LMFDB - Embedded newform 8027.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71035 q^{2} -1.96664 q^{3} +5.34597 q^{4} +2.92225 q^{5} +5.33028 q^{6} +3.98832 q^{7} -9.06874 q^{8} +0.867686 q^{9} +O(q^{10})$	\(q-2.71035 q^{2} -1.96664 q^{3} +5.34597 q^{4} +2.92225 q^{5} +5.33028 q^{6} +3.98832 q^{7} -9.06874 q^{8} +0.867686 q^{9} -7.92031 q^{10} -5.77891 q^{11} -10.5136 q^{12} -3.10160 q^{13} -10.8097 q^{14} -5.74703 q^{15} +13.8875 q^{16} -7.84184 q^{17} -2.35173 q^{18} +4.98645 q^{19} +15.6223 q^{20} -7.84361 q^{21} +15.6628 q^{22} -1.00000 q^{23} +17.8350 q^{24} +3.53956 q^{25} +8.40640 q^{26} +4.19350 q^{27} +21.3215 q^{28} -3.29033 q^{29} +15.5764 q^{30} -5.20258 q^{31} -19.5023 q^{32} +11.3651 q^{33} +21.2541 q^{34} +11.6549 q^{35} +4.63862 q^{36} +4.96112 q^{37} -13.5150 q^{38} +6.09974 q^{39} -26.5011 q^{40} -5.41518 q^{41} +21.2589 q^{42} -10.2102 q^{43} -30.8939 q^{44} +2.53560 q^{45} +2.71035 q^{46} +4.75647 q^{47} -27.3117 q^{48} +8.90673 q^{49} -9.59344 q^{50} +15.4221 q^{51} -16.5811 q^{52} -3.54675 q^{53} -11.3658 q^{54} -16.8874 q^{55} -36.1691 q^{56} -9.80656 q^{57} +8.91793 q^{58} -8.68327 q^{59} -30.7235 q^{60} -10.0960 q^{61} +14.1008 q^{62} +3.46061 q^{63} +25.0832 q^{64} -9.06365 q^{65} -30.8032 q^{66} +13.3138 q^{67} -41.9222 q^{68} +1.96664 q^{69} -31.5888 q^{70} -3.25235 q^{71} -7.86882 q^{72} -8.60558 q^{73} -13.4463 q^{74} -6.96106 q^{75} +26.6574 q^{76} -23.0482 q^{77} -16.5324 q^{78} +11.9125 q^{79} +40.5827 q^{80} -10.8502 q^{81} +14.6770 q^{82} +13.7921 q^{83} -41.9317 q^{84} -22.9158 q^{85} +27.6733 q^{86} +6.47091 q^{87} +52.4074 q^{88} -3.40388 q^{89} -6.87235 q^{90} -12.3702 q^{91} -5.34597 q^{92} +10.2316 q^{93} -12.8917 q^{94} +14.5717 q^{95} +38.3542 q^{96} +6.73076 q^{97} -24.1403 q^{98} -5.01428 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) $ 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * 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 $

$2$	−2.71035	−1.91650	−0.958252	−	0.285926i	$-0.907699\pi$
$2$	−2.71035	−1.91650	−0.958252	+	0.285926i	$0.907699\pi$
$3$	−1.96664	−1.13544	−0.567721	−	0.823221i	$-0.692175\pi$
$3$	−1.96664	−1.13544	−0.567721	+	0.823221i	$0.692175\pi$
$4$	5.34597	2.67299
$5$	2.92225	1.30687	0.653436	−	0.756982i	$-0.273327\pi$
$5$	2.92225	1.30687	0.653436	+	0.756982i	$0.273327\pi$
$6$	5.33028	2.17608
$7$	3.98832	1.50744	0.753722	−	0.657193i	$-0.228256\pi$
$7$	3.98832	1.50744	0.753722	+	0.657193i	$0.228256\pi$
$8$	−9.06874	−3.20628
$9$	0.867686	0.289229
$10$	−7.92031	−2.50462
$11$	−5.77891	−1.74241	−0.871203	−	0.490922i	$-0.836660\pi$
$11$	−5.77891	−1.74241	−0.871203	+	0.490922i	$0.836660\pi$
$12$	−10.5136	−3.03502
$13$	−3.10160	−0.860228	−0.430114	−	0.902774i	$-0.641527\pi$
$13$	−3.10160	−0.860228	−0.430114	+	0.902774i	$0.641527\pi$
$14$	−10.8097	−2.88902
$15$	−5.74703	−1.48388
$16$	13.8875	3.47187
$17$	−7.84184	−1.90193	−0.950963	−	0.309305i	$-0.899903\pi$
$17$	−7.84184	−1.90193	−0.950963	+	0.309305i	$0.899903\pi$
$18$	−2.35173	−0.554308
$19$	4.98645	1.14397	0.571985	−	0.820264i	$-0.306174\pi$
$19$	4.98645	1.14397	0.571985	+	0.820264i	$0.306174\pi$
$20$	15.6223	3.49325
$21$	−7.84361	−1.71162
$22$	15.6628	3.33933
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	17.8350	3.64055
$25$	3.53956	0.707913
$26$	8.40640	1.64863
$27$	4.19350	0.807040
$28$	21.3215	4.02938
$29$	−3.29033	−0.610999	−0.305500	−	0.952192i	$-0.598823\pi$
$29$	−3.29033	−0.610999	−0.305500	+	0.952192i	$0.598823\pi$
$30$	15.5764	2.84385
$31$	−5.20258	−0.934411	−0.467206	−	0.884149i	$-0.654739\pi$
$31$	−5.20258	−0.934411	−0.467206	+	0.884149i	$0.654739\pi$
$32$	−19.5023	−3.44756
$33$	11.3651	1.97840
$34$	21.2541	3.64505
$35$	11.6549	1.97004
$36$	4.63862	0.773104
$37$	4.96112	0.815603	0.407801	−	0.913071i	$-0.366296\pi$
$37$	4.96112	0.815603	0.407801	+	0.913071i	$0.366296\pi$
$38$	−13.5150	−2.19242
$39$	6.09974	0.976740
$40$	−26.5011	−4.19020
$41$	−5.41518	−0.845710	−0.422855	−	0.906197i	$-0.638972\pi$
$41$	−5.41518	−0.845710	−0.422855	+	0.906197i	$0.638972\pi$
$42$	21.2589	3.28032
$43$	−10.2102	−1.55705	−0.778523	−	0.627616i	$-0.784031\pi$
$43$	−10.2102	−1.55705	−0.778523	+	0.627616i	$0.784031\pi$
$44$	−30.8939	−4.65743
$45$	2.53560	0.377985
$46$	2.71035	0.399619
$47$	4.75647	0.693802	0.346901	−	0.937902i	$-0.387234\pi$
$47$	4.75647	0.693802	0.346901	+	0.937902i	$0.387234\pi$
$48$	−27.3117	−3.94210
$49$	8.90673	1.27239
$50$	−9.59344	−1.35672
$51$	15.4221	2.15953
$52$	−16.5811	−2.29938
$53$	−3.54675	−0.487183	−0.243592	−	0.969878i	$-0.578326\pi$
$53$	−3.54675	−0.487183	−0.243592	+	0.969878i	$0.578326\pi$
$54$	−11.3658	−1.54669
$55$	−16.8874	−2.27710
$56$	−36.1691	−4.83329
$57$	−9.80656	−1.29891
$58$	8.91793	1.17098
$59$	−8.68327	−1.13047	−0.565233	−	0.824931i	$-0.691214\pi$
$59$	−8.68327	−1.13047	−0.565233	+	0.824931i	$0.691214\pi$
$60$	−30.7235	−3.96638
$61$	−10.0960	−1.29266	−0.646328	−	0.763060i	$-0.723696\pi$
$61$	−10.0960	−1.29266	−0.646328	+	0.763060i	$0.723696\pi$
$62$	14.1008	1.79080
$63$	3.46061	0.435996
$64$	25.0832	3.13540
$65$	−9.06365	−1.12421
$66$	−30.8032	−3.79161
$67$	13.3138	1.62654	0.813271	−	0.581885i	$-0.197685\pi$
$67$	13.3138	1.62654	0.813271	+	0.581885i	$0.197685\pi$
$68$	−41.9222	−5.08382
$69$	1.96664	0.236756
$70$	−31.5888	−3.77558
$71$	−3.25235	−0.385983	−0.192991	−	0.981200i	$-0.561819\pi$
$71$	−3.25235	−0.385983	−0.192991	+	0.981200i	$0.561819\pi$
$72$	−7.86882	−0.927349
$73$	−8.60558	−1.00721	−0.503604	−	0.863935i	$-0.667993\pi$
$73$	−8.60558	−1.00721	−0.503604	+	0.863935i	$0.667993\pi$
$74$	−13.4463	−1.56311
$75$	−6.96106	−0.803794
$76$	26.6574	3.05781
$77$	−23.0482	−2.62658
$78$	−16.5324	−1.87192
$79$	11.9125	1.34026	0.670128	−	0.742246i	$-0.266239\pi$
$79$	11.9125	1.34026	0.670128	+	0.742246i	$0.266239\pi$
$80$	40.5827	4.53728
$81$	−10.8502	−1.20558
$82$	14.6770	1.62081
$83$	13.7921	1.51388	0.756939	−	0.653486i	$-0.226694\pi$
$83$	13.7921	1.51388	0.756939	+	0.653486i	$0.226694\pi$
$84$	−41.9317	−4.57512
$85$	−22.9158	−2.48557
$86$	27.6733	2.98408
$87$	6.47091	0.693754
$88$	52.4074	5.58665
$89$	−3.40388	−0.360810	−0.180405	−	0.983592i	$-0.557741\pi$
$89$	−3.40388	−0.360810	−0.180405	+	0.983592i	$0.557741\pi$
$90$	−6.87235	−0.724409
$91$	−12.3702	−1.29675
$92$	−5.34597	−0.557356
$93$	10.2316	1.06097
$94$	−12.8917	−1.32967
$95$	14.5717	1.49502
$96$	38.3542	3.91450
$97$	6.73076	0.683405	0.341703	−	0.939808i	$-0.388996\pi$
$97$	6.73076	0.683405	0.341703	+	0.939808i	$0.388996\pi$
$98$	−24.1403	−2.43854
$99$	−5.01428	−0.503954
$100$	18.9224	1.89224
$101$	−3.68682	−0.366853	−0.183426	−	0.983033i	$-0.558719\pi$
$101$	−3.68682	−0.366853	−0.183426	+	0.983033i	$0.558719\pi$
$102$	−41.7992	−4.13874
$103$	7.24539	0.713910	0.356955	−	0.934122i	$-0.383815\pi$
$103$	7.24539	0.713910	0.356955	+	0.934122i	$0.383815\pi$
$104$	28.1276	2.75814
$105$	−22.9210	−2.23686
$106$	9.61291	0.933688
$107$	−14.1301	−1.36601	−0.683006	−	0.730413i	$-0.739328\pi$
$107$	−14.1301	−1.36601	−0.683006	+	0.730413i	$0.739328\pi$
$108$	22.4183	2.15721
$109$	14.1661	1.35686	0.678432	−	0.734663i	$-0.262660\pi$
$109$	14.1661	1.35686	0.678432	+	0.734663i	$0.262660\pi$
$110$	45.7708	4.36407
$111$	−9.75675	−0.926070
$112$	55.3877	5.23365
$113$	17.6312	1.65860	0.829301	−	0.558803i	$-0.188739\pi$
$113$	17.6312	1.65860	0.829301	+	0.558803i	$0.188739\pi$
$114$	26.5792	2.48937
$115$	−2.92225	−0.272502
$116$	−17.5900	−1.63319
$117$	−2.69121	−0.248803
$118$	23.5347	2.16654
$119$	−31.2758	−2.86705
$120$	52.1183	4.75773
$121$	22.3958	2.03598
$122$	27.3636	2.47738
$123$	10.6497	0.960254
$124$	−27.8129	−2.49767
$125$	−4.26776	−0.381720
$126$	−9.37946	−0.835588
$127$	−13.6294	−1.20941	−0.604705	−	0.796449i	$-0.706709\pi$
$127$	−13.6294	−1.20941	−0.604705	+	0.796449i	$0.706709\pi$
$128$	−28.9793	−2.56144
$129$	20.0799	1.76794
$130$	24.5656	2.15455
$131$	11.7740	1.02870	0.514350	−	0.857580i	$-0.328033\pi$
$131$	11.7740	1.02870	0.514350	+	0.857580i	$0.328033\pi$
$132$	60.7572	5.28824
$133$	19.8876	1.72447
$134$	−36.0851	−3.11727
$135$	12.2545	1.05470
$136$	71.1156	6.09811
$137$	9.83154	0.839965	0.419983	−	0.907532i	$-0.362036\pi$
$137$	9.83154	0.839965	0.419983	+	0.907532i	$0.362036\pi$
$138$	−5.33028	−0.453744
$139$	−20.0077	−1.69703	−0.848515	−	0.529171i	$-0.822503\pi$
$139$	−20.0077	−1.69703	−0.848515	+	0.529171i	$0.822503\pi$
$140$	62.3067	5.26588
$141$	−9.35427	−0.787772
$142$	8.81498	0.739737
$143$	17.9239	1.49887
$144$	12.0500	1.00416
$145$	−9.61518	−0.798497
$146$	23.3241	1.93032
$147$	−17.5164	−1.44472
$148$	26.5220	2.18009
$149$	−9.98907	−0.818337	−0.409168	−	0.912459i	$-0.634181\pi$
$149$	−9.98907	−0.818337	−0.409168	+	0.912459i	$0.634181\pi$
$150$	18.8669	1.54047
$151$	−1.26061	−0.102587	−0.0512935	−	0.998684i	$-0.516334\pi$
$151$	−1.26061	−0.102587	−0.0512935	+	0.998684i	$0.516334\pi$
$152$	−45.2208	−3.66789
$153$	−6.80426	−0.550091
$154$	62.4685	5.03385
$155$	−15.2033	−1.22116
$156$	32.6090	2.61081
$157$	−20.7695	−1.65759	−0.828795	−	0.559552i	$-0.810973\pi$
$157$	−20.7695	−1.65759	−0.828795	+	0.559552i	$0.810973\pi$
$158$	−32.2869	−2.56860
$159$	6.97519	0.553168
$160$	−56.9908	−4.50552
$161$	−3.98832	−0.314324
$162$	29.4077	2.31049
$163$	9.17272	0.718463	0.359232	−	0.933248i	$-0.383039\pi$
$163$	9.17272	0.718463	0.359232	+	0.933248i	$0.383039\pi$
$164$	−28.9494	−2.26057
$165$	33.2116	2.58552
$166$	−37.3813	−2.90135
$167$	6.62504	0.512661	0.256330	−	0.966589i	$-0.417486\pi$
$167$	6.62504	0.512661	0.256330	+	0.966589i	$0.417486\pi$
$168$	71.1316	5.48792
$169$	−3.38009	−0.260007
$170$	62.1098	4.76361
$171$	4.32667	0.330869
$172$	−54.5836	−4.16196
$173$	18.9578	1.44134	0.720668	−	0.693280i	$-0.243835\pi$
$173$	18.9578	1.44134	0.720668	+	0.693280i	$0.243835\pi$
$174$	−17.5384	−1.32958
$175$	14.1169	1.06714
$176$	−80.2544	−6.04940
$177$	17.0769	1.28358
$178$	9.22568	0.691494
$179$	18.1422	1.35601	0.678007	−	0.735055i	$-0.262844\pi$
$179$	18.1422	1.35601	0.678007	+	0.735055i	$0.262844\pi$
$180$	13.5552	1.01035
$181$	3.22796	0.239932	0.119966	−	0.992778i	$-0.461721\pi$
$181$	3.22796	0.239932	0.119966	+	0.992778i	$0.461721\pi$
$182$	33.5274	2.48522
$183$	19.8552	1.46774
$184$	9.06874	0.668556
$185$	14.4976	1.06589
$186$	−27.7312	−2.03335
$187$	45.3173	3.31393
$188$	25.4279	1.85452
$189$	16.7250	1.21657
$190$	−39.4942	−2.86521
$191$	−4.57203	−0.330820	−0.165410	−	0.986225i	$-0.552895\pi$
$191$	−4.57203	−0.330820	−0.165410	+	0.986225i	$0.552895\pi$
$192$	−49.3296	−3.56006
$193$	−2.12234	−0.152769	−0.0763845	−	0.997078i	$-0.524338\pi$
$193$	−2.12234	−0.152769	−0.0763845	+	0.997078i	$0.524338\pi$
$194$	−18.2427	−1.30975
$195$	17.8250	1.27647
$196$	47.6151	3.40108
$197$	20.1361	1.43464	0.717320	−	0.696744i	$-0.245369\pi$
$197$	20.1361	1.43464	0.717320	+	0.696744i	$0.245369\pi$
$198$	13.5904	0.965830
$199$	−3.23405	−0.229256	−0.114628	−	0.993408i	$-0.536568\pi$
$199$	−3.23405	−0.229256	−0.114628	+	0.993408i	$0.536568\pi$
$200$	−32.0994	−2.26977
$201$	−26.1835	−1.84684
$202$	9.99256	0.703074
$203$	−13.1229	−0.921047
$204$	82.4461	5.77238
$205$	−15.8245	−1.10523
$206$	−19.6375	−1.36821
$207$	−0.867686	−0.0603084
$208$	−43.0733	−2.98660
$209$	−28.8162	−1.99326
$210$	62.1239	4.28695
$211$	0.561681	0.0386677	0.0193338	−	0.999813i	$-0.493845\pi$
$211$	0.561681	0.0386677	0.0193338	+	0.999813i	$0.493845\pi$
$212$	−18.9608	−1.30223
$213$	6.39621	0.438261
$214$	38.2975	2.61797
$215$	−29.8369	−2.03486
$216$	−38.0298	−2.58760
$217$	−20.7496	−1.40857
$218$	−38.3950	−2.60044
$219$	16.9241	1.14363
$220$	−90.2797	−6.08666
$221$	24.3222	1.63609
$222$	26.4442	1.77482
$223$	2.69679	0.180590	0.0902951	−	0.995915i	$-0.471219\pi$
$223$	2.69679	0.180590	0.0902951	+	0.995915i	$0.471219\pi$
$224$	−77.7817	−5.19701
$225$	3.07123	0.204749
$226$	−47.7866	−3.17872
$227$	−11.5550	−0.766934	−0.383467	−	0.923554i	$-0.625270\pi$
$227$	−11.5550	−0.766934	−0.383467	+	0.923554i	$0.625270\pi$
$228$	−52.4256	−3.47197
$229$	19.2132	1.26964	0.634821	−	0.772660i	$-0.281074\pi$
$229$	19.2132	1.26964	0.634821	+	0.772660i	$0.281074\pi$
$230$	7.92031	0.522250
$231$	45.3275	2.98233
$232$	29.8391	1.95904
$233$	7.32393	0.479806	0.239903	−	0.970797i	$-0.422884\pi$
$233$	7.32393	0.479806	0.239903	+	0.970797i	$0.422884\pi$
$234$	7.29412	0.476831
$235$	13.8996	0.906710
$236$	−46.4205	−3.02172
$237$	−23.4275	−1.52178
$238$	84.7682	5.49471
$239$	11.0172	0.712646	0.356323	−	0.934363i	$-0.384030\pi$
$239$	11.0172	0.712646	0.356323	+	0.934363i	$0.384030\pi$
$240$	−79.8117	−5.15182
$241$	3.70965	0.238959	0.119480	−	0.992837i	$-0.461877\pi$
$241$	3.70965	0.238959	0.119480	+	0.992837i	$0.461877\pi$
$242$	−60.7003	−3.90196
$243$	8.75793	0.561821
$244$	−53.9727	−3.45525
$245$	26.0277	1.66285
$246$	−28.8645	−1.84033
$247$	−15.4660	−0.984075
$248$	47.1808	2.99599
$249$	−27.1241	−1.71892
$250$	11.5671	0.731568
$251$	24.6469	1.55570	0.777850	−	0.628450i	$-0.216310\pi$
$251$	24.6469	1.55570	0.777850	+	0.628450i	$0.216310\pi$
$252$	18.5003	1.16541
$253$	5.77891	0.363317
$254$	36.9403	2.31784
$255$	45.0673	2.82222
$256$	28.3777	1.77360
$257$	24.8192	1.54818	0.774090	−	0.633075i	$-0.218208\pi$
$257$	24.8192	1.54818	0.774090	+	0.633075i	$0.218208\pi$
$258$	−54.4234	−3.38826
$259$	19.7865	1.22948
$260$	−48.4540	−3.00499
$261$	−2.85497	−0.176718
$262$	−31.9116	−1.97151
$263$	5.39551	0.332702	0.166351	−	0.986067i	$-0.446802\pi$
$263$	5.39551	0.332702	0.166351	+	0.986067i	$0.446802\pi$
$264$	−103.067	−6.34331
$265$	−10.3645	−0.636686
$266$	−53.9022	−3.30495
$267$	6.69421	0.409679
$268$	71.1753	4.34772
$269$	27.5622	1.68050	0.840249	−	0.542200i	$-0.182409\pi$
$269$	27.5622	1.68050	0.840249	+	0.542200i	$0.182409\pi$
$270$	−33.2138	−2.02133
$271$	−19.8073	−1.20321	−0.601603	−	0.798795i	$-0.705471\pi$
$271$	−19.8073	−1.20321	−0.601603	+	0.798795i	$0.705471\pi$
$272$	−108.903	−6.60323
$273$	24.3277	1.47238
$274$	−26.6469	−1.60980
$275$	−20.4548	−1.23347
$276$	10.5136	0.632845
$277$	18.4574	1.10900	0.554499	−	0.832185i	$-0.312910\pi$
$277$	18.4574	1.10900	0.554499	+	0.832185i	$0.312910\pi$
$278$	54.2278	3.25236
$279$	−4.51421	−0.270259
$280$	−105.695	−6.31649
$281$	1.46811	0.0875799	0.0437900	−	0.999041i	$-0.486057\pi$
$281$	1.46811	0.0875799	0.0437900	+	0.999041i	$0.486057\pi$
$282$	25.3533	1.50977
$283$	−3.13897	−0.186593	−0.0932963	−	0.995638i	$-0.529740\pi$
$283$	−3.13897	−0.186593	−0.0932963	+	0.995638i	$0.529740\pi$
$284$	−17.3869	−1.03173
$285$	−28.6573	−1.69751
$286$	−48.5798	−2.87259
$287$	−21.5975	−1.27486
$288$	−16.9219	−0.997133
$289$	44.4945	2.61732
$290$	26.0605	1.53032
$291$	−13.2370	−0.775967
$292$	−46.0052	−2.69225
$293$	−20.4070	−1.19219	−0.596094	−	0.802914i	$-0.703282\pi$
$293$	−20.4070	−1.19219	−0.596094	+	0.802914i	$0.703282\pi$
$294$	47.4754	2.76882
$295$	−25.3747	−1.47737
$296$	−44.9911	−2.61505
$297$	−24.2339	−1.40619
$298$	27.0738	1.56835
$299$	3.10160	0.179370
$300$	−37.2136	−2.14853
$301$	−40.7217	−2.34716
$302$	3.41669	0.196608
$303$	7.25067	0.416540
$304$	69.2491	3.97171
$305$	−29.5030	−1.68934
$306$	18.4419	1.05425
$307$	−14.8051	−0.844971	−0.422485	−	0.906370i	$-0.638842\pi$
$307$	−14.8051	−0.844971	−0.422485	+	0.906370i	$0.638842\pi$
$308$	−123.215	−7.02081
$309$	−14.2491	−0.810603
$310$	41.2061	2.34035
$311$	−5.07180	−0.287595	−0.143798	−	0.989607i	$-0.545931\pi$
$311$	−5.07180	−0.287595	−0.143798	+	0.989607i	$0.545931\pi$
$312$	−55.3169	−3.13170
$313$	24.2824	1.37252	0.686261	−	0.727356i	$-0.259251\pi$
$313$	24.2824	1.37252	0.686261	+	0.727356i	$0.259251\pi$
$314$	56.2926	3.17678
$315$	10.1128	0.569791
$316$	63.6836	3.58248
$317$	28.4704	1.59906	0.799530	−	0.600627i	$-0.205082\pi$
$317$	28.4704	1.59906	0.799530	+	0.600627i	$0.205082\pi$
$318$	−18.9052	−1.06015
$319$	19.0145	1.06461
$320$	73.2993	4.09756
$321$	27.7889	1.55103
$322$	10.8097	0.602403
$323$	−39.1029	−2.17574
$324$	−58.0047	−3.22249
$325$	−10.9783	−0.608967
$326$	−24.8612	−1.37694
$327$	−27.8596	−1.54064
$328$	49.1089	2.71158
$329$	18.9703	1.04587
$330$	−90.0148	−4.95515
$331$	−6.04840	−0.332450	−0.166225	−	0.986088i	$-0.553158\pi$
$331$	−6.04840	−0.332450	−0.166225	+	0.986088i	$0.553158\pi$
$332$	73.7320	4.04657
$333$	4.30469	0.235896
$334$	−17.9561	−0.982516
$335$	38.9064	2.12568
$336$	−108.928	−5.94250
$337$	9.35898	0.509816	0.254908	−	0.966965i	$-0.417955\pi$
$337$	9.35898	0.509816	0.254908	+	0.966965i	$0.417955\pi$
$338$	9.16122	0.498304
$339$	−34.6742	−1.88325
$340$	−122.507	−6.64390
$341$	30.0652	1.62812
$342$	−11.7268	−0.634111
$343$	7.60464	0.410612
$344$	92.5939	4.99233
$345$	5.74703	0.309410
$346$	−51.3822	−2.76233
$347$	5.47360	0.293838	0.146919	−	0.989149i	$-0.453064\pi$
$347$	5.47360	0.293838	0.146919	+	0.989149i	$0.453064\pi$
$348$	34.5933	1.85439
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−38.2617	−2.04518
$351$	−13.0066	−0.694238
$352$	112.702	6.00705
$353$	−31.8834	−1.69698	−0.848492	−	0.529208i	$-0.822489\pi$
$353$	−31.8834	−1.69698	−0.848492	+	0.529208i	$0.822489\pi$
$354$	−46.2843	−2.45998
$355$	−9.50418	−0.504430
$356$	−18.1970	−0.964441
$357$	61.5083	3.25537
$358$	−49.1717	−2.59881
$359$	7.58959	0.400563	0.200282	−	0.979738i	$-0.435814\pi$
$359$	7.58959	0.400563	0.200282	+	0.979738i	$0.435814\pi$
$360$	−22.9947	−1.21193
$361$	5.86465	0.308666
$362$	−8.74888	−0.459831
$363$	−44.0445	−2.31174
$364$	−66.1306	−3.46618
$365$	−25.1477	−1.31629
$366$	−53.8143	−2.81292
$367$	5.10854	0.266664	0.133332	−	0.991071i	$-0.457432\pi$
$367$	5.10854	0.266664	0.133332	+	0.991071i	$0.457432\pi$
$368$	−13.8875	−0.723934
$369$	−4.69868	−0.244603
$370$	−39.2936	−2.04278
$371$	−14.1456	−0.734402
$372$	54.6980	2.83596
$373$	24.2696	1.25663	0.628317	−	0.777957i	$-0.283744\pi$
$373$	24.2696	1.25663	0.628317	+	0.777957i	$0.283744\pi$
$374$	−122.825	−6.35115
$375$	8.39317	0.433421
$376$	−43.1351	−2.22452
$377$	10.2053	0.525599
$378$	−45.3306	−2.33156
$379$	−16.1347	−0.828785	−0.414393	−	0.910098i	$-0.636006\pi$
$379$	−16.1347	−0.828785	−0.414393	+	0.910098i	$0.636006\pi$
$380$	77.8997	3.99617
$381$	26.8041	1.37322
$382$	12.3918	0.634018
$383$	24.7457	1.26445	0.632223	−	0.774787i	$-0.282143\pi$
$383$	24.7457	1.26445	0.632223	+	0.774787i	$0.282143\pi$
$384$	56.9920	2.90836
$385$	−67.3526	−3.43260
$386$	5.75226	0.292782
$387$	−8.85928	−0.450342
$388$	35.9825	1.82673
$389$	−16.1022	−0.816415	−0.408208	−	0.912889i	$-0.633846\pi$
$389$	−16.1022	−0.816415	−0.408208	+	0.912889i	$0.633846\pi$
$390$	−48.3118	−2.44636
$391$	7.84184	0.396579
$392$	−80.7727	−4.07964
$393$	−23.1553	−1.16803
$394$	−54.5759	−2.74949
$395$	34.8112	1.75154
$396$	−26.8062	−1.34706
$397$	35.3555	1.77444	0.887222	−	0.461344i	$-0.152632\pi$
$397$	35.3555	1.77444	0.887222	+	0.461344i	$0.152632\pi$
$398$	8.76540	0.439370
$399$	−39.1117	−1.95804
$400$	49.1556	2.45778
$401$	−10.8588	−0.542262	−0.271131	−	0.962542i	$-0.587398\pi$
$401$	−10.8588	−0.542262	−0.271131	+	0.962542i	$0.587398\pi$
$402$	70.9664	3.53948
$403$	16.1363	0.803807
$404$	−19.7096	−0.980592
$405$	−31.7070	−1.57553
$406$	35.5676	1.76519
$407$	−28.6699	−1.42111
$408$	−139.859	−6.92405
$409$	−5.88303	−0.290897	−0.145449	−	0.989366i	$-0.546463\pi$
$409$	−5.88303	−0.290897	−0.145449	+	0.989366i	$0.546463\pi$
$410$	42.8900	2.11818
$411$	−19.3351	−0.953732
$412$	38.7336	1.90827
$413$	−34.6317	−1.70411
$414$	2.35173	0.115581
$415$	40.3039	1.97844
$416$	60.4884	2.96569
$417$	39.3480	1.92688
$418$	78.1019	3.82009
$419$	−29.1878	−1.42592	−0.712959	−	0.701205i	$-0.752646\pi$
$419$	−29.1878	−1.42592	−0.712959	+	0.701205i	$0.752646\pi$
$420$	−122.535	−5.97910
$421$	15.1007	0.735964	0.367982	−	0.929833i	$-0.380049\pi$
$421$	15.1007	0.735964	0.367982	+	0.929833i	$0.380049\pi$
$422$	−1.52235	−0.0741068
$423$	4.12712	0.200667
$424$	32.1645	1.56205
$425$	−27.7567	−1.34640
$426$	−17.3359	−0.839928
$427$	−40.2660	−1.94861
$428$	−75.5393	−3.65133
$429$	−35.2498	−1.70188
$430$	80.8683	3.89981
$431$	13.4716	0.648905	0.324452	−	0.945902i	$-0.394820\pi$
$431$	13.4716	0.648905	0.324452	+	0.945902i	$0.394820\pi$
$432$	58.2371	2.80193
$433$	6.86286	0.329808	0.164904	−	0.986310i	$-0.447269\pi$
$433$	6.86286	0.329808	0.164904	+	0.986310i	$0.447269\pi$
$434$	56.2385	2.69954
$435$	18.9096	0.906647
$436$	75.7315	3.62688
$437$	−4.98645	−0.238534
$438$	−45.8702	−2.19176
$439$	−7.70147	−0.367571	−0.183785	−	0.982966i	$-0.558835\pi$
$439$	−7.70147	−0.367571	−0.183785	+	0.982966i	$0.558835\pi$
$440$	153.148	7.30103
$441$	7.72824	0.368012
$442$	−65.9216	−3.13557
$443$	26.8972	1.27792	0.638962	−	0.769239i	$-0.279364\pi$
$443$	26.8972	1.27792	0.638962	+	0.769239i	$0.279364\pi$
$444$	−52.1593	−2.47537
$445$	−9.94699	−0.471533
$446$	−7.30922	−0.346102
$447$	19.6449	0.929174
$448$	100.040	4.72643
$449$	−6.50539	−0.307009	−0.153504	−	0.988148i	$-0.549056\pi$
$449$	−6.50539	−0.307009	−0.153504	+	0.988148i	$0.549056\pi$
$450$	−8.32409	−0.392402
$451$	31.2939	1.47357
$452$	94.2557	4.43342
$453$	2.47917	0.116482
$454$	31.3181	1.46983
$455$	−36.1488	−1.69468
$456$	88.9331	4.16468
$457$	3.15393	0.147535	0.0737673	−	0.997275i	$-0.476498\pi$
$457$	3.15393	0.147535	0.0737673	+	0.997275i	$0.476498\pi$
$458$	−52.0743	−2.43327
$459$	−32.8848	−1.53493
$460$	−15.6223	−0.728393
$461$	16.0649	0.748216	0.374108	−	0.927385i	$-0.377949\pi$
$461$	16.0649	0.748216	0.374108	+	0.927385i	$0.377949\pi$
$462$	−122.853	−5.71565
$463$	15.9443	0.740995	0.370498	−	0.928833i	$-0.379187\pi$
$463$	15.9443	0.740995	0.370498	+	0.928833i	$0.379187\pi$
$464$	−45.6943	−2.12131
$465$	29.8994	1.38655
$466$	−19.8504	−0.919551
$467$	−5.04257	−0.233342	−0.116671	−	0.993171i	$-0.537222\pi$
$467$	−5.04257	−0.233342	−0.116671	+	0.993171i	$0.537222\pi$
$468$	−14.3871	−0.665046
$469$	53.0998	2.45192
$470$	−37.6727	−1.73771
$471$	40.8463	1.88210
$472$	78.7463	3.62459
$473$	59.0040	2.71301
$474$	63.4967	2.91650
$475$	17.6498	0.809831
$476$	−167.199	−7.66358
$477$	−3.07746	−0.140907
$478$	−29.8605	−1.36579
$479$	−7.74193	−0.353738	−0.176869	−	0.984234i	$-0.556597\pi$
$479$	−7.74193	−0.353738	−0.176869	+	0.984234i	$0.556597\pi$
$480$	112.081	5.11575
$481$	−15.3874	−0.701605
$482$	−10.0544	−0.457966
$483$	7.84361	0.356897
$484$	119.727	5.44215
$485$	19.6690	0.893123
$486$	−23.7370	−1.07673
$487$	−30.2471	−1.37063	−0.685313	−	0.728249i	$-0.740335\pi$
$487$	−30.2471	−1.37063	−0.685313	+	0.728249i	$0.740335\pi$
$488$	91.5576	4.14462
$489$	−18.0395	−0.815773
$490$	−70.5441	−3.18686
$491$	7.27267	0.328211	0.164106	−	0.986443i	$-0.447526\pi$
$491$	7.27267	0.328211	0.164106	+	0.986443i	$0.447526\pi$
$492$	56.9332	2.56675
$493$	25.8023	1.16207
$494$	41.9181	1.88598
$495$	−14.6530	−0.658603
$496$	−72.2507	−3.24415
$497$	−12.9714	−0.581847
$498$	73.5157	3.29432
$499$	−43.4784	−1.94636	−0.973180	−	0.230043i	$-0.926113\pi$
$499$	−43.4784	−1.94636	−0.973180	+	0.230043i	$0.926113\pi$
$500$	−22.8153	−1.02033
$501$	−13.0291	−0.582097
$502$	−66.8017	−2.98151
$503$	13.6377	0.608074	0.304037	−	0.952660i	$-0.401665\pi$
$503$	13.6377	0.608074	0.304037	+	0.952660i	$0.401665\pi$
$504$	−31.3834	−1.39793
$505$	−10.7738	−0.479429
$506$	−15.6628	−0.696298
$507$	6.64744	0.295223
$508$	−72.8622	−3.23274
$509$	−10.0558	−0.445713	−0.222857	−	0.974851i	$-0.571538\pi$
$509$	−10.0558	−0.445713	−0.222857	+	0.974851i	$0.571538\pi$
$510$	−122.148	−5.40880
$511$	−34.3218	−1.51831
$512$	−18.9546	−0.837684
$513$	20.9107	0.923229
$514$	−67.2687	−2.96709
$515$	21.1729	0.932988
$516$	107.347	4.72567
$517$	−27.4872	−1.20888
$518$	−53.6284	−2.35630
$519$	−37.2833	−1.63655
$520$	82.1959	3.60453
$521$	10.5660	0.462905	0.231452	−	0.972846i	$-0.425652\pi$
$521$	10.5660	0.462905	0.231452	+	0.972846i	$0.425652\pi$
$522$	7.73797	0.338682
$523$	12.5907	0.550551	0.275276	−	0.961365i	$-0.411231\pi$
$523$	12.5907	0.550551	0.275276	+	0.961365i	$0.411231\pi$
$524$	62.9435	2.74970
$525$	−27.7630	−1.21167
$526$	−14.6237	−0.637624
$527$	40.7978	1.77718
$528$	157.832	6.86875
$529$	1.00000	0.0434783
$530$	28.0914	1.22021
$531$	−7.53436	−0.326963
$532$	106.318	4.60948
$533$	16.7957	0.727503
$534$	−18.1436	−0.785152
$535$	−41.2918	−1.78520
$536$	−120.740	−5.21515
$537$	−35.6793	−1.53968
$538$	−74.7031	−3.22068
$539$	−51.4712	−2.21702
$540$	65.5120	2.81919
$541$	15.7408	0.676749	0.338374	−	0.941012i	$-0.390123\pi$
$541$	15.7408	0.676749	0.338374	+	0.941012i	$0.390123\pi$
$542$	53.6846	2.30595
$543$	−6.34824	−0.272429
$544$	152.934	6.55700
$545$	41.3969	1.77325
$546$	−65.9365	−2.82182
$547$	−20.6424	−0.882607	−0.441304	−	0.897358i	$-0.645484\pi$
$547$	−20.6424	−0.882607	−0.441304	+	0.897358i	$0.645484\pi$
$548$	52.5591	2.24521
$549$	−8.76013	−0.373873
$550$	55.4396	2.36395
$551$	−16.4071	−0.698964
$552$	−17.8350	−0.759107
$553$	47.5107	2.02036
$554$	−50.0259	−2.12540
$555$	−28.5117	−1.21025
$556$	−106.961	−4.53614
$557$	−11.1387	−0.471963	−0.235981	−	0.971758i	$-0.575830\pi$
$557$	−11.1387	−0.471963	−0.235981	+	0.971758i	$0.575830\pi$
$558$	12.2351	0.517952
$559$	31.6680	1.33942
$560$	161.857	6.83970
$561$	−89.1229	−3.76277
$562$	−3.97908	−0.167847
$563$	11.3392	0.477889	0.238944	−	0.971033i	$-0.423199\pi$
$563$	11.3392	0.477889	0.238944	+	0.971033i	$0.423199\pi$
$564$	−50.0077	−2.10570
$565$	51.5228	2.16758
$566$	8.50770	0.357605
$567$	−43.2740	−1.81734
$568$	29.4947	1.23757
$569$	22.7862	0.955245	0.477623	−	0.878565i	$-0.341499\pi$
$569$	22.7862	0.955245	0.477623	+	0.878565i	$0.341499\pi$
$570$	77.6711	3.25328
$571$	−12.4039	−0.519088	−0.259544	−	0.965731i	$-0.583572\pi$
$571$	−12.4039	−0.519088	−0.259544	+	0.965731i	$0.583572\pi$
$572$	95.8204	4.00645
$573$	8.99155	0.375627
$574$	58.5367	2.44327
$575$	−3.53956	−0.147610
$576$	21.7643	0.906846
$577$	−12.7244	−0.529723	−0.264861	−	0.964286i	$-0.585326\pi$
$577$	−12.7244	−0.529723	−0.264861	+	0.964286i	$0.585326\pi$
$578$	−120.595	−5.01610
$579$	4.17388	0.173460
$580$	−51.4025	−2.13437
$581$	55.0073	2.28209
$582$	35.8769	1.48714
$583$	20.4963	0.848871
$584$	78.0417	3.22939
$585$	−7.86441	−0.325153
$586$	55.3100	2.28483
$587$	18.3644	0.757981	0.378991	−	0.925400i	$-0.376271\pi$
$587$	18.3644	0.757981	0.378991	+	0.925400i	$0.376271\pi$
$588$	−93.6419	−3.86173
$589$	−25.9424	−1.06894
$590$	68.7743	2.83139
$591$	−39.6006	−1.62895
$592$	68.8974	2.83166
$593$	−18.8714	−0.774956	−0.387478	−	0.921879i	$-0.626654\pi$
$593$	−18.8714	−0.774956	−0.387478	+	0.921879i	$0.626654\pi$
$594$	65.6821	2.69497
$595$	−91.3958	−3.74686
$596$	−53.4013	−2.18740
$597$	6.36023	0.260307
$598$	−8.40640	−0.343763
$599$	−13.7784	−0.562969	−0.281485	−	0.959566i	$-0.590827\pi$
$599$	−13.7784	−0.562969	−0.281485	+	0.959566i	$0.590827\pi$
$600$	63.1280	2.57719
$601$	−3.52323	−0.143716	−0.0718579	−	0.997415i	$-0.522893\pi$
$601$	−3.52323	−0.143716	−0.0718579	+	0.997415i	$0.522893\pi$
$602$	110.370	4.49834
$603$	11.5522	0.470443
$604$	−6.73919	−0.274214
$605$	65.4462	2.66077
$606$	−19.6518	−0.798300
$607$	−16.3999	−0.665651	−0.332825	−	0.942988i	$-0.608002\pi$
$607$	−16.3999	−0.665651	−0.332825	+	0.942988i	$0.608002\pi$
$608$	−97.2474	−3.94390
$609$	25.8081	1.04580
$610$	79.9632	3.23762
$611$	−14.7526	−0.596828
$612$	−36.3754	−1.47039
$613$	40.9891	1.65553	0.827766	−	0.561073i	$-0.189611\pi$
$613$	40.9891	1.65553	0.827766	+	0.561073i	$0.189611\pi$
$614$	40.1269	1.61939
$615$	31.1212	1.25493
$616$	209.018	8.42156
$617$	13.5612	0.545952	0.272976	−	0.962021i	$-0.411992\pi$
$617$	13.5612	0.545952	0.272976	+	0.962021i	$0.411992\pi$
$618$	38.6200	1.55352
$619$	−12.6260	−0.507483	−0.253741	−	0.967272i	$-0.581661\pi$
$619$	−12.6260	−0.507483	−0.253741	+	0.967272i	$0.581661\pi$
$620$	−81.2762	−3.26413
$621$	−4.19350	−0.168279
$622$	13.7463	0.551177
$623$	−13.5758	−0.543902
$624$	84.7099	3.39111
$625$	−30.1693	−1.20677
$626$	−65.8136	−2.63044
$627$	56.6712	2.26323
$628$	−111.033	−4.43071
$629$	−38.9043	−1.55122
$630$	−27.4091	−1.09201
$631$	16.7096	0.665200	0.332600	−	0.943068i	$-0.392074\pi$
$631$	16.7096	0.665200	0.332600	+	0.943068i	$0.392074\pi$
$632$	−108.031	−4.29724
$633$	−1.10463	−0.0439049
$634$	−77.1647	−3.06460
$635$	−39.8284	−1.58054
$636$	37.2891	1.47861
$637$	−27.6251	−1.09455
$638$	−51.5359	−2.04033
$639$	−2.82202	−0.111637
$640$	−84.6849	−3.34747
$641$	1.91944	0.0758132	0.0379066	−	0.999281i	$-0.487931\pi$
$641$	1.91944	0.0758132	0.0379066	+	0.999281i	$0.487931\pi$
$642$	−75.3176	−2.97255
$643$	−41.0194	−1.61765	−0.808824	−	0.588051i	$-0.799895\pi$
$643$	−41.0194	−1.61765	−0.808824	+	0.588051i	$0.799895\pi$
$644$	−21.3215	−0.840183
$645$	58.6785	2.31046
$646$	105.982	4.16982
$647$	−37.5538	−1.47639	−0.738196	−	0.674586i	$-0.764322\pi$
$647$	−37.5538	−1.47639	−0.738196	+	0.674586i	$0.764322\pi$
$648$	98.3974	3.86542
$649$	50.1798	1.96973
$650$	29.7550	1.16709
$651$	40.8070	1.59935
$652$	49.0371	1.92044
$653$	17.0140	0.665808	0.332904	−	0.942961i	$-0.391971\pi$
$653$	17.0140	0.665808	0.332904	+	0.942961i	$0.391971\pi$
$654$	75.5092	2.95264
$655$	34.4066	1.34438
$656$	−75.2032	−2.93619
$657$	−7.46694	−0.291313
$658$	−51.4161	−2.00441
$659$	41.8377	1.62977	0.814884	−	0.579625i	$-0.196801\pi$
$659$	41.8377	1.62977	0.814884	+	0.579625i	$0.196801\pi$
$660$	177.548	6.91105
$661$	10.8354	0.421448	0.210724	−	0.977546i	$-0.432418\pi$
$661$	10.8354	0.421448	0.210724	+	0.977546i	$0.432418\pi$
$662$	16.3933	0.637142
$663$	−47.8332	−1.85769
$664$	−125.077	−4.85392
$665$	58.1165	2.25366
$666$	−11.6672	−0.452095
$667$	3.29033	0.127402
$668$	35.4173	1.37034
$669$	−5.30362	−0.205050
$670$	−105.450	−4.07388
$671$	58.3437	2.25233
$672$	152.969	5.90090
$673$	−27.7209	−1.06856	−0.534282	−	0.845307i	$-0.679418\pi$
$673$	−27.7209	−1.06856	−0.534282	+	0.845307i	$0.679418\pi$
$674$	−25.3661	−0.977064
$675$	14.8432	0.571314
$676$	−18.0699	−0.694995
$677$	−15.5485	−0.597578	−0.298789	−	0.954319i	$-0.596583\pi$
$677$	−15.5485	−0.597578	−0.298789	+	0.954319i	$0.596583\pi$
$678$	93.9791	3.60925
$679$	26.8445	1.03020
$680$	207.818	7.96945
$681$	22.7246	0.870810
$682$	−81.4872	−3.12031
$683$	32.7757	1.25413	0.627063	−	0.778969i	$-0.284257\pi$
$683$	32.7757	1.25413	0.627063	+	0.778969i	$0.284257\pi$
$684$	23.1303	0.884407
$685$	28.7302	1.09773
$686$	−20.6112	−0.786939
$687$	−37.7854	−1.44160
$688$	−141.794	−5.40586
$689$	11.0006	0.419089
$690$	−15.5764	−0.592985
$691$	−40.3317	−1.53429	−0.767146	−	0.641473i	$-0.778324\pi$
$691$	−40.3317	−1.53429	−0.767146	+	0.641473i	$0.778324\pi$
$692$	101.348	3.85267
$693$	−19.9986	−0.759683
$694$	−14.8353	−0.563142
$695$	−58.4676	−2.21780
$696$	−58.6830	−2.22437
$697$	42.4650	1.60848
$698$	−2.71035	−0.102588
$699$	−14.4036	−0.544792
$700$	75.4687	2.85245
$701$	−40.2242	−1.51925	−0.759624	−	0.650362i	$-0.774617\pi$
$701$	−40.2242	−1.51925	−0.759624	+	0.650362i	$0.774617\pi$
$702$	35.2522	1.33051
$703$	24.7384	0.933025
$704$	−144.953	−5.46313
$705$	−27.3356	−1.02952
$706$	86.4151	3.25228
$707$	−14.7042	−0.553010
$708$	91.2926	3.43099
$709$	33.9041	1.27329	0.636647	−	0.771155i	$-0.280321\pi$
$709$	33.9041	1.27329	0.636647	+	0.771155i	$0.280321\pi$
$710$	25.7596	0.966741
$711$	10.3363	0.387640
$712$	30.8689	1.15686
$713$	5.20258	0.194838
$714$	−166.709	−6.23892
$715$	52.3780	1.95883
$716$	96.9879	3.62461
$717$	−21.6670	−0.809168
$718$	−20.5704	−0.767681
$719$	−5.93545	−0.221355	−0.110678	−	0.993856i	$-0.535302\pi$
$719$	−5.93545	−0.221355	−0.110678	+	0.993856i	$0.535302\pi$
$720$	35.2130	1.31231
$721$	28.8970	1.07618
$722$	−15.8952	−0.591560
$723$	−7.29555	−0.271324
$724$	17.2566	0.641335
$725$	−11.6463	−0.432534
$726$	119.376	4.43045
$727$	−36.3140	−1.34681	−0.673407	−	0.739272i	$-0.735170\pi$
$727$	−36.3140	−1.34681	−0.673407	+	0.739272i	$0.735170\pi$
$728$	112.182	4.15774
$729$	15.3268	0.567660
$730$	68.1589	2.52267
$731$	80.0670	2.96139
$732$	106.145	3.92324
$733$	0.703511	0.0259848	0.0129924	−	0.999916i	$-0.495864\pi$
$733$	0.703511	0.0259848	0.0129924	+	0.999916i	$0.495864\pi$
$734$	−13.8459	−0.511062
$735$	−51.1872	−1.88807
$736$	19.5023	0.718866
$737$	−76.9394	−2.83410
$738$	12.7350	0.468783
$739$	12.8798	0.473791	0.236895	−	0.971535i	$-0.423870\pi$
$739$	12.8798	0.473791	0.236895	+	0.971535i	$0.423870\pi$
$740$	77.5040	2.84910
$741$	30.4160	1.11736
$742$	38.3394	1.40748
$743$	−42.0133	−1.54132	−0.770659	−	0.637248i	$-0.780073\pi$
$743$	−42.0133	−1.54132	−0.770659	+	0.637248i	$0.780073\pi$
$744$	−92.7879	−3.40177
$745$	−29.1906	−1.06946
$746$	−65.7791	−2.40834
$747$	11.9672	0.437857
$748$	242.265	8.85808
$749$	−56.3555	−2.05919
$750$	−22.7484	−0.830654
$751$	2.75427	0.100505	0.0502523	−	0.998737i	$-0.483997\pi$
$751$	2.75427	0.100505	0.0502523	+	0.998737i	$0.483997\pi$
$752$	66.0552	2.40879
$753$	−48.4717	−1.76641
$754$	−27.6598	−1.00731
$755$	−3.68382	−0.134068
$756$	89.4116	3.25187
$757$	−18.8747	−0.686014	−0.343007	−	0.939333i	$-0.611445\pi$
$757$	−18.8747	−0.686014	−0.343007	+	0.939333i	$0.611445\pi$
$758$	43.7307	1.58837
$759$	−11.3651	−0.412525
$760$	−132.147	−4.79346
$761$	14.9623	0.542384	0.271192	−	0.962525i	$-0.412582\pi$
$761$	14.9623	0.542384	0.271192	+	0.962525i	$0.412582\pi$
$762$	−72.6483	−2.63177
$763$	56.4989	2.04540
$764$	−24.4419	−0.884278
$765$	−19.8838	−0.718899
$766$	−67.0693	−2.42331
$767$	26.9320	0.972459
$768$	−55.8088	−2.01383
$769$	−34.2419	−1.23479	−0.617397	−	0.786651i	$-0.711813\pi$
$769$	−34.2419	−1.23479	−0.617397	+	0.786651i	$0.711813\pi$
$770$	182.549	6.57860
$771$	−48.8106	−1.75787
$772$	−11.3459	−0.408350
$773$	−0.999025	−0.0359324	−0.0179662	−	0.999839i	$-0.505719\pi$
$773$	−0.999025	−0.0359324	−0.0179662	+	0.999839i	$0.505719\pi$
$774$	24.0117	0.863083
$775$	−18.4149	−0.661482
$776$	−61.0395	−2.19119
$777$	−38.9131	−1.39600
$778$	43.6426	1.56466
$779$	−27.0025	−0.967466
$780$	95.2918	3.41199
$781$	18.7950	0.672538
$782$	−21.2541	−0.760045
$783$	−13.7980	−0.493101
$784$	123.692	4.41756
$785$	−60.6939	−2.16626
$786$	62.7588	2.23853
$787$	−35.4225	−1.26268	−0.631339	−	0.775507i	$-0.717494\pi$
$787$	−35.4225	−1.26268	−0.631339	+	0.775507i	$0.717494\pi$
$788$	107.647	3.83477
$789$	−10.6111	−0.377763
$790$	−94.3504	−3.35684
$791$	70.3188	2.50025
$792$	45.4732	1.61582
$793$	31.3136	1.11198
$794$	−95.8257	−3.40073
$795$	20.3833	0.722920
$796$	−17.2891	−0.612798
$797$	−3.27496	−0.116005	−0.0580025	−	0.998316i	$-0.518473\pi$
$797$	−3.27496	−0.116005	−0.0580025	+	0.998316i	$0.518473\pi$
$798$	106.006	3.75258
$799$	−37.2994	−1.31956
$800$	−69.0298	−2.44057
$801$	−2.95350	−0.104357
$802$	29.4311	1.03925
$803$	49.7309	1.75496
$804$	−139.976	−4.93659
$805$	−11.6549	−0.410781
$806$	−43.7350	−1.54050
$807$	−54.2051	−1.90811
$808$	33.4348	1.17623
$809$	−0.134513	−0.00472924	−0.00236462	−	0.999997i	$-0.500753\pi$
$809$	−0.134513	−0.00472924	−0.00236462	+	0.999997i	$0.500753\pi$
$810$	85.9368	3.01951
$811$	35.1363	1.23380	0.616902	−	0.787040i	$-0.288388\pi$
$811$	35.1363	1.23380	0.616902	+	0.787040i	$0.288388\pi$
$812$	−70.1547	−2.46195
$813$	38.9538	1.36617
$814$	77.7052	2.72357
$815$	26.8050	0.938939
$816$	214.174	7.49759
$817$	−50.9128	−1.78121
$818$	15.9450	0.557505
$819$	−10.7334	−0.375056
$820$	−84.5975	−2.95427
$821$	−47.7986	−1.66818	−0.834091	−	0.551628i	$-0.814007\pi$
$821$	−47.7986	−1.66818	−0.834091	+	0.551628i	$0.814007\pi$
$822$	52.4049	1.82783
$823$	−35.4319	−1.23508	−0.617539	−	0.786541i	$-0.711870\pi$
$823$	−35.4319	−1.23508	−0.617539	+	0.786541i	$0.711870\pi$
$824$	−65.7065	−2.28900
$825$	40.2273	1.40054
$826$	93.8639	3.26594
$827$	43.1919	1.50193	0.750965	−	0.660342i	$-0.229589\pi$
$827$	43.1919	1.50193	0.750965	+	0.660342i	$0.229589\pi$
$828$	−4.63862	−0.161203
$829$	9.92881	0.344842	0.172421	−	0.985023i	$-0.444841\pi$
$829$	9.92881	0.344842	0.172421	+	0.985023i	$0.444841\pi$
$830$	−109.238	−3.79169
$831$	−36.2991	−1.25920
$832$	−77.7979	−2.69716
$833$	−69.8451	−2.41999
$834$	−106.647	−3.69287
$835$	19.3600	0.669982
$836$	−154.051	−5.32795
$837$	−21.8170	−0.754107
$838$	79.1091	2.73278
$839$	10.9334	0.377463	0.188732	−	0.982029i	$-0.439562\pi$
$839$	10.9334	0.377463	0.188732	+	0.982029i	$0.439562\pi$
$840$	207.865	7.17201
$841$	−18.1737	−0.626680
$842$	−40.9282	−1.41048
$843$	−2.88724	−0.0994419
$844$	3.00273	0.103358
$845$	−9.87749	−0.339796
$846$	−11.1859	−0.384580
$847$	89.3217	3.06913
$848$	−49.2553	−1.69143
$849$	6.17324	0.211865
$850$	75.2302	2.58038
$851$	−4.96112	−0.170065
$852$	34.1939	1.17146
$853$	6.06738	0.207743	0.103872	−	0.994591i	$-0.466877\pi$
$853$	6.06738	0.207743	0.103872	+	0.994591i	$0.466877\pi$
$854$	109.135	3.73451
$855$	12.6436	0.432403
$856$	128.142	4.37982
$857$	−16.8086	−0.574172	−0.287086	−	0.957905i	$-0.592687\pi$
$857$	−16.8086	−0.574172	−0.287086	+	0.957905i	$0.592687\pi$
$858$	95.5392	3.26165
$859$	−11.0032	−0.375424	−0.187712	−	0.982224i	$-0.560107\pi$
$859$	−11.0032	−0.375424	−0.187712	+	0.982224i	$0.560107\pi$
$860$	−159.507	−5.43915
$861$	42.4746	1.44753
$862$	−36.5127	−1.24363
$863$	47.9067	1.63076	0.815381	−	0.578925i	$-0.196528\pi$
$863$	47.9067	1.63076	0.815381	+	0.578925i	$0.196528\pi$
$864$	−81.7831	−2.78232
$865$	55.3996	1.88364
$866$	−18.6007	−0.632078
$867$	−87.5047	−2.97182
$868$	−110.927	−3.76510
$869$	−68.8410	−2.33527
$870$	−51.2516	−1.73759
$871$	−41.2941	−1.39920
$872$	−128.468	−4.35049
$873$	5.84019	0.197660
$874$	13.5150	0.457151
$875$	−17.0212	−0.575422
$876$	90.4758	3.05689
$877$	36.5793	1.23520	0.617598	−	0.786494i	$-0.288106\pi$
$877$	36.5793	1.23520	0.617598	+	0.786494i	$0.288106\pi$
$878$	20.8736	0.704451
$879$	40.1333	1.35366
$880$	−234.524	−7.90579
$881$	−14.3640	−0.483934	−0.241967	−	0.970284i	$-0.577793\pi$
$881$	−14.3640	−0.483934	−0.241967	+	0.970284i	$0.577793\pi$
$882$	−20.9462	−0.705295
$883$	14.9218	0.502158	0.251079	−	0.967967i	$-0.419215\pi$
$883$	14.9218	0.502158	0.251079	+	0.967967i	$0.419215\pi$
$884$	130.026	4.37325
$885$	49.9030	1.67747
$886$	−72.9006	−2.44914
$887$	26.2369	0.880949	0.440475	−	0.897765i	$-0.354810\pi$
$887$	26.2369	0.880949	0.440475	+	0.897765i	$0.354810\pi$
$888$	88.4814	2.96924
$889$	−54.3583	−1.82312
$890$	26.9598	0.903694
$891$	62.7022	2.10060
$892$	14.4169	0.482715
$893$	23.7179	0.793688
$894$	−53.2446	−1.78077
$895$	53.0162	1.77214
$896$	−115.579	−3.86122
$897$	−6.09974	−0.203664
$898$	17.6319	0.588383
$899$	17.1182	0.570925
$900$	16.4187	0.547290
$901$	27.8130	0.926586
$902$	−84.8171	−2.82410
$903$	80.0851	2.66507
$904$	−159.892	−5.31794
$905$	9.43291	0.313561
$906$	−6.71941	−0.223237
$907$	−28.4627	−0.945088	−0.472544	−	0.881307i	$-0.656664\pi$
$907$	−28.4627	−0.945088	−0.472544	+	0.881307i	$0.656664\pi$
$908$	−61.7729	−2.05000
$909$	−3.19901	−0.106104
$910$	97.9757	3.24786
$911$	47.9648	1.58914	0.794572	−	0.607170i	$-0.207695\pi$
$911$	47.9648	1.58914	0.794572	+	0.607170i	$0.207695\pi$
$912$	−136.188	−4.50964
$913$	−79.7032	−2.63779
$914$	−8.54823	−0.282750
$915$	58.0218	1.91814
$916$	102.713	3.39373
$917$	46.9585	1.55071
$918$	89.1291	2.94170
$919$	47.0607	1.55239	0.776194	−	0.630494i	$-0.217148\pi$
$919$	47.0607	1.55239	0.776194	+	0.630494i	$0.217148\pi$
$920$	26.5011	0.873717
$921$	29.1163	0.959415
$922$	−43.5414	−1.43396
$923$	10.0875	0.332033
$924$	242.320	7.97173
$925$	17.5602	0.577376
$926$	−43.2146	−1.42012
$927$	6.28672	0.206483
$928$	64.1692	2.10646
$929$	26.6778	0.875271	0.437635	−	0.899153i	$-0.355816\pi$
$929$	26.6778	0.875271	0.437635	+	0.899153i	$0.355816\pi$
$930$	−81.0377	−2.65733
$931$	44.4129	1.45557
$932$	39.1535	1.28252
$933$	9.97441	0.326548
$934$	13.6671	0.447201
$935$	132.429	4.33088
$936$	24.4059	0.797732
$937$	12.4596	0.407036	0.203518	−	0.979071i	$-0.434762\pi$
$937$	12.4596	0.407036	0.203518	+	0.979071i	$0.434762\pi$
$938$	−143.919	−4.69912
$939$	−47.7548	−1.55842
$940$	74.3068	2.42362
$941$	−14.2678	−0.465116	−0.232558	−	0.972582i	$-0.574710\pi$
$941$	−14.2678	−0.465116	−0.232558	+	0.972582i	$0.574710\pi$
$942$	−110.708	−3.60705
$943$	5.41518	0.176343
$944$	−120.589	−3.92483
$945$	48.8748	1.58990
$946$	−159.921	−5.19949
$947$	−23.3559	−0.758963	−0.379482	−	0.925199i	$-0.623898\pi$
$947$	−23.3559	−0.758963	−0.379482	+	0.925199i	$0.623898\pi$
$948$	−125.243	−4.06770
$949$	26.6910	0.866428
$950$	−47.8372	−1.55204
$951$	−55.9912	−1.81564
$952$	283.632	9.19256
$953$	−39.8277	−1.29014	−0.645072	−	0.764122i	$-0.723173\pi$
$953$	−39.8277	−1.29014	−0.645072	+	0.764122i	$0.723173\pi$
$954$	8.34099	0.270049
$955$	−13.3606	−0.432339
$956$	58.8978	1.90489
$957$	−37.3948	−1.20880
$958$	20.9833	0.677939
$959$	39.2114	1.26620
$960$	−144.154	−4.65254
$961$	−3.93314	−0.126875
$962$	41.7052	1.34463
$963$	−12.2605	−0.395090
$964$	19.8317	0.638735
$965$	−6.20200	−0.199650
$966$	−21.2589	−0.683994
$967$	27.5225	0.885063	0.442532	−	0.896753i	$-0.354080\pi$
$967$	27.5225	0.885063	0.442532	+	0.896753i	$0.354080\pi$
$968$	−203.102	−6.52793
$969$	76.9015	2.47043
$970$	−53.3097	−1.71167
$971$	26.7626	0.858852	0.429426	−	0.903102i	$-0.358716\pi$
$971$	26.7626	0.858852	0.429426	+	0.903102i	$0.358716\pi$
$972$	46.8196	1.50174
$973$	−79.7972	−2.55818
$974$	81.9800	2.62681
$975$	21.5904	0.691446
$976$	−140.207	−4.48793
$977$	8.24581	0.263807	0.131903	−	0.991263i	$-0.457891\pi$
$977$	8.24581	0.263807	0.131903	+	0.991263i	$0.457891\pi$
$978$	48.8932	1.56343
$979$	19.6707	0.628678
$980$	139.143	4.44477
$981$	12.2917	0.392444
$982$	−19.7115	−0.629018
$983$	−26.8256	−0.855605	−0.427802	−	0.903872i	$-0.640712\pi$
$983$	−26.8256	−0.855605	−0.427802	+	0.903872i	$0.640712\pi$
$984$	−96.5796	−3.07885
$985$	58.8429	1.87489
$986$	−69.9330	−2.22712
$987$	−37.3079	−1.18752
$988$	−82.6805	−2.63042
$989$	10.2102	0.324667
$990$	39.7147	1.26222
$991$	−28.7600	−0.913591	−0.456795	−	0.889572i	$-0.651003\pi$
$991$	−28.7600	−0.913591	−0.456795	+	0.889572i	$0.651003\pi$
$992$	101.463	3.22144
$993$	11.8951	0.377478
$994$	35.1570	1.11511
$995$	−9.45072	−0.299608
$996$	−145.005	−4.59465
$997$	29.9574	0.948762	0.474381	−	0.880320i	$-0.342672\pi$
$997$	29.9574	0.948762	0.474381	+	0.880320i	$0.342672\pi$
$998$	117.841	3.73021
$999$	20.8045	0.658224

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.3	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.3	✓	169	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71035 q^{2} -1.96664 q^{3} +5.34597 q^{4} +2.92225 q^{5} +5.33028 q^{6} +3.98832 q^{7} -9.06874 q^{8} +0.867686 q^{9} +O(q^{10})\)	\(q-2.71035 q^{2} -1.96664 q^{3} +5.34597 q^{4} +2.92225 q^{5} +5.33028 q^{6} +3.98832 q^{7} -9.06874 q^{8} +0.867686 q^{9} -7.92031 q^{10} -5.77891 q^{11} -10.5136 q^{12} -3.10160 q^{13} -10.8097 q^{14} -5.74703 q^{15} +13.8875 q^{16} -7.84184 q^{17} -2.35173 q^{18} +4.98645 q^{19} +15.6223 q^{20} -7.84361 q^{21} +15.6628 q^{22} -1.00000 q^{23} +17.8350 q^{24} +3.53956 q^{25} +8.40640 q^{26} +4.19350 q^{27} +21.3215 q^{28} -3.29033 q^{29} +15.5764 q^{30} -5.20258 q^{31} -19.5023 q^{32} +11.3651 q^{33} +21.2541 q^{34} +11.6549 q^{35} +4.63862 q^{36} +4.96112 q^{37} -13.5150 q^{38} +6.09974 q^{39} -26.5011 q^{40} -5.41518 q^{41} +21.2589 q^{42} -10.2102 q^{43} -30.8939 q^{44} +2.53560 q^{45} +2.71035 q^{46} +4.75647 q^{47} -27.3117 q^{48} +8.90673 q^{49} -9.59344 q^{50} +15.4221 q^{51} -16.5811 q^{52} -3.54675 q^{53} -11.3658 q^{54} -16.8874 q^{55} -36.1691 q^{56} -9.80656 q^{57} +8.91793 q^{58} -8.68327 q^{59} -30.7235 q^{60} -10.0960 q^{61} +14.1008 q^{62} +3.46061 q^{63} +25.0832 q^{64} -9.06365 q^{65} -30.8032 q^{66} +13.3138 q^{67} -41.9222 q^{68} +1.96664 q^{69} -31.5888 q^{70} -3.25235 q^{71} -7.86882 q^{72} -8.60558 q^{73} -13.4463 q^{74} -6.96106 q^{75} +26.6574 q^{76} -23.0482 q^{77} -16.5324 q^{78} +11.9125 q^{79} +40.5827 q^{80} -10.8502 q^{81} +14.6770 q^{82} +13.7921 q^{83} -41.9317 q^{84} -22.9158 q^{85} +27.6733 q^{86} +6.47091 q^{87} +52.4074 q^{88} -3.40388 q^{89} -6.87235 q^{90} -12.3702 q^{91} -5.34597 q^{92} +10.2316 q^{93} -12.8917 q^{94} +14.5717 q^{95} +38.3542 q^{96} +6.73076 q^{97} -24.1403 q^{98} -5.01428 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * q^99

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