LMFDB - Embedded newform 1510.2.b.d.1209.35

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1510,2,Mod(1209,1510)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1510.1209"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1510, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1510 = 2 \cdot 5 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1510.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [38,0,0,-38,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.0574107052$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1209.35
Character	$\chi$	$=$	1510.1209
Dual form			1510.2.b.d.1209.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +2.00532i q^{3} -1.00000 q^{4} +(-2.18650 + 0.468193i) q^{5} -2.00532 q^{6} -2.17096i q^{7} -1.00000i q^{8} -1.02133 q^{9} +(-0.468193 - 2.18650i) q^{10} +5.84119 q^{11} -2.00532i q^{12} -6.75054i q^{13} +2.17096 q^{14} +(-0.938878 - 4.38465i) q^{15} +1.00000 q^{16} +6.66300i q^{17} -1.02133i q^{18} -1.60686 q^{19} +(2.18650 - 0.468193i) q^{20} +4.35347 q^{21} +5.84119i q^{22} +2.42865i q^{23} +2.00532 q^{24} +(4.56159 - 2.04741i) q^{25} +6.75054 q^{26} +3.96788i q^{27} +2.17096i q^{28} +8.38049 q^{29} +(4.38465 - 0.938878i) q^{30} +1.63097 q^{31} +1.00000i q^{32} +11.7135i q^{33} -6.66300 q^{34} +(1.01643 + 4.74680i) q^{35} +1.02133 q^{36} +2.82834i q^{37} -1.60686i q^{38} +13.5370 q^{39} +(0.468193 + 2.18650i) q^{40} -3.30357 q^{41} +4.35347i q^{42} -12.7163i q^{43} -5.84119 q^{44} +(2.23313 - 0.478178i) q^{45} -2.42865 q^{46} +1.23929i q^{47} +2.00532i q^{48} +2.28695 q^{49} +(2.04741 + 4.56159i) q^{50} -13.3615 q^{51} +6.75054i q^{52} -4.58108i q^{53} -3.96788 q^{54} +(-12.7718 + 2.73480i) q^{55} -2.17096 q^{56} -3.22228i q^{57} +8.38049i q^{58} +5.11750 q^{59} +(0.938878 + 4.38465i) q^{60} +2.82307 q^{61} +1.63097i q^{62} +2.21725i q^{63} -1.00000 q^{64} +(3.16055 + 14.7601i) q^{65} -11.7135 q^{66} +5.28369i q^{67} -6.66300i q^{68} -4.87023 q^{69} +(-4.74680 + 1.01643i) q^{70} +1.18017 q^{71} +1.02133i q^{72} +3.97394i q^{73} -2.82834 q^{74} +(4.10572 + 9.14747i) q^{75} +1.60686 q^{76} -12.6810i q^{77} +13.5370i q^{78} -12.3021 q^{79} +(-2.18650 + 0.468193i) q^{80} -11.0209 q^{81} -3.30357i q^{82} +15.2796i q^{83} -4.35347 q^{84} +(-3.11957 - 14.5687i) q^{85} +12.7163 q^{86} +16.8056i q^{87} -5.84119i q^{88} +12.8886 q^{89} +(0.478178 + 2.23313i) q^{90} -14.6551 q^{91} -2.42865i q^{92} +3.27061i q^{93} -1.23929 q^{94} +(3.51341 - 0.752321i) q^{95} -2.00532 q^{96} +7.19553i q^{97} +2.28695i q^{98} -5.96577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 38 q^{4} + 12 q^{6} - 42 q^{9} + 2 q^{10} + 28 q^{11} - 24 q^{14} - 6 q^{15} + 38 q^{16} - 20 q^{19} + 28 q^{21} - 12 q^{24} - 6 q^{25} + 44 q^{26} - 24 q^{29} + 2 q^{30} + 36 q^{31} - 36 q^{34}+ \cdots - 24 q^{99}+O(q^{100}) $ 38 * q - 38 * q^4 + 12 * q^6 - 42 * q^9 + 2 * q^10 + 28 * q^11 - 24 * q^14 - 6 * q^15 + 38 * q^16 - 20 * q^19 + 28 * q^21 - 12 * q^24 - 6 * q^25 + 44 * q^26 - 24 * q^29 + 2 * q^30 + 36 * q^31 - 36 * q^34 - 4 * q^35 + 42 * q^36 - 2 * q^40 - 4 * q^41 - 28 * q^44 - 8 * q^45 + 16 * q^46 - 10 * q^49 + 8 * q^50 - 48 * q^54 - 40 * q^55 + 24 * q^56 - 56 * q^59 + 6 * q^60 + 20 * q^61 - 38 * q^64 + 40 * q^66 + 100 * q^69 + 8 * q^70 + 52 * q^71 - 64 * q^74 - 60 * q^75 + 20 * q^76 + 4 * q^79 + 54 * q^81 - 28 * q^84 - 68 * q^85 + 68 * q^86 + 48 * q^89 - 6 * q^90 + 52 * q^91 - 44 * q^94 - 52 * q^95 + 12 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1510\mathbb{Z}\right)^\times$.

$n$	$761$	$907$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			2.00532i			1.15777i	0.815408	+	0.578887i	$0.196513\pi$
$3$			2.00532i			1.15777i	−0.815408	+	0.578887i	$0.803487\pi$
$4$	−1.00000			−0.500000
$5$	−2.18650	+	0.468193i	−0.977834	+	0.209382i
$5$	−2.18650	+	0.468193i	−0.977834	+	0.209382i
$6$	−2.00532			−0.818670
$7$		−	2.17096i		−	0.820544i	−0.911963	−	0.410272i	$-0.865434\pi$
$7$		−	2.17096i		−	0.820544i	0.911963	−	0.410272i	$-0.134566\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.02133			−0.340442
$10$	−0.468193	−	2.18650i	−0.148056	−	0.691433i
$11$	5.84119			1.76119			0.880593	−	0.473873i	$-0.157144\pi$
$11$	5.84119			1.76119			0.880593	+	0.473873i	$0.157144\pi$
$12$		−	2.00532i		−	0.578887i
$13$		−	6.75054i		−	1.87226i	−0.351650	−	0.936131i	$-0.614379\pi$
$13$		−	6.75054i		−	1.87226i	0.351650	−	0.936131i	$-0.385621\pi$
$14$	2.17096			0.580212
$15$	−0.938878	−	4.38465i	−0.242417	−	1.13211i
$16$	1.00000			0.250000
$17$			6.66300i			1.61601i	0.589172	+	0.808007i	$0.299454\pi$
$17$			6.66300i			1.61601i	−0.589172	+	0.808007i	$0.700546\pi$
$18$		−	1.02133i		−	0.240729i
$19$	−1.60686			−0.368639			−0.184320	−	0.982866i	$-0.559008\pi$
$19$	−1.60686			−0.368639			−0.184320	+	0.982866i	$0.559008\pi$
$20$	2.18650	−	0.468193i	0.488917	−	0.104691i
$21$	4.35347			0.950005
$22$			5.84119i			1.24535i
$23$			2.42865i			0.506409i	0.967413	+	0.253204i	$0.0814845\pi$
$23$			2.42865i			0.506409i	−0.967413	+	0.253204i	$0.918516\pi$
$24$	2.00532			0.409335
$25$	4.56159	−	2.04741i	0.912318	−	0.409482i
$26$	6.75054			1.32389
$27$			3.96788i			0.763619i
$28$			2.17096i			0.410272i
$29$	8.38049			1.55622			0.778109	−	0.628129i	$-0.216179\pi$
$29$	8.38049			1.55622			0.778109	+	0.628129i	$0.216179\pi$
$30$	4.38465	−	0.938878i	0.800524	−	0.171415i
$31$	1.63097			0.292930			0.146465	−	0.989216i	$-0.453210\pi$
$31$	1.63097			0.292930			0.146465	+	0.989216i	$0.453210\pi$
$32$			1.00000i			0.176777i
$33$			11.7135i			2.03906i
$34$	−6.66300			−1.14269
$35$	1.01643	+	4.74680i	0.171807	+	0.802356i
$36$	1.02133			0.170221
$37$			2.82834i			0.464977i	0.972599	+	0.232488i	$0.0746867\pi$
$37$			2.82834i			0.464977i	−0.972599	+	0.232488i	$0.925313\pi$
$38$		−	1.60686i		−	0.260667i
$39$	13.5370			2.16766
$40$	0.468193	+	2.18650i	0.0740278	+	0.345716i
$41$	−3.30357			−0.515931			−0.257965	−	0.966154i	$-0.583052\pi$
$41$	−3.30357			−0.515931			−0.257965	+	0.966154i	$0.583052\pi$
$42$			4.35347i			0.671755i
$43$		−	12.7163i		−	1.93922i	−0.244652	−	0.969611i	$-0.578674\pi$
$43$		−	12.7163i		−	1.93922i	0.244652	−	0.969611i	$-0.421326\pi$
$44$	−5.84119			−0.880593
$45$	2.23313	−	0.478178i	0.332896	−	0.0712825i
$46$	−2.42865			−0.358085
$47$			1.23929i			0.180770i	0.995907	+	0.0903848i	$0.0288097\pi$
$47$			1.23929i			0.180770i	−0.995907	+	0.0903848i	$0.971190\pi$
$48$			2.00532i			0.289444i
$49$	2.28695			0.326707
$50$	2.04741	+	4.56159i	0.289547	+	0.645106i
$51$	−13.3615			−1.87098
$52$			6.75054i			0.936131i
$53$		−	4.58108i		−	0.629260i	−0.949214	−	0.314630i	$-0.898120\pi$
$53$		−	4.58108i		−	0.629260i	0.949214	−	0.314630i	$-0.101880\pi$
$54$	−3.96788			−0.539960
$55$	−12.7718	+	2.73480i	−1.72215	+	0.368761i
$56$	−2.17096			−0.290106
$57$		−	3.22228i		−	0.426801i
$58$			8.38049i			1.10041i
$59$	5.11750			0.666242			0.333121	−	0.942884i	$-0.391898\pi$
$59$	5.11750			0.666242			0.333121	+	0.942884i	$0.391898\pi$
$60$	0.938878	+	4.38465i	0.121209	+	0.566056i
$61$	2.82307			0.361457			0.180728	−	0.983533i	$-0.442154\pi$
$61$	2.82307			0.361457			0.180728	+	0.983533i	$0.442154\pi$
$62$			1.63097i			0.207133i
$63$			2.21725i			0.279348i
$64$	−1.00000			−0.125000
$65$	3.16055	+	14.7601i	0.392018	+	1.83076i
$66$	−11.7135			−1.44183
$67$			5.28369i			0.645506i	0.946483	+	0.322753i	$0.104608\pi$
$67$			5.28369i			0.645506i	−0.946483	+	0.322753i	$0.895392\pi$
$68$		−	6.66300i		−	0.808007i
$69$	−4.87023			−0.586307
$70$	−4.74680	+	1.01643i	−0.567351	+	0.121486i
$71$	1.18017			0.140061			0.0700305	−	0.997545i	$-0.477690\pi$
$71$	1.18017			0.140061			0.0700305	+	0.997545i	$0.477690\pi$
$72$			1.02133i			0.120364i
$73$			3.97394i			0.465115i	0.972583	+	0.232557i	$0.0747094\pi$
$73$			3.97394i			0.465115i	−0.972583	+	0.232557i	$0.925291\pi$
$74$	−2.82834			−0.328788
$75$	4.10572	+	9.14747i	0.474088	+	1.05626i
$76$	1.60686			0.184320
$77$		−	12.6810i		−	1.44513i
$78$			13.5370i			1.53277i
$79$	−12.3021			−1.38409			−0.692047	−	0.721853i	$-0.743291\pi$
$79$	−12.3021			−1.38409			−0.692047	+	0.721853i	$0.743291\pi$
$80$	−2.18650	+	0.468193i	−0.244458	+	0.0523455i
$81$	−11.0209			−1.22454
$82$		−	3.30357i		−	0.364818i
$83$			15.2796i			1.67715i	0.544786	+	0.838575i	$0.316611\pi$
$83$			15.2796i			1.67715i	−0.544786	+	0.838575i	$0.683389\pi$
$84$	−4.35347			−0.475003
$85$	−3.11957	−	14.5687i	−0.338365	−	1.58019i
$86$	12.7163			1.37124
$87$			16.8056i			1.80175i
$88$		−	5.84119i		−	0.622673i
$89$	12.8886			1.36619			0.683096	−	0.730328i	$-0.260633\pi$
$89$	12.8886			1.36619			0.683096	+	0.730328i	$0.260633\pi$
$90$	0.478178	+	2.23313i	0.0504043	+	0.235393i
$91$	−14.6551			−1.53627
$92$		−	2.42865i		−	0.253204i
$93$			3.27061i			0.339147i
$94$	−1.23929			−0.127823
$95$	3.51341	−	0.752321i	0.360468	−	0.0771865i
$96$	−2.00532			−0.204668
$97$			7.19553i			0.730596i	0.930891	+	0.365298i	$0.119033\pi$
$97$			7.19553i			0.730596i	−0.930891	+	0.365298i	$0.880967\pi$
$98$			2.28695i			0.231017i
$99$	−5.96577			−0.599582
$100$	−4.56159	+	2.04741i	−0.456159	+	0.204741i
$101$	−8.65400			−0.861105			−0.430553	−	0.902565i	$-0.641681\pi$
$101$	−8.65400			−0.861105			−0.430553	+	0.902565i	$0.641681\pi$
$102$		−	13.3615i		−	1.32298i
$103$		−	4.40652i		−	0.434187i	−0.976151	−	0.217093i	$-0.930342\pi$
$103$		−	4.40652i		−	0.434187i	0.976151	−	0.217093i	$-0.0696576\pi$
$104$	−6.75054			−0.661945
$105$	−9.51888	+	2.03826i	−0.928947	+	0.198914i
$106$	4.58108			0.444954
$107$			0.374223i			0.0361775i	0.999836	+	0.0180887i	$0.00575814\pi$
$107$			0.374223i			0.0361775i	−0.999836	+	0.0180887i	$0.994242\pi$
$108$		−	3.96788i		−	0.381810i
$109$	18.3383			1.75649			0.878243	−	0.478214i	$-0.158716\pi$
$109$	18.3383			1.75649			0.878243	+	0.478214i	$0.158716\pi$
$110$	−2.73480	−	12.7718i	−0.260753	−	1.21774i
$111$	−5.67174			−0.538338
$112$		−	2.17096i		−	0.205136i
$113$		−	6.19114i		−	0.582414i	−0.956660	−	0.291207i	$-0.905943\pi$
$113$		−	6.19114i		−	0.582414i	0.956660	−	0.291207i	$-0.0940568\pi$
$114$	3.22228			0.301794
$115$	−1.13708	−	5.31025i	−0.106033	−	0.495183i
$116$	−8.38049			−0.778109
$117$			6.89450i			0.637397i
$118$			5.11750i			0.471104i
$119$	14.4651			1.32601
$120$	−4.38465	+	0.938878i	−0.400262	+	0.0857075i
$121$	23.1196			2.10178
$122$			2.82307i			0.255589i
$123$		−	6.62473i		−	0.597331i
$124$	−1.63097			−0.146465
$125$	−9.01535	+	6.61237i	−0.806357	+	0.591428i
$126$	−2.21725			−0.197529
$127$		−	5.74629i		−	0.509901i	−0.966954	−	0.254950i	$-0.917941\pi$
$127$		−	5.74629i		−	0.509901i	0.966954	−	0.254950i	$-0.0820591\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	25.5004			2.24518
$130$	−14.7601	+	3.16055i	−1.29454	+	0.277199i
$131$	4.63792			0.405217			0.202609	−	0.979260i	$-0.435058\pi$
$131$	4.63792			0.405217			0.202609	+	0.979260i	$0.435058\pi$
$132$		−	11.7135i		−	1.01953i
$133$			3.48842i			0.302485i
$134$	−5.28369			−0.456442
$135$	−1.85773	−	8.67579i	−0.159888	−	0.746693i
$136$	6.66300			0.571347
$137$		−	5.10212i		−	0.435903i	−0.975960	−	0.217952i	$-0.930062\pi$
$137$		−	5.10212i		−	0.435903i	0.975960	−	0.217952i	$-0.0699375\pi$
$138$		−	4.87023i		−	0.414582i
$139$	10.7091			0.908337			0.454169	−	0.890916i	$-0.349936\pi$
$139$	10.7091			0.908337			0.454169	+	0.890916i	$0.349936\pi$
$140$	−1.01643	−	4.74680i	−0.0859036	−	0.401178i
$141$	−2.48519			−0.209290
$142$			1.18017i			0.0990380i
$143$		−	39.4312i		−	3.29740i
$144$	−1.02133			−0.0851105
$145$	−18.3240	+	3.92368i	−1.52172	+	0.325844i
$146$	−3.97394			−0.328886
$147$			4.58608i			0.378254i
$148$		−	2.82834i		−	0.232488i
$149$	−4.84470			−0.396894			−0.198447	−	0.980112i	$-0.563590\pi$
$149$	−4.84470			−0.396894			−0.198447	+	0.980112i	$0.563590\pi$
$150$	−9.14747	+	4.10572i	−0.746888	+	0.335231i
$151$	1.00000			0.0813788
$151$	1.00000			0.0813788
$152$			1.60686i			0.130334i
$153$		−	6.80510i		−	0.550159i
$154$	12.6810			1.02186
$155$	−3.56611	+	0.763606i	−0.286437	+	0.0613343i
$156$	−13.5370			−1.08383
$157$			13.2890i			1.06058i	0.847818	+	0.530288i	$0.177916\pi$
$157$			13.2890i			1.06058i	−0.847818	+	0.530288i	$0.822084\pi$
$158$		−	12.3021i		−	0.978702i
$159$	9.18656			0.728542
$160$	−0.468193	−	2.18650i	−0.0370139	−	0.172858i
$161$	5.27249			0.415531
$162$		−	11.0209i		−	0.865881i
$163$			20.7783i			1.62748i	0.581227	+	0.813742i	$0.302573\pi$
$163$			20.7783i			1.62748i	−0.581227	+	0.813742i	$0.697427\pi$
$164$	3.30357			0.257965
$165$	−5.48417	−	25.6116i	−0.426942	−	1.99386i
$166$	−15.2796			−1.18592
$167$			14.0044i			1.08369i	0.840478	+	0.541845i	$0.182274\pi$
$167$			14.0044i			1.08369i	−0.840478	+	0.541845i	$0.817726\pi$
$168$		−	4.35347i		−	0.335878i
$169$	−32.5698			−2.50537
$170$	14.5687	−	3.11957i	1.11737	−	0.239260i
$171$	1.64113			0.125500
$172$			12.7163i			0.969611i
$173$			19.8339i			1.50794i	0.656909	+	0.753970i	$0.271864\pi$
$173$			19.8339i			1.50794i	−0.656909	+	0.753970i	$0.728136\pi$
$174$	−16.8056			−1.27403
$175$	−4.44484	−	9.90301i	−0.335998	−	0.748597i
$176$	5.84119			0.440297
$177$			10.2623i			0.771358i
$178$			12.8886i			0.966044i
$179$	−9.34255			−0.698295			−0.349147	−	0.937068i	$-0.613529\pi$
$179$	−9.34255			−0.698295			−0.349147	+	0.937068i	$0.613529\pi$
$180$	−2.23313	+	0.478178i	−0.166448	+	0.0356412i
$181$	7.36824			0.547677			0.273838	−	0.961776i	$-0.411707\pi$
$181$	7.36824			0.547677			0.273838	+	0.961776i	$0.411707\pi$
$182$		−	14.6551i		−	1.08631i
$183$			5.66117i			0.418486i
$184$	2.42865			0.179042
$185$	−1.32421	−	6.18418i	−0.0973578	−	0.454670i
$186$	−3.27061			−0.239813
$187$			38.9199i			2.84610i
$188$		−	1.23929i		−	0.0903848i
$189$	8.61410			0.626583
$190$	0.752321	+	3.51341i	0.0545791	+	0.254889i
$191$	19.6749			1.42363			0.711813	−	0.702369i	$-0.247874\pi$
$191$	19.6749			1.42363			0.711813	+	0.702369i	$0.247874\pi$
$192$		−	2.00532i		−	0.144722i
$193$		−	4.97202i		−	0.357894i	−0.983859	−	0.178947i	$-0.942731\pi$
$193$		−	4.97202i		−	0.357894i	0.983859	−	0.178947i	$-0.0572690\pi$
$194$	−7.19553			−0.516609
$195$	−29.5987	+	6.33794i	−2.11961	+	0.453869i
$196$	−2.28695			−0.163354
$197$		−	21.9808i		−	1.56607i	−0.621979	−	0.783034i	$-0.713671\pi$
$197$		−	21.9808i		−	1.56607i	0.621979	−	0.783034i	$-0.286329\pi$
$198$		−	5.96577i		−	0.423968i
$199$	14.5437			1.03098			0.515489	−	0.856896i	$-0.327610\pi$
$199$	14.5437			1.03098			0.515489	+	0.856896i	$0.327610\pi$
$200$	−2.04741	−	4.56159i	−0.144774	−	0.322553i
$201$	−10.5955			−0.747350
$202$		−	8.65400i		−	0.608893i
$203$		−	18.1937i		−	1.27695i
$204$	13.3615			0.935490
$205$	7.22326	−	1.54671i	0.504495	−	0.108027i
$206$	4.40652			0.307017
$207$		−	2.48044i		−	0.172403i
$208$		−	6.75054i		−	0.468066i
$209$	−9.38599			−0.649242
$210$	−2.03826	−	9.51888i	−0.140654	−	0.656865i
$211$	20.0494			1.38026			0.690130	−	0.723685i	$-0.257553\pi$
$211$	20.0494			1.38026			0.690130	+	0.723685i	$0.257553\pi$
$212$			4.58108i			0.314630i
$213$			2.36663i			0.162159i
$214$	−0.374223			−0.0255813
$215$	5.95369	+	27.8043i	0.406038	+	1.89624i
$216$	3.96788			0.269980
$217$		−	3.54075i		−	0.240362i
$218$			18.3383i			1.24202i
$219$	−7.96905			−0.538498
$220$	12.7718	−	2.73480i	0.861074	−	0.184381i
$221$	44.9788			3.02560
$222$		−	5.67174i		−	0.380662i
$223$		−	21.4376i		−	1.43557i	−0.696266	−	0.717784i	$-0.745157\pi$
$223$		−	21.4376i		−	1.43557i	0.696266	−	0.717784i	$-0.254843\pi$
$224$	2.17096			0.145053
$225$	−4.65887	+	2.09107i	−0.310592	+	0.139405i
$226$	6.19114			0.411829
$227$			22.5305i			1.49540i	0.664034	+	0.747702i	$0.268843\pi$
$227$			22.5305i			1.49540i	−0.664034	+	0.747702i	$0.731157\pi$
$228$			3.22228i			0.213401i
$229$	9.94967			0.657493			0.328746	−	0.944418i	$-0.393374\pi$
$229$	9.94967			0.657493			0.328746	+	0.944418i	$0.393374\pi$
$230$	5.31025	−	1.13708i	0.350148	−	0.0749766i
$231$	25.4295			1.67314
$232$		−	8.38049i		−	0.550206i
$233$		−	18.5365i		−	1.21436i	−0.794563	−	0.607182i	$-0.792300\pi$
$233$		−	18.5365i		−	1.21436i	0.794563	−	0.607182i	$-0.207700\pi$
$234$	−6.89450			−0.450708
$235$	−0.580228	−	2.70972i	−0.0378499	−	0.176763i
$236$	−5.11750			−0.333121
$237$		−	24.6697i		−	1.60247i
$238$			14.4651i			0.937632i
$239$	−10.3268			−0.667988			−0.333994	−	0.942575i	$-0.608396\pi$
$239$	−10.3268			−0.667988			−0.333994	+	0.942575i	$0.608396\pi$
$240$	−0.938878	−	4.38465i	−0.0606043	−	0.283028i
$241$	9.46248			0.609532			0.304766	−	0.952427i	$-0.401422\pi$
$241$	9.46248			0.609532			0.304766	+	0.952427i	$0.401422\pi$
$242$			23.1196i			1.48618i
$243$		−	10.1968i		−	0.654123i
$244$	−2.82307			−0.180728
$245$	−5.00043	+	1.07073i	−0.319466	+	0.0684067i
$246$	6.62473			0.422377
$247$			10.8472i			0.690189i
$248$		−	1.63097i		−	0.103566i
$249$	−30.6405			−1.94176
$250$	−6.61237	−	9.01535i	−0.418203	−	0.570181i
$251$	−1.73091			−0.109254			−0.0546271	−	0.998507i	$-0.517397\pi$
$251$	−1.73091			−0.109254			−0.0546271	+	0.998507i	$0.517397\pi$
$252$		−	2.21725i		−	0.139674i
$253$			14.1862i			0.891880i
$254$	5.74629			0.360554
$255$	29.2149	−	6.25575i	1.82951	−	0.391750i
$256$	1.00000			0.0625000
$257$		−	12.2712i		−	0.765454i	−0.923862	−	0.382727i	$-0.874985\pi$
$257$		−	12.2712i		−	0.765454i	0.923862	−	0.382727i	$-0.125015\pi$
$258$			25.5004i			1.58758i
$259$	6.14020			0.381534
$260$	−3.16055	−	14.7601i	−0.196009	−	0.915381i
$261$	−8.55921			−0.529802
$262$			4.63792i			0.286532i
$263$		−	3.08230i		−	0.190063i	−0.995474	−	0.0950314i	$-0.969705\pi$
$263$		−	3.08230i		−	0.190063i	0.995474	−	0.0950314i	$-0.0302951\pi$
$264$	11.7135			0.720915
$265$	2.14483	+	10.0166i	0.131756	+	0.615312i
$266$	−3.48842			−0.213889
$267$			25.8459i			1.58174i
$268$		−	5.28369i		−	0.322753i
$269$	−21.6437			−1.31964			−0.659820	−	0.751424i	$-0.729368\pi$
$269$	−21.6437			−1.31964			−0.659820	+	0.751424i	$0.729368\pi$
$270$	8.67579	−	1.85773i	0.527992	−	0.113058i
$271$	5.85686			0.355779			0.177890	−	0.984050i	$-0.443073\pi$
$271$	5.85686			0.355779			0.177890	+	0.984050i	$0.443073\pi$
$272$			6.66300i			0.404004i
$273$		−	29.3883i		−	1.77866i
$274$	5.10212			0.308230
$275$	26.6451	−	11.9593i	1.60676	−	0.721174i
$276$	4.87023			0.293154
$277$			0.238569i			0.0143342i	0.999974	+	0.00716711i	$0.00228138\pi$
$277$			0.238569i			0.0143342i	−0.999974	+	0.00716711i	$0.997719\pi$
$278$			10.7091i			0.642292i
$279$	−1.66575			−0.0997257
$280$	4.74680	−	1.01643i	0.283676	−	0.0607430i
$281$	−25.8471			−1.54191			−0.770954	−	0.636891i	$-0.780220\pi$
$281$	−25.8471			−1.54191			−0.770954	+	0.636891i	$0.780220\pi$
$282$		−	2.48519i		−	0.147991i
$283$		−	6.39123i		−	0.379919i	−0.981792	−	0.189960i	$-0.939164\pi$
$283$		−	6.39123i		−	0.379919i	0.981792	−	0.189960i	$-0.0608357\pi$
$284$	−1.18017			−0.0700305
$285$	1.50865	+	7.04552i	0.0893645	+	0.417341i
$286$	39.4312			2.33162
$287$			7.17190i			0.423344i
$288$		−	1.02133i		−	0.0601822i
$289$	−27.3956			−1.61150
$290$	−3.92368	−	18.3240i	−0.230407	−	1.07602i
$291$	−14.4294			−0.845865
$292$		−	3.97394i		−	0.232557i
$293$		−	11.0160i		−	0.643564i	−0.946814	−	0.321782i	$-0.895718\pi$
$293$		−	11.0160i		−	0.643564i	0.946814	−	0.321782i	$-0.104282\pi$
$294$	−4.58608			−0.267466
$295$	−11.1894	+	2.39598i	−0.651474	+	0.139499i
$296$	2.82834			0.164394
$297$			23.1772i			1.34488i
$298$		−	4.84470i		−	0.280646i
$299$	16.3947			0.948130
$300$	−4.10572	−	9.14747i	−0.237044	−	0.528129i
$301$	−27.6066			−1.59122
$302$			1.00000i			0.0575435i
$303$		−	17.3541i		−	0.996966i
$304$	−1.60686			−0.0921598
$305$	−6.17265	+	1.32174i	−0.353445	+	0.0756826i
$306$	6.80510			0.389021
$307$			8.74181i			0.498921i	0.968385	+	0.249461i	$0.0802533\pi$
$307$			8.74181i			0.498921i	−0.968385	+	0.249461i	$0.919747\pi$
$308$			12.6810i			0.722566i
$309$	8.83649			0.502691
$310$	−0.763606	−	3.56611i	−0.0433699	−	0.202541i
$311$	21.1421			1.19886			0.599430	−	0.800427i	$-0.295394\pi$
$311$	21.1421			1.19886			0.599430	+	0.800427i	$0.295394\pi$
$312$		−	13.5370i		−	0.766383i
$313$			16.3617i			0.924820i	0.886666	+	0.462410i	$0.153015\pi$
$313$			16.3617i			0.924820i	−0.886666	+	0.462410i	$0.846985\pi$
$314$	−13.2890			−0.749940
$315$	−1.03810	−	4.84803i	−0.0584904	−	0.273156i
$316$	12.3021			0.692047
$317$		−	20.3398i		−	1.14240i	−0.820811	−	0.571199i	$-0.806478\pi$
$317$		−	20.3398i		−	1.14240i	0.820811	−	0.571199i	$-0.193522\pi$
$318$			9.18656i			0.515157i
$319$	48.9521			2.74079
$320$	2.18650	−	0.468193i	0.122229	−	0.0261728i
$321$	−0.750438			−0.0418854
$322$			5.27249i			0.293824i
$323$		−	10.7065i		−	0.595726i
$324$	11.0209			0.612271
$325$	−13.8211	−	30.7932i	−0.766658	−	1.70810i
$326$	−20.7783			−1.15080
$327$			36.7742i			2.03362i
$328$			3.30357i			0.182409i
$329$	2.69045			0.148329
$330$	25.6116	−	5.48417i	1.40987	−	0.301894i
$331$	−21.7967			−1.19806			−0.599028	−	0.800728i	$-0.704446\pi$
$331$	−21.7967			−1.19806			−0.599028	+	0.800728i	$0.704446\pi$
$332$		−	15.2796i		−	0.838575i
$333$		−	2.88866i		−	0.158298i
$334$	−14.0044			−0.766285
$335$	−2.47379	−	11.5528i	−0.135157	−	0.631198i
$336$	4.35347			0.237501
$337$			0.0111359i			0.000606610i	1.00000		0.000303305i	$9.65449e-5\pi$
$337$			0.0111359i			0.000606610i	−1.00000		0.000303305i	$0.999903\pi$
$338$		−	32.5698i		−	1.77156i
$339$	12.4153			0.674304
$340$	3.11957	+	14.5687i	0.169182	+	0.790097i
$341$	9.52678			0.515904
$342$			1.64113i			0.0887421i
$343$		−	20.1616i		−	1.08862i
$344$	−12.7163			−0.685618
$345$	10.6488	−	2.28021i	0.573311	−	0.122762i
$346$	−19.8339			−1.06627
$347$			1.36755i			0.0734137i	0.999326	+	0.0367069i	$0.0116868\pi$
$347$			1.36755i			0.0734137i	−0.999326	+	0.0367069i	$0.988313\pi$
$348$		−	16.8056i		−	0.900875i
$349$	−21.6787			−1.16043			−0.580217	−	0.814462i	$-0.697032\pi$
$349$	−21.6787			−1.16043			−0.580217	+	0.814462i	$0.697032\pi$
$350$	9.90301	−	4.44484i	0.529338	−	0.237586i
$351$	26.7854			1.42970
$352$			5.84119i			0.311337i
$353$		−	5.23065i		−	0.278400i	−0.990264	−	0.139200i	$-0.955547\pi$
$353$		−	5.23065i		−	0.278400i	0.990264	−	0.139200i	$-0.0444530\pi$
$354$	−10.2623			−0.545433
$355$	−2.58045	+	0.552549i	−0.136956	+	0.0293263i
$356$	−12.8886			−0.683096
$357$			29.0072i			1.53522i
$358$		−	9.34255i		−	0.493769i
$359$	6.18172			0.326259			0.163129	−	0.986605i	$-0.447841\pi$
$359$	6.18172			0.326259			0.163129	+	0.986605i	$0.447841\pi$
$360$	−0.478178	−	2.23313i	−0.0252022	−	0.117696i
$361$	−16.4180			−0.864105
$362$			7.36824i			0.387266i
$363$			46.3622i			2.43338i
$364$	14.6551			0.768137
$365$	−1.86057	−	8.68904i	−0.0973868	−	0.454805i
$366$	−5.66117			−0.295914
$367$			14.1447i			0.738347i	0.929360	+	0.369174i	$0.120359\pi$
$367$			14.1447i			0.738347i	−0.929360	+	0.369174i	$0.879641\pi$
$368$			2.42865i			0.126602i
$369$	3.37402			0.175645
$370$	6.18418	−	1.32421i	0.321500	−	0.0688424i
$371$	−9.94533			−0.516336
$372$		−	3.27061i		−	0.169573i
$373$			16.1041i			0.833839i	0.908943	+	0.416920i	$0.136890\pi$
$373$			16.1041i			0.833839i	−0.908943	+	0.416920i	$0.863110\pi$
$374$	−38.9199			−2.01250
$375$	−13.2600	−	18.0787i	−0.684741	−	0.933580i
$376$	1.23929			0.0639117
$377$		−	56.5728i		−	2.91365i
$378$			8.61410i			0.443061i
$379$	−0.381999			−0.0196220			−0.00981099	−	0.999952i	$-0.503123\pi$
$379$	−0.381999			−0.0196220			−0.00981099	+	0.999952i	$0.503123\pi$
$380$	−3.51341	+	0.752321i	−0.180234	+	0.0385932i
$381$	11.5232			0.590350
$382$			19.6749i			1.00666i
$383$		−	11.8757i		−	0.606821i	−0.952860	−	0.303410i	$-0.901875\pi$
$383$		−	11.8757i		−	0.606821i	0.952860	−	0.303410i	$-0.0981253\pi$
$384$	2.00532			0.102334
$385$	5.93714	+	27.7270i	0.302585	+	1.41310i
$386$	4.97202			0.253069
$387$			12.9875i			0.660193i
$388$		−	7.19553i		−	0.365298i
$389$	−25.1152			−1.27339			−0.636695	−	0.771116i	$-0.719699\pi$
$389$	−25.1152			−1.27339			−0.636695	+	0.771116i	$0.719699\pi$
$390$	−6.33794	−	29.5987i	−0.320934	−	1.49879i
$391$	−16.1821			−0.818364
$392$		−	2.28695i		−	0.115509i
$393$			9.30054i			0.469150i
$394$	21.9808			1.10738
$395$	26.8986	−	5.75975i	1.35341	−	0.289805i
$396$	5.96577			0.299791
$397$		−	27.6815i		−	1.38929i	−0.719351	−	0.694647i	$-0.755561\pi$
$397$		−	27.6815i		−	1.38929i	0.719351	−	0.694647i	$-0.244439\pi$
$398$			14.5437i			0.729012i
$399$	−6.99542			−0.350209
$400$	4.56159	−	2.04741i	0.228080	−	0.102370i
$401$	−26.8220			−1.33943			−0.669714	−	0.742619i	$-0.733583\pi$
$401$	−26.8220			−1.33943			−0.669714	+	0.742619i	$0.733583\pi$
$402$		−	10.5955i		−	0.528457i
$403$		−	11.0099i		−	0.548442i
$404$	8.65400			0.430553
$405$	24.0972	−	5.15989i	1.19740	−	0.256397i
$406$	18.1937			0.902937
$407$			16.5209i			0.818910i
$408$			13.3615i			0.661492i
$409$	−22.0078			−1.08821			−0.544107	−	0.839016i	$-0.683132\pi$
$409$	−22.0078			−1.08821			−0.544107	+	0.839016i	$0.683132\pi$
$410$	1.54671	+	7.22326i	0.0763864	+	0.356731i
$411$	10.2314			0.504678
$412$			4.40652i			0.217093i
$413$		−	11.1099i		−	0.546681i
$414$	2.48044			0.121907
$415$	−7.15378	−	33.4088i	−0.351165	−	1.63997i
$416$	6.75054			0.330972
$417$			21.4753i			1.05165i
$418$		−	9.38599i		−	0.459084i
$419$	11.2304			0.548639			0.274320	−	0.961639i	$-0.411547\pi$
$419$	11.2304			0.548639			0.274320	+	0.961639i	$0.411547\pi$
$420$	9.51888	−	2.03826i	0.464474	−	0.0994571i
$421$	3.24051			0.157933			0.0789663	−	0.996877i	$-0.474838\pi$
$421$	3.24051			0.157933			0.0789663	+	0.996877i	$0.474838\pi$
$422$			20.0494i			0.975991i
$423$		−	1.26572i		−	0.0615416i
$424$	−4.58108			−0.222477
$425$	13.6419	+	30.3939i	0.661729	+	1.47432i
$426$	−2.36663			−0.114664
$427$		−	6.12876i		−	0.296591i
$428$		−	0.374223i		−	0.0180887i
$429$	79.0724			3.81765
$430$	−27.8043	+	5.95369i	−1.34084	+	0.287113i
$431$	1.56276			0.0752755			0.0376377	−	0.999291i	$-0.488017\pi$
$431$	1.56276			0.0752755			0.0376377	+	0.999291i	$0.488017\pi$
$432$			3.96788i			0.190905i
$433$		−	24.4974i		−	1.17727i	−0.808399	−	0.588635i	$-0.799666\pi$
$433$		−	24.4974i		−	1.17727i	0.808399	−	0.588635i	$-0.200334\pi$
$434$	3.54075			0.169962
$435$	−7.86826	−	36.7455i	−0.377254	−	1.76181i
$436$	−18.3383			−0.878243
$437$		−	3.90250i		−	0.186682i
$438$		−	7.96905i		−	0.380776i
$439$	21.0172			1.00310			0.501548	−	0.865130i	$-0.332764\pi$
$439$	21.0172			1.00310			0.501548	+	0.865130i	$0.332764\pi$
$440$	2.73480	+	12.7718i	0.130377	+	0.608871i
$441$	−2.33572			−0.111225
$442$			44.9788i			2.13943i
$443$			15.5229i			0.737513i	0.929526	+	0.368757i	$0.120216\pi$
$443$			15.5229i			0.737513i	−0.929526	+	0.368757i	$0.879784\pi$
$444$	5.67174			0.269169
$445$	−28.1810	+	6.03437i	−1.33591	+	0.286056i
$446$	21.4376			1.01510
$447$		−	9.71520i		−	0.459513i
$448$			2.17096i			0.102568i
$449$	21.2796			1.00425			0.502124	−	0.864796i	$-0.332552\pi$
$449$	21.2796			1.00425			0.502124	+	0.864796i	$0.332552\pi$
$450$	−2.09107	−	4.65887i	−0.0985741	−	0.219621i
$451$	−19.2968			−0.908650
$452$			6.19114i			0.291207i
$453$			2.00532i			0.0942184i
$454$	−22.5305			−1.05741
$455$	32.0435	−	6.86142i	1.50222	−	0.321668i
$456$	−3.22228			−0.150897
$457$		−	37.7848i		−	1.76750i	−0.467960	−	0.883750i	$-0.655011\pi$
$457$		−	37.7848i		−	1.76750i	0.467960	−	0.883750i	$-0.344989\pi$
$458$			9.94967i			0.464918i
$459$	−26.4380			−1.23402
$460$	1.13708	+	5.31025i	0.0530165	+	0.247592i
$461$	29.3240			1.36576			0.682878	−	0.730532i	$-0.260728\pi$
$461$	29.3240			1.36576			0.682878	+	0.730532i	$0.260728\pi$
$462$			25.4295i			1.18309i
$463$		−	15.1006i		−	0.701784i	−0.936416	−	0.350892i	$-0.885878\pi$
$463$		−	15.1006i		−	0.701784i	0.936416	−	0.350892i	$-0.114122\pi$
$464$	8.38049			0.389054
$465$	−1.53128	−	7.15121i	−0.0710113	−	0.331629i
$466$	18.5365			0.858685
$467$		−	6.33706i		−	0.293244i	−0.989193	−	0.146622i	$-0.953160\pi$
$467$		−	6.33706i		−	0.293244i	0.989193	−	0.146622i	$-0.0468401\pi$
$468$		−	6.89450i		−	0.318699i
$469$	11.4707			0.529666
$470$	2.70972	−	0.580228i	0.124990	−	0.0267639i
$471$	−26.6487			−1.22791
$472$		−	5.11750i		−	0.235552i
$473$		−	74.2785i		−	3.41533i
$474$	24.6697			1.13312
$475$	−7.32984	+	3.28990i	−0.336316	+	0.150951i
$476$	−14.4651			−0.663006
$477$			4.67878i			0.214227i
$478$		−	10.3268i		−	0.472339i
$479$	4.32184			0.197470			0.0987349	−	0.995114i	$-0.468520\pi$
$479$	4.32184			0.197470			0.0987349	+	0.995114i	$0.468520\pi$
$480$	4.38465	−	0.938878i	0.200131	−	0.0428537i
$481$	19.0928			0.870558
$482$			9.46248i			0.431004i
$483$			10.5731i			0.481091i
$484$	−23.1196			−1.05089
$485$	−3.36890	−	15.7331i	−0.152974	−	0.714401i
$486$	10.1968			0.462535
$487$		−	24.1218i		−	1.09306i	−0.837439	−	0.546531i	$-0.815948\pi$
$487$		−	24.1218i		−	1.09306i	0.837439	−	0.546531i	$-0.184052\pi$
$488$		−	2.82307i		−	0.127794i
$489$	−41.6673			−1.88426
$490$	−1.07073	−	5.00043i	−0.0483709	−	0.225896i
$491$	29.1609			1.31602			0.658008	−	0.753011i	$-0.271399\pi$
$491$	29.1609			1.31602			0.658008	+	0.753011i	$0.271399\pi$
$492$			6.62473i			0.298666i
$493$			55.8392i			2.51487i
$494$	−10.8472			−0.488038
$495$	13.0442	−	2.79313i	0.586292	−	0.125542i
$496$	1.63097			0.0732325
$497$		−	2.56211i		−	0.114926i
$498$		−	30.6405i		−	1.37303i
$499$	−36.9551			−1.65434			−0.827168	−	0.561954i	$-0.810050\pi$
$499$	−36.9551			−1.65434			−0.827168	+	0.561954i	$0.810050\pi$
$500$	9.01535	−	6.61237i	0.403179	−	0.295714i
$501$	−28.0833			−1.25467
$502$		−	1.73091i		−	0.0772544i
$503$		−	20.6421i		−	0.920385i	−0.887819	−	0.460192i	$-0.847780\pi$
$503$		−	20.6421i		−	0.920385i	0.887819	−	0.460192i	$-0.152220\pi$
$504$	2.21725			0.0987643
$505$	18.9220	−	4.05174i	0.842018	−	0.180300i
$506$	−14.1862			−0.630654
$507$		−	65.3130i		−	2.90065i
$508$			5.74629i			0.254950i
$509$	12.1937			0.540476			0.270238	−	0.962794i	$-0.412898\pi$
$509$	12.1937			0.540476			0.270238	+	0.962794i	$0.412898\pi$
$510$	6.25575	+	29.2149i	0.277009	+	1.29366i
$511$	8.62725			0.381647
$512$			1.00000i			0.0441942i
$513$		−	6.37584i		−	0.281500i
$514$	12.2712			0.541257
$515$	2.06310	+	9.63486i	0.0909110	+	0.424563i
$516$	−25.5004			−1.12259
$517$			7.23895i			0.318369i
$518$			6.14020i			0.269785i
$519$	−39.7733			−1.74585
$520$	14.7601	−	3.16055i	0.647272	−	0.138599i
$521$	3.21524			0.140862			0.0704310	−	0.997517i	$-0.477563\pi$
$521$	3.21524			0.140862			0.0704310	+	0.997517i	$0.477563\pi$
$522$		−	8.55921i		−	0.374627i
$523$		−	0.850486i		−	0.0371892i	−0.999827	−	0.0185946i	$-0.994081\pi$
$523$		−	0.850486i		−	0.0371892i	0.999827	−	0.0185946i	$-0.00591918\pi$
$524$	−4.63792			−0.202609
$525$	19.8588	−	8.91334i	0.866707	−	0.389010i
$526$	3.08230			0.134395
$527$			10.8671i			0.473379i
$528$			11.7135i			0.509764i
$529$	17.1017			0.743550
$530$	−10.0166	+	2.14483i	−0.435091	+	0.0931655i
$531$	−5.22664			−0.226817
$532$		−	3.48842i		−	0.151242i
$533$			22.3009i			0.965958i
$534$	−25.8459			−1.11846
$535$	−0.175208	−	0.818239i	−0.00757492	−	0.0353756i
$536$	5.28369			0.228221
$537$		−	18.7348i		−	0.808468i
$538$		−	21.6437i		−	0.933127i
$539$	13.3585			0.575393
$540$	1.85773	+	8.67579i	0.0799441	+	0.373346i
$541$	−3.39116			−0.145798			−0.0728988	−	0.997339i	$-0.523225\pi$
$541$	−3.39116			−0.145798			−0.0728988	+	0.997339i	$0.523225\pi$
$542$			5.85686i			0.251574i
$543$			14.7757i			0.634087i
$544$	−6.66300			−0.285674
$545$	−40.0967	+	8.58584i	−1.71755	+	0.367777i
$546$	29.3883			1.25770
$547$			28.7907i			1.23100i	0.788137	+	0.615500i	$0.211046\pi$
$547$			28.7907i			1.23100i	−0.788137	+	0.615500i	$0.788954\pi$
$548$			5.10212i			0.217952i
$549$	−2.88327			−0.123055
$550$	11.9593	+	26.6451i	0.509947	+	1.13615i
$551$	−13.4663			−0.573683
$552$			4.87023i			0.207291i
$553$			26.7073i			1.13571i
$554$	−0.238569			−0.0101358
$555$	12.4013	−	2.65547i	0.526405	−	0.112718i
$556$	−10.7091			−0.454169
$557$			19.3872i			0.821460i	0.911757	+	0.410730i	$0.134726\pi$
$557$			19.3872i			0.821460i	−0.911757	+	0.410730i	$0.865274\pi$
$558$		−	1.66575i		−	0.0705167i
$559$	−85.8421			−3.63073
$560$	1.01643	+	4.74680i	0.0429518	+	0.200589i
$561$	−78.0470			−3.29515
$562$		−	25.8471i		−	1.09029i
$563$			26.9603i			1.13624i	0.822945	+	0.568121i	$0.192329\pi$
$563$			26.9603i			1.13624i	−0.822945	+	0.568121i	$0.807671\pi$
$564$	2.48519			0.104645
$565$	2.89865	+	13.5370i	0.121947	+	0.569504i
$566$	6.39123			0.268643
$567$			23.9258i			1.00479i
$568$		−	1.18017i		−	0.0495190i
$569$	−12.0158			−0.503730			−0.251865	−	0.967762i	$-0.581044\pi$
$569$	−12.0158			−0.503730			−0.251865	+	0.967762i	$0.581044\pi$
$570$	−7.04552	+	1.50865i	−0.295104	+	0.0631903i
$571$	−21.2842			−0.890716			−0.445358	−	0.895353i	$-0.646924\pi$
$571$	−21.2842			−0.890716			−0.445358	+	0.895353i	$0.646924\pi$
$572$			39.4312i			1.64870i
$573$			39.4546i			1.64824i
$574$	−7.17190			−0.299349
$575$	4.97244	+	11.0785i	0.207365	+	0.462006i
$576$	1.02133			0.0425553
$577$		−	6.43692i		−	0.267972i	−0.990983	−	0.133986i	$-0.957222\pi$
$577$		−	6.43692i		−	0.267972i	0.990983	−	0.133986i	$-0.0427778\pi$
$578$		−	27.3956i		−	1.13951i
$579$	9.97051			0.414360
$580$	18.3240	−	3.92368i	0.760861	−	0.162922i
$581$	33.1713			1.37618
$582$		−	14.4294i		−	0.598117i
$583$		−	26.7590i		−	1.10824i
$584$	3.97394			0.164443
$585$	−3.22796	−	15.0749i	−0.133460	−	0.623268i
$586$	11.0160			0.455069
$587$		−	26.3841i		−	1.08899i	−0.838765	−	0.544493i	$-0.816722\pi$
$587$		−	26.3841i		−	1.08899i	0.838765	−	0.544493i	$-0.183278\pi$
$588$		−	4.58608i		−	0.189127i
$589$	−2.62073			−0.107985
$590$	−2.39598	−	11.1894i	−0.0986408	−	0.460662i
$591$	44.0787			1.81315
$592$			2.82834i			0.116244i
$593$		−	39.7404i		−	1.63194i	−0.578092	−	0.815972i	$-0.696202\pi$
$593$		−	39.7404i		−	1.63194i	0.578092	−	0.815972i	$-0.303798\pi$
$594$	−23.1772			−0.950971
$595$	−31.6279	+	6.77244i	−1.29662	+	0.277643i
$596$	4.84470			0.198447
$597$			29.1649i			1.19364i
$598$			16.3947i			0.670429i
$599$	−12.3856			−0.506061			−0.253030	−	0.967458i	$-0.581427\pi$
$599$	−12.3856			−0.506061			−0.253030	+	0.967458i	$0.581427\pi$
$600$	9.14747	−	4.10572i	0.373444	−	0.167615i
$601$	−35.4437			−1.44578			−0.722889	−	0.690964i	$-0.757186\pi$
$601$	−35.4437			−1.44578			−0.722889	+	0.690964i	$0.757186\pi$
$602$		−	27.6066i		−	1.12516i
$603$		−	5.39638i		−	0.219757i
$604$	−1.00000			−0.0406894
$605$	−50.5510	+	10.8244i	−2.05519	+	0.440075i
$606$	17.3541			0.704961
$607$			3.88739i			0.157784i	0.996883	+	0.0788921i	$0.0251383\pi$
$607$			3.88739i			0.157784i	−0.996883	+	0.0788921i	$0.974862\pi$
$608$		−	1.60686i		−	0.0651668i
$609$	36.4842			1.47841
$610$	−1.32174	−	6.17265i	−0.0535157	−	0.249923i
$611$	8.36590			0.338448
$612$			6.80510i			0.275080i
$613$		−	42.0739i		−	1.69935i	−0.527308	−	0.849674i	$-0.676798\pi$
$613$		−	42.0739i		−	1.69935i	0.527308	−	0.849674i	$-0.323202\pi$
$614$	−8.74181			−0.352791
$615$	3.10165	+	14.4850i	0.125071	+	0.584091i
$616$	−12.6810			−0.510931
$617$		−	40.1727i		−	1.61729i	−0.588295	−	0.808647i	$-0.700200\pi$
$617$		−	40.1727i		−	1.61729i	0.588295	−	0.808647i	$-0.299800\pi$
$618$			8.83649i			0.355456i
$619$	23.8946			0.960405			0.480202	−	0.877158i	$-0.340563\pi$
$619$	23.8946			0.960405			0.480202	+	0.877158i	$0.340563\pi$
$620$	3.56611	−	0.763606i	0.143218	−	0.0306672i
$621$	−9.63660			−0.386703
$622$			21.1421i			0.847722i
$623$		−	27.9807i		−	1.12102i
$624$	13.5370			0.541915
$625$	16.6162	−	18.6789i	0.664649	−	0.747156i
$626$	−16.3617			−0.653946
$627$		−	18.8220i		−	0.751676i
$628$		−	13.2890i		−	0.530288i
$629$	−18.8452			−0.751409
$630$	4.84803	−	1.03810i	0.193150	−	0.0413590i
$631$	−20.7451			−0.825851			−0.412925	−	0.910765i	$-0.635493\pi$
$631$	−20.7451			−0.825851			−0.412925	+	0.910765i	$0.635493\pi$
$632$			12.3021i			0.489351i
$633$			40.2056i			1.59803i
$634$	20.3398			0.807798
$635$	2.69037	+	12.5643i	0.106764	+	0.498598i
$636$	−9.18656			−0.364271
$637$		−	15.4382i		−	0.611682i
$638$			48.9521i			1.93803i
$639$	−1.20534			−0.0476826
$640$	0.468193	+	2.18650i	0.0185069	+	0.0864291i
$641$	−6.78473			−0.267981			−0.133990	−	0.990983i	$-0.542779\pi$
$641$	−6.78473			−0.267981			−0.133990	+	0.990983i	$0.542779\pi$
$642$		−	0.750438i		−	0.0296174i
$643$		−	6.81268i		−	0.268666i	−0.990936	−	0.134333i	$-0.957111\pi$
$643$		−	6.81268i		−	0.268666i	0.990936	−	0.134333i	$-0.0428891\pi$
$644$	−5.27249			−0.207765
$645$	−55.7566	+	11.9391i	−2.19541	+	0.470101i
$646$	10.7065			0.421242
$647$			9.28414i			0.364997i	0.983206	+	0.182499i	$0.0584185\pi$
$647$			9.28414i			0.364997i	−0.983206	+	0.182499i	$0.941581\pi$
$648$			11.0209i			0.432941i
$649$	29.8923			1.17338
$650$	30.7932	−	13.8211i	1.20781	−	0.542109i
$651$	7.10036			0.278285
$652$		−	20.7783i		−	0.813742i
$653$			30.4451i			1.19141i	0.803204	+	0.595704i	$0.203127\pi$
$653$			30.4451i			1.19141i	−0.803204	+	0.595704i	$0.796873\pi$
$654$	−36.7742			−1.43798
$655$	−10.1408	+	2.17144i	−0.396235	+	0.0848453i
$656$	−3.30357			−0.128983
$657$		−	4.05869i		−	0.158345i
$658$			2.69045i			0.104885i
$659$	47.4001			1.84644			0.923222	−	0.384266i	$-0.125546\pi$
$659$	47.4001			1.84644			0.923222	+	0.384266i	$0.125546\pi$
$660$	5.48417	+	25.6116i	0.213471	+	0.996929i
$661$	−19.5130			−0.758969			−0.379485	−	0.925198i	$-0.623899\pi$
$661$	−19.5130			−0.758969			−0.379485	+	0.925198i	$0.623899\pi$
$662$		−	21.7967i		−	0.847153i
$663$			90.1972i			3.50297i
$664$	15.2796			0.592962
$665$	−1.63325	−	7.62745i	−0.0633349	−	0.295780i
$666$	2.88866			0.111933
$667$			20.3533i			0.788082i
$668$		−	14.0044i		−	0.541845i
$669$	42.9893			1.66206
$670$	11.5528	−	2.47379i	0.446324	−	0.0955707i
$671$	16.4901			0.636593
$672$			4.35347i			0.167939i
$673$			13.6238i			0.525160i	0.964910	+	0.262580i	$0.0845734\pi$
$673$			13.6238i			0.525160i	−0.964910	+	0.262580i	$0.915427\pi$
$674$	−0.0111359			−0.000428938
$675$	8.12388	+	18.0999i	0.312688	+	0.696664i
$676$	32.5698			1.25268
$677$			44.5735i			1.71310i	0.516065	+	0.856550i	$0.327396\pi$
$677$			44.5735i			1.71310i	−0.516065	+	0.856550i	$0.672604\pi$
$678$			12.4153i			0.476805i
$679$	15.6212			0.599486
$680$	−14.5687	+	3.11957i	−0.558683	+	0.119630i
$681$	−45.1811			−1.73134
$682$			9.52678i			0.364799i
$683$			41.4737i			1.58695i	0.608606	+	0.793473i	$0.291729\pi$
$683$			41.4737i			1.58695i	−0.608606	+	0.793473i	$0.708271\pi$
$684$	−1.64113			−0.0627501
$685$	2.38878	+	11.1558i	0.0912704	+	0.426241i
$686$	20.1616			0.769772
$687$			19.9523i			0.761228i
$688$		−	12.7163i		−	0.484805i
$689$	−30.9248			−1.17814
$690$	2.28021	+	10.6488i	0.0868060	+	0.405392i
$691$	−18.6613			−0.709911			−0.354956	−	0.934883i	$-0.615504\pi$
$691$	−18.6613			−0.709911			−0.354956	+	0.934883i	$0.615504\pi$
$692$		−	19.8339i		−	0.753970i
$693$			12.9514i			0.491983i
$694$	−1.36755			−0.0519114
$695$	−23.4156	+	5.01394i	−0.888203	+	0.190190i
$696$	16.8056			0.637015
$697$		−	22.0117i		−	0.833752i
$698$		−	21.6787i		−	0.820551i
$699$	37.1716			1.40596
$700$	4.44484	+	9.90301i	0.167999	+	0.374299i
$701$	−30.9886			−1.17042			−0.585211	−	0.810881i	$-0.698988\pi$
$701$	−30.9886			−1.17042			−0.585211	+	0.810881i	$0.698988\pi$
$702$			26.7854i			1.01095i
$703$		−	4.54475i		−	0.171409i
$704$	−5.84119			−0.220148
$705$	5.43387	−	1.16355i	0.204651	−	0.0438217i
$706$	5.23065			0.196858
$707$			18.7875i			0.706575i
$708$		−	10.2623i		−	0.385679i
$709$	−14.5463			−0.546297			−0.273149	−	0.961972i	$-0.588065\pi$
$709$	−14.5463			−0.546297			−0.273149	+	0.961972i	$0.588065\pi$
$710$	−0.552549	−	2.58045i	−0.0207368	−	0.0968427i
$711$	12.5645			0.471204
$712$		−	12.8886i		−	0.483022i
$713$			3.96104i			0.148342i
$714$	−29.0072			−1.08557
$715$	18.4614	+	86.2165i	0.690418	+	3.22431i
$716$	9.34255			0.349147
$717$		−	20.7087i		−	0.773379i
$718$			6.18172i			0.230700i
$719$	−51.3573			−1.91530			−0.957651	−	0.287930i	$-0.907033\pi$
$719$	−51.3573			−1.91530			−0.957651	+	0.287930i	$0.907033\pi$
$720$	2.23313	−	0.478178i	0.0832240	−	0.0178206i
$721$	−9.56635			−0.356269
$722$		−	16.4180i		−	0.611015i
$723$			18.9753i			0.705701i
$724$	−7.36824			−0.273838
$725$	38.2284	−	17.1583i	1.41977	−	0.637243i
$726$	−46.3622			−1.72066
$727$			21.3938i			0.793452i	0.917937	+	0.396726i	$0.129854\pi$
$727$			21.3938i			0.793452i	−0.917937	+	0.396726i	$0.870146\pi$
$728$			14.6551i			0.543155i
$729$	−12.6148			−0.467214
$730$	8.68904	−	1.86057i	0.321596	−	0.0688628i
$731$	84.7289			3.13381
$732$		−	5.66117i		−	0.209243i
$733$		−	42.0285i		−	1.55236i	−0.630512	−	0.776179i	$-0.717155\pi$
$733$		−	42.0285i		−	1.55236i	0.630512	−	0.776179i	$-0.282845\pi$
$734$	−14.1447			−0.522090
$735$	−2.14717	−	10.0275i	−0.0791996	−	0.369869i
$736$	−2.42865			−0.0895212
$737$			30.8631i			1.13686i
$738$			3.37402i			0.124199i
$739$	49.3921			1.81692			0.908459	−	0.417975i	$-0.137260\pi$
$739$	49.3921			1.81692			0.908459	+	0.417975i	$0.137260\pi$
$740$	1.32421	+	6.18418i	0.0486789	+	0.227335i
$741$	−21.7521			−0.799084
$742$		−	9.94533i		−	0.365104i
$743$			23.1243i			0.848347i	0.905581	+	0.424173i	$0.139435\pi$
$743$			23.1243i			0.848347i	−0.905581	+	0.424173i	$0.860565\pi$
$744$	3.27061			0.119907
$745$	10.5930	−	2.26826i	0.388096	−	0.0831024i
$746$	−16.1041			−0.589613
$747$		−	15.6054i		−	0.570973i
$748$		−	38.9199i		−	1.42305i
$749$	0.812421			0.0296852
$750$	18.0787	−	13.2600i	0.660141	−	0.484185i
$751$	−14.2424			−0.519712			−0.259856	−	0.965647i	$-0.583675\pi$
$751$	−14.2424			−0.519712			−0.259856	+	0.965647i	$0.583675\pi$
$752$			1.23929i			0.0451924i
$753$		−	3.47104i		−	0.126492i
$754$	56.5728			2.06026
$755$	−2.18650	+	0.468193i	−0.0795750	+	0.0170393i
$756$	−8.61410			−0.313292
$757$			32.3970i			1.17749i	0.808319	+	0.588744i	$0.200377\pi$
$757$			32.3970i			1.17749i	−0.808319	+	0.588744i	$0.799623\pi$
$758$		−	0.381999i		−	0.0138748i
$759$	−28.4480			−1.03260
$760$	−0.752321	−	3.51341i	−0.0272895	−	0.127445i
$761$	−48.6975			−1.76528			−0.882641	−	0.470048i	$-0.844237\pi$
$761$	−48.6975			−1.76528			−0.882641	+	0.470048i	$0.844237\pi$
$762$			11.5232i			0.417440i
$763$		−	39.8115i		−	1.44127i
$764$	−19.6749			−0.711813
$765$	3.18610	+	14.8794i	0.115194	+	0.537965i
$766$	11.8757			0.429087
$767$		−	34.5459i		−	1.24738i
$768$			2.00532i			0.0723609i
$769$	23.2303			0.837706			0.418853	−	0.908054i	$-0.362432\pi$
$769$	23.2303			0.837706			0.418853	+	0.908054i	$0.362432\pi$
$770$	−27.7270	+	5.93714i	−0.999211	+	0.213960i
$771$	24.6076			0.886223
$772$			4.97202i			0.178947i
$773$			4.24863i			0.152813i	0.997077	+	0.0764063i	$0.0243446\pi$
$773$			4.24863i			0.152813i	−0.997077	+	0.0764063i	$0.975655\pi$
$774$	−12.9875			−0.466827
$775$	7.43980	−	3.33925i	0.267245	−	0.119950i
$776$	7.19553			0.258305
$777$			12.3131i			0.441730i
$778$		−	25.1152i		−	0.900422i
$779$	5.30838			0.190192
$780$	29.5987	−	6.33794i	1.05980	−	0.226935i
$781$	6.89363			0.246673
$782$		−	16.1821i		−	0.578671i
$783$			33.2528i			1.18836i
$784$	2.28695			0.0816769
$785$	−6.22180	−	29.0564i	−0.222065	−	1.03707i
$786$	−9.30054			−0.331739
$787$		−	29.6610i		−	1.05730i	−0.848840	−	0.528650i	$-0.822698\pi$
$787$		−	29.6610i		−	1.05730i	0.848840	−	0.528650i	$-0.177302\pi$
$788$			21.9808i			0.783034i
$789$	6.18101			0.220050
$790$	5.75975	+	26.8986i	0.204923	+	0.957008i
$791$	−13.4407			−0.477896
$792$			5.96577i			0.211984i
$793$		−	19.0572i		−	0.676742i
$794$	27.6815			0.982379
$795$	−20.0864	+	4.30108i	−0.712393	+	0.152544i
$796$	−14.5437			−0.515489
$797$		−	29.7577i		−	1.05407i	−0.849843	−	0.527037i	$-0.823303\pi$
$797$		−	29.7577i		−	1.05407i	0.849843	−	0.527037i	$-0.176697\pi$
$798$		−	6.99542i		−	0.247635i
$799$	−8.25741			−0.292126
$800$	2.04741	+	4.56159i	0.0723869	+	0.161277i
$801$	−13.1635			−0.465110
$802$		−	26.8220i		−	0.947119i
$803$			23.2126i			0.819154i
$804$	10.5955			0.373675
$805$	−11.5283	+	2.46854i	−0.406320	+	0.0870047i
$806$	11.0099			0.387807
$807$		−	43.4027i		−	1.52785i
$808$			8.65400i			0.304447i
$809$	1.36506			0.0479931			0.0239965	−	0.999712i	$-0.492361\pi$
$809$	1.36506			0.0479931			0.0239965	+	0.999712i	$0.492361\pi$
$810$	5.15989	+	24.0972i	0.181300	+	0.846688i
$811$	−38.0739			−1.33696			−0.668478	−	0.743732i	$-0.733054\pi$
$811$	−38.0739			−1.33696			−0.668478	+	0.743732i	$0.733054\pi$
$812$			18.1937i			0.638473i
$813$			11.7449i			0.411912i
$814$	−16.5209			−0.579057
$815$	−9.72826	−	45.4318i	−0.340766	−	1.59141i
$816$	−13.3615			−0.467745
$817$			20.4334i			0.714873i
$818$		−	22.0078i		−	0.769484i
$819$	14.9677			0.523012
$820$	−7.22326	+	1.54671i	−0.252247	+	0.0540133i
$821$	44.0762			1.53827			0.769135	−	0.639087i	$-0.220688\pi$
$821$	44.0762			1.53827			0.769135	+	0.639087i	$0.220688\pi$
$822$			10.2314i			0.356861i
$823$			2.45591i			0.0856075i	0.999083	+	0.0428038i	$0.0136290\pi$
$823$			2.45591i			0.0856075i	−0.999083	+	0.0428038i	$0.986371\pi$
$824$	−4.40652			−0.153508
$825$	23.9823	+	53.4322i	0.834957	+	1.86027i
$826$	11.1099			0.386562
$827$			48.4670i			1.68536i	0.538412	+	0.842681i	$0.319024\pi$
$827$			48.4670i			1.68536i	−0.538412	+	0.842681i	$0.680976\pi$
$828$			2.48044i			0.0862014i
$829$	−46.2142			−1.60509			−0.802543	−	0.596594i	$-0.796520\pi$
$829$	−46.2142			−1.60509			−0.802543	+	0.596594i	$0.796520\pi$
$830$	33.4088	−	7.15378i	1.15964	−	0.248311i
$831$	−0.478408			−0.0165958
$832$			6.75054i			0.234033i
$833$			15.2380i			0.527964i
$834$	−21.4753			−0.743629
$835$	−6.55675	−	30.6206i	−0.226906	−	1.05967i
$836$	9.38599			0.324621
$837$			6.47148i			0.223687i
$838$			11.2304i			0.387947i
$839$	−34.2715			−1.18318			−0.591592	−	0.806238i	$-0.701500\pi$
$839$	−34.2715			−1.18318			−0.591592	+	0.806238i	$0.701500\pi$
$840$	2.03826	+	9.51888i	0.0703268	+	0.328432i
$841$	41.2326			1.42181
$842$			3.24051i			0.111675i
$843$		−	51.8318i		−	1.78518i
$844$	−20.0494			−0.690130
$845$	71.2139	−	15.2489i	2.44983	−	0.524579i
$846$	1.26572			0.0435164
$847$		−	50.1915i		−	1.72460i
$848$		−	4.58108i		−	0.157315i
$849$	12.8165			0.439861
$850$	−30.3939	+	13.6419i	−1.04250	+	0.467913i
$851$	−6.86905			−0.235468
$852$		−	2.36663i		−	0.0810795i
$853$			29.3711i			1.00565i	0.864389	+	0.502824i	$0.167706\pi$
$853$			29.3711i			1.00565i	−0.864389	+	0.502824i	$0.832294\pi$
$854$	6.12876			0.209722
$855$	−3.58833	+	0.768365i	−0.122718	+	0.0262775i
$856$	0.374223			0.0127907
$857$			31.7951i			1.08610i	0.839700	+	0.543051i	$0.182731\pi$
$857$			31.7951i			1.08610i	−0.839700	+	0.543051i	$0.817269\pi$
$858$			79.0724i			2.69949i
$859$	−8.83827			−0.301558			−0.150779	−	0.988568i	$-0.548178\pi$
$859$	−8.83827			−0.301558			−0.150779	+	0.988568i	$0.548178\pi$
$860$	−5.95369	−	27.8043i	−0.203019	−	0.948118i
$861$	−14.3820			−0.490137
$862$			1.56276i			0.0532278i
$863$			6.60122i			0.224708i	0.993668	+	0.112354i	$0.0358391\pi$
$863$			6.60122i			0.224708i	−0.993668	+	0.112354i	$0.964161\pi$
$864$	−3.96788			−0.134990
$865$	−9.28607	−	43.3668i	−0.315736	−	1.47451i
$866$	24.4974			0.832456
$867$		−	54.9370i		−	1.86576i
$868$			3.54075i			0.120181i
$869$	−71.8589			−2.43765
$870$	36.7455	−	7.86826i	1.24579	−	0.266759i
$871$	35.6678			1.20856
$872$		−	18.3383i		−	0.621012i
$873$		−	7.34899i		−	0.248726i
$874$	3.90250			0.132004
$875$	14.3552	+	19.5719i	0.485293	+	0.661652i
$876$	7.96905			0.269249
$877$			39.0069i			1.31717i	0.752507	+	0.658584i	$0.228844\pi$
$877$			39.0069i			1.31717i	−0.752507	+	0.658584i	$0.771156\pi$
$878$			21.0172i			0.709295i
$879$	22.0907			0.745102
$880$	−12.7718	+	2.73480i	−0.430537	+	0.0921903i
$881$	9.22344			0.310746			0.155373	−	0.987856i	$-0.450342\pi$
$881$	9.22344			0.310746			0.155373	+	0.987856i	$0.450342\pi$
$882$		−	2.33572i		−	0.0786479i
$883$		−	7.16217i		−	0.241026i	−0.992712	−	0.120513i	$-0.961546\pi$
$883$		−	7.16217i		−	0.241026i	0.992712	−	0.120513i	$-0.0384540\pi$
$884$	−44.9788			−1.51280
$885$	−4.80471	−	22.4385i	−0.161509	−	0.754260i
$886$	−15.5229			−0.521501
$887$		−	40.6125i		−	1.36363i	−0.731523	−	0.681817i	$-0.761190\pi$
$887$		−	40.6125i		−	1.36363i	0.731523	−	0.681817i	$-0.238810\pi$
$888$			5.67174i			0.190331i
$889$	−12.4749			−0.418396
$890$	−6.03437	−	28.1810i	−0.202272	−	0.944631i
$891$	−64.3751			−2.15665
$892$			21.4376i			0.717784i
$893$		−	1.99137i		−	0.0666387i
$894$	9.71520			0.324925
$895$	20.4275	−	4.37411i	0.682816	−	0.146211i
$896$	−2.17096			−0.0725265
$897$			32.8767i			1.09772i
$898$			21.2796i			0.710111i
$899$	13.6683			0.455863
$900$	4.65887	−	2.09107i	0.155296	−	0.0697024i
$901$	30.5238			1.01689
$902$		−	19.2968i		−	0.642513i
$903$		−	55.3602i		−	1.84227i
$904$	−6.19114			−0.205914
$905$	−16.1107	+	3.44976i	−0.535537	+	0.114674i
$906$	−2.00532			−0.0666224
$907$			42.8468i			1.42271i	0.702835	+	0.711353i	$0.251917\pi$
$907$			42.8468i			1.42271i	−0.702835	+	0.711353i	$0.748083\pi$
$908$		−	22.5305i		−	0.747702i
$909$	8.83856			0.293156
$910$	6.86142	+	32.0435i	0.227454	+	1.06223i
$911$	41.4400			1.37297			0.686484	−	0.727145i	$-0.259153\pi$
$911$	41.4400			1.37297			0.686484	+	0.727145i	$0.259153\pi$
$912$		−	3.22228i		−	0.106700i
$913$			89.2509i			2.95377i
$914$	37.7848			1.24981
$915$	−2.65052	−	12.3782i	−0.0876234	−	0.409209i
$916$	−9.94967			−0.328746
$917$		−	10.0687i		−	0.332499i
$918$		−	26.4380i		−	0.872584i
$919$	22.8916			0.755123			0.377562	−	0.925984i	$-0.376763\pi$
$919$	22.8916			0.755123			0.377562	+	0.925984i	$0.376763\pi$
$920$	−5.31025	+	1.13708i	−0.175074	+	0.0374883i
$921$	−17.5302			−0.577638
$922$			29.3240i			0.965736i
$923$		−	7.96681i		−	0.262231i
$924$	−25.4295			−0.836568
$925$	5.79077	+	12.9017i	0.190399	+	0.424207i
$926$	15.1006			0.496237
$927$			4.50049i			0.147816i
$928$			8.38049i			0.275103i
$929$	18.9988			0.623331			0.311665	−	0.950192i	$-0.399113\pi$
$929$	18.9988			0.623331			0.311665	+	0.950192i	$0.399113\pi$
$930$	7.15121	−	1.53128i	0.234497	−	0.0502126i
$931$	−3.67481			−0.120437
$932$			18.5365i			0.607182i
$933$			42.3968i			1.38801i
$934$	6.33706			0.207355
$935$	−18.2220	−	85.0984i	−0.595923	−	2.78302i
$936$	6.89450			0.225354
$937$			39.5258i			1.29125i	0.763654	+	0.645626i	$0.223404\pi$
$937$			39.5258i			1.29125i	−0.763654	+	0.645626i	$0.776596\pi$
$938$			11.4707i			0.374530i
$939$	−32.8106			−1.07073
$940$	0.580228	+	2.70972i	0.0189250	+	0.0883813i
$941$	−43.9906			−1.43405			−0.717027	−	0.697046i	$-0.754498\pi$
$941$	−43.9906			−1.43405			−0.717027	+	0.697046i	$0.754498\pi$
$942$		−	26.6487i		−	0.868261i
$943$		−	8.02321i		−	0.261272i
$944$	5.11750			0.166561
$945$	−18.8347	+	4.03306i	−0.612694	+	0.131195i
$946$	74.2785			2.41500
$947$		−	50.1817i		−	1.63068i	−0.578979	−	0.815342i	$-0.696549\pi$
$947$		−	50.1817i		−	1.63068i	0.578979	−	0.815342i	$-0.303451\pi$
$948$			24.6697i			0.801234i
$949$	26.8263			0.870817
$950$	−3.28990	−	7.32984i	−0.106739	−	0.237812i
$951$	40.7879			1.32264
$952$		−	14.4651i		−	0.468816i
$953$		−	31.0453i		−	1.00566i	−0.864386	−	0.502828i	$-0.832293\pi$
$953$		−	31.0453i		−	1.00566i	0.864386	−	0.502828i	$-0.167707\pi$
$954$	−4.67878			−0.151481
$955$	−43.0192	+	9.21165i	−1.39207	+	0.298082i
$956$	10.3268			0.333994
$957$			98.1648i			3.17322i
$958$			4.32184i			0.139632i
$959$	−11.0765			−0.357678
$960$	0.938878	+	4.38465i	0.0303022	+	0.141514i
$961$	−28.3400			−0.914192
$962$			19.0928i			0.615578i
$963$		−	0.382204i		−	0.0123163i
$964$	−9.46248			−0.304766
$965$	2.32786	+	10.8713i	0.0749365	+	0.349961i
$966$	−10.5731			−0.340183
$967$			15.7277i			0.505769i	0.967496	+	0.252884i	$0.0813792\pi$
$967$			15.7277i			0.505769i	−0.967496	+	0.252884i	$0.918621\pi$
$968$		−	23.1196i		−	0.743091i
$969$	21.4700			0.689717
$970$	15.7331	−	3.36890i	0.505158	−	0.108169i
$971$	−30.5271			−0.979661			−0.489830	−	0.871818i	$-0.662941\pi$
$971$	−30.5271			−0.979661			−0.489830	+	0.871818i	$0.662941\pi$
$972$			10.1968i			0.327062i
$973$		−	23.2491i		−	0.745331i
$974$	24.1218			0.772912
$975$	61.7504	−	27.7158i	1.97759	−	0.887617i
$976$	2.82307			0.0903642
$977$		−	39.4721i		−	1.26283i	−0.775447	−	0.631413i	$-0.782475\pi$
$977$		−	39.4721i		−	1.26283i	0.775447	−	0.631413i	$-0.217525\pi$
$978$		−	41.6673i		−	1.33237i
$979$	75.2850			2.40612
$980$	5.00043	−	1.07073i	0.159733	−	0.0342034i
$981$	−18.7293			−0.597982
$982$			29.1609i			0.930563i
$983$		−	26.5056i		−	0.845398i	−0.906270	−	0.422699i	$-0.861083\pi$
$983$		−	26.5056i		−	0.845398i	0.906270	−	0.422699i	$-0.138917\pi$
$984$	−6.62473			−0.211189
$985$	10.2913	+	48.0611i	0.327907	+	1.53135i
$986$	−55.8392			−1.77828
$987$			5.39523i			0.171732i
$988$		−	10.8472i		−	0.345095i
$989$	30.8835			0.982039
$990$	2.79313	+	13.0442i	0.0887714	+	0.414571i
$991$	−3.03267			−0.0963358			−0.0481679	−	0.998839i	$-0.515338\pi$
$991$	−3.03267			−0.0963358			−0.0481679	+	0.998839i	$0.515338\pi$
$992$			1.63097i			0.0517832i
$993$		−	43.7095i		−	1.38708i
$994$	2.56211			0.0812651
$995$	−31.7999	+	6.80928i	−1.00813	+	0.215869i
$996$	30.6405			0.970881
$997$			4.98948i			0.158018i	0.996874	+	0.0790092i	$0.0251757\pi$
$997$			4.98948i			0.158018i	−0.996874	+	0.0790092i	$0.974824\pi$
$998$		−	36.9551i		−	1.16979i
$999$	−11.2225			−0.355065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1510.2.b.d.1209.35	yes	38
5.2	odd	4		7550.2.a.bj.1.16		19
5.3	odd	4		7550.2.a.bk.1.4		19
5.4	even	2	inner	1510.2.b.d.1209.4	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1510.2.b.d.1209.4	✓	38	5.4	even	2	inner
1510.2.b.d.1209.35	yes	38	1.1	even	1	trivial
7550.2.a.bj.1.16		19	5.2	odd	4
7550.2.a.bk.1.4		19	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1510 = 2 \cdot 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1510.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.00532i q^{3} -1.00000 q^{4} +(-2.18650 + 0.468193i) q^{5} -2.00532 q^{6} -2.17096i q^{7} -1.00000i q^{8} -1.02133 q^{9} +(-0.468193 - 2.18650i) q^{10} +5.84119 q^{11} -2.00532i q^{12} -6.75054i q^{13} +2.17096 q^{14} +(-0.938878 - 4.38465i) q^{15} +1.00000 q^{16} +6.66300i q^{17} -1.02133i q^{18} -1.60686 q^{19} +(2.18650 - 0.468193i) q^{20} +4.35347 q^{21} +5.84119i q^{22} +2.42865i q^{23} +2.00532 q^{24} +(4.56159 - 2.04741i) q^{25} +6.75054 q^{26} +3.96788i q^{27} +2.17096i q^{28} +8.38049 q^{29} +(4.38465 - 0.938878i) q^{30} +1.63097 q^{31} +1.00000i q^{32} +11.7135i q^{33} -6.66300 q^{34} +(1.01643 + 4.74680i) q^{35} +1.02133 q^{36} +2.82834i q^{37} -1.60686i q^{38} +13.5370 q^{39} +(0.468193 + 2.18650i) q^{40} -3.30357 q^{41} +4.35347i q^{42} -12.7163i q^{43} -5.84119 q^{44} +(2.23313 - 0.478178i) q^{45} -2.42865 q^{46} +1.23929i q^{47} +2.00532i q^{48} +2.28695 q^{49} +(2.04741 + 4.56159i) q^{50} -13.3615 q^{51} +6.75054i q^{52} -4.58108i q^{53} -3.96788 q^{54} +(-12.7718 + 2.73480i) q^{55} -2.17096 q^{56} -3.22228i q^{57} +8.38049i q^{58} +5.11750 q^{59} +(0.938878 + 4.38465i) q^{60} +2.82307 q^{61} +1.63097i q^{62} +2.21725i q^{63} -1.00000 q^{64} +(3.16055 + 14.7601i) q^{65} -11.7135 q^{66} +5.28369i q^{67} -6.66300i q^{68} -4.87023 q^{69} +(-4.74680 + 1.01643i) q^{70} +1.18017 q^{71} +1.02133i q^{72} +3.97394i q^{73} -2.82834 q^{74} +(4.10572 + 9.14747i) q^{75} +1.60686 q^{76} -12.6810i q^{77} +13.5370i q^{78} -12.3021 q^{79} +(-2.18650 + 0.468193i) q^{80} -11.0209 q^{81} -3.30357i q^{82} +15.2796i q^{83} -4.35347 q^{84} +(-3.11957 - 14.5687i) q^{85} +12.7163 q^{86} +16.8056i q^{87} -5.84119i q^{88} +12.8886 q^{89} +(0.478178 + 2.23313i) q^{90} -14.6551 q^{91} -2.42865i q^{92} +3.27061i q^{93} -1.23929 q^{94} +(3.51341 - 0.752321i) q^{95} -2.00532 q^{96} +7.19553i q^{97} +2.28695i q^{98} -5.96577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 38 q^{4} + 12 q^{6} - 42 q^{9} + 2 q^{10} + 28 q^{11} - 24 q^{14} - 6 q^{15} + 38 q^{16} - 20 q^{19} + 28 q^{21} - 12 q^{24} - 6 q^{25} + 44 q^{26} - 24 q^{29} + 2 q^{30} + 36 q^{31} - 36 q^{34}+ \cdots - 24 q^{99}+O(q^{100}) \) 38 * q - 38 * q^4 + 12 * q^6 - 42 * q^9 + 2 * q^10 + 28 * q^11 - 24 * q^14 - 6 * q^15 + 38 * q^16 - 20 * q^19 + 28 * q^21 - 12 * q^24 - 6 * q^25 + 44 * q^26 - 24 * q^29 + 2 * q^30 + 36 * q^31 - 36 * q^34 - 4 * q^35 + 42 * q^36 - 2 * q^40 - 4 * q^41 - 28 * q^44 - 8 * q^45 + 16 * q^46 - 10 * q^49 + 8 * q^50 - 48 * q^54 - 40 * q^55 + 24 * q^56 - 56 * q^59 + 6 * q^60 + 20 * q^61 - 38 * q^64 + 40 * q^66 + 100 * q^69 + 8 * q^70 + 52 * q^71 - 64 * q^74 - 60 * q^75 + 20 * q^76 + 4 * q^79 + 54 * q^81 - 28 * q^84 - 68 * q^85 + 68 * q^86 + 48 * q^89 - 6 * q^90 + 52 * q^91 - 44 * q^94 - 52 * q^95 + 12 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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