LMFDB - Embedded newform 211.3.b.b.210.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [211,3,Mod(210,211)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(211, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("211.210");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 211 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	211.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$5.74933357800$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			210.13
Character	$\chi$	$=$	211.210
Dual form			211.3.b.b.210.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.22244i q^{2} +3.54198i q^{3} +2.50564 q^{4} -4.86203 q^{5} +4.32986 q^{6} +11.8298i q^{7} -7.95275i q^{8} -3.54564 q^{9} +O(q^{10})$	\(q-1.22244i q^{2} +3.54198i q^{3} +2.50564 q^{4} -4.86203 q^{5} +4.32986 q^{6} +11.8298i q^{7} -7.95275i q^{8} -3.54564 q^{9} +5.94353i q^{10} -18.5677 q^{11} +8.87494i q^{12} -0.681531 q^{13} +14.4612 q^{14} -17.2212i q^{15} +0.300820 q^{16} +15.1426i q^{17} +4.33433i q^{18} +2.48599 q^{19} -12.1825 q^{20} -41.9009 q^{21} +22.6979i q^{22} -6.83460i q^{23} +28.1685 q^{24} -1.36068 q^{25} +0.833130i q^{26} +19.3192i q^{27} +29.6412i q^{28} +13.6141i q^{29} -21.0519 q^{30} +42.4006i q^{31} -32.1787i q^{32} -65.7664i q^{33} +18.5109 q^{34} -57.5168i q^{35} -8.88411 q^{36} +52.2386 q^{37} -3.03897i q^{38} -2.41397i q^{39} +38.6665i q^{40} +4.55079i q^{41} +51.2213i q^{42} +79.5072 q^{43} -46.5240 q^{44} +17.2390 q^{45} -8.35488 q^{46} +15.5899 q^{47} +1.06550i q^{48} -90.9438 q^{49} +1.66334i q^{50} -53.6348 q^{51} -1.70767 q^{52} -31.0354 q^{53} +23.6166 q^{54} +90.2766 q^{55} +94.0793 q^{56} +8.80534i q^{57} +16.6425 q^{58} +85.0925 q^{59} -43.1502i q^{60} -85.4066i q^{61} +51.8321 q^{62} -41.9442i q^{63} -38.1333 q^{64} +3.31362 q^{65} -80.3954 q^{66} -66.6424i q^{67} +37.9419i q^{68} +24.2080 q^{69} -70.3107 q^{70} -14.7734 q^{71} +28.1976i q^{72} -110.968 q^{73} -63.8584i q^{74} -4.81949i q^{75} +6.22901 q^{76} -219.652i q^{77} -2.95093 q^{78} +32.1023 q^{79} -1.46259 q^{80} -100.339 q^{81} +5.56306 q^{82} +49.1675 q^{83} -104.989 q^{84} -73.6237i q^{85} -97.1927i q^{86} -48.2211 q^{87} +147.664i q^{88} +154.890i q^{89} -21.0736i q^{90} -8.06236i q^{91} -17.1251i q^{92} -150.182 q^{93} -19.0577i q^{94} -12.0870 q^{95} +113.977 q^{96} -69.6446i q^{97} +111.173i q^{98} +65.8343 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 84 q^{4} - 2 q^{5} - 20 q^{6} - 118 q^{9}+O(q^{10}) $ 32 * q - 84 * q^4 - 2 * q^5 - 20 * q^6 - 118 * q^9	$ 32 q - 84 q^{4} - 2 q^{5} - 20 q^{6} - 118 q^{9} - 10 q^{11} - 24 q^{13} + 6 q^{14} + 80 q^{16} - 30 q^{19} - 68 q^{20} + 68 q^{21} + 76 q^{24} + 86 q^{25} - 74 q^{30} + 20 q^{34} + 60 q^{36} + 138 q^{37} - 54 q^{43} - 18 q^{44} + 28 q^{45} + 302 q^{46} - 84 q^{47} - 378 q^{49} - 452 q^{51} + 138 q^{52} + 254 q^{53} + 214 q^{54} + 146 q^{55} + 216 q^{56} + 226 q^{58} + 234 q^{59} - 720 q^{62} - 168 q^{64} + 156 q^{65} - 66 q^{66} - 22 q^{69} - 398 q^{70} - 240 q^{71} + 40 q^{73} + 342 q^{76} - 376 q^{78} + 360 q^{79} - 122 q^{80} + 320 q^{81} + 26 q^{82} + 150 q^{83} + 300 q^{84} + 220 q^{87} - 874 q^{93} + 272 q^{95} - 230 q^{96} + 434 q^{99}+O(q^{100}) $ 32 * q - 84 * q^4 - 2 * q^5 - 20 * q^6 - 118 * q^9 - 10 * q^11 - 24 * q^13 + 6 * q^14 + 80 * q^16 - 30 * q^19 - 68 * q^20 + 68 * q^21 + 76 * q^24 + 86 * q^25 - 74 * q^30 + 20 * q^34 + 60 * q^36 + 138 * q^37 - 54 * q^43 - 18 * q^44 + 28 * q^45 + 302 * q^46 - 84 * q^47 - 378 * q^49 - 452 * q^51 + 138 * q^52 + 254 * q^53 + 214 * q^54 + 146 * q^55 + 216 * q^56 + 226 * q^58 + 234 * q^59 - 720 * q^62 - 168 * q^64 + 156 * q^65 - 66 * q^66 - 22 * q^69 - 398 * q^70 - 240 * q^71 + 40 * q^73 + 342 * q^76 - 376 * q^78 + 360 * q^79 - 122 * q^80 + 320 * q^81 + 26 * q^82 + 150 * q^83 + 300 * q^84 + 220 * q^87 - 874 * q^93 + 272 * q^95 - 230 * q^96 + 434 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/211\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	1.22244i		−	0.611219i	−0.952157	−	0.305610i	$-0.901140\pi$
$2$		−	1.22244i		−	0.611219i	0.952157	−	0.305610i	$-0.0988603\pi$
$3$			3.54198i			1.18066i	0.807162	+	0.590330i	$0.201003\pi$
$3$			3.54198i			1.18066i	−0.807162	+	0.590330i	$0.798997\pi$
$4$	2.50564			0.626411
$5$	−4.86203			−0.972406			−0.486203	−	0.873846i	$-0.661618\pi$
$5$	−4.86203			−0.972406			−0.486203	+	0.873846i	$0.661618\pi$
$6$	4.32986			0.721643
$7$			11.8298i			1.68997i	0.534791	+	0.844985i	$0.320390\pi$
$7$			11.8298i			1.68997i	−0.534791	+	0.844985i	$0.679610\pi$
$8$		−	7.95275i		−	0.994094i
$9$	−3.54564			−0.393960
$10$			5.94353i			0.594353i
$11$	−18.5677			−1.68797			−0.843985	−	0.536366i	$-0.819797\pi$
$11$	−18.5677			−1.68797			−0.843985	+	0.536366i	$0.819797\pi$
$12$			8.87494i			0.739579i
$13$	−0.681531			−0.0524255			−0.0262127	−	0.999656i	$-0.508345\pi$
$13$	−0.681531			−0.0524255			−0.0262127	+	0.999656i	$0.508345\pi$
$14$	14.4612			1.03294
$15$		−	17.2212i		−	1.14808i
$16$	0.300820			0.0188012
$17$			15.1426i			0.890741i	0.895346	+	0.445370i	$0.146928\pi$
$17$			15.1426i			0.890741i	−0.895346	+	0.445370i	$0.853072\pi$
$18$			4.33433i			0.240796i
$19$	2.48599			0.130842			0.0654209	−	0.997858i	$-0.479161\pi$
$19$	2.48599			0.130842			0.0654209	+	0.997858i	$0.479161\pi$
$20$	−12.1825			−0.609125
$21$	−41.9009			−1.99528
$22$			22.6979i			1.03172i
$23$		−	6.83460i		−	0.297157i	−0.988901	−	0.148578i	$-0.952530\pi$
$23$		−	6.83460i		−	0.297157i	0.988901	−	0.148578i	$-0.0474697\pi$
$24$	28.1685			1.17369
$25$	−1.36068			−0.0544271
$26$			0.833130i			0.0320435i
$27$			19.3192i			0.715528i
$28$			29.6412i			1.05861i
$29$			13.6141i			0.469453i	0.972061	+	0.234727i	$0.0754195\pi$
$29$			13.6141i			0.469453i	−0.972061	+	0.234727i	$0.924580\pi$
$30$	−21.0519			−0.701730
$31$			42.4006i			1.36776i	0.729594	+	0.683880i	$0.239709\pi$
$31$			42.4006i			1.36776i	−0.729594	+	0.683880i	$0.760291\pi$
$32$		−	32.1787i		−	1.00559i
$33$		−	65.7664i		−	1.99292i
$34$	18.5109			0.544438
$35$		−	57.5168i		−	1.64334i
$36$	−8.88411			−0.246781
$37$	52.2386			1.41185			0.705926	−	0.708285i	$-0.250531\pi$
$37$	52.2386			1.41185			0.705926	+	0.708285i	$0.250531\pi$
$38$		−	3.03897i		−	0.0799730i
$39$		−	2.41397i		−	0.0618967i
$40$			38.6665i			0.966663i
$41$			4.55079i			0.110995i	0.998459	+	0.0554975i	$0.0176745\pi$
$41$			4.55079i			0.110995i	−0.998459	+	0.0554975i	$0.982326\pi$
$42$			51.2213i			1.21955i
$43$	79.5072			1.84901			0.924503	−	0.381175i	$-0.124481\pi$
$43$	79.5072			1.84901			0.924503	+	0.381175i	$0.124481\pi$
$44$	−46.5240			−1.05736
$45$	17.2390			0.383089
$46$	−8.35488			−0.181628
$47$	15.5899			0.331700			0.165850	−	0.986151i	$-0.446963\pi$
$47$	15.5899			0.331700			0.165850	+	0.986151i	$0.446963\pi$
$48$			1.06550i			0.0221979i
$49$	−90.9438			−1.85600
$50$			1.66334i			0.0332669i
$51$	−53.6348			−1.05166
$52$	−1.70767			−0.0328399
$53$	−31.0354			−0.585574			−0.292787	−	0.956178i	$-0.594583\pi$
$53$	−31.0354			−0.585574			−0.292787	+	0.956178i	$0.594583\pi$
$54$	23.6166			0.437344
$55$	90.2766			1.64139
$56$	94.0793			1.67999
$57$			8.80534i			0.154480i
$58$	16.6425			0.286939
$59$	85.0925			1.44225			0.721123	−	0.692807i	$-0.243626\pi$
$59$	85.0925			1.44225			0.721123	+	0.692807i	$0.243626\pi$
$60$		−	43.1502i		−	0.719171i
$61$		−	85.4066i		−	1.40011i	−0.714090	−	0.700054i	$-0.753159\pi$
$61$		−	85.4066i		−	1.40011i	0.714090	−	0.700054i	$-0.246841\pi$
$62$	51.8321			0.836002
$63$		−	41.9442i		−	0.665780i
$64$	−38.1333			−0.595832
$65$	3.31362			0.0509788
$66$	−80.3954			−1.21811
$67$		−	66.6424i		−	0.994663i	−0.867561	−	0.497331i	$-0.834313\pi$
$67$		−	66.6424i		−	0.994663i	0.867561	−	0.497331i	$-0.165687\pi$
$68$			37.9419i			0.557969i
$69$	24.2080			0.350841
$70$	−70.3107			−1.00444
$71$	−14.7734			−0.208075			−0.104038	−	0.994573i	$-0.533176\pi$
$71$	−14.7734			−0.208075			−0.104038	+	0.994573i	$0.533176\pi$
$72$			28.1976i			0.391633i
$73$	−110.968			−1.52011			−0.760054	−	0.649860i	$-0.774828\pi$
$73$	−110.968			−1.52011			−0.760054	+	0.649860i	$0.774828\pi$
$74$		−	63.8584i		−	0.862952i
$75$		−	4.81949i		−	0.0642599i
$76$	6.22901			0.0819607
$77$		−	219.652i		−	2.85262i
$78$	−2.95093			−0.0378325
$79$	32.1023			0.406358			0.203179	−	0.979142i	$-0.434873\pi$
$79$	32.1023			0.406358			0.203179	+	0.979142i	$0.434873\pi$
$80$	−1.46259			−0.0182824
$81$	−100.339			−1.23876
$82$	5.56306			0.0678423
$83$	49.1675			0.592379			0.296190	−	0.955129i	$-0.404284\pi$
$83$	49.1675			0.592379			0.296190	+	0.955129i	$0.404284\pi$
$84$	−104.989			−1.24987
$85$		−	73.6237i		−	0.866161i
$86$		−	97.1927i		−	1.13015i
$87$	−48.2211			−0.554265
$88$			147.664i			1.67800i
$89$			154.890i			1.74034i	0.492754	+	0.870169i	$0.335990\pi$
$89$			154.890i			1.74034i	−0.492754	+	0.870169i	$0.664010\pi$
$90$		−	21.0736i		−	0.234152i
$91$		−	8.06236i		−	0.0885974i
$92$		−	17.1251i		−	0.186142i
$93$	−150.182			−1.61486
$94$		−	19.0577i		−	0.202741i
$95$	−12.0870			−0.127231
$96$	113.977			1.18726
$97$		−	69.6446i		−	0.717985i	−0.933340	−	0.358993i	$-0.883120\pi$
$97$		−	69.6446i		−	0.717985i	0.933340	−	0.358993i	$-0.116880\pi$
$98$			111.173i			1.13442i
$99$	65.8343			0.664993
$100$	−3.40937			−0.0340937
$101$	68.1462			0.674715			0.337358	−	0.941377i	$-0.390467\pi$
$101$	68.1462			0.674715			0.337358	+	0.941377i	$0.390467\pi$
$102$			65.5653i			0.642797i
$103$	101.966			0.989957			0.494979	−	0.868905i	$-0.335176\pi$
$103$	101.966			0.989957			0.494979	+	0.868905i	$0.335176\pi$
$104$			5.42005i			0.0521158i
$105$	203.723			1.94022
$106$			37.9389i			0.357914i
$107$	5.84170			0.0545953			0.0272977	−	0.999627i	$-0.491310\pi$
$107$	5.84170			0.0545953			0.0272977	+	0.999627i	$0.491310\pi$
$108$			48.4071i			0.448214i
$109$	−116.712			−1.07075			−0.535377	−	0.844613i	$-0.679830\pi$
$109$	−116.712			−1.07075			−0.535377	+	0.844613i	$0.679830\pi$
$110$		−	110.358i		−	1.00325i
$111$			185.028i			1.66692i
$112$			3.55863i			0.0317735i
$113$	169.698			1.50175			0.750875	−	0.660445i	$-0.229632\pi$
$113$	169.698			1.50175			0.750875	+	0.660445i	$0.229632\pi$
$114$	10.7640			0.0944210
$115$			33.2300i			0.288957i
$116$			34.1122i			0.294071i
$117$	2.41646			0.0206535
$118$		−	104.020i		−	0.881529i
$119$	−179.134			−1.50532
$120$	−136.956			−1.14130
$121$	223.759			1.84925
$122$	−104.404			−0.855773
$123$	−16.1188			−0.131047
$124$			106.241i			0.856780i
$125$	128.166			1.02533
$126$	−51.2742			−0.406938
$127$			209.619i			1.65054i	0.564737	+	0.825271i	$0.308978\pi$
$127$			209.619i			1.65054i	−0.564737	+	0.825271i	$0.691022\pi$
$128$		−	82.0994i		−	0.641401i
$129$			281.613i			2.18305i
$130$		−	4.05070i		−	0.0311592i
$131$			182.249i			1.39121i	0.718424	+	0.695606i	$0.244864\pi$
$131$			182.249i			1.39121i	−0.718424	+	0.695606i	$0.755136\pi$
$132$		−	164.787i		−	1.24839i
$133$			29.4088i			0.221118i
$134$	−81.4663			−0.607957
$135$		−	93.9307i		−	0.695783i
$136$	120.425			0.885480
$137$	−79.5164			−0.580411			−0.290206	−	0.956964i	$-0.593724\pi$
$137$	−79.5164			−0.580411			−0.290206	+	0.956964i	$0.593724\pi$
$138$		−	29.5928i		−	0.214441i
$139$	173.728			1.24984			0.624920	−	0.780689i	$-0.285132\pi$
$139$	173.728			1.24984			0.624920	+	0.780689i	$0.285132\pi$
$140$		−	144.116i		−	1.02940i
$141$			55.2191i			0.391625i
$142$			18.0595i			0.127180i
$143$	12.6544			0.0884926
$144$	−1.06660			−0.00740694
$145$		−	66.1924i		−	0.456499i
$146$			135.652i			0.929120i
$147$		−	322.121i		−	2.19130i
$148$	130.891			0.884400
$149$		−	9.98193i		−	0.0669928i	−0.999439	−	0.0334964i	$-0.989336\pi$
$149$		−	9.98193i		−	0.0669928i	0.999439	−	0.0334964i	$-0.0106642\pi$
$150$	−5.89154			−0.0392769
$151$	−128.924			−0.853801			−0.426901	−	0.904299i	$-0.640395\pi$
$151$	−128.924			−0.853801			−0.426901	+	0.904299i	$0.640395\pi$
$152$		−	19.7705i		−	0.130069i
$153$		−	53.6902i		−	0.350916i
$154$	−268.511			−1.74358
$155$		−	206.153i		−	1.33002i
$156$		−	6.04855i		−	0.0387728i
$157$			161.512i			1.02874i	0.857569	+	0.514369i	$0.171974\pi$
$157$			161.512i			1.02874i	−0.857569	+	0.514369i	$0.828026\pi$
$158$		−	39.2431i		−	0.248374i
$159$		−	109.927i		−	0.691364i
$160$			156.454i			0.977837i
$161$	80.8519			0.502185
$162$			122.659i			0.757151i
$163$	−95.4990			−0.585883			−0.292942	−	0.956130i	$-0.594634\pi$
$163$	−95.4990			−0.585883			−0.292942	+	0.956130i	$0.594634\pi$
$164$			11.4027i			0.0695284i
$165$			319.758i			1.93793i
$166$		−	60.1043i		−	0.362074i
$167$		−	157.947i		−	0.945788i	−0.881119	−	0.472894i	$-0.843209\pi$
$167$		−	157.947i		−	0.945788i	0.881119	−	0.472894i	$-0.156791\pi$
$168$			333.227i			1.98350i
$169$	−168.536			−0.997252
$170$	−90.0005			−0.529415
$171$	−8.81444			−0.0515464
$172$	199.217			1.15824
$173$	−76.9084			−0.444557			−0.222279	−	0.974983i	$-0.571349\pi$
$173$	−76.9084			−0.444557			−0.222279	+	0.974983i	$0.571349\pi$
$174$			58.9473i			0.338778i
$175$		−	16.0965i		−	0.0919801i
$176$	−5.58552			−0.0317359
$177$			301.396i			1.70280i
$178$	189.344			1.06373
$179$	−221.067			−1.23501			−0.617505	−	0.786567i	$-0.711856\pi$
$179$	−221.067			−1.23501			−0.617505	+	0.786567i	$0.711856\pi$
$180$	43.1948			0.239971
$181$			162.750i			0.899170i	0.893238	+	0.449585i	$0.148428\pi$
$181$			162.750i			0.899170i	−0.893238	+	0.449585i	$0.851572\pi$
$182$	−9.85575			−0.0541525
$183$	302.509			1.65305
$184$	−54.3539			−0.295402
$185$	−253.985			−1.37289
$186$			183.588i			0.987035i
$187$		−	281.163i		−	1.50354i
$188$	39.0627			0.207780
$189$	−228.542			−1.20922
$190$			14.7756i			0.0777662i
$191$		−	143.789i		−	0.752823i	−0.926453	−	0.376411i	$-0.877158\pi$
$191$		−	143.789i		−	0.752823i	0.926453	−	0.376411i	$-0.122842\pi$
$192$		−	135.067i		−	0.703476i
$193$	0.420061			0.00217648			0.00108824	−	0.999999i	$-0.499654\pi$
$193$	0.420061			0.00217648			0.00108824	+	0.999999i	$0.499654\pi$
$194$	−85.1362			−0.438847
$195$			11.7368i			0.0601887i
$196$	−227.873			−1.16262
$197$		−	39.4901i		−	0.200457i	−0.994964	−	0.100229i	$-0.968043\pi$
$197$		−	39.4901i		−	0.200457i	0.994964	−	0.100229i	$-0.0319574\pi$
$198$		−	80.4784i		−	0.406457i
$199$	−118.109			−0.593512			−0.296756	−	0.954953i	$-0.595905\pi$
$199$	−118.109			−0.593512			−0.296756	+	0.954953i	$0.595905\pi$
$200$			10.8211i			0.0541056i
$201$	236.046			1.17436
$202$		−	83.3046i		−	0.412399i
$203$	−161.052			−0.793362
$204$	−134.390			−0.658773
$205$		−	22.1261i		−	0.107932i
$206$		−	124.647i		−	0.605081i
$207$			24.2330i			0.117068i
$208$	−0.205018			−0.000985663
$209$	−46.1591			−0.220857
$210$		−	249.039i		−	1.18590i
$211$	63.9249	+	201.084i	0.302962	+	0.953003i
$211$	63.9249	+	201.084i	0.302962	+	0.953003i
$212$	−77.7637			−0.366810
$213$		−	52.3270i		−	0.245667i
$214$		−	7.14112i		−	0.0333697i
$215$	−386.566			−1.79798
$216$	153.641			0.711302
$217$	−501.590			−2.31147
$218$			142.673i			0.654465i
$219$		−	393.046i		−	1.79473i
$220$	226.201			1.02819
$221$		−	10.3201i		−	0.0466975i
$222$	226.186			1.01885
$223$		−	222.654i		−	0.998450i	−0.866472	−	0.499225i	$-0.833618\pi$
$223$		−	222.654i		−	0.998450i	0.866472	−	0.499225i	$-0.166382\pi$
$224$	380.668			1.69941
$225$	4.82447			0.0214421
$226$		−	207.445i		−	0.917899i
$227$	314.757			1.38660			0.693298	−	0.720651i	$-0.256157\pi$
$227$	314.757			1.38660			0.693298	+	0.720651i	$0.256157\pi$
$228$			22.0630i			0.0967678i
$229$		−	225.754i		−	0.985824i	−0.870079	−	0.492912i	$-0.835933\pi$
$229$		−	225.754i		−	0.985824i	0.870079	−	0.492912i	$-0.164067\pi$
$230$	40.6217			0.176616
$231$	778.002			3.36798
$232$	108.270			0.466681
$233$			168.819i			0.724544i	0.932072	+	0.362272i	$0.117999\pi$
$233$			168.819i			0.724544i	−0.932072	+	0.362272i	$0.882001\pi$
$234$		−	2.95398i		−	0.0126238i
$235$	−75.7985			−0.322547
$236$	213.212			0.903439
$237$			113.706i			0.479771i
$238$			218.980i			0.920083i
$239$		−	93.1072i		−	0.389570i	−0.980846	−	0.194785i	$-0.937599\pi$
$239$		−	93.1072i		−	0.389570i	0.980846	−	0.194785i	$-0.0624009\pi$
$240$		−	5.18048i		−	0.0215853i
$241$	−94.2789			−0.391199			−0.195599	−	0.980684i	$-0.562665\pi$
$241$	−94.2789			−0.391199			−0.195599	+	0.980684i	$0.562665\pi$
$242$		−	273.531i		−	1.13029i
$243$		−	181.527i		−	0.747023i
$244$		−	213.998i		−	0.877042i
$245$	442.171			1.80478
$246$			19.7043i			0.0800987i
$247$	−1.69428			−0.00685944
$248$	337.201			1.35968
$249$			174.150i			0.699399i
$250$		−	156.676i		−	0.626702i
$251$		−	165.798i		−	0.660551i	−0.943885	−	0.330275i	$-0.892858\pi$
$251$		−	165.798i		−	0.660551i	0.943885	−	0.330275i	$-0.107142\pi$
$252$		−	105.097i		−	0.417052i
$253$			126.903i			0.501592i
$254$	256.246			1.00884
$255$	260.774			1.02264
$256$	−252.895			−0.987869
$257$	−499.595			−1.94395			−0.971975	−	0.235085i	$-0.924463\pi$
$257$	−499.595			−1.94395			−0.971975	+	0.235085i	$0.924463\pi$
$258$	344.255			1.33432
$259$			617.971i			2.38599i
$260$	8.30276			0.0319337
$261$		−	48.2709i		−	0.184946i
$262$	222.788			0.850335
$263$	4.14562			0.0157628			0.00788142	−	0.999969i	$-0.497491\pi$
$263$	4.14562			0.0157628			0.00788142	+	0.999969i	$0.497491\pi$
$264$	−523.024			−1.98115
$265$	150.895			0.569416
$266$	35.9504			0.135152
$267$	−548.618			−2.05475
$268$		−	166.982i		−	0.623067i
$269$	238.242			0.885658			0.442829	−	0.896606i	$-0.353975\pi$
$269$	238.242			0.885658			0.442829	+	0.896606i	$0.353975\pi$
$270$	−114.825			−0.425276
$271$			260.047i			0.959584i	0.877382	+	0.479792i	$0.159288\pi$
$271$			260.047i			0.959584i	−0.877382	+	0.479792i	$0.840712\pi$
$272$			4.55519i			0.0167470i
$273$	28.5568			0.104603
$274$			97.2039i			0.354759i
$275$	25.2646			0.0918713
$276$	60.6567			0.219771
$277$	303.516			1.09572			0.547862	−	0.836569i	$-0.315442\pi$
$277$	303.516			1.09572			0.547862	+	0.836569i	$0.315442\pi$
$278$		−	212.371i		−	0.763926i
$279$		−	150.337i		−	0.538843i
$280$	−457.416			−1.63363
$281$	144.026			0.512548			0.256274	−	0.966604i	$-0.417505\pi$
$281$	144.026			0.512548			0.256274	+	0.966604i	$0.417505\pi$
$282$	67.5020			0.239369
$283$		−	203.887i		−	0.720450i	−0.932865	−	0.360225i	$-0.882700\pi$
$283$		−	203.887i		−	0.720450i	0.932865	−	0.360225i	$-0.117300\pi$
$284$	−37.0168			−0.130341
$285$		−	42.8118i		−	0.150217i
$286$		−	15.4693i		−	0.0540884i
$287$	−53.8349			−0.187578
$288$			114.094i			0.396161i
$289$	59.7020			0.206581
$290$	−80.9162			−0.279021
$291$	246.680			0.847697
$292$	−278.046			−0.952212
$293$	−459.174			−1.56715			−0.783574	−	0.621298i	$-0.786606\pi$
$293$	−459.174			−1.56715			−0.783574	+	0.621298i	$0.786606\pi$
$294$	−393.774			−1.33937
$295$	−413.722			−1.40245
$296$		−	415.440i		−	1.40351i
$297$		−	358.714i		−	1.20779i
$298$	−12.2023			−0.0409473
$299$			4.65799i			0.0155786i
$300$		−	12.0759i		−	0.0402531i
$301$			940.553i			3.12476i
$302$			157.602i			0.521860i
$303$			241.373i			0.796610i
$304$	0.747836			0.00245999
$305$			415.249i			1.36147i
$306$	−65.6330			−0.214487
$307$	−274.722			−0.894860			−0.447430	−	0.894319i	$-0.647661\pi$
$307$	−274.722			−0.894860			−0.447430	+	0.894319i	$0.647661\pi$
$308$		−	550.369i		−	1.78691i
$309$			361.160i			1.16880i
$310$	−252.009			−0.812933
$311$	381.259			1.22591			0.612957	−	0.790116i	$-0.289980\pi$
$311$	381.259			1.22591			0.612957	+	0.790116i	$0.289980\pi$
$312$	−19.1977			−0.0615311
$313$		−	39.4335i		−	0.125986i	−0.998014	−	0.0629928i	$-0.979935\pi$
$313$		−	39.4335i		−	0.125986i	0.998014	−	0.0629928i	$-0.0200645\pi$
$314$	197.439			0.628785
$315$			203.934i			0.647409i
$316$	80.4369			0.254547
$317$		−	218.972i		−	0.690765i	−0.938462	−	0.345382i	$-0.887749\pi$
$317$		−	218.972i		−	0.690765i	0.938462	−	0.345382i	$-0.112251\pi$
$318$	−134.379			−0.422575
$319$		−	252.783i		−	0.792424i
$320$	185.405			0.579391
$321$			20.6912i			0.0644586i
$322$		−	98.8365i		−	0.306946i
$323$			37.6444i			0.116546i
$324$	−251.414			−0.775970
$325$	0.927343			0.00285336
$326$			116.742i			0.358103i
$327$		−	413.392i		−	1.26420i
$328$	36.1913			0.110339
$329$			184.425i			0.560563i
$330$	390.885			1.18450
$331$	151.409			0.457430			0.228715	−	0.973493i	$-0.426548\pi$
$331$	151.409			0.457430			0.228715	+	0.973493i	$0.426548\pi$
$332$	123.196			0.371073
$333$	−185.219			−0.556214
$334$	−193.080			−0.578084
$335$			324.017i			0.967216i
$336$	−12.6046			−0.0375137
$337$	310.324			0.920842			0.460421	−	0.887701i	$-0.347699\pi$
$337$	310.324			0.920842			0.460421	+	0.887701i	$0.347699\pi$
$338$			206.024i			0.609540i
$339$			601.066i			1.77306i
$340$		−	184.475i		−	0.542573i
$341$		−	787.280i		−	2.30874i
$342$			10.7751i			0.0315062i
$343$		−	496.186i		−	1.44661i
$344$		−	632.301i		−	1.83809i
$345$	−117.700			−0.341160
$346$			94.0158i			0.271722i
$347$	152.859			0.440516			0.220258	−	0.975442i	$-0.429310\pi$
$347$	152.859			0.440516			0.220258	+	0.975442i	$0.429310\pi$
$348$	−120.825			−0.347198
$349$			71.6495i			0.205300i	0.994718	+	0.102650i	$0.0327321\pi$
$349$			71.6495i			0.205300i	−0.994718	+	0.102650i	$0.967268\pi$
$350$	−19.6770			−0.0562200
$351$		−	13.1667i		−	0.0375119i
$352$			597.484i			1.69740i
$353$			269.623i			0.763804i	0.924203	+	0.381902i	$0.124731\pi$
$353$			269.623i			0.763804i	−0.924203	+	0.381902i	$0.875269\pi$
$354$	368.439			1.04079
$355$	71.8285			0.202334
$356$			388.099i			1.09017i
$357$		−	634.488i		−	1.77728i
$358$			270.241i			0.754862i
$359$	−56.8841			−0.158452			−0.0792258	−	0.996857i	$-0.525245\pi$
$359$	−56.8841			−0.158452			−0.0792258	+	0.996857i	$0.525245\pi$
$360$		−	137.098i		−	0.380827i
$361$	−354.820			−0.982880
$362$	198.952			0.549590
$363$			792.549i			2.18333i
$364$		−	20.2014i		−	0.0554984i
$365$	539.529			1.47816
$366$		−	369.798i		−	1.01038i
$367$		−	330.369i		−	0.900188i	−0.892981	−	0.450094i	$-0.851391\pi$
$367$		−	330.369i		−	0.900188i	0.892981	−	0.450094i	$-0.148609\pi$
$368$		−	2.05598i		−	0.00558691i
$369$		−	16.1355i		−	0.0437276i
$370$			310.482i			0.839139i
$371$		−	367.142i		−	0.989602i
$372$	−376.303			−1.01157
$373$		−	299.106i		−	0.801894i	−0.916101	−	0.400947i	$-0.868681\pi$
$373$		−	299.106i		−	0.801894i	0.916101	−	0.400947i	$-0.131319\pi$
$374$	−343.704			−0.918995
$375$			453.963i			1.21057i
$376$		−	123.983i		−	0.329741i
$377$		−	9.27846i		−	0.0246113i
$378$			279.379i			0.739099i
$379$		−	274.848i		−	0.725192i	−0.931946	−	0.362596i	$-0.881890\pi$
$379$		−	274.848i		−	0.725192i	0.931946	−	0.362596i	$-0.118110\pi$
$380$	−30.2856			−0.0796990
$381$	−742.466			−1.94873
$382$	−175.773			−0.460140
$383$	−90.3268			−0.235840			−0.117920	−	0.993023i	$-0.537623\pi$
$383$	−90.3268			−0.235840			−0.117920	+	0.993023i	$0.537623\pi$
$384$	290.795			0.757277
$385$			1067.95i			2.77390i
$386$		−	0.513499i		−	0.00133031i
$387$	−281.904			−0.728434
$388$		−	174.504i		−	0.449754i
$389$	421.184			1.08274			0.541368	−	0.840786i	$-0.317907\pi$
$389$	421.184			1.08274			0.541368	+	0.840786i	$0.317907\pi$
$390$	14.3475			0.0367885
$391$	103.494			0.264689
$392$			723.253i			1.84503i
$393$	−645.522			−1.64255
$394$	−48.2742			−0.122523
$395$	−156.082			−0.395145
$396$	164.957			0.416559
$397$		−	125.749i		−	0.316748i	−0.987379	−	0.158374i	$-0.949375\pi$
$397$		−	125.749i		−	0.316748i	0.987379	−	0.158374i	$-0.0506251\pi$
$398$			144.381i			0.362766i
$399$	−104.165			−0.261066
$400$	−0.409318			−0.00102330
$401$			766.100i			1.91047i	0.295843	+	0.955237i	$0.404400\pi$
$401$			766.100i			1.91047i	−0.295843	+	0.955237i	$0.595600\pi$
$402$		−	288.552i		−	0.717791i
$403$		−	28.8973i		−	0.0717055i
$404$	170.750			0.422649
$405$	487.852			1.20457
$406$			196.877i			0.484918i
$407$	−969.949			−2.38317
$408$			426.544i			1.04545i
$409$		−	578.057i		−	1.41334i	−0.707542	−	0.706671i	$-0.750196\pi$
$409$		−	578.057i		−	1.41334i	0.707542	−	0.706671i	$-0.249804\pi$
$410$	−27.0478			−0.0659702
$411$		−	281.646i		−	0.685269i
$412$	255.489			0.620120
$413$			1006.63i			2.43735i
$414$	29.6234			0.0715541
$415$	−239.054			−0.576033
$416$			21.9308i			0.0527183i
$417$			615.340i			1.47564i
$418$			56.4267i			0.134992i
$419$	210.206			0.501685			0.250843	−	0.968028i	$-0.419292\pi$
$419$	210.206			0.501685			0.250843	+	0.968028i	$0.419292\pi$
$420$	510.458			1.21538
$421$		−	766.459i		−	1.82057i	−0.413984	−	0.910284i	$-0.635863\pi$
$421$		−	766.459i		−	1.82057i	0.413984	−	0.910284i	$-0.364137\pi$
$422$	245.812	−	78.1443i	0.582494	−	0.185176i
$423$	−55.2762			−0.130677
$424$			246.817i			0.582116i
$425$		−	20.6042i		−	0.0484804i
$426$	−63.9665			−0.150156
$427$	1010.34			2.36614
$428$	14.6372			0.0341991
$429$			44.8218i			0.104480i
$430$			472.554i			1.09896i
$431$	−713.685			−1.65588			−0.827940	−	0.560816i	$-0.810487\pi$
$431$	−713.685			−1.65588			−0.827940	+	0.560816i	$0.810487\pi$
$432$			5.81161i			0.0134528i
$433$	734.106			1.69539			0.847697	−	0.530481i	$-0.177989\pi$
$433$	734.106			1.69539			0.847697	+	0.530481i	$0.177989\pi$
$434$			613.163i			1.41282i
$435$	234.452			0.538971
$436$	−292.439			−0.670732
$437$		−	16.9908i		−	0.0388805i
$438$	−480.475			−1.09698
$439$		−	1.58827i		−	0.00361794i	−0.999998	−	0.00180897i	$-0.999424\pi$
$439$		−	1.58827i		−	0.00361794i	0.999998	−	0.00180897i	$-0.000575813\pi$
$440$		−	717.947i		−	1.63170i
$441$	322.454			0.731188
$442$	−12.6157			−0.0285424
$443$	240.526			0.542948			0.271474	−	0.962446i	$-0.412489\pi$
$443$	240.526			0.542948			0.271474	+	0.962446i	$0.412489\pi$
$444$			463.614i			1.04418i
$445$		−	753.080i		−	1.69231i
$446$	−272.181			−0.610272
$447$	35.3558			0.0790958
$448$		−	451.108i		−	1.00694i
$449$			710.840i			1.58316i	0.611065	+	0.791581i	$0.290742\pi$
$449$			710.840i			1.58316i	−0.611065	+	0.791581i	$0.709258\pi$
$450$		−	5.89762i		−	0.0131058i
$451$		−	84.4976i		−	0.187356i
$452$	425.202			0.940712
$453$		−	456.646i		−	1.00805i
$454$		−	384.772i		−	0.847515i
$455$			39.1994i			0.0861526i
$456$	70.0267			0.153567
$457$			413.489i			0.904789i	0.891818	+	0.452395i	$0.149430\pi$
$457$			413.489i			0.904789i	−0.891818	+	0.452395i	$0.850570\pi$
$458$	−275.970			−0.602555
$459$	−292.543			−0.637349
$460$			83.2626i			0.181006i
$461$		−	684.958i		−	1.48581i	−0.669398	−	0.742904i	$-0.733448\pi$
$461$		−	684.958i		−	1.48581i	0.669398	−	0.742904i	$-0.266552\pi$
$462$		−	951.060i		−	2.05857i
$463$		−	605.572i		−	1.30793i	−0.756525	−	0.653965i	$-0.773104\pi$
$463$		−	605.572i		−	1.30793i	0.756525	−	0.653965i	$-0.226896\pi$
$464$			4.09540i			0.00882630i
$465$	730.190			1.57030
$466$	206.371			0.442856
$467$	868.334			1.85939			0.929694	−	0.368332i	$-0.120071\pi$
$467$	868.334			1.85939			0.929694	+	0.368332i	$0.120071\pi$
$468$	6.05480			0.0129376
$469$	788.365			1.68095
$470$			92.6591i			0.197147i
$471$	−572.073			−1.21459
$472$		−	676.720i		−	1.43373i
$473$	−1476.26			−3.12107
$474$	138.998			0.293245
$475$	−3.38263			−0.00712133
$476$	−448.845			−0.942951
$477$	110.040			0.230693
$478$	−113.818			−0.238113
$479$		−	322.377i		−	0.673021i	−0.941680	−	0.336510i	$-0.890753\pi$
$479$		−	322.377i		−	0.673021i	0.941680	−	0.336510i	$-0.109247\pi$
$480$	−554.157			−1.15449
$481$	−35.6022			−0.0740170
$482$			115.250i			0.239108i
$483$			286.376i			0.592911i
$484$	560.659			1.15839
$485$			338.614i			0.698173i
$486$	−221.905			−0.456595
$487$	813.798			1.67104			0.835522	−	0.549458i	$-0.185166\pi$
$487$	813.798			1.67104			0.835522	+	0.549458i	$0.185166\pi$
$488$	−679.217			−1.39184
$489$		−	338.256i		−	0.691730i
$490$		−	540.527i		−	1.10312i
$491$	−390.662			−0.795645			−0.397822	−	0.917462i	$-0.630234\pi$
$491$	−390.662			−0.795645			−0.397822	+	0.917462i	$0.630234\pi$
$492$	−40.3880			−0.0820895
$493$	−206.153			−0.418161
$494$			2.07116i			0.00419262i
$495$	−320.088			−0.646643
$496$			12.7549i			0.0257156i
$497$		−	174.766i		−	0.351641i
$498$	212.888			0.427486
$499$			840.503i			1.68438i	0.539184	+	0.842188i	$0.318733\pi$
$499$			840.503i			1.68438i	−0.539184	+	0.842188i	$0.681267\pi$
$500$	321.139			0.642278
$501$	559.444			1.11665
$502$	−202.678			−0.403742
$503$	−408.234			−0.811598			−0.405799	−	0.913962i	$-0.633007\pi$
$503$	−408.234			−0.811598			−0.405799	+	0.913962i	$0.633007\pi$
$504$	−333.572			−0.661848
$505$	−331.329			−0.656097
$506$	155.131			0.306583
$507$		−	596.950i		−	1.17742i
$508$			525.230i			1.03392i
$509$	−379.569			−0.745715			−0.372858	−	0.927889i	$-0.621622\pi$
$509$	−379.569			−0.745715			−0.372858	+	0.927889i	$0.621622\pi$
$510$		−	318.780i		−	0.625059i
$511$		−	1312.73i		−	2.56894i
$512$		−	19.2494i		−	0.0375964i
$513$			48.0275i			0.0936209i
$514$			610.724i			1.18818i
$515$	−495.760			−0.962640
$516$			705.622i			1.36749i
$517$	−289.468			−0.559900
$518$	755.432			1.45836
$519$		−	272.408i		−	0.524871i
$520$		−	26.3524i		−	0.0506777i
$521$	755.815			1.45070			0.725350	−	0.688380i	$-0.241678\pi$
$521$	755.815			1.45070			0.725350	+	0.688380i	$0.241678\pi$
$522$	−59.0082			−0.113043
$523$	531.121			1.01553			0.507764	−	0.861496i	$-0.330472\pi$
$523$	531.121			1.01553			0.507764	+	0.861496i	$0.330472\pi$
$524$			456.650i			0.871470i
$525$	57.0136			0.108597
$526$		−	5.06777i		−	0.00963455i
$527$	−642.055			−1.21832
$528$		−	19.7838i		−	0.0374694i
$529$	482.288			0.911698
$530$		−	184.460i		−	0.348038i
$531$	−301.708			−0.568188
$532$			73.6879i			0.138511i
$533$		−	3.10151i		−	0.00581896i
$534$			670.652i			1.25590i
$535$	−28.4025			−0.0530888
$536$	−529.990			−0.988788
$537$		−	783.014i		−	1.45813i
$538$		−	291.236i		−	0.541331i
$539$	1688.62			3.13287
$540$		−	235.357i		−	0.435846i
$541$	−834.199			−1.54196			−0.770978	−	0.636861i	$-0.780232\pi$
$541$	−834.199			−1.54196			−0.770978	+	0.636861i	$0.780232\pi$
$542$	317.892			0.586516
$543$	−576.457			−1.06161
$544$	487.269			0.895716
$545$	567.458			1.04121
$546$		−	34.9089i		−	0.0639357i
$547$	−35.9520			−0.0657258			−0.0328629	−	0.999460i	$-0.510462\pi$
$547$	−35.9520			−0.0657258			−0.0328629	+	0.999460i	$0.510462\pi$
$548$	−199.240			−0.363576
$549$			302.821i			0.551586i
$550$		−	30.8844i		−	0.0561535i
$551$			33.8447i			0.0614241i
$552$		−	192.521i		−	0.348769i
$553$			379.763i			0.686733i
$554$		−	371.029i		−	0.669728i
$555$		−	899.612i		−	1.62092i
$556$	435.300			0.782913
$557$		−	985.266i		−	1.76888i	−0.466653	−	0.884440i	$-0.654540\pi$
$557$		−	985.266i		−	1.76888i	0.466653	−	0.884440i	$-0.345460\pi$
$558$	−183.778			−0.329351
$559$	−54.1866			−0.0969350
$560$		−	17.3022i		−	0.0308967i
$561$	995.874			1.77518
$562$		−	176.063i		−	0.313279i
$563$			560.801i			0.996095i	0.867150	+	0.498047i	$0.165949\pi$
$563$			560.801i			0.996095i	−0.867150	+	0.498047i	$0.834051\pi$
$564$			138.359i			0.245318i
$565$	−825.075			−1.46031
$566$	−249.240			−0.440353
$567$		−	1186.99i		−	2.09346i
$568$			117.489i			0.206847i
$569$			354.951i			0.623816i	0.950112	+	0.311908i	$0.100968\pi$
$569$			354.951i			0.623816i	−0.950112	+	0.311908i	$0.899032\pi$
$570$	−52.3349			−0.0918155
$571$		−	191.549i		−	0.335462i	−0.985833	−	0.167731i	$-0.946356\pi$
$571$		−	191.549i		−	0.335462i	0.985833	−	0.167731i	$-0.0536441\pi$
$572$	31.7075			0.0554327
$573$	509.299			0.888828
$574$			65.8099i			0.114651i
$575$			9.29968i			0.0161734i
$576$	135.207			0.234734
$577$			274.941i			0.476501i	0.971204	+	0.238250i	$0.0765739\pi$
$577$			274.941i			0.476501i	−0.971204	+	0.238250i	$0.923426\pi$
$578$		−	72.9820i		−	0.126266i
$579$			1.48785i			0.00256969i
$580$		−	165.854i		−	0.285956i
$581$			581.641i			1.00110i
$582$		−	301.551i		−	0.518129i
$583$	576.256			0.988432
$584$			882.500i			1.51113i
$585$	−11.7489			−0.0200836
$586$			561.313i			0.957871i
$587$			1061.77i			1.80881i	0.426677	+	0.904404i	$0.359684\pi$
$587$			1061.77i			1.80881i	−0.426677	+	0.904404i	$0.640316\pi$
$588$		−	807.121i		−	1.37265i
$589$			105.408i			0.178960i
$590$			505.750i			0.857204i
$591$	139.873			0.236672
$592$	15.7144			0.0265446
$593$	494.862			0.834506			0.417253	−	0.908790i	$-0.362993\pi$
$593$	494.862			0.834506			0.417253	+	0.908790i	$0.362993\pi$
$594$	−438.505			−0.738225
$595$	870.953			1.46379
$596$		−	25.0111i		−	0.0419650i
$597$		−	418.340i		−	0.700736i
$598$	5.69411			0.00952192
$599$			1010.54i			1.68705i	0.537091	+	0.843524i	$0.319523\pi$
$599$			1010.54i			1.68705i	−0.537091	+	0.843524i	$0.680477\pi$
$600$	−38.3282			−0.0638804
$601$	118.670			0.197454			0.0987269	−	0.995115i	$-0.468523\pi$
$601$	118.670			0.197454			0.0987269	+	0.995115i	$0.468523\pi$
$602$	1149.77			1.90992
$603$			236.290i			0.391857i
$604$	−323.037			−0.534830
$605$	−1087.92			−1.79822
$606$	295.063			0.486903
$607$	−102.107			−0.168215			−0.0841077	−	0.996457i	$-0.526804\pi$
$607$	−102.107			−0.168215			−0.0841077	+	0.996457i	$0.526804\pi$
$608$		−	79.9961i		−	0.131573i
$609$		−	570.445i		−	0.936691i
$610$	507.617			0.832158
$611$	−10.6250			−0.0173895
$612$		−	134.528i		−	0.219818i
$613$		−	139.513i		−	0.227590i	−0.993504	−	0.113795i	$-0.963699\pi$
$613$		−	139.513i		−	0.227590i	0.993504	−	0.113795i	$-0.0363008\pi$
$614$			335.831i			0.546956i
$615$	78.3702			0.127431
$616$	−1746.83			−2.83577
$617$		−	1115.24i		−	1.80751i	−0.428047	−	0.903756i	$-0.640798\pi$
$617$		−	1115.24i		−	1.80751i	0.428047	−	0.903756i	$-0.359202\pi$
$618$	441.496			0.714395
$619$			694.243i			1.12156i	0.827966	+	0.560778i	$0.189498\pi$
$619$			694.243i			1.12156i	−0.827966	+	0.560778i	$0.810502\pi$
$620$		−	516.545i		−	0.833138i
$621$	132.039			0.212624
$622$		−	466.066i		−	0.749302i
$623$	−1832.32			−2.94112
$624$		−	0.726170i		−	0.00116373i
$625$	−589.132			−0.942611
$626$	−48.2051			−0.0770049
$627$		−	163.495i		−	0.260757i
$628$			404.691i			0.644413i
$629$			791.027i			1.25759i
$630$	249.297			0.395709
$631$	−364.441			−0.577560			−0.288780	−	0.957395i	$-0.593250\pi$
$631$	−364.441			−0.577560			−0.288780	+	0.957395i	$0.593250\pi$
$632$		−	255.302i		−	0.403958i
$633$	−712.235	+	226.421i	−1.12517	+	0.357695i
$634$	−267.680			−0.422209
$635$		−	1019.17i		−	1.60500i
$636$		−	275.438i		−	0.433078i
$637$	61.9810			0.0973014
$638$	−309.012			−0.484345
$639$	52.3810			0.0819734
$640$			399.169i			0.623702i
$641$		−	256.263i		−	0.399787i	−0.979818	−	0.199893i	$-0.935940\pi$
$641$		−	256.263i		−	0.399787i	0.979818	−	0.199893i	$-0.0640596\pi$
$642$	25.2937			0.0393983
$643$			779.614i			1.21246i	0.795288	+	0.606231i	$0.207320\pi$
$643$			779.614i			1.21246i	−0.795288	+	0.606231i	$0.792680\pi$
$644$	202.586			0.314574
$645$		−	1369.21i		−	2.12281i
$646$	46.0179			0.0712352
$647$	899.033			1.38954			0.694770	−	0.719232i	$-0.255506\pi$
$647$	899.033			1.38954			0.694770	+	0.719232i	$0.255506\pi$
$648$			797.973i			1.23144i
$649$	−1579.97			−2.43447
$650$		−	1.13362i		−	0.00174403i
$651$		−	1776.62i		−	2.72907i
$652$	−239.286			−0.367004
$653$	−242.793			−0.371811			−0.185906	−	0.982568i	$-0.559522\pi$
$653$	−242.793			−0.371811			−0.185906	+	0.982568i	$0.559522\pi$
$654$	−505.347			−0.772702
$655$		−	886.098i		−	1.35282i
$656$			1.36897i			0.00208684i
$657$	393.452			0.598862
$658$	225.448			0.342627
$659$		−	126.305i		−	0.191661i	−0.995398	−	0.0958307i	$-0.969449\pi$
$659$		−	126.305i		−	0.191661i	0.995398	−	0.0958307i	$-0.0305508\pi$
$660$			801.200i			1.21394i
$661$			632.493i			0.956873i	0.878122	+	0.478436i	$0.158796\pi$
$661$			632.493i			0.956873i	−0.878122	+	0.478436i	$0.841204\pi$
$662$		−	185.089i		−	0.279590i
$663$	36.5538			0.0551339
$664$		−	391.017i		−	0.588881i
$665$		−	142.986i		−	0.215017i
$666$			226.419i			0.339969i
$667$	93.0473			0.139501
$668$		−	395.758i		−	0.592452i
$669$	788.638			1.17883
$670$	396.091			0.591181
$671$			1585.80i			2.36334i
$672$			1348.32i			2.00643i
$673$		−	601.638i		−	0.893964i	−0.894543	−	0.446982i	$-0.852499\pi$
$673$		−	601.638i		−	0.893964i	0.894543	−	0.446982i	$-0.147501\pi$
$674$		−	379.352i		−	0.562836i
$675$		−	26.2872i		−	0.0389441i
$676$	−422.290			−0.624689
$677$	220.241			0.325318			0.162659	−	0.986682i	$-0.447993\pi$
$677$	220.241			0.325318			0.162659	+	0.986682i	$0.447993\pi$
$678$	734.767			1.08373
$679$	823.880			1.21337
$680$	−585.511			−0.861046
$681$			1114.87i			1.63710i
$682$	−962.402			−1.41115
$683$			830.505i			1.21597i	0.793950	+	0.607983i	$0.208021\pi$
$683$			830.505i			1.21597i	−0.793950	+	0.607983i	$0.791979\pi$
$684$	−22.0858			−0.0322892
$685$	386.611			0.564395
$686$	−606.557			−0.884194
$687$	799.615			1.16392
$688$	23.9173			0.0347636
$689$	21.1516			0.0306990
$690$			143.881i			0.208524i
$691$	−216.554			−0.313392			−0.156696	−	0.987647i	$-0.550084\pi$
$691$	−216.554			−0.313392			−0.156696	+	0.987647i	$0.550084\pi$
$692$	−192.705			−0.278475
$693$			778.806i			1.12382i
$694$		−	186.861i		−	0.269252i
$695$	−844.669			−1.21535
$696$			383.490i			0.550992i
$697$	−68.9108			−0.0988677
$698$	87.5872			0.125483
$699$	−597.953			−0.855441
$700$		−	40.3321i		−	0.0576173i
$701$		−	250.464i		−	0.357295i	−0.983913	−	0.178647i	$-0.942828\pi$
$701$		−	250.464i		−	0.357295i	0.983913	−	0.178647i	$-0.0571721\pi$
$702$	−16.0954			−0.0229280
$703$	129.865			0.184729
$704$	708.046			1.00575
$705$		−	268.477i		−	0.380819i
$706$	329.598			0.466852
$707$			806.155i			1.14025i
$708$			755.192i			1.06665i
$709$	995.009			1.40340			0.701699	−	0.712474i	$-0.252425\pi$
$709$	995.009			1.40340			0.701699	+	0.712474i	$0.252425\pi$
$710$		−	87.8059i		−	0.123670i
$711$	−113.823			−0.160089
$712$	1231.80			1.73006
$713$	289.791			0.406439
$714$	−775.623			−1.08631
$715$	−61.5263			−0.0860507
$716$	−553.914			−0.773623
$717$	329.784			0.459950
$718$			69.5374i			0.0968487i
$719$		−	191.938i		−	0.266951i	−0.991052	−	0.133476i	$-0.957386\pi$
$719$		−	191.938i		−	0.266951i	0.991052	−	0.133476i	$-0.0426138\pi$
$720$	5.18583			0.00720255
$721$			1206.23i			1.67300i
$722$			433.746i			0.600756i
$723$		−	333.934i		−	0.461873i
$724$			407.793i			0.563250i
$725$		−	18.5245i		−	0.0255510i
$726$	968.843			1.33449
$727$		−	859.636i		−	1.18244i	−0.806509	−	0.591221i	$-0.798646\pi$
$727$		−	859.636i		−	1.18244i	0.806509	−	0.591221i	$-0.201354\pi$
$728$	−64.1180			−0.0880741
$729$	−260.089			−0.356775
$730$		−	659.542i		−	0.903482i
$731$			1203.95i			1.64698i
$732$	757.978			1.03549
$733$	551.166			0.751932			0.375966	−	0.926633i	$-0.377311\pi$
$733$	551.166			0.751932			0.375966	+	0.926633i	$0.377311\pi$
$734$	−403.856			−0.550212
$735$			1566.16i			2.13083i
$736$	−219.929			−0.298816
$737$			1237.39i			1.67896i
$738$	−19.7246			−0.0267271
$739$			57.0583i			0.0772101i	0.999255	+	0.0386051i	$0.0122914\pi$
$739$			57.0583i			0.0772101i	−0.999255	+	0.0386051i	$0.987709\pi$
$740$	−636.397			−0.859996
$741$		−	6.00111i		−	0.00809867i
$742$	−448.809			−0.604864
$743$		−	1018.90i		−	1.37133i	−0.727918	−	0.685665i	$-0.759512\pi$
$743$		−	1018.90i		−	1.37133i	0.727918	−	0.685665i	$-0.240488\pi$
$744$			1194.36i			1.60532i
$745$			48.5324i			0.0651442i
$746$	−365.639			−0.490133
$747$	−174.330			−0.233374
$748$		−	704.493i		−	0.941836i
$749$			69.1060i			0.0922644i
$750$	554.942			0.739923
$751$		−	745.330i		−	0.992451i	−0.868194	−	0.496225i	$-0.834719\pi$
$751$		−	745.330i		−	0.992451i	0.868194	−	0.496225i	$-0.165281\pi$
$752$	4.68975			0.00623637
$753$	587.255			0.779887
$754$	−11.3424			−0.0150429
$755$	626.832			0.830241
$756$	−572.646			−0.757468
$757$			4.83528i			0.00638742i	0.999995	+	0.00319371i	$0.00101659\pi$
$757$			4.83528i			0.00638742i	−0.999995	+	0.00319371i	$0.998983\pi$
$758$	−335.985			−0.443251
$759$	−449.487			−0.592210
$760$			96.1247i			0.126480i
$761$		−	871.514i		−	1.14522i	−0.819827	−	0.572611i	$-0.805931\pi$
$761$		−	871.514i		−	1.14522i	0.819827	−	0.572611i	$-0.194069\pi$
$762$			907.620i			1.19110i
$763$		−	1380.68i		−	1.80954i
$764$		−	360.284i		−	0.471576i
$765$			261.043i			0.341233i
$766$			110.419i			0.144150i
$767$	−57.9932			−0.0756104
$768$		−	895.748i		−	1.16634i
$769$	−1111.34			−1.44517			−0.722587	−	0.691280i	$-0.757047\pi$
$769$	−1111.34			−1.44517			−0.722587	+	0.691280i	$0.757047\pi$
$770$	1305.51			1.69546
$771$		−	1769.56i		−	2.29515i
$772$	1.05252			0.00136337
$773$			311.752i			0.403301i	0.979457	+	0.201651i	$0.0646306\pi$
$773$			311.752i			0.403301i	−0.979457	+	0.201651i	$0.935369\pi$
$774$			344.611i			0.445233i
$775$		−	57.6935i		−	0.0744432i
$776$	−553.866			−0.713745
$777$	−2188.84			−2.81704
$778$		−	514.872i		−	0.661789i
$779$			11.3132i			0.0145228i
$780$			29.4082i			0.0377028i
$781$	274.307			0.351225
$782$		−	126.515i		−	0.161783i
$783$	−263.015			−0.335907
$784$	−27.3577			−0.0348950
$785$		−	785.276i		−	1.00035i
$786$			789.111i			1.00396i
$787$	456.562			0.580129			0.290065	−	0.957007i	$-0.406323\pi$
$787$	456.562			0.580129			0.290065	+	0.957007i	$0.406323\pi$
$788$		−	98.9481i		−	0.125569i
$789$			14.6837i			0.0186106i
$790$			190.801i			0.241520i
$791$			2007.49i			2.53791i
$792$		−	523.564i		−	0.661066i
$793$			58.2072i			0.0734013i
$794$	−153.720			−0.193602
$795$			534.468i			0.672287i
$796$	−295.939			−0.371782
$797$		−	651.367i		−	0.817274i	−0.912697	−	0.408637i	$-0.866004\pi$
$797$		−	651.367i		−	0.817274i	0.912697	−	0.408637i	$-0.133996\pi$
$798$			127.336i			0.159569i
$799$			236.071i			0.295459i
$800$			43.7849i			0.0547311i
$801$		−	549.185i		−	0.685624i
$802$	936.510			1.16772
$803$	2060.42			2.56590
$804$	591.448			0.735631
$805$	−393.104			−0.488328
$806$	−35.3252			−0.0438278
$807$			843.849i			1.04566i
$808$		−	541.950i		−	0.670730i
$809$	939.579			1.16141			0.580704	−	0.814115i	$-0.302777\pi$
$809$	939.579			1.16141			0.580704	+	0.814115i	$0.302777\pi$
$810$		−	596.369i		−	0.736258i
$811$	338.585			0.417491			0.208745	−	0.977970i	$-0.433062\pi$
$811$	338.585			0.417491			0.208745	+	0.977970i	$0.433062\pi$
$812$	−403.540			−0.496970
$813$	−921.083			−1.13294
$814$			1185.70i			1.45664i
$815$	464.319			0.569716
$816$	−16.1344			−0.0197726
$817$	197.654			0.241927
$818$	−706.639			−0.863862
$819$			28.5862i			0.0349038i
$820$		−	55.4401i		−	0.0676098i
$821$	−322.701			−0.393058			−0.196529	−	0.980498i	$-0.562967\pi$
$821$	−322.701			−0.393058			−0.196529	+	0.980498i	$0.562967\pi$
$822$	−344.294			−0.418850
$823$			468.901i			0.569747i	0.958565	+	0.284873i	$0.0919515\pi$
$823$			468.901i			0.569747i	−0.958565	+	0.284873i	$0.908048\pi$
$824$		−	810.907i		−	0.984110i
$825$			89.4868i			0.108469i
$826$	1230.54			1.48976
$827$	−169.013			−0.204369			−0.102185	−	0.994765i	$-0.532583\pi$
$827$	−169.013			−0.204369			−0.102185	+	0.994765i	$0.532583\pi$
$828$			60.7194i			0.0733326i
$829$	−440.344			−0.531174			−0.265587	−	0.964087i	$-0.585566\pi$
$829$	−440.344			−0.531174			−0.265587	+	0.964087i	$0.585566\pi$
$830$			292.229i			0.352083i
$831$			1075.05i			1.29368i
$832$	25.9890			0.0312368
$833$		−	1377.12i		−	1.65321i
$834$	752.216			0.901938
$835$			767.941i			0.919690i
$836$	−115.658			−0.138347
$837$	−819.147			−0.978670
$838$		−	256.964i		−	0.306640i
$839$			167.795i			0.199994i	0.994988	+	0.0999969i	$0.0318833\pi$
$839$			167.795i			0.199994i	−0.994988	+	0.0999969i	$0.968117\pi$
$840$		−	1620.16i		−	1.92876i
$841$	655.655			0.779613
$842$	−936.949			−1.11277
$843$			510.137i			0.605145i
$844$	160.173	+	503.844i	0.189778	+	0.596971i
$845$	819.425			0.969733
$846$			67.5718i			0.0798721i
$847$			2647.02i			3.12517i
$848$	−9.33607			−0.0110095
$849$	722.166			0.850607
$850$	−25.1873			−0.0296322
$851$		−	357.030i		−	0.419541i
$852$		−	131.113i		−	0.153888i
$853$	−132.728			−0.155601			−0.0778005	−	0.996969i	$-0.524790\pi$
$853$	−132.728			−0.155601			−0.0778005	+	0.996969i	$0.524790\pi$
$854$		−	1235.08i		−	1.44623i
$855$	42.8561			0.0501240
$856$		−	46.4576i		−	0.0542729i
$857$	−523.543			−0.610902			−0.305451	−	0.952208i	$-0.598807\pi$
$857$	−523.543			−0.610902			−0.305451	+	0.952208i	$0.598807\pi$
$858$	54.7920			0.0638601
$859$		−	813.815i		−	0.947398i	−0.880687	−	0.473699i	$-0.842918\pi$
$859$		−	813.815i		−	0.947398i	0.880687	−	0.473699i	$-0.157082\pi$
$860$	−968.598			−1.12628
$861$		−	190.682i		−	0.221466i
$862$			872.436i			1.01211i
$863$	1276.13			1.47871			0.739356	−	0.673315i	$-0.235130\pi$
$863$	1276.13			1.47871			0.739356	+	0.673315i	$0.235130\pi$
$864$	621.669			0.719524
$865$	373.931			0.432290
$866$		−	897.399i		−	1.03626i
$867$			211.463i			0.243902i
$868$	−1256.80			−1.44793
$869$	−596.065			−0.685921
$870$		−	286.604i		−	0.329429i
$871$			45.4189i			0.0521456i
$872$			928.183i			1.06443i
$873$			246.935i			0.282858i
$874$	−20.7702			−0.0237645
$875$			1516.18i			1.73278i
$876$		−	984.834i		−	1.12424i
$877$		−	1447.51i		−	1.65052i	−0.564752	−	0.825260i	$-0.691028\pi$
$877$		−	1447.51i		−	1.65052i	0.564752	−	0.825260i	$-0.308972\pi$
$878$	−1.94157			−0.00221135
$879$		−	1626.39i		−	1.85027i
$880$	27.1570			0.0308602
$881$	−559.327			−0.634877			−0.317439	−	0.948279i	$-0.602823\pi$
$881$	−559.327			−0.634877			−0.317439	+	0.948279i	$0.602823\pi$
$882$		−	394.180i		−	0.446917i
$883$		−	249.499i		−	0.282558i	−0.989970	−	0.141279i	$-0.954879\pi$
$883$		−	249.499i		−	0.282558i	0.989970	−	0.141279i	$-0.0451214\pi$
$884$		−	25.8586i		−	0.0292518i
$885$		−	1465.40i		−	1.65582i
$886$		−	294.028i		−	0.331860i
$887$	−284.512			−0.320757			−0.160379	−	0.987056i	$-0.551272\pi$
$887$	−284.512			−0.320757			−0.160379	+	0.987056i	$0.551272\pi$
$888$	1471.48			1.65707
$889$	−2479.75			−2.78936
$890$	−920.594			−1.03438
$891$	1863.07			2.09098
$892$		−	557.892i		−	0.625440i
$893$	38.7564			0.0434002
$894$		−	43.2203i		−	0.0483449i
$895$	1074.83			1.20093
$896$	971.218			1.08395
$897$	−16.4985			−0.0183930
$898$	868.958			0.967659
$899$	−577.248			−0.642100
$900$	12.0884			0.0134316
$901$		−	469.957i		−	0.521595i
$902$	−103.293			−0.114516
$903$	−3331.42			−3.68928
$904$		−	1349.56i		−	1.49288i
$905$		−	791.294i		−	0.874358i
$906$	−558.222			−0.616140
$907$		−	596.800i		−	0.657994i	−0.944331	−	0.328997i	$-0.893289\pi$
$907$		−	596.800i		−	0.657994i	0.944331	−	0.328997i	$-0.106711\pi$
$908$	788.670			0.868579
$909$	−241.622			−0.265811
$910$	47.9189			0.0526582
$911$			150.324i			0.165010i	0.996591	+	0.0825051i	$0.0262921\pi$
$911$			150.324i			0.165010i	−0.996591	+	0.0825051i	$0.973708\pi$
$912$			2.64882i			0.00290441i
$913$	−912.926			−0.999919
$914$	505.465			0.553025
$915$	−1470.81			−1.60744
$916$		−	565.658i		−	0.617531i
$917$	−2155.96			−2.35110
$918$			357.616i			0.389560i
$919$		−	1006.31i		−	1.09501i	−0.836804	−	0.547503i	$-0.815578\pi$
$919$		−	1006.31i		−	1.09501i	0.836804	−	0.547503i	$-0.184422\pi$
$920$	264.270			0.287250
$921$		−	973.061i		−	1.05653i
$922$	−837.319			−0.908155
$923$	10.0685			0.0109084
$924$	1949.40			2.10974
$925$	−71.0798			−0.0768430
$926$	−740.274			−0.799432
$927$	−361.533			−0.390004
$928$	438.086			0.472076
$929$			627.781i			0.675760i	0.941189	+	0.337880i	$0.109710\pi$
$929$			627.781i			0.675760i	−0.941189	+	0.337880i	$0.890290\pi$
$930$		−	892.612i		−	0.959798i
$931$	−226.086			−0.242842
$932$			423.000i			0.453862i
$933$			1350.41i			1.44739i
$934$		−	1061.49i		−	1.13649i
$935$			1367.02i			1.46205i
$936$		−	19.2175i		−	0.0205316i
$937$	1505.44			1.60665			0.803327	−	0.595538i	$-0.203061\pi$
$937$	1505.44			1.60665			0.803327	+	0.595538i	$0.203061\pi$
$938$		−	963.728i		−	1.02743i
$939$	139.673			0.148746
$940$	−189.924			−0.202047
$941$		−	236.413i		−	0.251236i	−0.992079	−	0.125618i	$-0.959909\pi$
$941$		−	236.413i		−	0.251236i	0.992079	−	0.125618i	$-0.0400914\pi$
$942$			699.324i			0.742382i
$943$	31.1028			0.0329829
$944$	25.5975			0.0271160
$945$	1111.18			1.17585
$946$			1804.64i			1.90766i
$947$	−7.95380			−0.00839895			−0.00419947	−	0.999991i	$-0.501337\pi$
$947$	−7.95380			−0.00839895			−0.00419947	+	0.999991i	$0.501337\pi$
$948$			284.906i			0.300534i
$949$	75.6281			0.0796924
$950$			4.13506i			0.00435270i
$951$	775.596			0.815559
$952$			1424.60i			1.49643i
$953$	−852.048			−0.894069			−0.447035	−	0.894517i	$-0.647520\pi$
$953$	−852.048			−0.894069			−0.447035	+	0.894517i	$0.647520\pi$
$954$		−	134.518i		−	0.141004i
$955$			699.107i			0.732049i
$956$		−	233.293i		−	0.244031i
$957$	895.354			0.935584
$958$	−394.086			−0.411363
$959$		−	940.661i		−	0.980877i
$960$			656.701i			0.684064i
$961$	−836.809			−0.870769
$962$			43.5215i			0.0452407i
$963$	−20.7126			−0.0215084
$964$	−236.229			−0.245051
$965$	−2.04235			−0.00211642
$966$	350.077			0.362399
$967$	404.123			0.417914			0.208957	−	0.977925i	$-0.432993\pi$
$967$	404.123			0.417914			0.208957	+	0.977925i	$0.432993\pi$
$968$		−	1779.50i		−	1.83832i
$969$	−133.336			−0.137601
$970$	413.935			0.426737
$971$		−	1412.33i		−	1.45451i	−0.686367	−	0.727255i	$-0.740796\pi$
$971$		−	1412.33i		−	1.45451i	0.686367	−	0.727255i	$-0.259204\pi$
$972$		−	454.841i		−	0.467943i
$973$			2055.16i			2.11219i
$974$		−	994.818i		−	1.02137i
$975$			3.28463i			0.00336886i
$976$		−	25.6920i		−	0.0263237i
$977$		−	776.906i		−	0.795195i	−0.917560	−	0.397598i	$-0.869844\pi$
$977$		−	776.906i		−	0.795195i	0.917560	−	0.397598i	$-0.130156\pi$
$978$	−413.497			−0.422799
$979$		−	2875.95i		−	2.93764i
$980$	1107.92			1.13053
$981$	413.819			0.421834
$982$			477.560i			0.486314i
$983$	133.223			0.135527			0.0677635	−	0.997701i	$-0.478414\pi$
$983$	133.223			0.135527			0.0677635	+	0.997701i	$0.478414\pi$
$984$			128.189i			0.130273i
$985$			192.002i			0.194926i
$986$			252.010i			0.255588i
$987$	−653.231			−0.661834
$988$	−4.24526			−0.00429683
$989$		−	543.400i		−	0.549444i
$990$			391.288i			0.395241i
$991$			224.891i			0.226933i	0.993542	+	0.113467i	$0.0361955\pi$
$991$			224.891i			0.226933i	−0.993542	+	0.113467i	$0.963804\pi$
$992$	1364.40			1.37540
$993$			536.289i			0.540069i
$994$	−213.640			−0.214930
$995$	574.249			0.577135
$996$			436.359i			0.438111i
$997$		−	1752.70i		−	1.75797i	−0.476845	−	0.878987i	$-0.658220\pi$
$997$		−	1752.70i		−	1.75797i	0.476845	−	0.878987i	$-0.341780\pi$
$998$	1027.46			1.02952
$999$			1009.21i			1.01022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	211.3.b.b.210.13	✓	32
211.210	odd	2	inner	211.3.b.b.210.20	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
211.3.b.b.210.13	✓	32	1.1	even	1	trivial
211.3.b.b.210.20	yes	32	211.210	odd	2	inner

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:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	211.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.22244i q^{2} +3.54198i q^{3} +2.50564 q^{4} -4.86203 q^{5} +4.32986 q^{6} +11.8298i q^{7} -7.95275i q^{8} -3.54564 q^{9} +O(q^{10})\)	\(q-1.22244i q^{2} +3.54198i q^{3} +2.50564 q^{4} -4.86203 q^{5} +4.32986 q^{6} +11.8298i q^{7} -7.95275i q^{8} -3.54564 q^{9} +5.94353i q^{10} -18.5677 q^{11} +8.87494i q^{12} -0.681531 q^{13} +14.4612 q^{14} -17.2212i q^{15} +0.300820 q^{16} +15.1426i q^{17} +4.33433i q^{18} +2.48599 q^{19} -12.1825 q^{20} -41.9009 q^{21} +22.6979i q^{22} -6.83460i q^{23} +28.1685 q^{24} -1.36068 q^{25} +0.833130i q^{26} +19.3192i q^{27} +29.6412i q^{28} +13.6141i q^{29} -21.0519 q^{30} +42.4006i q^{31} -32.1787i q^{32} -65.7664i q^{33} +18.5109 q^{34} -57.5168i q^{35} -8.88411 q^{36} +52.2386 q^{37} -3.03897i q^{38} -2.41397i q^{39} +38.6665i q^{40} +4.55079i q^{41} +51.2213i q^{42} +79.5072 q^{43} -46.5240 q^{44} +17.2390 q^{45} -8.35488 q^{46} +15.5899 q^{47} +1.06550i q^{48} -90.9438 q^{49} +1.66334i q^{50} -53.6348 q^{51} -1.70767 q^{52} -31.0354 q^{53} +23.6166 q^{54} +90.2766 q^{55} +94.0793 q^{56} +8.80534i q^{57} +16.6425 q^{58} +85.0925 q^{59} -43.1502i q^{60} -85.4066i q^{61} +51.8321 q^{62} -41.9442i q^{63} -38.1333 q^{64} +3.31362 q^{65} -80.3954 q^{66} -66.6424i q^{67} +37.9419i q^{68} +24.2080 q^{69} -70.3107 q^{70} -14.7734 q^{71} +28.1976i q^{72} -110.968 q^{73} -63.8584i q^{74} -4.81949i q^{75} +6.22901 q^{76} -219.652i q^{77} -2.95093 q^{78} +32.1023 q^{79} -1.46259 q^{80} -100.339 q^{81} +5.56306 q^{82} +49.1675 q^{83} -104.989 q^{84} -73.6237i q^{85} -97.1927i q^{86} -48.2211 q^{87} +147.664i q^{88} +154.890i q^{89} -21.0736i q^{90} -8.06236i q^{91} -17.1251i q^{92} -150.182 q^{93} -19.0577i q^{94} -12.0870 q^{95} +113.977 q^{96} -69.6446i q^{97} +111.173i q^{98} +65.8343 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 84 q^{4} - 2 q^{5} - 20 q^{6} - 118 q^{9}+O(q^{10}) \) 32 * q - 84 * q^4 - 2 * q^5 - 20 * q^6 - 118 * q^9	\( 32 q - 84 q^{4} - 2 q^{5} - 20 q^{6} - 118 q^{9} - 10 q^{11} - 24 q^{13} + 6 q^{14} + 80 q^{16} - 30 q^{19} - 68 q^{20} + 68 q^{21} + 76 q^{24} + 86 q^{25} - 74 q^{30} + 20 q^{34} + 60 q^{36} + 138 q^{37} - 54 q^{43} - 18 q^{44} + 28 q^{45} + 302 q^{46} - 84 q^{47} - 378 q^{49} - 452 q^{51} + 138 q^{52} + 254 q^{53} + 214 q^{54} + 146 q^{55} + 216 q^{56} + 226 q^{58} + 234 q^{59} - 720 q^{62} - 168 q^{64} + 156 q^{65} - 66 q^{66} - 22 q^{69} - 398 q^{70} - 240 q^{71} + 40 q^{73} + 342 q^{76} - 376 q^{78} + 360 q^{79} - 122 q^{80} + 320 q^{81} + 26 q^{82} + 150 q^{83} + 300 q^{84} + 220 q^{87} - 874 q^{93} + 272 q^{95} - 230 q^{96} + 434 q^{99}+O(q^{100}) \) 32 * q - 84 * q^4 - 2 * q^5 - 20 * q^6 - 118 * q^9 - 10 * q^11 - 24 * q^13 + 6 * q^14 + 80 * q^16 - 30 * q^19 - 68 * q^20 + 68 * q^21 + 76 * q^24 + 86 * q^25 - 74 * q^30 + 20 * q^34 + 60 * q^36 + 138 * q^37 - 54 * q^43 - 18 * q^44 + 28 * q^45 + 302 * q^46 - 84 * q^47 - 378 * q^49 - 452 * q^51 + 138 * q^52 + 254 * q^53 + 214 * q^54 + 146 * q^55 + 216 * q^56 + 226 * q^58 + 234 * q^59 - 720 * q^62 - 168 * q^64 + 156 * q^65 - 66 * q^66 - 22 * q^69 - 398 * q^70 - 240 * q^71 + 40 * q^73 + 342 * q^76 - 376 * q^78 + 360 * q^79 - 122 * q^80 + 320 * q^81 + 26 * q^82 + 150 * q^83 + 300 * q^84 + 220 * q^87 - 874 * q^93 + 272 * q^95 - 230 * q^96 + 434 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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