LMFDB - Embedded newform 471.2.b.a.313.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(313,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("471.313");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 15x^{10} + 77x^{8} + 158x^{6} + 111x^{4} + 21x^{2} + 1 $ x^12 + 15x^10 + 77x^8 + 158x^6 + 111x^4 + 21*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			313.12
Root			$2.55080i$ of defining polynomial
Character	$\chi$	$=$	471.313
Dual form			471.2.b.a.313.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.55080i q^{2} -1.00000 q^{3} -4.50658 q^{4} -2.15877i q^{5} -2.55080i q^{6} -0.830530i q^{7} -6.39378i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.55080i q^{2} -1.00000 q^{3} -4.50658 q^{4} -2.15877i q^{5} -2.55080i q^{6} -0.830530i q^{7} -6.39378i q^{8} +1.00000 q^{9} +5.50658 q^{10} +5.63582 q^{11} +4.50658 q^{12} +2.11851 q^{13} +2.11851 q^{14} +2.15877i q^{15} +7.29608 q^{16} -5.31022 q^{17} +2.55080i q^{18} +1.13265 q^{19} +9.72864i q^{20} +0.830530i q^{21} +14.3758i q^{22} +0.00420436i q^{23} +6.39378i q^{24} +0.339732 q^{25} +5.40391i q^{26} -1.00000 q^{27} +3.74285i q^{28} -7.71647i q^{29} -5.50658 q^{30} +8.08900 q^{31} +5.82330i q^{32} -5.63582 q^{33} -13.5453i q^{34} -1.79292 q^{35} -4.50658 q^{36} +6.62168 q^{37} +2.88916i q^{38} -2.11851 q^{39} -13.8027 q^{40} +11.4129i q^{41} -2.11851 q^{42} -8.86459i q^{43} -25.3982 q^{44} -2.15877i q^{45} -0.0107245 q^{46} +4.90496 q^{47} -7.29608 q^{48} +6.31022 q^{49} +0.866588i q^{50} +5.31022 q^{51} -9.54725 q^{52} +1.61039i q^{53} -2.55080i q^{54} -12.1664i q^{55} -5.31022 q^{56} -1.13265 q^{57} +19.6832 q^{58} +0.544168i q^{59} -9.72864i q^{60} +0.548372i q^{61} +20.6334i q^{62} -0.830530i q^{63} -0.261890 q^{64} -4.57338i q^{65} -14.3758i q^{66} -7.34907 q^{67} +23.9309 q^{68} -0.00420436i q^{69} -4.57338i q^{70} -14.3837 q^{71} -6.39378i q^{72} +1.25126i q^{73} +16.8906i q^{74} -0.339732 q^{75} -5.10438 q^{76} -4.68071i q^{77} -5.40391i q^{78} -2.79324i q^{79} -15.7505i q^{80} +1.00000 q^{81} -29.1119 q^{82} -7.18759i q^{83} -3.74285i q^{84} +11.4635i q^{85} +22.6118 q^{86} +7.71647i q^{87} -36.0341i q^{88} -2.76971 q^{89} +5.50658 q^{90} -1.75949i q^{91} -0.0189473i q^{92} -8.08900 q^{93} +12.5116i q^{94} -2.44513i q^{95} -5.82330i q^{96} +10.7432i q^{97} +16.0961i q^{98} +5.63582 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9	$ 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9} + 18 q^{10} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} + 10 q^{16} + 2 q^{17} + 4 q^{19} + 12 q^{25} - 12 q^{27} - 18 q^{30} + 2 q^{31} + 2 q^{33} - 4 q^{35} - 6 q^{36} - 2 q^{37} - 4 q^{39} - 40 q^{40} - 4 q^{42} - 36 q^{44} + 34 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{51} - 6 q^{52} + 2 q^{56} - 4 q^{57} + 24 q^{58} + 28 q^{64} - 38 q^{67} + 32 q^{68} - 26 q^{71} - 12 q^{75} - 28 q^{76} + 12 q^{81} - 50 q^{82} + 6 q^{86} - 4 q^{89} + 18 q^{90} - 2 q^{93} - 2 q^{99}+O(q^{100}) $ 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9 + 18 * q^10 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 + 10 * q^16 + 2 * q^17 + 4 * q^19 + 12 * q^25 - 12 * q^27 - 18 * q^30 + 2 * q^31 + 2 * q^33 - 4 * q^35 - 6 * q^36 - 2 * q^37 - 4 * q^39 - 40 * q^40 - 4 * q^42 - 36 * q^44 + 34 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^51 - 6 * q^52 + 2 * q^56 - 4 * q^57 + 24 * q^58 + 28 * q^64 - 38 * q^67 + 32 * q^68 - 26 * q^71 - 12 * q^75 - 28 * q^76 + 12 * q^81 - 50 * q^82 + 6 * q^86 - 4 * q^89 + 18 * q^90 - 2 * q^93 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$-1$

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 $

$2$			2.55080i			1.80369i	0.432062	+	0.901844i	$0.357786\pi$
$2$			2.55080i			1.80369i	−0.432062	+	0.901844i	$0.642214\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−4.50658			−2.25329
$5$		−	2.15877i		−	0.965429i	−0.875778	−	0.482715i	$-0.839651\pi$
$5$		−	2.15877i		−	0.965429i	0.875778	−	0.482715i	$-0.160349\pi$
$6$		−	2.55080i		−	1.04136i
$7$		−	0.830530i		−	0.313911i	−0.987606	−	0.156955i	$-0.949832\pi$
$7$		−	0.830530i		−	0.313911i	0.987606	−	0.156955i	$-0.0501679\pi$
$8$		−	6.39378i		−	2.26054i
$9$	1.00000			0.333333
$10$	5.50658			1.74133
$11$	5.63582			1.69926			0.849631	−	0.527377i	$-0.176825\pi$
$11$	5.63582			1.69926			0.849631	+	0.527377i	$0.176825\pi$
$12$	4.50658			1.30094
$13$	2.11851			0.587570			0.293785	−	0.955871i	$-0.405085\pi$
$13$	2.11851			0.587570			0.293785	+	0.955871i	$0.405085\pi$
$14$	2.11851			0.566197
$15$			2.15877i			0.557391i
$16$	7.29608			1.82402
$17$	−5.31022			−1.28792			−0.643959	−	0.765060i	$-0.722709\pi$
$17$	−5.31022			−1.28792			−0.643959	+	0.765060i	$0.722709\pi$
$18$			2.55080i			0.601229i
$19$	1.13265			0.259848			0.129924	−	0.991524i	$-0.458527\pi$
$19$	1.13265			0.259848			0.129924	+	0.991524i	$0.458527\pi$
$20$			9.72864i			2.17539i
$21$			0.830530i			0.181236i
$22$			14.3758i			3.06494i
$23$			0.00420436i			0.000876669i	1.00000		0.000438334i	$0.000139526\pi$
$23$			0.00420436i			0.000876669i	−1.00000		0.000438334i	$0.999860\pi$
$24$			6.39378i			1.30512i
$25$	0.339732			0.0679464
$26$			5.40391i			1.05979i
$27$	−1.00000			−0.192450
$28$			3.74285i			0.707331i
$29$		−	7.71647i		−	1.43291i	−0.697632	−	0.716456i	$-0.745763\pi$
$29$		−	7.71647i		−	1.43291i	0.697632	−	0.716456i	$-0.254237\pi$
$30$	−5.50658			−1.00536
$31$	8.08900			1.45283			0.726414	−	0.687257i	$-0.241186\pi$
$31$	8.08900			1.45283			0.726414	+	0.687257i	$0.241186\pi$
$32$			5.82330i			1.02942i
$33$	−5.63582			−0.981070
$34$		−	13.5453i		−	2.32300i
$35$	−1.79292			−0.303059
$36$	−4.50658			−0.751096
$37$	6.62168			1.08860			0.544299	−	0.838891i	$-0.316796\pi$
$37$	6.62168			1.08860			0.544299	+	0.838891i	$0.316796\pi$
$38$			2.88916i			0.468684i
$39$	−2.11851			−0.339234
$40$	−13.8027			−2.18239
$41$			11.4129i			1.78239i	0.453622	+	0.891194i	$0.350132\pi$
$41$			11.4129i			1.78239i	−0.453622	+	0.891194i	$0.649868\pi$
$42$	−2.11851			−0.326894
$43$		−	8.86459i		−	1.35184i	−0.736976	−	0.675919i	$-0.763747\pi$
$43$		−	8.86459i		−	1.35184i	0.736976	−	0.675919i	$-0.236253\pi$
$44$	−25.3982			−3.82893
$45$		−	2.15877i		−	0.321810i
$46$	−0.0107245			−0.00158124
$47$	4.90496			0.715461			0.357731	−	0.933825i	$-0.383551\pi$
$47$	4.90496			0.715461			0.357731	+	0.933825i	$0.383551\pi$
$48$	−7.29608			−1.05310
$49$	6.31022			0.901460
$50$			0.866588i			0.122554i
$51$	5.31022			0.743580
$52$	−9.54725			−1.32397
$53$			1.61039i			0.221205i	0.993865	+	0.110602i	$0.0352780\pi$
$53$			1.61039i			0.221205i	−0.993865	+	0.110602i	$0.964722\pi$
$54$		−	2.55080i		−	0.347120i
$55$		−	12.1664i		−	1.64052i
$56$	−5.31022			−0.709608
$57$	−1.13265			−0.150023
$58$	19.6832			2.58453
$59$			0.544168i			0.0708446i	0.999372	+	0.0354223i	$0.0112776\pi$
$59$			0.544168i			0.0708446i	−0.999372	+	0.0354223i	$0.988722\pi$
$60$		−	9.72864i		−	1.25596i
$61$			0.548372i			0.0702119i	0.999384	+	0.0351059i	$0.0111769\pi$
$61$			0.548372i			0.0702119i	−0.999384	+	0.0351059i	$0.988823\pi$
$62$			20.6334i			2.62045i
$63$		−	0.830530i		−	0.104637i
$64$	−0.261890			−0.0327362
$65$		−	4.57338i		−	0.567257i
$66$		−	14.3758i		−	1.76954i
$67$	−7.34907			−0.897831			−0.448916	−	0.893574i	$-0.648190\pi$
$67$	−7.34907			−0.897831			−0.448916	+	0.893574i	$0.648190\pi$
$68$	23.9309			2.90205
$69$		−	0.00420436i		−	0.000506145i
$70$		−	4.57338i		−	0.546623i
$71$	−14.3837			−1.70703			−0.853514	−	0.521070i	$-0.825533\pi$
$71$	−14.3837			−1.70703			−0.853514	+	0.521070i	$0.825533\pi$
$72$		−	6.39378i		−	0.753514i
$73$			1.25126i			0.146449i	0.997315	+	0.0732243i	$0.0233289\pi$
$73$			1.25126i			0.146449i	−0.997315	+	0.0732243i	$0.976671\pi$
$74$			16.8906i			1.96349i
$75$	−0.339732			−0.0392289
$76$	−5.10438			−0.585512
$77$		−	4.68071i		−	0.533417i
$78$		−	5.40391i		−	0.611872i
$79$		−	2.79324i		−	0.314264i	−0.987578	−	0.157132i	$-0.949775\pi$
$79$		−	2.79324i		−	0.314264i	0.987578	−	0.157132i	$-0.0502248\pi$
$80$		−	15.7505i		−	1.76096i
$81$	1.00000			0.111111
$82$	−29.1119			−3.21487
$83$		−	7.18759i		−	0.788940i	−0.918909	−	0.394470i	$-0.870928\pi$
$83$		−	7.18759i		−	0.788940i	0.918909	−	0.394470i	$-0.129072\pi$
$84$		−	3.74285i		−	0.408378i
$85$			11.4635i			1.24339i
$86$	22.6118			2.43829
$87$			7.71647i			0.827292i
$88$		−	36.0341i		−	3.84125i
$89$	−2.76971			−0.293588			−0.146794	−	0.989167i	$-0.546895\pi$
$89$	−2.76971			−0.293588			−0.146794	+	0.989167i	$0.546895\pi$
$90$	5.50658			0.580444
$91$		−	1.75949i		−	0.184445i
$92$		−	0.0189473i		−	0.00197539i
$93$	−8.08900			−0.838791
$94$			12.5116i			1.29047i
$95$		−	2.44513i		−	0.250865i
$96$		−	5.82330i		−	0.594338i
$97$			10.7432i			1.09080i	0.838175	+	0.545401i	$0.183623\pi$
$97$			10.7432i			1.09080i	−0.838175	+	0.545401i	$0.816377\pi$
$98$			16.0961i			1.62595i
$99$	5.63582			0.566421
$100$	−1.53103			−0.153103
$101$	3.91143			0.389202			0.194601	−	0.980882i	$-0.437659\pi$
$101$	3.91143			0.389202			0.194601	+	0.980882i	$0.437659\pi$
$102$			13.5453i			1.34119i
$103$		−	15.6154i		−	1.53863i	−0.638872	−	0.769313i	$-0.720599\pi$
$103$		−	15.6154i		−	1.53863i	0.638872	−	0.769313i	$-0.279401\pi$
$104$		−	13.5453i		−	1.32823i
$105$	1.79292			0.174971
$106$	−4.10779			−0.398984
$107$		−	10.7855i		−	1.04268i	−0.853350	−	0.521339i	$-0.825433\pi$
$107$		−	10.7855i		−	1.04268i	0.853350	−	0.521339i	$-0.174567\pi$
$108$	4.50658			0.433646
$109$	13.7919			1.32103			0.660514	−	0.750814i	$-0.270338\pi$
$109$	13.7919			1.32103			0.660514	+	0.750814i	$0.270338\pi$
$110$	31.0341			2.95898
$111$	−6.62168			−0.628502
$112$		−	6.05961i		−	0.572580i
$113$	−11.2605			−1.05930			−0.529649	−	0.848217i	$-0.677676\pi$
$113$	−11.2605			−1.05930			−0.529649	+	0.848217i	$0.677676\pi$
$114$		−	2.88916i		−	0.270595i
$115$	0.00907622			0.000846362
$116$			34.7749i			3.22877i
$117$	2.11851			0.195857
$118$	−1.38806			−0.127782
$119$			4.41030i			0.404291i
$120$	13.8027			1.26000
$121$	20.7624			1.88749
$122$	−1.39879			−0.126640
$123$		−	11.4129i		−	1.02906i
$124$	−36.4537			−3.27364
$125$		−	11.5272i		−	1.03103i
$126$	2.11851			0.188732
$127$	2.45177			0.217559			0.108780	−	0.994066i	$-0.465306\pi$
$127$	2.45177			0.217559			0.108780	+	0.994066i	$0.465306\pi$
$128$			10.9786i			0.970377i
$129$			8.86459i			0.780484i
$130$	11.6658			1.02316
$131$			3.09663i			0.270554i	0.990808	+	0.135277i	$0.0431924\pi$
$131$			3.09663i			0.270554i	−0.990808	+	0.135277i	$0.956808\pi$
$132$	25.3982			2.21063
$133$		−	0.940700i		−	0.0815690i
$134$		−	18.7460i		−	1.61941i
$135$			2.15877i			0.185797i
$136$			33.9524i			2.91139i
$137$			0.826325i			0.0705977i	0.999377	+	0.0352989i	$0.0112383\pi$
$137$			0.826325i			0.0705977i	−0.999377	+	0.0352989i	$0.988762\pi$
$138$	0.0107245			0.000912927
$139$			16.0486i			1.36123i	0.732642	+	0.680614i	$0.238287\pi$
$139$			16.0486i			1.36123i	−0.732642	+	0.680614i	$0.761713\pi$
$140$	8.07993			0.682878
$141$	−4.90496			−0.413072
$142$		−	36.6899i		−	3.07894i
$143$	11.9396			0.998436
$144$	7.29608			0.608007
$145$	−16.6580			−1.38338
$146$	−3.19171			−0.264147
$147$	−6.31022			−0.520458
$148$	−29.8411			−2.45292
$149$			7.38785i			0.605236i	0.953112	+	0.302618i	$0.0978607\pi$
$149$			7.38785i			0.605236i	−0.953112	+	0.302618i	$0.902139\pi$
$150$		−	0.866588i		−	0.0707566i
$151$			4.79088i			0.389877i	0.980816	+	0.194938i	$0.0624507\pi$
$151$			4.79088i			0.389877i	−0.980816	+	0.194938i	$0.937549\pi$
$152$		−	7.24192i		−	0.587397i
$153$	−5.31022			−0.429306
$154$	11.9396			0.962117
$155$		−	17.4623i		−	1.40260i
$156$	9.54725			0.764392
$157$	−3.44411	+	12.0473i	−0.274870	+	0.961481i
$157$	−3.44411	+	12.0473i	−0.274870	+	0.961481i
$158$	7.12499			0.566834
$159$		−	1.61039i		−	0.127712i
$160$	12.5711			0.993835
$161$	0.00349184			0.000275196
$162$			2.55080i			0.200410i
$163$		−	22.3904i		−	1.75375i	−0.480717	−	0.876876i	$-0.659623\pi$
$163$		−	22.3904i		−	1.75375i	0.480717	−	0.876876i	$-0.340377\pi$
$164$		−	51.4329i		−	4.01624i
$165$			12.1664i			0.947153i
$166$	18.3341			1.42300
$167$	0.292156			0.0226077			0.0113039	−	0.999936i	$-0.496402\pi$
$167$	0.292156			0.0226077			0.0113039	+	0.999936i	$0.496402\pi$
$168$	5.31022			0.409692
$169$	−8.51190			−0.654761
$170$	−29.2411			−2.24269
$171$	1.13265			0.0866160
$172$			39.9490i			3.04608i
$173$	−25.6407			−1.94942			−0.974712	−	0.223464i	$-0.928264\pi$
$173$	−25.6407			−1.94942			−0.974712	+	0.223464i	$0.928264\pi$
$174$	−19.6832			−1.49218
$175$		−	0.282158i		−	0.0213291i
$176$	41.1194			3.09949
$177$		−	0.544168i		−	0.0409022i
$178$		−	7.06496i		−	0.529542i
$179$		−	15.0829i		−	1.12735i	−0.825996	−	0.563675i	$-0.809387\pi$
$179$		−	15.0829i		−	1.12735i	0.825996	−	0.563675i	$-0.190613\pi$
$180$			9.72864i			0.725130i
$181$			15.1857i			1.12875i	0.825520	+	0.564373i	$0.190882\pi$
$181$			15.1857i			1.12875i	−0.825520	+	0.564373i	$0.809118\pi$
$182$	4.48810			0.332680
$183$		−	0.548372i		−	0.0405368i
$184$	0.0268817			0.00198175
$185$		−	14.2947i		−	1.05096i
$186$		−	20.6334i		−	1.51292i
$187$	−29.9274			−2.18851
$188$	−22.1046			−1.61214
$189$			0.830530i			0.0604121i
$190$	6.23703			0.452482
$191$		−	9.42950i		−	0.682294i	−0.940010	−	0.341147i	$-0.889185\pi$
$191$		−	9.42950i		−	0.682294i	0.940010	−	0.341147i	$-0.110815\pi$
$192$	0.261890			0.0189003
$193$	−12.2617			−0.882614			−0.441307	−	0.897356i	$-0.645485\pi$
$193$	−12.2617			−0.882614			−0.441307	+	0.897356i	$0.645485\pi$
$194$	−27.4036			−1.96747
$195$			4.57338i			0.327506i
$196$	−28.4375			−2.03125
$197$	−4.32534			−0.308168			−0.154084	−	0.988058i	$-0.549243\pi$
$197$	−4.32534			−0.308168			−0.154084	+	0.988058i	$0.549243\pi$
$198$			14.3758i			1.02165i
$199$	5.24168			0.371573			0.185787	−	0.982590i	$-0.440517\pi$
$199$	5.24168			0.371573			0.185787	+	0.982590i	$0.440517\pi$
$200$		−	2.17217i		−	0.153596i
$201$	7.34907			0.518363
$202$			9.97728i			0.701999i
$203$	−6.40876			−0.449807
$204$	−23.9309			−1.67550
$205$	24.6377			1.72077
$206$	39.8316			2.77520
$207$			0.00420436i			0.000292223i
$208$	15.4569			1.07174
$209$	6.38341			0.441550
$210$			4.57338i			0.315593i
$211$		−	0.0206476i		−	0.00142144i	−1.00000		0.000710718i	$-0.999774\pi$
$211$		−	0.0206476i		−	0.00142144i	1.00000		0.000710718i	$-0.000226229\pi$
$212$		−	7.25736i		−	0.498438i
$213$	14.3837			0.985553
$214$	27.5118			1.88067
$215$	−19.1366			−1.30510
$216$			6.39378i			0.435041i
$217$		−	6.71816i		−	0.456058i
$218$			35.1805i			2.38272i
$219$		−	1.25126i		−	0.0845521i
$220$			54.8288i			3.69656i
$221$	−11.2498			−0.756742
$222$		−	16.8906i		−	1.13362i
$223$			20.0265i			1.34107i	0.741877	+	0.670536i	$0.233936\pi$
$223$			20.0265i			1.34107i	−0.741877	+	0.670536i	$0.766064\pi$
$224$	4.83642			0.323147
$225$	0.339732			0.0226488
$226$		−	28.7233i		−	1.91064i
$227$			19.0262i			1.26281i	0.775452	+	0.631406i	$0.217522\pi$
$227$			19.0262i			1.26281i	−0.775452	+	0.631406i	$0.782478\pi$
$228$	5.10438			0.338046
$229$			17.2569i			1.14037i	0.821517	+	0.570185i	$0.193128\pi$
$229$			17.2569i			1.14037i	−0.821517	+	0.570185i	$0.806872\pi$
$230$			0.0231516i			0.00152657i
$231$			4.68071i			0.307968i
$232$	−49.3374			−3.23916
$233$	9.44224			0.618581			0.309291	−	0.950968i	$-0.399908\pi$
$233$	9.44224			0.618581			0.309291	+	0.950968i	$0.399908\pi$
$234$			5.40391i			0.353264i
$235$		−	10.5886i		−	0.690727i
$236$		−	2.45233i		−	0.159633i
$237$			2.79324i			0.181440i
$238$	−11.2498			−0.729215
$239$	−10.1650			−0.657519			−0.328760	−	0.944414i	$-0.606631\pi$
$239$	−10.1650			−0.657519			−0.328760	+	0.944414i	$0.606631\pi$
$240$			15.7505i			1.01669i
$241$		−	14.4832i		−	0.932943i	−0.884536	−	0.466472i	$-0.845525\pi$
$241$		−	14.4832i		−	0.932943i	0.884536	−	0.466472i	$-0.154475\pi$
$242$			52.9608i			3.40445i
$243$	−1.00000			−0.0641500
$244$		−	2.47128i		−	0.158208i
$245$		−	13.6223i		−	0.870296i
$246$	29.1119			1.85611
$247$	2.39954			0.152679
$248$		−	51.7193i		−	3.28418i
$249$			7.18759i			0.455495i
$250$	29.4036			1.85965
$251$			21.0817i			1.33066i	0.746548	+	0.665331i	$0.231710\pi$
$251$			21.0817i			1.33066i	−0.746548	+	0.665331i	$0.768290\pi$
$252$			3.74285i			0.235777i
$253$			0.0236950i			0.00148969i
$254$			6.25397i			0.392409i
$255$		−	11.4635i		−	0.717873i
$256$	−28.5279			−1.78299
$257$	21.1912			1.32187			0.660934	−	0.750444i	$-0.270160\pi$
$257$	21.1912			1.32187			0.660934	+	0.750444i	$0.270160\pi$
$258$	−22.6118			−1.40775
$259$		−	5.49950i		−	0.341722i
$260$			20.6103i			1.27819i
$261$		−	7.71647i		−	0.477637i
$262$	−7.89889			−0.487995
$263$	−7.64122			−0.471178			−0.235589	−	0.971853i	$-0.575702\pi$
$263$	−7.64122			−0.471178			−0.235589	+	0.971853i	$0.575702\pi$
$264$			36.0341i			2.21775i
$265$	3.47646			0.213557
$266$	2.39954			0.147125
$267$	2.76971			0.169503
$268$	33.1191			2.02307
$269$			21.7817i			1.32806i	0.747707	+	0.664028i	$0.231155\pi$
$269$			21.7817i			1.32806i	−0.747707	+	0.664028i	$0.768845\pi$
$270$	−5.50658			−0.335120
$271$			1.53341i			0.0931483i	0.998915	+	0.0465742i	$0.0148304\pi$
$271$			1.53341i			0.0931483i	−0.998915	+	0.0465742i	$0.985170\pi$
$272$	−38.7438			−2.34919
$273$			1.75949i			0.106489i
$274$	−2.10779			−0.127336
$275$	1.91467			0.115459
$276$			0.0189473i			0.00114049i
$277$	−3.86007			−0.231929			−0.115965	−	0.993253i	$-0.536996\pi$
$277$	−3.86007			−0.231929			−0.115965	+	0.993253i	$0.536996\pi$
$278$	−40.9369			−2.45523
$279$	8.08900			0.484276
$280$			11.4635i			0.685076i
$281$	−31.2546			−1.86450			−0.932248	−	0.361821i	$-0.882155\pi$
$281$	−31.2546			−1.86450			−0.932248	+	0.361821i	$0.882155\pi$
$282$		−	12.5116i		−	0.745052i
$283$	−22.9451			−1.36394			−0.681971	−	0.731379i	$-0.738877\pi$
$283$	−22.9451			−1.36394			−0.681971	+	0.731379i	$0.738877\pi$
$284$	64.8211			3.84643
$285$			2.44513i			0.144837i
$286$			30.4554i			1.80087i
$287$	9.47871			0.559511
$288$			5.82330i			0.343141i
$289$	11.1984			0.658732
$290$		−	42.4913i		−	2.49518i
$291$		−	10.7432i		−	0.629775i
$292$		−	5.63889i		−	0.329991i
$293$			30.5271i			1.78341i	0.452614	+	0.891706i	$0.350491\pi$
$293$			30.5271i			1.78341i	−0.452614	+	0.891706i	$0.649509\pi$
$294$		−	16.0961i		−	0.938744i
$295$	1.17473			0.0683955
$296$		−	42.3375i		−	2.46082i
$297$	−5.63582			−0.327023
$298$	−18.8449			−1.09166
$299$			0.00890699i			0.000515104i
$300$	1.53103			0.0883940
$301$	−7.36231			−0.424356
$302$	−12.2206			−0.703215
$303$	−3.91143			−0.224706
$304$	8.26392			0.473968
$305$	1.18381			0.0677846
$306$		−	13.5453i		−	0.774334i
$307$			22.2588i			1.27038i	0.772358	+	0.635188i	$0.219077\pi$
$307$			22.2588i			1.27038i	−0.772358	+	0.635188i	$0.780923\pi$
$308$			21.0940i			1.20194i
$309$			15.6154i			0.888326i
$310$	44.5427			2.52986
$311$	14.7778			0.837972			0.418986	−	0.907993i	$-0.362386\pi$
$311$	14.7778			0.837972			0.418986	+	0.907993i	$0.362386\pi$
$312$			13.5453i			0.766852i
$313$	6.04874			0.341895			0.170947	−	0.985280i	$-0.445317\pi$
$313$	6.04874			0.341895			0.170947	+	0.985280i	$0.445317\pi$
$314$	−30.7303	−	8.78523i	−1.73421	−	0.495779i
$315$	−1.79292			−0.101020
$316$			12.5879i			0.708127i
$317$	14.8240			0.832600			0.416300	−	0.909227i	$-0.363327\pi$
$317$	14.8240			0.832600			0.416300	+	0.909227i	$0.363327\pi$
$318$	4.10779			0.230353
$319$		−	43.4886i		−	2.43489i
$320$			0.565359i			0.0316045i
$321$			10.7855i			0.601990i
$322$			0.00890699i			0.000496367i
$323$	−6.01463			−0.334663
$324$	−4.50658			−0.250365
$325$	0.719727			0.0399233
$326$	57.1134			3.16322
$327$	−13.7919			−0.762696
$328$	72.9712			4.02916
$329$		−	4.07371i		−	0.224591i
$330$	−31.0341			−1.70837
$331$	17.0292			0.936009			0.468005	−	0.883726i	$-0.344973\pi$
$331$	17.0292			0.936009			0.468005	+	0.883726i	$0.344973\pi$
$332$			32.3914i			1.77771i
$333$	6.62168			0.362866
$334$			0.745232i			0.0407773i
$335$			15.8649i			0.866793i
$336$			6.05961i			0.330579i
$337$		−	13.7391i		−	0.748418i	−0.927344	−	0.374209i	$-0.877914\pi$
$337$		−	13.7391i		−	0.748418i	0.927344	−	0.374209i	$-0.122086\pi$
$338$		−	21.7121i		−	1.18098i
$339$	11.2605			0.611586
$340$		−	51.6612i		−	2.80172i
$341$	45.5881			2.46874
$342$			2.88916i			0.156228i
$343$		−	11.0545i		−	0.596889i
$344$	−56.6782			−3.05589
$345$	−0.00907622			−0.000488647
$346$		−	65.4042i		−	3.51615i
$347$	25.7325			1.38139			0.690696	−	0.723145i	$-0.257304\pi$
$347$	25.7325			1.38139			0.690696	+	0.723145i	$0.257304\pi$
$348$		−	34.7749i		−	1.86413i
$349$	23.4171			1.25349			0.626743	−	0.779226i	$-0.284388\pi$
$349$	23.4171			1.25349			0.626743	+	0.779226i	$0.284388\pi$
$350$	0.719727			0.0384710
$351$	−2.11851			−0.113078
$352$			32.8190i			1.74926i
$353$	−36.8326			−1.96040			−0.980202	−	0.198001i	$-0.936555\pi$
$353$	−36.8326			−1.96040			−0.980202	+	0.198001i	$0.936555\pi$
$354$	1.38806			0.0737747
$355$			31.0510i			1.64801i
$356$	12.4819			0.661539
$357$		−	4.41030i		−	0.233418i
$358$	38.4735			2.03339
$359$		−	31.6195i		−	1.66881i	−0.551150	−	0.834406i	$-0.685811\pi$
$359$		−	31.6195i		−	1.66881i	0.551150	−	0.834406i	$-0.314189\pi$
$360$	−13.8027			−0.727464
$361$	−17.7171			−0.932479
$362$	−38.7357			−2.03590
$363$	−20.7624			−1.08974
$364$			7.92927i			0.415607i
$365$	2.70117			0.141386
$366$	1.39879			0.0731158
$367$			22.2038i			1.15903i	0.814961	+	0.579516i	$0.196758\pi$
$367$			22.2038i			1.15903i	−0.814961	+	0.579516i	$0.803242\pi$
$368$			0.0306753i			0.00159906i
$369$			11.4129i			0.594129i
$370$	36.4628			1.89561
$371$	1.33748			0.0694385
$372$	36.4537			1.89004
$373$			23.5653i			1.22016i	0.792338	+	0.610082i	$0.208863\pi$
$373$			23.5653i			1.22016i	−0.792338	+	0.610082i	$0.791137\pi$
$374$		−	76.3389i		−	3.94739i
$375$			11.5272i			0.595264i
$376$		−	31.3612i		−	1.61733i
$377$		−	16.3475i		−	0.841937i
$378$	−2.11851			−0.108965
$379$			7.06496i			0.362903i	0.983400	+	0.181451i	$0.0580795\pi$
$379$			7.06496i			0.362903i	−0.983400	+	0.181451i	$0.941920\pi$
$380$			11.0192i			0.565271i
$381$	−2.45177			−0.125608
$382$	24.0528			1.23065
$383$			19.9612i			1.01997i	0.860183	+	0.509986i	$0.170349\pi$
$383$			19.9612i			1.01997i	−0.860183	+	0.509986i	$0.829651\pi$
$384$		−	10.9786i		−	0.560247i
$385$	−10.1046			−0.514976
$386$		−	31.2770i		−	1.59196i
$387$		−	8.86459i		−	0.450613i
$388$		−	48.4149i		−	2.45789i
$389$	10.7797			0.546553			0.273277	−	0.961935i	$-0.411893\pi$
$389$	10.7797			0.546553			0.273277	+	0.961935i	$0.411893\pi$
$390$	−11.6658			−0.590719
$391$		−	0.0223261i		−	0.00112908i
$392$		−	40.3461i		−	2.03779i
$393$		−	3.09663i		−	0.156204i
$394$		−	11.0331i		−	0.555838i
$395$	−6.02995			−0.303400
$396$	−25.3982			−1.27631
$397$		−	13.6005i		−	0.682592i	−0.939956	−	0.341296i	$-0.889134\pi$
$397$		−	13.6005i		−	0.682592i	0.939956	−	0.341296i	$-0.110866\pi$
$398$			13.3705i			0.670202i
$399$			0.940700i			0.0470939i
$400$	2.47871			0.123936
$401$			31.6423i			1.58014i	0.613017	+	0.790069i	$0.289956\pi$
$401$			31.6423i			1.58014i	−0.613017	+	0.790069i	$0.710044\pi$
$402$			18.7460i			0.934965i
$403$	17.1367			0.853638
$404$	−17.6272			−0.876985
$405$		−	2.15877i		−	0.107270i
$406$		−	16.3475i		−	0.811310i
$407$	37.3186			1.84981
$408$		−	33.9524i		−	1.68089i
$409$		−	3.28116i		−	0.162243i	−0.996704	−	0.0811215i	$-0.974150\pi$
$409$		−	3.28116i		−	0.162243i	0.996704	−	0.0811215i	$-0.0258502\pi$
$410$			62.8458i			3.10373i
$411$		−	0.826325i		−	0.0407596i
$412$			70.3718i			3.46697i
$413$	0.451947			0.0222389
$414$	−0.0107245			−0.000527079
$415$	−15.5163			−0.761666
$416$			12.3367i			0.604858i
$417$		−	16.0486i		−	0.785905i
$418$			16.2828i			0.796418i
$419$	−11.2271			−0.548478			−0.274239	−	0.961662i	$-0.588426\pi$
$419$	−11.2271			−0.548478			−0.274239	+	0.961662i	$0.588426\pi$
$420$	−8.07993			−0.394260
$421$		−	22.6751i		−	1.10512i	−0.833474	−	0.552559i	$-0.813652\pi$
$421$		−	22.6751i		−	1.10512i	0.833474	−	0.552559i	$-0.186348\pi$
$422$	0.0526678			0.00256383
$423$	4.90496			0.238487
$424$	10.2965			0.500042
$425$	−1.80405			−0.0875094
$426$			36.6899i			1.77763i
$427$	0.455439			0.0220403
$428$			48.6059i			2.34945i
$429$	−11.9396			−0.576447
$430$		−	48.8136i		−	2.35400i
$431$	−16.0716			−0.774140			−0.387070	−	0.922050i	$-0.626513\pi$
$431$	−16.0716			−0.774140			−0.387070	+	0.922050i	$0.626513\pi$
$432$	−7.29608			−0.351033
$433$		−	12.1664i		−	0.584680i	−0.956314	−	0.292340i	$-0.905566\pi$
$433$		−	12.1664i		−	0.584680i	0.956314	−	0.292340i	$-0.0944339\pi$
$434$	17.1367			0.822587
$435$	16.6580			0.798692
$436$	−62.1544			−2.97666
$437$			0.00476207i			0.000227801i
$438$	3.19171			0.152506
$439$		−	41.2080i		−	1.96675i	−0.181587	−	0.983375i	$-0.558123\pi$
$439$		−	41.2080i		−	1.96675i	0.181587	−	0.983375i	$-0.441877\pi$
$440$	−77.7893			−3.70846
$441$	6.31022			0.300487
$442$		−	28.6959i		−	1.36493i
$443$		−	5.62574i		−	0.267287i	−0.991029	−	0.133644i	$-0.957332\pi$
$443$		−	5.62574i		−	0.267287i	0.991029	−	0.133644i	$-0.0426677\pi$
$444$	29.8411			1.41620
$445$			5.97915i			0.283439i
$446$	−51.0835			−2.41887
$447$		−	7.38785i		−	0.349433i
$448$			0.217507i			0.0102763i
$449$			41.4212i			1.95479i	0.211424	+	0.977394i	$0.432190\pi$
$449$			41.4212i			1.95479i	−0.211424	+	0.977394i	$0.567810\pi$
$450$			0.866588i			0.0408514i
$451$			64.3207i			3.02875i
$452$	50.7463			2.38691
$453$		−	4.79088i		−	0.225095i
$454$	−48.5320			−2.27772
$455$	−3.79832			−0.178068
$456$			7.24192i			0.339134i
$457$	3.10288			0.145147			0.0725733	−	0.997363i	$-0.476879\pi$
$457$	3.10288			0.145147			0.0725733	+	0.997363i	$0.476879\pi$
$458$	−44.0189			−2.05687
$459$	5.31022			0.247860
$460$	−0.0409027			−0.00190710
$461$	31.2546			1.45567			0.727837	−	0.685750i	$-0.240526\pi$
$461$	31.2546			1.45567			0.727837	+	0.685750i	$0.240526\pi$
$462$	−11.9396			−0.555479
$463$			30.2123i			1.40409i	0.712134	+	0.702043i	$0.247729\pi$
$463$			30.2123i			1.40409i	−0.712134	+	0.702043i	$0.752271\pi$
$464$		−	56.3000i		−	2.61366i
$465$			17.4623i			0.809793i
$466$			24.0852i			1.11573i
$467$	−3.25215			−0.150491			−0.0752457	−	0.997165i	$-0.523974\pi$
$467$	−3.25215			−0.150491			−0.0752457	+	0.997165i	$0.523974\pi$
$468$	−9.54725			−0.441322
$469$			6.10362i			0.281839i
$470$	27.0095			1.24586
$471$	3.44411	−	12.0473i	0.158696	−	0.555112i
$472$	3.47929			0.160147
$473$		−	49.9592i		−	2.29713i
$474$	−7.12499			−0.327262
$475$	0.384798			0.0176557
$476$		−	19.8753i		−	0.910985i
$477$			1.61039i			0.0737348i
$478$		−	25.9289i		−	1.18596i
$479$		−	16.3429i		−	0.746727i	−0.927685	−	0.373363i	$-0.878205\pi$
$479$		−	16.3429i		−	0.746727i	0.927685	−	0.373363i	$-0.121795\pi$
$480$	−12.5711			−0.573791
$481$	14.0281			0.639627
$482$	36.9437			1.68274
$483$	−0.00349184			−0.000158884
$484$	−93.5675			−4.25307
$485$	23.1920			1.05309
$486$		−	2.55080i		−	0.115707i
$487$	−26.0219			−1.17916			−0.589581	−	0.807709i	$-0.700707\pi$
$487$	−26.0219			−1.17916			−0.589581	+	0.807709i	$0.700707\pi$
$488$	3.50617			0.158717
$489$			22.3904i			1.01253i
$490$	34.7477			1.56974
$491$		−	31.9500i		−	1.44188i	−0.692996	−	0.720942i	$-0.743709\pi$
$491$		−	31.9500i		−	1.44188i	0.692996	−	0.720942i	$-0.256291\pi$
$492$			51.4329i			2.31877i
$493$			40.9762i			1.84547i
$494$			6.12074i			0.275385i
$495$		−	12.1664i		−	0.546839i
$496$	59.0180			2.64999
$497$			11.9461i			0.535854i
$498$	−18.3341			−0.821571
$499$			11.5416i			0.516675i	0.966055	+	0.258337i	$0.0831746\pi$
$499$			11.5416i			0.516675i	−0.966055	+	0.258337i	$0.916825\pi$
$500$			51.9483i			2.32320i
$501$	−0.292156			−0.0130526
$502$	−53.7751			−2.40010
$503$		−	33.4290i		−	1.49052i	−0.666771	−	0.745262i	$-0.732324\pi$
$503$		−	33.4290i		−	1.49052i	0.666771	−	0.745262i	$-0.267676\pi$
$504$	−5.31022			−0.236536
$505$		−	8.44387i		−	0.375747i
$506$	−0.0604411			−0.00268694
$507$	8.51190			0.378027
$508$	−11.0491			−0.490224
$509$		−	28.8230i		−	1.27756i	−0.769390	−	0.638779i	$-0.779440\pi$
$509$		−	28.8230i		−	1.27756i	0.769390	−	0.638779i	$-0.220560\pi$
$510$	29.2411			1.29482
$511$	1.03921			0.0459718
$512$		−	50.8118i		−	2.24559i
$513$	−1.13265			−0.0500078
$514$			54.0544i			2.38424i
$515$	−33.7099			−1.48543
$516$		−	39.9490i		−	1.75866i
$517$	27.6434			1.21576
$518$	14.0281			0.616360
$519$	25.6407			1.12550
$520$	−29.2411			−1.28231
$521$		−	7.57790i		−	0.331994i	−0.986126	−	0.165997i	$-0.946916\pi$
$521$		−	7.57790i		−	0.331994i	0.986126	−	0.165997i	$-0.0530842\pi$
$522$	19.6832			0.861509
$523$	9.52704			0.416588			0.208294	−	0.978066i	$-0.433209\pi$
$523$	9.52704			0.416588			0.208294	+	0.978066i	$0.433209\pi$
$524$		−	13.9552i		−	0.609636i
$525$			0.282158i			0.0123144i
$526$		−	19.4912i		−	0.849858i
$527$	−42.9544			−1.87112
$528$	−41.1194			−1.78949
$529$	23.0000			0.999999
$530$			8.86775i			0.385191i
$531$			0.544168i			0.0236149i
$532$			4.23934i			0.183799i
$533$			24.1783i			1.04728i
$534$			7.06496i			0.305731i
$535$	−23.2835			−1.00663
$536$			46.9883i			2.02958i
$537$			15.0829i			0.650876i
$538$	−55.5609			−2.39540
$539$	35.5632			1.53182
$540$		−	9.72864i		−	0.418654i
$541$			33.4907i			1.43988i	0.694038	+	0.719938i	$0.255830\pi$
$541$			33.4907i			1.43988i	−0.694038	+	0.719938i	$0.744170\pi$
$542$	−3.91143			−0.168010
$543$		−	15.1857i		−	0.651682i
$544$		−	30.9230i		−	1.32581i
$545$		−	29.7736i		−	1.27536i
$546$	−4.48810			−0.192073
$547$	16.7151			0.714686			0.357343	−	0.933973i	$-0.383683\pi$
$547$	16.7151			0.714686			0.357343	+	0.933973i	$0.383683\pi$
$548$		−	3.72390i		−	0.159077i
$549$			0.548372i			0.0234040i
$550$			4.88393i			0.208252i
$551$		−	8.74007i		−	0.372339i
$552$	−0.0268817			−0.00114416
$553$	−2.31987			−0.0986508
$554$		−	9.84626i		−	0.418327i
$555$			14.2947i			0.606774i
$556$		−	72.3244i		−	3.06724i
$557$	−21.2109			−0.898736			−0.449368	−	0.893347i	$-0.648351\pi$
$557$	−21.2109			−0.898736			−0.449368	+	0.893347i	$0.648351\pi$
$558$			20.6334i			0.873482i
$559$		−	18.7798i		−	0.794300i
$560$	−13.0813			−0.552785
$561$	29.9274			1.26354
$562$		−	79.7243i		−	3.36297i
$563$			26.4063i			1.11289i	0.830884	+	0.556446i	$0.187835\pi$
$563$			26.4063i			1.11289i	−0.830884	+	0.556446i	$0.812165\pi$
$564$	22.1046			0.930770
$565$			24.3088i			1.02268i
$566$		−	58.5282i		−	2.46013i
$567$		−	0.830530i		−	0.0348790i
$568$			91.9660i			3.85881i
$569$		−	26.1149i		−	1.09479i	−0.836874	−	0.547396i	$-0.815619\pi$
$569$		−	26.1149i		−	1.09479i	0.836874	−	0.547396i	$-0.184381\pi$
$570$	−6.23703			−0.261240
$571$	−8.08498			−0.338346			−0.169173	−	0.985586i	$-0.554110\pi$
$571$	−8.08498			−0.338346			−0.169173	+	0.985586i	$0.554110\pi$
$572$	−53.8065			−2.24976
$573$			9.42950i			0.393923i
$574$			24.1783i			1.00918i
$575$			0.00142835i			5.95665e-5i
$576$	−0.261890			−0.0109121
$577$	−28.2121			−1.17449			−0.587243	−	0.809411i	$-0.699787\pi$
$577$	−28.2121			−1.17449			−0.587243	+	0.809411i	$0.699787\pi$
$578$			28.5650i			1.18815i
$579$	12.2617			0.509577
$580$	75.0708			3.11714
$581$	−5.96951			−0.247657
$582$	27.4036			1.13592
$583$			9.07588i			0.375885i
$584$	8.00026			0.331053
$585$		−	4.57338i		−	0.189086i
$586$	−77.8685			−3.21672
$587$			8.64427i			0.356787i	0.983959	+	0.178394i	$0.0570901\pi$
$587$			8.64427i			0.356787i	−0.983959	+	0.178394i	$0.942910\pi$
$588$	28.4375			1.17274
$589$	9.16202			0.377514
$590$			2.99650i			0.123364i
$591$	4.32534			0.177921
$592$	48.3123			1.98562
$593$	20.9709			0.861173			0.430586	−	0.902549i	$-0.358307\pi$
$593$	20.9709			0.861173			0.430586	+	0.902549i	$0.358307\pi$
$594$		−	14.3758i		−	0.589848i
$595$	9.52079			0.390314
$596$		−	33.2939i		−	1.36377i
$597$	−5.24168			−0.214528
$598$	−0.0227199			−0.000929087
$599$			40.7837i			1.66638i	0.552989	+	0.833189i	$0.313487\pi$
$599$			40.7837i			1.66638i	−0.552989	+	0.833189i	$0.686513\pi$
$600$			2.17217i			0.0886785i
$601$	−2.65666			−0.108368			−0.0541838	−	0.998531i	$-0.517256\pi$
$601$	−2.65666			−0.108368			−0.0541838	+	0.998531i	$0.517256\pi$
$602$		−	18.7798i		−	0.765406i
$603$	−7.34907			−0.299277
$604$		−	21.5905i		−	0.878504i
$605$		−	44.8212i		−	1.82224i
$606$		−	9.97728i		−	0.405299i
$607$		−	41.6416i		−	1.69018i	−0.534623	−	0.845090i	$-0.679547\pi$
$607$		−	41.6416i		−	1.69018i	0.534623	−	0.845090i	$-0.320453\pi$
$608$			6.59576i			0.267493i
$609$	6.40876			0.259696
$610$			3.01965i			0.122262i
$611$	10.3912			0.420384
$612$	23.9309			0.967350
$613$			6.25191i			0.252512i	0.991998	+	0.126256i	$0.0402961\pi$
$613$			6.25191i			0.252512i	−0.991998	+	0.126256i	$0.959704\pi$
$614$	−56.7777			−2.29136
$615$	−24.6377			−0.993487
$616$	−29.9274			−1.20581
$617$	−33.7784			−1.35987			−0.679934	−	0.733273i	$-0.737992\pi$
$617$	−33.7784			−1.35987			−0.679934	+	0.733273i	$0.737992\pi$
$618$	−39.8316			−1.60226
$619$	−34.9417			−1.40442			−0.702212	−	0.711968i	$-0.747804\pi$
$619$	−34.9417			−1.40442			−0.702212	+	0.711968i	$0.747804\pi$
$620$			78.6950i			3.16047i
$621$		−	0.00420436i		−	0.000168715i
$622$			37.6952i			1.51144i
$623$			2.30032i			0.0921605i
$624$	−15.4569			−0.618770
$625$	−23.1859			−0.927437
$626$			15.4291i			0.616672i
$627$	−6.38341			−0.254929
$628$	15.5211	−	54.2922i	0.619361	−	2.16650i
$629$	−35.1626			−1.40202
$630$		−	4.57338i		−	0.182208i
$631$	17.5143			0.697234			0.348617	−	0.937265i	$-0.386651\pi$
$631$	17.5143			0.697234			0.348617	+	0.937265i	$0.386651\pi$
$632$	−17.8593			−0.710407
$633$			0.0206476i			0.000820666i
$634$			37.8131i			1.50175i
$635$		−	5.29279i		−	0.210038i
$636$			7.25736i			0.287773i
$637$	13.3683			0.529671
$638$	110.931			4.39179
$639$	−14.3837			−0.569009
$640$	23.7001			0.936830
$641$	46.2206			1.82560			0.912802	−	0.408402i	$-0.133914\pi$
$641$	46.2206			1.82560			0.912802	+	0.408402i	$0.133914\pi$
$642$	−27.5118			−1.08580
$643$		−	39.5314i		−	1.55897i	−0.626423	−	0.779484i	$-0.715482\pi$
$643$		−	39.5314i		−	1.55897i	0.626423	−	0.779484i	$-0.284518\pi$
$644$	−0.0157363			−0.000620095
$645$	19.1366			0.753502
$646$		−	15.3421i		−	0.603627i
$647$	38.0424			1.49560			0.747802	−	0.663922i	$-0.231109\pi$
$647$	38.0424			1.49560			0.747802	+	0.663922i	$0.231109\pi$
$648$		−	6.39378i		−	0.251171i
$649$			3.06683i			0.120384i
$650$			1.83588i			0.0720091i
$651$			6.71816i			0.263305i
$652$			100.904i			3.95171i
$653$	18.0797			0.707512			0.353756	−	0.935338i	$-0.384904\pi$
$653$	18.0797			0.707512			0.353756	+	0.935338i	$0.384904\pi$
$654$		−	35.1805i		−	1.37566i
$655$	6.68490			0.261201
$656$			83.2691i			3.25111i
$657$			1.25126i			0.0488162i
$658$	10.3912			0.405092
$659$	32.4958			1.26586			0.632928	−	0.774211i	$-0.281853\pi$
$659$	32.4958			1.26586			0.632928	+	0.774211i	$0.281853\pi$
$660$		−	54.8288i		−	2.13421i
$661$	−8.74829			−0.340269			−0.170135	−	0.985421i	$-0.554420\pi$
$661$	−8.74829			−0.340269			−0.170135	+	0.985421i	$0.554420\pi$
$662$			43.4381i			1.68827i
$663$	11.2498			0.436905
$664$	−45.9558			−1.78343
$665$	−2.03075			−0.0787491
$666$			16.8906i			0.654497i
$667$	0.0324428			0.00125619
$668$	−1.31662			−0.0509417
$669$		−	20.0265i		−	0.774268i
$670$	−40.4682			−1.56342
$671$			3.09052i			0.119308i
$672$	−4.83642			−0.186569
$673$			22.6168i			0.871814i	0.899992	+	0.435907i	$0.143572\pi$
$673$			22.6168i			0.871814i	−0.899992	+	0.435907i	$0.856428\pi$
$674$	35.0457			1.34991
$675$	−0.339732			−0.0130763
$676$	38.3595			1.47537
$677$	5.92033			0.227537			0.113768	−	0.993507i	$-0.463708\pi$
$677$	5.92033			0.227537			0.113768	+	0.993507i	$0.463708\pi$
$678$			28.7233i			1.10311i
$679$	8.92251			0.342415
$680$	73.2952			2.81074
$681$		−	19.0262i		−	0.729085i
$682$			116.286i			4.45283i
$683$			40.9451i			1.56672i	0.621568	+	0.783360i	$0.286496\pi$
$683$			40.9451i			1.56672i	−0.621568	+	0.783360i	$0.713504\pi$
$684$	−5.10438			−0.195171
$685$	1.78384			0.0681571
$686$	28.1979			1.07660
$687$		−	17.2569i		−	0.658393i
$688$		−	64.6768i		−	2.46578i
$689$			3.41164i			0.129973i
$690$		−	0.0231516i		−	0.000881367i
$691$		−	3.24237i		−	0.123345i	−0.998096	−	0.0616727i	$-0.980357\pi$
$691$		−	3.24237i		−	0.123345i	0.998096	−	0.0616727i	$-0.0196435\pi$
$692$	115.552			4.39262
$693$		−	4.68071i		−	0.177806i
$694$			65.6384i			2.49160i
$695$	34.6452			1.31417
$696$	49.3374			1.87013
$697$		−	60.6048i		−	2.29557i
$698$			59.7322i			2.26090i
$699$	−9.44224			−0.357138
$700$			1.27156i			0.0480606i
$701$			16.9360i			0.639663i	0.947475	+	0.319831i	$0.103626\pi$
$701$			16.9360i			0.639663i	−0.947475	+	0.319831i	$0.896374\pi$
$702$		−	5.40391i		−	0.203957i
$703$	7.50005			0.282870
$704$	−1.47596			−0.0556274
$705$			10.5886i			0.398792i
$706$		−	93.9527i		−	3.53596i
$707$		−	3.24856i		−	0.122175i
$708$			2.45233i			0.0921644i
$709$	−24.4736			−0.919126			−0.459563	−	0.888145i	$-0.651994\pi$
$709$	−24.4736			−0.919126			−0.459563	+	0.888145i	$0.651994\pi$
$710$	−79.2048			−2.97250
$711$		−	2.79324i		−	0.104755i
$712$			17.7089i			0.663668i
$713$			0.0340090i			0.00127365i
$714$	11.2498			0.421012
$715$		−	25.7747i		−	0.963919i
$716$			67.9724i			2.54025i
$717$	10.1650			0.379619
$718$	80.6550			3.01002
$719$		−	21.7965i		−	0.812872i	−0.913679	−	0.406436i	$-0.866771\pi$
$719$		−	21.7965i		−	0.812872i	0.913679	−	0.406436i	$-0.133229\pi$
$720$		−	15.7505i		−	0.586988i
$721$	−12.9690			−0.482991
$722$		−	45.1928i		−	1.68190i
$723$			14.4832i			0.538635i
$724$		−	68.4356i		−	2.54339i
$725$		−	2.62153i		−	0.0973613i
$726$		−	52.9608i		−	1.96556i
$727$	24.1593			0.896019			0.448010	−	0.894029i	$-0.352133\pi$
$727$	24.1593			0.896019			0.448010	+	0.894029i	$0.352133\pi$
$728$	−11.2498			−0.416945
$729$	1.00000			0.0370370
$730$			6.89014i			0.255016i
$731$			47.0729i			1.74106i
$732$			2.47128i			0.0913412i
$733$	−33.0044			−1.21904			−0.609522	−	0.792769i	$-0.708639\pi$
$733$	−33.0044			−1.21904			−0.609522	+	0.792769i	$0.708639\pi$
$734$	−56.6376			−2.09053
$735$			13.6223i			0.502466i
$736$	−0.0244832			−0.000902463
$737$	−41.4180			−1.52565
$738$	−29.1119			−1.07162
$739$	6.03477			0.221993			0.110996	−	0.993821i	$-0.464596\pi$
$739$	6.03477			0.221993			0.110996	+	0.993821i	$0.464596\pi$
$740$			64.4200i			2.36812i
$741$	−2.39954			−0.0881492
$742$			3.41164i			0.125245i
$743$	8.33395			0.305743			0.152871	−	0.988246i	$-0.451148\pi$
$743$	8.33395			0.305743			0.152871	+	0.988246i	$0.451148\pi$
$744$			51.7193i			1.89612i
$745$	15.9486			0.584313
$746$	−60.1103			−2.20079
$747$		−	7.18759i		−	0.262980i
$748$	134.870			4.93135
$749$	−8.95771			−0.327308
$750$	−29.4036			−1.07367
$751$		−	8.12677i		−	0.296550i	−0.988946	−	0.148275i	$-0.952628\pi$
$751$		−	8.12677i		−	0.296550i	0.988946	−	0.148275i	$-0.0473721\pi$
$752$	35.7870			1.30502
$753$		−	21.0817i		−	0.768259i
$754$	41.6991			1.51859
$755$	10.3424			0.376398
$756$		−	3.74285i		−	0.136126i
$757$			46.8010i			1.70101i	0.525966	+	0.850506i	$0.323704\pi$
$757$			46.8010i			1.70101i	−0.525966	+	0.850506i	$0.676296\pi$
$758$	−18.0213			−0.654563
$759$		−	0.0236950i		−	0.000860073i
$760$	−15.6336			−0.567090
$761$		−	25.3894i		−	0.920366i	−0.887824	−	0.460183i	$-0.847784\pi$
$761$		−	25.3894i		−	0.920366i	0.887824	−	0.460183i	$-0.152216\pi$
$762$		−	6.25397i		−	0.226557i
$763$		−	11.4546i		−	0.414685i
$764$			42.4948i			1.53741i
$765$			11.4635i			0.414464i
$766$	−50.9171			−1.83971
$767$			1.15283i			0.0416262i
$768$	28.5279			1.02941
$769$	−38.1465			−1.37560			−0.687799	−	0.725902i	$-0.741423\pi$
$769$	−38.1465			−1.37560			−0.687799	+	0.725902i	$0.741423\pi$
$770$		−	25.7747i		−	0.928856i
$771$	−21.1912			−0.763181
$772$	55.2581			1.98878
$773$	11.7956			0.424259			0.212129	−	0.977242i	$-0.431960\pi$
$773$	11.7956			0.424259			0.212129	+	0.977242i	$0.431960\pi$
$774$	22.6118			0.812764
$775$	2.74809			0.0987144
$776$	68.6894			2.46580
$777$			5.49950i			0.197294i
$778$			27.4969i			0.985811i
$779$			12.9268i			0.463150i
$780$		−	20.6103i		−	0.737966i
$781$	−81.0637			−2.90069
$782$	0.0569493			0.00203650
$783$			7.71647i			0.275764i
$784$	46.0399			1.64428
$785$	26.0074	+	7.43503i	0.928242	+	0.265367i
$786$	7.89889			0.281744
$787$		−	16.9335i		−	0.603613i	−0.953369	−	0.301806i	$-0.902410\pi$
$787$		−	16.9335i		−	0.603613i	0.953369	−	0.301806i	$-0.0975896\pi$
$788$	19.4925			0.694391
$789$	7.64122			0.272035
$790$		−	15.3812i		−	0.547238i
$791$			9.35218i			0.332525i
$792$		−	36.0341i		−	1.28042i
$793$			1.16173i			0.0412544i
$794$	34.6923			1.23118
$795$	−3.47646			−0.123297
$796$	−23.6221			−0.837262
$797$	−9.72844			−0.344599			−0.172300	−	0.985045i	$-0.555120\pi$
$797$	−9.72844			−0.344599			−0.172300	+	0.985045i	$0.555120\pi$
$798$	−2.39954			−0.0849427
$799$	−26.0464			−0.921455
$800$			1.97836i			0.0699456i
$801$	−2.76971			−0.0978628
$802$	−80.7130			−2.85008
$803$			7.05186i			0.248855i
$804$	−33.1191			−1.16802
$805$		−	0.00753807i		−	0.000265682i
$806$			43.7122i			1.53970i
$807$		−	21.7817i		−	0.766754i
$808$		−	25.0088i		−	0.879807i
$809$		−	5.05013i		−	0.177553i	−0.996052	−	0.0887765i	$-0.971704\pi$
$809$		−	5.05013i		−	0.177553i	0.996052	−	0.0887765i	$-0.0282957\pi$
$810$	5.50658			0.193481
$811$		−	5.85639i		−	0.205646i	−0.994700	−	0.102823i	$-0.967213\pi$
$811$		−	5.85639i		−	0.205646i	0.994700	−	0.102823i	$-0.0327875\pi$
$812$	28.8816			1.01354
$813$		−	1.53341i		−	0.0537792i
$814$			95.1922i			3.33648i
$815$	−48.3356			−1.69312
$816$	38.7438			1.35630
$817$		−	10.0405i		−	0.351272i
$818$	8.36959			0.292636
$819$		−	1.75949i		−	0.0614815i
$820$	−111.032			−3.87739
$821$	−3.82070			−0.133343			−0.0666716	−	0.997775i	$-0.521238\pi$
$821$	−3.82070			−0.133343			−0.0666716	+	0.997775i	$0.521238\pi$
$822$	2.10779			0.0735176
$823$		−	42.0514i		−	1.46582i	−0.680326	−	0.732910i	$-0.738162\pi$
$823$		−	42.0514i		−	1.46582i	0.680326	−	0.732910i	$-0.261838\pi$
$824$	−99.8411			−3.47813
$825$	−1.91467			−0.0666602
$826$			1.15283i			0.0401120i
$827$	−15.6218			−0.543223			−0.271612	−	0.962407i	$-0.587557\pi$
$827$	−15.6218			−0.543223			−0.271612	+	0.962407i	$0.587557\pi$
$828$		−	0.0189473i		−	0.000658463i
$829$	−4.11180			−0.142809			−0.0714044	−	0.997447i	$-0.522748\pi$
$829$	−4.11180			−0.142809			−0.0714044	+	0.997447i	$0.522748\pi$
$830$		−	39.5790i		−	1.37381i
$831$	3.86007			0.133904
$832$	−0.554817			−0.0192348
$833$	−33.5087			−1.16101
$834$	40.9369			1.41753
$835$		−	0.630697i		−	0.0218262i
$836$	−28.7673			−0.994939
$837$	−8.08900			−0.279597
$838$		−	28.6380i		−	0.989282i
$839$			33.4430i			1.15458i	0.816539	+	0.577290i	$0.195890\pi$
$839$			33.4430i			1.15458i	−0.816539	+	0.577290i	$0.804110\pi$
$840$		−	11.4635i		−	0.395529i
$841$	−30.5439			−1.05324
$842$	57.8397			1.99329
$843$	31.2546			1.07647
$844$			0.0930498i			0.00320291i
$845$			18.3752i			0.632126i
$846$			12.5116i			0.430156i
$847$		−	17.2438i		−	0.592504i
$848$			11.7496i			0.403482i
$849$	22.9451			0.787472
$850$		−	4.60178i		−	0.157840i
$851$			0.0278399i			0.000954339i
$852$	−64.8211			−2.22073
$853$	−17.2620			−0.591040			−0.295520	−	0.955337i	$-0.595493\pi$
$853$	−17.2620			−0.591040			−0.295520	+	0.955337i	$0.595493\pi$
$854$			1.16173i			0.0397537i
$855$		−	2.44513i		−	0.0836216i
$856$	−68.9604			−2.35702
$857$		−	19.5442i		−	0.667617i	−0.942641	−	0.333808i	$-0.891666\pi$
$857$		−	19.5442i		−	0.667617i	0.942641	−	0.333808i	$-0.108334\pi$
$858$		−	30.4554i		−	1.03973i
$859$		−	20.9660i		−	0.715351i	−0.933846	−	0.357675i	$-0.883569\pi$
$859$		−	20.9660i		−	0.715351i	0.933846	−	0.357675i	$-0.116431\pi$
$860$	86.2405			2.94078
$861$	−9.47871			−0.323034
$862$		−	40.9954i		−	1.39631i
$863$			33.2578i			1.13211i	0.824368	+	0.566054i	$0.191531\pi$
$863$			33.2578i			1.13211i	−0.824368	+	0.566054i	$0.808469\pi$
$864$		−	5.82330i		−	0.198113i
$865$			55.3522i			1.88203i
$866$	31.0341			1.05458
$867$	−11.1984			−0.380319
$868$			30.2759i			1.02763i
$869$		−	15.7422i		−	0.534017i
$870$			42.4913i			1.44059i
$871$	−15.5691			−0.527539
$872$		−	88.1826i		−	2.98624i
$873$			10.7432i			0.363601i
$874$	−0.0121471			−0.000410881
$875$	−9.57371			−0.323650
$876$			5.63889i			0.190520i
$877$			20.5356i			0.693437i	0.937969	+	0.346718i	$0.112704\pi$
$877$			20.5356i			0.693437i	−0.937969	+	0.346718i	$0.887296\pi$
$878$	105.113			3.54740
$879$		−	30.5271i		−	1.02965i
$880$		−	88.7671i		−	2.99234i
$881$		−	30.4611i		−	1.02626i	−0.858311	−	0.513130i	$-0.828486\pi$
$881$		−	30.4611i		−	1.02626i	0.858311	−	0.513130i	$-0.171514\pi$
$882$			16.0961i			0.541984i
$883$			4.55251i			0.153204i	0.997062	+	0.0766022i	$0.0244071\pi$
$883$			4.55251i			0.153204i	−0.997062	+	0.0766022i	$0.975593\pi$
$884$	50.6980			1.70516
$885$	−1.17473			−0.0394881
$886$	14.3501			0.482102
$887$			25.4020i			0.852914i	0.904508	+	0.426457i	$0.140239\pi$
$887$			25.4020i			0.852914i	−0.904508	+	0.426457i	$0.859761\pi$
$888$			42.3375i			1.42075i
$889$		−	2.03627i		−	0.0682942i
$890$	−15.2516			−0.511235
$891$	5.63582			0.188807
$892$		−	90.2508i		−	3.02182i
$893$	5.55560			0.185911
$894$	18.8449			0.630269
$895$	−32.5605			−1.08838
$896$	9.11802			0.304612
$897$		−	0.00890699i		−	0.000297396i
$898$	−105.657			−3.52583
$899$		−	62.4185i		−	2.08178i
$900$	−1.53103			−0.0510343
$901$		−	8.55154i		−	0.284893i
$902$	−164.069			−5.46291
$903$	7.36231			0.245002
$904$			71.9971i			2.39459i
$905$	32.7824			1.08972
$906$	12.2206			0.406002
$907$	1.00411			0.0333409			0.0166705	−	0.999861i	$-0.494693\pi$
$907$	1.00411			0.0333409			0.0166705	+	0.999861i	$0.494693\pi$
$908$		−	85.7430i		−	2.84548i
$909$	3.91143			0.129734
$910$		−	9.68876i		−	0.321179i
$911$	16.5356			0.547850			0.273925	−	0.961751i	$-0.411678\pi$
$911$	16.5356			0.547850			0.273925	+	0.961751i	$0.411678\pi$
$912$	−8.26392			−0.273646
$913$		−	40.5079i		−	1.34062i
$914$			7.91483i			0.261799i
$915$	−1.18381			−0.0391354
$916$		−	77.7696i		−	2.56958i
$917$	2.57184			0.0849298
$918$			13.5453i			0.447062i
$919$			4.53794i			0.149693i	0.997195	+	0.0748464i	$0.0238467\pi$
$919$			4.53794i			0.149693i	−0.997195	+	0.0748464i	$0.976153\pi$
$920$		−	0.0580313i		−	0.00191324i
$921$		−	22.2588i		−	0.733452i
$922$			79.7243i			2.62558i
$923$	−30.4720			−1.00300
$924$		−	21.0940i		−	0.693941i
$925$	2.24960			0.0739663
$926$	−77.0656			−2.53253
$927$		−	15.6154i		−	0.512875i
$928$	44.9353			1.47507
$929$	29.7428			0.975830			0.487915	−	0.872891i	$-0.337758\pi$
$929$	29.7428			0.975830			0.487915	+	0.872891i	$0.337758\pi$
$930$	−44.5427			−1.46061
$931$	7.14728			0.234243
$932$	−42.5522			−1.39384
$933$	−14.7778			−0.483803
$934$		−	8.29557i		−	0.271439i
$935$			64.6063i			2.11285i
$936$		−	13.5453i		−	0.442742i
$937$			27.3424i			0.893237i	0.894724	+	0.446619i	$0.147372\pi$
$937$			27.3424i			0.893237i	−0.894724	+	0.446619i	$0.852628\pi$
$938$	−15.5691			−0.508349
$939$	−6.04874			−0.197393
$940$			47.7186i			1.55641i
$941$	−47.3999			−1.54519			−0.772597	−	0.634897i	$-0.781043\pi$
$941$	−47.3999			−1.54519			−0.772597	+	0.634897i	$0.781043\pi$
$942$	30.7303	+	8.78523i	1.00125	+	0.286238i
$943$	−0.0479837			−0.00156256
$944$			3.97029i			0.129222i
$945$	1.79292			0.0583236
$946$	127.436			4.14330
$947$		−	22.3815i		−	0.727301i	−0.931536	−	0.363650i	$-0.881530\pi$
$947$		−	22.3815i		−	0.727301i	0.931536	−	0.363650i	$-0.118470\pi$
$948$		−	12.5879i		−	0.408838i
$949$			2.65081i			0.0860488i
$950$			0.981542i			0.0318454i
$951$	−14.8240			−0.480702
$952$	28.1984			0.913917
$953$	−37.1158			−1.20230			−0.601149	−	0.799137i	$-0.705290\pi$
$953$	−37.1158			−1.20230			−0.601149	+	0.799137i	$0.705290\pi$
$954$	−4.10779			−0.132995
$955$	−20.3561			−0.658707
$956$	45.8094			1.48158
$957$			43.4886i			1.40579i
$958$	41.6875			1.34686
$959$	0.686288			0.0221614
$960$		−	0.565359i		−	0.0182469i
$961$	34.4320			1.11071
$962$			35.7829i			1.15369i
$963$		−	10.7855i		−	0.347559i
$964$			65.2695i			2.10219i
$965$			26.4701i			0.852101i
$966$		−	0.00890699i		−	0.000286578i
$967$	47.4875			1.52709			0.763547	−	0.645752i	$-0.223456\pi$
$967$	47.4875			1.52709			0.763547	+	0.645752i	$0.223456\pi$
$968$		−	132.750i		−	4.26676i
$969$	6.01463			0.193218
$970$			59.1580i			1.89945i
$971$			24.7866i			0.795440i	0.917507	+	0.397720i	$0.130199\pi$
$971$			24.7866i			0.795440i	−0.917507	+	0.397720i	$0.869801\pi$
$972$	4.50658			0.144549
$973$	13.3289			0.427304
$974$		−	66.3765i		−	2.12684i
$975$	−0.719727			−0.0230497
$976$			4.00097i			0.128068i
$977$	−22.4945			−0.719664			−0.359832	−	0.933017i	$-0.617166\pi$
$977$	−22.4945			−0.719664			−0.359832	+	0.933017i	$0.617166\pi$
$978$	−57.1134			−1.82629
$979$	−15.6096			−0.498884
$980$			61.3899i			1.96103i
$981$	13.7919			0.440343
$982$	81.4981			2.60071
$983$			38.6154i			1.23164i	0.787887	+	0.615820i	$0.211175\pi$
$983$			38.6154i			1.23164i	−0.787887	+	0.615820i	$0.788825\pi$
$984$	−72.9712			−2.32624
$985$			9.33739i			0.297514i
$986$	−104.522			−3.32866
$987$			4.07371i			0.129668i
$988$	−10.8137			−0.344030
$989$	0.0372699			0.00118511
$990$	31.0341			0.986327
$991$	−27.7847			−0.882610			−0.441305	−	0.897357i	$-0.645484\pi$
$991$	−27.7847			−0.882610			−0.441305	+	0.897357i	$0.645484\pi$
$992$			47.1047i			1.49557i
$993$	−17.0292			−0.540405
$994$	−30.4720			−0.966514
$995$		−	11.3156i		−	0.358728i
$996$		−	32.3914i		−	1.02636i
$997$		−	16.9853i		−	0.537931i	−0.963150	−	0.268966i	$-0.913318\pi$
$997$		−	16.9853i		−	0.537931i	0.963150	−	0.268966i	$-0.0866818\pi$
$998$	−29.4404			−0.931920
$999$	−6.62168			−0.209501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.b.a.313.12	yes	12
3.2	odd	2		1413.2.b.c.784.1		12
157.156	even	2	inner	471.2.b.a.313.1	✓	12
471.470	odd	2		1413.2.b.c.784.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.b.a.313.1	✓	12	157.156	even	2	inner
471.2.b.a.313.12	yes	12	1.1	even	1	trivial
1413.2.b.c.784.1		12	3.2	odd	2
1413.2.b.c.784.12		12	471.470	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.55080i q^{2} -1.00000 q^{3} -4.50658 q^{4} -2.15877i q^{5} -2.55080i q^{6} -0.830530i q^{7} -6.39378i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.55080i q^{2} -1.00000 q^{3} -4.50658 q^{4} -2.15877i q^{5} -2.55080i q^{6} -0.830530i q^{7} -6.39378i q^{8} +1.00000 q^{9} +5.50658 q^{10} +5.63582 q^{11} +4.50658 q^{12} +2.11851 q^{13} +2.11851 q^{14} +2.15877i q^{15} +7.29608 q^{16} -5.31022 q^{17} +2.55080i q^{18} +1.13265 q^{19} +9.72864i q^{20} +0.830530i q^{21} +14.3758i q^{22} +0.00420436i q^{23} +6.39378i q^{24} +0.339732 q^{25} +5.40391i q^{26} -1.00000 q^{27} +3.74285i q^{28} -7.71647i q^{29} -5.50658 q^{30} +8.08900 q^{31} +5.82330i q^{32} -5.63582 q^{33} -13.5453i q^{34} -1.79292 q^{35} -4.50658 q^{36} +6.62168 q^{37} +2.88916i q^{38} -2.11851 q^{39} -13.8027 q^{40} +11.4129i q^{41} -2.11851 q^{42} -8.86459i q^{43} -25.3982 q^{44} -2.15877i q^{45} -0.0107245 q^{46} +4.90496 q^{47} -7.29608 q^{48} +6.31022 q^{49} +0.866588i q^{50} +5.31022 q^{51} -9.54725 q^{52} +1.61039i q^{53} -2.55080i q^{54} -12.1664i q^{55} -5.31022 q^{56} -1.13265 q^{57} +19.6832 q^{58} +0.544168i q^{59} -9.72864i q^{60} +0.548372i q^{61} +20.6334i q^{62} -0.830530i q^{63} -0.261890 q^{64} -4.57338i q^{65} -14.3758i q^{66} -7.34907 q^{67} +23.9309 q^{68} -0.00420436i q^{69} -4.57338i q^{70} -14.3837 q^{71} -6.39378i q^{72} +1.25126i q^{73} +16.8906i q^{74} -0.339732 q^{75} -5.10438 q^{76} -4.68071i q^{77} -5.40391i q^{78} -2.79324i q^{79} -15.7505i q^{80} +1.00000 q^{81} -29.1119 q^{82} -7.18759i q^{83} -3.74285i q^{84} +11.4635i q^{85} +22.6118 q^{86} +7.71647i q^{87} -36.0341i q^{88} -2.76971 q^{89} +5.50658 q^{90} -1.75949i q^{91} -0.0189473i q^{92} -8.08900 q^{93} +12.5116i q^{94} -2.44513i q^{95} -5.82330i q^{96} +10.7432i q^{97} +16.0961i q^{98} +5.63582 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9	\( 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9} + 18 q^{10} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} + 10 q^{16} + 2 q^{17} + 4 q^{19} + 12 q^{25} - 12 q^{27} - 18 q^{30} + 2 q^{31} + 2 q^{33} - 4 q^{35} - 6 q^{36} - 2 q^{37} - 4 q^{39} - 40 q^{40} - 4 q^{42} - 36 q^{44} + 34 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{51} - 6 q^{52} + 2 q^{56} - 4 q^{57} + 24 q^{58} + 28 q^{64} - 38 q^{67} + 32 q^{68} - 26 q^{71} - 12 q^{75} - 28 q^{76} + 12 q^{81} - 50 q^{82} + 6 q^{86} - 4 q^{89} + 18 q^{90} - 2 q^{93} - 2 q^{99}+O(q^{100}) \) 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9 + 18 * q^10 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 + 10 * q^16 + 2 * q^17 + 4 * q^19 + 12 * q^25 - 12 * q^27 - 18 * q^30 + 2 * q^31 + 2 * q^33 - 4 * q^35 - 6 * q^36 - 2 * q^37 - 4 * q^39 - 40 * q^40 - 4 * q^42 - 36 * q^44 + 34 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^51 - 6 * q^52 + 2 * q^56 - 4 * q^57 + 24 * q^58 + 28 * q^64 - 38 * q^67 + 32 * q^68 - 26 * q^71 - 12 * q^75 - 28 * q^76 + 12 * q^81 - 50 * q^82 + 6 * q^86 - 4 * q^89 + 18 * q^90 - 2 * q^93 - 2 * q^99

Introduction

L-functions

Modular forms

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