LMFDB - Embedded newform 357.2.bh.a.100.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(25,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 16, 15]))

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

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

chi := DirichletCharacter("357.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$357 = 3 \cdot 7 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	357.bh (of order $24$ , degree $8$ , 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$24$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			100.6
Character	$\chi$	$=$	357.100
Dual form			357.2.bh.a.25.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68695 + 0.452018i) q^{2} +(0.608761 - 0.793353i) q^{3} +(0.909440 - 0.525065i) q^{4} +(0.277214 - 2.10565i) q^{5} +(-0.668342 + 1.61352i) q^{6} +(2.14198 - 1.55304i) q^{7} +(1.17303 - 1.17303i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(0.484144 + 3.67744i) q^{10} +(-5.06864 + 0.667299i) q^{11} +(0.137070 - 1.04115i) q^{12} +0.853029i q^{13} +(-2.91141 + 3.58812i) q^{14} +(-1.50177 - 1.50177i) q^{15} +(-2.49874 + 4.32795i) q^{16} +(2.60121 - 3.19902i) q^{17} +(0.873231 + 1.51248i) q^{18} +(-2.98493 + 0.799810i) q^{19} +(-0.853494 - 2.06052i) q^{20} +(0.0718432 - 2.64478i) q^{21} +(8.24893 - 3.41682i) q^{22} +(-3.68648 - 4.80431i) q^{23} +(-0.216531 - 1.64472i) q^{24} +(0.472715 + 0.126664i) q^{25} +(-0.385584 - 1.43902i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(1.13255 - 2.53707i) q^{28} +(-3.11130 + 1.28874i) q^{29} +(3.21224 + 1.85459i) q^{30} +(4.55776 - 5.93979i) q^{31} +(1.40024 - 5.22576i) q^{32} +(-2.55619 + 4.42745i) q^{33} +(-2.94210 + 6.57239i) q^{34} +(-2.67637 - 4.94078i) q^{35} +(-0.742554 - 0.742554i) q^{36} +(-3.99120 - 0.525452i) q^{37} +(4.67391 - 2.69848i) q^{38} +(0.676754 + 0.519291i) q^{39} +(-2.14481 - 2.79516i) q^{40} +(2.06379 + 0.854851i) q^{41} +(1.07429 + 4.49409i) q^{42} +(4.32276 - 4.32276i) q^{43} +(-4.25925 + 3.26823i) q^{44} +(-2.10565 + 0.277214i) q^{45} +(8.39054 + 6.43829i) q^{46} +(-1.22754 - 0.708719i) q^{47} +(1.91246 + 4.61708i) q^{48} +(2.17613 - 6.65315i) q^{49} -0.854702 q^{50} +(-0.954437 - 4.01112i) q^{51} +(0.447896 + 0.775779i) q^{52} +(2.02796 - 7.56844i) q^{53} +(1.73152 + 0.227959i) q^{54} +10.8578i q^{55} +(0.690839 - 4.33436i) q^{56} +(-1.18258 + 2.85500i) q^{57} +(4.66609 - 3.58041i) q^{58} +(-5.92312 - 1.58710i) q^{59} +(-2.15429 - 0.577241i) q^{60} +(-1.98003 + 1.51933i) q^{61} +(-5.00384 + 12.0803i) q^{62} +(-2.05451 - 1.66703i) q^{63} -0.546438i q^{64} +(1.79618 + 0.236472i) q^{65} +(2.31088 - 8.62434i) q^{66} +(3.97853 + 6.89102i) q^{67} +(0.685948 - 4.27512i) q^{68} -6.05570 q^{69} +(6.74824 + 7.12509i) q^{70} +(1.52214 + 3.67477i) q^{71} +(-1.43666 - 0.829456i) q^{72} +(4.66349 + 3.57842i) q^{73} +(6.97049 - 0.917682i) q^{74} +(0.388260 - 0.297922i) q^{75} +(-2.29466 + 2.29466i) q^{76} +(-9.82057 + 9.30114i) q^{77} +(-1.37638 - 0.570116i) q^{78} +(-1.69621 - 2.21054i) q^{79} +(8.42046 + 6.46125i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-3.86793 - 0.509222i) q^{82} +(8.40583 + 8.40583i) q^{83} +(-1.32334 - 2.44299i) q^{84} +(-6.01492 - 6.36405i) q^{85} +(-5.33833 + 9.24626i) q^{86} +(-0.871612 + 3.25290i) q^{87} +(-5.16289 + 6.72841i) q^{88} +(13.8392 + 7.99004i) q^{89} +(3.42683 - 1.41944i) q^{90} +(1.32479 + 1.82717i) q^{91} +(-5.87520 - 2.43359i) q^{92} +(-1.93776 - 7.23183i) q^{93} +(2.39115 + 0.640707i) q^{94} +(0.856654 + 6.50694i) q^{95} +(-3.29346 - 4.29212i) q^{96} +(-11.6960 + 4.84463i) q^{97} +(-0.663688 + 12.2072i) q^{98} +(1.95642 + 4.72322i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100})$ 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$ .

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{8}\right)$	$1$

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

)

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

$2$	−1.68695	+	0.452018i	−1.19286	+	0.319625i	−0.800014	−	0.599981i	$-0.795175\pi$
$2$	−1.68695	+	0.452018i	−1.19286	+	0.319625i	−0.392842	+	0.919606i	$0.628508\pi$
$3$	0.608761	−	0.793353i	0.351469	−	0.458043i
$3$	0.608761	−	0.793353i	0.351469	−	0.458043i
$4$	0.909440	−	0.525065i	0.454720	−	0.262533i
$5$	0.277214	−	2.10565i	0.123974	−	0.941675i	−0.810524	−	0.585706i	$-0.800817\pi$
$5$	0.277214	−	2.10565i	0.123974	−	0.941675i	0.934498	−	0.355969i	$-0.115849\pi$
$6$	−0.668342	+	1.61352i	−0.272850	+	0.658717i
$7$	2.14198	−	1.55304i	0.809591	−	0.586994i
$7$	2.14198	−	1.55304i	0.809591	−	0.586994i
$8$	1.17303	−	1.17303i	0.414728	−	0.414728i
$9$	−0.258819	−	0.965926i	−0.0862730	−	0.321975i
$10$	0.484144	+	3.67744i	0.153100	+	1.16291i
$11$	−5.06864	+	0.667299i	−1.52825	+	0.201198i	−0.847294	−	0.531124i	$-0.821770\pi$
$11$	−5.06864	+	0.667299i	−1.52825	+	0.201198i	−0.680958	+	0.732322i	$0.738436\pi$
$12$	0.137070	−	1.04115i	0.0395686	−	0.300553i
$13$			0.853029i			0.236588i	0.992979	+	0.118294i	$0.0377425\pi$
$13$			0.853029i			0.236588i	−0.992979	+	0.118294i	$0.962258\pi$
$14$	−2.91141	+	3.58812i	−0.778108	+	0.958965i
$15$	−1.50177	−	1.50177i	−0.387755	−	0.387755i
$16$	−2.49874	+	4.32795i	−0.624686	+	1.08199i
$17$	2.60121	−	3.19902i	0.630886	−	0.775876i
$17$	2.60121	−	3.19902i	0.630886	−	0.775876i
$18$	0.873231	+	1.51248i	0.205823	+	0.356495i
$19$	−2.98493	+	0.799810i	−0.684790	+	0.183489i	−0.584408	−	0.811460i	$-0.698673\pi$
$19$	−2.98493	+	0.799810i	−0.684790	+	0.183489i	−0.100382	+	0.994949i	$0.532007\pi$
$20$	−0.853494	−	2.06052i	−0.190847	−	0.460746i
$21$	0.0718432	−	2.64478i	0.0156775	−	0.577137i
$22$	8.24893	−	3.41682i	1.75868	−	0.728468i
$23$	−3.68648	−	4.80431i	−0.768683	−	1.00177i	−0.999585	−	0.0287905i	$-0.990834\pi$
$23$	−3.68648	−	4.80431i	−0.768683	−	1.00177i	0.230902	−	0.972977i	$-0.425832\pi$
$24$	−0.216531	−	1.64472i	−0.0441993	−	0.335727i
$25$	0.472715	+	0.126664i	0.0945430	+	0.0253327i
$26$	−0.385584	−	1.43902i	−0.0756193	−	0.282215i
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	1.13255	−	2.53707i	0.214032	−	0.479462i
$29$	−3.11130	+	1.28874i	−0.577754	+	0.239314i	−0.652373	−	0.757898i	$-0.726226\pi$
$29$	−3.11130	+	1.28874i	−0.577754	+	0.239314i	0.0746181	+	0.997212i	$0.476226\pi$
$30$	3.21224	+	1.85459i	0.586471	+	0.338599i
$31$	4.55776	−	5.93979i	0.818598	−	1.06682i	−0.177969	−	0.984036i	$-0.556953\pi$
$31$	4.55776	−	5.93979i	0.818598	−	1.06682i	0.996568	−	0.0827822i	$-0.0263806\pi$
$32$	1.40024	−	5.22576i	0.247529	−	0.923792i
$33$	−2.55619	+	4.42745i	−0.444975	+	0.770720i
$34$	−2.94210	+	6.57239i	−0.504566	+	1.12715i
$35$	−2.67637	−	4.94078i	−0.452390	−	0.835144i
$36$	−0.742554	−	0.742554i	−0.123759	−	0.123759i
$37$	−3.99120	−	0.525452i	−0.656150	−	0.0863837i	−0.204902	−	0.978782i	$-0.565688\pi$
$37$	−3.99120	−	0.525452i	−0.656150	−	0.0863837i	−0.451248	+	0.892399i	$0.649021\pi$
$38$	4.67391	−	2.69848i	0.758208	−	0.437752i
$39$	0.676754	+	0.519291i	0.108367	+	0.0831532i
$40$	−2.14481	−	2.79516i	−0.339124	−	0.441954i
$41$	2.06379	+	0.854851i	0.322310	+	0.133505i	0.537972	−	0.842963i	$-0.319191\pi$
$41$	2.06379	+	0.854851i	0.322310	+	0.133505i	−0.215661	+	0.976468i	$0.569191\pi$
$42$	1.07429	+	4.49409i	0.165766	+	0.693453i
$43$	4.32276	−	4.32276i	0.659215	−	0.659215i	−0.295979	−	0.955194i	$-0.595646\pi$
$43$	4.32276	−	4.32276i	0.659215	−	0.659215i	0.955194	+	0.295979i	$0.0956459\pi$
$44$	−4.25925	+	3.26823i	−0.642106	+	0.492705i
$45$	−2.10565	+	0.277214i	−0.313892	+	0.0413246i
$46$	8.39054	+	6.43829i	1.23712	+	0.949274i
$47$	−1.22754	−	0.708719i	−0.179055	−	0.103377i	0.407794	−	0.913074i	$-0.366298\pi$
$47$	−1.22754	−	0.708719i	−0.179055	−	0.103377i	−0.586848	+	0.809697i	$0.699632\pi$
$48$	1.91246	+	4.61708i	0.276039	+	0.666418i
$49$	2.17613	−	6.65315i	0.310876	−	0.950451i
$50$	−0.854702			−0.120873
$51$	−0.954437	−	4.01112i	−0.133648	−	0.561669i
$52$	0.447896	+	0.775779i	0.0621120	+	0.107581i
$53$	2.02796	−	7.56844i	0.278561	−	1.03961i	−0.674856	−	0.737950i	$-0.735794\pi$
$53$	2.02796	−	7.56844i	0.278561	−	1.03961i	0.953417	−	0.301655i	$-0.0975392\pi$
$54$	1.73152	+	0.227959i	0.235630	+	0.0310213i
$55$			10.8578i			1.46406i
$56$	0.690839	−	4.33436i	0.0923172	−	0.579203i
$57$	−1.18258	+	2.85500i	−0.156636	+	0.378154i
$58$	4.66609	−	3.58041i	0.612687	−	0.470131i
$59$	−5.92312	−	1.58710i	−0.771125	−	0.206622i	−0.148256	−	0.988949i	$-0.547366\pi$
$59$	−5.92312	−	1.58710i	−0.771125	−	0.206622i	−0.622868	+	0.782327i	$0.714033\pi$
$60$	−2.15429	−	0.577241i	−0.278118	−	0.0745215i
$61$	−1.98003	+	1.51933i	−0.253517	+	0.194530i	−0.727699	−	0.685896i	$-0.759410\pi$
$61$	−1.98003	+	1.51933i	−0.253517	+	0.194530i	0.474183	+	0.880427i	$0.342744\pi$
$62$	−5.00384	+	12.0803i	−0.635488	+	1.53420i
$63$	−2.05451	−	1.66703i	−0.258843	−	0.210027i
$64$		−	0.546438i		−	0.0683048i
$65$	1.79618	+	0.236472i	0.222789	+	0.0293307i
$66$	2.31088	−	8.62434i	0.284450	−	1.06158i
$67$	3.97853	+	6.89102i	0.486055	+	0.841872i	0.999872	−	0.0160281i	$-0.00510213\pi$
$67$	3.97853	+	6.89102i	0.486055	+	0.841872i	−0.513817	+	0.857900i	$0.671769\pi$
$68$	0.685948	−	4.27512i	0.0831834	−	0.518434i
$69$	−6.05570			−0.729020
$70$	6.74824	+	7.12509i	0.806568	+	0.851612i
$71$	1.52214	+	3.67477i	0.180645	+	0.436115i	0.988100	−	0.153814i	$-0.0491557\pi$
$71$	1.52214	+	3.67477i	0.180645	+	0.436115i	−0.807455	+	0.589929i	$0.799156\pi$
$72$	−1.43666	−	0.829456i	−0.169312	−	0.0977523i
$73$	4.66349	+	3.57842i	0.545820	+	0.418823i	0.844520	−	0.535525i	$-0.179886\pi$
$73$	4.66349	+	3.57842i	0.545820	+	0.418823i	−0.298699	+	0.954347i	$0.596553\pi$
$74$	6.97049	−	0.917682i	0.810302	−	0.106678i
$75$	0.388260	−	0.297922i	0.0448324	−	0.0344011i
$76$	−2.29466	+	2.29466i	−0.263216	+	0.263216i
$77$	−9.82057	+	9.30114i	−1.11916	+	1.05996i
$78$	−1.37638	−	0.570116i	−0.155844	−	0.0645529i
$79$	−1.69621	−	2.21054i	−0.190838	−	0.248705i	0.688128	−	0.725589i	$-0.258433\pi$
$79$	−1.69621	−	2.21054i	−0.190838	−	0.248705i	−0.878966	+	0.476884i	$0.841766\pi$
$80$	8.42046	+	6.46125i	0.941436	+	0.722389i
$81$	−0.866025	+	0.500000i	−0.0962250	+	0.0555556i
$82$	−3.86793	−	0.509222i	−0.427141	−	0.0562342i
$83$	8.40583	+	8.40583i	0.922659	+	0.922659i	0.997217	−	0.0745575i	$-0.0237544\pi$
$83$	8.40583	+	8.40583i	0.922659	+	0.922659i	−0.0745575	+	0.997217i	$0.523754\pi$
$84$	−1.32334	−	2.44299i	−0.144389	−	0.266552i
$85$	−6.01492	−	6.36405i	−0.652410	−	0.690278i
$86$	−5.33833	+	9.24626i	−0.575647	+	0.997050i
$87$	−0.871612	+	3.25290i	−0.0934466	+	0.348747i
$88$	−5.16289	+	6.72841i	−0.550366	+	0.717251i
$89$	13.8392	+	7.99004i	1.46695	+	0.846943i	0.999316	−	0.0369808i	$-0.0117740\pi$
$89$	13.8392	+	7.99004i	1.46695	+	0.846943i	0.467632	+	0.883923i	$0.345107\pi$
$90$	3.42683	−	1.41944i	0.361219	−	0.149622i
$91$	1.32479	+	1.82717i	0.138876	+	0.191539i
$92$	−5.87520	−	2.43359i	−0.612532	−	0.253719i
$93$	−1.93776	−	7.23183i	−0.200937	−	0.749906i
$94$	2.39115	+	0.640707i	0.246628	+	0.0660839i
$95$	0.856654	+	6.50694i	0.0878909	+	0.667598i
$96$	−3.29346	−	4.29212i	−0.336137	−	0.438063i
$97$	−11.6960	+	4.84463i	−1.18755	+	0.491898i	−0.886955	−	0.461856i	$-0.847184\pi$
$97$	−11.6960	+	4.84463i	−1.18755	+	0.491898i	−0.300591	+	0.953753i	$0.597184\pi$
$98$	−0.663688	+	12.2072i	−0.0670426	+	1.23311i
$99$	1.95642	+	4.72322i	0.196628	+	0.474701i
$100$	0.496412	−	0.133013i	0.0496412	−	0.0133013i
$101$	7.50365	+	12.9967i	0.746641	+	1.29322i	0.949424	+	0.313996i	$0.101668\pi$
$101$	7.50365	+	12.9967i	0.746641	+	1.29322i	−0.202783	+	0.979224i	$0.564999\pi$
$102$	3.42319	+	6.33514i	0.338946	+	0.627272i
$103$	−0.846362	+	1.46594i	−0.0833945	+	0.144443i	−0.904706	−	0.426037i	$-0.859909\pi$
$103$	−0.846362	+	1.46594i	−0.0833945	+	0.144443i	0.821311	+	0.570480i	$0.193243\pi$
$104$	1.00063	+	1.00063i	0.0981195	+	0.0981195i
$105$	−5.54906	−	0.884446i	−0.541532	−	0.0863131i
$106$			13.6843i			1.32913i
$107$	−2.08709	+	15.8530i	−0.201767	+	1.53257i	0.528219	+	0.849108i	$0.322860\pi$
$107$	−2.08709	+	15.8530i	−0.201767	+	1.53257i	−0.729986	+	0.683462i	$0.760473\pi$
$108$	−1.04115	+	0.137070i	−0.100184	+	0.0131895i
$109$	−2.40923	−	18.2999i	−0.230762	−	1.75281i	−0.578925	−	0.815381i	$-0.696528\pi$
$109$	−2.40923	−	18.2999i	−0.230762	−	1.75281i	0.348163	−	0.937434i	$-0.386806\pi$
$110$	−4.90790	−	18.3165i	−0.467950	−	1.74641i
$111$	−2.84656	+	2.84656i	−0.270183	+	0.270183i
$112$	1.36923	+	13.1510i	0.129380	+	1.24265i
$113$	3.24517	−	7.83452i	0.305280	−	0.737010i	−0.694566	−	0.719429i	$-0.744404\pi$
$113$	3.24517	−	7.83452i	0.305280	−	0.737010i	0.999845	−	0.0175809i	$-0.00559647\pi$
$114$	0.704445	−	5.35079i	0.0659773	−	0.501148i
$115$	−11.1381	+	6.43060i	−1.03864	+	0.599657i
$116$	−2.15287	+	2.80567i	−0.199889	+	0.260500i
$117$	0.823963	−	0.220780i	0.0761754	−	0.0204111i
$118$	10.7094			0.985882
$119$	0.603522	−	10.8920i	0.0553248	−	0.998468i
$120$	−3.52323			−0.321625
$121$	14.6206	−	3.91759i	1.32915	−	0.356144i
$122$	2.65345	−	3.45805i	0.240232	−	0.313077i
$123$	1.93456	−	1.11692i	0.174433	−	0.100709i
$124$	1.02623	−	7.79501i	0.0921584	−	0.700012i
$125$	4.46151	−	10.7710i	0.399049	−	0.963390i
$126$	4.21938	+	1.88354i	0.375893	+	0.167799i
$127$	1.82255	−	1.82255i	0.161725	−	0.161725i	−0.621605	−	0.783331i	$-0.713519\pi$
$127$	1.82255	−	1.82255i	0.161725	−	0.161725i	0.783331	+	0.621605i	$0.213519\pi$
$128$	3.04747	+	11.3733i	0.269361	+	1.00527i
$129$	−0.797947	−	6.06101i	−0.0702553	−	0.533642i
$130$	−3.13696	+	0.412989i	−0.275130	+	0.0362215i
$131$	2.04668	−	15.5461i	0.178819	−	1.35827i	−0.632906	−	0.774229i	$-0.718138\pi$
$131$	2.04668	−	15.5461i	0.178819	−	1.35827i	0.811725	−	0.584040i	$-0.198529\pi$
$132$			5.36866i			0.467282i
$133$	−5.15152	+	6.34889i	−0.446693	+	0.550519i
$134$	−9.82646	−	9.82646i	−0.848877	−	0.848877i
$135$	−1.06191	+	1.83928i	−0.0913946	+	0.158300i
$136$	−0.701249	−	6.80382i	−0.0601316	−	0.583423i
$137$	8.37551	+	14.5068i	0.715569	+	1.23940i	0.962740	+	0.270429i	$0.0871656\pi$
$137$	8.37551	+	14.5068i	0.715569	+	1.23940i	−0.247171	+	0.968972i	$0.579501\pi$
$138$	10.2157	−	2.73728i	0.869616	−	0.233013i
$139$	−7.40536	−	17.8781i	−0.628114	−	1.51640i	−0.841963	−	0.539535i	$-0.818600\pi$
$139$	−7.40536	−	17.8781i	−0.628114	−	1.51640i	0.213849	−	0.976867i	$-0.431400\pi$
$140$	−5.02823	−	3.08807i	−0.424963	−	0.260990i
$141$	−1.30954	+	0.542430i	−0.110283	+	0.0456808i
$142$	−4.22884	−	5.51113i	−0.354876	−	0.462484i
$143$	−0.569226	−	4.32370i	−0.0476010	−	0.361566i
$144$	4.82720	+	1.29344i	0.402267	+	0.107787i
$145$	1.85115	+	6.90857i	0.153729	+	0.573726i
$146$	−9.48460	−	3.92865i	−0.784951	−	0.325137i
$147$	−3.95356	−	5.77662i	−0.326084	−	0.476448i
$148$	−3.90565	+	1.61778i	−0.321043	+	0.132980i
$149$	18.2103	+	10.5137i	1.49185	+	0.861318i	0.999956	−	0.00933956i	$-0.00297292\pi$
$149$	18.2103	+	10.5137i	1.49185	+	0.861318i	0.491890	+	0.870657i	$0.336306\pi$
$150$	−0.520310	+	0.678081i	−0.0424831	+	0.0553651i
$151$	3.68147	−	13.7394i	0.299593	−	1.11810i	−0.637907	−	0.770114i	$-0.720200\pi$
$151$	3.68147	−	13.7394i	0.299593	−	1.11810i	0.937500	−	0.347985i	$-0.113134\pi$
$152$	−2.56321	+	4.43960i	−0.207903	+	0.360099i
$153$	−3.76326	−	1.68461i	−0.304241	−	0.136192i
$154$	12.3626	−	20.1297i	0.996203	−	1.62209i
$155$	−11.2436	−	11.2436i	−0.903112	−	0.903112i
$156$	0.888129	+	0.116924i	0.0711072	+	0.00936144i
$157$	13.5740	−	7.83695i	1.08332	−	0.625457i	0.151532	−	0.988452i	$-0.451579\pi$
$157$	13.5740	−	7.83695i	1.08332	−	0.625457i	0.931791	+	0.362995i	$0.118246\pi$
$158$	3.86063	+	2.96236i	0.307135	+	0.235673i
$159$	−4.76990	−	6.21626i	−0.378278	−	0.492982i
$160$	−10.6154	−	4.39706i	−0.839225	−	0.347618i
$161$	−15.3576	−	4.56547i	−1.21035	−	0.359810i
$162$	1.23494	−	1.23494i	0.0970257	−	0.0970257i
$163$	−4.32731	+	3.32046i	−0.338941	+	0.260079i	−0.764181	−	0.645002i	$-0.776856\pi$
$163$	−4.32731	+	3.32046i	−0.338941	+	0.260079i	0.425240	+	0.905081i	$0.360190\pi$
$164$	2.32575	−	0.306190i	0.181610	−	0.0239095i
$165$	8.61404	+	6.60979i	0.670602	+	0.514571i
$166$	−17.9798	−	10.3807i	−1.39550	−	0.805695i
$167$	−0.320783	−	0.774438i	−0.0248229	−	0.0599278i	0.910982	−	0.412446i	$-0.135325\pi$
$167$	−0.320783	−	0.774438i	−0.0248229	−	0.0599278i	−0.935805	+	0.352518i	$0.885325\pi$
$168$	−3.01812	−	3.18667i	−0.232853	−	0.245857i
$169$	12.2723			0.944026
$170$	13.0236	+	8.01699i	0.998861	+	0.614875i
$171$	1.54511	+	2.67622i	0.118158	+	0.204655i
$172$	1.66156	−	6.20103i	0.126693	−	0.472824i
$173$	−3.24712	−	0.427492i	−0.246874	−	0.0325016i	0.00607347	−	0.999982i	$-0.498067\pi$
$173$	−3.24712	−	0.427492i	−0.246874	−	0.0325016i	−0.252948	+	0.967480i	$0.581400\pi$
$174$		−	5.88147i		−	0.445873i
$175$	1.20926	−	0.462835i	0.0914113	−	0.0349870i
$176$	9.77719	−	23.6042i	0.736984	−	1.77924i
$177$	−4.86490	+	3.73297i	−0.365668	+	0.280587i
$178$	−26.9576	−	7.22328i	−2.02056	−	0.541408i
$179$	−2.42169	−	0.648890i	−0.181006	−	0.0485003i	0.167178	−	0.985927i	$-0.446535\pi$
$179$	−2.42169	−	0.648890i	−0.181006	−	0.0485003i	−0.348183	+	0.937426i	$0.613201\pi$
$180$	−1.76941	+	1.35771i	−0.131884	+	0.101198i
$181$	−8.68431	+	20.9658i	−0.645499	+	1.55837i	0.173659	+	0.984806i	$0.444441\pi$
$181$	−8.68431	+	20.9658i	−0.645499	+	1.55837i	−0.819158	+	0.573568i	$0.805559\pi$
$182$	−3.06077	−	2.48352i	−0.226879	−	0.184091i
$183$			2.49577i			0.184493i
$184$	−9.95992	−	1.31125i	−0.734255	−	0.0966665i
$185$	−2.21284	+	8.25841i	−0.162691	+	0.607171i
$186$	6.53783	+	11.3239i	0.479377	+	0.830306i
$187$	−11.0499	+	17.9505i	−0.808047	+	1.31267i
$188$	−1.48849			−0.108560
$189$	−2.57325	+	0.615123i	−0.187177	+	0.0447436i
$190$	−4.38639	−	10.5897i	−0.318222	−	0.768256i
$191$	−0.906882	−	0.523588i	−0.0656197	−	0.0378855i	0.466831	−	0.884346i	$-0.345396\pi$
$191$	−0.906882	−	0.523588i	−0.0656197	−	0.0378855i	−0.532451	+	0.846461i	$0.678729\pi$
$192$	−0.433519	−	0.332651i	−0.0312865	−	0.0240070i
$193$	19.1229	−	2.51758i	1.37650	−	0.181219i	0.594295	−	0.804247i	$-0.297431\pi$
$193$	19.1229	−	2.51758i	1.37650	−	0.181219i	0.782200	+	0.623028i	$0.214098\pi$
$194$	17.5407	−	13.4594i	1.25935	−	0.966332i
$195$	1.28105	−	1.28105i	0.0917380	−	0.0917380i
$196$	−1.51428	−	7.19325i	−0.108163	−	0.513804i
$197$	12.4697	+	5.16513i	0.888431	+	0.368000i	0.779761	−	0.626078i	$-0.215341\pi$
$197$	12.4697	+	5.16513i	0.888431	+	0.368000i	0.108670	+	0.994078i	$0.465341\pi$
$198$	−5.43537	−	7.08351i	−0.386275	−	0.503403i
$199$	−1.38114	−	1.05979i	−0.0979066	−	0.0751264i	0.558648	−	0.829405i	$-0.311320\pi$
$199$	−1.38114	−	1.05979i	−0.0979066	−	0.0751264i	−0.656555	+	0.754278i	$0.727987\pi$
$200$	0.703087	−	0.405928i	0.0497158	−	0.0287034i
$201$	7.88899	+	1.03861i	0.556446	+	0.0732576i
$202$	−18.5330	−	18.5330i	−1.30398	−	1.30398i
$203$	−4.66287	+	7.59244i	−0.327269	+	0.532885i
$204$	−2.97410	−	3.14673i	−0.208229	−	0.220315i
$205$	2.37213	−	4.10865i	0.165677	−	0.286960i
$206$	0.765141	−	2.85554i	0.0533099	−	0.198955i
$207$	−3.68648	+	4.80431i	−0.256228	+	0.333922i
$208$	−3.69187	−	2.13150i	−0.255985	−	0.147793i
$209$	14.5958	−	6.04579i	1.00961	−	0.418196i
$210$	9.76078	−	1.01625i	0.673558	−	0.0701281i
$211$	13.7888	+	5.71150i	0.949258	+	0.393196i	0.802952	−	0.596044i	$-0.203262\pi$
$211$	13.7888	+	5.71150i	0.949258	+	0.393196i	0.146306	+	0.989239i	$0.453262\pi$
$212$	−2.12962	−	7.94785i	−0.146263	−	0.545860i
$213$	3.84201	+	1.02946i	0.263250	+	0.0705377i
$214$	−3.64503	−	27.6867i	−0.249169	−	1.89262i
$215$	−7.90390	−	10.3006i	−0.539041	−	0.702492i
$216$	−1.53263	+	0.634838i	−0.104283	+	0.0431952i
$217$	0.537886	−	19.8013i	0.0365141	−	1.34420i
$218$	12.3361	+	29.7821i	0.835509	+	2.01710i
$219$	5.67791	−	1.52139i	0.383677	−	0.102806i
$220$	5.70104	+	9.87448i	0.384364	+	0.665737i
$221$	2.72886	+	2.21891i	0.183563	+	0.149260i
$222$	3.51532	−	6.08871i	0.235933	−	0.408647i
$223$	6.35941	+	6.35941i	0.425857	+	0.425857i	0.887215	−	0.461357i	$-0.152637\pi$
$223$	6.35941	+	6.35941i	0.425857	+	0.425857i	−0.461357	+	0.887215i	$0.652637\pi$
$224$	−5.11653	−	13.3681i	−0.341863	−	0.893192i
$225$		−	0.489391i		−	0.0326260i
$226$	−1.93310	+	14.6833i	−0.128588	+	0.976722i
$227$	−2.56388	+	0.337541i	−0.170171	+	0.0224034i	−0.215130	−	0.976585i	$-0.569018\pi$
$227$	−2.56388	+	0.337541i	−0.170171	+	0.0224034i	0.0449592	+	0.998989i	$0.485684\pi$
$228$	0.423576	+	3.21738i	0.0280520	+	0.213076i
$229$	3.53552	+	13.1947i	0.233634	+	0.871932i	0.978760	+	0.205009i	$0.0657224\pi$
$229$	3.53552	+	13.1947i	0.233634	+	0.871932i	−0.745126	+	0.666923i	$0.767611\pi$
$230$	15.8828	−	15.8828i	1.04728	−	1.04728i
$231$	1.40071	+	13.4534i	0.0921599	+	0.885166i
$232$	−2.13791	+	5.16138i	−0.140361	+	0.338861i
$233$	2.99590	−	22.7561i	0.196268	−	1.49080i	−0.555579	−	0.831464i	$-0.687503\pi$
$233$	2.99590	−	22.7561i	0.196268	−	1.49080i	0.751846	−	0.659338i	$-0.229163\pi$
$234$	−1.29019	+	0.744892i	−0.0843424	+	0.0486951i
$235$	−1.83260	+	2.38830i	−0.119546	+	0.155795i
$236$	−6.22005	+	1.66666i	−0.404891	+	0.108490i
$237$	−2.78633			−0.180991
$238$	3.90527	+	18.6471i	0.253141	+	1.20871i
$239$	8.95308			0.579127			0.289563	−	0.957159i	$-0.406490\pi$
$239$	8.95308			0.579127			0.289563	+	0.957159i	$0.406490\pi$
$240$	10.2521	−	2.74704i	0.661771	−	0.177321i
$241$	−3.22689	+	4.20536i	−0.207862	+	0.270891i	−0.885637	−	0.464378i	$-0.846278\pi$
$241$	−3.22689	+	4.20536i	−0.207862	+	0.270891i	0.677775	+	0.735270i	$0.262944\pi$
$242$	−22.8935	+	13.2176i	−1.47165	+	0.849658i
$243$	−0.130526	+	0.991445i	−0.00837326	+	0.0636012i
$244$	−1.00297	+	2.42138i	−0.0642086	+	0.155013i
$245$	−13.4060	−	6.42652i	−0.856475	−	0.410575i
$246$	−2.75864	+	2.75864i	−0.175884	+	0.175884i
$247$	−0.682261	−	2.54623i	−0.0434112	−	0.162013i
$248$	−1.62116	−	12.3139i	−0.102944	−	0.781935i
$249$	11.7859	−	1.55165i	0.746903	−	0.0983317i
$250$	−2.65766	+	20.1869i	−0.168085	+	1.27673i
$251$			6.18240i			0.390230i	0.980780	+	0.195115i	$0.0625079\pi$
$251$			6.18240i			0.390230i	−0.980780	+	0.195115i	$0.937492\pi$
$252$	−2.74375	−	0.437317i	−0.172840	−	0.0275484i
$253$	21.8913	+	21.8913i	1.37630	+	1.37630i
$254$	−2.25074	+	3.89839i	−0.141224	+	0.244607i
$255$	−8.71059	+	0.897773i	−0.545478	+	0.0562207i
$256$	−9.73545	−	16.8623i	−0.608466	−	1.05389i
$257$	−17.2782	+	4.62968i	−1.07778	+	0.288791i	−0.753688	−	0.657233i	$-0.771727\pi$
$257$	−17.2782	+	4.62968i	−1.07778	+	0.288791i	−0.324097	+	0.946024i	$0.605060\pi$
$258$	4.08578	+	9.86395i	0.254370	+	0.614103i
$259$	−9.36511	+	5.07299i	−0.581920	+	0.315220i
$260$	1.75768	−	0.728056i	0.109007	−	0.0451521i
$261$	2.05010	+	2.67174i	0.126898	+	0.165376i
$262$	3.57445	+	27.1507i	0.220831	+	1.67737i
$263$	−30.1737	−	8.08501i	−1.86059	−	0.498543i	−0.860644	−	0.509206i	$-0.829939\pi$
$263$	−30.1737	−	8.08501i	−1.86059	−	0.498543i	−0.999943	+	0.0106635i	$0.996606\pi$
$264$	2.19504	+	8.19200i	0.135095	+	0.504183i
$265$	−15.3743	−	6.36825i	−0.944436	−	0.391198i
$266$	5.82055	−	13.0389i	0.356881	−	0.799464i
$267$	14.7637	−	6.11531i	0.903522	−	0.374251i
$268$	7.23647	+	4.17798i	0.442038	+	0.255211i
$269$	−13.1100	+	17.0853i	−0.799333	+	1.04171i	0.198764	+	0.980047i	$0.436307\pi$
$269$	−13.1100	+	17.0853i	−0.799333	+	1.04171i	−0.998097	+	0.0616638i	$0.980359\pi$
$270$	0.960004	−	3.58278i	0.0584240	−	0.218041i
$271$	−0.747499	+	1.29471i	−0.0454073	+	0.0786478i	−0.887836	−	0.460160i	$-0.847792\pi$
$271$	−0.747499	+	1.29471i	−0.0454073	+	0.0786478i	0.842428	+	0.538808i	$0.181125\pi$
$272$	7.34544	+	19.2514i	0.445383	+	1.16729i
$273$	2.25607	+	0.0612844i	0.136544	+	0.00370910i
$274$	−20.6864	−	20.6864i	−1.24971	−	1.24971i
$275$	−2.48054	−	0.326570i	−0.149582	−	0.0196929i
$276$	−5.50729	+	3.17964i	−0.331500	+	0.191392i
$277$	13.6673	+	10.4873i	0.821189	+	0.630121i	0.931486	−	0.363778i	$-0.118513\pi$
$277$	13.6673	+	10.4873i	0.821189	+	0.630121i	−0.110296	+	0.993899i	$0.535180\pi$
$278$	20.5737	+	26.8122i	1.23393	+	1.60809i
$279$	−6.91704	−	2.86513i	−0.414112	−	0.171531i
$280$	−8.93513	−	2.65621i	−0.533976	−	0.158739i
$281$	−6.19304	+	6.19304i	−0.369446	+	0.369446i	−0.867275	−	0.497829i	$-0.834131\pi$
$281$	−6.19304	+	6.19304i	−0.369446	+	0.369446i	0.497829	+	0.867275i	$0.334131\pi$
$282$	1.96395	−	1.50699i	0.116951	−	0.0897399i
$283$	−19.6653	+	2.58899i	−1.16898	+	0.153900i	−0.689923	−	0.723883i	$-0.742356\pi$
$283$	−19.6653	+	2.58899i	−1.16898	+	0.153900i	−0.479060	+	0.877782i	$0.659022\pi$
$284$	3.31379	+	2.54276i	0.196637	+	0.150885i
$285$	5.68380	+	3.28154i	0.336679	+	0.194382i
$286$	2.91465	+	7.03658i	0.172347	+	0.416081i
$287$	5.74821	−	1.37408i	0.339306	−	0.0811095i
$288$	−5.41010			−0.318793
$289$	−3.46744	−	16.6426i	−0.203967	−	0.978978i
$290$	−6.24559	−	10.8177i	−0.366754	−	0.635236i
$291$	−3.27655	+	12.2283i	−0.192075	+	0.716833i
$292$	6.12007	+	0.805722i	0.358150	+	0.0471513i
$293$		−	32.7527i		−	1.91343i	−0.291019	−	0.956717i	$-0.593994\pi$
$293$		−	32.7527i		−	1.91343i	0.291019	−	0.956717i	$-0.406006\pi$
$294$	9.28060	+	7.95782i	0.541256	+	0.464109i
$295$	−4.98384	+	12.0321i	−0.290170	+	0.700533i
$296$	−5.29816	+	4.06542i	−0.307949	+	0.236298i
$297$	4.93818	+	1.32318i	0.286542	+	0.0767787i
$298$	−35.4723	−	9.50478i	−2.05486	−	0.550597i
$299$	4.09822	−	3.14467i	0.237006	−	0.181861i
$300$	0.196670	−	0.474804i	0.0113548	−	0.0274128i
$301$	2.54583	−	15.9727i	0.146739	−	0.920650i
$302$			24.8418i			1.42949i
$303$	14.8789	+	1.95885i	0.854771	+	0.112533i
$304$	3.99704	−	14.9171i	0.229246	−	0.855557i
$305$	2.65028	+	4.59043i	0.151755	+	0.262847i
$306$	7.10991	+	1.14079i	0.406446	+	0.0652148i
$307$	−12.0880			−0.689898			−0.344949	−	0.938621i	$-0.612104\pi$
$307$	−12.0880			−0.689898			−0.344949	+	0.938621i	$0.612104\pi$
$308$	−4.04751	+	13.6153i	−0.230628	+	0.775802i
$309$	0.647777	+	1.56387i	0.0368507	+	0.0889656i
$310$	24.0498	+	13.8852i	1.36594	+	0.788625i
$311$	3.70408	+	2.84224i	0.210039	+	0.161168i	0.708424	−	0.705787i	$-0.249407\pi$
$311$	3.70408	+	2.84224i	0.210039	+	0.161168i	−0.498385	+	0.866956i	$0.666073\pi$
$312$	1.40299	−	0.184708i	0.0794289	−	0.0104570i
$313$	17.1108	−	13.1296i	0.967161	−	0.742129i	0.000981626	−	1.00000i	$-0.499688\pi$
$313$	17.1108	−	13.1296i	0.967161	−	0.742129i	0.966179	+	0.257871i	$0.0830209\pi$
$314$	−19.3563	+	19.3563i	−1.09234	+	1.09234i
$315$	−4.07973	+	3.86395i	−0.229867	+	0.217709i
$316$	−2.70328	−	1.11973i	−0.152071	−	0.0629900i
$317$	14.1556	+	18.4479i	0.795056	+	1.03614i	0.998373	+	0.0570237i	$0.0181611\pi$
$317$	14.1556	+	18.4479i	0.795056	+	1.03614i	−0.203317	+	0.979113i	$0.565172\pi$
$318$	10.8565	+	8.33046i	0.608800	+	0.467149i
$319$	14.9101	−	8.60835i	0.834805	−	0.481975i
$320$	−1.15061	−	0.151480i	−0.0643210	−	0.00846801i
$321$	11.3065	+	11.3065i	0.631068	+	0.631068i
$322$	27.9713	+	0.759817i	1.55878	+	0.0423430i
$323$	−5.20582	+	11.6293i	−0.289659	+	0.647073i
$324$	−0.525065	+	0.909440i	−0.0291703	+	0.0505244i
$325$	−0.108048	+	0.403240i	−0.00599341	+	0.0223677i
$326$	5.79906	−	7.55748i	0.321180	−	0.418570i
$327$	−15.9850	−	9.22892i	−0.883970	−	0.510360i
$328$	3.42365	−	1.41812i	0.189039	−	0.0783027i
$329$	−3.73002	+	0.388355i	−0.205643	+	0.0214107i
$330$	−17.5192	−	7.25670i	−0.964402	−	0.399468i
$331$	5.40573	+	20.1744i	0.297126	+	1.10889i	0.939514	+	0.342509i	$0.111277\pi$
$331$	5.40573	+	20.1744i	0.297126	+	1.10889i	−0.642389	+	0.766379i	$0.722057\pi$
$332$	12.0582	+	3.23098i	0.661780	+	0.177323i
$333$	0.525452	+	3.99120i	0.0287946	+	0.218717i
$334$	0.891205	+	1.16144i	0.0487646	+	0.0635512i
$335$	15.6130	−	6.46711i	0.853028	−	0.353336i
$336$	11.2669	+	6.91955i	0.614662	+	0.377492i
$337$	3.46056	+	8.35453i	0.188509	+	0.455100i	0.989673	−	0.143344i	$-0.0457856\pi$
$337$	3.46056	+	8.35453i	0.188509	+	0.455100i	−0.801164	+	0.598445i	$0.795786\pi$
$338$	−20.7029	+	5.54732i	−1.12609	+	0.301734i
$339$	−4.24001	−	7.34392i	−0.230286	−	0.398867i
$340$	−8.81175	−	2.62949i	−0.477884	−	0.142604i
$341$	−19.1380	+	33.1481i	−1.03638	+	1.79507i
$342$	−3.81623	−	3.81623i	−0.206358	−	0.206358i
$343$	−5.67139	−	17.6305i	−0.306226	−	0.951959i
$344$		−	10.1414i		−	0.546790i
$345$	−1.67872	+	12.7512i	−0.0903795	+	0.686500i
$346$	5.67098	−	0.746599i	0.304874	−	0.0401374i
$347$	1.28228	+	9.73991i	0.0688366	+	0.522866i	0.990774	+	0.135526i	$0.0432725\pi$
$347$	1.28228	+	9.73991i	0.0688366	+	0.522866i	−0.921937	+	0.387339i	$0.873394\pi$
$348$	0.915306	+	3.41597i	0.0490656	+	0.183115i
$349$	16.5993	−	16.5993i	0.888542	−	0.888542i	−0.105841	−	0.994383i	$-0.533753\pi$
$349$	16.5993	−	16.5993i	0.888542	−	0.888542i	0.994383	+	0.105841i	$0.0337534\pi$
$350$	−1.83075	+	1.32739i	−0.0978578	+	0.0709518i
$351$	0.326440	−	0.788096i	0.0174241	−	0.0420655i
$352$	−3.61015	+	27.4218i	−0.192422	+	1.46159i
$353$	−26.5641	+	15.3368i	−1.41386	+	0.816294i	−0.995750	−	0.0921004i	$-0.970642\pi$
$353$	−26.5641	+	15.3368i	−1.41386	+	0.816294i	−0.418114	+	0.908395i	$0.637309\pi$
$354$	6.51948	−	8.49636i	0.346507	−	0.451576i
$355$	8.15974	−	2.18639i	0.433074	−	0.116042i
$356$	16.7812			0.889400
$357$	−8.27381	−	7.10944i	−0.437896	−	0.376271i
$358$	4.37859			0.231416
$359$	22.0096	−	5.89746i	1.16162	−	0.311256i	0.374009	−	0.927425i	$-0.377983\pi$
$359$	22.0096	−	5.89746i	1.16162	−	0.311256i	0.787614	+	0.616169i	$0.211316\pi$
$360$	−2.14481	+	2.79516i	−0.113041	+	0.147318i
$361$	−8.18437	+	4.72525i	−0.430756	+	0.248697i
$362$	5.17312	−	39.2937i	0.271893	−	2.06523i
$363$	5.79245	−	13.9842i	0.304025	−	0.733980i
$364$	2.16420	+	0.966100i	0.113435	+	0.0506374i
$365$	8.82769	−	8.82769i	0.462062	−	0.462062i
$366$	−1.12813	−	4.21025i	−0.0589685	−	0.220073i
$367$	−0.373911	−	2.84013i	−0.0195180	−	0.148254i	0.978911	−	0.204288i	$-0.0654878\pi$
$367$	−0.373911	−	2.84013i	−0.0195180	−	0.148254i	−0.998429	+	0.0560339i	$0.982154\pi$
$368$	30.0044	−	3.95015i	1.56409	−	0.205916i
$369$	0.291574	−	2.21472i	0.0151787	−	0.115294i
$370$		−	14.9318i		−	0.776267i
$371$	−7.41025	−	19.3609i	−0.384721	−	1.00517i
$372$	−5.55946	−	5.55946i	−0.288245	−	0.288245i
$373$	14.7967	−	25.6287i	0.766145	−	1.32700i	−0.173494	−	0.984835i	$-0.555506\pi$
$373$	14.7967	−	25.6287i	0.766145	−	1.32700i	0.939639	−	0.342167i	$-0.111161\pi$
$374$	10.5267	−	35.2763i	0.544323	−	1.82409i
$375$	−5.82924	−	10.0965i	−0.301021	−	0.521383i
$376$	−2.27128	+	0.608588i	−0.117132	+	0.0313855i
$377$	−1.09934	−	2.65403i	−0.0566187	−	0.136690i
$378$	4.06291	−	2.20084i	0.208973	−	0.113199i
$379$	−18.3943	+	7.61918i	−0.944854	+	0.391371i	−0.801294	−	0.598271i	$-0.795855\pi$
$379$	−18.3943	+	7.61918i	−0.944854	+	0.391371i	−0.143559	+	0.989642i	$0.545855\pi$
$380$	4.19564	+	5.46787i	0.215232	+	0.280496i
$381$	−0.336429	−	2.55543i	−0.0172358	−	0.130919i
$382$	1.76654	+	0.473342i	0.0903840	+	0.0242183i
$383$	−1.74357	−	6.50708i	−0.0890921	−	0.332496i	0.906966	−	0.421205i	$-0.138393\pi$
$383$	−1.74357	−	6.50708i	−0.0890921	−	0.332496i	−0.996058	+	0.0887087i	$0.971726\pi$
$384$	10.8783	+	4.50592i	0.555128	+	0.229942i
$385$	16.8625	+	23.2571i	0.859395	+	1.18529i
$386$	−31.1214	+	12.8909i	−1.58404	+	0.656130i
$387$	−5.29428	−	3.05666i	−0.269123	−	0.155379i
$388$	−8.09303	+	10.5470i	−0.410862	+	0.535445i
$389$	5.62263	−	20.9839i	0.285079	−	1.06393i	−0.663703	−	0.747996i	$-0.731016\pi$
$389$	5.62263	−	20.9839i	0.285079	−	1.06393i	0.948782	−	0.315932i	$-0.102317\pi$
$390$	−1.58202	+	2.74013i	−0.0801085	+	0.138752i
$391$	−24.9584	−	0.703900i	−1.26220	−	0.0355978i
$392$	−5.25167	−	10.3570i	−0.265249	−	0.523107i
$393$	−11.0876	−	11.0876i	−0.559296	−	0.559296i
$394$	−23.3706	−	3.07679i	−1.17739	−	0.155007i
$395$	−5.12484	+	2.95883i	−0.257859	+	0.148875i
$396$	4.25925	+	3.26823i	0.214035	+	0.164235i
$397$	15.1662	+	19.7649i	0.761168	+	0.991974i	0.999782	+	0.0208593i	$0.00664021\pi$
$397$	15.1662	+	19.7649i	0.761168	+	0.991974i	−0.238614	+	0.971114i	$0.576693\pi$
$398$	2.80897	+	1.16351i	0.140801	+	0.0583216i
$399$	1.90087	+	7.95193i	0.0951625	+	0.398095i
$400$	−1.72939	+	1.72939i	−0.0864694	+	0.0864694i
$401$	19.0488	−	14.6167i	0.951251	−	0.729921i	−0.0116057	−	0.999933i	$-0.503694\pi$
$401$	19.0488	−	14.6167i	0.951251	−	0.729921i	0.962857	+	0.270012i	$0.0870276\pi$
$402$	−13.7778	+	1.81388i	−0.687175	+	0.0904683i
$403$	5.06682	+	3.88791i	0.252396	+	0.193670i
$404$	13.6482	+	7.87981i	0.679025	+	0.392035i
$405$	0.812751	+	1.96215i	0.0403859	+	0.0975002i
$406$	4.43412	−	14.9158i	0.220062	−	0.740258i
$407$	20.5806			1.02014
$408$	−5.82473	−	3.58557i	−0.288367	−	0.177512i
$409$	7.05930	+	12.2271i	0.349060	+	0.604589i	0.986083	−	0.166256i	$-0.0531677\pi$
$409$	7.05930	+	12.2271i	0.349060	+	0.604589i	−0.637023	+	0.770845i	$0.719834\pi$
$410$	−2.14449	+	8.00334i	−0.105909	+	0.395257i
$411$	16.6077	+	2.18645i	0.819199	+	0.107850i
$412$			1.77758i			0.0875751i
$413$	−15.1520	+	5.79932i	−0.745582	+	0.285366i
$414$	4.04728	−	9.77099i	0.198913	−	0.480218i
$415$	20.0299	−	15.3695i	0.983231	−	0.754460i
$416$	4.45772	+	1.19444i	0.218558	+	0.0585624i
$417$	−18.6918	−	5.00844i	−0.915339	−	0.245264i
$418$	−21.8897	+	16.7965i	−1.07066	+	0.821545i
$419$	4.00889	−	9.67833i	0.195847	−	0.472817i	−0.795197	−	0.606351i	$-0.792633\pi$
$419$	4.00889	−	9.67833i	0.195847	−	0.472817i	0.991044	+	0.133534i	$0.0426325\pi$
$420$	−5.51092	+	2.10927i	−0.268906	+	0.102922i
$421$			10.8298i			0.527814i	0.964548	+	0.263907i	$0.0850113\pi$
$421$			10.8298i			0.527814i	−0.964548	+	0.263907i	$0.914989\pi$
$422$	−25.8427	−	3.40226i	−1.25800	−	0.165619i
$423$	−0.366860	+	1.36914i	−0.0178373	+	0.0665698i
$424$	−6.49914	−	11.2568i	−0.315626	−	0.546680i
$425$	1.63483	−	1.18275i	0.0793008	−	0.0573716i
$426$	−6.94663			−0.336565
$427$	−1.88160	+	6.32943i	−0.0910568	+	0.306303i
$428$	6.42579	+	15.5132i	0.310602	+	0.749860i
$429$	−3.77674	−	2.18050i	−0.182343	−	0.105276i
$430$	17.9895	+	13.8039i	0.867532	+	0.665681i
$431$	−8.39852	+	1.10569i	−0.404543	+	0.0532591i	−0.330052	−	0.943963i	$-0.607066\pi$
$431$	−8.39852	+	1.10569i	−0.404543	+	0.0532591i	−0.0744904	+	0.997222i	$0.523733\pi$
$432$	3.96477	−	3.04228i	0.190755	−	0.146372i
$433$	15.7387	−	15.7387i	0.756353	−	0.756353i	−0.219304	−	0.975657i	$-0.570379\pi$
$433$	15.7387	−	15.7387i	0.756353	−	0.756353i	0.975657	+	0.219304i	$0.0703786\pi$
$434$	8.04314	+	33.6470i	0.386083	+	1.61511i
$435$	6.60785	+	2.73706i	0.316822	+	0.131232i
$436$	−11.7997	−	15.3777i	−0.565103	−	0.736457i
$437$	14.8464	+	11.3920i	0.710200	+	0.544955i
$438$	−8.89066	+	5.13303i	−0.424812	+	0.245266i
$439$	−7.72189	−	1.01661i	−0.368546	−	0.0485200i	−0.0560210	−	0.998430i	$-0.517841\pi$
$439$	−7.72189	−	1.01661i	−0.368546	−	0.0485200i	−0.312525	+	0.949910i	$0.601175\pi$
$440$	12.7365	+	12.7365i	0.607187	+	0.607187i
$441$	−6.98968	−	0.380018i	−0.332842	−	0.0180961i
$442$	−5.60644	−	2.50970i	−0.266671	−	0.119374i
$443$	−0.0838013	+	0.145148i	−0.00398152	+	0.00689619i	−0.868009	−	0.496548i	$-0.834601\pi$
$443$	−0.0838013	+	0.145148i	−0.00398152	+	0.00689619i	0.864028	+	0.503444i	$0.167934\pi$
$444$	−1.09414	+	4.08340i	−0.0519258	+	0.193790i
$445$	20.6606	−	26.9255i	0.979408	−	1.27639i
$446$	−13.6026	−	7.85346i	−0.644101	−	0.371872i
$447$	19.4268	−	8.04686i	0.918857	−	0.380603i
$448$	−0.848641	−	1.17046i	−0.0400945	−	0.0552990i
$449$	−21.2301	−	8.79381i	−1.00191	−	0.415006i	−0.179414	−	0.983774i	$-0.557420\pi$
$449$	−21.2301	−	8.79381i	−1.00191	−	0.415006i	−0.822498	+	0.568768i	$0.807420\pi$
$450$	0.221213	+	0.825579i	0.0104281	+	0.0389182i
$451$	−11.0311	−	2.95576i	−0.519432	−	0.139181i
$452$	−1.16235	−	8.82895i	−0.0546725	−	0.415279i
$453$	−8.65908	−	11.2847i	−0.406839	−	0.530203i
$454$	4.17257	−	1.72834i	0.195829	−	0.0811148i
$455$	4.21463	−	2.28303i	0.197585	−	0.107030i
$456$	1.96179	+	4.73619i	0.0918694	+	0.221792i
$457$	−20.8091	+	5.57578i	−0.973409	+	0.260824i	−0.710267	−	0.703933i	$-0.751426\pi$
$457$	−20.8091	+	5.57578i	−0.973409	+	0.260824i	−0.263142	+	0.964757i	$0.584759\pi$
$458$	−11.9285	−	20.6608i	−0.557382	−	0.965415i
$459$	−3.62741	+	1.96007i	−0.169313	+	0.0914882i
$460$	−6.75297	+	11.6965i	−0.314859	+	0.545352i
$461$	−6.88128	−	6.88128i	−0.320493	−	0.320493i	0.528463	−	0.848956i	$-0.322768\pi$
$461$	−6.88128	−	6.88128i	−0.320493	−	0.320493i	−0.848956	+	0.528463i	$0.822768\pi$
$462$	−8.44408	−	22.0620i	−0.392854	−	1.02642i
$463$			14.7056i			0.683429i	0.939804	+	0.341714i	$0.111008\pi$
$463$			14.7056i			0.683429i	−0.939804	+	0.341714i	$0.888992\pi$
$464$	2.19673	−	16.6858i	0.101981	−	0.774619i
$465$	−15.7649	+	2.07549i	−0.731079	+	0.0962484i
$466$	5.23222	+	39.7427i	0.242378	+	1.84104i
$467$	6.45656	+	24.0962i	0.298774	+	1.11504i	0.938173	+	0.346166i	$0.112516\pi$
$467$	6.45656	+	24.0962i	0.298774	+	1.11504i	−0.639399	+	0.768875i	$0.720817\pi$
$468$	0.633421	−	0.633421i	0.0292799	−	0.0292799i
$469$	19.2240	+	8.58158i	0.887680	+	0.396261i
$470$	2.01196	−	4.85731i	0.0928050	−	0.224051i
$471$	2.04586	−	15.5398i	0.0942681	−	0.716037i
$472$	−8.80969	+	5.08628i	−0.405499	+	0.234115i
$473$	−19.0260	+	24.7951i	−0.874814	+	1.14008i
$474$	4.70040	−	1.25947i	0.215897	−	0.0578493i
$475$	−1.51233			−0.0693904
$476$	−5.17015	−	10.2225i	−0.236973	−	0.468548i
$477$	−7.83542			−0.358759
$478$	−15.1034	+	4.04695i	−0.690815	+	0.185103i
$479$	4.66618	−	6.08109i	0.213203	−	0.277852i	−0.674493	−	0.738281i	$-0.735638\pi$
$479$	4.66618	−	6.08109i	0.213203	−	0.277852i	0.887696	+	0.460429i	$0.152304\pi$
$480$	−9.95070	+	5.74504i	−0.454185	+	0.262224i
$481$	0.448226	−	3.40461i	0.0204373	−	0.155237i
$482$	3.54271	−	8.55286i	0.161366	−	0.389572i
$483$	−12.9712	+	9.40474i	−0.590208	+	0.427931i
$484$	11.2396	−	11.2396i	0.510891	−	0.510891i
$485$	6.95881	+	25.9706i	0.315983	+	1.17927i
$486$	−0.227959	−	1.73152i	−0.0103404	−	0.0785434i
$487$	−28.5121	+	3.75369i	−1.29201	+	0.170096i	−0.745018	−	0.667045i	$-0.767559\pi$
$487$	−28.5121	+	3.75369i	−1.29201	+	0.170096i	−0.546988	+	0.837140i	$0.684226\pi$
$488$	−0.540413	+	4.10484i	−0.0244633	+	0.185818i
$489$			5.45445i			0.246659i
$490$	25.5201	+	4.78150i	1.15288	+	0.216006i
$491$	−16.9095	−	16.9095i	−0.763114	−	0.763114i	0.213770	−	0.976884i	$-0.431426\pi$
$491$	−16.9095	−	16.9095i	−0.763114	−	0.763114i	−0.976884	+	0.213770i	$0.931426\pi$
$492$	1.17291	−	2.03154i	0.0528788	−	0.0915887i
$493$	−3.97043	+	13.3054i	−0.178819	+	0.599245i
$494$	2.30189	+	3.98698i	0.103567	+	0.179383i
$495$	10.4878	−	2.81020i	0.471391	−	0.126309i
$496$	14.3184	+	34.5678i	0.642917	+	1.55214i
$497$	8.96745	+	5.50733i	0.402245	+	0.247037i
$498$	−19.1809	+	7.94501i	−0.859519	+	0.356024i
$499$	−26.0788	−	33.9866i	−1.16745	−	1.52145i	−0.808909	−	0.587934i	$-0.799941\pi$
$499$	−26.0788	−	33.9866i	−1.16745	−	1.52145i	−0.358540	−	0.933515i	$-0.616725\pi$
$500$	−1.59802	−	12.1382i	−0.0714657	−	0.542836i
$501$	−0.809683	−	0.216954i	−0.0361740	−	0.00969279i
$502$	−2.79455	−	10.4294i	−0.124727	−	0.465488i
$503$	17.0199	+	7.04989i	0.758881	+	0.314339i	0.728360	−	0.685195i	$-0.240283\pi$
$503$	17.0199	+	7.04989i	0.758881	+	0.314339i	0.0305218	+	0.999534i	$0.490283\pi$
$504$	−4.36547	+	0.454515i	−0.194453	+	0.0202457i
$505$	29.4466	−	12.1972i	1.31036	−	0.542768i
$506$	−46.8249	−	27.0344i	−2.08162	−	1.20182i
$507$	7.47093	−	9.73630i	0.331796	−	0.432404i
$508$	0.700543	−	2.61446i	0.0310816	−	0.115998i
$509$	−2.38543	+	4.13168i	−0.105732	+	0.183134i	−0.914037	−	0.405631i	$-0.867052\pi$
$509$	−2.38543	+	4.13168i	−0.105732	+	0.183134i	0.808305	+	0.588764i	$0.200385\pi$
$510$	14.2885	−	5.45184i	0.632707	−	0.241412i
$511$	15.5465	+	0.422309i	0.687738	+	0.0186818i
$512$	7.39360	+	7.39360i	0.326754	+	0.326754i
$513$	3.06379	+	0.403356i	0.135270	+	0.0178086i
$514$	27.0548	−	15.6201i	1.19334	−	0.688973i
$515$	2.85214	+	2.18852i	0.125680	+	0.0964377i
$516$	−3.90811	−	5.09315i	−0.172045	−	0.224213i
$517$	6.69487	+	2.77311i	0.294440	+	0.121961i
$518$	13.5054	−	12.7911i	0.593394	−	0.562009i
$519$	−2.31588	+	2.31588i	−0.101656	+	0.101656i
$520$	2.38436	−	1.82958i	0.104561	−	0.0802325i
$521$	0.562089	−	0.0740004i	0.0246255	−	0.00324201i	−0.118203	−	0.992989i	$-0.537713\pi$
$521$	0.562089	−	0.0740004i	0.0246255	−	0.00324201i	0.142829	+	0.989747i	$0.454380\pi$
$522$	−4.66609	−	3.58041i	−0.204229	−	0.156710i
$523$	−12.7271	−	7.34801i	−0.556518	−	0.321306i	0.195229	−	0.980758i	$-0.437455\pi$
$523$	−12.7271	−	7.34801i	−0.556518	−	0.321306i	−0.751747	+	0.659452i	$0.770788\pi$
$524$	−6.30138	−	15.2129i	−0.275277	−	0.664578i
$525$	0.368958	−	1.24113i	0.0161027	−	0.0541671i
$526$	54.5561			2.37876
$527$	−7.14582	−	30.0310i	−0.311277	−	1.30817i
$528$	−12.7745	−	22.1261i	−0.555940	−	0.962915i
$529$	−3.53844	+	13.2056i	−0.153845	+	0.574158i
$530$	28.8143	+	3.79347i	1.25161	+	0.164778i
$531$			6.13207i			0.266109i
$532$	−1.35141	+	8.47881i	−0.0585911	+	0.367603i
$533$	−0.729213	+	1.76048i	−0.0315857	+	0.0762547i
$534$	−22.1414	+	16.9897i	−0.958152	+	0.735216i
$535$	32.8024	+	8.78937i	1.41817	+	0.379997i
$536$	12.7503	+	3.41643i	0.550728	+	0.147567i
$537$	−1.98903	+	1.52624i	−0.0858331	+	0.0658620i
$538$	14.3931	−	34.7481i	0.620533	−	1.49810i
$539$	−6.59038	+	35.1746i	−0.283868	+	1.51508i
$540$			2.23029i			0.0959763i
$541$	−29.8326	−	3.92754i	−1.28260	−	0.168858i	−0.541759	−	0.840534i	$-0.682241\pi$
$541$	−29.8326	−	3.92754i	−1.28260	−	0.168858i	−0.740845	+	0.671676i	$0.765575\pi$
$542$	0.675766	−	2.52199i	0.0290266	−	0.108329i
$543$	11.3466	+	19.6529i	0.486929	+	0.843386i
$544$	−13.0750	−	18.0727i	−0.560585	−	0.774859i
$545$	−39.2011			−1.67919
$546$	−3.83359	+	0.916400i	−0.164062	+	0.0392183i
$547$	−4.73826	−	11.4392i	−0.202593	−	0.489104i	0.789629	−	0.613585i	$-0.210273\pi$
$547$	−4.73826	−	11.4392i	−0.202593	−	0.489104i	−0.992222	+	0.124481i	$0.960273\pi$
$548$	15.2341	+	8.79538i	0.650766	+	0.375720i
$549$	1.98003	+	1.51933i	0.0845056	+	0.0648434i
$550$	4.33218	−	0.570342i	0.184725	−	0.0243195i
$551$	8.25627	−	6.33526i	0.351729	−	0.269891i
$552$	−7.10350	+	7.10350i	−0.302345	+	0.302345i
$553$	−7.06630	−	2.10065i	−0.300490	−	0.0893287i
$554$	−27.7966	−	11.5137i	−1.18096	−	0.489171i
$555$	5.20475	+	6.78296i	0.220929	+	0.287921i
$556$	−16.1219	−	12.3708i	−0.683721	−	0.524638i
$557$	19.9975	−	11.5455i	0.847319	−	0.489200i	−0.0124263	−	0.999923i	$-0.503956\pi$
$557$	19.9975	−	11.5455i	0.847319	−	0.489200i	0.859745	+	0.510723i	$0.170622\pi$
$558$	12.9638	+	1.70672i	0.548802	+	0.0722511i
$559$	3.68744	+	3.68744i	0.155962	+	0.155962i
$560$	28.0710	+	0.762527i	1.18622	+	0.0322226i
$561$	7.51431	+	19.6940i	0.317254	+	0.831482i
$562$	7.64801	−	13.2467i	0.322612	−	0.558780i
$563$	−5.87269	+	21.9172i	−0.247505	+	0.923700i	0.724603	+	0.689166i	$0.242023\pi$
$563$	−5.87269	+	21.9172i	−0.247505	+	0.923700i	−0.972108	+	0.234534i	$0.924644\pi$
$564$	−0.906138	+	1.18090i	−0.0381553	+	0.0497249i
$565$	−15.5972	−	9.00502i	−0.656177	−	0.378844i
$566$	32.0042	−	13.2566i	1.34524	−	0.557216i
$567$	−1.07849	+	2.41596i	−0.0452922	+	0.101461i
$568$	6.09612	+	2.52509i	0.255787	+	0.105951i
$569$	2.39012	+	8.92005i	0.100199	+	0.373948i	0.997756	−	0.0669498i	$-0.0213267\pi$
$569$	2.39012	+	8.92005i	0.100199	+	0.373948i	−0.897557	+	0.440898i	$0.854660\pi$
$570$	−11.0716	−	2.96663i	−0.463739	−	0.124258i
$571$	−1.08630	−	8.25127i	−0.0454602	−	0.345305i	−0.999026	−	0.0441206i	$-0.985951\pi$
$571$	−1.08630	−	8.25127i	−0.0454602	−	0.345305i	0.953566	−	0.301184i	$-0.0973819\pi$
$572$	−2.78790	−	3.63326i	−0.116568	−	0.151914i
$573$	−0.967465	+	0.400737i	−0.0404164	+	0.0167410i
$574$	−9.07586	+	4.91631i	−0.378819	+	0.205203i
$575$	−1.13412	−	2.73801i	−0.0472961	−	0.114183i
$576$	−0.527819	+	0.141429i	−0.0219925	+	0.00589286i
$577$	−10.6947	−	18.5237i	−0.445224	−	0.771151i	0.552844	−	0.833285i	$-0.313543\pi$
$577$	−10.6947	−	18.5237i	−0.445224	−	0.771151i	−0.998068	+	0.0621341i	$0.980209\pi$
$578$	13.3722	+	26.5080i	0.556209	+	1.10259i
$579$	9.64395	−	16.7038i	0.400789	−	0.694186i
$580$	5.31096	+	5.31096i	0.220525	+	0.220525i
$581$	31.0597	+	4.95050i	1.28857	+	0.205381i
$582$		−	22.1096i		−	0.916471i
$583$	−5.22857	+	39.7149i	−0.216545	+	1.64482i
$584$	9.66799	−	1.27281i	0.400064	−	0.0526694i
$585$	−0.236472	−	1.79618i	−0.00977690	−	0.0742630i
$586$	14.8048	+	55.2523i	0.611581	+	2.28245i
$587$	−19.3255	+	19.3255i	−0.797650	+	0.797650i	−0.982724	−	0.185075i	$-0.940747\pi$
$587$	−19.3255	+	19.3255i	−0.797650	+	0.797650i	0.185075	+	0.982724i	$0.440747\pi$
$588$	−6.62863	−	3.17762i	−0.273360	−	0.131043i
$589$	−8.85390	+	21.3752i	−0.364819	+	0.880750i
$590$	2.96880	−	22.5503i	0.122224	−	0.928381i
$591$	11.6889	−	6.74856i	0.480815	−	0.277599i
$592$	12.2471	−	15.9608i	0.503354	−	0.655983i
$593$	−32.7867	+	8.78518i	−1.34639	+	0.360764i	−0.858801	−	0.512309i	$-0.828790\pi$
$593$	−32.7867	+	8.78518i	−1.34639	+	0.360764i	−0.487589	+	0.873073i	$0.662123\pi$
$594$	−8.92857			−0.366344
$595$	−22.7674	−	4.29022i	−0.933374	−	0.175882i
$596$	22.0816			0.904496
$597$	−1.68157	+	0.450576i	−0.0688222	+	0.0184408i
$598$	−5.49205	+	7.15738i	−0.224587	+	0.292687i
$599$	−28.6865	+	16.5622i	−1.17210	+	0.676711i	−0.954173	−	0.299254i	$-0.903262\pi$
$599$	−28.6865	+	16.5622i	−1.17210	+	0.676711i	−0.217925	+	0.975966i	$0.569929\pi$
$600$	0.105968	−	0.804910i	0.00432614	−	0.0328603i
$601$	9.67351	−	23.3539i	0.394591	−	0.952626i	−0.594336	−	0.804217i	$-0.702585\pi$
$601$	9.67351	−	23.3539i	0.394591	−	0.952626i	0.988926	−	0.148409i	$-0.0474151\pi$
$602$	2.92524	+	28.0959i	0.119224	+	1.14510i
$603$	5.62649	−	5.62649i	0.229129	−	0.229129i
$604$	−3.86602	−	14.4282i	−0.157306	−	0.587074i
$605$	−4.19602	−	31.8719i	−0.170593	−	1.29578i
$606$	−25.9854	+	3.42105i	−1.05559	+	0.138971i
$607$	2.95522	−	22.4472i	0.119949	−	0.911102i	−0.820614	−	0.571483i	$-0.806368\pi$
$607$	2.95522	−	22.4472i	0.119949	−	0.911102i	0.940563	−	0.339619i	$-0.110298\pi$
$608$			16.7184i			0.678022i
$609$	3.18491	+	8.32129i	0.129059	+	0.337195i
$610$	−6.54586	−	6.54586i	−0.265034	−	0.265034i
$611$	0.604558	−	1.04713i	0.0244578	−	0.0423621i
$612$	−4.30698	+	0.443907i	−0.174099	+	0.0179439i
$613$	−6.19005	−	10.7215i	−0.250014	−	0.433036i	0.713516	−	0.700639i	$-0.247102\pi$
$613$	−6.19005	−	10.7215i	−0.250014	−	0.433036i	−0.963529	+	0.267603i	$0.913768\pi$
$614$	20.3919	−	5.46399i	0.822949	−	0.220509i
$615$	−1.81555	−	4.38312i	−0.0732100	−	0.176745i
$616$	−0.609301	+	22.4303i	−0.0245494	+	0.903742i
$617$	−19.4379	+	8.05144i	−0.782541	+	0.324139i	−0.737940	−	0.674866i	$-0.764201\pi$
$617$	−19.4379	+	8.05144i	−0.782541	+	0.324139i	−0.0446003	+	0.999005i	$0.514201\pi$
$618$	−1.79967	−	2.34537i	−0.0723932	−	0.0943447i
$619$	2.15520	+	16.3704i	0.0866249	+	0.657981i	0.978581	+	0.205860i	$0.0659992\pi$
$619$	2.15520	+	16.3704i	0.0866249	+	0.657981i	−0.891956	+	0.452121i	$0.850667\pi$
$620$	−16.1291	−	4.32177i	−0.647759	−	0.173566i
$621$	1.56733	+	5.84935i	0.0628948	+	0.234727i
$622$	−7.53334	−	3.12041i	−0.302059	−	0.125117i
$623$	42.0520	−	4.37829i	1.68478	−	0.175412i
$624$	−3.93850	+	1.63138i	−0.157666	+	0.0653075i
$625$	−19.3241	−	11.1568i	−0.772964	−	0.446271i
$626$	−22.9303	+	29.8834i	−0.916481	+	1.19438i
$627$	4.08893	−	15.2601i	0.163296	−	0.609429i
$628$	8.22983	−	14.2545i	0.328406	−	0.568815i
$629$	−12.0629	+	11.4011i	−0.480978	+	0.454593i
$630$	5.13574	−	8.36240i	0.204613	−	0.333166i
$631$	−17.0999	−	17.0999i	−0.680736	−	0.680736i	0.279430	−	0.960166i	$-0.409855\pi$
$631$	−17.0999	−	17.0999i	−0.680736	−	0.680736i	−0.960166	+	0.279430i	$0.909855\pi$
$632$	−4.58273	−	0.603327i	−0.182291	−	0.0239991i
$633$	12.9253	−	7.46243i	0.513735	−	0.296605i
$634$	−32.2185	−	24.7222i	−1.27956	−	0.981842i
$635$	−3.33242	−	4.34290i	−0.132243	−	0.172343i
$636$	−7.60188	−	3.14880i	−0.301434	−	0.124858i
$637$	5.67534	+	1.85630i	0.224865	+	0.0735494i
$638$	−21.2615	+	21.2615i	−0.841751	+	0.841751i
$639$	3.15560	−	2.42137i	0.124833	−	0.0957881i
$640$	24.7930	−	3.26407i	0.980031	−	0.129024i
$641$	−23.4068	−	17.9607i	−0.924515	−	0.709405i	0.0324918	−	0.999472i	$-0.489656\pi$
$641$	−23.4068	−	17.9607i	−0.924515	−	0.709405i	−0.957006	+	0.290067i	$0.906322\pi$
$642$	−24.1843	−	13.9628i	−0.954478	−	0.551068i
$643$	−0.690671	−	1.66743i	−0.0272374	−	0.0657569i	0.909676	−	0.415319i	$-0.136330\pi$
$643$	−0.690671	−	1.66743i	−0.0272374	−	0.0657569i	−0.936913	+	0.349563i	$0.886330\pi$
$644$	−16.3640	+	3.91174i	−0.644832	+	0.154144i
$645$	−12.9836			−0.511228
$646$	3.52531	−	21.9712i	0.138702	−	0.864447i
$647$	1.37700	+	2.38504i	0.0541355	+	0.0937655i	0.891823	−	0.452384i	$-0.149426\pi$
$647$	1.37700	+	2.38504i	0.0541355	+	0.0937655i	−0.837688	+	0.546150i	$0.816093\pi$
$648$	−0.429358	+	1.60239i	−0.0168668	+	0.0629476i
$649$	31.0812	+	4.09192i	1.22005	+	0.160622i
$650$		−	0.729086i		−	0.0285971i
$651$	−15.3820	−	12.4810i	−0.602867	−	0.489169i
$652$	−2.19197	+	5.29188i	−0.0858441	+	0.207246i
$653$	21.3113	−	16.3527i	0.833976	−	0.639932i	−0.100904	−	0.994896i	$-0.532174\pi$
$653$	21.3113	−	16.3527i	0.833976	−	0.639932i	0.934880	+	0.354964i	$0.115507\pi$
$654$	31.1375	+	8.34327i	1.21757	+	0.326248i
$655$	−32.1673	−	8.61919i	−1.25688	−	0.336780i
$656$	−8.85664	+	6.79594i	−0.345794	+	0.265337i
$657$	2.24949	−	5.43075i	0.0877610	−	0.211874i
$658$	6.11683	−	2.34117i	0.238459	−	0.0912685i
$659$		−	45.0417i		−	1.75458i	−0.479965	−	0.877288i	$-0.659351\pi$
$659$		−	45.0417i		−	1.75458i	0.479965	−	0.877288i	$-0.340649\pi$
$660$	11.3045	+	1.48827i	0.440028	+	0.0579308i
$661$	−6.46359	+	24.1224i	−0.251404	+	0.938254i	0.718651	+	0.695371i	$0.244760\pi$
$661$	−6.46359	+	24.1224i	−0.251404	+	0.938254i	−0.970056	+	0.242883i	$0.921907\pi$
$662$	−18.2384	−	31.5899i	−0.708856	−	1.22777i
$663$	3.42160	−	0.814163i	0.132884	−	0.0316195i
$664$	19.7205			0.765305
$665$	11.9405	+	12.6073i	0.463032	+	0.488890i
$666$	−2.69051	−	6.49546i	−0.104255	−	0.251694i
$667$	17.6613	+	10.1967i	0.683847	+	0.394819i
$668$	−0.698363	−	0.535873i	−0.0270205	−	0.0207335i
$669$	8.91662	−	1.17390i	0.344736	−	0.0453854i
$670$	−23.4151	+	17.9670i	−0.904605	+	0.694128i
$671$	9.02221	−	9.02221i	0.348298	−	0.348298i
$672$	−13.7204	−	4.07875i	−0.529274	−	0.157341i
$673$	23.7568	+	9.84040i	0.915759	+	0.379320i	0.790258	−	0.612774i	$-0.209946\pi$
$673$	23.7568	+	9.84040i	0.915759	+	0.379320i	0.125500	+	0.992094i	$0.459946\pi$
$674$	−9.61420	−	12.5295i	−0.370325	−	0.482617i
$675$	−0.388260	−	0.297922i	−0.0149441	−	0.0114670i
$676$	11.1610	−	6.44378i	0.429267	−	0.247838i
$677$	35.3571	+	4.65485i	1.35888	+	0.178901i	0.774499	−	0.632575i	$-0.218002\pi$
$677$	35.3571	+	4.65485i	1.35888	+	0.178901i	0.584386	+	0.811476i	$0.301335\pi$
$678$	10.4723	+	10.4723i	0.402186	+	0.402186i
$679$	−17.5286	+	28.5414i	−0.672686	+	1.09532i
$680$	−14.5209	−	0.409532i	−0.556850	−	0.0157048i
$681$	−1.29300	+	2.23955i	−0.0495480	+	0.0858196i
$682$	17.3015	−	64.5700i	0.662507	−	2.47251i
$683$	19.5371	−	25.4612i	0.747565	−	0.974245i	−0.252413	−	0.967619i	$-0.581224\pi$
$683$	19.5371	−	25.4612i	0.747565	−	0.974245i	0.999978	−	0.00662563i	$-0.00210902\pi$
$684$	2.81038	+	1.62257i	0.107457	+	0.0620405i
$685$	32.8681	−	13.6144i	1.25583	−	0.520180i
$686$	17.5367	+	27.1783i	0.669554	+	1.03767i
$687$	12.6204	+	5.22753i	0.481497	+	0.199443i
$688$	7.90723	+	29.5102i	0.301460	+	1.12507i
$689$	6.45610	+	1.72991i	0.245958	+	0.0659042i
$690$	−2.93183	−	22.2695i	−0.111613	−	0.847784i
$691$	26.4628	+	34.4870i	1.00669	+	1.31195i	0.949561	+	0.313582i	$0.101529\pi$
$691$	26.4628	+	34.4870i	1.00669	+	1.31195i	0.0571328	+	0.998367i	$0.481804\pi$
$692$	−3.17752	+	1.31617i	−0.120791	+	0.0500334i
$693$	11.5260	+	7.07863i	0.437835	+	0.268895i
$694$	−6.56576	−	15.8512i	−0.249233	−	0.601702i
$695$	−39.6979	+	10.6370i	−1.50583	+	0.403485i
$696$	2.79332	+	4.83817i	0.105880	+	0.183390i
$697$	8.10304	−	4.37847i	0.306924	−	0.165846i
$698$	−20.4991	+	35.5055i	−0.775903	+	1.34390i
$699$	−16.2298	−	16.2298i	−0.613869	−	0.613869i
$700$	0.856729	−	1.05586i	0.0323813	−	0.0399078i
$701$		−	33.9412i		−	1.28194i	−0.767566	−	0.640970i	$-0.778532\pi$
$701$		−	33.9412i		−	1.28194i	0.767566	−	0.640970i	$-0.221468\pi$
$702$	−0.194456	+	1.47704i	−0.00733926	+	0.0557472i
$703$	12.3337	−	1.62377i	0.465175	−	0.0612415i
$704$	0.364638	+	2.76970i	0.0137428	+	0.104387i
$705$	0.779144	+	2.90781i	0.0293443	+	0.109514i
$706$	37.8799	−	37.8799i	1.42563	−	1.42563i
$707$	36.2570	+	16.1852i	1.36359	+	0.608706i
$708$	−2.46428	+	5.94929i	−0.0926133	+	0.223588i
$709$	−3.92502	+	29.8135i	−0.147407	+	1.11967i	0.744556	+	0.667560i	$0.232661\pi$
$709$	−3.92502	+	29.8135i	−0.147407	+	1.11967i	−0.891963	+	0.452109i	$0.850672\pi$
$710$	−12.7768	+	7.37669i	−0.479505	+	0.276842i
$711$	−1.69621	+	2.21054i	−0.0636128	+	0.0829018i
$712$	25.6062	−	6.86117i	0.959635	−	0.257133i
$713$	−45.3387			−1.69795
$714$	17.1711	+	8.25338i	0.642613	+	0.308875i
$715$	−9.26199			−0.346379
$716$	−2.54309	+	0.681420i	−0.0950398	+	0.0254658i
$717$	5.45029	−	7.10296i	0.203545	−	0.265265i
$718$	−34.4634	+	19.8975i	−1.28616	+	0.742567i
$719$	3.40041	−	25.8287i	0.126814	−	0.963246i	−0.803197	−	0.595714i	$-0.796869\pi$
$719$	3.40041	−	25.8287i	0.126814	−	0.963246i	0.930011	−	0.367533i	$-0.119797\pi$
$720$	4.06171	−	9.80584i	0.151371	−	0.365442i
$721$	0.463779	+	4.45445i	0.0172720	+	0.165892i
$722$	11.6708	−	11.6708i	0.434340	−	0.434340i
$723$	1.37193	+	5.12013i	0.0510228	+	0.190420i
$724$	3.11054	+	23.6269i	0.115602	+	0.878088i
$725$	−1.63400	+	0.215120i	−0.0606851	+	0.00798934i
$726$	−3.45048	+	26.2090i	−0.128059	+	0.972707i
$727$			12.1979i			0.452396i	0.974081	+	0.226198i	$0.0726296\pi$
$727$			12.1979i			0.452396i	−0.974081	+	0.226198i	$0.927370\pi$
$728$	3.69733	+	0.589306i	0.137032	+	0.0218411i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	−10.9016	+	18.8822i	−0.403487	+	0.698860i
$731$	−2.58419	−	25.0730i	−0.0955799	−	0.927359i
$732$	1.31044	+	2.26975i	0.0484354	+	0.0838925i
$733$	−36.6391	+	9.81742i	−1.35330	+	0.362615i	−0.861351	−	0.508011i	$-0.830381\pi$
$733$	−36.6391	+	9.81742i	−1.35330	+	0.362615i	−0.491946	+	0.870626i	$0.663714\pi$
$734$	1.91456	+	4.62216i	0.0706677	+	0.170607i
$735$	−13.2595	+	6.72345i	−0.489085	+	0.247998i
$736$	−30.2681	+	12.5374i	−1.11570	+	0.462136i
$737$	−24.7641	−	32.2732i	−0.912198	−	1.18880i
$738$	0.509222	+	3.86793i	0.0187447	+	0.142380i
$739$	−23.8191	−	6.38232i	−0.876201	−	0.234777i	−0.207434	−	0.978249i	$-0.566511\pi$
$739$	−23.8191	−	6.38232i	−0.876201	−	0.234777i	−0.668767	+	0.743472i	$0.733178\pi$
$740$	2.32377	+	8.67241i	0.0854233	+	0.318804i
$741$	−2.43540	−	1.00877i	−0.0894665	−	0.0370583i
$742$	21.2522	+	29.3114i	0.780194	+	1.07606i
$743$	12.5777	−	5.20985i	0.461431	−	0.191131i	−0.139843	−	0.990174i	$-0.544660\pi$
$743$	12.5777	−	5.20985i	0.461431	−	0.191131i	0.601274	+	0.799043i	$0.294660\pi$
$744$	−10.7562	−	6.21009i	−0.394341	−	0.227673i
$745$	27.1864	−	35.4300i	0.996032	−	1.29805i
$746$	−13.3768	+	49.9227i	−0.489758	+	1.82780i
$747$	5.94382	−	10.2950i	0.217473	−	0.376674i
$748$	−0.624041	+	22.1268i	−0.0228172	+	0.809035i
$749$	20.1499	+	37.1982i	0.736261	+	1.35919i
$750$	14.3975	+	14.3975i	0.525721	+	0.525721i
$751$	40.0667	+	5.27488i	1.46205	+	0.192483i	0.819201	−	0.573507i	$-0.194418\pi$
$751$	40.0667	+	5.27488i	1.46205	+	0.192483i	0.642852	+	0.765990i	$0.277751\pi$
$752$	6.13460	−	3.54181i	0.223706	−	0.129157i
$753$	4.90483	+	3.76361i	0.178742	+	0.137153i
$754$	3.05420	+	3.98031i	0.111227	+	0.144954i
$755$	−27.9099	−	11.5606i	−1.01574	−	0.420735i
$756$	−2.01724	+	1.91054i	−0.0733662	+	0.0694858i
$757$	29.4891	−	29.4891i	1.07180	−	1.07180i	0.0745835	−	0.997215i	$-0.476237\pi$
$757$	29.4891	−	29.4891i	1.07180	−	1.07180i	0.997215	−	0.0745835i	$-0.0237627\pi$
$758$	27.5864	−	21.1678i	1.00198	−	0.768848i
$759$	30.6941	−	4.04096i	1.11413	−	0.146678i
$760$	8.63769	+	6.62794i	0.313322	+	0.240420i
$761$	−0.249169	−	0.143858i	−0.00903237	−	0.00521484i	0.495477	−	0.868621i	$-0.334993\pi$
$761$	−0.249169	−	0.143858i	−0.00903237	−	0.00521484i	−0.504509	+	0.863406i	$0.668327\pi$
$762$	1.72264	+	4.15882i	0.0624046	+	0.150658i
$763$	−33.5810	−	35.4564i	−1.21572	−	1.28361i
$764$	−1.09967			−0.0397848
$765$	−4.59042	+	7.45710i	−0.165967	+	0.269612i
$766$	5.88263	+	10.1890i	0.212548	+	0.368144i
$767$	1.35384	−	5.05260i	0.0488843	−	0.182439i
$768$	−19.3043	−	2.54146i	−0.696585	−	0.0917071i
$769$			23.4436i			0.845400i	0.906270	+	0.422700i	$0.138918\pi$
$769$			23.4436i			0.845400i	−0.906270	+	0.422700i	$0.861082\pi$
$770$	−38.9589	−	31.6114i	−1.40398	−	1.13920i
$771$	−6.84533	+	16.5261i	−0.246529	+	0.595173i
$772$	16.0692	−	12.3303i	0.578344	−	0.443779i
$773$	4.27059	+	1.14430i	0.153603	+	0.0411577i	0.334801	−	0.942289i	$-0.391331\pi$
$773$	4.27059	+	1.14430i	0.153603	+	0.0411577i	−0.181198	+	0.983447i	$0.557998\pi$
$774$	10.3129	+	2.76332i	0.370688	+	0.0993257i
$775$	2.90688	−	2.23053i	0.104418	−	0.0801229i
$776$	−8.03681	+	19.4026i	−0.288505	+	0.696512i
$777$	−1.67644	+	10.5181i	−0.0601421	+	0.377334i
$778$			37.9404i			1.36023i
$779$	−6.84399	−	0.901029i	−0.245212	−	0.0322827i
$780$	0.492404	−	1.83767i	0.0176309	−	0.0657993i
$781$	−10.1673	−	17.6104i	−0.363816	−	0.630148i
$782$	42.4218	−	10.0942i	1.51700	−	0.360967i
$783$	3.36765			0.120350
$784$	23.3569	+	26.0427i	0.834176	+	0.930097i
$785$	−12.7390	−	30.7546i	−0.454674	−	1.09768i
$786$	23.7161	+	13.6925i	0.845924	+	0.488395i
$787$	13.5000	+	10.3589i	0.481224	+	0.369257i	0.820701	−	0.571358i	$-0.193583\pi$
$787$	13.5000	+	10.3589i	0.481224	+	0.369257i	−0.339476	+	0.940615i	$0.610250\pi$
$788$	14.0525	−	1.85005i	0.500599	−	0.0659051i
$789$	−24.7828	+	19.0165i	−0.882292	+	0.677006i
$790$	7.30792	−	7.30792i	0.260004	−	0.260004i
$791$	−5.21626	−	21.8212i	−0.185469	−	0.775874i
$792$	7.83540	+	3.24553i	0.278419	+	0.115325i
$793$	−1.29603	−	1.68902i	−0.0460235	−	0.0599790i
$794$	−34.5187	−	26.4871i	−1.22502	−	0.939994i
$795$	−14.4116	+	8.32051i	−0.511125	+	0.295098i
$796$	−1.81252	−	0.238623i	−0.0642432	−	0.00845778i
$797$	28.3126	+	28.3126i	1.00288	+	1.00288i	0.999996	+	0.00288799i	$0.000919278\pi$
$797$	28.3126	+	28.3126i	1.00288	+	1.00288i	0.00288799	+	0.999996i	$0.499081\pi$
$798$	−6.80109	−	12.5553i	−0.240756	−	0.444453i
$799$	−5.46028	+	2.08339i	−0.193171	+	0.0737050i
$800$	1.32383	−	2.29293i	0.0468043	−	0.0810674i
$801$	4.13595	−	15.4356i	0.146137	−	0.545389i
$802$	−25.5274	+	33.2680i	−0.901405	+	1.17473i
$803$	−26.0254	−	15.0258i	−0.918417	−	0.530248i
$804$	7.71990	−	3.19769i	0.272260	−	0.112774i
$805$	−13.8706	+	31.0722i	−0.488876	+	1.09515i
$806$	−10.3049	−	4.26842i	−0.362974	−	0.150349i
$807$	5.57382	+	20.8018i	0.196208	+	0.732258i
$808$	24.0475	+	6.44350i	0.845987	+	0.226682i
$809$	−0.558952	−	4.24566i	−0.0196517	−	0.149269i	0.978806	−	0.204791i	$-0.0656513\pi$
$809$	−0.558952	−	4.24566i	−0.0196517	−	0.149269i	−0.998458	+	0.0555211i	$0.982318\pi$
$810$	−2.25800	−	2.94268i	−0.0793380	−	0.103395i
$811$	−30.0965	+	12.4664i	−1.05683	+	0.437754i	−0.842326	−	0.538968i	$-0.818814\pi$
$811$	−30.0965	+	12.4664i	−1.05683	+	0.437754i	−0.214506	+	0.976723i	$0.568814\pi$
$812$	−0.254071	+	9.35317i	−0.00891616	+	0.328232i
$813$	0.572111	+	1.38120i	0.0200648	+	0.0484407i
$814$	−34.7185	+	9.30280i	−1.21688	+	0.326063i
$815$	5.79214	+	10.0323i	0.202890	+	0.351415i
$816$	19.7448	+	5.89199i	0.691206	+	0.206261i
$817$	−9.44576	+	16.3605i	−0.330465	+	0.572383i
$818$	−17.4355	−	17.4355i	−0.609620	−	0.609620i
$819$	1.42203	−	1.75255i	0.0496897	−	0.0612392i
$820$		−	4.98209i		−	0.173982i
$821$	1.54174	−	11.7107i	0.0538073	−	0.408707i	−0.943252	−	0.332077i	$-0.892251\pi$
$821$	1.54174	−	11.7107i	0.0538073	−	0.408707i	0.997060	−	0.0766299i	$-0.0244160\pi$
$822$	−29.0048	+	3.81855i	−1.01166	+	0.133187i
$823$	3.28442	+	24.9476i	0.114488	+	0.869620i	0.948256	+	0.317506i	$0.102845\pi$
$823$	3.28442	+	24.9476i	0.114488	+	0.869620i	−0.833769	+	0.552114i	$0.813821\pi$
$824$	0.726784	+	2.71239i	0.0253187	+	0.0944907i
$825$	−1.76914	+	1.76914i	−0.0615937	+	0.0615937i
$826$	22.9393	−	16.6322i	0.798162	−	0.578707i
$827$	−18.6913	+	45.1249i	−0.649962	+	1.56915i	0.162870	+	0.986648i	$0.447925\pi$
$827$	−18.6913	+	45.1249i	−0.649962	+	1.56915i	−0.812831	+	0.582499i	$0.802075\pi$
$828$	−0.830052	+	6.30487i	−0.0288463	+	0.219109i
$829$	−29.0542	+	16.7745i	−1.00909	+	0.582601i	−0.910927	−	0.412569i	$-0.864632\pi$
$829$	−29.0542	+	16.7745i	−1.00909	+	0.582601i	−0.0981684	+	0.995170i	$0.531298\pi$
$830$	−26.8423	+	34.9815i	−0.931709	+	1.21423i
$831$	16.6403	−	4.45875i	0.577244	−	0.154672i
$832$	0.466128			0.0161601
$833$	−15.6230	−	24.2677i	−0.541305	−	0.840827i
$834$	33.7960			1.17026
$835$	−1.71962	+	0.460771i	−0.0595099	+	0.0159456i
$836$	10.0996	−	13.1620i	0.349302	−	0.455219i
$837$	−6.48388	+	3.74347i	−0.224116	+	0.129393i
$838$	−2.38804	+	18.1390i	−0.0824935	+	0.626600i
$839$	−10.4496	+	25.2277i	−0.360762	+	0.870956i	0.634427	+	0.772983i	$0.281236\pi$
$839$	−10.4496	+	25.2277i	−0.360762	+	0.870956i	−0.995189	+	0.0979733i	$0.968764\pi$
$840$	−7.54667	+	5.47172i	−0.260385	+	0.188792i
$841$	−12.4868	+	12.4868i	−0.430578	+	0.430578i
$842$	−4.89528	−	18.2694i	−0.168703	−	0.629606i
$843$	1.14319	+	8.68336i	0.0393734	+	0.299071i
$844$	15.5390	−	2.04574i	0.534873	−	0.0704174i
$845$	3.40207	−	25.8413i	0.117035	−	0.888966i
$846$		−	2.47550i		−	0.0851095i
$847$	25.2329	−	31.0978i	0.867012	−	1.06853i
$848$	27.6885	+	27.6885i	0.950827	+	0.950827i
$849$	−9.91751	+	17.1776i	−0.340368	+	0.589535i
$850$	−2.22326	+	2.73421i	−0.0762571	+	0.0937825i
$851$	12.1890	+	21.1120i	0.417835	+	0.723711i
$852$	4.03461	−	1.08107i	0.138224	−	0.0370369i
$853$	16.9691	+	40.9671i	0.581012	+	1.40269i	0.891896	+	0.452240i	$0.149375\pi$
$853$	16.9691	+	40.9671i	0.581012	+	1.40269i	−0.310884	+	0.950448i	$0.600625\pi$
$854$	0.313148	−	11.5280i	0.0107157	−	0.394479i
$855$	6.06350	−	2.51158i	0.207367	−	0.0858944i
$856$	16.1478	+	21.0443i	0.551921	+	0.719278i
$857$	−1.47039	−	11.1687i	−0.0502277	−	0.381517i	−0.998034	−	0.0626712i	$-0.980038\pi$
$857$	−1.47039	−	11.1687i	−0.0502277	−	0.381517i	0.947807	−	0.318846i	$-0.103295\pi$
$858$	7.35682	+	1.97125i	0.251158	+	0.0672975i
$859$	−2.30421	−	8.59944i	−0.0786187	−	0.293409i	0.915411	−	0.402521i	$-0.131866\pi$
$859$	−2.30421	−	8.59944i	−0.0786187	−	0.293409i	−0.994029	+	0.109112i	$0.965199\pi$
$860$	−12.5966	−	5.21767i	−0.429540	−	0.177921i
$861$	2.40916	−	5.39685i	0.0821039	−	0.183924i
$862$	13.6681	−	5.66152i	0.465538	−	0.192832i
$863$	39.0655	+	22.5545i	1.32981	+	0.767764i	0.985269	−	0.171009i	$-0.0547028\pi$
$863$	39.0655	+	22.5545i	1.32981	+	0.767764i	0.344536	+	0.938773i	$0.388036\pi$
$864$	−3.29346	+	4.29212i	−0.112046	+	0.146021i
$865$	−1.80030	+	6.71880i	−0.0612119	+	0.228446i
$866$	−19.4362	+	33.6646i	−0.660471	+	1.14397i
$867$	−15.3143	−	7.38048i	−0.520102	−	0.250654i
$868$	−9.90779	−	18.2905i	−0.336292	−	0.620820i
$869$	10.0726	+	10.0726i	0.341688	+	0.341688i
$870$	−12.3843	−	1.63043i	−0.419868	−	0.0552767i
$871$	−5.87824	+	3.39380i	−0.199177	+	0.114995i
$872$	−24.2924	−	18.6402i	−0.822645	−	0.631237i
$873$	7.70669	+	10.0436i	0.260832	+	0.339923i
$874$	−30.1946	−	12.5070i	−1.02135	−	0.423056i
$875$	−7.17140	−	30.0002i	−0.242437	−	1.01419i
$876$	4.36488	−	4.36488i	0.147476	−	0.147476i
$877$	2.08201	−	1.59758i	0.0703043	−	0.0539464i	−0.573011	−	0.819547i	$-0.694225\pi$
$877$	2.08201	−	1.59758i	0.0703043	−	0.0539464i	0.643316	+	0.765601i	$0.277558\pi$
$878$	13.4860	−	1.77546i	0.455130	−	0.0599190i
$879$	−25.9845	−	19.9386i	−0.876435	−	0.672512i
$880$	−46.9919	−	27.1308i	−1.58410	−	0.914578i
$881$	5.61447	+	13.5545i	0.189156	+	0.456664i	0.989798	−	0.142480i	$-0.0455078\pi$
$881$	5.61447	+	13.5545i	0.189156	+	0.456664i	−0.800641	+	0.599144i	$0.795508\pi$
$882$	11.9630	−	2.51838i	0.402816	−	0.0847984i
$883$	−37.2088			−1.25218			−0.626088	−	0.779753i	$-0.715345\pi$
$883$	−37.2088			−1.25218			−0.626088	+	0.779753i	$0.715345\pi$
$884$	3.64680	+	0.585134i	0.122655	+	0.0196802i
$885$	6.51170	+	11.2786i	0.218888	+	0.379126i
$886$	0.0757593	−	0.282738i	0.00254518	−	0.00949876i
$887$	31.7188	+	4.17585i	1.06501	+	0.140211i	0.642607	−	0.766196i	$-0.277853\pi$
$887$	31.7188	+	4.17585i	1.06501	+	0.140211i	0.422405	+	0.906407i	$0.361186\pi$
$888$			6.67818i			0.224105i
$889$	1.07337	−	6.73437i	0.0359996	−	0.225863i
$890$	−22.6827	+	54.7610i	−0.760327	+	1.83559i
$891$	4.05592	−	3.11222i	0.135878	−	0.104263i
$892$	9.12260	+	2.44439i	0.305447	+	0.0818443i
$893$	4.23095	+	1.13368i	0.141583	+	0.0379372i
$894$	−29.1348	+	22.3559i	−0.974414	+	0.747694i
$895$	−2.03766	+	4.91935i	−0.0681116	+	0.164436i
$896$	24.1909	+	19.6286i	0.808160	+	0.655744i
$897$		−	5.16569i		−	0.172477i
$898$	39.7892	+	5.23835i	1.32778	+	0.174806i
$899$	−6.52571	+	24.3543i	−0.217645	+	0.812261i
$900$	−0.256962	−	0.445071i	−0.00856540	−	0.0148357i
$901$	−18.9364	−	26.1746i	−0.630864	−	0.872001i
$902$	19.9449			0.664094
$903$	−11.1222	−	11.7433i	−0.370123	−	0.390793i
$904$	−5.38344	−	12.9968i	−0.179051	−	0.432266i
$905$	41.7392	+	24.0981i	1.38746	+	0.801048i
$906$	19.7084	+	15.1228i	0.654766	+	0.502420i
$907$	42.9881	−	5.65949i	1.42740	−	0.187920i	0.623097	−	0.782145i	$-0.285874\pi$
$907$	42.9881	−	5.65949i	1.42740	−	0.187920i	0.804299	+	0.594224i	$0.202541\pi$
$908$	−2.15446	+	1.65318i	−0.0714984	+	0.0548627i
$909$	10.6118	−	10.6118i	0.351970	−	0.351970i
$910$	−6.07791	+	5.75644i	−0.201481	+	0.190824i
$911$	14.8839	+	6.16510i	0.493125	+	0.204259i	0.615366	−	0.788241i	$-0.289008\pi$
$911$	14.8839	+	6.16510i	0.493125	+	0.204259i	−0.122241	+	0.992500i	$0.539008\pi$
$912$	−9.40133	−	12.2520i	−0.311309	−	0.405706i
$913$	−48.2153	−	36.9969i	−1.59569	−	1.22442i
$914$	32.5836	−	18.8122i	1.07777	−	0.622251i
$915$	5.25522	+	0.691863i	0.173732	+	0.0228723i
$916$	10.1434	+	10.1434i	0.335148	+	0.335148i
$917$	−19.7598	−	36.4780i	−0.652525	−	1.20461i
$918$	5.23329	−	4.94620i	0.172724	−	0.163249i
$919$	10.2156	−	17.6939i	0.336980	−	0.583667i	−0.646883	−	0.762589i	$-0.723928\pi$
$919$	10.2156	−	17.6939i	0.336980	−	0.583667i	0.983863	+	0.178923i	$0.0572612\pi$
$920$	−5.52206	+	20.6086i	−0.182057	+	0.679446i
$921$	−7.35871	+	9.59005i	−0.242478	+	0.316003i
$922$	14.7189	+	8.49793i	0.484740	+	0.279865i
$923$	−3.13469	+	1.29843i	−0.103179	+	0.0427383i
$924$	8.33775	+	11.4996i	0.274292	+	0.378307i
$925$	−1.82015	−	0.753929i	−0.0598460	−	0.0247890i
$926$	−6.64721	−	24.8077i	−0.218441	−	0.815232i
$927$	1.63504	+	0.438109i	0.0537019	+	0.0143894i
$928$	2.37810	+	18.0635i	0.0780649	+	0.592962i
$929$	27.7387	+	36.1498i	0.910077	+	1.18604i	0.982048	+	0.188629i	$0.0604044\pi$
$929$	27.7387	+	36.1498i	0.910077	+	1.18604i	−0.0719709	+	0.997407i	$0.522929\pi$
$930$	25.6565	−	10.6273i	0.841309	−	0.348481i
$931$	−1.17434	+	21.5997i	−0.0384875	+	0.707901i
$932$	−9.22385	−	22.2683i	−0.302137	−	0.729424i
$933$	4.50980	−	1.20840i	0.147644	−	0.0395611i
$934$	−21.7838	−	37.7307i	−0.712789	−	1.23459i
$935$	34.7342	+	28.2433i	1.13593	+	0.923655i
$936$	0.707550	−	1.22551i	0.0231270	−	0.0400571i
$937$	−4.93588	−	4.93588i	−0.161248	−	0.161248i	0.621871	−	0.783119i	$-0.286373\pi$
$937$	−4.93588	−	4.93588i	−0.161248	−	0.161248i	−0.783119	+	0.621871i	$0.786373\pi$
$938$	−36.3089	−	5.78716i	−1.18553	−	0.188958i
$939$		−	21.5677i		−	0.703836i
$940$	−0.412632	+	3.13425i	−0.0134586	+	0.102228i
$941$	−13.4577	+	1.77175i	−0.438710	+	0.0577572i	−0.346646	−	0.937996i	$-0.612680\pi$
$941$	−13.4577	+	1.77175i	−0.438710	+	0.0577572i	−0.0920635	+	0.995753i	$0.529346\pi$
$942$	3.57301	+	27.1397i	0.116415	+	0.884259i
$943$	−3.50115	−	13.0665i	−0.114013	−	0.425503i
$944$	21.6692	−	21.6692i	0.705273	−	0.705273i
$945$	0.581892	+	5.58889i	0.0189290	+	0.181807i
$946$	20.8881	−	50.4282i	0.679130	−	1.63956i
$947$	5.78933	−	43.9744i	0.188128	−	1.42897i	−0.593301	−	0.804981i	$-0.702176\pi$
$947$	5.78933	−	43.9744i	0.188128	−	1.42897i	0.781429	−	0.623994i	$-0.214491\pi$
$948$	−2.53400	+	1.46300i	−0.0823004	+	0.0475162i
$949$	−3.05250	+	3.97809i	−0.0990883	+	0.129134i
$950$	2.55123	−	0.683599i	0.0827727	−	0.0221789i
$951$	23.2531			0.754032
$952$	−12.0687	−	13.4846i	−0.391148	−	0.437037i
$953$	−15.1891			−0.492022			−0.246011	−	0.969267i	$-0.579120\pi$
$953$	−15.1891			−0.492022			−0.246011	+	0.969267i	$0.579120\pi$
$954$	13.2180	−	3.54175i	0.427948	−	0.114668i
$955$	−1.35389	+	1.76443i	−0.0438110	+	0.0570956i
$956$	8.14229	−	4.70095i	0.263341	−	0.152040i
$957$	2.24723	−	17.0694i	0.0726426	−	0.551775i
$958$	−5.12287	+	12.3677i	−0.165512	+	0.399582i
$959$	40.4698	+	18.0658i	1.30684	+	0.583374i
$960$	−0.820623	+	0.820623i	−0.0264855	+	0.0264855i
$961$	−6.48454	−	24.2006i	−0.209179	−	0.780666i
$962$	0.782810	+	5.94603i	0.0252388	+	0.191708i
$963$	15.8530	−	2.08709i	0.510857	−	0.0672556i
$964$	−0.726571	+	5.51885i	−0.0234013	+	0.177750i
$965$		−	40.9640i		−	1.31868i
$966$	17.6306	−	21.7286i	0.567256	−	0.699105i
$967$	38.6487	+	38.6487i	1.24286	+	1.24286i	0.958810	+	0.284049i	$0.0916777\pi$
$967$	38.6487	+	38.6487i	1.24286	+	1.24286i	0.284049	+	0.958810i	$0.408322\pi$
$968$	12.5550	−	21.7458i	0.403532	−	0.698938i
$969$	6.05706	+	11.2095i	0.194581	+	0.360102i
$970$	−23.4784	−	40.6657i	−0.753845	−	1.30570i
$971$	−21.4163	+	5.73847i	−0.687281	+	0.184156i	−0.585527	−	0.810653i	$-0.699112\pi$
$971$	−21.4163	+	5.73847i	−0.687281	+	0.184156i	−0.101754	+	0.994810i	$0.532446\pi$
$972$	0.401868	+	0.970194i	0.0128899	+	0.0311190i
$973$	−43.6275	−	26.7937i	−1.39863	−	0.858966i
$974$	46.4018	−	19.2203i	1.48681	−	0.615857i
$975$	0.254136	+	0.331197i	0.00813888	+	0.0106068i
$976$	−1.62800	−	12.3659i	−0.0521110	−	0.395822i
$977$	−8.92735	−	2.39208i	−0.285611	−	0.0765293i	0.113169	−	0.993576i	$-0.463900\pi$
$977$	−8.92735	−	2.39208i	−0.285611	−	0.0765293i	−0.398780	+	0.917046i	$0.630566\pi$
$978$	−2.46551	−	9.20141i	−0.0788383	−	0.294229i
$979$	−75.4774	−	31.2638i	−2.41227	−	0.999195i
$980$	−15.5663	+	1.19447i	−0.497246	+	0.0381560i
$981$	−17.0528	+	7.06351i	−0.544454	+	0.225520i
$982$	36.1689	+	20.8821i	1.15419	+	0.666375i
$983$	−5.72855	+	7.46560i	−0.182712	+	0.238116i	−0.875725	−	0.482810i	$-0.839616\pi$
$983$	−5.72855	+	7.46560i	−0.182712	+	0.238116i	0.693013	+	0.720925i	$0.256283\pi$
$984$	0.959114	−	3.57946i	0.0305754	−	0.114109i
$985$	14.3327	−	24.8250i	0.456679	−	0.790991i
$986$	0.683649	−	24.2403i	0.0217718	−	0.771968i
$987$	−1.96259	+	3.19564i	−0.0624700	+	0.101718i
$988$	−1.95741	−	1.95741i	−0.0622736	−	0.0622736i
$989$	−36.7036	−	4.83213i	−1.16711	−	0.153653i
$990$	−16.4222	+	9.48134i	−0.521931	+	0.301337i
$991$	−32.5302	−	24.9613i	−1.03335	−	0.792921i	−0.0547147	−	0.998502i	$-0.517425\pi$
$991$	−32.5302	−	24.9613i	−1.03335	−	0.792921i	−0.978640	+	0.205581i	$0.934092\pi$
$992$	−24.6580	−	32.1349i	−0.782891	−	1.02028i
$993$	19.2963	+	7.99277i	0.612348	+	0.253643i
$994$	−17.6171	−	5.23716i	−0.558780	−	0.166112i
$995$	−2.61441	+	2.61441i	−0.0828825	+	0.0828825i
$996$	9.90388	−	7.59951i	0.313816	−	0.240800i
$997$	−51.6201	+	6.79591i	−1.63482	+	0.215229i	−0.891279	−	0.453456i	$-0.850191\pi$
$997$	−51.6201	+	6.79591i	−1.63482	+	0.215229i	−0.743546	+	0.668685i	$0.766858\pi$
$998$	59.3563	+	45.5457i	1.87889	+	1.44172i
$999$	3.48631	+	2.01282i	0.110302	+	0.0636829i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bh.a.100.6	yes	192
7.4	even	3	inner	357.2.bh.a.151.19	yes	192
17.8	even	8	inner	357.2.bh.a.331.19	yes	192
119.25	even	24	inner	357.2.bh.a.25.6	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bh.a.25.6	✓	192	119.25	even	24	inner
357.2.bh.a.100.6	yes	192	1.1	even	1	trivial
357.2.bh.a.151.19	yes	192	7.4	even	3	inner
357.2.bh.a.331.19	yes	192	17.8	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

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	357.2.bh.a.100.6

Level	$357$
Weight	$2$
Character	357.100
Analytic conductor	$2.851$
Analytic rank	$0$
Dimension	$192$
Inner twists	$4$