LMFDB - Embedded newform 133.2.s.d.103.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(31,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("133.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$133 = 7 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	133.s (of order $6$ , 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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} + 26x^{14} + 265x^{12} + 1335x^{10} + 3450x^{8} + 4344x^{6} + 2376x^{4} + 423x^{2} + 9$ x^16 + 26x^14 + 265x^12 + 1335x^10 + 3450x^8 + 4344x^6 + 2376x^4 + 423*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.7
Root			$-2.43648i$ of defining polynomial
Character	$\chi$	$=$	133.103
Dual form			133.2.s.d.31.7

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11006 - 1.21824i) q^{2} +0.519505 q^{3} +(1.96822 - 3.40907i) q^{4} +(-2.56167 + 1.47898i) q^{5} +(1.09618 - 0.632882i) q^{6} +(0.877506 + 2.49599i) q^{7} -4.71813i q^{8} -2.73011 q^{9} +(-3.60351 + 6.24146i) q^{10} +(-2.13212 - 3.69294i) q^{11} +(1.02250 - 1.77103i) q^{12} +(0.490112 + 0.848899i) q^{13} +(4.89231 + 4.19767i) q^{14} +(-1.33080 + 0.768337i) q^{15} +(-1.81137 - 3.13738i) q^{16} -4.99613i q^{17} +(-5.76070 + 3.32594i) q^{18} +(1.53917 + 4.07811i) q^{19} +11.6439i q^{20} +(0.455869 + 1.29668i) q^{21} +(-8.99779 - 5.19488i) q^{22} +7.91309 q^{23} -2.45109i q^{24} +(1.87477 - 3.24719i) q^{25} +(2.06833 + 1.19415i) q^{26} -2.97682 q^{27} +(10.2361 + 1.92120i) q^{28} +(1.16758 - 0.674101i) q^{29} +(-1.87204 + 3.24247i) q^{30} +(-2.73769 - 4.74181i) q^{31} +(0.527856 + 0.304758i) q^{32} +(-1.10765 - 1.91850i) q^{33} +(-6.08649 - 10.5421i) q^{34} +(-5.93941 - 5.09609i) q^{35} +(-5.37348 + 9.30714i) q^{36} +(-1.05910 - 0.611469i) q^{37} +(8.21585 + 6.72996i) q^{38} +(0.254615 + 0.441007i) q^{39} +(6.97802 + 12.0863i) q^{40} +(-1.34076 + 2.32227i) q^{41} +(2.54158 + 2.18071i) q^{42} +(-2.72284 + 4.71610i) q^{43} -16.7860 q^{44} +(6.99365 - 4.03779i) q^{45} +(16.6971 - 9.64005i) q^{46} -4.39134i q^{47} +(-0.941015 - 1.62988i) q^{48} +(-5.45996 + 4.38050i) q^{49} -9.13568i q^{50} -2.59551i q^{51} +3.85860 q^{52} +(6.59523 + 3.80776i) q^{53} +(-6.28126 + 3.62649i) q^{54} +(10.9236 + 6.30673i) q^{55} +(11.7764 - 4.14019i) q^{56} +(0.799605 + 2.11860i) q^{57} +(1.64243 - 2.84478i) q^{58} -9.34345 q^{59} +6.04904i q^{60} +3.37328i q^{61} +(-11.5533 - 6.67033i) q^{62} +(-2.39569 - 6.81435i) q^{63} +8.73055 q^{64} +(-2.51101 - 1.44973i) q^{65} +(-4.67440 - 2.69876i) q^{66} +(-1.50548 - 0.869188i) q^{67} +(-17.0321 - 9.83350i) q^{68} +4.11088 q^{69} +(-18.7408 - 3.51741i) q^{70} +(-12.4289 - 7.17583i) q^{71} +12.8810i q^{72} -4.63227i q^{73} -2.97967 q^{74} +(0.973950 - 1.68693i) q^{75} +(16.9320 + 2.77951i) q^{76} +(7.34661 - 8.56234i) q^{77} +(1.07451 + 0.620366i) q^{78} +(-4.21472 + 2.43337i) q^{79} +(9.28026 + 5.35796i) q^{80} +6.64387 q^{81} +6.53348i q^{82} +2.39463i q^{83} +(5.31772 + 0.998072i) q^{84} +(7.38917 + 12.7984i) q^{85} +13.2683i q^{86} +(0.606561 - 0.350198i) q^{87} +(-17.4238 + 10.0596i) q^{88} +14.4359 q^{89} +(9.83800 - 17.0399i) q^{90} +(-1.68877 + 1.96823i) q^{91} +(15.5747 - 26.9762i) q^{92} +(-1.42224 - 2.46339i) q^{93} +(-5.34972 - 9.26598i) q^{94} +(-9.97428 - 8.17037i) q^{95} +(0.274224 + 0.158323i) q^{96} +(7.58396 - 13.1358i) q^{97} +(-6.18433 + 15.8947i) q^{98} +(5.82094 + 10.0822i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 8 q^{3} + 10 q^{4} + 9 q^{5} - 6 q^{6} + 2 q^{7} + 16 q^{9} - 2 q^{10} - 9 q^{11} - 17 q^{12} + 15 q^{13} + 3 q^{14} - 12 q^{15} - 22 q^{16} - 3 q^{18} + 8 q^{19} - 10 q^{21} - 27 q^{22} + 30 q^{23}+ \cdots + 18 q^{99}+O(q^{100})$ 16 * q - 8 * q^3 + 10 * q^4 + 9 * q^5 - 6 * q^6 + 2 * q^7 + 16 * q^9 - 2 * q^10 - 9 * q^11 - 17 * q^12 + 15 * q^13 + 3 * q^14 - 12 * q^15 - 22 * q^16 - 3 * q^18 + 8 * q^19 - 10 * q^21 - 27 * q^22 + 30 * q^23 + 13 * q^25 - 9 * q^26 - 38 * q^27 + 35 * q^28 - 18 * q^29 - 32 * q^30 - 27 * q^31 + 27 * q^32 - 12 * q^33 - 16 * q^34 - 6 * q^35 + 4 * q^36 - 39 * q^37 + 27 * q^38 - 9 * q^39 + 9 * q^40 + 9 * q^41 + 48 * q^42 - 9 * q^43 + 18 * q^44 + 75 * q^45 - 36 * q^46 + 35 * q^48 - 8 * q^49 + 18 * q^53 - 18 * q^54 + 15 * q^56 - 22 * q^57 - 20 * q^58 + 18 * q^59 - 45 * q^62 - 46 * q^63 - 22 * q^64 - 36 * q^65 - 45 * q^66 + 18 * q^67 + 63 * q^68 + 30 * q^69 - 19 * q^70 - 9 * q^71 + 18 * q^74 + 10 * q^75 + 98 * q^76 + 30 * q^77 + 54 * q^78 + 21 * q^79 + 27 * q^80 + 40 * q^81 - 34 * q^84 + 31 * q^85 - 48 * q^87 + 18 * q^88 + 24 * q^89 + 28 * q^90 + 15 * q^91 + 54 * q^92 + 6 * q^93 - 49 * q^94 - 66 * q^95 - 69 * q^96 + q^97 + 15 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$ .

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	2.11006	−	1.21824i	1.49204	−	0.861427i	0.492077	−	0.870552i	$-0.336238\pi$
$2$	2.11006	−	1.21824i	1.49204	−	0.861427i	0.999958	+	0.00912499i	$0.00290461\pi$
$3$	0.519505			0.299936			0.149968	−	0.988691i	$-0.452083\pi$
$3$	0.519505			0.299936			0.149968	+	0.988691i	$0.452083\pi$
$4$	1.96822	−	3.40907i	0.984112	−	1.70453i
$5$	−2.56167	+	1.47898i	−1.14561	+	0.661420i	−0.947814	−	0.318822i	$-0.896713\pi$
$5$	−2.56167	+	1.47898i	−1.14561	+	0.661420i	−0.197799	+	0.980243i	$0.563379\pi$
$6$	1.09618	−	0.632882i	0.447515	−	0.258373i
$7$	0.877506	+	2.49599i	0.331666	+	0.943397i
$7$	0.877506	+	2.49599i	0.331666	+	0.943397i
$8$		−	4.71813i		−	1.66811i
$9$	−2.73011			−0.910038
$10$	−3.60351	+	6.24146i	−1.13953	+	1.97372i
$11$	−2.13212	−	3.69294i	−0.642859	−	1.11346i	−0.984792	−	0.173740i	$-0.944415\pi$
$11$	−2.13212	−	3.69294i	−0.642859	−	1.11346i	0.341933	−	0.939724i	$-0.388919\pi$
$12$	1.02250	−	1.77103i	0.295171	−	0.511251i
$13$	0.490112	+	0.848899i	0.135933	+	0.235442i	0.925953	−	0.377638i	$-0.123264\pi$
$13$	0.490112	+	0.848899i	0.135933	+	0.235442i	−0.790021	+	0.613080i	$0.789930\pi$
$14$	4.89231	+	4.19767i	1.30753	+	1.12187i
$15$	−1.33080	+	0.768337i	−0.343611	+	0.198384i
$16$	−1.81137	−	3.13738i	−0.452842	−	0.784346i
$17$		−	4.99613i		−	1.21174i	−0.795564	−	0.605869i	$-0.792825\pi$
$17$		−	4.99613i		−	1.21174i	0.795564	−	0.605869i	$-0.207175\pi$
$18$	−5.76070	+	3.32594i	−1.35781	+	0.783931i
$19$	1.53917	+	4.07811i	0.353109	+	0.935582i
$19$	1.53917	+	4.07811i	0.353109	+	0.935582i
$20$			11.6439i			2.60365i
$21$	0.455869	+	1.29668i	0.0994787	+	0.282959i
$22$	−8.99779	−	5.19488i	−1.91834	−	1.10755i
$23$	7.91309			1.64999			0.824996	−	0.565138i	$-0.191177\pi$
$23$	7.91309			1.64999			0.824996	+	0.565138i	$0.191177\pi$
$24$		−	2.45109i		−	0.500326i
$25$	1.87477	−	3.24719i	0.374953	−	0.649438i
$26$	2.06833	+	1.19415i	0.405632	+	0.234192i
$27$	−2.97682			−0.572890
$28$	10.2361	+	1.92120i	1.93445	+	0.363073i
$29$	1.16758	−	0.674101i	0.216813	−	0.125177i	−0.387660	−	0.921802i	$-0.626717\pi$
$29$	1.16758	−	0.674101i	0.216813	−	0.125177i	0.604474	+	0.796625i	$0.293383\pi$
$30$	−1.87204	+	3.24247i	−0.341786	+	0.591991i
$31$	−2.73769	−	4.74181i	−0.491703	−	0.851655i	0.508251	−	0.861209i	$-0.330292\pi$
$31$	−2.73769	−	4.74181i	−0.491703	−	0.851655i	−0.999954	+	0.00955415i	$0.996959\pi$
$32$	0.527856	+	0.304758i	0.0933127	+	0.0538741i
$33$	−1.10765	−	1.91850i	−0.192817	−	0.333968i
$34$	−6.08649	−	10.5421i	−1.04382	−	1.80796i
$35$	−5.93941	−	5.09609i	−1.00394	−	0.861397i
$36$	−5.37348	+	9.30714i	−0.895580	+	1.55119i
$37$	−1.05910	−	0.611469i	−0.174114	−	0.100525i	0.410410	−	0.911901i	$-0.365386\pi$
$37$	−1.05910	−	0.611469i	−0.174114	−	0.100525i	−0.584524	+	0.811376i	$0.698719\pi$
$38$	8.21585	+	6.72996i	1.33279	+	1.09174i
$39$	0.254615	+	0.441007i	0.0407711	+	0.0706176i
$40$	6.97802	+	12.0863i	1.10332	+	1.91101i
$41$	−1.34076	+	2.32227i	−0.209392	+	0.362677i	−0.951523	−	0.307577i	$-0.900482\pi$
$41$	−1.34076	+	2.32227i	−0.209392	+	0.362677i	0.742131	+	0.670254i	$0.233815\pi$
$42$	2.54158	+	2.18071i	0.392174	+	0.336491i
$43$	−2.72284	+	4.71610i	−0.415229	+	0.719198i	−0.995452	−	0.0952593i	$-0.969632\pi$
$43$	−2.72284	+	4.71610i	−0.415229	+	0.719198i	0.580223	+	0.814457i	$0.302965\pi$
$44$	−16.7860			−2.53058
$45$	6.99365	−	4.03779i	1.04255	−	0.601918i
$46$	16.6971	−	9.64005i	2.46185	−	1.42135i
$47$		−	4.39134i		−	0.640543i	−0.947326	−	0.320272i	$-0.896226\pi$
$47$		−	4.39134i		−	0.640543i	0.947326	−	0.320272i	$-0.103774\pi$
$48$	−0.941015	−	1.62988i	−0.135824	−	0.235254i
$49$	−5.45996	+	4.38050i	−0.779995	+	0.625786i
$50$		−	9.13568i		−	1.29198i
$51$		−	2.59551i		−	0.363444i
$52$	3.85860			0.535092
$53$	6.59523	+	3.80776i	0.905925	+	0.523036i	0.879118	−	0.476605i	$-0.158133\pi$
$53$	6.59523	+	3.80776i	0.905925	+	0.523036i	0.0268069	+	0.999641i	$0.491466\pi$
$54$	−6.28126	+	3.62649i	−0.854771	+	0.493502i
$55$	10.9236	+	6.30673i	1.47294	+	0.850400i
$56$	11.7764	−	4.14019i	1.57369	−	0.553256i
$57$	0.799605	+	2.11860i	0.105910	+	0.280615i
$58$	1.64243	−	2.84478i	0.215662	−	0.373538i
$59$	−9.34345			−1.21641			−0.608207	−	0.793779i	$-0.708111\pi$
$59$	−9.34345			−1.21641			−0.608207	+	0.793779i	$0.708111\pi$
$60$			6.04904i			0.780928i
$61$			3.37328i			0.431904i	0.976404	+	0.215952i	$0.0692855\pi$
$61$			3.37328i			0.431904i	−0.976404	+	0.215952i	$0.930715\pi$
$62$	−11.5533	−	6.67033i	−1.46728	−	0.847132i
$63$	−2.39569	−	6.81435i	−0.301829	−	0.858527i
$64$	8.73055			1.09132
$65$	−2.51101	−	1.44973i	−0.311452	−	0.179817i
$66$	−4.67440	−	2.69876i	−0.575378	−	0.332195i
$67$	−1.50548	−	0.869188i	−0.183923	−	0.106188i	0.405211	−	0.914223i	$-0.367198\pi$
$67$	−1.50548	−	0.869188i	−0.183923	−	0.106188i	−0.589135	+	0.808035i	$0.700531\pi$
$68$	−17.0321	−	9.83350i	−2.06545	−	1.19249i
$69$	4.11088			0.494892
$70$	−18.7408	−	3.51741i	−2.23995	−	0.420411i
$71$	−12.4289	−	7.17583i	−1.47504	−	0.851614i	−0.475435	−	0.879751i	$-0.657709\pi$
$71$	−12.4289	−	7.17583i	−1.47504	−	0.851614i	−0.999604	+	0.0281369i	$0.991043\pi$
$72$			12.8810i			1.51804i
$73$		−	4.63227i		−	0.542167i	−0.962556	−	0.271083i	$-0.912618\pi$
$73$		−	4.63227i		−	0.542167i	0.962556	−	0.271083i	$-0.0873819\pi$
$74$	−2.97967			−0.346379
$75$	0.973950	−	1.68693i	0.112462	−	0.194790i
$76$	16.9320	+	2.77951i	1.94223	+	0.318832i
$77$	7.34661	−	8.56234i	0.837224	−	0.975770i
$78$	1.07451	+	0.620366i	0.121664	+	0.0702427i
$79$	−4.21472	+	2.43337i	−0.474193	+	0.273775i	−0.717993	−	0.696050i	$-0.754939\pi$
$79$	−4.21472	+	2.43337i	−0.474193	+	0.273775i	0.243800	+	0.969825i	$0.421606\pi$
$80$	9.28026	+	5.35796i	1.03756	+	0.599038i
$81$	6.64387			0.738208
$82$			6.53348i			0.721503i
$83$			2.39463i			0.262845i	0.991326	+	0.131422i	$0.0419544\pi$
$83$			2.39463i			0.262845i	−0.991326	+	0.131422i	$0.958046\pi$
$84$	5.31772	+	0.998072i	0.580211	+	0.108899i
$85$	7.38917	+	12.7984i	0.801469	+	1.38818i
$86$			13.2683i			1.43076i
$87$	0.606561	−	0.350198i	0.0650302	−	0.0375452i
$88$	−17.4238	+	10.0596i	−1.85738	+	1.07236i
$89$	14.4359			1.53020			0.765101	−	0.643910i	$-0.222689\pi$
$89$	14.4359			1.53020			0.765101	+	0.643910i	$0.222689\pi$
$90$	9.83800	−	17.0399i	1.03702	−	1.79616i
$91$	−1.68877	+	1.96823i	−0.177031	+	0.206327i
$92$	15.5747	−	26.9762i	1.62378	−	2.81247i
$93$	−1.42224	−	2.46339i	−0.147480	−	0.255442i
$94$	−5.34972	−	9.26598i	−0.551781	−	0.955713i
$95$	−9.97428	−	8.17037i	−1.02334	−	0.838262i
$96$	0.274224	+	0.158323i	0.0279878	+	0.0161588i
$97$	7.58396	−	13.1358i	0.770035	−	1.33374i	−0.167508	−	0.985871i	$-0.553572\pi$
$97$	7.58396	−	13.1358i	0.770035	−	1.33374i	0.937543	−	0.347869i	$-0.113095\pi$
$98$	−6.18433	+	15.8947i	−0.624711	+	1.60560i
$99$	5.82094	+	10.0822i	0.585026	+	1.01330i
$100$	−7.37993	−	12.7824i	−0.737993	−	1.27824i
$101$	4.32394	+	2.49643i	0.430248	+	0.248404i	0.699452	−	0.714679i	$-0.253427\pi$
$101$	4.32394	+	2.49643i	0.430248	+	0.248404i	−0.269204	+	0.963083i	$0.586761\pi$
$102$	−3.16196	−	5.47667i	−0.313081	−	0.542272i
$103$	−4.27296	+	7.40099i	−0.421027	+	0.729241i	−0.996040	−	0.0889036i	$-0.971664\pi$
$103$	−4.27296	+	7.40099i	−0.421027	+	0.729241i	0.575013	+	0.818144i	$0.304997\pi$
$104$	4.00521	−	2.31241i	0.392743	−	0.226751i
$105$	−3.08555	−	2.64745i	−0.301119	−	0.258364i
$106$	18.5551			1.80223
$107$	3.83188	+	2.21233i	0.370441	+	0.213874i	0.673651	−	0.739049i	$-0.264725\pi$
$107$	3.83188	+	2.21233i	0.370441	+	0.213874i	−0.303210	+	0.952924i	$0.598058\pi$
$108$	−5.85905	+	10.1482i	−0.563788	+	0.976509i
$109$			2.52839i			0.242176i	0.992642	+	0.121088i	$0.0386383\pi$
$109$			2.52839i			0.242176i	−0.992642	+	0.121088i	$0.961362\pi$
$110$	30.7325			2.93023
$111$	−0.550205	−	0.317661i	−0.0522231	−	0.0301510i
$112$	6.24140	−	7.27424i	0.589757	−	0.687351i
$113$			16.0323i			1.50820i	0.656762	+	0.754098i	$0.271925\pi$
$113$			16.0323i			1.50820i	−0.656762	+	0.754098i	$0.728075\pi$
$114$	4.26817	+	3.49625i	0.399751	+	0.327453i
$115$	−20.2707	+	11.7033i	−1.89025	+	1.09134i
$116$		−	5.30713i		−	0.492754i
$117$	−1.33806	−	2.31759i	−0.123704	−	0.214261i
$118$	−19.7152	+	11.3826i	−1.81493	+	1.04785i
$119$	12.4703	−	4.38413i	1.14315	−	0.401893i
$120$	3.62511	+	6.27888i	0.330926	+	0.573181i
$121$	−3.59189	+	6.22133i	−0.326535	+	0.565576i
$122$	4.10947	+	7.11781i	0.372054	+	0.644416i
$123$	−0.696532	+	1.20643i	−0.0628042	+	0.108780i
$124$	−21.5535			−1.93556
$125$		−	3.69883i		−	0.330833i
$126$	−13.3566	−	11.4601i	−1.18990	−	1.02095i
$127$	−6.21062	+	3.58570i	−0.551104	+	0.318180i	−0.749567	−	0.661929i	$-0.769738\pi$
$127$	−6.21062	+	3.58570i	−0.551104	+	0.318180i	0.198463	+	0.980108i	$0.436405\pi$
$128$	17.3662	−	10.0264i	1.53497	−	0.886217i
$129$	−1.41453	+	2.45003i	−0.124542	+	0.215714i
$130$	−7.06450			−0.619597
$131$	−14.8952	+	8.59975i	−1.30140	+	0.751364i	−0.980644	−	0.195798i	$-0.937270\pi$
$131$	−14.8952	+	8.59975i	−1.30140	+	0.751364i	−0.320756	+	0.947162i	$0.603937\pi$
$132$	−8.72040			−0.759013
$133$	−8.82830	+	7.42032i	−0.765511	+	0.643423i
$134$	−4.23552			−0.365893
$135$	7.62563	−	4.40266i	0.656310	−	0.378921i
$136$	−23.5724			−2.02131
$137$	−3.20193	+	5.54590i	−0.273559	+	0.473818i	−0.969771	−	0.244019i	$-0.921534\pi$
$137$	−3.20193	+	5.54590i	−0.273559	+	0.473818i	0.696212	+	0.717837i	$0.254868\pi$
$138$	8.67420	−	5.00805i	0.738397	−	0.426314i
$139$	1.06133	−	0.612762i	0.0900212	−	0.0519738i	−0.454314	−	0.890842i	$-0.650115\pi$
$139$	1.06133	−	0.612762i	0.0900212	−	0.0519738i	0.544335	+	0.838868i	$0.316782\pi$
$140$	−29.0630	+	10.2176i	−2.45627	+	0.863542i
$141$		−	2.28132i		−	0.192122i
$142$	−34.9676			−2.93441
$143$	2.08996	−	3.61991i	0.174771	−	0.302712i
$144$	4.94524	+	8.56542i	0.412104	+	0.713785i
$145$	−1.99396	+	3.45365i	−0.165590	+	0.286810i
$146$	−5.64323	−	9.77436i	−0.467037	−	0.808932i
$147$	−2.83648	+	2.27569i	−0.233949	+	0.187696i
$148$	−4.16908	+	2.40702i	−0.342696	+	0.197856i
$149$	1.11809	+	1.93659i	0.0915973	+	0.158651i	0.908183	−	0.418572i	$-0.137469\pi$
$149$	1.11809	+	1.93659i	0.0915973	+	0.158651i	−0.816586	+	0.577224i	$0.804136\pi$
$150$		−	4.74603i		−	0.387511i
$151$	18.6079	−	10.7433i	1.51429	−	0.874275i	0.514429	−	0.857533i	$-0.328004\pi$
$151$	18.6079	−	10.7433i	1.51429	−	0.874275i	0.999860	−	0.0167425i	$-0.00532954\pi$
$152$	19.2410	−	7.26199i	1.56065	−	0.589025i
$153$			13.6400i			1.10273i
$154$	5.07076	−	27.0170i	0.408614	−	2.17709i
$155$	14.0261	+	8.09797i	1.12660	+	0.650445i
$156$	2.00456			0.160493
$157$			2.18736i			0.174571i	0.996183	+	0.0872853i	$0.0278192\pi$
$157$			2.18736i			0.174571i	−0.996183	+	0.0872853i	$0.972181\pi$
$158$	−5.92886	+	10.2691i	−0.471675	+	0.816965i
$159$	3.42625	+	1.97815i	0.271720	+	0.156877i
$160$	−1.80292			−0.142534
$161$	6.94378	+	19.7510i	0.547247	+	1.55660i
$162$	14.0189	−	8.09384i	1.10143	−	0.635912i
$163$	−1.15162	+	1.99467i	−0.0902021	+	0.156235i	−0.907596	−	0.419844i	$-0.862085\pi$
$163$	−1.15162	+	1.99467i	−0.0902021	+	0.156235i	0.817394	+	0.576079i	$0.195418\pi$
$164$	5.27784	+	9.14149i	0.412130	+	0.713830i
$165$	5.67485	+	3.27638i	0.441787	+	0.255066i
$166$	2.91724	+	5.05281i	0.226422	+	0.392174i
$167$	−2.71065	−	4.69499i	−0.209756	−	0.363309i	0.741881	−	0.670531i	$-0.233934\pi$
$167$	−2.71065	−	4.69499i	−0.209756	−	0.363309i	−0.951638	+	0.307222i	$0.900600\pi$
$168$	6.11790	−	2.15085i	0.472006	−	0.165941i
$169$	6.01958	−	10.4262i	0.463045	−	0.802017i
$170$	31.1831	+	18.0036i	2.39164	+	1.38081i
$171$	−4.20210	−	11.1337i	−0.321343	−	0.851416i
$172$	10.7183	+	18.5647i	0.817265	+	1.41554i
$173$	−9.45972	−	16.3847i	−0.719209	−	1.24571i	−0.961314	−	0.275457i	$-0.911171\pi$
$173$	−9.45972	−	16.3847i	−0.719209	−	1.24571i	0.242104	−	0.970250i	$-0.422162\pi$
$174$	0.853252	−	1.47788i	0.0646849	−	0.112038i
$175$	9.75009	+	1.82997i	0.737037	+	0.138333i
$176$	−7.72412	+	13.3786i	−0.582227	+	1.00845i
$177$	−4.85397			−0.364846
$178$	30.4606	−	17.5864i	2.28312	−	1.31816i
$179$	−0.738758	+	0.426522i	−0.0552173	+	0.0318797i	−0.527355	−	0.849645i	$-0.676816\pi$
$179$	−0.738758	+	0.426522i	−0.0552173	+	0.0318797i	0.472137	+	0.881525i	$0.343483\pi$
$180$		−	31.7891i		−	2.36942i
$181$	9.12286	+	15.8013i	0.678097	+	1.17450i	0.975553	+	0.219763i	$0.0705284\pi$
$181$	9.12286	+	15.8013i	0.678097	+	1.17450i	−0.297456	+	0.954735i	$0.596138\pi$
$182$	−1.16562	+	6.21041i	−0.0864014	+	0.460346i
$183$			1.75243i			0.129544i
$184$		−	37.3349i		−	2.75237i
$185$	3.61740			0.265957
$186$	−6.00202	−	3.46527i	−0.440089	−	0.254086i
$187$	−18.4504	+	10.6524i	−1.34923	+	0.778977i
$188$	−14.9704	−	8.64315i	−1.09183	−	0.630366i
$189$	−2.61218	−	7.43013i	−0.190008	−	0.540462i
$190$	−30.9998	−	5.08885i	−2.24896	−	0.369184i
$191$	7.10389	−	12.3043i	0.514020	−	0.890308i	−0.485848	−	0.874043i	$-0.661489\pi$
$191$	7.10389	−	12.3043i	0.514020	−	0.890308i	0.999868	−	0.0162649i	$-0.00517749\pi$
$192$	4.53556			0.327326
$193$			11.6210i			0.836498i	0.908332	+	0.418249i	$0.137356\pi$
$193$			11.6210i			0.836498i	−0.908332	+	0.418249i	$0.862644\pi$
$194$		−	36.9564i		−	2.65331i
$195$	−1.30448	−	0.753143i	−0.0934159	−	0.0539337i
$196$	4.18697	+	27.2352i	0.299070	+	1.94537i
$197$	−23.6941			−1.68814			−0.844068	−	0.536236i	$-0.819846\pi$
$197$	−23.6941			−1.68814			−0.844068	+	0.536236i	$0.819846\pi$
$198$	24.5650	+	14.1826i	1.74576	+	1.00791i
$199$	11.1859	+	6.45816i	0.792945	+	0.457807i	0.840998	−	0.541038i	$-0.181968\pi$
$199$	11.1859	+	6.45816i	0.792945	+	0.457807i	−0.0480533	+	0.998845i	$0.515302\pi$
$200$	−15.3207	−	8.84539i	−1.08333	−	0.625463i
$201$	−0.782102	−	0.451547i	−0.0551653	−	0.0318497i
$202$	12.1650			0.855927
$203$	2.70711	+	2.32274i	0.190002	+	0.163024i
$204$	−8.84827	−	5.10855i	−0.619503	−	0.357670i
$205$		−	7.93184i		−	0.553984i
$206$			20.8220i			1.45074i
$207$	−21.6036			−1.50156
$208$	1.77555	−	3.07534i	0.123112	−	0.213236i
$209$	11.7785	−	14.3791i	0.814738	−	0.994622i
$210$	−9.73591	−	1.82731i	−0.671842	−	0.126097i
$211$	−3.64879	−	2.10663i	−0.251193	−	0.145026i	0.369117	−	0.929383i	$-0.379660\pi$
$211$	−3.64879	−	2.10663i	−0.251193	−	0.145026i	−0.620310	+	0.784356i	$0.712993\pi$
$212$	25.9618	−	14.9890i	1.78306	−	1.02945i
$213$	−6.45687	−	3.72788i	−0.442417	−	0.255430i
$214$	10.7806			0.736949
$215$		−	16.1081i		−	1.09856i
$216$			14.0450i			0.955643i
$217$	9.43319	−	10.9942i	0.640367	−	0.746336i
$218$	3.08019	+	5.33505i	0.208617	+	0.361335i
$219$		−	2.40649i		−	0.162615i
$220$	43.0001	−	24.8261i	2.89907	−	1.67378i
$221$	4.24121	−	2.44866i	0.285294	−	0.164715i
$222$	−1.54795			−0.103892
$223$	2.30802	−	3.99761i	0.154557	−	0.267700i	−0.778341	−	0.627842i	$-0.783938\pi$
$223$	2.30802	−	3.99761i	0.154557	−	0.267700i	0.932897	+	0.360142i	$0.117272\pi$
$224$	−0.297477	+	1.58495i	−0.0198760	+	0.105899i
$225$	−5.11833	+	8.86521i	−0.341222	+	0.591014i
$226$	19.5313	+	33.8291i	1.29920	+	2.25028i
$227$	−13.3601	−	23.1404i	−0.886744	−	1.53589i	−0.843702	−	0.536812i	$-0.819628\pi$
$227$	−13.3601	−	23.1404i	−0.886744	−	1.53589i	−0.0430420	−	0.999073i	$-0.513705\pi$
$228$	8.79623	+	1.44397i	0.582545	+	0.0956292i
$229$	3.97646	+	2.29581i	0.262772	+	0.151711i	0.625598	−	0.780145i	$-0.284855\pi$
$229$	3.97646	+	2.29581i	0.262772	+	0.151711i	−0.362827	+	0.931857i	$0.618188\pi$
$230$	−28.5149	+	49.3892i	−1.88022	+	3.25663i
$231$	3.81660	−	4.44818i	0.251114	−	0.292669i
$232$	−3.18049	−	5.50877i	−0.208810	−	0.361669i
$233$	−3.96470	−	6.86706i	−0.259736	−	0.449876i	0.706435	−	0.707778i	$-0.250302\pi$
$233$	−3.96470	−	6.86706i	−0.259736	−	0.449876i	−0.966171	+	0.257902i	$0.916969\pi$
$234$	−5.64677	−	3.26017i	−0.369141	−	0.213124i
$235$	6.49471	+	11.2492i	0.423668	+	0.733815i
$236$	−18.3900	+	31.8524i	−1.19709	+	2.07342i
$237$	−2.18957	+	1.26415i	−0.142228	+	0.0821152i
$238$	20.9721	−	24.4426i	1.35942	−	1.58438i
$239$	−1.68928			−0.109270			−0.0546351	−	0.998506i	$-0.517400\pi$
$239$	−1.68928			−0.109270			−0.0546351	+	0.998506i	$0.517400\pi$
$240$	4.82114	+	2.78348i	0.311203	+	0.179673i
$241$	13.2765	−	22.9956i	0.855216	−	1.48128i	−0.0212286	−	0.999775i	$-0.506758\pi$
$241$	13.2765	−	22.9956i	0.855216	−	1.48128i	0.876445	−	0.481503i	$-0.159909\pi$
$242$			17.5031i			1.12514i
$243$	12.3820			0.794305
$244$	11.4997	+	6.63937i	0.736195	+	0.425042i
$245$	7.50795	−	19.2966i	0.479665	−	1.23281i
$246$			3.39418i			0.216405i
$247$	−2.70754	+	3.30533i	−0.172276	+	0.210313i
$248$	−22.3725	+	12.9168i	−1.42065	+	0.820215i
$249$			1.24402i			0.0788367i
$250$	−4.50607	−	7.80474i	−0.284989	−	0.493615i
$251$	−9.03338	+	5.21543i	−0.570182	+	0.329195i	−0.757222	−	0.653158i	$-0.773444\pi$
$251$	−9.03338	+	5.21543i	−0.570182	+	0.329195i	0.187040	+	0.982352i	$0.440111\pi$
$252$	−27.9458	−	5.24509i	−1.76042	−	0.330410i
$253$	−16.8717	−	29.2226i	−1.06071	−	1.83721i
$254$	−8.73651	+	15.1321i	−0.548177	+	0.949471i
$255$	3.83871	+	6.64884i	0.240389	+	0.416367i
$256$	15.6986	−	27.1908i	0.981163	−	1.69942i
$257$	9.84420			0.614065			0.307032	−	0.951699i	$-0.400664\pi$
$257$	9.84420			0.614065			0.307032	+	0.951699i	$0.400664\pi$
$258$			6.89295i			0.429136i
$259$	0.596860	−	3.18006i	0.0370870	−	0.197600i
$260$	−9.88446	+	5.70680i	−0.613008	+	0.353921i
$261$	−3.18762	+	1.84037i	−0.197309	+	0.113916i
$262$	−20.9531	+	36.2919i	−1.29449	+	2.24212i
$263$	−5.91445			−0.364701			−0.182350	−	0.983234i	$-0.558370\pi$
$263$	−5.91445			−0.364701			−0.182350	+	0.983234i	$0.558370\pi$
$264$	−9.05173	+	5.22602i	−0.557096	+	0.321639i
$265$	−22.5264			−1.38379
$266$	−9.58847	+	26.4123i	−0.587907	+	1.61944i
$267$	7.49952			0.458963
$268$	−5.92624	+	3.42151i	−0.362002	+	0.209002i
$269$	20.7687			1.26629			0.633144	−	0.774034i	$-0.281764\pi$
$269$	20.7687			1.26629			0.633144	+	0.774034i	$0.281764\pi$
$270$	10.7270	−	18.5797i	0.652825	−	1.13073i
$271$	10.7055	−	6.18082i	0.650313	−	0.375458i	−0.138263	−	0.990396i	$-0.544152\pi$
$271$	10.7055	−	6.18082i	0.650313	−	0.375458i	0.788576	+	0.614937i	$0.210819\pi$
$272$	−15.6748	+	9.04983i	−0.950422	+	0.548726i
$273$	−0.877324	+	1.02250i	−0.0530980	+	0.0618848i
$274$			15.6029i			0.942604i
$275$	−15.9889			−0.964169
$276$	8.09115	−	14.0143i	0.487030	−	0.843560i
$277$	−7.72105	−	13.3732i	−0.463913	−	0.803521i	0.535239	−	0.844701i	$-0.320222\pi$
$277$	−7.72105	−	13.3732i	−0.463913	−	0.803521i	−0.999152	+	0.0411801i	$0.986888\pi$
$278$	1.49298	−	2.58592i	0.0895432	−	0.155093i
$279$	7.47420	+	12.9457i	0.447469	+	0.775038i
$280$	−24.0440	+	28.0229i	−1.43691	+	1.67469i
$281$	−19.4675	+	11.2395i	−1.16133	+	0.670495i	−0.951623	−	0.307269i	$-0.900585\pi$
$281$	−19.4675	+	11.2395i	−1.16133	+	0.670495i	−0.209709	+	0.977764i	$0.567252\pi$
$282$	−2.77920	−	4.81372i	−0.165499	−	0.286653i
$283$			20.9466i			1.24515i	0.782562	+	0.622573i	$0.213912\pi$
$283$			20.9466i			1.24515i	−0.782562	+	0.622573i	$0.786088\pi$
$284$	−48.9257	+	28.2473i	−2.90321	+	1.67617i
$285$	−5.18169	−	4.24454i	−0.306937	−	0.251425i
$286$		−	10.1843i		−	0.602210i
$287$	−6.97289	−	1.30873i	−0.411597	−	0.0772517i
$288$	−1.44111	−	0.832024i	−0.0849181	−	0.0490275i
$289$	−7.96129			−0.468311
$290$			9.71652i			0.570573i
$291$	3.93990	−	6.82412i	0.230961	−	0.400037i
$292$	−15.7917	−	9.11736i	−0.924141	−	0.533553i
$293$	11.0045			0.642889			0.321445	−	0.946928i	$-0.395832\pi$
$293$	11.0045			0.642889			0.321445	+	0.946928i	$0.395832\pi$
$294$	−3.21279	+	8.25735i	−0.187373	+	0.481578i
$295$	23.9348	−	13.8188i	1.39354	−	0.804561i
$296$	−2.88499	+	4.99695i	−0.167687	+	0.290442i
$297$	6.34695	+	10.9932i	0.368287	+	0.637892i
$298$	4.71846	+	2.72420i	0.273333	+	0.157809i
$299$	3.87830	+	6.71741i	0.224288	+	0.388478i
$300$	−3.83391	−	6.64052i	−0.221351	−	0.383391i
$301$	−14.1607	−	2.65779i	−0.816207	−	0.153192i
$302$	26.1758	−	45.3378i	1.50625	−	2.60890i
$303$	2.24631	+	1.29691i	0.129047	+	0.0745053i
$304$	10.0066	−	12.2159i	0.573917	−	0.700631i
$305$	−4.98901	−	8.64122i	−0.285670	−	0.494795i
$306$	16.6168	+	28.7812i	0.949920	+	1.64531i
$307$	0.280430	−	0.485719i	0.0160050	−	0.0277215i	−0.857912	−	0.513797i	$-0.828239\pi$
$307$	0.280430	−	0.485719i	0.0160050	−	0.0277215i	0.873917	+	0.486075i	$0.161572\pi$
$308$	−14.7298	−	41.8977i	−0.839309	−	2.38734i
$309$	−2.21982	+	3.84485i	−0.126281	+	0.218726i
$310$	39.4611			2.24124
$311$	−22.5185	+	13.0010i	−1.27690	+	0.737221i	−0.976278	−	0.216520i	$-0.930529\pi$
$311$	−22.5185	+	13.0010i	−1.27690	+	0.737221i	−0.300627	+	0.953742i	$0.597196\pi$
$312$	2.08073	−	1.20131i	0.117798	−	0.0680107i
$313$		−	14.2755i		−	0.806897i	−0.915002	−	0.403449i	$-0.867811\pi$
$313$		−	14.2755i		−	0.806897i	0.915002	−	0.403449i	$-0.132189\pi$
$314$	2.66474	+	4.61546i	0.150380	+	0.260465i
$315$	16.2153	+	13.9129i	0.913627	+	0.783904i
$316$			19.1577i			1.07770i
$317$		−	25.0580i		−	1.40740i	−0.710498	−	0.703699i	$-0.751530\pi$
$317$		−	25.0580i		−	1.40740i	0.710498	−	0.703699i	$-0.248470\pi$
$318$	9.63945			0.540553
$319$	−4.97883	−	2.87453i	−0.278761	−	0.160943i
$320$	−22.3648	+	12.9123i	−1.25023	+	0.721820i
$321$	1.99068	+	1.14932i	0.111109	+	0.0641487i
$322$	38.7133	+	33.2165i	2.15741	+	1.85109i
$323$	20.3747	−	7.68988i	1.13368	−	0.427876i
$324$	13.0766	−	22.6494i	0.726480	−	1.25830i
$325$	3.67538			0.203874
$326$			5.61182i			0.310810i
$327$			1.31351i			0.0726374i
$328$	10.9568	+	6.32588i	0.604985	+	0.349288i
$329$	10.9608	−	3.85343i	0.604286	−	0.212447i
$330$	15.9657			0.878882
$331$	−5.26615	−	3.04041i	−0.289454	−	0.167116i	0.348242	−	0.937405i	$-0.386779\pi$
$331$	−5.26615	−	3.04041i	−0.289454	−	0.167116i	−0.637695	+	0.770289i	$0.720112\pi$
$332$	8.16346	+	4.71317i	0.448028	+	0.258669i
$333$	2.89145	+	1.66938i	0.158451	+	0.0914815i
$334$	−11.4393	−	6.60446i	−0.625928	−	0.361380i
$335$	5.14205			0.280940
$336$	3.24244	−	3.77900i	0.176889	−	0.206161i
$337$	−3.04940	−	1.76057i	−0.166111	−	0.0959044i	0.414640	−	0.909986i	$-0.363908\pi$
$337$	−3.04940	−	1.76057i	−0.166111	−	0.0959044i	−0.580751	+	0.814081i	$0.697241\pi$
$338$		−	29.3332i		−	1.59552i
$339$			8.32887i			0.452362i
$340$	58.1742			3.15494
$341$	−11.6742	+	20.2202i	−0.632191	+	1.09499i
$342$	−22.4302	−	18.3736i	−1.21289	−	0.993528i
$343$	−15.7249	−	9.78412i	−0.849062	−	0.528293i
$344$	22.2511	+	12.8467i	1.19970	+	0.692648i
$345$	−10.5307	+	6.07992i	−0.566955	+	0.327332i
$346$	−39.9211	−	23.0484i	−2.14617	−	1.23909i
$347$	−30.9642			−1.66225			−0.831123	−	0.556088i	$-0.812302\pi$
$347$	−30.9642			−1.66225			−0.831123	+	0.556088i	$0.812302\pi$
$348$		−	2.75708i		−	0.147795i
$349$			10.6995i			0.572734i	0.958120	+	0.286367i	$0.0924476\pi$
$349$			10.6995i			0.572734i	−0.958120	+	0.286367i	$0.907552\pi$
$350$	22.8026	−	8.01661i	1.21885	−	0.428506i
$351$	−1.45898	−	2.52702i	−0.0778744	−	0.134882i
$352$		−	2.59912i		−	0.138534i
$353$	−8.50793	+	4.91206i	−0.452832	+	0.261442i	−0.709025	−	0.705183i	$-0.750865\pi$
$353$	−8.50793	+	4.91206i	−0.452832	+	0.261442i	0.256194	+	0.966625i	$0.417532\pi$
$354$	−10.2421	+	5.91330i	−0.544364	+	0.314289i
$355$	42.4516			2.25310
$356$	28.4131	−	49.2129i	1.50589	−	2.60828i
$357$	6.47838	−	2.27758i	0.342872	−	0.120542i
$358$	−1.03921	+	1.79997i	−0.0549241	+	0.0951314i
$359$	−1.73994	−	3.01367i	−0.0918306	−	0.159055i	0.816451	−	0.577415i	$-0.195939\pi$
$359$	−1.73994	−	3.01367i	−0.0918306	−	0.159055i	−0.908281	+	0.418360i	$0.862605\pi$
$360$	−19.0508	−	32.9969i	−1.00406	−	1.73909i
$361$	−14.2619	+	12.5538i	−0.750628	+	0.660725i
$362$	38.4995	+	22.2277i	2.02349	+	1.16826i
$363$	−1.86600	+	3.23201i	−0.0979397	+	0.169637i
$364$	3.38595	+	9.63105i	0.177472	+	0.504804i
$365$	6.85104	+	11.8664i	0.358600	+	0.621113i
$366$	2.13489	+	3.69773i	0.111592	+	0.193284i
$367$	23.5835	+	13.6160i	1.23105	+	0.710747i	0.967249	−	0.253830i	$-0.0816904\pi$
$367$	23.5835	+	13.6160i	1.23105	+	0.710747i	0.263801	+	0.964577i	$0.415024\pi$
$368$	−14.3335	−	24.8264i	−0.747186	−	1.29416i
$369$	3.66043	−	6.34006i	0.190555	−	0.330050i
$370$	7.63292	−	4.40687i	0.396817	−	0.229102i
$371$	−3.71678	+	19.8030i	−0.192966	+	1.02812i
$372$	−11.1972			−0.580546
$373$	27.0858	+	15.6380i	1.40245	+	0.809704i	0.994643	−	0.103366i	$-0.0329613\pi$
$373$	27.0858	+	15.6380i	1.40245	+	0.809704i	0.407804	+	0.913069i	$0.366295\pi$
$374$	−25.9543	+	44.9541i	−1.34206	+	2.32452i
$375$		−	1.92156i		−	0.0992289i
$376$	−20.7189			−1.06850
$377$	1.14449	+	0.660770i	0.0589441	+	0.0340314i
$378$	−14.5635	−	12.4957i	−0.749067	−	0.642710i
$379$		−	24.5248i		−	1.25975i	−0.776695	−	0.629877i	$-0.783105\pi$
$379$		−	24.5248i		−	1.25975i	0.776695	−	0.629877i	$-0.216895\pi$
$380$	−47.4849	+	17.9219i	−2.43593	+	0.919372i
$381$	−3.22645	+	1.86279i	−0.165296	+	0.0954336i
$382$		−	34.6170i		−	1.77116i
$383$	−4.86814	−	8.43186i	−0.248750	−	0.430848i	0.714429	−	0.699708i	$-0.246686\pi$
$383$	−4.86814	−	8.43186i	−0.248750	−	0.430848i	−0.963179	+	0.268860i	$0.913353\pi$
$384$	9.02184	−	5.20876i	0.460394	−	0.265809i
$385$	−6.15605	+	32.7994i	−0.313741	+	1.67161i
$386$	14.1572	+	24.5210i	0.720582	+	1.24808i
$387$	7.43367	−	12.8755i	0.377875	−	0.654498i
$388$	−29.8539	−	51.7085i	−1.51560	−	2.62510i
$389$	−9.49619	+	16.4479i	−0.481476	+	0.833941i	−0.999774	−	0.0212591i	$-0.993233\pi$
$389$	−9.49619	+	16.4479i	−0.481476	+	0.833941i	0.518298	+	0.855200i	$0.326566\pi$
$390$	−3.67004			−0.185840
$391$		−	39.5348i		−	1.99936i
$392$	20.6678	+	25.7608i	1.04388	+	1.30112i
$393$	−7.73813	+	4.46761i	−0.390337	+	0.225361i
$394$	−49.9959	+	28.8652i	−2.51876	+	1.45421i
$395$	7.19781	−	12.4670i	0.362161	−	0.627282i
$396$	45.8277			2.30293
$397$	−13.3890	+	7.73015i	−0.671975	+	0.387965i	−0.796825	−	0.604211i	$-0.793489\pi$
$397$	−13.3890	+	7.73015i	−0.671975	+	0.387965i	0.124850	+	0.992176i	$0.460155\pi$
$398$	31.4704			1.57747
$399$	−4.58634	+	3.85489i	−0.229604	+	0.192986i
$400$	−13.5836			−0.679179
$401$	−4.59237	+	2.65140i	−0.229332	+	0.132405i	−0.610264	−	0.792198i	$-0.708937\pi$
$401$	−4.59237	+	2.65140i	−0.229332	+	0.132405i	0.380932	+	0.924603i	$0.375603\pi$
$402$	−2.20037			−0.109745
$403$	2.68355	−	4.64804i	0.133677	−	0.231535i
$404$	17.0210	−	9.82706i	0.846825	−	0.488915i
$405$	−17.0194	+	9.82616i	−0.845701	+	0.488266i
$406$	8.54180	+	1.60319i	0.423922	+	0.0795651i
$407$			5.21491i			0.258493i
$408$	−12.2460			−0.606265
$409$	3.01207	−	5.21706i	0.148937	−	0.257967i	−0.781898	−	0.623407i	$-0.785748\pi$
$409$	3.01207	−	5.21706i	0.148937	−	0.257967i	0.930835	+	0.365440i	$0.119081\pi$
$410$	−9.66290	−	16.7366i	−0.477216	−	0.826563i
$411$	−1.66342	+	2.88112i	−0.0820502	+	0.142115i
$412$	16.8203	+	29.1336i	0.828676	+	1.43531i
$413$	−8.19894	−	23.3212i	−0.403443	−	1.14756i
$414$	−45.5849	+	26.3184i	−2.24037	+	1.29348i
$415$	−3.54161	−	6.13426i	−0.173851	−	0.301119i
$416$			0.597462i			0.0292930i
$417$	0.551368	−	0.318333i	0.0270006	−	0.0155888i
$418$	7.33616	−	44.6898i	0.358824	−	2.18585i
$419$			15.6997i			0.766981i	0.923545	+	0.383491i	$0.125278\pi$
$419$			15.6997i			0.766981i	−0.923545	+	0.383491i	$0.874722\pi$
$420$	−15.0984	+	5.30807i	−0.736725	+	0.259007i
$421$	6.64289	+	3.83528i	0.323755	+	0.186920i	0.653065	−	0.757302i	$-0.273483\pi$
$421$	6.64289	+	3.83528i	0.323755	+	0.186920i	−0.329310	+	0.944222i	$0.606816\pi$
$422$	−10.2655			−0.499719
$423$			11.9889i			0.582919i
$424$	17.9655	−	31.1171i	0.872481	−	1.51118i
$425$	−16.2234	−	9.36657i	−0.786950	−	0.454346i
$426$	−18.1658			−0.880137
$427$	−8.41968	+	2.96007i	−0.407457	+	0.143248i
$428$	15.0840	−	8.70874i	0.729112	−	0.420953i
$429$	1.08574	−	1.88056i	0.0524201	−	0.0907943i
$430$	−19.6236	−	33.9890i	−0.946333	−	1.63910i
$431$	8.55529	+	4.93940i	0.412094	+	0.237922i	0.691689	−	0.722196i	$-0.256867\pi$
$431$	8.55529	+	4.93940i	0.412094	+	0.237922i	−0.279595	+	0.960118i	$0.590200\pi$
$432$	5.39212	+	9.33943i	0.259429	+	0.449343i
$433$	−12.6770	−	21.9572i	−0.609218	−	1.05520i	−0.991370	−	0.131097i	$-0.958150\pi$
$433$	−12.6770	−	21.9572i	−0.609218	−	1.05520i	0.382151	−	0.924100i	$-0.375183\pi$
$434$	6.51096	−	34.6903i	0.312536	−	1.66519i
$435$	−1.03587	+	1.79419i	−0.0496663	+	0.0860246i
$436$	8.61946	+	4.97645i	0.412797	+	0.238329i
$437$	12.1796	+	32.2704i	0.582628	+	1.54370i
$438$	−2.93168	−	5.07782i	−0.140081	−	0.242628i
$439$	12.5014	+	21.6531i	0.596660	+	1.03345i	0.993310	+	0.115476i	$0.0368392\pi$
$439$	12.5014	+	21.6531i	0.596660	+	1.03345i	−0.396650	+	0.917970i	$0.629827\pi$
$440$	29.7560	−	51.5389i	1.41856	−	2.45702i
$441$	14.9063	−	11.9593i	0.709825	−	0.569489i
$442$	5.96612	−	10.3336i	0.283780	−	0.491521i
$443$	−9.64018			−0.458019			−0.229010	−	0.973424i	$-0.573549\pi$
$443$	−9.64018			−0.458019			−0.229010	+	0.973424i	$0.573549\pi$
$444$	−2.16585	+	1.25046i	−0.102787	+	0.0593440i
$445$	−36.9800	+	21.3504i	−1.75302	+	1.01211i
$446$		−	11.2469i		−	0.532557i
$447$	0.580852	+	1.00606i	0.0274734	+	0.0475852i
$448$	7.66111	+	21.7914i	0.361954	+	1.02955i
$449$		−	3.27174i		−	0.154403i	−0.997016	−	0.0772015i	$-0.975402\pi$
$449$		−	3.27174i		−	0.154403i	0.997016	−	0.0772015i	$-0.0245985\pi$
$450$			24.9414i			1.17575i
$451$	11.4347			0.538437
$452$	54.6553	+	31.5552i	2.57077	+	1.48423i
$453$	9.66689	−	5.58118i	0.454190	−	0.262227i
$454$	−56.3813	−	32.5518i	−2.64611	−	1.52773i
$455$	1.41509	−	7.53961i	0.0663407	−	0.353463i
$456$	9.99581	−	3.77264i	0.468096	−	0.176670i
$457$	−9.80301	+	16.9793i	−0.458566	+	0.794259i	−0.998885	−	0.0472008i	$-0.984970\pi$
$457$	−9.80301	+	16.9793i	−0.458566	+	0.794259i	0.540320	+	0.841460i	$0.318303\pi$
$458$	11.1874			0.522753
$459$			14.8726i			0.694192i
$460$			92.1389i			4.29600i
$461$	24.6424	+	14.2273i	1.14771	+	0.662633i	0.948329	−	0.317289i	$-0.102772\pi$
$461$	24.6424	+	14.2273i	1.14771	+	0.662633i	0.199384	+	0.979921i	$0.436106\pi$
$462$	2.63428	−	14.0354i	0.122558	−	0.652988i
$463$	27.2689			1.26729			0.633647	−	0.773623i	$-0.281557\pi$
$463$	27.2689			1.26729			0.633647	+	0.773623i	$0.281557\pi$
$464$	−4.22982	−	2.44209i	−0.196365	−	0.113371i
$465$	7.28662	+	4.20693i	0.337909	+	0.195092i
$466$	−16.7315	−	9.65992i	−0.775070	−	0.447487i
$467$	17.7429	+	10.2438i	0.821042	+	0.474029i	0.850776	−	0.525529i	$-0.176133\pi$
$467$	17.7429	+	10.2438i	0.821042	+	0.474029i	−0.0297338	+	0.999558i	$0.509466\pi$
$468$	−10.5344			−0.486954
$469$	0.848421	−	4.52038i	0.0391764	−	0.208732i
$470$	27.4084	+	15.8243i	1.26426	+	0.729918i
$471$			1.13635i			0.0523600i
$472$			44.0836i			2.02911i
$473$	23.2217			1.06774
$474$	−3.08007	+	5.33484i	−0.141472	+	0.245037i
$475$	16.1280	+	2.64753i	0.740002	+	0.121477i
$476$	9.59856	−	51.1410i	0.439949	−	2.34405i
$477$	−18.0057	−	10.3956i	−0.824426	−	0.475983i
$478$	−3.56447	+	2.05795i	−0.163035	+	0.0941283i
$479$	16.0235	+	9.25116i	0.732132	+	0.422697i	0.819202	−	0.573506i	$-0.194417\pi$
$479$	16.0235	+	9.25116i	0.732132	+	0.422697i	−0.0870697	+	0.996202i	$0.527750\pi$
$480$	−0.936628			−0.0427510
$481$		−	1.19875i		−	0.0546584i
$482$		−	64.6960i		−	2.94682i
$483$	3.60733	+	10.2607i	0.164139	+	0.466880i
$484$	14.1393	+	24.4900i	0.642695	+	1.11318i
$485$			44.8661i			2.03727i
$486$	26.1267	−	15.0843i	1.18513	−	0.684236i
$487$	−0.0383399	+	0.0221355i	−0.00173734	+	0.00100306i	−0.500868	−	0.865523i	$-0.666986\pi$
$487$	−0.0383399	+	0.0221355i	−0.00173734	+	0.00100306i	0.499131	+	0.866526i	$0.333653\pi$
$488$	15.9156			0.720463
$489$	−0.598274	+	1.03624i	−0.0270549	+	0.0468604i
$490$	−7.66569	−	49.8634i	−0.346301	−	2.25260i
$491$	−8.80924	+	15.2581i	−0.397556	+	0.688586i	−0.993424	−	0.114496i	$-0.963475\pi$
$491$	−8.80924	+	15.2581i	−0.397556	+	0.688586i	0.595868	+	0.803082i	$0.296808\pi$
$492$	2.74186	+	4.74905i	0.123613	+	0.214103i
$493$	−3.36789	−	5.83336i	−0.151682	−	0.262721i
$494$	−1.68637	+	10.2729i	−0.0758733	+	0.462198i
$495$	−29.8226	−	17.2181i	−1.34043	−	0.773896i
$496$	−9.91792	+	17.1783i	−0.445328	+	0.771330i
$497$	7.00438	−	37.3193i	0.314189	−	1.67400i
$498$	1.51552	+	2.62496i	0.0679121	+	0.117627i
$499$	−3.31085	−	5.73456i	−0.148214	−	0.256714i	0.782353	−	0.622835i	$-0.214019\pi$
$499$	−3.31085	−	5.73456i	−0.148214	−	0.256714i	−0.930567	+	0.366121i	$0.880686\pi$
$500$	−12.6096	−	7.28013i	−0.563916	−	0.325577i
$501$	−1.40820	−	2.43907i	−0.0629136	−	0.108969i
$502$	−12.7073	+	22.0097i	−0.567154	+	0.982340i
$503$	−3.91107	+	2.25806i	−0.174386	+	0.100682i	−0.584652	−	0.811284i	$-0.698769\pi$
$503$	−3.91107	+	2.25806i	−0.174386	+	0.100682i	0.410266	+	0.911966i	$0.365436\pi$
$504$	−32.1510	+	11.3032i	−1.43212	+	0.503484i
$505$	−14.7687			−0.657197
$506$	−71.2003	−	41.1075i	−3.16524	−	1.82745i
$507$	3.12720	−	5.41647i	0.138884	−	0.240554i
$508$			28.2299i			1.25250i
$509$	13.7406			0.609039			0.304520	−	0.952506i	$-0.401504\pi$
$509$	13.7406			0.609039			0.304520	+	0.952506i	$0.401504\pi$
$510$	16.1998	+	9.35295i	0.717339	+	0.414156i
$511$	11.5621	−	4.06485i	0.511478	−	0.179818i
$512$		−	36.3932i		−	1.60837i
$513$	−4.58183	−	12.1398i	−0.202293	−	0.535985i
$514$	20.7718	−	11.9926i	0.916206	−	0.528972i
$515$		−	25.2785i		−	1.11390i
$516$	5.56822	+	9.64444i	0.245127	+	0.424573i
$517$	−16.2170	+	9.36288i	−0.713222	+	0.411779i
$518$	−2.61468	−	7.43723i	−0.114882	−	0.326773i
$519$	−4.91437	−	8.51194i	−0.215717	−	0.373632i
$520$	−6.84002	+	11.8473i	−0.299955	+	0.519537i
$521$	−12.3020	−	21.3077i	−0.538961	−	0.933509i	−0.998960	−	0.0455891i	$-0.985484\pi$
$521$	−12.3020	−	21.3077i	−0.538961	−	0.933509i	0.459999	−	0.887920i	$-0.347850\pi$
$522$	−4.48404	+	7.76658i	−0.196261	+	0.339934i
$523$	−33.1553			−1.44978			−0.724889	−	0.688866i	$-0.758109\pi$
$523$	−33.1553			−1.44978			−0.724889	+	0.688866i	$0.758109\pi$
$524$			67.7050i			2.95771i
$525$	5.06522	+	0.950680i	0.221064	+	0.0414911i
$526$	−12.4798	+	7.20523i	−0.544146	+	0.314163i
$527$	−23.6907	+	13.6778i	−1.03198	+	0.595816i
$528$	−4.01272	+	6.95023i	−0.174631	+	0.302470i
$529$	39.6169			1.72248
$530$	−47.5320	+	27.4426i	−2.06466	+	1.19203i
$531$	25.5087			1.10698
$532$	7.92027	+	44.7011i	0.343387	+	1.93804i
$533$	−2.62849			−0.113853
$534$	15.8244	−	9.13622i	0.684789	−	0.395363i
$535$	−13.0880			−0.565844
$536$	−4.10094	+	7.10303i	−0.177134	+	0.306804i
$537$	−0.383788	+	0.221580i	−0.0165617	+	0.00956189i
$538$	43.8230	−	25.3012i	1.88934	−	1.09081i
$539$	27.8183	+	10.8236i	1.19822	+	0.466205i
$540$		−	34.6617i		−	1.49160i
$541$	7.44415			0.320049			0.160025	−	0.987113i	$-0.448843\pi$
$541$	7.44415			0.320049			0.160025	+	0.987113i	$0.448843\pi$
$542$	15.0595	−	26.0838i	0.646860	−	1.12039i
$543$	4.73937	+	8.20883i	0.203386	+	0.352274i
$544$	1.52261	−	2.63724i	0.0652813	−	0.113071i
$545$	−3.73944	−	6.47691i	−0.160180	−	0.277440i
$546$	−0.605544	+	3.22634i	−0.0259149	+	0.138074i
$547$	24.2379	−	13.9938i	1.03634	−	0.598330i	0.117544	−	0.993068i	$-0.462498\pi$
$547$	24.2379	−	13.9938i	1.03634	−	0.598330i	0.918794	+	0.394738i	$0.129165\pi$
$548$	12.6042	+	21.8311i	0.538426	+	0.932580i
$549$		−	9.20944i		−	0.393049i
$550$	−33.7375	+	19.4784i	−1.43857	+	0.830561i
$551$	4.54615	+	3.72395i	0.193673	+	0.158646i
$552$		−	19.3957i		−	0.825535i
$553$	−9.77212	−	8.38461i	−0.415553	−	0.356550i
$554$	−32.5837	−	18.8122i	−1.38435	−	0.799254i
$555$	1.87926			0.0797701
$556$		−	4.82421i		−	0.204592i
$557$	−9.42909	+	16.3317i	−0.399523	+	0.691995i	−0.993667	−	0.112364i	$-0.964158\pi$
$557$	−9.42909	+	16.3317i	−0.399523	+	0.691995i	0.594144	+	0.804359i	$0.297491\pi$
$558$	31.5420	+	18.2108i	1.33528	+	0.770923i
$559$	−5.33799			−0.225773
$560$	−5.22994	+	27.8651i	−0.221005	+	1.17752i
$561$	−9.58508	+	5.53395i	−0.404682	+	0.233643i
$562$	−27.3850	+	47.4321i	−1.15516	+	2.00080i
$563$	3.06569	+	5.30994i	0.129204	+	0.223787i	0.923368	−	0.383915i	$-0.125425\pi$
$563$	3.06569	+	5.30994i	0.129204	+	0.223787i	−0.794165	+	0.607703i	$0.792091\pi$
$564$	−7.77718	−	4.49016i	−0.327478	−	0.189070i
$565$	−23.7115	−	41.0695i	−0.997551	−	1.72781i
$566$	25.5180	+	44.1985i	1.07260	+	1.85780i
$567$	5.83004	+	16.5831i	0.244839	+	0.696423i
$568$	−33.8565	+	58.6411i	−1.42059	+	2.46053i
$569$	13.9939	+	8.07939i	0.586655	+	0.338706i	0.763774	−	0.645484i	$-0.223344\pi$
$569$	13.9939	+	8.07939i	0.586655	+	0.338706i	−0.177119	+	0.984190i	$0.556678\pi$
$570$	−16.1045	−	2.64368i	−0.674544	−	0.110732i
$571$	8.74774	+	15.1515i	0.366081	+	0.634071i	0.988949	−	0.148256i	$-0.0473659\pi$
$571$	8.74774	+	15.1515i	0.366081	+	0.634071i	−0.622868	+	0.782327i	$0.714033\pi$
$572$	−8.22701	−	14.2496i	−0.343989	−	0.595806i
$573$	3.69051	−	6.39214i	0.154173	−	0.267036i
$574$	−16.3075	+	5.73317i	−0.680663	+	0.239298i
$575$	14.8352	−	25.6953i	0.618670	−	1.07157i
$576$	−23.8354			−0.993142
$577$	6.64834	−	3.83842i	0.276774	−	0.159796i	−0.355188	−	0.934795i	$-0.615583\pi$
$577$	6.64834	−	3.83842i	0.276774	−	0.159796i	0.631962	+	0.774999i	$0.282250\pi$
$578$	−16.7988	+	9.69877i	−0.698736	+	0.403416i
$579$			6.03716i			0.250896i
$580$	7.84914	+	13.5951i	0.325918	+	0.564506i
$581$	−5.97698	+	2.10130i	−0.247967	+	0.0871768i
$582$		−	19.1990i		−	0.795825i
$583$		−	32.4744i		−	1.34495i
$584$	−21.8557			−0.904393
$585$	6.85535	+	3.95794i	0.283434	+	0.163641i
$586$	23.2201	−	13.4061i	0.959213	−	0.553802i
$587$	−9.28923	−	5.36314i	−0.383408	−	0.221360i	0.295892	−	0.955221i	$-0.404383\pi$
$587$	−9.28923	−	5.36314i	−0.383408	−	0.221360i	−0.679300	+	0.733861i	$0.737716\pi$
$588$	2.17515	+	14.1488i	0.0897018	+	0.583487i
$589$	15.1239	−	18.4630i	0.623168	−	0.760756i
$590$	33.6692	−	58.3168i	1.38614	−	2.40087i
$591$	−12.3092			−0.506333
$592$			4.43038i			0.182088i
$593$			19.7527i			0.811148i	0.914062	+	0.405574i	$0.132928\pi$
$593$			19.7527i			0.811148i	−0.914062	+	0.405574i	$0.867072\pi$
$594$	26.7848	+	15.4642i	1.09899	+	0.634505i
$595$	−25.4607	+	29.6740i	−1.04379	+	1.21652i
$596$	8.80259			0.360568
$597$	5.81111	+	3.35505i	0.237833	+	0.137313i
$598$	16.3669	+	9.44941i	0.669290	+	0.386415i
$599$	−18.5280	−	10.6971i	−0.757033	−	0.437073i	0.0711966	−	0.997462i	$-0.477318\pi$
$599$	−18.5280	−	10.6971i	−0.757033	−	0.437073i	−0.828229	+	0.560389i	$0.810652\pi$
$600$	−7.95916	−	4.59522i	−0.324931	−	0.187599i
$601$	−41.2626			−1.68313			−0.841567	−	0.540152i	$-0.818367\pi$
$601$	−41.2626			−1.68313			−0.841567	+	0.540152i	$0.818367\pi$
$602$	−33.1176	+	11.6430i	−1.34977	+	0.474534i
$603$	4.11013	+	2.37298i	0.167377	+	0.0966353i
$604$		−	84.5807i		−	3.44154i
$605$		−	21.2493i		−	0.863908i
$606$	6.31978			0.256724
$607$	2.49028	−	4.31329i	0.101077	−	0.175071i	−0.811051	−	0.584975i	$-0.801104\pi$
$607$	2.49028	−	4.31329i	0.101077	−	0.175071i	0.912129	+	0.409904i	$0.134438\pi$
$608$	−0.430377	+	2.62173i	−0.0174541	+	0.106325i
$609$	1.40635	+	1.20667i	0.0569884	+	0.0488968i
$610$	−21.0542	−	12.1556i	−0.852459	−	0.492168i
$611$	3.72781	−	2.15225i	0.150811	−	0.0870707i
$612$	46.4997	+	26.8466i	1.87964	+	1.08521i
$613$	5.70975			0.230615			0.115307	−	0.993330i	$-0.463215\pi$
$613$	5.70975			0.230615			0.115307	+	0.993330i	$0.463215\pi$
$614$		−	1.36653i		−	0.0551485i
$615$		−	4.12063i		−	0.166160i
$616$	−40.3982	−	34.6622i	−1.62769	−	1.39658i
$617$	−10.4082	−	18.0275i	−0.419019	−	0.725761i	0.576822	−	0.816870i	$-0.304292\pi$
$617$	−10.4082	−	18.0275i	−0.419019	−	0.725761i	−0.995841	+	0.0911081i	$0.970959\pi$
$618$			10.8171i			0.435128i
$619$	−20.3009	+	11.7208i	−0.815963	+	0.471097i	−0.849023	−	0.528357i	$-0.822808\pi$
$619$	−20.3009	+	11.7208i	−0.815963	+	0.471097i	0.0330590	+	0.999453i	$0.489475\pi$
$620$	55.2130	−	31.8773i	2.21741	−	1.28022i
$621$	−23.5558			−0.945263
$622$	−31.6768	+	54.8659i	−1.27012	+	2.19992i
$623$	12.6676	+	36.0319i	0.507516	+	1.44359i
$624$	0.922405	−	1.59765i	0.0369258	−	0.0639573i
$625$	14.8443	+	25.7111i	0.593773	+	1.02845i
$626$	−17.3910	−	30.1220i	−0.695083	−	1.20392i
$627$	6.11900	−	7.47000i	0.244369	−	0.298323i
$628$	7.45687	+	4.30522i	0.297561	+	0.171797i
$629$	−3.05498	+	5.29138i	−0.121810	+	0.210981i
$630$	51.1644	+	9.60295i	2.03844	+	0.382591i
$631$	9.85289	+	17.0657i	0.392238	+	0.679375i	0.992744	−	0.120244i	$-0.0383678\pi$
$631$	9.85289	+	17.0657i	0.392238	+	0.679375i	−0.600507	+	0.799620i	$0.705034\pi$
$632$	11.4809	+	19.8856i	0.456688	+	0.791006i
$633$	−1.89556	−	1.09440i	−0.0753419	−	0.0434987i
$634$	−30.5267	−	52.8738i	−1.21237	−	2.09989i
$635$	10.6064	−	18.3708i	0.420901	−	0.729022i
$636$	13.4873	−	7.78688i	0.534805	−	0.308770i
$637$	−6.39460	−	2.48802i	−0.253363	−	0.0985790i
$638$	−14.0075			−0.554562
$639$	33.9323	+	19.5908i	1.34234	+	0.775001i
$640$	−29.6577	+	51.3687i	−1.17232	+	2.03052i
$641$		−	38.2301i		−	1.51000i	−0.655725	−	0.755000i	$-0.727637\pi$
$641$		−	38.2301i		−	1.51000i	0.655725	−	0.755000i	$-0.272363\pi$
$642$	5.60059			0.221038
$643$	−30.6174	−	17.6770i	−1.20743	−	0.697113i	−0.245236	−	0.969463i	$-0.578866\pi$
$643$	−30.6174	−	17.6770i	−1.20743	−	0.697113i	−0.962198	+	0.272351i	$0.912199\pi$
$644$	80.9994	+	15.2026i	3.19182	+	0.599067i
$645$		−	8.36824i		−	0.329499i
$646$	33.6237	−	41.0474i	1.32291	−	1.61499i
$647$	−14.9202	+	8.61417i	−0.586573	+	0.338658i	−0.763741	−	0.645522i	$-0.776640\pi$
$647$	−14.9202	+	8.61417i	−0.586573	+	0.338658i	0.177168	+	0.984181i	$0.443306\pi$
$648$		−	31.3466i		−	1.23141i
$649$	19.9214	+	34.5048i	0.781982	+	1.35443i
$650$	7.75527	−	4.47750i	0.304187	−	0.175622i
$651$	4.90059	−	5.71155i	0.192069	−	0.223853i
$652$	4.53331	+	7.85192i	0.177538	+	0.307505i
$653$	−3.97065	+	6.87736i	−0.155383	+	0.269132i	−0.933199	−	0.359361i	$-0.882995\pi$
$653$	−3.97065	+	6.87736i	−0.155383	+	0.269132i	0.777815	+	0.628493i	$0.216328\pi$
$654$	1.60017	+	2.77158i	0.0625718	+	0.108378i
$655$	25.4377	−	44.0594i	0.993934	−	1.72154i
$656$	9.71445			0.379286
$657$			12.6466i			0.493392i
$658$	18.4334	−	21.4838i	0.718609	−	0.837526i
$659$	−22.9605	+	13.2563i	−0.894415	+	0.516391i	−0.875384	−	0.483428i	$-0.839391\pi$
$659$	−22.9605	+	13.2563i	−0.894415	+	0.516391i	−0.0190311	+	0.999819i	$0.506058\pi$
$660$	22.3388	−	12.8973i	0.869536	−	0.502027i
$661$	−0.612406	+	1.06072i	−0.0238198	+	0.0412572i	−0.877690	−	0.479230i	$-0.840916\pi$
$661$	−0.612406	+	1.06072i	−0.0238198	+	0.0412572i	0.853870	+	0.520487i	$0.174249\pi$
$662$	−14.8158			−0.575833
$663$	2.20333	−	1.27209i	0.0855701	−	0.0494039i
$664$	11.2982			0.438454
$665$	11.6407	−	32.0653i	0.451406	−	1.24344i
$666$	8.13484			0.315218
$667$	9.23913	−	5.33422i	0.357741	−	0.206542i
$668$	−21.3407			−0.825696
$669$	1.19903	−	2.07678i	0.0463571	−	0.0802929i
$670$	10.8500	−	6.26425i	0.419172	−	0.242009i
$671$	12.4573	−	7.19224i	0.480910	−	0.277653i
$672$	−0.154540	+	0.823390i	−0.00596153	+	0.0317630i
$673$		−	3.42896i		−	0.132177i	−0.997814	−	0.0660883i	$-0.978948\pi$
$673$		−	3.42896i		−	0.132177i	0.997814	−	0.0660883i	$-0.0210519\pi$
$674$	−8.57921			−0.330459
$675$	−5.58085	+	9.66631i	−0.214807	+	0.372056i
$676$	−23.6958	−	41.0423i	−0.911376	−	1.57855i
$677$	4.04989	−	7.01461i	0.155650	−	0.269593i	−0.777646	−	0.628703i	$-0.783586\pi$
$677$	4.04989	−	7.01461i	0.155650	−	0.269593i	0.933295	+	0.359110i	$0.116920\pi$
$678$	10.1466	+	17.5744i	0.389677	+	0.674940i
$679$	39.4419	+	7.40277i	1.51364	+	0.284092i
$680$	60.3846	−	34.8631i	2.31564	−	1.33694i
$681$	−6.94066	−	12.0216i	−0.265967	−	0.460668i
$682$			56.8878i			2.17835i
$683$	−15.4107	+	8.89736i	−0.589673	+	0.340448i	−0.764968	−	0.644068i	$-0.777245\pi$
$683$	−15.4107	+	8.89736i	−0.589673	+	0.340448i	0.175295	+	0.984516i	$0.443912\pi$
$684$	−46.2262	−	7.58838i	−1.76750	−	0.290149i
$685$		−	18.9423i		−	0.723750i
$686$	−45.0997	−	1.48837i	−1.72192	−	0.0568263i
$687$	2.06579	+	1.19268i	0.0788147	+	0.0455037i
$688$	19.7283			0.752133
$689$			7.46491i			0.284390i
$690$	−14.8136	+	25.6579i	−0.563945	+	0.976781i
$691$	3.33249	+	1.92402i	0.126774	+	0.0731930i	0.562046	−	0.827106i	$-0.310014\pi$
$691$	3.33249	+	1.92402i	0.126774	+	0.0731930i	−0.435272	+	0.900299i	$0.643348\pi$
$692$	−74.4754			−2.83113
$693$	−20.0571	+	23.3762i	−0.761906	+	0.887988i
$694$	−65.3362	+	37.7219i	−2.48013	+	1.43190i
$695$	−1.81253	+	3.13939i	−0.0687530	+	0.119084i
$696$	−1.65228	−	2.86183i	−0.0626295	−	0.108478i
$697$	11.6023	+	6.69861i	0.439470	+	0.253728i
$698$	13.0346	+	22.5766i	0.493368	+	0.854539i
$699$	−2.05968	−	3.56747i	−0.0779042	−	0.134934i
$700$	25.4289	−	29.6369i	0.961121	−	1.12017i
$701$	3.04331	−	5.27117i	0.114944	−	0.199089i	−0.802813	−	0.596231i	$-0.796664\pi$
$701$	3.04331	−	5.27117i	0.114944	−	0.199089i	0.917757	+	0.397141i	$0.129998\pi$
$702$	−6.15704	−	3.55477i	−0.232383	−	0.134166i
$703$	0.863511	−	5.26026i	0.0325680	−	0.198394i
$704$	−18.6146	−	32.2414i	−0.701564	−	1.21514i
$705$	3.37403	+	5.84399i	0.127073	+	0.220098i
$706$	−11.9681	+	20.7294i	−0.450427	+	0.780163i
$707$	−2.43678	+	12.9832i	−0.0916446	+	0.488282i
$708$	−9.55370	+	16.5475i	−0.359050	+	0.621893i
$709$	22.1358			0.831326			0.415663	−	0.909519i	$-0.363550\pi$
$709$	22.1358			0.831326			0.415663	+	0.909519i	$0.363550\pi$
$710$	89.5753	−	51.7164i	3.36170	−	1.94088i
$711$	11.5067	−	6.64338i	0.431534	−	0.249146i
$712$		−	68.1104i		−	2.55255i
$713$	−21.6635	−	37.5224i	−0.811306	−	1.40522i
$714$	10.8951	−	12.6980i	0.407739	−	0.475212i
$715$			12.3640i			0.462388i
$716$			3.35796i			0.125493i
$717$	−0.877587			−0.0327741
$718$	−7.34275	−	4.23934i	−0.274029	−	0.158211i
$719$	36.6113	−	21.1375i	1.36537	−	0.788297i	0.375038	−	0.927010i	$-0.377630\pi$
$719$	36.6113	−	21.1375i	1.36537	−	0.788297i	0.990333	+	0.138713i	$0.0442964\pi$
$720$	−25.3362	−	14.6278i	−0.944223	−	0.545147i
$721$	−22.2224	−	4.17087i	−0.827604	−	0.155331i
$722$	−14.7999	+	43.8637i	−0.550796	+	1.63244i
$723$	6.89722	−	11.9463i	0.256510	−	0.444289i
$724$	71.8234			2.66929
$725$		−	5.05513i		−	0.187743i
$726$			9.09297i			0.337472i
$727$	−0.271061	−	0.156497i	−0.0100531	−	0.00580415i	0.494965	−	0.868913i	$-0.335181\pi$
$727$	−0.271061	−	0.156497i	−0.0100531	−	0.00580415i	−0.505018	+	0.863109i	$0.668514\pi$
$728$	9.28636	+	7.96783i	0.344175	+	0.295307i
$729$	−13.4991			−0.499967
$730$	28.9122	+	16.6924i	1.07009	+	0.617815i
$731$	23.5622	+	13.6037i	0.871480	+	0.503149i
$732$	5.97416	+	3.44918i	0.220811	+	0.127486i
$733$	3.86773	+	2.23304i	0.142858	+	0.0824791i	0.569725	−	0.821835i	$-0.307050\pi$
$733$	3.86773	+	2.23304i	0.142858	+	0.0824791i	−0.426867	+	0.904314i	$0.640383\pi$
$734$	66.3501			2.44903
$735$	3.90042	−	10.0247i	0.143869	−	0.369765i
$736$	4.17697	+	2.41158i	0.153965	+	0.0888919i
$737$			7.41286i			0.273056i
$738$		−	17.8372i		−	0.656595i
$739$	−26.8374			−0.987231			−0.493615	−	0.869680i	$-0.664325\pi$
$739$	−26.8374			−0.987231			−0.493615	+	0.869680i	$0.664325\pi$
$740$	7.11986	−	12.3320i	0.261731	−	0.453332i
$741$	−1.40658	+	1.71713i	−0.0516719	+	0.0630805i
$742$	16.2822	+	46.3133i	0.597738	+	1.70022i
$743$	19.0495	+	10.9982i	0.698859	+	0.403486i	0.806922	−	0.590658i	$-0.201132\pi$
$743$	19.0495	+	10.9982i	0.698859	+	0.403486i	−0.108063	+	0.994144i	$0.534465\pi$
$744$	−11.6226	+	6.71031i	−0.426105	+	0.246012i
$745$	−5.72834	−	3.30726i	−0.209870	−	0.121169i
$746$	76.2033			2.79000
$747$		−	6.53762i		−	0.239199i
$748$			83.8649i			3.06640i
$749$	−2.15948	+	11.5057i	−0.0789056	+	0.420408i
$750$	−2.34092	−	4.05460i	−0.0854785	−	0.148053i
$751$			17.7139i			0.646390i	0.946332	+	0.323195i	$0.104757\pi$
$751$			17.7139i			0.646390i	−0.946332	+	0.323195i	$0.895243\pi$
$752$	−13.7773	+	7.95434i	−0.502407	+	0.290065i
$753$	−4.69288	+	2.70944i	−0.171018	+	0.0987374i
$754$	3.21991			0.117262
$755$	−31.7782	+	55.0414i	−1.15653	+	2.00316i
$756$	−30.4711	−	5.71907i	−1.10822	−	0.208000i
$757$	14.3619	−	24.8756i	0.521994	−	0.904119i	−0.477679	−	0.878534i	$-0.658522\pi$
$757$	14.3619	−	24.8756i	0.521994	−	0.904119i	0.999673	−	0.0255850i	$-0.00814486\pi$
$758$	−29.8771	−	51.7487i	−1.08519	−	1.87960i
$759$	−8.76491	−	15.1813i	−0.318146	−	0.551045i
$760$	−38.5488	+	47.0599i	−1.39831	+	1.70704i
$761$	28.4338	+	16.4163i	1.03073	+	0.595090i	0.917192	−	0.398445i	$-0.130450\pi$
$761$	28.4338	+	16.4163i	1.03073	+	0.595090i	0.113533	+	0.993534i	$0.463783\pi$
$762$	−4.53866	+	7.86118i	−0.164418	+	0.284781i
$763$	−6.31085	+	2.21868i	−0.228468	+	0.0803216i
$764$	−27.9641	−	48.4353i	−1.01171	−	1.75233i
$765$	−20.1733	−	34.9412i	−0.729367	−	1.26330i
$766$	−20.5441	−	11.8611i	−0.742288	−	0.428560i
$767$	−4.57934	−	7.93165i	−0.165350	−	0.286395i
$768$	8.15550	−	14.1257i	0.294286	−	0.509719i
$769$	16.1652	−	9.33300i	0.582933	−	0.336556i	−0.179365	−	0.983783i	$-0.557404\pi$
$769$	16.1652	−	9.33300i	0.582933	−	0.336556i	0.762298	+	0.647226i	$0.224071\pi$
$770$	26.9680	+	76.7081i	0.971858	+	2.76437i
$771$	5.11411			0.184180
$772$	39.6168	+	22.8727i	1.42584	+	0.823208i
$773$	−19.2824	+	33.3981i	−0.693540	+	1.20125i	0.277130	+	0.960832i	$0.410617\pi$
$773$	−19.2824	+	33.3981i	−0.693540	+	1.20125i	−0.970670	+	0.240415i	$0.922717\pi$
$774$		−	36.2240i		−	1.30205i
$775$	−20.5301			−0.737463
$776$	−61.9764	−	35.7821i	−2.22482	−	1.28450i
$777$	0.310071	−	1.65206i	0.0111237	−	0.0592672i
$778$			46.2746i			1.65903i
$779$	−11.5341	−	1.89341i	−0.413252	−	0.0678385i
$780$	−5.13503	+	2.96471i	−0.183863	+	0.106154i
$781$			61.1990i			2.18987i
$782$	−48.1629	−	83.4206i	−1.72230	−	2.98312i
$783$	−3.47567	+	2.00668i	−0.124210	+	0.0717128i
$784$	23.6333	+	9.19530i	0.844047	+	0.328404i
$785$	−3.23507	−	5.60330i	−0.115465	−	0.199990i
$786$	−10.8853	+	18.8538i	−0.388264	+	0.672494i
$787$	−5.45291	−	9.44471i	−0.194375	−	0.336668i	0.752320	−	0.658797i	$-0.228935\pi$
$787$	−5.45291	−	9.44471i	−0.194375	−	0.336668i	−0.946695	+	0.322130i	$0.895601\pi$
$788$	−46.6354	+	80.7748i	−1.66132	+	2.87748i
$789$	−3.07258			−0.109387
$790$		−	35.0747i		−	1.24790i
$791$	−40.0166	+	14.0685i	−1.42283	+	0.500217i
$792$	47.5689	−	27.4639i	1.69029	−	0.975888i
$793$	−2.86357	+	1.65328i	−0.101688	+	0.0587098i
$794$	−18.8344	+	32.6221i	−0.668407	+	1.15771i
$795$	−11.7026			−0.415047
$796$	44.0326	−	25.4222i	1.56069	−	0.901067i
$797$	14.3886			0.509670			0.254835	−	0.966985i	$-0.417979\pi$
$797$	14.3886			0.509670			0.254835	+	0.966985i	$0.417979\pi$
$798$	−4.98126	+	13.7213i	−0.176335	+	0.485729i
$799$	−21.9397			−0.776171
$800$	1.97921	−	1.14270i	0.0699758	−	0.0404006i
$801$	−39.4117			−1.39254
$802$	−6.46010	+	11.1892i	−0.228114	+	0.395105i
$803$	−17.1067	+	9.87657i	−0.603683	+	0.348537i
$804$	−3.07871	+	1.77749i	−0.108578	+	0.0626873i
$805$	−46.9990	−	40.3258i	−1.65650	−	1.42130i
$806$		−	13.0768i		−	0.460612i
$807$	10.7894			0.379805
$808$	11.7785	−	20.4009i	0.414365	−	0.717701i
$809$	9.85366	+	17.0670i	0.346436	+	0.600045i	0.985614	−	0.169014i	$-0.0540584\pi$
$809$	9.85366	+	17.0670i	0.346436	+	0.600045i	−0.639177	+	0.769059i	$0.720725\pi$
$810$	−23.9413	+	41.4675i	−0.841210	+	1.45702i
$811$	−19.1598	−	33.1858i	−0.672793	−	1.16531i	−0.977109	−	0.212740i	$-0.931761\pi$
$811$	−19.1598	−	33.1858i	−0.672793	−	1.16531i	0.304316	−	0.952571i	$-0.401572\pi$
$812$	13.2466	−	4.65704i	0.464863	−	0.163430i
$813$	5.56156	−	3.21097i	0.195052	−	0.112614i
$814$	6.35302	+	11.0037i	0.222673	+	0.385681i
$815$		−	6.81291i		−	0.238646i
$816$	−8.14311	+	4.70143i	−0.285066	+	0.164583i
$817$	−23.4237	−	3.84517i	−0.819490	−	0.134526i
$818$		−	14.6777i		−	0.513195i
$819$	4.61053	−	5.37350i	0.161105	−	0.187765i
$820$	−27.0402	−	15.6116i	−0.944283	−	0.545182i
$821$	52.5846			1.83521			0.917607	−	0.397489i	$-0.130118\pi$
$821$	52.5846			1.83521			0.917607	+	0.397489i	$0.130118\pi$
$822$			8.10577i			0.282721i
$823$	0.743147	−	1.28717i	0.0259045	−	0.0448679i	−0.852783	−	0.522266i	$-0.825087\pi$
$823$	0.743147	−	1.28717i	0.0259045	−	0.0448679i	0.878687	+	0.477398i	$0.158420\pi$
$824$	34.9188	+	20.1604i	1.21645	+	0.702320i
$825$	−8.30632			−0.289189
$826$	−45.7111	−	39.2207i	−1.59049	−	1.36466i
$827$	−13.9727	+	8.06715i	−0.485879	+	0.280522i	−0.722863	−	0.690991i	$-0.757174\pi$
$827$	−13.9727	+	8.06715i	−0.485879	+	0.280522i	0.236984	+	0.971513i	$0.423841\pi$
$828$	−42.5208	+	73.6482i	−1.47770	+	2.55945i
$829$	−12.6886	−	21.9774i	−0.440694	−	0.763305i	0.557047	−	0.830481i	$-0.311934\pi$
$829$	−12.6886	−	21.9774i	−0.440694	−	0.763305i	−0.997741	+	0.0671760i	$0.978601\pi$
$830$	−14.9460	−	8.62908i	−0.518784	−	0.299520i
$831$	−4.01112	−	6.94746i	−0.139144	−	0.241005i
$832$	4.27895	+	7.41135i	0.148346	+	0.256942i
$833$	21.8855	+	27.2787i	0.758289	+	0.945150i
$834$	0.775612	−	1.34340i	0.0268572	−	0.0465181i
$835$	13.8876	+	8.01800i	0.480600	+	0.277474i
$836$	−25.8364	−	68.4550i	−0.893572	−	2.36757i
$837$	8.14960	+	14.1155i	0.281692	+	0.487904i
$838$	19.1260	+	33.1273i	0.660698	+	1.14436i
$839$	−4.29661	+	7.44195i	−0.148335	+	0.256924i	−0.930612	−	0.366006i	$-0.880725\pi$
$839$	−4.29661	+	7.44195i	−0.148335	+	0.256924i	0.782277	+	0.622931i	$0.214058\pi$
$840$	−12.4910	+	14.5580i	−0.430980	+	0.502299i
$841$	−13.5912	+	23.5406i	−0.468661	+	0.811745i
$842$	18.6892			0.644071
$843$	−10.1134	+	5.83900i	−0.348325	+	0.201106i
$844$	−14.3633	+	8.29264i	−0.494405	+	0.285445i
$845$			35.6114i			1.22507i
$846$	14.6053	+	25.2972i	0.502142	+	0.869735i
$847$	−18.6803	−	3.50607i	−0.641863	−	0.120470i
$848$		−	27.5890i		−	0.947411i
$849$			10.8818i			0.373464i
$850$	−45.6430			−1.56554
$851$	−8.38071	−	4.83861i	−0.287287	−	0.165865i
$852$	−25.4171	+	14.6746i	−0.870777	+	0.502743i
$853$	49.0168	+	28.2998i	1.67830	+	0.968968i	0.962744	+	0.270415i	$0.0871609\pi$
$853$	49.0168	+	28.2998i	1.67830	+	0.968968i	0.715558	+	0.698553i	$0.246172\pi$
$854$	−14.1599	+	16.5031i	−0.484542	+	0.564725i
$855$	27.2309	+	22.3060i	0.931278	+	0.762850i
$856$	10.4381	−	18.0793i	0.356766	−	0.617937i
$857$	53.3644			1.82289			0.911447	−	0.411417i	$-0.134966\pi$
$857$	53.3644			1.82289			0.911447	+	0.411417i	$0.134966\pi$
$858$		−	5.29079i		−	0.180624i
$859$		−	54.3500i		−	1.85440i	−0.374568	−	0.927199i	$-0.622209\pi$
$859$		−	54.3500i		−	1.85440i	0.374568	−	0.927199i	$-0.377791\pi$
$860$	−54.9136	−	31.7044i	−1.87254	−	1.08111i
$861$	−3.62245	−	0.679890i	−0.123453	−	0.0231706i
$862$	24.0695			0.819811
$863$	−23.3409	−	13.4759i	−0.794532	−	0.458723i	0.0470234	−	0.998894i	$-0.485026\pi$
$863$	−23.3409	−	13.4759i	−0.794532	−	0.458723i	−0.841556	+	0.540170i	$0.818360\pi$
$864$	−1.57133	−	0.907210i	−0.0534579	−	0.0308639i
$865$	48.4653	+	27.9815i	1.64787	+	0.951399i
$866$	−53.4984	−	30.8873i	−1.81795	−	1.04959i
$867$	−4.13592			−0.140463
$868$	−18.9134	−	53.7975i	−0.641961	−	1.82601i
$869$	17.9726	+	10.3765i	0.609678	+	0.351998i
$870$			5.04778i			0.171136i
$871$		−	1.70400i		−	0.0577377i
$872$	11.9293			0.403976
$873$	−20.7051	+	35.8623i	−0.700761	+	1.21375i
$874$	65.0127	+	53.2547i	2.19909	+	1.80137i
$875$	9.23226	−	3.24575i	0.312107	−	0.109726i
$876$	−8.20387	−	4.73651i	−0.277183	−	0.160032i
$877$	28.6106	−	16.5183i	0.966112	−	0.557785i	0.0680630	−	0.997681i	$-0.478318\pi$
$877$	28.6106	−	16.5183i	0.966112	−	0.557785i	0.898049	+	0.439896i	$0.144985\pi$
$878$	52.7574	+	30.4595i	1.78047	+	1.02796i
$879$	5.71688			0.192826
$880$		−	45.6953i		−	1.54039i
$881$			35.4655i			1.19486i	0.801920	+	0.597431i	$0.203812\pi$
$881$			35.4655i			1.19486i	−0.801920	+	0.597431i	$0.796188\pi$
$882$	16.8839	−	43.3942i	0.568511	−	1.46116i
$883$	−7.78226	−	13.4793i	−0.261894	−	0.453614i	0.704851	−	0.709355i	$-0.251014\pi$
$883$	−7.78226	−	13.4793i	−0.261894	−	0.453614i	−0.966745	+	0.255742i	$0.917680\pi$
$884$		−	19.2781i		−	0.648392i
$885$	12.4343	−	7.17892i	0.417973	−	0.241317i
$886$	−20.3413	+	11.7441i	−0.683380	+	0.394550i
$887$	33.4585			1.12343			0.561714	−	0.827331i	$-0.310142\pi$
$887$	33.4585			1.12343			0.561714	+	0.827331i	$0.310142\pi$
$888$	−1.49877	+	2.59594i	−0.0502953	+	0.0871139i
$889$	−14.3998	−	12.3552i	−0.482952	−	0.414380i
$890$	−52.0199	+	90.1011i	−1.74371	+	3.02020i
$891$	−14.1655	−	24.5354i	−0.474564	−	0.821968i
$892$	−9.08541	−	15.7364i	−0.304202	−	0.526894i
$893$	17.9084	−	6.75901i	0.599281	−	0.226182i
$894$	2.45126	+	1.41524i	0.0819824	+	0.0473326i
$895$	1.26164	−	2.18522i	0.0421718	−	0.0730437i
$896$	40.2648	+	34.5478i	1.34515	+	1.15416i
$897$	2.01479	+	3.48973i	0.0672720	+	0.116519i
$898$	−3.98577	−	6.90356i	−0.133007	−	0.230375i
$899$	−6.39292	−	3.69095i	−0.213216	−	0.123100i
$900$	20.1480	+	34.8974i	0.671602	+	1.16325i
$901$	19.0240	−	32.9506i	0.633783	−	1.09774i
$902$	24.1278	−	13.9302i	0.803368	−	0.463824i
$903$	−7.35653	−	1.38073i	−0.244810	−	0.0459479i
$904$	75.6426			2.51584
$905$	−46.7395	−	26.9851i	−1.55367	−	0.897014i
$906$	13.5985	−	23.5532i	0.451778	−	0.782503i
$907$			30.4404i			1.01076i	0.862898	+	0.505378i	$0.168647\pi$
$907$			30.4404i			1.01076i	−0.862898	+	0.505378i	$0.831353\pi$
$908$	−105.183			−3.49062
$909$	−11.8049	−	6.81554i	−0.391542	−	0.226057i
$910$	−6.19914	−	17.6329i	−0.205500	−	0.584526i
$911$		−	41.7075i		−	1.38183i	−0.722936	−	0.690915i	$-0.757208\pi$
$911$		−	41.7075i		−	1.38183i	0.722936	−	0.690915i	$-0.242792\pi$
$912$	5.19847	−	6.34622i	0.172138	−	0.210144i
$913$	8.84324	−	5.10565i	0.292669	−	0.168972i
$914$			47.7698i			1.58008i
$915$	−2.59182	−	4.48916i	−0.0856828	−	0.148407i
$916$	15.6531	−	9.03733i	0.517194	−	0.298602i
$917$	−34.5356	−	29.6320i	−1.14046	−	0.978535i
$918$	18.1184	+	31.3820i	0.597996	+	1.03576i
$919$	0.724144	−	1.25425i	0.0238873	−	0.0413740i	−0.853835	−	0.520544i	$-0.825729\pi$
$919$	0.724144	−	1.25425i	0.0238873	−	0.0413740i	0.877722	+	0.479170i	$0.159062\pi$
$920$	55.2177	+	95.6398i	1.82047	+	3.15315i
$921$	0.145685	−	0.252333i	0.00480047	−	0.00831467i
$922$	69.3293			2.28324
$923$		−	14.0678i		−	0.463049i
$924$	−7.65220	−	21.7660i	−0.251739	−	0.716050i
$925$	−3.97111	+	2.29272i	−0.130569	+	0.0753843i
$926$	57.5389	−	33.2201i	1.89085	−	1.09168i
$927$	11.6657	−	20.2055i	0.383151	−	0.663637i
$928$	0.821750			0.0269753
$929$	−42.4110	+	24.4860i	−1.39146	+	0.803359i	−0.993477	−	0.114034i	$-0.963623\pi$
$929$	−42.4110	+	24.4860i	−1.39146	+	0.803359i	−0.397982	+	0.917393i	$0.630289\pi$
$930$	20.5002			0.672230
$931$	−26.2680	−	15.5240i	−0.860897	−	0.508779i
$932$	−31.2137			−1.02244
$933$	−11.6984	+	6.75410i	−0.382990	+	0.221119i
$934$	49.9179			1.63336
$935$	31.5092	−	54.5756i	1.03046	−	1.78481i
$936$	−10.9347	+	6.31315i	−0.357412	+	0.206352i
$937$	29.7790	−	17.1929i	0.972837	−	0.561668i	0.0727371	−	0.997351i	$-0.476827\pi$
$937$	29.7790	−	17.1929i	0.972837	−	0.561668i	0.900100	+	0.435683i	$0.143493\pi$
$938$	−3.71670	−	10.5718i	−0.121354	−	0.345183i
$939$		−	7.41617i		−	0.242018i
$940$	51.1322			1.66775
$941$	29.7704	−	51.5638i	0.970487	−	1.68093i	0.276397	−	0.961044i	$-0.410860\pi$
$941$	29.7704	−	51.5638i	0.970487	−	1.68093i	0.694090	−	0.719888i	$-0.255807\pi$
$942$	1.38434	+	2.39775i	0.0451043	+	0.0781230i
$943$	−10.6096	+	18.3763i	−0.345495	+	0.598415i
$944$	16.9244	+	29.3140i	0.550843	+	0.954089i
$945$	17.6806	+	15.1702i	0.575148	+	0.493485i
$946$	48.9991	−	28.2897i	1.59310	−	0.919776i
$947$	19.9213	+	34.5047i	0.647356	+	1.12125i	0.983752	+	0.179532i	$0.0574584\pi$
$947$	19.9213	+	34.5047i	0.647356	+	1.12125i	−0.336397	+	0.941720i	$0.609208\pi$
$948$			9.95250i			0.323242i
$949$	3.93233	−	2.27033i	0.127649	−	0.0736981i
$950$	37.2563	−	14.0613i	1.20875	−	0.456210i
$951$		−	13.0177i		−	0.422129i
$952$	−20.6849	−	58.8365i	−0.670401	−	1.90690i
$953$	17.0187	+	9.82575i	0.551290	+	0.318287i	0.749642	−	0.661843i	$-0.230226\pi$
$953$	17.0187	+	9.82575i	0.551290	+	0.318287i	−0.198352	+	0.980131i	$0.563559\pi$
$954$	−50.6575			−1.64010
$955$			42.0261i			1.35993i
$956$	−3.32487	+	5.75885i	−0.107534	+	0.186255i
$957$	−2.58653	−	1.49333i	−0.0836105	−	0.0482725i
$958$	45.0806			1.45649
$959$	−16.6522	−	3.12542i	−0.537729	−	0.100925i
$960$	−11.6186	+	6.70801i	−0.374989	+	0.216500i
$961$	0.510143	−	0.883594i	0.0164562	−	0.0285030i
$962$	−1.46037	−	2.52944i	−0.0470843	−	0.0815523i
$963$	−10.4615	−	6.03993i	−0.337116	−	0.194634i
$964$	−52.2624	−	90.5211i	−1.68326	−	2.91549i
$965$	−17.1872	−	29.7692i	−0.553277	−	0.958303i
$966$	20.1117	+	17.2561i	0.647084	+	0.555207i
$967$	−0.115397	+	0.199874i	−0.00371092	+	0.00642750i	−0.867875	−	0.496783i	$-0.834515\pi$
$967$	−0.115397	+	0.199874i	−0.00371092	+	0.00642750i	0.864164	+	0.503210i	$0.167848\pi$
$968$	29.3530	+	16.9470i	0.943442	+	0.544697i
$969$	10.5848	−	3.99493i	0.340032	−	0.128336i
$970$	54.6578	+	94.6701i	1.75496	+	3.03967i
$971$	12.8070	+	22.1824i	0.410997	+	0.711868i	0.994999	−	0.0998844i	$-0.0318473\pi$
$971$	12.8070	+	22.1824i	0.410997	+	0.711868i	−0.584002	+	0.811752i	$0.698514\pi$
$972$	24.3705	−	42.2110i	0.781685	−	1.35392i
$973$	2.46078	+	2.11138i	0.0788889	+	0.0676878i
$974$	−0.0539328	+	0.0934144i	−0.00172812	+	0.00299319i
$975$	1.90938			0.0611491
$976$	10.5833	−	6.11025i	0.338762	−	0.195584i
$977$	43.2838	−	24.9899i	1.38477	−	0.799498i	0.392051	−	0.919943i	$-0.371766\pi$
$977$	43.2838	−	24.9899i	1.38477	−	0.799498i	0.992720	+	0.120445i	$0.0384322\pi$
$978$			2.91537i			0.0932232i
$979$	−30.7791	−	53.3110i	−0.983704	−	1.70383i
$980$	−51.0060	−	63.5751i	−1.62933	−	2.03083i
$981$		−	6.90280i		−	0.220390i
$982$			42.9271i			1.36986i
$983$	−49.1757			−1.56846			−0.784230	−	0.620470i	$-0.786942\pi$
$983$	−49.1757			−1.56846			−0.784230	+	0.620470i	$0.786942\pi$
$984$	5.69208	+	3.28633i	0.181457	+	0.104764i
$985$	60.6965	−	35.0431i	1.93395	−	1.11657i
$986$	−14.2129	−	8.20581i	−0.452630	−	0.261326i
$987$	5.69417	−	2.00188i	0.181247	−	0.0637204i
$988$	5.93904	+	15.7358i	0.188946	+	0.500622i
$989$	−21.5461	+	37.3189i	−0.685125	+	1.18667i
$990$	−83.9033			−2.66662
$991$		−	33.3875i		−	1.06059i	−0.847814	−	0.530294i	$-0.822082\pi$
$991$		−	33.3875i		−	1.06059i	0.847814	−	0.530294i	$-0.177918\pi$
$992$		−	3.33733i		−	0.105960i
$993$	−2.73579	−	1.57951i	−0.0868176	−	0.0501242i
$994$	−30.6843	−	87.2788i	−0.973246	−	2.76832i
$995$	−38.2060			−1.21121
$996$	4.24095	+	2.44852i	0.134380	+	0.0775842i
$997$	−5.02512	−	2.90126i	−0.159147	−	0.0918837i	0.418311	−	0.908304i	$-0.362622\pi$
$997$	−5.02512	−	2.90126i	−0.159147	−	0.0918837i	−0.577458	+	0.816420i	$0.695955\pi$
$998$	−13.9722	−	8.06683i	−0.442281	−	0.255351i
$999$	3.15274	+	1.82023i	0.0997482	+	0.0575897i

Display

a_p

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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

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.s.d.103.7	yes	16
7.2	even	3		931.2.p.h.293.2		16
7.3	odd	6		133.2.i.d.122.7	yes	16
7.4	even	3		931.2.i.g.521.7		16
7.5	odd	6		931.2.p.g.293.2		16
7.6	odd	2		931.2.s.g.901.7		16
19.12	odd	6		133.2.i.d.12.2	✓	16
133.12	even	6		931.2.p.h.734.2		16
133.31	even	6	inner	133.2.s.d.31.7	yes	16
133.69	even	6		931.2.i.g.411.2		16
133.88	odd	6		931.2.s.g.31.7		16
133.107	odd	6		931.2.p.g.734.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.i.d.12.2	✓	16	19.12	odd	6
133.2.i.d.122.7	yes	16	7.3	odd	6
133.2.s.d.31.7	yes	16	133.31	even	6	inner
133.2.s.d.103.7	yes	16	1.1	even	1	trivial
931.2.i.g.411.2		16	133.69	even	6
931.2.i.g.521.7		16	7.4	even	3
931.2.p.g.293.2		16	7.5	odd	6
931.2.p.g.734.2		16	133.107	odd	6
931.2.p.h.293.2		16	7.2	even	3
931.2.p.h.734.2		16	133.12	even	6
931.2.s.g.31.7		16	133.88	odd	6
931.2.s.g.901.7		16	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	133.2.s.d.103.7

Level	$133$
Weight	$2$
Character	133.103
Analytic conductor	$1.062$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$