LMFDB - Embedded newform 230.2.b.b.139.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(139,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, 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("230.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.11574317056.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 45x^{4} + 4 $ x^8 + 45*x^4 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.4
Root			$0.386289 - 0.386289i$ of defining polynomial
Character	$\chi$	$=$	230.139
Dual form			230.2.b.b.139.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +3.25886i q^{3} -1.00000 q^{4} +(0.386289 + 2.20245i) q^{5} +3.25886 q^{6} -1.44270i q^{7} +1.00000i q^{8} -7.62018 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +3.25886i q^{3} -1.00000 q^{4} +(0.386289 + 2.20245i) q^{5} +3.25886 q^{6} -1.44270i q^{7} +1.00000i q^{8} -7.62018 q^{9} +(2.20245 - 0.386289i) q^{10} -2.03144 q^{11} -3.25886i q^{12} +0.557299i q^{13} -1.44270 q^{14} +(-7.17748 + 1.25886i) q^{15} +1.00000 q^{16} +3.91861i q^{17} +7.62018i q^{18} +6.73300 q^{19} +(-0.386289 - 2.20245i) q^{20} +4.70156 q^{21} +2.03144i q^{22} +1.00000i q^{23} -3.25886 q^{24} +(-4.70156 + 1.70156i) q^{25} +0.557299 q^{26} -15.0565i q^{27} +1.44270i q^{28} +9.69520 q^{29} +(1.25886 + 7.17748i) q^{30} -3.07502 q^{31} -1.00000i q^{32} -6.62018i q^{33} +3.91861 q^{34} +(3.17748 - 0.557299i) q^{35} +7.62018 q^{36} +3.65798i q^{37} -6.73300i q^{38} -1.81616 q^{39} +(-2.20245 + 0.386289i) q^{40} +7.03321 q^{41} -4.70156i q^{42} -5.06465i q^{43} +2.03144 q^{44} +(-2.94359 - 16.7830i) q^{45} +1.00000 q^{46} -0.659753i q^{47} +3.25886i q^{48} +4.91861 q^{49} +(1.70156 + 4.70156i) q^{50} -12.7702 q^{51} -0.557299i q^{52} +11.1275i q^{53} -15.0565 q^{54} +(-0.784722 - 4.47414i) q^{55} +1.44270 q^{56} +21.9419i q^{57} -9.69520i q^{58} -10.7226 q^{59} +(7.17748 - 1.25886i) q^{60} +1.73937 q^{61} +3.07502i q^{62} +10.9936i q^{63} -1.00000 q^{64} +(-1.22742 + 0.215278i) q^{65} -6.62018 q^{66} -12.0129i q^{67} -3.91861i q^{68} -3.25886 q^{69} +(-0.557299 - 3.17748i) q^{70} +12.4363 q^{71} -7.62018i q^{72} -9.26464i q^{73} +3.65798 q^{74} +(-5.54515 - 15.3217i) q^{75} -6.73300 q^{76} +2.93076i q^{77} +1.81616i q^{78} -5.92439 q^{79} +(0.386289 + 2.20245i) q^{80} +26.2066 q^{81} -7.03321i q^{82} -11.3775i q^{83} -4.70156 q^{84} +(-8.63055 + 1.51372i) q^{85} -5.06465 q^{86} +31.5953i q^{87} -2.03144i q^{88} -5.25308 q^{89} +(-16.7830 + 2.94359i) q^{90} +0.804016 q^{91} -1.00000i q^{92} -10.0211i q^{93} -0.659753 q^{94} +(2.60088 + 14.8291i) q^{95} +3.25886 q^{96} +0.0813861i q^{97} -4.91861i q^{98} +15.4799 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 6 q^{6} - 14 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 + 6 * q^6 - 14 * q^9	$ 8 q - 8 q^{4} + 6 q^{6} - 14 q^{9} + 10 q^{11} - 6 q^{14} - 16 q^{15} + 8 q^{16} + 2 q^{19} + 12 q^{21} - 6 q^{24} - 12 q^{25} + 10 q^{26} - 4 q^{29} - 10 q^{30} + 10 q^{31} + 10 q^{34} - 16 q^{35} + 14 q^{36} + 46 q^{41} - 10 q^{44} - 26 q^{45} + 8 q^{46} + 18 q^{49} - 12 q^{50} + 14 q^{51} - 12 q^{54} - 18 q^{55} + 6 q^{56} - 32 q^{59} + 16 q^{60} + 18 q^{61} - 8 q^{64} - 16 q^{65} - 6 q^{66} - 6 q^{69} - 10 q^{70} + 38 q^{71} + 12 q^{74} - 32 q^{75} - 2 q^{76} + 12 q^{79} + 32 q^{81} - 12 q^{84} - 24 q^{85} - 4 q^{86} - 60 q^{89} - 24 q^{90} - 26 q^{91} - 4 q^{94} + 18 q^{95} + 6 q^{96} + 54 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 6 * q^6 - 14 * q^9 + 10 * q^11 - 6 * q^14 - 16 * q^15 + 8 * q^16 + 2 * q^19 + 12 * q^21 - 6 * q^24 - 12 * q^25 + 10 * q^26 - 4 * q^29 - 10 * q^30 + 10 * q^31 + 10 * q^34 - 16 * q^35 + 14 * q^36 + 46 * q^41 - 10 * q^44 - 26 * q^45 + 8 * q^46 + 18 * q^49 - 12 * q^50 + 14 * q^51 - 12 * q^54 - 18 * q^55 + 6 * q^56 - 32 * q^59 + 16 * q^60 + 18 * q^61 - 8 * q^64 - 16 * q^65 - 6 * q^66 - 6 * q^69 - 10 * q^70 + 38 * q^71 + 12 * q^74 - 32 * q^75 - 2 * q^76 + 12 * q^79 + 32 * q^81 - 12 * q^84 - 24 * q^85 - 4 * q^86 - 60 * q^89 - 24 * q^90 - 26 * q^91 - 4 * q^94 + 18 * q^95 + 6 * q^96 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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
$3$			3.25886i			1.88150i	0.339095	+	0.940752i	$0.389879\pi$
$3$			3.25886i			1.88150i	−0.339095	+	0.940752i	$0.610121\pi$
$4$	−1.00000			−0.500000
$5$	0.386289	+	2.20245i	0.172754	+	0.984965i
$5$	0.386289	+	2.20245i	0.172754	+	0.984965i
$6$	3.25886			1.33042
$7$		−	1.44270i		−	0.545290i	−0.962115	−	0.272645i	$-0.912102\pi$
$7$		−	1.44270i		−	0.545290i	0.962115	−	0.272645i	$-0.0878984\pi$
$8$			1.00000i			0.353553i
$9$	−7.62018			−2.54006
$10$	2.20245	−	0.386289i	0.696475	−	0.122155i
$11$	−2.03144			−0.612502			−0.306251	−	0.951951i	$-0.599075\pi$
$11$	−2.03144			−0.612502			−0.306251	+	0.951951i	$0.599075\pi$
$12$		−	3.25886i		−	0.940752i
$13$			0.557299i			0.154567i	0.997009	+	0.0772835i	$0.0246246\pi$
$13$			0.557299i			0.154567i	−0.997009	+	0.0772835i	$0.975375\pi$
$14$	−1.44270			−0.385578
$15$	−7.17748	+	1.25886i	−1.85322	+	0.325037i
$16$	1.00000			0.250000
$17$			3.91861i			0.950403i	0.879877	+	0.475202i	$0.157625\pi$
$17$			3.91861i			0.950403i	−0.879877	+	0.475202i	$0.842375\pi$
$18$			7.62018i			1.79609i
$19$	6.73300			1.54466			0.772328	−	0.635224i	$-0.219092\pi$
$19$	6.73300			1.54466			0.772328	+	0.635224i	$0.219092\pi$
$20$	−0.386289	−	2.20245i	−0.0863768	−	0.492483i
$21$	4.70156			1.02596
$22$			2.03144i			0.433104i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	−3.25886			−0.665212
$25$	−4.70156	+	1.70156i	−0.940312	+	0.340312i
$26$	0.557299			0.109295
$27$		−	15.0565i		−	2.89763i
$28$			1.44270i			0.272645i
$29$	9.69520			1.80035			0.900176	−	0.435525i	$-0.143437\pi$
$29$	9.69520			1.80035			0.900176	+	0.435525i	$0.143437\pi$
$30$	1.25886	+	7.17748i	0.229836	+	1.31042i
$31$	−3.07502			−0.552290			−0.276145	−	0.961116i	$-0.589057\pi$
$31$	−3.07502			−0.552290			−0.276145	+	0.961116i	$0.589057\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	6.62018i		−	1.15242i
$34$	3.91861			0.672037
$35$	3.17748	−	0.557299i	0.537091	−	0.0942007i
$36$	7.62018			1.27003
$37$			3.65798i			0.601368i	0.953724	+	0.300684i	$0.0972150\pi$
$37$			3.65798i			0.601368i	−0.953724	+	0.300684i	$0.902785\pi$
$38$		−	6.73300i		−	1.09224i
$39$	−1.81616			−0.290818
$40$	−2.20245	+	0.386289i	−0.348238	+	0.0610776i
$41$	7.03321			1.09840			0.549202	−	0.835690i	$-0.314932\pi$
$41$	7.03321			1.09840			0.549202	+	0.835690i	$0.314932\pi$
$42$		−	4.70156i		−	0.725467i
$43$		−	5.06465i		−	0.772352i	−0.922425	−	0.386176i	$-0.873796\pi$
$43$		−	5.06465i		−	0.772352i	0.922425	−	0.386176i	$-0.126204\pi$
$44$	2.03144			0.306251
$45$	−2.94359	−	16.7830i	−0.438804	−	2.50187i
$46$	1.00000			0.147442
$47$		−	0.659753i		−	0.0962348i	−0.998842	−	0.0481174i	$-0.984678\pi$
$47$		−	0.659753i		−	0.0962348i	0.998842	−	0.0481174i	$-0.0153222\pi$
$48$			3.25886i			0.470376i
$49$	4.91861			0.702659
$50$	1.70156	+	4.70156i	0.240637	+	0.664901i
$51$	−12.7702			−1.78819
$52$		−	0.557299i		−	0.0772835i
$53$			11.1275i			1.52848i	0.644930	+	0.764242i	$0.276887\pi$
$53$			11.1275i			1.52848i	−0.644930	+	0.764242i	$0.723113\pi$
$54$	−15.0565			−2.04893
$55$	−0.784722	−	4.47414i	−0.105812	−	0.603293i
$56$	1.44270			0.192789
$57$			21.9419i			2.90628i
$58$		−	9.69520i		−	1.27304i
$59$	−10.7226			−1.39597			−0.697984	−	0.716114i	$-0.745919\pi$
$59$	−10.7226			−1.39597			−0.697984	+	0.716114i	$0.745919\pi$
$60$	7.17748	−	1.25886i	0.926608	−	0.162518i
$61$	1.73937			0.222703			0.111351	−	0.993781i	$-0.464482\pi$
$61$	1.73937			0.222703			0.111351	+	0.993781i	$0.464482\pi$
$62$			3.07502i			0.390528i
$63$			10.9936i			1.38507i
$64$	−1.00000			−0.125000
$65$	−1.22742	+	0.215278i	−0.152243	+	0.0267020i
$66$	−6.62018			−0.814887
$67$		−	12.0129i		−	1.46761i	−0.679359	−	0.733806i	$-0.737742\pi$
$67$		−	12.0129i		−	1.46761i	0.679359	−	0.733806i	$-0.262258\pi$
$68$		−	3.91861i		−	0.475202i
$69$	−3.25886			−0.392321
$70$	−0.557299	−	3.17748i	−0.0666100	−	0.379781i
$71$	12.4363			1.47592			0.737961	−	0.674844i	$-0.235789\pi$
$71$	12.4363			1.47592			0.737961	+	0.674844i	$0.235789\pi$
$72$		−	7.62018i		−	0.898046i
$73$		−	9.26464i		−	1.08434i	−0.840267	−	0.542172i	$-0.817602\pi$
$73$		−	9.26464i		−	1.08434i	0.840267	−	0.542172i	$-0.182398\pi$
$74$	3.65798			0.425231
$75$	−5.54515	−	15.3217i	−0.640299	−	1.76920i
$76$	−6.73300			−0.772328
$77$			2.93076i			0.333991i
$78$			1.81616i			0.205640i
$79$	−5.92439			−0.666546			−0.333273	−	0.942830i	$-0.608153\pi$
$79$	−5.92439			−0.666546			−0.333273	+	0.942830i	$0.608153\pi$
$80$	0.386289	+	2.20245i	0.0431884	+	0.246241i
$81$	26.2066			2.91184
$82$		−	7.03321i		−	0.776688i
$83$		−	11.3775i		−	1.24884i	−0.781089	−	0.624420i	$-0.785336\pi$
$83$		−	11.3775i		−	1.24884i	0.781089	−	0.624420i	$-0.214664\pi$
$84$	−4.70156			−0.512982
$85$	−8.63055	+	1.51372i	−0.936114	+	0.164186i
$86$	−5.06465			−0.546135
$87$			31.5953i			3.38737i
$88$		−	2.03144i		−	0.216552i
$89$	−5.25308			−0.556826			−0.278413	−	0.960462i	$-0.589808\pi$
$89$	−5.25308			−0.556826			−0.278413	+	0.960462i	$0.589808\pi$
$90$	−16.7830	+	2.94359i	−1.76909	+	0.310281i
$91$	0.804016			0.0842838
$92$		−	1.00000i		−	0.104257i
$93$		−	10.0211i		−	1.03914i
$94$	−0.659753			−0.0680483
$95$	2.60088	+	14.8291i	0.266845	+	1.52143i
$96$	3.25886			0.332606
$97$			0.0813861i			0.00826350i	0.999991	+	0.00413175i	$0.00131518\pi$
$97$			0.0813861i			0.00826350i	−0.999991	+	0.00413175i	$0.998685\pi$
$98$		−	4.91861i		−	0.496855i
$99$	15.4799			1.55579
$100$	4.70156	−	1.70156i	0.470156	−	0.170156i
$101$	8.31281			0.827156			0.413578	−	0.910469i	$-0.364279\pi$
$101$	8.31281			0.827156			0.413578	+	0.910469i	$0.364279\pi$
$102$			12.7702i			1.26444i
$103$		−	6.36991i		−	0.627646i	−0.949481	−	0.313823i	$-0.898390\pi$
$103$		−	6.36991i		−	0.627646i	0.949481	−	0.313823i	$-0.101610\pi$
$104$	−0.557299			−0.0546477
$105$	1.81616	+	10.3550i	0.177239	+	1.01054i
$106$	11.1275			1.08080
$107$			16.9226i			1.63597i	0.575239	+	0.817986i	$0.304909\pi$
$107$			16.9226i			1.63597i	−0.575239	+	0.817986i	$0.695091\pi$
$108$			15.0565i			1.44881i
$109$	0.218825			0.0209597			0.0104798	−	0.999945i	$-0.496664\pi$
$109$	0.218825			0.0209597			0.0104798	+	0.999945i	$0.496664\pi$
$110$	−4.47414	+	0.784722i	−0.426592	+	0.0748203i
$111$	−11.9208			−1.13148
$112$		−	1.44270i		−	0.136322i
$113$			0.580599i			0.0546182i	0.999627	+	0.0273091i	$0.00869384\pi$
$113$			0.580599i			0.0546182i	−0.999627	+	0.0273091i	$0.991306\pi$
$114$	21.9419			2.05505
$115$	−2.20245	+	0.386289i	−0.205379	+	0.0360216i
$116$	−9.69520			−0.900176
$117$		−	4.24672i		−	0.392609i
$118$			10.7226i			0.987098i
$119$	5.65339			0.518245
$120$	−1.25886	−	7.17748i	−0.114918	−	0.655211i
$121$	−6.87326			−0.624842
$122$		−	1.73937i		−	0.157475i
$123$			22.9203i			2.06665i
$124$	3.07502			0.276145
$125$	−5.56376	−	9.69766i	−0.497638	−	0.867385i
$126$	10.9936			0.979391
$127$		−	1.56944i		−	0.139266i	−0.997573	−	0.0696328i	$-0.977817\pi$
$127$		−	1.56944i		−	0.139266i	0.997573	−	0.0696328i	$-0.0221828\pi$
$128$			1.00000i			0.0883883i
$129$	16.5050			1.45318
$130$	0.215278	+	1.22742i	0.0188812	+	0.107652i
$131$	15.9208			1.39101			0.695505	−	0.718521i	$-0.255181\pi$
$131$	15.9208			1.39101			0.695505	+	0.718521i	$0.255181\pi$
$132$			6.62018i			0.576212i
$133$		−	9.71371i		−	0.842285i
$134$	−12.0129			−1.03776
$135$	33.1612	−	5.81616i	2.85406	−	0.500575i
$136$	−3.91861			−0.336018
$137$			6.47013i			0.552781i	0.961045	+	0.276390i	$0.0891383\pi$
$137$			6.47013i			0.552781i	−0.961045	+	0.276390i	$0.910862\pi$
$138$			3.25886i			0.277413i
$139$	0.656206			0.0556586			0.0278293	−	0.999613i	$-0.491141\pi$
$139$	0.656206			0.0556586			0.0278293	+	0.999613i	$0.491141\pi$
$140$	−3.17748	+	0.557299i	−0.268546	+	0.0471004i
$141$	2.15004			0.181066
$142$		−	12.4363i		−	1.04363i
$143$		−	1.13212i		−	0.0946725i
$144$	−7.62018			−0.635015
$145$	3.74514	+	21.3532i	0.311017	+	1.77328i
$146$	−9.26464			−0.766747
$147$			16.0291i			1.32206i
$148$		−	3.65798i		−	0.300684i
$149$	−23.8349			−1.95263			−0.976314	−	0.216357i	$-0.930582\pi$
$149$	−23.8349			−1.95263			−0.976314	+	0.216357i	$0.930582\pi$
$150$	−15.3217	+	5.54515i	−1.25101	+	0.452760i
$151$	−14.8669			−1.20985			−0.604925	−	0.796282i	$-0.706797\pi$
$151$	−14.8669			−1.20985			−0.604925	+	0.796282i	$0.706797\pi$
$152$			6.73300i			0.546118i
$153$		−	29.8605i		−	2.41408i
$154$	2.93076			0.236167
$155$	−1.18785	−	6.77258i	−0.0954101	−	0.543987i
$156$	1.81616			0.145409
$157$		−	8.24213i		−	0.657793i	−0.944366	−	0.328897i	$-0.893323\pi$
$157$		−	8.24213i		−	0.657793i	0.944366	−	0.328897i	$-0.106677\pi$
$158$			5.92439i			0.471319i
$159$	−36.2631			−2.87585
$160$	2.20245	−	0.386289i	0.174119	−	0.0305388i
$161$	1.44270			0.113701
$162$		−	26.2066i		−	2.05898i
$163$		−	10.3154i		−	0.807962i	−0.914767	−	0.403981i	$-0.867626\pi$
$163$		−	10.3154i		−	0.807962i	0.914767	−	0.403981i	$-0.132374\pi$
$164$	−7.03321			−0.549202
$165$	14.5806	−	2.55730i	1.13510	−	0.199085i
$166$	−11.3775			−0.883063
$167$			4.65975i			0.360582i	0.983613	+	0.180291i	$0.0577040\pi$
$167$			4.65975i			0.360582i	−0.983613	+	0.180291i	$0.942296\pi$
$168$			4.70156i			0.362733i
$169$	12.6894			0.976109
$170$	1.51372	+	8.63055i	0.116097	+	0.661933i
$171$	−51.3067			−3.92352
$172$			5.06465i			0.386176i
$173$			2.80402i			0.213185i	0.994303	+	0.106593i	$0.0339941\pi$
$173$			2.80402i			0.213185i	−0.994303	+	0.106593i	$0.966006\pi$
$174$	31.5953			2.39523
$175$	2.45485	+	6.78295i	0.185569	+	0.512743i
$176$	−2.03144			−0.153125
$177$		−	34.9436i		−	2.62652i
$178$			5.25308i			0.393735i
$179$	4.44212			0.332019			0.166010	−	0.986124i	$-0.446912\pi$
$179$	4.44212			0.332019			0.166010	+	0.986124i	$0.446912\pi$
$180$	2.94359	+	16.7830i	0.219402	+	1.25093i
$181$	2.42019			0.179891			0.0899455	−	0.995947i	$-0.471331\pi$
$181$	2.42019			0.179891			0.0899455	+	0.995947i	$0.471331\pi$
$182$		−	0.804016i		−	0.0595976i
$183$			5.66835i			0.419016i
$184$	−1.00000			−0.0737210
$185$	−8.05651	+	1.41304i	−0.592327	+	0.103888i
$186$	−10.0211			−0.734780
$187$		−	7.96042i		−	0.582124i
$188$			0.659753i			0.0481174i
$189$	−21.7220			−1.58005
$190$	14.8291	−	2.60088i	1.07582	−	0.188688i
$191$	−20.8934			−1.51179			−0.755897	−	0.654690i	$-0.772799\pi$
$191$	−20.8934			−1.51179			−0.755897	+	0.654690i	$0.772799\pi$
$192$		−	3.25886i		−	0.235188i
$193$		−	2.88540i		−	0.207696i	−0.994593	−	0.103848i	$-0.966884\pi$
$193$		−	2.88540i		−	0.207696i	0.994593	−	0.103848i	$-0.0331155\pi$
$194$	0.0813861			0.00584318
$195$	−0.701562	−	4.00000i	−0.0502399	−	0.286446i
$196$	−4.91861			−0.351330
$197$		−	19.0925i		−	1.36029i	−0.733079	−	0.680144i	$-0.761917\pi$
$197$		−	19.0925i		−	1.36029i	0.733079	−	0.680144i	$-0.238083\pi$
$198$		−	15.4799i		−	1.10011i
$199$	−6.58060			−0.466486			−0.233243	−	0.972418i	$-0.574934\pi$
$199$	−6.58060			−0.466486			−0.233243	+	0.972418i	$0.574934\pi$
$200$	−1.70156	−	4.70156i	−0.120319	−	0.332451i
$201$	39.1485			2.76132
$202$		−	8.31281i		−	0.584888i
$203$		−	13.9873i		−	0.981714i
$204$	12.7702			0.894094
$205$	2.71685	+	15.4903i	0.189753	+	1.08189i
$206$	−6.36991			−0.443813
$207$		−	7.62018i		−	0.529639i
$208$			0.557299i			0.0386417i
$209$	−13.6777			−0.946105
$210$	10.3550	−	1.81616i	0.714559	−	0.125327i
$211$	6.55986			0.451599			0.225800	−	0.974174i	$-0.427501\pi$
$211$	6.55986			0.451599			0.225800	+	0.974174i	$0.427501\pi$
$212$		−	11.1275i		−	0.764242i
$213$			40.5283i			2.77695i
$214$	16.9226			1.15681
$215$	11.1546	−	1.95642i	0.760740	−	0.133427i
$216$	15.0565			1.02447
$217$			4.43634i			0.301158i
$218$		−	0.218825i		−	0.0148207i
$219$	30.1922			2.04020
$220$	0.784722	+	4.47414i	0.0529059	+	0.301646i
$221$	−2.18384			−0.146901
$222$			11.9208i			0.800075i
$223$			20.2094i			1.35332i	0.736296	+	0.676660i	$0.236573\pi$
$223$			20.2094i			1.35332i	−0.736296	+	0.676660i	$0.763427\pi$
$224$	−1.44270			−0.0963945
$225$	35.8267	−	12.9662i	2.38845	−	0.864414i
$226$	0.580599			0.0386209
$227$		−	15.0098i		−	0.996234i	−0.867110	−	0.498117i	$-0.834025\pi$
$227$		−	15.0098i		−	0.996234i	0.867110	−	0.498117i	$-0.165975\pi$
$228$		−	21.9419i		−	1.45314i
$229$	−13.7081			−0.905859			−0.452929	−	0.891546i	$-0.649621\pi$
$229$	−13.7081			−0.905859			−0.452929	+	0.891546i	$0.649621\pi$
$230$	0.386289	+	2.20245i	0.0254711	+	0.145225i
$231$	−9.55093			−0.628405
$232$			9.69520i			0.636521i
$233$		−	9.19822i		−	0.602595i	−0.953530	−	0.301298i	$-0.902580\pi$
$233$		−	9.19822i		−	0.602595i	0.953530	−	0.301298i	$-0.0974198\pi$
$234$	−4.24672			−0.277617
$235$	1.45307	−	0.254855i	0.0947880	−	0.0166249i
$236$	10.7226			0.697984
$237$		−	19.3068i		−	1.25411i
$238$		−	5.65339i		−	0.366455i
$239$	2.72618			0.176342			0.0881709	−	0.996105i	$-0.471898\pi$
$239$	2.72618			0.176342			0.0881709	+	0.996105i	$0.471898\pi$
$240$	−7.17748	+	1.25886i	−0.463304	+	0.0812591i
$241$	3.26109			0.210066			0.105033	−	0.994469i	$-0.466505\pi$
$241$	3.26109			0.210066			0.105033	+	0.994469i	$0.466505\pi$
$242$			6.87326i			0.441830i
$243$			40.2340i			2.58101i
$244$	−1.73937			−0.111351
$245$	1.90000	+	10.8330i	0.121387	+	0.692095i
$246$	22.9203			1.46134
$247$			3.75229i			0.238753i
$248$		−	3.07502i		−	0.195264i
$249$	37.0776			2.34970
$250$	−9.69766	+	5.56376i	−0.613334	+	0.351883i
$251$	19.9941			1.26202			0.631008	−	0.775776i	$-0.282641\pi$
$251$	19.9941			1.26202			0.631008	+	0.775776i	$0.282641\pi$
$252$		−	10.9936i		−	0.692534i
$253$		−	2.03144i		−	0.127715i
$254$	−1.56944			−0.0984756
$255$	−4.93299	−	28.1258i	−0.308916	−	1.76130i
$256$	1.00000			0.0625000
$257$			26.7935i			1.67133i	0.549237	+	0.835667i	$0.314919\pi$
$257$			26.7935i			1.67133i	−0.549237	+	0.835667i	$0.685081\pi$
$258$		−	16.5050i		−	1.02756i
$259$	5.27737			0.327920
$260$	1.22742	−	0.215278i	0.0761215	−	0.0133510i
$261$	−73.8791			−4.57300
$262$		−	15.9208i		−	0.983593i
$263$		−	15.8267i		−	0.975918i	−0.872867	−	0.487959i	$-0.837742\pi$
$263$		−	15.8267i		−	0.975918i	0.872867	−	0.487959i	$-0.162258\pi$
$264$	6.62018			0.407444
$265$	−24.5078	+	4.29844i	−1.50550	+	0.264051i
$266$	−9.71371			−0.595586
$267$		−	17.1191i		−	1.04767i
$268$			12.0129i			0.733806i
$269$	−12.0872			−0.736967			−0.368484	−	0.929634i	$-0.620123\pi$
$269$	−12.0872			−0.736967			−0.368484	+	0.929634i	$0.620123\pi$
$270$	−5.81616	−	33.1612i	−0.353960	−	2.01813i
$271$	8.40254			0.510418			0.255209	−	0.966886i	$-0.417856\pi$
$271$	8.40254			0.510418			0.255209	+	0.966886i	$0.417856\pi$
$272$			3.91861i			0.237601i
$273$			2.62018i			0.158580i
$274$	6.47013			0.390875
$275$	9.55093	−	3.45662i	0.575943	−	0.208442i
$276$	3.25886			0.196160
$277$			13.8488i			0.832093i	0.909343	+	0.416046i	$0.136585\pi$
$277$			13.8488i			0.832093i	−0.909343	+	0.416046i	$0.863415\pi$
$278$		−	0.656206i		−	0.0393566i
$279$	23.4322			1.40285
$280$	0.557299	+	3.17748i	0.0333050	+	0.189890i
$281$	−8.15004			−0.486191			−0.243095	−	0.970002i	$-0.578163\pi$
$281$	−8.15004			−0.486191			−0.243095	+	0.970002i	$0.578163\pi$
$282$		−	2.15004i		−	0.128033i
$283$		−	17.3532i		−	1.03154i	−0.856727	−	0.515770i	$-0.827506\pi$
$283$		−	17.3532i		−	1.03154i	0.856727	−	0.515770i	$-0.172494\pi$
$284$	−12.4363			−0.737961
$285$	−48.3259	+	8.47591i	−2.86258	+	0.502070i
$286$	−1.13212			−0.0669436
$287$		−	10.1468i		−	0.598948i
$288$			7.62018i			0.449023i
$289$	1.64446			0.0967332
$290$	21.3532	−	3.74514i	1.25390	−	0.219922i
$291$	−0.265226			−0.0155478
$292$			9.26464i			0.542172i
$293$			7.02252i			0.410260i	0.978735	+	0.205130i	$0.0657617\pi$
$293$			7.02252i			0.410260i	−0.978735	+	0.205130i	$0.934238\pi$
$294$	16.0291			0.934835
$295$	−4.14203	−	23.6160i	−0.241158	−	1.37498i
$296$	−3.65798			−0.212616
$297$			30.5864i			1.77480i
$298$			23.8349i			1.38072i
$299$	−0.557299			−0.0322294
$300$	5.54515	+	15.3217i	0.320150	+	0.884601i
$301$	−7.30678			−0.421156
$302$			14.8669i			0.855494i
$303$			27.0903i			1.55630i
$304$	6.73300			0.386164
$305$	0.671897	+	3.83086i	0.0384727	+	0.219355i
$306$	−29.8605			−1.70701
$307$		−	16.4156i		−	0.936887i	−0.883493	−	0.468444i	$-0.844815\pi$
$307$		−	16.4156i		−	0.936887i	0.883493	−	0.468444i	$-0.155185\pi$
$308$		−	2.93076i		−	0.166995i
$309$	20.7587			1.18092
$310$	−6.77258	+	1.18785i	−0.384657	+	0.0674651i
$311$	7.35181			0.416883			0.208441	−	0.978035i	$-0.433161\pi$
$311$	7.35181			0.416883			0.208441	+	0.978035i	$0.433161\pi$
$312$		−	1.81616i		−	0.102820i
$313$			4.08972i			0.231165i	0.993298	+	0.115582i	$0.0368734\pi$
$313$			4.08972i			0.231165i	−0.993298	+	0.115582i	$0.963127\pi$
$314$	−8.24213			−0.465130
$315$	−24.2129	+	4.24672i	−1.36424	+	0.239275i
$316$	5.92439			0.333273
$317$		−	8.91580i		−	0.500761i	−0.968148	−	0.250381i	$-0.919444\pi$
$317$		−	8.91580i		−	0.500761i	0.968148	−	0.250381i	$-0.0805557\pi$
$318$			36.2631i			2.03353i
$319$	−19.6952			−1.10272
$320$	−0.386289	−	2.20245i	−0.0215942	−	0.123121i
$321$	−55.1485			−3.07809
$322$		−	1.44270i		−	0.0803986i
$323$			26.3840i			1.46805i
$324$	−26.2066			−1.45592
$325$	−0.948279	−	2.62018i	−0.0526011	−	0.145341i
$326$	−10.3154			−0.571316
$327$			0.713121i			0.0394357i
$328$			7.03321i			0.388344i
$329$	−0.951826			−0.0524759
$330$	−2.55730	−	14.5806i	−0.140775	−	0.802636i
$331$	21.3240			1.17207			0.586036	−	0.810285i	$-0.300688\pi$
$331$	21.3240			1.17207			0.586036	+	0.810285i	$0.300688\pi$
$332$			11.3775i			0.624420i
$333$		−	27.8744i		−	1.52751i
$334$	4.65975			0.254970
$335$	26.4579	−	4.64046i	1.44555	−	0.253535i
$336$	4.70156			0.256491
$337$			3.15417i			0.171819i	0.996303	+	0.0859094i	$0.0273796\pi$
$337$			3.15417i			0.171819i	−0.996303	+	0.0859094i	$0.972620\pi$
$338$		−	12.6894i		−	0.690213i
$339$	−1.89209			−0.102764
$340$	8.63055	−	1.51372i	0.468057	−	0.0820928i
$341$	6.24672			0.338279
$342$			51.3067i			2.77435i
$343$		−	17.1950i		−	0.928443i
$344$	5.06465			0.273068
$345$	−1.25886	−	7.17748i	−0.0677748	−	0.386422i
$346$	2.80402			0.150745
$347$			3.54739i			0.190434i	0.995457	+	0.0952169i	$0.0303545\pi$
$347$			3.54739i			0.190434i	−0.995457	+	0.0952169i	$0.969646\pi$
$348$		−	31.5953i		−	1.69369i
$349$	18.9726			1.01558			0.507789	−	0.861481i	$-0.330463\pi$
$349$	18.9726			1.01558			0.507789	+	0.861481i	$0.330463\pi$
$350$	6.78295	−	2.45485i	0.362564	−	0.131217i
$351$	8.39098			0.447877
$352$			2.03144i			0.108276i
$353$		−	33.5710i		−	1.78680i	−0.449257	−	0.893402i	$-0.648311\pi$
$353$		−	33.5710i		−	1.78680i	0.449257	−	0.893402i	$-0.351689\pi$
$354$	−34.9436			−1.85723
$355$	4.80402	+	27.3904i	0.254971	+	1.45373i
$356$	5.25308			0.278413
$357$			18.4236i			0.975081i
$358$		−	4.44212i		−	0.234773i
$359$	3.53243			0.186434			0.0932171	−	0.995646i	$-0.470285\pi$
$359$	3.53243			0.186434			0.0932171	+	0.995646i	$0.470285\pi$
$360$	16.7830	−	2.94359i	0.884544	−	0.155141i
$361$	26.3333			1.38596
$362$		−	2.42019i		−	0.127202i
$363$		−	22.3990i		−	1.17564i
$364$	−0.804016			−0.0421419
$365$	20.4049	−	3.57883i	1.06804	−	0.187324i
$366$	5.66835			0.296289
$367$			8.07444i			0.421482i	0.977542	+	0.210741i	$0.0675877\pi$
$367$			8.07444i			0.421482i	−0.977542	+	0.210741i	$0.932412\pi$
$368$			1.00000i			0.0521286i
$369$	−53.5943			−2.79001
$370$	1.41304	+	8.05651i	0.0734602	+	0.418838i
$371$	16.0537			0.833466
$372$			10.0211i			0.519568i
$373$			1.31459i			0.0680668i	0.999421	+	0.0340334i	$0.0108353\pi$
$373$			1.31459i			0.0680668i	−0.999421	+	0.0340334i	$0.989165\pi$
$374$	−7.96042			−0.411624
$375$	31.6033	−	18.1315i	1.63199	−	0.936308i
$376$	0.659753			0.0340242
$377$			5.40312i			0.278275i
$378$			21.7220i			1.11726i
$379$	−0.311952			−0.0160239			−0.00801196	−	0.999968i	$-0.502550\pi$
$379$	−0.311952			−0.0160239			−0.00801196	+	0.999968i	$0.502550\pi$
$380$	−2.60088	−	14.8291i	−0.133422	−	0.760716i
$381$	5.11460			0.262029
$382$			20.8934i			1.06900i
$383$		−	10.6805i		−	0.545748i	−0.962050	−	0.272874i	$-0.912026\pi$
$383$		−	10.6805i		−	0.545748i	0.962050	−	0.272874i	$-0.0879742\pi$
$384$	−3.25886			−0.166303
$385$	−6.45485	+	1.13212i	−0.328969	+	0.0576981i
$386$	−2.88540			−0.146863
$387$			38.5935i			1.96182i
$388$		−	0.0813861i		−	0.00413175i
$389$	7.86867			0.398957			0.199479	−	0.979902i	$-0.436075\pi$
$389$	7.86867			0.398957			0.199479	+	0.979902i	$0.436075\pi$
$390$	−4.00000	+	0.701562i	−0.202548	+	0.0355250i
$391$	−3.91861			−0.198173
$392$			4.91861i			0.248428i
$393$			51.8838i			2.61719i
$394$	−19.0925			−0.961868
$395$	−2.28853	−	13.0482i	−0.115148	−	0.656525i
$396$	−15.4799			−0.777895
$397$			29.2334i			1.46718i	0.679591	+	0.733591i	$0.262157\pi$
$397$			29.2334i			1.46718i	−0.679591	+	0.733591i	$0.737843\pi$
$398$			6.58060i			0.329856i
$399$	31.6556			1.58476
$400$	−4.70156	+	1.70156i	−0.235078	+	0.0850781i
$401$	23.7130			1.18417			0.592086	−	0.805874i	$-0.298304\pi$
$401$	23.7130			1.18417			0.592086	+	0.805874i	$0.298304\pi$
$402$		−	39.1485i		−	1.95255i
$403$		−	1.71371i		−	0.0853658i
$404$	−8.31281			−0.413578
$405$	10.1233	+	57.7186i	0.503031	+	2.86806i
$406$	−13.9873			−0.694177
$407$		−	7.43096i		−	0.368339i
$408$		−	12.7702i		−	0.632220i
$409$	33.2509			1.64415			0.822076	−	0.569378i	$-0.192816\pi$
$409$	33.2509			1.64415			0.822076	+	0.569378i	$0.192816\pi$
$410$	15.4903	−	2.71685i	0.765011	−	0.134176i
$411$	−21.0853			−1.04006
$412$			6.36991i			0.313823i
$413$			15.4695i			0.761207i
$414$	−7.62018			−0.374511
$415$	25.0583	−	4.39499i	1.23006	−	0.215741i
$416$	0.557299			0.0273238
$417$			2.13848i			0.104722i
$418$			13.6777i			0.668997i
$419$	−7.28229			−0.355763			−0.177882	−	0.984052i	$-0.556924\pi$
$419$	−7.28229			−0.355763			−0.177882	+	0.984052i	$0.556924\pi$
$420$	−1.81616	−	10.3550i	−0.0886195	−	0.505270i
$421$	−2.71515			−0.132329			−0.0661643	−	0.997809i	$-0.521076\pi$
$421$	−2.71515			−0.132329			−0.0661643	+	0.997809i	$0.521076\pi$
$422$		−	6.55986i		−	0.319329i
$423$			5.02743i			0.244442i
$424$	−11.1275			−0.540401
$425$	−6.66777	−	18.4236i	−0.323434	−	0.893676i
$426$	40.5283			1.96360
$427$		−	2.50938i		−	0.121438i
$428$		−	16.9226i		−	0.817986i
$429$	3.68942			0.178127
$430$	−1.95642	−	11.1546i	−0.0943468	−	0.537924i
$431$	10.3336			0.497750			0.248875	−	0.968536i	$-0.419939\pi$
$431$	10.3336			0.497750			0.248875	+	0.968536i	$0.419939\pi$
$432$		−	15.0565i		−	0.724407i
$433$		−	28.4153i		−	1.36555i	−0.730628	−	0.682775i	$-0.760773\pi$
$433$		−	28.4153i		−	1.36555i	0.730628	−	0.682775i	$-0.239227\pi$
$434$	4.43634			0.212951
$435$	−69.5870	+	12.2049i	−3.33644	+	0.585181i
$436$	−0.218825			−0.0104798
$437$			6.73300i			0.322083i
$438$		−	30.1922i		−	1.44264i
$439$	−6.37313			−0.304173			−0.152087	−	0.988367i	$-0.548599\pi$
$439$	−6.37313			−0.304173			−0.152087	+	0.988367i	$0.548599\pi$
$440$	4.47414	−	0.784722i	0.213296	−	0.0374101i
$441$	−37.4807			−1.78480
$442$			2.18384i			0.103875i
$443$			9.43114i			0.448087i	0.974579	+	0.224044i	$0.0719258\pi$
$443$			9.43114i			0.448087i	−0.974579	+	0.224044i	$0.928074\pi$
$444$	11.9208			0.565738
$445$	−2.02921	−	11.5696i	−0.0961936	−	0.548454i
$446$	20.2094			0.956942
$447$		−	77.6745i		−	3.67388i
$448$			1.44270i			0.0681612i
$449$	−11.3185			−0.534154			−0.267077	−	0.963675i	$-0.586058\pi$
$449$	−11.3185			−0.534154			−0.267077	+	0.963675i	$0.586058\pi$
$450$	−12.9662	−	35.8267i	−0.611233	−	1.68889i
$451$	−14.2875			−0.672774
$452$		−	0.580599i		−	0.0273091i
$453$		−	48.4491i		−	2.27634i
$454$	−15.0098			−0.704444
$455$	0.310582	+	1.77080i	0.0145603	+	0.0830166i
$456$	−21.9419			−1.02752
$457$			4.96456i			0.232232i	0.993236	+	0.116116i	$0.0370445\pi$
$457$			4.96456i			0.232232i	−0.993236	+	0.116116i	$0.962956\pi$
$458$			13.7081i			0.640539i
$459$	59.0007			2.75391
$460$	2.20245	−	0.386289i	0.102690	−	0.0180108i
$461$	19.9128			0.927433			0.463717	−	0.885984i	$-0.346516\pi$
$461$	19.9128			0.927433			0.463717	+	0.885984i	$0.346516\pi$
$462$			9.55093i			0.444350i
$463$			29.9046i			1.38978i	0.719114	+	0.694892i	$0.244548\pi$
$463$			29.9046i			1.38978i	−0.719114	+	0.694892i	$0.755452\pi$
$464$	9.69520			0.450088
$465$	22.0709	−	3.87102i	1.02351	−	0.179514i
$466$	−9.19822			−0.426099
$467$			15.1032i			0.698895i	0.936956	+	0.349447i	$0.113631\pi$
$467$			15.1032i			0.698895i	−0.936956	+	0.349447i	$0.886369\pi$
$468$			4.24672i			0.196305i
$469$	−17.3311			−0.800274
$470$	−0.254855	−	1.45307i	−0.0117556	−	0.0670252i
$471$	26.8599			1.23764
$472$		−	10.7226i		−	0.493549i
$473$			10.2885i			0.473067i
$474$	−19.3068			−0.886790
$475$	−31.6556	+	11.4566i	−1.45246	+	0.525666i
$476$	−5.65339			−0.259123
$477$		−	84.7937i		−	3.88244i
$478$		−	2.72618i		−	0.124692i
$479$	−28.6678			−1.30986			−0.654932	−	0.755688i	$-0.727303\pi$
$479$	−28.6678			−1.30986			−0.654932	+	0.755688i	$0.727303\pi$
$480$	1.25886	+	7.17748i	0.0574589	+	0.327605i
$481$	−2.03859			−0.0929516
$482$		−	3.26109i		−	0.148539i
$483$			4.70156i			0.213928i
$484$	6.87326			0.312421
$485$	−0.179249	+	0.0314385i	−0.00813926	+	0.00142755i
$486$	40.2340			1.82505
$487$			9.15319i			0.414770i	0.978259	+	0.207385i	$0.0664954\pi$
$487$			9.15319i			0.414770i	−0.978259	+	0.207385i	$0.933505\pi$
$488$			1.73937i			0.0787374i
$489$	33.6164			1.52018
$490$	10.8330	−	1.90000i	0.489385	−	0.0858335i
$491$	−20.8098			−0.939133			−0.469566	−	0.882897i	$-0.655590\pi$
$491$	−20.8098			−0.939133			−0.469566	+	0.882897i	$0.655590\pi$
$492$		−	22.9203i		−	1.03333i
$493$			37.9917i			1.71106i
$494$	3.75229			0.168824
$495$	5.97972	+	34.0937i	0.268768	+	1.53240i
$496$	−3.07502			−0.138073
$497$		−	17.9419i		−	0.804805i
$498$		−	37.0776i		−	1.66149i
$499$	18.1293			0.811579			0.405789	−	0.913967i	$-0.366997\pi$
$499$	18.1293			0.811579			0.405789	+	0.913967i	$0.366997\pi$
$500$	5.56376	+	9.69766i	0.248819	+	0.433692i
$501$	−15.1855			−0.678438
$502$		−	19.9941i		−	0.892380i
$503$			26.4296i			1.17844i	0.807974	+	0.589218i	$0.200564\pi$
$503$			26.4296i			1.17844i	−0.807974	+	0.589218i	$0.799436\pi$
$504$	−10.9936			−0.489695
$505$	3.21115	+	18.3085i	0.142894	+	0.814720i
$506$	−2.03144			−0.0903085
$507$			41.3531i			1.83655i
$508$			1.56944i			0.0696328i
$509$	12.0501			0.534113			0.267057	−	0.963681i	$-0.413949\pi$
$509$	12.0501			0.534113			0.267057	+	0.963681i	$0.413949\pi$
$510$	−28.1258	+	4.93299i	−1.24543	+	0.218437i
$511$	−13.3661			−0.591282
$512$		−	1.00000i		−	0.0441942i
$513$		−	101.376i		−	4.47584i
$514$	26.7935			1.18181
$515$	14.0294	−	2.46062i	0.618209	−	0.108428i
$516$	−16.5050			−0.726592
$517$			1.34025i			0.0589440i
$518$		−	5.27737i		−	0.231874i
$519$	−9.13790			−0.401109
$520$	−0.215278	−	1.22742i	−0.00944058	−	0.0538260i
$521$	−25.3697			−1.11146			−0.555732	−	0.831361i	$-0.687562\pi$
$521$	−25.3697			−1.11146			−0.555732	+	0.831361i	$0.687562\pi$
$522$			73.8791i			3.23360i
$523$			25.0018i			1.09325i	0.837377	+	0.546626i	$0.184088\pi$
$523$			25.0018i			1.09325i	−0.837377	+	0.546626i	$0.815912\pi$
$524$	−15.9208			−0.695505
$525$	−22.1047	+	8.00000i	−0.964728	+	0.349149i
$526$	−15.8267			−0.690078
$527$		−	12.0498i		−	0.524898i
$528$		−	6.62018i		−	0.288106i
$529$	−1.00000			−0.0434783
$530$	4.29844	+	24.5078i	0.186712	+	1.06455i
$531$	81.7083			3.54584
$532$			9.71371i			0.421143i
$533$			3.91960i			0.169777i
$534$	−17.1191			−0.740814
$535$	−37.2712	+	6.53702i	−1.61137	+	0.282620i
$536$	12.0129			0.518880
$537$			14.4762i			0.624696i
$538$			12.0872i			0.521115i
$539$	−9.99186			−0.430380
$540$	−33.1612	+	5.81616i	−1.42703	+	0.250288i
$541$	24.7900			1.06580			0.532902	−	0.846177i	$-0.321101\pi$
$541$	24.7900			1.06580			0.532902	+	0.846177i	$0.321101\pi$
$542$		−	8.40254i		−	0.360920i
$543$			7.88705i			0.338466i
$544$	3.91861			0.168009
$545$	0.0845298	+	0.481952i	0.00362086	+	0.0206445i
$546$	2.62018			0.112133
$547$		−	30.9508i		−	1.32336i	−0.749785	−	0.661681i	$-0.769843\pi$
$547$		−	30.9508i		−	1.32336i	0.749785	−	0.661681i	$-0.230157\pi$
$548$		−	6.47013i		−	0.276390i
$549$	−13.2543			−0.565678
$550$	−3.45662	−	9.55093i	−0.147391	−	0.407253i
$551$	65.2778			2.78093
$552$		−	3.25886i		−	0.138706i
$553$			8.54713i			0.363461i
$554$	13.8488			0.588379
$555$	−4.60489	−	26.2551i	−0.195467	−	1.11447i
$556$	−0.656206			−0.0278293
$557$		−	7.45307i		−	0.315797i	−0.987455	−	0.157898i	$-0.949528\pi$
$557$		−	7.45307i		−	0.315797i	0.987455	−	0.157898i	$-0.0504718\pi$
$558$		−	23.4322i		−	0.991964i
$559$	2.82252			0.119380
$560$	3.17748	−	0.557299i	0.134273	−	0.0235502i
$561$	25.9419			1.09527
$562$			8.15004i			0.343789i
$563$			7.96161i			0.335542i	0.985826	+	0.167771i	$0.0536569\pi$
$563$			7.96161i			0.335542i	−0.985826	+	0.167771i	$0.946343\pi$
$564$	−2.15004			−0.0905331
$565$	−1.27874	+	0.224279i	−0.0537970	+	0.00943549i
$566$	−17.3532			−0.729408
$567$		−	37.8082i		−	1.58780i
$568$			12.4363i			0.521817i
$569$	−32.3873			−1.35774			−0.678872	−	0.734257i	$-0.737531\pi$
$569$	−32.3873			−1.35774			−0.678872	+	0.734257i	$0.737531\pi$
$570$	8.47591	+	48.3259i	0.355017	+	2.02415i
$571$	−6.38994			−0.267410			−0.133705	−	0.991021i	$-0.542688\pi$
$571$	−6.38994			−0.267410			−0.133705	+	0.991021i	$0.542688\pi$
$572$			1.13212i			0.0473363i
$573$		−	68.0887i		−	2.84445i
$574$	−10.1468			−0.423520
$575$	−1.70156	−	4.70156i	−0.0709600	−	0.196069i
$576$	7.62018			0.317507
$577$		−	39.1728i		−	1.63078i	−0.578910	−	0.815392i	$-0.696522\pi$
$577$		−	39.1728i		−	1.63078i	0.578910	−	0.815392i	$-0.303478\pi$
$578$		−	1.64446i		−	0.0684007i
$579$	9.40312			0.390781
$580$	−3.74514	−	21.3532i	−0.155509	−	0.886642i
$581$	−16.4143			−0.680979
$582$			0.265226i			0.0109940i
$583$		−	22.6049i		−	0.936199i
$584$	9.26464			0.383374
$585$	9.35318	−	1.64046i	0.386706	−	0.0678246i
$586$	7.02252			0.290097
$587$		−	21.3811i		−	0.882491i	−0.897386	−	0.441246i	$-0.854537\pi$
$587$		−	21.3811i		−	0.882491i	0.897386	−	0.441246i	$-0.145463\pi$
$588$		−	16.0291i		−	0.661028i
$589$	−20.7041			−0.853098
$590$	−23.6160	+	4.14203i	−0.972257	+	0.170525i
$591$	62.2199			2.55939
$592$			3.65798i			0.150342i
$593$			2.45130i			0.100663i	0.998733	+	0.0503314i	$0.0160277\pi$
$593$			2.45130i			0.100663i	−0.998733	+	0.0503314i	$0.983972\pi$
$594$	30.5864			1.25497
$595$	2.18384	+	12.4513i	0.0895287	+	0.510453i
$596$	23.8349			0.976314
$597$		−	21.4453i		−	0.877696i
$598$			0.557299i			0.0227897i
$599$	−38.5828			−1.57645			−0.788226	−	0.615386i	$-0.789000\pi$
$599$	−38.5828			−1.57645			−0.788226	+	0.615386i	$0.789000\pi$
$600$	15.3217	−	5.54515i	0.625507	−	0.226380i
$601$	−35.3416			−1.44162			−0.720808	−	0.693135i	$-0.756229\pi$
$601$	−35.3416			−1.44162			−0.720808	+	0.693135i	$0.756229\pi$
$602$			7.30678i			0.297802i
$603$			91.5406i			3.72782i
$604$	14.8669			0.604925
$605$	−2.65506	−	15.1380i	−0.107944	−	0.615447i
$606$	27.0903			1.10047
$607$		−	17.8129i		−	0.723005i	−0.932371	−	0.361502i	$-0.882264\pi$
$607$		−	17.8129i		−	0.723005i	0.932371	−	0.361502i	$-0.117736\pi$
$608$		−	6.73300i		−	0.273059i
$609$	45.5826			1.84710
$610$	3.83086	−	0.671897i	0.155107	−	0.0272043i
$611$	0.367680			0.0148747
$612$			29.8605i			1.20704i
$613$			37.7547i			1.52490i	0.647048	+	0.762450i	$0.276003\pi$
$613$			37.7547i			1.52490i	−0.647048	+	0.762450i	$0.723997\pi$
$614$	−16.4156			−0.662479
$615$	−50.4807	+	8.85384i	−2.03558	+	0.357021i
$616$	−2.93076			−0.118084
$617$			23.1248i			0.930971i	0.885055	+	0.465486i	$0.154120\pi$
$617$			23.1248i			0.930971i	−0.885055	+	0.465486i	$0.845880\pi$
$618$		−	20.7587i		−	0.835036i
$619$	−19.5428			−0.785491			−0.392746	−	0.919647i	$-0.628475\pi$
$619$	−19.5428			−0.785491			−0.392746	+	0.919647i	$0.628475\pi$
$620$	1.18785	+	6.77258i	0.0477050	+	0.271993i
$621$	15.0565			0.604197
$622$		−	7.35181i		−	0.294781i
$623$			7.57863i			0.303631i
$624$	−1.81616			−0.0727046
$625$	19.2094	−	16.0000i	0.768375	−	0.640000i
$626$	4.08972			0.163458
$627$		−	44.5736i		−	1.78010i
$628$			8.24213i			0.328897i
$629$	−14.3342			−0.571542
$630$	4.24672	+	24.2129i	0.169193	+	0.964666i
$631$	−26.4807			−1.05418			−0.527090	−	0.849809i	$-0.676717\pi$
$631$	−26.4807			−1.05418			−0.527090	+	0.849809i	$0.676717\pi$
$632$		−	5.92439i		−	0.235660i
$633$			21.3777i			0.849686i
$634$	−8.91580			−0.354092
$635$	3.45662	−	0.606258i	0.137172	−	0.0240586i
$636$	36.2631			1.43792
$637$			2.74114i			0.108608i
$638$			19.6952i			0.779740i
$639$	−94.7671			−3.74893
$640$	−2.20245	+	0.386289i	−0.0870594	+	0.0152694i
$641$	−35.9594			−1.42031			−0.710156	−	0.704044i	$-0.751376\pi$
$641$	−35.9594			−1.42031			−0.710156	+	0.704044i	$0.751376\pi$
$642$			55.1485i			2.17654i
$643$		−	14.6934i		−	0.579452i	−0.957110	−	0.289726i	$-0.906436\pi$
$643$		−	14.6934i		−	0.579452i	0.957110	−	0.289726i	$-0.0935642\pi$
$644$	−1.44270			−0.0568504
$645$	6.37569	+	36.3514i	0.251043	+	1.43134i
$646$	26.3840			1.03807
$647$			26.7763i			1.05269i	0.850272	+	0.526343i	$0.176437\pi$
$647$			26.7763i			1.05269i	−0.850272	+	0.526343i	$0.823563\pi$
$648$			26.2066i			1.02949i
$649$	21.7824			0.855033
$650$	−2.62018	+	0.948279i	−0.102772	+	0.0371946i
$651$	−14.4574			−0.566630
$652$			10.3154i			0.403981i
$653$		−	18.8331i		−	0.736996i	−0.929629	−	0.368498i	$-0.879872\pi$
$653$		−	18.8331i		−	0.736996i	0.929629	−	0.368498i	$-0.120128\pi$
$654$	0.713121			0.0278853
$655$	6.15004	+	35.0649i	0.240302	+	1.37010i
$656$	7.03321			0.274601
$657$			70.5982i			2.75430i
$658$			0.951826i			0.0371060i
$659$	18.0885			0.704629			0.352315	−	0.935882i	$-0.385395\pi$
$659$	18.0885			0.704629			0.352315	+	0.935882i	$0.385395\pi$
$660$	−14.5806	+	2.55730i	−0.567549	+	0.0995427i
$661$	30.3235			1.17945			0.589724	−	0.807605i	$-0.299237\pi$
$661$	30.3235			1.17945			0.589724	+	0.807605i	$0.299237\pi$
$662$		−	21.3240i		−	0.828780i
$663$		−	7.11683i		−	0.276395i
$664$	11.3775			0.441531
$665$	21.3939	−	3.75229i	0.829621	−	0.145508i
$666$	−27.8744			−1.08011
$667$			9.69520i			0.375400i
$668$		−	4.65975i		−	0.180291i
$669$	−65.8595			−2.54628
$670$	−4.64046	−	26.4579i	−0.179277	−	1.02216i
$671$	−3.53341			−0.136406
$672$		−	4.70156i		−	0.181367i
$673$		−	11.1496i		−	0.429787i	−0.976637	−	0.214894i	$-0.931060\pi$
$673$		−	11.1496i		−	0.429787i	0.976637	−	0.214894i	$-0.0689404\pi$
$674$	3.15417			0.121494
$675$	25.6196	+	70.7891i	0.986099	+	2.72467i
$676$	−12.6894			−0.488055
$677$		−	43.5275i		−	1.67290i	−0.548045	−	0.836449i	$-0.684628\pi$
$677$		−	43.5275i		−	1.67290i	0.548045	−	0.836449i	$-0.315372\pi$
$678$			1.89209i			0.0726654i
$679$	0.117416			0.00450600
$680$	−1.51372	−	8.63055i	−0.0580484	−	0.330966i
$681$	48.9148			1.87442
$682$		−	6.24672i		−	0.239199i
$683$		−	24.1375i		−	0.923596i	−0.886985	−	0.461798i	$-0.847205\pi$
$683$		−	24.1375i		−	0.923596i	0.886985	−	0.461798i	$-0.152795\pi$
$684$	51.3067			1.96176
$685$	−14.2501	+	2.49934i	−0.544470	+	0.0954948i
$686$	−17.1950			−0.656508
$687$		−	44.6729i		−	1.70438i
$688$		−	5.06465i		−	0.193088i
$689$	−6.20136			−0.236253
$690$	−7.17748	+	1.25886i	−0.273242	+	0.0479240i
$691$	−20.8241			−0.792186			−0.396093	−	0.918210i	$-0.629634\pi$
$691$	−20.8241			−0.792186			−0.396093	+	0.918210i	$0.629634\pi$
$692$		−	2.80402i		−	0.106593i
$693$		−	22.3329i		−	0.848356i
$694$	3.54739			0.134657
$695$	0.253485	+	1.44526i	0.00961523	+	0.0548218i
$696$	−31.5953			−1.19762
$697$			27.5604i			1.04393i
$698$		−	18.9726i		−	0.718122i
$699$	29.9757			1.13379
$700$	−2.45485	−	6.78295i	−0.0927844	−	0.256371i
$701$	−31.5301			−1.19087			−0.595437	−	0.803402i	$-0.703021\pi$
$701$	−31.5301			−1.19087			−0.595437	+	0.803402i	$0.703021\pi$
$702$		−	8.39098i		−	0.316697i
$703$			24.6292i			0.928907i
$704$	2.03144			0.0765627
$705$	0.830537	+	4.73536i	0.0312798	+	0.178344i
$706$	−33.5710			−1.26346
$707$		−	11.9929i		−	0.451040i
$708$			34.9436i			1.31326i
$709$	−3.12175			−0.117240			−0.0586199	−	0.998280i	$-0.518670\pi$
$709$	−3.12175			−0.117240			−0.0586199	+	0.998280i	$0.518670\pi$
$710$	27.3904	−	4.80402i	1.02794	−	0.180292i
$711$	45.1449			1.69307
$712$		−	5.25308i		−	0.196868i
$713$		−	3.07502i		−	0.115160i
$714$	18.4236			0.689486
$715$	2.49343	−	0.437325i	0.0932491	−	0.0163550i
$716$	−4.44212			−0.166010
$717$			8.88423i			0.331788i
$718$		−	3.53243i		−	0.131829i
$719$	−20.3945			−0.760588			−0.380294	−	0.924866i	$-0.624177\pi$
$719$	−20.3945			−0.760588			−0.380294	+	0.924866i	$0.624177\pi$
$720$	−2.94359	−	16.7830i	−0.109701	−	0.625467i
$721$	−9.18988			−0.342249
$722$		−	26.3333i		−	0.980024i
$723$			10.6275i			0.395239i
$724$	−2.42019			−0.0899455
$725$	−45.5826	+	16.4970i	−1.69289	+	0.612682i
$726$	−22.3990			−0.831305
$727$			39.8896i			1.47942i	0.672924	+	0.739712i	$0.265038\pi$
$727$			39.8896i			1.47942i	−0.672924	+	0.739712i	$0.734962\pi$
$728$			0.804016i			0.0297988i
$729$	−52.4973			−1.94434
$730$	−3.57883	−	20.4049i	−0.132458	−	0.755219i
$731$	19.8464			0.734046
$732$		−	5.66835i		−	0.209508i
$733$		−	22.7761i		−	0.841255i	−0.907233	−	0.420628i	$-0.861810\pi$
$733$		−	22.7761i		−	0.841255i	0.907233	−	0.420628i	$-0.138190\pi$
$734$	8.07444			0.298033
$735$	−35.3032	+	6.19185i	−1.30218	+	0.228390i
$736$	1.00000			0.0368605
$737$			24.4035i			0.898915i
$738$			53.5943i			1.97283i
$739$	−33.7661			−1.24211			−0.621053	−	0.783769i	$-0.713295\pi$
$739$	−33.7661			−1.24211			−0.621053	+	0.783769i	$0.713295\pi$
$740$	8.05651	−	1.41304i	0.296163	−	0.0519442i
$741$	−12.2282			−0.449214
$742$		−	16.0537i		−	0.589350i
$743$			47.5880i			1.74584i	0.487868	+	0.872918i	$0.337775\pi$
$743$			47.5880i			1.74584i	−0.487868	+	0.872918i	$0.662225\pi$
$744$	10.0211			0.367390
$745$	−9.20714	−	52.4951i	−0.337324	−	1.92327i
$746$	1.31459			0.0481305
$747$			86.6983i			3.17212i
$748$			7.96042i			0.291062i
$749$	24.4143			0.892078
$750$	−18.1315	−	31.6033i	−0.662070	−	1.15399i
$751$	51.2698			1.87086			0.935430	−	0.353512i	$-0.115013\pi$
$751$	51.2698			1.87086			0.935430	+	0.353512i	$0.115013\pi$
$752$		−	0.659753i		−	0.0240587i
$753$			65.1580i			2.37449i
$754$	5.40312			0.196770
$755$	−5.74291	−	32.7436i	−0.209006	−	1.19166i
$756$	21.7220			0.790023
$757$			26.2807i			0.955189i	0.878580	+	0.477594i	$0.158491\pi$
$757$			26.2807i			0.955189i	−0.878580	+	0.477594i	$0.841509\pi$
$758$			0.311952i			0.0113306i
$759$	6.62018			0.240297
$760$	−14.8291	+	2.60088i	−0.537908	+	0.0943439i
$761$	−7.18003			−0.260276			−0.130138	−	0.991496i	$-0.541542\pi$
$761$	−7.18003			−0.260276			−0.130138	+	0.991496i	$0.541542\pi$
$762$		−	5.11460i		−	0.185282i
$763$		−	0.315700i		−	0.0114291i
$764$	20.8934			0.755897
$765$	65.7663	−	11.5348i	2.37779	−	0.417041i
$766$	−10.6805			−0.385902
$767$		−	5.97571i		−	0.215770i
$768$			3.25886i			0.117594i
$769$	32.2666			1.16356			0.581782	−	0.813345i	$-0.302356\pi$
$769$	32.2666			1.16356			0.581782	+	0.813345i	$0.302356\pi$
$770$	1.13212	+	6.45485i	0.0407987	+	0.232616i
$771$	−87.3164			−3.14462
$772$			2.88540i			0.103848i
$773$			3.75316i			0.134992i	0.997720	+	0.0674958i	$0.0215009\pi$
$773$			3.75316i			0.134992i	−0.997720	+	0.0674958i	$0.978499\pi$
$774$	38.5935			1.38722
$775$	14.4574	−	5.23234i	0.519325	−	0.187951i
$776$	−0.0813861			−0.00292159
$777$			17.1982i			0.616983i
$778$		−	7.86867i		−	0.282105i
$779$	47.3546			1.69666
$780$	0.701562	+	4.00000i	0.0251200	+	0.143223i
$781$	−25.2637			−0.904005
$782$			3.91861i			0.140129i
$783$		−	145.976i		−	5.21675i
$784$	4.91861			0.175665
$785$	18.1529	−	3.18384i	0.647903	−	0.113636i
$786$	51.8838			1.85063
$787$			21.9373i			0.781981i	0.920395	+	0.390991i	$0.127867\pi$
$787$			21.9373i			0.781981i	−0.920395	+	0.390991i	$0.872133\pi$
$788$			19.0925i			0.680144i
$789$	51.5771			1.83619
$790$	−13.0482	+	2.28853i	−0.464233	+	0.0814221i
$791$	0.837631			0.0297827
$792$			15.4799i			0.550055i
$793$			0.969347i			0.0344225i
$794$	29.2334			1.03745
$795$	−14.0080	−	79.8676i	−0.496813	−	2.83261i
$796$	6.58060			0.233243
$797$			7.57883i			0.268456i	0.990950	+	0.134228i	$0.0428554\pi$
$797$			7.57883i			0.268456i	−0.990950	+	0.134228i	$0.957145\pi$
$798$		−	31.6556i		−	1.12060i
$799$	2.58532			0.0914619
$800$	1.70156	+	4.70156i	0.0601593	+	0.166225i
$801$	40.0294			1.41437
$802$		−	23.7130i		−	0.837337i
$803$			18.8205i			0.664163i
$804$	−39.1485			−1.38066
$805$	0.557299	+	3.17748i	0.0196422	+	0.111991i
$806$	−1.71371			−0.0603627
$807$		−	39.3904i		−	1.38661i
$808$			8.31281i			0.292444i
$809$	−18.9835			−0.667423			−0.333712	−	0.942675i	$-0.608301\pi$
$809$	−18.9835			−0.667423			−0.333712	+	0.942675i	$0.608301\pi$
$810$	57.7186	−	10.1233i	2.02802	−	0.355696i
$811$	14.1851			0.498106			0.249053	−	0.968490i	$-0.419881\pi$
$811$	14.1851			0.498106			0.249053	+	0.968490i	$0.419881\pi$
$812$			13.9873i			0.490857i
$813$			27.3827i			0.960354i
$814$	−7.43096			−0.260455
$815$	22.7191	−	3.98471i	0.795815	−	0.139578i
$816$	−12.7702			−0.447047
$817$		−	34.1003i		−	1.19302i
$818$		−	33.2509i		−	1.16259i
$819$	−6.12674			−0.214086
$820$	−2.71685	−	15.4903i	−0.0948765	−	0.540944i
$821$	−44.8294			−1.56456			−0.782278	−	0.622930i	$-0.785942\pi$
$821$	−44.8294			−1.56456			−0.782278	+	0.622930i	$0.785942\pi$
$822$			21.0853i			0.735433i
$823$			15.7652i			0.549539i	0.961510	+	0.274770i	$0.0886016\pi$
$823$			15.7652i			0.549539i	−0.961510	+	0.274770i	$0.911398\pi$
$824$	6.36991			0.221906
$825$	11.2646	+	31.1252i	0.392184	+	1.08364i
$826$	15.4695			0.538254
$827$			11.4332i			0.397573i	0.980043	+	0.198786i	$0.0637000\pi$
$827$			11.4332i			0.397573i	−0.980043	+	0.198786i	$0.936300\pi$
$828$			7.62018i			0.264819i
$829$	28.3924			0.986108			0.493054	−	0.869999i	$-0.335881\pi$
$829$	28.3924			0.986108			0.493054	+	0.869999i	$0.335881\pi$
$830$	−4.39499	−	25.0583i	−0.152552	−	0.869786i
$831$	−45.1313			−1.56559
$832$		−	0.557299i		−	0.0193209i
$833$			19.2741i			0.667810i
$834$	2.13848			0.0740496
$835$	−10.2629	+	1.80001i	−0.355161	+	0.0622919i
$836$	13.6777			0.473052
$837$			46.2991i			1.60033i
$838$			7.28229i			0.251562i
$839$	−54.3340			−1.87582			−0.937908	−	0.346883i	$-0.887240\pi$
$839$	−54.3340			−1.87582			−0.937908	+	0.346883i	$0.887240\pi$
$840$	−10.3550	+	1.81616i	−0.357280	+	0.0626635i
$841$	64.9969			2.24127
$842$			2.71515i			0.0935704i
$843$		−	26.5599i		−	0.914770i
$844$	−6.55986			−0.225800
$845$	4.90178	+	27.9478i	0.168626	+	0.961433i
$846$	5.02743			0.172847
$847$			9.91606i			0.340720i
$848$			11.1275i			0.382121i
$849$	56.5516			1.94085
$850$	−18.4236	+	6.66777i	−0.631925	+	0.228702i
$851$	−3.65798			−0.125394
$852$		−	40.5283i		−	1.38848i
$853$		−	46.8542i		−	1.60426i	−0.597150	−	0.802129i	$-0.703700\pi$
$853$		−	46.8542i		−	1.60426i	0.597150	−	0.802129i	$-0.296300\pi$
$854$	−2.50938			−0.0858694
$855$	−19.8192	−	113.000i	−0.677802	−	3.86453i
$856$	−16.9226			−0.578403
$857$		−	28.5356i		−	0.974756i	−0.873191	−	0.487378i	$-0.837953\pi$
$857$		−	28.5356i		−	0.974756i	0.873191	−	0.487378i	$-0.162047\pi$
$858$		−	3.68942i		−	0.125955i
$859$	−19.4417			−0.663343			−0.331671	−	0.943395i	$-0.607613\pi$
$859$	−19.4417			−0.663343			−0.331671	+	0.943395i	$0.607613\pi$
$860$	−11.1546	+	1.95642i	−0.380370	+	0.0667133i
$861$	33.0671			1.12692
$862$		−	10.3336i		−	0.351962i
$863$			1.94514i			0.0662132i	0.999452	+	0.0331066i	$0.0105401\pi$
$863$			1.94514i			0.0662132i	−0.999452	+	0.0331066i	$0.989460\pi$
$864$	−15.0565			−0.512233
$865$	−6.17570	+	1.08316i	−0.209980	+	0.0368285i
$866$	−28.4153			−0.965590
$867$			5.35908i			0.182004i
$868$		−	4.43634i		−	0.150579i
$869$	12.0350			0.408261
$870$	12.2049	+	69.5870i	0.413785	+	2.35922i
$871$	6.69479			0.226844
$872$			0.218825i			0.00741036i
$873$		−	0.620176i		−	0.0209898i
$874$	6.73300			0.227747
$875$	−13.9908	+	8.02685i	−0.472976	+	0.271357i
$876$	−30.1922			−1.02010
$877$			38.6457i			1.30497i	0.757800	+	0.652486i	$0.226274\pi$
$877$			38.6457i			1.30497i	−0.757800	+	0.652486i	$0.773726\pi$
$878$			6.37313i			0.215083i
$879$	−22.8854			−0.771905
$880$	−0.784722	−	4.47414i	−0.0264530	−	0.150823i
$881$	−54.6889			−1.84252			−0.921258	−	0.388952i	$-0.872837\pi$
$881$	−54.6889			−1.84252			−0.921258	+	0.388952i	$0.872837\pi$
$882$			37.4807i			1.26204i
$883$		−	14.6273i		−	0.492247i	−0.969238	−	0.246123i	$-0.920843\pi$
$883$		−	14.6273i		−	0.492247i	0.969238	−	0.246123i	$-0.0791569\pi$
$884$	2.18384			0.0734505
$885$	76.9614	−	13.4983i	2.58703	−	0.453740i
$886$	9.43114			0.316845
$887$		−	40.2666i		−	1.35202i	−0.736892	−	0.676010i	$-0.763707\pi$
$887$		−	40.2666i		−	1.35202i	0.736892	−	0.676010i	$-0.236293\pi$
$888$		−	11.9208i		−	0.400037i
$889$	−2.26424			−0.0759401
$890$	−11.5696	+	2.02921i	−0.387815	+	0.0680191i
$891$	−53.2370			−1.78351
$892$		−	20.2094i		−	0.676660i
$893$		−	4.44212i		−	0.148650i
$894$	−77.6745			−2.59782
$895$	1.71594	+	9.78353i	0.0573575	+	0.327027i
$896$	1.44270			0.0481973
$897$		−	1.81616i		−	0.0606398i
$898$			11.3185i			0.377704i
$899$	−29.8129			−0.994317
$900$	−35.8267	+	12.9662i	−1.19422	+	0.432207i
$901$	−43.6045			−1.45268
$902$			14.2875i			0.475723i
$903$		−	23.8118i		−	0.792406i
$904$	−0.580599			−0.0193104
$905$	0.934890	+	5.33034i	0.0310768	+	0.177186i
$906$	−48.4491			−1.60961
$907$		−	7.87090i		−	0.261349i	−0.991425	−	0.130674i	$-0.958286\pi$
$907$		−	7.87090i		−	0.261349i	0.991425	−	0.130674i	$-0.0417143\pi$
$908$			15.0098i			0.498117i
$909$	−63.3451			−2.10102
$910$	1.77080	−	0.310582i	0.0587016	−	0.0102957i
$911$	0.586235			0.0194228			0.00971141	−	0.999953i	$-0.496909\pi$
$911$	0.586235			0.0194228			0.00971141	+	0.999953i	$0.496909\pi$
$912$			21.9419i			0.726569i
$913$			23.1126i			0.764916i
$914$	4.96456			0.164213
$915$	−12.4843	+	2.18962i	−0.412717	+	0.0723866i
$916$	13.7081			0.452929
$917$		−	22.9690i		−	0.758504i
$918$		−	59.0007i		−	1.94731i
$919$	27.9422			0.921729			0.460865	−	0.887470i	$-0.347539\pi$
$919$	27.9422			0.921729			0.460865	+	0.887470i	$0.347539\pi$
$920$	−0.386289	−	2.20245i	−0.0127356	−	0.0726126i
$921$	53.4961			1.76276
$922$		−	19.9128i		−	0.655794i
$923$			6.93076i			0.228129i
$924$	9.55093			0.314203
$925$	−6.22428	−	17.1982i	−0.204653	−	0.565474i
$926$	29.9046			0.982725
$927$			48.5399i			1.59426i
$928$		−	9.69520i		−	0.318260i
$929$	4.79352			0.157270			0.0786351	−	0.996903i	$-0.474944\pi$
$929$	4.79352			0.157270			0.0786351	+	0.996903i	$0.474944\pi$
$930$	−3.87102	−	22.0709i	−0.126936	−	0.723733i
$931$	33.1170			1.08537
$932$			9.19822i			0.301298i
$933$			23.9585i			0.784367i
$934$	15.1032			0.494193
$935$	17.5324	−	3.07502i	0.573372	−	0.100564i
$936$	4.24672			0.138808
$937$		−	0.110466i		−	0.00360877i	−0.999998	−	0.00180438i	$-0.999426\pi$
$937$		−	0.110466i		−	0.00360877i	0.999998	−	0.00180438i	$-0.000574353\pi$
$938$			17.3311i			0.565879i
$939$	−13.3278			−0.434938
$940$	−1.45307	+	0.254855i	−0.0473940	+	0.00831245i
$941$	19.2077			0.626155			0.313077	−	0.949728i	$-0.398640\pi$
$941$	19.2077			0.626155			0.313077	+	0.949728i	$0.398640\pi$
$942$		−	26.8599i		−	0.875144i
$943$			7.03321i			0.229033i
$944$	−10.7226			−0.348992
$945$	−8.39098	−	47.8417i	−0.272959	−	1.55629i
$946$	10.2885			0.334509
$947$		−	20.0933i		−	0.652944i	−0.945207	−	0.326472i	$-0.894140\pi$
$947$		−	20.0933i		−	0.652944i	0.945207	−	0.326472i	$-0.105860\pi$
$948$			19.3068i			0.627055i
$949$	5.16318			0.167604
$950$	11.4566	+	31.6556i	0.371702	+	1.02704i
$951$	29.0553			0.942184
$952$			5.65339i			0.183227i
$953$			55.4762i			1.79705i	0.438920	+	0.898526i	$0.355361\pi$
$953$			55.4762i			1.79705i	−0.438920	+	0.898526i	$0.644639\pi$
$954$	−84.7937			−2.74530
$955$	−8.07089	−	46.0167i	−0.261168	−	1.48906i
$956$	−2.72618			−0.0881709
$957$		−	64.1839i		−	2.07477i
$958$			28.6678i			0.926213i
$959$	9.33447			0.301426
$960$	7.17748	−	1.25886i	0.231652	−	0.0406296i
$961$	−21.5442			−0.694976
$962$			2.03859i			0.0657267i
$963$		−	128.953i		−	4.15546i
$964$	−3.26109			−0.105033
$965$	6.35495	−	1.11460i	0.204573	−	0.0358802i
$966$	4.70156			0.151270
$967$			2.86228i			0.0920448i	0.998940	+	0.0460224i	$0.0146546\pi$
$967$			2.86228i			0.0920448i	−0.998940	+	0.0460224i	$0.985345\pi$
$968$		−	6.87326i		−	0.220915i
$969$	−85.9819			−2.76214
$970$	0.0314385	+	0.179249i	0.00100943	+	0.00575533i
$971$	42.5901			1.36678			0.683391	−	0.730052i	$-0.260504\pi$
$971$	42.5901			1.36678			0.683391	+	0.730052i	$0.260504\pi$
$972$		−	40.2340i		−	1.29051i
$973$		−	0.946709i		−	0.0303501i
$974$	9.15319			0.293287
$975$	8.53879	−	3.09031i	0.273460	−	0.0989691i
$976$	1.73937			0.0556757
$977$		−	42.5633i		−	1.36172i	−0.732413	−	0.680861i	$-0.761606\pi$
$977$		−	42.5633i		−	1.36172i	0.732413	−	0.680861i	$-0.238394\pi$
$978$		−	33.6164i		−	1.07493i
$979$	10.6713			0.341057
$980$	−1.90000	−	10.8330i	−0.0606934	−	0.346047i
$981$	−1.66749			−0.0532388
$982$			20.8098i			0.664067i
$983$			32.6691i			1.04198i	0.853562	+	0.520991i	$0.174437\pi$
$983$			32.6691i			1.04198i	−0.853562	+	0.520991i	$0.825563\pi$
$984$	−22.9203			−0.730671
$985$	42.0503	−	7.37523i	1.33984	−	0.234994i
$986$	37.9917			1.20990
$987$		−	3.10187i		−	0.0987336i
$988$		−	3.75229i		−	0.119376i
$989$	5.06465			0.161047
$990$	34.0937	−	5.97972i	1.08357	−	0.190048i
$991$	−4.39775			−0.139699			−0.0698495	−	0.997558i	$-0.522252\pi$
$991$	−4.39775			−0.139699			−0.0698495	+	0.997558i	$0.522252\pi$
$992$			3.07502i			0.0976320i
$993$			69.4919i			2.20526i
$994$	−17.9419			−0.569083
$995$	−2.54201	−	14.4934i	−0.0805872	−	0.459473i
$996$	−37.0776			−1.17485
$997$		−	33.4135i		−	1.05822i	−0.848554	−	0.529108i	$-0.822527\pi$
$997$		−	33.4135i		−	1.05822i	0.848554	−	0.529108i	$-0.177473\pi$
$998$		−	18.1293i		−	0.573873i
$999$	55.0764			1.74254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.b.b.139.4	✓	8
3.2	odd	2		2070.2.d.f.829.6		8
4.3	odd	2		1840.2.e.e.369.1		8
5.2	odd	4		1150.2.a.s.1.4		4
5.3	odd	4		1150.2.a.r.1.1		4
5.4	even	2	inner	230.2.b.b.139.5	yes	8
15.14	odd	2		2070.2.d.f.829.2		8
20.3	even	4		9200.2.a.cr.1.4		4
20.7	even	4		9200.2.a.cj.1.1		4
20.19	odd	2		1840.2.e.e.369.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.b.b.139.4	✓	8	1.1	even	1	trivial
230.2.b.b.139.5	yes	8	5.4	even	2	inner
1150.2.a.r.1.1		4	5.3	odd	4
1150.2.a.s.1.4		4	5.2	odd	4
1840.2.e.e.369.1		8	4.3	odd	2
1840.2.e.e.369.8		8	20.19	odd	2
2070.2.d.f.829.2		8	15.14	odd	2
2070.2.d.f.829.6		8	3.2	odd	2
9200.2.a.cj.1.1		4	20.7	even	4
9200.2.a.cr.1.4		4	20.3	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +3.25886i q^{3} -1.00000 q^{4} +(0.386289 + 2.20245i) q^{5} +3.25886 q^{6} -1.44270i q^{7} +1.00000i q^{8} -7.62018 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +3.25886i q^{3} -1.00000 q^{4} +(0.386289 + 2.20245i) q^{5} +3.25886 q^{6} -1.44270i q^{7} +1.00000i q^{8} -7.62018 q^{9} +(2.20245 - 0.386289i) q^{10} -2.03144 q^{11} -3.25886i q^{12} +0.557299i q^{13} -1.44270 q^{14} +(-7.17748 + 1.25886i) q^{15} +1.00000 q^{16} +3.91861i q^{17} +7.62018i q^{18} +6.73300 q^{19} +(-0.386289 - 2.20245i) q^{20} +4.70156 q^{21} +2.03144i q^{22} +1.00000i q^{23} -3.25886 q^{24} +(-4.70156 + 1.70156i) q^{25} +0.557299 q^{26} -15.0565i q^{27} +1.44270i q^{28} +9.69520 q^{29} +(1.25886 + 7.17748i) q^{30} -3.07502 q^{31} -1.00000i q^{32} -6.62018i q^{33} +3.91861 q^{34} +(3.17748 - 0.557299i) q^{35} +7.62018 q^{36} +3.65798i q^{37} -6.73300i q^{38} -1.81616 q^{39} +(-2.20245 + 0.386289i) q^{40} +7.03321 q^{41} -4.70156i q^{42} -5.06465i q^{43} +2.03144 q^{44} +(-2.94359 - 16.7830i) q^{45} +1.00000 q^{46} -0.659753i q^{47} +3.25886i q^{48} +4.91861 q^{49} +(1.70156 + 4.70156i) q^{50} -12.7702 q^{51} -0.557299i q^{52} +11.1275i q^{53} -15.0565 q^{54} +(-0.784722 - 4.47414i) q^{55} +1.44270 q^{56} +21.9419i q^{57} -9.69520i q^{58} -10.7226 q^{59} +(7.17748 - 1.25886i) q^{60} +1.73937 q^{61} +3.07502i q^{62} +10.9936i q^{63} -1.00000 q^{64} +(-1.22742 + 0.215278i) q^{65} -6.62018 q^{66} -12.0129i q^{67} -3.91861i q^{68} -3.25886 q^{69} +(-0.557299 - 3.17748i) q^{70} +12.4363 q^{71} -7.62018i q^{72} -9.26464i q^{73} +3.65798 q^{74} +(-5.54515 - 15.3217i) q^{75} -6.73300 q^{76} +2.93076i q^{77} +1.81616i q^{78} -5.92439 q^{79} +(0.386289 + 2.20245i) q^{80} +26.2066 q^{81} -7.03321i q^{82} -11.3775i q^{83} -4.70156 q^{84} +(-8.63055 + 1.51372i) q^{85} -5.06465 q^{86} +31.5953i q^{87} -2.03144i q^{88} -5.25308 q^{89} +(-16.7830 + 2.94359i) q^{90} +0.804016 q^{91} -1.00000i q^{92} -10.0211i q^{93} -0.659753 q^{94} +(2.60088 + 14.8291i) q^{95} +3.25886 q^{96} +0.0813861i q^{97} -4.91861i q^{98} +15.4799 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 + 6 * q^6 - 14 * q^9	\( 8 q - 8 q^{4} + 6 q^{6} - 14 q^{9} + 10 q^{11} - 6 q^{14} - 16 q^{15} + 8 q^{16} + 2 q^{19} + 12 q^{21} - 6 q^{24} - 12 q^{25} + 10 q^{26} - 4 q^{29} - 10 q^{30} + 10 q^{31} + 10 q^{34} - 16 q^{35} + 14 q^{36} + 46 q^{41} - 10 q^{44} - 26 q^{45} + 8 q^{46} + 18 q^{49} - 12 q^{50} + 14 q^{51} - 12 q^{54} - 18 q^{55} + 6 q^{56} - 32 q^{59} + 16 q^{60} + 18 q^{61} - 8 q^{64} - 16 q^{65} - 6 q^{66} - 6 q^{69} - 10 q^{70} + 38 q^{71} + 12 q^{74} - 32 q^{75} - 2 q^{76} + 12 q^{79} + 32 q^{81} - 12 q^{84} - 24 q^{85} - 4 q^{86} - 60 q^{89} - 24 q^{90} - 26 q^{91} - 4 q^{94} + 18 q^{95} + 6 q^{96} + 54 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 6 * q^6 - 14 * q^9 + 10 * q^11 - 6 * q^14 - 16 * q^15 + 8 * q^16 + 2 * q^19 + 12 * q^21 - 6 * q^24 - 12 * q^25 + 10 * q^26 - 4 * q^29 - 10 * q^30 + 10 * q^31 + 10 * q^34 - 16 * q^35 + 14 * q^36 + 46 * q^41 - 10 * q^44 - 26 * q^45 + 8 * q^46 + 18 * q^49 - 12 * q^50 + 14 * q^51 - 12 * q^54 - 18 * q^55 + 6 * q^56 - 32 * q^59 + 16 * q^60 + 18 * q^61 - 8 * q^64 - 16 * q^65 - 6 * q^66 - 6 * q^69 - 10 * q^70 + 38 * q^71 + 12 * q^74 - 32 * q^75 - 2 * q^76 + 12 * q^79 + 32 * q^81 - 12 * q^84 - 24 * q^85 - 4 * q^86 - 60 * q^89 - 24 * q^90 - 26 * q^91 - 4 * q^94 + 18 * q^95 + 6 * q^96 + 54 * q^99

Introduction

L-functions

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