LMFDB - Embedded newform 985.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [985,2,Mod(1,985)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(985, 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("985.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 985 = 5 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	985.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:	$7.86526459910$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - x^{12} + 66 x^{11} - 83 x^{10} - 218 x^{9} + 446 x^{8} + 178 x^{7} - 782 x^{6} + \cdots - 1 $ x^14 - 6x^13 - x^12 + 66x^11 - 83x^10 - 218x^9 + 446x^8 + 178x^7 - 782x^6 + 205x^5 + 408x^4 - 216x^3 - 4x^2 + 11x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.236045$ of defining polynomial
Character	$\chi$	$=$	985.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.236045 q^{2} -2.87112 q^{3} -1.94428 q^{4} -1.00000 q^{5} -0.677712 q^{6} +1.02221 q^{7} -0.931027 q^{8} +5.24331 q^{9} -0.236045 q^{10} +0.916844 q^{11} +5.58226 q^{12} +4.99719 q^{13} +0.241286 q^{14} +2.87112 q^{15} +3.66880 q^{16} +0.345734 q^{17} +1.23766 q^{18} -5.30778 q^{19} +1.94428 q^{20} -2.93487 q^{21} +0.216416 q^{22} -7.21308 q^{23} +2.67309 q^{24} +1.00000 q^{25} +1.17956 q^{26} -6.44081 q^{27} -1.98746 q^{28} +4.17022 q^{29} +0.677712 q^{30} +9.99162 q^{31} +2.72806 q^{32} -2.63237 q^{33} +0.0816088 q^{34} -1.02221 q^{35} -10.1945 q^{36} +2.64110 q^{37} -1.25287 q^{38} -14.3475 q^{39} +0.931027 q^{40} -9.80072 q^{41} -0.692761 q^{42} -12.7545 q^{43} -1.78260 q^{44} -5.24331 q^{45} -1.70261 q^{46} -8.43174 q^{47} -10.5336 q^{48} -5.95510 q^{49} +0.236045 q^{50} -0.992644 q^{51} -9.71595 q^{52} -3.66822 q^{53} -1.52032 q^{54} -0.916844 q^{55} -0.951701 q^{56} +15.2393 q^{57} +0.984359 q^{58} +4.19018 q^{59} -5.58226 q^{60} +2.70353 q^{61} +2.35847 q^{62} +5.35974 q^{63} -6.69366 q^{64} -4.99719 q^{65} -0.621356 q^{66} +9.72899 q^{67} -0.672205 q^{68} +20.7096 q^{69} -0.241286 q^{70} +0.435154 q^{71} -4.88167 q^{72} -6.14822 q^{73} +0.623419 q^{74} -2.87112 q^{75} +10.3198 q^{76} +0.937203 q^{77} -3.38665 q^{78} -4.36466 q^{79} -3.66880 q^{80} +2.76239 q^{81} -2.31341 q^{82} -9.26666 q^{83} +5.70622 q^{84} -0.345734 q^{85} -3.01064 q^{86} -11.9732 q^{87} -0.853607 q^{88} +14.2366 q^{89} -1.23766 q^{90} +5.10815 q^{91} +14.0243 q^{92} -28.6871 q^{93} -1.99027 q^{94} +5.30778 q^{95} -7.83257 q^{96} -11.0151 q^{97} -1.40567 q^{98} +4.80730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 6 q^{2} - 7 q^{3} + 10 q^{4} - 14 q^{5} + 5 q^{6} - 4 q^{7} - 12 q^{8} + 13 q^{9} + 6 q^{10} - 5 q^{11} - 10 q^{12} - 15 q^{13} - 15 q^{14} + 7 q^{15} + 18 q^{16} - 18 q^{17} - 29 q^{18} + 20 q^{19}+ \cdots + 32 q^{99}+O(q^{100}) $ 14 * q - 6 * q^2 - 7 * q^3 + 10 * q^4 - 14 * q^5 + 5 * q^6 - 4 * q^7 - 12 * q^8 + 13 * q^9 + 6 * q^10 - 5 * q^11 - 10 * q^12 - 15 * q^13 - 15 * q^14 + 7 * q^15 + 18 * q^16 - 18 * q^17 - 29 * q^18 + 20 * q^19 - 10 * q^20 - 5 * q^21 + 12 * q^22 - 42 * q^23 + 7 * q^24 + 14 * q^25 - 13 * q^26 - 19 * q^27 - 3 * q^28 - 2 * q^29 - 5 * q^30 - 40 * q^32 - 10 * q^33 + 13 * q^34 + 4 * q^35 + q^36 - 15 * q^37 - 3 * q^38 - 19 * q^39 + 12 * q^40 + 3 * q^41 - 9 * q^42 - 15 * q^43 - 29 * q^44 - 13 * q^45 - 8 * q^46 - 40 * q^47 - 28 * q^48 + 12 * q^49 - 6 * q^50 - 13 * q^51 - 17 * q^52 - 39 * q^53 + 28 * q^54 + 5 * q^55 - 41 * q^56 - 17 * q^57 - 10 * q^58 + 19 * q^59 + 10 * q^60 - 18 * q^61 + 26 * q^62 - 28 * q^63 + 36 * q^64 + 15 * q^65 - 8 * q^66 - 22 * q^67 - 57 * q^68 + 12 * q^69 + 15 * q^70 - 50 * q^71 - 37 * q^72 - 10 * q^73 - 3 * q^74 - 7 * q^75 - 3 * q^76 - 36 * q^77 + 10 * q^78 + q^79 - 18 * q^80 - 42 * q^81 - 40 * q^82 - 12 * q^83 + 35 * q^84 + 18 * q^85 + 5 * q^86 - 35 * q^87 + 13 * q^88 + 7 * q^89 + 29 * q^90 + 16 * q^91 - 4 * q^92 - 37 * q^93 + 27 * q^94 - 20 * q^95 + 16 * q^96 + 2 * q^97 + 13 * q^98 + 32 * q^99

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 $

$2$	0.236045	0.166909	0.0834544	−	0.996512i	$-0.473405\pi$
$2$	0.236045	0.166909	0.0834544	+	0.996512i	$0.473405\pi$
$3$	−2.87112	−1.65764	−0.828820	−	0.559515i	$-0.810987\pi$
$3$	−2.87112	−1.65764	−0.828820	+	0.559515i	$0.810987\pi$
$4$	−1.94428	−0.972141
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.677712	−0.276675
$7$	1.02221	0.386357	0.193179	−	0.981164i	$-0.438120\pi$
$7$	1.02221	0.386357	0.193179	+	0.981164i	$0.438120\pi$
$8$	−0.931027	−0.329168
$9$	5.24331	1.74777
$10$	−0.236045	−0.0746439
$11$	0.916844	0.276439	0.138219	−	0.990402i	$-0.455862\pi$
$11$	0.916844	0.276439	0.138219	+	0.990402i	$0.455862\pi$
$12$	5.58226	1.61146
$13$	4.99719	1.38597	0.692985	−	0.720952i	$-0.256295\pi$
$13$	4.99719	1.38597	0.692985	+	0.720952i	$0.256295\pi$
$14$	0.241286	0.0644864
$15$	2.87112	0.741319
$16$	3.66880	0.917200
$17$	0.345734	0.0838529	0.0419264	−	0.999121i	$-0.486650\pi$
$17$	0.345734	0.0838529	0.0419264	+	0.999121i	$0.486650\pi$
$18$	1.23766	0.291718
$19$	−5.30778	−1.21769	−0.608845	−	0.793290i	$-0.708367\pi$
$19$	−5.30778	−1.21769	−0.608845	+	0.793290i	$0.708367\pi$
$20$	1.94428	0.434755
$21$	−2.93487	−0.640441
$22$	0.216416	0.0461401
$23$	−7.21308	−1.50403	−0.752015	−	0.659146i	$-0.770918\pi$
$23$	−7.21308	−1.50403	−0.752015	+	0.659146i	$0.770918\pi$
$24$	2.67309	0.545642
$25$	1.00000	0.200000
$26$	1.17956	0.231331
$27$	−6.44081	−1.23953
$28$	−1.98746	−0.375594
$29$	4.17022	0.774391	0.387195	−	0.921998i	$-0.373444\pi$
$29$	4.17022	0.774391	0.387195	+	0.921998i	$0.373444\pi$
$30$	0.677712	0.123733
$31$	9.99162	1.79455	0.897274	−	0.441474i	$-0.145544\pi$
$31$	9.99162	1.79455	0.897274	+	0.441474i	$0.145544\pi$
$32$	2.72806	0.482257
$33$	−2.63237	−0.458236
$34$	0.0816088	0.0139958
$35$	−1.02221	−0.172784
$36$	−10.1945	−1.69908
$37$	2.64110	0.434195	0.217097	−	0.976150i	$-0.430341\pi$
$37$	2.64110	0.434195	0.217097	+	0.976150i	$0.430341\pi$
$38$	−1.25287	−0.203243
$39$	−14.3475	−2.29744
$40$	0.931027	0.147208
$41$	−9.80072	−1.53061	−0.765307	−	0.643665i	$-0.777413\pi$
$41$	−9.80072	−1.53061	−0.765307	+	0.643665i	$0.777413\pi$
$42$	−0.692761	−0.106895
$43$	−12.7545	−1.94505	−0.972524	−	0.232804i	$-0.925210\pi$
$43$	−12.7545	−1.94505	−0.972524	+	0.232804i	$0.925210\pi$
$44$	−1.78260	−0.268738
$45$	−5.24331	−0.781627
$46$	−1.70261	−0.251036
$47$	−8.43174	−1.22990	−0.614948	−	0.788568i	$-0.710823\pi$
$47$	−8.43174	−1.22990	−0.614948	+	0.788568i	$0.710823\pi$
$48$	−10.5336	−1.52039
$49$	−5.95510	−0.850728
$50$	0.236045	0.0333818
$51$	−0.992644	−0.138998
$52$	−9.71595	−1.34736
$53$	−3.66822	−0.503869	−0.251935	−	0.967744i	$-0.581067\pi$
$53$	−3.66822	−0.503869	−0.251935	+	0.967744i	$0.581067\pi$
$54$	−1.52032	−0.206889
$55$	−0.916844	−0.123627
$56$	−0.951701	−0.127176
$57$	15.2393	2.01849
$58$	0.984359	0.129253
$59$	4.19018	0.545515	0.272757	−	0.962083i	$-0.412064\pi$
$59$	4.19018	0.545515	0.272757	+	0.962083i	$0.412064\pi$
$60$	−5.58226	−0.720667
$61$	2.70353	0.346152	0.173076	−	0.984908i	$-0.444629\pi$
$61$	2.70353	0.346152	0.173076	+	0.984908i	$0.444629\pi$
$62$	2.35847	0.299526
$63$	5.35974	0.675264
$64$	−6.69366	−0.836708
$65$	−4.99719	−0.619825
$66$	−0.621356	−0.0764837
$67$	9.72899	1.18859	0.594293	−	0.804249i	$-0.297432\pi$
$67$	9.72899	1.18859	0.594293	+	0.804249i	$0.297432\pi$
$68$	−0.672205	−0.0815169
$69$	20.7096	2.49314
$70$	−0.241286	−0.0288392
$71$	0.435154	0.0516432	0.0258216	−	0.999667i	$-0.491780\pi$
$71$	0.435154	0.0516432	0.0258216	+	0.999667i	$0.491780\pi$
$72$	−4.88167	−0.575310
$73$	−6.14822	−0.719595	−0.359797	−	0.933030i	$-0.617154\pi$
$73$	−6.14822	−0.719595	−0.359797	+	0.933030i	$0.617154\pi$
$74$	0.623419	0.0724709
$75$	−2.87112	−0.331528
$76$	10.3198	1.18377
$77$	0.937203	0.106804
$78$	−3.38665	−0.383463
$79$	−4.36466	−0.491063	−0.245531	−	0.969389i	$-0.578962\pi$
$79$	−4.36466	−0.491063	−0.245531	+	0.969389i	$0.578962\pi$
$80$	−3.66880	−0.410185
$81$	2.76239	0.306932
$82$	−2.31341	−0.255473
$83$	−9.26666	−1.01715	−0.508574	−	0.861018i	$-0.669827\pi$
$83$	−9.26666	−1.01715	−0.508574	+	0.861018i	$0.669827\pi$
$84$	5.70622	0.622600
$85$	−0.345734	−0.0375002
$86$	−3.01064	−0.324646
$87$	−11.9732	−1.28366
$88$	−0.853607	−0.0909948
$89$	14.2366	1.50908	0.754538	−	0.656256i	$-0.227861\pi$
$89$	14.2366	1.50908	0.754538	+	0.656256i	$0.227861\pi$
$90$	−1.23766	−0.130460
$91$	5.10815	0.535480
$92$	14.0243	1.46213
$93$	−28.6871	−2.97471
$94$	−1.99027	−0.205281
$95$	5.30778	0.544567
$96$	−7.83257	−0.799408
$97$	−11.0151	−1.11842	−0.559209	−	0.829027i	$-0.688895\pi$
$97$	−11.0151	−1.11842	−0.559209	+	0.829027i	$0.688895\pi$
$98$	−1.40567	−0.141994
$99$	4.80730	0.483152
$100$	−1.94428	−0.194428
$101$	11.5252	1.14680	0.573400	−	0.819276i	$-0.305624\pi$
$101$	11.5252	1.14680	0.573400	+	0.819276i	$0.305624\pi$
$102$	−0.234308	−0.0232000
$103$	4.12363	0.406313	0.203157	−	0.979146i	$-0.434880\pi$
$103$	4.12363	0.406313	0.203157	+	0.979146i	$0.434880\pi$
$104$	−4.65252	−0.456217
$105$	2.93487	0.286414
$106$	−0.865864	−0.0841002
$107$	−10.2697	−0.992805	−0.496402	−	0.868092i	$-0.665346\pi$
$107$	−10.2697	−0.992805	−0.496402	+	0.868092i	$0.665346\pi$
$108$	12.5228	1.20500
$109$	19.6212	1.87937	0.939685	−	0.342041i	$-0.111118\pi$
$109$	19.6212	1.87937	0.939685	+	0.342041i	$0.111118\pi$
$110$	−0.216416	−0.0206345
$111$	−7.58292	−0.719739
$112$	3.75027	0.354367
$113$	−14.9685	−1.40812	−0.704058	−	0.710142i	$-0.748631\pi$
$113$	−14.9685	−1.40812	−0.704058	+	0.710142i	$0.748631\pi$
$114$	3.59715	0.336904
$115$	7.21308	0.672623
$116$	−8.10809	−0.752817
$117$	26.2018	2.42236
$118$	0.989070	0.0910512
$119$	0.353411	0.0323972
$120$	−2.67309	−0.244018
$121$	−10.1594	−0.923582
$122$	0.638154	0.0577758
$123$	28.1390	2.53721
$124$	−19.4265	−1.74455
$125$	−1.00000	−0.0894427
$126$	1.26514	0.112708
$127$	5.21953	0.463159	0.231579	−	0.972816i	$-0.425611\pi$
$127$	5.21953	0.463159	0.231579	+	0.972816i	$0.425611\pi$
$128$	−7.03611	−0.621910
$129$	36.6197	3.22419
$130$	−1.17956	−0.103454
$131$	−1.76360	−0.154087	−0.0770433	−	0.997028i	$-0.524548\pi$
$131$	−1.76360	−0.154087	−0.0770433	+	0.997028i	$0.524548\pi$
$132$	5.11807	0.445470
$133$	−5.42564	−0.470463
$134$	2.29648	0.198385
$135$	6.44081	0.554337
$136$	−0.321888	−0.0276017
$137$	−14.9252	−1.27514	−0.637571	−	0.770392i	$-0.720061\pi$
$137$	−14.9252	−1.27514	−0.637571	+	0.770392i	$0.720061\pi$
$138$	4.88839	0.416127
$139$	−10.6367	−0.902195	−0.451097	−	0.892475i	$-0.648967\pi$
$139$	−10.6367	−0.902195	−0.451097	+	0.892475i	$0.648967\pi$
$140$	1.98746	0.167971
$141$	24.2085	2.03873
$142$	0.102716	0.00861971
$143$	4.58164	0.383136
$144$	19.2367	1.60306
$145$	−4.17022	−0.346318
$146$	−1.45125	−0.120107
$147$	17.0978	1.41020
$148$	−5.13505	−0.422099
$149$	−7.93007	−0.649656	−0.324828	−	0.945773i	$-0.605306\pi$
$149$	−7.93007	−0.649656	−0.324828	+	0.945773i	$0.605306\pi$
$150$	−0.677712	−0.0553349
$151$	−23.5423	−1.91584	−0.957921	−	0.287033i	$-0.907331\pi$
$151$	−23.5423	−1.91584	−0.957921	+	0.287033i	$0.907331\pi$
$152$	4.94169	0.400824
$153$	1.81279	0.146556
$154$	0.221222	0.0178266
$155$	−9.99162	−0.802546
$156$	27.8956	2.23344
$157$	6.13158	0.489353	0.244677	−	0.969605i	$-0.421318\pi$
$157$	6.13158	0.489353	0.244677	+	0.969605i	$0.421318\pi$
$158$	−1.03025	−0.0819627
$159$	10.5319	0.835234
$160$	−2.72806	−0.215672
$161$	−7.37325	−0.581093
$162$	0.652047	0.0512297
$163$	−7.33018	−0.574144	−0.287072	−	0.957909i	$-0.592682\pi$
$163$	−7.33018	−0.574144	−0.287072	+	0.957909i	$0.592682\pi$
$164$	19.0554	1.48797
$165$	2.63237	0.204929
$166$	−2.18735	−0.169771
$167$	−10.1434	−0.784921	−0.392461	−	0.919769i	$-0.628376\pi$
$167$	−10.1434	−0.784921	−0.392461	+	0.919769i	$0.628376\pi$
$168$	2.73244	0.210813
$169$	11.9719	0.920915
$170$	−0.0816088	−0.00625911
$171$	−27.8304	−2.12824
$172$	24.7984	1.89086
$173$	2.03837	0.154975	0.0774873	−	0.996993i	$-0.475310\pi$
$173$	2.03837	0.154975	0.0774873	+	0.996993i	$0.475310\pi$
$174$	−2.82621	−0.214254
$175$	1.02221	0.0772715
$176$	3.36372	0.253550
$177$	−12.0305	−0.904267
$178$	3.36047	0.251878
$179$	0.681587	0.0509442	0.0254721	−	0.999676i	$-0.491891\pi$
$179$	0.681587	0.0509442	0.0254721	+	0.999676i	$0.491891\pi$
$180$	10.1945	0.759852
$181$	3.58428	0.266417	0.133209	−	0.991088i	$-0.457472\pi$
$181$	3.58428	0.266417	0.133209	+	0.991088i	$0.457472\pi$
$182$	1.20575	0.0893763
$183$	−7.76216	−0.573795
$184$	6.71557	0.495078
$185$	−2.64110	−0.194178
$186$	−6.77144	−0.496506
$187$	0.316985	0.0231802
$188$	16.3937	1.19563
$189$	−6.58383	−0.478903
$190$	1.25287	0.0908930
$191$	15.4485	1.11782	0.558908	−	0.829229i	$-0.311220\pi$
$191$	15.4485	1.11782	0.558908	+	0.829229i	$0.311220\pi$
$192$	19.2183	1.38696
$193$	−4.87672	−0.351034	−0.175517	−	0.984476i	$-0.556160\pi$
$193$	−4.87672	−0.351034	−0.175517	+	0.984476i	$0.556160\pi$
$194$	−2.60006	−0.186674
$195$	14.3475	1.02745
$196$	11.5784	0.827028
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	1.13474	0.0806423
$199$	−20.0659	−1.42244	−0.711218	−	0.702971i	$-0.751856\pi$
$199$	−20.0659	−1.42244	−0.711218	+	0.702971i	$0.751856\pi$
$200$	−0.931027	−0.0658336
$201$	−27.9331	−1.97025
$202$	2.72046	0.191411
$203$	4.26282	0.299192
$204$	1.92998	0.135126
$205$	9.80072	0.684512
$206$	0.973361	0.0678173
$207$	−37.8204	−2.62870
$208$	18.3337	1.27121
$209$	−4.86641	−0.336617
$210$	0.692761	0.0478050
$211$	−4.29538	−0.295706	−0.147853	−	0.989009i	$-0.547236\pi$
$211$	−4.29538	−0.295706	−0.147853	+	0.989009i	$0.547236\pi$
$212$	7.13206	0.489832
$213$	−1.24938	−0.0856059
$214$	−2.42410	−0.165708
$215$	12.7545	0.869852
$216$	5.99657	0.408015
$217$	10.2135	0.693337
$218$	4.63148	0.313683
$219$	17.6523	1.19283
$220$	1.78260	0.120183
$221$	1.72770	0.116218
$222$	−1.78991	−0.120131
$223$	13.6428	0.913589	0.456795	−	0.889572i	$-0.348997\pi$
$223$	13.6428	0.913589	0.456795	+	0.889572i	$0.348997\pi$
$224$	2.78863	0.186323
$225$	5.24331	0.349554
$226$	−3.53323	−0.235027
$227$	−8.32757	−0.552720	−0.276360	−	0.961054i	$-0.589128\pi$
$227$	−8.32757	−0.552720	−0.276360	+	0.961054i	$0.589128\pi$
$228$	−29.6294	−1.96226
$229$	−27.7853	−1.83611	−0.918053	−	0.396458i	$-0.870239\pi$
$229$	−27.7853	−1.83611	−0.918053	+	0.396458i	$0.870239\pi$
$230$	1.70261	0.112267
$231$	−2.69082	−0.177043
$232$	−3.88259	−0.254904
$233$	−15.7592	−1.03242	−0.516211	−	0.856462i	$-0.672658\pi$
$233$	−15.7592	−1.03242	−0.516211	+	0.856462i	$0.672658\pi$
$234$	6.18480	0.404313
$235$	8.43174	0.550026
$236$	−8.14689	−0.530318
$237$	12.5314	0.814005
$238$	0.0834209	0.00540737
$239$	−26.6777	−1.72564	−0.862818	−	0.505515i	$-0.831303\pi$
$239$	−26.6777	−1.72564	−0.862818	+	0.505515i	$0.831303\pi$
$240$	10.5336	0.679938
$241$	7.59582	0.489290	0.244645	−	0.969613i	$-0.421329\pi$
$241$	7.59582	0.489290	0.244645	+	0.969613i	$0.421329\pi$
$242$	−2.39807	−0.154154
$243$	11.3913	0.730752
$244$	−5.25643	−0.336509
$245$	5.95510	0.380457
$246$	6.64206	0.423482
$247$	−26.5240	−1.68768
$248$	−9.30247	−0.590707
$249$	26.6057	1.68607
$250$	−0.236045	−0.0149288
$251$	−10.2993	−0.650088	−0.325044	−	0.945699i	$-0.605379\pi$
$251$	−10.2993	−0.650088	−0.325044	+	0.945699i	$0.605379\pi$
$252$	−10.4209	−0.656452
$253$	−6.61327	−0.415773
$254$	1.23204	0.0773053
$255$	0.992644	0.0621618
$256$	11.7265	0.732905
$257$	−16.8749	−1.05263	−0.526315	−	0.850290i	$-0.676427\pi$
$257$	−16.8749	−1.05263	−0.526315	+	0.850290i	$0.676427\pi$
$258$	8.64390	0.538146
$259$	2.69975	0.167754
$260$	9.71595	0.602557
$261$	21.8658	1.35346
$262$	−0.416289	−0.0257184
$263$	8.57005	0.528452	0.264226	−	0.964461i	$-0.414884\pi$
$263$	8.57005	0.528452	0.264226	+	0.964461i	$0.414884\pi$
$264$	2.45080	0.150837
$265$	3.66822	0.225337
$266$	−1.28069	−0.0785244
$267$	−40.8749	−2.50151
$268$	−18.9159	−1.15547
$269$	26.3927	1.60919	0.804596	−	0.593822i	$-0.202382\pi$
$269$	26.3927	1.60919	0.804596	+	0.593822i	$0.202382\pi$
$270$	1.52032	0.0925237
$271$	27.5722	1.67489	0.837447	−	0.546518i	$-0.184047\pi$
$271$	27.5722	1.67489	0.837447	+	0.546518i	$0.184047\pi$
$272$	1.26843	0.0769099
$273$	−14.6661	−0.887633
$274$	−3.52300	−0.212832
$275$	0.916844	0.0552878
$276$	−40.2653	−2.42369
$277$	9.89475	0.594518	0.297259	−	0.954797i	$-0.403928\pi$
$277$	9.89475	0.594518	0.297259	+	0.954797i	$0.403928\pi$
$278$	−2.51074	−0.150584
$279$	52.3892	3.13646
$280$	0.951701	0.0568750
$281$	27.3790	1.63330	0.816648	−	0.577135i	$-0.195830\pi$
$281$	27.3790	1.63330	0.816648	+	0.577135i	$0.195830\pi$
$282$	5.71429	0.340281
$283$	−7.11007	−0.422650	−0.211325	−	0.977416i	$-0.567778\pi$
$283$	−7.11007	−0.422650	−0.211325	+	0.977416i	$0.567778\pi$
$284$	−0.846062	−0.0502045
$285$	−15.2393	−0.902696
$286$	1.08147	0.0639488
$287$	−10.0183	−0.591364
$288$	14.3040	0.842874
$289$	−16.8805	−0.992969
$290$	−0.984359	−0.0578035
$291$	31.6257	1.85393
$292$	11.9539	0.699548
$293$	15.7053	0.917512	0.458756	−	0.888562i	$-0.348295\pi$
$293$	15.7053	0.917512	0.458756	+	0.888562i	$0.348295\pi$
$294$	4.03584	0.235375
$295$	−4.19018	−0.243962
$296$	−2.45894	−0.142923
$297$	−5.90522	−0.342656
$298$	−1.87185	−0.108433
$299$	−36.0451	−2.08454
$300$	5.58226	0.322292
$301$	−13.0377	−0.751483
$302$	−5.55702	−0.319771
$303$	−33.0902	−1.90098
$304$	−19.4732	−1.11686
$305$	−2.70353	−0.154804
$306$	0.427900	0.0244614
$307$	−8.97401	−0.512174	−0.256087	−	0.966654i	$-0.582433\pi$
$307$	−8.97401	−0.512174	−0.256087	+	0.966654i	$0.582433\pi$
$308$	−1.82219	−0.103829
$309$	−11.8394	−0.673521
$310$	−2.35847	−0.133952
$311$	−9.76960	−0.553983	−0.276992	−	0.960872i	$-0.589337\pi$
$311$	−9.76960	−0.553983	−0.276992	+	0.960872i	$0.589337\pi$
$312$	13.3579	0.756243
$313$	−0.449986	−0.0254347	−0.0127174	−	0.999919i	$-0.504048\pi$
$313$	−0.449986	−0.0254347	−0.0127174	+	0.999919i	$0.504048\pi$
$314$	1.44733	0.0816773
$315$	−5.35974	−0.301987
$316$	8.48613	0.477382
$317$	−27.2882	−1.53266	−0.766330	−	0.642447i	$-0.777919\pi$
$317$	−27.2882	−1.53266	−0.766330	+	0.642447i	$0.777919\pi$
$318$	2.48600	0.139408
$319$	3.82344	0.214072
$320$	6.69366	0.374187
$321$	29.4854	1.64571
$322$	−1.74042	−0.0969896
$323$	−1.83508	−0.102107
$324$	−5.37087	−0.298381
$325$	4.99719	0.277194
$326$	−1.73025	−0.0958297
$327$	−56.3348	−3.11532
$328$	9.12473	0.503829
$329$	−8.61897	−0.475179
$330$	0.621356	0.0342045
$331$	4.69448	0.258032	0.129016	−	0.991643i	$-0.458818\pi$
$331$	4.69448	0.258032	0.129016	+	0.991643i	$0.458818\pi$
$332$	18.0170	0.988812
$333$	13.8481	0.758873
$334$	−2.39430	−0.131010
$335$	−9.72899	−0.531551
$336$	−10.7675	−0.587413
$337$	−1.18729	−0.0646760	−0.0323380	−	0.999477i	$-0.510295\pi$
$337$	−1.18729	−0.0646760	−0.0323380	+	0.999477i	$0.510295\pi$
$338$	2.82590	0.153709
$339$	42.9763	2.33415
$340$	0.672205	0.0364555
$341$	9.16076	0.496083
$342$	−6.56921	−0.355222
$343$	−13.2428	−0.715042
$344$	11.8748	0.640247
$345$	−20.7096	−1.11497
$346$	0.481147	0.0258666
$347$	2.21480	0.118896	0.0594482	−	0.998231i	$-0.481066\pi$
$347$	2.21480	0.118896	0.0594482	+	0.998231i	$0.481066\pi$
$348$	23.2793	1.24790
$349$	22.6828	1.21418	0.607092	−	0.794632i	$-0.292336\pi$
$349$	22.6828	1.21418	0.607092	+	0.794632i	$0.292336\pi$
$350$	0.241286	0.0128973
$351$	−32.1860	−1.71796
$352$	2.50120	0.133315
$353$	−12.2691	−0.653016	−0.326508	−	0.945194i	$-0.605872\pi$
$353$	−12.2691	−0.653016	−0.326508	+	0.945194i	$0.605872\pi$
$354$	−2.83973	−0.150930
$355$	−0.435154	−0.0230956
$356$	−27.6800	−1.46704
$357$	−1.01469	−0.0537029
$358$	0.160885	0.00850304
$359$	−18.9950	−1.00252	−0.501258	−	0.865298i	$-0.667129\pi$
$359$	−18.9950	−1.00252	−0.501258	+	0.865298i	$0.667129\pi$
$360$	4.88167	0.257286
$361$	9.17256	0.482767
$362$	0.846050	0.0444674
$363$	29.1688	1.53097
$364$	−9.93169	−0.520562
$365$	6.14822	0.321812
$366$	−1.83222	−0.0957715
$367$	35.4991	1.85304	0.926519	−	0.376249i	$-0.122786\pi$
$367$	35.4991	1.85304	0.926519	+	0.376249i	$0.122786\pi$
$368$	−26.4633	−1.37950
$369$	−51.3882	−2.67516
$370$	−0.623419	−0.0324100
$371$	−3.74968	−0.194673
$372$	55.7759	2.89184
$373$	22.1497	1.14687	0.573434	−	0.819252i	$-0.305611\pi$
$373$	22.1497	1.14687	0.573434	+	0.819252i	$0.305611\pi$
$374$	0.0748225	0.00386898
$375$	2.87112	0.148264
$376$	7.85018	0.404842
$377$	20.8394	1.07328
$378$	−1.55408	−0.0799332
$379$	−0.0471576	−0.00242232	−0.00121116	−	0.999999i	$-0.500386\pi$
$379$	−0.0471576	−0.00242232	−0.00121116	+	0.999999i	$0.500386\pi$
$380$	−10.3198	−0.529396
$381$	−14.9859	−0.767750
$382$	3.64654	0.186573
$383$	−27.8084	−1.42094	−0.710470	−	0.703727i	$-0.751518\pi$
$383$	−27.8084	−1.42094	−0.710470	+	0.703727i	$0.751518\pi$
$384$	20.2015	1.03090
$385$	−0.937203	−0.0477643
$386$	−1.15112	−0.0585907
$387$	−66.8760	−3.39950
$388$	21.4165	1.08726
$389$	−5.91034	−0.299666	−0.149833	−	0.988711i	$-0.547874\pi$
$389$	−5.91034	−0.299666	−0.149833	+	0.988711i	$0.547874\pi$
$390$	3.38665	0.171490
$391$	−2.49381	−0.126117
$392$	5.54436	0.280032
$393$	5.06351	0.255420
$394$	−0.236045	−0.0118918
$395$	4.36466	0.219610
$396$	−9.34675	−0.469692
$397$	−10.7928	−0.541673	−0.270836	−	0.962625i	$-0.587300\pi$
$397$	−10.7928	−0.541673	−0.270836	+	0.962625i	$0.587300\pi$
$398$	−4.73646	−0.237417
$399$	15.5777	0.779858
$400$	3.66880	0.183440
$401$	−25.3129	−1.26407	−0.632034	−	0.774941i	$-0.717780\pi$
$401$	−25.3129	−1.26407	−0.632034	+	0.774941i	$0.717780\pi$
$402$	−6.59345	−0.328851
$403$	49.9300	2.48719
$404$	−22.4082	−1.11485
$405$	−2.76239	−0.137264
$406$	1.00622	0.0499377
$407$	2.42148	0.120028
$408$	0.924178	0.0457536
$409$	11.0910	0.548415	0.274207	−	0.961671i	$-0.411585\pi$
$409$	11.0910	0.548415	0.274207	+	0.961671i	$0.411585\pi$
$410$	2.31341	0.114251
$411$	42.8519	2.11373
$412$	−8.01750	−0.394994
$413$	4.28322	0.210764
$414$	−8.92731	−0.438753
$415$	9.26666	0.454883
$416$	13.6326	0.668394
$417$	30.5393	1.49551
$418$	−1.14869	−0.0561843
$419$	−29.8386	−1.45771	−0.728856	−	0.684667i	$-0.759947\pi$
$419$	−29.8386	−1.45771	−0.728856	+	0.684667i	$0.759947\pi$
$420$	−5.70622	−0.278435
$421$	−31.3685	−1.52881	−0.764403	−	0.644739i	$-0.776966\pi$
$421$	−31.3685	−1.52881	−0.764403	+	0.644739i	$0.776966\pi$
$422$	−1.01390	−0.0493560
$423$	−44.2103	−2.14958
$424$	3.41521	0.165857
$425$	0.345734	0.0167706
$426$	−0.294909	−0.0142884
$427$	2.76356	0.133738
$428$	19.9671	0.965147
$429$	−13.1544	−0.635102
$430$	3.01064	0.145186
$431$	−28.4126	−1.36859	−0.684293	−	0.729207i	$-0.739889\pi$
$431$	−28.4126	−1.36859	−0.684293	+	0.729207i	$0.739889\pi$
$432$	−23.6301	−1.13690
$433$	29.6797	1.42631	0.713157	−	0.701005i	$-0.247265\pi$
$433$	29.6797	1.42631	0.713157	+	0.701005i	$0.247265\pi$
$434$	2.41084	0.115724
$435$	11.9732	0.574071
$436$	−38.1492	−1.82701
$437$	38.2855	1.83144
$438$	4.16672	0.199094
$439$	19.0177	0.907664	0.453832	−	0.891087i	$-0.350057\pi$
$439$	19.0177	0.907664	0.453832	+	0.891087i	$0.350057\pi$
$440$	0.853607	0.0406941
$441$	−31.2244	−1.48688
$442$	0.407814	0.0193977
$443$	−12.5365	−0.595628	−0.297814	−	0.954624i	$-0.596258\pi$
$443$	−12.5365	−0.595628	−0.297814	+	0.954624i	$0.596258\pi$
$444$	14.7433	0.699688
$445$	−14.2366	−0.674879
$446$	3.22031	0.152486
$447$	22.7681	1.07690
$448$	−6.84230	−0.323268
$449$	17.9879	0.848900	0.424450	−	0.905451i	$-0.360467\pi$
$449$	17.9879	0.848900	0.424450	+	0.905451i	$0.360467\pi$
$450$	1.23766	0.0583437
$451$	−8.98573	−0.423122
$452$	29.1030	1.36889
$453$	67.5926	3.17578
$454$	−1.96568	−0.0922539
$455$	−5.10815	−0.239474
$456$	−14.1882	−0.664422
$457$	−27.3085	−1.27744	−0.638718	−	0.769441i	$-0.720535\pi$
$457$	−27.3085	−1.27744	−0.638718	+	0.769441i	$0.720535\pi$
$458$	−6.55858	−0.306462
$459$	−2.22681	−0.103939
$460$	−14.0243	−0.653885
$461$	−8.85519	−0.412427	−0.206214	−	0.978507i	$-0.566114\pi$
$461$	−8.85519	−0.412427	−0.206214	+	0.978507i	$0.566114\pi$
$462$	−0.635154	−0.0295500
$463$	−17.7027	−0.822714	−0.411357	−	0.911474i	$-0.634945\pi$
$463$	−17.7027	−0.822714	−0.411357	+	0.911474i	$0.634945\pi$
$464$	15.2997	0.710271
$465$	28.6871	1.33033
$466$	−3.71988	−0.172320
$467$	−12.5779	−0.582035	−0.291018	−	0.956718i	$-0.593994\pi$
$467$	−12.5779	−0.582035	−0.291018	+	0.956718i	$0.593994\pi$
$468$	−50.9437	−2.35488
$469$	9.94502	0.459219
$470$	1.99027	0.0918042
$471$	−17.6045	−0.811171
$472$	−3.90117	−0.179566
$473$	−11.6939	−0.537687
$474$	2.95798	0.135865
$475$	−5.30778	−0.243538
$476$	−0.687132	−0.0314946
$477$	−19.2336	−0.880648
$478$	−6.29713	−0.288024
$479$	21.5408	0.984224	0.492112	−	0.870532i	$-0.336225\pi$
$479$	21.5408	0.984224	0.492112	+	0.870532i	$0.336225\pi$
$480$	7.83257	0.357506
$481$	13.1981	0.601781
$482$	1.79295	0.0816668
$483$	21.1695	0.963243
$484$	19.7527	0.897852
$485$	11.0151	0.500171
$486$	2.68886	0.121969
$487$	4.30185	0.194935	0.0974677	−	0.995239i	$-0.468926\pi$
$487$	4.30185	0.194935	0.0974677	+	0.995239i	$0.468926\pi$
$488$	−2.51706	−0.113942
$489$	21.0458	0.951724
$490$	1.40567	0.0635016
$491$	−7.55139	−0.340789	−0.170395	−	0.985376i	$-0.554504\pi$
$491$	−7.55139	−0.340789	−0.170395	+	0.985376i	$0.554504\pi$
$492$	−54.7102	−2.46653
$493$	1.44179	0.0649349
$494$	−6.26085	−0.281689
$495$	−4.80730	−0.216072
$496$	36.6573	1.64596
$497$	0.444816	0.0199527
$498$	6.28013	0.281419
$499$	37.8523	1.69450	0.847250	−	0.531194i	$-0.178256\pi$
$499$	37.8523	1.69450	0.847250	+	0.531194i	$0.178256\pi$
$500$	1.94428	0.0869510
$501$	29.1229	1.30112
$502$	−2.43110	−0.108505
$503$	20.1705	0.899360	0.449680	−	0.893190i	$-0.351538\pi$
$503$	20.1705	0.899360	0.449680	+	0.893190i	$0.351538\pi$
$504$	−4.99007	−0.222275
$505$	−11.5252	−0.512864
$506$	−1.56103	−0.0693961
$507$	−34.3727	−1.52654
$508$	−10.1483	−0.450256
$509$	19.5293	0.865623	0.432811	−	0.901484i	$-0.357522\pi$
$509$	19.5293	0.865623	0.432811	+	0.901484i	$0.357522\pi$
$510$	0.234308	0.0103753
$511$	−6.28474	−0.278021
$512$	16.8402	0.744239
$513$	34.1864	1.50937
$514$	−3.98324	−0.175693
$515$	−4.12363	−0.181709
$516$	−71.1991	−3.13437
$517$	−7.73060	−0.339991
$518$	0.637262	0.0279997
$519$	−5.85241	−0.256892
$520$	4.65252	0.204026
$521$	19.9256	0.872958	0.436479	−	0.899714i	$-0.356225\pi$
$521$	19.9256	0.872958	0.436479	+	0.899714i	$0.356225\pi$
$522$	5.16130	0.225904
$523$	0.645222	0.0282136	0.0141068	−	0.999900i	$-0.495510\pi$
$523$	0.645222	0.0282136	0.0141068	+	0.999900i	$0.495510\pi$
$524$	3.42894	0.149794
$525$	−2.93487	−0.128088
$526$	2.02291	0.0882033
$527$	3.45445	0.150478
$528$	−9.65763	−0.420295
$529$	29.0285	1.26211
$530$	0.865864	0.0376107
$531$	21.9704	0.953435
$532$	10.5490	0.457357
$533$	−48.9760	−2.12139
$534$	−9.64831	−0.417523
$535$	10.2697	0.443996
$536$	−9.05795	−0.391244
$537$	−1.95692	−0.0844472
$538$	6.22986	0.268588
$539$	−5.45990	−0.235174
$540$	−12.5228	−0.538894
$541$	0.776828	0.0333984	0.0166992	−	0.999861i	$-0.494684\pi$
$541$	0.776828	0.0333984	0.0166992	+	0.999861i	$0.494684\pi$
$542$	6.50828	0.279555
$543$	−10.2909	−0.441624
$544$	0.943182	0.0404386
$545$	−19.6212	−0.840480
$546$	−3.46186	−0.148154
$547$	8.27780	0.353933	0.176967	−	0.984217i	$-0.443372\pi$
$547$	8.27780	0.353933	0.176967	+	0.984217i	$0.443372\pi$
$548$	29.0187	1.23962
$549$	14.1755	0.604994
$550$	0.216416	0.00922802
$551$	−22.1346	−0.942967
$552$	−19.2812	−0.820662
$553$	−4.46158	−0.189726
$554$	2.33560	0.0992303
$555$	7.58292	0.321877
$556$	20.6808	0.877061
$557$	−11.5911	−0.491130	−0.245565	−	0.969380i	$-0.578974\pi$
$557$	−11.5911	−0.491130	−0.245565	+	0.969380i	$0.578974\pi$
$558$	12.3662	0.523503
$559$	−63.7368	−2.69578
$560$	−3.75027	−0.158478
$561$	−0.910100	−0.0384244
$562$	6.46268	0.272612
$563$	13.9955	0.589840	0.294920	−	0.955522i	$-0.404707\pi$
$563$	13.9955	0.589840	0.294920	+	0.955522i	$0.404707\pi$
$564$	−47.0682	−1.98193
$565$	14.9685	0.629729
$566$	−1.67829	−0.0705440
$567$	2.82373	0.118585
$568$	−0.405140	−0.0169993
$569$	−40.7482	−1.70825	−0.854127	−	0.520065i	$-0.825908\pi$
$569$	−40.7482	−1.70825	−0.854127	+	0.520065i	$0.825908\pi$
$570$	−3.59715	−0.150668
$571$	−17.0553	−0.713742	−0.356871	−	0.934154i	$-0.616156\pi$
$571$	−17.0553	−0.713742	−0.356871	+	0.934154i	$0.616156\pi$
$572$	−8.90801	−0.372463
$573$	−44.3545	−1.85294
$574$	−2.36478	−0.0987039
$575$	−7.21308	−0.300806
$576$	−35.0970	−1.46237
$577$	23.5705	0.981255	0.490627	−	0.871369i	$-0.336768\pi$
$577$	23.5705	0.981255	0.490627	+	0.871369i	$0.336768\pi$
$578$	−3.98455	−0.165735
$579$	14.0016	0.581888
$580$	8.10809	0.336670
$581$	−9.47243	−0.392983
$582$	7.46509	0.309438
$583$	−3.36319	−0.139289
$584$	5.72416	0.236867
$585$	−26.2018	−1.08331
$586$	3.70715	0.153141
$587$	0.0140745	0.000580917 0	0.000290459	−	1.00000i	$-0.499908\pi$
$587$	0.0140745	0.000580917 0	0.000290459		1.00000i	$0.499908\pi$
$588$	−33.2429	−1.37091
$589$	−53.0334	−2.18520
$590$	−0.989070	−0.0407194
$591$	2.87112	0.118102
$592$	9.68969	0.398244
$593$	−7.67621	−0.315224	−0.157612	−	0.987501i	$-0.550380\pi$
$593$	−7.67621	−0.315224	−0.157612	+	0.987501i	$0.550380\pi$
$594$	−1.39390	−0.0571923
$595$	−0.353411	−0.0144885
$596$	15.4183	0.631558
$597$	57.6117	2.35789
$598$	−8.50826	−0.347928
$599$	−9.42711	−0.385181	−0.192591	−	0.981279i	$-0.561689\pi$
$599$	−9.42711	−0.385181	−0.192591	+	0.981279i	$0.561689\pi$
$600$	2.67309	0.109128
$601$	3.49753	0.142667	0.0713337	−	0.997453i	$-0.477274\pi$
$601$	3.49753	0.142667	0.0713337	+	0.997453i	$0.477274\pi$
$602$	−3.07749	−0.125429
$603$	51.0121	2.07737
$604$	45.7728	1.86247
$605$	10.1594	0.413038
$606$	−7.81076	−0.317290
$607$	11.1635	0.453112	0.226556	−	0.973998i	$-0.427253\pi$
$607$	11.1635	0.453112	0.226556	+	0.973998i	$0.427253\pi$
$608$	−14.4799	−0.587239
$609$	−12.2391	−0.495952
$610$	−0.638154	−0.0258381
$611$	−42.1350	−1.70460
$612$	−3.52458	−0.142473
$613$	44.5755	1.80039	0.900193	−	0.435490i	$-0.143425\pi$
$613$	44.5755	1.80039	0.900193	+	0.435490i	$0.143425\pi$
$614$	−2.11827	−0.0854864
$615$	−28.1390	−1.13467
$616$	−0.872561	−0.0351565
$617$	25.3603	1.02097	0.510484	−	0.859887i	$-0.329466\pi$
$617$	25.3603	1.02097	0.510484	+	0.859887i	$0.329466\pi$
$618$	−2.79463	−0.112417
$619$	17.2831	0.694667	0.347333	−	0.937742i	$-0.387087\pi$
$619$	17.2831	0.694667	0.347333	+	0.937742i	$0.387087\pi$
$620$	19.4265	0.780188
$621$	46.4581	1.86430
$622$	−2.30606	−0.0924647
$623$	14.5527	0.583043
$624$	−52.6382	−2.10721
$625$	1.00000	0.0400000
$626$	−0.106217	−0.00424528
$627$	13.9720	0.557989
$628$	−11.9215	−0.475720
$629$	0.913120	0.0364085
$630$	−1.26514	−0.0504043
$631$	13.6827	0.544700	0.272350	−	0.962198i	$-0.412199\pi$
$631$	13.6827	0.544700	0.272350	+	0.962198i	$0.412199\pi$
$632$	4.06362	0.161642
$633$	12.3325	0.490175
$634$	−6.44124	−0.255814
$635$	−5.21953	−0.207131
$636$	−20.4770	−0.811965
$637$	−29.7587	−1.17908
$638$	0.902504	0.0357305
$639$	2.28165	0.0902606
$640$	7.03611	0.278127
$641$	4.80495	0.189784	0.0948921	−	0.995488i	$-0.469749\pi$
$641$	4.80495	0.189784	0.0948921	+	0.995488i	$0.469749\pi$
$642$	6.95987	0.274684
$643$	−11.5218	−0.454376	−0.227188	−	0.973851i	$-0.572953\pi$
$643$	−11.5218	−0.454376	−0.227188	+	0.973851i	$0.572953\pi$
$644$	14.3357	0.564905
$645$	−36.6197	−1.44190
$646$	−0.433162	−0.0170425
$647$	−19.8337	−0.779742	−0.389871	−	0.920870i	$-0.627480\pi$
$647$	−19.8337	−0.779742	−0.389871	+	0.920870i	$0.627480\pi$
$648$	−2.57186	−0.101032
$649$	3.84174	0.150802
$650$	1.17956	0.0462661
$651$	−29.3241	−1.14930
$652$	14.2519	0.558149
$653$	37.8833	1.48249	0.741244	−	0.671235i	$-0.234236\pi$
$653$	37.8833	1.48249	0.741244	+	0.671235i	$0.234236\pi$
$654$	−13.2975	−0.519974
$655$	1.76360	0.0689097
$656$	−35.9569	−1.40388
$657$	−32.2370	−1.25769
$658$	−2.03446	−0.0793116
$659$	−18.2539	−0.711072	−0.355536	−	0.934663i	$-0.615702\pi$
$659$	−18.2539	−0.711072	−0.355536	+	0.934663i	$0.615702\pi$
$660$	−5.11807	−0.199220
$661$	39.5364	1.53779	0.768895	−	0.639375i	$-0.220807\pi$
$661$	39.5364	1.53779	0.768895	+	0.639375i	$0.220807\pi$
$662$	1.10811	0.0430678
$663$	−4.96043	−0.192647
$664$	8.62751	0.334813
$665$	5.42564	0.210397
$666$	3.26878	0.126663
$667$	−30.0801	−1.16471
$668$	19.7217	0.763055
$669$	−39.1701	−1.51440
$670$	−2.29648	−0.0887206
$671$	2.47872	0.0956898
$672$	−8.00649	−0.308857
$673$	14.7965	0.570364	0.285182	−	0.958473i	$-0.407946\pi$
$673$	14.7965	0.570364	0.285182	+	0.958473i	$0.407946\pi$
$674$	−0.280254	−0.0107950
$675$	−6.44081	−0.247907
$676$	−23.2767	−0.895259
$677$	37.1563	1.42803	0.714017	−	0.700128i	$-0.246874\pi$
$677$	37.1563	1.42803	0.714017	+	0.700128i	$0.246874\pi$
$678$	10.1443	0.389590
$679$	−11.2597	−0.432109
$680$	0.321888	0.0123438
$681$	23.9094	0.916212
$682$	2.16235	0.0828006
$683$	−29.5420	−1.13039	−0.565196	−	0.824957i	$-0.691199\pi$
$683$	−29.5420	−1.13039	−0.565196	+	0.824957i	$0.691199\pi$
$684$	54.1101	2.06895
$685$	14.9252	0.570261
$686$	−3.12589	−0.119347
$687$	79.7749	3.04360
$688$	−46.7938	−1.78400
$689$	−18.3308	−0.698348
$690$	−4.88839	−0.186098
$691$	24.4783	0.931198	0.465599	−	0.884996i	$-0.345839\pi$
$691$	24.4783	0.931198	0.465599	+	0.884996i	$0.345839\pi$
$692$	−3.96317	−0.150657
$693$	4.91405	0.186669
$694$	0.522791	0.0198449
$695$	10.6367	0.403474
$696$	11.1474	0.422540
$697$	−3.38844	−0.128346
$698$	5.35416	0.202658
$699$	45.2466	1.71138
$700$	−1.98746	−0.0751188
$701$	21.2361	0.802077	0.401039	−	0.916061i	$-0.368649\pi$
$701$	21.2361	0.802077	0.401039	+	0.916061i	$0.368649\pi$
$702$	−7.59732	−0.286742
$703$	−14.0184	−0.528714
$704$	−6.13704	−0.231299
$705$	−24.2085	−0.911746
$706$	−2.89605	−0.108994
$707$	11.7811	0.443074
$708$	23.3907	0.879076
$709$	−10.4005	−0.390599	−0.195300	−	0.980744i	$-0.562568\pi$
$709$	−10.4005	−0.390599	−0.195300	+	0.980744i	$0.562568\pi$
$710$	−0.102716	−0.00385485
$711$	−22.8853	−0.858265
$712$	−13.2547	−0.496739
$713$	−72.0703	−2.69905
$714$	−0.239511	−0.00896348
$715$	−4.58164	−0.171344
$716$	−1.32520	−0.0495250
$717$	76.5948	2.86048
$718$	−4.48366	−0.167329
$719$	−35.5394	−1.32540	−0.662698	−	0.748887i	$-0.730589\pi$
$719$	−35.5394	−1.32540	−0.662698	+	0.748887i	$0.730589\pi$
$720$	−19.2367	−0.716909
$721$	4.21520	0.156982
$722$	2.16514	0.0805780
$723$	−21.8085	−0.811067
$724$	−6.96885	−0.258995
$725$	4.17022	0.154878
$726$	6.88514	0.255532
$727$	−20.0589	−0.743944	−0.371972	−	0.928244i	$-0.621318\pi$
$727$	−20.0589	−0.743944	−0.371972	+	0.928244i	$0.621318\pi$
$728$	−4.75583	−0.176263
$729$	−40.9929	−1.51826
$730$	1.45125	0.0537133
$731$	−4.40968	−0.163098
$732$	15.0918	0.557810
$733$	−7.54137	−0.278547	−0.139273	−	0.990254i	$-0.544477\pi$
$733$	−7.54137	−0.278547	−0.139273	+	0.990254i	$0.544477\pi$
$734$	8.37937	0.309288
$735$	−17.0978	−0.630661
$736$	−19.6777	−0.725329
$737$	8.91997	0.328571
$738$	−12.1299	−0.446508
$739$	−2.97975	−0.109612	−0.0548059	−	0.998497i	$-0.517454\pi$
$739$	−2.97975	−0.109612	−0.0548059	+	0.998497i	$0.517454\pi$
$740$	5.13505	0.188768
$741$	76.1535	2.79757
$742$	−0.885091	−0.0324927
$743$	50.0156	1.83490	0.917448	−	0.397856i	$-0.130246\pi$
$743$	50.0156	1.83490	0.917448	+	0.397856i	$0.130246\pi$
$744$	26.7085	0.979180
$745$	7.93007	0.290535
$746$	5.22832	0.191422
$747$	−48.5880	−1.77774
$748$	−0.616308	−0.0225344
$749$	−10.4977	−0.383577
$750$	0.677712	0.0247465
$751$	25.8694	0.943989	0.471995	−	0.881601i	$-0.343534\pi$
$751$	25.8694	0.943989	0.471995	+	0.881601i	$0.343534\pi$
$752$	−30.9344	−1.12806
$753$	29.5706	1.07761
$754$	4.91903	0.179140
$755$	23.5423	0.856790
$756$	12.8008	0.465562
$757$	−52.5795	−1.91103	−0.955517	−	0.294936i	$-0.904702\pi$
$757$	−52.5795	−1.91103	−0.955517	+	0.294936i	$0.904702\pi$
$758$	−0.0111313	−0.000404307 0
$759$	18.9875	0.689201
$760$	−4.94169	−0.179254
$761$	−47.2393	−1.71242	−0.856211	−	0.516626i	$-0.827188\pi$
$761$	−47.2393	−1.71242	−0.856211	+	0.516626i	$0.827188\pi$
$762$	−3.53734	−0.128144
$763$	20.0569	0.726109
$764$	−30.0363	−1.08668
$765$	−1.81279	−0.0655417
$766$	−6.56402	−0.237168
$767$	20.9391	0.756068
$768$	−33.6681	−1.21489
$769$	19.1183	0.689425	0.344712	−	0.938708i	$-0.387976\pi$
$769$	19.1183	0.689425	0.344712	+	0.938708i	$0.387976\pi$
$770$	−0.221222	−0.00797228
$771$	48.4499	1.74488
$772$	9.48172	0.341255
$773$	−35.0337	−1.26007	−0.630037	−	0.776565i	$-0.716960\pi$
$773$	−35.0337	−1.26007	−0.630037	+	0.776565i	$0.716960\pi$
$774$	−15.7857	−0.567406
$775$	9.99162	0.358910
$776$	10.2554	0.368147
$777$	−7.75130	−0.278076
$778$	−1.39510	−0.0500169
$779$	52.0201	1.86381
$780$	−27.8956	−0.998823
$781$	0.398968	0.0142762
$782$	−0.588650	−0.0210501
$783$	−26.8596	−0.959884
$784$	−21.8481	−0.780288
$785$	−6.13158	−0.218845
$786$	1.19521	0.0426319
$787$	31.2968	1.11561	0.557806	−	0.829971i	$-0.311643\pi$
$787$	31.2968	1.11561	0.557806	+	0.829971i	$0.311643\pi$
$788$	1.94428	0.0692622
$789$	−24.6056	−0.875983
$790$	1.03025	0.0366548
$791$	−15.3009	−0.544036
$792$	−4.47573	−0.159038
$793$	13.5101	0.479756
$794$	−2.54757	−0.0904099
$795$	−10.5319	−0.373528
$796$	39.0139	1.38281
$797$	31.3216	1.10947	0.554734	−	0.832027i	$-0.312820\pi$
$797$	31.3216	1.10947	0.554734	+	0.832027i	$0.312820\pi$
$798$	3.67702	0.130165
$799$	−2.91514	−0.103130
$800$	2.72806	0.0964513
$801$	74.6469	2.63752
$802$	−5.97498	−0.210984
$803$	−5.63696	−0.198924
$804$	54.3098	1.91536
$805$	7.37325	0.259873
$806$	11.7857	0.415134
$807$	−75.7766	−2.66746
$808$	−10.7303	−0.377489
$809$	4.76429	0.167504	0.0837518	−	0.996487i	$-0.473310\pi$
$809$	4.76429	0.167504	0.0837518	+	0.996487i	$0.473310\pi$
$810$	−0.652047	−0.0229106
$811$	−0.713408	−0.0250511	−0.0125256	−	0.999922i	$-0.503987\pi$
$811$	−0.713408	−0.0250511	−0.0125256	+	0.999922i	$0.503987\pi$
$812$	−8.28813	−0.290856
$813$	−79.1631	−2.77637
$814$	0.571578	0.0200338
$815$	7.33018	0.256765
$816$	−3.64181	−0.127489
$817$	67.6983	2.36846
$818$	2.61797	0.0915352
$819$	26.7836	0.935896
$820$	−19.0554	−0.665442
$821$	1.05247	0.0367315	0.0183658	−	0.999831i	$-0.494154\pi$
$821$	1.05247	0.0367315	0.0183658	+	0.999831i	$0.494154\pi$
$822$	10.1150	0.352800
$823$	36.9290	1.28726	0.643631	−	0.765336i	$-0.277427\pi$
$823$	36.9290	1.28726	0.643631	+	0.765336i	$0.277427\pi$
$824$	−3.83921	−0.133745
$825$	−2.63237	−0.0916473
$826$	1.01103	0.0351783
$827$	−10.4375	−0.362948	−0.181474	−	0.983396i	$-0.558087\pi$
$827$	−10.4375	−0.362948	−0.181474	+	0.983396i	$0.558087\pi$
$828$	73.5336	2.55547
$829$	−17.5141	−0.608291	−0.304145	−	0.952626i	$-0.598371\pi$
$829$	−17.5141	−0.608291	−0.304145	+	0.952626i	$0.598371\pi$
$830$	2.18735	0.0759239
$831$	−28.4090	−0.985497
$832$	−33.4495	−1.15965
$833$	−2.05888	−0.0713360
$834$	7.20863	0.249614
$835$	10.1434	0.351028
$836$	9.46168	0.327239
$837$	−64.3541	−2.22440
$838$	−7.04325	−0.243305
$839$	23.0283	0.795026	0.397513	−	0.917597i	$-0.369873\pi$
$839$	23.0283	0.795026	0.397513	+	0.917597i	$0.369873\pi$
$840$	−2.73244	−0.0942783
$841$	−11.6093	−0.400319
$842$	−7.40436	−0.255171
$843$	−78.6084	−2.70742
$844$	8.35144	0.287468
$845$	−11.9719	−0.411845
$846$	−10.4356	−0.358783
$847$	−10.3850	−0.356832
$848$	−13.4580	−0.462149
$849$	20.4138	0.700601
$850$	0.0816088	0.00279916
$851$	−19.0505	−0.653042
$852$	2.42914	0.0832211
$853$	41.3312	1.41515	0.707577	−	0.706637i	$-0.249788\pi$
$853$	41.3312	1.41515	0.707577	+	0.706637i	$0.249788\pi$
$854$	0.652325	0.0223221
$855$	27.8304	0.951778
$856$	9.56133	0.326799
$857$	−14.1899	−0.484718	−0.242359	−	0.970187i	$-0.577921\pi$
$857$	−14.1899	−0.484718	−0.242359	+	0.970187i	$0.577921\pi$
$858$	−3.10503	−0.106004
$859$	−15.4345	−0.526618	−0.263309	−	0.964712i	$-0.584814\pi$
$859$	−15.4345	−0.526618	−0.263309	+	0.964712i	$0.584814\pi$
$860$	−24.7984	−0.845619
$861$	28.7638	0.980269
$862$	−6.70664	−0.228429
$863$	−3.73755	−0.127228	−0.0636138	−	0.997975i	$-0.520263\pi$
$863$	−3.73755	−0.127228	−0.0636138	+	0.997975i	$0.520263\pi$
$864$	−17.5709	−0.597774
$865$	−2.03837	−0.0693068
$866$	7.00573	0.238064
$867$	48.4658	1.64598
$868$	−19.8579	−0.674021
$869$	−4.00171	−0.135749
$870$	2.82621	0.0958175
$871$	48.6176	1.64734
$872$	−18.2679	−0.618628
$873$	−57.7558	−1.95474
$874$	9.03708	0.305684
$875$	−1.02221	−0.0345568
$876$	−34.3210	−1.15960
$877$	−37.4630	−1.26504	−0.632518	−	0.774546i	$-0.717978\pi$
$877$	−37.4630	−1.26504	−0.632518	+	0.774546i	$0.717978\pi$
$878$	4.48902	0.151497
$879$	−45.0917	−1.52091
$880$	−3.36372	−0.113391
$881$	−21.1306	−0.711907	−0.355953	−	0.934504i	$-0.615844\pi$
$881$	−21.1306	−0.711907	−0.355953	+	0.934504i	$0.615844\pi$
$882$	−7.37036	−0.248173
$883$	−21.3153	−0.717317	−0.358658	−	0.933469i	$-0.616766\pi$
$883$	−21.3153	−0.717317	−0.358658	+	0.933469i	$0.616766\pi$
$884$	−3.35914	−0.112980
$885$	12.0305	0.404401
$886$	−2.95918	−0.0994156
$887$	28.5267	0.957834	0.478917	−	0.877860i	$-0.341029\pi$
$887$	28.5267	0.957834	0.478917	+	0.877860i	$0.341029\pi$
$888$	7.05990	0.236915
$889$	5.33544	0.178945
$890$	−3.36047	−0.112643
$891$	2.53268	0.0848480
$892$	−26.5255	−0.888138
$893$	44.7539	1.49763
$894$	5.37430	0.179743
$895$	−0.681587	−0.0227829
$896$	−7.19235	−0.240280
$897$	103.490	3.45542
$898$	4.24594	0.141689
$899$	41.6673	1.38968
$900$	−10.1945	−0.339816
$901$	−1.26823	−0.0422509
$902$	−2.12103	−0.0706227
$903$	37.4329	1.24569
$904$	13.9361	0.463507
$905$	−3.58428	−0.119145
$906$	15.9549	0.530065
$907$	−7.24122	−0.240441	−0.120220	−	0.992747i	$-0.538360\pi$
$907$	−7.24122	−0.240441	−0.120220	+	0.992747i	$0.538360\pi$
$908$	16.1912	0.537322
$909$	60.4302	2.00434
$910$	−1.20575	−0.0399703
$911$	−30.4699	−1.00951	−0.504756	−	0.863262i	$-0.668418\pi$
$911$	−30.4699	−1.00951	−0.504756	+	0.863262i	$0.668418\pi$
$912$	55.9098	1.85136
$913$	−8.49609	−0.281179
$914$	−6.44602	−0.213215
$915$	7.76216	0.256609
$916$	54.0225	1.78495
$917$	−1.80276	−0.0595325
$918$	−0.525627	−0.0173483
$919$	−56.0316	−1.84831	−0.924157	−	0.382013i	$-0.875231\pi$
$919$	−56.0316	−1.84831	−0.924157	+	0.382013i	$0.875231\pi$
$920$	−6.71557	−0.221406
$921$	25.7654	0.849000
$922$	−2.09022	−0.0688378
$923$	2.17454	0.0715760
$924$	5.23171	0.172111
$925$	2.64110	0.0868390
$926$	−4.17863	−0.137318
$927$	21.6215	0.710142
$928$	11.3766	0.373455
$929$	−17.8294	−0.584963	−0.292481	−	0.956271i	$-0.594481\pi$
$929$	−17.8294	−0.584963	−0.292481	+	0.956271i	$0.594481\pi$
$930$	6.77144	0.222044
$931$	31.6084	1.03592
$932$	30.6404	1.00366
$933$	28.0497	0.918305
$934$	−2.96894	−0.0971468
$935$	−0.316985	−0.0103665
$936$	−24.3946	−0.797363
$937$	10.3366	0.337681	0.168841	−	0.985643i	$-0.445998\pi$
$937$	10.3366	0.337681	0.168841	+	0.985643i	$0.445998\pi$
$938$	2.34747	0.0766476
$939$	1.29196	0.0421616
$940$	−16.3937	−0.534703
$941$	4.39565	0.143294	0.0716470	−	0.997430i	$-0.477174\pi$
$941$	4.39565	0.143294	0.0716470	+	0.997430i	$0.477174\pi$
$942$	−4.15544	−0.135392
$943$	70.6933	2.30209
$944$	15.3729	0.500347
$945$	6.58383	0.214172
$946$	−2.76029	−0.0897447
$947$	−13.1530	−0.427415	−0.213708	−	0.976898i	$-0.568554\pi$
$947$	−13.1530	−0.427415	−0.213708	+	0.976898i	$0.568554\pi$
$948$	−24.3647	−0.791328
$949$	−30.7238	−0.997337
$950$	−1.25287	−0.0406486
$951$	78.3477	2.54060
$952$	−0.329036	−0.0106641
$953$	52.7707	1.70941	0.854706	−	0.519113i	$-0.173738\pi$
$953$	52.7707	1.70941	0.854706	+	0.519113i	$0.173738\pi$
$954$	−4.54000	−0.146988
$955$	−15.4485	−0.499903
$956$	51.8690	1.67756
$957$	−10.9776	−0.354854
$958$	5.08459	0.164276
$959$	−15.2566	−0.492661
$960$	−19.2183	−0.620267
$961$	68.8325	2.22040
$962$	3.11534	0.100443
$963$	−53.8470	−1.73520
$964$	−14.7684	−0.475659
$965$	4.87672	0.156987
$966$	4.99694	0.160774
$967$	40.7983	1.31198	0.655992	−	0.754768i	$-0.272250\pi$
$967$	40.7983	1.31198	0.655992	+	0.754768i	$0.272250\pi$
$968$	9.45867	0.304013
$969$	5.26874	0.169256
$970$	2.60006	0.0834830
$971$	59.3602	1.90496	0.952479	−	0.304603i	$-0.0985239\pi$
$971$	59.3602	1.90496	0.952479	+	0.304603i	$0.0985239\pi$
$972$	−22.1479	−0.710394
$973$	−10.8729	−0.348569
$974$	1.01543	0.0325364
$975$	−14.3475	−0.459488
$976$	9.91872	0.317491
$977$	−21.8738	−0.699806	−0.349903	−	0.936786i	$-0.613785\pi$
$977$	−21.8738	−0.699806	−0.349903	+	0.936786i	$0.613785\pi$
$978$	4.96775	0.158851
$979$	13.0527	0.417167
$980$	−11.5784	−0.369858
$981$	102.880	3.28471
$982$	−1.78247	−0.0568808
$983$	−32.5706	−1.03884	−0.519421	−	0.854519i	$-0.673852\pi$
$983$	−32.5706	−1.03884	−0.519421	+	0.854519i	$0.673852\pi$
$984$	−26.1982	−0.835167
$985$	1.00000	0.0318626
$986$	0.340327	0.0108382
$987$	24.7461	0.787677
$988$	51.5701	1.64066
$989$	91.9994	2.92541
$990$	−1.13474	−0.0360643
$991$	−0.493203	−0.0156671	−0.00783356	−	0.999969i	$-0.502494\pi$
$991$	−0.493203	−0.0156671	−0.00783356	+	0.999969i	$0.502494\pi$
$992$	27.2577	0.865433
$993$	−13.4784	−0.427724
$994$	0.104997	0.00333029
$995$	20.0659	0.636133
$996$	−51.7290	−1.63909
$997$	19.0675	0.603872	0.301936	−	0.953328i	$-0.402367\pi$
$997$	19.0675	0.603872	0.301936	+	0.953328i	$0.402367\pi$
$998$	8.93483	0.282827
$999$	−17.0109	−0.538200

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	985.2.a.f.1.10	✓	14
3.2	odd	2		8865.2.a.v.1.5		14
5.4	even	2		4925.2.a.k.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
985.2.a.f.1.10	✓	14	1.1	even	1	trivial
4925.2.a.k.1.5		14	5.4	even	2
8865.2.a.v.1.5		14	3.2	odd	2

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:	\( N \)	\(=\)	\( 985 = 5 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	985.a (trivial)

\(f(q)\)	\(=\)	\(q+0.236045 q^{2} -2.87112 q^{3} -1.94428 q^{4} -1.00000 q^{5} -0.677712 q^{6} +1.02221 q^{7} -0.931027 q^{8} +5.24331 q^{9} -0.236045 q^{10} +0.916844 q^{11} +5.58226 q^{12} +4.99719 q^{13} +0.241286 q^{14} +2.87112 q^{15} +3.66880 q^{16} +0.345734 q^{17} +1.23766 q^{18} -5.30778 q^{19} +1.94428 q^{20} -2.93487 q^{21} +0.216416 q^{22} -7.21308 q^{23} +2.67309 q^{24} +1.00000 q^{25} +1.17956 q^{26} -6.44081 q^{27} -1.98746 q^{28} +4.17022 q^{29} +0.677712 q^{30} +9.99162 q^{31} +2.72806 q^{32} -2.63237 q^{33} +0.0816088 q^{34} -1.02221 q^{35} -10.1945 q^{36} +2.64110 q^{37} -1.25287 q^{38} -14.3475 q^{39} +0.931027 q^{40} -9.80072 q^{41} -0.692761 q^{42} -12.7545 q^{43} -1.78260 q^{44} -5.24331 q^{45} -1.70261 q^{46} -8.43174 q^{47} -10.5336 q^{48} -5.95510 q^{49} +0.236045 q^{50} -0.992644 q^{51} -9.71595 q^{52} -3.66822 q^{53} -1.52032 q^{54} -0.916844 q^{55} -0.951701 q^{56} +15.2393 q^{57} +0.984359 q^{58} +4.19018 q^{59} -5.58226 q^{60} +2.70353 q^{61} +2.35847 q^{62} +5.35974 q^{63} -6.69366 q^{64} -4.99719 q^{65} -0.621356 q^{66} +9.72899 q^{67} -0.672205 q^{68} +20.7096 q^{69} -0.241286 q^{70} +0.435154 q^{71} -4.88167 q^{72} -6.14822 q^{73} +0.623419 q^{74} -2.87112 q^{75} +10.3198 q^{76} +0.937203 q^{77} -3.38665 q^{78} -4.36466 q^{79} -3.66880 q^{80} +2.76239 q^{81} -2.31341 q^{82} -9.26666 q^{83} +5.70622 q^{84} -0.345734 q^{85} -3.01064 q^{86} -11.9732 q^{87} -0.853607 q^{88} +14.2366 q^{89} -1.23766 q^{90} +5.10815 q^{91} +14.0243 q^{92} -28.6871 q^{93} -1.99027 q^{94} +5.30778 q^{95} -7.83257 q^{96} -11.0151 q^{97} -1.40567 q^{98} +4.80730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 6 q^{2} - 7 q^{3} + 10 q^{4} - 14 q^{5} + 5 q^{6} - 4 q^{7} - 12 q^{8} + 13 q^{9} + 6 q^{10} - 5 q^{11} - 10 q^{12} - 15 q^{13} - 15 q^{14} + 7 q^{15} + 18 q^{16} - 18 q^{17} - 29 q^{18} + 20 q^{19}+ \cdots + 32 q^{99}+O(q^{100}) \) 14 * q - 6 * q^2 - 7 * q^3 + 10 * q^4 - 14 * q^5 + 5 * q^6 - 4 * q^7 - 12 * q^8 + 13 * q^9 + 6 * q^10 - 5 * q^11 - 10 * q^12 - 15 * q^13 - 15 * q^14 + 7 * q^15 + 18 * q^16 - 18 * q^17 - 29 * q^18 + 20 * q^19 - 10 * q^20 - 5 * q^21 + 12 * q^22 - 42 * q^23 + 7 * q^24 + 14 * q^25 - 13 * q^26 - 19 * q^27 - 3 * q^28 - 2 * q^29 - 5 * q^30 - 40 * q^32 - 10 * q^33 + 13 * q^34 + 4 * q^35 + q^36 - 15 * q^37 - 3 * q^38 - 19 * q^39 + 12 * q^40 + 3 * q^41 - 9 * q^42 - 15 * q^43 - 29 * q^44 - 13 * q^45 - 8 * q^46 - 40 * q^47 - 28 * q^48 + 12 * q^49 - 6 * q^50 - 13 * q^51 - 17 * q^52 - 39 * q^53 + 28 * q^54 + 5 * q^55 - 41 * q^56 - 17 * q^57 - 10 * q^58 + 19 * q^59 + 10 * q^60 - 18 * q^61 + 26 * q^62 - 28 * q^63 + 36 * q^64 + 15 * q^65 - 8 * q^66 - 22 * q^67 - 57 * q^68 + 12 * q^69 + 15 * q^70 - 50 * q^71 - 37 * q^72 - 10 * q^73 - 3 * q^74 - 7 * q^75 - 3 * q^76 - 36 * q^77 + 10 * q^78 + q^79 - 18 * q^80 - 42 * q^81 - 40 * q^82 - 12 * q^83 + 35 * q^84 + 18 * q^85 + 5 * q^86 - 35 * q^87 + 13 * q^88 + 7 * q^89 + 29 * q^90 + 16 * q^91 - 4 * q^92 - 37 * q^93 + 27 * q^94 - 20 * q^95 + 16 * q^96 + 2 * q^97 + 13 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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