LMFDB - Embedded newform 416.2.bf.a.157.5

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			157.5
Character	$\chi$	$=$	416.157
Dual form			416.2.bf.a.53.5

$q$-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 $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$1$

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	−0.995224	−	0.0976183i	$-0.968878\pi$
$3$	−3.06223	−	1.26842i	−1.76798	−	0.732321i	−0.772756	−	0.634703i	$-0.781122\pi$
$4$	1.58703	−	1.21710i	0.793516	−	0.608550i
$5$	−0.807892	−	1.95042i	−0.361300	−	0.872256i	−0.995111	−	0.0987676i	$-0.968510\pi$
$5$	−0.807892	−	1.95042i	−0.361300	−	0.872256i	0.633810	−	0.773489i	$-0.281490\pi$
$6$	4.67738	+	0.307199i	1.90953	+	0.125414i
$7$	2.62405	−	2.62405i	0.991799	−	0.991799i	−0.00816797	−	0.999967i	$-0.502600\pi$
$7$	2.62405	−	2.62405i	0.991799	−	0.991799i	0.999967	+	0.00816797i	$0.00259997\pi$
$8$	−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	0.315959	−	0.948773i	$-0.397674\pi$
$11$	4.01397	−	1.66264i	1.21026	−	0.501306i	0.894300	+	0.447467i	$0.147674\pi$
$12$	−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	$0.0889777\pi$
$17$			2.27517i			0.551811i	−0.961185	+	0.275905i	$0.911022\pi$
$18$	−10.1287	−	4.99661i	−2.38736	−	1.17771i
$19$	2.76406	−	6.67304i	0.634120	−	1.53090i	−0.200279	−	0.979739i	$-0.564185\pi$
$19$	2.76406	−	6.67304i	0.634120	−	1.53090i	0.834399	−	0.551161i	$-0.185815\pi$
$20$	−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	0.688137	−	0.725580i	$-0.258429\pi$
$23$	−0.179570	−	0.179570i	−0.0374429	−	0.0374429i	−0.725580	+	0.688137i	$0.758429\pi$
$24$	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	0.780282	−	0.625427i	$-0.215075\pi$
$29$	4.79162	+	1.98475i	0.889781	+	0.368560i	0.109499	+	0.993987i	$0.465075\pi$
$30$	−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	0.941775	−	0.336242i	$-0.109156\pi$
$37$	0.231634	+	0.559213i	0.0380803	+	0.0919340i	−0.903695	+	0.428176i	$0.859156\pi$
$38$	−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	0.476399	−	0.879229i	$-0.341942\pi$
$41$	−2.57937	−	2.57937i	−0.402830	−	0.402830i	−0.879229	+	0.476399i	$0.841942\pi$
$42$	13.0798	−	11.4676i	2.01826	−	1.76949i
$43$	−0.449620	+	0.186239i	−0.0685664	+	0.0284011i	−0.416703	−	0.909043i	$-0.636815\pi$
$43$	−0.449620	+	0.186239i	−0.0685664	+	0.0284011i	0.348137	+	0.937444i	$0.386815\pi$
$44$	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	$-0.894468\pi$
$47$		−	4.46300i		−	0.650996i	0.945543	−	0.325498i	$-0.105532\pi$
$48$	−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	−0.927262	−	0.374413i	$-0.877844\pi$
$53$	−9.59654	+	3.97502i	−1.31819	+	0.546010i	−0.390923	+	0.920423i	$0.627844\pi$
$54$	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	0.998498	+	0.0547808i	$0.0174460\pi$
$59$	2.54391	+	6.14155i	0.331189	+	0.799562i	−0.667309	+	0.744781i	$0.732554\pi$
$60$	8.51652	+	11.1051i	1.09948	+	1.43366i
$61$	−2.20636	−	0.913906i	−0.282496	−	0.117014i	0.236937	−	0.971525i	$-0.423857\pi$
$61$	−2.20636	−	0.913906i	−0.282496	−	0.117014i	−0.519433	+	0.854511i	$0.673857\pi$
$62$	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	0.0244206	−	0.999702i	$-0.492226\pi$
$67$	−5.44496	−	2.25538i	−0.665207	−	0.275538i	−0.689628	+	0.724164i	$0.742226\pi$
$68$	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	−0.973658	−	0.228013i	$-0.926777\pi$
$71$	−6.28291	+	6.28291i	−0.745645	+	0.745645i	0.228013	+	0.973658i	$0.426777\pi$
$72$	−22.1560	+	4.39787i	−2.61111	+	0.518294i
$73$	8.07849	+	8.07849i	0.945515	+	0.945515i	0.998591	−	0.0530751i	$-0.0169023\pi$
$73$	8.07849	+	8.07849i	0.945515	+	0.945515i	−0.0530751	+	0.998591i	$0.516902\pi$
$74$	−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	$0.0552264\pi$
$79$			3.06873i			0.345259i	−0.984987	+	0.172630i	$0.944774\pi$
$80$	−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	−0.924698	−	0.380701i	$-0.875683\pi$
$83$	−0.0149546	+	0.0361037i	−0.00164149	+	0.00396290i	0.923057	+	0.384664i	$0.125683\pi$
$84$	−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	−0.180235	−	0.983624i	$-0.557686\pi$
$89$	7.57915	−	7.57915i	0.803389	−	0.803389i	0.983624	+	0.180235i	$0.0576858\pi$
$90$	−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	0.992699	−	0.120621i	$-0.0384886\pi$
$101$	2.06487	+	4.98505i	0.205463	+	0.496031i	−0.787236	+	0.616652i	$0.788489\pi$
$102$	−0.698932	+	10.6419i	−0.0692046	+	1.05370i
$103$	5.39113	−	5.39113i	0.531203	−	0.531203i	−0.389727	−	0.920930i	$-0.627431\pi$
$103$	5.39113	−	5.39113i	0.531203	−	0.531203i	0.920930	+	0.389727i	$0.127431\pi$
$104$	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	−0.885750	−	0.464163i	$-0.846355\pi$
$107$	−12.2459	+	5.07242i	−1.18386	+	0.490369i	−0.298107	+	0.954533i	$0.596355\pi$
$108$	−28.6208	−	16.5344i	−2.75403	−	1.59102i
$109$	−7.33872	+	17.7172i	−0.702922	+	1.69700i	0.0140484	+	0.999901i	$0.495528\pi$
$109$	−7.33872	+	17.7172i	−0.702922	+	1.69700i	−0.716971	+	0.697103i	$0.754472\pi$
$110$	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	$-0.580870\pi$
$113$		−	20.5778i		−	1.93580i	0.251336	−	0.967900i	$-0.419130\pi$
$114$	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	0.0701270	−	0.997538i	$-0.477660\pi$
$131$	−6.70309	−	2.77651i	−0.585652	−	0.242585i	−0.655779	+	0.754953i	$0.727660\pi$
$132$	−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	0.553546	−	0.832819i	$-0.313274\pi$
$137$	−3.26880	−	3.26880i	−0.279272	−	0.279272i	−0.832819	+	0.553546i	$0.813274\pi$
$138$	−0.784753	−	0.895080i	−0.0668026	−	0.0761943i
$139$	−12.0720	+	5.00038i	−1.02393	+	0.424127i	−0.830519	−	0.556990i	$-0.811956\pi$
$139$	−12.0720	+	5.00038i	−1.02393	+	0.424127i	−0.193414	+	0.981117i	$0.561956\pi$
$140$	−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	0.441588	−	0.897218i	$-0.354415\pi$
$149$	16.9460	−	7.01924i	1.38827	−	0.575039i	0.946679	+	0.322179i	$0.104415\pi$
$150$	1.91442	−	1.67845i	0.156312	−	0.137045i
$151$	−5.03561	−	5.03561i	−0.409792	−	0.409792i	0.471874	−	0.881666i	$-0.343578\pi$
$151$	−5.03561	−	5.03561i	−0.409792	−	0.409792i	−0.881666	+	0.471874i	$0.843578\pi$
$152$	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	0.126256	−	0.991998i	$-0.459704\pi$
$157$	−6.08850	−	2.52194i	−0.485915	−	0.201273i	−0.612172	+	0.790725i	$0.709704\pi$
$158$	−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	0.867854	−	0.496820i	$-0.165499\pi$
$163$	14.4296	+	5.97694i	1.13021	+	0.468150i	0.262360	+	0.964970i	$0.415499\pi$
$164$	−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	−0.983439	−	0.181238i	$-0.941989\pi$
$167$	−10.3667	+	10.3667i	−0.802201	+	0.802201i	0.181238	+	0.983439i	$0.441989\pi$
$168$	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	−0.586391	−	0.810028i	$-0.699452\pi$
$173$	5.27468	−	12.7342i	0.401027	−	0.968164i	0.987417	−	0.158136i	$-0.0505483\pi$
$174$	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	−0.656939	−	0.753943i	$-0.728149\pi$
$179$	4.55833	−	11.0048i	0.340705	−	0.822536i	0.997645	−	0.0685922i	$-0.0218507\pi$
$180$	−8.71855	−	32.5728i	−0.649842	−	2.42784i
$181$	−11.1086	+	4.60132i	−0.825694	+	0.342014i	−0.755197	−	0.655498i	$-0.772459\pi$
$181$	−11.1086	+	4.60132i	−0.825694	+	0.342014i	−0.0704974	+	0.997512i	$0.522459\pi$
$182$	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	0.997622	+	0.0689264i	$0.0219574\pi$
$197$	4.78525	+	11.5526i	0.340935	+	0.823090i	−0.656687	+	0.754163i	$0.728043\pi$
$198$	−48.9640	−	3.21584i	−3.47972	−	0.228539i
$199$	−3.42010	+	3.42010i	−0.242444	+	0.242444i	−0.817861	−	0.575416i	$-0.804840\pi$
$199$	−3.42010	+	3.42010i	−0.242444	+	0.242444i	0.575416	+	0.817861i	$0.304840\pi$
$200$	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	−0.923675	−	0.383178i	$-0.874830\pi$
$211$	0.00594991	−	0.0143644i	0.000409609	−	0.000988884i	0.924084	+	0.382189i	$0.124830\pi$
$212$	−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	0.732608	−	0.680651i	$-0.238303\pi$
$227$	11.5914	+	4.80131i	0.769348	+	0.318674i	0.0367394	+	0.999325i	$0.488303\pi$
$228$	−6.26237	+	47.4695i	−0.414736	+	3.14374i
$229$	−6.53886	−	15.7862i	−0.432100	−	1.04318i	−0.978609	−	0.205729i	$-0.934044\pi$
$229$	−6.53886	−	15.7862i	−0.432100	−	1.04318i	0.546509	−	0.837453i	$-0.315956\pi$
$230$	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	0.971815	−	0.235744i	$-0.0757526\pi$
$233$	11.2356	+	11.2356i	0.736072	+	0.736072i	−0.235744	+	0.971815i	$0.575753\pi$
$234$	−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	$-0.933867\pi$
$239$		−	6.37778i		−	0.412544i	0.978495	−	0.206272i	$-0.0661332\pi$
$240$	27.0320	+	7.25868i	1.74491	+	0.468546i
$241$			4.23046i			0.272508i	0.990674	+	0.136254i	$0.0435063\pi$
$241$			4.23046i			0.272508i	−0.990674	+	0.136254i	$0.956494\pi$
$242$	−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	0.819587	+	0.572954i	$0.194203\pi$
$251$	10.2218	+	24.6775i	0.645192	+	1.55763i	−0.174396	+	0.984676i	$0.555797\pi$
$252$	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	−0.791135	−	0.611642i	$-0.790509\pi$
$263$	−2.91088	+	2.91088i	−0.179493	+	0.179493i	0.611642	+	0.791135i	$0.290509\pi$
$264$	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	0.668169	+	0.744009i	$0.267078\pi$
$269$	−5.41883	+	13.0822i	−0.330392	+	0.797636i	−0.998561	+	0.0536268i	$0.982922\pi$
$270$	21.8293	−	44.2505i	1.32849	−	2.69300i
$271$		−	0.945391i		−	0.0574284i	−0.999588	−	0.0287142i	$-0.990859\pi$
$271$		−	0.945391i		−	0.0574284i	0.999588	−	0.0287142i	$-0.00914127\pi$
$272$	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	−0.856524	−	0.516108i	$-0.827380\pi$
$277$	−18.2616	+	7.56421i	−1.09723	+	0.454489i	−0.240710	+	0.970597i	$0.577380\pi$
$278$	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	−0.186976	+	0.982364i	$0.559869\pi$
$281$	−19.6017	+	19.6017i	−1.16934	+	1.16934i	−0.982364	+	0.186976i	$0.940131\pi$
$282$	1.37103	−	20.8752i	0.0816437	−	1.24310i
$283$	3.18385	+	7.68649i	0.189260	+	0.456915i	0.989818	−	0.142342i	$-0.0454631\pi$
$283$	3.18385	+	7.68649i	0.189260	+	0.456915i	−0.800557	+	0.599256i	$0.795463\pi$
$284$	−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	0.876663	−	0.481104i	$-0.159764\pi$
$293$	−1.42798	−	3.44745i	−0.0834235	−	0.201402i	−0.960087	+	0.279702i	$0.909764\pi$
$294$	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	−0.784895	−	0.619629i	$-0.787283\pi$
$307$	3.64890	−	8.80921i	0.208253	−	0.502768i	0.993148	+	0.116861i	$0.0372831\pi$
$308$	−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	−0.875634	−	0.482975i	$-0.839556\pi$
$311$	−23.9593	−	23.9593i	−1.35861	−	1.35861i	−0.482975	−	0.875634i	$-0.660444\pi$
$312$	−1.82527	−	9.19552i	−0.103336	−	0.520594i
$313$	−2.80015	+	2.80015i	−0.158274	+	0.158274i	−0.781801	−	0.623528i	$-0.785699\pi$
$313$	−2.80015	+	2.80015i	−0.158274	+	0.158274i	0.623528	+	0.781801i	$0.285699\pi$
$314$	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	0.448388	−	0.893839i	$-0.351998\pi$
$317$	2.37525	+	0.983862i	0.133408	+	0.0552592i	−0.314981	+	0.949098i	$0.601998\pi$
$318$	−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	0.0222952	−	0.999751i	$-0.492903\pi$
$331$	13.5539	−	5.61422i	0.744991	−	0.308585i	0.722696	+	0.691166i	$0.242903\pi$
$332$	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	$0.204449\pi$
$337$			21.9936i			1.19807i	−0.800723	+	0.599035i	$0.795551\pi$
$338$	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	0.974078	−	0.226211i	$-0.0726339\pi$
$347$	2.33493	+	5.63701i	0.125345	+	0.302611i	−0.848733	+	0.528822i	$0.822634\pi$
$348$	−34.0858	−	4.49674i	−1.82719	−	0.241050i
$349$	8.24827	+	3.41654i	0.441520	+	0.182883i	0.592358	−	0.805675i	$-0.298197\pi$
$349$	8.24827	+	3.41654i	0.441520	+	0.182883i	−0.150838	+	0.988558i	$0.548197\pi$
$350$	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	−0.729584	−	0.683891i	$-0.760287\pi$
$359$	−0.865773	+	0.865773i	−0.0456938	+	0.0456938i	0.683891	+	0.729584i	$0.260287\pi$
$360$	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	$0.0138362\pi$
$367$			1.66492i			0.0869083i	−0.999055	+	0.0434542i	$0.986164\pi$
$368$	−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	0.689868	−	0.723935i	$-0.257669\pi$
$373$	32.6312	−	13.5163i	1.68958	−	0.699846i	0.999710	+	0.0240896i	$0.00766869\pi$
$374$	−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	0.964746	+	0.263183i	$0.0847722\pi$
$379$	9.12395	+	22.0272i	0.468666	+	1.13146i	−0.496080	+	0.868277i	$0.665228\pi$
$380$	−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	0.980152	−	0.198247i	$-0.0635248\pi$
$389$	2.89728	+	6.99466i	0.146898	+	0.354644i	−0.833254	+	0.552890i	$0.813525\pi$
$390$	−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	−0.997743	−	0.0671427i	$-0.978612\pi$
$397$	−4.87671	+	11.7734i	−0.244755	+	0.590891i	0.752988	+	0.658034i	$0.228612\pi$
$398$	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	$-0.949675\pi$
$401$		−	6.30559i		−	0.314886i	0.987528	−	0.157443i	$-0.0503251\pi$
$402$	−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	−0.835607	−	0.549328i	$-0.814884\pi$
$409$	−5.78963	+	5.78963i	−0.286279	+	0.286279i	0.549328	+	0.835607i	$0.314884\pi$
$410$	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	0.737522	−	0.675323i	$-0.235996\pi$
$419$	15.9970	+	6.62617i	0.781504	+	0.323710i	0.0439817	+	0.999032i	$0.485996\pi$
$420$	51.4881	+	6.79253i	2.51236	+	0.331442i
$421$	2.84659	+	6.87227i	0.138734	+	0.334934i	0.977942	−	0.208877i	$-0.0669809\pi$
$421$	2.84659	+	6.87227i	0.138734	+	0.334934i	−0.839208	+	0.543811i	$0.816981\pi$
$422$	−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	$-0.830841\pi$
$431$		−	21.0415i		−	1.01353i	0.862083	−	0.506767i	$-0.169159\pi$
$432$	−65.5460	+	8.59369i	−3.15359	+	0.413464i
$433$			20.1730i			0.969450i	0.874667	+	0.484725i	$0.161080\pi$
$433$			20.1730i			0.969450i	−0.874667	+	0.484725i	$0.838920\pi$
$434$	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	0.585879	−	0.810398i	$-0.300749\pi$
$439$	−4.70420	−	4.70420i	−0.224519	−	0.224519i	−0.810398	+	0.585879i	$0.800749\pi$
$440$	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	0.727102	−	0.686529i	$-0.240867\pi$
$443$	−5.73517	−	13.8459i	−0.272486	−	0.657840i	−0.999588	+	0.0286891i	$0.990867\pi$
$444$	−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	0.573005	−	0.819552i	$-0.305778\pi$
$457$	−5.27059	−	5.27059i	−0.246548	−	0.246548i	−0.819552	+	0.573005i	$0.805778\pi$
$458$	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	−0.205494	−	0.978658i	$-0.565880\pi$
$461$	13.5659	−	32.7510i	0.631828	−	1.52537i	0.837322	−	0.546710i	$-0.184120\pi$
$462$	33.4355	−	67.7777i	1.55556	−	3.15330i
$463$			35.1174i			1.63204i	0.578022	+	0.816021i	$0.303825\pi$
$463$			35.1174i			1.63204i	−0.578022	+	0.816021i	$0.696175\pi$
$464$	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	−0.881231	−	0.472686i	$-0.843285\pi$
$467$	1.64524	−	3.97197i	0.0761329	−	0.183801i	0.957364	+	0.288885i	$0.0932845\pi$
$468$	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	−0.657364	−	0.753573i	$-0.728329\pi$
$487$	2.12314	−	2.12314i	0.0962087	−	0.0962087i	0.753573	+	0.657364i	$0.228329\pi$
$488$	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	0.101111	−	0.994875i	$-0.467760\pi$
$491$	19.4129	−	8.04107i	0.876090	−	0.362888i	0.774979	+	0.631987i	$0.217760\pi$
$492$	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	−0.961663	−	0.274234i	$-0.911576\pi$
$499$	−1.96023	+	4.73242i	−0.0877520	+	0.211852i	0.873911	+	0.486086i	$0.161576\pi$
$500$	−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	−0.974203	−	0.225674i	$-0.927541\pi$
$503$	−26.9104	−	26.9104i	−1.19988	−	1.19988i	−0.225674	−	0.974203i	$-0.572459\pi$
$504$	−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	0.407244	−	0.913319i	$-0.366490\pi$
$509$	1.11439	+	0.461596i	0.0493945	+	0.0204599i	−0.357849	+	0.933779i	$0.616490\pi$
$510$	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	0.937521	−	0.347928i	$-0.113114\pi$
$521$	13.4577	+	13.4577i	0.589594	+	0.589594i	−0.347928	+	0.937521i	$0.613114\pi$
$522$	−38.6159	−	44.0449i	−1.69017	−	1.92779i
$523$	−7.38695	+	3.05977i	−0.323009	+	0.133795i	−0.538295	−	0.842756i	$-0.680931\pi$
$523$	−7.38695	+	3.05977i	−0.323009	+	0.133795i	0.215286	+	0.976551i	$0.430931\pi$
$524$	−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	0.208471	−	0.978029i	$-0.433151\pi$
$541$	−7.80793	−	3.23415i	−0.335689	−	0.139047i	−0.544160	+	0.838982i	$0.683151\pi$
$542$	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	0.341363	−	0.939932i	$-0.389112\pi$
$547$	−1.91523	−	0.793314i	−0.0818893	−	0.0339197i	−0.423252	+	0.906012i	$0.639112\pi$
$548$	−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	−0.118451	−	0.992960i	$-0.537793\pi$
$557$	15.7520	−	38.0288i	0.667435	−	1.61133i	0.785886	−	0.618371i	$-0.212207\pi$
$558$	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	−0.617135	−	0.786857i	$-0.711707\pi$
$563$	8.91298	−	21.5178i	0.375637	−	0.906868i	0.992773	−	0.120011i	$-0.0382931\pi$
$564$	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	−0.0396342	−	0.999214i	$-0.512619\pi$
$569$	22.8896	−	22.8896i	0.959580	−	0.959580i	0.999214	+	0.0396342i	$0.0126193\pi$
$570$	−71.3223	−	4.68427i	−2.98736	−	0.196203i
$571$	−13.2380	−	31.9594i	−0.553993	−	1.33746i	−0.914456	−	0.404685i	$-0.867381\pi$
$571$	−13.2380	−	31.9594i	−0.553993	−	1.33746i	0.360463	−	0.932774i	$-0.382619\pi$
$572$	−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	−0.657916	−	0.753091i	$-0.728562\pi$
$587$	−14.3095	+	5.92719i	−0.590617	+	0.244641i	0.0672993	+	0.997733i	$0.478562\pi$
$588$	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	$-0.930431\pi$
$593$		−	10.5599i		−	0.433643i	0.976211	−	0.216822i	$-0.0695690\pi$
$594$	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	0.746150	−	0.665778i	$-0.231900\pi$
$599$	1.96704	+	1.96704i	0.0803713	+	0.0803713i	−0.665778	+	0.746150i	$0.731900\pi$
$600$	0.995408	−	4.99380i	0.0406374	−	0.203871i
$601$	7.27349	−	7.27349i	0.296692	−	0.296692i	−0.543025	−	0.839717i	$-0.682721\pi$
$601$	7.27349	−	7.27349i	0.296692	−	0.296692i	0.839717	+	0.543025i	$0.182721\pi$
$602$	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	0.774064	+	0.633108i	$0.218221\pi$
$613$	16.6972	+	40.3106i	0.674393	+	1.62813i	−0.0996712	+	0.995020i	$0.531779\pi$
$614$	−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	0.957351	−	0.288928i	$-0.0932987\pi$
$617$	16.6033	+	16.6033i	0.668423	+	0.668423i	−0.288928	+	0.957351i	$0.593299\pi$
$618$	26.8725	−	23.5602i	1.08097	−	0.947731i
$619$	−23.7648	+	9.84372i	−0.955189	+	0.395652i	−0.805179	−	0.593032i	$-0.797931\pi$
$619$	−23.7648	+	9.84372i	−0.955189	+	0.395652i	−0.150010	+	0.988684i	$0.547931\pi$
$620$	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	−0.999218	−	0.0395308i	$-0.987414\pi$
$631$	−26.0931	−	26.0931i	−1.03875	−	1.03875i	−0.0395308	−	0.999218i	$-0.512586\pi$
$632$	−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	0.976356	−	0.216169i	$-0.0693564\pi$
$643$	38.3884	+	15.9010i	1.51389	+	0.627073i	0.537533	+	0.843243i	$0.319356\pi$
$644$	−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	−0.497076	−	0.867707i	$-0.665593\pi$
$647$	9.42745	−	9.42745i	0.370631	−	0.370631i	0.867707	+	0.497076i	$0.165593\pi$
$648$	−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	−0.876381	−	0.481618i	$-0.840049\pi$
$653$	2.14317	−	5.17408i	0.0838688	−	0.202477i	0.960250	+	0.279140i	$0.0900494\pi$
$654$	−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	−0.931626	−	0.363418i	$-0.881610\pi$
$659$	−0.407950	+	0.984879i	−0.0158915	+	0.0383654i	0.915735	+	0.401784i	$0.131610\pi$
$660$	52.6489	+	30.4156i	2.04936	+	1.18393i
$661$	11.1147	−	4.60384i	0.432310	−	0.179069i	−0.155907	−	0.987772i	$-0.549830\pi$
$661$	11.1147	−	4.60384i	0.432310	−	0.179069i	0.588217	+	0.808703i	$0.299830\pi$
$662$	−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	−0.801631	−	0.597819i	$-0.796034\pi$
$677$	−17.1080	−	41.3024i	−0.657514	−	1.58738i	0.144117	−	0.989561i	$-0.453966\pi$
$678$	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	−0.972987	−	0.230858i	$-0.925847\pi$
$683$	−39.1427	+	16.2134i	−1.49775	+	0.620389i	−0.524765	+	0.851247i	$0.675847\pi$
$684$	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	−0.930920	−	0.365222i	$-0.880993\pi$
$691$	−0.378773	+	0.914440i	−0.0144092	+	0.0347869i	0.916511	+	0.400009i	$0.130993\pi$
$692$	−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	0.0825187	−	0.996590i	$-0.473704\pi$
$701$	−14.9281	−	6.18343i	−0.563827	−	0.233545i	−0.646346	+	0.763045i	$0.723704\pi$
$702$	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	0.998550	−	0.0538316i	$-0.0171434\pi$
$709$	6.77403	+	16.3539i	0.254404	+	0.614185i	−0.744146	+	0.668017i	$0.767143\pi$
$710$	−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	$0.00854881\pi$
$719$			1.44012i			0.0537073i	−0.999639	+	0.0268536i	$0.991451\pi$
$720$	−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	0.999284	−	0.0378417i	$-0.0120483\pi$
$727$	25.9233	+	25.9233i	0.961442	+	0.961442i	−0.0378417	+	0.999284i	$0.512048\pi$
$728$	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	0.996748	−	0.0805793i	$-0.0256770\pi$
$733$	44.5252	+	18.4430i	1.64458	+	0.681206i	0.647829	+	0.761786i	$0.275677\pi$
$734$	−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	0.794115	−	0.607768i	$-0.207935\pi$
$739$	25.1697	+	10.4256i	0.925882	+	0.383513i	0.131767	+	0.991281i	$0.457935\pi$
$740$	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	−0.992683	−	0.120749i	$-0.961470\pi$
$743$	−23.7672	+	23.7672i	−0.871934	+	0.871934i	0.120749	+	0.992683i	$0.461470\pi$
$744$	−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	$0.00781623\pi$
$751$			1.34572i			0.0491059i	−0.999699	+	0.0245529i	$0.992184\pi$
$752$	−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	−0.787764	−	0.615977i	$-0.788761\pi$
$757$	−25.0164	+	10.3621i	−0.909235	+	0.376618i	−0.121471	+	0.992595i	$0.538761\pi$
$758$	−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	−0.810335	−	0.585966i	$-0.800715\pi$
$761$	−6.18950	+	6.18950i	−0.224369	+	0.224369i	0.585966	+	0.810335i	$0.300715\pi$
$762$	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	0.999925	−	0.0122536i	$-0.00390053\pi$
$773$	7.90176	+	19.0765i	0.284207	+	0.686136i	−0.715718	+	0.698389i	$0.753901\pi$
$774$	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	−0.255667	−	0.966765i	$-0.582295\pi$
$787$	17.0768	−	41.2271i	0.608723	−	1.46959i	0.864390	−	0.502822i	$-0.167705\pi$
$788$	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	0.809224	−	0.587501i	$-0.199888\pi$
$797$	27.2715	+	11.2962i	0.966006	+	0.400133i	0.156782	+	0.987633i	$0.449888\pi$
$798$	−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	0.790977	−	0.611846i	$-0.209573\pi$
$809$	5.09501	+	5.09501i	0.179131	+	0.179131i	−0.611846	+	0.790977i	$0.709573\pi$
$810$	−69.1892	+	60.6610i	−2.43106	+	2.13141i
$811$	5.21299	−	2.15929i	0.183053	−	0.0758230i	−0.289274	−	0.957246i	$-0.593414\pi$
$811$	5.21299	−	2.15929i	0.183053	−	0.0758230i	0.472327	+	0.881423i	$0.343414\pi$
$812$	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	−0.219971	−	0.975506i	$-0.570596\pi$
$821$	9.00488	−	3.72994i	0.314272	−	0.130176i	0.534244	+	0.845330i	$0.320596\pi$
$822$	−14.2853	−	16.2936i	−0.498256	−	0.568305i
$823$	13.6368	+	13.6368i	0.475349	+	0.475349i	0.903641	−	0.428292i	$-0.140884\pi$
$823$	13.6368	+	13.6368i	0.475349	+	0.475349i	−0.428292	+	0.903641i	$0.640884\pi$
$824$	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	0.994824	−	0.101612i	$-0.0324000\pi$
$827$	6.31306	+	15.2411i	0.219527	+	0.529984i	−0.775297	+	0.631596i	$0.782400\pi$
$828$	−2.46838	−	3.21863i	−0.0857820	−	0.111855i
$829$	16.0447	+	6.64592i	0.557255	+	0.230822i	0.643493	−	0.765452i	$-0.277485\pi$
$829$	16.0447	+	6.64592i	0.557255	+	0.230822i	−0.0862381	+	0.996275i	$0.527485\pi$
$830$	−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	−0.501398	−	0.865217i	$-0.667181\pi$
$839$	10.5382	−	10.5382i	0.363819	−	0.363819i	0.865217	+	0.501398i	$0.167181\pi$
$840$	−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	−0.671068	−	0.741396i	$-0.734164\pi$
$853$	−18.1469	+	7.51669i	−0.621338	+	0.257367i	0.0497297	+	0.998763i	$0.484164\pi$
$854$	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	−0.627585	−	0.778548i	$-0.715957\pi$
$857$	4.41936	−	4.41936i	0.150962	−	0.150962i	0.778548	+	0.627585i	$0.215957\pi$
$858$	1.33469	−	20.3218i	0.0455655	−	0.693775i
$859$	13.3415	+	32.2093i	0.455207	+	1.09897i	0.970316	+	0.241842i	$0.0777515\pi$
$859$	13.3415	+	32.2093i	0.455207	+	1.09897i	−0.515109	+	0.857125i	$0.672249\pi$
$860$	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	−0.952438	−	0.304732i	$-0.901433\pi$
$877$	−1.88005	+	4.53883i	−0.0634846	+	0.153265i	0.888954	+	0.457997i	$0.151433\pi$
$878$	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	$0.193068\pi$
$881$			33.8388i			1.14006i	−0.821624	+	0.570030i	$0.806932\pi$
$882$	−33.8336	+	68.5846i	−1.13924	+	2.30936i
$883$	16.6773	−	40.2626i	0.561236	−	1.35494i	−0.347542	−	0.937665i	$-0.612984\pi$
$883$	16.6773	−	40.2626i	0.561236	−	1.35494i	0.908778	−	0.417280i	$-0.137016\pi$
$884$	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	0.526664	−	0.850074i	$-0.323443\pi$
$887$	−9.63198	−	9.63198i	−0.323410	−	0.323410i	−0.850074	+	0.526664i	$0.823443\pi$
$888$	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	−0.0884617	−	0.996080i	$-0.528195\pi$
$907$	16.6641	−	6.90248i	0.553321	−	0.229193i	0.641783	+	0.766886i	$0.278195\pi$
$908$	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	$0.103915\pi$
$911$			19.3587i			0.641381i	−0.947184	+	0.320690i	$0.896085\pi$
$912$	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	0.525490	−	0.850800i	$-0.323882\pi$
$919$	−9.86175	−	9.86175i	−0.325309	−	0.325309i	−0.850800	+	0.525490i	$0.823882\pi$
$920$	−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	0.910808	−	0.412831i	$-0.135460\pi$
$937$	15.2433	+	15.2433i	0.497977	+	0.497977i	−0.412831	+	0.910808i	$0.635460\pi$
$938$	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	−0.929194	−	0.369592i	$-0.879497\pi$
$941$	−0.331709	+	0.800816i	−0.0108134	+	0.0261058i	0.918381	+	0.395698i	$0.129497\pi$
$942$	−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	−0.944274	−	0.329159i	$-0.893235\pi$
$947$	−1.34851	+	3.25559i	−0.0438206	+	0.105792i	0.900454	+	0.434952i	$0.143235\pi$
$948$	−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	−0.850529	−	0.525929i	$-0.823718\pi$
$953$	−10.0206	+	10.0206i	−0.324600	+	0.324600i	0.525929	+	0.850529i	$0.323718\pi$
$954$	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	0.204516	−	0.978863i	$-0.434438\pi$
$967$	36.7991	−	36.7991i	1.18338	−	1.18338i	0.978863	−	0.204516i	$-0.0655620\pi$
$968$	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	−0.878151	−	0.478384i	$-0.841223\pi$
$971$	−36.1724	+	14.9831i	−1.16083	+	0.480831i	−0.282678	+	0.959215i	$0.591223\pi$
$972$	−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	$-0.759406\pi$
$977$		−	42.8788i		−	1.37181i	0.727689	−	0.685907i	$-0.240594\pi$
$978$	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	0.897798	−	0.440408i	$-0.145166\pi$
$983$	14.3404	+	14.3404i	0.457389	+	0.457389i	−0.440408	+	0.897798i	$0.645166\pi$
$984$	−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	0.974614	+	0.223893i	$0.0718767\pi$
$997$	14.0123	+	33.8287i	0.443774	+	1.07137i	−0.530840	+	0.847472i	$0.678123\pi$
$998$	0.474750	−	7.22850i	0.0150280	−	0.228814i
$999$	7.07350	−	7.07350i	0.223796	−	0.223796i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bf.a.53.5	✓	192	32.21	even	8	inner
416.2.bf.a.157.5	yes	192	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bf (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(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

Introduction

L-functions

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