LMFDB - Embedded newform 1334.2.c.b.231.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(231,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1334.231");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.c (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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			231.2
Character	$\chi$	$=$	1334.231
Dual form			1334.2.c.b.231.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -2.92171i q^{3} -1.00000 q^{4} +1.71359 q^{5} -2.92171 q^{6} +4.94068 q^{7} +1.00000i q^{8} -5.53640 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -2.92171i q^{3} -1.00000 q^{4} +1.71359 q^{5} -2.92171 q^{6} +4.94068 q^{7} +1.00000i q^{8} -5.53640 q^{9} -1.71359i q^{10} +2.54827i q^{11} +2.92171i q^{12} +6.82697 q^{13} -4.94068i q^{14} -5.00662i q^{15} +1.00000 q^{16} +1.44230i q^{17} +5.53640i q^{18} -2.89320i q^{19} -1.71359 q^{20} -14.4353i q^{21} +2.54827 q^{22} -1.00000 q^{23} +2.92171 q^{24} -2.06360 q^{25} -6.82697i q^{26} +7.41062i q^{27} -4.94068 q^{28} +(3.77291 + 3.84254i) q^{29} -5.00662 q^{30} +3.14151i q^{31} -1.00000i q^{32} +7.44532 q^{33} +1.44230 q^{34} +8.46632 q^{35} +5.53640 q^{36} -4.59544i q^{37} -2.89320 q^{38} -19.9464i q^{39} +1.71359i q^{40} -11.3733i q^{41} -14.4353 q^{42} +6.85278i q^{43} -2.54827i q^{44} -9.48713 q^{45} +1.00000i q^{46} -7.23490i q^{47} -2.92171i q^{48} +17.4104 q^{49} +2.06360i q^{50} +4.21400 q^{51} -6.82697 q^{52} -6.48011 q^{53} +7.41062 q^{54} +4.36670i q^{55} +4.94068i q^{56} -8.45309 q^{57} +(3.84254 - 3.77291i) q^{58} -4.25517 q^{59} +5.00662i q^{60} +10.3277i q^{61} +3.14151 q^{62} -27.3536 q^{63} -1.00000 q^{64} +11.6986 q^{65} -7.44532i q^{66} -8.15926 q^{67} -1.44230i q^{68} +2.92171i q^{69} -8.46632i q^{70} -12.5382 q^{71} -5.53640i q^{72} +10.8854i q^{73} -4.59544 q^{74} +6.02925i q^{75} +2.89320i q^{76} +12.5902i q^{77} -19.9464 q^{78} +3.82311i q^{79} +1.71359 q^{80} +5.04251 q^{81} -11.3733 q^{82} -2.37162 q^{83} +14.4353i q^{84} +2.47152i q^{85} +6.85278 q^{86} +(11.2268 - 11.0234i) q^{87} -2.54827 q^{88} +2.27002i q^{89} +9.48713i q^{90} +33.7299 q^{91} +1.00000 q^{92} +9.17859 q^{93} -7.23490 q^{94} -4.95776i q^{95} -2.92171 q^{96} +8.75975i q^{97} -17.4104i q^{98} -14.1083i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} - 54 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 2 * q^5 + 2 * q^6 - 8 * q^7 - 54 * q^9	$ 28 q - 28 q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} - 54 q^{9} - 2 q^{13} + 28 q^{16} - 2 q^{20} + 6 q^{22} - 28 q^{23} - 2 q^{24} + 38 q^{25} + 8 q^{28} - 2 q^{29} + 2 q^{30} + 30 q^{33} + 12 q^{34} + 56 q^{35} + 54 q^{36} + 12 q^{38} + 16 q^{42} - 52 q^{45} + 76 q^{49} - 60 q^{51} + 2 q^{52} - 22 q^{53} - 14 q^{54} + 72 q^{57} - 18 q^{58} - 12 q^{59} + 14 q^{62} + 24 q^{63} - 28 q^{64} - 42 q^{65} - 16 q^{67} - 4 q^{71} - 32 q^{74} - 34 q^{78} + 2 q^{80} + 116 q^{81} - 68 q^{82} - 48 q^{83} + 46 q^{86} + 12 q^{87} - 6 q^{88} + 96 q^{91} + 28 q^{92} + 70 q^{93} - 10 q^{94} + 2 q^{96}+O(q^{100}) $ 28 * q - 28 * q^4 + 2 * q^5 + 2 * q^6 - 8 * q^7 - 54 * q^9 - 2 * q^13 + 28 * q^16 - 2 * q^20 + 6 * q^22 - 28 * q^23 - 2 * q^24 + 38 * q^25 + 8 * q^28 - 2 * q^29 + 2 * q^30 + 30 * q^33 + 12 * q^34 + 56 * q^35 + 54 * q^36 + 12 * q^38 + 16 * q^42 - 52 * q^45 + 76 * q^49 - 60 * q^51 + 2 * q^52 - 22 * q^53 - 14 * q^54 + 72 * q^57 - 18 * q^58 - 12 * q^59 + 14 * q^62 + 24 * q^63 - 28 * q^64 - 42 * q^65 - 16 * q^67 - 4 * q^71 - 32 * q^74 - 34 * q^78 + 2 * q^80 + 116 * q^81 - 68 * q^82 - 48 * q^83 + 46 * q^86 + 12 * q^87 - 6 * q^88 + 96 * q^91 + 28 * q^92 + 70 * q^93 - 10 * q^94 + 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1334\mathbb{Z}\right)^\times$.

$n$	$465$	$553$
$\chi(n)$	$1$	$-1$

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
$3$		−	2.92171i		−	1.68685i	−0.537246	−	0.843425i	$-0.680535\pi$
$3$		−	2.92171i		−	1.68685i	0.537246	−	0.843425i	$-0.319465\pi$
$4$	−1.00000			−0.500000
$5$	1.71359			0.766342			0.383171	−	0.923677i	$-0.374832\pi$
$5$	1.71359			0.766342			0.383171	+	0.923677i	$0.374832\pi$
$6$	−2.92171			−1.19278
$7$	4.94068			1.86740			0.933701	−	0.358052i	$-0.116559\pi$
$7$	4.94068			1.86740			0.933701	+	0.358052i	$0.116559\pi$
$8$			1.00000i			0.353553i
$9$	−5.53640			−1.84547
$10$		−	1.71359i		−	0.541886i
$11$			2.54827i			0.768334i	0.923264	+	0.384167i	$0.125511\pi$
$11$			2.54827i			0.768334i	−0.923264	+	0.384167i	$0.874489\pi$
$12$			2.92171i			0.843425i
$13$	6.82697			1.89346			0.946730	−	0.322028i	$-0.104364\pi$
$13$	6.82697			1.89346			0.946730	+	0.322028i	$0.104364\pi$
$14$		−	4.94068i		−	1.32045i
$15$		−	5.00662i		−	1.29270i
$16$	1.00000			0.250000
$17$			1.44230i			0.349810i	0.984585	+	0.174905i	$0.0559619\pi$
$17$			1.44230i			0.349810i	−0.984585	+	0.174905i	$0.944038\pi$
$18$			5.53640i			1.30494i
$19$		−	2.89320i		−	0.663745i	−0.943324	−	0.331873i	$-0.892320\pi$
$19$		−	2.89320i		−	0.663745i	0.943324	−	0.331873i	$-0.107680\pi$
$20$	−1.71359			−0.383171
$21$		−	14.4353i		−	3.15003i
$22$	2.54827			0.543294
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	2.92171			0.596392
$25$	−2.06360			−0.412720
$26$		−	6.82697i		−	1.33888i
$27$			7.41062i			1.42618i
$28$	−4.94068			−0.933701
$29$	3.77291	+	3.84254i	0.700612	+	0.713542i
$29$	3.77291	+	3.84254i	0.700612	+	0.713542i
$30$	−5.00662			−0.914080
$31$			3.14151i			0.564232i	0.959380	+	0.282116i	$0.0910363\pi$
$31$			3.14151i			0.564232i	−0.959380	+	0.282116i	$0.908964\pi$
$32$		−	1.00000i		−	0.176777i
$33$	7.44532			1.29606
$34$	1.44230			0.247353
$35$	8.46632			1.43107
$36$	5.53640			0.922733
$37$		−	4.59544i		−	0.755486i	−0.925910	−	0.377743i	$-0.876700\pi$
$37$		−	4.59544i		−	0.755486i	0.925910	−	0.377743i	$-0.123300\pi$
$38$	−2.89320			−0.469339
$39$		−	19.9464i		−	3.19399i
$40$			1.71359i			0.270943i
$41$		−	11.3733i		−	1.77621i	−0.459639	−	0.888106i	$-0.652021\pi$
$41$		−	11.3733i		−	1.77621i	0.459639	−	0.888106i	$-0.347979\pi$
$42$	−14.4353			−2.22741
$43$			6.85278i			1.04504i	0.852627	+	0.522520i	$0.175008\pi$
$43$			6.85278i			1.04504i	−0.852627	+	0.522520i	$0.824992\pi$
$44$		−	2.54827i		−	0.384167i
$45$	−9.48713			−1.41426
$46$			1.00000i			0.147442i
$47$		−	7.23490i		−	1.05532i	−0.849456	−	0.527659i	$-0.823070\pi$
$47$		−	7.23490i		−	1.05532i	0.849456	−	0.527659i	$-0.176930\pi$
$48$		−	2.92171i		−	0.421713i
$49$	17.4104			2.48719
$50$			2.06360i			0.291837i
$51$	4.21400			0.590078
$52$	−6.82697			−0.946730
$53$	−6.48011			−0.890111			−0.445055	−	0.895503i	$-0.646816\pi$
$53$	−6.48011			−0.890111			−0.445055	+	0.895503i	$0.646816\pi$
$54$	7.41062			1.00846
$55$			4.36670i			0.588806i
$56$			4.94068i			0.660227i
$57$	−8.45309			−1.11964
$58$	3.84254	−	3.77291i	0.504551	−	0.495407i
$59$	−4.25517			−0.553976			−0.276988	−	0.960873i	$-0.589336\pi$
$59$	−4.25517			−0.553976			−0.276988	+	0.960873i	$0.589336\pi$
$60$			5.00662i			0.646352i
$61$			10.3277i			1.32233i	0.750241	+	0.661165i	$0.229938\pi$
$61$			10.3277i			1.32233i	−0.750241	+	0.661165i	$0.770062\pi$
$62$	3.14151			0.398972
$63$	−27.3536			−3.44623
$64$	−1.00000			−0.125000
$65$	11.6986			1.45104
$66$		−	7.44532i		−	0.916456i
$67$	−8.15926			−0.996813			−0.498406	−	0.866944i	$-0.666081\pi$
$67$	−8.15926			−0.996813			−0.498406	+	0.866944i	$0.666081\pi$
$68$		−	1.44230i		−	0.174905i
$69$			2.92171i			0.351733i
$70$		−	8.46632i		−	1.01192i
$71$	−12.5382			−1.48801			−0.744007	−	0.668172i	$-0.767077\pi$
$71$	−12.5382			−1.48801			−0.744007	+	0.668172i	$0.767077\pi$
$72$		−	5.53640i		−	0.652471i
$73$			10.8854i			1.27403i	0.770849	+	0.637017i	$0.219832\pi$
$73$			10.8854i			1.27403i	−0.770849	+	0.637017i	$0.780168\pi$
$74$	−4.59544			−0.534210
$75$			6.02925i			0.696197i
$76$			2.89320i			0.331873i
$77$			12.5902i			1.43479i
$78$	−19.9464			−2.25849
$79$			3.82311i			0.430133i	0.976599	+	0.215066i	$0.0689968\pi$
$79$			3.82311i			0.430133i	−0.976599	+	0.215066i	$0.931003\pi$
$80$	1.71359			0.191585
$81$	5.04251			0.560279
$82$	−11.3733			−1.25597
$83$	−2.37162			−0.260319			−0.130160	−	0.991493i	$-0.541549\pi$
$83$	−2.37162			−0.260319			−0.130160	+	0.991493i	$0.541549\pi$
$84$			14.4353i			1.57502i
$85$			2.47152i			0.268074i
$86$	6.85278			0.738955
$87$	11.2268	−	11.0234i	1.20364	−	1.18183i
$88$	−2.54827			−0.271647
$89$			2.27002i			0.240621i	0.992736	+	0.120311i	$0.0383891\pi$
$89$			2.27002i			0.240621i	−0.992736	+	0.120311i	$0.961611\pi$
$90$			9.48713i			1.00003i
$91$	33.7299			3.53585
$92$	1.00000			0.104257
$93$	9.17859			0.951775
$94$	−7.23490			−0.746223
$95$		−	4.95776i		−	0.508656i
$96$	−2.92171			−0.298196
$97$			8.75975i			0.889418i	0.895675	+	0.444709i	$0.146693\pi$
$97$			8.75975i			0.889418i	−0.895675	+	0.444709i	$0.853307\pi$
$98$		−	17.4104i		−	1.75871i
$99$		−	14.1083i		−	1.41793i
$100$	2.06360			0.206360
$101$			10.3781i			1.03266i	0.856391	+	0.516328i	$0.172701\pi$
$101$			10.3781i			1.03266i	−0.856391	+	0.516328i	$0.827299\pi$
$102$		−	4.21400i		−	0.417248i
$103$	−1.47855			−0.145686			−0.0728431	−	0.997343i	$-0.523207\pi$
$103$	−1.47855			−0.145686			−0.0728431	+	0.997343i	$0.523207\pi$
$104$			6.82697i			0.669439i
$105$		−	24.7361i		−	2.41400i
$106$			6.48011i			0.629403i
$107$	−13.9184			−1.34554			−0.672771	−	0.739851i	$-0.734896\pi$
$107$	−13.9184			−1.34554			−0.672771	+	0.739851i	$0.734896\pi$
$108$		−	7.41062i		−	0.713088i
$109$	−6.46947			−0.619663			−0.309832	−	0.950791i	$-0.600273\pi$
$109$	−6.46947			−0.619663			−0.309832	+	0.950791i	$0.600273\pi$
$110$	4.36670			0.416349
$111$	−13.4266			−1.27439
$112$	4.94068			0.466851
$113$			3.27697i			0.308272i	0.988050	+	0.154136i	$0.0492593\pi$
$113$			3.27697i			0.308272i	−0.988050	+	0.154136i	$0.950741\pi$
$114$			8.45309i			0.791704i
$115$	−1.71359			−0.159793
$116$	−3.77291	−	3.84254i	−0.350306	−	0.356771i
$117$	−37.7968			−3.49432
$118$			4.25517i			0.391720i
$119$			7.12597i			0.653237i
$120$	5.00662			0.457040
$121$	4.50630			0.409663
$122$	10.3277			0.935028
$123$	−33.2295			−2.99621
$124$		−	3.14151i		−	0.282116i
$125$	−12.1041			−1.08263
$126$			27.3536i			2.43685i
$127$		−	0.721234i		−	0.0639991i	−0.999488	−	0.0319996i	$-0.989812\pi$
$127$		−	0.721234i		−	0.0639991i	0.999488	−	0.0319996i	$-0.0101875\pi$
$128$			1.00000i			0.0883883i
$129$	20.0219			1.76283
$130$		−	11.6986i		−	1.02604i
$131$		−	11.7636i		−	1.02779i	−0.857852	−	0.513897i	$-0.828201\pi$
$131$		−	11.7636i		−	1.02779i	0.857852	−	0.513897i	$-0.171799\pi$
$132$	−7.44532			−0.648032
$133$		−	14.2944i		−	1.23948i
$134$			8.15926i			0.704853i
$135$			12.6988i			1.09294i
$136$	−1.44230			−0.123677
$137$			1.75414i			0.149866i	0.997189	+	0.0749332i	$0.0238743\pi$
$137$			1.75414i			0.149866i	−0.997189	+	0.0749332i	$0.976126\pi$
$138$	2.92171			0.248713
$139$	0.970744			0.0823374			0.0411687	−	0.999152i	$-0.486892\pi$
$139$	0.970744			0.0823374			0.0411687	+	0.999152i	$0.486892\pi$
$140$	−8.46632			−0.715535
$141$	−21.1383			−1.78016
$142$			12.5382i			1.05218i
$143$			17.3970i			1.45481i
$144$	−5.53640			−0.461367
$145$	6.46523	+	6.58455i	0.536908	+	0.546817i
$146$	10.8854			0.900879
$147$		−	50.8680i		−	4.19553i
$148$			4.59544i			0.377743i
$149$	17.4823			1.43221			0.716103	−	0.697995i	$-0.245924\pi$
$149$	17.4823			1.43221			0.716103	+	0.697995i	$0.245924\pi$
$150$	6.02925			0.492286
$151$	−11.5608			−0.940801			−0.470400	−	0.882453i	$-0.655891\pi$
$151$	−11.5608			−0.940801			−0.470400	+	0.882453i	$0.655891\pi$
$152$	2.89320			0.234669
$153$		−	7.98517i		−	0.645563i
$154$	12.5902			1.01455
$155$			5.38327i			0.432395i
$156$			19.9464i			1.59699i
$157$		−	14.0075i		−	1.11792i	−0.829196	−	0.558959i	$-0.811201\pi$
$157$		−	14.0075i		−	1.11792i	0.829196	−	0.558959i	$-0.188799\pi$
$158$	3.82311			0.304150
$159$			18.9330i			1.50148i
$160$		−	1.71359i		−	0.135471i
$161$	−4.94068			−0.389380
$162$		−	5.04251i		−	0.396177i
$163$		−	10.9022i		−	0.853923i	−0.904270	−	0.426961i	$-0.859584\pi$
$163$		−	10.9022i		−	0.853923i	0.904270	−	0.426961i	$-0.140416\pi$
$164$			11.3733i			0.888106i
$165$	12.7582			0.993228
$166$			2.37162i			0.184074i
$167$	−12.9995			−1.00593			−0.502966	−	0.864306i	$-0.667758\pi$
$167$	−12.9995			−1.00593			−0.502966	+	0.864306i	$0.667758\pi$
$168$	14.4353			1.11370
$169$	33.6075			2.58519
$170$	2.47152			0.189557
$171$			16.0179i			1.22492i
$172$		−	6.85278i		−	0.522520i
$173$	−4.73181			−0.359753			−0.179876	−	0.983689i	$-0.557570\pi$
$173$	−4.73181			−0.359753			−0.179876	+	0.983689i	$0.557570\pi$
$174$	−11.0234	−	11.2268i	−0.835679	−	0.851102i
$175$	−10.1956			−0.770715
$176$			2.54827i			0.192083i
$177$			12.4324i			0.934475i
$178$	2.27002			0.170145
$179$	1.47498			0.110245			0.0551227	−	0.998480i	$-0.482445\pi$
$179$	1.47498			0.110245			0.0551227	+	0.998480i	$0.482445\pi$
$180$	9.48713			0.707129
$181$	−10.7212			−0.796902			−0.398451	−	0.917190i	$-0.630452\pi$
$181$	−10.7212			−0.796902			−0.398451	+	0.917190i	$0.630452\pi$
$182$		−	33.7299i		−	2.50023i
$183$	30.1746			2.23057
$184$		−	1.00000i		−	0.0737210i
$185$		−	7.87472i		−	0.578961i
$186$		−	9.17859i		−	0.673007i
$187$	−3.67539			−0.268771
$188$			7.23490i			0.527659i
$189$			36.6136i			2.66324i
$190$	−4.95776			−0.359674
$191$			7.55274i			0.546497i	0.961944	+	0.273248i	$0.0880981\pi$
$191$			7.55274i			0.546497i	−0.961944	+	0.273248i	$0.911902\pi$
$192$			2.92171i			0.210856i
$193$		−	25.2068i		−	1.81442i	−0.420673	−	0.907212i	$-0.638206\pi$
$193$		−	25.2068i		−	1.81442i	0.420673	−	0.907212i	$-0.361794\pi$
$194$	8.75975			0.628913
$195$		−	34.1801i		−	2.44768i
$196$	−17.4104			−1.24360
$197$	−19.5702			−1.39432			−0.697161	−	0.716915i	$-0.745554\pi$
$197$	−19.5702			−1.39432			−0.697161	+	0.716915i	$0.745554\pi$
$198$	−14.1083			−1.00263
$199$	21.9077			1.55300			0.776498	−	0.630120i	$-0.216994\pi$
$199$	21.9077			1.55300			0.776498	+	0.630120i	$0.216994\pi$
$200$		−	2.06360i		−	0.145919i
$201$			23.8390i			1.68147i
$202$	10.3781			0.730198
$203$	18.6408	+	18.9848i	1.30832	+	1.33247i
$204$	−4.21400			−0.295039
$205$		−	19.4892i		−	1.36119i
$206$			1.47855i			0.103016i
$207$	5.53640			0.384806
$208$	6.82697			0.473365
$209$	7.37266			0.509978
$210$	−24.7361			−1.70696
$211$		−	24.8500i		−	1.71074i	−0.518016	−	0.855371i	$-0.673329\pi$
$211$		−	24.8500i		−	1.71074i	0.518016	−	0.855371i	$-0.326671\pi$
$212$	6.48011			0.445055
$213$			36.6331i			2.51006i
$214$			13.9184i			0.951442i
$215$			11.7429i			0.800858i
$216$	−7.41062			−0.504229
$217$			15.5212i			1.05365i
$218$			6.46947i			0.438168i
$219$	31.8039			2.14911
$220$		−	4.36670i		−	0.294403i
$221$			9.84657i			0.662352i
$222$			13.4266i			0.901132i
$223$	−5.43376			−0.363871			−0.181936	−	0.983310i	$-0.558236\pi$
$223$	−5.43376			−0.363871			−0.181936	+	0.983310i	$0.558236\pi$
$224$		−	4.94068i		−	0.330113i
$225$	11.4249			0.761661
$226$	3.27697			0.217981
$227$	17.8375			1.18392			0.591959	−	0.805968i	$-0.298355\pi$
$227$	17.8375			1.18392			0.591959	+	0.805968i	$0.298355\pi$
$228$	8.45309			0.559820
$229$			28.4244i			1.87834i	0.343452	+	0.939170i	$0.388404\pi$
$229$			28.4244i			1.87834i	−0.343452	+	0.939170i	$0.611596\pi$
$230$			1.71359i			0.112991i
$231$	36.7850			2.42027
$232$	−3.84254	+	3.77291i	−0.252275	+	0.247704i
$233$	−12.2982			−0.805683			−0.402841	−	0.915270i	$-0.631977\pi$
$233$	−12.2982			−0.805683			−0.402841	+	0.915270i	$0.631977\pi$
$234$			37.7968i			2.47086i
$235$		−	12.3977i		−	0.808734i
$236$	4.25517			0.276988
$237$	11.1700			0.725570
$238$	7.12597			0.461908
$239$	−3.43906			−0.222454			−0.111227	−	0.993795i	$-0.535478\pi$
$239$	−3.43906			−0.222454			−0.111227	+	0.993795i	$0.535478\pi$
$240$		−	5.00662i		−	0.323176i
$241$	−15.7949			−1.01744			−0.508719	−	0.860932i	$-0.669881\pi$
$241$	−15.7949			−1.01744			−0.508719	+	0.860932i	$0.669881\pi$
$242$		−	4.50630i		−	0.289676i
$243$			7.49911i			0.481068i
$244$		−	10.3277i		−	0.661165i
$245$	29.8343			1.90604
$246$			33.2295i			2.11864i
$247$		−	19.7518i		−	1.25678i
$248$	−3.14151			−0.199486
$249$			6.92920i			0.439120i
$250$			12.1041i			0.765533i
$251$		−	14.6244i		−	0.923082i	−0.887119	−	0.461541i	$-0.847297\pi$
$251$		−	14.6244i		−	0.923082i	0.887119	−	0.461541i	$-0.152703\pi$
$252$	27.3536			1.72311
$253$		−	2.54827i		−	0.160209i
$254$	−0.721234			−0.0452542
$255$	7.22107			0.452201
$256$	1.00000			0.0625000
$257$	26.1130			1.62889			0.814443	−	0.580243i	$-0.197043\pi$
$257$	26.1130			1.62889			0.814443	+	0.580243i	$0.197043\pi$
$258$		−	20.0219i		−	1.24651i
$259$		−	22.7046i		−	1.41080i
$260$	−11.6986			−0.725519
$261$	−20.8883	−	21.2739i	−1.29296	−	1.31682i
$262$	−11.7636			−0.726760
$263$		−	0.0897845i		−	0.00553635i	−0.999996	−	0.00276818i	$-0.999119\pi$
$263$		−	0.0897845i		−	0.00553635i	0.999996	−	0.00276818i	$-0.000881139\pi$
$264$			7.44532i			0.458228i
$265$	−11.1043			−0.682129
$266$	−14.2944			−0.876445
$267$	6.63233			0.405892
$268$	8.15926			0.498406
$269$			5.89155i			0.359214i	0.983738	+	0.179607i	$0.0574826\pi$
$269$			5.89155i			0.359214i	−0.983738	+	0.179607i	$0.942517\pi$
$270$	12.6988			0.772824
$271$		−	20.1216i		−	1.22230i	−0.791516	−	0.611149i	$-0.790708\pi$
$271$		−	20.1216i		−	1.22230i	0.791516	−	0.611149i	$-0.209292\pi$
$272$			1.44230i			0.0874525i
$273$		−	98.5490i		−	5.96446i
$274$	1.75414			0.105972
$275$		−	5.25862i		−	0.317107i
$276$		−	2.92171i		−	0.175866i
$277$	−24.3694			−1.46422			−0.732109	−	0.681188i	$-0.761464\pi$
$277$	−24.3694			−1.46422			−0.732109	+	0.681188i	$0.761464\pi$
$278$		−	0.970744i		−	0.0582214i
$279$		−	17.3927i		−	1.04127i
$280$			8.46632i			0.505959i
$281$	−17.7309			−1.05774			−0.528869	−	0.848703i	$-0.677384\pi$
$281$	−17.7309			−1.05774			−0.528869	+	0.848703i	$0.677384\pi$
$282$			21.1383i			1.25877i
$283$	12.0039			0.713557			0.356779	−	0.934189i	$-0.383875\pi$
$283$	12.0039			0.713557			0.356779	+	0.934189i	$0.383875\pi$
$284$	12.5382			0.744007
$285$	−14.4852			−0.858026
$286$	17.3970			1.02871
$287$		−	56.1919i		−	3.31690i
$288$			5.53640i			0.326235i
$289$	14.9198			0.877633
$290$	6.58455	−	6.46523i	0.386658	−	0.379652i
$291$	25.5935			1.50031
$292$		−	10.8854i		−	0.637017i
$293$		−	1.47987i		−	0.0864551i	−0.999065	−	0.0432275i	$-0.986236\pi$
$293$		−	1.47987i		−	0.0864551i	0.999065	−	0.0432275i	$-0.0137640\pi$
$294$	−50.8680			−2.96668
$295$	−7.29163			−0.424535
$296$	4.59544			0.267105
$297$	−18.8843			−1.09578
$298$		−	17.4823i		−	1.01272i
$299$	−6.82697			−0.394814
$300$		−	6.02925i		−	0.348099i
$301$			33.8574i			1.95151i
$302$			11.5608i			0.665247i
$303$	30.3217			1.74194
$304$		−	2.89320i		−	0.165936i
$305$			17.6975i			1.01336i
$306$	−7.98517			−0.456482
$307$		−	7.63351i		−	0.435668i	−0.975986	−	0.217834i	$-0.930101\pi$
$307$		−	7.63351i		−	0.435668i	0.975986	−	0.217834i	$-0.0698991\pi$
$308$		−	12.5902i		−	0.717394i
$309$			4.31990i			0.245751i
$310$	5.38327			0.305749
$311$			22.9722i			1.30263i	0.758807	+	0.651316i	$0.225783\pi$
$311$			22.9722i			1.30263i	−0.758807	+	0.651316i	$0.774217\pi$
$312$	19.9464			1.12924
$313$	26.0728			1.47372			0.736862	−	0.676044i	$-0.236307\pi$
$313$	26.0728			1.47372			0.736862	+	0.676044i	$0.236307\pi$
$314$	−14.0075			−0.790487
$315$	−46.8729			−2.64099
$316$		−	3.82311i		−	0.215066i
$317$			13.3224i			0.748259i	0.927376	+	0.374130i	$0.122058\pi$
$317$			13.3224i			0.748259i	−0.927376	+	0.374130i	$0.877942\pi$
$318$	18.9330			1.06171
$319$	−9.79186	+	9.61441i	−0.548239	+	0.538304i
$320$	−1.71359			−0.0957927
$321$			40.6656i			2.26973i
$322$			4.94068i			0.275334i
$323$	4.17287			0.232185
$324$	−5.04251			−0.280140
$325$	−14.0881			−0.781469
$326$	−10.9022			−0.603815
$327$			18.9019i			1.04528i
$328$	11.3733			0.627986
$329$		−	35.7453i		−	1.97070i
$330$		−	12.7582i		−	0.702318i
$331$			2.07268i			0.113925i	0.998376	+	0.0569623i	$0.0181415\pi$
$331$			2.07268i			0.113925i	−0.998376	+	0.0569623i	$0.981859\pi$
$332$	2.37162			0.130160
$333$			25.4422i			1.39422i
$334$			12.9995i			0.711301i
$335$	−13.9817			−0.763899
$336$		−	14.4353i		−	0.787508i
$337$		−	8.73944i		−	0.476068i	−0.971257	−	0.238034i	$-0.923497\pi$
$337$		−	8.73944i		−	0.476068i	0.971257	−	0.238034i	$-0.0765029\pi$
$338$		−	33.6075i		−	1.82801i
$339$	9.57437			0.520008
$340$		−	2.47152i		−	0.134037i
$341$	−8.00543			−0.433518
$342$	16.0179			0.866149
$343$	51.4343			2.77719
$344$	−6.85278			−0.369477
$345$			5.00662i			0.269548i
$346$			4.73181i			0.254384i
$347$	−5.59753			−0.300491			−0.150246	−	0.988649i	$-0.548006\pi$
$347$	−5.59753			−0.300491			−0.150246	+	0.988649i	$0.548006\pi$
$348$	−11.2268	+	11.0234i	−0.601820	+	0.590914i
$349$	22.4862			1.20366			0.601829	−	0.798625i	$-0.294439\pi$
$349$	22.4862			1.20366			0.601829	+	0.798625i	$0.294439\pi$
$350$			10.1956i			0.544978i
$351$			50.5921i			2.70041i
$352$	2.54827			0.135823
$353$	−26.6846			−1.42028			−0.710139	−	0.704061i	$-0.751368\pi$
$353$	−26.6846			−1.42028			−0.710139	+	0.704061i	$0.751368\pi$
$354$	12.4324			0.660773
$355$	−21.4854			−1.14033
$356$		−	2.27002i		−	0.120311i
$357$	20.8200			1.10191
$358$		−	1.47498i		−	0.0779553i
$359$		−	18.4391i		−	0.973179i	−0.873631	−	0.486589i	$-0.838241\pi$
$359$		−	18.4391i		−	0.973179i	0.873631	−	0.486589i	$-0.161759\pi$
$360$		−	9.48713i		−	0.500016i
$361$	10.6294			0.559442
$362$			10.7212i			0.563495i
$363$		−	13.1661i		−	0.691041i
$364$	−33.7299			−1.76793
$365$			18.6531i			0.976346i
$366$		−	30.1746i		−	1.57725i
$367$			18.0715i			0.943326i	0.881779	+	0.471663i	$0.156346\pi$
$367$			18.0715i			0.943326i	−0.881779	+	0.471663i	$0.843654\pi$
$368$	−1.00000			−0.0521286
$369$			62.9672i			3.27794i
$370$	−7.87472			−0.409387
$371$	−32.0162			−1.66220
$372$	−9.17859			−0.475888
$373$	19.8078			1.02561			0.512806	−	0.858505i	$-0.328606\pi$
$373$	19.8078			1.02561			0.512806	+	0.858505i	$0.328606\pi$
$374$			3.67539i			0.190050i
$375$			35.3648i			1.82623i
$376$	7.23490			0.373111
$377$	25.7575	+	26.2329i	1.32658	+	1.35106i
$378$	36.6136			1.88320
$379$		−	14.5934i		−	0.749612i	−0.927103	−	0.374806i	$-0.877709\pi$
$379$		−	14.5934i		−	0.749612i	0.927103	−	0.374806i	$-0.122291\pi$
$380$			4.95776i			0.254328i
$381$	−2.10724			−0.107957
$382$	7.55274			0.386432
$383$	−12.7651			−0.652268			−0.326134	−	0.945324i	$-0.605746\pi$
$383$	−12.7651			−0.652268			−0.326134	+	0.945324i	$0.605746\pi$
$384$	2.92171			0.149098
$385$			21.5745i			1.09954i
$386$	−25.2068			−1.28299
$387$		−	37.9397i		−	1.92859i
$388$		−	8.75975i		−	0.444709i
$389$		−	5.11627i		−	0.259405i	−0.991553	−	0.129703i	$-0.958598\pi$
$389$		−	5.11627i		−	0.259405i	0.991553	−	0.129703i	$-0.0414023\pi$
$390$	−34.1801			−1.73077
$391$		−	1.44230i		−	0.0729405i
$392$			17.4104i			0.879356i
$393$	−34.3699			−1.73373
$394$			19.5702i			0.985934i
$395$			6.55125i			0.329629i
$396$			14.1083i			0.708967i
$397$	15.2291			0.764327			0.382163	−	0.924095i	$-0.375179\pi$
$397$	15.2291			0.764327			0.382163	+	0.924095i	$0.375179\pi$
$398$		−	21.9077i		−	1.09813i
$399$	−41.7640			−2.09082
$400$	−2.06360			−0.103180
$401$	−15.0188			−0.750002			−0.375001	−	0.927024i	$-0.622358\pi$
$401$	−15.0188			−0.750002			−0.375001	+	0.927024i	$0.622358\pi$
$402$	23.8390			1.18898
$403$			21.4470i			1.06835i
$404$		−	10.3781i		−	0.516328i
$405$	8.64081			0.429365
$406$	18.9848	−	18.6408i	0.942199	−	0.925125i
$407$	11.7105			0.580466
$408$			4.21400i			0.208624i
$409$		−	1.47010i		−	0.0726919i	−0.999339	−	0.0363459i	$-0.988428\pi$
$409$		−	1.47010i		−	0.0726919i	0.999339	−	0.0363459i	$-0.0115718\pi$
$410$	−19.4892			−0.962504
$411$	5.12509			0.252802
$412$	1.47855			0.0728431
$413$	−21.0234			−1.03450
$414$		−	5.53640i		−	0.272099i
$415$	−4.06400			−0.199494
$416$		−	6.82697i		−	0.334720i
$417$		−	2.83623i		−	0.138891i
$418$		−	7.37266i		−	0.360609i
$419$	10.6262			0.519124			0.259562	−	0.965726i	$-0.416422\pi$
$419$	10.6262			0.519124			0.259562	+	0.965726i	$0.416422\pi$
$420$			24.7361i			1.20700i
$421$		−	12.7131i		−	0.619597i	−0.950802	−	0.309799i	$-0.899738\pi$
$421$		−	12.7131i		−	0.619597i	0.950802	−	0.309799i	$-0.100262\pi$
$422$	−24.8500			−1.20968
$423$			40.0553i			1.94755i
$424$		−	6.48011i		−	0.314702i
$425$		−	2.97634i		−	0.144374i
$426$	36.6331			1.77488
$427$			51.0260i			2.46932i
$428$	13.9184			0.672771
$429$	50.8290			2.45405
$430$	11.7429			0.566292
$431$	19.5280			0.940631			0.470316	−	0.882498i	$-0.344140\pi$
$431$	19.5280			0.940631			0.470316	+	0.882498i	$0.344140\pi$
$432$			7.41062i			0.356544i
$433$			38.9477i			1.87171i	0.352389	+	0.935854i	$0.385369\pi$
$433$			38.9477i			1.87171i	−0.352389	+	0.935854i	$0.614631\pi$
$434$	15.5212			0.745042
$435$	19.2382	−	18.8895i	0.922400	−	0.905684i
$436$	6.46947			0.309832
$437$			2.89320i			0.138400i
$438$		−	31.8039i		−	1.51965i
$439$	13.5439			0.646417			0.323209	−	0.946328i	$-0.395238\pi$
$439$	13.5439			0.646417			0.323209	+	0.946328i	$0.395238\pi$
$440$	−4.36670			−0.208174
$441$	−96.3907			−4.59003
$442$	9.84657			0.468353
$443$		−	21.3433i		−	1.01405i	−0.861931	−	0.507025i	$-0.830745\pi$
$443$		−	21.3433i		−	1.01405i	0.861931	−	0.507025i	$-0.169255\pi$
$444$	13.4266			0.637196
$445$			3.88988i			0.184398i
$446$			5.43376i			0.257296i
$447$		−	51.0782i		−	2.41592i
$448$	−4.94068			−0.233425
$449$			29.0633i			1.37158i	0.727798	+	0.685792i	$0.240544\pi$
$449$			29.0633i			1.37158i	−0.727798	+	0.685792i	$0.759456\pi$
$450$		−	11.4249i		−	0.538576i
$451$	28.9823			1.36472
$452$		−	3.27697i		−	0.154136i
$453$			33.7772i			1.58699i
$454$		−	17.8375i		−	0.837156i
$455$	57.7993			2.70967
$456$		−	8.45309i		−	0.395852i
$457$	3.39653			0.158883			0.0794416	−	0.996840i	$-0.474686\pi$
$457$	3.39653			0.158883			0.0794416	+	0.996840i	$0.474686\pi$
$458$	28.4244			1.32819
$459$	−10.6884			−0.498891
$460$	1.71359			0.0798967
$461$		−	6.60253i		−	0.307510i	−0.988109	−	0.153755i	$-0.950863\pi$
$461$		−	6.60253i		−	0.307510i	0.988109	−	0.153755i	$-0.0491367\pi$
$462$		−	36.7850i		−	1.71139i
$463$	22.8065			1.05991			0.529953	−	0.848027i	$-0.322210\pi$
$463$	22.8065			1.05991			0.529953	+	0.848027i	$0.322210\pi$
$464$	3.77291	+	3.84254i	0.175153	+	0.178386i
$465$	15.7284			0.729385
$466$			12.2982i			0.569704i
$467$			0.338478i			0.0156629i	0.999969	+	0.00783144i	$0.00249285\pi$
$467$			0.338478i			0.0156629i	−0.999969	+	0.00783144i	$0.997507\pi$
$468$	37.7968			1.74716
$469$	−40.3123			−1.86145
$470$	−12.3977			−0.571862
$471$	−40.9258			−1.88576
$472$		−	4.25517i		−	0.195860i
$473$	−17.4628			−0.802939
$474$		−	11.1700i		−	0.513056i
$475$			5.97041i			0.273941i
$476$		−	7.12597i		−	0.326618i
$477$	35.8764			1.64267
$478$			3.43906i			0.157299i
$479$		−	38.1372i		−	1.74254i	−0.490808	−	0.871268i	$-0.663298\pi$
$479$		−	38.1372i		−	1.74254i	0.490808	−	0.871268i	$-0.336702\pi$
$480$	−5.00662			−0.228520
$481$		−	31.3730i		−	1.43048i
$482$			15.7949i			0.719438i
$483$			14.4353i			0.656827i
$484$	−4.50630			−0.204832
$485$			15.0106i			0.681598i
$486$	7.49911			0.340167
$487$	−31.1164			−1.41002			−0.705009	−	0.709198i	$-0.749057\pi$
$487$	−31.1164			−1.41002			−0.705009	+	0.709198i	$0.749057\pi$
$488$	−10.3277			−0.467514
$489$	−31.8530			−1.44044
$490$		−	29.8343i		−	1.34777i
$491$			10.5325i			0.475324i	0.971348	+	0.237662i	$0.0763810\pi$
$491$			10.5325i			0.475324i	−0.971348	+	0.237662i	$0.923619\pi$
$492$	33.2295			1.49810
$493$	−5.54212	+	5.44169i	−0.249604	+	0.245081i
$494$	−19.7518			−0.888674
$495$		−	24.1758i		−	1.08662i
$496$			3.14151i			0.141058i
$497$	−61.9474			−2.77872
$498$	6.92920			0.310505
$499$	12.4186			0.555932			0.277966	−	0.960591i	$-0.410340\pi$
$499$	12.4186			0.555932			0.277966	+	0.960591i	$0.410340\pi$
$500$	12.1041			0.541313
$501$			37.9808i			1.69686i
$502$	−14.6244			−0.652718
$503$			9.50805i			0.423943i	0.977276	+	0.211972i	$0.0679884\pi$
$503$			9.50805i			0.423943i	−0.977276	+	0.211972i	$0.932012\pi$
$504$		−	27.3536i		−	1.21843i
$505$			17.7838i			0.791367i
$506$	−2.54827			−0.113285
$507$		−	98.1914i		−	4.36083i
$508$			0.721234i			0.0319996i
$509$	−15.5860			−0.690838			−0.345419	−	0.938449i	$-0.612263\pi$
$509$	−15.5860			−0.690838			−0.345419	+	0.938449i	$0.612263\pi$
$510$		−	7.22107i		−	0.319755i
$511$			53.7811i			2.37914i
$512$		−	1.00000i		−	0.0441942i
$513$	21.4404			0.946617
$514$		−	26.1130i		−	1.15180i
$515$	−2.53364			−0.111645
$516$	−20.0219			−0.881413
$517$	18.4365			0.810836
$518$	−22.7046			−0.997584
$519$			13.8250i			0.606849i
$520$			11.6986i			0.513019i
$521$	4.92853			0.215923			0.107961	−	0.994155i	$-0.465568\pi$
$521$	4.92853			0.215923			0.107961	+	0.994155i	$0.465568\pi$
$522$	−21.2739	+	20.8883i	−0.931131	+	0.914258i
$523$	−42.7689			−1.87015			−0.935076	−	0.354446i	$-0.884669\pi$
$523$	−42.7689			−1.87015			−0.935076	+	0.354446i	$0.884669\pi$
$524$			11.7636i			0.513897i
$525$			29.7886i			1.30008i
$526$	−0.0897845			−0.00391479
$527$	−4.53101			−0.197374
$528$	7.44532			0.324016
$529$	1.00000			0.0434783
$530$			11.1043i			0.482338i
$531$	23.5583			1.02234
$532$			14.2944i			0.619740i
$533$		−	77.6452i		−	3.36319i
$534$		−	6.63233i		−	0.287009i
$535$	−23.8505			−1.03115
$536$		−	8.15926i		−	0.352427i
$537$		−	4.30947i		−	0.185968i
$538$	5.89155			0.254003
$539$			44.3664i			1.91099i
$540$		−	12.6988i		−	0.546469i
$541$		−	35.3121i		−	1.51818i	−0.650983	−	0.759092i	$-0.725643\pi$
$541$		−	35.3121i		−	1.51818i	0.650983	−	0.759092i	$-0.274357\pi$
$542$	−20.1216			−0.864295
$543$			31.3243i			1.34425i
$544$	1.44230			0.0618383
$545$	−11.0860			−0.474874
$546$	−98.5490			−4.21751
$547$	−29.4432			−1.25890			−0.629451	−	0.777040i	$-0.716720\pi$
$547$	−29.4432			−1.25890			−0.629451	+	0.777040i	$0.716720\pi$
$548$		−	1.75414i		−	0.0749332i
$549$		−	57.1784i		−	2.44031i
$550$	−5.25862			−0.224228
$551$	11.1172	−	10.9158i	0.473610	−	0.465028i
$552$	−2.92171			−0.124356
$553$			18.8888i			0.803232i
$554$			24.3694i			1.03536i
$555$	−23.0077			−0.976621
$556$	−0.970744			−0.0411687
$557$	−19.8512			−0.841124			−0.420562	−	0.907264i	$-0.638167\pi$
$557$	−19.8512			−0.841124			−0.420562	+	0.907264i	$0.638167\pi$
$558$	−17.3927			−0.736290
$559$			46.7837i			1.97874i
$560$	8.46632			0.357767
$561$			10.7384i			0.453376i
$562$			17.7309i			0.747934i
$563$			30.3496i			1.27908i	0.768757	+	0.639541i	$0.220876\pi$
$563$			30.3496i			1.27908i	−0.768757	+	0.639541i	$0.779124\pi$
$564$	21.1383			0.890082
$565$			5.61539i			0.236241i
$566$		−	12.0039i		−	0.504561i
$567$	24.9135			1.04627
$568$		−	12.5382i		−	0.526092i
$569$			39.6101i			1.66054i	0.557360	+	0.830271i	$0.311814\pi$
$569$			39.6101i			1.66054i	−0.557360	+	0.830271i	$0.688186\pi$
$570$			14.4852i			0.606716i
$571$	29.4953			1.23434			0.617170	−	0.786830i	$-0.288279\pi$
$571$	29.4953			1.23434			0.617170	+	0.786830i	$0.288279\pi$
$572$		−	17.3970i		−	0.727405i
$573$	22.0669			0.921859
$574$	−56.1919			−2.34541
$575$	2.06360			0.0860581
$576$	5.53640			0.230683
$577$			4.71064i			0.196106i	0.995181	+	0.0980532i	$0.0312615\pi$
$577$			4.71064i			0.196106i	−0.995181	+	0.0980532i	$0.968738\pi$
$578$		−	14.9198i		−	0.620580i
$579$	−73.6470			−3.06066
$580$	−6.46523	−	6.58455i	−0.268454	−	0.273409i
$581$	−11.7174			−0.486121
$582$		−	25.5935i		−	1.06088i
$583$		−	16.5131i		−	0.683902i
$584$	−10.8854			−0.450439
$585$	−64.7683			−2.67784
$586$	−1.47987			−0.0611330
$587$	32.7925			1.35349			0.676745	−	0.736218i	$-0.263390\pi$
$587$	32.7925			1.35349			0.676745	+	0.736218i	$0.263390\pi$
$588$			50.8680i			2.09776i
$589$	9.08901			0.374506
$590$			7.29163i			0.300192i
$591$			57.1786i			2.35201i
$592$		−	4.59544i		−	0.188872i
$593$	11.7730			0.483460			0.241730	−	0.970344i	$-0.422285\pi$
$593$	11.7730			0.483460			0.241730	+	0.970344i	$0.422285\pi$
$594$			18.8843i			0.774832i
$595$			12.2110i			0.500603i
$596$	−17.4823			−0.716103
$597$		−	64.0080i		−	2.61967i
$598$			6.82697i			0.279176i
$599$		−	30.8580i		−	1.26082i	−0.776262	−	0.630411i	$-0.782886\pi$
$599$		−	30.8580i		−	1.26082i	0.776262	−	0.630411i	$-0.217114\pi$
$600$	−6.02925			−0.246143
$601$		−	41.1878i		−	1.68008i	−0.542522	−	0.840042i	$-0.682530\pi$
$601$		−	41.1878i		−	1.68008i	0.542522	−	0.840042i	$-0.317470\pi$
$602$	33.8574			1.37993
$603$	45.1729			1.83958
$604$	11.5608			0.470400
$605$	7.72196			0.313942
$606$		−	30.3217i		−	1.23173i
$607$			15.8398i			0.642920i	0.946923	+	0.321460i	$0.104173\pi$
$607$			15.8398i			0.642920i	−0.946923	+	0.321460i	$0.895827\pi$
$608$	−2.89320			−0.117335
$609$	55.4681	−	54.4629i	2.24768	−	2.20695i
$610$	17.6975			0.716551
$611$		−	49.3924i		−	1.99820i
$612$			7.98517i			0.322781i
$613$	−17.9048			−0.723167			−0.361583	−	0.932340i	$-0.617764\pi$
$613$	−17.9048			−0.723167			−0.361583	+	0.932340i	$0.617764\pi$
$614$	−7.63351			−0.308064
$615$	−56.9419			−2.29612
$616$	−12.5902			−0.507274
$617$		−	29.5701i		−	1.19045i	−0.803560	−	0.595224i	$-0.797063\pi$
$617$		−	29.5701i		−	1.19045i	0.803560	−	0.595224i	$-0.202937\pi$
$618$	4.31990			0.173772
$619$			12.9604i			0.520924i	0.965484	+	0.260462i	$0.0838748\pi$
$619$			12.9604i			0.520924i	−0.965484	+	0.260462i	$0.916125\pi$
$620$		−	5.38327i		−	0.216197i
$621$		−	7.41062i		−	0.297378i
$622$	22.9722			0.921100
$623$			11.2154i			0.449337i
$624$		−	19.9464i		−	0.798496i
$625$	−10.4235			−0.416942
$626$		−	26.0728i		−	1.04208i
$627$		−	21.5408i		−	0.860256i
$628$			14.0075i			0.558959i
$629$	6.62803			0.264277
$630$			46.8729i			1.86746i
$631$	−13.5715			−0.540272			−0.270136	−	0.962822i	$-0.587069\pi$
$631$	−13.5715			−0.540272			−0.270136	+	0.962822i	$0.587069\pi$
$632$	−3.82311			−0.152075
$633$	−72.6044			−2.88577
$634$	13.3224			0.529099
$635$		−	1.23590i		−	0.0490452i
$636$		−	18.9330i		−	0.750742i
$637$	118.860			4.70940
$638$	9.61441	+	9.79186i	0.380638	+	0.387663i
$639$	69.4166			2.74608
$640$			1.71359i			0.0677357i
$641$			30.3669i			1.19942i	0.800217	+	0.599711i	$0.204718\pi$
$641$			30.3669i			1.19942i	−0.800217	+	0.599711i	$0.795282\pi$
$642$	40.6656			1.60494
$643$	−16.3637			−0.645321			−0.322660	−	0.946515i	$-0.604577\pi$
$643$	−16.3637			−0.645321			−0.322660	+	0.946515i	$0.604577\pi$
$644$	4.94068			0.194690
$645$	34.3093			1.35093
$646$		−	4.17287i		−	0.164179i
$647$	−23.8576			−0.937940			−0.468970	−	0.883214i	$-0.655375\pi$
$647$	−23.8576			−0.937940			−0.468970	+	0.883214i	$0.655375\pi$
$648$			5.04251i			0.198089i
$649$		−	10.8433i		−	0.425638i
$650$			14.0881i			0.552582i
$651$	45.3485			1.77735
$652$			10.9022i			0.426961i
$653$		−	3.07304i		−	0.120257i	−0.998191	−	0.0601286i	$-0.980849\pi$
$653$		−	3.07304i		−	0.120257i	0.998191	−	0.0601286i	$-0.0191511\pi$
$654$	18.9019			0.739124
$655$		−	20.1581i		−	0.787641i
$656$		−	11.3733i		−	0.444053i
$657$		−	60.2657i		−	2.35119i
$658$	−35.7453			−1.39350
$659$			46.0852i			1.79522i	0.440787	+	0.897612i	$0.354699\pi$
$659$			46.0852i			1.79522i	−0.440787	+	0.897612i	$0.645301\pi$
$660$	−12.7582			−0.496614
$661$	−32.4263			−1.26124			−0.630619	−	0.776093i	$-0.717199\pi$
$661$	−32.4263			−1.26124			−0.630619	+	0.776093i	$0.717199\pi$
$662$	2.07268			0.0805568
$663$	28.7688			1.11729
$664$		−	2.37162i		−	0.0920368i
$665$		−	24.4947i		−	0.949865i
$666$	25.4422			0.985866
$667$	−3.77291	−	3.84254i	−0.146088	−	0.148784i
$668$	12.9995			0.502966
$669$			15.8759i			0.613797i
$670$			13.9817i			0.540158i
$671$	−26.3179			−1.01599
$672$	−14.4353			−0.556852
$673$	21.0663			0.812045			0.406023	−	0.913863i	$-0.366915\pi$
$673$	21.0663			0.812045			0.406023	+	0.913863i	$0.366915\pi$
$674$	−8.73944			−0.336631
$675$		−	15.2926i		−	0.588611i
$676$	−33.6075			−1.29260
$677$		−	16.6179i		−	0.638677i	−0.947641	−	0.319338i	$-0.896539\pi$
$677$		−	16.6179i		−	0.638677i	0.947641	−	0.319338i	$-0.103461\pi$
$678$		−	9.57437i		−	0.367701i
$679$			43.2791i			1.66090i
$680$	−2.47152			−0.0947785
$681$		−	52.1161i		−	1.99709i
$682$			8.00543i			0.306544i
$683$	6.94145			0.265607			0.132804	−	0.991142i	$-0.457602\pi$
$683$	6.94145			0.265607			0.132804	+	0.991142i	$0.457602\pi$
$684$		−	16.0179i		−	0.612460i
$685$			3.00588i			0.114849i
$686$		−	51.4343i		−	1.96377i
$687$	83.0480			3.16848
$688$			6.85278i			0.261260i
$689$	−44.2395			−1.68539
$690$	5.00662			0.190599
$691$	30.3928			1.15619			0.578097	−	0.815968i	$-0.303795\pi$
$691$	30.3928			1.15619			0.578097	+	0.815968i	$0.303795\pi$
$692$	4.73181			0.179876
$693$		−	69.7045i		−	2.64785i
$694$			5.59753i			0.212479i
$695$	1.66346			0.0630986
$696$	11.0234	+	11.2268i	0.417839	+	0.425551i
$697$	16.4038			0.621337
$698$		−	22.4862i		−	0.851115i
$699$			35.9318i			1.35907i
$700$	10.1956			0.385357
$701$	33.4924			1.26499			0.632495	−	0.774564i	$-0.282031\pi$
$701$	33.4924			1.26499			0.632495	+	0.774564i	$0.282031\pi$
$702$	50.5921			1.90948
$703$	−13.2955			−0.501450
$704$		−	2.54827i		−	0.0960417i
$705$	−36.2224			−1.36421
$706$			26.6846i			1.00429i
$707$			51.2747i			1.92838i
$708$		−	12.4324i		−	0.467237i
$709$	3.94472			0.148147			0.0740735	−	0.997253i	$-0.476400\pi$
$709$	3.94472			0.148147			0.0740735	+	0.997253i	$0.476400\pi$
$710$			21.4854i			0.806333i
$711$		−	21.1662i		−	0.793796i
$712$	−2.27002			−0.0850725
$713$		−	3.14151i		−	0.117651i
$714$		−	20.8200i		−	0.779170i
$715$			29.8114i			1.11488i
$716$	−1.47498			−0.0551227
$717$			10.0479i			0.375247i
$718$	−18.4391			−0.688141
$719$	7.59323			0.283180			0.141590	−	0.989925i	$-0.454779\pi$
$719$	7.59323			0.283180			0.141590	+	0.989925i	$0.454779\pi$
$720$	−9.48713			−0.353564
$721$	−7.30506			−0.272055
$722$		−	10.6294i		−	0.395585i
$723$			46.1481i			1.71627i
$724$	10.7212			0.398451
$725$	−7.78578	−	7.92948i	−0.289157	−	0.294493i
$726$	−13.1661			−0.488640
$727$			41.1658i			1.52676i	0.645952	+	0.763378i	$0.276461\pi$
$727$			41.1658i			1.52676i	−0.645952	+	0.763378i	$0.723539\pi$
$728$			33.7299i			1.25011i
$729$	37.0378			1.37177
$730$	18.6531			0.690381
$731$	−9.88380			−0.365566
$732$	−30.1746			−1.11529
$733$		−	1.54061i		−	0.0569039i	−0.999595	−	0.0284519i	$-0.990942\pi$
$733$		−	1.54061i		−	0.0569039i	0.999595	−	0.0284519i	$-0.00905776\pi$
$734$	18.0715			0.667032
$735$		−	87.1671i		−	3.21521i
$736$			1.00000i			0.0368605i
$737$		−	20.7920i		−	0.765885i
$738$	62.9672			2.31785
$739$		−	43.4126i		−	1.59696i	−0.602022	−	0.798480i	$-0.705638\pi$
$739$		−	43.4126i		−	1.59696i	0.602022	−	0.798480i	$-0.294362\pi$
$740$			7.87472i			0.289480i
$741$	−57.7090			−2.11999
$742$			32.0162i			1.17535i
$743$		−	2.38541i		−	0.0875123i	−0.999042	−	0.0437561i	$-0.986068\pi$
$743$		−	2.38541i		−	0.0875123i	0.999042	−	0.0437561i	$-0.0139325\pi$
$744$			9.17859i			0.336503i
$745$	29.9575			1.09756
$746$		−	19.8078i		−	0.725217i
$747$	13.1303			0.480411
$748$	3.67539			0.134385
$749$	−68.7664			−2.51267
$750$	35.3648			1.29134
$751$		−	31.9064i		−	1.16428i	−0.813088	−	0.582140i	$-0.802215\pi$
$751$		−	31.9064i		−	1.16428i	0.813088	−	0.582140i	$-0.197785\pi$
$752$		−	7.23490i		−	0.263830i
$753$	−42.7282			−1.55710
$754$	26.2329	−	25.7575i	0.955347	−	0.938035i
$755$	−19.8104			−0.720975
$756$		−	36.6136i		−	1.33162i
$757$			6.11862i			0.222385i	0.993799	+	0.111192i	$0.0354670\pi$
$757$			6.11862i			0.222385i	−0.993799	+	0.111192i	$0.964533\pi$
$758$	−14.5934			−0.530055
$759$	−7.44532			−0.270248
$760$	4.95776			0.179837
$761$	46.3877			1.68155			0.840776	−	0.541384i	$-0.182099\pi$
$761$	46.3877			1.68155			0.840776	+	0.541384i	$0.182099\pi$
$762$			2.10724i			0.0763371i
$763$	−31.9636			−1.15716
$764$		−	7.55274i		−	0.273248i
$765$		−	13.6833i		−	0.494722i
$766$			12.7651i			0.461223i
$767$	−29.0499			−1.04893
$768$		−	2.92171i		−	0.105428i
$769$			38.3492i			1.38291i	0.722421	+	0.691454i	$0.243029\pi$
$769$			38.3492i			1.38291i	−0.722421	+	0.691454i	$0.756971\pi$
$770$	21.5745			0.777491
$771$		−	76.2948i		−	2.74769i
$772$			25.2068i			0.907212i
$773$		−	25.1798i		−	0.905655i	−0.891598	−	0.452827i	$-0.850415\pi$
$773$		−	25.1798i		−	0.905655i	0.891598	−	0.452827i	$-0.149585\pi$
$774$	−37.9397			−1.36372
$775$		−	6.48282i		−	0.232870i
$776$	−8.75975			−0.314457
$777$	−66.3364			−2.37981
$778$	−5.11627			−0.183427
$779$	−32.9052			−1.17895
$780$			34.1801i			1.22384i
$781$		−	31.9508i		−	1.14329i
$782$	−1.44230			−0.0515767
$783$	−28.4756	+	27.9596i	−1.01764	+	0.999196i
$784$	17.4104			0.621798
$785$		−	24.0031i		−	0.856707i
$786$			34.3699i			1.22594i
$787$	35.6976			1.27248			0.636242	−	0.771490i	$-0.280488\pi$
$787$	35.6976			1.27248			0.636242	+	0.771490i	$0.280488\pi$
$788$	19.5702			0.697161
$789$	−0.262324			−0.00933900
$790$	6.55125			0.233083
$791$			16.1905i			0.575667i
$792$	14.1083			0.501315
$793$			70.5070i			2.50378i
$794$		−	15.2291i		−	0.540461i
$795$			32.4434i			1.15065i
$796$	−21.9077			−0.776498
$797$			28.4237i			1.00682i	0.864048	+	0.503410i	$0.167921\pi$
$797$			28.4237i			1.00682i	−0.864048	+	0.503410i	$0.832079\pi$
$798$			41.7640i			1.47843i
$799$	10.4349			0.369161
$800$			2.06360i			0.0729593i
$801$		−	12.5677i		−	0.444058i
$802$			15.0188i			0.530332i
$803$	−27.7389			−0.978884
$804$		−	23.8390i		−	0.840737i
$805$	−8.46632			−0.298399
$806$	21.4470			0.755438
$807$	17.2134			0.605941
$808$	−10.3781			−0.365099
$809$			41.5912i			1.46227i	0.682233	+	0.731134i	$0.261009\pi$
$809$			41.5912i			1.46227i	−0.682233	+	0.731134i	$0.738991\pi$
$810$		−	8.64081i		−	0.303607i
$811$	−25.2570			−0.886893			−0.443446	−	0.896301i	$-0.646244\pi$
$811$	−25.2570			−0.886893			−0.443446	+	0.896301i	$0.646244\pi$
$812$	−18.6408	−	18.9848i	−0.654162	−	0.666236i
$813$	−58.7894			−2.06183
$814$		−	11.7105i		−	0.410451i
$815$		−	18.6819i		−	0.654397i
$816$	4.21400			0.147519
$817$	19.8265			0.693640
$818$	−1.47010			−0.0514009
$819$	−186.742			−6.52530
$820$			19.4892i			0.680593i
$821$	13.5680			0.473528			0.236764	−	0.971567i	$-0.423913\pi$
$821$	13.5680			0.473528			0.236764	+	0.971567i	$0.423913\pi$
$822$		−	5.12509i		−	0.178758i
$823$			49.5557i			1.72740i	0.504003	+	0.863702i	$0.331860\pi$
$823$			49.5557i			1.72740i	−0.504003	+	0.863702i	$0.668140\pi$
$824$		−	1.47855i		−	0.0515078i
$825$	−15.3642			−0.534912
$826$			21.0234i			0.731499i
$827$			18.0519i			0.627727i	0.949468	+	0.313863i	$0.101623\pi$
$827$			18.0519i			0.627727i	−0.949468	+	0.313863i	$0.898377\pi$
$828$	−5.53640			−0.192403
$829$		−	49.3366i		−	1.71353i	−0.515707	−	0.856765i	$-0.672471\pi$
$829$		−	49.3366i		−	1.71353i	0.515707	−	0.856765i	$-0.327529\pi$
$830$			4.06400i			0.141063i
$831$			71.2005i			2.46992i
$832$	−6.82697			−0.236683
$833$			25.1110i			0.870046i
$834$	−2.83623			−0.0982108
$835$	−22.2758			−0.770887
$836$	−7.37266			−0.254989
$837$	−23.2806			−0.804694
$838$		−	10.6262i		−	0.367076i
$839$		−	49.4365i		−	1.70674i	−0.521306	−	0.853370i	$-0.674555\pi$
$839$		−	49.4365i		−	1.70674i	0.521306	−	0.853370i	$-0.325445\pi$
$840$	24.7361			0.853478
$841$	−0.530284	+	28.9952i	−0.0182857	+	0.999833i
$842$	−12.7131			−0.438122
$843$			51.8047i			1.78425i
$844$			24.8500i			0.855371i
$845$	57.5896			1.98114
$846$	40.0553			1.37713
$847$	22.2642			0.765007
$848$	−6.48011			−0.222528
$849$		−	35.0719i		−	1.20366i
$850$	−2.97634			−0.102088
$851$			4.59544i			0.157530i
$852$		−	36.6331i		−	1.25503i
$853$		−	0.0751253i		−	0.00257224i	−0.999999	−	0.00128612i	$-0.999591\pi$
$853$		−	0.0751253i		−	0.00257224i	0.999999	−	0.00128612i	$-0.000409385\pi$
$854$	51.0260			1.74607
$855$			27.4481i			0.938707i
$856$		−	13.9184i		−	0.475721i
$857$	13.5050			0.461321			0.230661	−	0.973034i	$-0.425911\pi$
$857$	13.5050			0.461321			0.230661	+	0.973034i	$0.425911\pi$
$858$		−	50.8290i		−	1.73527i
$859$		−	43.1137i		−	1.47102i	−0.677513	−	0.735511i	$-0.736942\pi$
$859$		−	43.1137i		−	1.47102i	0.677513	−	0.735511i	$-0.263058\pi$
$860$		−	11.7429i		−	0.400429i
$861$	−164.177			−5.59512
$862$		−	19.5280i		−	0.665127i
$863$	35.5713			1.21086			0.605430	−	0.795898i	$-0.293001\pi$
$863$	35.5713			1.21086			0.605430	+	0.795898i	$0.293001\pi$
$864$	7.41062			0.252115
$865$	−8.10839			−0.275694
$866$	38.9477			1.32350
$867$		−	43.5912i		−	1.48044i
$868$		−	15.5212i		−	0.526824i
$869$	−9.74232			−0.330486
$870$	−18.8895	−	19.2382i	−0.640415	−	0.652235i
$871$	−55.7030			−1.88743
$872$		−	6.46947i		−	0.219084i
$873$		−	48.4975i		−	1.64139i
$874$	2.89320			0.0978639
$875$	−59.8027			−2.02170
$876$	−31.8039			−1.07455
$877$	32.2167			1.08788			0.543939	−	0.839124i	$-0.316932\pi$
$877$	32.2167			1.08788			0.543939	+	0.839124i	$0.316932\pi$
$878$		−	13.5439i		−	0.457086i
$879$	−4.32376			−0.145837
$880$			4.36670i			0.147202i
$881$			21.2323i			0.715333i	0.933849	+	0.357667i	$0.116428\pi$
$881$			21.2323i			0.715333i	−0.933849	+	0.357667i	$0.883572\pi$
$882$			96.3907i			3.24564i
$883$	38.2410			1.28691			0.643455	−	0.765484i	$-0.277500\pi$
$883$	38.2410			1.28691			0.643455	+	0.765484i	$0.277500\pi$
$884$		−	9.84657i		−	0.331176i
$885$			21.3040i			0.716127i
$886$	−21.3433			−0.717042
$887$		−	6.06703i		−	0.203711i	−0.994799	−	0.101856i	$-0.967522\pi$
$887$		−	6.06703i		−	0.203711i	0.994799	−	0.101856i	$-0.0324779\pi$
$888$		−	13.4266i		−	0.450566i
$889$		−	3.56339i		−	0.119512i
$890$	3.88988			0.130389
$891$			12.8497i			0.430481i
$892$	5.43376			0.181936
$893$	−20.9320			−0.700462
$894$	−51.0782			−1.70831
$895$	2.52752			0.0844857
$896$			4.94068i			0.165057i
$897$			19.9464i			0.665992i
$898$	29.0633			0.969856
$899$	−12.0714	+	11.8526i	−0.402603	+	0.395308i
$900$	−11.4249			−0.380831
$901$		−	9.34628i		−	0.311370i
$902$		−	28.9823i		−	0.965005i
$903$	98.9217			3.29191
$904$	−3.27697			−0.108990
$905$	−18.3718			−0.610699
$906$	33.7772			1.12217
$907$		−	50.3573i		−	1.67209i	−0.548663	−	0.836044i	$-0.684863\pi$
$907$		−	50.3573i		−	1.67209i	0.548663	−	0.836044i	$-0.315137\pi$
$908$	−17.8375			−0.591959
$909$		−	57.4571i		−	1.90573i
$910$		−	57.7993i		−	1.91603i
$911$			18.8278i			0.623794i	0.950116	+	0.311897i	$0.100964\pi$
$911$			18.8278i			0.623794i	−0.950116	+	0.311897i	$0.899036\pi$
$912$	−8.45309			−0.279910
$913$		−	6.04355i		−	0.200012i
$914$		−	3.39653i		−	0.112347i
$915$	51.7070			1.70938
$916$		−	28.4244i		−	0.939170i
$917$		−	58.1204i		−	1.91930i
$918$			10.6884i			0.352769i
$919$	24.6608			0.813486			0.406743	−	0.913543i	$-0.366664\pi$
$919$	24.6608			0.813486			0.406743	+	0.913543i	$0.366664\pi$
$920$		−	1.71359i		−	0.0564955i
$921$	−22.3029			−0.734906
$922$	−6.60253			−0.217443
$923$	−85.5981			−2.81749
$924$	−36.7850			−1.21014
$925$			9.48316i			0.311804i
$926$		−	22.8065i		−	0.749467i
$927$	8.18586			0.268859
$928$	3.84254	−	3.77291i	0.126138	−	0.123852i
$929$	46.0971			1.51240			0.756198	−	0.654343i	$-0.227055\pi$
$929$	46.0971			1.51240			0.756198	+	0.654343i	$0.227055\pi$
$930$		−	15.7284i		−	0.515753i
$931$		−	50.3716i		−	1.65086i
$932$	12.2982			0.402841
$933$	67.1180			2.19735
$934$	0.338478			0.0110753
$935$	−6.29812			−0.205970
$936$		−	37.7968i		−	1.23543i
$937$	41.6519			1.36071			0.680354	−	0.732884i	$-0.261826\pi$
$937$	41.6519			1.36071			0.680354	+	0.732884i	$0.261826\pi$
$938$			40.3123i			1.31624i
$939$		−	76.1773i		−	2.48595i
$940$			12.3977i			0.404367i
$941$	46.4597			1.51454			0.757272	−	0.653099i	$-0.226532\pi$
$941$	46.4597			1.51454			0.757272	+	0.653099i	$0.226532\pi$
$942$			40.9258i			1.33343i
$943$			11.3733i			0.370366i
$944$	−4.25517			−0.138494
$945$			62.7407i			2.04096i
$946$			17.4628i			0.567764i
$947$		−	14.7338i		−	0.478785i	−0.970923	−	0.239392i	$-0.923052\pi$
$947$		−	14.7338i		−	0.478785i	0.970923	−	0.239392i	$-0.0769482\pi$
$948$	−11.1700			−0.362785
$949$			74.3140i			2.41233i
$950$	5.97041			0.193706
$951$	38.9241			1.26220
$952$	−7.12597			−0.230954
$953$	47.1165			1.52625			0.763126	−	0.646249i	$-0.223663\pi$
$953$	47.1165			1.52625			0.763126	+	0.646249i	$0.223663\pi$
$954$		−	35.8764i		−	1.16154i
$955$			12.9423i			0.418803i
$956$	3.43906			0.111227
$957$	28.0905	+	28.6090i	0.908038	+	0.924797i
$958$	−38.1372			−1.23216
$959$			8.66665i			0.279861i
$960$			5.00662i			0.161588i
$961$	21.1309			0.681642
$962$	−31.3730			−1.01150
$963$	77.0578			2.48315
$964$	15.7949			0.508719
$965$		−	43.1942i		−	1.39047i
$966$	14.4353			0.464447
$967$			9.31632i			0.299593i	0.988717	+	0.149796i	$0.0478618\pi$
$967$			9.31632i			0.299593i	−0.988717	+	0.149796i	$0.952138\pi$
$968$			4.50630i			0.144838i
$969$		−	12.1919i		−	0.391661i
$970$	15.0106			0.481963
$971$			0.211486i			0.00678691i	0.999994	+	0.00339345i	$0.00108017\pi$
$971$			0.211486i			0.00678691i	−0.999994	+	0.00339345i	$0.998920\pi$
$972$		−	7.49911i		−	0.240534i
$973$	4.79614			0.153757
$974$			31.1164i			0.997034i
$975$			41.1615i			1.31822i
$976$			10.3277i			0.330582i
$977$	−59.8721			−1.91548			−0.957740	−	0.287636i	$-0.907131\pi$
$977$	−59.8721			−1.91548			−0.957740	+	0.287636i	$0.907131\pi$
$978$			31.8530i			1.01855i
$979$	−5.78462			−0.184877
$980$	−29.8343			−0.953020
$981$	35.8176			1.14357
$982$	10.5325			0.336105
$983$		−	19.9121i		−	0.635097i	−0.948242	−	0.317548i	$-0.897140\pi$
$983$		−	19.9121i		−	0.635097i	0.948242	−	0.317548i	$-0.102860\pi$
$984$		−	33.2295i		−	1.05932i
$985$	−33.5354			−1.06853
$986$	5.44169	+	5.54212i	0.173299	+	0.176497i
$987$	−104.438			−3.32428
$988$			19.7518i			0.628388i
$989$		−	6.85278i		−	0.217906i
$990$	−24.1758			−0.768358
$991$	−20.9143			−0.664363			−0.332182	−	0.943215i	$-0.607785\pi$
$991$	−20.9143			−0.664363			−0.332182	+	0.943215i	$0.607785\pi$
$992$	3.14151			0.0997431
$993$	6.05576			0.192174
$994$			61.9474i			1.96485i
$995$	37.5409			1.19013
$996$		−	6.92920i		−	0.219560i
$997$			12.8727i			0.407681i	0.979004	+	0.203841i	$0.0653424\pi$
$997$			12.8727i			0.407681i	−0.979004	+	0.203841i	$0.934658\pi$
$998$		−	12.4186i		−	0.393103i
$999$	34.0551			1.07746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.c.b.231.2	✓	28
29.28	even	2	inner	1334.2.c.b.231.27	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.c.b.231.2	✓	28	1.1	even	1	trivial
1334.2.c.b.231.27	yes	28	29.28	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -2.92171i q^{3} -1.00000 q^{4} +1.71359 q^{5} -2.92171 q^{6} +4.94068 q^{7} +1.00000i q^{8} -5.53640 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -2.92171i q^{3} -1.00000 q^{4} +1.71359 q^{5} -2.92171 q^{6} +4.94068 q^{7} +1.00000i q^{8} -5.53640 q^{9} -1.71359i q^{10} +2.54827i q^{11} +2.92171i q^{12} +6.82697 q^{13} -4.94068i q^{14} -5.00662i q^{15} +1.00000 q^{16} +1.44230i q^{17} +5.53640i q^{18} -2.89320i q^{19} -1.71359 q^{20} -14.4353i q^{21} +2.54827 q^{22} -1.00000 q^{23} +2.92171 q^{24} -2.06360 q^{25} -6.82697i q^{26} +7.41062i q^{27} -4.94068 q^{28} +(3.77291 + 3.84254i) q^{29} -5.00662 q^{30} +3.14151i q^{31} -1.00000i q^{32} +7.44532 q^{33} +1.44230 q^{34} +8.46632 q^{35} +5.53640 q^{36} -4.59544i q^{37} -2.89320 q^{38} -19.9464i q^{39} +1.71359i q^{40} -11.3733i q^{41} -14.4353 q^{42} +6.85278i q^{43} -2.54827i q^{44} -9.48713 q^{45} +1.00000i q^{46} -7.23490i q^{47} -2.92171i q^{48} +17.4104 q^{49} +2.06360i q^{50} +4.21400 q^{51} -6.82697 q^{52} -6.48011 q^{53} +7.41062 q^{54} +4.36670i q^{55} +4.94068i q^{56} -8.45309 q^{57} +(3.84254 - 3.77291i) q^{58} -4.25517 q^{59} +5.00662i q^{60} +10.3277i q^{61} +3.14151 q^{62} -27.3536 q^{63} -1.00000 q^{64} +11.6986 q^{65} -7.44532i q^{66} -8.15926 q^{67} -1.44230i q^{68} +2.92171i q^{69} -8.46632i q^{70} -12.5382 q^{71} -5.53640i q^{72} +10.8854i q^{73} -4.59544 q^{74} +6.02925i q^{75} +2.89320i q^{76} +12.5902i q^{77} -19.9464 q^{78} +3.82311i q^{79} +1.71359 q^{80} +5.04251 q^{81} -11.3733 q^{82} -2.37162 q^{83} +14.4353i q^{84} +2.47152i q^{85} +6.85278 q^{86} +(11.2268 - 11.0234i) q^{87} -2.54827 q^{88} +2.27002i q^{89} +9.48713i q^{90} +33.7299 q^{91} +1.00000 q^{92} +9.17859 q^{93} -7.23490 q^{94} -4.95776i q^{95} -2.92171 q^{96} +8.75975i q^{97} -17.4104i q^{98} -14.1083i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} - 54 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 2 * q^5 + 2 * q^6 - 8 * q^7 - 54 * q^9	\( 28 q - 28 q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} - 54 q^{9} - 2 q^{13} + 28 q^{16} - 2 q^{20} + 6 q^{22} - 28 q^{23} - 2 q^{24} + 38 q^{25} + 8 q^{28} - 2 q^{29} + 2 q^{30} + 30 q^{33} + 12 q^{34} + 56 q^{35} + 54 q^{36} + 12 q^{38} + 16 q^{42} - 52 q^{45} + 76 q^{49} - 60 q^{51} + 2 q^{52} - 22 q^{53} - 14 q^{54} + 72 q^{57} - 18 q^{58} - 12 q^{59} + 14 q^{62} + 24 q^{63} - 28 q^{64} - 42 q^{65} - 16 q^{67} - 4 q^{71} - 32 q^{74} - 34 q^{78} + 2 q^{80} + 116 q^{81} - 68 q^{82} - 48 q^{83} + 46 q^{86} + 12 q^{87} - 6 q^{88} + 96 q^{91} + 28 q^{92} + 70 q^{93} - 10 q^{94} + 2 q^{96}+O(q^{100}) \) 28 * q - 28 * q^4 + 2 * q^5 + 2 * q^6 - 8 * q^7 - 54 * q^9 - 2 * q^13 + 28 * q^16 - 2 * q^20 + 6 * q^22 - 28 * q^23 - 2 * q^24 + 38 * q^25 + 8 * q^28 - 2 * q^29 + 2 * q^30 + 30 * q^33 + 12 * q^34 + 56 * q^35 + 54 * q^36 + 12 * q^38 + 16 * q^42 - 52 * q^45 + 76 * q^49 - 60 * q^51 + 2 * q^52 - 22 * q^53 - 14 * q^54 + 72 * q^57 - 18 * q^58 - 12 * q^59 + 14 * q^62 + 24 * q^63 - 28 * q^64 - 42 * q^65 - 16 * q^67 - 4 * q^71 - 32 * q^74 - 34 * q^78 + 2 * q^80 + 116 * q^81 - 68 * q^82 - 48 * q^83 + 46 * q^86 + 12 * q^87 - 6 * q^88 + 96 * q^91 + 28 * q^92 + 70 * q^93 - 10 * q^94 + 2 * q^96

Introduction

L-functions

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