LMFDB - Embedded newform 570.2.bf.a.269.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			269.37
Character	$\chi$	$=$	570.269
Dual form			570.2.bf.a.89.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(1.59691 + 0.670720i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.906623 - 2.04402i) q^{5} +(1.54028 - 0.792176i) q^{6} +(-0.609399 + 0.351837i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.10027 + 2.14217i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(1.59691 + 0.670720i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.906623 - 2.04402i) q^{5} +(1.54028 - 0.792176i) q^{6} +(-0.609399 + 0.351837i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.10027 + 2.14217i) q^{9} +(-0.983047 - 2.00839i) q^{10} +(-0.509726 - 0.294290i) q^{11} +(0.383229 - 1.68912i) q^{12} +(4.66104 + 1.69648i) q^{13} +(-0.122192 + 0.692983i) q^{14} +(2.81877 - 2.65604i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-2.98678 - 2.50621i) q^{17} +(2.99102 - 0.231942i) q^{18} +(4.25849 - 0.930206i) q^{19} +(-2.17040 - 0.537909i) q^{20} +(-1.20914 + 0.153117i) q^{21} +(-0.553085 + 0.201306i) q^{22} +(-0.920024 - 5.21772i) q^{23} +(-1.04761 - 1.37932i) q^{24} +(-3.35607 - 3.70632i) q^{25} +(4.29564 - 2.48009i) q^{26} +(1.91715 + 4.82955i) q^{27} +(0.452313 + 0.539045i) q^{28} +(-5.26885 + 4.42109i) q^{29} +(-0.222775 - 3.86657i) q^{30} +(-3.31909 + 1.91628i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-0.616602 - 0.811840i) q^{33} +(-3.83973 + 0.677048i) q^{34} +(0.166667 + 1.56461i) q^{35} +(1.74491 - 2.44034i) q^{36} +4.06006 q^{37} +(2.02472 - 3.86012i) q^{38} +(6.30541 + 5.83539i) q^{39} +(-1.80717 + 1.31686i) q^{40} +(-11.2584 + 4.09772i) q^{41} +(-0.659928 + 1.02468i) q^{42} +(6.70173 + 1.18170i) q^{43} +(-0.201306 + 0.553085i) q^{44} +(6.28279 - 2.35086i) q^{45} +(-4.58838 - 2.64910i) q^{46} +(3.96405 - 3.32623i) q^{47} +(-1.73001 - 0.0840942i) q^{48} +(-3.25242 + 5.63336i) q^{49} +(-4.99644 + 0.188521i) q^{50} +(-3.08867 - 6.00549i) q^{51} +(0.861325 - 4.88482i) q^{52} +(-1.73263 + 0.305510i) q^{53} +(4.93197 + 1.63575i) q^{54} +(-1.06367 + 0.775081i) q^{55} +0.703674 q^{56} +(7.42435 + 1.37080i) q^{57} +6.87799i q^{58} +(6.40650 + 5.37569i) q^{59} +(-3.10516 - 2.31473i) q^{60} +(0.127441 + 0.722753i) q^{61} +(-0.665517 + 3.77433i) q^{62} +(-2.03359 - 0.566482i) q^{63} +(0.500000 + 0.866025i) q^{64} +(7.69345 - 7.98921i) q^{65} +(-1.01825 - 0.0494963i) q^{66} +(-9.62563 + 8.07686i) q^{67} +(-1.94948 + 3.37660i) q^{68} +(2.03043 - 8.94933i) q^{69} +(1.30569 + 0.878037i) q^{70} +(-0.366606 + 2.07913i) q^{71} +(-0.747803 - 2.90530i) q^{72} +(-2.97621 - 8.17708i) q^{73} +(2.60975 - 3.11018i) q^{74} +(-2.87345 - 8.16966i) q^{75} +(-1.65555 - 4.03226i) q^{76} +0.414169 q^{77} +(8.52321 - 1.07931i) q^{78} +(4.37816 + 12.0289i) q^{79} +(-0.152850 + 2.23084i) q^{80} +(-0.177746 + 8.99824i) q^{81} +(-4.09772 + 11.2584i) q^{82} +(6.11594 + 10.5931i) q^{83} +(0.360756 + 1.16418i) q^{84} +(-7.83063 + 3.83287i) q^{85} +(5.21302 - 4.37424i) q^{86} +(-11.3792 + 3.52617i) q^{87} +(0.294290 + 0.509726i) q^{88} +(-8.31122 - 3.02504i) q^{89} +(2.23764 - 6.32400i) q^{90} +(-3.43732 + 0.606092i) q^{91} +(-4.97869 + 1.81209i) q^{92} +(-6.58559 + 0.833950i) q^{93} -5.17470i q^{94} +(1.95948 - 9.54780i) q^{95} +(-1.17645 + 1.27121i) q^{96} +(-8.74575 - 7.33855i) q^{97} +(2.22479 + 6.11255i) q^{98} +(-0.440143 - 1.71001i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	1.59691	+	0.670720i	0.921979	+	0.387241i
$3$	1.59691	+	0.670720i	0.921979	+	0.387241i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	0.906623	−	2.04402i	0.405454	−	0.914115i
$5$	0.906623	−	2.04402i	0.405454	−	0.914115i
$6$	1.54028	−	0.792176i	0.628816	−	0.323405i
$7$	−0.609399	+	0.351837i	−0.230331	+	0.132982i	−0.610725	−	0.791843i	$-0.709122\pi$
$7$	−0.609399	+	0.351837i	−0.230331	+	0.132982i	0.380394	+	0.924825i	$0.375789\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	2.10027	+	2.14217i	0.700089	+	0.714055i
$10$	−0.983047	−	2.00839i	−0.310867	−	0.635108i
$11$	−0.509726	−	0.294290i	−0.153688	−	0.0887319i	0.421184	−	0.906975i	$-0.361615\pi$
$11$	−0.509726	−	0.294290i	−0.153688	−	0.0887319i	−0.574872	+	0.818243i	$0.694948\pi$
$12$	0.383229	−	1.68912i	0.110629	−	0.487608i
$13$	4.66104	+	1.69648i	1.29274	+	0.470519i	0.894625	−	0.446817i	$-0.147443\pi$
$13$	4.66104	+	1.69648i	1.29274	+	0.470519i	0.398114	+	0.917336i	$0.369665\pi$
$14$	−0.122192	+	0.692983i	−0.0326571	+	0.185208i
$15$	2.81877	−	2.65604i	0.727803	−	0.685786i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−2.98678	−	2.50621i	−0.724401	−	0.607845i	0.204198	−	0.978930i	$-0.434541\pi$
$17$	−2.98678	−	2.50621i	−0.724401	−	0.607845i	−0.928599	+	0.371085i	$0.878986\pi$
$18$	2.99102	−	0.231942i	0.704990	−	0.0546691i
$19$	4.25849	−	0.930206i	0.976964	−	0.213404i
$19$	4.25849	−	0.930206i	0.976964	−	0.213404i
$20$	−2.17040	−	0.537909i	−0.485317	−	0.120280i
$21$	−1.20914	+	0.153117i	−0.263856	+	0.0334128i
$22$	−0.553085	+	0.201306i	−0.117918	+	0.0429187i
$23$	−0.920024	−	5.21772i	−0.191838	−	1.08797i	−0.916850	−	0.399233i	$-0.869277\pi$
$23$	−0.920024	−	5.21772i	−0.191838	−	1.08797i	0.725011	−	0.688737i	$-0.241834\pi$
$24$	−1.04761	−	1.37932i	−0.213842	−	0.281552i
$25$	−3.35607	−	3.70632i	−0.671214	−	0.741264i
$26$	4.29564	−	2.48009i	0.842444	−	0.486385i
$27$	1.91715	+	4.82955i	0.368956	+	0.929447i
$28$	0.452313	+	0.539045i	0.0854791	+	0.101870i
$29$	−5.26885	+	4.42109i	−0.978400	+	0.820975i	−0.983847	−	0.179010i	$-0.942711\pi$
$29$	−5.26885	+	4.42109i	−0.978400	+	0.820975i	0.00544697	+	0.999985i	$0.498266\pi$
$30$	−0.222775	−	3.86657i	−0.0406730	−	0.705936i
$31$	−3.31909	+	1.91628i	−0.596127	+	0.344174i	−0.767516	−	0.641029i	$-0.778508\pi$
$31$	−3.31909	+	1.91628i	−0.596127	+	0.344174i	0.171390	+	0.985203i	$0.445174\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	−0.616602	−	0.811840i	−0.107337	−	0.141323i
$34$	−3.83973	+	0.677048i	−0.658509	+	0.116113i
$35$	0.166667	+	1.56461i	0.0281719	+	0.264467i
$36$	1.74491	−	2.44034i	0.290819	−	0.406724i
$37$	4.06006			0.667469			0.333735	−	0.942667i	$-0.391691\pi$
$37$	4.06006			0.667469			0.333735	+	0.942667i	$0.391691\pi$
$38$	2.02472	−	3.86012i	0.328454	−	0.626193i
$39$	6.30541	+	5.83539i	1.00967	+	0.934409i
$40$	−1.80717	+	1.31686i	−0.285739	+	0.208215i
$41$	−11.2584	+	4.09772i	−1.75827	+	0.639957i	−0.999929	−	0.0119057i	$-0.996210\pi$
$41$	−11.2584	+	4.09772i	−1.75827	+	0.639957i	−0.758337	+	0.651862i	$0.773988\pi$
$42$	−0.659928	+	1.02468i	−0.101829	+	0.158111i
$43$	6.70173	+	1.18170i	1.02200	+	0.180207i	0.659444	−	0.751754i	$-0.270792\pi$
$43$	6.70173	+	1.18170i	1.02200	+	0.180207i	0.362560	+	0.931961i	$0.381903\pi$
$44$	−0.201306	+	0.553085i	−0.0303481	+	0.0833807i
$45$	6.28279	−	2.35086i	0.936583	−	0.350446i
$46$	−4.58838	−	2.64910i	−0.676520	−	0.390589i
$47$	3.96405	−	3.32623i	0.578216	−	0.485181i	−0.306144	−	0.951985i	$-0.599039\pi$
$47$	3.96405	−	3.32623i	0.578216	−	0.485181i	0.884361	+	0.466804i	$0.154595\pi$
$48$	−1.73001	−	0.0840942i	−0.249705	−	0.0121380i
$49$	−3.25242	+	5.63336i	−0.464632	+	0.804766i
$50$	−4.99644	+	0.188521i	−0.706604	+	0.0266609i
$51$	−3.08867	−	6.00549i	−0.432500	−	0.840937i
$52$	0.861325	−	4.88482i	0.119444	−	0.677402i
$53$	−1.73263	+	0.305510i	−0.237996	+	0.0419650i	−0.291374	−	0.956609i	$-0.594112\pi$
$53$	−1.73263	+	0.305510i	−0.237996	+	0.0419650i	0.0533780	+	0.998574i	$0.483001\pi$
$54$	4.93197	+	1.63575i	0.671156	+	0.222597i
$55$	−1.06367	+	0.775081i	−0.143425	+	0.104512i
$56$	0.703674			0.0940323
$57$	7.42435	+	1.37080i	0.983379	+	0.181566i
$58$			6.87799i			0.903124i
$59$	6.40650	+	5.37569i	0.834056	+	0.699856i	0.956218	−	0.292654i	$-0.0945385\pi$
$59$	6.40650	+	5.37569i	0.834056	+	0.699856i	−0.122163	+	0.992510i	$0.538983\pi$
$60$	−3.10516	−	2.31473i	−0.400875	−	0.298830i
$61$	0.127441	+	0.722753i	0.0163171	+	0.0925390i	0.991879	−	0.127187i	$-0.0405948\pi$
$61$	0.127441	+	0.722753i	0.0163171	+	0.0925390i	−0.975562	+	0.219726i	$0.929484\pi$
$62$	−0.665517	+	3.77433i	−0.0845207	+	0.479341i
$63$	−2.03359	−	0.566482i	−0.256209	−	0.0713701i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	7.69345	−	7.98921i	0.954255	−	0.990939i
$66$	−1.01825	−	0.0494963i	−0.125338	−	0.00609257i
$67$	−9.62563	+	8.07686i	−1.17596	+	0.986745i	−0.175960	+	0.984397i	$0.556303\pi$
$67$	−9.62563	+	8.07686i	−1.17596	+	0.986745i	−0.999997	+	0.00234801i	$0.999253\pi$
$68$	−1.94948	+	3.37660i	−0.236410	+	0.409473i
$69$	2.03043	−	8.94933i	0.244435	−	1.07737i
$70$	1.30569	+	0.878037i	0.156060	+	0.104946i
$71$	−0.366606	+	2.07913i	−0.0435082	+	0.246747i	−0.998803	−	0.0489066i	$-0.984426\pi$
$71$	−0.366606	+	2.07913i	−0.0435082	+	0.246747i	0.955295	+	0.295654i	$0.0955374\pi$
$72$	−0.747803	−	2.90530i	−0.0881294	−	0.342393i
$73$	−2.97621	−	8.17708i	−0.348339	−	0.957055i	−0.982893	−	0.184176i	$-0.941038\pi$
$73$	−2.97621	−	8.17708i	−0.348339	−	0.957055i	0.634554	−	0.772879i	$-0.281184\pi$
$74$	2.60975	−	3.11018i	0.303378	−	0.361551i
$75$	−2.87345	−	8.16966i	−0.331797	−	0.943351i
$76$	−1.65555	−	4.03226i	−0.189905	−	0.462532i
$77$	0.414169			0.0471989
$78$	8.52321	−	1.07931i	0.965063	−	0.122208i
$79$	4.37816	+	12.0289i	0.492582	+	1.35336i	0.898309	+	0.439364i	$0.144796\pi$
$79$	4.37816	+	12.0289i	0.492582	+	1.35336i	−0.405727	+	0.913994i	$0.632982\pi$
$80$	−0.152850	+	2.23084i	−0.0170891	+	0.249415i
$81$	−0.177746	+	8.99824i	−0.0197495	+	0.999805i
$82$	−4.09772	+	11.2584i	−0.452518	+	1.24328i
$83$	6.11594	+	10.5931i	0.671311	+	1.16275i	0.977532	+	0.210785i	$0.0676020\pi$
$83$	6.11594	+	10.5931i	0.671311	+	1.16275i	−0.306221	+	0.951960i	$0.599065\pi$
$84$	0.360756	+	1.16418i	0.0393617	+	0.127023i
$85$	−7.83063	+	3.83287i	−0.849352	+	0.415733i
$86$	5.21302	−	4.37424i	0.562134	−	0.471687i
$87$	−11.3792	+	3.52617i	−1.21998	+	0.378045i
$88$	0.294290	+	0.509726i	0.0313715	+	0.0543370i
$89$	−8.31122	−	3.02504i	−0.880988	−	0.320653i	−0.138379	−	0.990379i	$-0.544189\pi$
$89$	−8.31122	−	3.02504i	−0.880988	−	0.320653i	−0.742608	+	0.669726i	$0.766412\pi$
$90$	2.23764	−	6.32400i	0.235867	−	0.666608i
$91$	−3.43732	+	0.606092i	−0.360329	+	0.0635357i
$92$	−4.97869	+	1.81209i	−0.519064	+	0.188924i
$93$	−6.58559	+	0.833950i	−0.682894	+	0.0864766i
$94$		−	5.17470i		−	0.533730i
$95$	1.95948	−	9.54780i	0.201038	−	0.979583i
$96$	−1.17645	+	1.27121i	−0.120071	+	0.129742i
$97$	−8.74575	−	7.33855i	−0.887996	−	0.745117i	0.0798111	−	0.996810i	$-0.474568\pi$
$97$	−8.74575	−	7.33855i	−0.887996	−	0.745117i	−0.967807	+	0.251693i	$0.919013\pi$
$98$	2.22479	+	6.11255i	0.224737	+	0.617461i
$99$	−0.440143	−	1.71001i	−0.0442360	−	0.171862i
$100$	−3.06724	+	3.94868i	−0.306724	+	0.394868i
$101$	3.34255	−	9.18357i	0.332596	−	0.913799i	−0.654839	−	0.755769i	$-0.727263\pi$
$101$	3.34255	−	9.18357i	0.332596	−	0.913799i	0.987434	−	0.158030i	$-0.0505144\pi$
$102$	−6.58583	−	1.49420i	−0.652095	−	0.147948i
$103$	−1.81980	+	3.15198i	−0.179310	+	0.310574i	−0.941644	−	0.336609i	$-0.890720\pi$
$103$	−1.81980	+	3.15198i	−0.179310	+	0.310574i	0.762334	+	0.647183i	$0.224053\pi$
$104$	−3.18834	−	3.79971i	−0.312642	−	0.372593i
$105$	−0.783263	+	2.61033i	−0.0764386	+	0.254743i
$106$	−0.879681	+	1.52365i	−0.0854422	+	0.147990i
$107$	−1.34242	+	0.775048i	−0.129777	+	0.0749267i	−0.563483	−	0.826128i	$-0.690539\pi$
$107$	−1.34242	+	0.775048i	−0.129777	+	0.0749267i	0.433706	+	0.901054i	$0.357206\pi$
$108$	4.42326	−	2.72667i	0.425629	−	0.262374i
$109$	1.82397	+	0.321615i	0.174704	+	0.0308051i	0.260316	−	0.965523i	$-0.416173\pi$
$109$	1.82397	+	0.321615i	0.174704	+	0.0308051i	−0.0856115	+	0.996329i	$0.527284\pi$
$110$	−0.0899645	+	1.31303i	−0.00857778	+	0.125192i
$111$	6.48356	+	2.72316i	0.615392	+	0.258471i
$112$	0.452313	−	0.539045i	0.0427395	−	0.0509350i
$113$			4.64466i			0.436933i	0.975844	+	0.218467i	$0.0701054\pi$
$113$			4.64466i			0.436933i	−0.975844	+	0.218467i	$0.929895\pi$
$114$	5.82237	−	4.80625i	0.545315	−	0.450146i
$115$	−11.4993	−	2.84995i	−1.07231	−	0.265760i
$116$	5.26885	+	4.42109i	0.489200	+	0.410488i
$117$	6.15529	+	13.5478i	0.569057	+	1.25249i
$118$	8.23604	−	1.45224i	0.758189	−	0.133689i
$119$	2.70192	+	0.476421i	0.247684	+	0.0436735i
$120$	−3.76914	+	0.890814i	−0.344074	+	0.0813198i
$121$	−5.32679	−	9.22626i	−0.484253	−	0.838751i
$122$	0.635578	+	0.366951i	0.0575426	+	0.0332222i
$123$	−20.7271	−	1.00753i	−1.86890	−	0.0908457i
$124$	2.46352	+	2.93591i	0.221231	+	0.263653i
$125$	−10.6185	+	3.49965i	−0.949747	+	0.313018i
$126$	−1.74112	+	1.19370i	−0.155111	+	0.106343i
$127$	2.33456	+	0.849710i	0.207159	+	0.0753995i	0.443515	−	0.896267i	$-0.353731\pi$
$127$	2.33456	+	0.849710i	0.207159	+	0.0753995i	−0.236357	+	0.971666i	$0.575953\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	9.90949	+	6.38205i	0.872482	+	0.561908i
$130$	−1.17483	−	11.0289i	−0.103040	−	0.967298i
$131$	6.62454	−	7.89481i	0.578788	−	0.689773i	−0.394621	−	0.918844i	$-0.629124\pi$
$131$	6.62454	−	7.89481i	0.578788	−	0.689773i	0.973410	+	0.229071i	$0.0735687\pi$
$132$	−0.692435	+	0.748209i	−0.0602687	+	0.0651232i
$133$	−2.26784	+	2.06516i	−0.196647	+	0.179072i
$134$			12.5654i			1.08548i
$135$	11.6098	+	0.459872i	0.999216	+	0.0395794i
$136$	1.33353	+	3.66383i	0.114349	+	0.314171i
$137$	−1.14740	−	6.50725i	−0.0980294	−	0.555952i	−0.993777	−	0.111389i	$-0.964470\pi$
$137$	−1.14740	−	6.50725i	−0.0980294	−	0.555952i	0.895747	−	0.444563i	$-0.146641\pi$
$138$	−5.55045	−	7.30792i	−0.472485	−	0.622091i
$139$	−1.68475	−	0.613197i	−0.142898	−	0.0520107i	0.269581	−	0.962978i	$-0.413115\pi$
$139$	−1.68475	−	0.613197i	−0.142898	−	0.0520107i	−0.412479	+	0.910967i	$0.635337\pi$
$140$	1.51190	−	0.435827i	0.127779	−	0.0368341i
$141$	8.56122	−	2.65294i	0.720985	−	0.223418i
$142$	1.35705	+	1.61727i	0.113881	+	0.135719i
$143$	−1.87659	−	2.23644i	−0.156929	−	0.187020i
$144$	−2.70627	−	1.29464i	−0.225523	−	0.107887i
$145$	4.25995	+	14.7779i	0.353770	+	1.22724i
$146$	−8.17708	−	2.97621i	−0.676740	−	0.246313i
$147$	−8.97225	+	6.81453i	−0.740018	+	0.562053i
$148$	−0.705021	−	3.99837i	−0.0579524	−	0.328664i
$149$	7.58551	+	20.8410i	0.621429	+	1.70736i	0.703461	+	0.710734i	$0.251637\pi$
$149$	7.58551	+	20.8410i	0.621429	+	1.70736i	−0.0820319	+	0.996630i	$0.526141\pi$
$150$	−8.10534	−	3.05017i	−0.661798	−	0.249045i
$151$		−	6.14590i		−	0.500146i	−0.968227	−	0.250073i	$-0.919545\pi$
$151$		−	6.14590i		−	0.500146i	0.968227	−	0.250073i	$-0.0804546\pi$
$152$	−4.15306	−	1.32366i	−0.336858	−	0.107363i
$153$	−0.904332	−	11.6619i	−0.0731109	−	0.942808i
$154$	0.266223	−	0.317272i	0.0214528	−	0.0255665i
$155$	0.907754	+	8.52165i	0.0729125	+	0.684475i
$156$	4.65181	−	7.22292i	0.372443	−	0.578297i
$157$	6.47768	+	1.14219i	0.516975	+	0.0911567i	0.426048	−	0.904701i	$-0.359906\pi$
$157$	6.47768	+	1.14219i	0.516975	+	0.0911567i	0.0909278	+	0.995857i	$0.471017\pi$
$158$	12.0289	+	4.37816i	0.956968	+	0.348308i
$159$	−2.97178	−	0.674240i	−0.235677	−	0.0534707i
$160$	1.61067	+	1.55104i	0.127335	+	0.122621i
$161$	2.39645	+	2.85597i	0.188867	+	0.225082i
$162$	6.77880	+	5.92012i	0.532593	+	0.465129i
$163$	−19.0197	−	10.9810i	−1.48974	−	0.860101i	−0.489807	−	0.871831i	$-0.662933\pi$
$163$	−19.0197	−	10.9810i	−1.48974	−	0.860101i	−0.999931	+	0.0117299i	$0.996266\pi$
$164$	5.99047	+	10.3758i	0.467777	+	0.810214i
$165$	−2.21845	+	0.524316i	−0.172706	+	0.0408179i
$166$	12.0460	+	2.12404i	0.934954	+	0.164858i
$167$	23.6287	−	4.16638i	1.82844	−	0.322404i	0.849665	−	0.527324i	$-0.176804\pi$
$167$	23.6287	−	4.16638i	1.82844	−	0.322404i	0.978779	+	0.204920i	$0.0656933\pi$
$168$	1.12371	+	0.471968i	0.0866958	+	0.0364131i
$169$	8.88866	+	7.45847i	0.683743	+	0.573729i
$170$	−2.09729	+	8.46233i	−0.160855	+	0.649031i
$171$	10.9366	+	7.16870i	0.836344	+	0.548204i
$172$		−	6.80511i		−	0.518885i
$173$	−3.40469	+	4.05756i	−0.258854	+	0.308490i	−0.879782	−	0.475377i	$-0.842312\pi$
$173$	−3.40469	+	4.05756i	−0.258854	+	0.308490i	0.620928	+	0.783868i	$0.286756\pi$
$174$	−4.61321	+	10.9836i	−0.349726	+	0.832662i
$175$	3.34921	+	1.07784i	0.253176	+	0.0814771i
$176$	0.579639	+	0.102206i	0.0436919	+	0.00770407i
$177$	6.62505	+	12.8815i	0.497969	+	0.968232i
$178$	−7.65966	+	4.42231i	−0.574116	+	0.331466i
$179$	−2.94985	+	5.10930i	−0.220482	+	0.381887i	−0.954955	−	0.296752i	$-0.904096\pi$
$179$	−2.94985	+	5.10930i	−0.220482	+	0.381887i	0.734472	+	0.678639i	$0.237430\pi$
$180$	−3.40614	−	5.77912i	−0.253879	−	0.430750i
$181$	−3.53877	−	4.21734i	−0.263035	−	0.313473i	0.618321	−	0.785926i	$-0.287813\pi$
$181$	−3.53877	−	4.21734i	−0.263035	−	0.313473i	−0.881356	+	0.472453i	$0.843369\pi$
$182$	−1.74517	+	3.02273i	−0.129361	+	0.224059i
$183$	−0.281253	+	1.23965i	−0.0207908	+	0.0916377i
$184$	−1.81209	+	4.97869i	−0.133589	+	0.367034i
$185$	3.68094	−	8.29885i	0.270628	−	0.610144i
$186$	−3.59430	+	5.58091i	−0.263547	+	0.409212i
$187$	0.784887	+	2.15646i	0.0573966	+	0.157696i
$188$	−3.96405	−	3.32623i	−0.289108	−	0.242591i
$189$	−2.86752	−	2.26860i	−0.208582	−	0.165016i
$190$	−6.05451	−	7.63826i	−0.439240	−	0.554137i
$191$			18.7407i			1.35603i	0.735050	+	0.678013i	$0.237159\pi$
$191$			18.7407i			1.35603i	−0.735050	+	0.678013i	$0.762841\pi$
$192$	0.217596	+	1.71833i	0.0157036	+	0.124010i
$193$	−16.0122	+	5.82795i	−1.15258	+	0.419505i	−0.846442	−	0.532481i	$-0.821260\pi$
$193$	−16.0122	+	5.82795i	−1.15258	+	0.419505i	−0.306140	+	0.951987i	$0.599037\pi$
$194$	−11.2433	+	1.98250i	−0.807223	+	0.142335i
$195$	17.6443	−	7.59792i	1.26353	−	0.544098i
$196$	6.11255	+	2.22479i	0.436611	+	0.158913i
$197$	−10.5344	−	18.2460i	−0.750542	−	1.29998i	−0.947561	−	0.319576i	$-0.896459\pi$
$197$	−10.5344	−	18.2460i	−0.750542	−	1.29998i	0.197019	−	0.980400i	$-0.436874\pi$
$198$	−1.59286	−	0.762002i	−0.113200	−	0.0541531i
$199$	19.4953	−	16.3585i	1.38198	−	1.15962i	0.413510	−	0.910500i	$-0.364303\pi$
$199$	19.4953	−	16.3585i	1.38198	−	1.15962i	0.968472	−	0.249121i	$-0.0801417\pi$
$200$	1.05328	+	4.88780i	0.0744782	+	0.345620i
$201$	−20.7886	+	6.44195i	−1.46632	+	0.454380i
$202$	−4.88647	−	8.46362i	−0.343811	−	0.595498i
$203$	1.65533	−	4.54798i	0.116181	−	0.319206i
$204$	−5.37791	+	4.08459i	−0.376529	+	0.285978i
$205$	−1.83129	+	26.7275i	−0.127903	+	1.86673i
$206$	1.24482	+	3.42010i	0.0867304	+	0.238290i
$207$	9.24492	−	12.9295i	0.642566	−	0.898659i
$208$	−4.96017			−0.343926
$209$	−2.44441	−	0.779082i	−0.169084	−	0.0538902i
$210$	1.49616	+	2.27790i	0.103245	+	0.157190i
$211$	1.95426	−	2.32899i	0.134537	−	0.160334i	−0.694570	−	0.719425i	$-0.744405\pi$
$211$	1.95426	−	2.32899i	0.134537	−	0.160334i	0.829106	+	0.559091i	$0.188850\pi$
$212$	0.601737	+	1.65326i	0.0413275	+	0.113546i
$213$	−1.97995	+	3.07430i	−0.135664	+	0.210647i
$214$	−0.269171	+	1.52655i	−0.0184002	+	0.104353i
$215$	8.49136	−	12.6271i	0.579106	−	0.861164i
$216$	0.754469	−	5.14109i	0.0513351	−	0.349807i
$217$	1.34844	−	2.33556i	0.0915378	−	0.158548i
$218$	1.41879	−	1.19051i	0.0960929	−	0.0806315i
$219$	0.731777	−	15.0543i	0.0494489	−	1.01728i
$220$	0.948010	+	0.912915i	0.0639148	+	0.0615487i
$221$	−9.66978	−	16.7485i	−0.650460	−	1.12663i
$222$	6.25362	−	3.21628i	0.419715	−	0.215863i
$223$	1.16123	−	6.58567i	0.0777617	−	0.441009i	−0.920923	−	0.389744i	$-0.872564\pi$
$223$	1.16123	−	6.58567i	0.0777617	−	0.441009i	0.998685	−	0.0512650i	$-0.0163253\pi$
$224$	−0.122192	−	0.692983i	−0.00816427	−	0.0463019i
$225$	0.890907	−	14.9735i	0.0593938	−	0.998235i
$226$	3.55802	+	2.98553i	0.236676	+	0.198595i
$227$		−	5.39883i		−	0.358333i	−0.983819	−	0.179167i	$-0.942660\pi$
$227$		−	5.39883i		−	0.358333i	0.983819	−	0.179167i	$-0.0573401\pi$
$228$	0.0607453	−	7.54959i	0.00402296	−	0.499984i
$229$	−11.7777			−0.778291			−0.389145	−	0.921176i	$-0.627230\pi$
$229$	−11.7777			−0.778291			−0.389145	+	0.921176i	$0.627230\pi$
$230$	−9.57477	+	6.97703i	−0.631342	+	0.460052i
$231$	0.661392	+	0.277791i	0.0435164	+	0.0182773i
$232$	6.77350	−	1.19435i	0.444702	−	0.0784130i
$233$	0.777687	−	4.41048i	0.0509479	−	0.288940i	−0.948679	−	0.316240i	$-0.897580\pi$
$233$	0.777687	−	4.41048i	0.0509479	−	0.288940i	0.999627	+	0.0272994i	$0.00869076\pi$
$234$	14.3347	+	3.99312i	0.937092	+	0.261038i
$235$	−3.20500	−	11.1183i	−0.209071	−	0.725275i
$236$	4.18155	−	7.24265i	0.272196	−	0.471457i
$237$	−1.07648	+	22.1457i	−0.0699250	+	1.43851i
$238$	2.10172	−	1.76355i	0.136234	−	0.114314i
$239$	−10.5453	−	6.08831i	−0.682117	−	0.393820i	0.118535	−	0.992950i	$-0.462180\pi$
$239$	−10.5453	−	6.08831i	−0.682117	−	0.393820i	−0.800652	+	0.599129i	$0.795513\pi$
$240$	−1.74036	+	3.45994i	−0.112340	+	0.223338i
$241$	−0.389462	+	1.07004i	−0.0250874	+	0.0689272i	−0.951604	−	0.307326i	$-0.900566\pi$
$241$	−0.389462	+	1.07004i	−0.0250874	+	0.0689272i	0.926517	+	0.376254i	$0.122788\pi$
$242$	−10.4917	−	1.84997i	−0.674433	−	0.118921i
$243$	−6.31915	+	14.2502i	−0.405374	+	0.914151i
$244$	0.689643	−	0.251009i	0.0441499	−	0.0160692i
$245$	8.56600	+	11.7554i	0.547262	+	0.751023i
$246$	−14.0949	+	15.2303i	−0.898661	+	0.971046i
$247$	21.4271	+	2.88871i	1.36337	+	0.183804i
$248$	3.83256			0.243368
$249$	2.66161	+	21.0184i	0.168673	+	1.33199i
$250$	−4.14455	+	10.3838i	−0.262125	+	0.656727i
$251$	13.2982	−	2.34483i	0.839373	−	0.148004i	0.262596	−	0.964906i	$-0.415421\pi$
$251$	13.2982	−	2.34483i	0.839373	−	0.148004i	0.576777	+	0.816902i	$0.304310\pi$
$252$	−0.204746	+	2.10107i	−0.0128978	+	0.132355i
$253$	−1.06656	+	2.93036i	−0.0670543	+	0.184230i
$254$	2.15154	−	1.24219i	0.135000	−	0.0779421i
$255$	−15.0756	+	0.868593i	−0.944073	+	0.0543934i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−10.1630	−	12.1118i	−0.633953	−	0.755516i	0.349449	−	0.936955i	$-0.386369\pi$
$257$	−10.1630	−	12.1118i	−0.633953	−	0.755516i	−0.983402	+	0.181439i	$0.941924\pi$
$258$	11.2586	−	3.48881i	0.700932	−	0.217204i
$259$	−2.47420	+	1.42848i	−0.153739	+	0.0887613i
$260$	−9.20379	−	6.18926i	−0.570795	−	0.383842i
$261$	−20.5367	−	2.00127i	−1.27119	−	0.123876i
$262$	−1.78961	−	10.1494i	−0.110562	−	0.627031i
$263$	−0.882759	+	0.321298i	−0.0544333	+	0.0198121i	−0.369093	−	0.929392i	$-0.620332\pi$
$263$	−0.882759	+	0.321298i	−0.0544333	+	0.0198121i	0.314660	+	0.949204i	$0.398109\pi$
$264$	0.128073	+	1.01137i	0.00788234	+	0.0622458i
$265$	−0.946377	+	3.81853i	−0.0581354	+	0.234570i
$266$	0.124266	+	3.06472i	0.00761922	+	0.187910i
$267$	−11.2433	−	10.4052i	−0.688082	−	0.636790i
$268$	9.62563	+	8.07686i	0.587979	+	0.493373i
$269$	5.95522	−	2.16752i	0.363096	−	0.132156i	−0.154028	−	0.988066i	$-0.549225\pi$
$269$	5.95522	−	2.16752i	0.363096	−	0.132156i	0.517125	+	0.855910i	$0.327002\pi$
$270$	7.81495	−	8.59806i	0.475603	−	0.523261i
$271$	4.73123	−	26.8321i	0.287402	−	1.62994i	−0.409177	−	0.912455i	$-0.634184\pi$
$271$	4.73123	−	26.8321i	0.287402	−	1.62994i	0.696578	−	0.717481i	$-0.254705\pi$
$272$	3.66383	+	1.33353i	0.222152	+	0.0808568i
$273$	−5.89562	−	1.33760i	−0.356819	−	0.0809554i
$274$	−5.72238	−	3.30382i	−0.345702	−	0.199591i
$275$	0.619941	+	2.87687i	0.0373838	+	0.173482i
$276$	−9.16595	−	0.445549i	−0.551725	−	0.0268189i
$277$	19.9332	+	11.5084i	1.19767	+	0.691475i	0.960035	−	0.279880i	$-0.0902947\pi$
$277$	19.9332	+	11.5084i	1.19767	+	0.691475i	0.237634	+	0.971355i	$0.423628\pi$
$278$	−1.55267	+	0.896434i	−0.0931230	+	0.0537646i
$279$	−11.0760	−	3.08535i	−0.663101	−	0.184715i
$280$	0.637967	−	1.43833i	0.0381258	−	0.0859564i
$281$	−4.36041	−	24.7291i	−0.260120	−	1.47522i	−0.782579	−	0.622551i	$-0.786096\pi$
$281$	−4.36041	−	24.7291i	−0.260120	−	1.47522i	0.522459	−	0.852665i	$-0.325015\pi$
$282$	3.47078	−	8.26355i	0.206682	−	0.492088i
$283$	14.8470	−	17.6939i	0.882561	−	1.05180i	−0.115726	−	0.993281i	$-0.536919\pi$
$283$	14.8470	−	17.6939i	0.882561	−	1.05180i	0.998287	−	0.0585140i	$-0.0186362\pi$
$284$	2.11120			0.125277
$285$	9.53302	−	13.9327i	0.564688	−	0.825305i
$286$	−2.91946			−0.172631
$287$	5.41913	−	6.45827i	0.319881	−	0.381219i
$288$	−2.73131	+	1.24094i	−0.160944	+	0.0731233i
$289$	−0.312230	−	1.77074i	−0.0183664	−	0.104161i
$290$	14.0588	+	6.23575i	0.825560	+	0.366176i
$291$	−9.04409	−	17.5850i	−0.530174	−	1.03085i
$292$	−7.53604	+	4.35093i	−0.441013	+	0.254619i
$293$	5.40430	+	3.12017i	0.315723	+	0.182283i	0.649484	−	0.760375i	$-0.274985\pi$
$293$	5.40430	+	3.12017i	0.315723	+	0.182283i	−0.333762	+	0.942657i	$0.608318\pi$
$294$	−0.547020	+	11.2534i	−0.0319028	+	0.656313i
$295$	16.7963	−	8.22132i	0.977920	−	0.478664i
$296$	−3.51611	−	2.03003i	−0.204370	−	0.117993i
$297$	0.444066	−	3.02595i	0.0257673	−	0.175583i
$298$	20.8410	+	7.58551i	1.20729	+	0.439417i
$299$	4.56348	−	25.8808i	0.263913	−	1.49672i
$300$	−7.54657	+	4.24844i	−0.435702	+	0.245284i
$301$	−4.49979	+	1.63779i	−0.259364	+	0.0944006i
$302$	−4.70803	−	3.95051i	−0.270917	−	0.227326i
$303$	11.4974	−	12.4235i	0.660506	−	0.713709i
$304$	−3.68352	+	2.33060i	−0.211264	+	0.133669i
$305$	1.59287	+	0.394773i	0.0912072	+	0.0226046i
$306$	−9.51482	−	6.80336i	−0.543926	−	0.388922i
$307$	−7.16687	+	2.60853i	−0.409035	+	0.148876i	−0.538339	−	0.842729i	$-0.680948\pi$
$307$	−7.16687	+	2.60853i	−0.409035	+	0.148876i	0.129304	+	0.991605i	$0.458726\pi$
$308$	−0.0719197	−	0.407877i	−0.00409800	−	0.0232409i
$309$	−5.02016	+	3.81287i	−0.285587	+	0.216907i
$310$	7.11146	+	4.78223i	0.403904	+	0.271613i
$311$	−5.76904	+	3.33076i	−0.327132	+	0.188870i	−0.654567	−	0.756004i	$-0.727149\pi$
$311$	−5.76904	+	3.33076i	−0.327132	+	0.188870i	0.327435	+	0.944874i	$0.393816\pi$
$312$	−2.54296	−	8.20630i	−0.143967	−	0.464590i
$313$	−15.0195	−	17.8995i	−0.848951	−	1.01174i	−0.999731	−	0.0231728i	$-0.992623\pi$
$313$	−15.0195	−	17.8995i	−0.848951	−	1.01174i	0.150781	−	0.988567i	$-0.451821\pi$
$314$	5.03874	−	4.22801i	0.284353	−	0.238600i
$315$	−3.00161	+	3.64313i	−0.169121	+	0.205267i
$316$	11.0859	−	6.40045i	0.623631	−	0.360053i
$317$	10.4152	−	28.6155i	0.584974	−	1.60720i	−0.194592	−	0.980884i	$-0.562338\pi$
$317$	10.4152	−	28.6155i	0.584974	−	1.60720i	0.779566	−	0.626320i	$-0.215440\pi$
$318$	−2.42672	+	1.84312i	−0.136084	+	0.103357i
$319$	3.98675	−	0.702972i	0.223215	−	0.0393589i
$320$	2.22349	−	0.236853i	0.124297	−	0.0132405i
$321$	−2.66357	+	0.337295i	−0.148666	+	0.0188260i
$322$	3.72821			0.207765
$323$	−15.0505	−	7.89433i	−0.837430	−	0.439252i
$324$	8.89241	−	1.38748i	0.494023	−	0.0770824i
$325$	−9.35507	−	22.9688i	−0.518926	−	1.27408i
$326$	−20.6376	+	7.51147i	−1.14301	+	0.416022i
$327$	2.69701	+	1.73696i	0.149145	+	0.0960543i
$328$	11.7989	+	2.08047i	0.651486	+	0.114875i
$329$	−1.24540	+	3.42170i	−0.0686610	+	0.188645i
$330$	−1.02434	+	2.03645i	−0.0563881	+	0.112103i
$331$	19.5324	+	11.2770i	1.07360	+	0.619842i	0.929162	−	0.369672i	$-0.120530\pi$
$331$	19.5324	+	11.2770i	1.07360	+	0.619842i	0.144436	+	0.989514i	$0.453863\pi$
$332$	9.37016	−	7.86250i	0.514254	−	0.431511i
$333$	8.52721	+	8.69731i	0.467288	+	0.476610i
$334$	11.9966	−	20.7787i	0.656425	−	1.13696i
$335$	7.78248	+	26.9977i	0.425202	+	1.47504i
$336$	1.08385	−	0.557434i	0.0591290	−	0.0304105i
$337$	3.31113	−	18.7784i	0.180369	−	1.02292i	−0.751394	−	0.659854i	$-0.770618\pi$
$337$	3.31113	−	18.7784i	0.180369	−	1.02292i	0.931763	−	0.363068i	$-0.118271\pi$
$338$	11.4270	−	2.01490i	0.621549	−	0.109596i
$339$	−3.11527	+	7.41712i	−0.169198	+	0.402843i
$340$	5.13441	+	7.04610i	0.278453	+	0.382128i
$341$	2.25577			0.122157
$342$	12.5215	−	3.76999i	0.677084	−	0.203857i
$343$		−	9.50300i		−	0.513114i
$344$	−5.21302	−	4.37424i	−0.281067	−	0.235843i
$345$	−16.4518	−	12.2639i	−0.885735	−	0.660267i
$346$	0.919773	+	5.21629i	0.0494473	+	0.280430i
$347$	3.48284	−	19.7522i	0.186968	−	1.06035i	−0.736432	−	0.676512i	$-0.763491\pi$
$347$	3.48284	−	19.7522i	0.186968	−	1.06035i	0.923400	−	0.383839i	$-0.125398\pi$
$348$	5.44858	+	10.5940i	0.292075	+	0.567899i
$349$	15.0305	+	26.0337i	0.804566	+	1.39355i	0.916583	+	0.399844i	$0.130936\pi$
$349$	15.0305	+	26.0337i	0.804566	+	1.39355i	−0.112017	+	0.993706i	$0.535731\pi$
$350$	2.97850	−	1.87282i	0.159208	−	0.100106i
$351$	0.742702	+	25.7631i	0.0396425	+	1.37513i
$352$	0.450879	−	0.378332i	0.0240319	−	0.0201652i
$353$	−13.2934	+	23.0249i	−0.707538	+	1.22549i	0.258230	+	0.966084i	$0.416861\pi$
$353$	−13.2934	+	23.0249i	−0.707538	+	1.22549i	−0.965768	+	0.259408i	$0.916472\pi$
$354$	14.1263	+	3.20498i	0.750804	+	0.170343i
$355$	3.91741	+	2.63434i	0.207915	+	0.139816i
$356$	−1.53585	+	8.71025i	−0.0814000	+	0.461642i
$357$	3.99519	+	2.57304i	0.211448	+	0.136179i
$358$	2.01782	+	5.54391i	0.106645	+	0.293005i
$359$	−8.34454	+	9.94464i	−0.440408	+	0.524858i	−0.939895	−	0.341463i	$-0.889077\pi$
$359$	−8.34454	+	9.94464i	−0.440408	+	0.524858i	0.499487	+	0.866321i	$0.333522\pi$
$360$	−6.61649	−	1.10549i	−0.348719	−	0.0582644i
$361$	17.2694	−	7.92254i	0.908918	−	0.416976i
$362$	−5.50535			−0.289355
$363$	−2.31818	−	18.3063i	−0.121673	−	0.960833i
$364$	1.19377	+	3.27985i	0.0625704	+	0.171911i
$365$	−19.4124	−	1.33008i	−1.01609	−	0.0696195i
$366$	0.768842	+	1.01228i	0.0401880	+	0.0529130i
$367$	−8.24108	+	22.6422i	−0.430181	+	1.18191i	0.515521	+	0.856877i	$0.327598\pi$
$367$	−8.24108	+	22.6422i	−0.430181	+	1.18191i	−0.945702	+	0.325035i	$0.894624\pi$
$368$	2.64910	+	4.58838i	0.138094	+	0.239186i
$369$	−32.4237	−	15.5110i	−1.68791	−	0.807472i
$370$	−3.99123	−	8.15416i	−0.207494	−	0.423915i
$371$	0.948376	−	0.795782i	0.0492372	−	0.0413149i
$372$	1.96486	+	6.34073i	0.101873	+	0.328752i
$373$	1.51941	+	2.63170i	0.0786722	+	0.136264i	0.902677	−	0.430318i	$-0.141599\pi$
$373$	1.51941	+	2.63170i	0.0786722	+	0.136264i	−0.824005	+	0.566582i	$0.808265\pi$
$374$	2.15646	+	0.784887i	0.111508	+	0.0405856i
$375$	−19.3041	−	1.53341i	−0.996860	−	0.0791848i
$376$	−5.09609	+	0.898578i	−0.262811	+	0.0463406i
$377$	−32.0586	+	11.6684i	−1.65110	+	0.600952i
$378$	−3.58106	+	0.738425i	−0.184190	+	0.0379805i
$379$		−	26.7261i		−	1.37283i	−0.727211	−	0.686414i	$-0.759184\pi$
$379$		−	26.7261i		−	1.37283i	0.727211	−	0.686414i	$-0.240816\pi$
$380$	−9.74301	−	0.271754i	−0.499806	−	0.0139407i
$381$	3.15817	+	2.92275i	0.161798	+	0.149737i
$382$	14.3562	+	12.0463i	0.734526	+	0.616340i
$383$	11.4573	+	31.4788i	0.585442	+	1.60849i	0.778738	+	0.627349i	$0.215860\pi$
$383$	11.4573	+	31.4788i	0.585442	+	1.60849i	−0.193296	+	0.981141i	$0.561918\pi$
$384$	1.45618	+	0.937832i	0.0743106	+	0.0478585i
$385$	0.375495	−	0.846571i	0.0191370	−	0.0431452i
$386$	−5.82795	+	16.0122i	−0.296635	+	0.814998i
$387$	11.5440	+	16.8381i	0.586816	+	0.855928i
$388$	−5.70838	+	9.88721i	−0.289799	+	0.501947i
$389$	13.0474	+	15.5493i	0.661529	+	0.788380i	0.987604	−	0.156964i	$-0.0501706\pi$
$389$	13.0474	+	15.5493i	0.661529	+	0.788380i	−0.326075	+	0.945344i	$0.605726\pi$
$390$	5.52119	−	18.4002i	0.279577	−	0.931729i
$391$	−10.3288	+	17.8900i	−0.522348	+	0.904734i
$392$	5.63336	−	3.25242i	0.284528	−	0.164272i
$393$	15.8740	−	8.16413i	0.800739	−	0.411826i
$394$	−20.7486	−	3.65854i	−1.04530	−	0.184315i
$395$	28.5567	+	1.95662i	1.43684	+	0.0984480i
$396$	−1.60760	+	0.730395i	−0.0807848	+	0.0367037i
$397$	5.98357	−	7.13094i	0.300307	−	0.357892i	−0.594697	−	0.803950i	$-0.702728\pi$
$397$	5.98357	−	7.13094i	0.300307	−	0.357892i	0.895004	+	0.446058i	$0.147173\pi$
$398$		−	25.4493i		−	1.27566i
$399$	−5.00669	+	1.77680i	−0.250648	+	0.0889511i
$400$	4.42131	+	2.33496i	0.221065	+	0.116748i
$401$	17.9233	+	15.0395i	0.895049	+	0.751035i	0.969216	−	0.246210i	$-0.0791854\pi$
$401$	17.9233	+	15.0395i	0.895049	+	0.751035i	−0.0741673	+	0.997246i	$0.523630\pi$
$402$	−8.42784	+	20.0658i	−0.420343	+	1.00079i
$403$	−18.7214	+	3.30108i	−0.932577	+	0.164438i
$404$	−9.62448	−	1.69705i	−0.478836	−	0.0844316i
$405$	18.2315	+	8.52134i	0.905929	+	0.423429i
$406$	−2.41993	−	4.19144i	−0.120099	−	0.208018i
$407$	−2.06952	−	1.19484i	−0.102582	−	0.0592258i
$408$	−0.327881	+	6.74524i	−0.0162325	+	0.333939i
$409$	8.83396	+	10.5279i	0.436811	+	0.520571i	0.938874	−	0.344260i	$-0.111870\pi$
$409$	8.83396	+	10.5279i	0.436811	+	0.520571i	−0.502063	+	0.864831i	$0.667426\pi$
$410$	19.2973	+	18.5830i	0.953028	+	0.917747i
$411$	2.53224	−	11.1611i	0.124906	−	0.550537i
$412$	3.42010	+	1.24482i	0.168496	+	0.0613277i
$413$	−5.79549	−	1.02190i	−0.285177	−	0.0502844i
$414$	−3.96202	−	15.3929i	−0.194723	−	0.756520i
$415$	27.1974	−	2.89716i	1.33507	−	0.142216i
$416$	−3.18834	+	3.79971i	−0.156321	+	0.186296i
$417$	−2.27911	−	2.10922i	−0.111608	−	0.103289i
$418$	−2.16805	+	1.37174i	−0.106043	+	0.0670942i
$419$		−	31.0113i		−	1.51500i	−0.652836	−	0.757500i	$-0.726421\pi$
$419$		−	31.0113i		−	1.51500i	0.652836	−	0.757500i	$-0.273579\pi$
$420$	2.70669	+	0.318083i	0.132073	+	0.0155209i
$421$	1.29022	+	3.54484i	0.0628813	+	0.172765i	0.967154	−	0.254190i	$-0.0818087\pi$
$421$	1.29022	+	3.54484i	0.0628813	+	0.172765i	−0.904273	+	0.426954i	$0.859586\pi$
$422$	−0.527940	−	2.99410i	−0.0256997	−	0.145750i
$423$	15.4509	+	1.50567i	0.751249	+	0.0732082i
$424$	1.65326	+	0.601737i	0.0802894	+	0.0292230i
$425$	0.735036	+	19.4810i	0.0356545	+	0.944966i
$426$	1.08236	+	3.49285i	0.0524405	+	0.169229i
$427$	−0.331953	−	0.395607i	−0.0160644	−	0.0191448i
$428$	0.996383	+	1.18744i	0.0481620	+	0.0573972i
$429$	−1.49674	−	4.83007i	−0.0722631	−	0.233198i
$430$	−4.21481	−	14.6213i	−0.203256	−	0.705103i
$431$	16.6213	+	6.04965i	0.800619	+	0.291401i	0.709743	−	0.704461i	$-0.248811\pi$
$431$	16.6213	+	6.04965i	0.800619	+	0.291401i	0.0908758	+	0.995862i	$0.471033\pi$
$432$	−3.45334	−	3.88258i	−0.166149	−	0.186801i
$433$	5.52724	+	31.3465i	0.265622	+	1.50642i	0.767258	+	0.641338i	$0.221621\pi$
$433$	5.52724	+	31.3465i	0.265622	+	1.50642i	−0.501636	+	0.865079i	$0.667268\pi$
$434$	−0.922384	−	2.53423i	−0.0442759	−	0.121647i
$435$	−3.10907	+	26.4563i	−0.149069	+	1.26848i
$436$		−	1.85210i		−	0.0886997i
$437$	−8.77147	−	21.3638i	−0.419596	−	1.02197i
$438$	−11.0619	−	10.2373i	−0.528557	−	0.489157i
$439$	−1.67532	+	1.99656i	−0.0799585	+	0.0952908i	−0.804541	−	0.593898i	$-0.797588\pi$
$439$	−1.67532	+	1.99656i	−0.0799585	+	0.0952908i	0.724582	+	0.689189i	$0.242033\pi$
$440$	1.30870	−	0.139407i	0.0623899	−	0.00664598i
$441$	−18.8985	+	4.86434i	−0.899931	+	0.231635i
$442$	−19.0457	−	3.35828i	−0.905914	−	0.159737i
$443$	−2.66945	−	0.971602i	−0.126830	−	0.0461622i	0.277826	−	0.960632i	$-0.410386\pi$
$443$	−2.66945	−	0.971602i	−0.126830	−	0.0461622i	−0.404655	+	0.914469i	$0.632608\pi$
$444$	1.55593	−	6.85793i	0.0738413	−	0.325463i
$445$	−13.7184	+	14.2458i	−0.650314	+	0.675314i
$446$	−4.29849	−	5.12274i	−0.203539	−	0.242569i
$447$	−1.86509	+	38.3691i	−0.0882157	+	1.81480i
$448$	−0.609399	−	0.351837i	−0.0287914	−	0.0166227i
$449$	−2.32272	−	4.02306i	−0.109616	−	0.189860i	0.805999	−	0.591917i	$-0.201629\pi$
$449$	−2.32272	−	4.02306i	−0.109616	−	0.189860i	−0.915615	+	0.402057i	$0.868295\pi$
$450$	−10.8977	−	10.3073i	−0.513723	−	0.485889i
$451$	6.94462	+	1.22452i	0.327009	+	0.0576606i
$452$	4.57410	−	0.806537i	0.215148	−	0.0379363i
$453$	4.12218	−	9.81447i	0.193677	−	0.461124i
$454$	−4.13575	−	3.47030i	−0.194100	−	0.162869i
$455$	−1.87749	+	7.57546i	−0.0880179	+	0.355143i
$456$	−5.74428	−	4.89932i	−0.269000	−	0.229432i
$457$		−	33.8451i		−	1.58321i	−0.611036	−	0.791603i	$-0.709247\pi$
$457$		−	33.8451i		−	1.58321i	0.611036	−	0.791603i	$-0.290753\pi$
$458$	−7.57054	+	9.02222i	−0.353748	+	0.421581i
$459$	6.37773	−	19.2296i	0.297687	−	0.897560i
$460$	−0.809831	+	11.8194i	−0.0377586	+	0.551085i
$461$	1.14556	+	0.201994i	0.0533543	+	0.00940779i	0.200262	−	0.979742i	$-0.435821\pi$
$461$	1.14556	+	0.201994i	0.0533543	+	0.00940779i	−0.146907	+	0.989150i	$0.546932\pi$
$462$	0.637935	−	0.328095i	0.0296794	−	0.0152643i
$463$	2.91055	−	1.68041i	0.135265	−	0.0780951i	−0.430841	−	0.902428i	$-0.641783\pi$
$463$	2.91055	−	1.68041i	0.135265	−	0.0780951i	0.566105	+	0.824333i	$0.308450\pi$
$464$	3.43900	−	5.95652i	0.159651	−	0.276524i
$465$	−4.26604	+	14.2172i	−0.197833	+	0.659306i
$466$	−2.87874	−	3.43074i	−0.133355	−	0.158926i
$467$	−5.04251	+	8.73388i	−0.233339	+	0.404156i	−0.958789	−	0.284120i	$-0.908299\pi$
$467$	−5.04251	+	8.73388i	−0.233339	+	0.404156i	0.725449	+	0.688275i	$0.241632\pi$
$468$	12.2731	−	8.41433i	0.567324	−	0.388952i
$469$	3.02411	−	8.30868i	0.139641	−	0.383659i
$470$	−10.5772	−	4.69151i	−0.487891	−	0.216403i
$471$	9.57821	+	6.16869i	0.441341	+	0.284238i
$472$	−2.86035	−	7.85874i	−0.131658	−	0.361728i
$473$	−3.06828	−	2.57459i	−0.141080	−	0.118380i
$474$	16.2726	+	15.0596i	0.747426	+	0.691710i
$475$	−17.7394	−	12.6615i	−0.813940	−	0.580949i
$476$		−	2.74360i		−	0.125753i
$477$	−4.29345	−	3.06994i	−0.196584	−	0.140563i
$478$	−11.4423	+	4.16465i	−0.523358	+	0.190487i
$479$	−17.0808	+	3.01180i	−0.780440	+	0.137613i	−0.549655	−	0.835392i	$-0.685241\pi$
$479$	−17.0808	+	3.01180i	−0.780440	+	0.137613i	−0.230785	+	0.973005i	$0.574130\pi$
$480$	1.53179	+	3.55719i	0.0699161	+	0.162363i
$481$	18.9241	+	6.88780i	0.862864	+	0.314057i
$482$	0.569355	+	0.986152i	0.0259334	+	0.0449180i
$483$	1.91136	+	6.16809i	0.0869699	+	0.280658i
$484$	−8.16111	+	6.84798i	−0.370960	+	0.311272i
$485$	−22.9293	+	11.2232i	−1.04116	+	0.509620i
$486$	6.85442	+	14.0006i	0.310923	+	0.635080i
$487$	−16.4000	−	28.4057i	−0.743157	−	1.28719i	−0.951051	−	0.309034i	$-0.899994\pi$
$487$	−16.4000	−	28.4057i	−0.743157	−	1.28719i	0.207894	−	0.978151i	$-0.433339\pi$
$488$	0.251009	−	0.689643i	0.0113627	−	0.0312187i
$489$	−23.0076	−	30.2927i	−1.04044	−	1.36988i
$490$	14.5113	+	0.994265i	0.655551	+	0.0449163i
$491$	−2.66282	−	7.31603i	−0.120171	−	0.330168i	0.864992	−	0.501785i	$-0.167323\pi$
$491$	−2.66282	−	7.31603i	−0.120171	−	0.330168i	−0.985164	+	0.171617i	$0.945101\pi$
$492$	2.60701	+	20.5872i	0.117533	+	0.928142i
$493$	26.8171			1.20778
$494$	15.9859	−	14.5572i	0.719241	−	0.654962i
$495$	−3.89434	−	0.650670i	−0.175037	−	0.0292454i
$496$	2.46352	−	2.93591i	0.110615	−	0.131826i
$497$	−0.508104	−	1.39600i	−0.0227916	−	0.0626194i
$498$	17.8119	+	11.4714i	0.798168	+	0.514048i
$499$	1.88699	−	10.7017i	0.0844733	−	0.479072i	−0.912996	−	0.407969i	$-0.866237\pi$
$499$	1.88699	−	10.7017i	0.0844733	−	0.479072i	0.997469	−	0.0711028i	$-0.0226518\pi$
$500$	5.29036	+	9.84947i	0.236592	+	0.440482i
$501$	40.5275	+	9.19490i	1.81063	+	0.410798i
$502$	6.75166	−	11.6942i	0.301341	−	0.521938i
$503$	−2.59237	+	2.17526i	−0.115588	+	0.0969899i	−0.698750	−	0.715366i	$-0.746260\pi$
$503$	−2.59237	+	2.17526i	−0.115588	+	0.0969899i	0.583162	+	0.812356i	$0.301815\pi$
$504$	1.47790	+	1.50739i	0.0658311	+	0.0671443i
$505$	−15.7410	−	15.1583i	−0.700465	−	0.674535i
$506$	1.55921	+	2.70063i	0.0693154	+	0.120058i
$507$	9.19188	+	17.8723i	0.408226	+	0.793739i
$508$	0.431409	−	2.44664i	0.0191407	−	0.108552i
$509$	−0.888374	−	5.03822i	−0.0393765	−	0.223315i	0.958769	−	0.284186i	$-0.0917233\pi$
$509$	−0.888374	−	5.03822i	−0.0393765	−	0.223315i	−0.998146	+	0.0608709i	$0.980612\pi$
$510$	−9.02505	+	12.1069i	−0.399636	+	0.536104i
$511$	4.69070	+	3.93596i	0.207504	+	0.174117i
$512$		−	1.00000i		−	0.0441942i
$513$	12.6567	+	18.7832i	0.558805	+	0.829299i
$514$	−15.8109			−0.697388
$515$	4.79286	+	6.57737i	0.211199	+	0.289834i
$516$	4.56433	−	10.8672i	0.200933	−	0.478401i
$517$	−2.99946	+	0.528886i	−0.131916	+	0.0232604i
$518$	−0.496105	+	2.81355i	−0.0217976	+	0.123620i
$519$	−8.15849	+	4.19597i	−0.358118	+	0.184183i
$520$	−10.6573	+	3.07213i	−0.467355	+	0.134722i
$521$	−8.32550	+	14.4202i	−0.364747	+	0.631760i	−0.988735	−	0.149673i	$-0.952178\pi$
$521$	−8.32550	+	14.4202i	−0.364747	+	0.631760i	0.623989	+	0.781433i	$0.285511\pi$
$522$	−14.7338	+	14.4456i	−0.644881	+	0.632268i
$523$	−4.88617	+	4.09999i	−0.213657	+	0.179280i	−0.743335	−	0.668919i	$-0.766757\pi$
$523$	−4.88617	+	4.09999i	−0.213657	+	0.179280i	0.529678	+	0.848199i	$0.322313\pi$
$524$	−8.92521	−	5.15297i	−0.389900	−	0.225109i
$525$	4.62546	+	3.96760i	0.201872	+	0.173160i
$526$	−0.321298	+	0.882759i	−0.0140093	+	0.0384901i
$527$	14.7160	+	2.59483i	0.641039	+	0.113032i
$528$	0.857082	+	0.551990i	0.0372997	+	0.0240223i
$529$	−4.76521	+	1.73439i	−0.207183	+	0.0754084i
$530$	2.31684	+	3.17947i	0.100637	+	0.138107i
$531$	1.93975	+	25.0142i	0.0841779	+	1.08552i
$532$	2.42759	+	1.87477i	0.105249	+	0.0812817i
$533$	−59.4275			−2.57409
$534$	−15.1980	+	1.92455i	−0.657680	+	0.0832836i
$535$	0.367145	+	3.44662i	0.0158731	+	0.149010i
$536$	12.3745	−	2.18195i	0.534495	−	0.0942460i
$537$	−8.13757	+	6.18058i	−0.351162	+	0.266712i
$538$	2.16752	−	5.95522i	0.0934486	−	0.256748i
$539$	3.31569	−	1.91431i	0.142817	−	0.0824553i
$540$	−1.56314	−	11.5133i	−0.0672670	−	0.495454i
$541$	26.2558	−	22.0313i	1.12883	−	0.947198i	0.129810	−	0.991539i	$-0.458563\pi$
$541$	26.2558	−	22.0313i	1.12883	−	0.947198i	0.999016	+	0.0443409i	$0.0141188\pi$
$542$	−17.5134	−	20.8717i	−0.752266	−	0.896516i
$543$	−2.82246	−	9.10826i	−0.121123	−	0.390873i
$544$	3.37660	−	1.94948i	0.144771	−	0.0835834i
$545$	2.31104	−	3.43665i	0.0989941	−	0.147210i
$546$	−4.81429	+	3.65651i	−0.206033	+	0.156484i
$547$	6.32651	+	35.8794i	0.270502	+	1.53409i	0.752896	+	0.658139i	$0.228656\pi$
$547$	6.32651	+	35.8794i	0.270502	+	1.53409i	−0.482394	+	0.875954i	$0.660233\pi$
$548$	−6.20915	+	2.25995i	−0.265242	+	0.0965401i
$549$	−1.28060	+	1.79097i	−0.0546545	+	0.0764369i
$550$	2.60230	+	1.37431i	0.110962	+	0.0586009i
$551$	−18.3248	+	23.7283i	−0.780663	+	1.01086i
$552$	−6.23307	+	6.73513i	−0.265297	+	0.286666i
$553$	−6.90026	−	5.79001i	−0.293429	−	0.246216i
$554$	21.6288	−	7.87223i	0.918919	−	0.334459i
$555$	11.4444	−	10.7837i	0.485786	−	0.457741i
$556$	−0.311328	+	1.76563i	−0.0132033	+	0.0748794i
$557$	6.08867	+	2.21609i	0.257985	+	0.0938989i	0.467775	−	0.883848i	$-0.345056\pi$
$557$	6.08867	+	2.21609i	0.257985	+	0.0938989i	−0.209790	+	0.977746i	$0.567278\pi$
$558$	−9.48301	+	6.50147i	−0.401448	+	0.275229i
$559$	29.2323	+	16.8773i	1.23639	+	0.713832i
$560$	−0.691744	−	1.41325i	−0.0292315	−	0.0597207i
$561$	−0.192984	+	3.97012i	−0.00814780	+	0.167619i
$562$	−21.7464	−	12.5553i	−0.917317	−	0.529613i
$563$	18.1512	−	10.4796i	0.764981	−	0.441662i	−0.0661006	−	0.997813i	$-0.521056\pi$
$563$	18.1512	−	10.4796i	0.764981	−	0.441662i	0.831081	+	0.556151i	$0.187722\pi$
$564$	−4.09928	−	7.97048i	−0.172611	−	0.335618i
$565$	9.49380	+	4.21096i	0.399407	+	0.177156i
$566$	−4.01089	−	22.7469i	−0.168590	−	0.956123i
$567$	−3.05760	−	5.54606i	−0.128407	−	0.232913i
$568$	1.35705	−	1.61727i	0.0569407	−	0.0678593i
$569$	16.6126			0.696435			0.348217	−	0.937414i	$-0.386787\pi$
$569$	16.6126			0.696435			0.348217	+	0.937414i	$0.386787\pi$
$570$	−4.54539	−	16.2585i	−0.190386	−	0.680994i
$571$	−24.5511			−1.02743			−0.513716	−	0.857960i	$-0.671732\pi$
$571$	−24.5511			−1.02743			−0.513716	+	0.857960i	$0.671732\pi$
$572$	−1.87659	+	2.23644i	−0.0784644	+	0.0935102i
$573$	−12.5697	+	29.9272i	−0.525108	+	1.25023i
$574$	−1.46397	−	8.30259i	−0.0611049	−	0.346543i
$575$	−16.2509	+	20.9209i	−0.677708	+	0.872463i
$576$	−0.805036	+	2.88997i	−0.0335431	+	0.120415i
$577$	−10.0080	+	5.77810i	−0.416637	+	0.240546i	−0.693637	−	0.720324i	$-0.743993\pi$
$577$	−10.0080	+	5.77810i	−0.416637	+	0.240546i	0.277000	+	0.960870i	$0.410660\pi$
$578$	−1.55716	−	0.899029i	−0.0647695	−	0.0373947i
$579$	−29.4790	−	1.43295i	−1.22510	−	0.0595513i
$580$	13.8137	−	6.76139i	0.573581	−	0.280751i
$581$	−7.45409	−	4.30362i	−0.309248	−	0.178544i
$582$	−19.2843	−	4.37524i	−0.799360	−	0.181360i
$583$	0.973077	+	0.354171i	0.0403007	+	0.0146683i
$584$	−1.51106	+	8.56966i	−0.0625282	+	0.354615i
$585$	33.2725	−	0.298833i	1.37565	−	0.0123552i
$586$	5.86401	−	2.13432i	0.242240	−	0.0881681i
$587$	21.0811	+	17.6891i	0.870109	+	0.730108i	0.964121	−	0.265463i	$-0.0855249\pi$
$587$	21.0811	+	17.6891i	0.870109	+	0.730108i	−0.0940123	+	0.995571i	$0.529969\pi$
$588$	8.26901	+	7.65261i	0.341008	+	0.315588i
$589$	−12.3518	+	11.2479i	−0.508946	+	0.463461i
$590$	4.49858	−	18.1513i	0.185204	−	0.747277i
$591$	−4.58447	−	36.2030i	−0.188580	−	1.48919i
$592$	−3.81520	+	1.38862i	−0.156804	+	0.0570720i
$593$	2.79635	+	15.8589i	0.114832	+	0.651246i	0.986833	+	0.161742i	$0.0517112\pi$
$593$	2.79635	+	15.8589i	0.114832	+	0.651246i	−0.872001	+	0.489504i	$0.837178\pi$
$594$	−2.03257	−	2.28521i	−0.0833973	−	0.0937635i
$595$	3.42344	−	5.09085i	0.140347	−	0.208705i
$596$	19.2072	−	11.0893i	0.786757	−	0.454235i
$597$	42.1042	−	13.0472i	1.72321	−	0.533986i
$598$	−16.8925	−	20.1317i	−0.690785	−	0.823246i
$599$	20.3906	−	17.1098i	0.833138	−	0.699086i	−0.122871	−	0.992423i	$-0.539210\pi$
$599$	20.3906	−	17.1098i	0.833138	−	0.699086i	0.956009	+	0.293337i	$0.0947656\pi$
$600$	−1.59635	+	8.51185i	−0.0651707	+	0.347495i
$601$	−19.4310	+	11.2185i	−0.792606	+	0.457611i	−0.840879	−	0.541223i	$-0.817961\pi$
$601$	−19.4310	+	11.2185i	−0.792606	+	0.457611i	0.0482733	+	0.998834i	$0.484628\pi$
$602$	−1.63779	+	4.49979i	−0.0667513	+	0.183398i
$603$	−37.5184	−	3.65611i	−1.52787	−	0.148888i
$604$	−6.05253	+	1.06722i	−0.246274	+	0.0434247i
$605$	−23.6881	+	2.52333i	−0.963058	+	0.102588i
$606$	−2.12656	−	16.7931i	−0.0863854	−	0.682174i
$607$	−35.9563			−1.45942			−0.729711	−	0.683756i	$-0.760345\pi$
$607$	−35.9563			−1.45942			−0.729711	+	0.683756i	$0.760345\pi$
$608$	−0.582381	+	4.31982i	−0.0236187	+	0.175192i
$609$	5.69384	−	6.15247i	0.230726	−	0.249311i
$610$	1.32629	−	0.966451i	0.0536998	−	0.0391304i
$611$	24.1195	−	8.77878i	0.975770	−	0.355151i
$612$	−11.3277	+	2.91566i	−0.457894	+	0.117859i
$613$	7.22022	+	1.27312i	0.291622	+	0.0514208i	0.317545	−	0.948243i	$-0.397141\pi$
$613$	7.22022	+	1.27312i	0.291622	+	0.0514208i	−0.0259232	+	0.999664i	$0.508253\pi$
$614$	−2.60853	+	7.16687i	−0.105272	+	0.289231i
$615$	−20.8511	+	41.4533i	−0.840798	+	1.67156i
$616$	−0.358681	−	0.207084i	−0.0144517	−	0.00834367i
$617$	−6.29623	+	5.28317i	−0.253477	+	0.212692i	−0.760668	−	0.649141i	$-0.775128\pi$
$617$	−6.29623	+	5.28317i	−0.253477	+	0.212692i	0.507191	+	0.861834i	$0.330684\pi$
$618$	−0.306069	+	6.29653i	−0.0123119	+	0.253284i
$619$	−24.0373	+	41.6339i	−0.966142	+	1.67341i	−0.259628	+	0.965709i	$0.583600\pi$
$619$	−24.0373	+	41.6339i	−0.966142	+	1.67341i	−0.706514	+	0.707699i	$0.749733\pi$
$620$	8.23456	−	2.37373i	0.330708	−	0.0953314i
$621$	23.4354	−	14.4465i	0.940430	−	0.579717i
$622$	−1.15676	+	6.56031i	−0.0463818	+	0.263044i
$623$	6.12917	−	1.08074i	0.245560	−	0.0432989i
$624$	−7.92097	−	3.32689i	−0.317093	−	0.133182i
$625$	−2.47361	+	24.8773i	−0.0989446	+	0.995093i
$626$	−23.3661			−0.933899
$627$	−3.38097	−	2.88364i	−0.135023	−	0.115162i
$628$		−	6.57761i		−	0.262475i
$629$	−12.1265	−	10.1753i	−0.483515	−	0.405717i
$630$	0.861403	+	4.64112i	0.0343191	+	0.184907i
$631$	1.11777	+	6.33918i	0.0444977	+	0.252359i	0.998940	−	0.0460375i	$-0.0146594\pi$
$631$	1.11777	+	6.33918i	0.0444977	+	0.252359i	−0.954442	+	0.298396i	$0.903548\pi$
$632$	2.22285	−	12.6064i	0.0884203	−	0.501457i
$633$	4.68288	−	2.40844i	0.186128	−	0.0957269i
$634$	−15.2260	−	26.3721i	−0.604700	−	1.04737i
$635$	3.85339	−	4.00153i	0.152917	−	0.158796i
$636$	−0.147952	+	3.04371i	−0.00586669	+	0.120691i
$637$	−24.7165	+	20.7396i	−0.979305	+	0.821734i
$638$	2.02413	−	3.50589i	0.0801359	−	0.138800i
$639$	−5.22381	+	3.58139i	−0.206651	+	0.141678i
$640$	1.24779	−	1.85554i	0.0493233	−	0.0733465i
$641$	−5.59910	+	31.7541i	−0.221151	+	1.25421i	0.648756	+	0.760996i	$0.275290\pi$
$641$	−5.59910	+	31.7541i	−0.221151	+	1.25421i	−0.869907	+	0.493215i	$0.835822\pi$
$642$	−1.45373	+	2.25723i	−0.0573741	+	0.0890856i
$643$	11.1669	+	30.6808i	0.440380	+	1.20993i	0.939243	+	0.343253i	$0.111529\pi$
$643$	11.1669	+	30.6808i	0.440380	+	1.20993i	−0.498863	+	0.866681i	$0.666249\pi$
$644$	2.39645	−	2.85597i	0.0944333	−	0.112541i
$645$	22.0292	−	14.4691i	0.867401	−	0.569721i
$646$	−15.7217	+	6.45495i	−0.618560	+	0.253966i
$647$	0.721070			0.0283482			0.0141741	−	0.999900i	$-0.495488\pi$
$647$	0.721070			0.0283482			0.0141741	+	0.999900i	$0.495488\pi$
$648$	4.65305	−	7.70384i	0.182789	−	0.302635i
$649$	−1.68355	−	4.62550i	−0.0660849	−	0.181567i
$650$	−23.6084	−	7.59766i	−0.925999	−	0.298005i
$651$	3.71984	−	2.82526i	0.145792	−	0.110731i
$652$	−7.51147	+	20.6376i	−0.294172	+	0.808230i
$653$	18.1847	+	31.4968i	0.711622	+	1.23257i	0.964248	+	0.265002i	$0.0853726\pi$
$653$	18.1847	+	31.4968i	0.711622	+	1.23257i	−0.252625	+	0.967564i	$0.581294\pi$
$654$	3.06419	−	0.949528i	0.119819	−	0.0371295i
$655$	−10.1312	−	20.6983i	−0.395860	−	0.808751i
$656$	9.17793	−	7.70120i	0.358338	−	0.300681i
$657$	11.2658	−	23.5496i	0.439521	−	0.918757i
$658$	1.82065	+	3.15346i	0.0709764	+	0.122935i
$659$	5.08952	+	1.85243i	0.198260	+	0.0721606i	0.439242	−	0.898369i	$-0.355247\pi$
$659$	5.08952	+	1.85243i	0.198260	+	0.0721606i	−0.240982	+	0.970530i	$0.577469\pi$
$660$	0.901579	+	2.09370i	0.0350939	+	0.0814970i
$661$	−45.1136	+	7.95474i	−1.75471	+	0.309404i	−0.956231	−	0.292613i	$-0.905475\pi$
$661$	−45.1136	+	7.95474i	−1.75471	+	0.309404i	−0.798484	+	0.602017i	$0.794364\pi$
$662$	21.1939	−	7.71395i	0.823724	−	0.299811i
$663$	−4.20821	−	33.2317i	−0.163433	−	1.29061i
$664$		−	12.2319i		−	0.474689i
$665$	2.16516	+	6.50784i	0.0839613	+	0.252363i
$666$	12.1437	−	0.941696i	0.470559	−	0.0364900i
$667$	27.9155	+	23.4238i	1.08089	+	0.906975i
$668$	−8.20616	−	22.5462i	−0.317506	−	0.872340i
$669$	6.27152	−	9.73788i	0.242471	−	0.376488i
$670$	25.6839	+	11.3921i	0.992256	+	0.440113i
$671$	0.147739	−	0.405911i	0.00570341	−	0.0156700i
$672$	0.269668	−	1.18859i	0.0104027	−	0.0458509i
$673$	19.4385	−	33.6685i	0.749299	−	1.29782i	−0.198860	−	0.980028i	$-0.563724\pi$
$673$	19.4385	−	33.6685i	0.749299	−	1.29782i	0.948159	−	0.317796i	$-0.102943\pi$
$674$	−12.2567	−	14.6070i	−0.472111	−	0.562640i
$675$	11.4657	−	23.3139i	0.441317	−	0.897351i
$676$	5.80166	−	10.0488i	0.223141	−	0.386491i
$677$	−20.1798	+	11.6508i	−0.775573	+	0.447777i	−0.834859	−	0.550464i	$-0.814451\pi$
$677$	−20.1798	+	11.6508i	−0.775573	+	0.447777i	0.0592860	+	0.998241i	$0.481118\pi$
$678$	3.67939	+	7.15407i	0.141306	+	0.274750i
$679$	7.91163	+	1.39503i	0.303620	+	0.0535365i
$680$	8.69796	+	0.595957i	0.333552	+	0.0228539i
$681$	3.62111	−	8.62147i	0.138761	−	0.330375i
$682$	1.44998	−	1.72802i	0.0555227	−	0.0661693i
$683$			4.43162i			0.169571i	0.996399	+	0.0847856i	$0.0270205\pi$
$683$			4.43162i			0.169571i	−0.996399	+	0.0847856i	$0.972979\pi$
$684$	5.16067	−	12.0153i	0.197323	−	0.459417i
$685$	−14.3412	−	3.55431i	−0.547951	−	0.135803i
$686$	−7.27972	−	6.10841i	−0.277941	−	0.233220i
$687$	−18.8079	−	7.89953i	−0.717567	−	0.301386i
$688$	−6.70173	+	1.18170i	−0.255501	+	0.0450517i
$689$	−8.59417	−	1.51538i	−0.327412	−	0.0577315i
$690$	−19.9697	+	4.71972i	−0.760234	+	0.179677i
$691$	−12.5291	−	21.7010i	−0.476628	−	0.825545i	0.523013	−	0.852325i	$-0.324808\pi$
$691$	−12.5291	−	21.7010i	−0.476628	−	0.825545i	−0.999641	+	0.0267801i	$0.991475\pi$
$692$	4.58713	+	2.64838i	0.174377	+	0.100676i
$693$	0.869866	+	0.887218i	0.0330435	+	0.0337026i
$694$	−12.8923	−	15.3644i	−0.489385	−	0.583226i
$695$	−2.78082	+	2.88772i	−0.105483	+	0.109538i
$696$	11.6178	+	2.63585i	0.440370	+	0.0999116i
$697$	43.8961	+	15.9769i	1.66268	+	0.605168i
$698$	29.6044	+	5.22005i	1.12054	+	0.197582i
$699$	4.20010	−	6.52155i	0.158862	−	0.246668i
$700$	0.479882	−	3.48549i	0.0181378	−	0.131739i
$701$	−17.4000	+	20.7365i	−0.657188	+	0.783206i	−0.986979	−	0.160848i	$-0.948577\pi$
$701$	−17.4000	+	20.7365i	−0.657188	+	0.783206i	0.329791	+	0.944054i	$0.393022\pi$
$702$	20.2131	+	15.9913i	0.762894	+	0.603552i
$703$	17.2897	−	3.77669i	0.652093	−	0.142441i
$704$		−	0.588581i		−	0.0221830i
$705$	2.33913	−	19.9046i	0.0880968	−	0.749649i
$706$	9.09324	+	24.9835i	0.342229	+	0.940266i
$707$	1.19417	+	6.77249i	0.0449115	+	0.254706i
$708$	11.5354	−	8.76125i	0.433526	−	0.329268i
$709$	−21.1852	−	7.71080i	−0.795628	−	0.289585i	−0.0879546	−	0.996124i	$-0.528033\pi$
$709$	−21.1852	−	7.71080i	−0.795628	−	0.289585i	−0.707674	+	0.706539i	$0.750255\pi$
$710$	4.53608	−	1.30759i	0.170236	−	0.0490731i
$711$	−16.5726	+	34.6427i	−0.621521	+	1.29920i
$712$	5.68521	+	6.77537i	0.213062	+	0.253918i
$713$	13.0523	+	15.5551i	0.488811	+	0.582542i
$714$	4.53912	−	1.40657i	0.169872	−	0.0526397i
$715$	−6.27270	+	1.80820i	−0.234586	+	0.0676227i
$716$	5.54391	+	2.01782i	0.207186	+	0.0754094i
$717$	−12.7563	−	16.7954i	−0.476394	−	0.627237i
$718$	2.25427	+	12.7846i	0.0841285	+	0.477116i
$719$	−4.35482	−	11.9648i	−0.162408	−	0.446211i	0.831619	−	0.555346i	$-0.187414\pi$
$719$	−4.35482	−	11.9648i	−0.162408	−	0.446211i	−0.994027	+	0.109135i	$0.965192\pi$
$720$	−5.09985	+	4.35793i	−0.190060	+	0.162410i
$721$		−	2.56109i		−	0.0953799i
$722$	5.03156	−	18.3217i	0.187255	−	0.681862i
$723$	−1.33963	+	1.44754i	−0.0498215	+	0.0538345i
$724$	−3.53877	+	4.21734i	−0.131517	+	0.156736i
$725$	34.0686	+	4.69056i	1.26528	+	0.174203i
$726$	−15.5136	−	9.99126i	−0.575762	−	0.370810i
$727$	−51.8091	−	9.13534i	−1.92149	−	0.338811i	−0.922596	−	0.385767i	$-0.873937\pi$
$727$	−51.8091	−	9.13534i	−1.92149	−	0.338811i	−0.998897	+	0.0469563i	$0.985048\pi$
$728$	3.27985	+	1.19377i	0.121559	+	0.0442440i
$729$	−19.6490	+	18.5180i	−0.727742	+	0.685851i
$730$	−13.4970	+	14.0158i	−0.499546	+	0.518750i
$731$	−17.0550	−	20.3254i	−0.630803	−	0.751761i
$732$	1.26966	+	0.0617170i	0.0469279	+	0.00228113i
$733$	1.86260	+	1.07537i	0.0687968	+	0.0397199i	0.534004	−	0.845482i	$-0.320687\pi$
$733$	1.86260	+	1.07537i	0.0687968	+	0.0397199i	−0.465207	+	0.885202i	$0.654020\pi$
$734$	12.0477	+	20.8672i	0.444687	+	0.770221i
$735$	5.79460	+	24.5177i	0.213737	+	0.904349i
$736$	5.21772	+	0.920024i	0.192328	+	0.0339126i
$737$	7.28337	−	1.28426i	0.268286	−	0.0473061i
$738$	−32.7237	+	14.8677i	−1.20457	+	0.547286i
$739$	−26.1969	−	21.9818i	−0.963667	−	0.808613i	0.0178787	−	0.999840i	$-0.494309\pi$
$739$	−26.1969	−	21.9818i	−0.963667	−	0.808613i	−0.981546	+	0.191228i	$0.938753\pi$
$740$	−8.81196	−	2.18394i	−0.323934	−	0.0802832i
$741$	32.2796	+	18.9846i	1.18582	+	0.697416i
$742$		−	1.23802i		−	0.0454490i
$743$	2.40055	−	2.86086i	0.0880675	−	0.104955i	−0.720211	−	0.693755i	$-0.755955\pi$
$743$	2.40055	−	2.86086i	0.0880675	−	0.104955i	0.808279	+	0.588800i	$0.200400\pi$
$744$	6.12027	+	2.57058i	0.224380	+	0.0942419i
$745$	49.4768	+	3.38999i	1.81269	+	0.124200i
$746$	2.99266	+	0.527686i	0.109569	+	0.0193200i
$747$	−9.84709	+	35.3497i	−0.360286	+	1.29338i
$748$	1.98740	−	1.14743i	0.0726667	−	0.0419541i
$749$	0.545381	−	0.944628i	0.0199278	−	0.0345159i
$750$	−13.5831	+	13.8022i	−0.495985	+	0.503983i
$751$	25.8996	+	30.8659i	0.945089	+	1.12631i	0.991850	+	0.127408i	$0.0406656\pi$
$751$	25.8996	+	30.8659i	0.945089	+	1.12631i	−0.0467611	+	0.998906i	$0.514890\pi$
$752$	−2.58735	+	4.48142i	−0.0943510	+	0.163421i
$753$	22.8087	+	5.17487i	0.831197	+	0.188583i
$754$	−11.6684	+	32.0586i	−0.424937	+	1.16750i
$755$	−12.5624	−	5.57201i	−0.457191	−	0.202786i
$756$	−1.73619	+	3.21790i	−0.0631447	+	0.117034i
$757$	−14.4394	−	39.6718i	−0.524808	−	1.44190i	−0.865111	−	0.501581i	$-0.832752\pi$
$757$	−14.4394	−	39.6718i	−0.524808	−	1.44190i	0.340303	−	0.940316i	$-0.389470\pi$
$758$	−20.4734	−	17.1792i	−0.743627	−	0.623977i
$759$	−3.66866	+	3.96417i	−0.133164	+	0.143890i
$760$	−6.47086	+	7.28889i	−0.234723	+	0.264396i
$761$			14.1016i			0.511181i	0.966785	+	0.255590i	$0.0822699\pi$
$761$			14.1016i			0.511181i	−0.966785	+	0.255590i	$0.917730\pi$
$762$	4.26899	−	0.540593i	0.154649	−	0.0195836i
$763$	−1.22468	+	0.445747i	−0.0443364	+	0.0161371i
$764$	18.4559	−	3.25428i	0.667712	−	0.117736i
$765$	−24.6571	−	8.72446i	−0.891478	−	0.315434i
$766$	31.4788	+	11.4573i	1.13737	+	0.413970i
$767$	20.7412	+	35.9248i	0.748921	+	1.29717i
$768$	1.65444	−	0.512675i	0.0596994	−	0.0184996i
$769$	25.0246	−	20.9982i	0.902411	−	0.757213i	−0.0682489	−	0.997668i	$-0.521741\pi$
$769$	25.0246	−	20.9982i	0.902411	−	0.757213i	0.970660	+	0.240455i	$0.0772968\pi$
$770$	−0.407147	−	0.831811i	−0.0146726	−	0.0299764i
$771$	−8.10585	−	26.1581i	−0.291925	−	0.942062i
$772$	8.51990	+	14.7569i	0.306638	+	0.531112i
$773$	17.0769	−	46.9183i	0.614212	−	1.68753i	−0.106512	−	0.994311i	$-0.533968\pi$
$773$	17.0769	−	46.9183i	0.614212	−	1.68753i	0.720724	−	0.693222i	$-0.243810\pi$
$774$	20.3191	+	1.98007i	0.730354	+	0.0711720i
$775$	18.2414	+	5.87046i	0.655252	+	0.210873i
$776$	3.90476	+	10.7282i	0.140173	+	0.385122i
$777$	−4.90919	+	0.621662i	−0.176116	+	0.0223020i
$778$	20.2982			0.727724
$779$	−44.1320	+	27.9227i	−1.58119	+	1.00044i
$780$	−10.5464	−	16.0569i	−0.377621	−	0.574929i
$781$	0.798736	−	0.951897i	0.0285810	−	0.0340615i
$782$	7.06530	+	19.4117i	0.252654	+	0.694162i
$783$	−31.4530	−	16.9702i	−1.12404	−	0.606467i
$784$	1.12955	−	6.40602i	0.0403412	−	0.228786i
$785$	8.20748	−	12.2050i	0.292938	−	0.435615i
$786$	3.94954	−	17.4080i	0.140876	−	0.620923i
$787$	0.615944	−	1.06685i	0.0219560	−	0.0380290i	−0.854839	−	0.518894i	$-0.826344\pi$
$787$	0.615944	−	1.06685i	0.0219560	−	0.0380290i	0.876795	+	0.480865i	$0.159677\pi$
$788$	−16.1396	+	13.5427i	−0.574948	+	0.482439i
$789$	−1.62519	−	0.0789992i	−0.0578584	−	0.00281245i
$790$	19.8548	−	20.6180i	0.706401	−	0.733557i
$791$	−1.63416	−	2.83045i	−0.0581041	−	0.100639i
$792$	−0.473828	+	1.70098i	−0.0168368	+	0.0604417i
$793$	−0.632129	+	3.58498i	−0.0224475	+	0.127306i
$794$	−1.61645	−	9.16736i	−0.0573658	−	0.325337i
$795$	−4.07245	+	5.46311i	−0.144435	+	0.193756i
$796$	−19.4953	−	16.3585i	−0.690991	−	0.579810i
$797$		−	29.3150i		−	1.03839i	−0.854656	−	0.519195i	$-0.826232\pi$
$797$		−	29.3150i		−	1.03839i	0.854656	−	0.519195i	$-0.173768\pi$
$798$	−1.85713	+	4.97745i	−0.0657417	+	0.176200i
$799$	−20.1760			−0.713775
$800$	4.63064	−	1.88604i	0.163718	−	0.0666815i
$801$	−10.9757	−	24.1574i	−0.387806	−	0.853560i
$802$	23.0418	−	4.06289i	0.813635	−	0.143466i
$803$	−0.889383	+	5.04394i	−0.0313856	+	0.177997i
$804$	9.95398	+	19.3542i	0.351050	+	0.682568i
$805$	8.01036	−	2.30910i	0.282328	−	0.0813852i
$806$	−9.50508	+	16.4633i	−0.334802	+	0.579894i
$807$	10.9638	+	0.532940i	0.385943	+	0.0187604i
$808$	−7.48651	+	6.28193i	−0.263375	+	0.220998i
$809$	40.0141	+	23.1022i	1.40682	+	0.812229i	0.995080	−	0.0990719i	$-0.0315874\pi$
$809$	40.0141	+	23.1022i	1.40682	+	0.812229i	0.411741	+	0.911301i	$0.364921\pi$
$810$	18.2467	−	8.48871i	0.641123	−	0.298263i
$811$	4.74079	−	13.0252i	0.166472	−	0.457377i	−0.828205	−	0.560426i	$-0.810637\pi$
$811$	4.74079	−	13.0252i	0.166472	−	0.457377i	0.994676	+	0.103049i	$0.0328597\pi$
$812$	−4.76633	−	0.840433i	−0.167265	−	0.0294934i
$813$	25.5522	−	39.6753i	0.896156	−	1.39147i
$814$	−2.24556	+	0.817316i	−0.0787067	+	0.0286469i
$815$	−39.6892	+	28.9211i	−1.39025	+	1.01306i
$816$	4.95640	+	4.58693i	0.173509	+	0.160575i
$817$	29.6384	−	1.20175i	1.03692	−	0.0420440i
$818$	13.7432			0.480520
$819$	−8.51764	−	6.09035i	−0.297630	−	0.212814i
$820$	26.6395	−	2.83772i	0.930291	−	0.0990976i
$821$	49.9134	−	8.80108i	1.74199	−	0.307160i	0.789958	−	0.613161i	$-0.210102\pi$
$821$	49.9134	−	8.80108i	1.74199	−	0.307160i	0.952031	+	0.306001i	$0.0989912\pi$
$822$	−6.92221	−	9.11403i	−0.241440	−	0.317888i
$823$	−2.12828	+	5.84741i	−0.0741873	+	0.203828i	−0.971243	−	0.238089i	$-0.923479\pi$
$823$	−2.12828	+	5.84741i	−0.0741873	+	0.203828i	0.897056	+	0.441917i	$0.145701\pi$
$824$	3.15198	−	1.81980i	0.109805	−	0.0633957i
$825$	−0.939581	+	5.00991i	−0.0327120	+	0.174423i
$826$	−4.50809	+	3.78273i	−0.156856	+	0.131618i
$827$	5.05972	+	6.02994i	0.175944	+	0.209682i	0.846808	−	0.531898i	$-0.178521\pi$
$827$	5.05972	+	6.02994i	0.175944	+	0.209682i	−0.670864	+	0.741580i	$0.734077\pi$
$828$	−14.3384	−	6.85929i	−0.498293	−	0.238377i
$829$	−16.1201	+	9.30696i	−0.559875	+	0.323244i	−0.753095	−	0.657911i	$-0.771440\pi$
$829$	−16.1201	+	9.30696i	−0.559875	+	0.323244i	0.193220	+	0.981155i	$0.438107\pi$
$830$	15.2628	−	22.6967i	0.529780	−	0.787814i
$831$	24.1126	+	31.7476i	0.836458	+	1.10131i
$832$	0.861325	+	4.88482i	0.0298611	+	0.169351i
$833$	23.8326	−	8.67437i	0.825752	−	0.300549i
$834$	−3.08074	+	0.390121i	−0.106677	+	0.0135088i
$835$	12.9062	−	52.0750i	0.446636	−	1.80213i
$836$	−0.342778	+	2.54256i	−0.0118552	+	0.0879364i
$837$	−15.6180	−	12.3559i	−0.539836	−	0.427083i
$838$	−23.7560	−	19.9337i	−0.820637	−	0.688597i
$839$	13.2225	−	4.81261i	0.456493	−	0.166150i	−0.103531	−	0.994626i	$-0.533014\pi$
$839$	13.2225	−	4.81261i	0.456493	−	0.166150i	0.560024	+	0.828477i	$0.310792\pi$
$840$	1.98349	−	1.86899i	0.0684370	−	0.0644861i
$841$	3.17894	−	18.0286i	0.109618	−	0.621677i
$842$	3.54484	+	1.29022i	0.122163	+	0.0444638i
$843$	9.62312	−	42.4149i	0.331438	−	1.46085i
$844$	−2.63296	−	1.52014i	−0.0906303	−	0.0523255i
$845$	23.3040	−	11.4066i	0.801681	−	0.392399i
$846$	11.0851	−	10.8683i	0.381113	−	0.373659i
$847$	6.49228	+	3.74832i	0.223077	+	0.128794i
$848$	1.52365	−	0.879681i	0.0523225	−	0.0302084i
$849$	35.5770	−	18.2975i	1.22100	−	0.627969i
$850$	15.3958	+	11.9591i	0.528070	+	0.410192i
$851$	−3.73535	−	21.1842i	−0.128046	−	0.726186i
$852$	3.37141	+	1.41603i	0.115503	+	0.0485122i
$853$	−16.4517	+	19.6064i	−0.563295	+	0.671309i	−0.970240	−	0.242144i	$-0.922149\pi$
$853$	−16.4517	+	19.6064i	−0.563295	+	0.671309i	0.406945	+	0.913452i	$0.366594\pi$
$854$	−0.516428			−0.0176718
$855$	24.5684	−	15.8554i	0.840221	−	0.542243i
$856$	1.55010			0.0529812
$857$	−17.7479	+	21.1511i	−0.606256	+	0.722508i	−0.978642	−	0.205570i	$-0.934095\pi$
$857$	−17.7479	+	21.1511i	−0.606256	+	0.722508i	0.372386	+	0.928078i	$0.378540\pi$
$858$	−4.66213	−	1.95814i	−0.159163	−	0.0668499i
$859$	2.57398	+	14.5977i	0.0878229	+	0.498069i	0.996712	+	0.0810299i	$0.0258209\pi$
$859$	2.57398	+	14.5977i	0.0878229	+	0.498069i	−0.908889	+	0.417039i	$0.863068\pi$
$860$	−13.9098	−	6.16967i	−0.474321	−	0.210384i
$861$	12.9856	−	6.67858i	0.442547	−	0.227605i
$862$	15.3182	−	8.84399i	0.521742	−	0.301228i
$863$	−22.9942	−	13.2757i	−0.782733	−	0.451911i	0.0546650	−	0.998505i	$-0.482591\pi$
$863$	−22.9942	−	13.2757i	−0.782733	−	0.451911i	−0.837398	+	0.546594i	$0.815924\pi$
$864$	−5.19399	+	0.149733i	−0.176703	+	0.00509402i
$865$	5.20697	+	10.6379i	0.177042	+	0.361701i
$866$	27.5657	+	15.9150i	0.936719	+	0.540815i
$867$	0.689069	−	3.03714i	0.0234020	−	0.103147i
$868$	−2.53423	−	0.922384i	−0.0860174	−	0.0313078i
$869$	1.30833	−	7.41990i	0.0443820	−	0.251703i
$870$	18.2682	+	19.3875i	0.619351	+	0.657297i
$871$	−58.5676	+	21.3169i	−1.98449	+	0.722295i
$872$	−1.41879	−	1.19051i	−0.0480465	−	0.0403158i
$873$	−2.64802	−	34.1478i	−0.0896219	−	1.15573i
$874$	−22.0038	−	7.01304i	−0.744289	−	0.237219i
$875$	5.23960	−	5.86866i	0.177131	−	0.198397i
$876$	−14.9527	+	1.89349i	−0.505204	+	0.0639752i
$877$	10.1316	−	3.68761i	0.342121	−	0.124522i	−0.165245	−	0.986253i	$-0.552841\pi$
$877$	10.1316	−	3.68761i	0.342121	−	0.124522i	0.507366	+	0.861731i	$0.330619\pi$
$878$	0.452584	+	2.56673i	0.0152740	+	0.0866231i
$879$	6.53744	+	8.60742i	0.220502	+	0.290321i
$880$	0.734426	−	1.09213i	0.0247575	−	0.0368158i
$881$	−17.2780	+	9.97546i	−0.582111	+	0.336082i	−0.761972	−	0.647610i	$-0.775768\pi$
$881$	−17.2780	+	9.97546i	−0.582111	+	0.336082i	0.179861	+	0.983692i	$0.442435\pi$
$882$	−8.42145	+	17.6039i	−0.283565	+	0.592753i
$883$	−32.9420	−	39.2587i	−1.10859	−	1.32116i	−0.942181	−	0.335103i	$-0.891229\pi$
$883$	−32.9420	−	39.2587i	−1.10859	−	1.32116i	−0.166404	−	0.986058i	$-0.553216\pi$
$884$	−14.8150	+	12.4312i	−0.498281	+	0.418107i
$885$	32.3365	−	1.86309i	1.08698	−	0.0626271i
$886$	−2.46018	+	1.42039i	−0.0826515	+	0.0477188i
$887$	3.66402	−	10.0668i	0.123026	−	0.338010i	−0.862857	−	0.505448i	$-0.831327\pi$
$887$	3.66402	−	10.0668i	0.123026	−	0.338010i	0.985883	+	0.167438i	$0.0535494\pi$
$888$	−4.25335	−	5.60011i	−0.142733	−	0.187927i
$889$	−1.72164	+	0.303571i	−0.0577419	+	0.0101814i
$890$	2.09487	+	19.6659i	0.0702204	+	0.659202i
$891$	2.73870	−	4.53433i	0.0917499	−	0.151906i
$892$	−6.68726			−0.223906
$893$	13.7868	−	17.8521i	0.461357	−	0.597398i
$894$	28.1936	+	26.0919i	0.942934	+	0.872644i
$895$	7.76912	+	10.6618i	0.259693	+	0.356384i
$896$	−0.661237	+	0.240671i	−0.0220904	+	0.00804024i
$897$	24.6463	−	38.2686i	0.822915	−	1.27775i
$898$	−4.57486	−	0.806671i	−0.152665	−	0.0269190i
$899$	9.01576	−	24.7706i	0.300692	−	0.826145i
$900$	−14.9007	+	1.72275i	−0.496691	+	0.0574251i
$901$	5.94067	+	3.42985i	0.197912	+	0.114265i
$902$	5.40195	−	4.53278i	0.179865	−	0.150925i
$903$	−8.28428	−	0.402692i	−0.275683	−	0.0134007i
$904$	2.32233	−	4.02239i	0.0772396	−	0.133783i
$905$	−11.8287	+	3.40979i	−0.393199	+	0.113345i
$906$	−4.86863	−	9.46639i	−0.161750	−	0.314500i
$907$	5.55087	−	31.4806i	0.184314	−	1.04530i	−0.742520	−	0.669824i	$-0.766370\pi$
$907$	5.55087	−	31.4806i	0.184314	−	1.04530i	0.926834	−	0.375472i	$-0.122519\pi$
$908$	−5.31681	+	0.937497i	−0.176445	+	0.0311119i
$909$	26.6930	−	12.1277i	0.885350	−	0.402249i
$910$	4.59631	+	6.30765i	0.152366	+	0.209096i
$911$	−4.89999			−0.162344			−0.0811720	−	0.996700i	$-0.525866\pi$
$911$	−4.89999			−0.162344			−0.0811720	+	0.996700i	$0.525866\pi$
$912$	−7.44544	+	1.25115i	−0.246543	+	0.0414297i
$913$		−	7.19945i		−	0.238267i
$914$	−25.9268	−	21.7552i	−0.857583	−	0.719598i
$915$	2.27889	+	1.69878i	0.0753377	+	0.0561601i
$916$	2.04517	+	11.5987i	0.0675744	+	0.383233i
$917$	−1.25930	+	7.14185i	−0.0415858	+	0.235845i
$918$	−10.6312	−	17.2462i	−0.350882	−	0.569208i
$919$	2.35783	+	4.08388i	0.0777777	+	0.134715i	0.902291	−	0.431128i	$-0.141884\pi$
$919$	2.35783	+	4.08388i	0.0777777	+	0.134715i	−0.824513	+	0.565843i	$0.808551\pi$
$920$	8.53367	+	8.21776i	0.281347	+	0.270932i
$921$	−13.1945	−	0.641372i	−0.434772	−	0.0211339i
$922$	0.891091	−	0.747714i	0.0293465	−	0.0246246i
$923$	−5.23596	+	9.06895i	−0.172344	+	0.298508i
$924$	0.158722	−	0.699582i	0.00522156	−	0.0230146i
$925$	−13.6258	−	15.0479i	−0.448014	−	0.494771i
$926$	0.583599	−	3.30975i	0.0191782	−	0.108765i
$927$	−10.5741	+	2.72170i	−0.347300	+	0.0893924i
$928$	−2.35241	−	6.46320i	−0.0772217	−	0.212165i
$929$	22.8776	−	27.2644i	0.750589	−	0.894517i	−0.246625	−	0.969111i	$-0.579322\pi$
$929$	22.8776	−	27.2644i	0.750589	−	0.894517i	0.997214	+	0.0745936i	$0.0237659\pi$
$930$	8.14884	+	12.4066i	0.267211	+	0.406829i
$931$	−8.61021	+	27.0150i	−0.282188	+	0.885381i
$932$	−4.47852			−0.146699
$933$	−11.4467	+	1.44952i	−0.374747	+	0.0474551i
$934$	3.44928	+	9.47681i	0.112864	+	0.310091i
$935$	5.11945	+	0.350769i	0.167424	+	0.0114714i
$936$	1.44325	−	14.8104i	0.0471741	−	0.484092i
$937$	−11.2142	+	30.8107i	−0.366351	+	1.00654i	0.610387	+	0.792103i	$0.291014\pi$
$937$	−11.2142	+	30.8107i	−0.366351	+	1.00654i	−0.976738	+	0.214437i	$0.931208\pi$
$938$	−4.42096	−	7.65732i	−0.144349	−	0.250020i
$939$	−11.9792	−	38.6578i	−0.390928	−	1.26155i
$940$	−10.3928	+	5.08698i	−0.338976	+	0.165919i
$941$	3.90814	−	3.27932i	0.127402	−	0.106903i	−0.576861	−	0.816843i	$-0.695722\pi$
$941$	3.90814	−	3.27932i	0.127402	−	0.106903i	0.704262	+	0.709940i	$0.251278\pi$
$942$	10.8822	−	3.37218i	0.354563	−	0.109871i
$943$	31.7388	+	54.9731i	1.03356	+	1.79017i
$944$	−7.85874	−	2.86035i	−0.255780	−	0.0930964i
$945$	−7.23683	+	3.80453i	−0.235414	+	0.123761i
$946$	−3.94451	+	0.695523i	−0.128247	+	0.0226134i
$947$	−8.73107	+	3.17785i	−0.283722	+	0.103266i	−0.479961	−	0.877290i	$-0.659349\pi$
$947$	−8.73107	+	3.17785i	−0.283722	+	0.103266i	0.196239	+	0.980556i	$0.437127\pi$
$948$	21.9961	−	2.78543i	0.714401	−	0.0904664i
$949$		−	43.1628i		−	1.40112i
$950$	−21.1019	+	5.45054i	−0.684637	+	0.176839i
$951$	35.8251	−	38.7108i	1.16171	−	1.25528i
$952$	−2.10172	−	1.76355i	−0.0681171	−	0.0571571i
$953$	−5.80437	−	15.9474i	−0.188022	−	0.516586i	0.809486	−	0.587139i	$-0.199746\pi$
$953$	−5.80437	−	15.9474i	−0.188022	−	0.516586i	−0.997508	+	0.0705532i	$0.977524\pi$
$954$	−5.11148	+	1.31566i	−0.165490	+	0.0425960i
$955$	38.3063	+	16.9907i	1.23956	+	0.549807i
$956$	−4.16465	+	11.4423i	−0.134694	+	0.370070i
$957$	6.83800	+	1.55141i	0.221041	+	0.0501500i
$958$	−8.67213	+	15.0206i	−0.280184	+	0.485293i
$959$	2.98872	+	3.56182i	0.0965108	+	0.115017i
$960$	3.70958	+	1.11310i	0.119726	+	0.0359253i
$961$	−8.15575	+	14.1262i	−0.263089	+	0.455683i
$962$	17.4405	−	10.0693i	0.562305	−	0.324647i
$963$	−4.47973	−	1.24788i	−0.144357	−	0.0402125i
$964$	1.12141	+	0.197735i	0.0361182	+	0.00636861i
$965$	−2.60453	+	38.0130i	−0.0838429	+	1.22368i
$966$	5.95363	+	2.50059i	0.191555	+	0.0804551i
$967$	22.9935	−	27.4026i	0.739421	−	0.881208i	−0.256941	−	0.966427i	$-0.582715\pi$
$967$	22.9935	−	27.4026i	0.739421	−	0.881208i	0.996362	+	0.0852189i	$0.0271590\pi$
$968$			10.6536i			0.342419i
$969$	−18.7394	−	22.7012i	−0.601996	−	0.729268i
$970$	−6.14118	+	24.7790i	−0.197181	+	0.795605i
$971$	−23.5966	−	19.7999i	−0.757250	−	0.635409i	0.180159	−	0.983637i	$-0.442339\pi$
$971$	−23.5966	−	19.7999i	−0.757250	−	0.635409i	−0.937410	+	0.348229i	$0.886783\pi$
$972$	15.1310	+	3.74863i	0.485328	+	0.120237i
$973$	1.24243	−	0.219074i	0.0398304	−	0.00702318i
$974$	−32.3018	−	5.69568i	−1.03502	−	0.182501i
$975$	0.466404	−	42.9538i	0.0149369	−	1.37562i
$976$	−0.366951	−	0.635578i	−0.0117458	−	0.0203444i
$977$	−31.1019	−	17.9567i	−0.995038	−	0.574486i	−0.0882617	−	0.996097i	$-0.528131\pi$
$977$	−31.1019	−	17.9567i	−0.995038	−	0.574486i	−0.906776	+	0.421612i	$0.861465\pi$
$978$	−37.9946	−	1.84688i	−1.21493	−	0.0590568i
$979$	3.34621	+	3.98785i	0.106945	+	0.127452i
$980$	10.0893	−	10.4772i	0.322291	−	0.334681i
$981$	3.14187	+	4.58272i	0.100312	+	0.146315i
$982$	−7.31603	−	2.66282i	−0.233464	−	0.0849740i
$983$	38.3234	+	6.75745i	1.22233	+	0.215529i	0.747327	−	0.664457i	$-0.231337\pi$
$983$	38.3234	+	6.75745i	1.22233	+	0.215529i	0.475000	+	0.879986i	$0.342448\pi$
$984$	17.4464	+	11.2361i	0.556172	+	0.358194i
$985$	−46.8460	+	4.99019i	−1.49264	+	0.159001i
$986$	17.2377	−	20.5431i	0.548959	−	0.654224i
$987$	−4.28380	+	4.62885i	−0.136355	+	0.147338i
$988$	−0.875945	−	21.6031i	−0.0278675	−	0.687288i
$989$		−	36.0549i		−	1.14648i
$990$	−3.00167	+	2.56499i	−0.0953994	+	0.0815208i
$991$	8.44615	+	23.2056i	0.268301	+	0.737150i	0.998543	+	0.0539619i	$0.0171849\pi$
$991$	8.44615	+	23.2056i	0.268301	+	0.737150i	−0.730242	+	0.683188i	$0.760593\pi$
$992$	−0.665517	−	3.77433i	−0.0211302	−	0.119835i
$993$	23.6278	+	31.1092i	0.749807	+	0.987222i
$994$	−1.39600	−	0.508104i	−0.0442786	−	0.0161161i
$995$	−15.7622	−	54.6797i	−0.499696	−	1.73346i
$996$	20.2369	−	6.27097i	0.641230	−	0.198703i
$997$	26.5334	+	31.6212i	0.840320	+	1.00145i	0.999898	+	0.0142691i	$0.00454216\pi$
$997$	26.5334	+	31.6212i	0.840320	+	1.00145i	−0.159578	+	0.987185i	$0.551013\pi$
$998$	−6.98501	−	8.32441i	−0.221107	−	0.263505i
$999$	7.78375	+	19.6082i	0.246267	+	0.620377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.269.37	yes	240
3.2	odd	2	inner	570.2.bf.a.269.13	yes	240
5.4	even	2	inner	570.2.bf.a.269.4	yes	240
15.14	odd	2	inner	570.2.bf.a.269.28	yes	240
19.13	odd	18	inner	570.2.bf.a.89.28	yes	240
57.32	even	18	inner	570.2.bf.a.89.4	✓	240
95.89	odd	18	inner	570.2.bf.a.89.13	yes	240
285.89	even	18	inner	570.2.bf.a.89.37	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.89.4	✓	240	57.32	even	18	inner
570.2.bf.a.89.13	yes	240	95.89	odd	18	inner
570.2.bf.a.89.28	yes	240	19.13	odd	18	inner
570.2.bf.a.89.37	yes	240	285.89	even	18	inner
570.2.bf.a.269.4	yes	240	5.4	even	2	inner
570.2.bf.a.269.13	yes	240	3.2	odd	2	inner
570.2.bf.a.269.28	yes	240	15.14	odd	2	inner
570.2.bf.a.269.37	yes	240	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(1.59691 + 0.670720i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.906623 - 2.04402i) q^{5} +(1.54028 - 0.792176i) q^{6} +(-0.609399 + 0.351837i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.10027 + 2.14217i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(1.59691 + 0.670720i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.906623 - 2.04402i) q^{5} +(1.54028 - 0.792176i) q^{6} +(-0.609399 + 0.351837i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(2.10027 + 2.14217i) q^{9} +(-0.983047 - 2.00839i) q^{10} +(-0.509726 - 0.294290i) q^{11} +(0.383229 - 1.68912i) q^{12} +(4.66104 + 1.69648i) q^{13} +(-0.122192 + 0.692983i) q^{14} +(2.81877 - 2.65604i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-2.98678 - 2.50621i) q^{17} +(2.99102 - 0.231942i) q^{18} +(4.25849 - 0.930206i) q^{19} +(-2.17040 - 0.537909i) q^{20} +(-1.20914 + 0.153117i) q^{21} +(-0.553085 + 0.201306i) q^{22} +(-0.920024 - 5.21772i) q^{23} +(-1.04761 - 1.37932i) q^{24} +(-3.35607 - 3.70632i) q^{25} +(4.29564 - 2.48009i) q^{26} +(1.91715 + 4.82955i) q^{27} +(0.452313 + 0.539045i) q^{28} +(-5.26885 + 4.42109i) q^{29} +(-0.222775 - 3.86657i) q^{30} +(-3.31909 + 1.91628i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-0.616602 - 0.811840i) q^{33} +(-3.83973 + 0.677048i) q^{34} +(0.166667 + 1.56461i) q^{35} +(1.74491 - 2.44034i) q^{36} +4.06006 q^{37} +(2.02472 - 3.86012i) q^{38} +(6.30541 + 5.83539i) q^{39} +(-1.80717 + 1.31686i) q^{40} +(-11.2584 + 4.09772i) q^{41} +(-0.659928 + 1.02468i) q^{42} +(6.70173 + 1.18170i) q^{43} +(-0.201306 + 0.553085i) q^{44} +(6.28279 - 2.35086i) q^{45} +(-4.58838 - 2.64910i) q^{46} +(3.96405 - 3.32623i) q^{47} +(-1.73001 - 0.0840942i) q^{48} +(-3.25242 + 5.63336i) q^{49} +(-4.99644 + 0.188521i) q^{50} +(-3.08867 - 6.00549i) q^{51} +(0.861325 - 4.88482i) q^{52} +(-1.73263 + 0.305510i) q^{53} +(4.93197 + 1.63575i) q^{54} +(-1.06367 + 0.775081i) q^{55} +0.703674 q^{56} +(7.42435 + 1.37080i) q^{57} +6.87799i q^{58} +(6.40650 + 5.37569i) q^{59} +(-3.10516 - 2.31473i) q^{60} +(0.127441 + 0.722753i) q^{61} +(-0.665517 + 3.77433i) q^{62} +(-2.03359 - 0.566482i) q^{63} +(0.500000 + 0.866025i) q^{64} +(7.69345 - 7.98921i) q^{65} +(-1.01825 - 0.0494963i) q^{66} +(-9.62563 + 8.07686i) q^{67} +(-1.94948 + 3.37660i) q^{68} +(2.03043 - 8.94933i) q^{69} +(1.30569 + 0.878037i) q^{70} +(-0.366606 + 2.07913i) q^{71} +(-0.747803 - 2.90530i) q^{72} +(-2.97621 - 8.17708i) q^{73} +(2.60975 - 3.11018i) q^{74} +(-2.87345 - 8.16966i) q^{75} +(-1.65555 - 4.03226i) q^{76} +0.414169 q^{77} +(8.52321 - 1.07931i) q^{78} +(4.37816 + 12.0289i) q^{79} +(-0.152850 + 2.23084i) q^{80} +(-0.177746 + 8.99824i) q^{81} +(-4.09772 + 11.2584i) q^{82} +(6.11594 + 10.5931i) q^{83} +(0.360756 + 1.16418i) q^{84} +(-7.83063 + 3.83287i) q^{85} +(5.21302 - 4.37424i) q^{86} +(-11.3792 + 3.52617i) q^{87} +(0.294290 + 0.509726i) q^{88} +(-8.31122 - 3.02504i) q^{89} +(2.23764 - 6.32400i) q^{90} +(-3.43732 + 0.606092i) q^{91} +(-4.97869 + 1.81209i) q^{92} +(-6.58559 + 0.833950i) q^{93} -5.17470i q^{94} +(1.95948 - 9.54780i) q^{95} +(-1.17645 + 1.27121i) q^{96} +(-8.74575 - 7.33855i) q^{97} +(2.22479 + 6.11255i) q^{98} +(-0.440143 - 1.71001i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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