LMFDB - Embedded newform 416.2.bf.a.53.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(53,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("416.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$416 = 2^{5} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	416.bf (of order $8$ , 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			53.5
Character	$\chi$	$=$	416.53
Dual form			416.2.bf.a.157.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33922 - 0.454405i) q^{2} +(-3.06223 + 1.26842i) q^{3} +(1.58703 + 1.21710i) q^{4} +(-0.807892 + 1.95042i) q^{5} +(4.67738 - 0.307199i) q^{6} +(2.62405 + 2.62405i) q^{7} +(-1.57233 - 2.35112i) q^{8} +(5.64706 - 5.64706i) q^{9} +(1.96823 - 2.24494i) q^{10} +(4.01397 + 1.66264i) q^{11} +(-6.40365 - 1.71402i) q^{12} +(0.382683 + 0.923880i) q^{13} +(-2.32181 - 4.70657i) q^{14} -6.99740i q^{15} +(1.03734 + 3.86315i) q^{16} -2.27517i q^{17} +(-10.1287 + 4.99661i) q^{18} +(2.76406 + 6.67304i) q^{19} +(-3.65601 + 2.11210i) q^{20} +(-11.3639 - 4.70706i) q^{21} +(-4.62009 - 4.05062i) q^{22} +(-0.179570 + 0.179570i) q^{23} +(7.79705 + 5.20530i) q^{24} +(0.384069 + 0.384069i) q^{25} +(-0.0926824 - 1.41117i) q^{26} +(-6.32451 + 15.2687i) q^{27} +(0.970723 + 7.35819i) q^{28} +(4.79162 - 1.98475i) q^{29} +(-3.17965 + 9.37107i) q^{30} -1.08028 q^{31} +(0.366207 - 5.64499i) q^{32} -14.4006 q^{33} +(-1.03385 + 3.04696i) q^{34} +(-7.23797 + 2.99806i) q^{35} +(15.8351 - 2.08903i) q^{36} +(0.231634 - 0.559213i) q^{37} +(-0.669431 - 10.1927i) q^{38} +(-2.34373 - 2.34373i) q^{39} +(5.85596 - 1.16726i) q^{40} +(-2.57937 + 2.57937i) q^{41} +(13.0798 + 11.4676i) q^{42} +(-0.449620 - 0.186239i) q^{43} +(4.34670 + 7.52407i) q^{44} +(6.45194 + 15.5764i) q^{45} +(0.322081 - 0.158886i) q^{46} +4.46300i q^{47} +(-8.07666 - 10.5141i) q^{48} +6.77130i q^{49} +(-0.339831 - 0.688876i) q^{50} +(2.88587 + 6.96711i) q^{51} +(-0.517122 + 1.93199i) q^{52} +(-9.59654 - 3.97502i) q^{53} +(15.4081 - 17.5743i) q^{54} +(-6.48572 + 6.48572i) q^{55} +(2.04358 - 10.2953i) q^{56} +(-16.9284 - 16.9284i) q^{57} +(-7.31893 + 0.480689i) q^{58} +(2.54391 - 6.14155i) q^{59} +(8.51652 - 11.1051i) q^{60} +(-2.20636 + 0.913906i) q^{61} +(1.44674 + 0.490887i) q^{62} +29.6363 q^{63} +(-3.05554 + 7.39349i) q^{64} -2.11112 q^{65} +(19.2857 + 6.54373i) q^{66} +(-5.44496 + 2.25538i) q^{67} +(2.76911 - 3.61077i) q^{68} +(0.322115 - 0.777654i) q^{69} +(11.0556 - 0.726104i) q^{70} +(-6.28291 - 6.28291i) q^{71} +(-22.1560 - 4.39787i) q^{72} +(8.07849 - 8.07849i) q^{73} +(-0.564318 + 0.643655i) q^{74} +(-1.66327 - 0.688948i) q^{75} +(-3.73509 + 13.9545i) q^{76} +(6.17002 + 14.8957i) q^{77} +(2.07377 + 4.20378i) q^{78} -3.06873i q^{79} +(-8.37284 - 1.09776i) q^{80} -30.8201i q^{81} +(4.62643 - 2.28227i) q^{82} +(-0.0149546 - 0.0361037i) q^{83} +(-12.3058 - 21.3012i) q^{84} +(4.43756 + 1.83810i) q^{85} +(0.517513 + 0.453725i) q^{86} +(-12.1555 + 12.1555i) q^{87} +(-2.40223 - 12.0516i) q^{88} +(7.57915 + 7.57915i) q^{89} +(-1.56260 - 23.7920i) q^{90} +(-1.42013 + 3.42849i) q^{91} +(-0.503537 + 0.0664287i) q^{92} +(3.30808 - 1.37025i) q^{93} +(2.02801 - 5.97695i) q^{94} -15.2483 q^{95} +(6.03879 + 17.7508i) q^{96} +11.5489 q^{97} +(3.07692 - 9.06828i) q^{98} +(32.0562 - 13.2781i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51}+ \cdots + 56 q^{98}+O(q^{100})$ 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$ .

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.33922	−	0.454405i	−0.946973	−	0.321313i
$2$	−1.33922	−	0.454405i	−0.946973	−	0.321313i
$3$	−3.06223	+	1.26842i	−1.76798	+	0.732321i	−0.772756	+	0.634703i	$0.781122\pi$
$3$	−3.06223	+	1.26842i	−1.76798	+	0.732321i	−0.995224	+	0.0976183i	$0.968878\pi$
$4$	1.58703	+	1.21710i	0.793516	+	0.608550i
$5$	−0.807892	+	1.95042i	−0.361300	+	0.872256i	0.633810	+	0.773489i	$0.281490\pi$
$5$	−0.807892	+	1.95042i	−0.361300	+	0.872256i	−0.995111	+	0.0987676i	$0.968510\pi$
$6$	4.67738	−	0.307199i	1.90953	−	0.125414i
$7$	2.62405	+	2.62405i	0.991799	+	0.991799i	0.999967	−	0.00816797i	$-0.00259997\pi$
$7$	2.62405	+	2.62405i	0.991799	+	0.991799i	−0.00816797	+	0.999967i	$0.502600\pi$
$8$	−1.57233	−	2.35112i	−0.555903	−	0.831247i
$9$	5.64706	−	5.64706i	1.88235	−	1.88235i
$10$	1.96823	−	2.24494i	0.622409	−	0.709913i
$11$	4.01397	+	1.66264i	1.21026	+	0.501306i	0.894300	−	0.447467i	$-0.147674\pi$
$11$	4.01397	+	1.66264i	1.21026	+	0.501306i	0.315959	+	0.948773i	$0.397674\pi$
$12$	−6.40365	−	1.71402i	−1.84857	−	0.494795i
$13$	0.382683	+	0.923880i	0.106137	+	0.256238i
$13$	0.382683	+	0.923880i	0.106137	+	0.256238i
$14$	−2.32181	−	4.70657i	−0.620529	−	1.25788i
$15$		−	6.99740i		−	1.80672i
$16$	1.03734	+	3.86315i	0.259335	+	0.965787i
$17$		−	2.27517i		−	0.551811i	−0.961185	−	0.275905i	$-0.911022\pi$
$17$		−	2.27517i		−	0.551811i	0.961185	−	0.275905i	$-0.0889777\pi$
$18$	−10.1287	+	4.99661i	−2.38736	+	1.17771i
$19$	2.76406	+	6.67304i	0.634120	+	1.53090i	0.834399	+	0.551161i	$0.185815\pi$
$19$	2.76406	+	6.67304i	0.634120	+	1.53090i	−0.200279	+	0.979739i	$0.564185\pi$
$20$	−3.65601	+	2.11210i	−0.817509	+	0.472280i
$21$	−11.3639	−	4.70706i	−2.47980	−	1.02716i
$22$	−4.62009	−	4.05062i	−0.985007	−	0.863595i
$23$	−0.179570	+	0.179570i	−0.0374429	+	0.0374429i	−0.725580	−	0.688137i	$-0.758429\pi$
$23$	−0.179570	+	0.179570i	−0.0374429	+	0.0374429i	0.688137	+	0.725580i	$0.258429\pi$
$24$	7.79705	+	5.20530i	1.59157	+	1.06253i
$25$	0.384069	+	0.384069i	0.0768138	+	0.0768138i
$26$	−0.0926824	−	1.41117i	−0.0181765	−	0.276754i
$27$	−6.32451	+	15.2687i	−1.21715	+	2.93847i
$28$	0.970723	+	7.35819i	0.183449	+	1.39057i
$29$	4.79162	−	1.98475i	0.889781	−	0.368560i	0.109499	−	0.993987i	$-0.465075\pi$
$29$	4.79162	−	1.98475i	0.889781	−	0.368560i	0.780282	+	0.625427i	$0.215075\pi$
$30$	−3.17965	+	9.37107i	−0.580523	+	1.71091i
$31$	−1.08028			−0.194025			−0.0970124	−	0.995283i	$-0.530929\pi$
$31$	−1.08028			−0.194025			−0.0970124	+	0.995283i	$0.530929\pi$
$32$	0.366207	−	5.64499i	0.0647369	−	0.997902i
$33$	−14.4006			−2.50683
$34$	−1.03385	+	3.04696i	−0.177304	+	0.522550i
$35$	−7.23797	+	2.99806i	−1.22344	+	0.506765i
$36$	15.8351	−	2.08903i	2.63918	−	0.348172i
$37$	0.231634	−	0.559213i	0.0380803	−	0.0919340i	−0.903695	−	0.428176i	$-0.859156\pi$
$37$	0.231634	−	0.559213i	0.0380803	−	0.0919340i	0.941775	+	0.336242i	$0.109156\pi$
$38$	−0.669431	−	10.1927i	−0.108596	−	1.65347i
$39$	−2.34373	−	2.34373i	−0.375297	−	0.375297i
$40$	5.85596	−	1.16726i	0.925908	−	0.184560i
$41$	−2.57937	+	2.57937i	−0.402830	+	0.402830i	−0.879229	−	0.476399i	$-0.841942\pi$
$41$	−2.57937	+	2.57937i	−0.402830	+	0.402830i	0.476399	+	0.879229i	$0.341942\pi$
$42$	13.0798	+	11.4676i	2.01826	+	1.76949i
$43$	−0.449620	−	0.186239i	−0.0685664	−	0.0284011i	0.348137	−	0.937444i	$-0.386815\pi$
$43$	−0.449620	−	0.186239i	−0.0685664	−	0.0284011i	−0.416703	+	0.909043i	$0.636815\pi$
$44$	4.34670	+	7.52407i	0.655290	+	1.13430i
$45$	6.45194	+	15.5764i	0.961799	+	2.32199i
$46$	0.322081	−	0.158886i	0.0474883	−	0.0234265i
$47$			4.46300i			0.650996i	0.945543	+	0.325498i	$0.105532\pi$
$47$			4.46300i			0.650996i	−0.945543	+	0.325498i	$0.894468\pi$
$48$	−8.07666	−	10.5141i	−1.16577	−	1.51758i
$49$			6.77130i			0.967329i
$50$	−0.339831	−	0.688876i	−0.0480593	−	0.0974218i
$51$	2.88587	+	6.96711i	0.404103	+	0.975591i
$52$	−0.517122	+	1.93199i	−0.0717119	+	0.267919i
$53$	−9.59654	−	3.97502i	−1.31819	−	0.546010i	−0.390923	−	0.920423i	$-0.627844\pi$
$53$	−9.59654	−	3.97502i	−1.31819	−	0.546010i	−0.927262	+	0.374413i	$0.877844\pi$
$54$	15.4081	−	17.5743i	2.09678	−	2.39156i
$55$	−6.48572	+	6.48572i	−0.874534	+	0.874534i
$56$	2.04358	−	10.2953i	0.273086	−	1.37577i
$57$	−16.9284	−	16.9284i	−2.24222	−	2.24222i
$58$	−7.31893	+	0.480689i	−0.961022	+	0.0631176i
$59$	2.54391	−	6.14155i	0.331189	−	0.799562i	−0.667309	−	0.744781i	$-0.732554\pi$
$59$	2.54391	−	6.14155i	0.331189	−	0.799562i	0.998498	−	0.0547808i	$-0.0174460\pi$
$60$	8.51652	−	11.1051i	1.09948	−	1.43366i
$61$	−2.20636	+	0.913906i	−0.282496	+	0.117014i	−0.519433	−	0.854511i	$-0.673857\pi$
$61$	−2.20636	+	0.913906i	−0.282496	+	0.117014i	0.236937	+	0.971525i	$0.423857\pi$
$62$	1.44674	+	0.490887i	0.183736	+	0.0623427i
$63$	29.6363			3.73383
$64$	−3.05554	+	7.39349i	−0.381943	+	0.924186i
$65$	−2.11112			−0.261853
$66$	19.2857	+	6.54373i	2.37390	+	0.805477i
$67$	−5.44496	+	2.25538i	−0.665207	+	0.275538i	−0.689628	−	0.724164i	$-0.742226\pi$
$67$	−5.44496	+	2.25538i	−0.665207	+	0.275538i	0.0244206	+	0.999702i	$0.492226\pi$
$68$	2.76911	−	3.61077i	0.335804	−	0.437871i
$69$	0.322115	−	0.777654i	0.0387781	−	0.0936185i
$70$	11.0556	−	0.726104i	1.32139	−	0.0867860i
$71$	−6.28291	−	6.28291i	−0.745645	−	0.745645i	0.228013	−	0.973658i	$-0.426777\pi$
$71$	−6.28291	−	6.28291i	−0.745645	−	0.745645i	−0.973658	+	0.228013i	$0.926777\pi$
$72$	−22.1560	−	4.39787i	−2.61111	−	0.518294i
$73$	8.07849	−	8.07849i	0.945515	−	0.945515i	−0.0530751	−	0.998591i	$-0.516902\pi$
$73$	8.07849	−	8.07849i	0.945515	−	0.945515i	0.998591	+	0.0530751i	$0.0169023\pi$
$74$	−0.564318	+	0.643655i	−0.0656006	+	0.0748234i
$75$	−1.66327	−	0.688948i	−0.192058	−	0.0795529i
$76$	−3.73509	+	13.9545i	−0.428445	+	1.60069i
$77$	6.17002	+	14.8957i	0.703139	+	1.69753i
$78$	2.07377	+	4.20378i	0.234808	+	0.475984i
$79$		−	3.06873i		−	0.345259i	−0.984987	−	0.172630i	$-0.944774\pi$
$79$		−	3.06873i		−	0.345259i	0.984987	−	0.172630i	$-0.0552264\pi$
$80$	−8.37284	−	1.09776i	−0.936112	−	0.122733i
$81$		−	30.8201i		−	3.42445i
$82$	4.62643	−	2.28227i	0.510904	−	0.252035i
$83$	−0.0149546	−	0.0361037i	−0.00164149	−	0.00396290i	0.923057	−	0.384664i	$-0.125683\pi$
$83$	−0.0149546	−	0.0361037i	−0.00164149	−	0.00396290i	−0.924698	+	0.380701i	$0.875683\pi$
$84$	−12.3058	−	21.3012i	−1.34268	−	2.32415i
$85$	4.43756	+	1.83810i	0.481320	+	0.199369i
$86$	0.517513	+	0.453725i	0.0558049	+	0.0489264i
$87$	−12.1555	+	12.1555i	−1.30321	+	1.30321i
$88$	−2.40223	−	12.0516i	−0.256078	−	1.28470i
$89$	7.57915	+	7.57915i	0.803389	+	0.803389i	0.983624	−	0.180235i	$-0.0576858\pi$
$89$	7.57915	+	7.57915i	0.803389	+	0.803389i	−0.180235	+	0.983624i	$0.557686\pi$
$90$	−1.56260	−	23.7920i	−0.164713	−	2.50790i
$91$	−1.42013	+	3.42849i	−0.148870	+	0.359403i
$92$	−0.503537	+	0.0664287i	−0.0524974	+	0.00692567i
$93$	3.30808	−	1.37025i	0.343032	−	0.142088i
$94$	2.02801	−	5.97695i	0.209173	−	0.616476i
$95$	−15.2483			−1.56445
$96$	6.03879	+	17.7508i	0.616332	+	1.81168i
$97$	11.5489			1.17262			0.586308	−	0.810088i	$-0.300581\pi$
$97$	11.5489			1.17262			0.586308	+	0.810088i	$0.300581\pi$
$98$	3.07692	−	9.06828i	0.310815	−	0.916035i
$99$	32.0562	−	13.2781i	3.22177	−	1.33450i
$100$	0.142080	+	1.07698i	0.0142080	+	0.107698i
$101$	2.06487	−	4.98505i	0.205463	−	0.496031i	−0.787236	−	0.616652i	$-0.788489\pi$
$101$	2.06487	−	4.98505i	0.205463	−	0.496031i	0.992699	+	0.120621i	$0.0384886\pi$
$102$	−0.698932	−	10.6419i	−0.0692046	−	1.05370i
$103$	5.39113	+	5.39113i	0.531203	+	0.531203i	0.920930	−	0.389727i	$-0.127431\pi$
$103$	5.39113	+	5.39113i	0.531203	+	0.531203i	−0.389727	+	0.920930i	$0.627431\pi$
$104$	1.57045	−	2.35238i	0.153995	−	0.230670i
$105$	18.3615	−	18.3615i	1.79190	−	1.79190i
$106$	11.0456	+	9.68414i	1.07285	+	0.940607i
$107$	−12.2459	−	5.07242i	−1.18386	−	0.490369i	−0.298107	−	0.954533i	$-0.596355\pi$
$107$	−12.2459	−	5.07242i	−1.18386	−	0.490369i	−0.885750	+	0.464163i	$0.846355\pi$
$108$	−28.6208	+	16.5344i	−2.75403	+	1.59102i
$109$	−7.33872	−	17.7172i	−0.702922	−	1.69700i	−0.716971	−	0.697103i	$-0.754472\pi$
$109$	−7.33872	−	17.7172i	−0.702922	−	1.69700i	0.0140484	−	0.999901i	$-0.495528\pi$
$110$	11.6330	−	5.73867i	1.10916	−	0.547161i
$111$			2.00625i			0.190425i
$112$	−7.41507	+	12.8591i	−0.700659	+	1.21507i
$113$			20.5778i			1.93580i	0.251336	+	0.967900i	$0.419130\pi$
$113$			20.5778i			1.93580i	−0.251336	+	0.967900i	$0.580870\pi$
$114$	14.9785	+	30.3633i	1.40287	+	2.84378i
$115$	−0.205164	−	0.495310i	−0.0191317	−	0.0461879i
$116$	10.0201	+	2.68201i	0.930342	+	0.249018i
$117$	7.37824	+	3.05617i	0.682118	+	0.282543i
$118$	−6.19762	+	7.06893i	−0.570537	+	0.650748i
$119$	5.97018	−	5.97018i	0.547285	−	0.547285i
$120$	−16.4517	+	11.0022i	−1.50183	+	1.00436i
$121$	5.56944	+	5.56944i	0.506313	+	0.506313i
$122$	3.37009	−	0.221340i	0.305114	−	0.0200391i
$123$	4.62691	−	11.1704i	0.417195	−	1.00720i
$124$	−1.71445	−	1.31481i	−0.153962	−	0.118074i
$125$	−10.8115	+	4.47827i	−0.967010	+	0.400549i
$126$	−39.6897	−	13.4669i	−3.53584	−	1.19973i
$127$	13.3495			1.18457			0.592287	−	0.805727i	$-0.298225\pi$
$127$	13.3495			1.18457			0.592287	+	0.805727i	$0.298225\pi$
$128$	7.45169	−	8.51307i	0.658643	−	0.752456i
$129$	1.61307			0.142023
$130$	2.82726	+	0.959306i	0.247967	+	0.0841367i
$131$	−6.70309	+	2.77651i	−0.585652	+	0.242585i	−0.655779	−	0.754953i	$-0.727660\pi$
$131$	−6.70309	+	2.77651i	−0.585652	+	0.242585i	0.0701270	+	0.997538i	$0.477660\pi$
$132$	−22.8543	−	17.5270i	−1.98921	−	1.52553i
$133$	−10.2574	+	24.7635i	−0.889426	+	2.14726i
$134$	8.31686	−	0.546231i	0.718467	−	0.0471872i
$135$	−24.6710	−	24.6710i	−2.12334	−	2.12334i
$136$	−5.34921	+	3.57733i	−0.458691	+	0.306753i
$137$	−3.26880	+	3.26880i	−0.279272	+	0.279272i	−0.832819	−	0.553546i	$-0.813274\pi$
$137$	−3.26880	+	3.26880i	−0.279272	+	0.279272i	0.553546	+	0.832819i	$0.313274\pi$
$138$	−0.784753	+	0.895080i	−0.0668026	+	0.0761943i
$139$	−12.0720	−	5.00038i	−1.02393	−	0.424127i	−0.193414	−	0.981117i	$-0.561956\pi$
$139$	−12.0720	−	5.00038i	−1.02393	−	0.424127i	−0.830519	+	0.556990i	$0.811956\pi$
$140$	−15.1358	−	4.05130i	−1.27921	−	0.342397i
$141$	−5.66095	−	13.6667i	−0.476738	−	1.15095i
$142$	5.55923	+	11.2692i	0.466520	+	0.945691i
$143$			4.34470i			0.363322i
$144$	27.6733	+	15.9575i	2.30611	+	1.32979i
$145$			10.9492i			0.909278i
$146$	−14.4898	+	7.14798i	−1.19918	+	0.591571i
$147$	−8.58884	−	20.7353i	−0.708396	−	1.71022i
$148$	1.04823	−	0.605568i	0.0861638	−	0.0497774i
$149$	16.9460	+	7.01924i	1.38827	+	0.575039i	0.946679	−	0.322179i	$-0.104415\pi$
$149$	16.9460	+	7.01924i	1.38827	+	0.575039i	0.441588	+	0.897218i	$0.354415\pi$
$150$	1.91442	+	1.67845i	0.156312	+	0.137045i
$151$	−5.03561	+	5.03561i	−0.409792	+	0.409792i	−0.881666	−	0.471874i	$-0.843578\pi$
$151$	−5.03561	+	5.03561i	−0.409792	+	0.409792i	0.471874	+	0.881666i	$0.343578\pi$
$152$	11.3431	−	16.9909i	0.920047	−	1.37814i
$153$	−12.8480	−	12.8480i	−1.03870	−	1.03870i
$154$	−1.49432	−	22.7524i	−0.120416	−	1.83344i
$155$	0.872753	−	2.10701i	0.0701012	−	0.169239i
$156$	−0.867023	−	6.57213i	−0.0694174	−	0.526191i
$157$	−6.08850	+	2.52194i	−0.485915	+	0.201273i	−0.612172	−	0.790725i	$-0.709704\pi$
$157$	−6.08850	+	2.52194i	−0.485915	+	0.201273i	0.126256	+	0.991998i	$0.459704\pi$
$158$	−1.39445	+	4.10971i	−0.110936	+	0.326951i
$159$	34.4288			2.73038
$160$	10.7143	+	5.27480i	0.847037	+	0.417010i
$161$	−0.942401			−0.0742716
$162$	−14.0048	+	41.2749i	−1.10032	+	3.24286i
$163$	14.4296	−	5.97694i	1.13021	−	0.468150i	0.262360	−	0.964970i	$-0.415499\pi$
$163$	14.4296	−	5.97694i	1.13021	−	0.468150i	0.867854	+	0.496820i	$0.165499\pi$
$164$	−7.23290	+	0.954194i	−0.564795	+	0.0745101i
$165$	11.6342	−	28.0874i	0.905719	−	2.18660i
$166$	0.00362188	+	0.0551464i	0.000281112	+	0.00428019i
$167$	−10.3667	−	10.3667i	−0.802201	−	0.802201i	0.181238	−	0.983439i	$-0.441989\pi$
$167$	−10.3667	−	10.3667i	−0.802201	−	0.802201i	−0.983439	+	0.181238i	$0.941989\pi$
$168$	6.80087	+	34.1189i	0.524699	+	2.63233i
$169$	−0.707107	+	0.707107i	−0.0543928	+	0.0543928i
$170$	−5.10763	−	4.47807i	−0.391738	−	0.343452i
$171$	53.2919	+	22.0742i	4.07533	+	1.68806i
$172$	−0.486890	−	0.842799i	−0.0371250	−	0.0642628i
$173$	5.27468	+	12.7342i	0.401027	+	0.968164i	0.987417	+	0.158136i	$0.0505483\pi$
$173$	5.27468	+	12.7342i	0.401027	+	0.968164i	−0.586391	+	0.810028i	$0.699452\pi$
$174$	21.8025	−	10.7554i	1.65285	−	0.815367i
$175$			2.01563i			0.152368i
$176$	−2.25918	+	17.2313i	−0.170292	+	1.29886i
$177$			22.0336i			1.65615i
$178$	−6.70616	−	13.5942i	−0.502648	−	1.01893i
$179$	4.55833	+	11.0048i	0.340705	+	0.822536i	0.997645	+	0.0685922i	$0.0218507\pi$
$179$	4.55833	+	11.0048i	0.340705	+	0.822536i	−0.656939	+	0.753943i	$0.728149\pi$
$180$	−8.71855	+	32.5728i	−0.649842	+	2.42784i
$181$	−11.1086	−	4.60132i	−0.825694	−	0.342014i	−0.0704974	−	0.997512i	$-0.522459\pi$
$181$	−11.1086	−	4.60132i	−0.825694	−	0.342014i	−0.755197	+	0.655498i	$0.772459\pi$
$182$	3.45979	−	3.94620i	0.256457	−	0.292512i
$183$	5.59718	−	5.59718i	0.413756	−	0.413756i
$184$	0.704534	+	0.139847i	0.0519389	+	0.0103097i
$185$	0.903568	+	0.903568i	0.0664316	+	0.0664316i
$186$	−5.05290	+	0.331862i	−0.370497	+	0.0243333i
$187$	3.78280	−	9.13249i	0.276626	−	0.667834i
$188$	−5.43192	+	7.08293i	−0.396163	+	0.516576i
$189$	−56.6618	+	23.4701i	−4.12154	+	1.70720i
$190$	20.4209	+	6.92892i	1.48149	+	0.502677i
$191$	−7.64117			−0.552896			−0.276448	−	0.961029i	$-0.589157\pi$
$191$	−7.64117			−0.552896			−0.276448	+	0.961029i	$0.589157\pi$
$192$	−0.0212446	−	26.5163i	−0.00153320	−	1.91365i
$193$	17.6216			1.26843			0.634214	−	0.773158i	$-0.281324\pi$
$193$	17.6216			1.26843			0.634214	+	0.773158i	$0.281324\pi$
$194$	−15.4666	−	5.24789i	−1.11044	−	0.376777i
$195$	6.46475	−	2.67779i	0.462950	−	0.191760i
$196$	−8.24135	+	10.7463i	−0.588668	+	0.767591i
$197$	4.78525	−	11.5526i	0.340935	−	0.823090i	−0.656687	−	0.754163i	$-0.728043\pi$
$197$	4.78525	−	11.5526i	0.340935	−	0.823090i	0.997622	−	0.0689264i	$-0.0219574\pi$
$198$	−48.9640	+	3.21584i	−3.47972	+	0.228539i
$199$	−3.42010	−	3.42010i	−0.242444	−	0.242444i	0.575416	−	0.817861i	$-0.304840\pi$
$199$	−3.42010	−	3.42010i	−0.242444	−	0.242444i	−0.817861	+	0.575416i	$0.804840\pi$
$200$	0.299109	−	1.50688i	0.0211502	−	0.106552i
$201$	13.8130	−	13.8130i	0.974291	−	0.974291i
$202$	−5.03056	+	5.73780i	−0.353949	+	0.403710i
$203$	17.7816	+	7.36536i	1.24802	+	0.516947i
$204$	−3.89969	+	14.5694i	−0.273033	+	1.02006i
$205$	−2.94702	−	7.11473i	−0.205829	−	0.496914i
$206$	−4.77016	−	9.66967i	−0.332353	−	0.673718i
$207$			2.02808i			0.140961i
$208$	−3.17211	+	2.43674i	−0.219946	+	0.168958i
$209$			31.3811i			2.17067i
$210$	−32.9337	+	16.2466i	−2.27264	+	1.12112i
$211$	0.00594991	+	0.0143644i	0.000409609	+	0.000988884i	0.924084	−	0.382189i	$-0.124830\pi$
$211$	0.00594991	+	0.0143644i	0.000409609	+	0.000988884i	−0.923675	+	0.383178i	$0.874830\pi$
$212$	−10.3920	−	17.9884i	−0.713727	−	1.23545i
$213$	27.2091	+	11.2704i	1.86434	+	0.772233i
$214$	14.0951	+	12.3577i	0.963518	+	0.844755i
$215$	0.726489	−	0.726489i	0.0495461	−	0.0495461i
$216$	45.8429	−	9.13781i	3.11921	−	0.621749i
$217$	−2.83472	−	2.83472i	−0.192433	−	0.192433i
$218$	1.77737	+	27.0621i	0.120379	+	1.83288i
$219$	−14.4913	+	34.9851i	−0.979231	+	2.36407i
$220$	−18.1868	+	2.39928i	−1.22615	+	0.161759i
$221$	2.10199	−	0.870672i	0.141395	−	0.0585677i
$222$	0.911649	−	2.68681i	0.0611859	−	0.180327i
$223$	−23.6463			−1.58347			−0.791736	−	0.610864i	$-0.790822\pi$
$223$	−23.6463			−1.58347			−0.791736	+	0.610864i	$0.790822\pi$
$224$	15.7737	−	13.8518i	1.05392	−	0.925512i
$225$	4.33772			0.289181
$226$	9.35068	−	27.5583i	0.621998	−	1.83315i
$227$	11.5914	−	4.80131i	0.769348	−	0.318674i	0.0367394	−	0.999325i	$-0.488303\pi$
$227$	11.5914	−	4.80131i	0.769348	−	0.318674i	0.732608	+	0.680651i	$0.238303\pi$
$228$	−6.26237	−	47.4695i	−0.414736	−	3.14374i
$229$	−6.53886	+	15.7862i	−0.432100	+	1.04318i	0.546509	+	0.837453i	$0.315956\pi$
$229$	−6.53886	+	15.7862i	−0.432100	+	1.04318i	−0.978609	+	0.205729i	$0.934044\pi$
$230$	0.0496889	+	0.756558i	0.00327639	+	0.0498860i
$231$	−37.7881	−	37.7881i	−2.48627	−	2.48627i
$232$	−12.2004	−	8.14499i	−0.800996	−	0.534745i
$233$	11.2356	−	11.2356i	0.736072	−	0.736072i	−0.235744	−	0.971815i	$-0.575753\pi$
$233$	11.2356	−	11.2356i	0.736072	−	0.736072i	0.971815	+	0.235744i	$0.0757526\pi$
$234$	−8.49236	−	7.44559i	−0.555163	−	0.486734i
$235$	−8.70475	−	3.60563i	−0.567835	−	0.235205i
$236$	11.5121	−	6.65064i	0.749377	−	0.432920i
$237$	3.89243	+	9.39716i	0.252841	+	0.610411i
$238$	−10.7083	+	5.28251i	−0.694114	+	0.342415i
$239$			6.37778i			0.412544i	0.978495	+	0.206272i	$0.0661332\pi$
$239$			6.37778i			0.412544i	−0.978495	+	0.206272i	$0.933867\pi$
$240$	27.0320	−	7.25868i	1.74491	−	0.468546i
$241$		−	4.23046i		−	0.272508i	−0.990674	−	0.136254i	$-0.956494\pi$
$241$		−	4.23046i		−	0.272508i	0.990674	−	0.136254i	$-0.0435063\pi$
$242$	−4.92793	−	9.98950i	−0.316780	−	0.642149i
$243$	20.1192	+	48.5720i	1.29065	+	3.11589i
$244$	−4.61388	−	1.23497i	−0.295374	−	0.0790606i
$245$	−13.2069	−	5.47048i	−0.843759	−	0.349496i
$246$	−11.2723	+	12.8571i	−0.718698	+	0.819739i
$247$	−5.10732	+	5.10732i	−0.324971	+	0.324971i
$248$	1.69857	+	2.53988i	0.107859	+	0.161282i
$249$	0.0915892	+	0.0915892i	0.00580423	+	0.00580423i
$250$	16.5140	−	1.08460i	1.04443	−	0.0685959i
$251$	10.2218	−	24.6775i	0.645192	−	1.55763i	−0.174396	−	0.984676i	$-0.555797\pi$
$251$	10.2218	−	24.6775i	0.645192	−	1.55763i	0.819587	−	0.572954i	$-0.194203\pi$
$252$	47.0338	+	36.0704i	2.96285	+	2.27222i
$253$	−1.01935	+	0.422228i	−0.0640859	+	0.0265453i
$254$	−17.8779	−	6.06607i	−1.12176	−	0.380619i
$255$	−15.9203			−0.996968
$256$	−13.8479	+	8.01480i	−0.865491	+	0.500925i
$257$	−6.87592			−0.428908			−0.214454	−	0.976734i	$-0.568797\pi$
$257$	−6.87592			−0.428908			−0.214454	+	0.976734i	$0.568797\pi$
$258$	−2.16026	−	0.732987i	−0.134492	−	0.0456338i
$259$	2.07522	−	0.859585i	0.128948	−	0.0534120i
$260$	−3.35042	−	2.56945i	−0.207784	−	0.159350i
$261$	15.8505	−	38.2666i	0.981123	−	2.36864i
$262$	10.2386	−	0.672445i	0.632542	−	0.0415438i
$263$	−2.91088	−	2.91088i	−0.179493	−	0.179493i	0.611642	−	0.791135i	$-0.290509\pi$
$263$	−2.91088	−	2.91088i	−0.179493	−	0.179493i	−0.791135	+	0.611642i	$0.790509\pi$
$264$	22.6426	+	33.8577i	1.39356	+	2.08380i
$265$	15.5059	−	15.5059i	0.952522	−	0.952522i
$266$	24.9895	−	28.5028i	1.53221	−	1.74762i
$267$	−32.8227	−	13.5956i	−2.00871	−	0.832037i
$268$	−11.3863	−	3.04770i	−0.695531	−	0.186168i
$269$	−5.41883	−	13.0822i	−0.330392	−	0.797636i	−0.998561	−	0.0536268i	$-0.982922\pi$
$269$	−5.41883	−	13.0822i	−0.330392	−	0.797636i	0.668169	−	0.744009i	$-0.267078\pi$
$270$	21.8293	+	44.2505i	1.32849	+	2.69300i
$271$			0.945391i			0.0574284i	0.999588	+	0.0287142i	$0.00914127\pi$
$271$			0.945391i			0.0574284i	−0.999588	+	0.0287142i	$0.990859\pi$
$272$	8.78934	−	2.36013i	0.532932	−	0.143104i
$273$		−	12.3001i		−	0.744439i
$274$	5.86301	−	2.89229i	0.354197	−	0.174730i
$275$	0.903073	+	2.18021i	0.0544574	+	0.131472i
$276$	1.45769	−	0.842116i	0.0877425	−	0.0506894i
$277$	−18.2616	−	7.56421i	−1.09723	−	0.454489i	−0.240710	−	0.970597i	$-0.577380\pi$
$277$	−18.2616	−	7.56421i	−1.09723	−	0.454489i	−0.856524	+	0.516108i	$0.827380\pi$
$278$	13.8949	+	12.1822i	0.833359	+	0.730640i
$279$	−6.10043	+	6.10043i	−0.365223	+	0.365223i
$280$	18.4293	+	12.3034i	1.10136	+	0.735268i
$281$	−19.6017	−	19.6017i	−1.16934	−	1.16934i	−0.982364	−	0.186976i	$-0.940131\pi$
$281$	−19.6017	−	19.6017i	−1.16934	−	1.16934i	−0.186976	−	0.982364i	$-0.559869\pi$
$282$	1.37103	+	20.8752i	0.0816437	+	1.24310i
$283$	3.18385	−	7.68649i	0.189260	−	0.456915i	−0.800557	−	0.599256i	$-0.795463\pi$
$283$	3.18385	−	7.68649i	0.189260	−	0.456915i	0.989818	+	0.142342i	$0.0454631\pi$
$284$	−2.32426	−	17.6181i	−0.137919	−	1.04544i
$285$	46.6939	−	19.3412i	2.76591	−	1.14568i
$286$	1.97425	−	5.81851i	0.116740	−	0.344056i
$287$	−13.5368			−0.799053
$288$	−29.8096	−	33.9456i	−1.75655	−	2.00026i
$289$	11.8236			0.695505
$290$	4.97535	−	14.6634i	0.292163	−	0.861062i
$291$	−35.3655	+	14.6489i	−2.07316	+	0.858731i
$292$	22.6531	−	2.98850i	1.32567	−	0.174889i
$293$	−1.42798	+	3.44745i	−0.0834235	+	0.201402i	−0.960087	−	0.279702i	$-0.909764\pi$
$293$	−1.42798	+	3.44745i	−0.0834235	+	0.201402i	0.876663	+	0.481104i	$0.159764\pi$
$294$	2.08014	+	31.6720i	0.121316	+	1.84715i
$295$	9.92342	+	9.92342i	0.577764	+	0.577764i
$296$	−1.67898	+	0.334670i	−0.0975889	+	0.0194523i
$297$	−50.7729	+	50.7729i	−2.94614	+	2.94614i
$298$	−19.5048	−	17.1007i	−1.12988	−	0.990615i
$299$	−0.234619	−	0.0971825i	−0.0135684	−	0.00562021i
$300$	−1.80114	−	3.11774i	−0.103989	−	0.180003i
$301$	−0.691126	−	1.66853i	−0.0398359	−	0.0961723i
$302$	9.03201	−	4.45559i	0.519734	−	0.256391i
$303$			17.8845i			1.02744i
$304$	−22.9117	+	17.6002i	−1.31408	+	1.00944i
$305$		−	5.04168i		−	0.288686i
$306$	11.3682	+	23.0446i	0.649875	+	1.31737i
$307$	3.64890	+	8.80921i	0.208253	+	0.502768i	0.993148	−	0.116861i	$-0.0372831\pi$
$307$	3.64890	+	8.80921i	0.208253	+	0.502768i	−0.784895	+	0.619629i	$0.787283\pi$
$308$	−8.33758	+	31.1495i	−0.475078	+	1.77491i
$309$	−23.3471	−	9.67067i	−1.32817	−	0.550145i
$310$	−2.12625	+	2.42517i	−0.120763	+	0.137741i
$311$	−23.9593	+	23.9593i	−1.35861	+	1.35861i	−0.482975	+	0.875634i	$0.660444\pi$
$311$	−23.9593	+	23.9593i	−1.35861	+	1.35861i	−0.875634	+	0.482975i	$0.839556\pi$
$312$	−1.82527	+	9.19552i	−0.103336	+	0.520594i
$313$	−2.80015	−	2.80015i	−0.158274	−	0.158274i	0.623528	−	0.781801i	$-0.285699\pi$
$313$	−2.80015	−	2.80015i	−0.158274	−	0.158274i	−0.781801	+	0.623528i	$0.785699\pi$
$314$	9.29983	−	0.610791i	0.524820	−	0.0344689i
$315$	−23.9430	+	57.8035i	−1.34903	+	3.25686i
$316$	3.73495	−	4.87017i	0.210107	−	0.273969i
$317$	2.37525	−	0.983862i	0.133408	−	0.0552592i	−0.314981	−	0.949098i	$-0.601998\pi$
$317$	2.37525	−	0.983862i	0.133408	−	0.0552592i	0.448388	+	0.893839i	$0.351998\pi$
$318$	−46.1078	−	15.6446i	−2.58560	−	0.877307i
$319$	22.5334			1.26163
$320$	−11.9519	−	11.9327i	−0.668131	−	0.667061i
$321$	43.9337			2.45214
$322$	1.26208	+	0.428232i	0.0703332	+	0.0238644i
$323$	15.1823	−	6.28873i	0.844767	−	0.349914i
$324$	37.5111	−	48.9124i	2.08395	−	2.71736i
$325$	−0.207857	+	0.501810i	−0.0115298	+	0.0278354i
$326$	−22.0404	+	1.44756i	−1.22070	+	0.0801729i
$327$	44.9457	+	44.9457i	2.48551	+	2.48551i
$328$	10.1200	+	2.00879i	0.558786	+	0.110917i
$329$	−11.7112	+	11.7112i	−0.645657	+	0.645657i
$330$	−28.3438	+	32.3286i	−1.56027	+	1.77963i
$331$	13.5539	+	5.61422i	0.744991	+	0.308585i	0.722696	−	0.691166i	$-0.242903\pi$
$331$	13.5539	+	5.61422i	0.744991	+	0.308585i	0.0222952	+	0.999751i	$0.492903\pi$
$332$	0.0202083	−	0.0754990i	0.00110907	−	0.00414355i
$333$	−1.84986	−	4.46596i	−0.101372	−	0.244733i
$334$	9.17265	+	18.5940i	0.501905	+	1.01742i
$335$		−	12.4421i		−	0.679783i
$336$	6.39591	−	48.7831i	0.348925	−	2.66134i
$337$		−	21.9936i		−	1.19807i	−0.800723	−	0.599035i	$-0.795551\pi$
$337$		−	21.9936i		−	1.19807i	0.800723	−	0.599035i	$-0.204449\pi$
$338$	1.26829	−	0.625660i	0.0689857	−	0.0340314i
$339$	−26.1013	−	63.0141i	−1.41763	−	3.42246i
$340$	4.80540	+	8.31806i	0.260609	+	0.451110i
$341$	−4.33623	−	1.79613i	−0.234820	−	0.0972657i
$342$	−61.3390	−	53.7784i	−3.31683	−	2.90800i
$343$	0.600109	−	0.600109i	0.0324028	−	0.0324028i
$344$	0.269082	+	1.34994i	0.0145079	+	0.0727839i
$345$	1.25652	+	1.25652i	0.0676488	+	0.0676488i
$346$	−1.27748	−	19.4508i	−0.0686777	−	1.04568i
$347$	2.33493	−	5.63701i	0.125345	−	0.302611i	−0.848733	−	0.528822i	$-0.822634\pi$
$347$	2.33493	−	5.63701i	0.125345	−	0.302611i	0.974078	+	0.226211i	$0.0726339\pi$
$348$	−34.0858	+	4.49674i	−1.82719	+	0.241050i
$349$	8.24827	−	3.41654i	0.441520	−	0.182883i	−0.150838	−	0.988558i	$-0.548197\pi$
$349$	8.24827	−	3.41654i	0.441520	−	0.182883i	0.592358	+	0.805675i	$0.298197\pi$
$350$	0.915915	−	2.69938i	0.0489577	−	0.144288i
$351$	−16.5268			−0.882133
$352$	10.8555	−	22.0500i	0.578603	−	1.17527i
$353$	20.8347			1.10892			0.554459	−	0.832211i	$-0.312925\pi$
$353$	20.8347			1.10892			0.554459	+	0.832211i	$0.312925\pi$
$354$	10.0122	−	29.5079i	0.532141	−	1.56833i
$355$	17.3303	−	7.17843i	0.919795	−	0.380992i
$356$	2.80378	+	21.2529i	0.148600	+	1.12640i
$357$	−10.7094	+	25.8547i	−0.566801	+	1.36838i
$358$	−1.10399	−	16.8092i	−0.0583474	−	0.888392i
$359$	−0.865773	−	0.865773i	−0.0456938	−	0.0456938i	0.683891	−	0.729584i	$-0.260287\pi$
$359$	−0.865773	−	0.865773i	−0.0456938	−	0.0456938i	−0.729584	+	0.683891i	$0.760287\pi$
$360$	26.4773	−	39.6605i	1.39548	−	2.09029i
$361$	−23.4544	+	23.4544i	−1.23444	+	1.23444i
$362$	12.7860	+	11.2100i	0.672017	+	0.589184i
$363$	−24.1193	−	9.99053i	−1.26593	−	0.524367i
$364$	−6.42660	+	3.71269i	−0.336845	+	0.194598i
$365$	9.22993	+	22.2830i	0.483117	+	1.16635i
$366$	−10.0393	+	4.95248i	−0.524760	+	0.258870i
$367$		−	1.66492i		−	0.0869083i	−0.999055	−	0.0434542i	$-0.986164\pi$
$367$		−	1.66492i		−	0.0869083i	0.999055	−	0.0434542i	$-0.0138362\pi$
$368$	−0.879980	−	0.507430i	−0.0458721	−	0.0264516i
$369$			29.1317i			1.51654i
$370$	−0.799492	−	1.62066i	−0.0415636	−	0.0842543i
$371$	−14.7512	−	35.6125i	−0.765842	−	1.84891i
$372$	6.91776	+	1.85163i	0.358669	+	0.0960024i
$373$	32.6312	+	13.5163i	1.68958	+	0.699846i	0.999710	−	0.0240896i	$-0.00766869\pi$
$373$	32.6312	+	13.5163i	1.68958	+	0.699846i	0.689868	+	0.723935i	$0.257669\pi$
$374$	−9.21587	+	10.5115i	−0.476541	+	0.543537i
$375$	27.4270	−	27.4270i	1.41632	−	1.41632i
$376$	10.4931	−	7.01732i	0.541138	−	0.361891i
$377$	3.66735	+	3.66735i	0.188878	+	0.188878i
$378$	86.5477	−	5.68424i	4.45153	−	0.292366i
$379$	9.12395	−	22.0272i	0.468666	−	1.13146i	−0.496080	−	0.868277i	$-0.665228\pi$
$379$	9.12395	−	22.0272i	0.468666	−	1.13146i	0.964746	−	0.263183i	$-0.0847722\pi$
$380$	−24.1996	−	18.5587i	−1.24141	−	0.952042i
$381$	−40.8792	+	16.9327i	−2.09430	+	0.867489i
$382$	10.2332	+	3.47219i	0.523577	+	0.177653i
$383$	6.28890			0.321348			0.160674	−	0.987008i	$-0.448633\pi$
$383$	6.28890			0.321348			0.160674	+	0.987008i	$0.448633\pi$
$384$	−12.0207	+	35.5208i	−0.613428	+	1.81266i
$385$	−34.0377			−1.73472
$386$	−23.5992	−	8.00733i	−1.20117	−	0.407562i
$387$	−3.59073	+	1.48733i	−0.182527	+	0.0756052i
$388$	18.3285	+	14.0562i	0.930489	+	0.713595i
$389$	2.89728	−	6.99466i	0.146898	−	0.354644i	−0.833254	−	0.552890i	$-0.813525\pi$
$389$	2.89728	−	6.99466i	0.146898	−	0.354644i	0.980152	+	0.198247i	$0.0635248\pi$
$390$	−9.87454	+	0.648536i	−0.500017	+	0.0328399i
$391$	0.408553	+	0.408553i	0.0206614	+	0.0206614i
$392$	15.9202	−	10.6467i	0.804090	−	0.537741i
$393$	17.0046	−	17.0046i	0.857770	−	0.857770i
$394$	−11.6581	+	13.2971i	−0.587326	+	0.669897i
$395$	5.98533	+	2.47920i	0.301154	+	0.124742i
$396$	67.0349	+	17.9428i	3.36863	+	0.901658i
$397$	−4.87671	−	11.7734i	−0.244755	−	0.590891i	0.752988	−	0.658034i	$-0.228612\pi$
$397$	−4.87671	−	11.7734i	−0.244755	−	0.590891i	−0.997743	+	0.0671427i	$0.978612\pi$
$398$	3.02616	+	6.13438i	0.151688	+	0.307489i
$399$		−	88.8421i		−	4.44767i
$400$	−1.08531	+	1.88213i	−0.0542653	+	0.0941063i
$401$			6.30559i			0.314886i	0.987528	+	0.157443i	$0.0503251\pi$
$401$			6.30559i			0.314886i	−0.987528	+	0.157443i	$0.949675\pi$
$402$	−24.7753	+	12.2219i	−1.23568	+	0.609575i
$403$	−0.413407	−	0.998052i	−0.0205933	−	0.0497165i
$404$	9.34432	−	5.39827i	0.464897	−	0.268574i
$405$	60.1122	+	24.8993i	2.98700	+	1.23726i
$406$	−20.4666	−	17.9439i	−1.01574	−	0.890540i
$407$	1.85954	−	1.85954i	0.0921741	−	0.0921741i
$408$	11.8430	−	17.7396i	0.586315	−	0.878243i
$409$	−5.78963	−	5.78963i	−0.286279	−	0.286279i	0.549328	−	0.835607i	$-0.314884\pi$
$409$	−5.78963	−	5.78963i	−0.286279	−	0.286279i	−0.835607	+	0.549328i	$0.814884\pi$
$410$	0.713740	+	10.8673i	0.0352491	+	0.536700i
$411$	5.86362	−	14.1560i	0.289231	−	0.698265i
$412$	1.99435	+	15.1174i	0.0982547	+	0.744782i
$413$	22.7911	−	9.44039i	1.12148	−	0.464531i
$414$	0.921571	−	2.71605i	0.0452927	−	0.133487i
$415$	0.0824993			0.00404973
$416$	5.35543	−	1.82191i	0.262572	−	0.0893266i
$417$	43.3098			2.12089
$418$	14.2597	−	42.0262i	0.697466	−	2.05557i
$419$	15.9970	−	6.62617i	0.781504	−	0.323710i	0.0439817	−	0.999032i	$-0.485996\pi$
$419$	15.9970	−	6.62617i	0.781504	−	0.323710i	0.737522	+	0.675323i	$0.235996\pi$
$420$	51.4881	−	6.79253i	2.51236	−	0.331442i
$421$	2.84659	−	6.87227i	0.138734	−	0.334934i	−0.839208	−	0.543811i	$-0.816981\pi$
$421$	2.84659	−	6.87227i	0.138734	−	0.334934i	0.977942	+	0.208877i	$0.0669809\pi$
$422$	−0.00144101	−	0.0219407i	−7.01475e−5	−	0.00106806i
$423$	25.2028	+	25.2028i	1.22540	+	1.22540i
$424$	5.74320	+	28.8127i	0.278914	+	1.39927i
$425$	0.873824	−	0.873824i	0.0423867	−	0.0423867i
$426$	−31.3177	−	27.4575i	−1.51735	−	1.33032i
$427$	−8.18775	−	3.39148i	−0.396233	−	0.164125i
$428$	−13.2610	−	22.9546i	−0.640995	−	1.10955i
$429$	−5.51089	−	13.3045i	−0.266068	−	0.642345i
$430$	−1.30305	+	0.642810i	−0.0628387	+	0.0309990i
$431$			21.0415i			1.01353i	0.862083	+	0.506767i	$0.169159\pi$
$431$			21.0415i			1.01353i	−0.862083	+	0.506767i	$0.830841\pi$
$432$	−65.5460	−	8.59369i	−3.15359	−	0.413464i
$433$		−	20.1730i		−	0.969450i	−0.874667	−	0.484725i	$-0.838920\pi$
$433$		−	20.1730i		−	0.969450i	0.874667	−	0.484725i	$-0.161080\pi$
$434$	2.50821	+	5.08444i	0.120398	+	0.244061i
$435$	−13.8881	−	33.5289i	−0.665884	−	1.60759i
$436$	9.91686	−	37.0498i	0.474931	−	1.77436i
$437$	−1.69462	−	0.701934i	−0.0810646	−	0.0335781i
$438$	35.3045	−	40.2679i	1.68691	−	1.92407i
$439$	−4.70420	+	4.70420i	−0.224519	+	0.224519i	−0.810398	−	0.585879i	$-0.800749\pi$
$439$	−4.70420	+	4.70420i	−0.224519	+	0.224519i	0.585879	+	0.810398i	$0.300749\pi$
$440$	25.4464	+	5.05101i	1.21311	+	0.240797i
$441$	38.2379	+	38.2379i	1.82085	+	1.82085i
$442$	−3.21067	+	0.210869i	−0.152716	+	0.0100300i
$443$	−5.73517	+	13.8459i	−0.272486	+	0.657840i	−0.999588	−	0.0286891i	$-0.990867\pi$
$443$	−5.73517	+	13.8459i	−0.272486	+	0.657840i	0.727102	+	0.686529i	$0.240867\pi$
$444$	−2.44180	+	3.18398i	−0.115883	+	0.151105i
$445$	−20.9057	+	8.65943i	−0.991025	+	0.410496i
$446$	31.6676	+	10.7450i	1.49950	+	0.508790i
$447$	−60.7958			−2.87554
$448$	−27.4188	+	11.3830i	−1.29542	+	0.537796i
$449$	29.8475			1.40859			0.704295	−	0.709908i	$-0.251263\pi$
$449$	29.8475			1.40859			0.704295	+	0.709908i	$0.251263\pi$
$450$	−5.80917	−	1.97108i	−0.273847	−	0.0929177i
$451$	−14.6421	+	6.06496i	−0.689470	+	0.285588i
$452$	−25.0453	+	32.6577i	−1.17803	+	1.53609i
$453$	9.03295	−	21.8075i	0.424405	−	1.02460i
$454$	−17.7052	+	1.16283i	−0.830946	+	0.0545745i
$455$	−5.53970	−	5.53970i	−0.259705	−	0.259705i
$456$	−13.1837	+	66.4178i	−0.617382	+	3.11030i
$457$	−5.27059	+	5.27059i	−0.246548	+	0.246548i	−0.819552	−	0.573005i	$-0.805778\pi$
$457$	−5.27059	+	5.27059i	−0.246548	+	0.246548i	0.573005	+	0.819552i	$0.305778\pi$
$458$	15.9303	−	18.1699i	0.744375	−	0.849026i
$459$	34.7390	+	14.3894i	1.62148	+	0.671638i
$460$	0.277240	−	1.03578i	0.0129264	−	0.0482934i
$461$	13.5659	+	32.7510i	0.631828	+	1.52537i	0.837322	+	0.546710i	$0.184120\pi$
$461$	13.5659	+	32.7510i	0.631828	+	1.52537i	−0.205494	+	0.978658i	$0.565880\pi$
$462$	33.4355	+	67.7777i	1.55556	+	3.15330i
$463$		−	35.1174i		−	1.63204i	−0.578022	−	0.816021i	$-0.696175\pi$
$463$		−	35.1174i		−	1.63204i	0.578022	−	0.816021i	$-0.303825\pi$
$464$	12.6379	+	16.4519i	0.586702	+	0.763759i
$465$			7.55917i			0.350548i
$466$	−20.1526	+	9.94149i	−0.933549	+	0.460531i
$467$	1.64524	+	3.97197i	0.0761329	+	0.183801i	0.957364	−	0.288885i	$-0.0932845\pi$
$467$	1.64524	+	3.97197i	0.0761329	+	0.183801i	−0.881231	+	0.472686i	$0.843285\pi$
$468$	7.98984	+	13.8303i	0.369330	+	0.639305i
$469$	−20.2061	−	8.36963i	−0.933030	−	0.386474i
$470$	10.0192	+	8.78422i	0.462150	+	0.405186i
$471$	15.4455	−	15.4455i	0.711692	−	0.711692i
$472$	−18.4394	+	3.67551i	−0.848742	+	0.169179i
$473$	−1.49511	−	1.49511i	−0.0687454	−	0.0687454i
$474$	−0.942711	−	14.3536i	−0.0433002	−	0.659284i
$475$	−1.50132	+	3.62450i	−0.0688851	+	0.166303i
$476$	16.7412	−	2.20856i	0.767330	−	0.101229i
$477$	−76.6393	+	31.7450i	−3.50907	+	1.45351i
$478$	2.89810	−	8.54127i	0.132556	−	0.390668i
$479$	−9.66724			−0.441708			−0.220854	−	0.975307i	$-0.570884\pi$
$479$	−9.66724			−0.441708			−0.220854	+	0.975307i	$0.570884\pi$
$480$	−39.5002	−	2.56250i	−1.80293	−	0.116961i
$481$	0.605288			0.0275987
$482$	−1.92234	+	5.66552i	−0.0875603	+	0.258057i
$483$	2.88585	−	1.19536i	0.131311	−	0.0543907i
$484$	2.06032	+	15.6174i	0.0936508	+	0.709883i
$485$	−9.33029	+	22.5253i	−0.423666	+	1.02282i
$486$	−4.87268	−	74.1909i	−0.221029	−	3.36537i
$487$	2.12314	+	2.12314i	0.0962087	+	0.0962087i	0.753573	−	0.657364i	$-0.228329\pi$
$487$	2.12314	+	2.12314i	0.0962087	+	0.0962087i	−0.657364	+	0.753573i	$0.728329\pi$
$488$	5.61784	+	3.75047i	0.254308	+	0.169776i
$489$	−36.6055	+	36.6055i	−1.65536	+	1.65536i
$490$	15.2012	+	13.3275i	0.686719	+	0.602074i
$491$	19.4129	+	8.04107i	0.876090	+	0.362888i	0.774979	−	0.631987i	$-0.217760\pi$
$491$	19.4129	+	8.04107i	0.876090	+	0.362888i	0.101111	+	0.994875i	$0.467760\pi$
$492$	20.9385	−	12.0963i	0.943980	−	0.545343i
$493$	−4.51566	−	10.9018i	−0.203375	−	0.490991i
$494$	9.16064	−	4.51905i	0.412156	−	0.203322i
$495$			73.2504i			3.29236i
$496$	−1.12062	−	4.17330i	−0.0503174	−	0.187387i
$497$		−	32.9734i		−	1.47906i
$498$	−0.0810397	−	0.164277i	−0.00363147	−	0.00736142i
$499$	−1.96023	−	4.73242i	−0.0877520	−	0.211852i	0.873911	−	0.486086i	$-0.161576\pi$
$499$	−1.96023	−	4.73242i	−0.0877520	−	0.211852i	−0.961663	+	0.274234i	$0.911576\pi$
$500$	−22.6087	−	6.05151i	−1.01109	−	0.270632i
$501$	44.8946	+	18.5960i	2.00574	+	0.830806i
$502$	−24.9028	+	28.4038i	−1.11147	+	1.26773i
$503$	−26.9104	+	26.9104i	−1.19988	+	1.19988i	−0.225674	+	0.974203i	$0.572459\pi$
$503$	−26.9104	+	26.9104i	−1.19988	+	1.19988i	−0.974203	+	0.225674i	$0.927541\pi$
$504$	−46.5982	−	69.6787i	−2.07565	−	3.10373i
$505$	8.05476	+	8.05476i	0.358432	+	0.358432i
$506$	1.55700	−	0.102260i	0.0692170	−	0.00454600i
$507$	1.26842	−	3.06223i	0.0563324	−	0.135998i
$508$	21.1860	+	16.2476i	0.939978	+	0.720872i
$509$	1.11439	−	0.461596i	0.0493945	−	0.0204599i	−0.357849	−	0.933779i	$-0.616490\pi$
$509$	1.11439	−	0.461596i	0.0493945	−	0.0204599i	0.407244	+	0.913319i	$0.366490\pi$
$510$	21.3208	+	7.23427i	0.944101	+	0.320339i
$511$	42.3968			1.87552
$512$	22.1873	−	4.44106i	0.980550	−	0.196269i
$513$	−119.370			−5.27032
$514$	9.20838	+	3.12445i	0.406164	+	0.137814i
$515$	−14.8704	+	6.15953i	−0.655269	+	0.271421i
$516$	2.55999	+	1.96326i	0.112697	+	0.0864279i
$517$	−7.42038	+	17.9144i	−0.326348	+	0.787874i
$518$	−3.16978	+	0.208184i	−0.139272	+	0.00914707i
$519$	−32.3046	−	32.3046i	−1.41801	−	1.41801i
$520$	3.31939	+	4.96351i	0.145565	+	0.217664i
$521$	13.4577	−	13.4577i	0.589594	−	0.589594i	−0.347928	−	0.937521i	$-0.613114\pi$
$521$	13.4577	−	13.4577i	0.589594	−	0.589594i	0.937521	+	0.347928i	$0.113114\pi$
$522$	−38.6159	+	44.0449i	−1.69017	+	1.92779i
$523$	−7.38695	−	3.05977i	−0.323009	−	0.133795i	0.215286	−	0.976551i	$-0.430931\pi$
$523$	−7.38695	−	3.05977i	−0.323009	−	0.133795i	−0.538295	+	0.842756i	$0.680931\pi$
$524$	−14.0173	−	3.75191i	−0.612349	−	0.163903i
$525$	−2.55667	−	6.17234i	−0.111582	−	0.269383i
$526$	2.57560	+	5.22104i	0.112301	+	0.227648i
$527$			2.45783i			0.107065i
$528$	−14.9384	−	55.6318i	−0.650109	−	2.42107i
$529$			22.9355i			0.997196i
$530$	−27.8119	+	13.7199i	−1.20807	+	0.595955i
$531$	−20.3161	−	49.0473i	−0.881642	−	2.12847i
$532$	−46.4183	+	26.8162i	−2.01249	+	1.16263i
$533$	−3.37011	−	1.39595i	−0.145976	−	0.0604652i
$534$	37.7789	+	33.1223i	1.63485	+	1.43334i
$535$	19.7867	−	19.7867i	0.855456	−	0.855456i
$536$	13.8639	+	9.25556i	0.598831	+	0.399779i
$537$	−27.9173	−	27.9173i	−1.20472	−	1.20472i
$538$	1.31239	+	19.9823i	0.0565812	+	0.861499i
$539$	−11.2583	+	27.1798i	−0.484928	+	1.17072i
$540$	−9.12660	−	69.1806i	−0.392746	−	2.97706i
$541$	−7.80793	+	3.23415i	−0.335689	+	0.139047i	−0.544160	−	0.838982i	$-0.683151\pi$
$541$	−7.80793	+	3.23415i	−0.335689	+	0.139047i	0.208471	+	0.978029i	$0.433151\pi$
$542$	0.429591	−	1.26609i	0.0184525	−	0.0543832i
$543$	39.8534			1.71027
$544$	−12.8433	−	0.833185i	−0.550653	−	0.0357225i
$545$	40.4850			1.73419
$546$	−5.58925	+	16.4726i	−0.239198	+	0.704963i
$547$	−1.91523	+	0.793314i	−0.0818893	+	0.0339197i	−0.423252	−	0.906012i	$-0.639112\pi$
$547$	−1.91523	+	0.793314i	−0.0818893	+	0.0339197i	0.341363	+	0.939932i	$0.389112\pi$
$548$	−9.16614	+	1.20924i	−0.391558	+	0.0516560i
$549$	−7.29858	+	17.6203i	−0.311496	+	0.752018i
$550$	−0.218716	−	3.33015i	−0.00932609	−	0.141998i
$551$	26.4887	+	26.4887i	1.12846	+	1.12846i
$552$	−2.33483	+	0.465399i	−0.0993769	+	0.0198087i
$553$	8.05251	−	8.05251i	0.342428	−	0.342428i
$554$	21.0191	+	18.4283i	0.893018	+	0.782944i
$555$	−3.91303	−	1.62083i	−0.166099	−	0.0688005i
$556$	−13.0727	−	22.6286i	−0.554405	−	0.959665i
$557$	15.7520	+	38.0288i	0.667435	+	1.61133i	0.785886	+	0.618371i	$0.212207\pi$
$557$	15.7520	+	38.0288i	0.667435	+	1.61133i	−0.118451	+	0.992960i	$0.537793\pi$
$558$	10.9419	−	5.39776i	0.463207	−	0.228505i
$559$		−	0.486665i		−	0.0205837i
$560$	−19.0902	−	24.8513i	−0.806708	−	1.05016i
$561$			32.7640i			1.38330i
$562$	17.3439	+	35.1582i	0.731610	+	1.48306i
$563$	8.91298	+	21.5178i	0.375637	+	0.906868i	0.992773	+	0.120011i	$0.0382931\pi$
$563$	8.91298	+	21.5178i	0.375637	+	0.906868i	−0.617135	+	0.786857i	$0.711707\pi$
$564$	7.64967	−	28.5795i	0.322109	−	1.20341i
$565$	−40.1355	−	16.6247i	−1.68851	−	0.699405i
$566$	−7.75666	+	8.84716i	−0.326037	+	0.371874i
$567$	80.8735	−	80.8735i	3.39637	−	3.39637i
$568$	−4.89307	+	24.6507i	−0.205309	+	1.03432i
$569$	22.8896	+	22.8896i	0.959580	+	0.959580i	0.999214	−	0.0396342i	$-0.0126193\pi$
$569$	22.8896	+	22.8896i	0.959580	+	0.959580i	−0.0396342	+	0.999214i	$0.512619\pi$
$570$	−71.3223	+	4.68427i	−2.98736	+	0.196203i
$571$	−13.2380	+	31.9594i	−0.553993	+	1.33746i	0.360463	+	0.932774i	$0.382619\pi$
$571$	−13.2380	+	31.9594i	−0.553993	+	1.33746i	−0.914456	+	0.404685i	$0.867381\pi$
$572$	−5.28792	+	6.89517i	−0.221099	+	0.288302i
$573$	23.3990	−	9.69219i	0.977508	−	0.404897i
$574$	18.1288	+	6.15120i	0.756682	+	0.256746i
$575$	−0.137934			−0.00575226
$576$	24.4966	+	59.0063i	1.02069	+	2.45859i
$577$	−15.2240			−0.633784			−0.316892	−	0.948462i	$-0.602639\pi$
$577$	−15.2240			−0.633784			−0.316892	+	0.948462i	$0.602639\pi$
$578$	−15.8344	−	5.37270i	−0.658624	−	0.223475i
$579$	−53.9613	+	22.3515i	−2.24256	+	0.928897i
$580$	−13.3262	+	17.3767i	−0.553341	+	0.721527i
$581$	0.0554963	−	0.133980i	0.00230237	−	0.00555842i
$582$	54.0187	−	3.54782i	2.23915	−	0.147062i
$583$	−31.9112	−	31.9112i	−1.32163	−	1.32163i
$584$	−31.6956	−	6.29144i	−1.31157	−	0.260342i
$585$	−11.9216	+	11.9216i	−0.492899	+	0.492899i
$586$	3.47892	−	3.96802i	0.143713	−	0.163917i
$587$	−14.3095	−	5.92719i	−0.590617	−	0.244641i	0.0672993	−	0.997733i	$-0.478562\pi$
$587$	−14.3095	−	5.92719i	−0.590617	−	0.244641i	−0.657916	+	0.753091i	$0.728562\pi$
$588$	11.6061	−	43.3611i	0.478630	−	1.78818i
$589$	−2.98597	−	7.20878i	−0.123035	−	0.297033i
$590$	−8.78041	−	17.7989i	−0.361484	−	0.732770i
$591$			41.4465i			1.70488i
$592$	2.40061	+	0.314741i	0.0986643	+	0.0129358i
$593$			10.5599i			0.433643i	0.976211	+	0.216822i	$0.0695690\pi$
$593$			10.5599i			0.433643i	−0.976211	+	0.216822i	$0.930431\pi$
$594$	91.0676	−	44.9247i	3.73655	−	1.84328i
$595$	6.82112	+	16.4676i	0.279639	+	0.675107i
$596$	18.3507	+	31.7647i	0.751672	+	1.30113i
$597$	14.8112	+	6.13502i	0.606184	+	0.251090i
$598$	0.270047	+	0.236761i	0.0110430	+	0.00968188i
$599$	1.96704	−	1.96704i	0.0803713	−	0.0803713i	−0.665778	−	0.746150i	$-0.731900\pi$
$599$	1.96704	−	1.96704i	0.0803713	−	0.0803713i	0.746150	+	0.665778i	$0.231900\pi$
$600$	0.995408	+	4.99380i	0.0406374	+	0.203871i
$601$	7.27349	+	7.27349i	0.296692	+	0.296692i	0.839717	−	0.543025i	$-0.182721\pi$
$601$	7.27349	+	7.27349i	0.296692	+	0.296692i	−0.543025	+	0.839717i	$0.682721\pi$
$602$	0.167384	+	2.54858i	0.00682208	+	0.103872i
$603$	−18.0117	+	43.4842i	−0.733495	+	1.77081i
$604$	−14.1205	+	1.86284i	−0.574556	+	0.0757978i
$605$	−15.3623	+	6.36326i	−0.624565	+	0.258703i
$606$	8.12681	−	23.9513i	0.330129	−	0.972956i
$607$	42.7662			1.73583			0.867914	−	0.496715i	$-0.165460\pi$
$607$	42.7662			1.73583			0.867914	+	0.496715i	$0.165460\pi$
$608$	38.6815	−	13.1594i	1.56874	−	0.533684i
$609$	−63.7936			−2.58505
$610$	−2.29097	+	6.75193i	−0.0927585	+	0.273378i
$611$	−4.12328	+	1.70792i	−0.166810	+	0.0690949i
$612$	−4.75291	−	36.0276i	−0.192125	−	1.45633i
$613$	16.6972	−	40.3106i	0.674393	−	1.62813i	−0.0996712	−	0.995020i	$-0.531779\pi$
$613$	16.6972	−	40.3106i	0.674393	−	1.62813i	0.774064	−	0.633108i	$-0.218221\pi$
$614$	−0.883729	−	13.4556i	−0.0356644	−	0.543023i
$615$	18.0489	+	18.0489i	0.727802	+	0.727802i
$616$	25.3204	−	37.9275i	1.02019	−	1.52814i
$617$	16.6033	−	16.6033i	0.668423	−	0.668423i	−0.288928	−	0.957351i	$-0.593299\pi$
$617$	16.6033	−	16.6033i	0.668423	−	0.668423i	0.957351	+	0.288928i	$0.0932987\pi$
$618$	26.8725	+	23.5602i	1.08097	+	0.947731i
$619$	−23.7648	−	9.84372i	−0.955189	−	0.395652i	−0.150010	−	0.988684i	$-0.547931\pi$
$619$	−23.7648	−	9.84372i	−0.955189	−	0.395652i	−0.805179	+	0.593032i	$0.797931\pi$
$620$	3.94953	−	2.28167i	0.158617	−	0.0916340i
$621$	−1.60611	−	3.87749i	−0.0644510	−	0.155598i
$622$	42.9741	−	21.1996i	1.72311	−	0.850028i
$623$			39.7762i			1.59360i
$624$	6.62294	−	11.4854i	0.265130	−	0.459785i
$625$		−	21.9892i		−	0.879568i
$626$	2.47762	+	5.02242i	0.0990255	+	0.200736i
$627$	−39.8043	−	96.0961i	−1.58963	−	3.83771i
$628$	−12.7321	−	3.40791i	−0.508066	−	0.135990i
$629$	−1.27231	−	0.527007i	−0.0507302	−	0.0210131i
$630$	58.3312	−	66.5318i	2.32397	−	2.65069i
$631$	−26.0931	+	26.0931i	−1.03875	+	1.03875i	−0.0395308	+	0.999218i	$0.512586\pi$
$631$	−26.0931	+	26.0931i	−1.03875	+	1.03875i	−0.999218	+	0.0395308i	$0.987414\pi$
$632$	−7.21496	+	4.82506i	−0.286996	+	0.191931i
$633$	−0.0364400	−	0.0364400i	−0.00144836	−	0.00144836i
$634$	−3.62806	+	0.238282i	−0.144089	+	0.00946340i
$635$	−10.7849	+	26.0371i	−0.427987	+	1.03325i
$636$	54.6396	+	41.9033i	2.16660	+	1.66157i
$637$	−6.25587	+	2.59127i	−0.247867	+	0.102670i
$638$	−30.1772	−	10.2393i	−1.19473	−	0.405377i
$639$	−70.9599			−2.80713
$640$	10.5839	+	21.4116i	0.418366	+	0.846368i
$641$	22.0961			0.872742			0.436371	−	0.899767i	$-0.356264\pi$
$641$	22.0961			0.872742			0.436371	+	0.899767i	$0.356264\pi$
$642$	−58.8370	−	19.9637i	−2.32211	−	0.787905i
$643$	38.3884	−	15.9010i	1.51389	−	0.627073i	0.537533	−	0.843243i	$-0.319356\pi$
$643$	38.3884	−	15.9010i	1.51389	−	0.627073i	0.976356	+	0.216169i	$0.0693564\pi$
$644$	−1.49562	−	1.14700i	−0.0589357	−	0.0451980i
$645$	−1.30319	+	3.14617i	−0.0513129	+	0.123880i
$646$	−23.1901	+	1.52307i	−0.912404	+	0.0599245i
$647$	9.42745	+	9.42745i	0.370631	+	0.370631i	0.867707	−	0.497076i	$-0.165593\pi$
$647$	9.42745	+	9.42745i	0.370631	+	0.370631i	−0.497076	+	0.867707i	$0.665593\pi$
$648$	−72.4617	+	48.4594i	−2.84657	+	1.90366i
$649$	20.4224	−	20.4224i	0.801650	−	0.801650i
$650$	0.506391	−	0.577584i	0.0198623	−	0.0226547i
$651$	12.2762	+	5.08496i	0.481142	+	0.199295i
$652$	30.1748	+	8.07667i	1.18174	+	0.316307i
$653$	2.14317	+	5.17408i	0.0838688	+	0.202477i	0.960250	−	0.279140i	$-0.0900494\pi$
$653$	2.14317	+	5.17408i	0.0838688	+	0.202477i	−0.876381	+	0.481618i	$0.840049\pi$
$654$	−39.7688	−	80.6159i	−1.55508	−	3.15233i
$655$		−	15.3170i		−	0.598484i
$656$	−12.6402	−	7.28882i	−0.493516	−	0.284581i
$657$		−	91.2394i		−	3.55959i
$658$	21.0054	−	10.3622i	0.818878	−	0.403962i
$659$	−0.407950	−	0.984879i	−0.0158915	−	0.0383654i	0.915735	−	0.401784i	$-0.131610\pi$
$659$	−0.407950	−	0.984879i	−0.0158915	−	0.0383654i	−0.931626	+	0.363418i	$0.881610\pi$
$660$	52.6489	−	30.4156i	2.04936	−	1.18393i
$661$	11.1147	+	4.60384i	0.432310	+	0.179069i	0.588217	−	0.808703i	$-0.299830\pi$
$661$	11.1147	+	4.60384i	0.432310	+	0.179069i	−0.155907	+	0.987772i	$0.549830\pi$
$662$	−15.6006	−	13.6777i	−0.606334	−	0.531598i
$663$	−5.33240	+	5.33240i	−0.207093	+	0.207093i
$664$	−0.0613706	+	0.0919272i	−0.00238164	+	0.00356747i
$665$	−40.0124	−	40.0124i	−1.55161	−	1.55161i
$666$	0.448019	+	6.82149i	0.0173604	+	0.264327i
$667$	−0.504028	+	1.21683i	−0.0195161	+	0.0471159i
$668$	−3.83499	−	29.0696i	−0.148380	−	1.12474i
$669$	72.4103	−	29.9933i	2.79955	−	1.15961i
$670$	−5.65374	+	16.6627i	−0.218423	+	0.643736i
$671$	−10.3758			−0.400553
$672$	−30.7328	+	62.4250i	−1.18554	+	2.40810i
$673$	−31.4632			−1.21282			−0.606409	−	0.795153i	$-0.707390\pi$
$673$	−31.4632			−1.21282			−0.606409	+	0.795153i	$0.707390\pi$
$674$	−9.99403	+	29.4544i	−0.384956	+	1.13454i
$675$	−8.29329	+	3.43519i	−0.319209	+	0.132221i
$676$	−1.98282	+	0.261582i	−0.0762623	+	0.0100608i
$677$	−17.1080	+	41.3024i	−0.657514	+	1.58738i	0.144117	+	0.989561i	$0.453966\pi$
$677$	−17.1080	+	41.3024i	−0.657514	+	1.58738i	−0.801631	+	0.597819i	$0.796034\pi$
$678$	6.32149	+	96.2504i	0.242776	+	3.69648i
$679$	30.3050	+	30.3050i	1.16300	+	1.16300i
$680$	−2.65572	−	13.3233i	−0.101842	−	0.510926i
$681$	−29.4054	+	29.4054i	−1.12682	+	1.12682i
$682$	4.99101	+	4.37582i	0.191116	+	0.167559i
$683$	−39.1427	−	16.2134i	−1.49775	−	0.620389i	−0.524765	−	0.851247i	$-0.675847\pi$
$683$	−39.1427	−	16.2134i	−1.49775	−	0.620389i	−0.972987	+	0.230858i	$0.925847\pi$
$684$	57.7094	+	99.8939i	2.20657	+	3.81954i
$685$	−3.73471	−	9.01638i	−0.142696	−	0.344498i
$686$	−1.07637	+	0.530986i	−0.0410961	+	0.0202732i
$687$		−	56.6350i		−	2.16076i
$688$	0.253059	−	1.93014i	0.00964779	−	0.0735860i
$689$		−	10.3872i		−	0.395721i
$690$	−1.11179	−	2.25373i	−0.0423251	−	0.0857980i
$691$	−0.378773	−	0.914440i	−0.0144092	−	0.0347869i	0.916511	−	0.400009i	$-0.130993\pi$
$691$	−0.378773	−	0.914440i	−0.0144092	−	0.0347869i	−0.930920	+	0.365222i	$0.880993\pi$
$692$	−7.12771	+	26.6294i	−0.270955	+	1.01230i
$693$	118.960	+	49.2747i	4.51890	+	1.87179i
$694$	−5.68848	+	6.48821i	−0.215932	+	0.246289i
$695$	19.5057	−	19.5057i	0.739895	−	0.739895i
$696$	47.6917	+	9.46662i	1.80775	+	0.358831i
$697$	5.86852	+	5.86852i	0.222286	+	0.222286i
$698$	−12.5988	+	0.827456i	−0.476870	+	0.0313197i
$699$	−20.1547	+	48.6576i	−0.762319	+	1.84040i
$700$	−2.45323	+	3.19887i	−0.0927232	+	0.120906i
$701$	−14.9281	+	6.18343i	−0.563827	+	0.233545i	−0.646346	−	0.763045i	$-0.723704\pi$
$701$	−14.9281	+	6.18343i	−0.563827	+	0.233545i	0.0825187	+	0.996590i	$0.473704\pi$
$702$	22.1330	+	7.50984i	0.835356	+	0.283441i
$703$	4.37190			0.164889
$704$	−24.5576	+	24.5970i	−0.925550	+	0.927034i
$705$	31.2294			1.17617
$706$	−27.9023	−	9.46739i	−1.05012	−	0.356310i
$707$	18.4994	−	7.66269i	0.695740	−	0.288185i
$708$	−26.8171	+	34.9680i	−1.00785	+	1.31418i
$709$	6.77403	−	16.3539i	0.254404	−	0.614185i	−0.744146	−	0.668017i	$-0.767143\pi$
$709$	6.77403	−	16.3539i	0.254404	−	0.614185i	0.998550	+	0.0538316i	$0.0171434\pi$
$710$	−26.4710	+	1.73855i	−0.993439	+	0.0652466i
$711$	−17.3293	−	17.3293i	−0.649899	−	0.649899i
$712$	5.90257	−	29.7365i	0.221208	−	1.11442i
$713$	0.193986	−	0.193986i	0.00726485	−	0.00726485i
$714$	26.0908	−	29.7588i	0.976423	−	1.11370i
$715$	−8.47400	−	3.51005i	−0.316910	−	0.131268i
$716$	−6.15969	+	23.0129i	−0.230199	+	0.860031i
$717$	−8.08969	−	19.5302i	−0.302115	−	0.729370i
$718$	0.766051	+	1.55287i	0.0285888	+	0.0579528i
$719$		−	1.44012i		−	0.0537073i	−0.999639	−	0.0268536i	$-0.991451\pi$
$719$		−	1.44012i		−	0.0537073i	0.999639	−	0.0268536i	$-0.00854881\pi$
$720$	−53.4810	+	41.0828i	−1.99312	+	1.53107i
$721$			28.2932i			1.05369i
$722$	42.0684	−	20.7528i	1.56562	−	0.772341i
$723$	5.36599	+	12.9546i	0.199563	+	0.481788i
$724$	−12.0294	−	20.8227i	−0.447069	−	0.773869i
$725$	2.60259	+	1.07803i	0.0966579	+	0.0400370i
$726$	27.7613	+	24.3395i	1.03032	+	0.903323i
$727$	25.9233	−	25.9233i	0.961442	−	0.961442i	−0.0378417	−	0.999284i	$-0.512048\pi$
$727$	25.9233	−	25.9233i	0.961442	−	0.961442i	0.999284	+	0.0378417i	$0.0120483\pi$
$728$	10.2937	−	2.05183i	0.381510	−	0.0760460i
$729$	−57.8399	−	57.8399i	−2.14222	−	2.14222i
$730$	−2.23540	−	34.0360i	−0.0827360	−	1.25973i
$731$	−0.423725	+	1.02296i	−0.0156721	+	0.0378357i
$732$	15.6952	−	2.07058i	0.580112	−	0.0765309i
$733$	44.5252	−	18.4430i	1.64458	−	0.681206i	0.647829	−	0.761786i	$-0.275677\pi$
$733$	44.5252	−	18.4430i	1.64458	−	0.681206i	0.996748	+	0.0805793i	$0.0256770\pi$
$734$	−0.756550	+	2.22970i	−0.0279248	+	0.0822998i
$735$	47.3815			1.74769
$736$	0.947910	+	1.07943i	0.0349404	+	0.0397883i
$737$	−25.6058			−0.943202
$738$	13.2376	−	39.0139i	0.487283	−	1.43612i
$739$	25.1697	−	10.4256i	0.925882	−	0.383513i	0.131767	−	0.991281i	$-0.457935\pi$
$739$	25.1697	−	10.4256i	0.925882	−	0.383513i	0.794115	+	0.607768i	$0.207935\pi$
$740$	0.334259	+	2.53372i	0.0122876	+	0.0931415i
$741$	9.16159	−	22.1180i	0.336559	−	0.812526i
$742$	3.57260	+	54.3960i	0.131154	+	1.99694i
$743$	−23.7672	−	23.7672i	−0.871934	−	0.871934i	0.120749	−	0.992683i	$-0.461470\pi$
$743$	−23.7672	−	23.7672i	−0.871934	−	0.871934i	−0.992683	+	0.120749i	$0.961470\pi$
$744$	−8.42303	−	5.62321i	−0.308803	−	0.206157i
$745$	−27.3810	+	27.3810i	−1.00316	+	1.00316i
$746$	−37.5585	−	32.9291i	−1.37511	−	1.20562i
$747$	−0.288329	−	0.119430i	−0.0105494	−	0.00436971i
$748$	17.1186	−	9.88951i	0.625917	−	0.361596i
$749$	−18.8236	−	45.4442i	−0.687800	−	1.66050i
$750$	−49.1938	+	24.2679i	−1.79630	+	0.886138i
$751$		−	1.34572i		−	0.0491059i	−0.999699	−	0.0245529i	$-0.992184\pi$
$751$		−	1.34572i		−	0.0491059i	0.999699	−	0.0245529i	$-0.00781623\pi$
$752$	−17.2412	+	4.62965i	−0.628724	+	0.168826i
$753$			88.5337i			3.22635i
$754$	−3.24493	−	6.57785i	−0.118173	−	0.239551i
$755$	−5.75335	−	13.8898i	−0.209386	−	0.505502i
$756$	−118.489	−	31.7153i	−4.30942	−	1.15347i
$757$	−25.0164	−	10.3621i	−0.909235	−	0.376618i	−0.121471	−	0.992595i	$-0.538761\pi$
$757$	−25.0164	−	10.3621i	−0.909235	−	0.376618i	−0.787764	+	0.615977i	$0.788761\pi$
$758$	−22.2283	+	25.3533i	−0.807366	+	0.920873i
$759$	2.58592	−	2.58592i	0.0938630	−	0.0938630i
$760$	23.9754	+	35.8507i	0.869680	+	1.30044i
$761$	−6.18950	−	6.18950i	−0.224369	−	0.224369i	0.585966	−	0.810335i	$-0.300715\pi$
$761$	−6.18950	−	6.18950i	−0.224369	−	0.224369i	−0.810335	+	0.585966i	$0.800715\pi$
$762$	62.4406	−	4.10095i	2.26198	−	0.148562i
$763$	27.2338	−	65.7482i	0.985930	−	2.38024i
$764$	−12.1268	−	9.30006i	−0.438731	−	0.336464i
$765$	35.4390	−	14.6793i	1.28130	−	0.530731i
$766$	−8.42224	−	2.85771i	−0.304308	−	0.103253i
$767$	6.64756			0.240030
$768$	32.2392	−	42.1080i	1.16333	−	1.51944i
$769$	−21.1914			−0.764180			−0.382090	−	0.924125i	$-0.624796\pi$
$769$	−21.1914			−0.764180			−0.382090	+	0.924125i	$0.624796\pi$
$770$	45.5841	+	15.4669i	1.64274	+	0.557389i
$771$	21.0556	−	8.72153i	0.758301	−	0.314098i
$772$	27.9660	+	21.4472i	1.00652	+	0.771901i
$773$	7.90176	−	19.0765i	0.284207	−	0.686136i	−0.715718	−	0.698389i	$-0.753901\pi$
$773$	7.90176	−	19.0765i	0.284207	−	0.686136i	0.999925	+	0.0122536i	$0.00390053\pi$
$774$	5.48463	−	0.360217i	0.197141	−	0.0129477i
$775$	−0.414903	−	0.414903i	−0.0149038	−	0.0149038i
$776$	−18.1587	−	27.1529i	−0.651861	−	0.974733i
$777$	−5.26450	+	5.26450i	−0.188863	+	0.188863i
$778$	−7.05852	+	8.05087i	−0.253060	+	0.288638i
$779$	−24.3418	−	10.0827i	−0.872136	−	0.361250i
$780$	13.5189	+	3.61851i	0.484054	+	0.129563i
$781$	−14.7732	−	35.6657i	−0.528627	−	1.27622i
$782$	−0.361494	−	0.732791i	−0.0129270	−	0.0262046i
$783$			85.7145i			3.06319i
$784$	−26.1586	+	7.02414i	−0.934234	+	0.250862i
$785$		−	13.9126i		−	0.496562i
$786$	−30.5000	+	15.0460i	−1.08790	+	0.536673i
$787$	17.0768	+	41.2271i	0.608723	+	1.46959i	0.864390	+	0.502822i	$0.167705\pi$
$787$	17.0768	+	41.2271i	0.608723	+	1.46959i	−0.255667	+	0.966765i	$0.582295\pi$
$788$	21.6550	−	12.5102i	0.771428	−	0.445659i
$789$	12.6060	+	5.22158i	0.448786	+	0.185893i
$790$	−6.88912	−	6.03997i	−0.245104	−	0.214892i
$791$	−53.9973	+	53.9973i	−1.91992	+	1.91992i
$792$	−81.6214	−	54.4904i	−2.90029	−	1.93623i
$793$	−1.68868	−	1.68868i	−0.0599667	−	0.0599667i
$794$	1.18110	+	17.9832i	0.0419155	+	0.638201i
$795$	−27.8148	+	67.1508i	−0.986488	+	2.38159i
$796$	−1.26521	−	9.59040i	−0.0448440	−	0.339923i
$797$	27.2715	−	11.2962i	0.966006	−	0.400133i	0.156782	−	0.987633i	$-0.449888\pi$
$797$	27.2715	−	11.2962i	0.966006	−	0.400133i	0.809224	+	0.587501i	$0.199888\pi$
$798$	−40.3703	+	118.979i	−1.42909	+	4.21182i
$799$	10.1541			0.359227
$800$	2.30871	−	2.02742i	0.0816253	−	0.0716800i
$801$	85.5998			3.02452
$802$	2.86529	−	8.44459i	0.101177	−	0.298189i
$803$	45.8585	−	18.9952i	1.61831	−	0.670326i
$804$	38.7333	−	5.10987i	1.36602	−	0.180211i
$805$	0.761358	−	1.83808i	0.0268344	−	0.0647839i
$806$	0.100123	+	1.52447i	0.00352669	+	0.0536971i
$807$	33.1874	+	33.1874i	1.16825	+	1.16825i
$808$	−14.9671	+	2.98338i	−0.526542	+	0.104955i
$809$	5.09501	−	5.09501i	0.179131	−	0.179131i	−0.611846	−	0.790977i	$-0.709573\pi$
$809$	5.09501	−	5.09501i	0.179131	−	0.179131i	0.790977	+	0.611846i	$0.209573\pi$
$810$	−69.1892	−	60.6610i	−2.43106	−	2.13141i
$811$	5.21299	+	2.15929i	0.183053	+	0.0758230i	0.472327	−	0.881423i	$-0.343414\pi$
$811$	5.21299	+	2.15929i	0.183053	+	0.0758230i	−0.289274	+	0.957246i	$0.593414\pi$
$812$	19.2555	+	33.3310i	0.675736	+	1.16969i
$813$	−1.19915	−	2.89501i	−0.0420561	−	0.101532i
$814$	−3.33533	+	1.64535i	−0.116903	+	0.0576697i
$815$			32.9726i			1.15498i
$816$	−23.9214	+	18.3758i	−0.837415	+	0.643282i
$817$		−	3.51511i		−	0.122978i
$818$	5.12276	+	10.3844i	0.179113	+	0.363083i
$819$	11.3413	+	27.3804i	0.396298	+	0.956749i
$820$	3.98232	−	14.8781i	0.139069	−	0.519566i
$821$	9.00488	+	3.72994i	0.314272	+	0.130176i	0.534244	−	0.845330i	$-0.320596\pi$
$821$	9.00488	+	3.72994i	0.314272	+	0.130176i	−0.219971	+	0.975506i	$0.570596\pi$
$822$	−14.2853	+	16.2936i	−0.498256	+	0.568305i
$823$	13.6368	−	13.6368i	0.475349	−	0.475349i	−0.428292	−	0.903641i	$-0.640884\pi$
$823$	13.6368	−	13.6368i	0.475349	−	0.475349i	0.903641	+	0.428292i	$0.140884\pi$
$824$	4.19855	−	21.1518i	0.146263	−	0.736859i
$825$	−5.53084	−	5.53084i	−0.192559	−	0.192559i
$826$	−34.8121	+	2.28638i	−1.21127	+	0.0795532i
$827$	6.31306	−	15.2411i	0.219527	−	0.529984i	−0.775297	−	0.631596i	$-0.782400\pi$
$827$	6.31306	−	15.2411i	0.219527	−	0.529984i	0.994824	+	0.101612i	$0.0324000\pi$
$828$	−2.46838	+	3.21863i	−0.0857820	+	0.111855i
$829$	16.0447	−	6.64592i	0.557255	−	0.230822i	−0.0862381	−	0.996275i	$-0.527485\pi$
$829$	16.0447	−	6.64592i	0.557255	−	0.230822i	0.643493	+	0.765452i	$0.277485\pi$
$830$	−0.110485	−	0.0374881i	−0.00383499	−	0.00130123i
$831$	65.5159			2.27272
$832$	−8.00000	+	0.00640954i	−0.277350	+	0.000222211i
$833$	15.4059			0.533783
$834$	−58.0015	−	19.6802i	−2.00843	−	0.681470i
$835$	28.5947	−	11.8443i	0.989560	−	0.409889i
$836$	−38.1939	+	49.8027i	−1.32096	+	1.72246i
$837$	6.83227	−	16.4946i	0.236158	−	0.570135i
$838$	−24.4345	+	1.60480i	−0.844075	+	0.0554368i
$839$	10.5382	+	10.5382i	0.363819	+	0.363819i	0.865217	−	0.501398i	$-0.167181\pi$
$839$	10.5382	+	10.5382i	0.363819	+	0.363819i	−0.501398	+	0.865217i	$0.667181\pi$
$840$	−72.0406	−	14.2998i	−2.48564	−	0.493389i
$841$	−1.48573	+	1.48573i	−0.0512320	+	0.0512320i
$842$	−6.93501	+	7.90999i	−0.238996	+	0.272596i
$843$	84.8882	+	35.1618i	2.92370	+	1.21104i
$844$	−0.00804015	+	0.0300383i	−0.000276753	+	0.00103396i
$845$	−0.807892	−	1.95042i	−0.0277923	−	0.0670966i
$846$	−22.2999	−	45.2045i	−0.766686	−	1.55416i
$847$			29.2290i			1.00432i
$848$	5.40121	−	41.1963i	0.185478	−	1.41469i
$849$			27.5763i			0.946415i
$850$	−1.56731	+	0.773174i	−0.0537584	+	0.0265196i
$851$	0.0588234	+	0.142012i	0.00201644	+	0.00486811i
$852$	29.4645	+	51.0026i	1.00944	+	1.74732i
$853$	−18.1469	−	7.51669i	−0.621338	−	0.257367i	0.0497297	−	0.998763i	$-0.484164\pi$
$853$	−18.1469	−	7.51669i	−0.621338	−	0.257367i	−0.671068	+	0.741396i	$0.734164\pi$
$854$	9.42411	+	8.26250i	0.322487	+	0.282737i
$855$	−86.1082	+	86.1082i	−2.94484	+	2.94484i
$856$	7.32875	+	36.7671i	0.250492	+	1.25668i
$857$	4.41936	+	4.41936i	0.150962	+	0.150962i	0.778548	−	0.627585i	$-0.215957\pi$
$857$	4.41936	+	4.41936i	0.150962	+	0.150962i	−0.627585	+	0.778548i	$0.715957\pi$
$858$	1.33469	+	20.3218i	0.0455655	+	0.693775i
$859$	13.3415	−	32.2093i	0.455207	−	1.09897i	−0.515109	−	0.857125i	$-0.672249\pi$
$859$	13.3415	−	32.2093i	0.455207	−	1.09897i	0.970316	−	0.241842i	$-0.0777515\pi$
$860$	2.03717	−	0.268752i	0.0694669	−	0.00916437i
$861$	41.4529	−	17.1703i	1.41271	−	0.585164i
$862$	9.56136	−	28.1792i	0.325661	−	0.959789i
$863$	37.5914			1.27963			0.639813	−	0.768530i	$-0.279012\pi$
$863$	37.5914			1.27963			0.639813	+	0.768530i	$0.279012\pi$
$864$	83.8757	+	41.2933i	2.85351	+	1.40483i
$865$	−29.0985			−0.989378
$866$	−9.16669	+	27.0161i	−0.311497	+	0.918043i
$867$	−36.2065	+	14.9972i	−1.22964	+	0.509333i
$868$	−1.04866	−	7.94893i	−0.0355937	−	0.269804i
$869$	5.10220	−	12.3178i	0.173080	−	0.417853i
$870$	3.36357	+	51.2134i	0.114036	+	1.73630i
$871$	−4.16739	−	4.16739i	−0.141207	−	0.141207i
$872$	−30.1165	+	45.1116i	−1.01987	+	1.52767i
$873$	65.2174	−	65.2174i	2.20728	−	2.20728i
$874$	1.95051	+	1.71009i	0.0659769	+	0.0578446i
$875$	−40.1212	−	16.6187i	−1.35634	−	0.561816i
$876$	−65.5785	+	37.8851i	−2.21569	+	1.28002i
$877$	−1.88005	−	4.53883i	−0.0634846	−	0.153265i	0.888954	−	0.457997i	$-0.151433\pi$
$877$	−1.88005	−	4.53883i	−0.0634846	−	0.153265i	−0.952438	+	0.304732i	$0.901433\pi$
$878$	8.43759	−	4.16236i	0.284755	−	0.140473i
$879$		−	12.3682i		−	0.417168i
$880$	−31.7832	−	18.3274i	−1.07141	−	0.617817i
$881$		−	33.8388i		−	1.14006i	−0.821624	−	0.570030i	$-0.806932\pi$
$881$		−	33.8388i		−	1.14006i	0.821624	−	0.570030i	$-0.193068\pi$
$882$	−33.8336	−	68.5846i	−1.13924	−	2.30936i
$883$	16.6773	+	40.2626i	0.561236	+	1.35494i	0.908778	+	0.417280i	$0.137016\pi$
$883$	16.6773	+	40.2626i	0.561236	+	1.35494i	−0.347542	+	0.937665i	$0.612984\pi$
$884$	4.39561	+	1.17654i	0.147840	+	0.0395714i
$885$	−42.9748	−	17.8008i	−1.44458	−	0.598366i
$886$	13.9723	−	15.9367i	0.469410	−	0.535404i
$887$	−9.63198	+	9.63198i	−0.323410	+	0.323410i	−0.850074	−	0.526664i	$-0.823443\pi$
$887$	−9.63198	+	9.63198i	−0.323410	+	0.323410i	0.526664	+	0.850074i	$0.323443\pi$
$888$	4.71693	−	3.15449i	0.158290	−	0.105858i
$889$	35.0297	+	35.0297i	1.17486	+	1.17486i
$890$	31.9323	−	2.09723i	1.07037	−	0.0702994i
$891$	51.2428	−	123.711i	1.71670	−	4.14447i
$892$	−37.5274	−	28.7798i	−1.25651	−	0.963621i
$893$	−29.7818	+	12.3360i	−0.996610	+	0.412809i
$894$	81.4190	+	27.6259i	2.72306	+	0.923949i
$895$	−25.1466			−0.840559
$896$	41.8924	−	2.78510i	1.39953	−	0.0930436i
$897$	0.841726			0.0281044
$898$	−39.9724	−	13.5628i	−1.33390	−	0.452598i
$899$	−5.17631	+	2.14410i	−0.172640	+	0.0715097i
$900$	6.88409	+	5.27943i	0.229470	+	0.175981i
$901$	−9.04385	+	21.8338i	−0.301294	+	0.727389i
$902$	22.3650	−	1.46888i	0.744673	−	0.0489083i
$903$	4.23278	+	4.23278i	0.140858	+	0.140858i
$904$	48.3810	−	32.3552i	1.60913	−	1.07612i
$905$	17.9491	−	17.9491i	0.596647	−	0.596647i
$906$	−22.0065	+	25.1004i	−0.731119	+	0.833906i
$907$	16.6641	+	6.90248i	0.553321	+	0.229193i	0.641783	−	0.766886i	$-0.278195\pi$
$907$	16.6641	+	6.90248i	0.553321	+	0.229193i	−0.0884617	+	0.996080i	$0.528195\pi$
$908$	24.2396	+	6.48804i	0.804419	+	0.215313i
$909$	−16.4904	−	39.8113i	−0.546952	−	1.32046i
$910$	4.90162	+	9.93616i	0.162487	+	0.329380i
$911$		−	19.3587i		−	0.641381i	−0.947184	−	0.320690i	$-0.896085\pi$
$911$		−	19.3587i		−	0.641381i	0.947184	−	0.320690i	$-0.103915\pi$
$912$	47.8365	−	82.9575i	1.58402	−	2.74700i
$913$		−	0.169784i		−	0.00561902i
$914$	9.45347	−	4.66350i	0.312693	−	0.154255i
$915$	6.39496	+	15.4388i	0.211411	+	0.510391i
$916$	−29.5908	+	17.0948i	−0.977706	+	0.564827i
$917$	−24.8750	−	10.3035i	−0.821444	−	0.340253i
$918$	−39.9847	−	35.0562i	−1.31969	−	1.15703i
$919$	−9.86175	+	9.86175i	−0.325309	+	0.325309i	−0.850800	−	0.525490i	$-0.823882\pi$
$919$	−9.86175	+	9.86175i	−0.325309	+	0.325309i	0.525490	+	0.850800i	$0.323882\pi$
$920$	−0.841948	+	1.26116i	−0.0277582	+	0.0415792i
$921$	−22.3475	−	22.3475i	−0.736376	−	0.736376i
$922$	−3.28554	−	50.0254i	−0.108204	−	1.64750i
$923$	3.40029	−	8.20902i	0.111922	−	0.270203i
$924$	−13.9790	−	105.963i	−0.459877	−	3.48591i
$925$	0.303740	−	0.125813i	0.00998689	−	0.00413671i
$926$	−15.9575	+	47.0299i	−0.524396	+	1.54550i
$927$	60.8880			1.99982
$928$	−9.44919	−	27.7755i	−0.310185	−	0.911774i
$929$	−4.67531			−0.153392			−0.0766960	−	0.997055i	$-0.524437\pi$
$929$	−4.67531			−0.153392			−0.0766960	+	0.997055i	$0.524437\pi$
$930$	3.43493	−	10.1234i	0.112636	−	0.331960i
$931$	−45.1852	+	18.7163i	−1.48088	+	0.613403i
$932$	31.5062	−	4.15643i	1.03202	−	0.136148i
$933$	42.9786	−	103.759i	1.40706	−	3.39693i
$934$	−0.398463	−	6.06696i	−0.0130381	−	0.198517i
$935$	14.7561	+	14.7561i	0.482577	+	0.482577i
$936$	−4.41562	−	22.1524i	−0.144329	−	0.724075i
$937$	15.2433	−	15.2433i	0.497977	−	0.497977i	−0.412831	−	0.910808i	$-0.635460\pi$
$937$	15.2433	−	15.2433i	0.497977	−	0.497977i	0.910808	+	0.412831i	$0.135460\pi$
$938$	23.2572	+	20.3905i	0.759375	+	0.665775i
$939$	12.1264	+	5.02294i	0.395732	+	0.163917i
$940$	−9.42631	−	16.3168i	−0.307452	−	0.532195i
$941$	−0.331709	−	0.800816i	−0.0108134	−	0.0261058i	0.918381	−	0.395698i	$-0.129497\pi$
$941$	−0.331709	−	0.800816i	−0.0108134	−	0.0261058i	−0.929194	+	0.369592i	$0.879497\pi$
$942$	−27.7035	+	13.6665i	−0.902629	+	0.445277i
$943$		−	0.926355i		−	0.0301663i
$944$	26.3646	+	3.45664i	0.858095	+	0.112504i
$945$		−	129.476i		−	4.21185i
$946$	1.32290	+	2.68168i	0.0430113	+	0.0871889i
$947$	−1.34851	−	3.25559i	−0.0438206	−	0.105792i	0.900454	−	0.434952i	$-0.143235\pi$
$947$	−1.34851	−	3.25559i	−0.0438206	−	0.105792i	−0.944274	+	0.329159i	$0.893235\pi$
$948$	−5.25986	+	19.6511i	−0.170832	+	0.638237i
$949$	10.5551	+	4.37205i	0.342631	+	0.141923i
$950$	3.65759	−	4.17180i	0.118668	−	0.135351i
$951$	−6.02563	+	6.02563i	−0.195394	+	0.195394i
$952$	−23.4237	−	4.64951i	−0.759167	−	0.150692i
$953$	−10.0206	−	10.0206i	−0.324600	−	0.324600i	0.525929	−	0.850529i	$-0.323718\pi$
$953$	−10.0206	−	10.0206i	−0.324600	−	0.324600i	−0.850529	+	0.525929i	$0.823718\pi$
$954$	117.062	−	7.68836i	3.79003	−	0.248920i
$955$	6.17324	−	14.9035i	0.199761	−	0.482267i
$956$	−7.76239	+	10.1217i	−0.251054	+	0.327361i
$957$	−69.0024	+	28.5817i	−2.23053	+	0.923916i
$958$	12.9466	+	4.39284i	0.418285	+	0.141926i
$959$	−17.1550			−0.553964
$960$	51.7351	+	21.3809i	1.66974	+	0.690064i
$961$	−29.8330			−0.962354
$962$	−0.810615	−	0.275046i	−0.0261353	−	0.00886784i
$963$	−97.7976	+	40.5091i	−3.15148	+	1.30539i
$964$	5.14888	−	6.71387i	0.165834	−	0.216239i
$965$	−14.2363	+	34.3695i	−0.458284	+	1.10639i
$966$	−4.40797	+	0.289505i	−0.141824	+	0.00931467i
$967$	36.7991	+	36.7991i	1.18338	+	1.18338i	0.978863	+	0.204516i	$0.0655620\pi$
$967$	36.7991	+	36.7991i	1.18338	+	1.18338i	0.204516	+	0.978863i	$0.434438\pi$
$968$	4.33742	−	21.8514i	0.139410	−	0.702332i
$969$	−38.5151	+	38.5151i	−1.23728	+	1.23728i
$970$	22.7309	−	25.9267i	0.729847	−	0.832455i
$971$	−36.1724	−	14.9831i	−1.16083	−	0.480831i	−0.282678	−	0.959215i	$-0.591223\pi$
$971$	−36.1724	−	14.9831i	−1.16083	−	0.480831i	−0.878151	+	0.478384i	$0.841223\pi$
$972$	−27.1871	+	101.572i	−0.872028	+	3.25793i
$973$	−18.5563	−	44.7988i	−0.594887	−	1.43618i
$974$	−1.87859	−	3.80812i	−0.0601939	−	0.122020i
$975$		−	1.80031i		−	0.0576560i
$976$	−5.81930	−	7.57548i	−0.186271	−	0.242485i
$977$			42.8788i			1.37181i	0.727689	+	0.685907i	$0.240594\pi$
$977$			42.8788i			1.37181i	−0.727689	+	0.685907i	$0.759406\pi$
$978$	65.6567	−	32.3892i	2.09947	−	1.03569i
$979$	17.8211	+	43.0240i	0.569565	+	1.37505i
$980$	−14.3017	−	24.7560i	−0.456850	−	0.790800i
$981$	−141.492	−	58.6081i	−4.51751	−	1.87121i
$982$	−22.3442	−	19.5901i	−0.713033	−	0.625145i
$983$	14.3404	−	14.3404i	0.457389	−	0.457389i	−0.440408	−	0.897798i	$-0.645166\pi$
$983$	14.3404	−	14.3404i	0.457389	−	0.457389i	0.897798	+	0.440408i	$0.145166\pi$
$984$	−33.5379	+	6.68507i	−1.06915	+	0.213112i
$985$	18.6665	+	18.6665i	0.594765	+	0.594765i
$986$	1.09365	+	16.6518i	0.0348290	+	0.530302i
$987$	21.0076	−	50.7169i	0.668680	−	1.61434i
$988$	−14.3216	+	1.88937i	−0.455631	+	0.0601087i
$989$	0.114181	−	0.0472953i	0.00363074	−	0.00150390i
$990$	33.2854	−	98.0986i	1.05788	−	3.11778i
$991$	−9.32899			−0.296345			−0.148173	−	0.988962i	$-0.547339\pi$
$991$	−9.32899			−0.296345			−0.148173	+	0.988962i	$0.547339\pi$
$992$	−0.395608	+	6.09819i	−0.0125606	+	0.193618i
$993$	−48.6264			−1.54311
$994$	−14.9833	+	44.1587i	−0.475241	+	1.40063i
$995$	9.43371	−	3.90757i	0.299069	−	0.123878i
$996$	0.0338818	+	0.256828i	0.00107359	+	0.00813791i
$997$	14.0123	−	33.8287i	0.443774	−	1.07137i	−0.530840	−	0.847472i	$-0.678123\pi$
$997$	14.0123	−	33.8287i	0.443774	−	1.07137i	0.974614	−	0.223893i	$-0.0718767\pi$
$998$	0.474750	+	7.22850i	0.0150280	+	0.228814i
$999$	7.07350	+	7.07350i	0.223796	+	0.223796i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bf.a.53.5	✓	192
32.29	even	8	inner	416.2.bf.a.157.5	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bf.a.53.5	✓	192	1.1	even	1	trivial
416.2.bf.a.157.5	yes	192	32.29	even	8	inner

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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

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Fields

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Groups

Database

Properties

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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	416.2.bf.a.53.5

Level	$416$
Weight	$2$
Character	416.53
Analytic conductor	$3.322$
Analytic rank	$0$
Dimension	$192$
Inner twists	$2$