LMFDB - Embedded newform 8018.2.a.i.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.06580 q^{3} +1.00000 q^{4} +4.42069 q^{5} +2.06580 q^{6} -2.80943 q^{7} -1.00000 q^{8} +1.26754 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.06580 q^{3} +1.00000 q^{4} +4.42069 q^{5} +2.06580 q^{6} -2.80943 q^{7} -1.00000 q^{8} +1.26754 q^{9} -4.42069 q^{10} -2.99482 q^{11} -2.06580 q^{12} -6.22957 q^{13} +2.80943 q^{14} -9.13227 q^{15} +1.00000 q^{16} -7.11307 q^{17} -1.26754 q^{18} +1.00000 q^{19} +4.42069 q^{20} +5.80373 q^{21} +2.99482 q^{22} +5.90443 q^{23} +2.06580 q^{24} +14.5425 q^{25} +6.22957 q^{26} +3.57892 q^{27} -2.80943 q^{28} -9.83172 q^{29} +9.13227 q^{30} -5.77790 q^{31} -1.00000 q^{32} +6.18670 q^{33} +7.11307 q^{34} -12.4196 q^{35} +1.26754 q^{36} -1.47032 q^{37} -1.00000 q^{38} +12.8691 q^{39} -4.42069 q^{40} -3.05509 q^{41} -5.80373 q^{42} +5.28995 q^{43} -2.99482 q^{44} +5.60340 q^{45} -5.90443 q^{46} +0.800480 q^{47} -2.06580 q^{48} +0.892914 q^{49} -14.5425 q^{50} +14.6942 q^{51} -6.22957 q^{52} -11.6805 q^{53} -3.57892 q^{54} -13.2391 q^{55} +2.80943 q^{56} -2.06580 q^{57} +9.83172 q^{58} -10.7432 q^{59} -9.13227 q^{60} -0.0750006 q^{61} +5.77790 q^{62} -3.56107 q^{63} +1.00000 q^{64} -27.5390 q^{65} -6.18670 q^{66} -5.36291 q^{67} -7.11307 q^{68} -12.1974 q^{69} +12.4196 q^{70} -0.743092 q^{71} -1.26754 q^{72} +6.76896 q^{73} +1.47032 q^{74} -30.0419 q^{75} +1.00000 q^{76} +8.41373 q^{77} -12.8691 q^{78} -3.13679 q^{79} +4.42069 q^{80} -11.1960 q^{81} +3.05509 q^{82} +10.9284 q^{83} +5.80373 q^{84} -31.4447 q^{85} -5.28995 q^{86} +20.3104 q^{87} +2.99482 q^{88} +12.2467 q^{89} -5.60340 q^{90} +17.5015 q^{91} +5.90443 q^{92} +11.9360 q^{93} -0.800480 q^{94} +4.42069 q^{95} +2.06580 q^{96} +8.07910 q^{97} -0.892914 q^{98} -3.79605 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.06580	−1.19269	−0.596346	−	0.802728i	$-0.703381\pi$
$3$	−2.06580	−1.19269	−0.596346	+	0.802728i	$0.703381\pi$
$4$	1.00000	0.500000
$5$	4.42069	1.97699	0.988496	−	0.151249i	$-0.0483296\pi$
$5$	4.42069	1.97699	0.988496	+	0.151249i	$0.0483296\pi$
$6$	2.06580	0.843360
$7$	−2.80943	−1.06187	−0.530933	−	0.847414i	$-0.678158\pi$
$7$	−2.80943	−1.06187	−0.530933	+	0.847414i	$0.678158\pi$
$8$	−1.00000	−0.353553
$9$	1.26754	0.422513
$10$	−4.42069	−1.39794
$11$	−2.99482	−0.902971	−0.451485	−	0.892278i	$-0.649106\pi$
$11$	−2.99482	−0.902971	−0.451485	+	0.892278i	$0.649106\pi$
$12$	−2.06580	−0.596346
$13$	−6.22957	−1.72777	−0.863885	−	0.503689i	$-0.831976\pi$
$13$	−6.22957	−1.72777	−0.863885	+	0.503689i	$0.831976\pi$
$14$	2.80943	0.750853
$15$	−9.13227	−2.35794
$16$	1.00000	0.250000
$17$	−7.11307	−1.72517	−0.862586	−	0.505910i	$-0.831157\pi$
$17$	−7.11307	−1.72517	−0.862586	+	0.505910i	$0.831157\pi$
$18$	−1.26754	−0.298762
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	4.42069	0.988496
$21$	5.80373	1.26648
$22$	2.99482	0.638497
$23$	5.90443	1.23116	0.615580	−	0.788075i	$-0.288922\pi$
$23$	5.90443	1.23116	0.615580	+	0.788075i	$0.288922\pi$
$24$	2.06580	0.421680
$25$	14.5425	2.90849
$26$	6.22957	1.22172
$27$	3.57892	0.688763
$28$	−2.80943	−0.530933
$29$	−9.83172	−1.82571	−0.912853	−	0.408289i	$-0.866126\pi$
$29$	−9.83172	−1.82571	−0.912853	+	0.408289i	$0.866126\pi$
$30$	9.13227	1.66732
$31$	−5.77790	−1.03774	−0.518871	−	0.854853i	$-0.673648\pi$
$31$	−5.77790	−1.03774	−0.518871	+	0.854853i	$0.673648\pi$
$32$	−1.00000	−0.176777
$33$	6.18670	1.07697
$34$	7.11307	1.21988
$35$	−12.4196	−2.09930
$36$	1.26754	0.211257
$37$	−1.47032	−0.241718	−0.120859	−	0.992670i	$-0.538565\pi$
$37$	−1.47032	−0.241718	−0.120859	+	0.992670i	$0.538565\pi$
$38$	−1.00000	−0.162221
$39$	12.8691	2.06070
$40$	−4.42069	−0.698972
$41$	−3.05509	−0.477125	−0.238563	−	0.971127i	$-0.576676\pi$
$41$	−3.05509	−0.477125	−0.238563	+	0.971127i	$0.576676\pi$
$42$	−5.80373	−0.895536
$43$	5.28995	0.806709	0.403355	−	0.915044i	$-0.367844\pi$
$43$	5.28995	0.806709	0.403355	+	0.915044i	$0.367844\pi$
$44$	−2.99482	−0.451485
$45$	5.60340	0.835305
$46$	−5.90443	−0.870561
$47$	0.800480	0.116762	0.0583810	−	0.998294i	$-0.481406\pi$
$47$	0.800480	0.116762	0.0583810	+	0.998294i	$0.481406\pi$
$48$	−2.06580	−0.298173
$49$	0.892914	0.127559
$50$	−14.5425	−2.05662
$51$	14.6942	2.05760
$52$	−6.22957	−0.863885
$53$	−11.6805	−1.60443	−0.802217	−	0.597033i	$-0.796346\pi$
$53$	−11.6805	−1.60443	−0.802217	+	0.597033i	$0.796346\pi$
$54$	−3.57892	−0.487029
$55$	−13.2391	−1.78517
$56$	2.80943	0.375426
$57$	−2.06580	−0.273622
$58$	9.83172	1.29097
$59$	−10.7432	−1.39865	−0.699324	−	0.714805i	$-0.746515\pi$
$59$	−10.7432	−1.39865	−0.699324	+	0.714805i	$0.746515\pi$
$60$	−9.13227	−1.17897
$61$	−0.0750006	−0.00960285	−0.00480142	−	0.999988i	$-0.501528\pi$
$61$	−0.0750006	−0.00960285	−0.00480142	+	0.999988i	$0.501528\pi$
$62$	5.77790	0.733794
$63$	−3.56107	−0.448653
$64$	1.00000	0.125000
$65$	−27.5390	−3.41579
$66$	−6.18670	−0.761530
$67$	−5.36291	−0.655184	−0.327592	−	0.944819i	$-0.606237\pi$
$67$	−5.36291	−0.655184	−0.327592	+	0.944819i	$0.606237\pi$
$68$	−7.11307	−0.862586
$69$	−12.1974	−1.46839
$70$	12.4196	1.48443
$71$	−0.743092	−0.0881888	−0.0440944	−	0.999027i	$-0.514040\pi$
$71$	−0.743092	−0.0881888	−0.0440944	+	0.999027i	$0.514040\pi$
$72$	−1.26754	−0.149381
$73$	6.76896	0.792246	0.396123	−	0.918197i	$-0.370355\pi$
$73$	6.76896	0.792246	0.396123	+	0.918197i	$0.370355\pi$
$74$	1.47032	0.170921
$75$	−30.0419	−3.46894
$76$	1.00000	0.114708
$77$	8.41373	0.958834
$78$	−12.8691	−1.45713
$79$	−3.13679	−0.352916	−0.176458	−	0.984308i	$-0.556464\pi$
$79$	−3.13679	−0.352916	−0.176458	+	0.984308i	$0.556464\pi$
$80$	4.42069	0.494248
$81$	−11.1960	−1.24400
$82$	3.05509	0.337378
$83$	10.9284	1.19955	0.599775	−	0.800169i	$-0.295257\pi$
$83$	10.9284	1.19955	0.599775	+	0.800169i	$0.295257\pi$
$84$	5.80373	0.633239
$85$	−31.4447	−3.41065
$86$	−5.28995	−0.570429
$87$	20.3104	2.17750
$88$	2.99482	0.319248
$89$	12.2467	1.29815	0.649073	−	0.760726i	$-0.275157\pi$
$89$	12.2467	1.29815	0.649073	+	0.760726i	$0.275157\pi$
$90$	−5.60340	−0.590650
$91$	17.5015	1.83466
$92$	5.90443	0.615580
$93$	11.9360	1.23771
$94$	−0.800480	−0.0825632
$95$	4.42069	0.453553
$96$	2.06580	0.210840
$97$	8.07910	0.820308	0.410154	−	0.912016i	$-0.365475\pi$
$97$	8.07910	0.820308	0.410154	+	0.912016i	$0.365475\pi$
$98$	−0.892914	−0.0901979
$99$	−3.79605	−0.381517
$100$	14.5425	1.45425
$101$	−12.5009	−1.24389	−0.621945	−	0.783061i	$-0.713657\pi$
$101$	−12.5009	−1.24389	−0.621945	+	0.783061i	$0.713657\pi$
$102$	−14.6942	−1.45494
$103$	17.2999	1.70461	0.852303	−	0.523048i	$-0.175205\pi$
$103$	17.2999	1.70461	0.852303	+	0.523048i	$0.175205\pi$
$104$	6.22957	0.610859
$105$	25.6565	2.50382
$106$	11.6805	1.13451
$107$	−2.05867	−0.199019	−0.0995094	−	0.995037i	$-0.531727\pi$
$107$	−2.05867	−0.199019	−0.0995094	+	0.995037i	$0.531727\pi$
$108$	3.57892	0.344382
$109$	−9.48547	−0.908544	−0.454272	−	0.890863i	$-0.650101\pi$
$109$	−9.48547	−0.908544	−0.454272	+	0.890863i	$0.650101\pi$
$110$	13.2391	1.26230
$111$	3.03738	0.288296
$112$	−2.80943	−0.265466
$113$	8.22581	0.773819	0.386910	−	0.922118i	$-0.373543\pi$
$113$	8.22581	0.773819	0.386910	+	0.922118i	$0.373543\pi$
$114$	2.06580	0.193480
$115$	26.1017	2.43399
$116$	−9.83172	−0.912853
$117$	−7.89623	−0.730006
$118$	10.7432	0.988993
$119$	19.9837	1.83190
$120$	9.13227	0.833658
$121$	−2.03108	−0.184643
$122$	0.0750006	0.00679024
$123$	6.31122	0.569063
$124$	−5.77790	−0.518871
$125$	42.1843	3.77308
$126$	3.56107	0.317245
$127$	9.60279	0.852110	0.426055	−	0.904697i	$-0.359903\pi$
$127$	9.60279	0.852110	0.426055	+	0.904697i	$0.359903\pi$
$128$	−1.00000	−0.0883883
$129$	−10.9280	−0.962155
$130$	27.5390	2.41533
$131$	5.68488	0.496690	0.248345	−	0.968672i	$-0.420113\pi$
$131$	5.68488	0.496690	0.248345	+	0.968672i	$0.420113\pi$
$132$	6.18670	0.538483
$133$	−2.80943	−0.243609
$134$	5.36291	0.463285
$135$	15.8213	1.36168
$136$	7.11307	0.609941
$137$	−11.6764	−0.997583	−0.498791	−	0.866722i	$-0.666223\pi$
$137$	−11.6764	−0.997583	−0.498791	+	0.866722i	$0.666223\pi$
$138$	12.1974	1.03831
$139$	0.382890	0.0324763	0.0162382	−	0.999868i	$-0.494831\pi$
$139$	0.382890	0.0324763	0.0162382	+	0.999868i	$0.494831\pi$
$140$	−12.4196	−1.04965
$141$	−1.65363	−0.139261
$142$	0.743092	0.0623589
$143$	18.6564	1.56013
$144$	1.26754	0.105628
$145$	−43.4630	−3.60940
$146$	−6.76896	−0.560203
$147$	−1.84458	−0.152139
$148$	−1.47032	−0.120859
$149$	−17.5403	−1.43696	−0.718479	−	0.695548i	$-0.755162\pi$
$149$	−17.5403	−1.43696	−0.718479	+	0.695548i	$0.755162\pi$
$150$	30.0419	2.45291
$151$	−3.02278	−0.245990	−0.122995	−	0.992407i	$-0.539250\pi$
$151$	−3.02278	−0.245990	−0.122995	+	0.992407i	$0.539250\pi$
$152$	−1.00000	−0.0811107
$153$	−9.01610	−0.728909
$154$	−8.41373	−0.677998
$155$	−25.5423	−2.05161
$156$	12.8691	1.03035
$157$	−12.8870	−1.02850	−0.514249	−	0.857641i	$-0.671929\pi$
$157$	−12.8870	−1.02850	−0.514249	+	0.857641i	$0.671929\pi$
$158$	3.13679	0.249549
$159$	24.1295	1.91360
$160$	−4.42069	−0.349486
$161$	−16.5881	−1.30733
$162$	11.1960	0.879638
$163$	−18.9641	−1.48538	−0.742690	−	0.669636i	$-0.766450\pi$
$163$	−18.9641	−1.48538	−0.742690	+	0.669636i	$0.766450\pi$
$164$	−3.05509	−0.238563
$165$	27.3495	2.12915
$166$	−10.9284	−0.848209
$167$	17.9963	1.39260	0.696298	−	0.717753i	$-0.254829\pi$
$167$	17.9963	1.39260	0.696298	+	0.717753i	$0.254829\pi$
$168$	−5.80373	−0.447768
$169$	25.8075	1.98519
$170$	31.4447	2.41169
$171$	1.26754	0.0969312
$172$	5.28995	0.403355
$173$	20.8415	1.58455	0.792277	−	0.610162i	$-0.208896\pi$
$173$	20.8415	1.58455	0.792277	+	0.610162i	$0.208896\pi$
$174$	−20.3104	−1.53973
$175$	−40.8561	−3.08843
$176$	−2.99482	−0.225743
$177$	22.1934	1.66816
$178$	−12.2467	−0.917928
$179$	19.5525	1.46142	0.730712	−	0.682686i	$-0.239188\pi$
$179$	19.5525	1.46142	0.730712	+	0.682686i	$0.239188\pi$
$180$	5.60340	0.417653
$181$	−8.08279	−0.600789	−0.300395	−	0.953815i	$-0.597118\pi$
$181$	−8.08279	−0.600789	−0.300395	+	0.953815i	$0.597118\pi$
$182$	−17.5015	−1.29730
$183$	0.154936	0.0114532
$184$	−5.90443	−0.435281
$185$	−6.49981	−0.477875
$186$	−11.9360	−0.875190
$187$	21.3023	1.55778
$188$	0.800480	0.0583810
$189$	−10.0547	−0.731374
$190$	−4.42069	−0.320710
$191$	−2.89450	−0.209438	−0.104719	−	0.994502i	$-0.533394\pi$
$191$	−2.89450	−0.209438	−0.104719	+	0.994502i	$0.533394\pi$
$192$	−2.06580	−0.149086
$193$	17.8104	1.28202	0.641012	−	0.767531i	$-0.278515\pi$
$193$	17.8104	1.28202	0.641012	+	0.767531i	$0.278515\pi$
$194$	−8.07910	−0.580045
$195$	56.8901	4.07398
$196$	0.892914	0.0637795
$197$	−27.7506	−1.97715	−0.988573	−	0.150745i	$-0.951833\pi$
$197$	−27.7506	−1.97715	−0.988573	+	0.150745i	$0.951833\pi$
$198$	3.79605	0.269773
$199$	15.0811	1.06907	0.534535	−	0.845146i	$-0.320487\pi$
$199$	15.0811	1.06907	0.534535	+	0.845146i	$0.320487\pi$
$200$	−14.5425	−1.02831
$201$	11.0787	0.781433
$202$	12.5009	0.879563
$203$	27.6216	1.93865
$204$	14.6942	1.02880
$205$	−13.5056	−0.943272
$206$	−17.2999	−1.20534
$207$	7.48411	0.520181
$208$	−6.22957	−0.431943
$209$	−2.99482	−0.207156
$210$	−25.6565	−1.77047
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−11.6805	−0.802217
$213$	1.53508	0.105182
$214$	2.05867	0.140728
$215$	23.3852	1.59486
$216$	−3.57892	−0.243515
$217$	16.2326	1.10194
$218$	9.48547	0.642437
$219$	−13.9833	−0.944906
$220$	−13.2391	−0.892583
$221$	44.3113	2.98070
$222$	−3.03738	−0.203856
$223$	−28.1859	−1.88747	−0.943735	−	0.330704i	$-0.892714\pi$
$223$	−28.1859	−1.88747	−0.943735	+	0.330704i	$0.892714\pi$
$224$	2.80943	0.187713
$225$	18.4332	1.22888
$226$	−8.22581	−0.547173
$227$	−11.1123	−0.737547	−0.368773	−	0.929519i	$-0.620222\pi$
$227$	−11.1123	−0.737547	−0.368773	+	0.929519i	$0.620222\pi$
$228$	−2.06580	−0.136811
$229$	27.2900	1.80337	0.901687	−	0.432389i	$-0.142329\pi$
$229$	27.2900	1.80337	0.901687	+	0.432389i	$0.142329\pi$
$230$	−26.1017	−1.72109
$231$	−17.3811	−1.14359
$232$	9.83172	0.645484
$233$	−3.37265	−0.220950	−0.110475	−	0.993879i	$-0.535237\pi$
$233$	−3.37265	−0.220950	−0.110475	+	0.993879i	$0.535237\pi$
$234$	7.89623	0.516192
$235$	3.53867	0.230837
$236$	−10.7432	−0.699324
$237$	6.47998	0.420920
$238$	−19.9837	−1.29535
$239$	−9.16352	−0.592739	−0.296369	−	0.955073i	$-0.595776\pi$
$239$	−9.16352	−0.592739	−0.296369	+	0.955073i	$0.595776\pi$
$240$	−9.13227	−0.589485
$241$	−23.1567	−1.49165	−0.745826	−	0.666141i	$-0.767945\pi$
$241$	−23.1567	−1.49165	−0.745826	+	0.666141i	$0.767945\pi$
$242$	2.03108	0.130563
$243$	12.3919	0.794940
$244$	−0.0750006	−0.00480142
$245$	3.94729	0.252183
$246$	−6.31122	−0.402388
$247$	−6.22957	−0.396378
$248$	5.77790	0.366897
$249$	−22.5759	−1.43069
$250$	−42.1843	−2.66797
$251$	28.9951	1.83016	0.915079	−	0.403275i	$-0.132128\pi$
$251$	28.9951	1.83016	0.915079	+	0.403275i	$0.132128\pi$
$252$	−3.56107	−0.224326
$253$	−17.6827	−1.11170
$254$	−9.60279	−0.602533
$255$	64.9584	4.06786
$256$	1.00000	0.0625000
$257$	16.5764	1.03401	0.517003	−	0.855984i	$-0.327048\pi$
$257$	16.5764	1.03401	0.517003	+	0.855984i	$0.327048\pi$
$258$	10.9280	0.680346
$259$	4.13075	0.256673
$260$	−27.5390	−1.70789
$261$	−12.4621	−0.771385
$262$	−5.68488	−0.351213
$263$	9.71752	0.599208	0.299604	−	0.954064i	$-0.403145\pi$
$263$	9.71752	0.599208	0.299604	+	0.954064i	$0.403145\pi$
$264$	−6.18670	−0.380765
$265$	−51.6356	−3.17195
$266$	2.80943	0.172257
$267$	−25.2992	−1.54829
$268$	−5.36291	−0.327592
$269$	10.1573	0.619304	0.309652	−	0.950850i	$-0.399787\pi$
$269$	10.1573	0.619304	0.309652	+	0.950850i	$0.399787\pi$
$270$	−15.8213	−0.962853
$271$	4.07158	0.247331	0.123665	−	0.992324i	$-0.460535\pi$
$271$	4.07158	0.247331	0.123665	+	0.992324i	$0.460535\pi$
$272$	−7.11307	−0.431293
$273$	−36.1547	−2.18818
$274$	11.6764	0.705398
$275$	−43.5520	−2.62629
$276$	−12.1974	−0.734197
$277$	23.1976	1.39381	0.696905	−	0.717163i	$-0.254560\pi$
$277$	23.1976	1.39381	0.696905	+	0.717163i	$0.254560\pi$
$278$	−0.382890	−0.0229642
$279$	−7.32372	−0.438460
$280$	12.4196	0.742215
$281$	−3.50191	−0.208907	−0.104453	−	0.994530i	$-0.533309\pi$
$281$	−3.50191	−0.208907	−0.104453	+	0.994530i	$0.533309\pi$
$282$	1.65363	0.0984724
$283$	0.687159	0.0408474	0.0204237	−	0.999791i	$-0.493498\pi$
$283$	0.687159	0.0408474	0.0204237	+	0.999791i	$0.493498\pi$
$284$	−0.743092	−0.0440944
$285$	−9.13227	−0.540949
$286$	−18.6564	−1.10318
$287$	8.58308	0.506643
$288$	−1.26754	−0.0746905
$289$	33.5958	1.97622
$290$	43.4630	2.55223
$291$	−16.6898	−0.978375
$292$	6.76896	0.396123
$293$	−0.0439727	−0.00256891	−0.00128446	−	0.999999i	$-0.500409\pi$
$293$	−0.0439727	−0.00256891	−0.00128446	+	0.999999i	$0.500409\pi$
$294$	1.84458	0.107578
$295$	−47.4924	−2.76511
$296$	1.47032	0.0854604
$297$	−10.7182	−0.621933
$298$	17.5403	1.01608
$299$	−36.7821	−2.12716
$300$	−30.0419	−1.73447
$301$	−14.8617	−0.856617
$302$	3.02278	0.173941
$303$	25.8245	1.48358
$304$	1.00000	0.0573539
$305$	−0.331554	−0.0189847
$306$	9.01610	0.515416
$307$	−3.67747	−0.209884	−0.104942	−	0.994478i	$-0.533466\pi$
$307$	−3.67747	−0.209884	−0.104942	+	0.994478i	$0.533466\pi$
$308$	8.41373	0.479417
$309$	−35.7381	−2.03307
$310$	25.5423	1.45071
$311$	−6.82968	−0.387276	−0.193638	−	0.981073i	$-0.562029\pi$
$311$	−6.82968	−0.387276	−0.193638	+	0.981073i	$0.562029\pi$
$312$	−12.8691	−0.728567
$313$	22.3104	1.26106	0.630530	−	0.776165i	$-0.282838\pi$
$313$	22.3104	1.26106	0.630530	+	0.776165i	$0.282838\pi$
$314$	12.8870	0.727258
$315$	−15.7424	−0.886982
$316$	−3.13679	−0.176458
$317$	6.37463	0.358035	0.179018	−	0.983846i	$-0.442708\pi$
$317$	6.37463	0.358035	0.179018	+	0.983846i	$0.442708\pi$
$318$	−24.1295	−1.35312
$319$	29.4442	1.64856
$320$	4.42069	0.247124
$321$	4.25280	0.237368
$322$	16.5881	0.924419
$323$	−7.11307	−0.395782
$324$	−11.1960	−0.621998
$325$	−90.5933	−5.02521
$326$	18.9641	1.05032
$327$	19.5951	1.08361
$328$	3.05509	0.168689
$329$	−2.24889	−0.123986
$330$	−27.3495	−1.50554
$331$	−14.3025	−0.786137	−0.393068	−	0.919509i	$-0.628586\pi$
$331$	−14.3025	−0.786137	−0.393068	+	0.919509i	$0.628586\pi$
$332$	10.9284	0.599775
$333$	−1.86368	−0.102129
$334$	−17.9963	−0.984714
$335$	−23.7078	−1.29529
$336$	5.80373	0.316620
$337$	8.29814	0.452028	0.226014	−	0.974124i	$-0.427430\pi$
$337$	8.29814	0.452028	0.226014	+	0.974124i	$0.427430\pi$
$338$	−25.8075	−1.40374
$339$	−16.9929	−0.922928
$340$	−31.4447	−1.70533
$341$	17.3038	0.937051
$342$	−1.26754	−0.0685407
$343$	17.1574	0.926415
$344$	−5.28995	−0.285215
$345$	−53.9209	−2.90300
$346$	−20.8415	−1.12045
$347$	11.3694	0.610340	0.305170	−	0.952298i	$-0.401287\pi$
$347$	11.3694	0.610340	0.305170	+	0.952298i	$0.401287\pi$
$348$	20.3104	1.08875
$349$	−22.4739	−1.20300	−0.601499	−	0.798874i	$-0.705430\pi$
$349$	−22.4739	−1.20300	−0.601499	+	0.798874i	$0.705430\pi$
$350$	40.8561	2.18385
$351$	−22.2951	−1.19003
$352$	2.99482	0.159624
$353$	−24.1879	−1.28739	−0.643695	−	0.765282i	$-0.722599\pi$
$353$	−24.1879	−1.28739	−0.643695	+	0.765282i	$0.722599\pi$
$354$	−22.1934	−1.17956
$355$	−3.28498	−0.174349
$356$	12.2467	0.649073
$357$	−41.2824	−2.18489
$358$	−19.5525	−1.03338
$359$	33.2857	1.75675	0.878375	−	0.477972i	$-0.158628\pi$
$359$	33.2857	1.75675	0.878375	+	0.477972i	$0.158628\pi$
$360$	−5.60340	−0.295325
$361$	1.00000	0.0526316
$362$	8.08279	0.424822
$363$	4.19581	0.220223
$364$	17.5015	0.917330
$365$	29.9234	1.56626
$366$	−0.154936	−0.00809866
$367$	13.7063	0.715464	0.357732	−	0.933824i	$-0.383550\pi$
$367$	13.7063	0.715464	0.357732	+	0.933824i	$0.383550\pi$
$368$	5.90443	0.307790
$369$	−3.87245	−0.201592
$370$	6.49981	0.337909
$371$	32.8155	1.70369
$372$	11.9360	0.618853
$373$	−9.68666	−0.501556	−0.250778	−	0.968045i	$-0.580686\pi$
$373$	−9.68666	−0.501556	−0.250778	+	0.968045i	$0.580686\pi$
$374$	−21.3023	−1.10152
$375$	−87.1444	−4.50012
$376$	−0.800480	−0.0412816
$377$	61.2474	3.15440
$378$	10.0547	0.517160
$379$	−12.5029	−0.642232	−0.321116	−	0.947040i	$-0.604058\pi$
$379$	−12.5029	−0.642232	−0.321116	+	0.947040i	$0.604058\pi$
$380$	4.42069	0.226776
$381$	−19.8375	−1.01630
$382$	2.89450	0.148095
$383$	34.5514	1.76549	0.882747	−	0.469849i	$-0.155692\pi$
$383$	34.5514	1.76549	0.882747	+	0.469849i	$0.155692\pi$
$384$	2.06580	0.105420
$385$	37.1945	1.89561
$386$	−17.8104	−0.906528
$387$	6.70522	0.340845
$388$	8.07910	0.410154
$389$	5.62122	0.285007	0.142504	−	0.989794i	$-0.454485\pi$
$389$	5.62122	0.285007	0.142504	+	0.989794i	$0.454485\pi$
$390$	−56.8901	−2.88074
$391$	−41.9986	−2.12396
$392$	−0.892914	−0.0450989
$393$	−11.7438	−0.592399
$394$	27.7506	1.39805
$395$	−13.8668	−0.697712
$396$	−3.79605	−0.190759
$397$	−1.86619	−0.0936616	−0.0468308	−	0.998903i	$-0.514912\pi$
$397$	−1.86619	−0.0936616	−0.0468308	+	0.998903i	$0.514912\pi$
$398$	−15.0811	−0.755947
$399$	5.80373	0.290550
$400$	14.5425	0.727124
$401$	2.91604	0.145620	0.0728100	−	0.997346i	$-0.476803\pi$
$401$	2.91604	0.145620	0.0728100	+	0.997346i	$0.476803\pi$
$402$	−11.0787	−0.552556
$403$	35.9938	1.79298
$404$	−12.5009	−0.621945
$405$	−49.4938	−2.45937
$406$	−27.6216	−1.37084
$407$	4.40333	0.218265
$408$	−14.6942	−0.727471
$409$	−21.8874	−1.08226	−0.541130	−	0.840939i	$-0.682003\pi$
$409$	−21.8874	−1.08226	−0.541130	+	0.840939i	$0.682003\pi$
$410$	13.5056	0.666994
$411$	24.1212	1.18981
$412$	17.2999	0.852303
$413$	30.1823	1.48518
$414$	−7.48411	−0.367824
$415$	48.3111	2.37150
$416$	6.22957	0.305430
$417$	−0.790975	−0.0387342
$418$	2.99482	0.146481
$419$	−36.4874	−1.78253	−0.891264	−	0.453485i	$-0.850180\pi$
$419$	−36.4874	−1.78253	−0.891264	+	0.453485i	$0.850180\pi$
$420$	25.6565	1.25191
$421$	9.54776	0.465330	0.232665	−	0.972557i	$-0.425256\pi$
$421$	9.54776	0.465330	0.232665	+	0.972557i	$0.425256\pi$
$422$	1.00000	0.0486792
$423$	1.01464	0.0493335
$424$	11.6805	0.567253
$425$	−103.442	−5.01766
$426$	−1.53508	−0.0743750
$427$	0.210709	0.0101969
$428$	−2.05867	−0.0995094
$429$	−38.5404	−1.86075
$430$	−23.3852	−1.12773
$431$	24.0497	1.15843	0.579217	−	0.815173i	$-0.303358\pi$
$431$	24.0497	1.15843	0.579217	+	0.815173i	$0.303358\pi$
$432$	3.57892	0.172191
$433$	25.7203	1.23604	0.618019	−	0.786164i	$-0.287936\pi$
$433$	25.7203	1.23604	0.618019	+	0.786164i	$0.287936\pi$
$434$	−16.2326	−0.779191
$435$	89.7859	4.30491
$436$	−9.48547	−0.454272
$437$	5.90443	0.282447
$438$	13.9833	0.668149
$439$	−39.3535	−1.87824	−0.939120	−	0.343589i	$-0.888357\pi$
$439$	−39.3535	−1.87824	−0.939120	+	0.343589i	$0.888357\pi$
$440$	13.2391	0.631151
$441$	1.13180	0.0538954
$442$	−44.3113	−2.10768
$443$	−7.83612	−0.372305	−0.186153	−	0.982521i	$-0.559602\pi$
$443$	−7.83612	−0.372305	−0.186153	+	0.982521i	$0.559602\pi$
$444$	3.03738	0.144148
$445$	54.1388	2.56642
$446$	28.1859	1.33464
$447$	36.2348	1.71385
$448$	−2.80943	−0.132733
$449$	−28.9861	−1.36794	−0.683970	−	0.729510i	$-0.739748\pi$
$449$	−28.9861	−1.36794	−0.683970	+	0.729510i	$0.739748\pi$
$450$	−18.4332	−0.868948
$451$	9.14944	0.430830
$452$	8.22581	0.386910
$453$	6.24447	0.293391
$454$	11.1123	0.521524
$455$	77.3689	3.62711
$456$	2.06580	0.0967401
$457$	20.4124	0.954854	0.477427	−	0.878671i	$-0.341570\pi$
$457$	20.4124	0.954854	0.477427	+	0.878671i	$0.341570\pi$
$458$	−27.2900	−1.27518
$459$	−25.4571	−1.18824
$460$	26.1017	1.21700
$461$	9.29921	0.433107	0.216554	−	0.976271i	$-0.430518\pi$
$461$	9.29921	0.433107	0.216554	+	0.976271i	$0.430518\pi$
$462$	17.3811	0.808643
$463$	−1.46590	−0.0681261	−0.0340630	−	0.999420i	$-0.510845\pi$
$463$	−1.46590	−0.0681261	−0.0340630	+	0.999420i	$0.510845\pi$
$464$	−9.83172	−0.456426
$465$	52.7654	2.44693
$466$	3.37265	0.156235
$467$	−17.8383	−0.825460	−0.412730	−	0.910853i	$-0.635425\pi$
$467$	−17.8383	−0.825460	−0.412730	+	0.910853i	$0.635425\pi$
$468$	−7.89623	−0.365003
$469$	15.0667	0.695718
$470$	−3.53867	−0.163227
$471$	26.6221	1.22668
$472$	10.7432	0.494497
$473$	−15.8424	−0.728435
$474$	−6.47998	−0.297635
$475$	14.5425	0.667254
$476$	19.9837	0.915951
$477$	−14.8054	−0.677895
$478$	9.16352	0.419130
$479$	11.0384	0.504356	0.252178	−	0.967681i	$-0.418853\pi$
$479$	11.0384	0.504356	0.252178	+	0.967681i	$0.418853\pi$
$480$	9.13227	0.416829
$481$	9.15943	0.417634
$482$	23.1567	1.05476
$483$	34.2678	1.55924
$484$	−2.03108	−0.0923217
$485$	35.7152	1.62174
$486$	−12.3919	−0.562107
$487$	31.6453	1.43398	0.716992	−	0.697081i	$-0.245518\pi$
$487$	31.6453	1.43398	0.716992	+	0.697081i	$0.245518\pi$
$488$	0.0750006	0.00339512
$489$	39.1760	1.77160
$490$	−3.94729	−0.178320
$491$	−15.9688	−0.720662	−0.360331	−	0.932825i	$-0.617336\pi$
$491$	−15.9688	−0.720662	−0.360331	+	0.932825i	$0.617336\pi$
$492$	6.31122	0.284532
$493$	69.9337	3.14966
$494$	6.22957	0.280281
$495$	−16.7811	−0.754256
$496$	−5.77790	−0.259436
$497$	2.08767	0.0936447
$498$	22.5759	1.01165
$499$	26.6651	1.19369	0.596846	−	0.802356i	$-0.296420\pi$
$499$	26.6651	1.19369	0.596846	+	0.802356i	$0.296420\pi$
$500$	42.1843	1.88654
$501$	−37.1768	−1.66094
$502$	−28.9951	−1.29412
$503$	1.54497	0.0688869	0.0344434	−	0.999407i	$-0.489034\pi$
$503$	1.54497	0.0688869	0.0344434	+	0.999407i	$0.489034\pi$
$504$	3.56107	0.158623
$505$	−55.2627	−2.45916
$506$	17.6827	0.786092
$507$	−53.3132	−2.36772
$508$	9.60279	0.426055
$509$	13.9287	0.617380	0.308690	−	0.951163i	$-0.400109\pi$
$509$	13.9287	0.617380	0.308690	+	0.951163i	$0.400109\pi$
$510$	−64.9584	−2.87641
$511$	−19.0169	−0.841259
$512$	−1.00000	−0.0441942
$513$	3.57892	0.158013
$514$	−16.5764	−0.731153
$515$	76.4773	3.36999
$516$	−10.9280	−0.481078
$517$	−2.39729	−0.105433
$518$	−4.13075	−0.181495
$519$	−43.0545	−1.88988
$520$	27.5390	1.20766
$521$	−17.0116	−0.745290	−0.372645	−	0.927974i	$-0.621549\pi$
$521$	−17.0116	−0.745290	−0.372645	+	0.927974i	$0.621549\pi$
$522$	12.4621	0.545452
$523$	−15.6969	−0.686377	−0.343189	−	0.939267i	$-0.611507\pi$
$523$	−15.6969	−0.686377	−0.343189	+	0.939267i	$0.611507\pi$
$524$	5.68488	0.248345
$525$	84.4007	3.68355
$526$	−9.71752	−0.423704
$527$	41.0986	1.79028
$528$	6.18670	0.269241
$529$	11.8623	0.515754
$530$	51.6356	2.24291
$531$	−13.6175	−0.590947
$532$	−2.80943	−0.121804
$533$	19.0319	0.824363
$534$	25.2992	1.09481
$535$	−9.10072	−0.393459
$536$	5.36291	0.231643
$537$	−40.3916	−1.74303
$538$	−10.1573	−0.437914
$539$	−2.67411	−0.115182
$540$	15.8213	0.680840
$541$	−8.84667	−0.380348	−0.190174	−	0.981750i	$-0.560905\pi$
$541$	−8.84667	−0.380348	−0.190174	+	0.981750i	$0.560905\pi$
$542$	−4.07158	−0.174889
$543$	16.6974	0.716556
$544$	7.11307	0.304970
$545$	−41.9323	−1.79618
$546$	36.1547	1.54728
$547$	−34.1498	−1.46014	−0.730071	−	0.683372i	$-0.760513\pi$
$547$	−34.1498	−1.46014	−0.730071	+	0.683372i	$0.760513\pi$
$548$	−11.6764	−0.498791
$549$	−0.0950663	−0.00405733
$550$	43.5520	1.85706
$551$	−9.83172	−0.418846
$552$	12.1974	0.519156
$553$	8.81259	0.374749
$554$	−23.1976	−0.985573
$555$	13.4273	0.569958
$556$	0.382890	0.0162382
$557$	−12.4370	−0.526972	−0.263486	−	0.964663i	$-0.584872\pi$
$557$	−12.4370	−0.526972	−0.263486	+	0.964663i	$0.584872\pi$
$558$	7.32372	0.310038
$559$	−32.9541	−1.39381
$560$	−12.4196	−0.524825
$561$	−44.0064	−1.85795
$562$	3.50191	0.147719
$563$	6.39726	0.269612	0.134806	−	0.990872i	$-0.456959\pi$
$563$	6.39726	0.269612	0.134806	+	0.990872i	$0.456959\pi$
$564$	−1.65363	−0.0696305
$565$	36.3637	1.52983
$566$	−0.687159	−0.0288834
$567$	31.4543	1.32096
$568$	0.743092	0.0311795
$569$	−11.5041	−0.482276	−0.241138	−	0.970491i	$-0.577521\pi$
$569$	−11.5041	−0.482276	−0.241138	+	0.970491i	$0.577521\pi$
$570$	9.13227	0.382509
$571$	18.0200	0.754115	0.377057	−	0.926190i	$-0.376936\pi$
$571$	18.0200	0.754115	0.377057	+	0.926190i	$0.376936\pi$
$572$	18.6564	0.780063
$573$	5.97946	0.249795
$574$	−8.58308	−0.358251
$575$	85.8651	3.58082
$576$	1.26754	0.0528142
$577$	7.19748	0.299635	0.149817	−	0.988714i	$-0.452131\pi$
$577$	7.19748	0.299635	0.149817	+	0.988714i	$0.452131\pi$
$578$	−33.5958	−1.39740
$579$	−36.7929	−1.52906
$580$	−43.4630	−1.80470
$581$	−30.7026	−1.27376
$582$	16.6898	0.691815
$583$	34.9808	1.44876
$584$	−6.76896	−0.280101
$585$	−34.9067	−1.44322
$586$	0.0439727	0.00181650
$587$	5.82462	0.240408	0.120204	−	0.992749i	$-0.461645\pi$
$587$	5.82462	0.240408	0.120204	+	0.992749i	$0.461645\pi$
$588$	−1.84458	−0.0760693
$589$	−5.77790	−0.238074
$590$	47.4924	1.95523
$591$	57.3272	2.35812
$592$	−1.47032	−0.0604296
$593$	41.9142	1.72121	0.860606	−	0.509272i	$-0.170085\pi$
$593$	41.9142	1.72121	0.860606	+	0.509272i	$0.170085\pi$
$594$	10.7182	0.439773
$595$	88.3417	3.62165
$596$	−17.5403	−0.718479
$597$	−31.1546	−1.27507
$598$	36.7821	1.50413
$599$	13.6133	0.556224	0.278112	−	0.960549i	$-0.410291\pi$
$599$	13.6133	0.556224	0.278112	+	0.960549i	$0.410291\pi$
$600$	30.0419	1.22645
$601$	−16.9930	−0.693159	−0.346579	−	0.938021i	$-0.612657\pi$
$601$	−16.9930	−0.693159	−0.346579	+	0.938021i	$0.612657\pi$
$602$	14.8617	0.605720
$603$	−6.79771	−0.276824
$604$	−3.02278	−0.122995
$605$	−8.97876	−0.365039
$606$	−25.8245	−1.04905
$607$	−16.2606	−0.659998	−0.329999	−	0.943981i	$-0.607048\pi$
$607$	−16.2606	−0.659998	−0.329999	+	0.943981i	$0.607048\pi$
$608$	−1.00000	−0.0405554
$609$	−57.0607	−2.31222
$610$	0.331554	0.0134242
$611$	−4.98664	−0.201738
$612$	−9.01610	−0.364454
$613$	1.73001	0.0698743	0.0349372	−	0.999390i	$-0.488877\pi$
$613$	1.73001	0.0698743	0.0349372	+	0.999390i	$0.488877\pi$
$614$	3.67747	0.148410
$615$	27.8999	1.12503
$616$	−8.41373	−0.338999
$617$	−21.5864	−0.869037	−0.434519	−	0.900663i	$-0.643081\pi$
$617$	−21.5864	−0.869037	−0.434519	+	0.900663i	$0.643081\pi$
$618$	35.7381	1.43760
$619$	6.35215	0.255314	0.127657	−	0.991818i	$-0.459254\pi$
$619$	6.35215	0.255314	0.127657	+	0.991818i	$0.459254\pi$
$620$	−25.5423	−1.02580
$621$	21.1315	0.847978
$622$	6.82968	0.273845
$623$	−34.4062	−1.37846
$624$	12.8691	0.515174
$625$	113.771	4.55085
$626$	−22.3104	−0.891704
$627$	6.18670	0.247073
$628$	−12.8870	−0.514249
$629$	10.4585	0.417006
$630$	15.7424	0.627191
$631$	−29.0008	−1.15450	−0.577252	−	0.816566i	$-0.695875\pi$
$631$	−29.0008	−1.15450	−0.577252	+	0.816566i	$0.695875\pi$
$632$	3.13679	0.124775
$633$	2.06580	0.0821083
$634$	−6.37463	−0.253169
$635$	42.4509	1.68461
$636$	24.1295	0.956798
$637$	−5.56246	−0.220393
$638$	−29.4442	−1.16571
$639$	−0.941900	−0.0372610
$640$	−4.42069	−0.174743
$641$	−38.4964	−1.52052	−0.760258	−	0.649621i	$-0.774928\pi$
$641$	−38.4964	−1.52052	−0.760258	+	0.649621i	$0.774928\pi$
$642$	−4.25280	−0.167845
$643$	−2.65218	−0.104592	−0.0522959	−	0.998632i	$-0.516654\pi$
$643$	−2.65218	−0.104592	−0.0522959	+	0.998632i	$0.516654\pi$
$644$	−16.5881	−0.653663
$645$	−48.3092	−1.90217
$646$	7.11307	0.279860
$647$	8.46850	0.332931	0.166466	−	0.986047i	$-0.446765\pi$
$647$	8.46850	0.332931	0.166466	+	0.986047i	$0.446765\pi$
$648$	11.1960	0.439819
$649$	32.1740	1.26294
$650$	90.5933	3.55336
$651$	−33.5334	−1.31428
$652$	−18.9641	−0.742690
$653$	41.9383	1.64117	0.820586	−	0.571523i	$-0.193647\pi$
$653$	41.9383	1.64117	0.820586	+	0.571523i	$0.193647\pi$
$654$	−19.5951	−0.766230
$655$	25.1311	0.981953
$656$	−3.05509	−0.119281
$657$	8.57992	0.334735
$658$	2.24889	0.0876710
$659$	15.4355	0.601283	0.300641	−	0.953737i	$-0.402799\pi$
$659$	15.4355	0.601283	0.300641	+	0.953737i	$0.402799\pi$
$660$	27.3495	1.06458
$661$	24.8678	0.967246	0.483623	−	0.875276i	$-0.339321\pi$
$661$	24.8678	0.967246	0.483623	+	0.875276i	$0.339321\pi$
$662$	14.3025	0.555883
$663$	−91.5385	−3.55506
$664$	−10.9284	−0.424105
$665$	−12.4196	−0.481612
$666$	1.86368	0.0722163
$667$	−58.0508	−2.24773
$668$	17.9963	0.696298
$669$	58.2266	2.25117
$670$	23.7078	0.915911
$671$	0.224613	0.00867109
$672$	−5.80373	−0.223884
$673$	9.48454	0.365602	0.182801	−	0.983150i	$-0.441484\pi$
$673$	9.48454	0.365602	0.182801	+	0.983150i	$0.441484\pi$
$674$	−8.29814	−0.319632
$675$	52.0464	2.00326
$676$	25.8075	0.992596
$677$	−15.7370	−0.604820	−0.302410	−	0.953178i	$-0.597791\pi$
$677$	−15.7370	−0.604820	−0.302410	+	0.953178i	$0.597791\pi$
$678$	16.9929	0.652608
$679$	−22.6977	−0.871057
$680$	31.4447	1.20585
$681$	22.9557	0.879666
$682$	−17.3038	−0.662595
$683$	−48.5904	−1.85926	−0.929629	−	0.368496i	$-0.879873\pi$
$683$	−48.5904	−1.85926	−0.929629	+	0.368496i	$0.879873\pi$
$684$	1.26754	0.0484656
$685$	−51.6177	−1.97221
$686$	−17.1574	−0.655074
$687$	−56.3758	−2.15087
$688$	5.28995	0.201677
$689$	72.7642	2.77209
$690$	53.9209	2.05273
$691$	−11.4589	−0.435916	−0.217958	−	0.975958i	$-0.569940\pi$
$691$	−11.4589	−0.435916	−0.217958	+	0.975958i	$0.569940\pi$
$692$	20.8415	0.792277
$693$	10.6647	0.405120
$694$	−11.3694	−0.431576
$695$	1.69264	0.0642054
$696$	−20.3104	−0.769864
$697$	21.7311	0.823123
$698$	22.4739	0.850648
$699$	6.96724	0.263525
$700$	−40.8561	−1.54422
$701$	−3.53726	−0.133601	−0.0668003	−	0.997766i	$-0.521279\pi$
$701$	−3.53726	−0.133601	−0.0668003	+	0.997766i	$0.521279\pi$
$702$	22.2951	0.841475
$703$	−1.47032	−0.0554540
$704$	−2.99482	−0.112871
$705$	−7.31019	−0.275318
$706$	24.1879	0.910322
$707$	35.1206	1.32084
$708$	22.1934	0.834078
$709$	13.0978	0.491897	0.245949	−	0.969283i	$-0.420901\pi$
$709$	13.0978	0.491897	0.245949	+	0.969283i	$0.420901\pi$
$710$	3.28498	0.123283
$711$	−3.97600	−0.149112
$712$	−12.2467	−0.458964
$713$	−34.1152	−1.27763
$714$	41.2824	1.54495
$715$	82.4741	3.08436
$716$	19.5525	0.730712
$717$	18.9300	0.706955
$718$	−33.2857	−1.24221
$719$	−19.5189	−0.727931	−0.363965	−	0.931412i	$-0.618577\pi$
$719$	−19.5189	−0.727931	−0.363965	+	0.931412i	$0.618577\pi$
$720$	5.60340	0.208826
$721$	−48.6028	−1.81006
$722$	−1.00000	−0.0372161
$723$	47.8371	1.77908
$724$	−8.08279	−0.300395
$725$	−142.978	−5.31005
$726$	−4.19581	−0.155721
$727$	−8.33362	−0.309077	−0.154539	−	0.987987i	$-0.549389\pi$
$727$	−8.33362	−0.309077	−0.154539	+	0.987987i	$0.549389\pi$
$728$	−17.5015	−0.648651
$729$	7.98869	0.295878
$730$	−29.9234	−1.10752
$731$	−37.6277	−1.39171
$732$	0.154936	0.00572662
$733$	13.0894	0.483469	0.241734	−	0.970342i	$-0.422284\pi$
$733$	13.0894	0.483469	0.241734	+	0.970342i	$0.422284\pi$
$734$	−13.7063	−0.505909
$735$	−8.15433	−0.300777
$736$	−5.90443	−0.217640
$737$	16.0609	0.591612
$738$	3.87245	0.142547
$739$	−26.0861	−0.959592	−0.479796	−	0.877380i	$-0.659289\pi$
$739$	−26.0861	−0.959592	−0.479796	+	0.877380i	$0.659289\pi$
$740$	−6.49981	−0.238938
$741$	12.8691	0.472756
$742$	−32.8155	−1.20469
$743$	2.06650	0.0758127	0.0379063	−	0.999281i	$-0.487931\pi$
$743$	2.06650	0.0758127	0.0379063	+	0.999281i	$0.487931\pi$
$744$	−11.9360	−0.437595
$745$	−77.5403	−2.84086
$746$	9.68666	0.354654
$747$	13.8522	0.506826
$748$	21.3023	0.778890
$749$	5.78369	0.211331
$750$	87.1444	3.18206
$751$	6.93696	0.253133	0.126567	−	0.991958i	$-0.459604\pi$
$751$	6.93696	0.253133	0.126567	+	0.991958i	$0.459604\pi$
$752$	0.800480	0.0291905
$753$	−59.8982	−2.18281
$754$	−61.2474	−2.23050
$755$	−13.3628	−0.486321
$756$	−10.0547	−0.365687
$757$	33.9622	1.23438	0.617189	−	0.786815i	$-0.288272\pi$
$757$	33.9622	1.23438	0.617189	+	0.786815i	$0.288272\pi$
$758$	12.5029	0.454127
$759$	36.5289	1.32592
$760$	−4.42069	−0.160355
$761$	24.9625	0.904891	0.452445	−	0.891792i	$-0.350552\pi$
$761$	24.9625	0.904891	0.452445	+	0.891792i	$0.350552\pi$
$762$	19.8375	0.718636
$763$	26.6488	0.964752
$764$	−2.89450	−0.104719
$765$	−39.8574	−1.44105
$766$	−34.5514	−1.24839
$767$	66.9256	2.41654
$768$	−2.06580	−0.0745432
$769$	−47.1555	−1.70047	−0.850235	−	0.526404i	$-0.823540\pi$
$769$	−47.1555	−1.70047	−0.850235	+	0.526404i	$0.823540\pi$
$770$	−37.1945	−1.34040
$771$	−34.2435	−1.23325
$772$	17.8104	0.641012
$773$	−35.5839	−1.27986	−0.639931	−	0.768432i	$-0.721037\pi$
$773$	−35.5839	−1.27986	−0.639931	+	0.768432i	$0.721037\pi$
$774$	−6.70522	−0.241014
$775$	−84.0250	−3.01827
$776$	−8.07910	−0.290023
$777$	−8.53332	−0.306131
$778$	−5.62122	−0.201530
$779$	−3.05509	−0.109460
$780$	56.8901	2.03699
$781$	2.22542	0.0796320
$782$	41.9986	1.50187
$783$	−35.1870	−1.25748
$784$	0.892914	0.0318898
$785$	−56.9696	−2.03333
$786$	11.7438	0.418889
$787$	42.5807	1.51784	0.758919	−	0.651185i	$-0.225728\pi$
$787$	42.5807	1.51784	0.758919	+	0.651185i	$0.225728\pi$
$788$	−27.7506	−0.988573
$789$	−20.0745	−0.714670
$790$	13.8668	0.493357
$791$	−23.1099	−0.821692
$792$	3.79605	0.134887
$793$	0.467221	0.0165915
$794$	1.86619	0.0662288
$795$	106.669	3.78316
$796$	15.0811	0.534535
$797$	−22.8260	−0.808538	−0.404269	−	0.914640i	$-0.632474\pi$
$797$	−22.8260	−0.808538	−0.404269	+	0.914640i	$0.632474\pi$
$798$	−5.80373	−0.205450
$799$	−5.69387	−0.201435
$800$	−14.5425	−0.514154
$801$	15.5232	0.548484
$802$	−2.91604	−0.102969
$803$	−20.2718	−0.715376
$804$	11.0787	0.390716
$805$	−73.3308	−2.58457
$806$	−35.9938	−1.26783
$807$	−20.9831	−0.738639
$808$	12.5009	0.439782
$809$	−8.25173	−0.290116	−0.145058	−	0.989423i	$-0.546337\pi$
$809$	−8.25173	−0.290116	−0.145058	+	0.989423i	$0.546337\pi$
$810$	49.4938	1.73904
$811$	3.46922	0.121821	0.0609104	−	0.998143i	$-0.480600\pi$
$811$	3.46922	0.121821	0.0609104	+	0.998143i	$0.480600\pi$
$812$	27.6216	0.969327
$813$	−8.41108	−0.294989
$814$	−4.40333	−0.154336
$815$	−83.8341	−2.93658
$816$	14.6942	0.514400
$817$	5.28995	0.185072
$818$	21.8874	0.765274
$819$	22.1839	0.775169
$820$	−13.5056	−0.471636
$821$	14.4251	0.503439	0.251720	−	0.967800i	$-0.419004\pi$
$821$	14.4251	0.503439	0.251720	+	0.967800i	$0.419004\pi$
$822$	−24.1212	−0.841322
$823$	−12.8692	−0.448592	−0.224296	−	0.974521i	$-0.572008\pi$
$823$	−12.8692	−0.448592	−0.224296	+	0.974521i	$0.572008\pi$
$824$	−17.2999	−0.602669
$825$	89.9699	3.13235
$826$	−30.1823	−1.05018
$827$	40.0027	1.39103	0.695514	−	0.718512i	$-0.255177\pi$
$827$	40.0027	1.39103	0.695514	+	0.718512i	$0.255177\pi$
$828$	7.48411	0.260091
$829$	44.8202	1.55667	0.778335	−	0.627850i	$-0.216065\pi$
$829$	44.8202	1.55667	0.778335	+	0.627850i	$0.216065\pi$
$830$	−48.3111	−1.67690
$831$	−47.9217	−1.66239
$832$	−6.22957	−0.215971
$833$	−6.35136	−0.220061
$834$	0.790975	0.0273892
$835$	79.5561	2.75315
$836$	−2.99482	−0.103578
$837$	−20.6787	−0.714759
$838$	36.4874	1.26044
$839$	−52.7321	−1.82052	−0.910258	−	0.414042i	$-0.864117\pi$
$839$	−52.7321	−1.82052	−0.910258	+	0.414042i	$0.864117\pi$
$840$	−25.6565	−0.885233
$841$	67.6628	2.33320
$842$	−9.54776	−0.329038
$843$	7.23426	0.249161
$844$	−1.00000	−0.0344214
$845$	114.087	3.92471
$846$	−1.01464	−0.0348840
$847$	5.70618	0.196067
$848$	−11.6805	−0.401109
$849$	−1.41953	−0.0487183
$850$	103.442	3.54802
$851$	−8.68138	−0.297594
$852$	1.53508	0.0525911
$853$	12.8468	0.439867	0.219934	−	0.975515i	$-0.429416\pi$
$853$	12.8468	0.439867	0.219934	+	0.975515i	$0.429416\pi$
$854$	−0.210709	−0.00721032
$855$	5.60340	0.191632
$856$	2.05867	0.0703638
$857$	−30.8498	−1.05381	−0.526904	−	0.849925i	$-0.676647\pi$
$857$	−30.8498	−1.05381	−0.526904	+	0.849925i	$0.676647\pi$
$858$	38.5404	1.31575
$859$	41.1487	1.40397	0.701987	−	0.712189i	$-0.252296\pi$
$859$	41.1487	1.40397	0.701987	+	0.712189i	$0.252296\pi$
$860$	23.3852	0.797428
$861$	−17.7309	−0.604269
$862$	−24.0497	−0.819136
$863$	23.6379	0.804645	0.402322	−	0.915498i	$-0.368203\pi$
$863$	23.6379	0.804645	0.402322	+	0.915498i	$0.368203\pi$
$864$	−3.57892	−0.121757
$865$	92.1339	3.13265
$866$	−25.7203	−0.874010
$867$	−69.4022	−2.35702
$868$	16.2326	0.550971
$869$	9.39410	0.318673
$870$	−89.7859	−3.04403
$871$	33.4086	1.13201
$872$	9.48547	0.321219
$873$	10.2406	0.346591
$874$	−5.90443	−0.199720
$875$	−118.514	−4.00650
$876$	−13.9833	−0.472453
$877$	−7.92482	−0.267602	−0.133801	−	0.991008i	$-0.542718\pi$
$877$	−7.92482	−0.267602	−0.133801	+	0.991008i	$0.542718\pi$
$878$	39.3535	1.32812
$879$	0.0908389	0.00306392
$880$	−13.2391	−0.446291
$881$	23.5649	0.793920	0.396960	−	0.917836i	$-0.370065\pi$
$881$	23.5649	0.793920	0.396960	+	0.917836i	$0.370065\pi$
$882$	−1.13180	−0.0381098
$883$	−15.5916	−0.524700	−0.262350	−	0.964973i	$-0.584497\pi$
$883$	−15.5916	−0.524700	−0.262350	+	0.964973i	$0.584497\pi$
$884$	44.3113	1.49035
$885$	98.1099	3.29793
$886$	7.83612	0.263260
$887$	6.72571	0.225827	0.112914	−	0.993605i	$-0.463982\pi$
$887$	6.72571	0.225827	0.112914	+	0.993605i	$0.463982\pi$
$888$	−3.03738	−0.101928
$889$	−26.9784	−0.904827
$890$	−54.1388	−1.81474
$891$	33.5298	1.12329
$892$	−28.1859	−0.943735
$893$	0.800480	0.0267870
$894$	−36.2348	−1.21187
$895$	86.4355	2.88922
$896$	2.80943	0.0938566
$897$	75.9845	2.53705
$898$	28.9861	0.967280
$899$	56.8068	1.89461
$900$	18.4332	0.614439
$901$	83.0839	2.76793
$902$	−9.14944	−0.304643
$903$	30.7014	1.02168
$904$	−8.22581	−0.273586
$905$	−35.7315	−1.18775
$906$	−6.24447	−0.207458
$907$	6.25551	0.207711	0.103855	−	0.994592i	$-0.466882\pi$
$907$	6.25551	0.207711	0.103855	+	0.994592i	$0.466882\pi$
$908$	−11.1123	−0.368773
$909$	−15.8454	−0.525560
$910$	−77.3689	−2.56475
$911$	31.7553	1.05210	0.526049	−	0.850454i	$-0.323673\pi$
$911$	31.7553	1.05210	0.526049	+	0.850454i	$0.323673\pi$
$912$	−2.06580	−0.0684056
$913$	−32.7286	−1.08316
$914$	−20.4124	−0.675184
$915$	0.684926	0.0226429
$916$	27.2900	0.901687
$917$	−15.9713	−0.527419
$918$	25.4571	0.840210
$919$	45.1762	1.49022	0.745112	−	0.666939i	$-0.232396\pi$
$919$	45.1762	1.49022	0.745112	+	0.666939i	$0.232396\pi$
$920$	−26.1017	−0.860546
$921$	7.59692	0.250327
$922$	−9.29921	−0.306253
$923$	4.62914	0.152370
$924$	−17.3811	−0.571797
$925$	−21.3820	−0.703037
$926$	1.46590	0.0481724
$927$	21.9283	0.720219
$928$	9.83172	0.322742
$929$	−18.3820	−0.603094	−0.301547	−	0.953451i	$-0.597503\pi$
$929$	−18.3820	−0.603094	−0.301547	+	0.953451i	$0.597503\pi$
$930$	−52.7654	−1.73024
$931$	0.892914	0.0292641
$932$	−3.37265	−0.110475
$933$	14.1088	0.461900
$934$	17.8383	0.583688
$935$	94.1709	3.07972
$936$	7.89623	0.258096
$937$	18.4700	0.603390	0.301695	−	0.953404i	$-0.402448\pi$
$937$	18.4700	0.603390	0.301695	+	0.953404i	$0.402448\pi$
$938$	−15.0667	−0.491947
$939$	−46.0889	−1.50406
$940$	3.53867	0.115419
$941$	33.0789	1.07834	0.539171	−	0.842196i	$-0.318738\pi$
$941$	33.0789	1.07834	0.539171	+	0.842196i	$0.318738\pi$
$942$	−26.6221	−0.867395
$943$	−18.0386	−0.587417
$944$	−10.7432	−0.349662
$945$	−44.4488	−1.44592
$946$	15.8424	0.515081
$947$	−23.8401	−0.774700	−0.387350	−	0.921933i	$-0.626610\pi$
$947$	−23.8401	−0.774700	−0.387350	+	0.921933i	$0.626610\pi$
$948$	6.47998	0.210460
$949$	−42.1677	−1.36882
$950$	−14.5425	−0.471820
$951$	−13.1687	−0.427025
$952$	−19.9837	−0.647675
$953$	21.7252	0.703749	0.351874	−	0.936047i	$-0.385544\pi$
$953$	21.7252	0.703749	0.351874	+	0.936047i	$0.385544\pi$
$954$	14.8054	0.479344
$955$	−12.7957	−0.414058
$956$	−9.16352	−0.296369
$957$	−60.8259	−1.96622
$958$	−11.0384	−0.356634
$959$	32.8041	1.05930
$960$	−9.13227	−0.294743
$961$	2.38416	0.0769085
$962$	−9.15943	−0.295312
$963$	−2.60944	−0.0840881
$964$	−23.1567	−0.745826
$965$	78.7344	2.53455
$966$	−34.2678	−1.10255
$967$	60.8730	1.95754	0.978771	−	0.204956i	$-0.0657051\pi$
$967$	60.8730	1.95754	0.978771	+	0.204956i	$0.0657051\pi$
$968$	2.03108	0.0652813
$969$	14.6942	0.472046
$970$	−35.7152	−1.14674
$971$	20.0956	0.644899	0.322450	−	0.946587i	$-0.395494\pi$
$971$	20.0956	0.644899	0.322450	+	0.946587i	$0.395494\pi$
$972$	12.3919	0.397470
$973$	−1.07570	−0.0344855
$974$	−31.6453	−1.01398
$975$	187.148	5.99353
$976$	−0.0750006	−0.00240071
$977$	−2.36121	−0.0755417	−0.0377709	−	0.999286i	$-0.512026\pi$
$977$	−2.36121	−0.0755417	−0.0377709	+	0.999286i	$0.512026\pi$
$978$	−39.1760	−1.25271
$979$	−36.6766	−1.17219
$980$	3.94729	0.126092
$981$	−12.0232	−0.383872
$982$	15.9688	0.509585
$983$	−14.1864	−0.452476	−0.226238	−	0.974072i	$-0.572643\pi$
$983$	−14.1864	−0.452476	−0.226238	+	0.974072i	$0.572643\pi$
$984$	−6.31122	−0.201194
$985$	−122.677	−3.90880
$986$	−69.9337	−2.22714
$987$	4.64577	0.147877
$988$	−6.22957	−0.198189
$989$	31.2341	0.993188
$990$	16.7811	0.533340
$991$	8.51600	0.270520	0.135260	−	0.990810i	$-0.456813\pi$
$991$	8.51600	0.270520	0.135260	+	0.990810i	$0.456813\pi$
$992$	5.77790	0.183449
$993$	29.5462	0.937619
$994$	−2.08767	−0.0662168
$995$	66.6688	2.11354
$996$	−22.5759	−0.715346
$997$	28.2844	0.895775	0.447888	−	0.894090i	$-0.352176\pi$
$997$	28.2844	0.895775	0.447888	+	0.894090i	$0.352176\pi$
$998$	−26.6651	−0.844068
$999$	−5.26214	−0.166487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.i.1.10	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.i.1.10	✓	43	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.06580 q^{3} +1.00000 q^{4} +4.42069 q^{5} +2.06580 q^{6} -2.80943 q^{7} -1.00000 q^{8} +1.26754 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.06580 q^{3} +1.00000 q^{4} +4.42069 q^{5} +2.06580 q^{6} -2.80943 q^{7} -1.00000 q^{8} +1.26754 q^{9} -4.42069 q^{10} -2.99482 q^{11} -2.06580 q^{12} -6.22957 q^{13} +2.80943 q^{14} -9.13227 q^{15} +1.00000 q^{16} -7.11307 q^{17} -1.26754 q^{18} +1.00000 q^{19} +4.42069 q^{20} +5.80373 q^{21} +2.99482 q^{22} +5.90443 q^{23} +2.06580 q^{24} +14.5425 q^{25} +6.22957 q^{26} +3.57892 q^{27} -2.80943 q^{28} -9.83172 q^{29} +9.13227 q^{30} -5.77790 q^{31} -1.00000 q^{32} +6.18670 q^{33} +7.11307 q^{34} -12.4196 q^{35} +1.26754 q^{36} -1.47032 q^{37} -1.00000 q^{38} +12.8691 q^{39} -4.42069 q^{40} -3.05509 q^{41} -5.80373 q^{42} +5.28995 q^{43} -2.99482 q^{44} +5.60340 q^{45} -5.90443 q^{46} +0.800480 q^{47} -2.06580 q^{48} +0.892914 q^{49} -14.5425 q^{50} +14.6942 q^{51} -6.22957 q^{52} -11.6805 q^{53} -3.57892 q^{54} -13.2391 q^{55} +2.80943 q^{56} -2.06580 q^{57} +9.83172 q^{58} -10.7432 q^{59} -9.13227 q^{60} -0.0750006 q^{61} +5.77790 q^{62} -3.56107 q^{63} +1.00000 q^{64} -27.5390 q^{65} -6.18670 q^{66} -5.36291 q^{67} -7.11307 q^{68} -12.1974 q^{69} +12.4196 q^{70} -0.743092 q^{71} -1.26754 q^{72} +6.76896 q^{73} +1.47032 q^{74} -30.0419 q^{75} +1.00000 q^{76} +8.41373 q^{77} -12.8691 q^{78} -3.13679 q^{79} +4.42069 q^{80} -11.1960 q^{81} +3.05509 q^{82} +10.9284 q^{83} +5.80373 q^{84} -31.4447 q^{85} -5.28995 q^{86} +20.3104 q^{87} +2.99482 q^{88} +12.2467 q^{89} -5.60340 q^{90} +17.5015 q^{91} +5.90443 q^{92} +11.9360 q^{93} -0.800480 q^{94} +4.42069 q^{95} +2.06580 q^{96} +8.07910 q^{97} -0.892914 q^{98} -3.79605 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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