LMFDB - Embedded newform 731.2.d.d.560.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(560,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("731.560");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.d (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			560.11
Character	$\chi$	$=$	731.560
Dual form			731.2.d.d.560.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.28013 q^{2} -2.62270i q^{3} -0.361257 q^{4} +1.51509i q^{5} +3.35741i q^{6} -3.46119i q^{7} +3.02273 q^{8} -3.87855 q^{9} +O(q^{10})$	\(q-1.28013 q^{2} -2.62270i q^{3} -0.361257 q^{4} +1.51509i q^{5} +3.35741i q^{6} -3.46119i q^{7} +3.02273 q^{8} -3.87855 q^{9} -1.93952i q^{10} -2.66241i q^{11} +0.947467i q^{12} +6.10034 q^{13} +4.43079i q^{14} +3.97362 q^{15} -3.14698 q^{16} +(3.82369 - 1.54252i) q^{17} +4.96506 q^{18} -5.46605 q^{19} -0.547335i q^{20} -9.07766 q^{21} +3.40824i q^{22} -4.54632i q^{23} -7.92770i q^{24} +2.70451 q^{25} -7.80925 q^{26} +2.30417i q^{27} +1.25038i q^{28} -5.97832i q^{29} -5.08677 q^{30} +4.36450i q^{31} -2.01689 q^{32} -6.98270 q^{33} +(-4.89484 + 1.97463i) q^{34} +5.24401 q^{35} +1.40115 q^{36} +7.49162i q^{37} +6.99728 q^{38} -15.9994i q^{39} +4.57970i q^{40} -2.38851i q^{41} +11.6206 q^{42} -1.00000 q^{43} +0.961813i q^{44} -5.87634i q^{45} +5.81990i q^{46} +4.98403 q^{47} +8.25358i q^{48} -4.97985 q^{49} -3.46213 q^{50} +(-4.04556 - 10.0284i) q^{51} -2.20379 q^{52} -13.2213 q^{53} -2.94964i q^{54} +4.03379 q^{55} -10.4622i q^{56} +14.3358i q^{57} +7.65305i q^{58} -15.3242 q^{59} -1.43550 q^{60} +3.31531i q^{61} -5.58714i q^{62} +13.4244i q^{63} +8.87585 q^{64} +9.24255i q^{65} +8.93880 q^{66} -2.45525 q^{67} +(-1.38133 + 0.557245i) q^{68} -11.9236 q^{69} -6.71304 q^{70} +12.5902i q^{71} -11.7238 q^{72} -1.13325i q^{73} -9.59027i q^{74} -7.09311i q^{75} +1.97465 q^{76} -9.21512 q^{77} +20.4813i q^{78} -6.56332i q^{79} -4.76795i q^{80} -5.59251 q^{81} +3.05761i q^{82} +9.61700 q^{83} +3.27936 q^{84} +(2.33705 + 5.79323i) q^{85} +1.28013 q^{86} -15.6793 q^{87} -8.04774i q^{88} -14.4993 q^{89} +7.52251i q^{90} -21.1144i q^{91} +1.64239i q^{92} +11.4468 q^{93} -6.38023 q^{94} -8.28155i q^{95} +5.28970i q^{96} -16.0845i q^{97} +6.37487 q^{98} +10.3263i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) $ 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9	$ 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 14 q^{18} + 16 q^{19} + 20 q^{21} - 44 q^{25} - 26 q^{26} + 88 q^{30} - 42 q^{32} + 12 q^{33} - 42 q^{34} + 22 q^{35} + 34 q^{38} - 14 q^{42} - 34 q^{43} + 30 q^{47} - 62 q^{49} - 46 q^{50} - 10 q^{51} + 26 q^{52} - 46 q^{53} + 16 q^{55} - 20 q^{59} - 42 q^{60} + 102 q^{64} - 70 q^{66} - 32 q^{67} - 10 q^{68} + 74 q^{69} + 130 q^{70} + 22 q^{72} + 38 q^{76} - 78 q^{77} + 46 q^{81} - 60 q^{83} - 98 q^{84} - 38 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{89} + 14 q^{93} - 78 q^{94} + 78 q^{98}+O(q^{100}) $ 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 14 * q^18 + 16 * q^19 + 20 * q^21 - 44 * q^25 - 26 * q^26 + 88 * q^30 - 42 * q^32 + 12 * q^33 - 42 * q^34 + 22 * q^35 + 34 * q^38 - 14 * q^42 - 34 * q^43 + 30 * q^47 - 62 * q^49 - 46 * q^50 - 10 * q^51 + 26 * q^52 - 46 * q^53 + 16 * q^55 - 20 * q^59 - 42 * q^60 + 102 * q^64 - 70 * q^66 - 32 * q^67 - 10 * q^68 + 74 * q^69 + 130 * q^70 + 22 * q^72 + 38 * q^76 - 78 * q^77 + 46 * q^81 - 60 * q^83 - 98 * q^84 - 38 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^89 + 14 * q^93 - 78 * q^94 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.28013			−0.905192			−0.452596	−	0.891716i	$-0.649502\pi$
$2$	−1.28013			−0.905192			−0.452596	+	0.891716i	$0.649502\pi$
$3$		−	2.62270i		−	1.51422i	−0.653290	−	0.757108i	$-0.726612\pi$
$3$		−	2.62270i		−	1.51422i	0.653290	−	0.757108i	$-0.273388\pi$
$4$	−0.361257			−0.180628
$5$			1.51509i			0.677568i	0.940864	+	0.338784i	$0.110016\pi$
$5$			1.51509i			0.677568i	−0.940864	+	0.338784i	$0.889984\pi$
$6$			3.35741i			1.37066i
$7$		−	3.46119i		−	1.30821i	−0.756405	−	0.654104i	$-0.773046\pi$
$7$		−	3.46119i		−	1.30821i	0.756405	−	0.654104i	$-0.226954\pi$
$8$	3.02273			1.06869
$9$	−3.87855			−1.29285
$10$		−	1.93952i		−	0.613329i
$11$		−	2.66241i		−	0.802747i	−0.915914	−	0.401374i	$-0.868533\pi$
$11$		−	2.66241i		−	0.802747i	0.915914	−	0.401374i	$-0.131467\pi$
$12$			0.947467i			0.273510i
$13$	6.10034			1.69193			0.845965	−	0.533239i	$-0.179025\pi$
$13$	6.10034			1.69193			0.845965	+	0.533239i	$0.179025\pi$
$14$			4.43079i			1.18418i
$15$	3.97362			1.02598
$16$	−3.14698			−0.786745
$17$	3.82369	−	1.54252i	0.927382	−	0.374116i
$17$	3.82369	−	1.54252i	0.927382	−	0.374116i
$18$	4.96506			1.17028
$19$	−5.46605			−1.25400			−0.626999	−	0.779020i	$-0.715717\pi$
$19$	−5.46605			−1.25400			−0.626999	+	0.779020i	$0.715717\pi$
$20$		−	0.547335i		−	0.122388i
$21$	−9.07766			−1.98091
$22$			3.40824i			0.726640i
$23$		−	4.54632i		−	0.947974i	−0.880532	−	0.473987i	$-0.842814\pi$
$23$		−	4.54632i		−	0.947974i	0.880532	−	0.473987i	$-0.157186\pi$
$24$		−	7.92770i		−	1.61823i
$25$	2.70451			0.540902
$26$	−7.80925			−1.53152
$27$			2.30417i			0.443437i
$28$			1.25038i			0.236299i
$29$		−	5.97832i		−	1.11015i	−0.831801	−	0.555073i	$-0.812690\pi$
$29$		−	5.97832i		−	1.11015i	0.831801	−	0.555073i	$-0.187310\pi$
$30$	−5.08677			−0.928712
$31$			4.36450i			0.783887i	0.919989	+	0.391943i	$0.128197\pi$
$31$			4.36450i			0.783887i	−0.919989	+	0.391943i	$0.871803\pi$
$32$	−2.01689			−0.356540
$33$	−6.98270			−1.21553
$34$	−4.89484	+	1.97463i	−0.839458	+	0.338646i
$35$	5.24401			0.886399
$36$	1.40115			0.233525
$37$			7.49162i			1.23161i	0.787897	+	0.615807i	$0.211170\pi$
$37$			7.49162i			1.23161i	−0.787897	+	0.615807i	$0.788830\pi$
$38$	6.99728			1.13511
$39$		−	15.9994i		−	2.56195i
$40$			4.57970i			0.724113i
$41$		−	2.38851i		−	0.373022i	−0.982453	−	0.186511i	$-0.940282\pi$
$41$		−	2.38851i		−	0.373022i	0.982453	−	0.186511i	$-0.0597180\pi$
$42$	11.6206			1.79310
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$			0.961813i			0.144999i
$45$		−	5.87634i		−	0.875993i
$46$			5.81990i			0.858098i
$47$	4.98403			0.726995			0.363498	−	0.931595i	$-0.381582\pi$
$47$	4.98403			0.726995			0.363498	+	0.931595i	$0.381582\pi$
$48$			8.25358i			1.19130i
$49$	−4.97985			−0.711407
$50$	−3.46213			−0.489620
$51$	−4.04556	−	10.0284i	−0.566492	−	1.40426i
$52$	−2.20379			−0.305610
$53$	−13.2213			−1.81608			−0.908039	−	0.418885i	$-0.862421\pi$
$53$	−13.2213			−1.81608			−0.908039	+	0.418885i	$0.862421\pi$
$54$		−	2.94964i		−	0.401396i
$55$	4.03379			0.543916
$56$		−	10.4622i		−	1.39807i
$57$			14.3358i			1.89883i
$58$			7.65305i			1.00490i
$59$	−15.3242			−1.99504			−0.997521	−	0.0703656i	$-0.977583\pi$
$59$	−15.3242			−1.99504			−0.997521	+	0.0703656i	$0.977583\pi$
$60$	−1.43550			−0.185322
$61$			3.31531i			0.424483i	0.977217	+	0.212241i	$0.0680763\pi$
$61$			3.31531i			0.424483i	−0.977217	+	0.212241i	$0.931924\pi$
$62$		−	5.58714i		−	0.709567i
$63$			13.4244i			1.69132i
$64$	8.87585			1.10948
$65$			9.24255i			1.14640i
$66$	8.93880			1.10029
$67$	−2.45525			−0.299957			−0.149978	−	0.988689i	$-0.547920\pi$
$67$	−2.45525			−0.299957			−0.149978	+	0.988689i	$0.547920\pi$
$68$	−1.38133	+	0.557245i	−0.167511	+	0.0675758i
$69$	−11.9236			−1.43544
$70$	−6.71304			−0.802361
$71$			12.5902i			1.49418i	0.664723	+	0.747090i	$0.268550\pi$
$71$			12.5902i			1.49418i	−0.664723	+	0.747090i	$0.731450\pi$
$72$	−11.7238			−1.38166
$73$		−	1.13325i		−	0.132637i	−0.997799	−	0.0663184i	$-0.978875\pi$
$73$		−	1.13325i		−	0.132637i	0.997799	−	0.0663184i	$-0.0211253\pi$
$74$		−	9.59027i		−	1.11485i
$75$		−	7.09311i		−	0.819042i
$76$	1.97465			0.226508
$77$	−9.21512			−1.05016
$78$			20.4813i			2.31905i
$79$		−	6.56332i		−	0.738431i	−0.929344	−	0.369215i	$-0.879626\pi$
$79$		−	6.56332i		−	0.738431i	0.929344	−	0.369215i	$-0.120374\pi$
$80$		−	4.76795i		−	0.533073i
$81$	−5.59251			−0.621390
$82$			3.05761i			0.337656i
$83$	9.61700			1.05560			0.527802	−	0.849368i	$-0.323016\pi$
$83$	9.61700			1.05560			0.527802	+	0.849368i	$0.323016\pi$
$84$	3.27936			0.357808
$85$	2.33705	+	5.79323i	0.253489	+	0.628364i
$86$	1.28013			0.138040
$87$	−15.6793			−1.68100
$88$		−	8.04774i		−	0.857892i
$89$	−14.4993			−1.53693			−0.768463	−	0.639894i	$-0.778978\pi$
$89$	−14.4993			−1.53693			−0.768463	+	0.639894i	$0.778978\pi$
$90$			7.52251i			0.792942i
$91$		−	21.1144i		−	2.21340i
$92$			1.64239i			0.171231i
$93$	11.4468			1.18697
$94$	−6.38023			−0.658070
$95$		−	8.28155i		−	0.849670i
$96$			5.28970i			0.539878i
$97$		−	16.0845i		−	1.63313i	−0.577251	−	0.816567i	$-0.695875\pi$
$97$		−	16.0845i		−	1.63313i	0.577251	−	0.816567i	$-0.304125\pi$
$98$	6.37487			0.643959
$99$			10.3263i			1.03783i
$100$	−0.977021			−0.0977021
$101$	14.0733			1.40034			0.700172	−	0.713975i	$-0.253107\pi$
$101$	14.0733			1.40034			0.700172	+	0.713975i	$0.253107\pi$
$102$	5.17886	+	12.8377i	0.512783	+	1.27112i
$103$	10.2351			1.00850			0.504249	−	0.863559i	$-0.331770\pi$
$103$	10.2351			1.00850			0.504249	+	0.863559i	$0.331770\pi$
$104$	18.4397			1.80816
$105$		−	13.7535i		−	1.34220i
$106$	16.9250			1.64390
$107$		−	14.2104i		−	1.37377i	−0.726766	−	0.686886i	$-0.758977\pi$
$107$		−	14.2104i		−	1.37377i	0.726766	−	0.686886i	$-0.241023\pi$
$108$		−	0.832395i		−	0.0800973i
$109$			8.45781i			0.810111i	0.914292	+	0.405056i	$0.132748\pi$
$109$			8.45781i			0.810111i	−0.914292	+	0.405056i	$0.867252\pi$
$110$	−5.16379			−0.492348
$111$	19.6483			1.86493
$112$			10.8923i			1.02923i
$113$			15.9037i			1.49609i	0.663648	+	0.748045i	$0.269007\pi$
$113$			15.9037i			1.49609i	−0.663648	+	0.748045i	$0.730993\pi$
$114$		−	18.3518i		−	1.71880i
$115$	6.88808			0.642317
$116$			2.15971i			0.200524i
$117$	−23.6605			−2.18741
$118$	19.6170			1.80590
$119$	−5.33895	−	13.2345i	−0.489421	−	1.21321i
$120$	12.0112			1.09646
$121$	3.91156			0.355597
$122$		−	4.24405i		−	0.384238i
$123$	−6.26433			−0.564836
$124$		−	1.57670i		−	0.141592i
$125$			11.6730i			1.04407i
$126$		−	17.1850i		−	1.53096i
$127$	−8.12435			−0.720920			−0.360460	−	0.932775i	$-0.617380\pi$
$127$	−8.12435			−0.720920			−0.360460	+	0.932775i	$0.617380\pi$
$128$	−7.32850			−0.647754
$129$			2.62270i			0.230916i
$130$		−	11.8317i		−	1.03771i
$131$		−	10.8598i		−	0.948823i	−0.880303	−	0.474412i	$-0.842661\pi$
$131$		−	10.8598i		−	0.948823i	0.880303	−	0.474412i	$-0.157339\pi$
$132$	2.52255			0.219560
$133$			18.9191i			1.64049i
$134$	3.14305			0.271518
$135$	−3.49102			−0.300459
$136$	11.5580	−	4.66261i	0.991088	−	0.399815i
$137$	−1.11887			−0.0955913			−0.0477956	−	0.998857i	$-0.515220\pi$
$137$	−1.11887			−0.0955913			−0.0477956	+	0.998857i	$0.515220\pi$
$138$	15.2638			1.29934
$139$		−	16.0654i		−	1.36265i	−0.731981	−	0.681325i	$-0.761404\pi$
$139$		−	16.0654i		−	1.36265i	0.731981	−	0.681325i	$-0.238596\pi$
$140$	−1.89443			−0.160109
$141$		−	13.0716i		−	1.10083i
$142$		−	16.1171i		−	1.35252i
$143$		−	16.2416i		−	1.35819i
$144$	12.2057			1.01714
$145$	9.05768			0.752200
$146$			1.45071i			0.120062i
$147$			13.0606i			1.07722i
$148$		−	2.70640i		−	0.222464i
$149$	−1.71074			−0.140150			−0.0700748	−	0.997542i	$-0.522324\pi$
$149$	−1.71074			−0.140150			−0.0700748	+	0.997542i	$0.522324\pi$
$150$			9.08013i			0.741390i
$151$	1.11501			0.0907386			0.0453693	−	0.998970i	$-0.485554\pi$
$151$	1.11501			0.0907386			0.0453693	+	0.998970i	$0.485554\pi$
$152$	−16.5224			−1.34014
$153$	−14.8304	+	5.98273i	−1.19897	+	0.483675i
$154$	11.7966			0.950596
$155$	−6.61260			−0.531136
$156$			5.77987i			0.462760i
$157$	11.3659			0.907094			0.453547	−	0.891232i	$-0.350158\pi$
$157$	11.3659			0.907094			0.453547	+	0.891232i	$0.350158\pi$
$158$			8.40193i			0.668421i
$159$			34.6754i			2.74993i
$160$		−	3.05577i		−	0.241580i
$161$	−15.7357			−1.24015
$162$	7.15916			0.562477
$163$			14.6126i			1.14455i	0.820062	+	0.572274i	$0.193939\pi$
$163$			14.6126i			1.14455i	−0.820062	+	0.572274i	$0.806061\pi$
$164$			0.862863i			0.0673783i
$165$		−	10.5794i		−	0.823606i
$166$	−12.3111			−0.955523
$167$		−	12.0506i		−	0.932503i	−0.884652	−	0.466252i	$-0.845604\pi$
$167$		−	12.0506i		−	0.932503i	0.884652	−	0.466252i	$-0.154396\pi$
$168$	−27.4393			−2.11699
$169$	24.2141			1.86263
$170$	−2.99174	−	7.41612i	−0.229456	−	0.568790i
$171$	21.2004			1.62123
$172$	0.361257			0.0275456
$173$		−	9.12661i		−	0.693883i	−0.937887	−	0.346941i	$-0.887220\pi$
$173$		−	9.12661i		−	0.693883i	0.937887	−	0.346941i	$-0.112780\pi$
$174$	20.0717			1.52163
$175$		−	9.36082i		−	0.707611i
$176$			8.37856i			0.631558i
$177$			40.1908i			3.02092i
$178$	18.5611			1.39121
$179$	11.6309			0.869332			0.434666	−	0.900592i	$-0.356866\pi$
$179$	11.6309			0.869332			0.434666	+	0.900592i	$0.356866\pi$
$180$			2.12287i			0.158229i
$181$			21.8899i			1.62707i	0.581519	+	0.813533i	$0.302459\pi$
$181$			21.8899i			1.62707i	−0.581519	+	0.813533i	$0.697541\pi$
$182$			27.0293i			2.00355i
$183$	8.69507			0.642758
$184$		−	13.7423i		−	1.01309i
$185$	−11.3505			−0.834502
$186$	−14.6534			−1.07444
$187$	−4.10682	−	10.1802i	−0.300320	−	0.744453i
$188$	−1.80051			−0.131316
$189$	7.97516			0.580108
$190$			10.6015i			0.769114i
$191$	5.39365			0.390271			0.195136	−	0.980776i	$-0.437485\pi$
$191$	5.39365			0.390271			0.195136	+	0.980776i	$0.437485\pi$
$192$		−	23.2787i		−	1.67999i
$193$		−	7.05314i		−	0.507696i	−0.967244	−	0.253848i	$-0.918304\pi$
$193$		−	7.05314i		−	0.507696i	0.967244	−	0.253848i	$-0.0816964\pi$
$194$			20.5903i			1.47830i
$195$	24.2404			1.73589
$196$	1.79900			0.128500
$197$		−	23.1181i		−	1.64710i	−0.567247	−	0.823548i	$-0.691991\pi$
$197$		−	23.1181i		−	1.64710i	0.567247	−	0.823548i	$-0.308009\pi$
$198$		−	13.2190i		−	0.939436i
$199$			4.68934i			0.332419i	0.986090	+	0.166209i	$0.0531528\pi$
$199$			4.68934i			0.332419i	−0.986090	+	0.166209i	$0.946847\pi$
$200$	8.17498			0.578059
$201$			6.43939i			0.454200i
$202$	−18.0157			−1.26758
$203$	−20.6921			−1.45230
$204$	1.46148	+	3.62282i	0.102324	+	0.253648i
$205$	3.61880			0.252748
$206$	−13.1023			−0.912883
$207$			17.6331i			1.22559i
$208$	−19.1977			−1.33112
$209$			14.5529i			1.00664i
$210$			17.6063i			1.21495i
$211$			15.9842i			1.10040i	0.835033	+	0.550200i	$0.185448\pi$
$211$			15.9842i			1.10040i	−0.835033	+	0.550200i	$0.814552\pi$
$212$	4.77626			0.328035
$213$	33.0203			2.26251
$214$			18.1912i			1.24353i
$215$		−	1.51509i		−	0.103328i
$216$			6.96487i			0.473899i
$217$	15.1064			1.02549
$218$		−	10.8271i		−	0.733306i
$219$	−2.97217			−0.200841
$220$	−1.45723			−0.0982466
$221$	23.3258	−	9.40988i	1.56907	−	0.632977i
$222$	−25.1524			−1.68812
$223$	19.4251			1.30080			0.650401	−	0.759591i	$-0.274601\pi$
$223$	19.4251			1.30080			0.650401	+	0.759591i	$0.274601\pi$
$224$			6.98085i			0.466428i
$225$	−10.4896			−0.699304
$226$		−	20.3588i		−	1.35425i
$227$			4.58898i			0.304582i	0.988336	+	0.152291i	$0.0486650\pi$
$227$			4.58898i			0.304582i	−0.988336	+	0.152291i	$0.951335\pi$
$228$		−	5.17891i		−	0.342981i
$229$	0.0701841			0.00463789			0.00231895	−	0.999997i	$-0.499262\pi$
$229$	0.0701841			0.00463789			0.00231895	+	0.999997i	$0.499262\pi$
$230$	−8.81766			−0.581420
$231$			24.1685i			1.59017i
$232$		−	18.0708i		−	1.18641i
$233$			5.00867i			0.328129i	0.986450	+	0.164064i	$0.0524605\pi$
$233$			5.00867i			0.328129i	−0.986450	+	0.164064i	$0.947539\pi$
$234$	30.2886			1.98003
$235$			7.55124i			0.492589i
$236$	5.53597			0.360361
$237$	−17.2136			−1.11814
$238$	6.83457	+	16.9420i	0.443019	+	1.09819i
$239$	6.50510			0.420780			0.210390	−	0.977618i	$-0.432527\pi$
$239$	6.50510			0.420780			0.210390	+	0.977618i	$0.432527\pi$
$240$	−12.5049			−0.807188
$241$			18.2783i			1.17741i	0.808348	+	0.588705i	$0.200362\pi$
$241$			18.2783i			1.17741i	−0.808348	+	0.588705i	$0.799638\pi$
$242$	−5.00733			−0.321883
$243$			21.5800i			1.38436i
$244$		−	1.19768i		−	0.0766735i
$245$		−	7.54491i		−	0.482026i
$246$	8.01918			0.511284
$247$	−33.3448			−2.12168
$248$			13.1927i			0.837735i
$249$		−	25.2225i		−	1.59841i
$250$		−	14.9430i		−	0.945079i
$251$	3.30184			0.208410			0.104205	−	0.994556i	$-0.466770\pi$
$251$	3.30184			0.208410			0.104205	+	0.994556i	$0.466770\pi$
$252$		−	4.84965i		−	0.305499i
$253$	−12.1042			−0.760983
$254$	10.4003			0.652571
$255$	15.1939	−	6.12938i	0.951479	−	0.383837i
$256$	−8.37025			−0.523140
$257$	−9.01893			−0.562585			−0.281293	−	0.959622i	$-0.590763\pi$
$257$	−9.01893			−0.562585			−0.281293	+	0.959622i	$0.590763\pi$
$258$		−	3.35741i		−	0.209023i
$259$	25.9299			1.61121
$260$		−	3.33893i		−	0.207072i
$261$			23.1872i			1.43525i
$262$			13.9020i			0.858867i
$263$	15.7533			0.971388			0.485694	−	0.874129i	$-0.338567\pi$
$263$	15.7533			0.971388			0.485694	+	0.874129i	$0.338567\pi$
$264$	−21.1068			−1.29903
$265$		−	20.0314i		−	1.23052i
$266$		−	24.2189i		−	1.48496i
$267$			38.0274i			2.32724i
$268$	0.886976			0.0541807
$269$		−	7.60244i		−	0.463529i	−0.972772	−	0.231765i	$-0.925550\pi$
$269$		−	7.60244i		−	0.463529i	0.972772	−	0.231765i	$-0.0744499\pi$
$270$	4.46897			0.271973
$271$	8.67242			0.526812			0.263406	−	0.964685i	$-0.415154\pi$
$271$	8.67242			0.526812			0.263406	+	0.964685i	$0.415154\pi$
$272$	−12.0331	+	4.85427i	−0.729613	+	0.294334i
$273$	−55.3768			−3.35156
$274$	1.43230			0.0865284
$275$		−	7.20051i		−	0.434207i
$276$	4.30749			0.259280
$277$		−	9.61388i		−	0.577642i	−0.957383	−	0.288821i	$-0.906737\pi$
$277$		−	9.61388i		−	0.577642i	0.957383	−	0.288821i	$-0.0932632\pi$
$278$			20.5659i			1.23346i
$279$		−	16.9279i		−	1.01345i
$280$	15.8512			0.947290
$281$	−10.0218			−0.597848			−0.298924	−	0.954277i	$-0.596628\pi$
$281$	−10.0218			−0.597848			−0.298924	+	0.954277i	$0.596628\pi$
$282$			16.7334i			0.996460i
$283$		−	4.97192i		−	0.295550i	−0.989021	−	0.147775i	$-0.952789\pi$
$283$		−	4.97192i		−	0.295550i	0.989021	−	0.147775i	$-0.0472111\pi$
$284$		−	4.54829i		−	0.269891i
$285$	−21.7200			−1.28658
$286$			20.7914i			1.22942i
$287$	−8.26708			−0.487990
$288$	7.82262			0.460952
$289$	12.2413	−	11.7962i	0.720075	−	0.693896i
$290$	−11.5951			−0.680885
$291$	−42.1848			−2.47292
$292$			0.409394i			0.0239580i
$293$	−15.0014			−0.876394			−0.438197	−	0.898879i	$-0.644383\pi$
$293$	−15.0014			−0.876394			−0.438197	+	0.898879i	$0.644383\pi$
$294$		−	16.7194i		−	0.975093i
$295$		−	23.2175i		−	1.35178i
$296$			22.6451i			1.31622i
$297$	6.13464			0.355968
$298$	2.18998			0.126862
$299$		−	27.7341i		−	1.60390i
$300$			2.56243i			0.147942i
$301$			3.46119i			0.199500i
$302$	−1.42737			−0.0821358
$303$		−	36.9100i		−	2.12042i
$304$	17.2016			0.986578
$305$	−5.02299			−0.287616
$306$	18.9849	−	7.65870i	1.08529	−	0.437819i
$307$	−10.9500			−0.624948			−0.312474	−	0.949926i	$-0.601158\pi$
$307$	−10.9500			−0.624948			−0.312474	+	0.949926i	$0.601158\pi$
$308$	3.32902			0.189689
$309$		−	26.8437i		−	1.52708i
$310$	8.46501			0.480780
$311$			0.0276932i			0.00157034i	1.00000		0.000785168i	$0.000249927\pi$
$311$			0.0276932i			0.00157034i	−1.00000		0.000785168i	$0.999750\pi$
$312$		−	48.3616i		−	2.73794i
$313$			1.35357i			0.0765081i	0.999268	+	0.0382540i	$0.0121796\pi$
$313$			1.35357i			0.0765081i	−0.999268	+	0.0382540i	$0.987820\pi$
$314$	−14.5498			−0.821094
$315$	−20.3391			−1.14598
$316$			2.37104i			0.133381i
$317$		−	16.7654i		−	0.941636i	−0.882230	−	0.470818i	$-0.843959\pi$
$317$		−	16.7654i		−	0.941636i	0.882230	−	0.470818i	$-0.156041\pi$
$318$		−	44.3891i		−	2.48922i
$319$	−15.9168			−0.891167
$320$			13.4477i			0.751749i
$321$	−37.2696			−2.08019
$322$	20.1438			1.12257
$323$	−20.9005	+	8.43149i	−1.16294	+	0.469140i
$324$	2.02033			0.112241
$325$	16.4984			0.915168
$326$		−	18.7061i		−	1.03604i
$327$	22.1823			1.22668
$328$		−	7.21980i		−	0.398647i
$329$		−	17.2507i		−	0.951061i
$330$			13.5431i			0.745521i
$331$	22.4753			1.23535			0.617677	−	0.786432i	$-0.288074\pi$
$331$	22.4753			1.23535			0.617677	+	0.786432i	$0.288074\pi$
$332$	−3.47420			−0.190672
$333$		−	29.0566i		−	1.59229i
$334$			15.4264i			0.844094i
$335$		−	3.71993i		−	0.203241i
$336$	28.5672			1.55847
$337$			29.2159i			1.59149i	0.605630	+	0.795747i	$0.292921\pi$
$337$			29.2159i			1.59149i	−0.605630	+	0.795747i	$0.707079\pi$
$338$	−30.9974			−1.68603
$339$	41.7105			2.26540
$340$	−0.844275	−	2.09284i	−0.0457872	−	0.113500i
$341$	11.6201			0.629263
$342$	−27.1393			−1.46753
$343$		−	6.99214i		−	0.377540i
$344$	−3.02273			−0.162974
$345$		−	18.0654i		−	0.972606i
$346$			11.6833i			0.628097i
$347$			26.0627i			1.39912i	0.714573	+	0.699561i	$0.246621\pi$
$347$			26.0627i			1.39912i	−0.714573	+	0.699561i	$0.753379\pi$
$348$	5.66426			0.303636
$349$	−18.2377			−0.976243			−0.488121	−	0.872776i	$-0.662318\pi$
$349$	−18.2377			−0.976243			−0.488121	+	0.872776i	$0.662318\pi$
$350$			11.9831i			0.640524i
$351$			14.0562i			0.750265i
$352$			5.36980i			0.286211i
$353$	4.68598			0.249409			0.124705	−	0.992194i	$-0.460202\pi$
$353$	4.68598			0.249409			0.124705	+	0.992194i	$0.460202\pi$
$354$		−	51.4496i		−	2.73452i
$355$	−19.0752			−1.01241
$356$	5.23798			0.277612
$357$	−34.7102	+	14.0025i	−1.83706	+	0.741089i
$358$	−14.8891			−0.786912
$359$	−22.4904			−1.18700			−0.593498	−	0.804836i	$-0.702253\pi$
$359$	−22.4904			−1.18700			−0.593498	+	0.804836i	$0.702253\pi$
$360$		−	17.7626i		−	0.936170i
$361$	10.8778			0.572513
$362$		−	28.0220i		−	1.47281i
$363$		−	10.2589i		−	0.538450i
$364$			7.62773i			0.399802i
$365$	1.71697			0.0898705
$366$	−11.1309			−0.581819
$367$			7.55139i			0.394179i	0.980385	+	0.197090i	$0.0631490\pi$
$367$			7.55139i			0.394179i	−0.980385	+	0.197090i	$0.936851\pi$
$368$			14.3072i			0.745814i
$369$			9.26393i			0.482261i
$370$	14.5301			0.755384
$371$			45.7613i			2.37581i
$372$	−4.13522			−0.214401
$373$	25.7297			1.33223			0.666116	−	0.745849i	$-0.267956\pi$
$373$	25.7297			1.33223			0.666116	+	0.745849i	$0.267956\pi$
$374$	5.25728	+	13.0321i	0.271847	+	0.673873i
$375$	30.6148			1.58094
$376$	15.0653			0.776936
$377$		−	36.4698i		−	1.87829i
$378$	−10.2093			−0.525109
$379$			16.6469i			0.855092i	0.903993	+	0.427546i	$0.140622\pi$
$379$			16.6469i			0.855092i	−0.903993	+	0.427546i	$0.859378\pi$
$380$			2.99177i			0.153474i
$381$			21.3077i			1.09163i
$382$	−6.90460			−0.353270
$383$	−4.19769			−0.214492			−0.107246	−	0.994233i	$-0.534203\pi$
$383$	−4.19769			−0.214492			−0.107246	+	0.994233i	$0.534203\pi$
$384$			19.2204i			0.980839i
$385$		−	13.9617i		−	0.711555i
$386$			9.02897i			0.459562i
$387$	3.87855			0.197158
$388$			5.81063i			0.294990i
$389$	−16.6484			−0.844106			−0.422053	−	0.906571i	$-0.638690\pi$
$389$	−16.6484			−0.844106			−0.422053	+	0.906571i	$0.638690\pi$
$390$	−31.0310			−1.57132
$391$	−7.01278	−	17.3837i	−0.354652	−	0.879134i
$392$	−15.0527			−0.760276
$393$	−28.4819			−1.43672
$394$			29.5943i			1.49094i
$395$	9.94400			0.500337
$396$		−	3.73044i		−	0.187462i
$397$			12.2218i			0.613397i	0.951807	+	0.306698i	$0.0992243\pi$
$397$			12.2218i			0.613397i	−0.951807	+	0.306698i	$0.900776\pi$
$398$		−	6.00299i		−	0.300903i
$399$	49.6190			2.48406
$400$	−8.51103			−0.425552
$401$		−	21.9077i		−	1.09402i	−0.837126	−	0.547010i	$-0.815766\pi$
$401$		−	21.9077i		−	1.09402i	0.837126	−	0.547010i	$-0.184234\pi$
$402$		−	8.24328i		−	0.411138i
$403$			26.6249i			1.32628i
$404$	−5.08406			−0.252942
$405$		−	8.47314i		−	0.421034i
$406$	26.4887			1.31461
$407$	19.9458			0.988675
$408$	−12.2286	−	30.3131i	−0.605407	−	1.50072i
$409$	26.0410			1.28764			0.643822	−	0.765175i	$-0.277348\pi$
$409$	26.0410			1.28764			0.643822	+	0.765175i	$0.277348\pi$
$410$	−4.63255			−0.228785
$411$			2.93445i			0.144746i
$412$	−3.69751			−0.182163
$413$			53.0400i			2.60993i
$414$		−	22.5728i		−	1.10939i
$415$			14.5706i			0.715243i
$416$	−12.3037			−0.603240
$417$	−42.1347			−2.06335
$418$		−	18.6296i		−	0.911206i
$419$		−	8.09530i		−	0.395481i	−0.980254	−	0.197741i	$-0.936640\pi$
$419$		−	8.09530i		−	0.395481i	0.980254	−	0.197741i	$-0.0633604\pi$
$420$			4.96853i			0.242439i
$421$	−21.6182			−1.05361			−0.526804	−	0.849987i	$-0.676610\pi$
$421$	−21.6182			−1.05361			−0.526804	+	0.849987i	$0.676610\pi$
$422$		−	20.4619i		−	0.996072i
$423$	−19.3308			−0.939896
$424$	−39.9642			−1.94083
$425$	10.3412	−	4.17175i	0.501622	−	0.202360i
$426$	−42.2704			−2.04801
$427$	11.4749			0.555311
$428$			5.13360i			0.248142i
$429$	−42.5969			−2.05660
$430$			1.93952i			0.0935318i
$431$			11.4664i			0.552316i	0.961112	+	0.276158i	$0.0890613\pi$
$431$			11.4664i			0.552316i	−0.961112	+	0.276158i	$0.910939\pi$
$432$		−	7.25117i		−	0.348872i
$433$	32.3443			1.55437			0.777185	−	0.629272i	$-0.216647\pi$
$433$	32.3443			1.55437			0.777185	+	0.629272i	$0.216647\pi$
$434$	−19.3382			−0.928261
$435$		−	23.7556i		−	1.13899i
$436$		−	3.05544i		−	0.146329i
$437$			24.8504i			1.18876i
$438$	3.80478			0.181799
$439$		−	28.2765i		−	1.34956i	−0.738017	−	0.674782i	$-0.764238\pi$
$439$		−	28.2765i		−	1.34956i	0.738017	−	0.674782i	$-0.235762\pi$
$440$	12.1930			0.581280
$441$	19.3146			0.919742
$442$	−29.8602	+	12.0459i	−1.42030	+	0.572966i
$443$	−14.6728			−0.697126			−0.348563	−	0.937285i	$-0.613330\pi$
$443$	−14.6728			−0.697126			−0.348563	+	0.937285i	$0.613330\pi$
$444$	−7.09806			−0.336859
$445$		−	21.9678i		−	1.04137i
$446$	−24.8667			−1.17747
$447$			4.48676i			0.212217i
$448$		−	30.7210i		−	1.45143i
$449$		−	24.1065i		−	1.13766i	−0.822457	−	0.568828i	$-0.807397\pi$
$449$		−	24.1065i		−	1.13766i	0.822457	−	0.568828i	$-0.192603\pi$
$450$	13.4280			0.633004
$451$	−6.35918			−0.299442
$452$		−	5.74530i		−	0.270236i
$453$		−	2.92435i		−	0.137398i
$454$		−	5.87451i		−	0.275705i
$455$	31.9902			1.49973
$456$			43.3332i			2.02926i
$457$	−12.7078			−0.594446			−0.297223	−	0.954808i	$-0.596060\pi$
$457$	−12.7078			−0.594446			−0.297223	+	0.954808i	$0.596060\pi$
$458$	−0.0898450			−0.00419818
$459$	3.55422	+	8.81043i	0.165897	+	0.411236i
$460$	−2.48836			−0.116021
$461$	17.1368			0.798141			0.399071	−	0.916920i	$-0.369333\pi$
$461$	17.1368			0.798141			0.399071	+	0.916920i	$0.369333\pi$
$462$		−	30.9389i		−	1.43941i
$463$	−5.87134			−0.272864			−0.136432	−	0.990649i	$-0.543564\pi$
$463$	−5.87134			−0.272864			−0.136432	+	0.990649i	$0.543564\pi$
$464$			18.8137i			0.873402i
$465$			17.3428i			0.804255i
$466$		−	6.41177i		−	0.297020i
$467$	28.7181			1.32892			0.664458	−	0.747326i	$-0.268662\pi$
$467$	28.7181			1.32892			0.664458	+	0.747326i	$0.268662\pi$
$468$	8.54750			0.395108
$469$			8.49810i			0.392406i
$470$		−	9.66660i		−	0.445887i
$471$		−	29.8092i		−	1.37354i
$472$	−46.3209			−2.13209
$473$			2.66241i			0.122418i
$474$	22.0357			1.01213
$475$	−14.7830			−0.678290
$476$	1.92873	+	4.78106i	0.0884032	+	0.219140i
$477$	51.2793			2.34792
$478$	−8.32741			−0.380887
$479$			11.7307i			0.535988i	0.963421	+	0.267994i	$0.0863608\pi$
$479$			11.7307i			0.535988i	−0.963421	+	0.267994i	$0.913639\pi$
$480$	−8.01436			−0.365804
$481$			45.7014i			2.08380i
$482$		−	23.3987i		−	1.06578i
$483$			41.2700i			1.87785i
$484$	−1.41308			−0.0642308
$485$	24.3694			1.10656
$486$		−	27.6253i		−	1.25311i
$487$			32.0620i			1.45287i	0.687237	+	0.726433i	$0.258823\pi$
$487$			32.0620i			1.45287i	−0.687237	+	0.726433i	$0.741177\pi$
$488$			10.0213i			0.453642i
$489$	38.3245			1.73309
$490$			9.65849i			0.436326i
$491$	9.29725			0.419579			0.209789	−	0.977747i	$-0.432722\pi$
$491$	9.29725			0.419579			0.209789	+	0.977747i	$0.432722\pi$
$492$	2.26303			0.102025
$493$	−9.22167	−	22.8593i	−0.415323	−	1.02953i
$494$	42.6858			1.92053
$495$	−15.6452			−0.703201
$496$		−	13.7350i		−	0.616719i
$497$	43.5770			1.95470
$498$			32.2882i			1.44687i
$499$			5.46640i			0.244709i	0.992486	+	0.122355i	$0.0390446\pi$
$499$			5.46640i			0.244709i	−0.992486	+	0.122355i	$0.960955\pi$
$500$		−	4.21695i		−	0.188588i
$501$	−31.6051			−1.41201
$502$	−4.22679			−0.188651
$503$		−	6.65578i		−	0.296766i	−0.988930	−	0.148383i	$-0.952593\pi$
$503$		−	6.65578i		−	0.296766i	0.988930	−	0.148383i	$-0.0474069\pi$
$504$			40.5783i			1.80750i
$505$			21.3223i			0.948828i
$506$	15.4950			0.688836
$507$		−	63.5064i		−	2.82042i
$508$	2.93498			0.130218
$509$	10.5299			0.466730			0.233365	−	0.972389i	$-0.425026\pi$
$509$	10.5299			0.466730			0.233365	+	0.972389i	$0.425026\pi$
$510$	−19.4502	+	7.84643i	−0.861271	+	0.347446i
$511$	−3.92239			−0.173516
$512$	25.3720			1.12130
$513$		−	12.5947i		−	0.556070i
$514$	11.5454			0.509248
$515$			15.5071i			0.683325i
$516$		−	0.947467i		−	0.0417099i
$517$		−	13.2695i		−	0.583594i
$518$	−33.1938			−1.45845
$519$	−23.9363			−1.05069
$520$			27.9377i			1.22515i
$521$		−	6.89084i		−	0.301893i	−0.988542	−	0.150947i	$-0.951768\pi$
$521$		−	6.89084i		−	0.301893i	0.988542	−	0.150947i	$-0.0482321\pi$
$522$		−	29.6827i		−	1.29918i
$523$	−24.0183			−1.05025			−0.525124	−	0.851026i	$-0.675981\pi$
$523$	−24.0183			−1.05025			−0.525124	+	0.851026i	$0.675981\pi$
$524$			3.92316i			0.171384i
$525$	−24.5506			−1.07148
$526$	−20.1663			−0.879292
$527$	6.73231	+	16.6885i	0.293264	+	0.726962i
$528$	21.9744			0.956314
$529$	2.33096			0.101346
$530$			25.6428i			1.11385i
$531$	59.4357			2.57929
$532$		−	6.83463i		−	0.296319i
$533$		−	14.5707i		−	0.631127i
$534$		−	48.6801i		−	2.10660i
$535$	21.5300			0.930823
$536$	−7.42156			−0.320562
$537$		−	30.5043i		−	1.31636i
$538$			9.73214i			0.419583i
$539$			13.2584i			0.571080i
$540$	1.26115			0.0542714
$541$		−	41.0051i		−	1.76295i	−0.472233	−	0.881474i	$-0.656552\pi$
$541$		−	41.0051i		−	1.76295i	0.472233	−	0.881474i	$-0.343448\pi$
$542$	−11.1019			−0.476866
$543$	57.4107			2.46373
$544$	−7.71198	+	3.11109i	−0.330648	+	0.133387i
$545$	−12.8143			−0.548905
$546$	70.8898			3.03380
$547$		−	1.34919i		−	0.0576874i	−0.999584	−	0.0288437i	$-0.990817\pi$
$547$		−	1.34919i		−	0.0576874i	0.999584	−	0.0288437i	$-0.00918251\pi$
$548$	0.404198			0.0172665
$549$		−	12.8586i		−	0.548792i
$550$			9.21762i			0.393041i
$551$			32.6778i			1.39212i
$552$	−36.0419			−1.53404
$553$	−22.7169			−0.966021
$554$			12.3071i			0.522876i
$555$			29.7688i			1.26362i
$556$			5.80373i			0.246133i
$557$	45.5959			1.93196			0.965980	−	0.258617i	$-0.0832667\pi$
$557$	45.5959			1.93196			0.965980	+	0.258617i	$0.0832667\pi$
$558$			21.6700i			0.917364i
$559$	−6.10034			−0.258017
$560$	−16.5028			−0.697371
$561$	−26.6997	+	10.7709i	−1.12726	+	0.454750i
$562$	12.8292			0.541167
$563$	0.928344			0.0391250			0.0195625	−	0.999809i	$-0.493773\pi$
$563$	0.928344			0.0391250			0.0195625	+	0.999809i	$0.493773\pi$
$564$			4.72220i			0.198841i
$565$	−24.0954			−1.01370
$566$			6.36472i			0.267529i
$567$			19.3567i			0.812907i
$568$			38.0567i			1.59682i
$569$	−1.32616			−0.0555954			−0.0277977	−	0.999614i	$-0.508849\pi$
$569$	−1.32616			−0.0555954			−0.0277977	+	0.999614i	$0.508849\pi$
$570$	27.8045			1.16460
$571$			2.57068i			0.107580i	0.998552	+	0.0537898i	$0.0171301\pi$
$571$			2.57068i			0.107580i	−0.998552	+	0.0537898i	$0.982870\pi$
$572$			5.86739i			0.245328i
$573$		−	14.1459i		−	0.590955i
$574$	10.5830			0.441724
$575$		−	12.2956i		−	0.512760i
$576$	−34.4254			−1.43439
$577$	1.48288			0.0617331			0.0308666	−	0.999524i	$-0.490173\pi$
$577$	1.48288			0.0617331			0.0308666	+	0.999524i	$0.490173\pi$
$578$	−15.6705	+	15.1008i	−0.651806	+	0.628109i
$579$	−18.4983			−0.768762
$580$	−3.27215			−0.135869
$581$		−	33.2863i		−	1.38095i
$582$	54.0022			2.23846
$583$			35.2004i			1.45785i
$584$		−	3.42550i		−	0.141748i
$585$		−	35.8477i		−	1.48212i
$586$	19.2039			0.793304
$587$	−43.6360			−1.80105			−0.900525	−	0.434804i	$-0.856818\pi$
$587$	−43.6360			−1.80105			−0.900525	+	0.434804i	$0.856818\pi$
$588$		−	4.71824i		−	0.194577i
$589$		−	23.8566i		−	0.982993i
$590$			29.7216i			1.22362i
$591$	−60.6318			−2.49406
$592$		−	23.5760i		−	0.968966i
$593$	22.0732			0.906439			0.453220	−	0.891399i	$-0.350275\pi$
$593$	22.0732			0.906439			0.453220	+	0.891399i	$0.350275\pi$
$594$	−7.85317			−0.322219
$595$	20.0515	−	8.08898i	0.822031	−	0.331616i
$596$	0.618017			0.0253150
$597$	12.2987			0.503354
$598$			35.5034i			1.45184i
$599$	−2.08703			−0.0852739			−0.0426369	−	0.999091i	$-0.513576\pi$
$599$	−2.08703			−0.0852739			−0.0426369	+	0.999091i	$0.513576\pi$
$600$		−	21.4405i		−	0.875306i
$601$			6.31049i			0.257410i	0.991683	+	0.128705i	$0.0410821\pi$
$601$			6.31049i			0.257410i	−0.991683	+	0.128705i	$0.958918\pi$
$602$		−	4.43079i		−	0.180585i
$603$	9.52282			0.387799
$604$	−0.402806			−0.0163900
$605$			5.92637i			0.240941i
$606$			47.2497i			1.91939i
$607$		−	9.22732i		−	0.374525i	−0.982310	−	0.187263i	$-0.940038\pi$
$607$		−	9.22732i		−	0.374525i	0.982310	−	0.187263i	$-0.0599615\pi$
$608$	11.0244			0.447100
$609$			54.2692i			2.19910i
$610$	6.43011			0.260347
$611$	30.4043			1.23003
$612$	5.35757	−	2.16130i	0.216567	−	0.0873654i
$613$	2.57474			0.103993			0.0519964	−	0.998647i	$-0.483442\pi$
$613$	2.57474			0.103993			0.0519964	+	0.998647i	$0.483442\pi$
$614$	14.0174			0.565698
$615$		−	9.49101i		−	0.382715i
$616$	−27.8548			−1.12230
$617$			18.3023i			0.736821i	0.929663	+	0.368411i	$0.120098\pi$
$617$			18.3023i			0.736821i	−0.929663	+	0.368411i	$0.879902\pi$
$618$			34.3635i			1.38230i
$619$			17.0256i			0.684315i	0.939643	+	0.342158i	$0.111158\pi$
$619$			17.0256i			0.684315i	−0.939643	+	0.342158i	$0.888842\pi$
$620$	2.38884			0.0959382
$621$	10.4755			0.420367
$622$		−	0.0354510i		−	0.00142145i
$623$			50.1850i			2.01062i
$624$			50.3497i			2.01560i
$625$	−4.16310			−0.166524
$626$		−	1.73275i		−	0.0692544i
$627$	38.1678			1.52428
$628$	−4.10599			−0.163847
$629$	11.5560	+	28.6457i	0.460766	+	1.14218i
$630$	26.0368			1.03733
$631$	31.2851			1.24544			0.622719	−	0.782445i	$-0.286028\pi$
$631$	31.2851			1.24544			0.622719	+	0.782445i	$0.286028\pi$
$632$		−	19.8391i		−	0.789157i
$633$	41.9218			1.66624
$634$			21.4619i			0.852361i
$635$		−	12.3091i		−	0.488472i
$636$		−	12.5267i		−	0.496716i
$637$	−30.3788			−1.20365
$638$	20.3756			0.806677
$639$		−	48.8317i		−	1.93175i
$640$		−	11.1033i		−	0.438897i
$641$		−	47.5282i		−	1.87725i	−0.344938	−	0.938625i	$-0.612100\pi$
$641$		−	47.5282i		−	1.87725i	0.344938	−	0.938625i	$-0.387900\pi$
$642$	47.7101			1.88297
$643$			41.4151i			1.63325i	0.577167	+	0.816626i	$0.304158\pi$
$643$			41.4151i			1.63325i	−0.577167	+	0.816626i	$0.695842\pi$
$644$	5.68462			0.224005
$645$	−3.97362			−0.156461
$646$	26.7555	−	10.7934i	1.05268	−	0.424662i
$647$	14.6255			0.574990			0.287495	−	0.957782i	$-0.407178\pi$
$647$	14.6255			0.574990			0.287495	+	0.957782i	$0.407178\pi$
$648$	−16.9046			−0.664076
$649$			40.7994i			1.60151i
$650$	−21.1202			−0.828402
$651$		−	39.6194i		−	1.55281i
$652$		−	5.27890i		−	0.206738i
$653$		−	0.959948i		−	0.0375657i	−0.999824	−	0.0187828i	$-0.994021\pi$
$653$		−	0.959948i		−	0.0375657i	0.999824	−	0.0187828i	$-0.00597911\pi$
$654$	−28.3963			−1.11038
$655$	16.4535			0.642892
$656$			7.51658i			0.293473i
$657$			4.39536i			0.171479i
$658$			22.0832i			0.860892i
$659$	18.8596			0.734666			0.367333	−	0.930090i	$-0.380271\pi$
$659$	18.8596			0.734666			0.367333	+	0.930090i	$0.380271\pi$
$660$			3.82188i			0.148767i
$661$	18.5981			0.723384			0.361692	−	0.932298i	$-0.382199\pi$
$661$	18.5981			0.723384			0.361692	+	0.932298i	$0.382199\pi$
$662$	−28.7714			−1.11823
$663$	−24.6793	−	61.1766i	−0.958464	−	2.37590i
$664$	29.0696			1.12812
$665$	−28.6640			−1.11154
$666$			37.1963i			1.44133i
$667$	−27.1794			−1.05239
$668$			4.35336i			0.168436i
$669$		−	50.9462i		−	1.96969i
$670$			4.76200i			0.183972i
$671$	8.82673			0.340752
$672$	18.3087			0.706272
$673$		−	11.9976i		−	0.462474i	−0.972897	−	0.231237i	$-0.925723\pi$
$673$		−	11.9976i		−	0.462474i	0.972897	−	0.231237i	$-0.0742772\pi$
$674$		−	37.4003i		−	1.44061i
$675$			6.23164i			0.239856i
$676$	−8.74752			−0.336443
$677$		−	0.181443i		−	0.00697343i	−0.999994	−	0.00348672i	$-0.998890\pi$
$677$		−	0.181443i		−	0.00697343i	0.999994	−	0.00348672i	$-0.00110986\pi$
$678$	−53.3950			−2.05062
$679$	−55.6715			−2.13648
$680$	7.06426	+	17.5114i	0.270902	+	0.671530i
$681$	12.0355			0.461202
$682$	−14.8753			−0.569603
$683$			5.11701i			0.195797i	0.995196	+	0.0978984i	$0.0312120\pi$
$683$			5.11701i			0.195797i	−0.995196	+	0.0978984i	$0.968788\pi$
$684$	−7.65877			−0.292840
$685$		−	1.69518i		−	0.0647696i
$686$			8.95088i			0.341746i
$687$		−	0.184072i		−	0.00702277i
$688$	3.14698			0.119978
$689$	−80.6541			−3.07268
$690$			23.1261i			0.880395i
$691$		−	20.1267i		−	0.765657i	−0.923819	−	0.382828i	$-0.874950\pi$
$691$		−	20.1267i		−	0.765657i	0.923819	−	0.382828i	$-0.125050\pi$
$692$			3.29705i			0.125335i
$693$	35.7413			1.35770
$694$		−	33.3638i		−	1.26647i
$695$	24.3405			0.923288
$696$	−47.3943			−1.79648
$697$	−3.68431	−	9.13292i	−0.139553	−	0.345934i
$698$	23.3467			0.883687
$699$	13.1362			0.496858
$700$			3.38166i			0.127815i
$701$	31.9434			1.20649			0.603244	−	0.797557i	$-0.293875\pi$
$701$	31.9434			1.20649			0.603244	+	0.797557i	$0.293875\pi$
$702$		−	17.9938i		−	0.679133i
$703$		−	40.9496i		−	1.54444i
$704$		−	23.6312i		−	0.890634i
$705$	19.8046			0.745886
$706$	−5.99868			−0.225763
$707$		−	48.7103i		−	1.83194i
$708$		−	14.5192i		−	0.545664i
$709$			49.8881i			1.87359i	0.349881	+	0.936794i	$0.386222\pi$
$709$			49.8881i			1.87359i	−0.349881	+	0.936794i	$0.613778\pi$
$710$	24.4189			0.916424
$711$			25.4561i			0.954680i
$712$	−43.8275			−1.64250
$713$	19.8424			0.743104
$714$	44.4337	−	17.9250i	1.66289	−	0.670827i
$715$	24.6075			0.920268
$716$	−4.20173			−0.157026
$717$		−	17.0609i		−	0.637152i
$718$	28.7907			1.07446
$719$		−	5.11125i		−	0.190618i	−0.995448	−	0.0953088i	$-0.969616\pi$
$719$		−	5.11125i		−	0.190618i	0.995448	−	0.0953088i	$-0.0303838\pi$
$720$			18.4927i			0.689184i
$721$		−	35.4257i		−	1.31932i
$722$	−13.9250			−0.518234
$723$	47.9385			1.78285
$724$		−	7.90788i		−	0.293894i
$725$		−	16.1684i		−	0.600480i
$726$			13.1327i			0.487401i
$727$	−32.0758			−1.18963			−0.594813	−	0.803864i	$-0.702774\pi$
$727$	−32.0758			−1.18963			−0.594813	+	0.803864i	$0.702774\pi$
$728$		−	63.8232i		−	2.36544i
$729$	39.8202			1.47482
$730$	−2.19796			−0.0813500
$731$	−3.82369	+	1.54252i	−0.141424	+	0.0570521i
$732$	−3.14115			−0.116100
$733$	−25.3673			−0.936961			−0.468480	−	0.883474i	$-0.655198\pi$
$733$	−25.3673			−0.936961			−0.468480	+	0.883474i	$0.655198\pi$
$734$		−	9.66680i		−	0.356808i
$735$	−19.7880			−0.729892
$736$			9.16944i			0.337990i
$737$			6.53689i			0.240790i
$738$		−	11.8591i		−	0.436539i
$739$	6.99714			0.257394			0.128697	−	0.991684i	$-0.458921\pi$
$739$	6.99714			0.257394			0.128697	+	0.991684i	$0.458921\pi$
$740$	4.10043			0.150735
$741$			87.4533i			3.21268i
$742$		−	58.5806i		−	2.15056i
$743$		−	43.3585i		−	1.59067i	−0.606170	−	0.795335i	$-0.707295\pi$
$743$		−	43.3585i		−	1.59067i	0.606170	−	0.795335i	$-0.292705\pi$
$744$	34.6004			1.26851
$745$		−	2.59193i		−	0.0949609i
$746$	−32.9374			−1.20592
$747$	−37.3000			−1.36474
$748$	1.48361	+	3.67768i	0.0542463	+	0.134469i
$749$	−49.1849			−1.79718
$750$	−39.1910			−1.43105
$751$			26.0320i			0.949923i	0.880007	+	0.474961i	$0.157538\pi$
$751$			26.0320i			0.949923i	−0.880007	+	0.474961i	$0.842462\pi$
$752$	−15.6846			−0.571960
$753$		−	8.65972i		−	0.315578i
$754$			46.6862i			1.70021i
$755$			1.68935i			0.0614816i
$756$	−2.88108			−0.104784
$757$	33.3983			1.21388			0.606941	−	0.794747i	$-0.292396\pi$
$757$	33.3983			1.21388			0.606941	+	0.794747i	$0.292396\pi$
$758$		−	21.3102i		−	0.774022i
$759$			31.7456i			1.15229i
$760$		−	25.0329i		−	0.908037i
$761$	13.4465			0.487436			0.243718	−	0.969846i	$-0.421633\pi$
$761$	13.4465			0.487436			0.243718	+	0.969846i	$0.421633\pi$
$762$		−	27.2768i		−	0.988133i
$763$	29.2741			1.05979
$764$	−1.94849			−0.0704940
$765$	−9.06436	−	22.4693i	−0.327723	−	0.812381i
$766$	5.37361			0.194156
$767$	−93.4829			−3.37547
$768$			21.9526i			0.792147i
$769$	26.5459			0.957270			0.478635	−	0.878014i	$-0.341132\pi$
$769$	26.5459			0.957270			0.478635	+	0.878014i	$0.341132\pi$
$770$			17.8729i			0.644093i
$771$			23.6539i			0.851876i
$772$			2.54799i			0.0917043i
$773$	16.3815			0.589202			0.294601	−	0.955620i	$-0.404813\pi$
$773$	16.3815			0.589202			0.294601	+	0.955620i	$0.404813\pi$
$774$	−4.96506			−0.178465
$775$			11.8038i			0.424005i
$776$		−	48.6190i		−	1.74532i
$777$		−	68.0064i		−	2.43971i
$778$	21.3121			0.764077
$779$			13.0557i			0.467769i
$780$	−8.75701			−0.313551
$781$	33.5203			1.19945
$782$	8.97730	+	22.2535i	0.321028	+	0.795784i
$783$	13.7751			0.492280
$784$	15.6715			0.559696
$785$			17.2203i			0.614618i
$786$	36.4607			1.30051
$787$			19.3877i			0.691095i	0.938401	+	0.345548i	$0.112307\pi$
$787$			19.3877i			0.691095i	−0.938401	+	0.345548i	$0.887693\pi$
$788$			8.35156i			0.297512i
$789$		−	41.3161i		−	1.47089i
$790$	−12.7297			−0.452901
$791$	55.0456			1.95720
$792$			31.2135i			1.10912i
$793$			20.2245i			0.718195i
$794$		−	15.6456i		−	0.555242i
$795$	−52.5362			−1.86327
$796$		−	1.69406i		−	0.0600442i
$797$	−7.51724			−0.266274			−0.133137	−	0.991098i	$-0.542505\pi$
$797$	−7.51724			−0.266274			−0.133137	+	0.991098i	$0.542505\pi$
$798$	−63.5190			−2.24855
$799$	19.0574	−	7.68795i	0.674202	−	0.271980i
$800$	−5.45470			−0.192853
$801$	56.2364			1.98701
$802$			28.0448i			0.990298i
$803$	−3.01718			−0.106474
$804$		−	2.32627i		−	0.0820413i
$805$		−	23.8410i		−	0.840283i
$806$		−	34.0835i		−	1.20054i
$807$	−19.9389			−0.701883
$808$	42.5396			1.49654
$809$			19.7384i			0.693965i	0.937872	+	0.346983i	$0.112794\pi$
$809$			19.7384i			0.693965i	−0.937872	+	0.346983i	$0.887206\pi$
$810$			10.8468i			0.381116i
$811$		−	25.2147i		−	0.885408i	−0.896668	−	0.442704i	$-0.854019\pi$
$811$		−	25.2147i		−	0.885408i	0.896668	−	0.442704i	$-0.145981\pi$
$812$	7.47516			0.262327
$813$		−	22.7452i		−	0.797707i
$814$	−25.5333			−0.894940
$815$	−22.1394			−0.775510
$816$	12.7313	+	31.5592i	0.445685	+	1.10479i
$817$	5.46605			0.191233
$818$	−33.3359			−1.16556
$819$			81.8934i			2.86159i
$820$	−1.30731			−0.0456534
$821$		−	19.8990i		−	0.694480i	−0.937776	−	0.347240i	$-0.887119\pi$
$821$		−	19.8990i		−	0.694480i	0.937776	−	0.347240i	$-0.112881\pi$
$822$		−	3.75649i		−	0.131023i
$823$		−	42.4083i		−	1.47826i	−0.673563	−	0.739130i	$-0.735237\pi$
$823$		−	42.4083i		−	1.47826i	0.673563	−	0.739130i	$-0.264763\pi$
$824$	30.9380			1.07778
$825$	−18.8848			−0.657483
$826$		−	67.8984i		−	2.36249i
$827$		−	22.3924i		−	0.778659i	−0.921099	−	0.389329i	$-0.872707\pi$
$827$		−	22.3924i		−	0.778659i	0.921099	−	0.389329i	$-0.127293\pi$
$828$		−	6.37008i		−	0.221376i
$829$	23.4993			0.816165			0.408083	−	0.912945i	$-0.366198\pi$
$829$	23.4993			0.816165			0.408083	+	0.912945i	$0.366198\pi$
$830$		−	18.6523i		−	0.647432i
$831$	−25.2143			−0.874674
$832$	54.1457			1.87717
$833$	−19.0414	+	7.68150i	−0.659746	+	0.266148i
$834$	53.9381			1.86772
$835$	18.2577			0.631834
$836$		−	5.25733i		−	0.181828i
$837$	−10.0565			−0.347604
$838$			10.3631i			0.357986i
$839$			5.48418i			0.189335i	0.995509	+	0.0946675i	$0.0301788\pi$
$839$			5.48418i			0.189335i	−0.995509	+	0.0946675i	$0.969821\pi$
$840$		−	41.5729i		−	1.43440i
$841$	−6.74033			−0.232425
$842$	27.6743			0.953718
$843$			26.2841i			0.905271i
$844$		−	5.77440i		−	0.198763i
$845$			36.6866i			1.26206i
$846$	24.7460			0.850785
$847$		−	13.5387i		−	0.465194i
$848$	41.6070			1.42879
$849$	−13.0398			−0.447526
$850$	−13.2381	+	5.34040i	−0.454064	+	0.183174i
$851$	34.0593			1.16754
$852$	−11.9288			−0.408673
$853$		−	32.4809i		−	1.11212i	−0.831141	−	0.556062i	$-0.812312\pi$
$853$		−	32.4809i		−	1.11212i	0.831141	−	0.556062i	$-0.187688\pi$
$854$	−14.6895			−0.502663
$855$			32.1204i			1.09849i
$856$		−	42.9541i		−	1.46814i
$857$			46.3843i			1.58446i	0.610225	+	0.792228i	$0.291079\pi$
$857$			46.3843i			1.58446i	−0.610225	+	0.792228i	$0.708921\pi$
$858$	54.5297			1.86161
$859$	23.8177			0.812650			0.406325	−	0.913729i	$-0.366810\pi$
$859$	23.8177			0.812650			0.406325	+	0.913729i	$0.366810\pi$
$860$			0.547335i			0.0186640i
$861$			21.6820i			0.738922i
$862$		−	14.6785i		−	0.499952i
$863$	−33.5399			−1.14171			−0.570856	−	0.821050i	$-0.693388\pi$
$863$	−33.5399			−1.14171			−0.570856	+	0.821050i	$0.693388\pi$
$864$		−	4.64726i		−	0.158103i
$865$	13.8276			0.470153
$866$	−41.4051			−1.40700
$867$	−30.9380	−	32.1052i	−1.05071	−	1.09035i
$868$	−5.45727			−0.185232
$869$	−17.4743			−0.592773
$870$			30.4103i			1.03101i
$871$	−14.9779			−0.507506
$872$			25.5656i			0.865762i
$873$			62.3845i			2.11140i
$874$		−	31.8119i		−	1.07605i
$875$	40.4025			1.36585
$876$	1.07372			0.0362775
$877$		−	26.6269i		−	0.899125i	−0.893249	−	0.449563i	$-0.851580\pi$
$877$		−	26.6269i		−	0.899125i	0.893249	−	0.449563i	$-0.148420\pi$
$878$			36.1977i			1.22161i
$879$			39.3443i			1.32705i
$880$	−12.6943			−0.427923
$881$			33.8092i			1.13906i	0.821970	+	0.569531i	$0.192875\pi$
$881$			33.8092i			1.13906i	−0.821970	+	0.569531i	$0.807125\pi$
$882$	−24.7252			−0.832542
$883$	−52.1957			−1.75652			−0.878262	−	0.478179i	$-0.841297\pi$
$883$	−52.1957			−1.75652			−0.878262	+	0.478179i	$0.841297\pi$
$884$	−8.42661	+	3.39938i	−0.283418	+	0.114334i
$885$	−60.8926			−2.04688
$886$	18.7832			0.631032
$887$			22.4878i			0.755065i	0.925996	+	0.377533i	$0.123227\pi$
$887$			22.4878i			0.755065i	−0.925996	+	0.377533i	$0.876773\pi$
$888$	59.3913			1.99304
$889$			28.1199i			0.943113i
$890$			28.1217i			0.942641i
$891$			14.8896i			0.498819i
$892$	−7.01745			−0.234961
$893$	−27.2430			−0.911651
$894$		−	5.74366i		−	0.192097i
$895$			17.6218i			0.589031i
$896$			25.3653i			0.847397i
$897$	−72.7382			−2.42866
$898$			30.8595i			1.02980i
$899$	26.0924			0.870229
$900$	3.78942			0.126314
$901$	−50.5540	+	20.3940i	−1.68420	+	0.679423i
$902$	8.14061			0.271053
$903$	9.07766			0.302086
$904$			48.0724i			1.59886i
$905$	−33.1652			−1.10245
$906$			3.74356i			0.124371i
$907$		−	5.20253i		−	0.172747i	−0.996263	−	0.0863735i	$-0.972472\pi$
$907$		−	5.20253i		−	0.172747i	0.996263	−	0.0863735i	$-0.0275278\pi$
$908$		−	1.65780i		−	0.0550160i
$909$	−54.5839			−1.81043
$910$	−40.9518			−1.35754
$911$		−	46.2267i		−	1.53156i	−0.643103	−	0.765780i	$-0.722353\pi$
$911$		−	46.2267i		−	1.53156i	0.643103	−	0.765780i	$-0.277647\pi$
$912$		−	45.1145i		−	1.49389i
$913$		−	25.6044i		−	0.847383i
$914$	16.2677			0.538087
$915$			13.1738i			0.435512i
$916$	−0.0253545			−0.000837735
$917$	−37.5878			−1.24126
$918$	−4.54988	−	11.2785i	−0.150168	−	0.372247i
$919$	48.2370			1.59119			0.795596	−	0.605828i	$-0.207158\pi$
$919$	48.2370			1.59119			0.795596	+	0.605828i	$0.207158\pi$
$920$	20.8208			0.686440
$921$			28.7185i			0.946307i
$922$	−21.9374			−0.722471
$923$			76.8044i			2.52805i
$924$		−	8.73102i		−	0.287229i
$925$			20.2611i			0.666182i
$926$	7.51610			0.246994
$927$	−39.6974			−1.30384
$928$			12.0576i			0.395811i
$929$			25.6952i			0.843032i	0.906821	+	0.421516i	$0.138502\pi$
$929$			25.6952i			0.843032i	−0.906821	+	0.421516i	$0.861498\pi$
$930$		−	22.2012i		−	0.728005i
$931$	27.2201			0.892103
$932$		−	1.80941i		−	0.0592693i
$933$	0.0726308			0.00237783
$934$	−36.7630			−1.20292
$935$	15.4240	−	6.22219i	0.504418	−	0.203487i
$936$	−71.5191			−2.33767
$937$	28.3246			0.925325			0.462662	−	0.886535i	$-0.346894\pi$
$937$	28.3246			0.925325			0.462662	+	0.886535i	$0.346894\pi$
$938$		−	10.8787i		−	0.355202i
$939$	3.54999			0.115850
$940$		−	2.72794i		−	0.0889755i
$941$			34.0431i			1.10977i	0.831926	+	0.554887i	$0.187238\pi$
$941$			34.0431i			1.10977i	−0.831926	+	0.554887i	$0.812762\pi$
$942$			38.1598i			1.24331i
$943$	−10.8589			−0.353615
$944$	48.2250			1.56959
$945$			12.0831i			0.393063i
$946$		−	3.40824i		−	0.110812i
$947$		−	45.3738i		−	1.47445i	−0.675647	−	0.737225i	$-0.736136\pi$
$947$		−	45.3738i		−	1.47445i	0.675647	−	0.737225i	$-0.263864\pi$
$948$	6.21853			0.201968
$949$		−	6.91321i		−	0.224412i
$950$	18.9242			0.613982
$951$	−43.9705			−1.42584
$952$	−16.1382	−	40.0044i	−0.523041	−	1.29655i
$953$	46.9785			1.52178			0.760892	−	0.648879i	$-0.224762\pi$
$953$	46.9785			1.52178			0.760892	+	0.648879i	$0.224762\pi$
$954$	−65.6443			−2.12531
$955$			8.17186i			0.264435i
$956$	−2.35001			−0.0760048
$957$			41.7448i			1.34942i
$958$		−	15.0168i		−	0.485172i
$959$			3.87261i			0.125053i
$960$	35.2693			1.13831
$961$	11.9512			0.385522
$962$		−	58.5039i		−	1.88624i
$963$			55.1157i			1.77608i
$964$		−	6.60316i		−	0.212674i
$965$	10.6861			0.343999
$966$		−	52.8311i		−	1.69981i
$967$	18.6557			0.599928			0.299964	−	0.953951i	$-0.403025\pi$
$967$	18.6557			0.599928			0.299964	+	0.953951i	$0.403025\pi$
$968$	11.8236			0.380024
$969$	22.1132	+	54.8158i	0.710380	+	1.76094i
$970$	−31.1961			−1.00165
$971$	−3.21144			−0.103060			−0.0515300	−	0.998671i	$-0.516410\pi$
$971$	−3.21144			−0.103060			−0.0515300	+	0.998671i	$0.516410\pi$
$972$		−	7.79590i		−	0.250054i
$973$	−55.6054			−1.78263
$974$		−	41.0436i		−	1.31512i
$975$		−	43.2704i		−	1.38576i
$976$		−	10.4332i		−	0.333960i
$977$	52.1502			1.66843			0.834216	−	0.551438i	$-0.185921\pi$
$977$	52.1502			1.66843			0.834216	+	0.551438i	$0.185921\pi$
$978$	−49.0605			−1.56878
$979$			38.6032i			1.23376i
$980$			2.72565i			0.0870676i
$981$		−	32.8040i		−	1.04735i
$982$	−11.9017			−0.379799
$983$			29.5038i			0.941023i	0.882394	+	0.470512i	$0.155931\pi$
$983$			29.5038i			0.941023i	−0.882394	+	0.470512i	$0.844069\pi$
$984$	−18.9353			−0.603637
$985$	35.0259			1.11602
$986$	11.8050	+	29.2629i	0.375947	+	0.931922i
$987$	−45.2433			−1.44011
$988$	12.0460			0.383235
$989$			4.54632i			0.144565i
$990$	20.0280			0.636532
$991$		−	28.8123i		−	0.915253i	−0.889145	−	0.457627i	$-0.848700\pi$
$991$		−	28.8123i		−	0.915253i	0.889145	−	0.457627i	$-0.151300\pi$
$992$		−	8.80272i		−	0.279487i
$993$		−	58.9459i		−	1.87059i
$994$	−55.7845			−1.76938
$995$	−7.10477			−0.225236
$996$			9.11179i			0.288718i
$997$		−	3.35222i		−	0.106166i	−0.998590	−	0.0530830i	$-0.983095\pi$
$997$		−	3.35222i		−	0.106166i	0.998590	−	0.0530830i	$-0.0169048\pi$
$998$		−	6.99772i		−	0.221509i
$999$	−17.2619			−0.546144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.d.560.11	✓	34
17.16	even	2	inner	731.2.d.d.560.12	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.d.560.11	✓	34	1.1	even	1	trivial
731.2.d.d.560.12	yes	34	17.16	even	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.28013 q^{2} -2.62270i q^{3} -0.361257 q^{4} +1.51509i q^{5} +3.35741i q^{6} -3.46119i q^{7} +3.02273 q^{8} -3.87855 q^{9} +O(q^{10})\)	\(q-1.28013 q^{2} -2.62270i q^{3} -0.361257 q^{4} +1.51509i q^{5} +3.35741i q^{6} -3.46119i q^{7} +3.02273 q^{8} -3.87855 q^{9} -1.93952i q^{10} -2.66241i q^{11} +0.947467i q^{12} +6.10034 q^{13} +4.43079i q^{14} +3.97362 q^{15} -3.14698 q^{16} +(3.82369 - 1.54252i) q^{17} +4.96506 q^{18} -5.46605 q^{19} -0.547335i q^{20} -9.07766 q^{21} +3.40824i q^{22} -4.54632i q^{23} -7.92770i q^{24} +2.70451 q^{25} -7.80925 q^{26} +2.30417i q^{27} +1.25038i q^{28} -5.97832i q^{29} -5.08677 q^{30} +4.36450i q^{31} -2.01689 q^{32} -6.98270 q^{33} +(-4.89484 + 1.97463i) q^{34} +5.24401 q^{35} +1.40115 q^{36} +7.49162i q^{37} +6.99728 q^{38} -15.9994i q^{39} +4.57970i q^{40} -2.38851i q^{41} +11.6206 q^{42} -1.00000 q^{43} +0.961813i q^{44} -5.87634i q^{45} +5.81990i q^{46} +4.98403 q^{47} +8.25358i q^{48} -4.97985 q^{49} -3.46213 q^{50} +(-4.04556 - 10.0284i) q^{51} -2.20379 q^{52} -13.2213 q^{53} -2.94964i q^{54} +4.03379 q^{55} -10.4622i q^{56} +14.3358i q^{57} +7.65305i q^{58} -15.3242 q^{59} -1.43550 q^{60} +3.31531i q^{61} -5.58714i q^{62} +13.4244i q^{63} +8.87585 q^{64} +9.24255i q^{65} +8.93880 q^{66} -2.45525 q^{67} +(-1.38133 + 0.557245i) q^{68} -11.9236 q^{69} -6.71304 q^{70} +12.5902i q^{71} -11.7238 q^{72} -1.13325i q^{73} -9.59027i q^{74} -7.09311i q^{75} +1.97465 q^{76} -9.21512 q^{77} +20.4813i q^{78} -6.56332i q^{79} -4.76795i q^{80} -5.59251 q^{81} +3.05761i q^{82} +9.61700 q^{83} +3.27936 q^{84} +(2.33705 + 5.79323i) q^{85} +1.28013 q^{86} -15.6793 q^{87} -8.04774i q^{88} -14.4993 q^{89} +7.52251i q^{90} -21.1144i q^{91} +1.64239i q^{92} +11.4468 q^{93} -6.38023 q^{94} -8.28155i q^{95} +5.28970i q^{96} -16.0845i q^{97} +6.37487 q^{98} +10.3263i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9}+O(q^{10}) \) 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9	\( 34 q - 6 q^{2} + 34 q^{4} - 18 q^{8} - 48 q^{9} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 14 q^{18} + 16 q^{19} + 20 q^{21} - 44 q^{25} - 26 q^{26} + 88 q^{30} - 42 q^{32} + 12 q^{33} - 42 q^{34} + 22 q^{35} + 34 q^{38} - 14 q^{42} - 34 q^{43} + 30 q^{47} - 62 q^{49} - 46 q^{50} - 10 q^{51} + 26 q^{52} - 46 q^{53} + 16 q^{55} - 20 q^{59} - 42 q^{60} + 102 q^{64} - 70 q^{66} - 32 q^{67} - 10 q^{68} + 74 q^{69} + 130 q^{70} + 22 q^{72} + 38 q^{76} - 78 q^{77} + 46 q^{81} - 60 q^{83} - 98 q^{84} - 38 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{89} + 14 q^{93} - 78 q^{94} + 78 q^{98}+O(q^{100}) \) 34 * q - 6 * q^2 + 34 * q^4 - 18 * q^8 - 48 * q^9 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 14 * q^18 + 16 * q^19 + 20 * q^21 - 44 * q^25 - 26 * q^26 + 88 * q^30 - 42 * q^32 + 12 * q^33 - 42 * q^34 + 22 * q^35 + 34 * q^38 - 14 * q^42 - 34 * q^43 + 30 * q^47 - 62 * q^49 - 46 * q^50 - 10 * q^51 + 26 * q^52 - 46 * q^53 + 16 * q^55 - 20 * q^59 - 42 * q^60 + 102 * q^64 - 70 * q^66 - 32 * q^67 - 10 * q^68 + 74 * q^69 + 130 * q^70 + 22 * q^72 + 38 * q^76 - 78 * q^77 + 46 * q^81 - 60 * q^83 - 98 * q^84 - 38 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^89 + 14 * q^93 - 78 * q^94 + 78 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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