LMFDB - Embedded newform 429.2.bd.a.76.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(76,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("429.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bd (of order $12$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			76.3
Character	$\chi$	$=$	429.76
Dual form			429.2.bd.a.175.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00245 - 0.536555i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.98987 + 1.14885i) q^{4} +(1.79777 + 1.79777i) q^{5} +(0.536555 + 2.00245i) q^{6} +(-3.46337 + 0.928006i) q^{7} +(-0.436407 - 0.436407i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.00245 - 0.536555i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.98987 + 1.14885i) q^{4} +(1.79777 + 1.79777i) q^{5} +(0.536555 + 2.00245i) q^{6} +(-3.46337 + 0.928006i) q^{7} +(-0.436407 - 0.436407i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.63535 - 4.56456i) q^{10} +(-3.28617 - 0.448433i) q^{11} -2.29771i q^{12} +(2.85516 - 2.20183i) q^{13} +7.43315 q^{14} +(0.658030 - 2.45580i) q^{15} +(-1.65798 - 2.87170i) q^{16} +(-1.36897 + 2.37113i) q^{17} +(1.46590 - 1.46590i) q^{18} +(-2.08672 - 7.78774i) q^{19} +(1.51196 + 5.64271i) q^{20} +(2.53536 + 2.53536i) q^{21} +(6.33979 + 2.66118i) q^{22} +(5.11558 - 2.95348i) q^{23} +(-0.159736 + 0.596144i) q^{24} +1.46396i q^{25} +(-6.89873 + 2.87710i) q^{26} +1.00000 q^{27} +(-7.95780 - 2.13229i) q^{28} +(1.82021 - 1.05090i) q^{29} +(-2.63535 + 4.56456i) q^{30} +(-3.95542 - 3.95542i) q^{31} +(2.09867 + 7.83233i) q^{32} +(1.25473 + 3.07012i) q^{33} +(4.01355 - 4.01355i) q^{34} +(-7.89468 - 4.55800i) q^{35} +(-1.98987 + 1.14885i) q^{36} +(-8.89501 - 2.38341i) q^{37} +16.7142i q^{38} +(-3.33442 - 1.37173i) q^{39} -1.56912i q^{40} +(-4.90808 - 1.31512i) q^{41} +(-3.71658 - 6.43730i) q^{42} +(3.91232 - 6.77635i) q^{43} +(-6.02387 - 4.66765i) q^{44} +(-2.45580 + 0.658030i) q^{45} +(-11.8284 + 3.16942i) q^{46} +(-1.59250 + 1.59250i) q^{47} +(-1.65798 + 2.87170i) q^{48} +(5.07153 - 2.92805i) q^{49} +(0.785498 - 2.93152i) q^{50} +2.73795 q^{51} +(8.21099 - 1.10119i) q^{52} -11.7365 q^{53} +(-2.00245 - 0.536555i) q^{54} +(-5.10160 - 6.71396i) q^{55} +(1.91643 + 1.10645i) q^{56} +(-5.70102 + 5.70102i) q^{57} +(-4.20875 + 1.12773i) q^{58} +(-2.29035 - 8.54770i) q^{59} +(4.13075 - 4.13075i) q^{60} +(2.38447 + 1.37667i) q^{61} +(5.79824 + 10.0428i) q^{62} +(0.928006 - 3.46337i) q^{63} -10.1780i q^{64} +(9.09131 + 1.17455i) q^{65} +(-0.865246 - 6.82101i) q^{66} +(-2.84470 + 10.6166i) q^{67} +(-5.44816 + 3.14550i) q^{68} +(-5.11558 - 2.95348i) q^{69} +(13.3631 + 13.3631i) q^{70} +(14.8218 - 3.97149i) q^{71} +(0.596144 - 0.159736i) q^{72} +(8.33912 + 8.33912i) q^{73} +(16.5330 + 9.54533i) q^{74} +(1.26783 - 0.731982i) q^{75} +(4.79467 - 17.8940i) q^{76} +(11.7974 - 1.49650i) q^{77} +(5.94100 + 4.53593i) q^{78} -5.17408i q^{79} +(2.18200 - 8.14333i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.12257 + 5.26692i) q^{82} +(-5.79897 + 5.79897i) q^{83} +(2.13229 + 7.95780i) q^{84} +(-6.72385 + 1.80165i) q^{85} +(-11.4701 + 11.4701i) q^{86} +(-1.82021 - 1.05090i) q^{87} +(1.23841 + 1.62981i) q^{88} +(-2.10392 - 0.563744i) q^{89} +5.27069 q^{90} +(-7.84517 + 10.2753i) q^{91} +13.5725 q^{92} +(-1.44778 + 5.40320i) q^{93} +(4.04337 - 2.33444i) q^{94} +(10.2491 - 17.7520i) q^{95} +(5.73367 - 5.73367i) q^{96} +(-0.395823 + 0.106060i) q^{97} +(-11.7266 + 3.14212i) q^{98} +(2.03144 - 2.62169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

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 $

$2$	−2.00245	−	0.536555i	−1.41595	−	0.379402i	−0.531903	−	0.846805i	$-0.678523\pi$
$2$	−2.00245	−	0.536555i	−1.41595	−	0.379402i	−0.884044	+	0.467403i	$0.845190\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.98987	+	1.14885i	0.994936	+	0.574427i
$5$	1.79777	+	1.79777i	0.803988	+	0.803988i	0.983716	−	0.179728i	$-0.0575219\pi$
$5$	1.79777	+	1.79777i	0.803988	+	0.803988i	−0.179728	+	0.983716i	$0.557522\pi$
$6$	0.536555	+	2.00245i	0.219048	+	0.817498i
$7$	−3.46337	+	0.928006i	−1.30903	+	0.350753i	−0.844857	−	0.534992i	$-0.820315\pi$
$7$	−3.46337	+	0.928006i	−1.30903	+	0.350753i	−0.464172	+	0.885745i	$0.653648\pi$
$8$	−0.436407	−	0.436407i	−0.154293	−	0.154293i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.63535	−	4.56456i	−0.833370	−	1.44344i
$11$	−3.28617	−	0.448433i	−0.990817	−	0.135208i
$11$	−3.28617	−	0.448433i	−0.990817	−	0.135208i
$12$		−	2.29771i		−	0.663291i
$13$	2.85516	−	2.20183i	0.791880	−	0.610676i
$13$	2.85516	−	2.20183i	0.791880	−	0.610676i
$14$	7.43315			1.98659
$15$	0.658030	−	2.45580i	0.169903	−	0.634085i
$16$	−1.65798	−	2.87170i	−0.414495	−	0.717926i
$17$	−1.36897	+	2.37113i	−0.332025	+	0.575084i	−0.982909	−	0.184094i	$-0.941065\pi$
$17$	−1.36897	+	2.37113i	−0.332025	+	0.575084i	0.650884	+	0.759177i	$0.274398\pi$
$18$	1.46590	−	1.46590i	0.345515	−	0.345515i
$19$	−2.08672	−	7.78774i	−0.478726	−	1.78663i	−0.606787	−	0.794865i	$-0.707542\pi$
$19$	−2.08672	−	7.78774i	−0.478726	−	1.78663i	0.128060	−	0.991766i	$-0.459125\pi$
$20$	1.51196	+	5.64271i	0.338085	+	1.26175i
$21$	2.53536	+	2.53536i	0.553261	+	0.553261i
$22$	6.33979	+	2.66118i	1.35165	+	0.567365i
$23$	5.11558	−	2.95348i	1.06667	−	0.615844i	0.139402	−	0.990236i	$-0.455482\pi$
$23$	5.11558	−	2.95348i	1.06667	−	0.615844i	0.927271	+	0.374392i	$0.122149\pi$
$24$	−0.159736	+	0.596144i	−0.0326060	+	0.121687i
$25$			1.46396i			0.292793i
$26$	−6.89873	+	2.87710i	−1.35295	+	0.564245i
$27$	1.00000			0.192450
$28$	−7.95780	−	2.13229i	−1.50388	−	0.402964i
$29$	1.82021	−	1.05090i	0.338005	−	0.195147i	−0.321385	−	0.946949i	$-0.604148\pi$
$29$	1.82021	−	1.05090i	0.338005	−	0.195147i	0.659389	+	0.751802i	$0.270815\pi$
$30$	−2.63535	+	4.56456i	−0.481146	+	0.833370i
$31$	−3.95542	−	3.95542i	−0.710414	−	0.710414i	0.256207	−	0.966622i	$-0.417527\pi$
$31$	−3.95542	−	3.95542i	−0.710414	−	0.710414i	−0.966622	+	0.256207i	$0.917527\pi$
$32$	2.09867	+	7.83233i	0.370995	+	1.38457i
$33$	1.25473	+	3.07012i	0.218420	+	0.534440i
$34$	4.01355	−	4.01355i	0.688317	−	0.688317i
$35$	−7.89468	−	4.55800i	−1.33445	−	0.770442i
$36$	−1.98987	+	1.14885i	−0.331645	+	0.191476i
$37$	−8.89501	−	2.38341i	−1.46233	−	0.391830i	−0.562037	−	0.827112i	$-0.689982\pi$
$37$	−8.89501	−	2.38341i	−1.46233	−	0.391830i	−0.900294	+	0.435282i	$0.856649\pi$
$38$			16.7142i			2.71141i
$39$	−3.33442	−	1.37173i	−0.533934	−	0.219653i
$40$		−	1.56912i		−	0.248100i
$41$	−4.90808	−	1.31512i	−0.766514	−	0.205387i	−0.145683	−	0.989331i	$-0.546538\pi$
$41$	−4.90808	−	1.31512i	−0.766514	−	0.205387i	−0.620831	+	0.783945i	$0.713205\pi$
$42$	−3.71658	−	6.43730i	−0.573480	−	0.993297i
$43$	3.91232	−	6.77635i	0.596624	−	1.03338i	−0.396692	−	0.917952i	$-0.629842\pi$
$43$	3.91232	−	6.77635i	0.596624	−	1.03338i	0.993316	−	0.115431i	$-0.0368249\pi$
$44$	−6.02387	−	4.66765i	−0.908133	−	0.703675i
$45$	−2.45580	+	0.658030i	−0.366089	+	0.0980933i
$46$	−11.8284	+	3.16942i	−1.74401	+	0.467305i
$47$	−1.59250	+	1.59250i	−0.232290	+	0.232290i	−0.813648	−	0.581358i	$-0.802522\pi$
$47$	−1.59250	+	1.59250i	−0.232290	+	0.232290i	0.581358	+	0.813648i	$0.302522\pi$
$48$	−1.65798	+	2.87170i	−0.239309	+	0.414495i
$49$	5.07153	−	2.92805i	0.724505	−	0.418293i
$50$	0.785498	−	2.93152i	0.111086	−	0.414579i
$51$	2.73795			0.383389
$52$	8.21099	−	1.10119i	1.13866	−	0.152707i
$53$	−11.7365			−1.61213			−0.806065	−	0.591827i	$-0.798407\pi$
$53$	−11.7365			−1.61213			−0.806065	+	0.591827i	$0.798407\pi$
$54$	−2.00245	−	0.536555i	−0.272499	−	0.0730160i
$55$	−5.10160	−	6.71396i	−0.687900	−	0.905310i
$56$	1.91643	+	1.10645i	0.256093	+	0.147856i
$57$	−5.70102	+	5.70102i	−0.755119	+	0.755119i
$58$	−4.20875	+	1.12773i	−0.552636	+	0.148078i
$59$	−2.29035	−	8.54770i	−0.298178	−	1.11282i	−0.938660	−	0.344843i	$-0.887932\pi$
$59$	−2.29035	−	8.54770i	−0.298178	−	1.11282i	0.640482	−	0.767973i	$-0.278734\pi$
$60$	4.13075	−	4.13075i	0.533278	−	0.533278i
$61$	2.38447	+	1.37667i	0.305300	+	0.176265i	0.644821	−	0.764333i	$-0.276932\pi$
$61$	2.38447	+	1.37667i	0.305300	+	0.176265i	−0.339521	+	0.940598i	$0.610265\pi$
$62$	5.79824	+	10.0428i	0.736377	+	1.27544i
$63$	0.928006	−	3.46337i	0.116918	−	0.436343i
$64$		−	10.1780i		−	1.27225i
$65$	9.09131	+	1.17455i	1.12764	+	0.145686i
$66$	−0.865246	−	6.82101i	−0.106504	−	0.839608i
$67$	−2.84470	+	10.6166i	−0.347535	+	1.29702i	0.542087	+	0.840322i	$0.317634\pi$
$67$	−2.84470	+	10.6166i	−0.347535	+	1.29702i	−0.889622	+	0.456697i	$0.849032\pi$
$68$	−5.44816	+	3.14550i	−0.660687	+	0.381448i
$69$	−5.11558	−	2.95348i	−0.615844	−	0.355558i
$70$	13.3631	+	13.3631i	1.59720	+	1.59720i
$71$	14.8218	−	3.97149i	1.75902	−	0.471329i	0.772509	−	0.635004i	$-0.219001\pi$
$71$	14.8218	−	3.97149i	1.75902	−	0.471329i	0.986514	+	0.163675i	$0.0523348\pi$
$72$	0.596144	−	0.159736i	0.0702562	−	0.0188251i
$73$	8.33912	+	8.33912i	0.976021	+	0.976021i	0.999719	−	0.0236984i	$-0.00754415\pi$
$73$	8.33912	+	8.33912i	0.976021	+	0.976021i	−0.0236984	+	0.999719i	$0.507544\pi$
$74$	16.5330	+	9.54533i	1.92192	+	1.10962i
$75$	1.26783	−	0.731982i	0.146396	−	0.0845220i
$76$	4.79467	−	17.8940i	0.549986	−	2.05258i
$77$	11.7974	−	1.49650i	1.34443	−	0.170542i
$78$	5.94100	+	4.53593i	0.672686	+	0.513593i
$79$		−	5.17408i		−	0.582129i	−0.956703	−	0.291065i	$-0.905991\pi$
$79$		−	5.17408i		−	0.582129i	0.956703	−	0.291065i	$-0.0940095\pi$
$80$	2.18200	−	8.14333i	0.243955	−	0.910452i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	9.12257	+	5.26692i	1.00742	+	0.581634i
$83$	−5.79897	+	5.79897i	−0.636520	+	0.636520i	−0.949695	−	0.313175i	$-0.898607\pi$
$83$	−5.79897	+	5.79897i	−0.636520	+	0.636520i	0.313175	+	0.949695i	$0.398607\pi$
$84$	2.13229	+	7.95780i	0.232652	+	0.868267i
$85$	−6.72385	+	1.80165i	−0.729304	+	0.195416i
$86$	−11.4701	+	11.4701i	−1.23686	+	1.23686i
$87$	−1.82021	−	1.05090i	−0.195147	−	0.112668i
$88$	1.23841	+	1.62981i	0.132015	+	0.173738i
$89$	−2.10392	−	0.563744i	−0.223015	−	0.0597568i	0.145581	−	0.989346i	$-0.453495\pi$
$89$	−2.10392	−	0.563744i	−0.223015	−	0.0597568i	−0.368596	+	0.929590i	$0.620162\pi$
$90$	5.27069			0.555580
$91$	−7.84517	+	10.2753i	−0.822398	+	1.07715i
$92$	13.5725			1.41503
$93$	−1.44778	+	5.40320i	−0.150128	+	0.560286i
$94$	4.04337	−	2.33444i	0.417041	−	0.240779i
$95$	10.2491	−	17.7520i	1.05154	−	1.82132i
$96$	5.73367	−	5.73367i	0.585190	−	0.585190i
$97$	−0.395823	+	0.106060i	−0.0401897	+	0.0107688i	−0.278858	−	0.960332i	$-0.589956\pi$
$97$	−0.395823	+	0.106060i	−0.0401897	+	0.0107688i	0.238668	+	0.971101i	$0.423289\pi$
$98$	−11.7266	+	3.14212i	−1.18456	+	0.317403i
$99$	2.03144	−	2.62169i	0.204167	−	0.263490i
$100$	−1.68188	+	2.91310i	−0.168188	+	0.291310i
$101$	−8.30829	−	14.3904i	−0.826706	−	1.43190i	−0.900608	−	0.434631i	$-0.856879\pi$
$101$	−8.30829	−	14.3904i	−0.826706	−	1.43190i	0.0739023	−	0.997265i	$-0.476455\pi$
$102$	−5.48261	−	1.46906i	−0.542859	−	0.145459i
$103$			4.32507i			0.426162i	0.977035	+	0.213081i	$0.0683498\pi$
$103$			4.32507i			0.426162i	−0.977035	+	0.213081i	$0.931650\pi$
$104$	−2.20691	−	0.285122i	−0.216405	−	0.0279585i
$105$			9.11600i			0.889630i
$106$	23.5018	+	6.29728i	2.28269	+	0.611645i
$107$	−4.28769	+	2.47550i	−0.414507	+	0.239316i	−0.692724	−	0.721203i	$-0.743590\pi$
$107$	−4.28769	+	2.47550i	−0.414507	+	0.239316i	0.278218	+	0.960518i	$0.410256\pi$
$108$	1.98987	+	1.14885i	0.191476	+	0.110548i
$109$	−0.920074	+	0.920074i	−0.0881271	+	0.0881271i	−0.749796	−	0.661669i	$-0.769848\pi$
$109$	−0.920074	+	0.920074i	−0.0881271	+	0.0881271i	0.661669	+	0.749796i	$0.269848\pi$
$110$	6.61330	+	16.1817i	0.630553	+	1.54286i
$111$	2.38341	+	8.89501i	0.226223	+	0.844277i
$112$	8.40715	+	8.40715i	0.794401	+	0.794401i
$113$	2.77367	−	4.80413i	0.260924	−	0.451934i	−0.705563	−	0.708647i	$-0.749306\pi$
$113$	2.77367	−	4.80413i	0.260924	−	0.451934i	0.966488	+	0.256712i	$0.0826393\pi$
$114$	14.4749	−	8.35711i	1.35570	−	0.782715i
$115$	14.5063	+	3.88696i	1.35272	+	0.362461i
$116$	4.82932			0.448391
$117$	0.479254	+	3.57356i	0.0443071	+	0.330376i
$118$			18.3453i			1.68882i
$119$	2.54083	−	9.48251i	0.232918	−	0.869260i
$120$	−1.35890	+	0.784561i	−0.124050	+	0.0716203i
$121$	10.5978	+	2.94725i	0.963438	+	0.267932i
$122$	−4.03613	−	4.03613i	−0.365414	−	0.365414i
$123$	1.31512	+	4.90808i	0.118580	+	0.442547i
$124$	−3.32658	−	12.4150i	−0.298736	−	1.11490i
$125$	6.35698	−	6.35698i	0.568586	−	0.568586i
$126$	−3.71658	+	6.43730i	−0.331099	+	0.573480i
$127$	−6.88197	−	11.9199i	−0.610676	−	1.05772i	−0.991127	−	0.132920i	$-0.957565\pi$
$127$	−6.88197	−	11.9199i	−0.610676	−	1.05772i	0.380451	−	0.924801i	$-0.375769\pi$
$128$	−1.26373	+	4.71631i	−0.111699	+	0.416867i
$129$	−7.82465			−0.688922
$130$	−17.5747	−	7.22998i	−1.54140	−	0.634111i
$131$			8.32581i			0.727429i	0.931510	+	0.363715i	$0.118492\pi$
$131$			8.32581i			0.727429i	−0.931510	+	0.363715i	$0.881508\pi$
$132$	−1.03037	+	7.55065i	−0.0896820	+	0.657200i
$133$	14.4542	+	25.0353i	1.25333	+	2.17084i
$134$	11.3927	−	19.7328i	0.984184	−	1.70466i
$135$	1.79777	+	1.79777i	0.154728	+	0.154728i
$136$	1.63221	−	0.437349i	0.139961	−	0.0375024i
$137$	0.0189132	+	0.0705850i	0.00161586	+	0.00603048i	0.966729	−	0.255803i	$-0.0823397\pi$
$137$	0.0189132	+	0.0705850i	0.00161586	+	0.00603048i	−0.965113	+	0.261833i	$0.915673\pi$
$138$	8.65900	+	8.65900i	0.737103	+	0.737103i
$139$	−7.61466	−	4.39632i	−0.645867	−	0.372891i	0.141004	−	0.990009i	$-0.454967\pi$
$139$	−7.61466	−	4.39632i	−0.645867	−	0.372891i	−0.786871	+	0.617118i	$0.788300\pi$
$140$	−10.4729	−	18.1397i	−0.885125	−	1.53308i
$141$	2.17539	+	0.582895i	0.183201	+	0.0490886i
$142$	−31.8109			−2.66951
$143$	−10.3699	+	5.95522i	−0.867177	+	0.498001i
$144$	3.31596			0.276330
$145$	5.16160	+	1.38305i	0.428648	+	0.114856i
$146$	−12.2243	−	21.1731i	−1.01169	−	1.75230i
$147$	−5.07153	−	2.92805i	−0.418293	−	0.241502i
$148$	−14.9617	−	14.9617i	−1.22985	−	1.22985i
$149$	1.63433	+	6.09941i	0.133890	+	0.499683i	1.00000		0.000169794i	$-5.40471e-5\pi$
$149$	1.63433	+	6.09941i	0.133890	+	0.499683i	−0.866110	+	0.499853i	$0.833387\pi$
$150$	−2.93152	+	0.785498i	−0.239358	+	0.0641357i
$151$	−9.96724	−	9.96724i	−0.811123	−	0.811123i	0.173680	−	0.984802i	$-0.444434\pi$
$151$	−9.96724	−	9.96724i	−0.811123	−	0.811123i	−0.984802	+	0.173680i	$0.944434\pi$
$152$	−2.48797	+	4.30929i	−0.201801	+	0.349529i
$153$	−1.36897	−	2.37113i	−0.110675	−	0.191695i
$154$	−24.4266	−	3.33327i	−1.96835	−	0.268603i
$155$		−	14.2219i		−	1.14233i
$156$	−5.05915	−	6.56033i	−0.405056	−	0.525247i
$157$	21.4725			1.71369			0.856846	−	0.515572i	$-0.172420\pi$
$157$	21.4725			1.71369			0.856846	+	0.515572i	$0.172420\pi$
$158$	−2.77618	+	10.3608i	−0.220861	+	0.824265i
$159$	5.86824	+	10.1641i	0.465382	+	0.806065i
$160$	−10.3078	+	17.8537i	−0.814905	+	1.41146i
$161$	−14.9763	+	14.9763i	−1.18030	+	1.18030i
$162$	0.536555	+	2.00245i	0.0421558	+	0.157328i
$163$	0.366328	+	1.36715i	0.0286930	+	0.107084i	0.978787	−	0.204879i	$-0.0656802\pi$
$163$	0.366328	+	1.36715i	0.0286930	+	0.107084i	−0.950094	+	0.311963i	$0.899013\pi$
$164$	−8.25558	−	8.25558i	−0.644652	−	0.644652i
$165$	−3.26366	+	7.77510i	−0.254076	+	0.605290i
$166$	14.7236	−	8.50070i	1.14278	−	0.659782i
$167$	−3.39164	+	12.6578i	−0.262453	+	0.979489i	0.701337	+	0.712829i	$0.252587\pi$
$167$	−3.39164	+	12.6578i	−0.262453	+	0.979489i	−0.963791	+	0.266660i	$0.914080\pi$
$168$		−	2.21290i		−	0.170729i
$169$	3.30393	−	12.5731i	0.254148	−	0.967165i
$170$	14.4309			1.10680
$171$	7.78774	+	2.08672i	0.595544	+	0.159575i
$172$	15.5701	−	8.98937i	1.18721	−	0.685433i
$173$	4.80536	−	8.32312i	0.365345	−	0.632795i	−0.623487	−	0.781834i	$-0.714285\pi$
$173$	4.80536	−	8.32312i	0.365345	−	0.632795i	0.988831	+	0.149039i	$0.0476178\pi$
$174$	3.08102	+	3.08102i	0.233572	+	0.233572i
$175$	−1.35857	−	5.07025i	−0.102698	−	0.383275i
$176$	4.16063	+	10.1804i	0.313619	+	0.767376i
$177$	−6.25735	+	6.25735i	−0.470331	+	0.470331i
$178$	3.91052	+	2.25774i	0.293106	+	0.169225i
$179$	−11.2783	+	6.51151i	−0.842978	+	0.486693i	−0.858275	−	0.513190i	$-0.828464\pi$
$179$	−11.2783	+	6.51151i	−0.842978	+	0.486693i	0.0152976	+	0.999883i	$0.495130\pi$
$180$	−5.64271	−	1.51196i	−0.420583	−	0.112695i
$181$		−	19.8522i		−	1.47560i	−0.675019	−	0.737800i	$-0.735865\pi$
$181$		−	19.8522i		−	1.47560i	0.675019	−	0.737800i	$-0.264135\pi$
$182$	21.2229	−	16.3665i	1.57314	−	1.21317i
$183$		−	2.75335i		−	0.203533i
$184$	−3.52140	−	0.943556i	−0.259601	−	0.0695599i
$185$	−11.7064	−	20.2760i	−0.860669	−	1.49072i
$186$	5.79824	−	10.0428i	0.425147	−	0.736377i
$187$	5.56197	−	7.17804i	0.406732	−	0.524911i
$188$	−4.99842	+	1.33932i	−0.364547	+	0.0976801i
$189$	−3.46337	+	0.928006i	−0.251923	+	0.0675025i
$190$	−30.0484	+	30.0484i	−2.17994	+	2.17994i
$191$	−9.50879	+	16.4697i	−0.688032	+	1.19171i	0.284442	+	0.958693i	$0.408192\pi$
$191$	−9.50879	+	16.4697i	−0.688032	+	1.19171i	−0.972474	+	0.233013i	$0.925142\pi$
$192$	−8.81442	+	5.08900i	−0.636126	+	0.367267i
$193$	3.02261	−	11.2805i	0.217573	−	0.811992i	−0.767673	−	0.640842i	$-0.778585\pi$
$193$	3.02261	−	11.2805i	0.217573	−	0.811992i	0.985245	−	0.171149i	$-0.0547481\pi$
$194$	0.849524			0.0609922
$195$	−3.52846	−	8.46058i	−0.252678	−	0.605875i
$196$	13.4556			0.961115
$197$	−3.37143	−	0.903371i	−0.240204	−	0.0643625i	0.136708	−	0.990611i	$-0.456348\pi$
$197$	−3.37143	−	0.903371i	−0.240204	−	0.0643625i	−0.376913	+	0.926249i	$0.623014\pi$
$198$	−5.47454	+	4.15983i	−0.389059	+	0.295626i
$199$	3.98358	+	2.29992i	0.282388	+	0.163037i	0.634504	−	0.772920i	$-0.281204\pi$
$199$	3.98358	+	2.29992i	0.282388	+	0.163037i	−0.352116	+	0.935956i	$0.614538\pi$
$200$	0.638885	−	0.638885i	0.0451760	−	0.0451760i
$201$	10.6166	−	2.84470i	0.748835	−	0.200650i
$202$	8.91572	+	33.2739i	0.627308	+	2.34114i
$203$	−5.32882	+	5.32882i	−0.374010	+	0.374010i
$204$	5.44816	+	3.14550i	0.381448	+	0.220229i
$205$	−6.45933	−	11.1879i	−0.451139	−	0.781396i
$206$	2.32064	−	8.66074i	0.161687	−	0.603422i
$207$			5.90697i			0.410563i
$208$	−11.0568	−	4.54861i	−0.766650	−	0.315389i
$209$	3.36503	+	26.5276i	0.232764	+	1.83495i
$210$	4.89124	−	18.2543i	0.337527	−	1.25967i
$211$	−6.74420	+	3.89377i	−0.464290	+	0.268058i	−0.713846	−	0.700302i	$-0.753049\pi$
$211$	−6.74420	+	3.89377i	−0.464290	+	0.268058i	0.249556	+	0.968360i	$0.419715\pi$
$212$	−23.3541	−	13.4835i	−1.60397	−	0.926051i
$213$	−10.8503	−	10.8503i	−0.743451	−	0.743451i
$214$	9.91414	−	2.65649i	0.677717	−	0.181594i
$215$	19.2158	−	5.14885i	1.31051	−	0.351149i
$216$	−0.436407	−	0.436407i	−0.0296938	−	0.0296938i
$217$	17.3697	+	10.0284i	1.17913	+	0.680773i
$218$	2.33608	−	1.34873i	0.158219	−	0.0913478i
$219$	3.05233	−	11.3915i	0.206257	−	0.769763i
$220$	−2.43818	−	19.2209i	−0.164382	−	1.29587i
$221$	1.31217	+	9.78421i	0.0882663	+	0.658157i
$222$		−	19.0907i		−	1.28128i
$223$	−1.70810	+	6.37471i	−0.114383	+	0.426882i	−0.999240	−	0.0389801i	$-0.987589\pi$
$223$	−1.70810	+	6.37471i	−0.114383	+	0.426882i	0.884857	+	0.465862i	$0.154256\pi$
$224$	−14.5369	−	25.1787i	−0.971288	−	1.68232i
$225$	−1.26783	−	0.731982i	−0.0845220	−	0.0487988i
$226$	−8.13181	+	8.13181i	−0.540920	+	0.540920i
$227$	1.29876	+	4.84703i	0.0862016	+	0.321709i	0.995539	−	0.0943507i	$-0.0300775\pi$
$227$	1.29876	+	4.84703i	0.0862016	+	0.321709i	−0.909337	+	0.416059i	$0.863411\pi$
$228$	−17.8940	+	4.79467i	−1.18506	+	0.317535i
$229$	−1.73497	+	1.73497i	−0.114650	+	0.114650i	−0.762104	−	0.647454i	$-0.775834\pi$
$229$	−1.73497	+	1.73497i	−0.114650	+	0.114650i	0.647454	+	0.762104i	$0.275834\pi$
$230$	−26.9627	−	15.5669i	−1.77787	−	1.02645i
$231$	−7.19468	−	9.46856i	−0.473375	−	0.622986i
$232$	−1.25297	−	0.335733i	−0.0822618	−	0.0220420i
$233$	7.45106			0.488135			0.244067	−	0.969758i	$-0.421518\pi$
$233$	7.45106			0.488135			0.244067	+	0.969758i	$0.421518\pi$
$234$	0.957728	−	7.41303i	0.0626086	−	0.484605i
$235$	−5.72590			−0.373516
$236$	5.26255	−	19.6401i	0.342563	−	1.27846i
$237$	−4.48088	+	2.58704i	−0.291065	+	0.168046i
$238$	−10.1758	+	17.6250i	−0.659598	+	1.14246i
$239$	−1.63279	+	1.63279i	−0.105617	+	0.105617i	−0.757940	−	0.652324i	$-0.773794\pi$
$239$	−1.63279	+	1.63279i	−0.105617	+	0.105617i	0.652324	+	0.757940i	$0.273794\pi$
$240$	−8.14333	+	2.18200i	−0.525650	+	0.140847i
$241$	−9.12434	+	2.44486i	−0.587751	+	0.157487i	−0.540425	−	0.841392i	$-0.681737\pi$
$241$	−9.12434	+	2.44486i	−0.587751	+	0.157487i	−0.0473257	+	0.998880i	$0.515070\pi$
$242$	−19.6403	−	11.5881i	−1.26252	−	0.744908i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	3.16319	+	5.47881i	0.202503	+	0.350745i
$245$	14.3814	+	3.85349i	0.918796	+	0.246191i
$246$		−	10.5338i		−	0.671613i
$247$	−23.1052	−	17.6407i	−1.47015	−	1.12245i
$248$			3.45235i			0.219224i
$249$	7.92155	+	2.12257i	0.502008	+	0.134513i
$250$	−16.1404	+	9.31868i	−1.02081	+	0.589365i
$251$	14.8888	+	8.59603i	0.939770	+	0.542577i	0.889888	−	0.456179i	$-0.150782\pi$
$251$	14.8888	+	8.59603i	0.939770	+	0.542577i	0.0498819	+	0.998755i	$0.484116\pi$
$252$	5.82551	−	5.82551i	0.366973	−	0.366973i
$253$	−18.1351	+	7.41165i	−1.14014	+	0.465966i
$254$	7.38511	+	27.5616i	0.463383	+	1.72937i
$255$	4.92220	+	4.92220i	0.308240	+	0.308240i
$256$	−5.11688	+	8.86270i	−0.319805	+	0.553919i
$257$	11.8934	−	6.86665i	0.741889	−	0.428330i	−0.0808667	−	0.996725i	$-0.525769\pi$
$257$	11.8934	−	6.86665i	0.741889	−	0.428330i	0.822756	+	0.568395i	$0.192435\pi$
$258$	15.6685	+	4.19836i	0.975477	+	0.261378i
$259$	33.0185			2.05167
$260$	16.7412	+	12.7818i	1.03824	+	0.792694i
$261$			2.10180i			0.130098i
$262$	4.46726	−	16.6720i	0.275988	−	1.03000i
$263$	−13.6608	+	7.88707i	−0.842362	+	0.486338i	−0.858066	−	0.513539i	$-0.828334\pi$
$263$	−13.6608	+	7.88707i	−0.842362	+	0.486338i	0.0157046	+	0.999877i	$0.495001\pi$
$264$	0.792251	−	1.88740i	0.0487597	−	0.116161i
$265$	−21.0995	−	21.0995i	−1.29613	−	1.29613i
$266$	−15.5109	−	57.8875i	−0.951035	−	3.54931i
$267$	0.563744	+	2.10392i	0.0345006	+	0.128758i
$268$	−17.8575	+	17.8575i	−1.09082	+	1.09082i
$269$	−12.7197	+	22.0312i	−0.775534	+	1.34326i	0.158959	+	0.987285i	$0.449186\pi$
$269$	−12.7197	+	22.0312i	−0.775534	+	1.34326i	−0.934494	+	0.355980i	$0.884147\pi$
$270$	−2.63535	−	4.56456i	−0.160382	−	0.277790i
$271$	1.94127	−	7.24493i	0.117924	−	0.440098i	−0.881565	−	0.472062i	$-0.843510\pi$
$271$	1.94127	−	7.24493i	0.117924	−	0.440098i	0.999489	+	0.0319644i	$0.0101763\pi$
$272$	9.07891			0.550490
$273$	12.8213	+	1.65645i	0.775980	+	0.100253i
$274$		−	0.151491i		−	0.00915191i
$275$	0.656490	−	4.81084i	0.0395878	−	0.290104i
$276$	−6.78624	−	11.7541i	−0.408484	−	0.707514i
$277$	−6.44371	+	11.1608i	−0.387165	+	0.670589i	−0.992067	−	0.125711i	$-0.959879\pi$
$277$	−6.44371	+	11.1608i	−0.387165	+	0.670589i	0.604902	+	0.796300i	$0.293212\pi$
$278$	12.8891	+	12.8891i	0.773038	+	0.773038i
$279$	5.40320	−	1.44778i	0.323481	−	0.0866766i
$280$	1.45615	+	5.43444i	0.0870219	+	0.324770i
$281$	−1.12663	−	1.12663i	−0.0672088	−	0.0672088i	0.672703	−	0.739912i	$-0.265133\pi$
$281$	−1.12663	−	1.12663i	−0.0672088	−	0.0672088i	−0.739912	+	0.672703i	$0.765133\pi$
$282$	−4.04337	−	2.33444i	−0.240779	−	0.139014i
$283$	6.39963	+	11.0845i	0.380419	+	0.658904i	0.991122	−	0.132955i	$-0.0424466\pi$
$283$	6.39963	+	11.0845i	0.380419	+	0.658904i	−0.610704	+	0.791859i	$0.709113\pi$
$284$	34.0561	+	9.12531i	2.02086	+	0.541488i
$285$	−20.4983			−1.21421
$286$	23.9606	−	6.36100i	1.41682	−	0.376134i
$287$	18.2189			1.07543
$288$	−7.83233	−	2.09867i	−0.461525	−	0.123665i
$289$	4.75183	+	8.23040i	0.279519	+	0.484141i
$290$	−9.59378	−	5.53897i	−0.563366	−	0.325260i
$291$	0.289762	+	0.289762i	0.0169862	+	0.0169862i
$292$	7.01336	+	26.1742i	0.410426	+	1.53173i
$293$	−5.33155	+	1.42858i	−0.311472	+	0.0834588i	−0.411169	−	0.911559i	$-0.634879\pi$
$293$	−5.33155	+	1.42858i	−0.311472	+	0.0834588i	0.0996967	+	0.995018i	$0.468213\pi$
$294$	8.58444	+	8.58444i	0.500655	+	0.500655i
$295$	11.2493	−	19.4843i	0.654959	−	1.13442i
$296$	2.84171	+	4.92199i	0.165171	+	0.286085i
$297$	−3.28617	−	0.448433i	−0.190683	−	0.0260207i
$298$		−	13.0907i		−	0.758323i
$299$	8.10278	−	19.6963i	0.468596	−	1.13907i
$300$	3.36376			0.194207
$301$	−7.26132	+	27.0996i	−0.418536	+	1.56200i
$302$	14.6109	+	25.3069i	0.840765	+	1.45625i
$303$	−8.30829	+	14.3904i	−0.477299	+	0.826706i
$304$	−18.9044	+	18.9044i	−1.08424	+	1.08424i
$305$	1.81179	+	6.76168i	0.103743	+	0.387173i
$306$	1.46906	+	5.48261i	0.0839806	+	0.313420i
$307$	0.832445	+	0.832445i	0.0475101	+	0.0475101i	0.730463	−	0.682953i	$-0.239304\pi$
$307$	0.832445	+	0.832445i	0.0475101	+	0.0475101i	−0.682953	+	0.730463i	$0.739304\pi$
$308$	25.1945	+	10.5756i	1.43559	+	0.602600i
$309$	3.74562	−	2.16253i	0.213081	−	0.123022i
$310$	−7.63083	+	28.4786i	−0.433402	+	1.61748i
$311$			0.521985i			0.0295990i	0.999890	+	0.0147995i	$0.00471100\pi$
$311$			0.521985i			0.0295990i	−0.999890	+	0.0147995i	$0.995289\pi$
$312$	0.856531	+	2.05380i	0.0484915	+	0.116273i
$313$	12.4320			0.702695			0.351348	−	0.936245i	$-0.385723\pi$
$313$	12.4320			0.702695			0.351348	+	0.936245i	$0.385723\pi$
$314$	−42.9977	−	11.5212i	−2.42650	−	0.650178i
$315$	7.89468	−	4.55800i	0.444815	−	0.256814i
$316$	5.94426	−	10.2958i	0.334391	−	0.579181i
$317$	−12.5213	−	12.5213i	−0.703265	−	0.703265i	0.261845	−	0.965110i	$-0.415669\pi$
$317$	−12.5213	−	12.5213i	−0.703265	−	0.703265i	−0.965110	+	0.261845i	$0.915669\pi$
$318$	−6.29728	−	23.5018i	−0.353134	−	1.31791i
$319$	−6.45278	+	2.63719i	−0.361286	+	0.147654i
$320$	18.2977	−	18.2977i	1.02287	−	1.02287i
$321$	4.28769	+	2.47550i	0.239316	+	0.138169i
$322$	38.0249	−	21.9537i	2.11905	−	1.22343i
$323$	21.3224	+	5.71333i	1.18641	+	0.317898i
$324$		−	2.29771i		−	0.127650i
$325$	3.22339	+	4.17986i	0.178802	+	0.231857i
$326$		−	2.93422i		−	0.162511i
$327$	1.25684	+	0.336771i	0.0695037	+	0.0186235i
$328$	1.56800	+	2.71585i	0.0865781	+	0.149958i
$329$	4.03756	−	6.99325i	0.222598	−	0.385551i
$330$	10.7071	−	13.8181i	0.589406	−	0.760663i
$331$	6.59575	−	1.76733i	0.362535	−	0.0971410i	−0.0729532	−	0.997335i	$-0.523242\pi$
$331$	6.59575	−	1.76733i	0.362535	−	0.0971410i	0.435488	+	0.900194i	$0.356576\pi$
$332$	−18.2014	+	4.87705i	−0.998931	+	0.267663i
$333$	6.51160	−	6.51160i	0.356833	−	0.356833i
$334$	13.5832	−	23.5268i	0.743240	−	1.28733i
$335$	−24.2003	+	13.9720i	−1.32220	+	0.763374i
$336$	3.07723	−	11.4844i	0.167877	−	0.626524i
$337$	30.0845			1.63881			0.819403	−	0.573218i	$-0.194305\pi$
$337$	30.0845			1.63881			0.819403	+	0.573218i	$0.194305\pi$
$338$	−13.3622	+	23.4044i	−0.726805	+	1.27303i
$339$	−5.54733			−0.301290
$340$	−15.4494	−	4.13966i	−0.837863	−	0.224505i
$341$	11.2244	+	14.7719i	0.607837	+	0.799944i
$342$	−14.4749	−	8.35711i	−0.782715	−	0.451901i
$343$	2.90019	−	2.90019i	0.156595	−	0.156595i
$344$	−4.66461	+	1.24988i	−0.251499	+	0.0673890i
$345$	−3.88696	−	14.5063i	−0.209267	−	0.780995i
$346$	−14.0883	+	14.0883i	−0.757393	+	0.757393i
$347$	−15.5560	−	8.98126i	−0.835090	−	0.482139i	0.0205024	−	0.999790i	$-0.493473\pi$
$347$	−15.5560	−	8.98126i	−0.835090	−	0.482139i	−0.855592	+	0.517650i	$0.826807\pi$
$348$	−2.41466	−	4.18231i	−0.129439	−	0.224195i
$349$	−3.15760	+	11.7843i	−0.169022	+	0.630800i	0.828470	+	0.560033i	$0.189211\pi$
$349$	−3.15760	+	11.7843i	−0.169022	+	0.630800i	−0.997493	+	0.0707674i	$0.977455\pi$
$350$			10.8819i			0.581661i
$351$	2.85516	−	2.20183i	0.152397	−	0.117525i
$352$	−3.38430	−	26.6795i	−0.180384	−	1.42202i
$353$	−4.05413	+	15.1302i	−0.215780	+	0.805301i	0.770111	+	0.637910i	$0.220201\pi$
$353$	−4.05413	+	15.1302i	−0.215780	+	0.805301i	−0.985891	+	0.167391i	$0.946466\pi$
$354$	15.8875	−	9.17263i	0.844409	−	0.487520i
$355$	33.7860	+	19.5064i	1.79318	+	1.03529i
$356$	−3.53888	−	3.53888i	−0.187560	−	0.187560i
$357$	−9.48251	+	2.54083i	−0.501868	+	0.134475i
$358$	26.0780	−	6.98758i	1.37826	−	0.369305i
$359$	4.92223	+	4.92223i	0.259785	+	0.259785i	0.824967	−	0.565181i	$-0.191194\pi$
$359$	4.92223	+	4.92223i	0.259785	+	0.259785i	−0.565181	+	0.824967i	$0.691194\pi$
$360$	1.35890	+	0.784561i	0.0716203	+	0.0413500i
$361$	−39.8401	+	23.0017i	−2.09685	+	1.21061i
$362$	−10.6518	+	39.7530i	−0.559846	+	2.08937i
$363$	−2.74651	−	10.6516i	−0.144154	−	0.559064i
$364$	−27.4158	+	11.4337i	−1.43698	+	0.599287i
$365$			29.9837i			1.56942i
$366$	−1.47732	+	5.51345i	−0.0772210	+	0.288193i
$367$	7.15964	+	12.4009i	0.373730	+	0.647319i	0.990136	−	0.140109i	$-0.0447453\pi$
$367$	7.15964	+	12.4009i	0.373730	+	0.647319i	−0.616406	+	0.787428i	$0.711412\pi$
$368$	−16.9631	−	9.79363i	−0.884260	−	0.510528i
$369$	3.59296	−	3.59296i	0.187042	−	0.187042i
$370$	12.5622	+	46.8829i	0.653079	+	2.43733i
$371$	40.6478	−	10.8915i	2.11033	−	0.565460i
$372$	−9.08840	+	9.08840i	−0.471211	+	0.471211i
$373$	5.69863	+	3.29011i	0.295064	+	0.170355i	0.640223	−	0.768189i	$-0.278842\pi$
$373$	5.69863	+	3.29011i	0.295064	+	0.170355i	−0.345159	+	0.938544i	$0.612175\pi$
$374$	−14.9890	+	11.3894i	−0.775063	+	0.588931i
$375$	−8.68380	−	2.32682i	−0.448430	−	0.120156i
$376$	1.38996			0.0716815
$377$	2.88311	−	7.00828i	0.148488	−	0.360945i
$378$	7.43315			0.382320
$379$	6.87917	−	25.6734i	0.353359	−	1.31875i	−0.529178	−	0.848511i	$-0.677500\pi$
$379$	6.87917	−	25.6734i	0.353359	−	1.31875i	0.882537	−	0.470243i	$-0.155834\pi$
$380$	40.7890	−	23.5495i	2.09243	−	1.20806i
$381$	−6.88197	+	11.9199i	−0.352574	+	0.610676i
$382$	27.8778	−	27.8778i	1.42635	−	1.42635i
$383$	−10.9639	+	2.93776i	−0.560227	+	0.150112i	−0.527811	−	0.849362i	$-0.676987\pi$
$383$	−10.9639	+	2.93776i	−0.560227	+	0.150112i	−0.0324165	+	0.999474i	$0.510320\pi$
$384$	4.71631	−	1.26373i	0.240678	−	0.0644896i
$385$	23.8993	+	18.5186i	1.21802	+	0.943795i
$386$	−12.1053	+	20.9670i	−0.616143	+	1.06719i
$387$	3.91232	+	6.77635i	0.198875	+	0.344461i
$388$	−0.909485	−	0.243696i	−0.0461721	−	0.0123718i
$389$		−	20.2722i		−	1.02784i	−0.857838	−	0.513920i	$-0.828193\pi$
$389$		−	20.2722i		−	1.02784i	0.857838	−	0.513920i	$-0.171807\pi$
$390$	2.52600	+	18.8351i	0.127909	+	0.953754i
$391$			16.1730i			0.817902i
$392$	−3.49108	−	0.935432i	−0.176326	−	0.0472464i
$393$	7.21036	−	4.16290i	0.363715	−	0.209991i
$394$	6.26641	+	3.61791i	0.315697	+	0.182268i
$395$	9.30181	−	9.30181i	0.468025	−	0.468025i
$396$	7.05424	−	2.88300i	0.354489	−	0.144876i
$397$	−8.46588	−	31.5951i	−0.424890	−	1.58571i	−0.764162	−	0.645024i	$-0.776847\pi$
$397$	−8.46588	−	31.5951i	−0.424890	−	1.58571i	0.339272	−	0.940688i	$-0.389819\pi$
$398$	−6.74289	−	6.74289i	−0.337990	−	0.337990i
$399$	14.4542	−	25.0353i	0.723613	−	1.25333i
$400$	4.20407	−	2.42722i	0.210204	−	0.121361i
$401$	4.24394	+	1.13716i	0.211932	+	0.0567871i	0.363223	−	0.931702i	$-0.381676\pi$
$401$	4.24394	+	1.13716i	0.211932	+	0.0567871i	−0.151291	+	0.988489i	$0.548343\pi$
$402$	−22.7855			−1.13644
$403$	−20.0025	−	2.58423i	−0.996396	−	0.128730i
$404$		−	38.1800i		−	1.89953i
$405$	0.658030	−	2.45580i	0.0326978	−	0.122030i
$406$	13.5299	−	7.81150i	0.671478	−	0.387678i
$407$	28.1617	+	11.8211i	1.39592	+	0.585951i
$408$	−1.19486	−	1.19486i	−0.0591544	−	0.0591544i
$409$	−9.64809	−	36.0071i	−0.477067	−	1.78044i	−0.613396	−	0.789775i	$-0.710197\pi$
$409$	−9.64809	−	36.0071i	−0.477067	−	1.78044i	0.136329	−	0.990664i	$-0.456470\pi$
$410$	6.93158	+	25.8690i	0.342326	+	1.27758i
$411$	0.0516718	−	0.0516718i	0.00254878	−	0.00254878i
$412$	−4.96887	+	8.60633i	−0.244799	+	0.424004i
$413$	15.8646	+	27.4784i	0.780648	+	1.35212i
$414$	3.16942	−	11.8284i	0.155768	−	0.581335i
$415$	−20.8505			−1.02351
$416$	23.2375	+	17.7417i	1.13931	+	0.869858i
$417$			8.79265i			0.430578i
$418$	7.49521	−	54.9258i	0.366603	−	2.68651i
$419$	−4.36045	−	7.55252i	−0.213022	−	0.368965i	0.739637	−	0.673006i	$-0.234997\pi$
$419$	−4.36045	−	7.55252i	−0.213022	−	0.368965i	−0.952659	+	0.304041i	$0.901664\pi$
$420$	−10.4729	+	18.1397i	−0.511027	+	0.885125i
$421$	8.15638	+	8.15638i	0.397518	+	0.397518i	0.877357	−	0.479839i	$-0.159305\pi$
$421$	8.15638	+	8.15638i	0.397518	+	0.397518i	−0.479839	+	0.877357i	$0.659305\pi$
$422$	15.5942	−	4.17844i	0.759112	−	0.203403i
$423$	−0.582895	−	2.17539i	−0.0283413	−	0.105771i
$424$	5.12189	+	5.12189i	0.248741	+	0.248741i
$425$	−3.47125	−	2.00413i	−0.168380	−	0.0972145i
$426$	15.9054	+	27.5490i	0.770621	+	1.33475i
$427$	−9.53586	−	2.55513i	−0.461473	−	0.123651i
$428$	−11.3759			−0.549877
$429$	10.3423	+	6.00301i	0.499333	+	0.289828i
$430$	−41.2413			−1.98883
$431$	35.3821	+	9.48061i	1.70430	+	0.456665i	0.974015	−	0.226482i	$-0.0727224\pi$
$431$	35.3821	+	9.48061i	1.70430	+	0.456665i	0.730281	+	0.683147i	$0.239389\pi$
$432$	−1.65798	−	2.87170i	−0.0797695	−	0.138165i
$433$	−9.37156	−	5.41067i	−0.450369	−	0.260020i	0.257617	−	0.966247i	$-0.417063\pi$
$433$	−9.37156	−	5.41067i	−0.450369	−	0.260020i	−0.707986	+	0.706227i	$0.750396\pi$
$434$	−29.4012	−	29.4012i	−1.41130	−	1.41130i
$435$	−1.38305	−	5.16160i	−0.0663120	−	0.247480i
$436$	−2.88786	+	0.773800i	−0.138303	+	0.0370583i
$437$	−33.6758	−	33.6758i	−1.61093	−	1.61093i
$438$	−12.2243	+	21.1731i	−0.584099	+	1.01169i
$439$	12.8123	+	22.1916i	0.611500	+	1.05915i	0.990988	+	0.133952i	$0.0427667\pi$
$439$	12.8123	+	22.1916i	0.611500	+	1.05915i	−0.379488	+	0.925197i	$0.623900\pi$
$440$	−0.703646	+	5.15640i	−0.0335450	+	0.245822i
$441$			5.85610i			0.278862i
$442$	2.62221	−	20.2965i	0.124726	−	0.965404i
$443$	−22.3406			−1.06144			−0.530718	−	0.847549i	$-0.678078\pi$
$443$	−22.3406			−1.06144			−0.530718	+	0.847549i	$0.678078\pi$
$444$	−5.47638	+	20.4381i	−0.259897	+	0.969951i
$445$	−2.76889	−	4.79585i	−0.131258	−	0.227345i
$446$	6.84077	−	11.8486i	0.323920	−	0.561046i
$447$	4.46508	−	4.46508i	0.211191	−	0.211191i
$448$	9.44526	+	35.2502i	0.446246	+	1.66541i
$449$	1.35064	+	5.04065i	0.0637405	+	0.237883i	0.990445	−	0.137908i	$-0.0440378\pi$
$449$	1.35064	+	5.04065i	0.0637405	+	0.237883i	−0.926705	+	0.375791i	$0.877371\pi$
$450$	2.14602	+	2.14602i	0.101164	+	0.101164i
$451$	15.5390	+	6.52264i	0.731705	+	0.307139i
$452$	11.0385	−	6.37307i	0.519206	−	0.299764i
$453$	−3.64826	+	13.6155i	−0.171410	+	0.639712i
$454$		−	10.4028i		−	0.488228i
$455$	−32.5765	+	4.36888i	−1.52721	+	0.204816i
$456$	4.97594			0.233020
$457$	26.0730	+	6.98623i	1.21964	+	0.326802i	0.810538	−	0.585686i	$-0.199175\pi$
$457$	26.0730	+	6.98623i	1.21964	+	0.326802i	0.409103	+	0.912488i	$0.365842\pi$
$458$	4.40509	−	2.54328i	0.205837	−	0.118840i
$459$	−1.36897	+	2.37113i	−0.0638982	+	0.110675i
$460$	24.4002	+	24.4002i	1.13767	+	1.13767i
$461$	−3.63876	−	13.5800i	−0.169474	−	0.632486i	−0.997427	−	0.0716883i	$-0.977161\pi$
$461$	−3.63876	−	13.5800i	−0.169474	−	0.632486i	0.827953	−	0.560797i	$-0.189505\pi$
$462$	9.32660	+	22.8207i	0.433913	+	1.06171i
$463$	−5.11693	+	5.11693i	−0.237804	+	0.237804i	−0.815940	−	0.578136i	$-0.803780\pi$
$463$	−5.11693	+	5.11693i	−0.237804	+	0.237804i	0.578136	+	0.815940i	$0.303780\pi$
$464$	−6.03574	−	3.48474i	−0.280202	−	0.161775i
$465$	−12.3165	+	7.11094i	−0.571165	+	0.329762i
$466$	−14.9204	−	3.99790i	−0.691173	−	0.185199i
$467$		−	25.7994i		−	1.19385i	−0.802296	−	0.596926i	$-0.796389\pi$
$467$		−	25.7994i		−	1.19385i	0.802296	−	0.596926i	$-0.203611\pi$
$468$	−3.15184	+	7.66152i	−0.145694	+	0.354154i
$469$		−	39.4089i		−	1.81974i
$470$	11.4658	+	3.07226i	0.528879	+	0.141713i
$471$	−10.7363	−	18.5957i	−0.494700	−	0.856846i
$472$	−2.73075	+	4.72980i	−0.125693	+	0.217707i
$473$	−15.8953	+	20.5138i	−0.730867	+	0.943226i
$474$	10.3608	−	2.77618i	0.475889	−	0.127514i
$475$	11.4010	−	3.05488i	0.523113	−	0.140168i
$476$	15.9499	−	15.9499i	0.731064	−	0.731064i
$477$	5.86824	−	10.1641i	0.268688	−	0.465382i
$478$	4.14568	−	2.39351i	0.189619	−	0.109477i
$479$	0.896045	−	3.34409i	0.0409414	−	0.152795i	−0.942429	−	0.334406i	$-0.891464\pi$
$479$	0.896045	−	3.34409i	0.0409414	−	0.152795i	0.983371	+	0.181611i	$0.0581310\pi$
$480$	20.6156			0.940971
$481$	−30.6446	+	12.7802i	−1.39727	+	0.582728i
$482$	19.5829			0.891975
$483$	20.4580	+	5.48170i	0.930871	+	0.249426i
$484$	17.7023	+	18.0400i	0.804652	+	0.820000i
$485$	−0.902271	−	0.520927i	−0.0409700	−	0.0236541i
$486$	1.46590	−	1.46590i	0.0664944	−	0.0664944i
$487$	−27.6019	+	7.39590i	−1.25076	+	0.335140i	−0.822630	−	0.568577i	$-0.807494\pi$
$487$	−27.6019	+	7.39590i	−1.25076	+	0.335140i	−0.428130	+	0.903717i	$0.640827\pi$
$488$	−0.439810	−	1.64139i	−0.0199092	−	0.0743023i
$489$	1.00083	−	1.00083i	0.0452589	−	0.0452589i
$490$	−26.7305	−	15.4329i	−1.20756	−	0.697186i
$491$	−3.92829	−	6.80400i	−0.177281	−	0.307060i	0.763667	−	0.645610i	$-0.223397\pi$
$491$	−3.92829	−	6.80400i	−0.177281	−	0.307060i	−0.940948	+	0.338550i	$0.890064\pi$
$492$	−3.02175	+	11.2773i	−0.136231	+	0.508421i
$493$			5.75461i			0.259175i
$494$	36.8018	+	47.7219i	1.65579	+	2.14711i
$495$	8.36526	−	1.06114i	0.375991	−	0.0476945i
$496$	−4.80079	+	17.9168i	−0.215562	+	0.804488i
$497$	−47.6477	+	27.5094i	−2.13729	+	1.23397i
$498$	−14.7236	−	8.50070i	−0.659782	−	0.380925i
$499$	4.94890	+	4.94890i	0.221543	+	0.221543i	0.809148	−	0.587605i	$-0.199929\pi$
$499$	4.94890	+	4.94890i	0.221543	+	0.221543i	−0.587605	+	0.809148i	$0.699929\pi$
$500$	19.9528	−	5.34634i	0.892318	−	0.239096i
$501$	12.6578	−	3.39164i	0.565508	−	0.151527i
$502$	−25.2018	−	25.2018i	−1.12481	−	1.12481i
$503$	−27.4130	−	15.8269i	−1.22228	−	0.705686i	−0.256880	−	0.966443i	$-0.582695\pi$
$503$	−27.4130	−	15.8269i	−1.22228	−	0.705686i	−0.965405	+	0.260757i	$0.916028\pi$
$504$	−1.91643	+	1.10645i	−0.0853645	+	0.0492852i
$505$	10.9342	−	40.8070i	0.486566	−	1.81589i
$506$	40.2915	−	5.11098i	1.79117	−	0.227211i
$507$	−12.5406	+	3.42529i	−0.556949	+	0.152122i
$508$		−	31.6255i		−	1.40315i
$509$	−2.21788	+	8.27724i	−0.0983058	+	0.366882i	−0.997500	−	0.0706677i	$-0.977487\pi$
$509$	−2.21788	+	8.27724i	−0.0983058	+	0.366882i	0.899194	+	0.437550i	$0.144154\pi$
$510$	−7.21544	−	12.4975i	−0.319505	−	0.553399i
$511$	−36.6202	−	21.1427i	−1.61998	−	0.935297i
$512$	21.9068	−	21.9068i	0.968153	−	0.968153i
$513$	−2.08672	−	7.78774i	−0.0921309	−	0.343837i
$514$	−27.5003	+	7.36868i	−1.21299	+	0.325018i
$515$	−7.77548	+	7.77548i	−0.342629	+	0.342629i
$516$	−15.5701	−	8.98937i	−0.685433	−	0.395735i
$517$	5.94735	−	4.51909i	0.261564	−	0.198749i
$518$	−66.1180	−	17.7163i	−2.90506	−	0.778408i
$519$	−9.61071			−0.421864
$520$	−3.45493	−	4.48010i	−0.151509	−	0.196465i
$521$	−15.3536			−0.672652			−0.336326	−	0.941746i	$-0.609184\pi$
$521$	−15.3536			−0.672652			−0.336326	+	0.941746i	$0.609184\pi$
$522$	1.12773	−	4.20875i	0.0493595	−	0.184212i
$523$	−31.9696	+	18.4576i	−1.39793	+	0.807096i	−0.994176	−	0.107770i	$-0.965629\pi$
$523$	−31.9696	+	18.4576i	−1.39793	+	0.807096i	−0.403756	+	0.914867i	$0.632296\pi$
$524$	−9.56513	+	16.5673i	−0.417855	+	0.723746i
$525$	−3.71168	+	3.71168i	−0.161991	+	0.161991i
$526$	31.5870	−	8.46370i	1.37726	−	0.369035i
$527$	14.7937	−	3.96395i	0.644423	−	0.172673i
$528$	6.73616	−	8.69341i	0.293154	−	0.378332i
$529$	5.94613	−	10.2990i	0.258528	−	0.447783i
$530$	30.9297	+	53.5718i	1.34350	+	2.32701i
$531$	8.54770	+	2.29035i	0.370939	+	0.0993927i
$532$			66.4228i			2.87979i
$533$	−16.9090	+	7.05186i	−0.732412	+	0.305450i
$534$		−	4.51548i		−	0.195404i
$535$	−12.1587	−	3.25791i	−0.525665	−	0.140852i
$536$	5.87459	−	3.39170i	0.253744	−	0.146499i
$537$	11.2783	+	6.51151i	0.486693	+	0.280993i
$538$	37.2916	−	37.2916i	1.60775	−	1.60775i
$539$	−17.9790	+	7.34783i	−0.774408	+	0.316493i
$540$	1.51196	+	5.64271i	0.0650644	+	0.242824i
$541$	−4.27417	−	4.27417i	−0.183761	−	0.183761i	0.609232	−	0.792992i	$-0.291478\pi$
$541$	−4.27417	−	4.27417i	−0.183761	−	0.183761i	−0.792992	+	0.609232i	$0.791478\pi$
$542$	−7.77461	+	13.4660i	−0.333948	+	0.578415i
$543$	−17.1925	+	9.92609i	−0.737800	+	0.425969i
$544$	−21.4445	−	5.74604i	−0.919425	−	0.246359i
$545$	−3.30817			−0.141706
$546$	−24.7852	−	10.1963i	−1.06071	−	0.436361i
$547$		−	21.1507i		−	0.904338i	−0.891932	−	0.452169i	$-0.850650\pi$
$547$		−	21.1507i		−	0.904338i	0.891932	−	0.452169i	$-0.149350\pi$
$548$	−0.0434570	+	0.162184i	−0.00185639	+	0.00692814i
$549$	−2.38447	+	1.37667i	−0.101767	+	0.0587550i
$550$	−3.89587	+	9.28122i	−0.166120	+	0.395753i
$551$	−11.9824	−	11.9824i	−0.510468	−	0.510468i
$552$	0.943556	+	3.52140i	0.0401604	+	0.149881i
$553$	4.80158	+	17.9197i	0.204184	+	0.762024i
$554$	18.8916	−	18.8916i	0.802628	−	0.802628i
$555$	−11.7064	+	20.2760i	−0.496908	+	0.860669i
$556$	−10.1015	−	17.4962i	−0.428397	−	0.742006i
$557$	−4.64876	+	17.3494i	−0.196974	+	0.735119i	0.794772	+	0.606908i	$0.207590\pi$
$557$	−4.64876	+	17.3494i	−0.196974	+	0.735119i	−0.991747	+	0.128211i	$0.959076\pi$
$558$	−11.5965			−0.490918
$559$	−3.75000	−	27.9618i	−0.158608	−	1.18266i
$560$			30.2283i			1.27738i
$561$	−8.99735	−	1.22779i	−0.379869	−	0.0518371i
$562$	1.65152	+	2.86051i	0.0696650	+	0.120663i
$563$	−1.48247	+	2.56771i	−0.0624786	+	0.108216i	−0.895573	−	0.444915i	$-0.853234\pi$
$563$	−1.48247	+	2.56771i	−0.0624786	+	0.108216i	0.833094	+	0.553131i	$0.186567\pi$
$564$	3.65909	+	3.65909i	0.154076	+	0.154076i
$565$	13.6231	−	3.65031i	0.573130	−	0.153570i
$566$	−6.86751	−	25.6299i	−0.288663	−	1.07731i
$567$	2.53536	+	2.53536i	0.106475	+	0.106475i
$568$	−8.20153	−	4.73515i	−0.344128	−	0.198683i
$569$	5.46077	+	9.45832i	0.228927	+	0.396514i	0.957490	−	0.288465i	$-0.0931449\pi$
$569$	5.46077	+	9.45832i	0.228927	+	0.396514i	−0.728563	+	0.684979i	$0.759812\pi$
$570$	41.0468	+	10.9985i	1.71926	+	0.460675i
$571$	−25.9256			−1.08495			−0.542477	−	0.840070i	$-0.682514\pi$
$571$	−25.9256			−1.08495			−0.542477	+	0.840070i	$0.682514\pi$
$572$	−27.4765	−	0.0633948i	−1.14885	−	0.00265067i
$573$	19.0176			0.794471
$574$	−36.4825	−	9.77546i	−1.52275	−	0.408020i
$575$	4.32380	+	7.48903i	0.180315	+	0.312314i
$576$	8.81442	+	5.08900i	0.367267	+	0.212042i
$577$	−18.3902	−	18.3902i	−0.765596	−	0.765596i	0.211732	−	0.977328i	$-0.432090\pi$
$577$	−18.3902	−	18.3902i	−0.765596	−	0.765596i	−0.977328	+	0.211732i	$0.932090\pi$
$578$	−5.09924	−	19.0306i	−0.212100	−	0.791569i
$579$	−11.2805	+	3.02261i	−0.468804	+	0.125616i
$580$	8.68201	+	8.68201i	0.360501	+	0.360501i
$581$	14.7025	−	25.4655i	0.609962	−	1.05649i
$582$	−0.424762	−	0.735709i	−0.0176069	−	0.0304961i
$583$	38.5681	+	5.26303i	1.59733	+	0.217972i
$584$		−	7.27851i		−	0.301187i
$585$	−5.56285	+	7.28603i	−0.229996	+	0.301240i
$586$	11.4427			0.472693
$587$	9.54896	−	35.6372i	0.394128	−	1.47091i	−0.429133	−	0.903241i	$-0.641181\pi$
$587$	9.54896	−	35.6372i	0.394128	−	1.47091i	0.823261	−	0.567664i	$-0.192153\pi$
$588$	−6.72780	−	11.6529i	−0.277450	−	0.480557i
$589$	−22.5499	+	39.0577i	−0.929154	+	1.60934i
$590$	−32.9806	+	32.9806i	−1.35779	+	1.35779i
$591$	0.903371	+	3.37143i	0.0371597	+	0.138682i
$592$	7.90329	+	29.4955i	0.324823	+	1.21226i
$593$	2.43714	+	2.43714i	0.100081	+	0.100081i	0.755375	−	0.655293i	$-0.227455\pi$
$593$	2.43714	+	2.43714i	0.100081	+	0.100081i	−0.655293	+	0.755375i	$0.727455\pi$
$594$	6.33979	+	2.66118i	0.260125	+	0.109189i
$595$	21.6152	−	12.4796i	0.886138	−	0.511612i
$596$	−3.75522	+	14.0147i	−0.153820	+	0.574063i
$597$		−	4.59984i		−	0.188259i
$598$	−26.7936	+	35.0933i	−1.09567	+	1.43507i
$599$	−1.53596			−0.0627578			−0.0313789	−	0.999508i	$-0.509990\pi$
$599$	−1.53596			−0.0627578			−0.0313789	+	0.999508i	$0.509990\pi$
$600$	−0.872733	−	0.233848i	−0.0356292	−	0.00954681i
$601$	17.4888	−	10.0971i	0.713382	−	0.411871i	−0.0989303	−	0.995094i	$-0.531542\pi$
$601$	17.4888	−	10.0971i	0.713382	−	0.411871i	0.812312	+	0.583223i	$0.198209\pi$
$602$	29.0809	−	50.3696i	1.18525	−	2.05291i
$603$	−7.77186	−	7.77186i	−0.316495	−	0.316495i
$604$	−8.38264	−	31.2844i	−0.341085	−	1.27295i
$605$	13.7540	+	24.3509i	0.559178	+	0.990006i
$606$	24.3582	−	24.3582i	0.989484	−	0.989484i
$607$	−11.4413	−	6.60565i	−0.464389	−	0.268115i	0.249499	−	0.968375i	$-0.419734\pi$
$607$	−11.4413	−	6.60565i	−0.464389	−	0.268115i	−0.713888	+	0.700260i	$0.753067\pi$
$608$	56.6169	−	32.6878i	2.29612	−	1.32566i
$609$	7.27930	+	1.95048i	0.294972	+	0.0790376i
$610$		−	14.5121i		−	0.587576i
$611$	−1.04044	+	8.05325i	−0.0420918	+	0.325800i
$612$		−	6.29100i		−	0.254298i
$613$	41.7690	+	11.1920i	1.68703	+	0.452039i	0.969621	−	0.244611i	$-0.0786604\pi$
$613$	41.7690	+	11.1920i	1.68703	+	0.452039i	0.717411	+	0.696650i	$0.245327\pi$
$614$	−1.22028	−	2.11358i	−0.0492464	−	0.0852973i
$615$	−6.45933	+	11.1879i	−0.260465	+	0.451139i
$616$	−5.80154	−	4.49537i	−0.233751	−	0.181124i
$617$	9.67250	−	2.59174i	0.389400	−	0.104339i	−0.0588066	−	0.998269i	$-0.518730\pi$
$617$	9.67250	−	2.59174i	0.389400	−	0.104339i	0.448207	+	0.893930i	$0.352063\pi$
$618$	−8.66074	+	2.32064i	−0.348386	+	0.0933498i
$619$	−11.0633	+	11.0633i	−0.444670	+	0.444670i	−0.893578	−	0.448908i	$-0.851813\pi$
$619$	−11.0633	+	11.0633i	−0.444670	+	0.444670i	0.448908	+	0.893578i	$0.351813\pi$
$620$	16.3389	−	28.2997i	0.656184	−	1.13654i
$621$	5.11558	−	2.95348i	0.205281	−	0.118519i
$622$	0.280074	−	1.04525i	0.0112299	−	0.0419107i
$623$	7.80981			0.312894
$624$	1.58919	+	11.8498i	0.0636184	+	0.474370i
$625$	30.1766			1.20707
$626$	−24.8944	−	6.67043i	−0.994980	−	0.266604i
$627$	21.2911	−	16.1780i	0.850283	−	0.646087i
$628$	42.7276	+	24.6688i	1.70501	+	0.984391i
$629$	17.8284	−	17.8284i	0.710865	−	0.710865i
$630$	−18.2543	+	4.89124i	−0.727271	+	0.194872i
$631$	3.10819	+	11.5999i	0.123735	+	0.461786i	0.999791	−	0.0204232i	$-0.00650135\pi$
$631$	3.10819	+	11.5999i	0.123735	+	0.461786i	−0.876056	+	0.482209i	$0.839835\pi$
$632$	−2.25801	+	2.25801i	−0.0898187	+	0.0898187i
$633$	6.74420	+	3.89377i	0.268058	+	0.154763i
$634$	18.3549	+	31.7916i	0.728966	+	1.26261i
$635$	9.05708	−	33.8015i	0.359419	−	1.34137i
$636$			26.9670i			1.06931i
$637$	8.03301	−	19.5267i	0.318279	−	0.773676i
$638$	14.3364	−	1.81857i	0.567583	−	0.0719980i
$639$	−3.97149	+	14.8218i	−0.157110	+	0.586341i
$640$	−10.7508	+	6.20695i	−0.424961	+	0.245351i
$641$	0.396844	+	0.229118i	0.0156744	+	0.00904962i	0.507817	−	0.861465i	$-0.330453\pi$
$641$	0.396844	+	0.229118i	0.0156744	+	0.00904962i	−0.492142	+	0.870515i	$0.663786\pi$
$642$	−7.25765	−	7.25765i	−0.286437	−	0.286437i
$643$	37.6209	−	10.0805i	1.48362	−	0.397536i	0.576046	−	0.817418i	$-0.304595\pi$
$643$	37.6209	−	10.0805i	1.48362	−	0.397536i	0.907579	+	0.419882i	$0.137928\pi$
$644$	−47.0065	+	12.5953i	−1.85231	+	0.496326i
$645$	−14.0669	−	14.0669i	−0.553885	−	0.553885i
$646$	−39.6316	−	22.8813i	−1.55929	−	0.900254i
$647$	28.3900	−	16.3910i	1.11613	−	0.644395i	0.175716	−	0.984441i	$-0.443776\pi$
$647$	28.3900	−	16.3910i	1.11613	−	0.644395i	0.940409	+	0.340046i	$0.110443\pi$
$648$	−0.159736	+	0.596144i	−0.00627503	+	0.0234187i
$649$	3.69340	+	29.1163i	0.144979	+	1.14291i
$650$	−4.21197	−	10.0995i	−0.165207	−	0.396135i
$651$		−	20.0568i		−	0.786089i
$652$	−0.841714	+	3.14132i	−0.0329641	+	0.123024i
$653$	−12.4464	−	21.5577i	−0.487063	−	0.843618i	0.512826	−	0.858493i	$-0.328599\pi$
$653$	−12.4464	−	21.5577i	−0.487063	−	0.843618i	−0.999889	+	0.0148741i	$0.995265\pi$
$654$	−2.33608	−	1.34873i	−0.0913478	−	0.0527397i
$655$	−14.9679	+	14.9679i	−0.584844	+	0.584844i
$656$	4.36087	+	16.2750i	0.170263	+	0.635431i
$657$	−11.3915	+	3.05233i	−0.444423	+	0.119083i
$658$	−11.8373	+	11.8373i	−0.461465	+	0.461465i
$659$	9.46147	+	5.46258i	0.368567	+	0.212792i	0.672832	−	0.739795i	$-0.265078\pi$
$659$	9.46147	+	5.46258i	0.368567	+	0.212792i	−0.304265	+	0.952587i	$0.598411\pi$
$660$	−15.4267	+	11.7220i	−0.600484	+	0.456278i
$661$	2.20949	+	0.592030i	0.0859390	+	0.0230273i	0.301532	−	0.953456i	$-0.402502\pi$
$661$	2.20949	+	0.592030i	0.0859390	+	0.0230273i	−0.215593	+	0.976483i	$0.569169\pi$
$662$	−14.1559			−0.550186
$663$	7.81729	−	6.02848i	0.303598	−	0.234127i
$664$	5.06143			0.196422
$665$	−19.0225	+	70.9931i	−0.737662	+	2.75299i
$666$	−16.5330	+	9.54533i	−0.640641	+	0.369874i
$667$	6.20763	−	10.7519i	0.240360	−	0.416316i
$668$	−21.2909	+	21.2909i	−0.823769	+	0.823769i
$669$	6.37471	−	1.70810i	0.246461	−	0.0660389i
$670$	55.9567	−	14.9935i	2.16179	−	0.579251i
$671$	−7.21843	−	5.59326i	−0.278664	−	0.215925i
$672$	−14.5369	+	25.1787i	−0.560773	+	0.971288i
$673$	3.63543	+	6.29675i	0.140135	+	0.242722i	0.927547	−	0.373705i	$-0.121913\pi$
$673$	3.63543	+	6.29675i	0.140135	+	0.242722i	−0.787412	+	0.616427i	$0.788580\pi$
$674$	−60.2427	−	16.1420i	−2.32046	−	0.621766i
$675$			1.46396i			0.0563480i
$676$	21.0191	−	21.2232i	0.808427	−	0.816278i
$677$		−	2.74868i		−	0.105640i	−0.998604	−	0.0528202i	$-0.983179\pi$
$677$		−	2.74868i		−	0.105640i	0.998604	−	0.0528202i	$-0.0168210\pi$
$678$	11.1083	+	2.97645i	0.426610	+	0.114310i
$679$	1.27245	−	0.734652i	0.0488323	−	0.0281934i
$680$	3.72059	+	2.14808i	0.142678	+	0.0823753i
$681$	3.54827	−	3.54827i	0.135970	−	0.135970i
$682$	−14.5504	−	35.6026i	−0.557165	−	1.36329i
$683$	−0.160240	−	0.598025i	−0.00613143	−	0.0228828i	0.962792	−	0.270242i	$-0.0871038\pi$
$683$	−0.160240	−	0.598025i	−0.00613143	−	0.0228828i	−0.968924	+	0.247359i	$0.920437\pi$
$684$	13.0993	+	13.0993i	0.500864	+	0.500864i
$685$	−0.0928941	+	0.160897i	−0.00354930	+	0.00614757i
$686$	−7.36360	+	4.25138i	−0.281144	+	0.162318i
$687$	2.37001	+	0.635042i	0.0904215	+	0.0242284i
$688$	−25.9462			−0.989190
$689$	−33.5096	+	25.8417i	−1.27661	+	0.984490i
$690$			31.1338i			1.18524i
$691$	3.30940	−	12.3509i	0.125896	−	0.469849i	−0.873974	−	0.485972i	$-0.838466\pi$
$691$	3.30940	−	12.3509i	0.125896	−	0.469849i	0.999870	+	0.0161232i	$0.00513238\pi$
$692$	19.1241	−	11.0413i	0.726989	−	0.419727i
$693$	−4.60267	+	10.9651i	−0.174841	+	0.416528i
$694$	26.3312	+	26.3312i	0.999519	+	0.999519i
$695$	−5.78583	−	21.5930i	−0.219469	−	0.819069i
$696$	0.335733	+	1.25297i	0.0127259	+	0.0474939i
$697$	9.83734	−	9.83734i	0.372616	−	0.372616i
$698$	12.6459	−	21.9033i	0.478654	−	0.829053i
$699$	−3.72553	−	6.45280i	−0.140912	−	0.244067i
$700$	3.12159	−	11.6499i	0.117985	−	0.440326i
$701$	7.20708			0.272208			0.136104	−	0.990695i	$-0.456542\pi$
$701$	7.20708			0.272208			0.136104	+	0.990695i	$0.456542\pi$
$702$	−6.89873	+	2.87710i	−0.260376	+	0.108589i
$703$			74.2456i			2.80022i
$704$	−4.56416	+	33.4467i	−0.172018	+	1.26057i
$705$	2.86295	+	4.95877i	0.107825	+	0.186758i
$706$	16.2364	−	28.1223i	0.611066	−	1.05840i
$707$	42.1290	+	42.1290i	1.58443	+	1.58443i
$708$	−19.6401	+	5.26255i	−0.738120	+	0.197779i
$709$	−2.69227	−	10.0477i	−0.101110	−	0.377349i	0.896765	−	0.442508i	$-0.145911\pi$
$709$	−2.69227	−	10.0477i	−0.101110	−	0.377349i	−0.997875	+	0.0651592i	$0.979244\pi$
$710$	−57.1887	−	57.1887i	−2.14625	−	2.14625i
$711$	4.48088	+	2.58704i	0.168046	+	0.0970215i
$712$	0.672145	+	1.16419i	0.0251897	+	0.0436298i
$713$	−31.9166	−	8.55201i	−1.19528	−	0.320275i
$714$	20.3516			0.761638
$715$	−29.3489	−	7.93663i	−1.09759	−	0.296813i
$716$	−29.9231			−1.11828
$717$	2.23044	+	0.597644i	0.0832973	+	0.0223194i
$718$	−7.21548	−	12.4976i	−0.269279	−	0.466406i
$719$	10.8367	+	6.25655i	0.404140	+	0.233330i	0.688269	−	0.725456i	$-0.258371\pi$
$719$	10.8367	+	6.25655i	0.404140	+	0.233330i	−0.284129	+	0.958786i	$0.591704\pi$
$720$	5.96133	+	5.96133i	0.222166	+	0.222166i
$721$	−4.01369	−	14.9793i	−0.149478	−	0.557858i
$722$	92.1195	−	24.6834i	3.42833	−	0.918619i
$723$	6.67948	+	6.67948i	0.248413	+	0.248413i
$724$	22.8072	−	39.5033i	0.847624	−	1.46813i
$725$	1.53848	+	2.66473i	0.0571377	+	0.0989654i
$726$	−0.215419	+	22.8030i	−0.00799496	+	0.846298i
$727$			35.9265i			1.33244i	0.745756	+	0.666219i	$0.232089\pi$
$727$			35.9265i			1.33244i	−0.745756	+	0.666219i	$0.767911\pi$
$728$	7.90793	−	1.06054i	0.293087	−	0.0393063i
$729$	1.00000			0.0370370
$730$	16.0879	−	60.0409i	0.595440	−	2.22221i
$731$	10.7117	+	18.5533i	0.396188	+	0.686217i
$732$	3.16319	−	5.47881i	0.116915	−	0.202503i
$733$	9.57425	−	9.57425i	0.353633	−	0.353633i	−0.507826	−	0.861459i	$-0.669551\pi$
$733$	9.57425	−	9.57425i	0.353633	−	0.353633i	0.861459	+	0.507826i	$0.169551\pi$
$734$	−7.68308	−	28.6737i	−0.283588	−	1.05836i
$735$	−3.85349	−	14.3814i	−0.142138	−	0.530467i
$736$	33.8686	+	33.8686i	1.24841	+	1.24841i
$737$	14.1090	−	33.6122i	0.519711	−	1.23812i
$738$	−9.12257	+	5.26692i	−0.335806	+	0.193878i
$739$	4.16556	−	15.5461i	0.153233	−	0.571872i	−0.846018	−	0.533155i	$-0.821006\pi$
$739$	4.16556	−	15.5461i	0.153233	−	0.571872i	0.999250	−	0.0387168i	$-0.0123270\pi$
$740$		−	53.7956i		−	1.97757i
$741$	−3.72470	+	28.8300i	−0.136830	+	1.05910i
$742$	−87.2391			−3.20265
$743$	−20.1572	−	5.40110i	−0.739495	−	0.198147i	−0.130641	−	0.991430i	$-0.541704\pi$
$743$	−20.1572	−	5.40110i	−0.739495	−	0.198147i	−0.608853	+	0.793283i	$0.708370\pi$
$744$	2.98982	−	1.72617i	0.109612	−	0.0632846i
$745$	−8.02719	+	13.9035i	−0.294093	+	0.509385i
$746$	−9.64592	−	9.64592i	−0.353162	−	0.353162i
$747$	−2.12257	−	7.92155i	−0.0776608	−	0.289834i
$748$	19.3141	−	7.89350i	0.706195	−	0.288615i
$749$	12.5526	−	12.5526i	0.458661	−	0.458661i
$750$	16.1404	+	9.31868i	0.589365	+	0.340270i
$751$	15.6602	−	9.04141i	0.571448	−	0.329926i	−0.186279	−	0.982497i	$-0.559643\pi$
$751$	15.6602	−	9.04141i	0.571448	−	0.329926i	0.757728	+	0.652571i	$0.226310\pi$
$752$	7.21351	+	1.93285i	0.263050	+	0.0704839i
$753$		−	17.1921i		−	0.626513i
$754$	−9.53361	+	12.4868i	−0.347194	+	0.454742i
$755$		−	35.8376i		−	1.30427i
$756$	−7.95780	−	2.13229i	−0.289422	−	0.0775505i
$757$	−5.72824	−	9.92161i	−0.208197	−	0.360607i	0.742950	−	0.669347i	$-0.233426\pi$
$757$	−5.72824	−	9.92161i	−0.208197	−	0.360607i	−0.951146	+	0.308740i	$0.900093\pi$
$758$	−27.5504	+	47.7187i	−1.00068	+	1.73322i
$759$	15.4862	+	11.9996i	0.562115	+	0.435559i
$760$	−12.2199	+	3.27432i	−0.443263	+	0.118772i
$761$	31.2900	−	8.38414i	1.13426	−	0.303925i	0.357621	−	0.933867i	$-0.383588\pi$
$761$	31.2900	−	8.38414i	1.13426	−	0.303925i	0.776642	+	0.629942i	$0.216921\pi$
$762$	20.1765	−	20.1765i	0.730918	−	0.730918i
$763$	2.33272	−	4.04039i	0.0844501	−	0.146272i
$764$	−37.8425	+	21.8484i	−1.36910	+	0.790448i
$765$	1.80165	−	6.72385i	0.0651388	−	0.243101i
$766$	23.5309			0.850205
$767$	−25.3599	−	19.3621i	−0.915692	−	0.699126i
$768$	10.2338			0.369279
$769$	23.4126	+	6.27339i	0.844280	+	0.226224i	0.654934	−	0.755686i	$-0.272696\pi$
$769$	23.4126	+	6.27339i	0.844280	+	0.226224i	0.189346	+	0.981910i	$0.439363\pi$
$770$	−37.9210	−	49.9059i	−1.36658	−	1.79848i
$771$	−11.8934	−	6.86665i	−0.428330	−	0.247296i
$772$	18.9743	−	18.9743i	0.682901	−	0.682901i
$773$	−38.1505	+	10.2224i	−1.37218	+	0.367674i	−0.868274	−	0.496085i	$-0.834770\pi$
$773$	−38.1505	+	10.2224i	−1.37218	+	0.367674i	−0.503905	+	0.863759i	$0.668104\pi$
$774$	−4.19836	−	15.6685i	−0.150907	−	0.563192i
$775$	5.79059	−	5.79059i	0.208004	−	0.208004i
$776$	0.219026	+	0.126454i	0.00786256	+	0.00453945i
$777$	−16.5093	−	28.5949i	−0.592266	−	1.02583i
$778$	−10.8772	+	40.5941i	−0.389965	+	1.45537i
$779$			40.9672i			1.46780i
$780$	2.69878	−	20.8892i	0.0966319	−	0.747952i
$781$	−50.4879	+	6.40440i	−1.80660	+	0.229167i
$782$	8.67769	−	32.3856i	0.310313	−	1.15811i
$783$	1.82021	−	1.05090i	0.0650491	−	0.0375561i
$784$	−16.8170	−	9.70929i	−0.600607	−	0.346761i
$785$	38.6027	+	38.6027i	1.37779	+	1.37779i
$786$	−16.6720	+	4.46726i	−0.594672	+	0.159342i
$787$	44.5357	−	11.9333i	1.58753	−	0.425376i	0.646281	−	0.763100i	$-0.276324\pi$
$787$	44.5357	−	11.9333i	1.58753	−	0.425376i	0.941245	+	0.337724i	$0.109657\pi$
$788$	−5.67087	−	5.67087i	−0.202016	−	0.202016i
$789$	13.6608	+	7.88707i	0.486338	+	0.280787i
$790$	−23.6174	+	13.6355i	−0.840268	+	0.485129i
$791$	−5.14796	+	19.2124i	−0.183040	+	0.683116i
$792$	−2.03066	+	0.257590i	−0.0721563	+	0.00915305i
$793$	9.83925	−	1.31955i	0.349402	−	0.0468588i
$794$			67.8101i			2.40649i
$795$	−7.72296	+	28.8225i	−0.273905	+	1.02223i
$796$	5.28454	+	9.15309i	0.187305	+	0.324423i
$797$	12.0999	+	6.98589i	0.428601	+	0.247453i	0.698750	−	0.715366i	$-0.253740\pi$
$797$	12.0999	+	6.98589i	0.428601	+	0.247453i	−0.270149	+	0.962818i	$0.587073\pi$
$798$	−42.3766	+	42.3766i	−1.50011	+	1.50011i
$799$	−1.59593	−	5.95611i	−0.0564601	−	0.210712i
$800$	−11.4663	+	3.07237i	−0.405393	+	0.108625i
$801$	1.54018	−	1.54018i	0.0544195	−	0.0544195i
$802$	−7.88814	−	4.55422i	−0.278540	−	0.160815i
$803$	−23.6642	−	31.1433i	−0.835093	−	1.09902i
$804$	24.3937	+	6.53629i	0.860301	+	0.230517i
$805$	−53.8479			−1.89789
$806$	38.6675	+	15.9073i	1.36200	+	0.560309i
$807$	25.4394			0.895510
$808$	−2.65427	+	9.90587i	−0.0933769	+	0.348487i
$809$	37.9647	−	21.9189i	1.33477	−	0.770628i	0.348740	−	0.937219i	$-0.386610\pi$
$809$	37.9647	−	21.9189i	1.33477	−	0.770628i	0.986026	+	0.166592i	$0.0532762\pi$
$810$	−2.63535	+	4.56456i	−0.0925967	+	0.160382i
$811$	23.1491	−	23.1491i	0.812875	−	0.812875i	−0.172189	−	0.985064i	$-0.555084\pi$
$811$	23.1491	−	23.1491i	0.812875	−	0.812875i	0.985064	+	0.172189i	$0.0550839\pi$
$812$	−16.7257	+	4.48164i	−0.586957	+	0.157275i
$813$	−7.24493	+	1.94127i	−0.254091	+	0.0680834i
$814$	−50.0498	−	38.7815i	−1.75424	−	1.35929i
$815$	−1.79926	+	3.11641i	−0.0630252	+	0.109163i
$816$	−4.53946	−	7.86257i	−0.158913	−	0.275245i
$817$	−60.9364	−	16.3279i	−2.13189	−	0.571239i
$818$			77.2793i			2.70201i
$819$	−4.97612	−	11.9318i	−0.173880	−	0.416930i
$820$		−	29.6833i		−	1.03659i
$821$	0.125986	+	0.0337579i	0.00439695	+	0.00117816i	0.261017	−	0.965334i	$-0.415942\pi$
$821$	0.125986	+	0.0337579i	0.00439695	+	0.00117816i	−0.256620	+	0.966512i	$0.582609\pi$
$822$	−0.131195	+	0.0757455i	−0.00457595	+	0.00264193i
$823$	1.59234	+	0.919336i	0.0555054	+	0.0320460i	0.527496	−	0.849558i	$-0.323131\pi$
$823$	1.59234	+	0.919336i	0.0555054	+	0.0320460i	−0.471991	+	0.881604i	$0.656464\pi$
$824$	1.88749	−	1.88749i	0.0657539	−	0.0657539i
$825$	−4.49455	+	1.83688i	−0.156480	+	0.0639520i
$826$	−17.0245	−	63.5364i	−0.592359	−	2.21071i
$827$	33.9178	+	33.9178i	1.17944	+	1.17944i	0.979887	+	0.199551i	$0.0639484\pi$
$827$	33.9178	+	33.9178i	1.17944	+	1.17944i	0.199551	+	0.979887i	$0.436052\pi$
$828$	−6.78624	+	11.7541i	−0.235838	+	0.408484i
$829$	19.3618	−	11.1785i	0.672462	−	0.388246i	−0.124547	−	0.992214i	$-0.539748\pi$
$829$	19.3618	−	11.1785i	0.672462	−	0.388246i	0.797009	+	0.603968i	$0.206414\pi$
$830$	41.7520	+	11.1874i	1.44923	+	0.388321i
$831$	12.8874			0.447059
$832$	−22.4102	−	29.0599i	−0.776934	−	1.00747i
$833$			16.0337i			0.555535i
$834$	4.71774	−	17.6069i	0.163362	−	0.609676i
$835$	−28.8532	+	16.6584i	−0.998507	+	0.576488i
$836$	−23.7803	+	56.6525i	−0.822460	+	1.95937i
$837$	−3.95542	−	3.95542i	−0.136719	−	0.136719i
$838$	4.67925	+	17.4632i	0.161642	+	0.603256i
$839$	−0.180459	−	0.673481i	−0.00623012	−	0.0232511i	0.962741	−	0.270426i	$-0.0871645\pi$
$839$	−0.180459	−	0.673481i	−0.00623012	−	0.0232511i	−0.968971	+	0.247175i	$0.920498\pi$
$840$	3.97829	−	3.97829i	0.137264	−	0.137264i
$841$	−12.2912	+	21.2890i	−0.423835	+	0.734104i
$842$	−11.9564	−	20.7091i	−0.412045	−	0.713683i
$843$	−0.412373	+	1.53900i	−0.0142029	+	0.0530059i
$844$	−17.8935			−0.615918
$845$	28.5434	−	16.6639i	0.981921	−	0.573257i
$846$			4.66888i			0.160519i
$847$	−39.4392	−	0.372581i	−1.35515	−	0.0128020i
$848$	19.4588	+	33.7037i	0.668219	+	1.15739i
$849$	6.39963	−	11.0845i	0.219635	−	0.380419i
$850$	5.87569	+	5.87569i	0.201534	+	0.201534i
$851$	−52.5425	+	14.0787i	−1.80113	+	0.482613i
$852$	−9.12531	−	34.0561i	−0.312628	−	1.16674i
$853$	4.09517	+	4.09517i	0.140216	+	0.140216i	0.773731	−	0.633515i	$-0.218388\pi$
$853$	4.09517	+	4.09517i	0.140216	+	0.140216i	−0.633515	+	0.773731i	$0.718388\pi$
$854$	17.7241	+	10.2330i	0.606507	+	0.350167i
$855$	10.2491	+	17.7520i	0.350513	+	0.607107i
$856$	2.95151	+	0.790854i	0.100880	+	0.0270308i
$857$	−24.6336			−0.841467			−0.420733	−	0.907184i	$-0.638227\pi$
$857$	−24.6336			−0.841467			−0.420733	+	0.907184i	$0.638227\pi$
$858$	−17.4891	−	17.5700i	−0.597068	−	0.599829i
$859$	9.87027			0.336769			0.168385	−	0.985721i	$-0.446145\pi$
$859$	9.87027			0.336769			0.168385	+	0.985721i	$0.446145\pi$
$860$	44.1522	+	11.8306i	1.50558	+	0.403419i
$861$	−9.10946	−	15.7780i	−0.310450	−	0.537714i
$862$	−65.7641	−	37.9689i	−2.23993	−	1.29323i
$863$	−21.6327	−	21.6327i	−0.736387	−	0.736387i	0.235490	−	0.971877i	$-0.424330\pi$
$863$	−21.6327	−	21.6327i	−0.736387	−	0.736387i	−0.971877	+	0.235490i	$0.924330\pi$
$864$	2.09867	+	7.83233i	0.0713981	+	0.266461i
$865$	23.6020	−	6.32414i	0.802492	−	0.215027i
$866$	15.8630	+	15.8630i	0.539046	+	0.539046i
$867$	4.75183	−	8.23040i	0.161380	−	0.279519i
$868$	23.0424	+	39.9105i	0.782109	+	1.35465i
$869$	−2.32023	+	17.0029i	−0.0787083	+	0.576784i
$870$			11.0779i			0.375577i
$871$	15.2537	+	36.5756i	0.516853	+	1.23932i
$872$	0.803054			0.0271949
$873$	0.106060	−	0.395823i	0.00358960	−	0.0133966i
$874$	49.3652	+	85.5030i	1.66980	+	2.89218i
$875$	−16.1172	+	27.9159i	−0.544862	+	0.943729i
$876$	19.1609	−	19.1609i	0.647386	−	0.647386i
$877$	−8.45317	−	31.5477i	−0.285443	−	1.06529i	−0.948515	−	0.316733i	$-0.897414\pi$
$877$	−8.45317	−	31.5477i	−0.285443	−	1.06529i	0.663071	−	0.748556i	$-0.269253\pi$
$878$	−13.7491	−	51.3122i	−0.464008	−	1.73170i
$879$	3.90297	+	3.90297i	0.131644	+	0.131644i
$880$	−10.8222	+	25.7819i	−0.364815	+	0.869107i
$881$	−49.6819	+	28.6839i	−1.67383	+	0.966384i	−0.708363	+	0.705849i	$0.750566\pi$
$881$	−49.6819	+	28.6839i	−1.67383	+	0.966384i	−0.965464	+	0.260536i	$0.916101\pi$
$882$	3.14212	−	11.7266i	0.105801	−	0.394854i
$883$		−	19.3540i		−	0.651314i	−0.945488	−	0.325657i	$-0.894415\pi$
$883$		−	19.3540i		−	0.651314i	0.945488	−	0.325657i	$-0.105585\pi$
$884$	−8.62956	+	20.9768i	−0.290244	+	0.705527i
$885$	−22.4986			−0.756281
$886$	44.7361	+	11.9870i	1.50294	+	0.402711i
$887$	−44.6589	+	25.7838i	−1.49950	+	0.865736i	−1.00000		0.000578975i	$-0.999816\pi$
$887$	−44.6589	+	25.7838i	−1.49950	+	0.865736i	−0.499499	+	0.866315i	$0.666482\pi$
$888$	2.84171	−	4.92199i	0.0953615	−	0.165171i
$889$	34.8965	+	34.8965i	1.17039	+	1.17039i
$890$	2.97132	+	11.0891i	0.0995990	+	0.371709i
$891$	1.25473	+	3.07012i	0.0420350	+	0.102853i
$892$	−10.7225	+	10.7225i	−0.359016	+	0.359016i
$893$	15.7251	+	9.07887i	0.526219	+	0.303813i
$894$	−11.3369	+	6.54534i	−0.379162	+	0.218909i
$895$	−31.9820	−	8.56954i	−1.06904	−	0.286448i
$896$		−	17.5071i		−	0.584870i
$897$	−21.1089	+	2.83094i	−0.704805	+	0.0945223i
$898$		−	10.8184i		−	0.361013i
$899$	−11.3565	−	3.04295i	−0.378759	−	0.101488i
$900$	−1.68188	−	2.91310i	−0.0560627	−	0.0971034i
$901$	16.0669	−	27.8287i	0.535267	−	0.927110i
$902$	−27.6164	−	21.3988i	−0.919527	−	0.712503i
$903$	27.0996	−	7.26132i	0.901819	−	0.241642i
$904$	−3.30701	+	0.886109i	−0.109989	+	0.0294716i
$905$	35.6897	−	35.6897i	1.18636	−	1.18636i
$906$	14.6109	−	25.3069i	0.485416	−	0.840765i
$907$	31.3309	−	18.0889i	1.04032	−	0.600632i	0.120399	−	0.992726i	$-0.461583\pi$
$907$	31.3309	−	18.0889i	1.04032	−	0.600632i	0.919925	+	0.392094i	$0.128249\pi$
$908$	−2.98416	+	11.1371i	−0.0990330	+	0.369596i
$909$	16.6166			0.551137
$910$	67.5771	+	8.73064i	2.24016	+	0.289418i
$911$	42.4782			1.40737			0.703683	−	0.710514i	$-0.251537\pi$
$911$	42.4782			1.40737			0.703683	+	0.710514i	$0.251537\pi$
$912$	25.8238	+	6.91947i	0.855112	+	0.229127i
$913$	21.6569	−	16.4560i	0.716737	−	0.544613i
$914$	−48.4614	−	27.9792i	−1.60296	−	0.925469i
$915$	4.94989	−	4.94989i	0.163638	−	0.163638i
$916$	−5.44559	+	1.45914i	−0.179927	+	0.0482113i
$917$	−7.72640	−	28.8353i	−0.255148	−	0.952226i
$918$	4.01355	−	4.01355i	0.132467	−	0.132467i
$919$	7.72336	+	4.45908i	0.254770	+	0.147092i	0.621946	−	0.783060i	$-0.286342\pi$
$919$	7.72336	+	4.45908i	0.254770	+	0.147092i	−0.367176	+	0.930151i	$0.619675\pi$
$920$	−4.63437	−	8.02697i	−0.152791	−	0.264641i
$921$	0.304696	−	1.13714i	0.0100401	−	0.0374701i
$922$			29.1458i			0.959865i
$923$	33.5741	−	43.9743i	1.10511	−	1.44743i
$924$	−3.43851	−	27.1069i	−0.113119	−	0.891750i
$925$	3.48923	−	13.0220i	0.114725	−	0.428160i
$926$	12.9919	−	7.50089i	0.426941	−	0.246495i
$927$	−3.74562	−	2.16253i	−0.123022	−	0.0710269i
$928$	12.0510	+	12.0510i	0.395594	+	0.395594i
$929$	8.78421	−	2.35372i	0.288200	−	0.0772231i	−0.111823	−	0.993728i	$-0.535669\pi$
$929$	8.78421	−	2.35372i	0.288200	−	0.0772231i	0.400023	+	0.916505i	$0.369002\pi$
$930$	28.4786	−	7.63083i	0.933851	−	0.250225i
$931$	−33.3858	−	33.3858i	−1.09418	−	1.09418i
$932$	14.8266	+	8.56017i	0.485663	+	0.280398i
$933$	0.452052	−	0.260992i	0.0147995	−	0.00854450i
$934$	−13.8428	+	51.6620i	−0.452950	+	1.69043i
$935$	22.9036	−	2.90533i	0.749029	−	0.0950145i
$936$	1.35038	−	1.76868i	0.0441384	−	0.0578110i
$937$			48.0553i			1.56990i	0.619560	+	0.784950i	$0.287311\pi$
$937$			48.0553i			1.56990i	−0.619560	+	0.784950i	$0.712689\pi$
$938$	−21.1451	+	78.9145i	−0.690412	+	2.57665i
$939$	−6.21598	−	10.7664i	−0.202851	−	0.351348i
$940$	−11.3938	−	6.57821i	−0.371625	−	0.214558i
$941$	15.8369	−	15.8369i	0.516269	−	0.516269i	−0.400171	−	0.916440i	$-0.631049\pi$
$941$	15.8369	−	15.8369i	0.516269	−	0.516269i	0.916440	+	0.400171i	$0.131049\pi$
$942$	11.5212	+	42.9977i	0.375381	+	1.40094i
$943$	−28.9919	+	7.76835i	−0.944105	+	0.252972i
$944$	−20.7491	+	20.7491i	−0.675326	+	0.675326i
$945$	−7.89468	−	4.55800i	−0.256814	−	0.148272i
$946$	42.8364	−	32.5492i	1.39273	−	1.05827i
$947$	36.3345	+	9.73580i	1.18071	+	0.316371i	0.795209	−	0.606335i	$-0.207361\pi$
$947$	36.3345	+	9.73580i	1.18071	+	0.316371i	0.385503	+	0.922706i	$0.374028\pi$
$948$	−11.8885			−0.386121
$949$	42.1709	+	5.44828i	1.36892	+	0.176859i
$950$	−24.4690			−0.793880
$951$	−4.58310	+	17.1044i	−0.148617	+	0.554647i
$952$	−5.24707	+	3.02940i	−0.170059	+	0.0981834i
$953$	−3.12814	+	5.41811i	−0.101331	+	0.175510i	−0.912233	−	0.409672i	$-0.865643\pi$
$953$	−3.12814	+	5.41811i	−0.101331	+	0.175510i	0.810903	+	0.585181i	$0.198977\pi$
$954$	−17.2045	+	17.2045i	−0.557015	+	0.557015i
$955$	−46.7034	+	12.5141i	−1.51129	+	0.404948i
$956$	−5.12489	+	1.37321i	−0.165751	+	0.0444128i
$957$	5.51026	+	4.26968i	0.178122	+	0.138019i
$958$	−3.58858	+	6.21560i	−0.115942	+	0.200817i
$959$	−0.131007	−	0.226910i	−0.00423042	−	0.00732731i
$960$	−24.9952	−	6.69744i	−0.806716	−	0.216159i
$961$			0.290695i			0.00937726i
$962$	68.2216	−	9.14929i	2.19955	−	0.294985i
$963$		−	4.95100i		−	0.159544i
$964$	−20.9651	−	5.61757i	−0.675239	−	0.180930i
$965$	25.7138	−	14.8459i	0.827757	−	0.477906i
$966$	−38.0249	−	21.9537i	−1.22343	−	0.706349i
$967$	−29.9334	+	29.9334i	−0.962594	+	0.962594i	−0.999325	−	0.0367313i	$-0.988305\pi$
$967$	−29.9334	+	29.9334i	−0.962594	+	0.962594i	0.0367313	+	0.999325i	$0.488305\pi$
$968$	−3.33876	−	5.91117i	−0.107312	−	0.189992i
$969$	−5.71333	−	21.3224i	−0.183538	−	0.684975i
$970$	1.52725	+	1.52725i	0.0490370	+	0.0490370i
$971$	−9.86003	+	17.0781i	−0.316423	+	0.548062i	−0.979739	−	0.200278i	$-0.935815\pi$
$971$	−9.86003	+	17.0781i	−0.316423	+	0.548062i	0.663316	+	0.748340i	$0.269149\pi$
$972$	−1.98987	+	1.14885i	−0.0638252	+	0.0368495i
$973$	30.4522	+	8.15963i	0.976251	+	0.261586i
$974$	59.2397			1.89816
$975$	2.00817	−	4.88147i	0.0643128	−	0.156332i
$976$		−	9.12999i		−	0.292244i
$977$	−5.91237	+	22.0653i	−0.189154	+	0.705931i	0.804550	+	0.593886i	$0.202407\pi$
$977$	−5.91237	+	22.0653i	−0.189154	+	0.705931i	−0.993703	+	0.112045i	$0.964260\pi$
$978$	−2.54111	+	1.46711i	−0.0812556	+	0.0469130i
$979$	6.66104	+	2.79603i	0.212888	+	0.0893614i
$980$	24.1901	+	24.1901i	0.772725	+	0.772725i
$981$	−0.336771	−	1.25684i	−0.0107523	−	0.0401280i
$982$	4.21549	+	15.7324i	0.134522	+	0.502042i
$983$	1.13899	−	1.13899i	0.0363282	−	0.0363282i	−0.688709	−	0.725038i	$-0.741822\pi$
$983$	1.13899	−	1.13899i	0.0363282	−	0.0363282i	0.725038	+	0.688709i	$0.241822\pi$
$984$	1.56800	−	2.71585i	0.0499859	−	0.0865781i
$985$	−4.43700	−	7.68511i	−0.141375	−	0.244868i
$986$	3.08767	−	11.5233i	0.0983314	−	0.366978i
$987$	−8.07511			−0.257034
$988$	−25.7098	−	61.6472i	−0.817937	−	1.96126i
$989$		−	46.2199i		−	1.46971i
$990$	−17.3204	−	2.36355i	−0.550478	−	0.0751187i
$991$	−21.3289	−	36.9427i	−0.677534	−	1.17352i	−0.975721	−	0.219016i	$-0.929715\pi$
$991$	−21.3289	−	36.9427i	−0.677534	−	1.17352i	0.298188	−	0.954507i	$-0.403618\pi$
$992$	22.6791	−	39.2813i	0.720061	−	1.24718i
$993$	−4.82842	−	4.82842i	−0.153225	−	0.153225i
$994$	110.173	−	29.5207i	3.49446	−	0.936339i
$995$	3.02683	+	11.2963i	0.0959570	+	0.358116i
$996$	13.3243	+	13.3243i	0.422198	+	0.422198i
$997$	−32.3113	−	18.6549i	−1.02331	−	0.590807i	−0.108247	−	0.994124i	$-0.534524\pi$
$997$	−32.3113	−	18.6549i	−1.02331	−	0.590807i	−0.915060	+	0.403317i	$0.867857\pi$
$998$	−7.25458	−	12.5653i	−0.229640	−	0.397748i
$999$	−8.89501	−	2.38341i	−0.281426	−	0.0754078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bd.a.76.3	✓	56
11.10	odd	2	inner	429.2.bd.a.76.12	yes	56
13.6	odd	12	inner	429.2.bd.a.175.12	yes	56
143.32	even	12	inner	429.2.bd.a.175.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.a.76.3	✓	56	1.1	even	1	trivial
429.2.bd.a.76.12	yes	56	11.10	odd	2	inner
429.2.bd.a.175.3	yes	56	143.32	even	12	inner
429.2.bd.a.175.12	yes	56	13.6	odd	12	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00245 - 0.536555i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.98987 + 1.14885i) q^{4} +(1.79777 + 1.79777i) q^{5} +(0.536555 + 2.00245i) q^{6} +(-3.46337 + 0.928006i) q^{7} +(-0.436407 - 0.436407i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.00245 - 0.536555i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.98987 + 1.14885i) q^{4} +(1.79777 + 1.79777i) q^{5} +(0.536555 + 2.00245i) q^{6} +(-3.46337 + 0.928006i) q^{7} +(-0.436407 - 0.436407i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.63535 - 4.56456i) q^{10} +(-3.28617 - 0.448433i) q^{11} -2.29771i q^{12} +(2.85516 - 2.20183i) q^{13} +7.43315 q^{14} +(0.658030 - 2.45580i) q^{15} +(-1.65798 - 2.87170i) q^{16} +(-1.36897 + 2.37113i) q^{17} +(1.46590 - 1.46590i) q^{18} +(-2.08672 - 7.78774i) q^{19} +(1.51196 + 5.64271i) q^{20} +(2.53536 + 2.53536i) q^{21} +(6.33979 + 2.66118i) q^{22} +(5.11558 - 2.95348i) q^{23} +(-0.159736 + 0.596144i) q^{24} +1.46396i q^{25} +(-6.89873 + 2.87710i) q^{26} +1.00000 q^{27} +(-7.95780 - 2.13229i) q^{28} +(1.82021 - 1.05090i) q^{29} +(-2.63535 + 4.56456i) q^{30} +(-3.95542 - 3.95542i) q^{31} +(2.09867 + 7.83233i) q^{32} +(1.25473 + 3.07012i) q^{33} +(4.01355 - 4.01355i) q^{34} +(-7.89468 - 4.55800i) q^{35} +(-1.98987 + 1.14885i) q^{36} +(-8.89501 - 2.38341i) q^{37} +16.7142i q^{38} +(-3.33442 - 1.37173i) q^{39} -1.56912i q^{40} +(-4.90808 - 1.31512i) q^{41} +(-3.71658 - 6.43730i) q^{42} +(3.91232 - 6.77635i) q^{43} +(-6.02387 - 4.66765i) q^{44} +(-2.45580 + 0.658030i) q^{45} +(-11.8284 + 3.16942i) q^{46} +(-1.59250 + 1.59250i) q^{47} +(-1.65798 + 2.87170i) q^{48} +(5.07153 - 2.92805i) q^{49} +(0.785498 - 2.93152i) q^{50} +2.73795 q^{51} +(8.21099 - 1.10119i) q^{52} -11.7365 q^{53} +(-2.00245 - 0.536555i) q^{54} +(-5.10160 - 6.71396i) q^{55} +(1.91643 + 1.10645i) q^{56} +(-5.70102 + 5.70102i) q^{57} +(-4.20875 + 1.12773i) q^{58} +(-2.29035 - 8.54770i) q^{59} +(4.13075 - 4.13075i) q^{60} +(2.38447 + 1.37667i) q^{61} +(5.79824 + 10.0428i) q^{62} +(0.928006 - 3.46337i) q^{63} -10.1780i q^{64} +(9.09131 + 1.17455i) q^{65} +(-0.865246 - 6.82101i) q^{66} +(-2.84470 + 10.6166i) q^{67} +(-5.44816 + 3.14550i) q^{68} +(-5.11558 - 2.95348i) q^{69} +(13.3631 + 13.3631i) q^{70} +(14.8218 - 3.97149i) q^{71} +(0.596144 - 0.159736i) q^{72} +(8.33912 + 8.33912i) q^{73} +(16.5330 + 9.54533i) q^{74} +(1.26783 - 0.731982i) q^{75} +(4.79467 - 17.8940i) q^{76} +(11.7974 - 1.49650i) q^{77} +(5.94100 + 4.53593i) q^{78} -5.17408i q^{79} +(2.18200 - 8.14333i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.12257 + 5.26692i) q^{82} +(-5.79897 + 5.79897i) q^{83} +(2.13229 + 7.95780i) q^{84} +(-6.72385 + 1.80165i) q^{85} +(-11.4701 + 11.4701i) q^{86} +(-1.82021 - 1.05090i) q^{87} +(1.23841 + 1.62981i) q^{88} +(-2.10392 - 0.563744i) q^{89} +5.27069 q^{90} +(-7.84517 + 10.2753i) q^{91} +13.5725 q^{92} +(-1.44778 + 5.40320i) q^{93} +(4.04337 - 2.33444i) q^{94} +(10.2491 - 17.7520i) q^{95} +(5.73367 - 5.73367i) q^{96} +(-0.395823 + 0.106060i) q^{97} +(-11.7266 + 3.14212i) q^{98} +(2.03144 - 2.62169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more