+	0.962135i	$0.587875\pi$
$60$	29.0102	3.74520
$61$	13.0226	1.66738	0.833689	−	0.552234i	$-0.186225\pi$
$61$	13.0226	1.66738	0.833689	+	0.552234i	$0.186225\pi$
$62$	7.90211	1.00357
$63$	5.76924	0.726856
$64$	−9.94728	−1.24341
$65$	−14.3101	−1.77495
$66$	−47.2418	−5.81506
$67$	−8.87285	−1.08399	−0.541995	−	0.840381i	$-0.682331\pi$
$67$	−8.87285	−1.08399	−0.541995	+	0.840381i	$0.682331\pi$
$68$	6.50155	0.788429
$69$	−18.0935	−2.17820
$70$	−6.06137	−0.724473
$71$	−8.36612	−0.992876	−0.496438	−	0.868072i	$-0.665359\pi$
$71$	−8.36612	−0.992876	−0.496438	+	0.868072i	$0.665359\pi$
$72$	−25.6669	−3.02487
$73$	−6.29778	−0.737099	−0.368550	−	0.929608i	$-0.620146\pi$
$73$	−6.29778	−0.737099	−0.368550	+	0.929608i	$0.620146\pi$
$74$	12.7274	1.47953
$75$	4.53351	0.523485
$76$	12.6575	1.45192
$77$	6.47610	0.738020
$78$	40.2246	4.55454
$79$	8.05893	0.906700	0.453350	−	0.891332i	$-0.350229\pi$
$79$	8.05893	0.906700	0.453350	+	0.891332i	$0.350229\pi$
$80$	7.47670	0.835920
$81$	7.77909	0.864343
$82$	−21.9008	−2.41854
$83$	14.7289	1.61670	0.808352	−	0.588699i	$-0.200360\pi$
$83$	14.7289	1.61670	0.808352	+	0.588699i	$0.200360\pi$
$84$	11.1786	1.21968
$85$	4.35187	0.472027
$86$	−15.4890	−1.67022
$87$	−2.97695	−0.319163
$88$	−28.8117	−3.07134
$89$	18.1388	1.92271	0.961353	−	0.275317i	$-0.0887828\pi$
$89$	18.1388	1.92271	0.961353	+	0.275317i	$0.0887828\pi$
$90$	−36.1060	−3.80590
$91$	−5.51416	−0.578041
$92$	−23.1906	−2.41778
$93$	−9.75480	−1.01153
$94$	−22.4479	−2.31532
$95$	8.47245	0.869255
$96$	5.05184	0.515602
$97$	13.8628	1.40755	0.703775	−	0.710423i	$-0.251496\pi$
$97$	13.8628	1.40755	0.703775	+	0.710423i	$0.251496\pi$
$98$	14.5452	1.46929
$99$	38.5764	3.87707
$100$	5.81063	0.581063
$101$	−12.6589	−1.25960	−0.629802	−	0.776755i	$-0.716864\pi$
$101$	−12.6589	−1.25960	−0.629802	+	0.776755i	$0.716864\pi$
$102$	−12.2328	−1.21122
$103$	15.5966	1.53678	0.768390	−	0.639982i	$-0.221058\pi$
$103$	15.5966	1.53678	0.768390	+	0.639982i	$0.221058\pi$
$104$	24.5321	2.40557
$105$	7.48249	0.730217
$106$	7.05414	0.685158
$107$	−11.4429	−1.10623	−0.553115	−	0.833105i	$-0.686561\pi$
$107$	−11.4429	−1.10623	−0.553115	+	0.833105i	$0.686561\pi$
$108$	32.5115	3.12842
$109$	1.79348	0.171784	0.0858921	−	0.996304i	$-0.472626\pi$
$109$	1.79348	0.171784	0.0858921	+	0.996304i	$0.472626\pi$
$110$	−40.5298	−3.86436
$111$	−15.7114	−1.49126
$112$	2.88102	0.272231
$113$	−20.8209	−1.95867	−0.979334	−	0.202250i	$-0.935175\pi$
$113$	−20.8209	−1.95867	−0.979334	+	0.202250i	$0.935175\pi$
$114$	−23.8154	−2.23052
$115$	−15.5228	−1.44751
$116$	−3.81557	−0.354267
$117$	−32.8464	−3.03665
$118$	10.0980	0.929596
$119$	1.67692	0.153723
$120$	−33.2890	−3.03886
$121$	32.3029	2.93663
$122$	−31.4048	−2.84325
$123$	27.0356	2.43772
$124$	−12.5028	−1.12278
$125$	−8.88055	−0.794301
$126$	−13.9128	−1.23945
$127$	4.91955	0.436539	0.218270	−	0.975888i	$-0.429959\pi$
$127$	4.91955	0.436539	0.218270	+	0.975888i	$0.429959\pi$
$128$	20.5944	1.82030
$129$	19.1205	1.68346
$130$	34.5096	3.02669
$131$	8.15696	0.712677	0.356338	−	0.934357i	$-0.384025\pi$
$131$	8.15696	0.712677	0.356338	+	0.934357i	$0.384025\pi$
$132$	74.7463	6.50583
$133$	3.26471	0.283087
$134$	21.3973	1.84845
$135$	21.7619	1.87296
$136$	−7.46049	−0.639732
$137$	11.5482	0.986633	0.493316	−	0.869850i	$-0.335785\pi$
$137$	11.5482	0.986633	0.493316	+	0.869850i	$0.335785\pi$
$138$	43.6334	3.71432
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	9.59035	0.810533
$141$	27.7109	2.33368
$142$	20.1753	1.69307
$143$	−36.8708	−3.08329
$144$	17.1614	1.43012
$145$	−2.55399	−0.212097
$146$	15.1874	1.25692
$147$	−17.9554	−1.48094
$148$	−20.1374	−1.65528
$149$	13.2390	1.08458	0.542292	−	0.840190i	$-0.317557\pi$
$149$	13.2390	1.08458	0.542292	+	0.840190i	$0.317557\pi$
$150$	−10.9328	−0.892659
$151$	5.72767	0.466111	0.233056	−	0.972463i	$-0.425128\pi$
$151$	5.72767	0.466111	0.233056	+	0.972463i	$0.425128\pi$
$152$	−14.5245	−1.17809
$153$	9.98896	0.807559
$154$	−15.6174	−1.25849
$155$	−8.36885	−0.672203
$156$	−63.6437	−5.09558
$157$	−18.7982	−1.50026	−0.750130	−	0.661290i	$-0.770009\pi$
$157$	−18.7982	−1.50026	−0.750130	+	0.661290i	$0.770009\pi$
$158$	−19.4345	−1.54613
$159$	−8.70801	−0.690590
$160$	4.33409	0.342640
$161$	−5.98146	−0.471405
$162$	−18.7597	−1.47390
$163$	11.6945	0.915988	0.457994	−	0.888955i	$-0.348568\pi$
$163$	11.6945	0.915988	0.457994	+	0.888955i	$0.348568\pi$
$164$	34.6517	2.70584
$165$	50.0322	3.89500
$166$	−35.5194	−2.75684
$167$	−9.28172	−0.718241	−0.359120	−	0.933291i	$-0.616923\pi$
$167$	−9.28172	−0.718241	−0.359120	+	0.933291i	$0.616923\pi$
$168$	−12.8274	−0.989652
$169$	18.3941	1.41493
$170$	−10.4948	−0.804912
$171$	19.4470	1.48715
$172$	24.5068	1.86863
$173$	−4.33926	−0.329908	−0.164954	−	0.986301i	$-0.552748\pi$
$173$	−4.33926	−0.329908	−0.164954	+	0.986301i	$0.552748\pi$
$174$	7.17907	0.544244
$175$	1.49871	0.113292
$176$	19.2641	1.45209
$177$	−12.4655	−0.936966
$178$	−43.7426	−3.27864
$179$	−21.8723	−1.63481	−0.817405	−	0.576063i	$-0.804588\pi$
$179$	−21.8723	−1.63481	−0.817405	+	0.576063i	$0.804588\pi$
$180$	57.1271	4.25801
$181$	−5.03954	−0.374586	−0.187293	−	0.982304i	$-0.559971\pi$
$181$	−5.03954	−0.374586	−0.187293	+	0.982304i	$0.559971\pi$
$182$	13.2977	0.985690
$183$	38.7678	2.86579
$184$	26.6110	1.96179
$185$	−13.4791	−0.991006
$186$	23.5242	1.72488
$187$	11.2128	0.819963
$188$	35.5172	2.59036
$189$	8.38556	0.609960
$190$	−20.4317	−1.48227
$191$	15.1279	1.09462	0.547309	−	0.836931i	$-0.315652\pi$
$191$	15.1279	1.09462	0.547309	+	0.836931i	$0.315652\pi$
$192$	−29.6126	−2.13710
$193$	−18.7042	−1.34636	−0.673178	−	0.739480i	$-0.735071\pi$
$193$	−18.7042	−1.34636	−0.673178	+	0.739480i	$0.735071\pi$
$194$	−33.4307	−2.40019
$195$	−42.6006	−3.05069
$196$	−23.0135	−1.64382
$197$	−10.7712	−0.767414	−0.383707	−	0.923455i	$-0.625353\pi$
$197$	−10.7712	−0.767414	−0.383707	+	0.923455i	$0.625353\pi$
$198$	−93.0289	−6.61128
$199$	18.2605	1.29445	0.647225	−	0.762299i	$-0.275930\pi$
$199$	18.2605	1.29445	0.647225	+	0.762299i	$0.275930\pi$
$200$	−6.66766	−0.471475
$201$	−26.4140	−1.86310
$202$	30.5275	2.14791
$203$	−0.984137	−0.0690728
$204$	19.3548	1.35511
$205$	23.1944	1.61997
$206$	−37.6120	−2.62055
$207$	−35.6299	−2.47645
$208$	−16.4027	−1.13732
$209$	21.8297	1.50999
$210$	−18.0444	−1.24518
$211$	−19.1629	−1.31923	−0.659614	−	0.751605i	$-0.729280\pi$
$211$	−19.1629	−1.31923	−0.659614	+	0.751605i	$0.729280\pi$
$212$	−11.1611	−0.766548
$213$	−24.9055	−1.70650
$214$	27.5952	1.88637
$215$	16.4039	1.11874
$216$	−37.3067	−2.53840
$217$	−3.22479	−0.218913
$218$	−4.32507	−0.292930
$219$	−18.7482	−1.26688
$220$	64.1265	4.32341
$221$	−9.54731	−0.642222
$222$	37.8888	2.54293
$223$	−3.53173	−0.236502	−0.118251	−	0.992984i	$-0.537729\pi$
$223$	−3.53173	−0.236502	−0.118251	+	0.992984i	$0.537729\pi$
$224$	1.67007	0.111586
$225$	8.92743	0.595162
$226$	50.2107	3.33997
$227$	1.64815	0.109391	0.0546957	−	0.998503i	$-0.482581\pi$
$227$	1.64815	0.109391	0.0546957	+	0.998503i	$0.482581\pi$
$228$	37.6809	2.49548
$229$	−17.0571	−1.12717	−0.563584	−	0.826059i	$-0.690578\pi$
$229$	−17.0571	−1.12717	−0.563584	+	0.826059i	$0.690578\pi$
$230$	37.4341	2.46833
$231$	19.2790	1.26847
$232$	4.37835	0.287453
$233$	11.5119	0.754167	0.377084	−	0.926179i	$-0.376927\pi$
$233$	11.5119	0.754167	0.377084	+	0.926179i	$0.376927\pi$
$234$	79.2107	5.17816
$235$	23.7738	1.55083
$236$	−15.9771	−1.04002
$237$	23.9910	1.55839
$238$	−4.04398	−0.262132
$239$	7.02240	0.454241	0.227121	−	0.973867i	$-0.427069\pi$
$239$	7.02240	0.454241	0.227121	+	0.973867i	$0.427069\pi$
$240$	22.2578	1.43673
$241$	8.57830	0.552577	0.276289	−	0.961075i	$-0.410895\pi$
$241$	8.57830	0.552577	0.276289	+	0.961075i	$0.410895\pi$
$242$	−77.9000	−5.00760
$243$	−2.40423	−0.154231
$244$	49.6888	3.18100
$245$	−15.4043	−0.984147
$246$	−65.1977	−4.15685
$247$	−18.5872	−1.18268
$248$	14.3469	0.911026
$249$	43.8472	2.77870
$250$	21.4159	1.35446
$251$	1.80845	0.114148	0.0570741	−	0.998370i	$-0.481823\pi$
$251$	1.80845	0.114148	0.0570741	+	0.998370i	$0.481823\pi$
$252$	22.0130	1.38669
$253$	−39.9954	−2.51449
$254$	−11.8637	−0.744397
$255$	12.9553	0.811293
$256$	−29.7699	−1.86062
$257$	−19.7244	−1.23038	−0.615189	−	0.788380i	$-0.710920\pi$
$257$	−19.7244	−1.23038	−0.615189	+	0.788380i	$0.710920\pi$
$258$	−46.1100	−2.87068
$259$	−5.19396	−0.322737
$260$	−54.6014	−3.38623
$261$	−5.86223	−0.362863
$262$	−19.6709	−1.21527
$263$	−9.55232	−0.589022	−0.294511	−	0.955648i	$-0.595157\pi$
$263$	−9.55232	−0.589022	−0.294511	+	0.955648i	$0.595157\pi$
$264$	−85.7710	−5.27884
$265$	−7.47080	−0.458927
$266$	−7.87302	−0.482726
$267$	53.9983	3.30464
$268$	−33.8550	−2.06802
$269$	−17.0996	−1.04258	−0.521290	−	0.853380i	$-0.674549\pi$
$269$	−17.0996	−1.04258	−0.521290	+	0.853380i	$0.674549\pi$
$270$	−52.4798	−3.19382
$271$	−9.83447	−0.597402	−0.298701	−	0.954347i	$-0.596553\pi$
$271$	−9.83447	−0.597402	−0.298701	+	0.954347i	$0.596553\pi$
$272$	4.98824	0.302457
$273$	−16.4154	−0.993505
$274$	−27.8492	−1.68243
$275$	10.0212	0.604304
$276$	−69.0372	−4.15555
$277$	−9.82153	−0.590119	−0.295059	−	0.955479i	$-0.595339\pi$
$277$	−9.82153	−0.590119	−0.295059	+	0.955479i	$0.595339\pi$
$278$	−2.41155	−0.144635
$279$	−19.2092	−1.15003
$280$	−11.0049	−0.657667
$281$	−20.4604	−1.22056	−0.610281	−	0.792185i	$-0.708944\pi$
$281$	−20.4604	−1.22056	−0.610281	+	0.792185i	$0.708944\pi$
$282$	−66.8262	−3.97944
$283$	9.70786	0.577073	0.288536	−	0.957469i	$-0.406831\pi$
$283$	9.70786	0.577073	0.288536	+	0.957469i	$0.406831\pi$
$284$	−31.9215	−1.89420
$285$	25.2221	1.49403
$286$	88.9158	5.25770
$287$	8.93757	0.527568
$288$	9.94813	0.586199
$289$	−14.0966	−0.829209
$290$	6.15908	0.361674
$291$	41.2687	2.41922
$292$	−24.0296	−1.40623
$293$	−16.4207	−0.959310	−0.479655	−	0.877457i	$-0.659238\pi$
$293$	−16.4207	−0.959310	−0.479655	+	0.877457i	$0.659238\pi$
$294$	43.3004	2.52533
$295$	−10.6944	−0.622655
$296$	23.1075	1.34310
$297$	56.0706	3.25355
$298$	−31.9266	−1.84946
$299$	34.0546	1.96943
$300$	17.2980	0.998698
$301$	6.32095	0.364334
$302$	−13.8126	−0.794824
$303$	−37.6848	−2.16494
$304$	9.71136	0.556985
$305$	33.2597	1.90445
$306$	−24.0889	−1.37707
$307$	−18.0462	−1.02995	−0.514974	−	0.857206i	$-0.672199\pi$
$307$	−18.0462	−1.02995	−0.514974	+	0.857206i	$0.672199\pi$
$308$	24.7100	1.40799
$309$	46.4303	2.64133
$310$	20.1819	1.14626
$311$	−13.8993	−0.788159	−0.394080	−	0.919076i	$-0.628937\pi$
$311$	−13.8993	−0.788159	−0.394080	+	0.919076i	$0.628937\pi$
$312$	73.0308	4.13456
$313$	−19.8011	−1.11923	−0.559614	−	0.828754i	$-0.689050\pi$
$313$	−19.8011	−1.11923	−0.559614	+	0.828754i	$0.689050\pi$
$314$	45.3328	2.55828
$315$	14.7346	0.830200
$316$	30.7494	1.72979
$317$	−8.76680	−0.492393	−0.246196	−	0.969220i	$-0.579181\pi$
$317$	−8.76680	−0.492393	−0.246196	+	0.969220i	$0.579181\pi$
$318$	20.9998	1.17761
$319$	−6.58049	−0.368437
$320$	−25.4053	−1.42020
$321$	−34.0651	−1.90133
$322$	14.4246	0.803850
$323$	5.65258	0.314518
$324$	29.6817	1.64898
$325$	−8.53272	−0.473310
$326$	−28.2020	−1.56196
$327$	5.33910	0.295253
$328$	−39.7626	−2.19552
$329$	9.16082	0.505052
$330$	−120.655	−6.64185
$331$	28.5451	1.56898	0.784490	−	0.620141i	$-0.212925\pi$
$331$	28.5451	1.56898	0.784490	+	0.620141i	$0.212925\pi$
$332$	56.1991	3.08433
$333$	−30.9390	−1.69545
$334$	22.3833	1.22476
$335$	−22.6612	−1.23811
$336$	8.57665	0.467894
$337$	−31.5528	−1.71879	−0.859394	−	0.511313i	$-0.829159\pi$
$337$	−31.5528	−1.71879	−0.859394	+	0.511313i	$0.829159\pi$
$338$	−44.3584	−2.41278
$339$	−61.9829	−3.36645
$340$	16.6049	0.900527
$341$	−21.5628	−1.16769
$342$	−46.8974	−2.53592
$343$	−12.8248	−0.692471
$344$	−28.1214	−1.51621
$345$	−46.2107	−2.48790
$346$	10.4643	0.562566
$347$	−13.1935	−0.708265	−0.354132	−	0.935195i	$-0.615224\pi$
$347$	−13.1935	−0.708265	−0.354132	+	0.935195i	$0.615224\pi$
$348$	−11.3588	−0.608894
$349$	−22.8263	−1.22186	−0.610931	−	0.791684i	$-0.709205\pi$
$349$	−22.8263	−1.22186	−0.610931	+	0.791684i	$0.709205\pi$
$350$	−3.61422	−0.193188
$351$	−47.7420	−2.54828
$352$	11.1670	0.595203
$353$	−2.63742	−0.140376	−0.0701879	−	0.997534i	$-0.522360\pi$
$353$	−2.63742	−0.140376	−0.0701879	+	0.997534i	$0.522360\pi$
$354$	30.0612	1.59774
$355$	−21.3670	−1.13404
$356$	69.2099	3.66812
$357$	4.99211	0.264210
$358$	52.7461	2.78772
$359$	−5.47111	−0.288754	−0.144377	−	0.989523i	$-0.546118\pi$
$359$	−5.47111	−0.288754	−0.144377	+	0.989523i	$0.546118\pi$
$360$	−65.5530	−3.45495
$361$	−7.99527	−0.420804
$362$	12.1531	0.638753
$363$	96.1641	5.04730
$364$	−21.0397	−1.10278
$365$	−16.0845	−0.841900
$366$	−93.4904	−4.88682
$367$	26.6690	1.39211	0.696056	−	0.717988i	$-0.254937\pi$
$367$	26.6690	1.39211	0.696056	+	0.717988i	$0.254937\pi$
$368$	−17.7927	−0.927509
$369$	53.2387	2.77149
$370$	32.5056	1.68989
$371$	−2.87874	−0.149457
$372$	−37.2201	−1.92977
$373$	−20.7078	−1.07221	−0.536104	−	0.844152i	$-0.680105\pi$
$373$	−20.7078	−1.07221	−0.536104	+	0.844152i	$0.680105\pi$
$374$	−27.0403	−1.39822
$375$	−26.4370	−1.36520
$376$	−40.7558	−2.10182
$377$	5.60305	0.288572
$378$	−20.2222	−1.04012
$379$	15.6061	0.801633	0.400817	−	0.916158i	$-0.368726\pi$
$379$	15.6061	0.801633	0.400817	+	0.916158i	$0.368726\pi$
$380$	32.3273	1.65835
$381$	14.6453	0.750299
$382$	−36.4817	−1.86657
$383$	1.68753	0.0862289	0.0431144	−	0.999070i	$-0.486272\pi$
$383$	1.68753	0.0862289	0.0431144	+	0.999070i	$0.486272\pi$
$384$	61.3085	3.12864
$385$	16.5399	0.842952
$386$	45.1061	2.29584
$387$	37.6522	1.91397
$388$	52.8944	2.68530
$389$	−21.9425	−1.11253	−0.556264	−	0.831006i	$-0.687766\pi$
$389$	−21.9425	−1.11253	−0.556264	+	0.831006i	$0.687766\pi$
$390$	102.733	5.20211
$391$	−10.3564	−0.523745
$392$	26.4079	1.33380
$393$	24.2829	1.22491
$394$	25.9752	1.30861
$395$	20.5824	1.03561
$396$	147.191	7.39663
$397$	1.12046	0.0562340	0.0281170	−	0.999605i	$-0.491049\pi$
$397$	1.12046	0.0562340	0.0281170	+	0.999605i	$0.491049\pi$
$398$	−44.0360	−2.20733
$399$	9.71889	0.486553
$400$	4.45814	0.222907
$401$	−22.5407	−1.12563	−0.562813	−	0.826584i	$-0.690281\pi$
$401$	−22.5407	−1.12563	−0.562813	+	0.826584i	$0.690281\pi$
$402$	63.6988	3.17701
$403$	18.3599	0.914573
$404$	−48.3009	−2.40306
$405$	19.8677	0.987235
$406$	2.37329	0.117785
$407$	−34.7297	−1.72149
$408$	−22.2095	−1.09953
$409$	29.2680	1.44721	0.723606	−	0.690214i	$-0.242484\pi$
$409$	29.2680	1.44721	0.723606	+	0.690214i	$0.242484\pi$
$410$	−55.9345	−2.76241
$411$	34.3785	1.69577
$412$	59.5100	2.93185
$413$	−4.12092	−0.202777
$414$	85.9233	4.22290
$415$	37.6174	1.84657
$416$	−9.50829	−0.466182
$417$	2.97695	0.145782
$418$	−52.6435	−2.57488
$419$	12.6001	0.615557	0.307778	−	0.951458i	$-0.400415\pi$
$419$	12.6001	0.615557	0.307778	+	0.951458i	$0.400415\pi$
$420$	28.5500	1.39310
$421$	23.7989	1.15989	0.579943	−	0.814657i	$-0.303075\pi$
$421$	23.7989	1.15989	0.579943	+	0.814657i	$0.303075\pi$
$422$	46.2122	2.24958
$423$	54.5685	2.65321
$424$	12.8073	0.621978
$425$	2.59490	0.125871
$426$	60.0609	2.90996
$427$	12.8161	0.620212
$428$	−43.6614	−2.11045
$429$	−109.763	−5.29939
$430$	−39.5588	−1.90769
$431$	5.72573	0.275799	0.137899	−	0.990446i	$-0.455965\pi$
$431$	5.72573	0.275799	0.137899	+	0.990446i	$0.455965\pi$
$432$	24.9441	1.20012
$433$	−13.5610	−0.651699	−0.325850	−	0.945422i	$-0.605650\pi$
$433$	−13.5610	−0.651699	−0.325850	+	0.945422i	$0.605650\pi$
$434$	7.77675	0.373296
$435$	−7.60311	−0.364541
$436$	6.84316	0.327728
$437$	−20.1624	−0.964496
$438$	45.2122	2.16032
$439$	11.8657	0.566317	0.283158	−	0.959073i	$-0.408618\pi$
$439$	11.8657	0.566317	0.283158	+	0.959073i	$0.408618\pi$
$440$	−73.5848	−3.50802
$441$	−35.3579	−1.68371
$442$	23.0238	1.09513
$443$	−5.95740	−0.283045	−0.141522	−	0.989935i	$-0.545200\pi$
$443$	−5.95740	−0.283045	−0.141522	+	0.989935i	$0.545200\pi$
$444$	−59.9480	−2.84500
$445$	46.3263	2.19608
$446$	8.51695	0.403289
$447$	39.4120	1.86412
$448$	−9.78948	−0.462510
$449$	13.4065	0.632692	0.316346	−	0.948644i	$-0.397544\pi$
$449$	13.4065	0.632692	0.316346	+	0.948644i	$0.397544\pi$
$450$	−21.5290	−1.01488
$451$	59.7616	2.81407
$452$	−79.4438	−3.73672
$453$	17.0510	0.801126
$454$	−3.97459	−0.186537
$455$	−14.0831	−0.660227
$456$	−43.2386	−2.02483
$457$	30.5928	1.43107	0.715535	−	0.698576i	$-0.246183\pi$
$457$	30.5928	1.43107	0.715535	+	0.698576i	$0.246183\pi$
$458$	41.1342	1.92207
$459$	14.5189	0.677684
$460$	−59.2285	−2.76154
$461$	−18.1146	−0.843679	−0.421840	−	0.906670i	$-0.638616\pi$
$461$	−18.1146	−0.843679	−0.421840	+	0.906670i	$0.638616\pi$
$462$	−46.4924	−2.16302
$463$	37.8503	1.75905	0.879526	−	0.475851i	$-0.157860\pi$
$463$	37.8503	1.75905	0.879526	+	0.475851i	$0.157860\pi$
$464$	−2.92746	−0.135904
$465$	−24.9137	−1.15534
$466$	−27.7614	−1.28602
$467$	36.4363	1.68607	0.843036	−	0.537858i	$-0.180766\pi$
$467$	36.4363	1.68607	0.843036	+	0.537858i	$0.180766\pi$
$468$	−125.328	−5.79328
$469$	−8.73209	−0.403211
$470$	−57.3317	−2.64451
$471$	−55.9613	−2.57856
$472$	18.3337	0.843875
$473$	42.2654	1.94337
$474$	−57.8556	−2.65740
$475$	5.05188	0.231796
$476$	6.39841	0.293271
$477$	−17.1479	−0.785148
$478$	−16.9349	−0.774583
$479$	−17.8368	−0.814985	−0.407493	−	0.913208i	$-0.633597\pi$
$479$	−17.8368	−0.814985	−0.407493	+	0.913208i	$0.633597\pi$
$480$	12.9024	0.588910
$481$	29.5711	1.34832
$482$	−20.6870	−0.942267
$483$	−17.8065	−0.810224
$484$	123.254	5.60246
$485$	35.4054	1.60767
$486$	5.79791	0.262999
$487$	−19.1219	−0.866496	−0.433248	−	0.901275i	$-0.642633\pi$
$487$	−19.1219	−0.866496	−0.433248	+	0.901275i	$0.642633\pi$
$488$	−57.0176	−2.58107
$489$	34.8141	1.57435
$490$	37.1483	1.67819
$491$	−4.04399	−0.182503	−0.0912515	−	0.995828i	$-0.529087\pi$
$491$	−4.04399	−0.182503	−0.0912515	+	0.995828i	$0.529087\pi$
$492$	103.156	4.65064
$493$	−1.70395	−0.0767421
$494$	44.8240	2.01673
$495$	98.5238	4.42831
$496$	−9.59262	−0.430721
$497$	−8.23340	−0.369319
$498$	−105.740	−4.73830
$499$	−16.9688	−0.759627	−0.379813	−	0.925063i	$-0.624012\pi$
$499$	−16.9688	−0.759627	−0.379813	+	0.925063i	$0.624012\pi$
$500$	−33.8844	−1.51536
$501$	−27.6312	−1.23447
$502$	−4.36116	−0.194648
$503$	12.3071	0.548748	0.274374	−	0.961623i	$-0.411529\pi$
$503$	12.3071	0.548748	0.274374	+	0.961623i	$0.411529\pi$
$504$	−25.2597	−1.12516
$505$	−32.3307	−1.43870
$506$	96.4509	4.28776
$507$	54.7584	2.43191
$508$	18.7709	0.832824
$509$	−9.49673	−0.420935	−0.210468	−	0.977601i	$-0.567499\pi$
$509$	−9.49673	−0.420935	−0.210468	+	0.977601i	$0.567499\pi$
$510$	−31.2424	−1.38344
$511$	−6.19788	−0.274178
$512$	30.6027	1.35246
$513$	28.2661	1.24798
$514$	47.5665	2.09807
$515$	39.8336	1.75528
$516$	72.9556	3.21169
$517$	61.2544	2.69397
$518$	12.5255	0.550338
$519$	−12.9178	−0.567026
$520$	62.6547	2.74759
$521$	37.4263	1.63968	0.819838	−	0.572596i	$-0.194063\pi$
$521$	37.4263	1.63968	0.819838	+	0.572596i	$0.194063\pi$
$522$	14.1371	0.618763
$523$	−0.781182	−0.0341587	−0.0170794	−	0.999854i	$-0.505437\pi$
$523$	−0.781182	−0.0341587	−0.0170794	+	0.999854i	$0.505437\pi$
$524$	31.1235	1.35964
$525$	4.46160	0.194720
$526$	23.0359	1.00441
$527$	−5.58346	−0.243219
$528$	57.3483	2.49576
$529$	13.9405	0.606110
$530$	18.0162	0.782574
$531$	−24.5472	−1.06526
$532$	12.4568	0.540069
$533$	−50.8848	−2.20407
$534$	−130.219	−5.63515
$535$	−29.2252	−1.26351
$536$	38.8484	1.67800
$537$	−65.1127	−2.80982
$538$	41.2365	1.77783
$539$	−39.6901	−1.70957
$540$	83.0340	3.57322
$541$	0.711324	0.0305822	0.0152911	−	0.999883i	$-0.495133\pi$
$541$	0.711324	0.0305822	0.0152911	+	0.999883i	$0.495133\pi$
$542$	23.7163	1.01870
$543$	−15.0025	−0.643817
$544$	2.89158	0.123975
$545$	4.58053	0.196208
$546$	39.5865	1.69415
$547$	8.05725	0.344503	0.172252	−	0.985053i	$-0.444896\pi$
$547$	8.05725	0.344503	0.172252	+	0.985053i	$0.444896\pi$
$548$	44.0632	1.88228
$549$	76.3418	3.25819
$550$	−24.1667	−1.03047
$551$	−3.31734	−0.141323
$552$	79.2197	3.37182
$553$	7.93109	0.337264
$554$	23.6851	1.00628
$555$	−40.1267	−1.70329
$556$	3.81557	0.161816
$557$	14.1408	0.599163	0.299581	−	0.954071i	$-0.403153\pi$
$557$	14.1408	0.599163	0.299581	+	0.954071i	$0.403153\pi$
$558$	46.3240	1.96105
$559$	−35.9875	−1.52211
$560$	7.35809	0.310936
$561$	33.3800	1.40931
$562$	49.3412	2.08133
$563$	11.2965	0.476090	0.238045	−	0.971254i	$-0.423493\pi$
$563$	11.2965	0.476090	0.238045	+	0.971254i	$0.423493\pi$
$564$	105.733	4.45216
$565$	−53.1765	−2.23715
$566$	−23.4110	−0.984038
$567$	7.65569	0.321509
$568$	36.6298	1.53695
$569$	−4.49306	−0.188359	−0.0941794	−	0.995555i	$-0.530023\pi$
$569$	−4.49306	−0.188359	−0.0941794	+	0.995555i	$0.530023\pi$
$570$	−60.8243	−2.54765
$571$	3.13847	0.131341	0.0656704	−	0.997841i	$-0.479081\pi$
$571$	3.13847	0.131341	0.0656704	+	0.997841i	$0.479081\pi$
$572$	−140.683	−5.88226
$573$	45.0350	1.88137
$574$	−21.5534	−0.899621
$575$	−9.25582	−0.385994
$576$	−58.3133	−2.42972
$577$	29.0973	1.21134	0.605668	−	0.795717i	$-0.292906\pi$
$577$	29.0973	1.21134	0.605668	+	0.795717i	$0.292906\pi$
$578$	33.9945	1.41399
$579$	−55.6814	−2.31404
$580$	−9.74494	−0.404637
$581$	14.4952	0.601363
$582$	−99.5216	−4.12530
$583$	−19.2489	−0.797208
$584$	27.5739	1.14101
$585$	−83.8893	−3.46840
$586$	39.5994	1.63584
$587$	−21.8382	−0.901360	−0.450680	−	0.892685i	$-0.648819\pi$
$587$	−21.8382	−0.901360	−0.450680	+	0.892685i	$0.648819\pi$
$588$	−68.5102	−2.82531
$589$	−10.8702	−0.447898
$590$	25.7902	1.06177
$591$	−32.0653	−1.31899
$592$	−15.4502	−0.634998
$593$	13.8595	0.569141	0.284571	−	0.958655i	$-0.408149\pi$
$593$	13.8595	0.569141	0.284571	+	0.958655i	$0.408149\pi$
$594$	−135.217	−5.54802
$595$	4.28284	0.175579
$596$	50.5145	2.06916
$597$	54.3605	2.22483
$598$	−82.1244	−3.35832
$599$	−22.3970	−0.915115	−0.457557	−	0.889180i	$-0.651276\pi$
$599$	−22.3970	−0.915115	−0.457557	+	0.889180i	$0.651276\pi$
$600$	−19.8493	−0.810344
$601$	38.6391	1.57612	0.788062	−	0.615596i	$-0.211085\pi$
$601$	38.6391	1.57612	0.788062	+	0.615596i	$0.211085\pi$
$602$	−15.2433	−0.621270
$603$	−52.0147	−2.11820
$604$	21.8544	0.889241
$605$	82.5013	3.35415
$606$	90.8789	3.69170
$607$	40.7542	1.65416	0.827081	−	0.562083i	$-0.190000\pi$
$607$	40.7542	1.65416	0.827081	+	0.562083i	$0.190000\pi$
$608$	5.62948	0.228305
$609$	−2.92973	−0.118718
$610$	−80.2075	−3.24751
$611$	−52.1559	−2.11000
$612$	38.1136	1.54065
$613$	7.93098	0.320329	0.160165	−	0.987090i	$-0.448797\pi$
$613$	7.93098	0.320329	0.160165	+	0.987090i	$0.448797\pi$
$614$	43.5192	1.75629
$615$	69.0486	2.78431
$616$	−28.3546	−1.14244
$617$	3.88610	0.156448	0.0782242	−	0.996936i	$-0.475075\pi$
$617$	3.88610	0.156448	0.0782242	+	0.996936i	$0.475075\pi$
$618$	−111.969	−4.50406
$619$	−21.1665	−0.850755	−0.425378	−	0.905016i	$-0.639859\pi$
$619$	−21.1665	−0.850755	−0.425378	+	0.905016i	$0.639859\pi$
$620$	−31.9320	−1.28242
$621$	−51.7879	−2.07818
$622$	33.5190	1.34399
$623$	17.8510	0.715187
$624$	−48.8300	−1.95476
$625$	−30.2952	−1.21181
$626$	47.7515	1.90853
$627$	64.9860	2.59529
$628$	−71.7259	−2.86218
$629$	−8.99290	−0.358570
$630$	−35.5332	−1.41568
$631$	7.87041	0.313316	0.156658	−	0.987653i	$-0.449928\pi$
$631$	7.87041	0.313316	0.156658	+	0.987653i	$0.449928\pi$
$632$	−35.2848	−1.40355
$633$	−57.0469	−2.26741
$634$	21.1416	0.839639
$635$	12.5645	0.498606
$636$	−33.2261	−1.31750
$637$	33.7946	1.33899
$638$	15.8692	0.628267
$639$	−49.0441	−1.94016
$640$	52.5979	2.07911
$641$	−15.4339	−0.609601	−0.304801	−	0.952416i	$-0.598590\pi$
$641$	−15.4339	−0.609601	−0.304801	+	0.952416i	$0.598590\pi$
$642$	82.1496	3.24219
$643$	−37.4522	−1.47697	−0.738486	−	0.674269i	$-0.764459\pi$
$643$	−37.4522	−1.47697	−0.738486	+	0.674269i	$0.764459\pi$
$644$	−22.8227	−0.899340
$645$	48.8335	1.92282
$646$	−13.6315	−0.536323
$647$	−1.72092	−0.0676562	−0.0338281	−	0.999428i	$-0.510770\pi$
$647$	−1.72092	−0.0676562	−0.0338281	+	0.999428i	$0.510770\pi$
$648$	−34.0596	−1.33799
$649$	−27.5548	−1.08162
$650$	20.5771	0.807100
$651$	−9.60005	−0.376256
$652$	44.6214	1.74751
$653$	−29.3431	−1.14828	−0.574141	−	0.818756i	$-0.694664\pi$
$653$	−29.3431	−1.14828	−0.574141	+	0.818756i	$0.694664\pi$
$654$	−12.8755	−0.503472
$655$	20.8328	0.814005
$656$	26.5861	1.03801
$657$	−36.9191	−1.44035
$658$	−22.0918	−0.861227
$659$	1.91595	0.0746348	0.0373174	−	0.999303i	$-0.488119\pi$
$659$	1.91595	0.0746348	0.0373174	+	0.999303i	$0.488119\pi$
$660$	190.901	7.43083
$661$	−22.7006	−0.882950	−0.441475	−	0.897274i	$-0.645545\pi$
$661$	−22.7006	−0.882950	−0.441475	+	0.897274i	$0.645545\pi$
$662$	−68.8379	−2.67546
$663$	−28.4219	−1.10381
$664$	−64.4882	−2.50263
$665$	8.33805	0.323336
$666$	74.6109	2.89111
$667$	6.07787	0.235336
$668$	−35.4151	−1.37025
$669$	−10.5138	−0.406487
$670$	54.6486	2.11126
$671$	85.6954	3.30823
$672$	4.97170	0.191788
$673$	−25.7822	−0.993831	−0.496916	−	0.867799i	$-0.665534\pi$
$673$	−25.7822	−0.993831	−0.496916	+	0.867799i	$0.665534\pi$
$674$	76.0911	2.93092
$675$	12.9760	0.499446
$676$	70.1842	2.69939
$677$	30.5774	1.17519	0.587593	−	0.809157i	$-0.300076\pi$
$677$	30.5774	1.17519	0.587593	+	0.809157i	$0.300076\pi$
$678$	149.475	5.74054
$679$	13.6428	0.523564
$680$	−19.0540	−0.730688
$681$	4.90645	0.188016
$682$	51.9997	1.99117
$683$	−24.1099	−0.922538	−0.461269	−	0.887260i	$-0.652606\pi$
$683$	−24.1099	−0.922538	−0.461269	+	0.887260i	$0.652606\pi$
$684$	74.2015	2.83717
$685$	29.4941	1.12691
$686$	30.9275	1.18082
$687$	−50.7783	−1.93731
$688$	18.8026	0.716842
$689$	16.3897	0.624399
$690$	111.439	4.24243
$691$	−9.55370	−0.363440	−0.181720	−	0.983350i	$-0.558166\pi$
$691$	−9.55370	−0.363440	−0.181720	+	0.983350i	$0.558166\pi$
$692$	−16.5568	−0.629393
$693$	37.9644	1.44215
$694$	31.8168	1.20775
$695$	2.55399	0.0968784
$696$	13.0341	0.494057
$697$	15.4747	0.586144
$698$	55.0467	2.08355
$699$	34.2702	1.29622
$700$	5.71845	0.216137
$701$	26.4434	0.998753	0.499376	−	0.866385i	$-0.333562\pi$
$701$	26.4434	0.998753	0.499376	+	0.866385i	$0.333562\pi$
$702$	115.132	4.34539
$703$	−17.5078	−0.660321
$704$	−65.4580	−2.46704
$705$	70.7734	2.66548
$706$	6.36028	0.239372
$707$	−12.4581	−0.468534
$708$	−47.5631	−1.78753
$709$	−30.9067	−1.16073	−0.580363	−	0.814358i	$-0.697089\pi$
$709$	−30.9067	−1.16073	−0.580363	+	0.814358i	$0.697089\pi$
$710$	51.5276	1.93380
$711$	47.2433	1.77176
$712$	−79.4179	−2.97631
$713$	19.9158	0.745853
$714$	−12.0387	−0.450538
$715$	−94.1677	−3.52167
$716$	−83.4553	−3.11887
$717$	20.9053	0.780724
$718$	13.1939	0.492390
$719$	−17.7183	−0.660781	−0.330391	−	0.943844i	$-0.607181\pi$
$719$	−17.7183	−0.660781	−0.330391	+	0.943844i	$0.607181\pi$
$720$	43.8302	1.63345
$721$	15.3492	0.571634
$722$	19.2810	0.717564
$723$	25.5372	0.949738
$724$	−19.2287	−0.714631
$725$	−1.52287	−0.0565580
$726$	−231.904	−8.60678
$727$	36.0694	1.33774	0.668870	−	0.743379i	$-0.266778\pi$
$727$	36.0694	1.33774	0.668870	+	0.743379i	$0.266778\pi$
$728$	24.1429	0.894796
$729$	−30.4945	−1.12943
$730$	38.7885	1.43563
$731$	10.9442	0.404786
$732$	147.921	5.46733
$733$	−4.12781	−0.152464	−0.0762321	−	0.997090i	$-0.524289\pi$
$733$	−4.12781	−0.152464	−0.0762321	+	0.997090i	$0.524289\pi$
$734$	−64.3137	−2.37386
$735$	−45.8579	−1.69150
$736$	−10.3141	−0.380181
$737$	−58.3877	−2.15074
$738$	−128.388	−4.72602
$739$	8.37073	0.307922	0.153961	−	0.988077i	$-0.450797\pi$
$739$	8.37073	0.307922	0.153961	+	0.988077i	$0.450797\pi$
$740$	−51.4307	−1.89063
$741$	−55.3332	−2.03271
$742$	6.94223	0.254857
$743$	−30.8629	−1.13225	−0.566124	−	0.824320i	$-0.691558\pi$
$743$	−30.8629	−1.13225	−0.566124	+	0.824320i	$0.691558\pi$
$744$	42.7099	1.56582
$745$	33.8124	1.23879
$746$	49.9378	1.82835
$747$	86.3442	3.15917
$748$	42.7834	1.56432
$749$	−11.2614	−0.411483
$750$	63.7541	2.32797
$751$	13.1883	0.481247	0.240624	−	0.970619i	$-0.422648\pi$
$751$	13.1883	0.481247	0.240624	+	0.970619i	$0.422648\pi$
$752$	27.2502	0.993712
$753$	5.38366	0.196192
$754$	−13.5120	−0.492079
$755$	14.6284	0.532383
$756$	31.9957	1.16367
$757$	16.8700	0.613152	0.306576	−	0.951846i	$-0.400817\pi$
$757$	16.8700	0.613152	0.306576	+	0.951846i	$0.400817\pi$
$758$	−37.6350	−1.36696
$759$	−119.064	−4.32176
$760$	−37.0953	−1.34559
$761$	−10.4682	−0.379473	−0.189737	−	0.981835i	$-0.560763\pi$
$761$	−10.4682	−0.379473	−0.189737	+	0.981835i	$0.560763\pi$
$762$	−35.3178	−1.27943
$763$	1.76503	0.0638983
$764$	57.7217	2.08830
$765$	25.5117	0.922378
$766$	−4.06957	−0.147039
$767$	23.4619	0.847160
$768$	−88.6234	−3.19792
$769$	−15.1924	−0.547850	−0.273925	−	0.961751i	$-0.588322\pi$
$769$	−15.1924	−0.547850	−0.273925	+	0.961751i	$0.588322\pi$
$770$	−39.8868	−1.43742
$771$	−58.7187	−2.11470
$772$	−71.3672	−2.56856
$773$	−18.0796	−0.650280	−0.325140	−	0.945666i	$-0.605411\pi$
$773$	−18.0796	−0.650280	−0.325140	+	0.945666i	$0.605411\pi$
$774$	−90.8001	−3.26374
$775$	−4.99011	−0.179250
$776$	−60.6960	−2.17886
$777$	−15.4621	−0.554701
$778$	52.9154	1.89711
$779$	30.1269	1.07941
$780$	−162.546	−5.82007
$781$	−55.0532	−1.96996
$782$	24.9750	0.893103
$783$	−8.52073	−0.304506
$784$	−17.6569	−0.630603
$785$	−48.0105	−1.71357
$786$	−58.5593	−2.08874
$787$	−37.6582	−1.34237	−0.671186	−	0.741289i	$-0.734215\pi$
$787$	−37.6582	−1.34237	−0.671186	+	0.741289i	$0.734215\pi$
$788$	−41.0982	−1.46406
$789$	−28.4368	−1.01238
$790$	−49.6356	−1.76595
$791$	−20.4906	−0.728563
$792$	−168.901	−6.00163
$793$	−72.9665	−2.59111
$794$	−2.70203	−0.0958916
$795$	−22.2402	−0.788778
$796$	69.6741	2.46953
$797$	−24.9058	−0.882209	−0.441104	−	0.897456i	$-0.645413\pi$
$797$	−24.9058	−0.882209	−0.441104	+	0.897456i	$0.645413\pi$
$798$	−23.4376	−0.829682
$799$	15.8612	0.561129
$800$	2.58429	0.0913685
$801$	106.334	3.75712
$802$	54.3579	1.91944
$803$	−41.4425	−1.46247
$804$	−100.785	−3.55440
$805$	−15.2766	−0.538429
$806$	−44.2759	−1.55955
$807$	−50.9046	−1.79193
$808$	55.4249	1.94984
$809$	42.1964	1.48355	0.741774	−	0.670650i	$-0.233985\pi$
$809$	42.1964	1.48355	0.741774	+	0.670650i	$0.233985\pi$
$810$	−47.9120	−1.68346
$811$	22.6981	0.797037	0.398519	−	0.917160i	$-0.369524\pi$
$811$	22.6981	0.797037	0.398519	+	0.917160i	$0.369524\pi$
$812$	−3.75505	−0.131776
$813$	−29.2767	−1.02678
$814$	83.7525	2.93552
$815$	29.8678	1.04622
$816$	14.8497	0.519845
$817$	21.3067	0.745428
$818$	−70.5813	−2.46782
$819$	−32.3253	−1.12954
$820$	88.5000	3.09055
$821$	−1.36935	−0.0477905	−0.0238953	−	0.999714i	$-0.507607\pi$
$821$	−1.36935	−0.0477905	−0.0238953	+	0.999714i	$0.507607\pi$
$822$	−82.9056	−2.89166
$823$	34.4023	1.19919	0.599595	−	0.800303i	$-0.295328\pi$
$823$	34.4023	1.19919	0.599595	+	0.800303i	$0.295328\pi$
$824$	−68.2874	−2.37890
$825$	29.8328	1.03864
$826$	9.93781	0.345780
$827$	−12.8014	−0.445150	−0.222575	−	0.974916i	$-0.571446\pi$
$827$	−12.8014	−0.445150	−0.222575	+	0.974916i	$0.571446\pi$
$828$	−135.949	−4.72454
$829$	−50.3176	−1.74760	−0.873801	−	0.486284i	$-0.838352\pi$
$829$	−50.3176	−1.74760	−0.873801	+	0.486284i	$0.838352\pi$
$830$	−90.7163	−3.14881
$831$	−29.2382	−1.01426
$832$	55.7351	1.93227
$833$	−10.2773	−0.356089
$834$	−7.17907	−0.248591
$835$	−23.7054	−0.820360
$836$	83.2929	2.88075
$837$	−27.9205	−0.965074
$838$	−30.3858	−1.04966
$839$	1.92110	0.0663237	0.0331619	−	0.999450i	$-0.489442\pi$
$839$	1.92110	0.0663237	0.0331619	+	0.999450i	$0.489442\pi$
$840$	−32.7610	−1.13036
$841$	1.00000	0.0344828
$842$	−57.3921	−1.97786
$843$	−60.9095	−2.09783
$844$	−73.1174	−2.51680
$845$	46.9784	1.61611
$846$	−131.595	−4.52432
$847$	31.7904	1.09233
$848$	−8.56324	−0.294063
$849$	28.8998	0.991840
$850$	−6.25773	−0.214638
$851$	32.0770	1.09959
$852$	−95.0289	−3.25563
$853$	−40.9520	−1.40217	−0.701085	−	0.713078i	$-0.747301\pi$
$853$	−40.9520	−1.40217	−0.701085	+	0.713078i	$0.747301\pi$
$854$	−30.9066	−1.05760
$855$	49.6675	1.69859
$856$	50.1012	1.71242
$857$	41.8356	1.42908	0.714539	−	0.699596i	$-0.246637\pi$
$857$	41.8356	1.42908	0.714539	+	0.699596i	$0.246637\pi$
$858$	264.698	9.03664
$859$	44.1672	1.50697	0.753483	−	0.657467i	$-0.228372\pi$
$859$	44.1672	1.50697	0.753483	+	0.657467i	$0.228372\pi$
$860$	62.5902	2.13431
$861$	26.6067	0.906754
$862$	−13.8079	−0.470299
$863$	−50.9051	−1.73283	−0.866415	−	0.499325i	$-0.833581\pi$
$863$	−50.9051	−1.73283	−0.866415	+	0.499325i	$0.833581\pi$
$864$	14.4596	0.491924
$865$	−11.0824	−0.376814
$866$	32.7030	1.11129
$867$	−41.9647	−1.42520
$868$	−12.3044	−0.417640
$869$	53.0317	1.79898
$870$	18.3353	0.621624
$871$	49.7150	1.68453
$872$	−7.85248	−0.265918
$873$	81.2667	2.75046
$874$	48.6225	1.64468
$875$	−8.73968	−0.295455
$876$	−71.5351	−2.41695
$877$	37.7123	1.27346	0.636728	−	0.771089i	$-0.280288\pi$
$877$	37.7123	1.27346	0.636728	+	0.771089i	$0.280288\pi$
$878$	−28.6146	−0.965696
$879$	−48.8837	−1.64881
$880$	49.2004	1.65854
$881$	33.2442	1.12003	0.560013	−	0.828484i	$-0.310796\pi$
$881$	33.2442	1.12003	0.560013	+	0.828484i	$0.310796\pi$
$882$	85.2674	2.87110
$883$	−13.3151	−0.448090	−0.224045	−	0.974579i	$-0.571926\pi$
$883$	−13.3151	−0.448090	−0.224045	+	0.974579i	$0.571926\pi$
$884$	−36.4285	−1.22522
$885$	−31.8368	−1.07018
$886$	14.3666	0.482655
$887$	4.68421	0.157280	0.0786402	−	0.996903i	$-0.474942\pi$
$887$	4.68421	0.157280	0.0786402	+	0.996903i	$0.474942\pi$
$888$	68.7899	2.30844
$889$	4.84151	0.162379
$890$	−111.718	−3.74480
$891$	51.1902	1.71494
$892$	−13.4756	−0.451196
$893$	30.8794	1.03334
$894$	−95.0439	−3.17874
$895$	−55.8616	−1.86725
$896$	20.2677	0.677096
$897$	101.379	3.38494
$898$	−32.3305	−1.07888
$899$	3.27677	0.109287
$900$	34.0633	1.13544
$901$	−4.98430	−0.166051
$902$	−144.118	−4.79861
$903$	18.8172	0.626196
$904$	91.1613	3.03198
$905$	−12.8709	−0.427845
$906$	−41.1193	−1.36610
$907$	−29.3849	−0.975711	−0.487855	−	0.872924i	$-0.662221\pi$
$907$	−29.3849	−0.975711	−0.487855	+	0.872924i	$0.662221\pi$
$908$	6.28863	0.208695
$909$	−74.2093	−2.46137
$910$	33.9622	1.12583
$911$	−37.1613	−1.23121	−0.615604	−	0.788055i	$-0.711088\pi$
$911$	−37.1613	−1.23121	−0.615604	+	0.788055i	$0.711088\pi$
$912$	28.9103	0.957314
$913$	96.9233	3.20769
$914$	−73.7761	−2.44030
$915$	99.0125	3.27325
$916$	−65.0828	−2.15040
$917$	8.02756	0.265093
$918$	−35.0131	−1.15560
$919$	−8.24216	−0.271884	−0.135942	−	0.990717i	$-0.543406\pi$
$919$	−8.24216	−0.271884	−0.135942	+	0.990717i	$0.543406\pi$
$920$	67.9644	2.24072
$921$	−53.7225	−1.77022
$922$	43.6842	1.43866
$923$	46.8757	1.54293
$924$	73.5606	2.41997
$925$	−8.03723	−0.264262
$926$	−91.2779	−2.99958
$927$	91.4310	3.00299
$928$	−1.69699	−0.0557063
$929$	−1.79090	−0.0587577	−0.0293788	−	0.999568i	$-0.509353\pi$
$929$	−1.79090	−0.0587577	−0.0293788	+	0.999568i	$0.509353\pi$
$930$	60.0806	1.97012
$931$	−20.0084	−0.655750
$932$	43.9244	1.43879
$933$	−41.3777	−1.35464
$934$	−87.8680	−2.87513
$935$	28.6375	0.936546
$936$	143.813	4.70067
$937$	5.68508	0.185723	0.0928617	−	0.995679i	$-0.470399\pi$
$937$	5.68508	0.185723	0.0928617	+	0.995679i	$0.470399\pi$
$938$	21.0579	0.687564
$939$	−58.9470	−1.92366
$940$	90.7107	2.95866
$941$	27.5721	0.898826	0.449413	−	0.893324i	$-0.351633\pi$
$941$	27.5721	0.898826	0.449413	+	0.893324i	$0.351633\pi$
$942$	134.954	4.39702
$943$	−55.1970	−1.79746
$944$	−12.2583	−0.398973
$945$	21.4167	0.696684
$946$	−101.925	−3.31388
$947$	−38.1581	−1.23997	−0.619986	−	0.784613i	$-0.712862\pi$
$947$	−38.1581	−1.23997	−0.619986	+	0.784613i	$0.712862\pi$
$948$	91.5396	2.97307
$949$	35.2868	1.14546
$950$	−12.1829	−0.395264
$951$	−26.0983	−0.846296
$952$	−7.34214	−0.237960
$953$	−17.1155	−0.554425	−0.277213	−	0.960809i	$-0.589411\pi$
$953$	−17.1155	−0.554425	−0.277213	+	0.960809i	$0.589411\pi$
$954$	41.3530	1.33885
$955$	38.6366	1.25025
$956$	26.7945	0.866595
$957$	−19.5898	−0.633248
$958$	43.0144	1.38973
$959$	11.3650	0.366996
$960$	−75.6302	−2.44096
$961$	−20.2627	−0.653637
$962$	−71.3121	−2.29920
$963$	−67.0812	−2.16166
$964$	32.7311	1.05420
$965$	−47.7703	−1.53778
$966$	42.9413	1.38161
$967$	−2.22190	−0.0714514	−0.0357257	−	0.999362i	$-0.511374\pi$
$967$	−2.22190	−0.0714514	−0.0357257	+	0.999362i	$0.511374\pi$
$968$	−141.433	−4.54584
$969$	16.8275	0.540576
$970$	−85.3818	−2.74144
$971$	−8.11794	−0.260517	−0.130259	−	0.991480i	$-0.541581\pi$
$971$	−8.11794	−0.260517	−0.130259	+	0.991480i	$0.541581\pi$
$972$	−9.17351	−0.294240
$973$	0.984137	0.0315500
$974$	46.1134	1.47757
$975$	−25.4015	−0.813499
$976$	38.1232	1.22029
$977$	18.0955	0.578927	0.289464	−	0.957189i	$-0.406523\pi$
$977$	18.0955	0.578927	0.289464	+	0.957189i	$0.406523\pi$
$978$	−83.9559	−2.68461
$979$	119.362	3.81483
$980$	−58.7764	−1.87754
$981$	10.5138	0.335680
$982$	9.75230	0.311208
$983$	8.52842	0.272014	0.136007	−	0.990708i	$-0.456573\pi$
$983$	8.52842	0.272014	0.136007	+	0.990708i	$0.456573\pi$
$984$	−118.371	−3.77353
$985$	−27.5095	−0.876525
$986$	4.10916	0.130862
$987$	27.2713	0.868055
$988$	−70.9208	−2.25629
$989$	−39.0372	−1.24131
$990$	−237.595	−7.55126
$991$	−34.9933	−1.11160	−0.555799	−	0.831317i	$-0.687588\pi$
$991$	−34.9933	−1.11160	−0.555799	+	0.831317i	$0.687588\pi$
$992$	−5.56064	−0.176551
$993$	84.9774	2.69667
$994$	19.8553	0.629771
$995$	46.6371	1.47849
$996$	167.302	5.30117
$997$	48.4491	1.53440	0.767199	−	0.641409i	$-0.221650\pi$
$997$	48.4491	1.53440	0.767199	+	0.641409i	$0.221650\pi$
$998$	40.9211	1.29533
$999$	−44.9697	−1.42278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.e.1.11	✓	103

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.e.1.11	✓	103	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41155 q^{2} +2.97695 q^{3} +3.81557 q^{4} +2.55399 q^{5} -7.17907 q^{6} +0.984137 q^{7} -4.37835 q^{8} +5.86223 q^{9} +O(q^{10})\)	\(q-2.41155 q^{2} +2.97695 q^{3} +3.81557 q^{4} +2.55399 q^{5} -7.17907 q^{6} +0.984137 q^{7} -4.37835 q^{8} +5.86223 q^{9} -6.15908 q^{10} +6.58049 q^{11} +11.3588 q^{12} -5.60305 q^{13} -2.37329 q^{14} +7.60311 q^{15} +2.92746 q^{16} +1.70395 q^{17} -14.1371 q^{18} +3.31734 q^{19} +9.74494 q^{20} +2.92973 q^{21} -15.8692 q^{22} -6.07787 q^{23} -13.0341 q^{24} +1.52287 q^{25} +13.5120 q^{26} +8.52073 q^{27} +3.75505 q^{28} -1.00000 q^{29} -18.3353 q^{30} -3.27677 q^{31} +1.69699 q^{32} +19.5898 q^{33} -4.10916 q^{34} +2.51348 q^{35} +22.3678 q^{36} -5.27768 q^{37} -7.99993 q^{38} -16.6800 q^{39} -11.1823 q^{40} +9.08164 q^{41} -7.06518 q^{42} +6.42284 q^{43} +25.1084 q^{44} +14.9721 q^{45} +14.6571 q^{46} +9.30849 q^{47} +8.71489 q^{48} -6.03148 q^{49} -3.67248 q^{50} +5.07258 q^{51} -21.3788 q^{52} -2.92515 q^{53} -20.5482 q^{54} +16.8065 q^{55} -4.30889 q^{56} +9.87555 q^{57} +2.41155 q^{58} -4.18735 q^{59} +29.0102 q^{60} +13.0226 q^{61} +7.90211 q^{62} +5.76924 q^{63} -9.94728 q^{64} -14.3101 q^{65} -47.2418 q^{66} -8.87285 q^{67} +6.50155 q^{68} -18.0935 q^{69} -6.06137 q^{70} -8.36612 q^{71} -25.6669 q^{72} -6.29778 q^{73} +12.7274 q^{74} +4.53351 q^{75} +12.6575 q^{76} +6.47610 q^{77} +40.2246 q^{78} +8.05893 q^{79} +7.47670 q^{80} +7.77909 q^{81} -21.9008 q^{82} +14.7289 q^{83} +11.1786 q^{84} +4.35187 q^{85} -15.4890 q^{86} -2.97695 q^{87} -28.8117 q^{88} +18.1388 q^{89} -36.1060 q^{90} -5.51416 q^{91} -23.1906 q^{92} -9.75480 q^{93} -22.4479 q^{94} +8.47245 q^{95} +5.05184 q^{96} +13.8628 q^{97} +14.5452 q^{98} +38.5764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * q^99

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