LMFDB - Embedded newform 4033.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36110 q^{2} +2.47312 q^{3} +3.57478 q^{4} +1.50101 q^{5} -5.83928 q^{6} +4.30200 q^{7} -3.71820 q^{8} +3.11634 q^{9} +O(q^{10})$	\(q-2.36110 q^{2} +2.47312 q^{3} +3.57478 q^{4} +1.50101 q^{5} -5.83928 q^{6} +4.30200 q^{7} -3.71820 q^{8} +3.11634 q^{9} -3.54403 q^{10} +4.62211 q^{11} +8.84086 q^{12} +5.87162 q^{13} -10.1574 q^{14} +3.71218 q^{15} +1.62947 q^{16} +2.60888 q^{17} -7.35798 q^{18} -5.21299 q^{19} +5.36577 q^{20} +10.6394 q^{21} -10.9132 q^{22} -7.81470 q^{23} -9.19557 q^{24} -2.74697 q^{25} -13.8635 q^{26} +0.287729 q^{27} +15.3787 q^{28} +2.26131 q^{29} -8.76482 q^{30} -2.47135 q^{31} +3.58906 q^{32} +11.4310 q^{33} -6.15982 q^{34} +6.45735 q^{35} +11.1402 q^{36} +1.00000 q^{37} +12.3084 q^{38} +14.5212 q^{39} -5.58105 q^{40} +10.2743 q^{41} -25.1206 q^{42} -0.898625 q^{43} +16.5230 q^{44} +4.67766 q^{45} +18.4513 q^{46} -1.07796 q^{47} +4.02989 q^{48} +11.5072 q^{49} +6.48586 q^{50} +6.45209 q^{51} +20.9897 q^{52} +0.859250 q^{53} -0.679356 q^{54} +6.93783 q^{55} -15.9957 q^{56} -12.8924 q^{57} -5.33917 q^{58} -1.53858 q^{59} +13.2702 q^{60} -14.6573 q^{61} +5.83510 q^{62} +13.4065 q^{63} -11.7331 q^{64} +8.81335 q^{65} -26.9898 q^{66} -3.71631 q^{67} +9.32617 q^{68} -19.3267 q^{69} -15.2464 q^{70} +7.76597 q^{71} -11.5872 q^{72} +2.36786 q^{73} -2.36110 q^{74} -6.79360 q^{75} -18.6353 q^{76} +19.8843 q^{77} -34.2860 q^{78} +1.30505 q^{79} +2.44585 q^{80} -8.63744 q^{81} -24.2587 q^{82} +15.6181 q^{83} +38.0334 q^{84} +3.91596 q^{85} +2.12174 q^{86} +5.59250 q^{87} -17.1859 q^{88} -5.39001 q^{89} -11.0444 q^{90} +25.2597 q^{91} -27.9358 q^{92} -6.11196 q^{93} +2.54518 q^{94} -7.82475 q^{95} +8.87618 q^{96} -9.56117 q^{97} -27.1697 q^{98} +14.4041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) $ 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * 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 $

$2$	−2.36110	−1.66955	−0.834774	−	0.550593i	$-0.814402\pi$
$2$	−2.36110	−1.66955	−0.834774	+	0.550593i	$0.814402\pi$
$3$	2.47312	1.42786	0.713929	−	0.700218i	$-0.246914\pi$
$3$	2.47312	1.42786	0.713929	+	0.700218i	$0.246914\pi$
$4$	3.57478	1.78739
$5$	1.50101	0.671272	0.335636	−	0.941992i	$-0.391049\pi$
$5$	1.50101	0.671272	0.335636	+	0.941992i	$0.391049\pi$
$6$	−5.83928	−2.38388
$7$	4.30200	1.62600	0.813002	−	0.582261i	$-0.197832\pi$
$7$	4.30200	1.62600	0.813002	+	0.582261i	$0.197832\pi$
$8$	−3.71820	−1.31458
$9$	3.11634	1.03878
$10$	−3.54403	−1.12072
$11$	4.62211	1.39362	0.696809	−	0.717257i	$-0.254602\pi$
$11$	4.62211	1.39362	0.696809	+	0.717257i	$0.254602\pi$
$12$	8.84086	2.55214
$13$	5.87162	1.62849	0.814247	−	0.580519i	$-0.197150\pi$
$13$	5.87162	1.62849	0.814247	+	0.580519i	$0.197150\pi$
$14$	−10.1574	−2.71469
$15$	3.71218	0.958481
$16$	1.62947	0.407368
$17$	2.60888	0.632747	0.316374	−	0.948635i	$-0.397535\pi$
$17$	2.60888	0.632747	0.316374	+	0.948635i	$0.397535\pi$
$18$	−7.35798	−1.73429
$19$	−5.21299	−1.19594	−0.597971	−	0.801517i	$-0.704026\pi$
$19$	−5.21299	−1.19594	−0.597971	+	0.801517i	$0.704026\pi$
$20$	5.36577	1.19982
$21$	10.6394	2.32170
$22$	−10.9132	−2.32671
$23$	−7.81470	−1.62948	−0.814738	−	0.579829i	$-0.803119\pi$
$23$	−7.81470	−1.62948	−0.814738	+	0.579829i	$0.803119\pi$
$24$	−9.19557	−1.87704
$25$	−2.74697	−0.549394
$26$	−13.8635	−2.71885
$27$	0.287729	0.0553735
$28$	15.3787	2.90630
$29$	2.26131	0.419915	0.209958	−	0.977711i	$-0.432667\pi$
$29$	2.26131	0.419915	0.209958	+	0.977711i	$0.432667\pi$
$30$	−8.76482	−1.60023
$31$	−2.47135	−0.443868	−0.221934	−	0.975062i	$-0.571237\pi$
$31$	−2.47135	−0.443868	−0.221934	+	0.975062i	$0.571237\pi$
$32$	3.58906	0.634461
$33$	11.4310	1.98989
$34$	−6.15982	−1.05640
$35$	6.45735	1.09149
$36$	11.1402	1.85670
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	12.3084	1.99668
$39$	14.5212	2.32526
$40$	−5.58105	−0.882442
$41$	10.2743	1.60458	0.802291	−	0.596933i	$-0.203614\pi$
$41$	10.2743	1.60458	0.802291	+	0.596933i	$0.203614\pi$
$42$	−25.1206	−3.87619
$43$	−0.898625	−0.137039	−0.0685195	−	0.997650i	$-0.521828\pi$
$43$	−0.898625	−0.137039	−0.0685195	+	0.997650i	$0.521828\pi$
$44$	16.5230	2.49094
$45$	4.67766	0.697304
$46$	18.4513	2.72049
$47$	−1.07796	−0.157237	−0.0786186	−	0.996905i	$-0.525051\pi$
$47$	−1.07796	−0.157237	−0.0786186	+	0.996905i	$0.525051\pi$
$48$	4.02989	0.581664
$49$	11.5072	1.64389
$50$	6.48586	0.917239
$51$	6.45209	0.903474
$52$	20.9897	2.91075
$53$	0.859250	0.118027	0.0590135	−	0.998257i	$-0.481204\pi$
$53$	0.859250	0.118027	0.0590135	+	0.998257i	$0.481204\pi$
$54$	−0.679356	−0.0924486
$55$	6.93783	0.935497
$56$	−15.9957	−2.13751
$57$	−12.8924	−1.70764
$58$	−5.33917	−0.701068
$59$	−1.53858	−0.200306	−0.100153	−	0.994972i	$-0.531933\pi$
$59$	−1.53858	−0.200306	−0.100153	+	0.994972i	$0.531933\pi$
$60$	13.2702	1.71318
$61$	−14.6573	−1.87667	−0.938336	−	0.345724i	$-0.887633\pi$
$61$	−14.6573	−1.87667	−0.938336	+	0.345724i	$0.887633\pi$
$62$	5.83510	0.741058
$63$	13.4065	1.68906
$64$	−11.7331	−1.46663
$65$	8.81335	1.09316
$66$	−26.9898	−3.32222
$67$	−3.71631	−0.454019	−0.227010	−	0.973893i	$-0.572895\pi$
$67$	−3.71631	−0.454019	−0.227010	+	0.973893i	$0.572895\pi$
$68$	9.32617	1.13096
$69$	−19.3267	−2.32666
$70$	−15.2464	−1.82230
$71$	7.76597	0.921651	0.460826	−	0.887491i	$-0.347553\pi$
$71$	7.76597	0.921651	0.460826	+	0.887491i	$0.347553\pi$
$72$	−11.5872	−1.36556
$73$	2.36786	0.277137	0.138569	−	0.990353i	$-0.455750\pi$
$73$	2.36786	0.277137	0.138569	+	0.990353i	$0.455750\pi$
$74$	−2.36110	−0.274472
$75$	−6.79360	−0.784457
$76$	−18.6353	−2.13761
$77$	19.8843	2.26603
$78$	−34.2860	−3.88213
$79$	1.30505	0.146829	0.0734146	−	0.997302i	$-0.476610\pi$
$79$	1.30505	0.146829	0.0734146	+	0.997302i	$0.476610\pi$
$80$	2.44585	0.273455
$81$	−8.63744	−0.959715
$82$	−24.2587	−2.67893
$83$	15.6181	1.71431	0.857154	−	0.515060i	$-0.172231\pi$
$83$	15.6181	1.71431	0.857154	+	0.515060i	$0.172231\pi$
$84$	38.0334	4.14979
$85$	3.91596	0.424745
$86$	2.12174	0.228793
$87$	5.59250	0.599579
$88$	−17.1859	−1.83203
$89$	−5.39001	−0.571339	−0.285670	−	0.958328i	$-0.592216\pi$
$89$	−5.39001	−0.571339	−0.285670	+	0.958328i	$0.592216\pi$
$90$	−11.0444	−1.16418
$91$	25.2597	2.64794
$92$	−27.9358	−2.91251
$93$	−6.11196	−0.633780
$94$	2.54518	0.262515
$95$	−7.82475	−0.802803
$96$	8.87618	0.905921
$97$	−9.56117	−0.970790	−0.485395	−	0.874295i	$-0.661324\pi$
$97$	−9.56117	−0.970790	−0.485395	+	0.874295i	$0.661324\pi$
$98$	−27.1697	−2.74455
$99$	14.4041	1.44766
$100$	−9.81980	−0.981980
$101$	5.05869	0.503359	0.251679	−	0.967811i	$-0.419017\pi$
$101$	5.05869	0.503359	0.251679	+	0.967811i	$0.419017\pi$
$102$	−15.2340	−1.50839
$103$	13.3101	1.31149	0.655743	−	0.754984i	$-0.272356\pi$
$103$	13.3101	1.31149	0.655743	+	0.754984i	$0.272356\pi$
$104$	−21.8318	−2.14079
$105$	15.9698	1.55849
$106$	−2.02877	−0.197052
$107$	−18.5742	−1.79564	−0.897818	−	0.440366i	$-0.854849\pi$
$107$	−18.5742	−1.79564	−0.897818	+	0.440366i	$0.854849\pi$
$108$	1.02857	0.0989739
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−16.3809	−1.56186
$111$	2.47312	0.234739
$112$	7.00999	0.662382
$113$	−5.63846	−0.530422	−0.265211	−	0.964190i	$-0.585442\pi$
$113$	−5.63846	−0.530422	−0.265211	+	0.964190i	$0.585442\pi$
$114$	30.4402	2.85098
$115$	−11.7299	−1.09382
$116$	8.08368	0.750551
$117$	18.2980	1.69165
$118$	3.63274	0.334420
$119$	11.2234	1.02885
$120$	−13.8026	−1.26000
$121$	10.3639	0.942172
$122$	34.6073	3.13319
$123$	25.4097	2.29112
$124$	−8.83453	−0.793364
$125$	−11.6283	−1.04006
$126$	−31.6541	−2.81997
$127$	−11.2276	−0.996288	−0.498144	−	0.867094i	$-0.665985\pi$
$127$	−11.2276	−0.996288	−0.498144	+	0.867094i	$0.665985\pi$
$128$	20.5248	1.81415
$129$	−2.22241	−0.195672
$130$	−20.8092	−1.82509
$131$	−6.04640	−0.528277	−0.264138	−	0.964485i	$-0.585088\pi$
$131$	−6.04640	−0.528277	−0.264138	+	0.964485i	$0.585088\pi$
$132$	40.8634	3.55671
$133$	−22.4263	−1.94461
$134$	8.77456	0.758006
$135$	0.431884	0.0371706
$136$	−9.70034	−0.831798
$137$	13.9498	1.19181	0.595904	−	0.803056i	$-0.296794\pi$
$137$	13.9498	1.19181	0.595904	+	0.803056i	$0.296794\pi$
$138$	45.6322	3.88447
$139$	−2.75928	−0.234039	−0.117019	−	0.993130i	$-0.537334\pi$
$139$	−2.75928	−0.234039	−0.117019	+	0.993130i	$0.537334\pi$
$140$	23.0836	1.95092
$141$	−2.66594	−0.224512
$142$	−18.3362	−1.53874
$143$	27.1393	2.26950
$144$	5.07799	0.423166
$145$	3.39425	0.281877
$146$	−5.59075	−0.462694
$147$	28.4588	2.34724
$148$	3.57478	0.293845
$149$	−4.50625	−0.369166	−0.184583	−	0.982817i	$-0.559094\pi$
$149$	−4.50625	−0.369166	−0.184583	+	0.982817i	$0.559094\pi$
$150$	16.0403	1.30969
$151$	12.1077	0.985308	0.492654	−	0.870225i	$-0.336027\pi$
$151$	12.1077	0.985308	0.492654	+	0.870225i	$0.336027\pi$
$152$	19.3829	1.57216
$153$	8.13017	0.657286
$154$	−46.9488	−3.78324
$155$	−3.70952	−0.297956
$156$	51.9102	4.15614
$157$	−24.1525	−1.92758	−0.963790	−	0.266661i	$-0.914080\pi$
$157$	−24.1525	−1.92758	−0.963790	+	0.266661i	$0.914080\pi$
$158$	−3.08134	−0.245138
$159$	2.12503	0.168526
$160$	5.38721	0.425896
$161$	−33.6188	−2.64954
$162$	20.3938	1.60229
$163$	8.98477	0.703741	0.351871	−	0.936049i	$-0.385546\pi$
$163$	8.98477	0.703741	0.351871	+	0.936049i	$0.385546\pi$
$164$	36.7285	2.86801
$165$	17.1581	1.33576
$166$	−36.8758	−2.86212
$167$	24.9208	1.92843	0.964214	−	0.265127i	$-0.0854139\pi$
$167$	24.9208	1.92843	0.964214	+	0.265127i	$0.0854139\pi$
$168$	−39.5593	−3.05207
$169$	21.4759	1.65199
$170$	−9.24595	−0.709132
$171$	−16.2455	−1.24232
$172$	−3.21238	−0.244942
$173$	−9.81065	−0.745890	−0.372945	−	0.927853i	$-0.621652\pi$
$173$	−9.81065	−0.745890	−0.372945	+	0.927853i	$0.621652\pi$
$174$	−13.2044	−1.00103
$175$	−11.8175	−0.893317
$176$	7.53160	0.567716
$177$	−3.80510	−0.286009
$178$	12.7263	0.953878
$179$	−15.4679	−1.15613	−0.578063	−	0.815992i	$-0.696191\pi$
$179$	−15.4679	−1.15613	−0.578063	+	0.815992i	$0.696191\pi$
$180$	16.7216	1.24635
$181$	−22.0026	−1.63544	−0.817721	−	0.575614i	$-0.804763\pi$
$181$	−22.0026	−1.63544	−0.817721	+	0.575614i	$0.804763\pi$
$182$	−59.6406	−4.42086
$183$	−36.2493	−2.67962
$184$	29.0566	2.14208
$185$	1.50101	0.110356
$186$	14.4309	1.05813
$187$	12.0585	0.881808
$188$	−3.85348	−0.281044
$189$	1.23781	0.0900375
$190$	18.4750	1.34032
$191$	20.1289	1.45647	0.728236	−	0.685326i	$-0.240340\pi$
$191$	20.1289	1.45647	0.728236	+	0.685326i	$0.240340\pi$
$192$	−29.0173	−2.09414
$193$	−27.0300	−1.94566	−0.972829	−	0.231524i	$-0.925629\pi$
$193$	−27.0300	−1.94566	−0.972829	+	0.231524i	$0.925629\pi$
$194$	22.5749	1.62078
$195$	21.7965	1.56088
$196$	41.1357	2.93827
$197$	9.53609	0.679419	0.339709	−	0.940530i	$-0.389671\pi$
$197$	9.53609	0.679419	0.339709	+	0.940530i	$0.389671\pi$
$198$	−34.0094	−2.41694
$199$	4.77168	0.338256	0.169128	−	0.985594i	$-0.445905\pi$
$199$	4.77168	0.338256	0.169128	+	0.985594i	$0.445905\pi$
$200$	10.2138	0.722223
$201$	−9.19089	−0.648275
$202$	−11.9441	−0.840381
$203$	9.72817	0.682783
$204$	23.0648	1.61486
$205$	15.4219	1.07711
$206$	−31.4265	−2.18959
$207$	−24.3533	−1.69267
$208$	9.56764	0.663396
$209$	−24.0950	−1.66669
$210$	−37.7063	−2.60198
$211$	−1.00217	−0.0689923	−0.0344961	−	0.999405i	$-0.510983\pi$
$211$	−1.00217	−0.0689923	−0.0344961	+	0.999405i	$0.510983\pi$
$212$	3.07163	0.210960
$213$	19.2062	1.31599
$214$	43.8555	2.99790
$215$	−1.34884	−0.0919904
$216$	−1.06983	−0.0727929
$217$	−10.6318	−0.721731
$218$	2.36110	0.159914
$219$	5.85601	0.395713
$220$	24.8012	1.67210
$221$	15.3184	1.03042
$222$	−5.83928	−0.391907
$223$	−24.7178	−1.65522	−0.827612	−	0.561300i	$-0.810301\pi$
$223$	−24.7178	−1.65522	−0.827612	+	0.561300i	$0.810301\pi$
$224$	15.4401	1.03164
$225$	−8.56050	−0.570700
$226$	13.3129	0.885564
$227$	−20.7197	−1.37522	−0.687609	−	0.726081i	$-0.741340\pi$
$227$	−20.7197	−1.37522	−0.687609	+	0.726081i	$0.741340\pi$
$228$	−46.0874	−3.05221
$229$	4.68363	0.309503	0.154751	−	0.987953i	$-0.450542\pi$
$229$	4.68363	0.309503	0.154751	+	0.987953i	$0.450542\pi$
$230$	27.6955	1.82619
$231$	49.1764	3.23557
$232$	−8.40800	−0.552013
$233$	10.6563	0.698118	0.349059	−	0.937101i	$-0.386501\pi$
$233$	10.6563	0.698118	0.349059	+	0.937101i	$0.386501\pi$
$234$	−43.2033	−2.82429
$235$	−1.61803	−0.105549
$236$	−5.50008	−0.358025
$237$	3.22754	0.209651
$238$	−26.4996	−1.71771
$239$	−11.2108	−0.725164	−0.362582	−	0.931952i	$-0.618105\pi$
$239$	−11.2108	−0.725164	−0.362582	+	0.931952i	$0.618105\pi$
$240$	6.04890	0.390455
$241$	−6.16588	−0.397179	−0.198590	−	0.980083i	$-0.563636\pi$
$241$	−6.16588	−0.397179	−0.198590	+	0.980083i	$0.563636\pi$
$242$	−24.4702	−1.57300
$243$	−22.2246	−1.42571
$244$	−52.3965	−3.35434
$245$	17.2724	1.10350
$246$	−59.9948	−3.82513
$247$	−30.6087	−1.94759
$248$	9.18897	0.583500
$249$	38.6255	2.44779
$250$	27.4555	1.73644
$251$	19.1910	1.21133	0.605663	−	0.795722i	$-0.292908\pi$
$251$	19.1910	1.21133	0.605663	+	0.795722i	$0.292908\pi$
$252$	47.9253	3.01901
$253$	−36.1204	−2.27087
$254$	26.5094	1.66335
$255$	9.68465	0.606476
$256$	−24.9948	−1.56218
$257$	−14.0876	−0.878760	−0.439380	−	0.898301i	$-0.644802\pi$
$257$	−14.0876	−0.878760	−0.439380	+	0.898301i	$0.644802\pi$
$258$	5.24733	0.326684
$259$	4.30200	0.267313
$260$	31.5058	1.95390
$261$	7.04702	0.436200
$262$	14.2761	0.881983
$263$	−26.9829	−1.66383	−0.831917	−	0.554900i	$-0.812757\pi$
$263$	−26.9829	−1.66383	−0.831917	+	0.554900i	$0.812757\pi$
$264$	−42.5029	−2.61587
$265$	1.28974	0.0792282
$266$	52.9507	3.24661
$267$	−13.3302	−0.815792
$268$	−13.2850	−0.811508
$269$	24.6682	1.50405	0.752024	−	0.659135i	$-0.229077\pi$
$269$	24.6682	1.50405	0.752024	+	0.659135i	$0.229077\pi$
$270$	−1.01972	−0.0620581
$271$	12.9297	0.785424	0.392712	−	0.919662i	$-0.371537\pi$
$271$	12.9297	0.785424	0.392712	+	0.919662i	$0.371537\pi$
$272$	4.25110	0.257761
$273$	62.4704	3.78088
$274$	−32.9367	−1.98978
$275$	−12.6968	−0.765646
$276$	−69.0887	−4.15865
$277$	0.940501	0.0565092	0.0282546	−	0.999601i	$-0.491005\pi$
$277$	0.940501	0.0565092	0.0282546	+	0.999601i	$0.491005\pi$
$278$	6.51492	0.390739
$279$	−7.70158	−0.461081
$280$	−24.0097	−1.43485
$281$	11.7996	0.703905	0.351953	−	0.936018i	$-0.385518\pi$
$281$	11.7996	0.703905	0.351953	+	0.936018i	$0.385518\pi$
$282$	6.29453	0.374834
$283$	−4.35529	−0.258895	−0.129447	−	0.991586i	$-0.541320\pi$
$283$	−4.35529	−0.258895	−0.129447	+	0.991586i	$0.541320\pi$
$284$	27.7616	1.64735
$285$	−19.3516	−1.14629
$286$	−64.0784	−3.78903
$287$	44.2002	2.60906
$288$	11.1847	0.659066
$289$	−10.1937	−0.599631
$290$	−8.01415	−0.470607
$291$	−23.6460	−1.38615
$292$	8.46457	0.495352
$293$	−15.9148	−0.929755	−0.464877	−	0.885375i	$-0.653902\pi$
$293$	−15.9148	−0.929755	−0.464877	+	0.885375i	$0.653902\pi$
$294$	−67.1939	−3.91883
$295$	−2.30942	−0.134460
$296$	−3.71820	−0.216116
$297$	1.32991	0.0771695
$298$	10.6397	0.616341
$299$	−45.8849	−2.65359
$300$	−24.2856	−1.40213
$301$	−3.86589	−0.222826
$302$	−28.5874	−1.64502
$303$	12.5108	0.718725
$304$	−8.49443	−0.487189
$305$	−22.0007	−1.25976
$306$	−19.1961	−1.09737
$307$	23.6562	1.35013	0.675066	−	0.737757i	$-0.264115\pi$
$307$	23.6562	1.35013	0.675066	+	0.737757i	$0.264115\pi$
$308$	71.0820	4.05027
$309$	32.9176	1.87262
$310$	8.75854	0.497451
$311$	22.2885	1.26386	0.631932	−	0.775024i	$-0.282262\pi$
$311$	22.2885	1.26386	0.631932	+	0.775024i	$0.282262\pi$
$312$	−53.9928	−3.05674
$313$	6.09388	0.344447	0.172223	−	0.985058i	$-0.444905\pi$
$313$	6.09388	0.344447	0.172223	+	0.985058i	$0.444905\pi$
$314$	57.0264	3.21819
$315$	20.1233	1.13382
$316$	4.66525	0.262441
$317$	−18.0982	−1.01650	−0.508249	−	0.861210i	$-0.669707\pi$
$317$	−18.0982	−1.01650	−0.508249	+	0.861210i	$0.669707\pi$
$318$	−5.01740	−0.281362
$319$	10.4520	0.585201
$320$	−17.6114	−0.984508
$321$	−45.9363	−2.56392
$322$	79.3773	4.42352
$323$	−13.6001	−0.756729
$324$	−30.8769	−1.71538
$325$	−16.1292	−0.894685
$326$	−21.2139	−1.17493
$327$	−2.47312	−0.136764
$328$	−38.2020	−2.10935
$329$	−4.63740	−0.255668
$330$	−40.5120	−2.23011
$331$	9.85043	0.541429	0.270714	−	0.962660i	$-0.412740\pi$
$331$	9.85043	0.541429	0.270714	+	0.962660i	$0.412740\pi$
$332$	55.8312	3.06413
$333$	3.11634	0.170775
$334$	−58.8403	−3.21960
$335$	−5.57821	−0.304770
$336$	17.3366	0.945788
$337$	20.4859	1.11594	0.557969	−	0.829862i	$-0.311581\pi$
$337$	20.4859	1.11594	0.557969	+	0.829862i	$0.311581\pi$
$338$	−50.7066	−2.75808
$339$	−13.9446	−0.757367
$340$	13.9987	0.759185
$341$	−11.4229	−0.618582
$342$	38.3571	2.07412
$343$	19.3901	1.04697
$344$	3.34127	0.180149
$345$	−29.0096	−1.56182
$346$	23.1639	1.24530
$347$	−19.7733	−1.06149	−0.530743	−	0.847533i	$-0.678087\pi$
$347$	−19.7733	−1.06149	−0.530743	+	0.847533i	$0.678087\pi$
$348$	19.9919	1.07168
$349$	19.8064	1.06021	0.530107	−	0.847931i	$-0.322152\pi$
$349$	19.8064	1.06021	0.530107	+	0.847931i	$0.322152\pi$
$350$	27.9022	1.49143
$351$	1.68943	0.0901753
$352$	16.5890	0.884197
$353$	8.59389	0.457407	0.228703	−	0.973496i	$-0.426551\pi$
$353$	8.59389	0.457407	0.228703	+	0.973496i	$0.426551\pi$
$354$	8.98421	0.477505
$355$	11.6568	0.618678
$356$	−19.2681	−1.02121
$357$	27.7569	1.46905
$358$	36.5212	1.93021
$359$	−9.58627	−0.505944	−0.252972	−	0.967474i	$-0.581408\pi$
$359$	−9.58627	−0.505944	−0.252972	+	0.967474i	$0.581408\pi$
$360$	−17.3925	−0.916663
$361$	8.17531	0.430279
$362$	51.9503	2.73045
$363$	25.6312	1.34529
$364$	90.2978	4.73289
$365$	3.55418	0.186034
$366$	85.5880	4.47376
$367$	−0.237967	−0.0124218	−0.00621089	−	0.999981i	$-0.501977\pi$
$367$	−0.237967	−0.0124218	−0.00621089	+	0.999981i	$0.501977\pi$
$368$	−12.7338	−0.663797
$369$	32.0184	1.66681
$370$	−3.54403	−0.184245
$371$	3.69649	0.191912
$372$	−21.8489	−1.13281
$373$	−21.2829	−1.10199	−0.550994	−	0.834509i	$-0.685751\pi$
$373$	−21.2829	−1.10199	−0.550994	+	0.834509i	$0.685751\pi$
$374$	−28.4714	−1.47222
$375$	−28.7582	−1.48507
$376$	4.00808	0.206701
$377$	13.2776	0.683829
$378$	−2.92259	−0.150322
$379$	35.9628	1.84728	0.923642	−	0.383257i	$-0.125198\pi$
$379$	35.9628	1.84728	0.923642	+	0.383257i	$0.125198\pi$
$380$	−27.9717	−1.43492
$381$	−27.7672	−1.42256
$382$	−47.5262	−2.43165
$383$	−7.84343	−0.400781	−0.200390	−	0.979716i	$-0.564221\pi$
$383$	−7.84343	−0.400781	−0.200390	+	0.979716i	$0.564221\pi$
$384$	50.7603	2.59035
$385$	29.8466	1.52112
$386$	63.8203	3.24837
$387$	−2.80042	−0.142353
$388$	−34.1791	−1.73518
$389$	−29.5129	−1.49636	−0.748182	−	0.663494i	$-0.769073\pi$
$389$	−29.5129	−1.49636	−0.748182	+	0.663494i	$0.769073\pi$
$390$	−51.4637	−2.60596
$391$	−20.3876	−1.03105
$392$	−42.7861	−2.16103
$393$	−14.9535	−0.754304
$394$	−22.5156	−1.13432
$395$	1.95889	0.0985623
$396$	51.4913	2.58754
$397$	21.9763	1.10296	0.551480	−	0.834188i	$-0.314063\pi$
$397$	21.9763	1.10296	0.551480	+	0.834188i	$0.314063\pi$
$398$	−11.2664	−0.564734
$399$	−55.4630	−2.77663
$400$	−4.47611	−0.223806
$401$	30.3076	1.51349	0.756744	−	0.653711i	$-0.226789\pi$
$401$	30.3076	1.51349	0.756744	+	0.653711i	$0.226789\pi$
$402$	21.7006	1.08233
$403$	−14.5108	−0.722836
$404$	18.0837	0.899698
$405$	−12.9649	−0.644230
$406$	−22.9691	−1.13994
$407$	4.62211	0.229109
$408$	−23.9902	−1.18769
$409$	17.2181	0.851383	0.425691	−	0.904868i	$-0.360031\pi$
$409$	17.2181	0.851383	0.425691	+	0.904868i	$0.360031\pi$
$410$	−36.4126	−1.79829
$411$	34.4995	1.70173
$412$	47.5807	2.34413
$413$	−6.61898	−0.325698
$414$	57.5004	2.82599
$415$	23.4429	1.15077
$416$	21.0736	1.03322
$417$	−6.82404	−0.334175
$418$	56.8907	2.78261
$419$	−22.9200	−1.11972	−0.559858	−	0.828589i	$-0.689144\pi$
$419$	−22.9200	−1.11972	−0.559858	+	0.828589i	$0.689144\pi$
$420$	57.0885	2.78563
$421$	−32.5918	−1.58843	−0.794214	−	0.607638i	$-0.792117\pi$
$421$	−32.5918	−1.58843	−0.794214	+	0.607638i	$0.792117\pi$
$422$	2.36622	0.115186
$423$	−3.35930	−0.163335
$424$	−3.19486	−0.155156
$425$	−7.16653	−0.347628
$426$	−45.3477	−2.19710
$427$	−63.0557	−3.05148
$428$	−66.3987	−3.20950
$429$	67.1187	3.24052
$430$	3.18475	0.153582
$431$	16.4811	0.793866	0.396933	−	0.917848i	$-0.370075\pi$
$431$	16.4811	0.793866	0.396933	+	0.917848i	$0.370075\pi$
$432$	0.468846	0.0225574
$433$	−12.8786	−0.618906	−0.309453	−	0.950915i	$-0.600146\pi$
$433$	−12.8786	−0.618906	−0.309453	+	0.950915i	$0.600146\pi$
$434$	25.1026	1.20496
$435$	8.39440	0.402481
$436$	−3.57478	−0.171201
$437$	40.7380	1.94876
$438$	−13.8266	−0.660661
$439$	−19.5107	−0.931196	−0.465598	−	0.884996i	$-0.654161\pi$
$439$	−19.5107	−0.931196	−0.465598	+	0.884996i	$0.654161\pi$
$440$	−25.7962	−1.22979
$441$	35.8604	1.70764
$442$	−36.1681	−1.72034
$443$	−14.6797	−0.697452	−0.348726	−	0.937225i	$-0.613386\pi$
$443$	−14.6797	−0.697452	−0.348726	+	0.937225i	$0.613386\pi$
$444$	8.84086	0.419569
$445$	−8.09045	−0.383524
$446$	58.3610	2.76348
$447$	−11.1445	−0.527118
$448$	−50.4756	−2.38475
$449$	−36.8808	−1.74051	−0.870255	−	0.492601i	$-0.836046\pi$
$449$	−36.8808	−1.74051	−0.870255	+	0.492601i	$0.836046\pi$
$450$	20.2122	0.952811
$451$	47.4891	2.23618
$452$	−20.1562	−0.948069
$453$	29.9438	1.40688
$454$	48.9213	2.29599
$455$	37.9151	1.77749
$456$	47.9364	2.24483
$457$	−2.37005	−0.110866	−0.0554332	−	0.998462i	$-0.517654\pi$
$457$	−2.37005	−0.110866	−0.0554332	+	0.998462i	$0.517654\pi$
$458$	−11.0585	−0.516730
$459$	0.750651	0.0350374
$460$	−41.9319	−1.95508
$461$	−17.8784	−0.832678	−0.416339	−	0.909209i	$-0.636687\pi$
$461$	−17.8784	−0.832678	−0.416339	+	0.909209i	$0.636687\pi$
$462$	−116.110	−5.40194
$463$	−22.9749	−1.06773	−0.533867	−	0.845569i	$-0.679262\pi$
$463$	−22.9749	−1.06773	−0.533867	+	0.845569i	$0.679262\pi$
$464$	3.68474	0.171060
$465$	−9.17411	−0.425439
$466$	−25.1606	−1.16554
$467$	7.27016	0.336423	0.168211	−	0.985751i	$-0.446201\pi$
$467$	7.27016	0.336423	0.168211	+	0.985751i	$0.446201\pi$
$468$	65.4111	3.02363
$469$	−15.9876	−0.738237
$470$	3.82033	0.176219
$471$	−59.7322	−2.75231
$472$	5.72075	0.263319
$473$	−4.15354	−0.190980
$474$	−7.62053	−0.350023
$475$	14.3199	0.657044
$476$	40.1212	1.83895
$477$	2.67772	0.122604
$478$	26.4697	1.21069
$479$	−13.6594	−0.624113	−0.312056	−	0.950064i	$-0.601018\pi$
$479$	−13.6594	−0.624113	−0.312056	+	0.950064i	$0.601018\pi$
$480$	13.3232	0.608119
$481$	5.87162	0.267723
$482$	14.5582	0.663109
$483$	−83.1436	−3.78316
$484$	37.0486	1.68403
$485$	−14.3514	−0.651664
$486$	52.4745	2.38029
$487$	34.0686	1.54379	0.771897	−	0.635747i	$-0.219308\pi$
$487$	34.0686	1.54379	0.771897	+	0.635747i	$0.219308\pi$
$488$	54.4987	2.46704
$489$	22.2204	1.00484
$490$	−40.7819	−1.84234
$491$	37.3457	1.68539	0.842693	−	0.538394i	$-0.180969\pi$
$491$	37.3457	1.68539	0.842693	+	0.538394i	$0.180969\pi$
$492$	90.8341	4.09512
$493$	5.89950	0.265700
$494$	72.2701	3.25159
$495$	21.6207	0.971776
$496$	−4.02700	−0.180818
$497$	33.4092	1.49861
$498$	−91.1984	−4.08670
$499$	−27.8793	−1.24805	−0.624025	−	0.781404i	$-0.714504\pi$
$499$	−27.8793	−1.24805	−0.624025	+	0.781404i	$0.714504\pi$
$500$	−41.5685	−1.85900
$501$	61.6322	2.75352
$502$	−45.3118	−2.02236
$503$	37.1164	1.65494	0.827470	−	0.561510i	$-0.189779\pi$
$503$	37.1164	1.65494	0.827470	+	0.561510i	$0.189779\pi$
$504$	−49.8481	−2.22041
$505$	7.59315	0.337891
$506$	85.2837	3.79132
$507$	53.1125	2.35881
$508$	−40.1361	−1.78075
$509$	15.6459	0.693494	0.346747	−	0.937959i	$-0.387286\pi$
$509$	15.6459	0.693494	0.346747	+	0.937959i	$0.387286\pi$
$510$	−22.8664	−1.01254
$511$	10.1865	0.450626
$512$	17.9657	0.793978
$513$	−1.49993	−0.0662235
$514$	33.2622	1.46713
$515$	19.9786	0.880363
$516$	−7.94462	−0.349742
$517$	−4.98246	−0.219129
$518$	−10.1574	−0.446292
$519$	−24.2630	−1.06503
$520$	−32.7698	−1.43705
$521$	2.27049	0.0994719	0.0497360	−	0.998762i	$-0.484162\pi$
$521$	2.27049	0.0994719	0.0497360	+	0.998762i	$0.484162\pi$
$522$	−16.6387	−0.728256
$523$	14.6636	0.641196	0.320598	−	0.947215i	$-0.396116\pi$
$523$	14.6636	0.641196	0.320598	+	0.947215i	$0.396116\pi$
$524$	−21.6145	−0.944235
$525$	−29.2261	−1.27553
$526$	63.7091	2.77785
$527$	−6.44747	−0.280856
$528$	18.6266	0.810618
$529$	38.0695	1.65519
$530$	−3.04521	−0.132275
$531$	−4.79474	−0.208074
$532$	−80.1690	−3.47577
$533$	60.3270	2.61305
$534$	31.4738	1.36200
$535$	−27.8801	−1.20536
$536$	13.8180	0.596845
$537$	−38.2541	−1.65079
$538$	−58.2441	−2.51108
$539$	53.1876	2.29095
$540$	1.54389	0.0664384
$541$	−30.8007	−1.32422	−0.662112	−	0.749405i	$-0.730340\pi$
$541$	−30.8007	−1.32422	−0.662112	+	0.749405i	$0.730340\pi$
$542$	−30.5283	−1.31130
$543$	−54.4152	−2.33518
$544$	9.36343	0.401454
$545$	−1.50101	−0.0642962
$546$	−147.499	−6.31236
$547$	1.18336	0.0505967	0.0252984	−	0.999680i	$-0.491946\pi$
$547$	1.18336	0.0505967	0.0252984	+	0.999680i	$0.491946\pi$
$548$	49.8673	2.13022
$549$	−45.6771	−1.94945
$550$	29.9784	1.27828
$551$	−11.7882	−0.502194
$552$	71.8605	3.05859
$553$	5.61431	0.238745
$554$	−2.22061	−0.0943448
$555$	3.71218	0.157573
$556$	−9.86380	−0.418318
$557$	22.9552	0.972641	0.486321	−	0.873780i	$-0.338339\pi$
$557$	22.9552	0.972641	0.486321	+	0.873780i	$0.338339\pi$
$558$	18.1842	0.769797
$559$	−5.27638	−0.223167
$560$	10.5221	0.444638
$561$	29.8223	1.25910
$562$	−27.8600	−1.17520
$563$	7.59833	0.320232	0.160116	−	0.987098i	$-0.448813\pi$
$563$	7.59833	0.320232	0.160116	+	0.987098i	$0.448813\pi$
$564$	−9.53013	−0.401291
$565$	−8.46338	−0.356057
$566$	10.2832	0.432237
$567$	−37.1583	−1.56050
$568$	−28.8754	−1.21159
$569$	33.8496	1.41905	0.709526	−	0.704680i	$-0.248909\pi$
$569$	33.8496	1.41905	0.709526	+	0.704680i	$0.248909\pi$
$570$	45.6910	1.91378
$571$	−4.08522	−0.170961	−0.0854806	−	0.996340i	$-0.527243\pi$
$571$	−4.08522	−0.170961	−0.0854806	+	0.996340i	$0.527243\pi$
$572$	97.0168	4.05647
$573$	49.7812	2.07964
$574$	−104.361	−4.35595
$575$	21.4667	0.895225
$576$	−36.5642	−1.52351
$577$	1.27687	0.0531569	0.0265784	−	0.999647i	$-0.491539\pi$
$577$	1.27687	0.0531569	0.0265784	+	0.999647i	$0.491539\pi$
$578$	24.0684	1.00111
$579$	−66.8484	−2.77813
$580$	12.1337	0.503824
$581$	67.1890	2.78747
$582$	55.8304	2.31425
$583$	3.97155	0.164485
$584$	−8.80418	−0.364319
$585$	27.4654	1.13556
$586$	37.5765	1.55227
$587$	−8.47671	−0.349871	−0.174936	−	0.984580i	$-0.555972\pi$
$587$	−8.47671	−0.349871	−0.174936	+	0.984580i	$0.555972\pi$
$588$	101.734	4.19543
$589$	12.8831	0.530840
$590$	5.45277	0.224487
$591$	23.5839	0.970114
$592$	1.62947	0.0669709
$593$	13.5113	0.554842	0.277421	−	0.960748i	$-0.410520\pi$
$593$	13.5113	0.554842	0.277421	+	0.960748i	$0.410520\pi$
$594$	−3.14006	−0.128838
$595$	16.8465	0.690638
$596$	−16.1088	−0.659844
$597$	11.8010	0.482981
$598$	108.339	4.43030
$599$	−8.69607	−0.355312	−0.177656	−	0.984093i	$-0.556851\pi$
$599$	−8.69607	−0.355312	−0.177656	+	0.984093i	$0.556851\pi$
$600$	25.2599	1.03123
$601$	14.2829	0.582612	0.291306	−	0.956630i	$-0.405910\pi$
$601$	14.2829	0.582612	0.291306	+	0.956630i	$0.405910\pi$
$602$	9.12773	0.372018
$603$	−11.5813	−0.471626
$604$	43.2822	1.76113
$605$	15.5563	0.632454
$606$	−29.5392	−1.19995
$607$	−23.8882	−0.969594	−0.484797	−	0.874627i	$-0.661106\pi$
$607$	−23.8882	−0.969594	−0.484797	+	0.874627i	$0.661106\pi$
$608$	−18.7097	−0.758780
$609$	24.0590	0.974918
$610$	51.9458	2.10322
$611$	−6.32939	−0.256060
$612$	29.0635	1.17482
$613$	27.4978	1.11063	0.555313	−	0.831641i	$-0.312598\pi$
$613$	27.4978	1.11063	0.555313	+	0.831641i	$0.312598\pi$
$614$	−55.8546	−2.25411
$615$	38.1402	1.53796
$616$	−73.9339	−2.97888
$617$	38.3367	1.54338	0.771689	−	0.636000i	$-0.219412\pi$
$617$	38.3367	1.54338	0.771689	+	0.636000i	$0.219412\pi$
$618$	−77.7216	−3.12642
$619$	36.3650	1.46163	0.730815	−	0.682575i	$-0.239140\pi$
$619$	36.3650	1.46163	0.730815	+	0.682575i	$0.239140\pi$
$620$	−13.2607	−0.532563
$621$	−2.24851	−0.0902298
$622$	−52.6252	−2.11008
$623$	−23.1878	−0.929000
$624$	23.6619	0.947236
$625$	−3.71930	−0.148772
$626$	−14.3882	−0.575070
$627$	−59.5900	−2.37980
$628$	−86.3398	−3.44533
$629$	2.60888	0.104023
$630$	−47.5130	−1.89297
$631$	−0.871490	−0.0346935	−0.0173467	−	0.999850i	$-0.505522\pi$
$631$	−0.871490	−0.0346935	−0.0173467	+	0.999850i	$0.505522\pi$
$632$	−4.85242	−0.193019
$633$	−2.47849	−0.0985113
$634$	42.7316	1.69709
$635$	−16.8527	−0.668780
$636$	7.59651	0.301221
$637$	67.5660	2.67706
$638$	−24.6782	−0.977021
$639$	24.2014	0.957393
$640$	30.8078	1.21779
$641$	13.7124	0.541608	0.270804	−	0.962635i	$-0.412711\pi$
$641$	13.7124	0.541608	0.270804	+	0.962635i	$0.412711\pi$
$642$	108.460	4.28058
$643$	−4.15838	−0.163991	−0.0819953	−	0.996633i	$-0.526129\pi$
$643$	−4.15838	−0.163991	−0.0819953	+	0.996633i	$0.526129\pi$
$644$	−120.180	−4.73575
$645$	−3.33586	−0.131349
$646$	32.1111	1.26340
$647$	47.6554	1.87353	0.936763	−	0.349965i	$-0.113807\pi$
$647$	47.6554	1.87353	0.936763	+	0.349965i	$0.113807\pi$
$648$	32.1157	1.26162
$649$	−7.11149	−0.279150
$650$	38.0825	1.49372
$651$	−26.2937	−1.03053
$652$	32.1185	1.25786
$653$	24.6399	0.964234	0.482117	−	0.876107i	$-0.339868\pi$
$653$	24.6399	0.964234	0.482117	+	0.876107i	$0.339868\pi$
$654$	5.83928	0.228334
$655$	−9.07571	−0.354617
$656$	16.7418	0.653656
$657$	7.37907	0.287885
$658$	10.9493	0.426850
$659$	30.3425	1.18197	0.590987	−	0.806681i	$-0.298738\pi$
$659$	30.3425	1.18197	0.590987	+	0.806681i	$0.298738\pi$
$660$	61.3364	2.38752
$661$	−12.3689	−0.481094	−0.240547	−	0.970638i	$-0.577327\pi$
$661$	−12.3689	−0.481094	−0.240547	+	0.970638i	$0.577327\pi$
$662$	−23.2578	−0.903941
$663$	37.8842	1.47130
$664$	−58.0711	−2.25360
$665$	−33.6621	−1.30536
$666$	−7.35798	−0.285116
$667$	−17.6715	−0.684242
$668$	89.0862	3.44685
$669$	−61.1301	−2.36343
$670$	13.1707	0.508828
$671$	−67.7476	−2.61537
$672$	38.1853	1.47303
$673$	−1.87876	−0.0724209	−0.0362105	−	0.999344i	$-0.511529\pi$
$673$	−1.87876	−0.0724209	−0.0362105	+	0.999344i	$0.511529\pi$
$674$	−48.3692	−1.86311
$675$	−0.790383	−0.0304218
$676$	76.7715	2.95275
$677$	−41.1934	−1.58319	−0.791595	−	0.611046i	$-0.790749\pi$
$677$	−41.1934	−1.58319	−0.791595	+	0.611046i	$0.790749\pi$
$678$	32.9246	1.26446
$679$	−41.1322	−1.57851
$680$	−14.5603	−0.558362
$681$	−51.2425	−1.96362
$682$	26.9705	1.03275
$683$	6.18362	0.236610	0.118305	−	0.992977i	$-0.462254\pi$
$683$	6.18362	0.236610	0.118305	+	0.992977i	$0.462254\pi$
$684$	−58.0739	−2.22051
$685$	20.9387	0.800027
$686$	−45.7818	−1.74796
$687$	11.5832	0.441926
$688$	−1.46428	−0.0558253
$689$	5.04519	0.192206
$690$	68.4944	2.60754
$691$	−3.47533	−0.132208	−0.0661040	−	0.997813i	$-0.521057\pi$
$691$	−3.47533	−0.132208	−0.0661040	+	0.997813i	$0.521057\pi$
$692$	−35.0709	−1.33319
$693$	61.9664	2.35391
$694$	46.6866	1.77220
$695$	−4.14170	−0.157104
$696$	−20.7940	−0.788196
$697$	26.8046	1.01530
$698$	−46.7649	−1.77008
$699$	26.3544	0.996814
$700$	−42.2448	−1.59670
$701$	−20.2744	−0.765752	−0.382876	−	0.923800i	$-0.625066\pi$
$701$	−20.2744	−0.765752	−0.382876	+	0.923800i	$0.625066\pi$
$702$	−3.98892	−0.150552
$703$	−5.21299	−0.196612
$704$	−54.2314	−2.04392
$705$	−4.00160	−0.150709
$706$	−20.2910	−0.763662
$707$	21.7625	0.818464
$708$	−13.6024	−0.511209
$709$	46.0586	1.72977	0.864883	−	0.501973i	$-0.167392\pi$
$709$	46.0586	1.72977	0.864883	+	0.501973i	$0.167392\pi$
$710$	−27.5228	−1.03291
$711$	4.06697	0.152523
$712$	20.0411	0.751072
$713$	19.3129	0.723272
$714$	−65.5367	−2.45265
$715$	40.7363	1.52345
$716$	−55.2943	−2.06645
$717$	−27.7256	−1.03543
$718$	22.6341	0.844697
$719$	−47.5246	−1.77237	−0.886184	−	0.463334i	$-0.846653\pi$
$719$	−47.5246	−1.77237	−0.886184	+	0.463334i	$0.846653\pi$
$720$	7.62212	0.284059
$721$	57.2602	2.13248
$722$	−19.3027	−0.718372
$723$	−15.2490	−0.567116
$724$	−78.6545	−2.92317
$725$	−6.21176	−0.230699
$726$	−60.5177	−2.24602
$727$	−21.7880	−0.808073	−0.404036	−	0.914743i	$-0.632393\pi$
$727$	−21.7880	−0.808073	−0.404036	+	0.914743i	$0.632393\pi$
$728$	−93.9206	−3.48093
$729$	−29.0520	−1.07600
$730$	−8.39177	−0.310593
$731$	−2.34441	−0.0867110
$732$	−129.583	−4.78953
$733$	−19.3869	−0.716070	−0.358035	−	0.933708i	$-0.616553\pi$
$733$	−19.3869	−0.716070	−0.358035	+	0.933708i	$0.616553\pi$
$734$	0.561863	0.0207387
$735$	42.7169	1.57564
$736$	−28.0474	−1.03384
$737$	−17.1772	−0.632729
$738$	−75.5985	−2.78282
$739$	14.8047	0.544601	0.272300	−	0.962212i	$-0.412216\pi$
$739$	14.8047	0.544601	0.272300	+	0.962212i	$0.412216\pi$
$740$	5.36577	0.197250
$741$	−75.6991	−2.78088
$742$	−8.72778	−0.320407
$743$	48.3474	1.77370	0.886848	−	0.462062i	$-0.152890\pi$
$743$	48.3474	1.77370	0.886848	+	0.462062i	$0.152890\pi$
$744$	22.7255	0.833156
$745$	−6.76393	−0.247811
$746$	50.2510	1.83982
$747$	48.6713	1.78079
$748$	43.1066	1.57613
$749$	−79.9063	−2.91971
$750$	67.9008	2.47939
$751$	−7.16431	−0.261429	−0.130715	−	0.991420i	$-0.541727\pi$
$751$	−7.16431	−0.261429	−0.130715	+	0.991420i	$0.541727\pi$
$752$	−1.75651	−0.0640534
$753$	47.4617	1.72960
$754$	−31.3496	−1.14168
$755$	18.1737	0.661409
$756$	4.42489	0.160932
$757$	−4.16381	−0.151336	−0.0756681	−	0.997133i	$-0.524109\pi$
$757$	−4.16381	−0.151336	−0.0756681	+	0.997133i	$0.524109\pi$
$758$	−84.9116	−3.08413
$759$	−89.3302	−3.24248
$760$	29.0940	1.05535
$761$	8.07829	0.292838	0.146419	−	0.989223i	$-0.453225\pi$
$761$	8.07829	0.292838	0.146419	+	0.989223i	$0.453225\pi$
$762$	65.5611	2.37503
$763$	−4.30200	−0.155743
$764$	71.9562	2.60328
$765$	12.2035	0.441217
$766$	18.5191	0.669122
$767$	−9.03395	−0.326197
$768$	−61.8153	−2.23057
$769$	−37.4024	−1.34876	−0.674382	−	0.738383i	$-0.735590\pi$
$769$	−37.4024	−1.34876	−0.674382	+	0.738383i	$0.735590\pi$
$770$	−70.4706	−2.53958
$771$	−34.8404	−1.25474
$772$	−96.6260	−3.47765
$773$	6.76505	0.243322	0.121661	−	0.992572i	$-0.461178\pi$
$773$	6.76505	0.243322	0.121661	+	0.992572i	$0.461178\pi$
$774$	6.61207	0.237666
$775$	6.78873	0.243858
$776$	35.5503	1.27618
$777$	10.6394	0.381686
$778$	69.6828	2.49825
$779$	−53.5601	−1.91899
$780$	77.9177	2.78990
$781$	35.8952	1.28443
$782$	48.1372	1.72138
$783$	0.650645	0.0232521
$784$	18.7507	0.669668
$785$	−36.2532	−1.29393
$786$	35.3067	1.25935
$787$	18.3861	0.655394	0.327697	−	0.944783i	$-0.393728\pi$
$787$	18.3861	0.655394	0.327697	+	0.944783i	$0.393728\pi$
$788$	34.0894	1.21438
$789$	−66.7320	−2.37572
$790$	−4.62512	−0.164554
$791$	−24.2567	−0.862467
$792$	−53.5572	−1.90307
$793$	−86.0619	−3.05615
$794$	−51.8882	−1.84144
$795$	3.18969	0.113127
$796$	17.0577	0.604594
$797$	50.8802	1.80227	0.901134	−	0.433540i	$-0.142736\pi$
$797$	50.8802	1.80227	0.901134	+	0.433540i	$0.142736\pi$
$798$	130.954	4.63571
$799$	−2.81228	−0.0994913
$800$	−9.85903	−0.348569
$801$	−16.7971	−0.593496
$802$	−71.5591	−2.52684
$803$	10.9445	0.386223
$804$	−32.8554	−1.15872
$805$	−50.4622	−1.77856
$806$	34.2615	1.20681
$807$	61.0076	2.14757
$808$	−18.8092	−0.661706
$809$	−45.7718	−1.60925	−0.804625	−	0.593783i	$-0.797634\pi$
$809$	−45.7718	−1.60925	−0.804625	+	0.593783i	$0.797634\pi$
$810$	30.6113	1.07557
$811$	5.63913	0.198017	0.0990083	−	0.995087i	$-0.468433\pi$
$811$	5.63913	0.198017	0.0990083	+	0.995087i	$0.468433\pi$
$812$	34.7760	1.22040
$813$	31.9768	1.12147
$814$	−10.9132	−0.382509
$815$	13.4862	0.472402
$816$	10.5135	0.368046
$817$	4.68453	0.163891
$818$	−40.6537	−1.42142
$819$	78.7179	2.75063
$820$	55.1298	1.92522
$821$	12.1929	0.425535	0.212768	−	0.977103i	$-0.431752\pi$
$821$	12.1929	0.425535	0.212768	+	0.977103i	$0.431752\pi$
$822$	−81.4566	−2.84113
$823$	1.97763	0.0689360	0.0344680	−	0.999406i	$-0.489026\pi$
$823$	1.97763	0.0689360	0.0344680	+	0.999406i	$0.489026\pi$
$824$	−49.4897	−1.72405
$825$	−31.4008	−1.09323
$826$	15.6280	0.543769
$827$	−17.9902	−0.625581	−0.312791	−	0.949822i	$-0.601264\pi$
$827$	−17.9902	−0.625581	−0.312791	+	0.949822i	$0.601264\pi$
$828$	−87.0575	−3.02546
$829$	−22.8362	−0.793135	−0.396567	−	0.918006i	$-0.629799\pi$
$829$	−22.8362	−0.793135	−0.396567	+	0.918006i	$0.629799\pi$
$830$	−55.3509	−1.92126
$831$	2.32598	0.0806872
$832$	−68.8920	−2.38840
$833$	30.0210	1.04017
$834$	16.1122	0.557920
$835$	37.4063	1.29450
$836$	−86.1343	−2.97902
$837$	−0.711079	−0.0245785
$838$	54.1163	1.86942
$839$	−48.3264	−1.66841	−0.834207	−	0.551452i	$-0.814074\pi$
$839$	−48.3264	−1.66841	−0.834207	+	0.551452i	$0.814074\pi$
$840$	−59.3789	−2.04877
$841$	−23.8865	−0.823671
$842$	76.9525	2.65196
$843$	29.1819	1.00508
$844$	−3.58254	−0.123316
$845$	32.2355	1.10894
$846$	7.93164	0.272695
$847$	44.5855	1.53198
$848$	1.40012	0.0480804
$849$	−10.7712	−0.369665
$850$	16.9209	0.580381
$851$	−7.81470	−0.267884
$852$	68.6579	2.35218
$853$	−28.1945	−0.965363	−0.482681	−	0.875796i	$-0.660337\pi$
$853$	−28.1945	−0.965363	−0.482681	+	0.875796i	$0.660337\pi$
$854$	148.880	5.09459
$855$	−24.3846	−0.833936
$856$	69.0626	2.36051
$857$	2.73685	0.0934889	0.0467445	−	0.998907i	$-0.485115\pi$
$857$	2.73685	0.0934889	0.0467445	+	0.998907i	$0.485115\pi$
$858$	−158.474	−5.41021
$859$	27.7729	0.947600	0.473800	−	0.880633i	$-0.342882\pi$
$859$	27.7729	0.947600	0.473800	+	0.880633i	$0.342882\pi$
$860$	−4.82182	−0.164423
$861$	109.313	3.72537
$862$	−38.9134	−1.32540
$863$	8.39284	0.285695	0.142848	−	0.989745i	$-0.454374\pi$
$863$	8.39284	0.285695	0.142848	+	0.989745i	$0.454374\pi$
$864$	1.03268	0.0351323
$865$	−14.7259	−0.500695
$866$	30.4076	1.03329
$867$	−25.2104	−0.856189
$868$	−38.0062	−1.29001
$869$	6.03206	0.204624
$870$	−19.8200	−0.671961
$871$	−21.8207	−0.739367
$872$	3.71820	0.125914
$873$	−29.7959	−1.00844
$874$	−96.1863	−3.25355
$875$	−50.0249	−1.69115
$876$	20.9339	0.707292
$877$	−9.57574	−0.323350	−0.161675	−	0.986844i	$-0.551690\pi$
$877$	−9.57574	−0.323350	−0.161675	+	0.986844i	$0.551690\pi$
$878$	46.0667	1.55468
$879$	−39.3594	−1.32756
$880$	11.3050	0.381091
$881$	6.48459	0.218471	0.109236	−	0.994016i	$-0.465160\pi$
$881$	6.48459	0.218471	0.109236	+	0.994016i	$0.465160\pi$
$882$	−84.6700	−2.85099
$883$	40.6313	1.36735	0.683676	−	0.729786i	$-0.260380\pi$
$883$	40.6313	1.36735	0.683676	+	0.729786i	$0.260380\pi$
$884$	54.7597	1.84177
$885$	−5.71149	−0.191990
$886$	34.6601	1.16443
$887$	7.96702	0.267507	0.133753	−	0.991015i	$-0.457297\pi$
$887$	7.96702	0.267507	0.133753	+	0.991015i	$0.457297\pi$
$888$	−9.19557	−0.308583
$889$	−48.3011	−1.61997
$890$	19.1023	0.640312
$891$	−39.9232	−1.33748
$892$	−88.3605	−2.95853
$893$	5.61942	0.188047
$894$	26.3133	0.880048
$895$	−23.2175	−0.776075
$896$	88.2975	2.94981
$897$	−113.479	−3.78896
$898$	87.0790	2.90586
$899$	−5.58849	−0.186387
$900$	−30.6019	−1.02006
$901$	2.24168	0.0746813
$902$	−112.126	−3.73340
$903$	−9.56081	−0.318164
$904$	20.9649	0.697282
$905$	−33.0262	−1.09783
$906$	−70.7001	−2.34885
$907$	−37.1979	−1.23514	−0.617569	−	0.786517i	$-0.711882\pi$
$907$	−37.1979	−1.23514	−0.617569	+	0.786517i	$0.711882\pi$
$908$	−74.0684	−2.45805
$909$	15.7646	0.522880
$910$	−89.5211	−2.96760
$911$	−7.36096	−0.243880	−0.121940	−	0.992538i	$-0.538911\pi$
$911$	−7.36096	−0.243880	−0.121940	+	0.992538i	$0.538911\pi$
$912$	−21.0078	−0.695637
$913$	72.1885	2.38909
$914$	5.59592	0.185097
$915$	−54.4105	−1.79876
$916$	16.7429	0.553202
$917$	−26.0116	−0.858980
$918$	−1.77236	−0.0584966
$919$	−17.5959	−0.580434	−0.290217	−	0.956961i	$-0.593727\pi$
$919$	−17.5959	−0.580434	−0.290217	+	0.956961i	$0.593727\pi$
$920$	43.6142	1.43792
$921$	58.5048	1.92780
$922$	42.2125	1.39020
$923$	45.5988	1.50090
$924$	175.795	5.78322
$925$	−2.74697	−0.0903198
$926$	54.2459	1.78263
$927$	41.4789	1.36235
$928$	8.11597	0.266420
$929$	0.662330	0.0217303	0.0108652	−	0.999941i	$-0.496541\pi$
$929$	0.662330	0.0217303	0.0108652	+	0.999941i	$0.496541\pi$
$930$	21.6609	0.710290
$931$	−59.9871	−1.96600
$932$	38.0939	1.24781
$933$	55.1222	1.80462
$934$	−17.1655	−0.561674
$935$	18.1000	0.591933
$936$	−68.0355	−2.22381
$937$	−56.3361	−1.84042	−0.920210	−	0.391424i	$-0.871983\pi$
$937$	−56.3361	−1.84042	−0.920210	+	0.391424i	$0.871983\pi$
$938$	37.7482	1.23252
$939$	15.0709	0.491821
$940$	−5.78411	−0.188657
$941$	17.7712	0.579325	0.289662	−	0.957129i	$-0.406457\pi$
$941$	17.7712	0.579325	0.289662	+	0.957129i	$0.406457\pi$
$942$	141.033	4.59512
$943$	−80.2909	−2.61463
$944$	−2.50707	−0.0815983
$945$	1.85797	0.0604396
$946$	9.80691	0.318850
$947$	10.1710	0.330514	0.165257	−	0.986251i	$-0.447155\pi$
$947$	10.1710	0.330514	0.165257	+	0.986251i	$0.447155\pi$
$948$	11.5377	0.374728
$949$	13.9032	0.451316
$950$	−33.8108	−1.09697
$951$	−44.7591	−1.45141
$952$	−41.7309	−1.35251
$953$	−36.9103	−1.19564	−0.597822	−	0.801629i	$-0.703967\pi$
$953$	−36.9103	−1.19564	−0.597822	+	0.801629i	$0.703967\pi$
$954$	−6.32235	−0.204694
$955$	30.2136	0.977689
$956$	−40.0759	−1.29615
$957$	25.8492	0.835585
$958$	32.2511	1.04199
$959$	60.0119	1.93789
$960$	−43.5552	−1.40574
$961$	−24.8924	−0.802981
$962$	−13.8635	−0.446976
$963$	−57.8836	−1.86527
$964$	−22.0416	−0.709913
$965$	−40.5722	−1.30607
$966$	196.310	6.31617
$967$	33.0803	1.06379	0.531896	−	0.846810i	$-0.321480\pi$
$967$	33.0803	1.06379	0.531896	+	0.846810i	$0.321480\pi$
$968$	−38.5350	−1.23856
$969$	−33.6347	−1.08050
$970$	33.8851	1.08798
$971$	8.41127	0.269931	0.134965	−	0.990850i	$-0.456908\pi$
$971$	8.41127	0.269931	0.134965	+	0.990850i	$0.456908\pi$
$972$	−79.4481	−2.54830
$973$	−11.8704	−0.380548
$974$	−80.4392	−2.57744
$975$	−39.8894	−1.27748
$976$	−23.8836	−0.764496
$977$	32.5930	1.04274	0.521371	−	0.853330i	$-0.325421\pi$
$977$	32.5930	1.04274	0.521371	+	0.853330i	$0.325421\pi$
$978$	−52.4646	−1.67763
$979$	−24.9132	−0.796229
$980$	61.7451	1.97238
$981$	−3.11634	−0.0994972
$982$	−88.1767	−2.81383
$983$	−9.87057	−0.314822	−0.157411	−	0.987533i	$-0.550315\pi$
$983$	−9.87057	−0.314822	−0.157411	+	0.987533i	$0.550315\pi$
$984$	−94.4784	−3.01186
$985$	14.3138	0.456075
$986$	−13.9293	−0.443599
$987$	−11.4689	−0.365058
$988$	−109.419	−3.48109
$989$	7.02248	0.223302
$990$	−51.0484	−1.62243
$991$	6.77425	0.215191	0.107596	−	0.994195i	$-0.465685\pi$
$991$	6.77425	0.215191	0.107596	+	0.994195i	$0.465685\pi$
$992$	−8.86982	−0.281617
$993$	24.3613	0.773084
$994$	−78.8824	−2.50200
$995$	7.16234	0.227061
$996$	138.077	4.37515
$997$	−42.8226	−1.35620	−0.678102	−	0.734968i	$-0.737197\pi$
$997$	−42.8226	−1.35620	−0.678102	+	0.734968i	$0.737197\pi$
$998$	65.8258	2.08368
$999$	0.287729	0.00910334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.f.1.7	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.f.1.7	✓	85	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36110 q^{2} +2.47312 q^{3} +3.57478 q^{4} +1.50101 q^{5} -5.83928 q^{6} +4.30200 q^{7} -3.71820 q^{8} +3.11634 q^{9} +O(q^{10})\)	\(q-2.36110 q^{2} +2.47312 q^{3} +3.57478 q^{4} +1.50101 q^{5} -5.83928 q^{6} +4.30200 q^{7} -3.71820 q^{8} +3.11634 q^{9} -3.54403 q^{10} +4.62211 q^{11} +8.84086 q^{12} +5.87162 q^{13} -10.1574 q^{14} +3.71218 q^{15} +1.62947 q^{16} +2.60888 q^{17} -7.35798 q^{18} -5.21299 q^{19} +5.36577 q^{20} +10.6394 q^{21} -10.9132 q^{22} -7.81470 q^{23} -9.19557 q^{24} -2.74697 q^{25} -13.8635 q^{26} +0.287729 q^{27} +15.3787 q^{28} +2.26131 q^{29} -8.76482 q^{30} -2.47135 q^{31} +3.58906 q^{32} +11.4310 q^{33} -6.15982 q^{34} +6.45735 q^{35} +11.1402 q^{36} +1.00000 q^{37} +12.3084 q^{38} +14.5212 q^{39} -5.58105 q^{40} +10.2743 q^{41} -25.1206 q^{42} -0.898625 q^{43} +16.5230 q^{44} +4.67766 q^{45} +18.4513 q^{46} -1.07796 q^{47} +4.02989 q^{48} +11.5072 q^{49} +6.48586 q^{50} +6.45209 q^{51} +20.9897 q^{52} +0.859250 q^{53} -0.679356 q^{54} +6.93783 q^{55} -15.9957 q^{56} -12.8924 q^{57} -5.33917 q^{58} -1.53858 q^{59} +13.2702 q^{60} -14.6573 q^{61} +5.83510 q^{62} +13.4065 q^{63} -11.7331 q^{64} +8.81335 q^{65} -26.9898 q^{66} -3.71631 q^{67} +9.32617 q^{68} -19.3267 q^{69} -15.2464 q^{70} +7.76597 q^{71} -11.5872 q^{72} +2.36786 q^{73} -2.36110 q^{74} -6.79360 q^{75} -18.6353 q^{76} +19.8843 q^{77} -34.2860 q^{78} +1.30505 q^{79} +2.44585 q^{80} -8.63744 q^{81} -24.2587 q^{82} +15.6181 q^{83} +38.0334 q^{84} +3.91596 q^{85} +2.12174 q^{86} +5.59250 q^{87} -17.1859 q^{88} -5.39001 q^{89} -11.0444 q^{90} +25.2597 q^{91} -27.9358 q^{92} -6.11196 q^{93} +2.54518 q^{94} -7.82475 q^{95} +8.87618 q^{96} -9.56117 q^{97} -27.1697 q^{98} +14.4041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

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