LMFDB - Embedded newform 310.2.b.b.249.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(249,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, 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("310.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2058981376.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 18x^{4} - 34x^{3} + 32x^{2} - 8x + 1 $ x^8 - 2x^7 + 2x^6 + 18x^4 - 34x^3 + 32x^2 - 8x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			249.4
Root			$0.769222 + 0.769222i$ of defining polynomial
Character	$\chi$	$=$	310.249
Dual form			310.2.b.b.249.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +2.51658i q^{3} -1.00000 q^{4} +(1.93581 + 1.11922i) q^{5} +2.51658 q^{6} -0.461555i q^{7} +1.00000i q^{8} -3.33317 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +2.51658i q^{3} -1.00000 q^{4} +(1.93581 + 1.11922i) q^{5} +2.51658 q^{6} -0.461555i q^{7} +1.00000i q^{8} -3.33317 q^{9} +(1.11922 - 1.93581i) q^{10} +0.183406 q^{11} -2.51658i q^{12} +3.35504i q^{13} -0.461555 q^{14} +(-2.81659 + 4.87162i) q^{15} +1.00000 q^{16} +2.33317i q^{17} +3.33317i q^{18} -2.79473 q^{19} +(-1.93581 - 1.11922i) q^{20} +1.16154 q^{21} -0.183406i q^{22} -1.25628i q^{23} -2.51658 q^{24} +(2.49472 + 4.33317i) q^{25} +3.35504 q^{26} -0.838459i q^{27} +0.461555i q^{28} +4.61132 q^{29} +(4.87162 + 2.81659i) q^{30} +1.00000 q^{31} -1.00000i q^{32} +0.461555i q^{33} +2.33317 q^{34} +(0.516580 - 0.893483i) q^{35} +3.33317 q^{36} -6.51658i q^{37} +2.79473i q^{38} -8.44322 q^{39} +(-1.11922 + 1.93581i) q^{40} +0.376903 q^{41} -1.16154i q^{42} -9.42136i q^{43} -0.183406 q^{44} +(-6.45239 - 3.73054i) q^{45} -1.25628 q^{46} -2.13847i q^{47} +2.51658i q^{48} +6.78697 q^{49} +(4.33317 - 2.49472i) q^{50} -5.87162 q^{51} -3.35504i q^{52} -11.0983i q^{53} -0.838459 q^{54} +(0.355039 + 0.205271i) q^{55} +0.461555 q^{56} -7.03316i q^{57} -4.61132i q^{58} -10.8201 q^{59} +(2.81659 - 4.87162i) q^{60} +12.3546 q^{61} -1.00000i q^{62} +1.53844i q^{63} -1.00000 q^{64} +(-3.75501 + 6.49472i) q^{65} +0.461555 q^{66} -1.80530i q^{67} -2.33317i q^{68} +3.16154 q^{69} +(-0.893483 - 0.516580i) q^{70} -5.18694 q^{71} -3.33317i q^{72} +11.5996i q^{73} -6.51658 q^{74} +(-10.9048 + 6.27815i) q^{75} +2.79473 q^{76} -0.0846520i q^{77} +8.44322i q^{78} +7.03316 q^{79} +(1.93581 + 1.11922i) q^{80} -7.88947 q^{81} -0.376903i q^{82} -6.70607i q^{83} -1.16154 q^{84} +(-2.61132 + 4.51658i) q^{85} -9.42136 q^{86} +11.6048i q^{87} +0.183406i q^{88} +12.8558 q^{89} +(-3.73054 + 6.45239i) q^{90} +1.54854 q^{91} +1.25628i q^{92} +2.51658i q^{93} -2.13847 q^{94} +(-5.41006 - 3.12790i) q^{95} +2.51658 q^{96} -12.3384i q^{97} -6.78697i q^{98} -0.611324 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6}+O(q^{10}) $ 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6	$ 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{10} + 12 q^{11} - 12 q^{14} - 12 q^{15} + 8 q^{16} - 4 q^{19} + 2 q^{20} + 12 q^{21} - 4 q^{24} - 4 q^{25} + 8 q^{26} + 8 q^{29} + 4 q^{30} + 8 q^{31} - 8 q^{34} - 12 q^{35} + 8 q^{39} - 2 q^{40} - 8 q^{41} - 12 q^{44} - 18 q^{45} + 8 q^{50} - 12 q^{51} - 4 q^{54} - 16 q^{55} + 12 q^{56} + 12 q^{60} - 8 q^{64} + 12 q^{66} + 28 q^{69} + 20 q^{70} + 24 q^{71} - 36 q^{74} - 20 q^{75} + 4 q^{76} + 24 q^{79} - 2 q^{80} - 32 q^{81} - 12 q^{84} + 8 q^{85} + 8 q^{86} + 24 q^{89} + 6 q^{90} - 28 q^{91} - 20 q^{94} + 4 q^{96} + 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^10 + 12 * q^11 - 12 * q^14 - 12 * q^15 + 8 * q^16 - 4 * q^19 + 2 * q^20 + 12 * q^21 - 4 * q^24 - 4 * q^25 + 8 * q^26 + 8 * q^29 + 4 * q^30 + 8 * q^31 - 8 * q^34 - 12 * q^35 + 8 * q^39 - 2 * q^40 - 8 * q^41 - 12 * q^44 - 18 * q^45 + 8 * q^50 - 12 * q^51 - 4 * q^54 - 16 * q^55 + 12 * q^56 + 12 * q^60 - 8 * q^64 + 12 * q^66 + 28 * q^69 + 20 * q^70 + 24 * q^71 - 36 * q^74 - 20 * q^75 + 4 * q^76 + 24 * q^79 - 2 * q^80 - 32 * q^81 - 12 * q^84 + 8 * q^85 + 8 * q^86 + 24 * q^89 + 6 * q^90 - 28 * q^91 - 20 * q^94 + 4 * q^96 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$-1$	$1$

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
$3$			2.51658i			1.45295i	0.687194	+	0.726474i	$0.258842\pi$
$3$			2.51658i			1.45295i	−0.687194	+	0.726474i	$0.741158\pi$
$4$	−1.00000			−0.500000
$5$	1.93581	+	1.11922i	0.865720	+	0.500528i
$5$	1.93581	+	1.11922i	0.865720	+	0.500528i
$6$	2.51658			1.02739
$7$		−	0.461555i		−	0.174452i	−0.996189	−	0.0872258i	$-0.972200\pi$
$7$		−	0.461555i		−	0.174452i	0.996189	−	0.0872258i	$-0.0278002\pi$
$8$			1.00000i			0.353553i
$9$	−3.33317			−1.11106
$10$	1.11922	−	1.93581i	0.353927	−	0.612157i
$11$	0.183406			0.0552989			0.0276495	−	0.999618i	$-0.491198\pi$
$11$	0.183406			0.0552989			0.0276495	+	0.999618i	$0.491198\pi$
$12$		−	2.51658i		−	0.726474i
$13$			3.35504i			0.930520i	0.885174	+	0.465260i	$0.154039\pi$
$13$			3.35504i			0.930520i	−0.885174	+	0.465260i	$0.845961\pi$
$14$	−0.461555			−0.123356
$15$	−2.81659	+	4.87162i	−0.727241	+	1.25785i
$16$	1.00000			0.250000
$17$			2.33317i			0.565878i	0.959138	+	0.282939i	$0.0913094\pi$
$17$			2.33317i			0.565878i	−0.959138	+	0.282939i	$0.908691\pi$
$18$			3.33317i			0.785637i
$19$	−2.79473			−0.641155			−0.320577	−	0.947222i	$-0.603877\pi$
$19$	−2.79473			−0.641155			−0.320577	+	0.947222i	$0.603877\pi$
$20$	−1.93581	−	1.11922i	−0.432860	−	0.250264i
$21$	1.16154			0.253469
$22$		−	0.183406i		−	0.0391023i
$23$		−	1.25628i		−	0.261953i	−0.991385	−	0.130977i	$-0.958189\pi$
$23$		−	1.25628i		−	0.261953i	0.991385	−	0.130977i	$-0.0418113\pi$
$24$	−2.51658			−0.513695
$25$	2.49472	+	4.33317i	0.498943	+	0.866635i
$26$	3.35504			0.657977
$27$		−	0.838459i		−	0.161361i
$28$			0.461555i			0.0872258i
$29$	4.61132			0.856301			0.428151	−	0.903707i	$-0.359165\pi$
$29$	4.61132			0.856301			0.428151	+	0.903707i	$0.359165\pi$
$30$	4.87162	+	2.81659i	0.889432	+	0.514237i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$		−	1.00000i		−	0.176777i
$33$			0.461555i			0.0803465i
$34$	2.33317			0.400136
$35$	0.516580	−	0.893483i	0.0873179	−	0.151026i
$36$	3.33317			0.555529
$37$		−	6.51658i		−	1.07132i	−0.844434	−	0.535660i	$-0.820063\pi$
$37$		−	6.51658i		−	1.07132i	0.844434	−	0.535660i	$-0.179937\pi$
$38$			2.79473i			0.453365i
$39$	−8.44322			−1.35200
$40$	−1.11922	+	1.93581i	−0.176963	+	0.306078i
$41$	0.376903			0.0588624			0.0294312	−	0.999567i	$-0.490630\pi$
$41$	0.376903			0.0588624			0.0294312	+	0.999567i	$0.490630\pi$
$42$		−	1.16154i		−	0.179230i
$43$		−	9.42136i		−	1.43674i	−0.695659	−	0.718372i	$-0.744888\pi$
$43$		−	9.42136i		−	1.43674i	0.695659	−	0.718372i	$-0.255112\pi$
$44$	−0.183406			−0.0276495
$45$	−6.45239	−	3.73054i	−0.961865	−	0.556116i
$46$	−1.25628			−0.185229
$47$		−	2.13847i		−	0.311928i	−0.987763	−	0.155964i	$-0.950152\pi$
$47$		−	2.13847i		−	0.311928i	0.987763	−	0.155964i	$-0.0498484\pi$
$48$			2.51658i			0.363237i
$49$	6.78697			0.969567
$50$	4.33317	−	2.49472i	0.612803	−	0.352806i
$51$	−5.87162			−0.822191
$52$		−	3.35504i		−	0.465260i
$53$		−	11.0983i		−	1.52447i	−0.647303	−	0.762233i	$-0.724103\pi$
$53$		−	11.0983i		−	1.52447i	0.647303	−	0.762233i	$-0.275897\pi$
$54$	−0.838459			−0.114100
$55$	0.355039	+	0.205271i	0.0478734	+	0.0276787i
$56$	0.461555			0.0616779
$57$		−	7.03316i		−	0.931565i
$58$		−	4.61132i		−	0.605496i
$59$	−10.8201			−1.40866			−0.704330	−	0.709872i	$-0.748753\pi$
$59$	−10.8201			−1.40866			−0.704330	+	0.709872i	$0.748753\pi$
$60$	2.81659	−	4.87162i	0.363621	−	0.628923i
$61$	12.3546			1.58184			0.790920	−	0.611920i	$-0.209603\pi$
$61$	12.3546			1.58184			0.790920	+	0.611920i	$0.209603\pi$
$62$		−	1.00000i		−	0.127000i
$63$			1.53844i			0.193826i
$64$	−1.00000			−0.125000
$65$	−3.75501	+	6.49472i	−0.465752	+	0.805570i
$66$	0.461555			0.0568135
$67$		−	1.80530i		−	0.220552i	−0.993901	−	0.110276i	$-0.964826\pi$
$67$		−	1.80530i		−	0.220552i	0.993901	−	0.110276i	$-0.0351735\pi$
$68$		−	2.33317i		−	0.282939i
$69$	3.16154			0.380605
$70$	−0.893483	−	0.516580i	−0.106792	−	0.0617431i
$71$	−5.18694			−0.615576			−0.307788	−	0.951455i	$-0.599589\pi$
$71$	−5.18694			−0.615576			−0.307788	+	0.951455i	$0.599589\pi$
$72$		−	3.33317i		−	0.392818i
$73$			11.5996i			1.35762i	0.734312	+	0.678812i	$0.237505\pi$
$73$			11.5996i			1.35762i	−0.734312	+	0.678812i	$0.762495\pi$
$74$	−6.51658			−0.757537
$75$	−10.9048	+	6.27815i	−1.25918	+	0.724938i
$76$	2.79473			0.320577
$77$		−	0.0846520i		−	0.00964699i
$78$			8.44322i			0.956007i
$79$	7.03316			0.791292			0.395646	−	0.918403i	$-0.370521\pi$
$79$	7.03316			0.791292			0.395646	+	0.918403i	$0.370521\pi$
$80$	1.93581	+	1.11922i	0.216430	+	0.125132i
$81$	−7.88947			−0.876608
$82$		−	0.376903i		−	0.0416220i
$83$		−	6.70607i		−	0.736087i	−0.929809	−	0.368043i	$-0.880028\pi$
$83$		−	6.70607i		−	0.736087i	0.929809	−	0.368043i	$-0.119972\pi$
$84$	−1.16154			−0.126735
$85$	−2.61132	+	4.51658i	−0.283238	+	0.489892i
$86$	−9.42136			−1.01593
$87$			11.6048i			1.24416i
$88$			0.183406i			0.0195511i
$89$	12.8558			1.36272			0.681358	−	0.731950i	$-0.261390\pi$
$89$	12.8558			1.36272			0.681358	+	0.731950i	$0.261390\pi$
$90$	−3.73054	+	6.45239i	−0.393233	+	0.680142i
$91$	1.54854			0.162331
$92$			1.25628i			0.130977i
$93$			2.51658i			0.260957i
$94$	−2.13847			−0.220567
$95$	−5.41006	−	3.12790i	−0.555061	−	0.320916i
$96$	2.51658			0.256847
$97$		−	12.3384i		−	1.25277i	−0.779512	−	0.626387i	$-0.784533\pi$
$97$		−	12.3384i		−	1.25277i	0.779512	−	0.626387i	$-0.215467\pi$
$98$		−	6.78697i		−	0.685587i
$99$	−0.611324			−0.0614403
$100$	−2.49472	−	4.33317i	−0.249472	−	0.433317i
$101$	−16.4585			−1.63768			−0.818842	−	0.574018i	$-0.805384\pi$
$101$	−16.4585			−1.63768			−0.818842	+	0.574018i	$0.805384\pi$
$102$			5.87162i			0.581377i
$103$			10.2558i			1.01053i	0.862963	+	0.505267i	$0.168606\pi$
$103$			10.2558i			1.01053i	−0.862963	+	0.505267i	$0.831394\pi$
$104$	−3.35504			−0.328989
$105$	2.24852	+	1.30001i	0.219433	+	0.126868i
$106$	−11.0983			−1.07796
$107$		−	17.2043i		−	1.66320i	−0.555372	−	0.831602i	$-0.687424\pi$
$107$		−	17.2043i		−	1.66320i	0.555372	−	0.831602i	$-0.312576\pi$
$108$			0.838459i			0.0806807i
$109$	15.3379			1.46911			0.734553	−	0.678552i	$-0.237392\pi$
$109$	15.3379			1.46911			0.734553	+	0.678552i	$0.237392\pi$
$110$	0.205271	−	0.355039i	0.0195718	−	0.0338516i
$111$	16.3995			1.55657
$112$		−	0.461555i		−	0.0436129i
$113$		−	2.01531i		−	0.189584i	−0.995497	−	0.0947920i	$-0.969781\pi$
$113$		−	2.01531i		−	0.189584i	0.995497	−	0.0947920i	$-0.0302186\pi$
$114$	−7.03316			−0.658716
$115$	1.40605	−	2.43193i	0.131115	−	0.226778i
$116$	−4.61132			−0.428151
$117$		−	11.1829i		−	1.03386i
$118$			10.8201i			0.996073i
$119$	1.07689			0.0987183
$120$	−4.87162	−	2.81659i	−0.444716	−	0.257119i
$121$	−10.9664			−0.996942
$122$		−	12.3546i		−	1.11853i
$123$			0.948508i			0.0855241i
$124$	−1.00000			−0.0898027
$125$	−0.0204612	+	11.1803i	−0.00183011	+	0.999998i
$126$	1.53844			0.137056
$127$			9.59955i			0.851822i	0.904765	+	0.425911i	$0.140046\pi$
$127$			9.59955i			0.851822i	−0.904765	+	0.425911i	$0.859954\pi$
$128$			1.00000i			0.0883883i
$129$	23.7096			2.08751
$130$	6.49472	+	3.75501i	0.569624	+	0.329336i
$131$	−3.91535			−0.342086			−0.171043	−	0.985264i	$-0.554714\pi$
$131$	−3.91535			−0.342086			−0.171043	+	0.985264i	$0.554714\pi$
$132$		−	0.461555i		−	0.0401732i
$133$			1.28992i			0.111850i
$134$	−1.80530			−0.155954
$135$	0.938416	−	1.62310i	0.0807660	−	0.139694i
$136$	−2.33317			−0.200068
$137$		−	6.81003i		−	0.581821i	−0.956750	−	0.290910i	$-0.906042\pi$
$137$		−	6.81003i		−	0.581821i	0.956750	−	0.290910i	$-0.0939581\pi$
$138$		−	3.16154i		−	0.269128i
$139$	21.5650			1.82912			0.914562	−	0.404447i	$-0.132536\pi$
$139$	21.5650			1.82912			0.914562	+	0.404447i	$0.132536\pi$
$140$	−0.516580	+	0.893483i	−0.0436590	+	0.0755131i
$141$	5.38164			0.453216
$142$			5.18694i			0.435278i
$143$			0.615334i			0.0514568i
$144$	−3.33317			−0.277764
$145$	8.92664	+	5.16106i	0.741317	+	0.428603i
$146$	11.5996			0.959986
$147$			17.0799i			1.40873i
$148$			6.51658i			0.535660i
$149$	−16.9222			−1.38632			−0.693158	−	0.720785i	$-0.743781\pi$
$149$	−16.9222			−1.38632			−0.693158	+	0.720785i	$0.743781\pi$
$150$	6.27815	+	10.9048i	0.512609	+	0.890371i
$151$	−3.35624			−0.273127			−0.136564	−	0.990631i	$-0.543606\pi$
$151$	−3.35624			−0.273127			−0.136564	+	0.990631i	$0.543606\pi$
$152$		−	2.79473i		−	0.226682i
$153$		−	7.77687i		−	0.628723i
$154$	−0.0846520			−0.00682145
$155$	1.93581	+	1.11922i	0.155488	+	0.0898975i
$156$	8.44322			0.675999
$157$		−	0.966840i		−	0.0771623i	−0.999255	−	0.0385811i	$-0.987716\pi$
$157$		−	0.966840i		−	0.0771623i	0.999255	−	0.0385811i	$-0.0122838\pi$
$158$		−	7.03316i		−	0.559528i
$159$	27.9297			2.21497
$160$	1.11922	−	1.93581i	0.0884817	−	0.153039i
$161$	−0.579845			−0.0456982
$162$			7.88947i			0.619856i
$163$		−	9.44274i		−	0.739613i	−0.929109	−	0.369806i	$-0.879424\pi$
$163$		−	9.44274i		−	0.739613i	0.929109	−	0.369806i	$-0.120576\pi$
$164$	−0.376903			−0.0294312
$165$	−0.516580	+	0.893483i	−0.0402157	+	0.0695576i
$166$	−6.70607			−0.520492
$167$			12.9995i			1.00593i	0.864306	+	0.502967i	$0.167758\pi$
$167$			12.9995i			1.00593i	−0.864306	+	0.502967i	$0.832242\pi$
$168$			1.16154i			0.0896148i
$169$	1.74372			0.134132
$170$	4.51658	+	2.61132i	0.346406	+	0.200279i
$171$	9.31532			0.712360
$172$			9.42136i			0.718372i
$173$		−	4.04373i		−	0.307439i	−0.988115	−	0.153720i	$-0.950875\pi$
$173$		−	4.04373i		−	0.307439i	0.988115	−	0.153720i	$-0.0491252\pi$
$174$	11.6048			0.879755
$175$	2.00000	−	1.15145i	0.151186	−	0.0870414i
$176$	0.183406			0.0138247
$177$		−	27.2297i		−	2.04671i
$178$		−	12.8558i		−	0.963586i
$179$	1.25749			0.0939891			0.0469945	−	0.998895i	$-0.485036\pi$
$179$	1.25749			0.0939891			0.0469945	+	0.998895i	$0.485036\pi$
$180$	6.45239	+	3.73054i	0.480933	+	0.278058i
$181$	5.06985			0.376839			0.188420	−	0.982089i	$-0.439664\pi$
$181$	5.06985			0.376839			0.188420	+	0.982089i	$0.439664\pi$
$182$		−	1.54854i		−	0.114785i
$183$			31.0912i			2.29833i
$184$	1.25628			0.0926145
$185$	7.29345	−	12.6149i	0.536225	−	0.927463i
$186$	2.51658			0.184525
$187$			0.427918i			0.0312924i
$188$			2.13847i			0.155964i
$189$	−0.386995			−0.0281498
$190$	−3.12790	+	5.41006i	−0.226922	+	0.392487i
$191$	−4.69999			−0.340079			−0.170040	−	0.985437i	$-0.554390\pi$
$191$	−4.69999			−0.340079			−0.170040	+	0.985437i	$0.554390\pi$
$192$		−	2.51658i		−	0.181619i
$193$			25.4865i			1.83456i	0.398247	+	0.917278i	$0.369619\pi$
$193$			25.4865i			1.83456i	−0.398247	+	0.917278i	$0.630381\pi$
$194$	−12.3384			−0.885845
$195$	−16.3445	−	9.44978i	−1.17045	−	0.676713i
$196$	−6.78697			−0.484783
$197$			9.30610i			0.663032i	0.943450	+	0.331516i	$0.107560\pi$
$197$			9.30610i			0.663032i	−0.943450	+	0.331516i	$0.892440\pi$
$198$			0.611324i			0.0434449i
$199$	−7.62007			−0.540172			−0.270086	−	0.962836i	$-0.587052\pi$
$199$	−7.62007			−0.540172			−0.270086	+	0.962836i	$0.587052\pi$
$200$	−4.33317	+	2.49472i	−0.306402	+	0.176403i
$201$	4.54318			0.320451
$202$			16.4585i			1.15802i
$203$		−	2.12838i		−	0.149383i
$204$	5.87162			0.411096
$205$	0.729613	+	0.421836i	0.0509584	+	0.0294623i
$206$	10.2558			0.714556
$207$			4.18742i			0.291046i
$208$			3.35504i			0.232630i
$209$	−0.512570			−0.0354552
$210$	1.30001	−	2.24852i	0.0897095	−	0.155163i
$211$	−21.0707			−1.45057			−0.725284	−	0.688450i	$-0.758292\pi$
$211$	−21.0707			−1.45057			−0.725284	+	0.688450i	$0.758292\pi$
$212$			11.0983i			0.762233i
$213$		−	13.0533i		−	0.894400i
$214$	−17.2043			−1.17606
$215$	10.5445	−	18.2380i	0.719131	−	1.24382i
$216$	0.838459			0.0570499
$217$		−	0.461555i		−	0.0313324i
$218$		−	15.3379i		−	1.03881i
$219$	−29.1912			−1.97256
$220$	−0.355039	−	0.205271i	−0.0239367	−	0.0138393i
$221$	−7.82789			−0.526561
$222$		−	16.3995i		−	1.10066i
$223$			20.3558i			1.36312i	0.731761	+	0.681561i	$0.238699\pi$
$223$			20.3558i			1.36312i	−0.731761	+	0.681561i	$0.761301\pi$
$224$	−0.461555			−0.0308390
$225$	−8.31532	−	14.4432i	−0.554355	−	0.962882i
$226$	−2.01531			−0.134056
$227$			20.4769i			1.35910i	0.733631	+	0.679548i	$0.237824\pi$
$227$			20.4769i			1.35910i	−0.733631	+	0.679548i	$0.762176\pi$
$228$			7.03316i			0.465782i
$229$	−8.16507			−0.539563			−0.269782	−	0.962922i	$-0.586952\pi$
$229$	−8.16507			−0.539563			−0.269782	+	0.962922i	$0.586952\pi$
$230$	−2.43193	−	1.40605i	−0.160357	−	0.0927124i
$231$	0.213033			0.0140166
$232$			4.61132i			0.302748i
$233$		−	7.60476i		−	0.498205i	−0.968477	−	0.249102i	$-0.919864\pi$
$233$		−	7.60476i		−	0.498205i	0.968477	−	0.249102i	$-0.0801355\pi$
$234$	−11.1829			−0.731051
$235$	2.39341	−	4.13968i	0.156129	−	0.270043i
$236$	10.8201			0.704330
$237$			17.6995i			1.14971i
$238$		−	1.07689i		−	0.0698044i
$239$	−13.9869			−0.904736			−0.452368	−	0.891831i	$-0.649421\pi$
$239$	−13.9869			−0.904736			−0.452368	+	0.891831i	$0.649421\pi$
$240$	−2.81659	+	4.87162i	−0.181810	+	0.314462i
$241$	−27.8839			−1.79616			−0.898080	−	0.439833i	$-0.855038\pi$
$241$	−27.8839			−1.79616			−0.898080	+	0.439833i	$0.855038\pi$
$242$			10.9664i			0.704944i
$243$		−	22.3699i		−	1.43503i
$244$	−12.3546			−0.790920
$245$	13.1383	+	7.59608i	0.839373	+	0.485295i
$246$	0.948508			0.0604746
$247$		−	9.37643i		−	0.596608i
$248$			1.00000i			0.0635001i
$249$	16.8764			1.06950
$250$	11.1803	+	0.0204612i	0.707106	+	0.00129408i
$251$	−17.7955			−1.12324			−0.561620	−	0.827396i	$-0.689822\pi$
$251$	−17.7955			−1.12324			−0.561620	+	0.827396i	$0.689822\pi$
$252$		−	1.53844i		−	0.0969129i
$253$		−	0.230410i		−	0.0144858i
$254$	9.59955			0.602329
$255$	−11.3663	−	6.57160i	−0.711787	−	0.411530i
$256$	1.00000			0.0625000
$257$		−	13.5528i		−	0.845400i	−0.906270	−	0.422700i	$-0.861082\pi$
$257$		−	13.5528i		−	0.845400i	0.906270	−	0.422700i	$-0.138918\pi$
$258$		−	23.7096i		−	1.47610i
$259$	−3.00776			−0.186893
$260$	3.75501	−	6.49472i	0.232876	−	0.402785i
$261$	−15.3703			−0.951400
$262$			3.91535i			0.241891i
$263$			19.2196i			1.18513i	0.805522	+	0.592566i	$0.201885\pi$
$263$			19.2196i			1.18513i	−0.805522	+	0.592566i	$0.798115\pi$
$264$	−0.461555			−0.0284068
$265$	12.4214	−	21.4841i	0.763038	−	1.31976i
$266$	1.28992			0.0790902
$267$			32.3527i			1.97996i
$268$			1.80530i			0.110276i
$269$	−26.7492			−1.63093			−0.815463	−	0.578809i	$-0.803518\pi$
$269$	−26.7492			−1.63093			−0.815463	+	0.578809i	$0.803518\pi$
$270$	−1.62310	−	0.938416i	−0.0987785	−	0.0571102i
$271$	23.0995			1.40319			0.701597	−	0.712574i	$-0.252471\pi$
$271$	23.0995			1.40319			0.701597	+	0.712574i	$0.252471\pi$
$272$			2.33317i			0.141469i
$273$			3.89702i			0.235858i
$274$	−6.81003			−0.411409
$275$	0.457545	+	0.794729i	0.0275910	+	0.0479240i
$276$	−3.16154			−0.190302
$277$		−	23.1410i		−	1.39041i	−0.718811	−	0.695205i	$-0.755313\pi$
$277$		−	23.1410i		−	1.39041i	0.718811	−	0.695205i	$-0.244687\pi$
$278$		−	21.5650i		−	1.29339i
$279$	−3.33317			−0.199552
$280$	0.893483	+	0.516580i	0.0533958	+	0.0308715i
$281$	8.25581			0.492500			0.246250	−	0.969206i	$-0.420802\pi$
$281$	8.25581			0.492500			0.246250	+	0.969206i	$0.420802\pi$
$282$		−	5.38164i		−	0.320472i
$283$			7.71263i			0.458468i	0.973371	+	0.229234i	$0.0736221\pi$
$283$			7.71263i			0.458468i	−0.973371	+	0.229234i	$0.926378\pi$
$284$	5.18694			0.307788
$285$	7.87162	−	13.6149i	0.466274	−	0.806474i
$286$	0.615334			0.0363854
$287$		−	0.173962i		−	0.0102686i
$288$			3.33317i			0.196409i
$289$	11.5563			0.679782
$290$	5.16106	−	8.92664i	0.303068	−	0.524191i
$291$	31.0505			1.82021
$292$		−	11.5996i		−	0.678812i
$293$			18.4811i			1.07968i	0.841768	+	0.539839i	$0.181515\pi$
$293$			18.4811i			1.07968i	−0.841768	+	0.539839i	$0.818485\pi$
$294$	17.0799			0.996123
$295$	−20.9457	−	12.1100i	−1.21951	−	0.705074i
$296$	6.51658			0.378769
$297$		−	0.153778i		−	0.00892312i
$298$			16.9222i			0.980274i
$299$	4.21488			0.243753
$300$	10.9048	−	6.27815i	0.629588	−	0.362469i
$301$	−4.34848			−0.250642
$302$			3.35624i			0.193130i
$303$		−	41.4192i		−	2.37947i
$304$	−2.79473			−0.160289
$305$	23.9161	+	13.8274i	1.36943	+	0.791755i
$306$	−7.77687			−0.444574
$307$		−	0.407734i		−	0.0232706i	−0.999932	−	0.0116353i	$-0.996296\pi$
$307$		−	0.407734i		−	0.0232706i	0.999932	−	0.0116353i	$-0.00370372\pi$
$308$			0.0846520i			0.00482349i
$309$	−25.8096			−1.46825
$310$	1.11922	−	1.93581i	0.0635671	−	0.109947i
$311$	10.1975			0.578248			0.289124	−	0.957292i	$-0.406636\pi$
$311$	10.1975			0.578248			0.289124	+	0.957292i	$0.406636\pi$
$312$		−	8.44322i		−	0.478003i
$313$		−	28.3322i		−	1.60143i	−0.599044	−	0.800716i	$-0.704453\pi$
$313$		−	28.3322i		−	1.60143i	0.599044	−	0.800716i	$-0.295547\pi$
$314$	−0.966840			−0.0545620
$315$	−1.72185	+	2.97814i	−0.0970153	+	0.167799i
$316$	−7.03316			−0.395646
$317$			11.0638i			0.621403i	0.950508	+	0.310702i	$0.100564\pi$
$317$			11.0638i			0.621403i	−0.950508	+	0.310702i	$0.899436\pi$
$318$		−	27.9297i		−	1.56622i
$319$	0.845744			0.0473526
$320$	−1.93581	−	1.11922i	−0.108215	−	0.0625660i
$321$	43.2960			2.41655
$322$			0.579845i			0.0323135i
$323$		−	6.52059i		−	0.362815i
$324$	7.88947			0.438304
$325$	−14.5380	+	8.36987i	−0.806421	+	0.464277i
$326$	−9.44274			−0.522985
$327$			38.5991i			2.13453i
$328$			0.376903i			0.0208110i
$329$	−0.987024			−0.0544164
$330$	0.893483	+	0.516580i	0.0491846	+	0.0284368i
$331$	14.3903			0.790961			0.395480	−	0.918474i	$-0.370578\pi$
$331$	14.3903			0.790961			0.395480	+	0.918474i	$0.370578\pi$
$332$			6.70607i			0.368043i
$333$			21.7209i			1.19030i
$334$	12.9995			0.711302
$335$	2.02052	−	3.49472i	0.110393	−	0.190937i
$336$	1.16154			0.0633673
$337$			4.50809i			0.245571i	0.992433	+	0.122786i	$0.0391828\pi$
$337$			4.50809i			0.245571i	−0.992433	+	0.122786i	$0.960817\pi$
$338$		−	1.74372i		−	0.0948456i
$339$	5.07168			0.275456
$340$	2.61132	−	4.51658i	0.141619	−	0.244946i
$341$	0.183406			0.00993198
$342$		−	9.31532i		−	0.503715i
$343$		−	6.36345i		−	0.343594i
$344$	9.42136			0.507966
$345$	6.12014	+	3.53844i	0.329497	+	0.190503i
$346$	−4.04373			−0.217392
$347$		−	23.2055i		−	1.24574i	−0.782326	−	0.622869i	$-0.785967\pi$
$347$		−	23.2055i		−	1.24574i	0.782326	−	0.622869i	$-0.214033\pi$
$348$		−	11.6048i		−	0.622081i
$349$	−21.0200			−1.12518			−0.562588	−	0.826737i	$-0.690194\pi$
$349$	−21.0200			−1.12518			−0.562588	+	0.826737i	$0.690194\pi$
$350$	−1.15145	−	2.00000i	−0.0615476	−	0.106904i
$351$	2.81306			0.150150
$352$		−	0.183406i		−	0.00977556i
$353$		−	10.0774i		−	0.536364i	−0.963368	−	0.268182i	$-0.913577\pi$
$353$		−	10.0774i		−	0.536364i	0.963368	−	0.268182i	$-0.0864229\pi$
$354$	−27.2297			−1.44724
$355$	−10.0409	−	5.80530i	−0.532917	−	0.308113i
$356$	−12.8558			−0.681358
$357$			2.71008i			0.143433i
$358$		−	1.25749i		−	0.0664603i
$359$	−22.5227			−1.18870			−0.594350	−	0.804206i	$-0.702591\pi$
$359$	−22.5227			−1.18870			−0.594350	+	0.804206i	$0.702591\pi$
$360$	3.73054	−	6.45239i	0.196617	−	0.340071i
$361$	−11.1895			−0.588920
$362$		−	5.06985i		−	0.266465i
$363$		−	27.5977i		−	1.44850i
$364$	−1.54854			−0.0811654
$365$	−12.9824	+	22.4545i	−0.679529	+	1.17532i
$366$	31.0912			1.62517
$367$		−	23.1402i		−	1.20791i	−0.797019	−	0.603954i	$-0.793591\pi$
$367$		−	23.1402i		−	1.20791i	0.797019	−	0.603954i	$-0.206409\pi$
$368$		−	1.25628i		−	0.0654884i
$369$	−1.25628			−0.0653996
$370$	−12.6149	−	7.29345i	−0.655815	−	0.379169i
$371$	−5.12247			−0.265945
$372$		−	2.51658i		−	0.130479i
$373$			22.4585i			1.16286i	0.813597	+	0.581429i	$0.197506\pi$
$373$			22.4585i			1.16286i	−0.813597	+	0.581429i	$0.802494\pi$
$374$	0.427918			0.0221271
$375$	−28.1362	−	0.0514923i	−1.45295	−	0.00265905i
$376$	2.13847			0.110283
$377$			15.4712i			0.796806i
$378$			0.386995i			0.0199049i
$379$	23.1301			1.18811			0.594056	−	0.804423i	$-0.297526\pi$
$379$	23.1301			1.18811			0.594056	+	0.804423i	$0.297526\pi$
$380$	5.41006	+	3.12790i	0.277530	+	0.160458i
$381$	−24.1580			−1.23765
$382$			4.69999i			0.240472i
$383$		−	11.6894i		−	0.597301i	−0.954363	−	0.298651i	$-0.903463\pi$
$383$		−	11.6894i		−	0.597301i	0.954363	−	0.298651i	$-0.0965365\pi$
$384$	−2.51658			−0.128424
$385$	0.0947438	−	0.163870i	0.00482859	−	0.00835159i
$386$	25.4865			1.29723
$387$			31.4030i			1.59631i
$388$			12.3384i			0.626387i
$389$	6.14770			0.311701			0.155850	−	0.987781i	$-0.450188\pi$
$389$	6.14770			0.311701			0.155850	+	0.987781i	$0.450188\pi$
$390$	−9.44978	+	16.3445i	−0.478508	+	0.827634i
$391$	2.93113			0.148234
$392$			6.78697i			0.342794i
$393$		−	9.85329i		−	0.497033i
$394$	9.30610			0.468834
$395$	13.6149	+	7.87162i	0.685038	+	0.396064i
$396$	0.611324			0.0307202
$397$			14.4176i			0.723599i	0.932256	+	0.361799i	$0.117837\pi$
$397$			14.4176i			0.723599i	−0.932256	+	0.361799i	$0.882163\pi$
$398$			7.62007i			0.381960i
$399$	−3.24619			−0.162513
$400$	2.49472	+	4.33317i	0.124736	+	0.216659i
$401$	−22.8437			−1.14076			−0.570379	−	0.821381i	$-0.693204\pi$
$401$	−22.8437			−1.14076			−0.570379	+	0.821381i	$0.693204\pi$
$402$		−	4.54318i		−	0.226593i
$403$			3.35504i			0.167126i
$404$	16.4585			0.818842
$405$	−15.2725	−	8.83002i	−0.758897	−	0.438767i
$406$	−2.12838			−0.105630
$407$		−	1.19518i		−	0.0592428i
$408$		−	5.87162i		−	0.290688i
$409$	−12.9302			−0.639356			−0.319678	−	0.947526i	$-0.603575\pi$
$409$	−12.9302			−0.639356			−0.319678	+	0.947526i	$0.603575\pi$
$410$	0.421836	−	0.729613i	0.0208330	−	0.0360330i
$411$	17.1380			0.845355
$412$		−	10.2558i		−	0.505267i
$413$			4.99409i			0.245743i
$414$	4.18742			0.205800
$415$	7.50553	−	12.9817i	0.368432	−	0.637245i
$416$	3.35504			0.164494
$417$			54.2702i			2.65762i
$418$			0.512570i			0.0250706i
$419$	6.45572			0.315383			0.157691	−	0.987488i	$-0.449595\pi$
$419$	6.45572			0.315383			0.157691	+	0.987488i	$0.449595\pi$
$420$	−2.24852	−	1.30001i	−0.109717	−	0.0634342i
$421$	6.17732			0.301064			0.150532	−	0.988605i	$-0.451901\pi$
$421$	6.17732			0.301064			0.150532	+	0.988605i	$0.451901\pi$
$422$			21.0707i			1.02571i
$423$			7.12790i			0.346571i
$424$	11.0983			0.538980
$425$	−10.1100	+	5.82060i	−0.490409	+	0.282341i
$426$	−13.0533			−0.632437
$427$		−	5.70231i		−	0.275954i
$428$			17.2043i			0.831602i
$429$	−1.54854			−0.0747640
$430$	−18.2380	−	10.5445i	−0.879512	−	0.508502i
$431$	13.6974			0.659782			0.329891	−	0.944019i	$-0.392988\pi$
$431$	13.6974			0.659782			0.329891	+	0.944019i	$0.392988\pi$
$432$		−	0.838459i		−	0.0403404i
$433$			8.09194i			0.388874i	0.980915	+	0.194437i	$0.0622879\pi$
$433$			8.09194i			0.388874i	−0.980915	+	0.194437i	$0.937712\pi$
$434$	−0.461555			−0.0221554
$435$	−12.9882	+	22.4646i	−0.622738	+	1.07710i
$436$	−15.3379			−0.734553
$437$			3.51098i			0.167953i
$438$			29.1912i			1.39481i
$439$	−29.5192			−1.40887			−0.704436	−	0.709767i	$-0.748800\pi$
$439$	−29.5192			−1.40887			−0.704436	+	0.709767i	$0.748800\pi$
$440$	−0.205271	+	0.355039i	−0.00978589	+	0.0169258i
$441$	−22.6221			−1.07724
$442$			7.82789i			0.372335i
$443$		−	15.3764i		−	0.730556i	−0.930898	−	0.365278i	$-0.880974\pi$
$443$		−	15.3764i		−	0.730556i	0.930898	−	0.365278i	$-0.119026\pi$
$444$	−16.3995			−0.778286
$445$	24.8864	+	14.3884i	1.17973	+	0.682078i
$446$	20.3558			0.963873
$447$		−	42.5860i		−	2.01425i
$448$			0.461555i			0.0218064i
$449$	20.6330			0.973734			0.486867	−	0.873476i	$-0.338140\pi$
$449$	20.6330			0.973734			0.486867	+	0.873476i	$0.338140\pi$
$450$	−14.4432	+	8.31532i	−0.680860	+	0.391988i
$451$	0.0691263			0.00325503
$452$			2.01531i			0.0947920i
$453$		−	8.44625i		−	0.396839i
$454$	20.4769			0.961027
$455$	2.99767	+	1.73315i	0.140533	+	0.0812511i
$456$	7.03316			0.329358
$457$			7.34519i			0.343594i	0.985132	+	0.171797i	$0.0549573\pi$
$457$			7.34519i			0.343594i	−0.985132	+	0.171797i	$0.945043\pi$
$458$			8.16507i			0.381529i
$459$	1.95627			0.0913109
$460$	−1.40605	+	2.43193i	−0.0655576	+	0.113389i
$461$	−2.15986			−0.100595			−0.0502974	−	0.998734i	$-0.516017\pi$
$461$	−2.15986			−0.100595			−0.0502974	+	0.998734i	$0.516017\pi$
$462$		−	0.213033i		−	0.00991121i
$463$			8.82315i			0.410047i	0.978757	+	0.205023i	$0.0657270\pi$
$463$			8.82315i			0.410047i	−0.978757	+	0.205023i	$0.934273\pi$
$464$	4.61132			0.214075
$465$	−2.81659	+	4.87162i	−0.130616	+	0.225916i
$466$	−7.60476			−0.352284
$467$		−	34.6245i		−	1.60223i	−0.598511	−	0.801115i	$-0.704241\pi$
$467$		−	34.6245i		−	1.60223i	0.598511	−	0.801115i	$-0.295759\pi$
$468$			11.1829i			0.516931i
$469$	−0.833246			−0.0384757
$470$	−4.13968	−	2.39341i	−0.190949	−	0.110400i
$471$	2.43313			0.112113
$472$		−	10.8201i		−	0.498037i
$473$		−	1.72793i		−	0.0794504i
$474$	17.6995			0.812965
$475$	−6.97205	−	12.1100i	−0.319900	−	0.555647i
$476$	−1.07689			−0.0493591
$477$			36.9925i			1.69377i
$478$			13.9869i			0.639745i
$479$	35.4879			1.62148			0.810742	−	0.585403i	$-0.199064\pi$
$479$	35.4879			1.62148			0.810742	+	0.585403i	$0.199064\pi$
$480$	4.87162	+	2.81659i	0.222358	+	0.128559i
$481$	21.8634			0.996884
$482$			27.8839i			1.27008i
$483$		−	1.45923i		−	0.0663971i
$484$	10.9664			0.498471
$485$	13.8093	−	23.8848i	0.627048	−	1.08455i
$486$	−22.3699			−1.01472
$487$		−	6.73569i		−	0.305223i	−0.988286	−	0.152612i	$-0.951232\pi$
$487$		−	6.73569i		−	0.305223i	0.988286	−	0.152612i	$-0.0487684\pi$
$488$			12.3546i			0.559265i
$489$	23.7634			1.07462
$490$	7.59608	−	13.1383i	0.343156	−	0.593527i
$491$	−8.12644			−0.366741			−0.183371	−	0.983044i	$-0.558701\pi$
$491$	−8.12644			−0.366741			−0.183371	+	0.983044i	$0.558701\pi$
$492$		−	0.948508i		−	0.0427620i
$493$			10.7590i			0.484562i
$494$	−9.37643			−0.421865
$495$	−1.18341	−	0.684203i	−0.0531901	−	0.0307526i
$496$	1.00000			0.0449013
$497$			2.39406i			0.107388i
$498$		−	16.8764i		−	0.756247i
$499$	28.0819			1.25712			0.628559	−	0.777762i	$-0.283645\pi$
$499$	28.0819			1.25712			0.628559	+	0.777762i	$0.283645\pi$
$500$	0.0204612	−	11.1803i	0.000915054	−	0.499999i
$501$	−32.7143			−1.46157
$502$			17.7955i			0.794250i
$503$		−	7.67692i		−	0.342297i	−0.985245	−	0.171148i	$-0.945252\pi$
$503$		−	7.67692i		−	0.342297i	0.985245	−	0.171148i	$-0.0547478\pi$
$504$	−1.53844			−0.0685278
$505$	−31.8606	−	18.4206i	−1.41778	−	0.819707i
$506$	−0.230410			−0.0102430
$507$			4.38820i			0.194887i
$508$		−	9.59955i		−	0.425911i
$509$	34.7895			1.54202			0.771010	−	0.636823i	$-0.219752\pi$
$509$	34.7895			1.54202			0.771010	+	0.636823i	$0.219752\pi$
$510$	−6.57160	+	11.3663i	−0.290996	+	0.503310i
$511$	5.35384			0.236840
$512$		−	1.00000i		−	0.0441942i
$513$			2.34327i			0.103458i
$514$	−13.5528			−0.597788
$515$	−11.4785	+	19.8533i	−0.505801	+	0.874840i
$516$	−23.7096			−1.04376
$517$		−	0.392208i		−	0.0172493i
$518$			3.00776i			0.132154i
$519$	10.1764			0.446693
$520$	−6.49472	−	3.75501i	−0.284812	−	0.164668i
$521$	27.7527			1.21587			0.607934	−	0.793987i	$-0.291998\pi$
$521$	27.7527			1.21587			0.607934	+	0.793987i	$0.291998\pi$
$522$			15.3703i			0.672742i
$523$		−	4.65539i		−	0.203566i	−0.994807	−	0.101783i	$-0.967545\pi$
$523$		−	4.65539i		−	0.203566i	0.994807	−	0.101783i	$-0.0324547\pi$
$524$	3.91535			0.171043
$525$	2.89771	+	5.03316i	0.126467	+	0.219665i
$526$	19.2196			0.838015
$527$			2.33317i			0.101635i
$528$			0.461555i			0.0200866i
$529$	21.4217			0.931380
$530$	−21.4841	−	12.4214i	−0.933212	−	0.539549i
$531$	36.0654			1.56510
$532$		−	1.28992i		−	0.0559252i
$533$			1.26453i			0.0547727i
$534$	32.3527			1.40004
$535$	19.2553	−	33.3043i	0.832480	−	1.43987i
$536$	1.80530			0.0779771
$537$			3.16457i			0.136561i
$538$			26.7492i			1.15324i
$539$	1.24477			0.0536160
$540$	−0.938416	+	1.62310i	−0.0403830	+	0.0698470i
$541$	−22.0908			−0.949756			−0.474878	−	0.880052i	$-0.657508\pi$
$541$	−22.0908			−0.949756			−0.474878	+	0.880052i	$0.657508\pi$
$542$		−	23.0995i		−	0.992208i
$543$			12.7587i			0.547528i
$544$	2.33317			0.100034
$545$	29.6913	+	17.1664i	1.27183	+	0.735329i
$546$	3.89702			0.166777
$547$		−	26.9894i		−	1.15398i	−0.816750	−	0.576992i	$-0.804226\pi$
$547$		−	26.9894i		−	1.15398i	0.816750	−	0.576992i	$-0.195774\pi$
$548$			6.81003i			0.290910i
$549$	−41.1799			−1.75752
$550$	0.794729	−	0.457545i	0.0338874	−	0.0195098i
$551$	−12.8874			−0.549022
$552$			3.16154i			0.134564i
$553$		−	3.24619i		−	0.138042i
$554$	−23.1410			−0.983169
$555$	31.7463	+	18.3546i	1.34756	+	0.779108i
$556$	−21.5650			−0.914562
$557$			8.86787i			0.375744i	0.982194	+	0.187872i	$0.0601589\pi$
$557$			8.86787i			0.375744i	−0.982194	+	0.187872i	$0.939841\pi$
$558$			3.33317i			0.141105i
$559$	31.6090			1.33692
$560$	0.516580	−	0.893483i	0.0218295	−	0.0377566i
$561$	−1.07689			−0.0454663
$562$		−	8.25581i		−	0.348250i
$563$		−	10.7143i		−	0.451555i	−0.974179	−	0.225778i	$-0.927508\pi$
$563$		−	10.7143i		−	0.451555i	0.974179	−	0.225778i	$-0.0724923\pi$
$564$	−5.38164			−0.226608
$565$	2.25556	−	3.90125i	0.0948921	−	0.164127i
$566$	7.71263			0.324186
$567$			3.64143i			0.152926i
$568$		−	5.18694i		−	0.217639i
$569$	−22.8225			−0.956770			−0.478385	−	0.878150i	$-0.658778\pi$
$569$	−22.8225			−0.956770			−0.478385	+	0.878150i	$0.658778\pi$
$570$	−13.6149	−	7.87162i	−0.570264	−	0.329706i
$571$	40.7354			1.70472			0.852361	−	0.522953i	$-0.175170\pi$
$571$	40.7354			1.70472			0.852361	+	0.522953i	$0.175170\pi$
$572$		−	0.615334i		−	0.0257284i
$573$		−	11.8279i		−	0.494117i
$574$	−0.173962			−0.00726103
$575$	5.44370	−	3.13407i	0.227018	−	0.130700i
$576$	3.33317			0.138882
$577$			2.27207i			0.0945874i	0.998881	+	0.0472937i	$0.0150597\pi$
$577$			2.27207i			0.0945874i	−0.998881	+	0.0472937i	$0.984940\pi$
$578$		−	11.5563i		−	0.480679i
$579$	−64.1387			−2.66552
$580$	−8.92664	−	5.16106i	−0.370659	−	0.214301i
$581$	−3.09522			−0.128411
$582$		−	31.0505i		−	1.28709i
$583$		−	2.03549i		−	0.0843013i
$584$	−11.5996			−0.479993
$585$	12.5161	−	21.6480i	0.517477	−	0.895035i
$586$	18.4811			0.763448
$587$			25.2360i			1.04160i	0.853678	+	0.520801i	$0.174367\pi$
$587$			25.2360i			1.04160i	−0.853678	+	0.520801i	$0.825633\pi$
$588$		−	17.0799i		−	0.704365i
$589$	−2.79473			−0.115155
$590$	−12.1100	+	20.9457i	−0.498563	+	0.862321i
$591$	−23.4195			−0.963351
$592$		−	6.51658i		−	0.267830i
$593$			8.80482i			0.361571i	0.983523	+	0.180785i	$0.0578639\pi$
$593$			8.80482i			0.361571i	−0.983523	+	0.180785i	$0.942136\pi$
$594$	−0.153778			−0.00630960
$595$	2.08465	+	1.20527i	0.0854624	+	0.0494113i
$596$	16.9222			0.693158
$597$		−	19.1765i		−	0.784842i
$598$		−	4.21488i		−	0.172359i
$599$	−17.9583			−0.733758			−0.366879	−	0.930269i	$-0.619574\pi$
$599$	−17.9583			−0.733758			−0.366879	+	0.930269i	$0.619574\pi$
$600$	−6.27815	−	10.9048i	−0.256304	−	0.445186i
$601$	−22.7327			−0.927285			−0.463642	−	0.886022i	$-0.653458\pi$
$601$	−22.7327			−0.927285			−0.463642	+	0.886022i	$0.653458\pi$
$602$			4.34848i			0.177231i
$603$			6.01738i			0.245047i
$604$	3.35624			0.136564
$605$	−21.2288	−	12.2737i	−0.863073	−	0.498998i
$606$	−41.4192			−1.68254
$607$		−	7.02100i		−	0.284973i	−0.989797	−	0.142487i	$-0.954490\pi$
$607$		−	7.02100i		−	0.284973i	0.989797	−	0.142487i	$-0.0455098\pi$
$608$			2.79473i			0.113341i
$609$	5.35624			0.217046
$610$	13.8274	−	23.9161i	0.559856	−	0.968333i
$611$	7.17466			0.290256
$612$			7.77687i			0.314362i
$613$			6.85278i			0.276781i	0.990378	+	0.138391i	$0.0441929\pi$
$613$			6.85278i			0.276781i	−0.990378	+	0.138391i	$0.955807\pi$
$614$	−0.407734			−0.0164548
$615$	−1.06158	+	1.83613i	−0.0428072	+	0.0740399i
$616$	0.0846520			0.00341072
$617$		−	35.4202i		−	1.42596i	−0.701183	−	0.712981i	$-0.747345\pi$
$617$		−	35.4202i		−	1.42596i	0.701183	−	0.712981i	$-0.252655\pi$
$618$			25.8096i			1.03821i
$619$	−30.9265			−1.24304			−0.621520	−	0.783398i	$-0.713485\pi$
$619$	−30.9265			−1.24304			−0.621520	+	0.783398i	$0.713485\pi$
$620$	−1.93581	−	1.11922i	−0.0777440	−	0.0449488i
$621$	−1.05334			−0.0422692
$622$		−	10.1975i		−	0.408883i
$623$		−	5.93368i		−	0.237728i
$624$	−8.44322			−0.337999
$625$	−12.5528	+	21.6201i	−0.502112	+	0.864803i
$626$	−28.3322			−1.13238
$627$		−	1.28992i		−	0.0515145i
$628$			0.966840i			0.0385811i
$629$	15.2043			0.606236
$630$	2.97814	+	1.72185i	0.118652	+	0.0686002i
$631$	44.6321			1.77678			0.888388	−	0.459094i	$-0.151826\pi$
$631$	44.6321			1.77678			0.888388	+	0.459094i	$0.151826\pi$
$632$			7.03316i			0.279764i
$633$		−	53.0261i		−	2.10760i
$634$	11.0638			0.439398
$635$	−10.7440	+	18.5829i	−0.426361	+	0.737440i
$636$	−27.9297			−1.10748
$637$			22.7705i			0.902201i
$638$		−	0.845744i		−	0.0334833i
$639$	17.2890			0.683941
$640$	−1.11922	+	1.93581i	−0.0442409	+	0.0765196i
$641$	−3.85424			−0.152233			−0.0761167	−	0.997099i	$-0.524252\pi$
$641$	−3.85424			−0.152233			−0.0761167	+	0.997099i	$0.524252\pi$
$642$		−	43.2960i		−	1.70876i
$643$			16.3830i			0.646082i	0.946385	+	0.323041i	$0.104705\pi$
$643$			16.3830i			0.646082i	−0.946385	+	0.323041i	$0.895295\pi$
$644$	0.579845			0.0228491
$645$	45.8973	+	26.5361i	1.80720	+	1.04486i
$646$	−6.52059			−0.256549
$647$			10.9689i			0.431232i	0.976478	+	0.215616i	$0.0691760\pi$
$647$			10.9689i			0.431232i	−0.976478	+	0.215616i	$0.930824\pi$
$648$		−	7.88947i		−	0.309928i
$649$	−1.98447			−0.0778974
$650$	8.36987	+	14.5380i	0.328293	+	0.570226i
$651$	1.16154			0.0455244
$652$			9.44274i			0.369806i
$653$		−	3.71784i		−	0.145490i	−0.997351	−	0.0727452i	$-0.976824\pi$
$653$		−	3.71784i		−	0.145490i	0.997351	−	0.0727452i	$-0.0231760\pi$
$654$	38.5991			1.50934
$655$	−7.57937	−	4.38212i	−0.296150	−	0.171223i
$656$	0.376903			0.0147156
$657$		−	38.6633i		−	1.50840i
$658$			0.987024i			0.0384782i
$659$	−25.9248			−1.00989			−0.504944	−	0.863152i	$-0.668487\pi$
$659$	−25.9248			−1.00989			−0.504944	+	0.863152i	$0.668487\pi$
$660$	0.516580	−	0.893483i	0.0201078	−	0.0347788i
$661$	12.1039			0.470786			0.235393	−	0.971900i	$-0.424362\pi$
$661$	12.1039			0.470786			0.235393	+	0.971900i	$0.424362\pi$
$662$		−	14.3903i		−	0.559294i
$663$		−	19.6995i		−	0.765065i
$664$	6.70607			0.260246
$665$	−1.44370	+	2.49704i	−0.0559843	+	0.0968312i
$666$	21.7209			0.841668
$667$		−	5.79314i		−	0.224311i
$668$		−	12.9995i		−	0.502967i
$669$	−51.2269			−1.98055
$670$	−3.49472	−	2.02052i	−0.135013	−	0.0780594i
$671$	2.26590			0.0874740
$672$		−	1.16154i		−	0.0448074i
$673$		−	8.56543i		−	0.330173i	−0.986279	−	0.165087i	$-0.947210\pi$
$673$		−	8.56543i		−	0.330173i	0.986279	−	0.165087i	$-0.0527904\pi$
$674$	4.50809			0.173645
$675$	3.63319	−	2.09172i	0.139841	−	0.0805102i
$676$	−1.74372			−0.0670660
$677$			28.0722i			1.07890i	0.842017	+	0.539451i	$0.181368\pi$
$677$			28.0722i			1.07890i	−0.842017	+	0.539451i	$0.818632\pi$
$678$		−	5.07168i		−	0.194777i
$679$	−5.69485			−0.218548
$680$	−4.51658	−	2.61132i	−0.173203	−	0.100140i
$681$	−51.5317			−1.97470
$682$		−	0.183406i		−	0.00702297i
$683$			49.5063i			1.89430i	0.320785	+	0.947152i	$0.396053\pi$
$683$			49.5063i			1.89430i	−0.320785	+	0.947152i	$0.603947\pi$
$684$	−9.31532			−0.356180
$685$	7.62189	−	13.1829i	0.291218	−	0.503694i
$686$	−6.36345			−0.242958
$687$		−	20.5481i		−	0.783957i
$688$		−	9.42136i		−	0.359186i
$689$	37.2351			1.41855
$690$	3.53844	−	6.12014i	0.134706	−	0.232990i
$691$	35.2890			1.34246			0.671228	−	0.741251i	$-0.265767\pi$
$691$	35.2890			1.34246			0.671228	+	0.741251i	$0.265767\pi$
$692$			4.04373i			0.153720i
$693$			0.282160i			0.0107184i
$694$	−23.2055			−0.880869
$695$	41.7458	+	24.1359i	1.58351	+	0.915528i
$696$	−11.6048			−0.439877
$697$			0.879381i			0.0333089i
$698$			21.0200i			0.795620i
$699$	19.1380			0.723865
$700$	−2.00000	+	1.15145i	−0.0755929	+	0.0435207i
$701$	−10.9207			−0.412469			−0.206235	−	0.978503i	$-0.566121\pi$
$701$	−10.9207			−0.412469			−0.206235	+	0.978503i	$0.566121\pi$
$702$		−	2.81306i		−	0.106172i
$703$			18.2121i			0.686882i
$704$	−0.183406			−0.00691237
$705$	10.4178	+	6.02321i	0.392358	+	0.226847i
$706$	−10.0774			−0.379267
$707$			7.59652i			0.285697i
$708$			27.2297i			1.02336i
$709$	−25.5241			−0.958579			−0.479289	−	0.877657i	$-0.659106\pi$
$709$	−25.5241			−0.958579			−0.479289	+	0.877657i	$0.659106\pi$
$710$	−5.80530	+	10.0409i	−0.217869	+	0.376829i
$711$	−23.4427			−0.879172
$712$			12.8558i			0.481793i
$713$		−	1.25628i		−	0.0470482i
$714$	2.71008			0.101422
$715$	−0.688691	+	1.19117i	−0.0257556	+	0.0445472i
$716$	−1.25749			−0.0469945
$717$		−	35.1991i		−	1.31453i
$718$			22.5227i			0.840538i
$719$	−40.0095			−1.49210			−0.746051	−	0.665889i	$-0.768052\pi$
$719$	−40.0095			−1.49210			−0.746051	+	0.665889i	$0.768052\pi$
$720$	−6.45239	−	3.73054i	−0.240466	−	0.139029i
$721$	4.73362			0.176289
$722$			11.1895i			0.416430i
$723$		−	70.1720i		−	2.60973i
$724$	−5.06985			−0.188420
$725$	11.5039	+	19.9817i	0.427246	+	0.742100i
$726$	−27.5977			−1.02425
$727$		−	49.6643i		−	1.84195i	−0.389626	−	0.920973i	$-0.627396\pi$
$727$		−	49.6643i		−	1.84195i	0.389626	−	0.920973i	$-0.372604\pi$
$728$			1.54854i			0.0573926i
$729$	32.6271			1.20841
$730$	22.4545	+	12.9824i	0.831079	+	0.480500i
$731$	21.9817			0.813021
$732$		−	31.0912i		−	1.14917i
$733$		−	7.49157i		−	0.276708i	−0.990383	−	0.138354i	$-0.955819\pi$
$733$		−	7.49157i		−	0.276708i	0.990383	−	0.138354i	$-0.0441811\pi$
$734$	−23.1402			−0.854120
$735$	−19.1161	+	33.0635i	−0.705109	+	1.21957i
$736$	−1.25628			−0.0463073
$737$		−	0.331102i		−	0.0121963i
$738$			1.25628i			0.0462445i
$739$	12.6089			0.463827			0.231913	−	0.972736i	$-0.425501\pi$
$739$	12.6089			0.463827			0.231913	+	0.972736i	$0.425501\pi$
$740$	−7.29345	+	12.6149i	−0.268113	+	0.463731i
$741$	23.5965			0.866840
$742$			5.12247i			0.188052i
$743$			42.8477i			1.57193i	0.618271	+	0.785965i	$0.287833\pi$
$743$			42.8477i			1.57193i	−0.618271	+	0.785965i	$0.712167\pi$
$744$	−2.51658			−0.0922623
$745$	−32.7581	−	18.9395i	−1.20016	−	0.693891i
$746$	22.4585			0.822265
$747$			22.3525i			0.817835i
$748$		−	0.427918i		−	0.0156462i
$749$	−7.94074			−0.290149
$750$	−0.0514923	+	28.1362i	−0.00188023	+	1.02739i
$751$	−40.3322			−1.47174			−0.735872	−	0.677121i	$-0.763227\pi$
$751$	−40.3322			−1.47174			−0.735872	+	0.677121i	$0.763227\pi$
$752$		−	2.13847i		−	0.0779821i
$753$		−	44.7837i		−	1.63201i
$754$	15.4712			0.563427
$755$	−6.49704	−	3.75636i	−0.236452	−	0.136708i
$756$	0.386995			0.0140749
$757$		−	46.9036i		−	1.70474i	−0.522940	−	0.852370i	$-0.675165\pi$
$757$		−	46.9036i		−	1.70474i	0.522940	−	0.852370i	$-0.324835\pi$
$758$		−	23.1301i		−	0.840123i
$759$	0.579845			0.0210470
$760$	3.12790	−	5.41006i	0.113461	−	0.196244i
$761$	−6.38795			−0.231563			−0.115782	−	0.993275i	$-0.536937\pi$
$761$	−6.38795			−0.231563			−0.115782	+	0.993275i	$0.536937\pi$
$762$			24.1580i			0.875153i
$763$		−	7.07930i		−	0.256288i
$764$	4.69999			0.170040
$765$	8.70400	−	15.0545i	0.314694	−	0.544298i
$766$	−11.6894			−0.422356
$767$		−	36.3019i		−	1.31079i
$768$			2.51658i			0.0908093i
$769$	−37.1905			−1.34112			−0.670561	−	0.741854i	$-0.733947\pi$
$769$	−37.1905			−1.34112			−0.670561	+	0.741854i	$0.733947\pi$
$770$	−0.163870	−	0.0947438i	−0.00590547	−	0.00341433i
$771$	34.1067			1.22832
$772$		−	25.4865i		−	0.917278i
$773$		−	38.0632i		−	1.36904i	−0.728995	−	0.684519i	$-0.760012\pi$
$773$		−	38.0632i		−	1.36904i	0.728995	−	0.684519i	$-0.239988\pi$
$774$	31.4030			1.12876
$775$	2.49472	+	4.33317i	0.0896128	+	0.155652i
$776$	12.3384			0.442922
$777$		−	7.56928i		−	0.271546i
$778$		−	6.14770i		−	0.220406i
$779$	−1.05334			−0.0377399
$780$	16.3445	+	9.44978i	0.585226	+	0.338356i
$781$	−0.951315			−0.0340407
$782$		−	2.93113i		−	0.104817i
$783$		−	3.86641i		−	0.138174i
$784$	6.78697			0.242392
$785$	1.08210	−	1.87162i	0.0386219	−	0.0668009i
$786$	−9.85329			−0.351455
$787$		−	19.0282i		−	0.678282i	−0.940736	−	0.339141i	$-0.889864\pi$
$787$		−	19.0282i		−	0.678282i	0.940736	−	0.339141i	$-0.110136\pi$
$788$		−	9.30610i		−	0.331516i
$789$	−48.3677			−1.72194
$790$	7.87162	−	13.6149i	0.280060	−	0.484395i
$791$	−0.930175			−0.0330732
$792$		−	0.611324i		−	0.0217224i
$793$			41.4500i			1.47193i
$794$	14.4176			0.511662
$795$	54.0666	+	31.2593i	1.91754	+	1.10865i
$796$	7.62007			0.270086
$797$		−	8.25837i		−	0.292526i	−0.989246	−	0.146263i	$-0.953275\pi$
$797$		−	8.25837i		−	0.292526i	0.989246	−	0.146263i	$-0.0467246\pi$
$798$			3.24619i			0.114914i
$799$	4.98943			0.176513
$800$	4.33317	−	2.49472i	0.153201	−	0.0882015i
$801$	−42.8507			−1.51406
$802$			22.8437i			0.806638i
$803$			2.12743i			0.0750752i
$804$	−4.54318			−0.160226
$805$	−1.12247	−	0.648971i	−0.0395619	−	0.0228732i
$806$	3.35504			0.118176
$807$		−	67.3164i		−	2.36965i
$808$		−	16.4585i		−	0.579009i
$809$	45.6417			1.60468			0.802338	−	0.596869i	$-0.203589\pi$
$809$	45.6417			1.60468			0.802338	+	0.596869i	$0.203589\pi$
$810$	−8.83002	+	15.2725i	−0.310255	+	0.536621i
$811$	−34.0047			−1.19407			−0.597033	−	0.802217i	$-0.703654\pi$
$811$	−34.0047			−1.19407			−0.597033	+	0.802217i	$0.703654\pi$
$812$			2.12838i			0.0746915i
$813$			58.1317i			2.03877i
$814$	−1.19518			−0.0418910
$815$	10.5685	−	18.2794i	0.370197	−	0.640298i
$816$	−5.87162			−0.205548
$817$			26.3301i			0.921175i
$818$			12.9302i			0.452093i
$819$	−5.16154			−0.180359
$820$	−0.729613	−	0.421836i	−0.0254792	−	0.0147312i
$821$	−29.7667			−1.03886			−0.519432	−	0.854512i	$-0.673857\pi$
$821$	−29.7667			−1.03886			−0.519432	+	0.854512i	$0.673857\pi$
$822$		−	17.1380i		−	0.597756i
$823$			6.72258i			0.234334i	0.993112	+	0.117167i	$0.0373813\pi$
$823$			6.72258i			0.234334i	−0.993112	+	0.117167i	$0.962619\pi$
$824$	−10.2558			−0.357278
$825$	−2.00000	+	1.15145i	−0.0696311	+	0.0400883i
$826$	4.99409			0.173767
$827$		−	0.490227i		−	0.0170469i	−0.999964	−	0.00852343i	$-0.997287\pi$
$827$		−	0.490227i		−	0.0170469i	0.999964	−	0.00852343i	$-0.00271312\pi$
$828$		−	4.18742i		−	0.145523i
$829$	−6.30657			−0.219036			−0.109518	−	0.993985i	$-0.534931\pi$
$829$	−6.30657			−0.219036			−0.109518	+	0.993985i	$0.534931\pi$
$830$	−12.9817	−	7.50553i	−0.450600	−	0.260521i
$831$	58.2363			2.02019
$832$		−	3.35504i		−	0.116315i
$833$			15.8352i			0.548656i
$834$	54.2702			1.87922
$835$	−14.5493	+	25.1646i	−0.503498	+	0.870857i
$836$	0.512570			0.0177276
$837$		−	0.838459i		−	0.0289814i
$838$		−	6.45572i		−	0.223009i
$839$	−52.4178			−1.80966			−0.904831	−	0.425771i	$-0.860003\pi$
$839$	−52.4178			−1.80966			−0.904831	+	0.425771i	$0.860003\pi$
$840$	−1.30001	+	2.24852i	−0.0448548	+	0.0775814i
$841$	−7.73569			−0.266748
$842$		−	6.17732i		−	0.212885i
$843$			20.7764i			0.715577i
$844$	21.0707			0.725284
$845$	3.37550	+	1.95159i	0.116121	+	0.0671368i
$846$	7.12790			0.245062
$847$			5.06158i			0.173918i
$848$		−	11.0983i		−	0.381116i
$849$	−19.4094			−0.666130
$850$	5.82060	+	10.1100i	0.199645	+	0.346772i
$851$	−8.18668			−0.280636
$852$			13.0533i			0.447200i
$853$			2.38929i			0.0818076i	0.999163	+	0.0409038i	$0.0130237\pi$
$853$			2.38929i			0.0818076i	−0.999163	+	0.0409038i	$0.986976\pi$
$854$	−5.70231			−0.195129
$855$	18.0327	+	10.4258i	0.616705	+	0.356556i
$856$	17.2043			0.588031
$857$		−	20.4509i		−	0.698590i	−0.937013	−	0.349295i	$-0.886421\pi$
$857$		−	20.4509i		−	0.698590i	0.937013	−	0.349295i	$-0.113579\pi$
$858$			1.54854i			0.0528662i
$859$	−47.8820			−1.63371			−0.816856	−	0.576842i	$-0.804285\pi$
$859$	−47.8820			−1.63371			−0.816856	+	0.576842i	$0.804285\pi$
$860$	−10.5445	+	18.2380i	−0.359565	+	0.621909i
$861$	0.437789			0.0149198
$862$		−	13.6974i		−	0.466537i
$863$			43.2544i			1.47240i	0.676766	+	0.736198i	$0.263381\pi$
$863$			43.2544i			1.47240i	−0.676766	+	0.736198i	$0.736619\pi$
$864$	−0.838459			−0.0285250
$865$	4.52580	−	7.82789i	0.153882	−	0.266156i
$866$	8.09194			0.274975
$867$			29.0823i			0.987688i
$868$			0.461555i			0.0156662i
$869$	1.28992			0.0437576
$870$	22.4646	+	12.9882i	0.761622	+	0.440342i
$871$	6.05685			0.205228
$872$			15.3379i			0.519407i
$873$			41.1260i			1.39190i
$874$	3.51098			0.118761
$875$	5.16034	+	0.00944399i	0.174451	+	0.000319265i
$876$	29.1912			0.986279
$877$			36.0663i			1.21787i	0.793219	+	0.608937i	$0.208404\pi$
$877$			36.0663i			1.21787i	−0.793219	+	0.608937i	$0.791596\pi$
$878$			29.5192i			0.996223i
$879$	−46.5092			−1.56872
$880$	0.355039	+	0.205271i	0.0119684	+	0.00691967i
$881$	19.7372			0.664963			0.332481	−	0.943110i	$-0.392114\pi$
$881$	19.7372			0.664963			0.332481	+	0.943110i	$0.392114\pi$
$882$			22.6221i			0.761727i
$883$			46.9281i			1.57926i	0.613585	+	0.789629i	$0.289727\pi$
$883$			46.9281i			1.57926i	−0.613585	+	0.789629i	$0.710273\pi$
$884$	7.82789			0.263280
$885$	30.4759	−	52.7115i	1.02444	−	1.77188i
$886$	−15.3764			−0.516581
$887$			38.4912i			1.29241i	0.763165	+	0.646204i	$0.223645\pi$
$887$			38.4912i			1.29241i	−0.763165	+	0.646204i	$0.776355\pi$
$888$			16.3995i			0.550331i
$889$	4.43072			0.148602
$890$	14.3884	−	24.8864i	0.482302	−	0.834196i
$891$	−1.44698			−0.0484755
$892$		−	20.3558i		−	0.681561i
$893$			5.97645i			0.199994i
$894$	−42.5860			−1.42429
$895$	2.43426	+	1.40740i	0.0813682	+	0.0470442i
$896$	0.461555			0.0154195
$897$			10.6071i			0.354161i
$898$		−	20.6330i		−	0.688534i
$899$	4.61132			0.153796
$900$	8.31532	+	14.4432i	0.277177	+	0.481441i
$901$	25.8942			0.862661
$902$		−	0.0691263i		−	0.00230165i
$903$		−	10.9433i		−	0.364170i
$904$	2.01531			0.0670280
$905$	9.81427	+	5.67425i	0.326237	+	0.188619i
$906$	−8.44625			−0.280608
$907$		−	14.9388i		−	0.496033i	−0.968756	−	0.248017i	$-0.920221\pi$
$907$		−	14.9388i		−	0.496033i	0.968756	−	0.248017i	$-0.0797787\pi$
$908$		−	20.4769i		−	0.679548i
$909$	54.8591			1.81956
$910$	1.73315	−	2.99767i	0.0574532	−	0.0993718i
$911$	9.34408			0.309583			0.154792	−	0.987947i	$-0.450529\pi$
$911$	9.34408			0.309583			0.154792	+	0.987947i	$0.450529\pi$
$912$		−	7.03316i		−	0.232891i
$913$		−	1.22993i		−	0.0407048i
$914$	7.34519			0.242957
$915$	−34.7978	+	60.1867i	−1.15038	+	1.98971i
$916$	8.16507			0.269782
$917$			1.80715i			0.0596774i
$918$		−	1.95627i		−	0.0645665i
$919$	13.8331			0.456312			0.228156	−	0.973625i	$-0.426730\pi$
$919$	13.8331			0.456312			0.228156	+	0.973625i	$0.426730\pi$
$920$	2.43193	+	1.40605i	0.0801783	+	0.0463562i
$921$	1.02610			0.0338110
$922$			2.15986i			0.0711312i
$923$		−	17.4024i		−	0.572806i
$924$	−0.213033			−0.00700828
$925$	28.2375	−	16.2570i	0.928442	−	0.534527i
$926$	8.82315			0.289947
$927$		−	34.1844i		−	1.12276i
$928$		−	4.61132i		−	0.151374i
$929$	−24.4312			−0.801562			−0.400781	−	0.916174i	$-0.631261\pi$
$929$	−24.4312			−0.801562			−0.400781	+	0.916174i	$0.631261\pi$
$930$	4.87162	+	2.81659i	0.159747	+	0.0923598i
$931$	−18.9677			−0.621642
$932$			7.60476i			0.249102i
$933$			25.6628i			0.840164i
$934$	−34.6245			−1.13295
$935$	−0.478932	+	0.828367i	−0.0156628	+	0.0270905i
$936$	11.1829			0.365525
$937$			31.4141i			1.02625i	0.858313	+	0.513127i	$0.171513\pi$
$937$			31.4141i			1.02625i	−0.858313	+	0.513127i	$0.828487\pi$
$938$			0.833246i			0.0272064i
$939$	71.3003			2.32680
$940$	−2.39341	+	4.13968i	−0.0780645	+	0.135021i
$941$	16.7373			0.545620			0.272810	−	0.962068i	$-0.412047\pi$
$941$	16.7373			0.545620			0.272810	+	0.962068i	$0.412047\pi$
$942$		−	2.43313i		−	0.0792757i
$943$		−	0.473498i		−	0.0154192i
$944$	−10.8201			−0.352165
$945$	−0.749149	−	0.433131i	−0.0243698	−	0.0140898i
$946$	−1.72793			−0.0561799
$947$		−	5.54878i		−	0.180311i	−0.995928	−	0.0901556i	$-0.971264\pi$
$947$		−	5.54878i		−	0.180311i	0.995928	−	0.0901556i	$-0.0287364\pi$
$948$		−	17.6995i		−	0.574853i
$949$	−38.9169			−1.26330
$950$	−12.1100	+	6.97205i	−0.392902	+	0.226203i
$951$	−27.8429			−0.902867
$952$			1.07689i			0.0349022i
$953$		−	33.5296i		−	1.08613i	−0.839691	−	0.543065i	$-0.817264\pi$
$953$		−	33.5296i		−	1.08613i	0.839691	−	0.543065i	$-0.182736\pi$
$954$	36.9925			1.19768
$955$	−9.09828	−	5.26029i	−0.294413	−	0.170219i
$956$	13.9869			0.452368
$957$			2.12838i			0.0688008i
$958$		−	35.4879i		−	1.14656i
$959$	−3.14321			−0.101499
$960$	2.81659	−	4.87162i	0.0909052	−	0.157231i
$961$	1.00000			0.0322581
$962$		−	21.8634i		−	0.704904i
$963$			57.3450i			1.84792i
$964$	27.8839			0.898080
$965$	−28.5248	+	49.3370i	−0.918247	+	1.58821i
$966$	−1.45923			−0.0469498
$967$			25.1472i			0.808681i	0.914609	+	0.404340i	$0.132499\pi$
$967$			25.1472i			0.808681i	−0.914609	+	0.404340i	$0.867501\pi$
$968$		−	10.9664i		−	0.352472i
$969$	16.4096			0.527152
$970$	−23.8848	−	13.8093i	−0.766894	−	0.443390i
$971$	24.5893			0.789109			0.394554	−	0.918873i	$-0.370899\pi$
$971$	24.5893			0.789109			0.394554	+	0.918873i	$0.370899\pi$
$972$			22.3699i			0.717514i
$973$		−	9.95346i		−	0.319093i
$974$	−6.73569			−0.215826
$975$	−21.0634	−	36.5860i	−0.674570	−	1.17169i
$976$	12.3546			0.395460
$977$		−	14.6777i		−	0.469582i	−0.972046	−	0.234791i	$-0.924559\pi$
$977$		−	14.6777i		−	0.469582i	0.972046	−	0.234791i	$-0.0754406\pi$
$978$		−	23.7634i		−	0.759870i
$979$	2.35784			0.0753567
$980$	−13.1383	−	7.59608i	−0.419687	−	0.242648i
$981$	−51.1239			−1.63226
$982$			8.12644i			0.259325i
$983$			38.5166i			1.22849i	0.789116	+	0.614244i	$0.210539\pi$
$983$			38.5166i			1.22849i	−0.789116	+	0.614244i	$0.789461\pi$
$984$	−0.948508			−0.0302373
$985$	−10.4155	+	18.0148i	−0.331866	+	0.574000i
$986$	10.7590			0.342637
$987$		−	2.48392i		−	0.0790642i
$988$			9.37643i			0.298304i
$989$	−11.8359			−0.376360
$990$	−0.684203	+	1.18341i	−0.0217454	+	0.0376111i
$991$	31.1432			0.989297			0.494648	−	0.869093i	$-0.335297\pi$
$991$	31.1432			0.989297			0.494648	+	0.869093i	$0.335297\pi$
$992$		−	1.00000i		−	0.0317500i
$993$			36.2143i			1.14922i
$994$	2.39406			0.0759350
$995$	−14.7510	−	8.52850i	−0.467638	−	0.270372i
$996$	−16.8764			−0.534748
$997$		−	3.79487i		−	0.120185i	−0.998193	−	0.0600924i	$-0.980860\pi$
$997$		−	3.79487i		−	0.120185i	0.998193	−	0.0600924i	$-0.0191395\pi$
$998$		−	28.0819i		−	0.888916i
$999$	−5.46388			−0.172870

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.b.b.249.4	✓	8
3.2	odd	2		2790.2.d.l.559.5		8
4.3	odd	2		2480.2.d.e.1489.1		8
5.2	odd	4		1550.2.a.q.1.4		4
5.3	odd	4		1550.2.a.n.1.1		4
5.4	even	2	inner	310.2.b.b.249.5	yes	8
15.14	odd	2		2790.2.d.l.559.1		8
20.19	odd	2		2480.2.d.e.1489.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.b.b.249.4	✓	8	1.1	even	1	trivial
310.2.b.b.249.5	yes	8	5.4	even	2	inner
1550.2.a.n.1.1		4	5.3	odd	4
1550.2.a.q.1.4		4	5.2	odd	4
2480.2.d.e.1489.1		8	4.3	odd	2
2480.2.d.e.1489.8		8	20.19	odd	2
2790.2.d.l.559.1		8	15.14	odd	2
2790.2.d.l.559.5		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +2.51658i q^{3} -1.00000 q^{4} +(1.93581 + 1.11922i) q^{5} +2.51658 q^{6} -0.461555i q^{7} +1.00000i q^{8} -3.33317 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +2.51658i q^{3} -1.00000 q^{4} +(1.93581 + 1.11922i) q^{5} +2.51658 q^{6} -0.461555i q^{7} +1.00000i q^{8} -3.33317 q^{9} +(1.11922 - 1.93581i) q^{10} +0.183406 q^{11} -2.51658i q^{12} +3.35504i q^{13} -0.461555 q^{14} +(-2.81659 + 4.87162i) q^{15} +1.00000 q^{16} +2.33317i q^{17} +3.33317i q^{18} -2.79473 q^{19} +(-1.93581 - 1.11922i) q^{20} +1.16154 q^{21} -0.183406i q^{22} -1.25628i q^{23} -2.51658 q^{24} +(2.49472 + 4.33317i) q^{25} +3.35504 q^{26} -0.838459i q^{27} +0.461555i q^{28} +4.61132 q^{29} +(4.87162 + 2.81659i) q^{30} +1.00000 q^{31} -1.00000i q^{32} +0.461555i q^{33} +2.33317 q^{34} +(0.516580 - 0.893483i) q^{35} +3.33317 q^{36} -6.51658i q^{37} +2.79473i q^{38} -8.44322 q^{39} +(-1.11922 + 1.93581i) q^{40} +0.376903 q^{41} -1.16154i q^{42} -9.42136i q^{43} -0.183406 q^{44} +(-6.45239 - 3.73054i) q^{45} -1.25628 q^{46} -2.13847i q^{47} +2.51658i q^{48} +6.78697 q^{49} +(4.33317 - 2.49472i) q^{50} -5.87162 q^{51} -3.35504i q^{52} -11.0983i q^{53} -0.838459 q^{54} +(0.355039 + 0.205271i) q^{55} +0.461555 q^{56} -7.03316i q^{57} -4.61132i q^{58} -10.8201 q^{59} +(2.81659 - 4.87162i) q^{60} +12.3546 q^{61} -1.00000i q^{62} +1.53844i q^{63} -1.00000 q^{64} +(-3.75501 + 6.49472i) q^{65} +0.461555 q^{66} -1.80530i q^{67} -2.33317i q^{68} +3.16154 q^{69} +(-0.893483 - 0.516580i) q^{70} -5.18694 q^{71} -3.33317i q^{72} +11.5996i q^{73} -6.51658 q^{74} +(-10.9048 + 6.27815i) q^{75} +2.79473 q^{76} -0.0846520i q^{77} +8.44322i q^{78} +7.03316 q^{79} +(1.93581 + 1.11922i) q^{80} -7.88947 q^{81} -0.376903i q^{82} -6.70607i q^{83} -1.16154 q^{84} +(-2.61132 + 4.51658i) q^{85} -9.42136 q^{86} +11.6048i q^{87} +0.183406i q^{88} +12.8558 q^{89} +(-3.73054 + 6.45239i) q^{90} +1.54854 q^{91} +1.25628i q^{92} +2.51658i q^{93} -2.13847 q^{94} +(-5.41006 - 3.12790i) q^{95} +2.51658 q^{96} -12.3384i q^{97} -6.78697i q^{98} -0.611324 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6}+O(q^{10}) \) 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6	\( 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{10} + 12 q^{11} - 12 q^{14} - 12 q^{15} + 8 q^{16} - 4 q^{19} + 2 q^{20} + 12 q^{21} - 4 q^{24} - 4 q^{25} + 8 q^{26} + 8 q^{29} + 4 q^{30} + 8 q^{31} - 8 q^{34} - 12 q^{35} + 8 q^{39} - 2 q^{40} - 8 q^{41} - 12 q^{44} - 18 q^{45} + 8 q^{50} - 12 q^{51} - 4 q^{54} - 16 q^{55} + 12 q^{56} + 12 q^{60} - 8 q^{64} + 12 q^{66} + 28 q^{69} + 20 q^{70} + 24 q^{71} - 36 q^{74} - 20 q^{75} + 4 q^{76} + 24 q^{79} - 2 q^{80} - 32 q^{81} - 12 q^{84} + 8 q^{85} + 8 q^{86} + 24 q^{89} + 6 q^{90} - 28 q^{91} - 20 q^{94} + 4 q^{96} + 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^10 + 12 * q^11 - 12 * q^14 - 12 * q^15 + 8 * q^16 - 4 * q^19 + 2 * q^20 + 12 * q^21 - 4 * q^24 - 4 * q^25 + 8 * q^26 + 8 * q^29 + 4 * q^30 + 8 * q^31 - 8 * q^34 - 12 * q^35 + 8 * q^39 - 2 * q^40 - 8 * q^41 - 12 * q^44 - 18 * q^45 + 8 * q^50 - 12 * q^51 - 4 * q^54 - 16 * q^55 + 12 * q^56 + 12 * q^60 - 8 * q^64 + 12 * q^66 + 28 * q^69 + 20 * q^70 + 24 * q^71 - 36 * q^74 - 20 * q^75 + 4 * q^76 + 24 * q^79 - 2 * q^80 - 32 * q^81 - 12 * q^84 + 8 * q^85 + 8 * q^86 + 24 * q^89 + 6 * q^90 - 28 * q^91 - 20 * q^94 + 4 * q^96 + 24 * q^99

Introduction

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