LMFDB - Embedded newform 105.2.m.a.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(13,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("105.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.m (of order $4$, degree $2$, 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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.2
Root			$0.517174 + 1.31626i$ of defining polynomial
Character	$\chi$	$=$	105.97
Dual form			105.2.m.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86147 - 1.86147i) q^{2} +(0.707107 + 0.707107i) q^{3} +4.93012i q^{4} +(1.50619 - 1.65269i) q^{5} -2.63251i q^{6} +(1.46123 - 2.20563i) q^{7} +(5.45433 - 5.45433i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.86147 - 1.86147i) q^{2} +(0.707107 + 0.707107i) q^{3} +4.93012i q^{4} +(1.50619 - 1.65269i) q^{5} -2.63251i q^{6} +(1.46123 - 2.20563i) q^{7} +(5.45433 - 5.45433i) q^{8} +1.00000i q^{9} +(-5.88016 + 0.272713i) q^{10} -1.46279 q^{11} +(-3.48612 + 3.48612i) q^{12} +(-0.887844 - 0.887844i) q^{13} +(-6.82574 + 1.38567i) q^{14} +(2.23367 - 0.103594i) q^{15} -10.4459 q^{16} +(2.10614 - 2.10614i) q^{17} +(1.86147 - 1.86147i) q^{18} +3.95987 q^{19} +(8.14798 + 7.42570i) q^{20} +(2.59286 - 0.526369i) q^{21} +(2.72294 + 2.72294i) q^{22} +(-4.13007 + 4.13007i) q^{23} +7.71359 q^{24} +(-0.462789 - 4.97854i) q^{25} +3.30539i q^{26} +(-0.707107 + 0.707107i) q^{27} +(10.8740 + 7.20405i) q^{28} +5.18572i q^{29} +(-4.35074 - 3.96506i) q^{30} +6.10346i q^{31} +(8.53599 + 8.53599i) q^{32} +(-1.03435 - 1.03435i) q^{33} -7.84104 q^{34} +(-1.44434 - 5.73706i) q^{35} -4.93012 q^{36} +(2.25560 + 2.25560i) q^{37} +(-7.37117 - 7.37117i) q^{38} -1.25560i q^{39} +(-0.799082 - 17.2296i) q^{40} -0.769968i q^{41} +(-5.80635 - 3.84671i) q^{42} +(-5.18572 + 5.18572i) q^{43} -7.21173i q^{44} +(1.65269 + 1.50619i) q^{45} +15.3760 q^{46} +(-8.57041 + 8.57041i) q^{47} +(-7.38635 - 7.38635i) q^{48} +(-2.72961 - 6.44587i) q^{49} +(-8.40592 + 10.1289i) q^{50} +2.97854 q^{51} +(4.37718 - 4.37718i) q^{52} +(-0.544449 + 0.544449i) q^{53} +2.63251 q^{54} +(-2.20324 + 2.41754i) q^{55} +(-4.06020 - 20.0003i) q^{56} +(2.80005 + 2.80005i) q^{57} +(9.65306 - 9.65306i) q^{58} +3.19633 q^{59} +(0.510732 + 11.0123i) q^{60} -1.42064i q^{61} +(11.3614 - 11.3614i) q^{62} +(2.20563 + 1.46123i) q^{63} -10.8872i q^{64} +(-2.80460 + 0.130073i) q^{65} +3.85081i q^{66} +(-5.93012 - 5.93012i) q^{67} +(10.3835 + 10.3835i) q^{68} -5.84081 q^{69} +(-7.99077 + 13.3679i) q^{70} +7.62611 q^{71} +(5.45433 + 5.45433i) q^{72} +(-6.81378 - 6.81378i) q^{73} -8.39746i q^{74} +(3.19312 - 3.84760i) q^{75} +19.5226i q^{76} +(-2.13747 + 3.22637i) q^{77} +(-2.33726 + 2.33726i) q^{78} +4.52029i q^{79} +(-15.7335 + 17.2638i) q^{80} -1.00000 q^{81} +(-1.43327 + 1.43327i) q^{82} +(6.75794 + 6.75794i) q^{83} +(2.59507 + 12.7831i) q^{84} +(-0.308559 - 6.65306i) q^{85} +19.3061 q^{86} +(-3.66686 + 3.66686i) q^{87} +(-7.97854 + 7.97854i) q^{88} -1.19991 q^{89} +(-0.272713 - 5.88016i) q^{90} +(-3.25560 + 0.660910i) q^{91} +(-20.3618 - 20.3618i) q^{92} +(-4.31580 + 4.31580i) q^{93} +31.9071 q^{94} +(5.96431 - 6.54445i) q^{95} +12.0717i q^{96} +(8.68829 - 8.68829i) q^{97} +(-6.91770 + 17.0799i) q^{98} -1.46279i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} + 24 q^{8}+O(q^{10}) $ 16 * q - 8 * q^7 + 24 * q^8	$ 16 q - 8 q^{7} + 24 q^{8} - 16 q^{11} + 8 q^{15} - 48 q^{16} + 8 q^{21} - 16 q^{22} - 40 q^{23} + 24 q^{28} - 8 q^{30} + 48 q^{32} - 8 q^{35} - 16 q^{36} + 32 q^{37} - 16 q^{42} - 16 q^{43} + 64 q^{46} - 72 q^{50} - 16 q^{51} + 24 q^{53} + 24 q^{56} + 8 q^{57} + 32 q^{58} + 40 q^{60} + 8 q^{63} + 40 q^{65} - 32 q^{67} - 40 q^{70} + 64 q^{71} + 24 q^{72} - 24 q^{77} - 8 q^{78} - 16 q^{81} + 48 q^{85} + 64 q^{86} - 64 q^{88} - 48 q^{91} - 40 q^{92} + 24 q^{93} - 72 q^{95} - 96 q^{98}+O(q^{100}) $ 16 * q - 8 * q^7 + 24 * q^8 - 16 * q^11 + 8 * q^15 - 48 * q^16 + 8 * q^21 - 16 * q^22 - 40 * q^23 + 24 * q^28 - 8 * q^30 + 48 * q^32 - 8 * q^35 - 16 * q^36 + 32 * q^37 - 16 * q^42 - 16 * q^43 + 64 * q^46 - 72 * q^50 - 16 * q^51 + 24 * q^53 + 24 * q^56 + 8 * q^57 + 32 * q^58 + 40 * q^60 + 8 * q^63 + 40 * q^65 - 32 * q^67 - 40 * q^70 + 64 * q^71 + 24 * q^72 - 24 * q^77 - 8 * q^78 - 16 * q^81 + 48 * q^85 + 64 * q^86 - 64 * q^88 - 48 * q^91 - 40 * q^92 + 24 * q^93 - 72 * q^95 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.86147	−	1.86147i	−1.31626	−	1.31626i	−0.916715	−	0.399541i	$-0.869169\pi$
$2$	−1.86147	−	1.86147i	−1.31626	−	1.31626i	−0.399541	−	0.916715i	$-0.630831\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			4.93012i			2.46506i
$5$	1.50619	−	1.65269i	0.673588	−	0.739107i
$5$	1.50619	−	1.65269i	0.673588	−	0.739107i
$6$		−	2.63251i		−	1.07472i
$7$	1.46123	−	2.20563i	0.552293	−	0.833650i
$7$	1.46123	−	2.20563i	0.552293	−	0.833650i
$8$	5.45433	−	5.45433i	1.92840	−	1.92840i
$9$			1.00000i			0.333333i
$10$	−5.88016	+	0.272713i	−1.85947	+	0.0862394i
$11$	−1.46279			−0.441048			−0.220524	−	0.975382i	$-0.570777\pi$
$11$	−1.46279			−0.441048			−0.220524	+	0.975382i	$0.570777\pi$
$12$	−3.48612	+	3.48612i	−1.00636	+	1.00636i
$13$	−0.887844	−	0.887844i	−0.246244	−	0.246244i	0.573183	−	0.819427i	$-0.305708\pi$
$13$	−0.887844	−	0.887844i	−0.246244	−	0.246244i	−0.819427	+	0.573183i	$0.805708\pi$
$14$	−6.82574	+	1.38567i	−1.82426	+	0.370337i
$15$	2.23367	−	0.103594i	0.576730	−	0.0267479i
$16$	−10.4459			−2.61147
$17$	2.10614	−	2.10614i	0.510815	−	0.510815i	−0.403961	−	0.914776i	$-0.632367\pi$
$17$	2.10614	−	2.10614i	0.510815	−	0.510815i	0.914776	+	0.403961i	$0.132367\pi$
$18$	1.86147	−	1.86147i	0.438752	−	0.438752i
$19$	3.95987			0.908456			0.454228	−	0.890885i	$-0.349915\pi$
$19$	3.95987			0.908456			0.454228	+	0.890885i	$0.349915\pi$
$20$	8.14798	+	7.42570i	1.82194	+	1.66044i
$21$	2.59286	−	0.526369i	0.565809	−	0.114863i
$22$	2.72294	+	2.72294i	0.580532	+	0.580532i
$23$	−4.13007	+	4.13007i	−0.861180	+	0.861180i	−0.991475	−	0.130295i	$-0.958407\pi$
$23$	−4.13007	+	4.13007i	−0.861180	+	0.861180i	0.130295	+	0.991475i	$0.458407\pi$
$24$	7.71359			1.57453
$25$	−0.462789	−	4.97854i	−0.0925579	−	0.995707i
$26$			3.30539i			0.648240i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	10.8740	+	7.20405i	2.05500	+	1.36144i
$29$			5.18572i			0.962965i	0.876456	+	0.481482i	$0.159901\pi$
$29$			5.18572i			0.962965i	−0.876456	+	0.481482i	$0.840099\pi$
$30$	−4.35074	−	3.96506i	−0.794332	−	0.723918i
$31$			6.10346i			1.09621i	0.836408	+	0.548107i	$0.184651\pi$
$31$			6.10346i			1.09621i	−0.836408	+	0.548107i	$0.815349\pi$
$32$	8.53599	+	8.53599i	1.50896	+	1.50896i
$33$	−1.03435	−	1.03435i	−0.180057	−	0.180057i
$34$	−7.84104			−1.34473
$35$	−1.44434	−	5.73706i	−0.244138	−	0.969741i
$36$	−4.93012			−0.821687
$37$	2.25560	+	2.25560i	0.370819	+	0.370819i	0.867775	−	0.496957i	$-0.165549\pi$
$37$	2.25560	+	2.25560i	0.370819	+	0.370819i	−0.496957	+	0.867775i	$0.665549\pi$
$38$	−7.37117	−	7.37117i	−1.19576	−	1.19576i
$39$		−	1.25560i		−	0.201057i
$40$	−0.799082	−	17.2296i	−0.126346	−	2.72424i
$41$		−	0.769968i		−	0.120249i	−0.998191	−	0.0601244i	$-0.980850\pi$
$41$		−	0.769968i		−	0.120249i	0.998191	−	0.0601244i	$-0.0191497\pi$
$42$	−5.80635	−	3.84671i	−0.895939	−	0.593560i
$43$	−5.18572	+	5.18572i	−0.790816	+	0.790816i	−0.981627	−	0.190811i	$-0.938888\pi$
$43$	−5.18572	+	5.18572i	−0.790816	+	0.790816i	0.190811	+	0.981627i	$0.438888\pi$
$44$		−	7.21173i		−	1.08721i
$45$	1.65269	+	1.50619i	0.246369	+	0.224529i
$46$	15.3760			2.26707
$47$	−8.57041	+	8.57041i	−1.25012	+	1.25012i	−0.294459	+	0.955664i	$0.595139\pi$
$47$	−8.57041	+	8.57041i	−1.25012	+	1.25012i	−0.955664	+	0.294459i	$0.904861\pi$
$48$	−7.38635	−	7.38635i	−1.06613	−	1.06613i
$49$	−2.72961	−	6.44587i	−0.389944	−	0.920839i
$50$	−8.40592	+	10.1289i	−1.18878	+	1.43244i
$51$	2.97854			0.417079
$52$	4.37718	−	4.37718i	0.607006	−	0.607006i
$53$	−0.544449	+	0.544449i	−0.0747859	+	0.0747859i	−0.743510	−	0.668724i	$-0.766841\pi$
$53$	−0.544449	+	0.544449i	−0.0747859	+	0.0747859i	0.668724	+	0.743510i	$0.266841\pi$
$54$	2.63251			0.358240
$55$	−2.20324	+	2.41754i	−0.297084	+	0.325981i
$56$	−4.06020	−	20.0003i	−0.542567	−	2.67265i
$57$	2.80005	+	2.80005i	0.370876	+	0.370876i
$58$	9.65306	−	9.65306i	1.26751	−	1.26751i
$59$	3.19633			0.416127			0.208063	−	0.978115i	$-0.433284\pi$
$59$	3.19633			0.416127			0.208063	+	0.978115i	$0.433284\pi$
$60$	0.510732	+	11.0123i	0.0659352	+	1.42168i
$61$		−	1.42064i		−	0.181894i	−0.995856	−	0.0909472i	$-0.971011\pi$
$61$		−	1.42064i		−	0.181894i	0.995856	−	0.0909472i	$-0.0289894\pi$
$62$	11.3614	−	11.3614i	1.44290	−	1.44290i
$63$	2.20563	+	1.46123i	0.277883	+	0.184098i
$64$		−	10.8872i		−	1.36090i
$65$	−2.80460	+	0.130073i	−0.347867	+	0.0161336i
$66$			3.85081i			0.474002i
$67$	−5.93012	−	5.93012i	−0.724480	−	0.724480i	0.245034	−	0.969514i	$-0.421201\pi$
$67$	−5.93012	−	5.93012i	−0.724480	−	0.724480i	−0.969514	+	0.245034i	$0.921201\pi$
$68$	10.3835	+	10.3835i	1.25919	+	1.25919i
$69$	−5.84081			−0.703150
$70$	−7.99077	+	13.3679i	−0.955079	+	1.59778i
$71$	7.62611			0.905053			0.452526	−	0.891751i	$-0.350523\pi$
$71$	7.62611			0.905053			0.452526	+	0.891751i	$0.350523\pi$
$72$	5.45433	+	5.45433i	0.642799	+	0.642799i
$73$	−6.81378	−	6.81378i	−0.797493	−	0.797493i	0.185207	−	0.982700i	$-0.440704\pi$
$73$	−6.81378	−	6.81378i	−0.797493	−	0.797493i	−0.982700	+	0.185207i	$0.940704\pi$
$74$		−	8.39746i		−	0.976185i
$75$	3.19312	−	3.84760i	0.368709	−	0.444282i
$76$			19.5226i			2.23940i
$77$	−2.13747	+	3.22637i	−0.243588	+	0.367679i
$78$	−2.33726	+	2.33726i	−0.264643	+	0.264643i
$79$			4.52029i			0.508573i	0.967129	+	0.254286i	$0.0818405\pi$
$79$			4.52029i			0.508573i	−0.967129	+	0.254286i	$0.918159\pi$
$80$	−15.7335	+	17.2638i	−1.75905	+	1.93015i
$81$	−1.00000			−0.111111
$82$	−1.43327	+	1.43327i	−0.158278	+	0.158278i
$83$	6.75794	+	6.75794i	0.741781	+	0.741781i	0.972921	−	0.231140i	$-0.0742455\pi$
$83$	6.75794	+	6.75794i	0.741781	+	0.741781i	−0.231140	+	0.972921i	$0.574246\pi$
$84$	2.59507	+	12.7831i	0.283145	+	1.39475i
$85$	−0.308559	−	6.65306i	−0.0334679	−	0.721626i
$86$	19.3061			2.08183
$87$	−3.66686	+	3.66686i	−0.393129	+	0.393129i
$88$	−7.97854	+	7.97854i	−0.850515	+	0.850515i
$89$	−1.19991			−0.127190			−0.0635950	−	0.997976i	$-0.520257\pi$
$89$	−1.19991			−0.127190			−0.0635950	+	0.997976i	$0.520257\pi$
$90$	−0.272713	−	5.88016i	−0.0287465	−	0.619823i
$91$	−3.25560	+	0.660910i	−0.341280	+	0.0692822i
$92$	−20.3618	−	20.3618i	−2.12286	−	2.12286i
$93$	−4.31580	+	4.31580i	−0.447527	+	0.447527i
$94$	31.9071			3.29096
$95$	5.96431	−	6.54445i	0.611925	−	0.671446i
$96$			12.0717i			1.23206i
$97$	8.68829	−	8.68829i	0.882162	−	0.882162i	−0.111592	−	0.993754i	$-0.535595\pi$
$97$	8.68829	−	8.68829i	0.882162	−	0.882162i	0.993754	+	0.111592i	$0.0355950\pi$
$98$	−6.91770	+	17.0799i	−0.698794	+	1.72533i
$99$		−	1.46279i		−	0.147016i
$100$	24.5448	−	2.28161i	2.45448	−	0.228161i
$101$		−	15.3420i		−	1.52659i	−0.646050	−	0.763295i	$-0.723580\pi$
$101$		−	15.3420i		−	1.52659i	0.646050	−	0.763295i	$-0.276420\pi$
$102$	−5.54445	−	5.54445i	−0.548982	−	0.548982i
$103$	−8.30776	−	8.30776i	−0.818588	−	0.818588i	0.167316	−	0.985903i	$-0.446490\pi$
$103$	−8.30776	−	8.30776i	−0.818588	−	0.818588i	−0.985903	+	0.167316i	$0.946490\pi$
$104$	−9.68519			−0.949711
$105$	3.03541	−	5.07802i	0.296226	−	0.495564i
$106$	2.02695			0.196875
$107$	4.39022	+	4.39022i	0.424418	+	0.424418i	0.886722	−	0.462303i	$-0.152977\pi$
$107$	4.39022	+	4.39022i	0.424418	+	0.424418i	−0.462303	+	0.886722i	$0.652977\pi$
$108$	−3.48612	−	3.48612i	−0.335452	−	0.335452i
$109$			7.44587i			0.713185i	0.934260	+	0.356593i	$0.116062\pi$
$109$			7.44587i			0.713185i	−0.934260	+	0.356593i	$0.883938\pi$
$110$	8.60143	−	0.398921i	0.820114	−	0.0380357i
$111$			3.18990i			0.302772i
$112$	−15.2638	+	23.0397i	−1.44230	+	2.17705i
$113$	2.54445	−	2.54445i	0.239362	−	0.239362i	−0.577224	−	0.816586i	$-0.695864\pi$
$113$	2.54445	−	2.54445i	0.239362	−	0.239362i	0.816586	+	0.577224i	$0.195864\pi$
$114$		−	10.4244i		−	0.976335i
$115$	0.605073	+	13.0464i	0.0564233	+	1.21658i
$116$	−25.5663			−2.37377
$117$	0.887844	−	0.887844i	0.0820812	−	0.0820812i
$118$	−5.94986	−	5.94986i	−0.547729	−	0.547729i
$119$	−1.56781	−	7.72294i	−0.143721	−	0.707960i
$120$	11.6181	−	12.7482i	1.06058	−	1.16375i
$121$	−8.86025			−0.805477
$122$	−2.64448	+	2.64448i	−0.239420	+	0.239420i
$123$	0.544449	−	0.544449i	0.0490913	−	0.0490913i
$124$	−30.0908			−2.70223
$125$	−8.92504	−	6.73377i	−0.798280	−	0.602287i
$126$	−1.38567	−	6.82574i	−0.123446	−	0.608086i
$127$	7.86025	+	7.86025i	0.697484	+	0.697484i	0.963867	−	0.266383i	$-0.0858286\pi$
$127$	7.86025	+	7.86025i	0.697484	+	0.697484i	−0.266383	+	0.963867i	$0.585829\pi$
$128$	−3.19418	+	3.19418i	−0.282329	+	0.282329i
$129$	−7.33372			−0.645698
$130$	5.46279	+	4.97854i	0.479118	+	0.436647i
$131$		−	6.18216i		−	0.540138i	−0.962841	−	0.270069i	$-0.912953\pi$
$131$		−	6.18216i		−	0.540138i	0.962841	−	0.270069i	$-0.0870465\pi$
$132$	5.09947	−	5.09947i	0.443851	−	0.443851i
$133$	5.78628	−	8.73401i	0.501735	−	0.757334i
$134$			22.0775i			1.90720i
$135$	0.103594	+	2.23367i	0.00891596	+	0.192243i
$136$		−	22.9752i		−	1.97011i
$137$	9.05565	+	9.05565i	0.773677	+	0.773677i	0.978747	−	0.205071i	$-0.0657424\pi$
$137$	9.05565	+	9.05565i	0.773677	+	0.773677i	−0.205071	+	0.978747i	$0.565742\pi$
$138$	10.8725	+	10.8725i	0.925526	+	0.925526i
$139$	11.9913			1.01709			0.508544	−	0.861036i	$-0.330184\pi$
$139$	11.9913			1.01709			0.508544	+	0.861036i	$0.330184\pi$
$140$	28.2844	−	7.12077i	2.39047	−	0.601815i
$141$	−12.1204			−1.02072
$142$	−14.1958	−	14.1958i	−1.19128	−	1.19128i
$143$	1.29873	+	1.29873i	0.108605	+	0.108605i
$144$		−	10.4459i		−	0.870489i
$145$	8.57041	+	7.81068i	0.711734	+	0.648642i
$146$			25.3673i			2.09941i
$147$	2.62780	−	6.48804i	0.216737	−	0.535125i
$148$	−11.1204	+	11.1204i	−0.914091	+	0.914091i
$149$		−	0.0968261i		−	0.00793230i	−0.999992	−	0.00396615i	$-0.998738\pi$
$149$		−	0.0968261i		−	0.00793230i	0.999992	−	0.00396615i	$-0.00126247\pi$
$150$	−13.1061	+	1.21830i	−1.07011	+	0.0994737i
$151$	−13.4550			−1.09495			−0.547475	−	0.836822i	$-0.684411\pi$
$151$	−13.4550			−1.09495			−0.547475	+	0.836822i	$0.684411\pi$
$152$	21.5984	−	21.5984i	1.75186	−	1.75186i
$153$	2.10614	+	2.10614i	0.170272	+	0.170272i
$154$	9.98463	−	2.02695i	0.804584	−	0.163336i
$155$	10.0871	+	9.19296i	0.810219	+	0.738397i
$156$	6.19027			0.495618
$157$	−1.64757	+	1.64757i	−0.131491	+	0.131491i	−0.769789	−	0.638298i	$-0.779639\pi$
$157$	−1.64757	+	1.64757i	−0.131491	+	0.131491i	0.638298	+	0.769789i	$0.279639\pi$
$158$	8.41438	−	8.41438i	0.669412	−	0.669412i
$159$	−0.769968			−0.0610624
$160$	26.9642	−	1.25056i	2.13171	−	0.0988653i
$161$	3.07442	+	15.1444i	0.242298	+	1.19355i
$162$	1.86147	+	1.86147i	0.146251	+	0.146251i
$163$	−10.2746	+	10.2746i	−0.804771	+	0.804771i	−0.983837	−	0.179066i	$-0.942692\pi$
$163$	−10.2746	+	10.2746i	−0.804771	+	0.804771i	0.179066	+	0.983837i	$0.442692\pi$
$164$	3.79604			0.296421
$165$	−3.26738	+	0.151536i	−0.254366	+	0.0117971i
$166$		−	25.1594i		−	1.95275i
$167$	−0.293008	+	0.293008i	−0.0226737	+	0.0226737i	−0.718353	−	0.695679i	$-0.755104\pi$
$167$	−0.293008	+	0.293008i	−0.0226737	+	0.0226737i	0.695679	+	0.718353i	$0.255104\pi$
$168$	11.2713	−	17.0133i	0.869602	−	1.31261i
$169$		−	11.4235i		−	0.878728i
$170$	−11.8101	+	12.9588i	−0.905792	+	0.993897i
$171$			3.95987i			0.302819i
$172$	−25.5663	−	25.5663i	−1.94941	−	1.94941i
$173$	3.45189	+	3.45189i	0.262442	+	0.262442i	0.826046	−	0.563603i	$-0.190585\pi$
$173$	3.45189	+	3.45189i	0.262442	+	0.262442i	−0.563603	+	0.826046i	$0.690585\pi$
$174$	13.6515			1.03492
$175$	−11.6571	−	6.25405i	−0.881190	−	0.472762i
$176$	15.2801			1.15178
$177$	2.26015	+	2.26015i	0.169883	+	0.169883i
$178$	2.23359	+	2.23359i	0.167415	+	0.167415i
$179$		−	1.99756i		−	0.149305i	−0.997210	−	0.0746523i	$-0.976215\pi$
$179$		−	1.99756i		−	0.149305i	0.997210	−	0.0746523i	$-0.0237847\pi$
$180$	−7.42570	+	8.14798i	−0.553479	+	0.607315i
$181$			8.48528i			0.630706i	0.948974	+	0.315353i	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$	7.29046	+	4.82993i	0.540405	+	0.358019i
$183$	1.00454	−	1.00454i	0.0742581	−	0.0742581i
$184$			45.0536i			3.32139i
$185$	7.12518	−	0.330455i	0.523854	−	0.0242955i
$186$	16.0674			1.17812
$187$	−3.08084	+	3.08084i	−0.225294	+	0.225294i
$188$	−42.2532	−	42.2532i	−3.08163	−	3.08163i
$189$	0.526369	+	2.59286i	0.0382877	+	0.188603i
$190$	−23.2847	+	1.07991i	−1.68925	+	0.0783447i
$191$	−7.83424			−0.566866			−0.283433	−	0.958992i	$-0.591473\pi$
$191$	−7.83424			−0.566866			−0.283433	+	0.958992i	$0.591473\pi$
$192$	7.69841	−	7.69841i	0.555585	−	0.555585i
$193$	13.5617	−	13.5617i	0.976194	−	0.976194i	−0.0235293	−	0.999723i	$-0.507490\pi$
$193$	13.5617	−	13.5617i	0.976194	−	0.976194i	0.999723	+	0.0235293i	$0.00749029\pi$
$194$	−32.3459			−2.32230
$195$	−2.07512	−	1.89117i	−0.148603	−	0.135430i
$196$	31.7789	−	13.4573i	2.26992	−	0.961236i
$197$	−11.4791	−	11.4791i	−0.817853	−	0.817853i	0.167943	−	0.985797i	$-0.446287\pi$
$197$	−11.4791	−	11.4791i	−0.817853	−	0.817853i	−0.985797	+	0.167943i	$0.946287\pi$
$198$	−2.72294	+	2.72294i	−0.193511	+	0.193511i
$199$	−20.1468			−1.42817			−0.714084	−	0.700061i	$-0.753156\pi$
$199$	−20.1468			−1.42817			−0.714084	+	0.700061i	$0.753156\pi$
$200$	−29.6788	−	24.6304i	−2.09861	−	1.74163i
$201$		−	8.38646i		−	0.591535i
$202$	−28.5587	+	28.5587i	−2.00938	+	2.00938i
$203$	11.4378	+	7.57754i	0.802775	+	0.531839i
$204$			14.6846i			1.02812i
$205$	−1.27252	−	1.15972i	−0.0888767	−	0.0809981i
$206$			30.9292i			2.15494i
$207$	−4.13007	−	4.13007i	−0.287060	−	0.287060i
$208$	9.27431	+	9.27431i	0.643057	+	0.643057i
$209$	−5.79246			−0.400673
$210$	−15.1029	+	3.80224i	−1.04220	+	0.262380i
$211$	11.9662			0.823785			0.411892	−	0.911233i	$-0.364868\pi$
$211$	11.9662			0.823785			0.411892	+	0.911233i	$0.364868\pi$
$212$	−2.68420	−	2.68420i	−0.184352	−	0.184352i
$213$	5.39247	+	5.39247i	0.369486	+	0.369486i
$214$		−	16.3445i		−	1.11729i
$215$	0.759730	+	16.3811i	0.0518132	+	1.11718i
$216$			7.71359i			0.524843i
$217$	13.4620	+	8.91857i	0.913858	+	0.605432i
$218$	13.8602	−	13.8602i	0.938734	−	0.938734i
$219$		−	9.63614i		−	0.651150i
$220$	−11.9188	−	10.8622i	−0.803564	−	0.732332i
$221$	−3.73985			−0.251570
$222$	5.93790	−	5.93790i	0.398526	−	0.398526i
$223$	0.660910	+	0.660910i	0.0442578	+	0.0442578i	0.728889	−	0.684632i	$-0.240037\pi$
$223$	0.660910	+	0.660910i	0.0442578	+	0.0442578i	−0.684632	+	0.728889i	$0.740037\pi$
$224$	31.3003	−	6.35418i	2.09134	−	0.424557i
$225$	4.97854	−	0.462789i	0.331902	−	0.0308526i
$226$	−9.47282			−0.630123
$227$	17.3487	−	17.3487i	1.15147	−	1.15147i	0.165216	−	0.986257i	$-0.447168\pi$
$227$	17.3487	−	17.3487i	1.15147	−	1.15147i	0.986257	−	0.165216i	$-0.0528323\pi$
$228$	−13.8046	+	13.8046i	−0.914232	+	0.914232i
$229$	25.0782			1.65721			0.828607	−	0.559831i	$-0.189134\pi$
$229$	25.0782			1.65721			0.828607	+	0.559831i	$0.189134\pi$
$230$	23.1592	−	25.4118i	1.52707	−	1.67560i
$231$	−3.79281	+	0.769968i	−0.249549	+	0.0506601i
$232$	28.2847	+	28.2847i	1.85698	+	1.85698i
$233$	2.24138	−	2.24138i	0.146837	−	0.146837i	−0.629866	−	0.776704i	$-0.716890\pi$
$233$	2.24138	−	2.24138i	0.146837	−	0.146837i	0.776704	+	0.629866i	$0.216890\pi$
$234$	−3.30539			−0.216080
$235$	1.25560	+	27.0729i	0.0819064	+	1.76604i
$236$			15.7583i			1.02578i
$237$	−3.19633	+	3.19633i	−0.207624	+	0.207624i
$238$	−11.4576	+	17.2944i	−0.742684	+	1.12103i
$239$		−	21.3769i		−	1.38276i	−0.722492	−	0.691380i	$-0.757003\pi$
$239$		−	21.3769i		−	1.38276i	0.722492	−	0.691380i	$-0.242997\pi$
$240$	−23.3326	+	1.08213i	−1.50611	+	0.0698512i
$241$			0.624129i			0.0402037i	0.999798	+	0.0201018i	$0.00639905\pi$
$241$			0.624129i			0.0402037i	−0.999798	+	0.0201018i	$0.993601\pi$
$242$	16.4931	+	16.4931i	1.06021	+	1.06021i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	7.00393			0.448381
$245$	−14.7643	−	5.19750i	−0.943260	−	0.332056i
$246$	−2.02695			−0.129234
$247$	−3.51575	−	3.51575i	−0.223702	−	0.223702i
$248$	33.2903	+	33.2903i	2.11394	+	2.11394i
$249$			9.55717i			0.605661i
$250$	4.07899	+	29.1484i	0.257978	+	1.84350i
$251$		−	16.3443i		−	1.03164i	−0.856696	−	0.515822i	$-0.827487\pi$
$251$		−	16.3443i		−	1.03164i	0.856696	−	0.515822i	$-0.172513\pi$
$252$	−7.20405	+	10.8740i	−0.453813	+	0.684999i
$253$	6.04143	−	6.04143i	0.379821	−	0.379821i
$254$		−	29.2632i		−	1.83614i
$255$	4.48624	−	4.92261i	0.280939	−	0.308266i
$256$	−9.88265			−0.617666
$257$	−21.3054	+	21.3054i	−1.32900	+	1.32900i	−0.422749	+	0.906247i	$0.638935\pi$
$257$	−21.3054	+	21.3054i	−1.32900	+	1.32900i	−0.906247	+	0.422749i	$0.861065\pi$
$258$	13.6515	+	13.6515i	0.849904	+	0.849904i
$259$	8.27098	−	1.67907i	0.513933	−	0.104332i
$260$	−0.641275	−	13.8270i	−0.0397702	−	0.857514i
$261$	−5.18572			−0.320988
$262$	−11.5079	+	11.5079i	−0.710960	+	0.710960i
$263$	−16.3449	+	16.3449i	−1.00787	+	1.00787i	−0.00789784	+	0.999969i	$0.502514\pi$
$263$	−16.3449	+	16.3449i	−1.00787	+	1.00787i	−0.999969	+	0.00789784i	$0.997486\pi$
$264$	−11.2834			−0.694442
$265$	0.0797641	+	1.71985i	0.00489987	+	0.105650i
$266$	−27.0291	+	5.48709i	−1.65726	+	0.336435i
$267$	−0.848464	−	0.848464i	−0.0519251	−	0.0519251i
$268$	29.2362	−	29.2362i	1.78589	−	1.78589i
$269$	16.5903			1.01153			0.505764	−	0.862672i	$-0.331211\pi$
$269$	16.5903			1.01153			0.505764	+	0.862672i	$0.331211\pi$
$270$	3.96506	−	4.35074i	0.241306	−	0.264777i
$271$		−	7.78033i		−	0.472621i	−0.971678	−	0.236311i	$-0.924062\pi$
$271$		−	7.78033i		−	0.472621i	0.971678	−	0.236311i	$-0.0759383\pi$
$272$	−22.0005	+	22.0005i	−1.33398	+	1.33398i
$273$	−2.76939	−	1.83472i	−0.167611	−	0.111043i
$274$		−	33.7136i		−	2.03671i
$275$	0.676964	+	7.28255i	0.0408224	+	0.439154i
$276$		−	28.7959i		−	1.73331i
$277$	21.3107	+	21.3107i	1.28043	+	1.28043i	0.940421	+	0.340013i	$0.110431\pi$
$277$	21.3107	+	21.3107i	1.28043	+	1.28043i	0.340013	+	0.940421i	$0.389569\pi$
$278$	−22.3214	−	22.3214i	−1.33875	−	1.33875i
$279$	−6.10346			−0.365405
$280$	−39.1697	−	23.4139i	−2.34084	−	1.39925i
$281$	−21.1519			−1.26182			−0.630908	−	0.775858i	$-0.717317\pi$
$281$	−21.1519			−1.26182			−0.630908	+	0.775858i	$0.717317\pi$
$282$	22.5617	+	22.5617i	1.34353	+	1.34353i
$283$	−2.65471	−	2.65471i	−0.157806	−	0.157806i	0.623788	−	0.781594i	$-0.285593\pi$
$283$	−2.65471	−	2.65471i	−0.157806	−	0.157806i	−0.781594	+	0.623788i	$0.785593\pi$
$284$			37.5977i			2.23101i
$285$	8.84503	−	0.410219i	0.523934	−	0.0242993i
$286$		−	4.83508i		−	0.285905i
$287$	−1.69826	−	1.12510i	−0.100245	−	0.0664126i
$288$	−8.53599	+	8.53599i	−0.502988	+	0.502988i
$289$			8.12832i			0.478136i
$290$	−1.41421	−	30.4929i	−0.0830455	−	1.79060i
$291$	12.2871			0.720282
$292$	33.5928	−	33.5928i	1.96587	−	1.96587i
$293$	1.56714	+	1.56714i	0.0915536	+	0.0915536i	0.751400	−	0.659847i	$-0.229379\pi$
$293$	1.56714	+	1.56714i	0.0915536	+	0.0915536i	−0.659847	+	0.751400i	$0.729379\pi$
$294$	−16.9688	+	7.18572i	−0.989643	+	0.419080i
$295$	4.81428	−	5.28255i	0.280298	−	0.307562i
$296$	24.6056			1.43017
$297$	1.03435	−	1.03435i	0.0600190	−	0.0600190i
$298$	−0.180239	+	0.180239i	−0.0104409	+	0.0104409i
$299$	7.33372			0.424120
$300$	18.9691	+	15.7425i	1.09518	+	0.908891i
$301$	3.86025	+	19.0153i	0.222501	+	1.09603i
$302$	25.0460	+	25.0460i	1.44123	+	1.44123i
$303$	10.8485	−	10.8485i	0.623228	−	0.623228i
$304$	−41.3643			−2.37240
$305$	−2.34788	−	2.13975i	−0.134439	−	0.122522i
$306$		−	7.84104i		−	0.448242i
$307$	17.3551	−	17.3551i	0.990510	−	0.990510i	−0.00944588	−	0.999955i	$-0.503007\pi$
$307$	17.3551	−	17.3551i	0.990510	−	0.990510i	0.999955	+	0.00944588i	$0.00300676\pi$
$308$	−15.9064	−	10.5380i	−0.906352	−	0.600459i
$309$		−	11.7489i		−	0.668374i
$310$	−1.66449	−	35.8893i	−0.0945368	−	2.03838i
$311$		−	31.0648i		−	1.76153i	−0.473558	−	0.880763i	$-0.657030\pi$
$311$		−	31.0648i		−	1.76153i	0.473558	−	0.880763i	$-0.342970\pi$
$312$	−6.84846	−	6.84846i	−0.387718	−	0.387718i
$313$	−5.72426	−	5.72426i	−0.323554	−	0.323554i	0.526575	−	0.850129i	$-0.323476\pi$
$313$	−5.72426	−	5.72426i	−0.323554	−	0.323554i	−0.850129	+	0.526575i	$0.823476\pi$
$314$	6.13381			0.346151
$315$	5.73706	−	1.44434i	0.323247	−	0.0813793i
$316$	−22.2856			−1.25366
$317$	0.752579	+	0.752579i	0.0422691	+	0.0422691i	0.727925	−	0.685656i	$-0.240485\pi$
$317$	0.752579	+	0.752579i	0.0422691	+	0.0422691i	−0.685656	+	0.727925i	$0.740485\pi$
$318$	1.43327	+	1.43327i	0.0803738	+	0.0803738i
$319$		−	7.58562i		−	0.424713i
$320$	−17.9932	−	16.3982i	−1.00585	−	0.916686i
$321$			6.20871i			0.346536i
$322$	22.4679	−	33.9138i	1.25209	−	1.88994i
$323$	8.34005	−	8.34005i	0.464053	−	0.464053i
$324$		−	4.93012i		−	0.273896i
$325$	−4.00928	+	4.83105i	−0.222395	+	0.267978i
$326$	38.2518			2.11857
$327$	−5.26503	+	5.26503i	−0.291157	+	0.291157i
$328$	−4.19966	−	4.19966i	−0.231887	−	0.231887i
$329$	6.37980	+	31.4265i	0.351730	+	1.73260i
$330$	6.36421	+	5.80005i	0.350338	+	0.319282i
$331$	15.8082			0.868899			0.434449	−	0.900696i	$-0.356943\pi$
$331$	15.8082			0.868899			0.434449	+	0.900696i	$0.356943\pi$
$332$	−33.3175	+	33.3175i	−1.82853	+	1.82853i
$333$	−2.25560	+	2.25560i	−0.123606	+	0.123606i
$334$	1.09085			0.0596887
$335$	−18.7326	+	0.868788i	−1.02347	+	0.0474670i
$336$	−27.0847	+	5.49839i	−1.47759	+	0.299962i
$337$	−20.0460	−	20.0460i	−1.09197	−	1.09197i	−0.995318	−	0.0966558i	$-0.969185\pi$
$337$	−20.0460	−	20.0460i	−1.09197	−	1.09197i	−0.0966558	−	0.995318i	$-0.530815\pi$
$338$	−21.2644	+	21.2644i	−1.15663	+	1.15663i
$339$	3.59839			0.195438
$340$	32.8004	−	1.52123i	1.77885	−	0.0825005i
$341$		−	8.92808i		−	0.483482i
$342$	7.37117	−	7.37117i	0.398587	−	0.398587i
$343$	−18.2058	−	3.39840i	−0.983020	−	0.183497i
$344$			56.5693i			3.05001i
$345$	−8.79736	+	9.65306i	−0.473634	+	0.519703i
$346$		−	12.8512i		−	0.690883i
$347$	−20.0847	−	20.0847i	−1.07820	−	1.07820i	−0.996671	−	0.0815328i	$-0.974018\pi$
$347$	−20.0847	−	20.0847i	−1.07820	−	1.07820i	−0.0815328	−	0.996671i	$-0.525982\pi$
$348$	−18.0781	−	18.0781i	−0.969087	−	0.969087i
$349$	−14.7663			−0.790420			−0.395210	−	0.918591i	$-0.629328\pi$
$349$	−14.7663			−0.790420			−0.395210	+	0.918591i	$0.629328\pi$
$350$	10.0575	+	33.3409i	0.537597	+	1.78215i
$351$	1.25560			0.0670190
$352$	−12.4864	−	12.4864i	−0.665525	−	0.665525i
$353$	12.4890	+	12.4890i	0.664724	+	0.664724i	0.956490	−	0.291766i	$-0.0942429\pi$
$353$	12.4890	+	12.4890i	0.664724	+	0.664724i	−0.291766	+	0.956490i	$0.594243\pi$
$354$		−	8.41438i		−	0.447219i
$355$	11.4864	−	12.6036i	0.609633	−	0.668931i
$356$		−	5.91570i		−	0.313531i
$357$	4.35233	−	6.56955i	0.230350	−	0.347697i
$358$	−3.71839	+	3.71839i	−0.196523	+	0.196523i
$359$		−	10.5372i		−	0.556133i	−0.960562	−	0.278066i	$-0.910306\pi$
$359$		−	10.5372i		−	0.556133i	0.960562	−	0.278066i	$-0.0896935\pi$
$360$	17.2296	−	0.799082i	0.908079	−	0.0421153i
$361$	−3.31943			−0.174707
$362$	15.7951	−	15.7951i	0.830171	−	0.830171i
$363$	−6.26514	−	6.26514i	−0.328835	−	0.328835i
$364$	−3.25837	−	16.0505i	−0.170785	−	0.841276i
$365$	−21.5239	+	0.998247i	−1.12661	+	0.0522507i
$366$	−3.73985			−0.195485
$367$	−11.1910	+	11.1910i	−0.584163	+	0.584163i	−0.936045	−	0.351881i	$-0.885542\pi$
$367$	−11.1910	+	11.1910i	−0.584163	+	0.584163i	0.351881	+	0.936045i	$0.385542\pi$
$368$	43.1422	−	43.1422i	2.24894	−	2.24894i
$369$	0.769968			0.0400829
$370$	−13.8784	−	12.6482i	−0.721505	−	0.657546i
$371$	0.405287	+	1.99642i	0.0210415	+	0.103649i
$372$	−21.2774	−	21.2774i	−1.10318	−	1.10318i
$373$	17.2746	−	17.2746i	0.894446	−	0.894446i	−0.100492	−	0.994938i	$-0.532042\pi$
$373$	17.2746	−	17.2746i	0.894446	−	0.894446i	0.994938	+	0.100492i	$0.0320416\pi$
$374$	11.4698			0.593088
$375$	−1.54946	−	11.0725i	−0.0800140	−	0.571779i
$376$			93.4917i			4.82147i
$377$	4.60412	−	4.60412i	0.237124	−	0.237124i
$378$	3.84671	−	5.80635i	0.197853	−	0.298646i
$379$			17.6237i			0.905267i	0.891697	+	0.452634i	$0.149515\pi$
$379$			17.6237i			0.905267i	−0.891697	+	0.452634i	$0.850485\pi$
$380$	32.2649	+	29.4048i	1.65516	+	1.50843i
$381$			11.1161i			0.569493i
$382$	14.5832	+	14.5832i	0.746141	+	0.746141i
$383$	−16.1249	−	16.1249i	−0.823942	−	0.823942i	0.162729	−	0.986671i	$-0.447970\pi$
$383$	−16.1249	−	16.1249i	−0.823942	−	0.823942i	−0.986671	+	0.162729i	$0.947970\pi$
$384$	−4.51726			−0.230520
$385$	2.11276	+	8.39211i	0.107676	+	0.427702i
$386$	−50.4894			−2.56984
$387$	−5.18572	−	5.18572i	−0.263605	−	0.263605i
$388$	42.8343	+	42.8343i	2.17458	+	2.17458i
$389$			15.4011i			0.780865i	0.920632	+	0.390432i	$0.127674\pi$
$389$			15.4011i			0.780865i	−0.920632	+	0.390432i	$0.872326\pi$
$390$	0.342419	+	7.38313i	0.0173390	+	0.373859i
$391$			17.3971i			0.879807i
$392$	−50.0461	−	20.2697i	−2.52771	−	1.02378i
$393$	4.37145	−	4.37145i	0.220510	−	0.220510i
$394$			42.7360i			2.15301i
$395$	7.47066	+	6.80841i	0.375889	+	0.342568i
$396$	7.21173			0.362403
$397$	−16.1781	+	16.1781i	−0.811955	+	0.811955i	−0.984927	−	0.172972i	$-0.944663\pi$
$397$	−16.1781	+	16.1781i	−0.811955	+	0.811955i	0.172972	+	0.984927i	$0.444663\pi$
$398$	37.5026	+	37.5026i	1.87983	+	1.87983i
$399$	10.2674	−	2.08435i	0.514013	−	0.104348i
$400$	4.83424	+	52.0051i	0.241712	+	2.60026i
$401$	−0.977595			−0.0488188			−0.0244094	−	0.999702i	$-0.507771\pi$
$401$	−0.977595			−0.0488188			−0.0244094	+	0.999702i	$0.507771\pi$
$402$	−15.6111	+	15.6111i	−0.778612	+	0.778612i
$403$	5.41892	−	5.41892i	0.269936	−	0.269936i
$404$	75.6382			3.76314
$405$	−1.50619	+	1.65269i	−0.0748431	+	0.0821230i
$406$	−7.18572	−	35.3964i	−0.356622	−	1.75670i
$407$	−3.29947	−	3.29947i	−0.163549	−	0.163549i
$408$	16.2459	−	16.2459i	0.804293	−	0.804293i
$409$	−24.3171			−1.20241			−0.601203	−	0.799097i	$-0.705312\pi$
$409$	−24.3171			−1.20241			−0.601203	+	0.799097i	$0.705312\pi$
$410$	0.209980	+	4.52753i	0.0103702	+	0.223599i
$411$			12.8066i			0.631704i
$412$	40.9583	−	40.9583i	2.01787	−	2.01787i
$413$	4.67058	−	7.04992i	0.229824	−	0.346904i
$414$			15.3760i			0.755689i
$415$	21.3475	−	0.990067i	1.04791	−	0.0486005i
$416$		−	15.1573i		−	0.743146i
$417$	8.47912	+	8.47912i	0.415224	+	0.415224i
$418$	10.7825	+	10.7825i	0.527388	+	0.527388i
$419$	−15.9893			−0.781127			−0.390563	−	0.920576i	$-0.627720\pi$
$419$	−15.9893			−0.781127			−0.390563	+	0.920576i	$0.627720\pi$
$420$	25.0353	+	14.9650i	1.22160	+	0.730215i
$421$	14.7000			0.716433			0.358216	−	0.933639i	$-0.383385\pi$
$421$	14.7000			0.716433			0.358216	+	0.933639i	$0.383385\pi$
$422$	−22.2746	−	22.2746i	−1.08431	−	1.08431i
$423$	−8.57041	−	8.57041i	−0.416708	−	0.416708i
$424$			5.93921i			0.288434i
$425$	−11.4602	−	9.51081i	−0.555902	−	0.461342i
$426$		−	20.0758i		−	0.972677i
$427$	−3.13341	−	2.07588i	−0.151636	−	0.100459i
$428$	−21.6443	+	21.6443i	−1.04622	+	1.04622i
$429$			1.83668i			0.0886758i
$430$	29.0787	−	31.9071i	1.40230	−	1.53870i
$431$	22.2722			1.07281			0.536407	−	0.843960i	$-0.319781\pi$
$431$	22.2722			1.07281			0.536407	+	0.843960i	$0.319781\pi$
$432$	7.38635	−	7.38635i	0.355376	−	0.355376i
$433$	28.0171	+	28.0171i	1.34642	+	1.34642i	0.889520	+	0.456896i	$0.151039\pi$
$433$	28.0171	+	28.0171i	1.34642	+	1.34642i	0.456896	+	0.889520i	$0.348961\pi$
$434$	−8.45741	−	41.6606i	−0.405968	−	1.99978i
$435$	0.537211	+	11.5832i	0.0257573	+	0.555371i
$436$	−36.7091			−1.75805
$437$	−16.3545	+	16.3545i	−0.782344	+	0.782344i
$438$	−17.9374	+	17.9374i	−0.857080	+	0.857080i
$439$	2.35656			0.112473			0.0562363	−	0.998417i	$-0.482090\pi$
$439$	2.35656			0.112473			0.0562363	+	0.998417i	$0.482090\pi$
$440$	1.16889	+	25.2033i	0.0557246	+	1.20152i
$441$	6.44587	−	2.72961i	0.306946	−	0.129981i
$442$	6.96162	+	6.96162i	0.331130	+	0.331130i
$443$	−5.47247	+	5.47247i	−0.260005	+	0.260005i	−0.825056	−	0.565051i	$-0.808856\pi$
$443$	−5.47247	+	5.47247i	−0.260005	+	0.260005i	0.565051	+	0.825056i	$0.308856\pi$
$444$	−15.7266			−0.746352
$445$	−1.80729	+	1.98308i	−0.0856737	+	0.0940071i
$446$		−	2.46053i		−	0.116509i
$447$	0.0684664	−	0.0684664i	0.00323835	−	0.00323835i
$448$	−24.0131	−	15.9087i	−1.13451	−	0.751616i
$449$		−	1.20020i		−	0.0566410i	−0.999599	−	0.0283205i	$-0.990984\pi$
$449$		−	1.20020i		−	0.0566410i	0.999599	−	0.0283205i	$-0.00901591\pi$
$450$	−10.1289	−	8.40592i	−0.477479	−	0.396259i
$451$			1.12630i			0.0530354i
$452$	12.5444	+	12.5444i	0.590041	+	0.590041i
$453$	−9.51409	−	9.51409i	−0.447011	−	0.447011i
$454$	−64.5881			−3.03127
$455$	−3.81127	+	6.37597i	−0.178675	+	0.298910i
$456$	30.5448			1.43039
$457$	−21.0775	−	21.0775i	−0.985962	−	0.985962i	0.0139406	−	0.999903i	$-0.495562\pi$
$457$	−21.0775	−	21.0775i	−0.985962	−	0.985962i	−0.999903	+	0.0139406i	$0.995562\pi$
$458$	−46.6823	−	46.6823i	−2.18132	−	2.18132i
$459$			2.97854i			0.139026i
$460$	−64.3204	+	2.98308i	−2.99896	+	0.139087i
$461$			21.9670i			1.02311i	0.859252	+	0.511553i	$0.170929\pi$
$461$			21.9670i			1.02311i	−0.859252	+	0.511553i	$0.829071\pi$
$462$	8.49347	+	5.62693i	0.395152	+	0.261788i
$463$	−21.6776	+	21.6776i	−1.00744	+	1.00744i	−0.00746987	+	0.999972i	$0.502378\pi$
$463$	−21.6776	+	21.6776i	−1.00744	+	1.00744i	−0.999972	+	0.00746987i	$0.997622\pi$
$464$		−	54.1694i		−	2.51475i
$465$	0.632282	+	13.6331i	0.0293214	+	0.632220i
$466$	−8.34450			−0.386551
$467$	−7.11299	+	7.11299i	−0.329150	+	0.329150i	−0.852263	−	0.523113i	$-0.824770\pi$
$467$	−7.11299	+	7.11299i	−0.329150	+	0.329150i	0.523113	+	0.852263i	$0.324770\pi$
$468$	4.37718	+	4.37718i	0.202335	+	0.202335i
$469$	−21.7449	+	4.41438i	−1.00409	+	0.203837i
$470$	48.0581	−	52.7326i	2.21676	−	2.43237i
$471$	−2.33002			−0.107362
$472$	17.4338	−	17.4338i	0.802457	−	0.802457i
$473$	7.58562	−	7.58562i	0.348787	−	0.348787i
$474$	11.8997			0.546572
$475$	−1.83259	−	19.7144i	−0.0840848	−	0.904557i
$476$	38.0750	−	7.72950i	1.74517	−	0.354281i
$477$	−0.544449	−	0.544449i	−0.0249286	−	0.0249286i
$478$	−39.7925	+	39.7925i	−1.82007	+	1.82007i
$479$	−31.7749			−1.45183			−0.725917	−	0.687782i	$-0.758584\pi$
$479$	−31.7749			−1.45183			−0.725917	+	0.687782i	$0.758584\pi$
$480$	19.9508	+	18.1823i	0.910627	+	0.829904i
$481$		−	4.00524i		−	0.182623i
$482$	1.16180	−	1.16180i	0.0529184	−	0.0529184i
$483$	−8.53477	+	12.8827i	−0.388345	+	0.586181i
$484$		−	43.6821i		−	1.98555i
$485$	−1.27287	−	27.4453i	−0.0577981	−	1.24623i
$486$			2.63251i			0.119413i
$487$	−4.81428	−	4.81428i	−0.218156	−	0.218156i	0.589565	−	0.807721i	$-0.299299\pi$
$487$	−4.81428	−	4.81428i	−0.218156	−	0.218156i	−0.807721	+	0.589565i	$0.799299\pi$
$488$	−7.74864	−	7.74864i	−0.350765	−	0.350765i
$489$	−14.5305			−0.657092
$490$	17.8084	+	37.1583i	0.804501	+	1.67864i
$491$	28.3401			1.27897			0.639484	−	0.768804i	$-0.279148\pi$
$491$	28.3401			1.27897			0.639484	+	0.768804i	$0.279148\pi$
$492$	2.68420	+	2.68420i	0.121013	+	0.121013i
$493$	10.9219	+	10.9219i	0.491897	+	0.491897i
$494$			13.0889i			0.588897i
$495$	−2.41754	−	2.20324i	−0.108660	−	0.0990282i
$496$		−	63.7559i		−	2.86273i
$497$	11.1435	−	16.8204i	0.499855	−	0.754497i
$498$	17.7904	−	17.7904i	0.797206	−	0.797206i
$499$			3.39197i			0.151845i	0.997114	+	0.0759227i	$0.0241902\pi$
$499$			3.39197i			0.151845i	−0.997114	+	0.0759227i	$0.975810\pi$
$500$	33.1983	−	44.0016i	1.48467	−	1.96781i
$501$	−0.414376			−0.0185130
$502$	−30.4244	+	30.4244i	−1.35791	+	1.35791i
$503$	8.32921	+	8.32921i	0.371381	+	0.371381i	0.867980	−	0.496599i	$-0.165418\pi$
$503$	8.32921	+	8.32921i	0.371381	+	0.371381i	−0.496599	+	0.867980i	$0.665418\pi$
$504$	20.0003	−	4.06020i	0.890883	−	0.180856i
$505$	−25.3557	−	23.1080i	−1.12831	−	1.02829i
$506$	−22.4918			−0.999884
$507$	8.07761	−	8.07761i	0.358739	−	0.358739i
$508$	−38.7520	+	38.7520i	−1.71934	+	1.71934i
$509$	38.9452			1.72622			0.863108	−	0.505020i	$-0.168515\pi$
$509$	38.9452			1.72622			0.863108	+	0.505020i	$0.168515\pi$
$510$	−17.5143	+	0.812285i	−0.775545	+	0.0359686i
$511$	−24.9852	+	5.07217i	−1.10528	+	0.224380i
$512$	24.7846	+	24.7846i	1.09534	+	1.09534i
$513$	−2.80005	+	2.80005i	−0.123625	+	0.123625i
$514$	79.3187			3.49860
$515$	−26.2432	+	1.21712i	−1.15641	+	0.0536328i
$516$		−	36.1562i		−	1.59169i
$517$	12.5367	−	12.5367i	0.551364	−	0.551364i
$518$	−18.5217	−	12.2706i	−0.813796	−	0.539140i
$519$			4.88171i			0.214283i
$520$	−14.5877	+	16.0066i	−0.639714	+	0.701938i
$521$			7.06726i			0.309622i	0.987944	+	0.154811i	$0.0494769\pi$
$521$			7.06726i			0.309622i	−0.987944	+	0.154811i	$0.950523\pi$
$522$	9.65306	+	9.65306i	0.422503	+	0.422503i
$523$	−14.5887	−	14.5887i	−0.637921	−	0.637921i	0.312121	−	0.950042i	$-0.398960\pi$
$523$	−14.5887	−	14.5887i	−0.637921	−	0.637921i	−0.950042	+	0.312121i	$0.898960\pi$
$524$	30.4788			1.33147
$525$	−3.82050	−	12.6651i	−0.166740	−	0.552749i
$526$	60.8508			2.65322
$527$	12.8548	+	12.8548i	0.559962	+	0.559962i
$528$	10.8047	+	10.8047i	0.470213	+	0.470213i
$529$		−	11.1150i		−	0.483261i
$530$	3.05297	−	3.34993i	0.132613	−	0.145511i
$531$			3.19633i			0.138709i
$532$	43.0597	+	28.5271i	1.86688	+	1.23681i
$533$	−0.683611	+	0.683611i	−0.0296105	+	0.0296105i
$534$			3.15878i			0.136694i
$535$	13.8682	−	0.643185i	0.599574	−	0.0278073i
$536$	−64.6897			−2.79417
$537$	1.41249	−	1.41249i	0.0609533	−	0.0609533i
$538$	−30.8823	−	30.8823i	−1.33143	−	1.33143i
$539$	3.99284	+	9.42895i	0.171984	+	0.406134i
$540$	−11.0123	+	0.510732i	−0.473892	+	0.0219784i
$541$	18.6013			0.799731			0.399865	−	0.916574i	$-0.369057\pi$
$541$	18.6013			0.799731			0.399865	+	0.916574i	$0.369057\pi$
$542$	−14.4828	+	14.4828i	−0.622091	+	0.622091i
$543$	−6.00000	+	6.00000i	−0.257485	+	0.257485i
$544$	35.9560			1.54160
$545$	12.3057	+	11.2149i	0.527120	+	0.480393i
$546$	1.73985	+	8.57041i	0.0744589	+	0.366780i
$547$	−7.22715	−	7.22715i	−0.309011	−	0.309011i	0.535515	−	0.844526i	$-0.320118\pi$
$547$	−7.22715	−	7.22715i	−0.309011	−	0.309011i	−0.844526	+	0.535515i	$0.820118\pi$
$548$	−44.6455	+	44.6455i	−1.90716	+	1.90716i
$549$	1.42064			0.0606315
$550$	12.2961	−	14.8164i	0.524307	−	0.631772i
$551$			20.5348i			0.874812i
$552$	−31.8577	+	31.8577i	−1.35595	+	1.35595i
$553$	9.97009	+	6.60519i	0.423971	+	0.280881i
$554$		−	79.3382i		−	3.37076i
$555$	5.27193	+	4.80460i	0.223781	+	0.203944i
$556$			59.1185i			2.50718i
$557$	−0.558927	−	0.558927i	−0.0236825	−	0.0236825i	0.695166	−	0.718849i	$-0.255331\pi$
$557$	−0.558927	−	0.558927i	−0.0236825	−	0.0236825i	−0.718849	+	0.695166i	$0.755331\pi$
$558$	11.3614	+	11.3614i	0.480966	+	0.480966i
$559$	9.20823			0.389467
$560$	15.0874	+	59.9286i	0.637558	+	2.53245i
$561$	−4.35697			−0.183951
$562$	39.3736	+	39.3736i	1.66087	+	1.66087i
$563$	−0.702475	−	0.702475i	−0.0296058	−	0.0296058i	0.692149	−	0.721755i	$-0.256664\pi$
$563$	−0.702475	−	0.702475i	−0.0296058	−	0.0296058i	−0.721755	+	0.692149i	$0.756664\pi$
$564$		−	59.7550i		−	2.51614i
$565$	−0.372772	−	8.03762i	−0.0156827	−	0.338145i
$566$			9.88333i			0.415427i
$567$	−1.46123	+	2.20563i	−0.0613659	+	0.0926278i
$568$	41.5953	−	41.5953i	1.74530	−	1.74530i
$569$			9.72049i			0.407504i	0.979023	+	0.203752i	$0.0653137\pi$
$569$			9.72049i			0.407504i	−0.979023	+	0.203752i	$0.934686\pi$
$570$	−17.2283	−	15.7011i	−0.721616	−	0.657648i
$571$	−0.986684			−0.0412914			−0.0206457	−	0.999787i	$-0.506572\pi$
$571$	−0.986684			−0.0412914			−0.0206457	+	0.999787i	$0.506572\pi$
$572$	−6.40289	+	6.40289i	−0.267718	+	0.267718i
$573$	−5.53964	−	5.53964i	−0.231422	−	0.231422i
$574$	1.06692	+	5.25560i	0.0445326	+	0.219365i
$575$	22.4731	+	18.6504i	0.937192	+	0.777774i
$576$	10.8872			0.453633
$577$	10.3510	−	10.3510i	0.430917	−	0.430917i	−0.458024	−	0.888940i	$-0.651442\pi$
$577$	10.3510	−	10.3510i	0.430917	−	0.430917i	0.888940	+	0.458024i	$0.151442\pi$
$578$	15.1306	−	15.1306i	0.629350	−	0.629350i
$579$	19.1792			0.797059
$580$	−38.5076	+	42.2532i	−1.59894	+	1.75447i
$581$	24.7804	−	5.03060i	1.02807	−	0.208705i
$582$	−22.8720	−	22.8720i	−0.948076	−	0.948076i
$583$	0.796415	−	0.796415i	0.0329841	−	0.0329841i
$584$	−74.3292			−3.07576
$585$	−0.130073	−	2.80460i	−0.00537785	−	0.115956i
$586$		−	5.83438i		−	0.241016i
$587$	21.1413	−	21.1413i	0.872594	−	0.872594i	−0.120160	−	0.992755i	$-0.538341\pi$
$587$	21.1413	−	21.1413i	0.872594	−	0.872594i	0.992755	+	0.120160i	$0.0383409\pi$
$588$	31.9868	+	12.9554i	1.31912	+	0.534270i
$589$			24.1689i			0.995862i
$590$	−18.7949	+	0.871680i	−0.773774	+	0.0358865i
$591$		−	16.2339i		−	0.667774i
$592$	−23.5617	−	23.5617i	−0.968381	−	0.968381i
$593$	−7.07816	−	7.07816i	−0.290665	−	0.290665i	0.546678	−	0.837343i	$-0.315892\pi$
$593$	−7.07816	−	7.07816i	−0.290665	−	0.290665i	−0.837343	+	0.546678i	$0.815892\pi$
$594$	−3.85081			−0.158001
$595$	−15.1251	−	9.04109i	−0.620067	−	0.370649i
$596$	0.477365			0.0195536
$597$	−14.2459	−	14.2459i	−0.583047	−	0.583047i
$598$	−13.6515	−	13.6515i	−0.558251	−	0.558251i
$599$		−	7.13847i		−	0.291670i	−0.989309	−	0.145835i	$-0.953413\pi$
$599$		−	7.13847i		−	0.291670i	0.989309	−	0.145835i	$-0.0465869\pi$
$600$	−3.56977	−	38.4024i	−0.145735	−	1.56777i
$601$		−	35.0829i		−	1.43106i	−0.698580	−	0.715532i	$-0.746185\pi$
$601$		−	35.0829i		−	1.43106i	0.698580	−	0.715532i	$-0.253815\pi$
$602$	28.2107	−	42.5822i	1.14978	−	1.73552i
$603$	5.93012	−	5.93012i	0.241493	−	0.241493i
$604$		−	66.3346i		−	2.69912i
$605$	−13.3452	+	14.6433i	−0.542560	+	0.595334i
$606$	−40.3881			−1.64066
$607$	5.36385	−	5.36385i	0.217712	−	0.217712i	−0.589822	−	0.807533i	$-0.700802\pi$
$607$	5.36385	−	5.36385i	0.217712	−	0.217712i	0.807533	+	0.589822i	$0.200802\pi$
$608$	33.8014	+	33.8014i	1.37083	+	1.37083i
$609$	2.72961	+	13.4459i	0.110609	+	0.544854i
$610$	0.387427	+	8.35359i	0.0156865	+	0.338227i
$611$	15.2184			0.615670
$612$	−10.3835	+	10.3835i	−0.419730	+	0.419730i
$613$	−10.4888	+	10.4888i	−0.423639	+	0.423639i	−0.886454	−	0.462816i	$-0.846839\pi$
$613$	−10.4888	+	10.4888i	−0.423639	+	0.423639i	0.462816	+	0.886454i	$0.346839\pi$
$614$	−64.6120			−2.60753
$615$	−0.0797641	−	1.71985i	−0.00321640	−	0.0693511i
$616$	5.93921	+	29.2562i	0.239298	+	1.17877i
$617$	19.7986	+	19.7986i	0.797060	+	0.797060i	0.982631	−	0.185571i	$-0.0594135\pi$
$617$	19.7986	+	19.7986i	0.797060	+	0.797060i	−0.185571	+	0.982631i	$0.559414\pi$
$618$	−21.8703	+	21.8703i	−0.879752	+	0.879752i
$619$	12.0675			0.485034			0.242517	−	0.970147i	$-0.422027\pi$
$619$	12.0675			0.485034			0.242517	+	0.970147i	$0.422027\pi$
$620$	−45.3224	+	49.7309i	−1.82019	+	1.99724i
$621$		−	5.84081i		−	0.234383i
$622$	−57.8262	+	57.8262i	−2.31862	+	2.31862i
$623$	−1.75334	+	2.64655i	−0.0702462	+	0.106032i
$624$			13.1158i			0.525054i
$625$	−24.5717	+	4.60803i	−0.982866	+	0.184321i
$626$			21.3110i			0.851761i
$627$	−4.09588	−	4.09588i	−0.163574	−	0.163574i
$628$	−8.12275	−	8.12275i	−0.324133	−	0.324133i
$629$	9.50124			0.378839
$630$	−13.3679	−	7.99077i	−0.532592	−	0.318360i
$631$	30.4435			1.21194			0.605969	−	0.795488i	$-0.292786\pi$
$631$	30.4435			1.21194			0.605969	+	0.795488i	$0.292786\pi$
$632$	24.6552	+	24.6552i	0.980730	+	0.980730i
$633$	8.46135	+	8.46135i	0.336309	+	0.336309i
$634$		−	2.80180i		−	0.111274i
$635$	24.8296	−	1.15156i	0.985332	−	0.0456982i
$636$		−	3.79604i		−	0.150523i
$637$	−3.29946	+	8.14639i	−0.130729	+	0.322772i
$638$	−14.1204	+	14.1204i	−0.559032	+	0.559032i
$639$			7.62611i			0.301684i
$640$	0.467961	+	10.0901i	0.0184978	+	0.398844i
$641$	36.5929			1.44533			0.722666	−	0.691198i	$-0.242917\pi$
$641$	36.5929			1.44533			0.722666	+	0.691198i	$0.242917\pi$
$642$	11.5573	−	11.5573i	0.456131	−	0.456131i
$643$	12.1140	+	12.1140i	0.477731	+	0.477731i	0.904405	−	0.426675i	$-0.140315\pi$
$643$	12.1140	+	12.1140i	0.477731	+	0.477731i	−0.426675	+	0.904405i	$0.640315\pi$
$644$	−74.6638	+	15.1573i	−2.94217	+	0.597280i
$645$	−11.0460	+	12.1204i	−0.434935	+	0.477240i
$646$	−31.0495			−1.22163
$647$	19.0978	−	19.0978i	0.750814	−	0.750814i	−0.223817	−	0.974631i	$-0.571852\pi$
$647$	19.0978	−	19.0978i	0.750814	−	0.750814i	0.974631	+	0.223817i	$0.0718519\pi$
$648$	−5.45433	+	5.45433i	−0.214266	+	0.214266i
$649$	−4.67556			−0.183532
$650$	16.4560	−	1.52970i	0.645457	−	0.0599997i
$651$	3.21267	+	15.8254i	0.125915	+	0.620248i
$652$	−50.6552	−	50.6552i	−1.98381	−	1.98381i
$653$	20.3709	−	20.3709i	0.797173	−	0.797173i	−0.185476	−	0.982649i	$-0.559383\pi$
$653$	20.3709	−	20.3709i	0.797173	−	0.797173i	0.982649	+	0.185476i	$0.0593826\pi$
$654$	19.6013			0.766473
$655$	−10.2172	−	9.31151i	−0.399220	−	0.363831i
$656$			8.04298i			0.314026i
$657$	6.81378	−	6.81378i	0.265831	−	0.265831i
$658$	46.6236	−	70.3752i	1.81758	−	2.74351i
$659$			31.4882i			1.22661i	0.789847	+	0.613304i	$0.210160\pi$
$659$			31.4882i			1.22661i	−0.789847	+	0.613304i	$0.789840\pi$
$660$	−0.747093	−	16.1086i	−0.0290806	−	0.627027i
$661$		−	48.1880i		−	1.87430i	−0.348931	−	0.937149i	$-0.613455\pi$
$661$		−	48.1880i		−	1.87430i	0.348931	−	0.937149i	$-0.386545\pi$
$662$	−29.4265	−	29.4265i	−1.14369	−	1.14369i
$663$	−2.64448	−	2.64448i	−0.102703	−	0.102703i
$664$	73.7201			2.86089
$665$	−5.71939	−	22.7180i	−0.221789	−	0.880967i
$666$	8.39746			0.325395
$667$	−21.4174	−	21.4174i	−0.829286	−	0.829286i
$668$	−1.44457	−	1.44457i	−0.0558920	−	0.0558920i
$669$			0.934668i			0.0361364i
$670$	36.4873	+	33.2528i	1.40963	+	1.28467i
$671$			2.07810i			0.0802241i
$672$	26.6257	+	17.6396i	1.02711	+	0.680461i
$673$	−30.6900	+	30.6900i	−1.18301	+	1.18301i	−0.204055	+	0.978960i	$0.565412\pi$
$673$	−30.6900	+	30.6900i	−1.18301	+	1.18301i	−0.978960	+	0.204055i	$0.934588\pi$
$674$			74.6299i			2.87463i
$675$	3.84760	+	3.19312i	0.148094	+	0.122903i
$676$	56.3191			2.16612
$677$	1.54060	−	1.54060i	0.0592101	−	0.0592101i	−0.676882	−	0.736092i	$-0.736669\pi$
$677$	1.54060	−	1.54060i	0.0592101	−	0.0592101i	0.736092	+	0.676882i	$0.236669\pi$
$678$	−6.69830	−	6.69830i	−0.257246	−	0.257246i
$679$	−6.46755	−	31.8587i	−0.248202	−	1.22263i
$680$	−37.9710	−	34.6050i	−1.45612	−	1.32704i
$681$	24.5348			0.940174
$682$	−16.6193	+	16.6193i	−0.636387	+	0.636387i
$683$	14.2154	−	14.2154i	0.543936	−	0.543936i	−0.380744	−	0.924680i	$-0.624332\pi$
$683$	14.2154	−	14.2154i	0.543936	−	0.543936i	0.924680	+	0.380744i	$0.124332\pi$
$684$	−19.5226			−0.746467
$685$	28.6057	−	1.32669i	1.09297	−	0.0506903i
$686$	27.5635	+	40.2155i	1.05238	+	1.53544i
$687$	17.7330	+	17.7330i	0.676555	+	0.676555i
$688$	54.1694	−	54.1694i	2.06519	−	2.06519i
$689$	0.966772			0.0368311
$690$	34.3449	−	1.59286i	1.30749	−	0.0606392i
$691$			10.2887i			0.391401i	0.980664	+	0.195700i	$0.0626980\pi$
$691$			10.2887i			0.391401i	−0.980664	+	0.195700i	$0.937302\pi$
$692$	−17.0182	+	17.0182i	−0.646937	+	0.646937i
$693$	−3.22637	−	2.13747i	−0.122560	−	0.0811959i
$694$			74.7741i			2.83838i
$695$	18.0611	−	19.8179i	0.685098	−	0.751736i
$696$			40.0005i			1.51622i
$697$	−1.62166	−	1.62166i	−0.0614248	−	0.0614248i
$698$	27.4869	+	27.4869i	1.04040	+	1.04040i
$699$	3.16979			0.119892
$700$	30.8332	−	57.4707i	1.16539	−	2.17219i
$701$	−44.3183			−1.67388			−0.836939	−	0.547297i	$-0.815657\pi$
$701$	−44.3183			−1.67388			−0.836939	+	0.547297i	$0.815657\pi$
$702$	−2.33726	−	2.33726i	−0.0882142	−	0.0882142i
$703$	8.93189	+	8.93189i	0.336872	+	0.336872i
$704$			15.9257i			0.600222i
$705$	−18.2556	+	20.0313i	−0.687546	+	0.754422i
$706$		−	46.4958i		−	1.74989i
$707$	−33.8389	−	22.4183i	−1.27264	−	0.843126i
$708$	−11.1428	+	11.1428i	−0.418772	+	0.418772i
$709$		−	0.817976i		−	0.0307197i	−0.999882	−	0.0153599i	$-0.995111\pi$
$709$		−	0.817976i		−	0.0307197i	0.999882	−	0.0153599i	$-0.00488939\pi$
$710$	−44.8427	+	2.07974i	−1.68292	+	0.0780512i
$711$	−4.52029			−0.169524
$712$	−6.54470	+	6.54470i	−0.245273	+	0.245273i
$713$	−25.2077	−	25.2077i	−0.944037	−	0.944037i
$714$	−20.3307	+	4.12728i	−0.760858	+	0.154460i
$715$	4.10253	−	0.190269i	0.153426	−	0.00711567i
$716$	9.84821			0.368045
$717$	15.1158	−	15.1158i	0.564509	−	0.564509i
$718$	−19.6147	+	19.6147i	−0.732013	+	0.732013i
$719$	−0.00762056			−0.000284199			−0.000142099	−	1.00000i	$-0.500045\pi$
$719$	−0.00762056			−0.000284199			−0.000142099		1.00000i	$0.500045\pi$
$720$	−17.2638	−	15.7335i	−0.643385	−	0.586351i
$721$	−30.4634	+	6.18428i	−1.13452	+	0.230315i
$722$	6.17902	+	6.17902i	0.229959	+	0.229959i
$723$	−0.441326	+	0.441326i	−0.0164131	+	0.0164131i
$724$	−41.8335			−1.55473
$725$	25.8173	−	2.39990i	0.958831	−	0.0891300i
$726$			23.3247i			0.865661i
$727$	−28.5738	+	28.5738i	−1.05974	+	1.05974i	−0.0616465	+	0.998098i	$0.519635\pi$
$727$	−28.5738	+	28.5738i	−1.05974	+	1.05974i	−0.998098	+	0.0616465i	$0.980365\pi$
$728$	−14.1523	+	21.3619i	−0.524519	+	0.791726i
$729$		−	1.00000i		−	0.0370370i
$730$	41.9243	+	38.2079i	1.55169	+	1.41414i
$731$			21.8438i			0.807921i
$732$	4.95253	+	4.95253i	0.183051	+	0.183051i
$733$	24.1522	+	24.1522i	0.892083	+	0.892083i	0.994719	−	0.102636i	$-0.0327275\pi$
$733$	24.1522	+	24.1522i	0.892083	+	0.892083i	−0.102636	+	0.994719i	$0.532728\pi$
$734$	41.6632			1.53782
$735$	−6.76479	−	14.1152i	−0.249523	−	0.520645i
$736$	−70.5085			−2.59898
$737$	8.67452	+	8.67452i	0.319530	+	0.319530i
$738$	−1.43327	−	1.43327i	−0.0527594	−	0.0527594i
$739$		−	37.9522i		−	1.39609i	−0.716052	−	0.698047i	$-0.754053\pi$
$739$		−	37.9522i		−	1.39609i	0.716052	−	0.698047i	$-0.245947\pi$
$740$	1.62918	+	35.1280i	0.0598900	+	1.29133i
$741$		−	4.97202i		−	0.182652i
$742$	2.96184	−	4.47070i	0.108733	−	0.164125i
$743$	−18.8022	+	18.8022i	−0.689784	+	0.689784i	−0.962184	−	0.272400i	$-0.912183\pi$
$743$	−18.8022	+	18.8022i	−0.689784	+	0.689784i	0.272400	+	0.962184i	$0.412183\pi$
$744$			47.0796i			1.72602i
$745$	−0.160024	−	0.145838i	−0.00586282	−	0.00534311i
$746$	−64.3123			−2.35464
$747$	−6.75794	+	6.75794i	−0.247260	+	0.247260i
$748$	−15.1889	−	15.1889i	−0.555363	−	0.555363i
$749$	16.0983	−	3.26807i	0.588220	−	0.119413i
$750$	−17.7267	+	23.4953i	−0.647289	+	0.857927i
$751$	0.105915			0.00386490			0.00193245	−	0.999998i	$-0.499385\pi$
$751$	0.105915			0.00386490			0.00193245	+	0.999998i	$0.499385\pi$
$752$	89.5254	−	89.5254i	3.26466	−	3.26466i
$753$	11.5572	−	11.5572i	0.421167	−	0.421167i
$754$	−17.1408			−0.624232
$755$	−20.2657	+	22.2369i	−0.737545	+	0.809284i
$756$	−12.7831	+	2.59507i	−0.464918	+	0.0943816i
$757$	3.14514	+	3.14514i	0.114312	+	0.114312i	0.761949	−	0.647637i	$-0.224243\pi$
$757$	3.14514	+	3.14514i	0.114312	+	0.114312i	−0.647637	+	0.761949i	$0.724243\pi$
$758$	32.8059	−	32.8059i	1.19156	−	1.19156i
$759$	8.54387			0.310123
$760$	−3.16426	−	68.2269i	−0.114780	−	2.47485i
$761$		−	35.1123i		−	1.27282i	−0.771351	−	0.636410i	$-0.780419\pi$
$761$		−	35.1123i		−	1.27282i	0.771351	−	0.636410i	$-0.219581\pi$
$762$	20.6922	−	20.6922i	0.749599	−	0.749599i
$763$	16.4228	+	10.8801i	0.594547	+	0.393887i
$764$		−	38.6238i		−	1.39736i
$765$	6.65306	−	0.308559i	0.240542	−	0.0111560i
$766$			60.0318i			2.16904i
$767$	−2.83784	−	2.83784i	−0.102469	−	0.102469i
$768$	−6.98809	−	6.98809i	−0.252161	−	0.252161i
$769$	−8.16835			−0.294558			−0.147279	−	0.989095i	$-0.547052\pi$
$769$	−8.16835			−0.294558			−0.147279	+	0.989095i	$0.547052\pi$
$770$	11.6888	−	19.5545i	0.421235	−	0.704695i
$771$	−30.1304			−1.08512
$772$	66.8609	+	66.8609i	2.40638	+	2.40638i
$773$	2.51166	+	2.51166i	0.0903382	+	0.0903382i	0.750832	−	0.660494i	$-0.229653\pi$
$773$	2.51166	+	2.51166i	0.0903382	+	0.0903382i	−0.660494	+	0.750832i	$0.729653\pi$
$774$			19.3061i			0.693944i
$775$	30.3863	−	2.82462i	1.09151	−	0.101463i
$776$		−	94.7776i		−	3.40232i
$777$	7.03574	+	4.66118i	0.252406	+	0.167219i
$778$	28.6686	−	28.6686i	1.02782	−	1.02782i
$779$		−	3.04897i		−	0.109241i
$780$	9.32372	−	10.2306i	0.333843	−	0.366315i
$781$	−11.1554			−0.399171
$782$	32.3840	−	32.3840i	1.15805	−	1.15805i
$783$	−3.66686	−	3.66686i	−0.131043	−	0.131043i
$784$	28.5131	+	67.3327i	1.01833	+	2.40474i
$785$	0.241377	+	5.20449i	0.00861510	+	0.185756i
$786$	−16.2746			−0.580497
$787$	−12.7347	+	12.7347i	−0.453943	+	0.453943i	−0.896661	−	0.442718i	$-0.854014\pi$
$787$	−12.7347	+	12.7347i	−0.453943	+	0.453943i	0.442718	+	0.896661i	$0.354014\pi$
$788$	56.5935	−	56.5935i	2.01606	−	2.01606i
$789$	−23.1151			−0.822920
$790$	−1.23274	−	26.5800i	−0.0438590	−	0.945675i
$791$	−1.89408	−	9.33014i	−0.0673459	−	0.331742i
$792$	−7.97854	−	7.97854i	−0.283505	−	0.283505i
$793$	−1.26131	+	1.26131i	−0.0447903	+	0.0447903i
$794$	60.2300			2.13748
$795$	−1.15972	+	1.27252i	−0.0411309	+	0.0451316i
$796$		−	99.3261i		−	3.52052i
$797$	−23.3462	+	23.3462i	−0.826967	+	0.826967i	−0.987096	−	0.160129i	$-0.948809\pi$
$797$	−23.3462	+	23.3462i	−0.826967	+	0.826967i	0.160129	+	0.987096i	$0.448809\pi$
$798$	−22.9924	−	15.2325i	−0.813922	−	0.539224i
$799$			36.1010i			1.27716i
$800$	38.5464	−	46.4471i	1.36282	−	1.64215i
$801$		−	1.19991i		−	0.0423967i
$802$	1.81976	+	1.81976i	0.0642580	+	0.0642580i
$803$	9.96713	+	9.96713i	0.351732	+	0.351732i
$804$	41.3463			1.45817
$805$	29.6597	+	17.7293i	1.04537	+	0.624874i
$806$	−20.1743			−0.710609
$807$	11.7311	+	11.7311i	0.412955	+	0.412955i
$808$	−83.6806	−	83.6806i	−2.94387	−	2.94387i
$809$		−	27.8210i		−	0.978135i	−0.872246	−	0.489067i	$-0.837337\pi$
$809$		−	27.8210i		−	0.978135i	0.872246	−	0.489067i	$-0.162663\pi$
$810$	5.88016	−	0.272713i	0.206608	−	0.00958215i
$811$			5.12216i			0.179863i	0.995948	+	0.0899317i	$0.0286649\pi$
$811$			5.12216i			0.179863i	−0.995948	+	0.0899317i	$0.971335\pi$
$812$	−37.3582	+	56.3897i	−1.31102	+	1.97889i
$813$	5.50152	−	5.50152i	0.192947	−	0.192947i
$814$			12.2837i			0.430544i
$815$	1.50528	+	32.4563i	0.0527275	+	1.13690i
$816$	−31.1134			−1.08919
$817$	−20.5348	+	20.5348i	−0.718421	+	0.718421i
$818$	45.2656	+	45.2656i	1.58267	+	1.58267i
$819$	−0.660910	−	3.25560i	−0.0230941	−	0.113760i
$820$	5.71755	−	6.27368i	0.199665	−	0.219086i
$821$	−26.1405			−0.912308			−0.456154	−	0.889901i	$-0.650773\pi$
$821$	−26.1405			−0.912308			−0.456154	+	0.889901i	$0.650773\pi$
$822$	23.8391	−	23.8391i	0.831485	−	0.831485i
$823$	13.7296	−	13.7296i	0.478583	−	0.478583i	−0.426095	−	0.904678i	$-0.640111\pi$
$823$	13.7296	−	13.7296i	0.478583	−	0.478583i	0.904678	+	0.426095i	$0.140111\pi$
$824$	−90.6265			−3.15712
$825$	−4.67086	+	5.62823i	−0.162618	+	0.195950i
$826$	−21.8173	+	4.42907i	−0.759122	+	0.154107i
$827$	15.7484	+	15.7484i	0.547624	+	0.547624i	0.925753	−	0.378129i	$-0.123432\pi$
$827$	15.7484	+	15.7484i	0.547624	+	0.547624i	−0.378129	+	0.925753i	$0.623432\pi$
$828$	20.3618	−	20.3618i	0.707620	−	0.707620i
$829$	−47.2996			−1.64278			−0.821392	−	0.570365i	$-0.806802\pi$
$829$	−47.2996			−1.64278			−0.821392	+	0.570365i	$0.806802\pi$
$830$	−41.5807	−	37.8948i	−1.44329	−	1.31535i
$831$			30.1378i			1.04547i
$832$	−9.66613	+	9.66613i	−0.335113	+	0.335113i
$833$	−19.3249	−	7.82698i	−0.669567	−	0.271189i
$834$		−	31.5672i		−	1.09308i
$835$	0.0429270	+	0.925579i	0.00148555	+	0.0320310i
$836$		−	28.5575i		−	0.987683i
$837$	−4.31580	−	4.31580i	−0.149176	−	0.149176i
$838$	29.7635	+	29.7635i	1.02816	+	1.02816i
$839$	−10.8244			−0.373699			−0.186850	−	0.982389i	$-0.559828\pi$
$839$	−10.8244			−0.373699			−0.186850	+	0.982389i	$0.559828\pi$
$840$	−11.1410	−	44.2533i	−0.384402	−	1.52689i
$841$	2.10826			0.0726986
$842$	−27.3635	−	27.3635i	−0.943009	−	0.943009i
$843$	−14.9566	−	14.9566i	−0.515134	−	0.515134i
$844$			58.9947i			2.03068i
$845$	−18.8795	−	17.2059i	−0.649474	−	0.591901i
$846$			31.9071i			1.09699i
$847$	−12.9469	+	19.5424i	−0.444860	+	0.671486i
$848$	5.68725	−	5.68725i	0.195301	−	0.195301i
$849$		−	3.75433i		−	0.128848i
$850$	3.62875	+	39.0369i	0.124465	+	1.33895i
$851$	−18.6316			−0.638683
$852$	−26.5856	+	26.5856i	−0.910806	+	0.910806i
$853$	−33.5751	−	33.5751i	−1.14959	−	1.14959i	−0.986633	−	0.162958i	$-0.947897\pi$
$853$	−33.5751	−	33.5751i	−1.14959	−	1.14959i	−0.162958	−	0.986633i	$-0.552103\pi$
$854$	1.96854	+	9.69693i	0.0673622	+	0.331822i
$855$	6.54445	+	5.96431i	0.223815	+	0.203975i
$856$	47.8914			1.63689
$857$	−8.92479	+	8.92479i	−0.304865	+	0.304865i	−0.842914	−	0.538049i	$-0.819162\pi$
$857$	−8.92479	+	8.92479i	−0.304865	+	0.304865i	0.538049	+	0.842914i	$0.319162\pi$
$858$	3.41892	−	3.41892i	0.116720	−	0.116720i
$859$	−20.3701			−0.695020			−0.347510	−	0.937676i	$-0.612973\pi$
$859$	−20.3701			−0.695020			−0.347510	+	0.937676i	$0.612973\pi$
$860$	−80.7608	+	3.74556i	−2.75392	+	0.127723i
$861$	−0.405287	−	1.99642i	−0.0138122	−	0.0680378i
$862$	−41.4589	−	41.4589i	−1.41210	−	1.41210i
$863$	−14.9014	+	14.9014i	−0.507250	+	0.507250i	−0.913681	−	0.406431i	$-0.866773\pi$
$863$	−14.9014	+	14.9014i	−0.507250	+	0.507250i	0.406431	+	0.913681i	$0.366773\pi$
$864$	−12.0717			−0.410688
$865$	10.9041	−	0.505716i	0.370751	−	0.0171949i
$866$		−	104.306i		−	3.54446i
$867$	−5.74759	+	5.74759i	−0.195198	+	0.195198i
$868$	−43.9696	+	66.3692i	−1.49243	+	2.25272i
$869$		−	6.61223i		−	0.224305i
$870$	20.5617	−	22.5617i	0.697108	−	0.764914i
$871$			10.5301i			0.356797i
$872$	40.6122	+	40.6122i	1.37530	+	1.37530i
$873$	8.68829	+	8.68829i	0.294054	+	0.294054i
$874$	60.8869			2.05953
$875$	−27.8937	+	9.84575i	−0.942981	+	0.332847i
$876$	47.5074			1.60512
$877$	23.4634	+	23.4634i	0.792302	+	0.792302i	0.981868	−	0.189566i	$-0.0607080\pi$
$877$	23.4634	+	23.4634i	0.792302	+	0.792302i	−0.189566	+	0.981868i	$0.560708\pi$
$878$	−4.38667	−	4.38667i	−0.148043	−	0.148043i
$879$			2.21628i			0.0747532i
$880$	23.0147	−	25.2533i	0.775826	−	0.851290i
$881$			34.9639i			1.17796i	0.808147	+	0.588981i	$0.200471\pi$
$881$			34.9639i			1.17796i	−0.808147	+	0.588981i	$0.799529\pi$
$882$	−17.0799	−	6.91770i	−0.575109	−	0.232931i
$883$	19.3814	−	19.3814i	0.652235	−	0.652235i	−0.301295	−	0.953531i	$-0.597419\pi$
$883$	19.3814	−	19.3814i	0.652235	−	0.652235i	0.953531	+	0.301295i	$0.0974190\pi$
$884$		−	18.4379i		−	0.620135i
$885$	7.13953	−	0.331121i	0.239993	−	0.0111305i
$886$	20.3737			0.684466
$887$	19.2450	−	19.2450i	0.646184	−	0.646184i	−0.305884	−	0.952069i	$-0.598952\pi$
$887$	19.2450	−	19.2450i	0.646184	−	0.646184i	0.952069	+	0.305884i	$0.0989521\pi$
$888$	17.3988	+	17.3988i	0.583865	+	0.583865i
$889$	28.8224	−	5.85116i	0.966673	−	0.196242i
$890$	7.05565	−	0.327230i	0.236506	−	0.0109688i
$891$	1.46279			0.0490053
$892$	−3.25837	+	3.25837i	−0.109098	+	0.109098i
$893$	−33.9377	+	33.9377i	−1.13568	+	1.13568i
$894$	−0.254896			−0.00852500
$895$	−3.30135	−	3.00870i	−0.110352	−	0.100570i
$896$	2.37775	+	11.7126i	0.0794349	+	0.391292i
$897$	5.18572	+	5.18572i	0.173146	+	0.173146i
$898$	−2.23414	+	2.23414i	−0.0745541	+	0.0745541i
$899$	−31.6509			−1.05562
$900$	2.28161	+	24.5448i	0.0760536	+	0.818160i
$901$			2.29338i			0.0764035i
$902$	2.09657	−	2.09657i	0.0698082	−	0.0698082i
$903$	−10.7163	+	16.1755i	−0.356615	+	0.538286i
$904$		−	27.7565i		−	0.923169i
$905$	14.0236	+	12.7804i	0.466159	+	0.424836i
$906$			35.4204i			1.17676i
$907$	−14.8842	−	14.8842i	−0.494220	−	0.494220i	0.415413	−	0.909633i	$-0.363637\pi$
$907$	−14.8842	−	14.8842i	−0.494220	−	0.494220i	−0.909633	+	0.415413i	$0.863637\pi$
$908$	85.5312	+	85.5312i	2.83845	+	2.83845i
$909$	15.3420			0.508863
$910$	18.9632	−	4.77410i	0.628624	−	0.158260i
$911$	−23.7484			−0.786819			−0.393410	−	0.919363i	$-0.628705\pi$
$911$	−23.7484			−0.786819			−0.393410	+	0.919363i	$0.628705\pi$
$912$	−29.2490	−	29.2490i	−0.968530	−	0.968530i
$913$	−9.88545	−	9.88545i	−0.327161	−	0.327161i
$914$			78.4700i			2.59556i
$915$	−0.147170	−	3.17324i	−0.00486529	−	0.104904i
$916$			123.639i			4.08514i
$917$	−13.6356	−	9.03357i	−0.450286	−	0.298315i
$918$	5.54445	−	5.54445i	0.182994	−	0.182994i
$919$		−	35.7695i		−	1.17993i	−0.807430	−	0.589964i	$-0.799142\pi$
$919$		−	35.7695i		−	1.17993i	0.807430	−	0.589964i	$-0.200858\pi$
$920$	74.4597	+	67.8592i	2.45486	+	2.23725i
$921$	24.5439			0.808748
$922$	40.8909	−	40.8909i	1.34667	−	1.34667i
$923$	−6.77080	−	6.77080i	−0.222863	−	0.222863i
$924$	−3.79604	−	18.6990i	−0.124880	−	0.615153i
$925$	10.1857	−	12.2735i	0.334905	−	0.403549i
$926$	80.7042			2.65210
$927$	8.30776	−	8.30776i	0.272863	−	0.272863i
$928$	−44.2653	+	44.2653i	−1.45308	+	1.45308i
$929$	5.58936			0.183381			0.0916905	−	0.995788i	$-0.470773\pi$
$929$	5.58936			0.183381			0.0916905	+	0.995788i	$0.470773\pi$
$930$	24.2006	−	26.5545i	0.793569	−	0.870758i
$931$	−10.8089	−	25.5248i	−0.354247	−	0.836542i
$932$	11.0503	+	11.0503i	0.361963	+	0.361963i
$933$	21.9662	−	21.9662i	0.719140	−	0.719140i
$934$	26.4812			0.866491
$935$	0.451357	+	9.73202i	0.0147609	+	0.318271i
$936$		−	9.68519i		−	0.316570i
$937$	20.4143	−	20.4143i	0.666906	−	0.666906i	−0.290092	−	0.956999i	$-0.593686\pi$
$937$	20.4143	−	20.4143i	0.666906	−	0.666906i	0.956999	+	0.290092i	$0.0936861\pi$
$938$	48.6947	+	32.2603i	1.58994	+	1.05334i
$939$		−	8.09533i		−	0.264181i
$940$	−133.473	+	6.19027i	−4.35340	+	0.201904i
$941$			17.1143i			0.557910i	0.960304	+	0.278955i	$0.0899880\pi$
$941$			17.1143i			0.557910i	−0.960304	+	0.278955i	$0.910012\pi$
$942$	4.33726	+	4.33726i	0.141316	+	0.141316i
$943$	3.18002	+	3.18002i	0.103556	+	0.103556i
$944$	−33.3884			−1.08670
$945$	5.07802	+	3.03541i	0.165188	+	0.0987420i
$946$	−28.2408			−0.918187
$947$	6.82151	+	6.82151i	0.221669	+	0.221669i	0.809201	−	0.587532i	$-0.199900\pi$
$947$	6.82151	+	6.82151i	0.221669	+	0.221669i	−0.587532	+	0.809201i	$0.699900\pi$
$948$	−15.7583	−	15.7583i	−0.511806	−	0.511806i
$949$			12.0991i			0.392755i
$950$	−33.2863	+	40.1089i	−1.07995	+	1.30131i
$951$			1.06431i			0.0345125i
$952$	−50.6748	−	33.5721i	−1.64238	−	1.08808i
$953$	30.7169	−	30.7169i	0.995017	−	0.995017i	−0.00497101	−	0.999988i	$-0.501582\pi$
$953$	30.7169	−	30.7169i	0.995017	−	0.995017i	0.999988	+	0.00497101i	$0.00158233\pi$
$954$			2.02695i			0.0656249i
$955$	−11.7998	+	12.9476i	−0.381834	+	0.418974i
$956$	105.391			3.40859
$957$	5.36385	−	5.36385i	0.173389	−	0.173389i
$958$	59.1480	+	59.1480i	1.91099	+	1.91099i
$959$	33.2058	−	6.74102i	1.07227	−	0.217679i
$960$	−1.12785	−	24.3184i	−0.0364012	−	0.784872i
$961$	−6.25222			−0.201684
$962$	−7.45563	+	7.45563i	−0.240379	+	0.240379i
$963$	−4.39022	+	4.39022i	−0.141473	+	0.141473i
$964$	−3.07703			−0.0991046
$965$	−1.98685	−	42.8399i	−0.0639589	−	1.37906i
$966$	39.8678	−	8.09345i	1.28273	−	0.260403i
$967$	24.6730	+	24.6730i	0.793431	+	0.793431i	0.982050	−	0.188619i	$-0.0604012\pi$
$967$	24.6730	+	24.6730i	0.793431	+	0.793431i	−0.188619	+	0.982050i	$0.560401\pi$
$968$	−48.3267	+	48.3267i	−1.55328	+	1.55328i
$969$	11.7946			0.378898
$970$	−48.7191	+	53.4579i	−1.56428	+	1.71643i
$971$			21.2020i			0.680404i	0.940352	+	0.340202i	$0.110496\pi$
$971$			21.2020i			0.680404i	−0.940352	+	0.340202i	$0.889504\pi$
$972$	3.48612	−	3.48612i	0.111817	−	0.111817i
$973$	17.5220	−	26.4483i	0.561731	−	0.847895i
$974$			17.9232i			0.574297i
$975$	−6.25106	+	0.581079i	−0.200194	+	0.0186094i
$976$			14.8398i			0.475011i
$977$	8.19657	+	8.19657i	0.262231	+	0.262231i	0.825960	−	0.563729i	$-0.190634\pi$
$977$	8.19657	+	8.19657i	0.262231	+	0.262231i	−0.563729	+	0.825960i	$0.690634\pi$
$978$	27.0481	+	27.0481i	0.864902	+	0.864902i
$979$	1.75521			0.0560969
$980$	25.6243	−	72.7901i	0.818538	−	2.32519i
$981$	−7.44587			−0.237728
$982$	−52.7541	−	52.7541i	−1.68345	−	1.68345i
$983$	1.74914	+	1.74914i	0.0557891	+	0.0557891i	0.734451	−	0.678662i	$-0.237440\pi$
$983$	1.74914	+	1.74914i	0.0557891	+	0.0557891i	−0.678662	+	0.734451i	$0.737440\pi$
$984$		−	5.93921i		−	0.189335i
$985$	−36.2612	+	1.68174i	−1.15538	+	0.0535847i
$986$		−	40.6615i		−	1.29492i
$987$	−17.7107	+	26.7331i	−0.563738	+	0.850924i
$988$	17.3331	−	17.3331i	0.551438	−	0.551438i
$989$		−	42.8348i		−	1.36207i
$990$	0.398921	+	8.60143i	0.0126786	+	0.273371i
$991$	−37.1253			−1.17932			−0.589662	−	0.807650i	$-0.700739\pi$
$991$	−37.1253			−1.17932			−0.589662	+	0.807650i	$0.700739\pi$
$992$	−52.0991	+	52.0991i	−1.65415	+	1.65415i
$993$	11.1781	+	11.1781i	0.354727	+	0.354727i
$994$	−52.0539	+	10.5673i	−1.65105	+	0.335174i
$995$	−30.3449	+	33.2964i	−0.961996	+	1.05557i
$996$	−47.1180			−1.49299
$997$	40.5538	−	40.5538i	1.28435	−	1.28435i	0.346186	−	0.938166i	$-0.387476\pi$
$997$	40.5538	−	40.5538i	1.28435	−	1.28435i	0.938166	−	0.346186i	$-0.112524\pi$
$998$	6.31404	−	6.31404i	0.199868	−	0.199868i
$999$	−3.18990			−0.100924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.m.a.97.2	yes	16
3.2	odd	2		315.2.p.e.307.7		16
4.3	odd	2		1680.2.cz.d.97.3		16
5.2	odd	4		525.2.m.b.118.8		16
5.3	odd	4	inner	105.2.m.a.13.1	✓	16
5.4	even	2		525.2.m.b.307.7		16
7.2	even	3		735.2.v.a.472.1		32
7.3	odd	6		735.2.v.a.607.7		32
7.4	even	3		735.2.v.a.607.8		32
7.5	odd	6		735.2.v.a.472.2		32
7.6	odd	2	inner	105.2.m.a.97.1	yes	16
15.8	even	4		315.2.p.e.118.8		16
20.3	even	4		1680.2.cz.d.433.6		16
21.20	even	2		315.2.p.e.307.8		16
28.27	even	2		1680.2.cz.d.97.6		16
35.3	even	12		735.2.v.a.313.1		32
35.13	even	4	inner	105.2.m.a.13.2	yes	16
35.18	odd	12		735.2.v.a.313.2		32
35.23	odd	12		735.2.v.a.178.7		32
35.27	even	4		525.2.m.b.118.7		16
35.33	even	12		735.2.v.a.178.8		32
35.34	odd	2		525.2.m.b.307.8		16
105.83	odd	4		315.2.p.e.118.7		16
140.83	odd	4		1680.2.cz.d.433.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.1	✓	16	5.3	odd	4	inner
105.2.m.a.13.2	yes	16	35.13	even	4	inner
105.2.m.a.97.1	yes	16	7.6	odd	2	inner
105.2.m.a.97.2	yes	16	1.1	even	1	trivial
315.2.p.e.118.7		16	105.83	odd	4
315.2.p.e.118.8		16	15.8	even	4
315.2.p.e.307.7		16	3.2	odd	2
315.2.p.e.307.8		16	21.20	even	2
525.2.m.b.118.7		16	35.27	even	4
525.2.m.b.118.8		16	5.2	odd	4
525.2.m.b.307.7		16	5.4	even	2
525.2.m.b.307.8		16	35.34	odd	2
735.2.v.a.178.7		32	35.23	odd	12
735.2.v.a.178.8		32	35.33	even	12
735.2.v.a.313.1		32	35.3	even	12
735.2.v.a.313.2		32	35.18	odd	12
735.2.v.a.472.1		32	7.2	even	3
735.2.v.a.472.2		32	7.5	odd	6
735.2.v.a.607.7		32	7.3	odd	6
735.2.v.a.607.8		32	7.4	even	3
1680.2.cz.d.97.3		16	4.3	odd	2
1680.2.cz.d.97.6		16	28.27	even	2
1680.2.cz.d.433.3		16	140.83	odd	4
1680.2.cz.d.433.6		16	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86147 - 1.86147i) q^{2} +(0.707107 + 0.707107i) q^{3} +4.93012i q^{4} +(1.50619 - 1.65269i) q^{5} -2.63251i q^{6} +(1.46123 - 2.20563i) q^{7} +(5.45433 - 5.45433i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.86147 - 1.86147i) q^{2} +(0.707107 + 0.707107i) q^{3} +4.93012i q^{4} +(1.50619 - 1.65269i) q^{5} -2.63251i q^{6} +(1.46123 - 2.20563i) q^{7} +(5.45433 - 5.45433i) q^{8} +1.00000i q^{9} +(-5.88016 + 0.272713i) q^{10} -1.46279 q^{11} +(-3.48612 + 3.48612i) q^{12} +(-0.887844 - 0.887844i) q^{13} +(-6.82574 + 1.38567i) q^{14} +(2.23367 - 0.103594i) q^{15} -10.4459 q^{16} +(2.10614 - 2.10614i) q^{17} +(1.86147 - 1.86147i) q^{18} +3.95987 q^{19} +(8.14798 + 7.42570i) q^{20} +(2.59286 - 0.526369i) q^{21} +(2.72294 + 2.72294i) q^{22} +(-4.13007 + 4.13007i) q^{23} +7.71359 q^{24} +(-0.462789 - 4.97854i) q^{25} +3.30539i q^{26} +(-0.707107 + 0.707107i) q^{27} +(10.8740 + 7.20405i) q^{28} +5.18572i q^{29} +(-4.35074 - 3.96506i) q^{30} +6.10346i q^{31} +(8.53599 + 8.53599i) q^{32} +(-1.03435 - 1.03435i) q^{33} -7.84104 q^{34} +(-1.44434 - 5.73706i) q^{35} -4.93012 q^{36} +(2.25560 + 2.25560i) q^{37} +(-7.37117 - 7.37117i) q^{38} -1.25560i q^{39} +(-0.799082 - 17.2296i) q^{40} -0.769968i q^{41} +(-5.80635 - 3.84671i) q^{42} +(-5.18572 + 5.18572i) q^{43} -7.21173i q^{44} +(1.65269 + 1.50619i) q^{45} +15.3760 q^{46} +(-8.57041 + 8.57041i) q^{47} +(-7.38635 - 7.38635i) q^{48} +(-2.72961 - 6.44587i) q^{49} +(-8.40592 + 10.1289i) q^{50} +2.97854 q^{51} +(4.37718 - 4.37718i) q^{52} +(-0.544449 + 0.544449i) q^{53} +2.63251 q^{54} +(-2.20324 + 2.41754i) q^{55} +(-4.06020 - 20.0003i) q^{56} +(2.80005 + 2.80005i) q^{57} +(9.65306 - 9.65306i) q^{58} +3.19633 q^{59} +(0.510732 + 11.0123i) q^{60} -1.42064i q^{61} +(11.3614 - 11.3614i) q^{62} +(2.20563 + 1.46123i) q^{63} -10.8872i q^{64} +(-2.80460 + 0.130073i) q^{65} +3.85081i q^{66} +(-5.93012 - 5.93012i) q^{67} +(10.3835 + 10.3835i) q^{68} -5.84081 q^{69} +(-7.99077 + 13.3679i) q^{70} +7.62611 q^{71} +(5.45433 + 5.45433i) q^{72} +(-6.81378 - 6.81378i) q^{73} -8.39746i q^{74} +(3.19312 - 3.84760i) q^{75} +19.5226i q^{76} +(-2.13747 + 3.22637i) q^{77} +(-2.33726 + 2.33726i) q^{78} +4.52029i q^{79} +(-15.7335 + 17.2638i) q^{80} -1.00000 q^{81} +(-1.43327 + 1.43327i) q^{82} +(6.75794 + 6.75794i) q^{83} +(2.59507 + 12.7831i) q^{84} +(-0.308559 - 6.65306i) q^{85} +19.3061 q^{86} +(-3.66686 + 3.66686i) q^{87} +(-7.97854 + 7.97854i) q^{88} -1.19991 q^{89} +(-0.272713 - 5.88016i) q^{90} +(-3.25560 + 0.660910i) q^{91} +(-20.3618 - 20.3618i) q^{92} +(-4.31580 + 4.31580i) q^{93} +31.9071 q^{94} +(5.96431 - 6.54445i) q^{95} +12.0717i q^{96} +(8.68829 - 8.68829i) q^{97} +(-6.91770 + 17.0799i) q^{98} -1.46279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 24 q^{8}+O(q^{10}) \) 16 * q - 8 * q^7 + 24 * q^8	\( 16 q - 8 q^{7} + 24 q^{8} - 16 q^{11} + 8 q^{15} - 48 q^{16} + 8 q^{21} - 16 q^{22} - 40 q^{23} + 24 q^{28} - 8 q^{30} + 48 q^{32} - 8 q^{35} - 16 q^{36} + 32 q^{37} - 16 q^{42} - 16 q^{43} + 64 q^{46} - 72 q^{50} - 16 q^{51} + 24 q^{53} + 24 q^{56} + 8 q^{57} + 32 q^{58} + 40 q^{60} + 8 q^{63} + 40 q^{65} - 32 q^{67} - 40 q^{70} + 64 q^{71} + 24 q^{72} - 24 q^{77} - 8 q^{78} - 16 q^{81} + 48 q^{85} + 64 q^{86} - 64 q^{88} - 48 q^{91} - 40 q^{92} + 24 q^{93} - 72 q^{95} - 96 q^{98}+O(q^{100}) \) 16 * q - 8 * q^7 + 24 * q^8 - 16 * q^11 + 8 * q^15 - 48 * q^16 + 8 * q^21 - 16 * q^22 - 40 * q^23 + 24 * q^28 - 8 * q^30 + 48 * q^32 - 8 * q^35 - 16 * q^36 + 32 * q^37 - 16 * q^42 - 16 * q^43 + 64 * q^46 - 72 * q^50 - 16 * q^51 + 24 * q^53 + 24 * q^56 + 8 * q^57 + 32 * q^58 + 40 * q^60 + 8 * q^63 + 40 * q^65 - 32 * q^67 - 40 * q^70 + 64 * q^71 + 24 * q^72 - 24 * q^77 - 8 * q^78 - 16 * q^81 + 48 * q^85 + 64 * q^86 - 64 * q^88 - 48 * q^91 - 40 * q^92 + 24 * q^93 - 72 * q^95 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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