LMFDB - Embedded newform 8027.2.a.d.1.5

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:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-2.63043 q^{2} +0.0298964 q^{3} +4.91916 q^{4} -2.77768 q^{5} -0.0786403 q^{6} -4.82248 q^{7} -7.67864 q^{8} -2.99911 q^{9} +O(q^{10})$	\(q-2.63043 q^{2} +0.0298964 q^{3} +4.91916 q^{4} -2.77768 q^{5} -0.0786403 q^{6} -4.82248 q^{7} -7.67864 q^{8} -2.99911 q^{9} +7.30650 q^{10} +4.52341 q^{11} +0.147065 q^{12} -2.29652 q^{13} +12.6852 q^{14} -0.0830427 q^{15} +10.3598 q^{16} -5.54708 q^{17} +7.88894 q^{18} -2.58452 q^{19} -13.6639 q^{20} -0.144175 q^{21} -11.8985 q^{22} -1.00000 q^{23} -0.229563 q^{24} +2.71553 q^{25} +6.04084 q^{26} -0.179352 q^{27} -23.7225 q^{28} +0.128996 q^{29} +0.218438 q^{30} +5.53653 q^{31} -11.8934 q^{32} +0.135234 q^{33} +14.5912 q^{34} +13.3953 q^{35} -14.7531 q^{36} -9.01931 q^{37} +6.79838 q^{38} -0.0686577 q^{39} +21.3288 q^{40} +6.64953 q^{41} +0.379241 q^{42} +7.27287 q^{43} +22.2514 q^{44} +8.33057 q^{45} +2.63043 q^{46} -0.251732 q^{47} +0.309720 q^{48} +16.2563 q^{49} -7.14300 q^{50} -0.165838 q^{51} -11.2969 q^{52} -11.6092 q^{53} +0.471772 q^{54} -12.5646 q^{55} +37.0300 q^{56} -0.0772677 q^{57} -0.339316 q^{58} -9.43292 q^{59} -0.408500 q^{60} +3.23426 q^{61} -14.5635 q^{62} +14.4631 q^{63} +10.5652 q^{64} +6.37901 q^{65} -0.355723 q^{66} +15.2765 q^{67} -27.2870 q^{68} -0.0298964 q^{69} -35.2354 q^{70} +5.64239 q^{71} +23.0290 q^{72} -7.79561 q^{73} +23.7247 q^{74} +0.0811845 q^{75} -12.7136 q^{76} -21.8140 q^{77} +0.180599 q^{78} -11.0532 q^{79} -28.7762 q^{80} +8.99196 q^{81} -17.4911 q^{82} -1.85819 q^{83} -0.709218 q^{84} +15.4080 q^{85} -19.1308 q^{86} +0.00385653 q^{87} -34.7336 q^{88} +12.0925 q^{89} -21.9130 q^{90} +11.0749 q^{91} -4.91916 q^{92} +0.165522 q^{93} +0.662162 q^{94} +7.17897 q^{95} -0.355571 q^{96} +1.98612 q^{97} -42.7610 q^{98} -13.5662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) $ 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * 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 $

$2$	−2.63043	−1.85999	−0.929997	−	0.367567i	$-0.880191\pi$
$2$	−2.63043	−1.85999	−0.929997	+	0.367567i	$0.880191\pi$
$3$	0.0298964	0.0172607	0.00863034	−	0.999963i	$-0.497253\pi$
$3$	0.0298964	0.0172607	0.00863034	+	0.999963i	$0.497253\pi$
$4$	4.91916	2.45958
$5$	−2.77768	−1.24222	−0.621109	−	0.783724i	$-0.713318\pi$
$5$	−2.77768	−1.24222	−0.621109	+	0.783724i	$0.713318\pi$
$6$	−0.0786403	−0.0321048
$7$	−4.82248	−1.82272	−0.911362	−	0.411605i	$-0.864968\pi$
$7$	−4.82248	−1.82272	−0.911362	+	0.411605i	$0.864968\pi$
$8$	−7.67864	−2.71481
$9$	−2.99911	−0.999702
$10$	7.30650	2.31052
$11$	4.52341	1.36386	0.681930	−	0.731418i	$-0.261141\pi$
$11$	4.52341	1.36386	0.681930	+	0.731418i	$0.261141\pi$
$12$	0.147065	0.0424540
$13$	−2.29652	−0.636940	−0.318470	−	0.947933i	$-0.603169\pi$
$13$	−2.29652	−0.636940	−0.318470	+	0.947933i	$0.603169\pi$
$14$	12.6852	3.39026
$15$	−0.0830427	−0.0214415
$16$	10.3598	2.58995
$17$	−5.54708	−1.34537	−0.672683	−	0.739931i	$-0.734858\pi$
$17$	−5.54708	−1.34537	−0.672683	+	0.739931i	$0.734858\pi$
$18$	7.88894	1.85944
$19$	−2.58452	−0.592928	−0.296464	−	0.955044i	$-0.595808\pi$
$19$	−2.58452	−0.592928	−0.296464	+	0.955044i	$0.595808\pi$
$20$	−13.6639	−3.05533
$21$	−0.144175	−0.0314615
$22$	−11.8985	−2.53677
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.229563	−0.0468595
$25$	2.71553	0.543106
$26$	6.04084	1.18471
$27$	−0.179352	−0.0345162
$28$	−23.7225	−4.48314
$29$	0.128996	0.0239540	0.0119770	−	0.999928i	$-0.496188\pi$
$29$	0.128996	0.0239540	0.0119770	+	0.999928i	$0.496188\pi$
$30$	0.218438	0.0398811
$31$	5.53653	0.994391	0.497195	−	0.867639i	$-0.334363\pi$
$31$	5.53653	0.994391	0.497195	+	0.867639i	$0.334363\pi$
$32$	−11.8934	−2.10248
$33$	0.135234	0.0235412
$34$	14.5912	2.50237
$35$	13.3953	2.26422
$36$	−14.7531	−2.45885
$37$	−9.01931	−1.48277	−0.741383	−	0.671082i	$-0.765830\pi$
$37$	−9.01931	−1.48277	−0.741383	+	0.671082i	$0.765830\pi$
$38$	6.79838	1.10284
$39$	−0.0686577	−0.0109940
$40$	21.3288	3.37238
$41$	6.64953	1.03848	0.519241	−	0.854628i	$-0.326215\pi$
$41$	6.64953	1.03848	0.519241	+	0.854628i	$0.326215\pi$
$42$	0.379241	0.0585182
$43$	7.27287	1.10910	0.554551	−	0.832150i	$-0.312890\pi$
$43$	7.27287	1.10910	0.554551	+	0.832150i	$0.312890\pi$
$44$	22.2514	3.35452
$45$	8.33057	1.24185
$46$	2.63043	0.387836
$47$	−0.251732	−0.0367188	−0.0183594	−	0.999831i	$-0.505844\pi$
$47$	−0.251732	−0.0367188	−0.0183594	+	0.999831i	$0.505844\pi$
$48$	0.309720	0.0447043
$49$	16.2563	2.32233
$50$	−7.14300	−1.01017
$51$	−0.165838	−0.0232219
$52$	−11.2969	−1.56660
$53$	−11.6092	−1.59464	−0.797322	−	0.603554i	$-0.793751\pi$
$53$	−11.6092	−1.59464	−0.797322	+	0.603554i	$0.793751\pi$
$54$	0.471772	0.0642000
$55$	−12.5646	−1.69421
$56$	37.0300	4.94835
$57$	−0.0772677	−0.0102344
$58$	−0.339316	−0.0445544
$59$	−9.43292	−1.22806	−0.614031	−	0.789282i	$-0.710453\pi$
$59$	−9.43292	−1.22806	−0.614031	+	0.789282i	$0.710453\pi$
$60$	−0.408500	−0.0527372
$61$	3.23426	0.414104	0.207052	−	0.978330i	$-0.433613\pi$
$61$	3.23426	0.414104	0.207052	+	0.978330i	$0.433613\pi$
$62$	−14.5635	−1.84956
$63$	14.4631	1.82218
$64$	10.5652	1.32065
$65$	6.37901	0.791219
$66$	−0.355723	−0.0437864
$67$	15.2765	1.86632	0.933159	−	0.359463i	$-0.117040\pi$
$67$	15.2765	1.86632	0.933159	+	0.359463i	$0.117040\pi$
$68$	−27.2870	−3.30903
$69$	−0.0298964	−0.00359910
$70$	−35.2354	−4.21144
$71$	5.64239	0.669628	0.334814	−	0.942284i	$-0.391326\pi$
$71$	5.64239	0.669628	0.334814	+	0.942284i	$0.391326\pi$
$72$	23.0290	2.71400
$73$	−7.79561	−0.912407	−0.456203	−	0.889876i	$-0.650791\pi$
$73$	−7.79561	−0.912407	−0.456203	+	0.889876i	$0.650791\pi$
$74$	23.7247	2.75794
$75$	0.0811845	0.00937438
$76$	−12.7136	−1.45835
$77$	−21.8140	−2.48594
$78$	0.180599	0.0204488
$79$	−11.0532	−1.24359	−0.621793	−	0.783181i	$-0.713596\pi$
$79$	−11.0532	−1.24359	−0.621793	+	0.783181i	$0.713596\pi$
$80$	−28.7762	−3.21728
$81$	8.99196	0.999106
$82$	−17.4911	−1.93157
$83$	−1.85819	−0.203963	−0.101981	−	0.994786i	$-0.532518\pi$
$83$	−1.85819	−0.203963	−0.101981	+	0.994786i	$0.532518\pi$
$84$	−0.709218	−0.0773820
$85$	15.4080	1.67124
$86$	−19.1308	−2.06292
$87$	0.00385653	0.000413463 0
$88$	−34.7336	−3.70262
$89$	12.0925	1.28180	0.640900	−	0.767624i	$-0.278561\pi$
$89$	12.0925	1.28180	0.640900	+	0.767624i	$0.278561\pi$
$90$	−21.9130	−2.30983
$91$	11.0749	1.16097
$92$	−4.91916	−0.512858
$93$	0.165522	0.0171639
$94$	0.662162	0.0682968
$95$	7.17897	0.736546
$96$	−0.355571	−0.0362903
$97$	1.98612	0.201660	0.100830	−	0.994904i	$-0.467850\pi$
$97$	1.98612	0.201660	0.100830	+	0.994904i	$0.467850\pi$
$98$	−42.7610	−4.31951
$99$	−13.5662	−1.36345
$100$	13.3581	1.33581
$101$	9.68506	0.963700	0.481850	−	0.876254i	$-0.339965\pi$
$101$	9.68506	0.963700	0.481850	+	0.876254i	$0.339965\pi$
$102$	0.436225	0.0431927
$103$	−14.2334	−1.40246	−0.701228	−	0.712937i	$-0.747365\pi$
$103$	−14.2334	−1.40246	−0.701228	+	0.712937i	$0.747365\pi$
$104$	17.6342	1.72917
$105$	0.400472	0.0390820
$106$	30.5371	2.96603
$107$	12.0814	1.16796	0.583978	−	0.811769i	$-0.301495\pi$
$107$	12.0814	1.16796	0.583978	+	0.811769i	$0.301495\pi$
$108$	−0.882259	−0.0848954
$109$	−0.269901	−0.0258518	−0.0129259	−	0.999916i	$-0.504115\pi$
$109$	−0.269901	−0.0258518	−0.0129259	+	0.999916i	$0.504115\pi$
$110$	33.0503	3.15122
$111$	−0.269645	−0.0255936
$112$	−49.9599	−4.72076
$113$	12.4214	1.16851	0.584254	−	0.811571i	$-0.301387\pi$
$113$	12.4214	1.16851	0.584254	+	0.811571i	$0.301387\pi$
$114$	0.203247	0.0190358
$115$	2.77768	0.259020
$116$	0.634553	0.0589168
$117$	6.88751	0.636751
$118$	24.8126	2.28419
$119$	26.7507	2.45223
$120$	0.637655	0.0582097
$121$	9.46124	0.860113
$122$	−8.50749	−0.770232
$123$	0.198797	0.0179249
$124$	27.2351	2.44578
$125$	6.34554	0.567562
$126$	−38.0442	−3.38925
$127$	−11.0894	−0.984021	−0.492010	−	0.870589i	$-0.663738\pi$
$127$	−11.0894	−0.984021	−0.492010	+	0.870589i	$0.663738\pi$
$128$	−4.00424	−0.353928
$129$	0.217432	0.0191439
$130$	−16.7795	−1.47166
$131$	10.3527	0.904522	0.452261	−	0.891886i	$-0.350618\pi$
$131$	10.3527	0.904522	0.452261	+	0.891886i	$0.350618\pi$
$132$	0.665236	0.0579013
$133$	12.4638	1.08075
$134$	−40.1837	−3.47134
$135$	0.498182	0.0428767
$136$	42.5940	3.65241
$137$	22.3028	1.90545	0.952726	−	0.303829i	$-0.0982653\pi$
$137$	22.3028	1.90545	0.952726	+	0.303829i	$0.0982653\pi$
$138$	0.0786403	0.00669431
$139$	17.9848	1.52545	0.762725	−	0.646723i	$-0.223861\pi$
$139$	17.9848	1.52545	0.762725	+	0.646723i	$0.223861\pi$
$140$	65.8937	5.56903
$141$	−0.00752587	−0.000633792 0
$142$	−14.8419	−1.24550
$143$	−10.3881	−0.868697
$144$	−31.0701	−2.58918
$145$	−0.358311	−0.0297561
$146$	20.5058	1.69707
$147$	0.486004	0.0400849
$148$	−44.3674	−3.64698
$149$	−12.6818	−1.03894	−0.519468	−	0.854490i	$-0.673870\pi$
$149$	−12.6818	−1.03894	−0.519468	+	0.854490i	$0.673870\pi$
$150$	−0.213550	−0.0174363
$151$	5.42398	0.441397	0.220699	−	0.975342i	$-0.429166\pi$
$151$	5.42398	0.441397	0.220699	+	0.975342i	$0.429166\pi$
$152$	19.8456	1.60969
$153$	16.6363	1.34496
$154$	57.3803	4.62384
$155$	−15.3787	−1.23525
$156$	−0.337738	−0.0270407
$157$	13.7363	1.09627	0.548137	−	0.836389i	$-0.315337\pi$
$157$	13.7363	1.09627	0.548137	+	0.836389i	$0.315337\pi$
$158$	29.0748	2.31306
$159$	−0.347073	−0.0275247
$160$	33.0362	2.61174
$161$	4.82248	0.380064
$162$	−23.6527	−1.85833
$163$	−20.2625	−1.58708	−0.793539	−	0.608520i	$-0.791764\pi$
$163$	−20.2625	−1.58708	−0.793539	+	0.608520i	$0.791764\pi$
$164$	32.7101	2.55423
$165$	−0.375636	−0.0292432
$166$	4.88783	0.379369
$167$	4.94744	0.382844	0.191422	−	0.981508i	$-0.438690\pi$
$167$	4.94744	0.382844	0.191422	+	0.981508i	$0.438690\pi$
$168$	1.10706	0.0854119
$169$	−7.72599	−0.594307
$170$	−40.5298	−3.10849
$171$	7.75124	0.592752
$172$	35.7764	2.72792
$173$	15.6220	1.18772	0.593860	−	0.804569i	$-0.297603\pi$
$173$	15.6220	1.18772	0.593860	+	0.804569i	$0.297603\pi$
$174$	−0.0101443	−0.000769039 0
$175$	−13.0956	−0.989932
$176$	46.8616	3.53233
$177$	−0.282010	−0.0211972
$178$	−31.8084	−2.38414
$179$	−25.5800	−1.91194	−0.955970	−	0.293464i	$-0.905192\pi$
$179$	−25.5800	−1.91194	−0.955970	+	0.293464i	$0.905192\pi$
$180$	40.9794	3.05442
$181$	−25.8508	−1.92147	−0.960736	−	0.277466i	$-0.910506\pi$
$181$	−25.8508	−1.92147	−0.960736	+	0.277466i	$0.910506\pi$
$182$	−29.1318	−2.15939
$183$	0.0966927	0.00714773
$184$	7.67864	0.566077
$185$	25.0528	1.84192
$186$	−0.435395	−0.0319247
$187$	−25.0917	−1.83489
$188$	−1.23831	−0.0903129
$189$	0.864919	0.0629136
$190$	−18.8838	−1.36997
$191$	−10.1336	−0.733244	−0.366622	−	0.930370i	$-0.619486\pi$
$191$	−10.1336	−0.733244	−0.366622	+	0.930370i	$0.619486\pi$
$192$	0.315862	0.0227954
$193$	12.5676	0.904634	0.452317	−	0.891857i	$-0.350597\pi$
$193$	12.5676	0.904634	0.452317	+	0.891857i	$0.350597\pi$
$194$	−5.22435	−0.375087
$195$	0.190709	0.0136570
$196$	79.9672	5.71194
$197$	15.8742	1.13099	0.565495	−	0.824751i	$-0.308685\pi$
$197$	15.8742	1.13099	0.565495	+	0.824751i	$0.308685\pi$
$198$	35.6849	2.53602
$199$	14.4921	1.02732	0.513659	−	0.857994i	$-0.328290\pi$
$199$	14.4921	1.02732	0.513659	+	0.857994i	$0.328290\pi$
$200$	−20.8516	−1.47443
$201$	0.456711	0.0322139
$202$	−25.4759	−1.79248
$203$	−0.622082	−0.0436616
$204$	−0.815782	−0.0571162
$205$	−18.4703	−1.29002
$206$	37.4399	2.60856
$207$	2.99911	0.208452
$208$	−23.7915	−1.64964
$209$	−11.6908	−0.808671
$210$	−1.05341	−0.0726923
$211$	6.36510	0.438191	0.219096	−	0.975703i	$-0.429689\pi$
$211$	6.36510	0.438191	0.219096	+	0.975703i	$0.429689\pi$
$212$	−57.1074	−3.92215
$213$	0.168687	0.0115582
$214$	−31.7794	−2.17239
$215$	−20.2017	−1.37775
$216$	1.37718	0.0937049
$217$	−26.6998	−1.81250
$218$	0.709954	0.0480842
$219$	−0.233060	−0.0157488
$220$	−61.8073	−4.16704
$221$	12.7390	0.856918
$222$	0.709282	0.0476039
$223$	−20.2063	−1.35311	−0.676557	−	0.736390i	$-0.736529\pi$
$223$	−20.2063	−1.35311	−0.676557	+	0.736390i	$0.736529\pi$
$224$	57.3558	3.83224
$225$	−8.14416	−0.542944
$226$	−32.6736	−2.17342
$227$	−10.8285	−0.718710	−0.359355	−	0.933201i	$-0.617003\pi$
$227$	−10.8285	−0.718710	−0.359355	+	0.933201i	$0.617003\pi$
$228$	−0.380092	−0.0251722
$229$	−0.00670486	−0.000443069 0	−0.000221535	−	1.00000i	$-0.500071\pi$
$229$	−0.00670486	−0.000443069 0	−0.000221535		1.00000i	$0.500071\pi$
$230$	−7.30650	−0.481776
$231$	−0.652161	−0.0429091
$232$	−0.990516	−0.0650306
$233$	26.9335	1.76447	0.882237	−	0.470805i	$-0.156037\pi$
$233$	26.9335	1.76447	0.882237	+	0.470805i	$0.156037\pi$
$234$	−18.1171	−1.18435
$235$	0.699231	0.0456128
$236$	−46.4020	−3.02051
$237$	−0.330452	−0.0214652
$238$	−70.3658	−4.56114
$239$	2.04365	0.132193	0.0660965	−	0.997813i	$-0.478945\pi$
$239$	2.04365	0.132193	0.0660965	+	0.997813i	$0.478945\pi$
$240$	−0.860305	−0.0555325
$241$	3.10823	0.200218	0.100109	−	0.994976i	$-0.468081\pi$
$241$	3.10823	0.200218	0.100109	+	0.994976i	$0.468081\pi$
$242$	−24.8871	−1.59981
$243$	0.806882	0.0517615
$244$	15.9098	1.01852
$245$	−45.1548	−2.88484
$246$	−0.522921	−0.0333402
$247$	5.93539	0.377660
$248$	−42.5130	−2.69958
$249$	−0.0555531	−0.00352054
$250$	−16.6915	−1.05566
$251$	−23.1131	−1.45888	−0.729442	−	0.684042i	$-0.760220\pi$
$251$	−23.1131	−1.45888	−0.729442	+	0.684042i	$0.760220\pi$
$252$	71.1464	4.48180
$253$	−4.52341	−0.284384
$254$	29.1698	1.83027
$255$	0.460645	0.0288467
$256$	−10.5976	−0.662350
$257$	9.78890	0.610614	0.305307	−	0.952254i	$-0.401241\pi$
$257$	9.78890	0.610614	0.305307	+	0.952254i	$0.401241\pi$
$258$	−0.571941	−0.0356075
$259$	43.4954	2.70267
$260$	31.3794	1.94606
$261$	−0.386874	−0.0239469
$262$	−27.2321	−1.68240
$263$	27.6060	1.70226	0.851129	−	0.524956i	$-0.175918\pi$
$263$	27.6060	1.70226	0.851129	+	0.524956i	$0.175918\pi$
$264$	−1.03841	−0.0639097
$265$	32.2466	1.98090
$266$	−32.7850	−2.01018
$267$	0.361522	0.0221248
$268$	75.1474	4.59036
$269$	12.9035	0.786740	0.393370	−	0.919380i	$-0.371309\pi$
$269$	12.9035	0.786740	0.393370	+	0.919380i	$0.371309\pi$
$270$	−1.31043	−0.0797504
$271$	15.8149	0.960685	0.480343	−	0.877081i	$-0.340512\pi$
$271$	15.8149	0.960685	0.480343	+	0.877081i	$0.340512\pi$
$272$	−57.4666	−3.48443
$273$	0.331100	0.0200391
$274$	−58.6658	−3.54413
$275$	12.2834	0.740720
$276$	−0.147065	−0.00885228
$277$	7.79346	0.468264	0.234132	−	0.972205i	$-0.424775\pi$
$277$	7.79346	0.468264	0.234132	+	0.972205i	$0.424775\pi$
$278$	−47.3077	−2.83733
$279$	−16.6047	−0.994095
$280$	−102.858	−6.14693
$281$	−8.24469	−0.491837	−0.245918	−	0.969291i	$-0.579090\pi$
$281$	−8.24469	−0.491837	−0.245918	+	0.969291i	$0.579090\pi$
$282$	0.0197963	0.00117885
$283$	−5.61461	−0.333754	−0.166877	−	0.985978i	$-0.553368\pi$
$283$	−5.61461	−0.333754	−0.166877	+	0.985978i	$0.553368\pi$
$284$	27.7558	1.64700
$285$	0.214625	0.0127133
$286$	27.3252	1.61577
$287$	−32.0672	−1.89287
$288$	35.6697	2.10185
$289$	13.7701	0.810008
$290$	0.942512	0.0553462
$291$	0.0593779	0.00348079
$292$	−38.3478	−2.24414
$293$	5.49347	0.320932	0.160466	−	0.987041i	$-0.448700\pi$
$293$	5.49347	0.320932	0.160466	+	0.987041i	$0.448700\pi$
$294$	−1.27840	−0.0745578
$295$	26.2017	1.52552
$296$	69.2560	4.02543
$297$	−0.811281	−0.0470753
$298$	33.3586	1.93241
$299$	2.29652	0.132811
$300$	0.399359	0.0230570
$301$	−35.0732	−2.02159
$302$	−14.2674	−0.820996
$303$	0.289548	0.0166341
$304$	−26.7750	−1.53565
$305$	−8.98375	−0.514408
$306$	−43.7606	−2.50163
$307$	−17.7653	−1.01392	−0.506958	−	0.861971i	$-0.669230\pi$
$307$	−17.7653	−1.01392	−0.506958	+	0.861971i	$0.669230\pi$
$308$	−107.307	−6.11437
$309$	−0.425527	−0.0242074
$310$	40.4527	2.29756
$311$	15.7639	0.893887	0.446943	−	0.894562i	$-0.352513\pi$
$311$	15.7639	0.893887	0.446943	+	0.894562i	$0.352513\pi$
$312$	0.527197	0.0298467
$313$	−9.98452	−0.564358	−0.282179	−	0.959362i	$-0.591057\pi$
$313$	−9.98452	−0.564358	−0.282179	+	0.959362i	$0.591057\pi$
$314$	−36.1323	−2.03906
$315$	−40.1740	−2.26355
$316$	−54.3726	−3.05870
$317$	−25.1536	−1.41277	−0.706383	−	0.707830i	$-0.749674\pi$
$317$	−25.1536	−1.41277	−0.706383	+	0.707830i	$0.749674\pi$
$318$	0.912950	0.0511957
$319$	0.583504	0.0326699
$320$	−29.3469	−1.64054
$321$	0.361191	0.0201597
$322$	−12.6852	−0.706918
$323$	14.3365	0.797705
$324$	44.2328	2.45738
$325$	−6.23627	−0.345926
$326$	53.2989	2.95196
$327$	−0.00806905	−0.000446220 0
$328$	−51.0593	−2.81928
$329$	1.21397	0.0669283
$330$	0.988085	0.0543923
$331$	−22.4976	−1.23658	−0.618289	−	0.785951i	$-0.712174\pi$
$331$	−22.4976	−1.23658	−0.618289	+	0.785951i	$0.712174\pi$
$332$	−9.14072	−0.501662
$333$	27.0499	1.48232
$334$	−13.0139	−0.712088
$335$	−42.4332	−2.31837
$336$	−1.49362	−0.0814836
$337$	−18.5308	−1.00944	−0.504718	−	0.863284i	$-0.668403\pi$
$337$	−18.5308	−1.00944	−0.504718	+	0.863284i	$0.668403\pi$
$338$	20.3227	1.10541
$339$	0.371355	0.0201693
$340$	75.7946	4.11054
$341$	25.0440	1.35621
$342$	−20.3891	−1.10251
$343$	−44.6382	−2.41024
$344$	−55.8457	−3.01100
$345$	0.0830427	0.00447087
$346$	−41.0926	−2.20915
$347$	31.9180	1.71345	0.856723	−	0.515777i	$-0.172497\pi$
$347$	31.9180	1.71345	0.856723	+	0.515777i	$0.172497\pi$
$348$	0.0189709	0.00101694
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	34.4470	1.84127
$351$	0.411885	0.0219848
$352$	−53.7989	−2.86749
$353$	5.35333	0.284929	0.142464	−	0.989800i	$-0.454497\pi$
$353$	5.35333	0.284929	0.142464	+	0.989800i	$0.454497\pi$
$354$	0.741808	0.0394266
$355$	−15.6728	−0.831824
$356$	59.4848	3.15269
$357$	0.799749	0.0423272
$358$	67.2864	3.55620
$359$	−32.7274	−1.72728	−0.863642	−	0.504105i	$-0.831822\pi$
$359$	−32.7274	−1.72728	−0.863642	+	0.504105i	$0.831822\pi$
$360$	−63.9674	−3.37138
$361$	−12.3203	−0.648436
$362$	67.9986	3.57393
$363$	0.282857	0.0148461
$364$	54.4793	2.85549
$365$	21.6537	1.13341
$366$	−0.254343	−0.0132947
$367$	25.5364	1.33299	0.666493	−	0.745511i	$-0.267794\pi$
$367$	25.5364	1.33299	0.666493	+	0.745511i	$0.267794\pi$
$368$	−10.3598	−0.540042
$369$	−19.9426	−1.03817
$370$	−65.8996	−3.42596
$371$	55.9850	2.90660
$372$	0.814231	0.0422159
$373$	−7.90506	−0.409309	−0.204654	−	0.978834i	$-0.565607\pi$
$373$	−7.90506	−0.409309	−0.204654	+	0.978834i	$0.565607\pi$
$374$	66.0020	3.41288
$375$	0.189709	0.00979652
$376$	1.93296	0.0996846
$377$	−0.296243	−0.0152573
$378$	−2.27511	−0.117019
$379$	−25.6682	−1.31848	−0.659242	−	0.751931i	$-0.729123\pi$
$379$	−25.6682	−1.31848	−0.659242	+	0.751931i	$0.729123\pi$
$380$	35.3145	1.81159
$381$	−0.331532	−0.0169849
$382$	26.6558	1.36383
$383$	8.52555	0.435635	0.217818	−	0.975989i	$-0.430106\pi$
$383$	8.52555	0.435635	0.217818	+	0.975989i	$0.430106\pi$
$384$	−0.119712	−0.00610905
$385$	60.5925	3.08808
$386$	−33.0581	−1.68261
$387$	−21.8121	−1.10877
$388$	9.77005	0.495999
$389$	−4.80560	−0.243653	−0.121827	−	0.992551i	$-0.538875\pi$
$389$	−4.80560	−0.243653	−0.121827	+	0.992551i	$0.538875\pi$
$390$	−0.501648	−0.0254019
$391$	5.54708	0.280528
$392$	−124.826	−6.30467
$393$	0.309509	0.0156127
$394$	−41.7560	−2.10364
$395$	30.7024	1.54481
$396$	−66.7342	−3.35352
$397$	−24.2929	−1.21922	−0.609612	−	0.792700i	$-0.708675\pi$
$397$	−24.2929	−1.21922	−0.609612	+	0.792700i	$0.708675\pi$
$398$	−38.1205	−1.91081
$399$	0.372622	0.0186544
$400$	28.1323	1.40662
$401$	−2.74107	−0.136883	−0.0684413	−	0.997655i	$-0.521803\pi$
$401$	−2.74107	−0.136883	−0.0684413	+	0.997655i	$0.521803\pi$
$402$	−1.20135	−0.0599178
$403$	−12.7148	−0.633368
$404$	47.6424	2.37030
$405$	−24.9768	−1.24111
$406$	1.63634	0.0812103
$407$	−40.7981	−2.02228
$408$	1.27341	0.0630431
$409$	−29.1075	−1.43927	−0.719637	−	0.694351i	$-0.755692\pi$
$409$	−29.1075	−1.43927	−0.719637	+	0.694351i	$0.755692\pi$
$410$	48.5848	2.39943
$411$	0.666772	0.0328894
$412$	−70.0162	−3.44945
$413$	45.4900	2.23842
$414$	−7.88894	−0.387720
$415$	5.16146	0.253366
$416$	27.3135	1.33916
$417$	0.537680	0.0263303
$418$	30.7519	1.50412
$419$	4.97464	0.243027	0.121513	−	0.992590i	$-0.461225\pi$
$419$	4.97464	0.243027	0.121513	+	0.992590i	$0.461225\pi$
$420$	1.96998	0.0961253
$421$	34.5634	1.68452	0.842259	−	0.539073i	$-0.181225\pi$
$421$	34.5634	1.68452	0.842259	+	0.539073i	$0.181225\pi$
$422$	−16.7429	−0.815033
$423$	0.754970	0.0367079
$424$	89.1427	4.32915
$425$	−15.0633	−0.730676
$426$	−0.443719	−0.0214983
$427$	−15.5971	−0.754799
$428$	59.4305	2.87268
$429$	−0.310567	−0.0149943
$430$	53.1392	2.56260
$431$	−8.70856	−0.419477	−0.209738	−	0.977758i	$-0.567261\pi$
$431$	−8.70856	−0.419477	−0.209738	+	0.977758i	$0.567261\pi$
$432$	−1.85805	−0.0893953
$433$	25.8686	1.24317	0.621583	−	0.783349i	$-0.286490\pi$
$433$	25.8686	1.24317	0.621583	+	0.783349i	$0.286490\pi$
$434$	70.2319	3.37124
$435$	−0.0107122	−0.000513611 0
$436$	−1.32768	−0.0635845
$437$	2.58452	0.123634
$438$	0.613049	0.0292926
$439$	13.9298	0.664831	0.332415	−	0.943133i	$-0.392136\pi$
$439$	13.9298	0.664831	0.332415	+	0.943133i	$0.392136\pi$
$440$	96.4790	4.59946
$441$	−48.7543	−2.32163
$442$	−33.5090	−1.59386
$443$	8.19290	0.389256	0.194628	−	0.980877i	$-0.437650\pi$
$443$	8.19290	0.389256	0.194628	+	0.980877i	$0.437650\pi$
$444$	−1.32643	−0.0629494
$445$	−33.5891	−1.59228
$446$	53.1513	2.51678
$447$	−0.379141	−0.0179327
$448$	−50.9506	−2.40719
$449$	20.2506	0.955685	0.477842	−	0.878446i	$-0.341419\pi$
$449$	20.2506	0.955685	0.477842	+	0.878446i	$0.341419\pi$
$450$	21.4226	1.00987
$451$	30.0786	1.41634
$452$	61.1029	2.87404
$453$	0.162157	0.00761882
$454$	28.4835	1.33680
$455$	−30.7626	−1.44217
$456$	0.593310	0.0277843
$457$	28.4135	1.32913	0.664563	−	0.747232i	$-0.268618\pi$
$457$	28.4135	1.32913	0.664563	+	0.747232i	$0.268618\pi$
$458$	0.0176366	0.000824106 0
$459$	0.994879	0.0464370
$460$	13.6639	0.637081
$461$	−18.3736	−0.855746	−0.427873	−	0.903839i	$-0.640737\pi$
$461$	−18.3736	−0.855746	−0.427873	+	0.903839i	$0.640737\pi$
$462$	1.71546	0.0798106
$463$	−21.2595	−0.988011	−0.494006	−	0.869459i	$-0.664468\pi$
$463$	−21.2595	−0.988011	−0.494006	+	0.869459i	$0.664468\pi$
$464$	1.33638	0.0620397
$465$	−0.459769	−0.0213213
$466$	−70.8468	−3.28191
$467$	20.5840	0.952516	0.476258	−	0.879306i	$-0.341993\pi$
$467$	20.5840	0.952516	0.476258	+	0.879306i	$0.341993\pi$
$468$	33.8808	1.56614
$469$	−73.6705	−3.40179
$470$	−1.83928	−0.0848395
$471$	0.410665	0.0189224
$472$	72.4319	3.33395
$473$	32.8982	1.51266
$474$	0.869230	0.0399251
$475$	−7.01832	−0.322023
$476$	131.591	6.03146
$477$	34.8172	1.59417
$478$	−5.37568	−0.245878
$479$	15.1849	0.693816	0.346908	−	0.937899i	$-0.387232\pi$
$479$	15.1849	0.693816	0.346908	+	0.937899i	$0.387232\pi$
$480$	0.987663	0.0450804
$481$	20.7130	0.944434
$482$	−8.17597	−0.372405
$483$	0.144175	0.00656017
$484$	46.5413	2.11552
$485$	−5.51682	−0.250506
$486$	−2.12245	−0.0962761
$487$	−36.8637	−1.67046	−0.835228	−	0.549904i	$-0.814664\pi$
$487$	−36.8637	−1.67046	−0.835228	+	0.549904i	$0.814664\pi$
$488$	−24.8347	−1.12421
$489$	−0.605774	−0.0273941
$490$	118.777	5.36578
$491$	−2.30164	−0.103871	−0.0519357	−	0.998650i	$-0.516539\pi$
$491$	−2.30164	−0.103871	−0.0519357	+	0.998650i	$0.516539\pi$
$492$	0.977914	0.0440877
$493$	−0.715554	−0.0322269
$494$	−15.6126	−0.702446
$495$	37.6826	1.69371
$496$	57.3573	2.57542
$497$	−27.2103	−1.22055
$498$	0.146129	0.00654818
$499$	5.96904	0.267211	0.133605	−	0.991035i	$-0.457345\pi$
$499$	5.96904	0.267211	0.133605	+	0.991035i	$0.457345\pi$
$500$	31.2147	1.39596
$501$	0.147911	0.00660816
$502$	60.7973	2.71352
$503$	21.3373	0.951383	0.475691	−	0.879612i	$-0.342198\pi$
$503$	21.3373	0.951383	0.475691	+	0.879612i	$0.342198\pi$
$504$	−111.057	−4.94687
$505$	−26.9020	−1.19713
$506$	11.8985	0.528953
$507$	−0.230979	−0.0102581
$508$	−54.5503	−2.42028
$509$	19.3799	0.858999	0.429499	−	0.903067i	$-0.358690\pi$
$509$	19.3799	0.858999	0.429499	+	0.903067i	$0.358690\pi$
$510$	−1.21169	−0.0536547
$511$	37.5941	1.66307
$512$	35.8847	1.58589
$513$	0.463537	0.0204657
$514$	−25.7490	−1.13574
$515$	39.5358	1.74216
$516$	1.06958	0.0470858
$517$	−1.13869	−0.0500793
$518$	−114.412	−5.02696
$519$	0.467042	0.0205009
$520$	−48.9821	−2.14801
$521$	−5.51547	−0.241637	−0.120819	−	0.992675i	$-0.538552\pi$
$521$	−5.51547	−0.241637	−0.120819	+	0.992675i	$0.538552\pi$
$522$	1.01764	0.0445411
$523$	36.3184	1.58809	0.794047	−	0.607857i	$-0.207970\pi$
$523$	36.3184	1.58809	0.794047	+	0.607857i	$0.207970\pi$
$524$	50.9267	2.22474
$525$	−0.391510	−0.0170869
$526$	−72.6156	−3.16619
$527$	−30.7116	−1.33782
$528$	1.40099	0.0609704
$529$	1.00000	0.0434783
$530$	−84.8225	−3.68445
$531$	28.2903	1.22770
$532$	61.3112	2.65818
$533$	−15.2708	−0.661451
$534$	−0.950957	−0.0411519
$535$	−33.5584	−1.45086
$536$	−117.302	−5.06670
$537$	−0.764750	−0.0330014
$538$	−33.9417	−1.46333
$539$	73.5338	3.16733
$540$	2.45064	0.105459
$541$	−17.5695	−0.755370	−0.377685	−	0.925934i	$-0.623280\pi$
$541$	−17.5695	−0.755370	−0.377685	+	0.925934i	$0.623280\pi$
$542$	−41.5999	−1.78687
$543$	−0.772844	−0.0331659
$544$	65.9738	2.82861
$545$	0.749699	0.0321136
$546$	−0.870935	−0.0372726
$547$	42.0697	1.79877	0.899385	−	0.437158i	$-0.144015\pi$
$547$	42.0697	1.79877	0.899385	+	0.437158i	$0.144015\pi$
$548$	109.711	4.68661
$549$	−9.69989	−0.413981
$550$	−32.3107	−1.37773
$551$	−0.333393	−0.0142030
$552$	0.229563	0.00977087
$553$	53.3040	2.26672
$554$	−20.5002	−0.870968
$555$	0.748988	0.0317928
$556$	88.4700	3.75197
$557$	−37.8585	−1.60412	−0.802058	−	0.597246i	$-0.796262\pi$
$557$	−37.8585	−1.60412	−0.802058	+	0.597246i	$0.796262\pi$
$558$	43.6774	1.84901
$559$	−16.7023	−0.706432
$560$	138.773	5.86422
$561$	−0.750152	−0.0316715
$562$	21.6871	0.914813
$563$	−13.8469	−0.583578	−0.291789	−	0.956483i	$-0.594251\pi$
$563$	−13.8469	−0.583578	−0.291789	+	0.956483i	$0.594251\pi$
$564$	−0.0370209	−0.00155886
$565$	−34.5028	−1.45154
$566$	14.7688	0.620780
$567$	−43.3635	−1.82110
$568$	−43.3258	−1.81791
$569$	−35.2212	−1.47655	−0.738276	−	0.674499i	$-0.764360\pi$
$569$	−35.2212	−1.47655	−0.738276	+	0.674499i	$0.764360\pi$
$570$	−0.564556	−0.0236467
$571$	−33.6767	−1.40933	−0.704664	−	0.709541i	$-0.748902\pi$
$571$	−33.6767	−1.40933	−0.704664	+	0.709541i	$0.748902\pi$
$572$	−51.1007	−2.13663
$573$	−0.302959	−0.0126563
$574$	84.3505	3.52072
$575$	−2.71553	−0.113245
$576$	−31.6863	−1.32026
$577$	−1.50897	−0.0628194	−0.0314097	−	0.999507i	$-0.510000\pi$
$577$	−1.50897	−0.0628194	−0.0314097	+	0.999507i	$0.510000\pi$
$578$	−36.2214	−1.50661
$579$	0.375725	0.0156146
$580$	−1.76259	−0.0731875
$581$	8.96107	0.371768
$582$	−0.156189	−0.00647425
$583$	−52.5131	−2.17487
$584$	59.8596	2.47701
$585$	−19.1313	−0.790983
$586$	−14.4502	−0.596931
$587$	−16.4705	−0.679812	−0.339906	−	0.940459i	$-0.610395\pi$
$587$	−16.4705	−0.679812	−0.339906	+	0.940459i	$0.610395\pi$
$588$	2.39073	0.0985921
$589$	−14.3093	−0.589603
$590$	−68.9216	−2.83746
$591$	0.474582	0.0195217
$592$	−93.4382	−3.84029
$593$	1.86844	0.0767277	0.0383638	−	0.999264i	$-0.487785\pi$
$593$	1.86844	0.0767277	0.0383638	+	0.999264i	$0.487785\pi$
$594$	2.13402	0.0875598
$595$	−74.3049	−3.04621
$596$	−62.3839	−2.55534
$597$	0.433262	0.0177322
$598$	−6.04084	−0.247028
$599$	21.9933	0.898624	0.449312	−	0.893375i	$-0.351669\pi$
$599$	21.9933	0.898624	0.449312	+	0.893375i	$0.351669\pi$
$600$	−0.623386	−0.0254496
$601$	12.2837	0.501064	0.250532	−	0.968108i	$-0.419394\pi$
$601$	12.2837	0.501064	0.250532	+	0.968108i	$0.419394\pi$
$602$	92.2576	3.76014
$603$	−45.8158	−1.86576
$604$	26.6814	1.08565
$605$	−26.2803	−1.06845
$606$	−0.761637	−0.0309394
$607$	25.8080	1.04751	0.523757	−	0.851868i	$-0.324530\pi$
$607$	25.8080	1.04751	0.523757	+	0.851868i	$0.324530\pi$
$608$	30.7387	1.24662
$609$	−0.0185980	−0.000753629 0
$610$	23.6311	0.956796
$611$	0.578107	0.0233877
$612$	81.8365	3.30805
$613$	−11.5290	−0.465650	−0.232825	−	0.972519i	$-0.574797\pi$
$613$	−11.5290	−0.465650	−0.232825	+	0.972519i	$0.574797\pi$
$614$	46.7303	1.88588
$615$	−0.552195	−0.0222667
$616$	167.502	6.74885
$617$	−2.96110	−0.119210	−0.0596048	−	0.998222i	$-0.518984\pi$
$617$	−2.96110	−0.119210	−0.0596048	+	0.998222i	$0.518984\pi$
$618$	1.11932	0.0450256
$619$	−10.6801	−0.429271	−0.214635	−	0.976694i	$-0.568856\pi$
$619$	−10.6801	−0.429271	−0.214635	+	0.976694i	$0.568856\pi$
$620$	−75.6504	−3.03819
$621$	0.179352	0.00719713
$622$	−41.4657	−1.66262
$623$	−58.3157	−2.33637
$624$	−0.711280	−0.0284740
$625$	−31.2035	−1.24814
$626$	26.2636	1.04970
$627$	−0.349513	−0.0139582
$628$	67.5709	2.69637
$629$	50.0309	1.99486
$630$	105.675	4.21018
$631$	−28.1193	−1.11941	−0.559706	−	0.828691i	$-0.689086\pi$
$631$	−28.1193	−1.11941	−0.559706	+	0.828691i	$0.689086\pi$
$632$	84.8738	3.37610
$633$	0.190293	0.00756348
$634$	66.1647	2.62774
$635$	30.8027	1.22237
$636$	−1.70731	−0.0676991
$637$	−37.3329	−1.47918
$638$	−1.53486	−0.0607659
$639$	−16.9221	−0.669429
$640$	11.1225	0.439656
$641$	12.5196	0.494493	0.247247	−	0.968953i	$-0.420474\pi$
$641$	12.5196	0.494493	0.247247	+	0.968953i	$0.420474\pi$
$642$	−0.950088	−0.0374970
$643$	−34.4916	−1.36022	−0.680108	−	0.733112i	$-0.738067\pi$
$643$	−34.4916	−1.36022	−0.680108	+	0.733112i	$0.738067\pi$
$644$	23.7225	0.934798
$645$	−0.603959	−0.0237808
$646$	−37.7112	−1.48373
$647$	7.28188	0.286280	0.143140	−	0.989702i	$-0.454280\pi$
$647$	7.28188	0.286280	0.143140	+	0.989702i	$0.454280\pi$
$648$	−69.0460	−2.71238
$649$	−42.6690	−1.67490
$650$	16.4041	0.643420
$651$	−0.798228	−0.0312850
$652$	−99.6742	−3.90354
$653$	41.6197	1.62870	0.814352	−	0.580371i	$-0.197092\pi$
$653$	41.6197	1.62870	0.814352	+	0.580371i	$0.197092\pi$
$654$	0.0212251	0.000829966 0
$655$	−28.7566	−1.12361
$656$	68.8878	2.68962
$657$	23.3798	0.912135
$658$	−3.19326	−0.124486
$659$	−14.9847	−0.583722	−0.291861	−	0.956461i	$-0.594274\pi$
$659$	−14.9847	−0.583722	−0.291861	+	0.956461i	$0.594274\pi$
$660$	−1.84781	−0.0719261
$661$	−28.5719	−1.11132	−0.555659	−	0.831411i	$-0.687534\pi$
$661$	−28.5719	−1.11132	−0.555659	+	0.831411i	$0.687534\pi$
$662$	59.1783	2.30003
$663$	0.380850	0.0147910
$664$	14.2684	0.553719
$665$	−34.6204	−1.34252
$666$	−71.1528	−2.75711
$667$	−0.128996	−0.00499476
$668$	24.3372	0.941636
$669$	−0.604096	−0.0233557
$670$	111.618	4.31216
$671$	14.6299	0.564780
$672$	1.71473	0.0661472
$673$	−8.67588	−0.334431	−0.167215	−	0.985920i	$-0.553478\pi$
$673$	−8.67588	−0.334431	−0.167215	+	0.985920i	$0.553478\pi$
$674$	48.7439	1.87754
$675$	−0.487034	−0.0187460
$676$	−38.0054	−1.46174
$677$	20.7098	0.795942	0.397971	−	0.917398i	$-0.369714\pi$
$677$	20.7098	0.795942	0.397971	+	0.917398i	$0.369714\pi$
$678$	−0.976824	−0.0375147
$679$	−9.57803	−0.367571
$680$	−118.313	−4.53709
$681$	−0.323732	−0.0124054
$682$	−65.8765	−2.52254
$683$	23.1388	0.885382	0.442691	−	0.896674i	$-0.354024\pi$
$683$	23.1388	0.885382	0.442691	+	0.896674i	$0.354024\pi$
$684$	38.1295	1.45792
$685$	−61.9500	−2.36699
$686$	117.418	4.48303
$687$	−0.000200451 0	−7.64768e−6 0
$688$	75.3454	2.87252
$689$	26.6607	1.01569
$690$	−0.218438	−0.00831579
$691$	32.2574	1.22713	0.613564	−	0.789645i	$-0.289735\pi$
$691$	32.2574	1.22713	0.613564	+	0.789645i	$0.289735\pi$
$692$	76.8471	2.92129
$693$	65.4226	2.48520
$694$	−83.9579	−3.18700
$695$	−49.9561	−1.89494
$696$	−0.0296129	−0.00112247
$697$	−36.8855	−1.39714
$698$	2.63043	0.0995632
$699$	0.805215	0.0304560
$700$	−64.4192	−2.43482
$701$	−15.4746	−0.584467	−0.292234	−	0.956347i	$-0.594398\pi$
$701$	−15.4746	−0.584467	−0.292234	+	0.956347i	$0.594398\pi$
$702$	−1.08343	−0.0408916
$703$	23.3106	0.879174
$704$	47.7909	1.80119
$705$	0.0209045	0.000787308 0
$706$	−14.0815	−0.529966
$707$	−46.7060	−1.75656
$708$	−1.38725	−0.0521361
$709$	−2.16607	−0.0813485	−0.0406743	−	0.999172i	$-0.512951\pi$
$709$	−2.16607	−0.0813485	−0.0406743	+	0.999172i	$0.512951\pi$
$710$	41.2261	1.54719
$711$	33.1498	1.24322
$712$	−92.8538	−3.47984
$713$	−5.53653	−0.207345
$714$	−2.10368	−0.0787283
$715$	28.8549	1.07911
$716$	−125.832	−4.70257
$717$	0.0610978	0.00228174
$718$	86.0870	3.21274
$719$	−34.0666	−1.27047	−0.635234	−	0.772319i	$-0.719097\pi$
$719$	−34.0666	−1.27047	−0.635234	+	0.772319i	$0.719097\pi$
$720$	86.3030	3.21632
$721$	68.6401	2.55629
$722$	32.4076	1.20609
$723$	0.0929247	0.00345591
$724$	−127.164	−4.72601
$725$	0.350293	0.0130096
$726$	−0.744035	−0.0276137
$727$	−21.7790	−0.807738	−0.403869	−	0.914817i	$-0.632335\pi$
$727$	−21.7790	−0.807738	−0.403869	+	0.914817i	$0.632335\pi$
$728$	−85.0403	−3.15180
$729$	−26.9517	−0.998213
$730$	−56.9586	−2.10813
$731$	−40.3432	−1.49215
$732$	0.475647	0.0175804
$733$	39.6531	1.46462	0.732310	−	0.680972i	$-0.238442\pi$
$733$	39.6531	1.46462	0.732310	+	0.680972i	$0.238442\pi$
$734$	−67.1716	−2.47935
$735$	−1.34997	−0.0497942
$736$	11.8934	0.438398
$737$	69.1018	2.54540
$738$	52.4577	1.93100
$739$	35.4213	1.30299	0.651496	−	0.758652i	$-0.274142\pi$
$739$	35.4213	1.30299	0.651496	+	0.758652i	$0.274142\pi$
$740$	123.239	4.53034
$741$	0.177447	0.00651867
$742$	−147.265	−5.40625
$743$	−36.0100	−1.32108	−0.660539	−	0.750792i	$-0.729672\pi$
$743$	−36.0100	−1.32108	−0.660539	+	0.750792i	$0.729672\pi$
$744$	−1.27099	−0.0465966
$745$	35.2261	1.29058
$746$	20.7937	0.761312
$747$	5.57290	0.203902
$748$	−123.430	−4.51306
$749$	−58.2624	−2.12886
$750$	−0.499015	−0.0182215
$751$	18.0855	0.659948	0.329974	−	0.943990i	$-0.392960\pi$
$751$	18.0855	0.659948	0.329974	+	0.943990i	$0.392960\pi$
$752$	−2.60789	−0.0950999
$753$	−0.690998	−0.0251814
$754$	0.779246	0.0283785
$755$	−15.0661	−0.548312
$756$	4.25467	0.154741
$757$	19.0225	0.691384	0.345692	−	0.938348i	$-0.387644\pi$
$757$	19.0225	0.691384	0.345692	+	0.938348i	$0.387644\pi$
$758$	67.5183	2.45237
$759$	−0.135234	−0.00490867
$760$	−55.1247	−1.99958
$761$	17.8329	0.646443	0.323221	−	0.946323i	$-0.395234\pi$
$761$	17.8329	0.646443	0.323221	+	0.946323i	$0.395234\pi$
$762$	0.872070	0.0315918
$763$	1.30159	0.0471207
$764$	−49.8489	−1.80347
$765$	−46.2104	−1.67074
$766$	−22.4259	−0.810279
$767$	21.6629	0.782202
$768$	−0.316830	−0.0114326
$769$	−29.3707	−1.05913	−0.529567	−	0.848268i	$-0.677646\pi$
$769$	−29.3707	−1.05913	−0.529567	+	0.848268i	$0.677646\pi$
$770$	−159.384	−5.74381
$771$	0.292653	0.0105396
$772$	61.8219	2.22502
$773$	−14.4907	−0.521193	−0.260597	−	0.965448i	$-0.583919\pi$
$773$	−14.4907	−0.521193	−0.260597	+	0.965448i	$0.583919\pi$
$774$	57.3752	2.06231
$775$	15.0346	0.540059
$776$	−15.2507	−0.547468
$777$	1.30036	0.0466500
$778$	12.6408	0.453194
$779$	−17.1858	−0.615746
$780$	0.938129	0.0335904
$781$	25.5228	0.913279
$782$	−14.5912	−0.521781
$783$	−0.0231357	−0.000826803 0
$784$	168.412	6.01470
$785$	−38.1550	−1.36181
$786$	−0.814142	−0.0290395
$787$	−30.9139	−1.10196	−0.550980	−	0.834518i	$-0.685746\pi$
$787$	−30.9139	−1.10196	−0.550980	+	0.834518i	$0.685746\pi$
$788$	78.0878	2.78176
$789$	0.825320	0.0293822
$790$	−80.7605	−2.87333
$791$	−59.9020	−2.12987
$792$	104.170	3.70151
$793$	−7.42755	−0.263760
$794$	63.9007	2.26775
$795$	0.964058	0.0341916
$796$	71.2890	2.52677
$797$	26.7211	0.946511	0.473255	−	0.880925i	$-0.343079\pi$
$797$	26.7211	0.946511	0.473255	+	0.880925i	$0.343079\pi$
$798$	−0.980155	−0.0346971
$799$	1.39638	0.0494002
$800$	−32.2969	−1.14187
$801$	−36.2666	−1.28142
$802$	7.21019	0.254601
$803$	−35.2627	−1.24439
$804$	2.24664	0.0792327
$805$	−13.3953	−0.472123
$806$	33.4453	1.17806
$807$	0.385768	0.0135797
$808$	−74.3681	−2.61626
$809$	20.2151	0.710727	0.355363	−	0.934728i	$-0.384357\pi$
$809$	20.2151	0.710727	0.355363	+	0.934728i	$0.384357\pi$
$810$	65.6997	2.30845
$811$	41.8232	1.46861	0.734306	−	0.678819i	$-0.237508\pi$
$811$	41.8232	1.46861	0.734306	+	0.678819i	$0.237508\pi$
$812$	−3.06012	−0.107389
$813$	0.472808	0.0165821
$814$	107.316	3.76144
$815$	56.2827	1.97150
$816$	−1.71805	−0.0601436
$817$	−18.7968	−0.657618
$818$	76.5652	2.67704
$819$	−33.2149	−1.16062
$820$	−90.8583	−3.17291
$821$	11.3612	0.396508	0.198254	−	0.980151i	$-0.436473\pi$
$821$	11.3612	0.396508	0.198254	+	0.980151i	$0.436473\pi$
$822$	−1.75390	−0.0611742
$823$	6.50093	0.226608	0.113304	−	0.993560i	$-0.463857\pi$
$823$	6.50093	0.226608	0.113304	+	0.993560i	$0.463857\pi$
$824$	109.293	3.80740
$825$	0.367231	0.0127853
$826$	−119.658	−4.16344
$827$	−41.8822	−1.45639	−0.728194	−	0.685371i	$-0.759640\pi$
$827$	−41.8822	−1.45639	−0.728194	+	0.685371i	$0.759640\pi$
$828$	14.7531	0.512705
$829$	29.8665	1.03731	0.518653	−	0.854985i	$-0.326434\pi$
$829$	29.8665	1.03731	0.518653	+	0.854985i	$0.326434\pi$
$830$	−13.5769	−0.471260
$831$	0.232996	0.00808256
$832$	−24.2633	−0.841178
$833$	−90.1750	−3.12438
$834$	−1.41433	−0.0489743
$835$	−13.7424	−0.475576
$836$	−57.5090	−1.98899
$837$	−0.992986	−0.0343226
$838$	−13.0854	−0.452029
$839$	−44.8575	−1.54865	−0.774326	−	0.632786i	$-0.781911\pi$
$839$	−44.8575	−1.54865	−0.774326	+	0.632786i	$0.781911\pi$
$840$	−3.07508	−0.106100
$841$	−28.9834	−0.999426
$842$	−90.9166	−3.13319
$843$	−0.246486	−0.00848944
$844$	31.3109	1.07777
$845$	21.4604	0.738259
$846$	−1.98589	−0.0682765
$847$	−45.6266	−1.56775
$848$	−120.269	−4.13005
$849$	−0.167856	−0.00576082
$850$	39.6228	1.35905
$851$	9.01931	0.309178
$852$	0.829798	0.0284284
$853$	8.90883	0.305032	0.152516	−	0.988301i	$-0.451262\pi$
$853$	8.90883	0.305032	0.152516	+	0.988301i	$0.451262\pi$
$854$	41.0272	1.40392
$855$	−21.5305	−0.736327
$856$	−92.7689	−3.17078
$857$	−49.4928	−1.69064	−0.845320	−	0.534260i	$-0.820590\pi$
$857$	−49.4928	−1.69064	−0.845320	+	0.534260i	$0.820590\pi$
$858$	0.816924	0.0278893
$859$	−17.1652	−0.585668	−0.292834	−	0.956163i	$-0.594598\pi$
$859$	−17.1652	−0.585668	−0.292834	+	0.956163i	$0.594598\pi$
$860$	−99.3755	−3.38868
$861$	−0.958694	−0.0326722
$862$	22.9073	0.780224
$863$	−32.2031	−1.09621	−0.548103	−	0.836411i	$-0.684650\pi$
$863$	−32.2031	−1.09621	−0.548103	+	0.836411i	$0.684650\pi$
$864$	2.13311	0.0725697
$865$	−43.3930	−1.47541
$866$	−68.0455	−2.31228
$867$	0.411677	0.0139813
$868$	−131.341	−4.45799
$869$	−49.9983	−1.69608
$870$	0.0281777	0.000955314 0
$871$	−35.0828	−1.18873
$872$	2.07247	0.0701826
$873$	−5.95659	−0.201600
$874$	−6.79838	−0.229959
$875$	−30.6012	−1.03451
$876$	−1.14646	−0.0387353
$877$	−5.94057	−0.200599	−0.100299	−	0.994957i	$-0.531980\pi$
$877$	−5.94057	−0.200599	−0.100299	+	0.994957i	$0.531980\pi$
$878$	−36.6412	−1.23658
$879$	0.164235	0.00553951
$880$	−130.167	−4.38792
$881$	−14.4430	−0.486598	−0.243299	−	0.969951i	$-0.578230\pi$
$881$	−14.4430	−0.486598	−0.243299	+	0.969951i	$0.578230\pi$
$882$	128.245	4.31823
$883$	15.5102	0.521959	0.260980	−	0.965344i	$-0.415954\pi$
$883$	15.5102	0.521959	0.260980	+	0.965344i	$0.415954\pi$
$884$	62.6651	2.10766
$885$	0.783335	0.0263315
$886$	−21.5508	−0.724014
$887$	−11.8805	−0.398907	−0.199453	−	0.979907i	$-0.563917\pi$
$887$	−11.8805	−0.398907	−0.199453	+	0.979907i	$0.563917\pi$
$888$	2.07051	0.0694816
$889$	53.4781	1.79360
$890$	88.3537	2.96162
$891$	40.6743	1.36264
$892$	−99.3980	−3.32809
$893$	0.650604	0.0217716
$894$	0.997303	0.0333548
$895$	71.0532	2.37505
$896$	19.3104	0.645114
$897$	0.0686577	0.00229241
$898$	−53.2678	−1.77757
$899$	0.714193	0.0238197
$900$	−40.0624	−1.33541
$901$	64.3971	2.14538
$902$	−79.1195	−2.63439
$903$	−1.04856	−0.0348940
$904$	−95.3795	−3.17228
$905$	71.8052	2.38689
$906$	−0.426544	−0.0141710
$907$	11.9265	0.396013	0.198006	−	0.980201i	$-0.436553\pi$
$907$	11.9265	0.396013	0.198006	+	0.980201i	$0.436553\pi$
$908$	−53.2669	−1.76772
$909$	−29.0465	−0.963413
$910$	80.9189	2.68244
$911$	−17.8766	−0.592278	−0.296139	−	0.955145i	$-0.595699\pi$
$911$	−17.8766	−0.592278	−0.296139	+	0.955145i	$0.595699\pi$
$912$	−0.800477	−0.0265064
$913$	−8.40535	−0.278176
$914$	−74.7396	−2.47217
$915$	−0.268582	−0.00887904
$916$	−0.0329822	−0.00108976
$917$	−49.9258	−1.64869
$918$	−2.61696	−0.0863725
$919$	−17.4145	−0.574450	−0.287225	−	0.957863i	$-0.592733\pi$
$919$	−17.4145	−0.574450	−0.287225	+	0.957863i	$0.592733\pi$
$920$	−21.3288	−0.703190
$921$	−0.531117	−0.0175009
$922$	48.3306	1.59168
$923$	−12.9579	−0.426513
$924$	−3.20808	−0.105538
$925$	−24.4922	−0.805299
$926$	55.9215	1.83769
$927$	42.6874	1.40204
$928$	−1.53421	−0.0503629
$929$	48.2881	1.58428	0.792141	−	0.610338i	$-0.208966\pi$
$929$	48.2881	1.58428	0.792141	+	0.610338i	$0.208966\pi$
$930$	1.20939	0.0396574
$931$	−42.0146	−1.37697
$932$	132.490	4.33986
$933$	0.471283	0.0154291
$934$	−54.1449	−1.77167
$935$	69.6969	2.27933
$936$	−52.8867	−1.72866
$937$	−12.1586	−0.397204	−0.198602	−	0.980080i	$-0.563640\pi$
$937$	−12.1586	−0.397204	−0.198602	+	0.980080i	$0.563640\pi$
$938$	193.785	6.32730
$939$	−0.298501	−0.00974121
$940$	3.43963	0.112188
$941$	41.7487	1.36097	0.680484	−	0.732763i	$-0.261769\pi$
$941$	41.7487	1.36097	0.680484	+	0.732763i	$0.261769\pi$
$942$	−1.08022	−0.0351956
$943$	−6.64953	−0.216539
$944$	−97.7231	−3.18061
$945$	−2.40247	−0.0781524
$946$	−86.5363	−2.81354
$947$	2.67143	0.0868098	0.0434049	−	0.999058i	$-0.486179\pi$
$947$	2.67143	0.0868098	0.0434049	+	0.999058i	$0.486179\pi$
$948$	−1.62554	−0.0527952
$949$	17.9028	0.581149
$950$	18.4612	0.598961
$951$	−0.752001	−0.0243853
$952$	−205.409	−6.65734
$953$	−16.2014	−0.524816	−0.262408	−	0.964957i	$-0.584517\pi$
$953$	−16.2014	−0.524816	−0.262408	+	0.964957i	$0.584517\pi$
$954$	−91.5841	−2.96514
$955$	28.1480	0.910849
$956$	10.0530	0.325139
$957$	0.0174447	0.000563906 0
$958$	−39.9428	−1.29049
$959$	−107.555	−3.47312
$960$	−0.877366	−0.0283169
$961$	−0.346793	−0.0111869
$962$	−54.4842	−1.75664
$963$	−36.2335	−1.16761
$964$	15.2899	0.492453
$965$	−34.9088	−1.12375
$966$	−0.379241	−0.0122019
$967$	48.3059	1.55341	0.776707	−	0.629862i	$-0.216889\pi$
$967$	48.3059	1.55341	0.776707	+	0.629862i	$0.216889\pi$
$968$	−72.6494	−2.33504
$969$	0.428610	0.0137689
$970$	14.5116	0.465939
$971$	10.3755	0.332965	0.166483	−	0.986044i	$-0.446759\pi$
$971$	10.3755	0.332965	0.166483	+	0.986044i	$0.446759\pi$
$972$	3.96918	0.127311
$973$	−86.7313	−2.78048
$974$	96.9674	3.10704
$975$	−0.186442	−0.00597092
$976$	33.5063	1.07251
$977$	−4.69085	−0.150074	−0.0750369	−	0.997181i	$-0.523907\pi$
$977$	−4.69085	−0.150074	−0.0750369	+	0.997181i	$0.523907\pi$
$978$	1.59345	0.0509528
$979$	54.6993	1.74820
$980$	−222.124	−7.09548
$981$	0.809461	0.0258441
$982$	6.05429	0.193200
$983$	17.2619	0.550571	0.275285	−	0.961363i	$-0.411228\pi$
$983$	17.2619	0.550571	0.275285	+	0.961363i	$0.411228\pi$
$984$	−1.52649	−0.0486627
$985$	−44.0936	−1.40494
$986$	1.88221	0.0599419
$987$	0.0362933	0.00115523
$988$	29.1971	0.928885
$989$	−7.27287	−0.231264
$990$	−99.1214	−3.15028
$991$	−29.4869	−0.936683	−0.468342	−	0.883547i	$-0.655148\pi$
$991$	−29.4869	−0.936683	−0.468342	+	0.883547i	$0.655148\pi$
$992$	−65.8484	−2.09069
$993$	−0.672596	−0.0213442
$994$	71.5747	2.27021
$995$	−40.2545	−1.27615
$996$	−0.273275	−0.00865904
$997$	−15.9325	−0.504588	−0.252294	−	0.967651i	$-0.581185\pi$
$997$	−15.9325	−0.504588	−0.252294	+	0.967651i	$0.581185\pi$
$998$	−15.7011	−0.497010
$999$	1.61763	0.0511795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.d.1.5	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.d.1.5	✓	149	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)

\(f(q)\)	\(=\)	\(q-2.63043 q^{2} +0.0298964 q^{3} +4.91916 q^{4} -2.77768 q^{5} -0.0786403 q^{6} -4.82248 q^{7} -7.67864 q^{8} -2.99911 q^{9} +O(q^{10})\)	\(q-2.63043 q^{2} +0.0298964 q^{3} +4.91916 q^{4} -2.77768 q^{5} -0.0786403 q^{6} -4.82248 q^{7} -7.67864 q^{8} -2.99911 q^{9} +7.30650 q^{10} +4.52341 q^{11} +0.147065 q^{12} -2.29652 q^{13} +12.6852 q^{14} -0.0830427 q^{15} +10.3598 q^{16} -5.54708 q^{17} +7.88894 q^{18} -2.58452 q^{19} -13.6639 q^{20} -0.144175 q^{21} -11.8985 q^{22} -1.00000 q^{23} -0.229563 q^{24} +2.71553 q^{25} +6.04084 q^{26} -0.179352 q^{27} -23.7225 q^{28} +0.128996 q^{29} +0.218438 q^{30} +5.53653 q^{31} -11.8934 q^{32} +0.135234 q^{33} +14.5912 q^{34} +13.3953 q^{35} -14.7531 q^{36} -9.01931 q^{37} +6.79838 q^{38} -0.0686577 q^{39} +21.3288 q^{40} +6.64953 q^{41} +0.379241 q^{42} +7.27287 q^{43} +22.2514 q^{44} +8.33057 q^{45} +2.63043 q^{46} -0.251732 q^{47} +0.309720 q^{48} +16.2563 q^{49} -7.14300 q^{50} -0.165838 q^{51} -11.2969 q^{52} -11.6092 q^{53} +0.471772 q^{54} -12.5646 q^{55} +37.0300 q^{56} -0.0772677 q^{57} -0.339316 q^{58} -9.43292 q^{59} -0.408500 q^{60} +3.23426 q^{61} -14.5635 q^{62} +14.4631 q^{63} +10.5652 q^{64} +6.37901 q^{65} -0.355723 q^{66} +15.2765 q^{67} -27.2870 q^{68} -0.0298964 q^{69} -35.2354 q^{70} +5.64239 q^{71} +23.0290 q^{72} -7.79561 q^{73} +23.7247 q^{74} +0.0811845 q^{75} -12.7136 q^{76} -21.8140 q^{77} +0.180599 q^{78} -11.0532 q^{79} -28.7762 q^{80} +8.99196 q^{81} -17.4911 q^{82} -1.85819 q^{83} -0.709218 q^{84} +15.4080 q^{85} -19.1308 q^{86} +0.00385653 q^{87} -34.7336 q^{88} +12.0925 q^{89} -21.9130 q^{90} +11.0749 q^{91} -4.91916 q^{92} +0.165522 q^{93} +0.662162 q^{94} +7.17897 q^{95} -0.355571 q^{96} +1.98612 q^{97} -42.7610 q^{98} -13.5662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * q^99

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