LMFDB - Embedded newform 256.2.m.a.5.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			5.17
Character	$\chi$	$=$	256.5
Dual form			256.2.m.a.205.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.101501 + 1.41057i) q^{2} +(0.345303 - 2.32784i) q^{3} +(-1.97939 + 0.286349i) q^{4} +(-1.81333 - 0.0890833i) q^{5} +(3.31862 + 0.250793i) q^{6} +(-2.21013 - 1.18134i) q^{7} +(-0.604825 - 2.76300i) q^{8} +(-2.42879 - 0.736767i) q^{9} +O(q^{10})$	\(q+(0.101501 + 1.41057i) q^{2} +(0.345303 - 2.32784i) q^{3} +(-1.97939 + 0.286349i) q^{4} +(-1.81333 - 0.0890833i) q^{5} +(3.31862 + 0.250793i) q^{6} +(-2.21013 - 1.18134i) q^{7} +(-0.604825 - 2.76300i) q^{8} +(-2.42879 - 0.736767i) q^{9} +(-0.0583977 - 2.56687i) q^{10} +(-1.66386 - 2.77598i) q^{11} +(-0.0169161 + 4.70660i) q^{12} +(-0.130100 + 0.143543i) q^{13} +(1.44203 - 3.23745i) q^{14} +(-0.833520 + 4.19039i) q^{15} +(3.83601 - 1.13359i) q^{16} +(0.207189 + 1.04161i) q^{17} +(0.792733 - 3.50076i) q^{18} +(-1.90474 - 4.02723i) q^{19} +(3.61481 - 0.342914i) q^{20} +(-3.51314 + 4.73692i) q^{21} +(3.74682 - 2.62875i) q^{22} +(-2.24444 - 1.84196i) q^{23} +(-6.64068 + 0.453864i) q^{24} +(-1.69569 - 0.167011i) q^{25} +(-0.215682 - 0.168944i) q^{26} +(0.464767 - 0.982667i) q^{27} +(4.71300 + 1.70547i) q^{28} +(0.948010 - 0.237464i) q^{29} +(-5.99543 - 0.750406i) q^{30} +(8.85870 + 3.66939i) q^{31} +(1.98837 + 5.29588i) q^{32} +(-7.03658 + 2.91465i) q^{33} +(-1.44823 + 0.397978i) q^{34} +(3.90247 + 2.33905i) q^{35} +(5.01852 + 0.762870i) q^{36} +(1.18907 + 3.32324i) q^{37} +(5.48734 - 3.09553i) q^{38} +(0.289221 + 0.352417i) q^{39} +(0.850611 + 5.06412i) q^{40} +(2.93118 - 0.288696i) q^{41} +(-7.03833 - 4.47471i) q^{42} +(11.6692 - 1.73096i) q^{43} +(4.08833 + 5.01832i) q^{44} +(4.33858 + 1.55237i) q^{45} +(2.37039 - 3.35289i) q^{46} +(-7.06692 + 10.5764i) q^{47} +(-1.31424 - 9.32106i) q^{48} +(-0.399870 - 0.598447i) q^{49} +(0.0634651 - 2.40883i) q^{50} +(2.49624 - 0.122633i) q^{51} +(0.216415 - 0.321382i) q^{52} +(-1.86050 - 0.466032i) q^{53} +(1.43329 + 0.555843i) q^{54} +(2.76983 + 5.18199i) q^{55} +(-1.92730 + 6.82111i) q^{56} +(-10.0325 + 3.04332i) q^{57} +(0.431183 + 1.31313i) q^{58} +(-7.39861 - 8.16311i) q^{59} +(0.449953 - 8.53311i) q^{60} +(-6.14803 - 8.28966i) q^{61} +(-4.27675 + 12.8682i) q^{62} +(4.49759 + 4.49759i) q^{63} +(-7.26837 + 3.34227i) q^{64} +(0.248701 - 0.248701i) q^{65} +(-4.82552 - 9.62972i) q^{66} +(11.0086 - 8.16451i) q^{67} +(-0.708372 - 2.00243i) q^{68} +(-5.06280 + 4.58866i) q^{69} +(-2.90328 + 5.74210i) q^{70} +(-2.37407 - 7.82625i) q^{71} +(-0.566693 + 7.15638i) q^{72} +(5.69942 - 3.04641i) q^{73} +(-4.56696 + 2.01458i) q^{74} +(-0.974300 + 3.88962i) q^{75} +(4.92342 + 7.42606i) q^{76} +(0.397970 + 8.10087i) q^{77} +(-0.467751 + 0.443736i) q^{78} +(-4.64124 + 3.10118i) q^{79} +(-7.05694 + 1.71386i) q^{80} +(-8.45803 - 5.65147i) q^{81} +(0.704743 + 4.10532i) q^{82} +(-1.15859 + 3.23804i) q^{83} +(5.59748 - 10.3822i) q^{84} +(-0.282912 - 1.90724i) q^{85} +(3.62607 + 16.2845i) q^{86} +(-0.225429 - 2.28881i) q^{87} +(-6.66370 + 6.27623i) q^{88} +(-0.401933 + 0.329858i) q^{89} +(-1.74935 + 6.27742i) q^{90} +(0.457110 - 0.163557i) q^{91} +(4.97007 + 3.00328i) q^{92} +(11.6007 - 19.3546i) q^{93} +(-15.6360 - 8.89484i) q^{94} +(3.09516 + 7.47239i) q^{95} +(13.0146 - 2.79993i) q^{96} +(-5.06179 + 12.2202i) q^{97} +(0.803562 - 0.624786i) q^{98} +(1.99592 + 7.96816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{64}\right)$	$1$

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 $

$2$	0.101501	+	1.41057i	0.0717723	+	0.997421i
$2$	0.101501	+	1.41057i	0.0717723	+	0.997421i
$3$	0.345303	−	2.32784i	0.199361	−	1.34398i	−0.626198	−	0.779664i	$-0.715390\pi$
$3$	0.345303	−	2.32784i	0.199361	−	1.34398i	0.825559	−	0.564316i	$-0.190860\pi$
$4$	−1.97939	+	0.286349i	−0.989697	+	0.143174i
$5$	−1.81333	−	0.0890833i	−0.810947	−	0.0398393i	−0.360631	−	0.932709i	$-0.617439\pi$
$5$	−1.81333	−	0.0890833i	−0.810947	−	0.0398393i	−0.450316	+	0.892869i	$0.648689\pi$
$6$	3.31862	+	0.250793i	1.35482	+	0.102386i
$7$	−2.21013	−	1.18134i	−0.835352	−	0.446505i	−0.00249731	−	0.999997i	$-0.500795\pi$
$7$	−2.21013	−	1.18134i	−0.835352	−	0.446505i	−0.832854	+	0.553492i	$0.813295\pi$
$8$	−0.604825	−	2.76300i	−0.213838	−	0.976869i
$9$	−2.42879	−	0.736767i	−0.809598	−	0.245589i
$10$	−0.0583977	−	2.56687i	−0.0184670	−	0.811715i
$11$	−1.66386	−	2.77598i	−0.501672	−	0.836989i	0.497870	−	0.867252i	$-0.334116\pi$
$11$	−1.66386	−	2.77598i	−0.501672	−	0.836989i	−0.999542	+	0.0302624i	$0.990366\pi$
$12$	−0.0169161	+	4.70660i	−0.00488325	+	1.35868i
$13$	−0.130100	+	0.143543i	−0.0360831	+	0.0398116i	−0.758725	−	0.651411i	$-0.774177\pi$
$13$	−0.130100	+	0.143543i	−0.0360831	+	0.0398116i	0.722642	+	0.691222i	$0.242927\pi$
$14$	1.44203	−	3.23745i	0.385398	−	0.865244i
$15$	−0.833520	+	4.19039i	−0.215214	+	1.08195i
$16$	3.83601	−	1.13359i	0.959002	−	0.283399i
$17$	0.207189	+	1.04161i	0.0502507	+	0.252627i	0.997743	−	0.0671520i	$-0.0213913\pi$
$17$	0.207189	+	1.04161i	0.0502507	+	0.252627i	−0.947492	+	0.319779i	$0.896391\pi$
$18$	0.792733	−	3.50076i	0.186849	−	0.825137i
$19$	−1.90474	−	4.02723i	−0.436977	−	0.923910i	−0.995530	−	0.0944417i	$-0.969893\pi$
$19$	−1.90474	−	4.02723i	−0.436977	−	0.923910i	0.558553	−	0.829469i	$-0.311357\pi$
$20$	3.61481	−	0.342914i	0.808296	−	0.0766779i
$21$	−3.51314	+	4.73692i	−0.766630	+	1.03368i
$22$	3.74682	−	2.62875i	0.798825	−	0.560451i
$23$	−2.24444	−	1.84196i	−0.467997	−	0.384075i	0.370631	−	0.928780i	$-0.379142\pi$
$23$	−2.24444	−	1.84196i	−0.467997	−	0.384075i	−0.838628	+	0.544705i	$0.816642\pi$
$24$	−6.64068	+	0.453864i	−1.35552	+	0.0926447i
$25$	−1.69569	−	0.167011i	−0.339137	−	0.0334021i
$26$	−0.215682	−	0.168944i	−0.0422987	−	0.0331327i
$27$	0.464767	−	0.982667i	0.0894444	−	0.189114i
$28$	4.71300	+	1.70547i	0.890674	+	0.322304i
$29$	0.948010	−	0.237464i	0.176041	−	0.0440960i	−0.153957	−	0.988078i	$-0.549202\pi$
$29$	0.948010	−	0.237464i	0.176041	−	0.0440960i	0.329998	+	0.943982i	$0.392952\pi$
$30$	−5.99543	−	0.750406i	−1.09461	−	0.137005i
$31$	8.85870	+	3.66939i	1.59107	+	0.659043i	0.990117	−	0.140242i	$-0.0447881\pi$
$31$	8.85870	+	3.66939i	1.59107	+	0.659043i	0.600952	+	0.799285i	$0.294788\pi$
$32$	1.98837	+	5.29588i	0.351497	+	0.936189i
$33$	−7.03658	+	2.91465i	−1.22491	+	0.507375i
$34$	−1.44823	+	0.397978i	−0.248369	+	0.0682527i
$35$	3.90247	+	2.33905i	0.659637	+	0.395371i
$36$	5.01852	+	0.762870i	0.836419	+	0.127145i
$37$	1.18907	+	3.32324i	0.195483	+	0.546338i	0.998787	−	0.0492306i	$-0.0156769\pi$
$37$	1.18907	+	3.32324i	0.195483	+	0.546338i	−0.803305	+	0.595568i	$0.796927\pi$
$38$	5.48734	−	3.09553i	0.890165	−	0.502161i
$39$	0.289221	+	0.352417i	0.0463125	+	0.0564319i
$40$	0.850611	+	5.06412i	0.134493	+	0.800708i
$41$	2.93118	−	0.288696i	0.457773	−	0.0450867i	0.133497	−	0.991049i	$-0.457379\pi$
$41$	2.93118	−	0.288696i	0.457773	−	0.0450867i	0.324276	+	0.945962i	$0.394879\pi$
$42$	−7.03833	−	4.47471i	−1.08604	−	0.690463i
$43$	11.6692	−	1.73096i	1.77953	−	0.263969i	0.825658	−	0.564172i	$-0.190804\pi$
$43$	11.6692	−	1.73096i	1.77953	−	0.263969i	0.953875	+	0.300203i	$0.0970543\pi$
$44$	4.08833	+	5.01832i	0.616339	+	0.756540i
$45$	4.33858	+	1.55237i	0.646757	+	0.231413i
$46$	2.37039	−	3.35289i	0.349496	−	0.494356i
$47$	−7.06692	+	10.5764i	−1.03082	+	1.54272i	−0.205018	+	0.978758i	$0.565725\pi$
$47$	−7.06692	+	10.5764i	−1.03082	+	1.54272i	−0.825798	+	0.563967i	$0.809275\pi$
$48$	−1.31424	−	9.32106i	−0.189695	−	1.34538i
$49$	−0.399870	−	0.598447i	−0.0571242	−	0.0854924i
$50$	0.0634651	−	2.40883i	0.00897532	−	0.340660i
$51$	2.49624	−	0.122633i	0.349544	−	0.0171720i
$52$	0.216415	−	0.321382i	0.0300114	−	0.0445676i
$53$	−1.86050	−	0.466032i	−0.255560	−	0.0640144i	0.113083	−	0.993586i	$-0.463927\pi$
$53$	−1.86050	−	0.466032i	−0.255560	−	0.0640144i	−0.368643	+	0.929571i	$0.620177\pi$
$54$	1.43329	+	0.555843i	0.195046	+	0.0756406i
$55$	2.76983	+	5.18199i	0.373484	+	0.698740i
$56$	−1.92730	+	6.82111i	−0.257547	+	0.911509i
$57$	−10.0325	+	3.04332i	−1.32883	+	0.403097i
$58$	0.431183	+	1.31313i	0.0566171	+	0.172422i
$59$	−7.39861	−	8.16311i	−0.963218	−	1.06275i	−0.997991	−	0.0633516i	$-0.979821\pi$
$59$	−7.39861	−	8.16311i	−0.963218	−	1.06275i	0.0347737	−	0.999395i	$-0.488929\pi$
$60$	0.449953	−	8.53311i	0.0580887	−	1.10162i
$61$	−6.14803	−	8.28966i	−0.787175	−	1.06138i	−0.996505	−	0.0835370i	$-0.973378\pi$
$61$	−6.14803	−	8.28966i	−0.787175	−	1.06138i	0.209330	−	0.977845i	$-0.432872\pi$
$62$	−4.27675	+	12.8682i	−0.543148	+	1.63427i
$63$	4.49759	+	4.49759i	0.566643	+	0.566643i
$64$	−7.26837	+	3.34227i	−0.908547	+	0.417783i
$65$	0.248701	−	0.248701i	0.0308476	−	0.0308476i
$66$	−4.82552	−	9.62972i	−0.593981	−	1.18534i
$67$	11.0086	−	8.16451i	1.34491	−	0.997454i	0.346680	−	0.937983i	$-0.387309\pi$
$67$	11.0086	−	8.16451i	1.34491	−	0.997454i	0.998230	−	0.0594703i	$-0.0189412\pi$
$68$	−0.708372	−	2.00243i	−0.0859027	−	0.242830i
$69$	−5.06280	+	4.58866i	−0.609490	+	0.552409i
$70$	−2.90328	+	5.74210i	−0.347008	+	0.686313i
$71$	−2.37407	−	7.82625i	−0.281750	−	0.928805i	−0.977574	−	0.210593i	$-0.932461\pi$
$71$	−2.37407	−	7.82625i	−0.281750	−	0.928805i	0.695824	−	0.718213i	$-0.255039\pi$
$72$	−0.566693	+	7.15638i	−0.0667855	+	0.843388i
$73$	5.69942	−	3.04641i	0.667067	−	0.356555i	−0.102852	−	0.994697i	$-0.532797\pi$
$73$	5.69942	−	3.04641i	0.667067	−	0.356555i	0.769919	+	0.638142i	$0.220297\pi$
$74$	−4.56696	+	2.01458i	−0.530898	+	0.234190i
$75$	−0.974300	+	3.88962i	−0.112502	+	0.449135i
$76$	4.92342	+	7.42606i	0.564755	+	0.851828i
$77$	0.397970	+	8.10087i	0.0453529	+	0.923179i
$78$	−0.467751	+	0.443736i	−0.0529624	+	0.0502433i
$79$	−4.64124	+	3.10118i	−0.522181	+	0.348910i	−0.788560	−	0.614958i	$-0.789173\pi$
$79$	−4.64124	+	3.10118i	−0.522181	+	0.348910i	0.266379	+	0.963868i	$0.414173\pi$
$80$	−7.05694	+	1.71386i	−0.788990	+	0.191615i
$81$	−8.45803	−	5.65147i	−0.939781	−	0.627941i
$82$	0.704743	+	4.10532i	0.0778259	+	0.453357i
$83$	−1.15859	+	3.23804i	−0.127172	+	0.355421i	−0.988207	−	0.153124i	$-0.951066\pi$
$83$	−1.15859	+	3.23804i	−0.127172	+	0.355421i	0.861035	+	0.508545i	$0.169816\pi$
$84$	5.59748	−	10.3822i	0.610735	−	1.13279i
$85$	−0.282912	−	1.90724i	−0.0306861	−	0.206869i
$86$	3.62607	+	16.2845i	0.391009	+	1.75600i
$87$	−0.225429	−	2.28881i	−0.0241685	−	0.245387i
$88$	−6.66370	+	6.27623i	−0.710353	+	0.669048i
$89$	−0.401933	+	0.329858i	−0.0426049	+	0.0349649i	−0.655455	−	0.755234i	$-0.727523\pi$
$89$	−0.401933	+	0.329858i	−0.0426049	+	0.0349649i	0.612850	+	0.790199i	$0.290023\pi$
$90$	−1.74935	+	6.27742i	−0.184397	+	0.661698i
$91$	0.457110	−	0.163557i	0.0479182	−	0.0171454i
$92$	4.97007	+	3.00328i	0.518165	+	0.313113i
$93$	11.6007	−	19.3546i	1.20294	−	2.00698i
$94$	−15.6360	−	8.89484i	−1.61273	−	0.917432i
$95$	3.09516	+	7.47239i	0.317557	+	0.766651i
$96$	13.0146	−	2.79993i	1.32829	−	0.285766i
$97$	−5.06179	+	12.2202i	−0.513947	+	1.24078i	0.427622	+	0.903958i	$0.359352\pi$
$97$	−5.06179	+	12.2202i	−0.513947	+	1.24078i	−0.941569	+	0.336820i	$0.890648\pi$
$98$	0.803562	−	0.624786i	0.0811720	−	0.0631129i
$99$	1.99592	+	7.96816i	0.200598	+	0.800830i
$100$	3.40426	−	0.154978i	0.340426	−	0.0154978i
$101$	−6.74825	−	3.19169i	−0.671476	−	0.317585i	0.0612358	−	0.998123i	$-0.480496\pi$
$101$	−6.74825	−	3.19169i	−0.671476	−	0.317585i	−0.732712	+	0.680539i	$0.761746\pi$
$102$	0.426353	+	3.50867i	0.0422153	+	0.347410i
$103$	0.738677	−	7.49991i	0.0727840	−	0.738988i	−0.887657	−	0.460505i	$-0.847668\pi$
$103$	0.738677	−	7.49991i	0.0727840	−	0.738988i	0.960441	−	0.278483i	$-0.0898317\pi$
$104$	0.475297	+	0.272647i	0.0466067	+	0.0267353i
$105$	6.79247	−	8.27665i	0.662877	−	0.807718i
$106$	0.468525	−	2.67167i	0.0455072	−	0.259495i
$107$	5.40783	+	4.01072i	0.522795	+	0.387731i	0.824668	−	0.565617i	$-0.191362\pi$
$107$	5.40783	+	4.01072i	0.522795	+	0.387731i	−0.301873	+	0.953348i	$0.597612\pi$
$108$	−0.638572	+	2.07817i	−0.0614466	+	0.199972i
$109$	9.79189	−	4.63122i	0.937893	−	0.443590i	0.103419	−	0.994638i	$-0.467022\pi$
$109$	9.79189	−	4.63122i	0.937893	−	0.443590i	0.834474	+	0.551047i	$0.185772\pi$
$110$	−7.02840	+	4.43301i	−0.670132	+	0.422671i
$111$	8.14657	−	1.62045i	0.773239	−	0.153807i
$112$	−9.81725	−	2.02624i	−0.927643	−	0.191462i
$113$	1.02113	+	0.203115i	0.0960595	+	0.0191074i	0.242886	−	0.970055i	$-0.421906\pi$
$113$	1.02113	+	0.203115i	0.0960595	+	0.0191074i	−0.146826	+	0.989162i	$0.546906\pi$
$114$	−5.31111	−	13.8426i	−0.497431	−	1.29648i
$115$	3.90582	+	3.54003i	0.364219	+	0.330109i
$116$	−1.80849	+	0.741497i	−0.167914	+	0.0688462i
$117$	0.421743	−	0.252783i	0.0389901	−	0.0233698i
$118$	10.7636	−	11.2648i	0.990874	−	1.03701i
$119$	0.772580	−	2.54685i	0.0708223	−	0.233470i
$120$	12.0822	−	0.231433i	1.10295	−	0.0211268i
$121$	0.247726	−	0.463462i	0.0225205	−	0.0421329i
$122$	11.0691	−	9.51362i	1.00215	−	0.861322i
$123$	0.340106	−	6.92301i	0.0306663	−	0.624227i
$124$	−18.5856	−	4.72650i	−1.66904	−	0.424453i
$125$	12.0393	+	1.78586i	1.07683	+	0.159732i
$126$	−5.88763	+	6.80066i	−0.524512	+	0.605851i
$127$		−	22.0006i		−	1.95223i	−0.217245	−	0.976117i	$-0.569707\pi$
$127$		−	22.0006i		−	1.95223i	0.217245	−	0.976117i	$-0.430293\pi$
$128$	−5.45224	−	9.91328i	−0.481914	−	0.876218i
$129$		−	27.7617i		−	2.44428i
$130$	0.376053	+	0.325566i	0.0329820	+	0.0285540i
$131$	−18.5034	−	2.74472i	−1.61665	−	0.239808i	−0.723751	−	0.690061i	$-0.757584\pi$
$131$	−18.5034	−	2.74472i	−1.61665	−	0.239808i	−0.892901	+	0.450253i	$0.851334\pi$
$132$	13.0936	−	7.78415i	1.13965	−	0.677523i
$133$	−0.547807	+	11.1509i	−0.0475009	+	0.966902i
$134$	12.6340	+	14.6996i	1.09141	+	1.26985i
$135$	−0.930316	+	1.74050i	−0.0800688	+	0.149798i
$136$	2.75266	−	1.20245i	0.236038	−	0.103110i
$137$	1.92509	−	6.34618i	0.164472	−	0.542191i	−0.835502	−	0.549488i	$-0.814823\pi$
$137$	1.92509	−	6.34618i	0.164472	−	0.542191i	0.999973	+	0.00729725i	$0.00232281\pi$
$138$	−6.98649	−	6.67567i	−0.594729	−	0.568270i
$139$	12.7958	−	7.66949i	1.08532	−	0.650517i	0.144530	−	0.989500i	$-0.453833\pi$
$139$	12.7958	−	7.66949i	1.08532	−	0.650517i	0.940793	+	0.338983i	$0.110083\pi$
$140$	−8.39431	−	3.51243i	−0.709448	−	0.296855i
$141$	22.1799	+	20.1027i	1.86789	+	1.69295i
$142$	10.7985	−	4.14316i	0.906188	−	0.347686i
$143$	0.614939	+	0.122319i	0.0514238	+	0.0102288i
$144$	−10.1521	−	0.0729765i	−0.846006	−	0.00608137i
$145$	−1.74021	+	0.346149i	−0.144517	+	0.0287461i
$146$	4.87566	+	7.73020i	0.403512	+	0.639756i
$147$	−1.53117	+	0.724188i	−0.126288	+	0.0597300i
$148$	−3.30525	−	6.23752i	−0.271690	−	0.512721i
$149$	11.9400	+	8.85529i	0.978160	+	0.725453i	0.961613	−	0.274410i	$-0.0884825\pi$
$149$	11.9400	+	8.85529i	0.978160	+	0.725453i	0.0165476	+	0.999863i	$0.494732\pi$
$150$	−5.58546	−	0.979513i	−0.456051	−	0.0799769i
$151$	0.887983	−	1.08201i	0.0722630	−	0.0880528i	−0.735624	−	0.677390i	$-0.763111\pi$
$151$	0.887983	−	1.08201i	0.0722630	−	0.0880528i	0.807887	+	0.589337i	$0.200611\pi$
$152$	−9.97522	+	7.69857i	−0.809097	+	0.624436i
$153$	0.264204	−	2.68250i	0.0213596	−	0.216868i
$154$	−11.3864	+	1.38361i	−0.917544	+	0.111495i
$155$	−15.7369	−	7.44299i	−1.26402	−	0.597835i
$156$	−0.673397	−	0.614754i	−0.0539149	−	0.0492197i
$157$	−0.347065	−	1.38556i	−0.0276988	−	0.110580i	0.954605	−	0.297875i	$-0.0962779\pi$
$157$	−0.347065	−	1.38556i	−0.0276988	−	0.110580i	−0.982304	+	0.187295i	$0.940028\pi$
$158$	−4.84551	−	6.23201i	−0.385488	−	0.495792i
$159$	−1.72729	+	4.17004i	−0.136983	+	0.330705i
$160$	−3.13380	−	9.78033i	−0.247749	−	0.773203i
$161$	2.78452	+	6.72242i	0.219451	+	0.529801i
$162$	7.11328	−	12.5042i	0.558872	−	0.982426i
$163$	−6.68518	+	11.1535i	−0.523624	+	0.873613i	−0.999984	−	0.00563685i	$-0.998206\pi$
$163$	−6.68518	+	11.1535i	−0.523624	+	0.873613i	0.476361	+	0.879250i	$0.341956\pi$
$164$	−5.71929	+	1.41078i	−0.446602	+	0.110164i
$165$	13.0193	−	4.65838i	1.01355	−	0.362654i
$166$	−4.68506	−	1.30560i	−0.363631	−	0.101334i
$167$	−6.08053	+	4.99016i	−0.470525	+	0.386150i	−0.839561	−	0.543265i	$-0.817188\pi$
$167$	−6.08053	+	4.99016i	−0.470525	+	0.386150i	0.369036	+	0.929415i	$0.379688\pi$
$168$	15.2130	+	6.84181i	1.17371	+	0.527857i
$169$	1.27054	+	12.9001i	0.0977342	+	0.992312i
$170$	2.66157	−	0.592654i	0.204133	−	0.0454545i
$171$	1.65909	+	11.1847i	0.126874	+	0.855313i
$172$	−22.6023	+	6.76771i	−1.72341	+	0.516033i
$173$	−4.11515	+	11.5011i	−0.312869	+	0.874411i	0.677446	+	0.735573i	$0.263087\pi$
$173$	−4.11515	+	11.5011i	−0.312869	+	0.874411i	−0.990315	+	0.138838i	$0.955663\pi$
$174$	3.20564	−	0.550300i	0.243019	−	0.0417181i
$175$	3.55040	+	2.37230i	0.268385	+	0.179329i
$176$	−9.52941	−	8.76254i	−0.718306	−	0.660501i
$177$	−21.5572	+	14.4041i	−1.62034	+	1.08268i
$178$	−0.506084	−	0.533473i	−0.0379326	−	0.0399855i
$179$	0.152236	+	3.09884i	0.0113787	+	0.231618i	0.997748	+	0.0670723i	$0.0213658\pi$
$179$	0.152236	+	3.09884i	0.0113787	+	0.231618i	−0.986369	+	0.164546i	$0.947384\pi$
$180$	−9.03228	−	1.83040i	−0.673226	−	0.136430i
$181$	3.43255	−	13.7035i	0.255139	−	1.01857i	−0.698013	−	0.716085i	$-0.745932\pi$
$181$	3.43255	−	13.7035i	0.255139	−	1.01857i	0.953153	−	0.302489i	$-0.0978176\pi$
$182$	0.277105	+	0.628183i	0.0205404	+	0.0465640i
$183$	−21.4200	+	11.4492i	−1.58341	+	0.846349i
$184$	−3.73185	+	7.31545i	−0.275116	+	0.539302i
$185$	−1.86014	−	6.13207i	−0.136760	−	0.450839i
$186$	28.4784	+	14.3990i	2.08814	+	1.05579i
$187$	2.54675	−	2.30824i	0.186237	−	0.168795i
$188$	10.9597	−	22.9585i	0.799317	−	1.67442i
$189$	−2.18806	+	1.62278i	−0.159158	+	0.118040i
$190$	−10.2261	+	5.12439i	−0.741882	+	0.371762i
$191$	14.0527	−	14.0527i	1.01681	−	1.01681i	0.0169583	−	0.999856i	$-0.494602\pi$
$191$	14.0527	−	14.0527i	1.01681	−	1.01681i	0.999856	−	0.0169583i	$-0.00539825\pi$
$192$	5.27048	+	18.0737i	0.380364	+	1.30436i
$193$	19.1046	+	19.1046i	1.37518	+	1.37518i	0.852571	+	0.522612i	$0.175042\pi$
$193$	19.1046	+	19.1046i	1.37518	+	1.37518i	0.522612	+	0.852571i	$0.324958\pi$
$194$	−17.7512	−	5.89962i	−1.27447	−	0.423568i
$195$	−0.493059	−	0.664814i	−0.0353087	−	0.0476083i
$196$	0.962864	+	1.07006i	0.0687760	+	0.0764329i
$197$	4.86979	+	5.37298i	0.346958	+	0.382809i	0.889281	−	0.457361i	$-0.151205\pi$
$197$	4.86979	+	5.37298i	0.346958	+	0.382809i	−0.542323	+	0.840170i	$0.682455\pi$
$198$	−11.0370	+	3.62416i	−0.784368	+	0.257558i
$199$	−3.31717	+	1.00625i	−0.235148	+	0.0713313i	−0.405659	−	0.914024i	$-0.632958\pi$
$199$	−3.31717	+	1.00625i	−0.235148	+	0.0713313i	0.170511	+	0.985356i	$0.445458\pi$
$200$	0.564143	+	4.78620i	0.0398909	+	0.338436i
$201$	−15.2044	−	28.4454i	−1.07244	−	2.00639i
$202$	3.81713	−	9.84282i	0.268572	−	0.692539i
$203$	−2.37575	−	0.595095i	−0.166745	−	0.0417675i
$204$	−4.90594	+	0.957534i	−0.343484	+	0.0670408i
$205$	−5.34092	+	0.262382i	−0.373026	+	0.0183256i
$206$	10.6541	+	0.280702i	0.742306	+	0.0195574i
$207$	4.09418	+	6.12737i	0.284565	+	0.425882i
$208$	−0.336344	+	0.698111i	−0.0233213	+	0.0484053i
$209$	−8.01030	+	11.9883i	−0.554084	+	0.829245i
$210$	12.3642	+	8.74114i	0.853211	+	0.603196i
$211$	−12.5539	−	4.49187i	−0.864248	−	0.309233i	−0.132810	−	0.991141i	$-0.542400\pi$
$211$	−12.5539	−	4.49187i	−0.864248	−	0.309233i	−0.731437	+	0.681909i	$0.761150\pi$
$212$	3.81612	+	0.389708i	0.262092	+	0.0267653i
$213$	−19.0381	+	2.82403i	−1.30447	+	0.193499i
$214$	−5.10849	+	8.03520i	−0.349209	+	0.549275i
$215$	−21.3143	+	2.09927i	−1.45362	+	0.143169i
$216$	−2.99621	−	0.689811i	−0.203867	−	0.0469357i
$217$	−15.2441	−	18.5750i	−1.03484	−	1.26095i
$218$	7.52653	+	13.3420i	0.509761	+	0.903637i
$219$	−5.12353	−	14.3193i	−0.346216	−	0.967608i
$220$	−6.96645	−	9.46407i	−0.469678	−	0.638068i
$221$	−0.176471	−	0.105772i	−0.0118707	−	0.00711502i
$222$	3.11265	+	11.3268i	0.208907	+	0.760205i
$223$	−13.4060	+	5.55295i	−0.897733	+	0.371853i	−0.783348	−	0.621583i	$-0.786490\pi$
$223$	−13.4060	+	5.55295i	−0.897733	+	0.371853i	−0.114385	+	0.993436i	$0.536490\pi$
$224$	1.86168	−	14.0535i	0.124389	−	0.938992i
$225$	3.99543	+	1.65496i	0.266362	+	0.110331i
$226$	−0.182861	+	1.46098i	−0.0121637	+	0.0971832i
$227$	−14.8255	+	3.71360i	−0.984004	+	0.246480i	−0.701409	−	0.712759i	$-0.747445\pi$
$227$	−14.8255	+	3.71360i	−0.984004	+	0.246480i	−0.282595	+	0.959239i	$0.591195\pi$
$228$	18.9868	−	8.89671i	1.25743	−	0.589199i
$229$	10.5659	−	22.3398i	0.698217	−	1.47626i	−0.172776	−	0.984961i	$-0.555274\pi$
$229$	10.5659	−	22.3398i	0.698217	−	1.47626i	0.870993	−	0.491295i	$-0.163476\pi$
$230$	−4.59700	+	5.86873i	−0.303117	+	0.386973i
$231$	18.9950	+	1.87084i	1.24978	+	0.123092i
$232$	−1.22949	−	2.47573i	−0.0807202	−	0.162540i
$233$	11.0398	+	9.06011i	0.723240	+	0.593548i	0.922316	−	0.386436i	$-0.126294\pi$
$233$	11.0398	+	9.06011i	0.723240	+	0.593548i	−0.199076	+	0.979984i	$0.563794\pi$
$234$	0.399374	+	0.569238i	0.0261079	+	0.0372123i
$235$	13.7568	−	18.5490i	0.897398	−	1.21000i
$236$	16.9823	+	14.0394i	1.10545	+	0.913890i
$237$	5.61642	+	11.8749i	0.364826	+	0.771360i
$238$	3.67093	+	0.831266i	0.237951	+	0.0538830i
$239$	1.53099	+	7.69679i	0.0990313	+	0.497864i	0.998185	+	0.0602299i	$0.0191834\pi$
$239$	1.53099	+	7.69679i	0.0990313	+	0.497864i	−0.899153	+	0.437634i	$0.855817\pi$
$240$	1.55281	+	17.0192i	0.100233	+	1.09859i
$241$	−1.48893	+	7.48536i	−0.0959104	+	0.482174i	0.902738	+	0.430192i	$0.141554\pi$
$241$	−1.48893	+	7.48536i	−0.0959104	+	0.482174i	−0.998648	+	0.0519826i	$0.983446\pi$
$242$	0.678889	+	0.302392i	0.0436406	+	0.0194385i
$243$	−13.8863	+	15.3212i	−0.890806	+	0.982853i
$244$	14.5431	+	14.6480i	0.931027	+	0.937744i
$245$	0.671785	+	1.12080i	0.0429187	+	0.0716056i
$246$	9.79988	−	0.222953i	0.624818	−	0.0142150i
$247$	0.825886	+	0.250530i	0.0525498	+	0.0159408i
$248$	4.78058	−	26.6960i	0.303567	−	1.69520i
$249$	7.13757	+	3.81511i	0.452325	+	0.241773i
$250$	−1.29707	+	17.1635i	−0.0820341	+	1.08552i
$251$	18.0446	+	0.886473i	1.13896	+	0.0559537i	0.609792	−	0.792561i	$-0.291253\pi$
$251$	18.0446	+	0.886473i	1.13896	+	0.0559537i	0.529171	+	0.848515i	$0.322503\pi$
$252$	−10.1904	−	7.61462i	−0.641933	−	0.479676i
$253$	−1.37882	+	9.29527i	−0.0866858	+	0.584388i
$254$	31.0333	−	2.23309i	1.94720	−	0.140116i
$255$	−4.53744			−0.284146
$256$	13.4299	−	8.69695i	0.839371	−	0.543560i
$257$	19.4020			1.21026			0.605132	−	0.796125i	$-0.293120\pi$
$257$	19.4020			1.21026			0.605132	+	0.796125i	$0.293120\pi$
$258$	39.1597	−	2.81785i	2.43798	−	0.175432i
$259$	1.29787	−	8.74951i	0.0806455	−	0.543668i
$260$	−0.421062	+	0.563493i	−0.0261132	+	0.0349463i
$261$	−2.47748	−	0.121711i	−0.153352	−	0.00753370i
$262$	1.99349	−	26.3789i	0.123158	−	1.62969i
$263$	−10.4314	−	5.57572i	−0.643230	−	0.343813i	0.117319	−	0.993094i	$-0.462570\pi$
$263$	−10.4314	−	5.57572i	−0.643230	−	0.343813i	−0.760549	+	0.649281i	$0.775070\pi$
$264$	12.3091	+	17.6792i	0.757571	+	1.08808i
$265$	3.33219	+	1.01081i	0.204695	+	0.0620936i
$266$	−15.7846	+	0.359109i	−0.967818	+	0.0220184i
$267$	0.629069	+	1.04954i	0.0384984	+	0.0642307i
$268$	−19.4524	+	19.3131i	−1.18824	+	1.17973i
$269$	7.82047	−	8.62856i	0.476822	−	0.526092i	−0.454276	−	0.890861i	$-0.650102\pi$
$269$	7.82047	−	8.62856i	0.476822	−	0.526092i	0.931098	+	0.364769i	$0.118852\pi$
$270$	−2.54952	−	1.13561i	−0.155159	−	0.0691110i
$271$	0.606286	−	3.04801i	0.0368293	−	0.185153i	−0.957992	−	0.286796i	$-0.907410\pi$
$271$	0.606286	−	3.04801i	0.0368293	−	0.185153i	0.994821	+	0.101643i	$0.0324098\pi$
$272$	1.97554	+	3.76075i	0.119785	+	0.228029i
$273$	−0.222893	−	1.12056i	−0.0134901	−	0.0678192i
$274$	9.14711	+	2.07133i	0.552597	+	0.125133i
$275$	2.35776	+	4.98507i	0.142179	+	0.300611i
$276$	8.70733	−	10.5325i	0.524120	−	0.633982i
$277$	−13.2510	+	17.8669i	−0.796175	+	1.07352i	0.199434	+	0.979911i	$0.436090\pi$
$277$	−13.2510	+	17.8669i	−0.796175	+	1.07352i	−0.995609	+	0.0936069i	$0.970160\pi$
$278$	12.1171	+	17.2708i	0.726736	+	1.03583i
$279$	−18.8125	−	15.4390i	−1.12627	−	0.924309i
$280$	4.10249	−	12.1972i	0.245171	−	0.728925i
$281$	−22.1530	−	2.18188i	−1.32154	−	0.130160i	−0.587476	−	0.809242i	$-0.699878\pi$
$281$	−22.1530	−	2.18188i	−1.32154	−	0.130160i	−0.734063	+	0.679082i	$0.762378\pi$
$282$	−26.1049	+	33.3267i	−1.55453	+	1.98458i
$283$	−5.99549	+	12.6764i	−0.356395	+	0.753533i	−0.999929	−	0.0118836i	$-0.996217\pi$
$283$	−5.99549	+	12.6764i	−0.356395	+	0.753533i	0.643535	+	0.765417i	$0.277467\pi$
$284$	6.94026	+	14.8114i	0.411828	+	0.878897i
$285$	18.4633	−	4.62482i	1.09367	−	0.273951i
$286$	−0.110122	+	0.879828i	−0.00651165	+	0.0520253i
$287$	−6.81934	−	2.82466i	−0.402533	−	0.166735i
$288$	−0.927510	−	14.3276i	−0.0546541	−	0.844261i
$289$	14.6639	−	6.07400i	0.862584	−	0.357294i
$290$	−0.664900	−	2.41955i	−0.0390443	−	0.142081i
$291$	26.6990	+	16.0027i	1.56512	+	0.938097i
$292$	−10.4091	+	7.66206i	−0.609145	+	0.448388i
$293$	−10.0617	−	28.1206i	−0.587812	−	1.64282i	−0.754109	−	0.656749i	$-0.771931\pi$
$293$	−10.0617	−	28.1206i	−0.587812	−	1.64282i	0.166297	−	0.986076i	$-0.446819\pi$
$294$	−1.17693	−	2.08631i	−0.0686400	−	0.121676i
$295$	12.6889	+	15.4615i	0.738779	+	0.900205i
$296$	8.46295	−	5.29540i	0.491899	−	0.307789i
$297$	−3.50117	+	0.344835i	−0.203158	+	0.0200094i
$298$	−11.2790	+	17.7409i	−0.653378	+	1.02771i
$299$	0.556400	−	0.0825342i	0.0321775	−	0.00477307i
$300$	0.814736	−	7.97809i	0.0470388	−	0.460615i
$301$	−27.8353	−	9.95963i	−1.60440	−	0.574063i
$302$	1.61638	+	1.14273i	0.0930122	+	0.0657569i
$303$	−9.75993	+	14.6068i	−0.560694	+	0.839137i
$304$	−11.8718	−	13.2893i	−0.680897	−	0.762193i
$305$	10.4099	+	15.5796i	0.596072	+	0.892085i
$306$	3.81067	+	0.100399i	0.217841	+	0.00573943i
$307$	−26.3011	+	1.29209i	−1.50108	+	0.0737434i	−0.782915	−	0.622129i	$-0.786268\pi$
$307$	−26.3011	+	1.29209i	−1.50108	+	0.0737434i	−0.718166	+	0.695872i	$0.755018\pi$
$308$	−3.10741	−	15.9209i	−0.177061	−	0.907175i
$309$	−17.2035	−	4.30926i	−0.978675	−	0.245145i
$310$	8.90152	−	22.9534i	0.505572	−	1.30367i
$311$	8.38224	+	15.6821i	0.475313	+	0.889249i	0.999296	+	0.0375196i	$0.0119457\pi$
$311$	8.38224	+	15.6821i	0.475313	+	0.889249i	−0.523983	+	0.851729i	$0.675554\pi$
$312$	0.798801	−	1.01227i	0.0452232	−	0.0573085i
$313$	1.16884	−	0.354563i	0.0660665	−	0.0200411i	−0.257078	−	0.966391i	$-0.582760\pi$
$313$	1.16884	−	0.354563i	0.0660665	−	0.0200411i	0.323145	+	0.946349i	$0.395260\pi$
$314$	1.91920	−	0.630195i	0.108307	−	0.0355640i
$315$	−7.75496	−	8.55628i	−0.436942	−	0.482092i
$316$	8.29884	−	7.46747i	0.466846	−	0.420078i
$317$	−7.47066	−	10.0730i	−0.419594	−	0.565757i	0.541949	−	0.840411i	$-0.317687\pi$
$317$	−7.47066	−	10.0730i	−0.419594	−	0.565757i	−0.961543	+	0.274654i	$0.911437\pi$
$318$	−6.05743	−	2.01319i	−0.339684	−	0.112894i
$319$	−2.23655	−	2.23655i	−0.125223	−	0.125223i
$320$	13.4777	−	5.41315i	0.753427	−	0.302604i
$321$	11.2037	−	11.2037i	0.625328	−	0.625328i
$322$	−9.19979	+	4.61008i	−0.512684	+	0.256910i
$323$	3.80016	−	2.81839i	0.211446	−	0.156819i
$324$	18.3601	+	8.76455i	1.02000	+	0.486920i
$325$	0.244581	−	0.221676i	0.0135669	−	0.0122964i
$326$	−16.4114	−	8.29779i	−0.908942	−	0.459572i
$327$	−7.39958	−	24.3932i	−0.409198	−	1.34894i
$328$	−2.57052	−	7.92424i	−0.141933	−	0.437543i
$329$	28.1131	−	15.0268i	1.54993	−	0.828454i
$330$	7.89243	+	17.8917i	0.434464	+	0.984908i
$331$	−7.70114	+	30.7447i	−0.423293	+	1.68988i	0.264836	+	0.964293i	$0.414682\pi$
$331$	−7.70114	+	30.7447i	−0.423293	+	1.68988i	−0.688130	+	0.725588i	$0.741568\pi$
$332$	1.36610	−	6.74111i	0.0749742	−	0.369967i
$333$	−0.439565	−	8.94754i	−0.0240880	−	0.490322i
$334$	−7.65614	−	8.07048i	−0.418925	−	0.441597i
$335$	−20.6895	+	13.8243i	−1.13039	+	0.755301i
$336$	−8.10669	+	22.1533i	−0.442256	+	1.20856i
$337$	24.2543	+	16.2062i	1.32122	+	0.882808i	0.997981	−	0.0635108i	$-0.0202297\pi$
$337$	24.2543	+	16.2062i	1.32122	+	0.882808i	0.323235	+	0.946319i	$0.395230\pi$
$338$	−18.0674	+	3.10156i	−0.982738	+	0.168703i
$339$	0.825417	−	2.30689i	0.0448305	−	0.125293i
$340$	1.10613	+	3.69417i	0.0599883	+	0.200344i
$341$	−4.55346	−	30.6969i	−0.246584	−	1.66233i
$342$	−15.6083	+	3.47551i	−0.844001	+	0.187934i
$343$	1.89624	+	19.2529i	0.102387	+	1.03956i
$344$	−11.8405	−	31.1951i	−0.638395	−	1.68192i
$345$	9.58931	−	7.86975i	0.516271	−	0.423693i
$346$	−16.6407	−	4.63732i	−0.894611	−	0.249304i
$347$	4.29600	−	1.53713i	0.230621	−	0.0825176i	−0.219043	−	0.975715i	$-0.570294\pi$
$347$	4.29600	−	1.53713i	0.230621	−	0.0825176i	0.449664	+	0.893198i	$0.351544\pi$
$348$	1.10161	+	4.46592i	0.0590526	+	0.239398i
$349$	0.587449	−	0.980099i	0.0314454	−	0.0524635i	−0.841605	−	0.540094i	$-0.818389\pi$
$349$	0.587449	−	0.980099i	0.0314454	−	0.0524635i	0.873050	+	0.487631i	$0.162139\pi$
$350$	−2.98592	+	5.24886i	−0.159604	+	0.280564i
$351$	0.0805888	+	0.194558i	0.00430151	+	0.0103848i
$352$	11.3929	−	14.3313i	0.607244	−	0.763859i
$353$	−5.25239	+	12.6804i	−0.279556	+	0.674909i	−0.999823	−	0.0187882i	$-0.994019\pi$
$353$	−5.25239	+	12.6804i	−0.279556	+	0.674909i	0.720267	+	0.693697i	$0.244019\pi$
$354$	−22.5060	−	28.9458i	−1.19618	−	1.53845i
$355$	3.60778	+	14.4031i	0.191481	+	0.764436i
$356$	0.701130	−	0.768013i	0.0371598	−	0.0407046i
$357$	−5.66190	−	2.67788i	−0.299660	−	0.141728i
$358$	−4.35567	+	0.529275i	−0.230204	+	0.0279731i
$359$	−1.94850	+	19.7835i	−0.102838	+	1.04413i	0.795835	+	0.605514i	$0.207032\pi$
$359$	−1.94850	+	19.7835i	−0.102838	+	1.04413i	−0.898673	+	0.438619i	$0.855468\pi$
$360$	1.66512	−	12.9264i	0.0877594	−	0.681282i
$361$	−0.537092	+	0.654448i	−0.0282680	+	0.0344446i
$362$	19.6781	+	3.45092i	1.03426	+	0.181376i
$363$	−0.993327	−	0.736701i	−0.0521361	−	0.0386668i
$364$	−0.857968	+	0.454636i	−0.0449697	+	0.0238294i
$365$	−10.6063	+	5.01642i	−0.555161	+	0.262571i
$366$	−18.3240	−	29.0522i	−0.957811	−	1.51858i
$367$	32.4565	−	6.45599i	1.69421	−	0.337000i	0.748781	−	0.662817i	$-0.230639\pi$
$367$	32.4565	−	6.45599i	1.69421	−	0.337000i	0.945433	+	0.325817i	$0.105639\pi$
$368$	−10.6977	−	4.52150i	−0.557657	−	0.235699i
$369$	−7.33193	−	1.45841i	−0.381685	−	0.0759219i
$370$	8.46088	−	3.24627i	0.439860	−	0.168765i
$371$	3.56142	+	3.22788i	0.184900	+	0.167583i
$372$	−17.4202	+	41.6323i	−0.903196	+	2.15853i
$373$	−8.35870	+	5.01001i	−0.432797	+	0.259408i	−0.713871	−	0.700278i	$-0.753060\pi$
$373$	−8.35870	+	5.01001i	−0.432797	+	0.259408i	0.281074	+	0.959686i	$0.409310\pi$
$374$	3.51443	+	3.35807i	0.181727	+	0.173642i
$375$	8.31441	−	27.4089i	0.429354	−	1.41539i
$376$	33.4968	+	13.1290i	1.72747	+	0.677079i
$377$	−0.0892494	+	0.166974i	−0.00459658	+	0.00859960i
$378$	−2.51113	−	2.92169i	−0.129158	−	0.150276i
$379$	−0.467551	+	9.51722i	−0.0240165	+	0.488867i	0.956416	+	0.292009i	$0.0943238\pi$
$379$	−0.467551	+	9.51722i	−0.0240165	+	0.488867i	−0.980432	+	0.196858i	$0.936926\pi$
$380$	−8.26626	−	13.9045i	−0.424050	−	0.713286i
$381$	−51.2138	−	7.59685i	−2.62376	−	0.389199i
$382$	21.2486	+	18.3958i	1.08717	+	0.941213i
$383$		−	15.3877i		−	0.786272i	−0.919480	−	0.393136i	$-0.871390\pi$
$383$		−	15.3877i		−	0.786272i	0.919480	−	0.393136i	$-0.128610\pi$
$384$	−24.9592	+	9.26887i	−1.27369	+	0.473000i
$385$		−	14.7250i		−	0.750456i
$386$	−25.0092	+	28.8875i	−1.27294	+	1.47034i
$387$	−29.6174	−	4.39332i	−1.50553	−	0.223325i
$388$	6.52003	−	25.6381i	0.331005	−	1.30158i
$389$	−0.319825	+	6.51018i	−0.0162158	+	0.330079i	0.976958	+	0.213433i	$0.0684645\pi$
$389$	−0.319825	+	6.51018i	−0.0162158	+	0.330079i	−0.993173	+	0.116647i	$0.962786\pi$
$390$	0.887718	−	0.762973i	0.0449513	−	0.0386346i
$391$	1.45358	−	2.71946i	0.0735107	−	0.137529i
$392$	−1.41166	+	1.46680i	−0.0712996	+	0.0740844i
$393$	−12.7786	+	42.1253i	−0.644594	+	2.12494i
$394$	−7.08466	+	7.41452i	−0.356920	+	0.373538i
$395$	8.69238	−	5.21001i	0.437361	−	0.262144i
$396$	−6.23239	−	15.2006i	−0.313189	−	0.763859i
$397$	4.68934	+	4.25017i	0.235351	+	0.213310i	0.780711	−	0.624892i	$-0.214857\pi$
$397$	4.68934	+	4.25017i	0.235351	+	0.213310i	−0.545360	+	0.838202i	$0.683607\pi$
$398$	−1.75608	−	4.57695i	−0.0880244	−	0.229422i
$399$	25.7683	+	5.12563i	1.29003	+	0.256603i
$400$	−6.69399	+	1.28157i	−0.334700	+	0.0640783i
$401$	30.2238	−	6.01189i	1.50931	−	0.300220i	0.630045	−	0.776559i	$-0.283037\pi$
$401$	30.2238	−	6.01189i	1.50931	−	0.300220i	0.879262	+	0.476339i	$0.158037\pi$
$402$	38.5809	−	24.3341i	1.92424	−	1.21367i
$403$	−1.67923	+	0.794216i	−0.0836483	+	0.0395627i
$404$	14.2714	+	4.38526i	0.710029	+	0.218175i
$405$	14.8338	+	11.0015i	0.737095	+	0.546667i
$406$	0.598279	−	3.41156i	0.0296921	−	0.169313i
$407$	7.24680	−	8.83025i	0.359211	−	0.437699i
$408$	−1.84862	−	6.82296i	−0.0915206	−	0.337787i
$409$	−0.567557	+	5.76251i	−0.0280639	+	0.284938i	0.970902	+	0.239476i	$0.0769758\pi$
$409$	−0.567557	+	5.76251i	−0.0280639	+	0.284938i	−0.998966	+	0.0454613i	$0.985524\pi$
$410$	−0.912218	−	7.50709i	−0.0450512	−	0.370749i
$411$	−14.1082	−	6.67267i	−0.695905	−	0.329138i
$412$	0.685456	+	15.0568i	0.0337700	+	0.741796i
$413$	6.70850	+	26.7819i	0.330104	+	1.31785i
$414$	−8.22750	+	6.39704i	−0.404359	+	0.314398i
$415$	2.38936	−	5.76842i	0.117289	−	0.283161i
$416$	−1.01887	−	0.403576i	−0.0499543	−	0.0197869i
$417$	−13.4349	−	32.4348i	−0.657912	−	1.58834i
$418$	−17.7233	−	10.0822i	−0.866874	−	0.493138i
$419$	16.9299	−	28.2458i	0.827079	−	1.37990i	−0.0960373	−	0.995378i	$-0.530617\pi$
$419$	16.9299	−	28.2458i	0.827079	−	1.37990i	0.923116	−	0.384521i	$-0.125633\pi$
$420$	−11.0750	+	18.3278i	−0.540403	+	0.894304i
$421$	−11.9271	+	4.26759i	−0.581292	+	0.207990i	−0.611083	−	0.791566i	$-0.709266\pi$
$421$	−11.9271	+	4.26759i	−0.581292	+	0.207990i	0.0297908	+	0.999556i	$0.490516\pi$
$422$	5.06184	−	18.1641i	0.246406	−	0.884213i
$423$	24.9564	−	20.4812i	1.21342	−	0.995830i
$424$	−0.162369	+	5.42244i	−0.00788531	+	0.263337i
$425$	−0.177368	−	1.80085i	−0.00860360	−	0.0873538i
$426$	−5.91587	−	26.5678i	−0.286625	−	1.28721i
$427$	3.79505	+	25.5842i	0.183655	+	1.23810i
$428$	−11.8527	−	6.39028i	−0.572922	−	0.308886i
$429$	0.497079	−	1.38924i	0.0239992	−	0.0670733i
$430$	−5.12459	−	29.8521i	−0.247130	−	1.43960i
$431$	−9.75432	−	6.51763i	−0.469849	−	0.313943i	0.298009	−	0.954563i	$-0.403677\pi$
$431$	−9.75432	−	6.51763i	−0.469849	−	0.313943i	−0.767858	+	0.640620i	$0.778677\pi$
$432$	0.668904	−	4.29638i	0.0321827	−	0.206710i
$433$	25.8243	−	17.2553i	1.24104	−	0.829235i	0.250721	−	0.968060i	$-0.419332\pi$
$433$	25.8243	−	17.2553i	1.24104	−	0.829235i	0.990317	+	0.138825i	$0.0443325\pi$
$434$	24.6540	−	23.3882i	1.18343	−	1.12267i
$435$	0.204882	+	4.17046i	0.00982332	+	0.199958i
$436$	−18.0559	+	11.9709i	−0.864720	+	0.573303i
$437$	−3.14294	+	12.5473i	−0.150347	+	0.600219i
$438$	19.6783	−	8.68050i	0.940264	−	0.414770i
$439$	12.4344	−	6.64635i	0.593464	−	0.317213i	−0.147181	−	0.989110i	$-0.547020\pi$
$439$	12.4344	−	6.64635i	0.593464	−	0.317213i	0.740645	+	0.671897i	$0.234520\pi$
$440$	12.6426	−	10.7873i	0.602712	−	0.514262i
$441$	0.530285	+	1.74812i	0.0252517	+	0.0832436i
$442$	0.131287	−	0.259660i	0.00624469	−	0.0123507i
$443$	23.7823	−	21.5550i	1.12993	−	1.02411i	0.130466	−	0.991453i	$-0.458353\pi$
$443$	23.7823	−	21.5550i	1.12993	−	1.02411i	0.999467	−	0.0326583i	$-0.0103973\pi$
$444$	−15.6613	+	5.54028i	−0.743251	+	0.262930i
$445$	0.758223	−	0.562337i	0.0359432	−	0.0266573i
$446$	−9.19354	−	18.3464i	−0.435327	−	0.868729i
$447$	24.7366	−	24.7366i	1.17000	−	1.17000i
$448$	20.0124	+	1.19957i	0.945498	+	0.0566744i
$449$	4.98783	+	4.98783i	0.235390	+	0.235390i	0.814938	−	0.579548i	$-0.196771\pi$
$449$	4.98783	+	4.98783i	0.235390	+	0.235390i	−0.579548	+	0.814938i	$0.696771\pi$
$450$	−1.92889	+	5.80380i	−0.0909288	+	0.273594i
$451$	−5.67848	−	7.65654i	−0.267389	−	0.360532i
$452$	−2.07937	−	0.109646i	−0.0978056	−	0.00515732i
$453$	−2.21213	−	2.44071i	−0.103935	−	0.114674i
$454$	−6.74309	−	20.5354i	−0.316469	−	0.963776i
$455$	−0.843463	+	0.255862i	−0.0395421	+	0.0119950i
$456$	14.4766	+	25.8791i	0.677928	+	1.21190i
$457$	7.60807	+	14.2337i	0.355891	+	0.665825i	0.994618	−	0.103608i	$-0.0330389\pi$
$457$	7.60807	+	14.2337i	0.355891	+	0.665825i	−0.638727	+	0.769433i	$0.720539\pi$
$458$	32.5842	+	12.6364i	1.52256	+	0.590462i
$459$	1.11985	+	0.280508i	0.0522701	+	0.0130930i
$460$	−8.74484	−	5.88869i	−0.407730	−	0.274561i
$461$	−16.4010	+	0.805730i	−0.763871	+	0.0375266i	−0.427274	−	0.904122i	$-0.640526\pi$
$461$	−16.4010	+	0.805730i	−0.763871	+	0.0375266i	−0.336597	+	0.941649i	$0.609276\pi$
$462$	−0.710931	+	26.9835i	−0.0330755	+	1.25539i
$463$	−3.36305	−	5.03316i	−0.156294	−	0.233911i	0.745056	−	0.667002i	$-0.232423\pi$
$463$	−3.36305	−	5.03316i	−0.156294	−	0.233911i	−0.901350	+	0.433091i	$0.857423\pi$
$464$	3.36739	−	1.98557i	0.156327	−	0.0921779i
$465$	−22.7601	+	34.0629i	−1.05547	+	1.57963i
$466$	−11.6593	+	16.4920i	−0.540109	+	0.763975i
$467$	−15.0027	−	5.36806i	−0.694244	−	0.248404i	−0.0339627	−	0.999423i	$-0.510813\pi$
$467$	−15.0027	−	5.36806i	−0.694244	−	0.248404i	−0.660281	+	0.751019i	$0.729563\pi$
$468$	−0.762411	+	0.621123i	−0.0352425	+	0.0287114i
$469$	−33.9755	+	5.03978i	−1.56884	+	0.232716i
$470$	27.5609	+	17.5222i	1.27129	+	0.808239i
$471$	−3.34521	+	0.329475i	−0.154139	+	0.0151814i
$472$	−18.0798	+	25.3797i	−0.832192	+	1.16819i
$473$	−24.2210	−	29.5133i	−1.11368	−	1.35702i
$474$	−16.1803	+	9.12766i	−0.743186	+	0.419247i
$475$	2.55725	+	7.14704i	0.117335	+	0.327929i
$476$	−0.799952	+	5.26246i	−0.0366658	+	0.241204i
$477$	4.17542	+	2.50265i	0.191179	+	0.114589i
$478$	−10.7014	+	2.94079i	−0.489472	+	0.134509i
$479$	9.95876	−	4.12505i	0.455027	−	0.188479i	−0.143385	−	0.989667i	$-0.545799\pi$
$479$	9.95876	−	4.12505i	0.455027	−	0.188479i	0.598412	+	0.801189i	$0.295799\pi$
$480$	−23.8492	+	3.91782i	−1.08856	+	0.178823i
$481$	−0.631726	−	0.261669i	−0.0288042	−	0.0119311i
$482$	−10.7097	−	1.34046i	−0.487814	−	0.0610563i
$483$	16.6102	−	4.16065i	0.755792	−	0.189316i
$484$	−0.357635	+	0.988311i	−0.0162562	+	0.0449232i
$485$	10.2673	−	21.7084i	0.466215	−	0.985730i
$486$	−23.0210	−	18.0324i	−1.04425	−	0.817967i
$487$	39.5206	+	3.89244i	1.79085	+	0.176383i	0.938198	−	0.346099i	$-0.112494\pi$
$487$	39.5206	+	3.89244i	1.79085	+	0.176383i	0.852650	+	0.522482i	$0.174994\pi$
$488$	−19.1859	+	22.0008i	−0.868504	+	0.995930i
$489$	23.6553	+	19.4134i	1.06973	+	0.877904i
$490$	−1.51278	+	1.06136i	−0.0683406	+	0.0479474i
$491$	7.60020	−	10.2477i	0.342992	−	0.462471i	−0.597706	−	0.801715i	$-0.703921\pi$
$491$	7.60020	−	10.2477i	0.342992	−	0.462471i	0.940698	+	0.339244i	$0.110171\pi$
$492$	1.30919	+	13.8008i	0.0590229	+	0.622186i
$493$	0.443762	+	0.938255i	0.0199860	+	0.0422569i
$494$	−0.269560	+	1.19040i	−0.0121281	+	0.0535584i
$495$	−2.90944	−	14.6267i	−0.130769	−	0.657422i
$496$	38.1417	+	4.03366i	1.71261	+	0.181117i
$497$	−3.99847	+	20.1016i	−0.179356	+	0.901682i
$498$	−4.65700	+	10.4553i	−0.208685	+	0.468511i
$499$	9.18656	−	10.1358i	0.411247	−	0.453741i	−0.499741	−	0.866175i	$-0.666571\pi$
$499$	9.18656	−	10.1358i	0.411247	−	0.453741i	0.910987	+	0.412434i	$0.135321\pi$
$500$	−24.3419	−	0.0874878i	−1.08860	−	0.00391257i
$501$	9.51668	+	15.8776i	0.425174	+	0.709360i
$502$	0.581119	+	25.5431i	0.0259366	+	1.14004i
$503$	−32.5584	−	9.87649i	−1.45171	−	0.440371i	−0.536688	−	0.843781i	$-0.680325\pi$
$503$	−32.5584	−	9.87649i	−1.45171	−	0.440371i	−0.915019	+	0.403410i	$0.867825\pi$
$504$	9.70659	−	15.1471i	0.432366	−	0.674705i
$505$	11.9525	+	6.38874i	0.531879	+	0.284295i
$506$	−13.2515	−	1.00144i	−0.589103	−	0.0445194i
$507$	30.4680	+	1.49680i	1.35313	+	0.0664751i
$508$	6.29983	+	43.5478i	0.279510	+	1.93212i
$509$	1.03436	−	6.97309i	0.0458472	−	0.309077i	−0.954107	−	0.299467i	$-0.903191\pi$
$509$	1.03436	−	6.97309i	0.0458472	−	0.309077i	0.999954	−	0.00960955i	$-0.00305886\pi$
$510$	−0.460556	−	6.40036i	−0.0203938	−	0.283413i
$511$	−16.1953			−0.716439
$512$	13.6308	+	18.0611i	0.602401	+	0.798193i
$513$	−4.84269			−0.213810
$514$	1.96933	+	27.3678i	0.0868634	+	1.20714i
$515$	−2.00758	+	13.5340i	−0.0884647	+	0.596380i
$516$	7.94953	+	54.9514i	0.349959	+	2.41910i
$517$	41.1182	+	2.02001i	1.80838	+	0.0888398i
$518$	12.4735	+	0.942641i	0.548054	+	0.0414173i
$519$	25.3517	+	13.5508i	1.11282	+	0.594813i
$520$	−0.837582	−	0.536741i	−0.0367304	−	0.0235377i
$521$	−10.4651	−	3.17455i	−0.458484	−	0.139080i	0.0525900	−	0.998616i	$-0.483252\pi$
$521$	−10.4651	−	3.17455i	−0.458484	−	0.139080i	−0.511074	+	0.859536i	$0.670752\pi$
$522$	−0.0797862	−	3.50700i	−0.00349215	−	0.153497i
$523$	−2.23200	−	3.72387i	−0.0975986	−	0.162833i	0.805056	−	0.593198i	$-0.202135\pi$
$523$	−2.23200	−	3.72387i	−0.0975986	−	0.162833i	−0.902655	+	0.430365i	$0.858385\pi$
$524$	37.4115	+	0.134462i	1.63433	+	0.00587398i
$525$	6.74830	−	7.44560i	0.294520	−	0.324953i
$526$	6.80611	−	15.2802i	0.296761	−	0.666247i
$527$	−1.98665	+	9.98756i	−0.0865398	+	0.435065i
$528$	−23.6883	+	19.1572i	−1.03090	+	0.833711i
$529$	−2.84241	−	14.2897i	−0.123583	−	0.621293i
$530$	−1.08759	+	4.80288i	−0.0472420	+	0.208624i
$531$	11.9554	+	25.2776i	0.518820	+	1.09695i
$532$	−2.10871	−	22.2288i	−0.0914241	−	0.963742i
$533$	−0.339905	+	0.458309i	−0.0147229	+	0.0198516i
$534$	−1.41659	+	0.993873i	−0.0613019	+	0.0430091i
$535$	−9.44891	−	7.75452i	−0.408512	−	0.335257i
$536$	−29.2168	−	25.4786i	−1.26197	−	1.10051i
$537$	7.26617	+	0.715656i	0.313559	+	0.0308828i
$538$	12.9649	+	10.1555i	0.558958	+	0.437834i
$539$	−0.995951	+	2.10576i	−0.0428986	+	0.0907015i
$540$	1.34307	−	3.71153i	0.0577967	−	0.159719i
$541$	−12.3367	+	3.09018i	−0.530396	+	0.132857i	−0.498921	−	0.866647i	$-0.666270\pi$
$541$	−12.3367	+	3.09018i	−0.530396	+	0.132857i	−0.0314746	+	0.999505i	$0.510020\pi$
$542$	4.36095	+	0.545830i	0.187319	+	0.0234454i
$543$	−30.7143	−	12.7223i	−1.31808	−	0.545966i
$544$	−5.10427	+	3.16835i	−0.218844	+	0.135842i
$545$	−18.1685	+	7.52564i	−0.778254	+	0.322363i
$546$	1.55800	−	0.428143i	0.0666761	−	0.0183228i
$547$	−1.28848	−	0.772287i	−0.0550915	−	0.0330206i	0.486292	−	0.873796i	$-0.338349\pi$
$547$	−1.28848	−	0.772287i	−0.0550915	−	0.0330206i	−0.541383	+	0.840776i	$0.682099\pi$
$548$	−1.99330	+	13.1128i	−0.0851495	+	0.560153i
$549$	8.82476	+	24.6635i	0.376631	+	1.05261i
$550$	−6.79246	+	3.83178i	−0.289632	+	0.163387i
$551$	−2.76203	−	3.36555i	−0.117667	−	0.143377i
$552$	15.7406	+	11.2132i	0.669964	+	0.477266i
$553$	13.9213	−	1.37113i	0.591995	−	0.0583064i
$554$	−26.5474	−	16.8779i	−1.12789	−	0.717073i
$555$	−14.9168	+	2.21270i	−0.633183	+	0.0939238i
$556$	−23.1317	+	18.8450i	−0.981004	+	0.799206i
$557$	35.9078	+	12.8480i	1.52146	+	0.544388i	0.959239	−	0.282598i	$-0.0911961\pi$
$557$	35.9078	+	12.8480i	1.52146	+	0.544388i	0.562223	+	0.826985i	$0.309946\pi$
$558$	19.8682	−	28.1033i	0.841090	−	1.18971i
$559$	−1.26969	+	1.90022i	−0.0537021	+	0.0803709i
$560$	17.6214	+	4.54880i	0.744641	+	0.192222i
$561$	−4.49382	−	6.72548i	−0.189729	−	0.283950i
$562$	0.829129	−	31.4698i	0.0349747	−	1.32747i
$563$	−42.8566	+	2.10541i	−1.80619	+	0.0887325i	−0.924055	−	0.382261i	$-0.875146\pi$
$563$	−42.8566	+	2.10541i	−1.80619	+	0.0887325i	−0.882137	+	0.470993i	$0.843896\pi$
$564$	−49.6592	−	33.4400i	−2.09103	−	1.40808i
$565$	−1.83355	−	0.459280i	−0.0771379	−	0.0193220i
$566$	−18.4894	−	7.17036i	−0.777169	−	0.301393i
$567$	12.0170	+	22.4823i	0.504669	+	0.944169i
$568$	−20.1881	+	11.2931i	−0.847073	+	0.473847i
$569$	9.56821	−	2.90248i	0.401120	−	0.121678i	−0.0832776	−	0.996526i	$-0.526539\pi$
$569$	9.56821	−	2.90248i	0.401120	−	0.121678i	0.484398	+	0.874848i	$0.339039\pi$
$570$	8.39766	+	25.5743i	0.351739	+	1.07119i
$571$	2.44731	+	2.70019i	0.102417	+	0.113000i	0.790002	−	0.613104i	$-0.210079\pi$
$571$	2.44731	+	2.70019i	0.102417	+	0.113000i	−0.687585	+	0.726103i	$0.741329\pi$
$572$	−1.25223	−	0.0660306i	−0.0523585	−	0.00276088i
$573$	−27.8599	−	37.5648i	−1.16387	−	1.56929i
$574$	3.29220	−	9.90584i	0.137414	−	0.413462i
$575$	3.49823	+	3.49823i	0.145886	+	0.145886i
$576$	20.1159	−	2.76258i	0.838161	−	0.115108i
$577$	−13.0836	+	13.0836i	−0.544679	+	0.544679i	−0.924897	−	0.380218i	$-0.875849\pi$
$577$	−13.0836	+	13.0836i	−0.544679	+	0.544679i	0.380218	+	0.924897i	$0.375849\pi$
$578$	10.0562	+	20.0679i	0.418282	+	0.834716i
$579$	51.0695	−	37.8757i	2.12238	−	1.57406i
$580$	3.34544	−	1.18347i	0.138912	−	0.0491411i
$581$	6.38586	−	5.78780i	0.264930	−	0.240119i
$582$	−19.8629	+	39.2850i	−0.823346	+	1.62841i
$583$	1.80192	+	5.94013i	0.0746278	+	0.246015i
$584$	−11.8644	−	13.9050i	−0.490952	−	0.575392i
$585$	−0.787278	+	0.420809i	−0.0325499	+	0.0173983i
$586$	38.6447	−	17.0470i	1.59640	−	0.704205i
$587$	−4.05493	+	16.1882i	−0.167365	+	0.668157i	0.827005	+	0.562194i	$0.190043\pi$
$587$	−4.05493	+	16.1882i	−0.167365	+	0.668157i	−0.994370	+	0.105963i	$0.966207\pi$
$588$	2.82341	−	1.87190i	0.116436	−	0.0771959i
$589$	−2.09601	−	42.6653i	−0.0863646	−	1.75799i
$590$	−20.5216	+	19.4680i	−0.844859	+	0.801483i
$591$	14.1890	−	9.48079i	0.583658	−	0.389988i
$592$	8.32851	+	11.4001i	0.342300	+	0.468539i
$593$	9.20043	+	6.14753i	0.377816	+	0.252449i	0.729950	−	0.683501i	$-0.239544\pi$
$593$	9.20043	+	6.14753i	0.377816	+	0.252449i	−0.352133	+	0.935950i	$0.614544\pi$
$594$	−0.841786	−	4.90363i	−0.0345389	−	0.201198i
$595$	−1.62783	+	4.54947i	−0.0667343	+	0.186510i
$596$	−26.1696	−	14.1091i	−1.07195	−	0.577932i
$597$	1.19697	+	8.06930i	0.0489886	+	0.330255i
$598$	0.172895	+	0.776462i	0.00707021	+	0.0317519i
$599$	−3.34199	−	33.9318i	−0.136550	−	1.38641i	−0.782317	−	0.622880i	$-0.785962\pi$
$599$	−3.34199	−	33.9318i	−0.136550	−	1.38641i	0.645768	−	0.763534i	$-0.276538\pi$
$600$	11.3363	+	0.339453i	0.462803	+	0.0138581i
$601$	10.2273	−	8.39332i	0.417180	−	0.342370i	−0.402271	−	0.915521i	$-0.631779\pi$
$601$	10.2273	−	8.39332i	0.417180	−	0.342370i	0.819450	+	0.573150i	$0.194279\pi$
$602$	11.2234	−	40.2744i	0.457431	−	1.64146i
$603$	−32.7529	+	11.7192i	−1.33380	+	0.477242i
$604$	−1.44784	+	2.39600i	−0.0589117	+	0.0974918i
$605$	−0.490496	+	0.818343i	−0.0199415	+	0.0332704i
$606$	−21.5945	−	12.2844i	−0.877215	−	0.499021i
$607$	−5.39399	−	13.0222i	−0.218935	−	0.528557i	0.775806	−	0.630971i	$-0.217343\pi$
$607$	−5.39399	−	13.0222i	−0.218935	−	0.528557i	−0.994742	+	0.102414i	$0.967343\pi$
$608$	17.5404	−	18.0949i	0.711358	−	0.733845i
$609$	−2.20564	+	5.32489i	−0.0893772	+	0.215776i
$610$	−20.9194	+	16.2653i	−0.847003	+	0.658562i
$611$	−0.598761	−	2.39039i	−0.0242233	−	0.0967048i
$612$	0.245168	+	5.38539i	0.00991033	+	0.217691i
$613$	1.68687	+	0.797829i	0.0681319	+	0.0322240i	0.461317	−	0.887235i	$-0.347377\pi$
$613$	1.68687	+	0.797829i	0.0681319	+	0.0322240i	−0.393185	+	0.919459i	$0.628627\pi$
$614$	−4.49217	−	36.9682i	−0.181289	−	1.49192i
$615$	−1.23345	+	12.5234i	−0.0497374	+	0.504993i
$616$	22.1420	−	5.99920i	0.892127	−	0.241715i
$617$	−5.44539	+	6.63523i	−0.219223	+	0.267124i	−0.870996	−	0.491290i	$-0.836526\pi$
$617$	−5.44539	+	6.63523i	−0.219223	+	0.267124i	0.651773	+	0.758414i	$0.274026\pi$
$618$	4.33232	−	24.7041i	0.174271	−	0.993746i
$619$	−1.94567	−	1.44300i	−0.0782029	−	0.0579992i	0.555892	−	0.831255i	$-0.312377\pi$
$619$	−1.94567	−	1.44300i	−0.0782029	−	0.0579992i	−0.634094	+	0.773256i	$0.718627\pi$
$620$	33.2808	+	10.2264i	1.33659	+	0.410701i
$621$	−2.85317	+	1.34945i	−0.114494	+	0.0541516i
$622$	−21.2698	+	13.4155i	−0.852841	+	0.537911i
$623$	1.27800	−	0.254210i	0.0512020	−	0.0101847i
$624$	1.50895	+	1.02402i	0.0604065	+	0.0409934i
$625$	−13.3164	−	2.64880i	−0.532656	−	0.105952i
$626$	0.618772	+	1.61273i	0.0247311	+	0.0644578i
$627$	25.1408	+	22.7863i	1.00403	+	0.909997i
$628$	1.08373	+	2.64319i	0.0432457	+	0.105475i
$629$	−3.21515	+	1.92709i	−0.128197	+	0.0768381i
$630$	11.2821	−	11.8074i	0.449488	−	0.470416i
$631$	10.3725	−	34.1936i	0.412924	−	1.36123i	−0.466220	−	0.884669i	$-0.654384\pi$
$631$	10.3725	−	34.1936i	0.412924	−	1.36123i	0.879143	−	0.476558i	$-0.158116\pi$
$632$	11.3757	+	10.9481i	0.452501	+	0.435492i
$633$	−14.7913	+	27.6725i	−0.587900	+	1.09988i
$634$	13.4504	−	11.5603i	0.534183	−	0.459118i
$635$	−1.95988	+	39.8943i	−0.0777755	+	1.58316i
$636$	2.22490	−	8.74875i	0.0882229	−	0.346911i
$637$	0.137926	+	0.0204593i	0.00546481	+	0.000810628i
$638$	2.92779	−	3.38181i	0.115912	−	0.133887i
$639$			20.7575i			0.821154i
$640$	9.00361	+	18.4618i	0.355899	+	0.729765i
$641$		−	38.1258i		−	1.50588i	−0.658089	−	0.752940i	$-0.728635\pi$
$641$		−	38.1258i		−	1.50588i	0.658089	−	0.752940i	$-0.271365\pi$
$642$	16.9407	+	14.6663i	0.668596	+	0.578834i
$643$	−0.684716	−	0.101568i	−0.0270026	−	0.00400545i	0.133216	−	0.991087i	$-0.457470\pi$
$643$	−0.684716	−	0.101568i	−0.0270026	−	0.00400545i	−0.160218	+	0.987082i	$0.551220\pi$
$644$	−7.43662	−	12.5090i	−0.293044	−	0.492923i
$645$	−2.47310	+	50.3412i	−0.0973784	+	1.98218i
$646$	4.36125	+	5.07431i	0.171591	+	0.199646i
$647$	−12.7171	+	23.7921i	−0.499962	+	0.935363i	0.497722	+	0.867337i	$0.334170\pi$
$647$	−12.7171	+	23.7921i	−0.499962	+	0.935363i	−0.997684	+	0.0680261i	$0.978330\pi$
$648$	−10.4994	+	26.7877i	−0.412456	+	1.05232i
$649$	−10.3504	+	34.1207i	−0.406288	+	1.33935i
$650$	0.337514	+	0.322498i	0.0132384	+	0.0126494i
$651$	−48.5035	+	29.0719i	−1.90100	+	1.13942i
$652$	10.0388	−	23.9916i	0.393150	−	0.939582i
$653$	5.88646	+	5.33518i	0.230355	+	0.208782i	0.778573	−	0.627554i	$-0.215944\pi$
$653$	5.88646	+	5.33518i	0.230355	+	0.208782i	−0.548218	+	0.836335i	$0.684694\pi$
$654$	33.6571	−	12.9135i	1.31610	−	0.504959i
$655$	33.3084	+	6.62544i	1.30147	+	0.258877i
$656$	10.9168	−	4.43021i	0.426228	−	0.172971i
$657$	−16.0872	+	3.19995i	−0.627622	+	0.124842i
$658$	24.0498	+	38.1302i	0.937559	+	1.48647i
$659$	14.8194	−	7.00904i	0.577281	−	0.273034i	−0.116534	−	0.993187i	$-0.537178\pi$
$659$	14.8194	−	7.00904i	0.577281	−	0.273034i	0.693815	+	0.720153i	$0.255928\pi$
$660$	−24.4364	+	12.9488i	−0.951186	+	0.504032i
$661$	−19.6260	−	14.5556i	−0.763362	−	0.566148i	0.142463	−	0.989800i	$-0.454498\pi$
$661$	−19.6260	−	14.5556i	−0.763362	−	0.566148i	−0.905825	+	0.423652i	$0.860748\pi$
$662$	−44.1491	−	7.74235i	−1.71590	−	0.300915i
$663$	−0.307157	+	0.374272i	−0.0119290	+	0.0145355i
$664$	9.64745	+	1.24274i	0.374394	+	0.0482275i
$665$	1.98671	−	20.1714i	0.0770413	−	0.782214i
$666$	12.5765	−	1.52822i	0.487329	−	0.0592174i
$667$	−2.56515	−	1.21322i	−0.0993229	−	0.0469762i
$668$	10.6068	−	11.6187i	0.410391	−	0.449539i
$669$	8.29726	+	33.1245i	0.320791	+	1.28067i
$670$	−21.6001	−	27.7807i	−0.834484	−	1.07326i
$671$	−12.7825	+	30.8596i	−0.493462	+	1.19132i
$672$	−32.0716	−	9.18643i	−1.23719	−	0.354374i
$673$	2.19303	+	5.29443i	0.0845349	+	0.204085i	0.960494	−	0.278299i	$-0.0897707\pi$
$673$	2.19303	+	5.29443i	0.0845349	+	0.204085i	−0.875959	+	0.482385i	$0.839771\pi$
$674$	−20.3981	+	35.8572i	−0.785705	+	1.38117i
$675$	−0.952215	+	1.58867i	−0.0366508	+	0.0611481i
$676$	−6.20882	−	25.1705i	−0.238801	−	0.968095i
$677$	−1.54888	+	0.554197i	−0.0595282	+	0.0212995i	−0.366486	−	0.930424i	$-0.619439\pi$
$677$	−1.54888	+	0.554197i	−0.0595282	+	0.0212995i	0.306957	+	0.951723i	$0.400689\pi$
$678$	3.33780	+	0.930154i	0.128187	+	0.0357223i
$679$	25.6235	−	21.0287i	0.983340	−	0.807006i
$680$	−5.09860	+	1.93523i	−0.195522	+	0.0742128i
$681$	3.52538	+	35.7938i	0.135093	+	1.37162i
$682$	42.8379	−	9.53873i	1.64035	−	0.365257i
$683$	−4.52899	−	30.5320i	−0.173297	−	1.16827i	−0.884931	−	0.465722i	$-0.845795\pi$
$683$	−4.52899	−	30.5320i	−0.173297	−	1.16827i	0.711634	−	0.702550i	$-0.247955\pi$
$684$	−6.48671	−	21.6638i	−0.248025	−	0.828336i
$685$	−4.05617	+	11.3362i	−0.154978	+	0.433135i
$686$	−26.9650	+	4.62897i	−1.02953	+	0.176735i
$687$	−48.3551	−	32.3098i	−1.84486	−	1.23270i
$688$	42.8009	−	19.8681i	1.63177	−	0.757464i
$689$	0.308946	−	0.206431i	0.0117699	−	0.00786440i
$690$	12.0741	+	12.7276i	0.459654	+	0.484530i
$691$	1.67640	+	34.1240i	0.0637734	+	1.29814i	0.791033	+	0.611774i	$0.209544\pi$
$691$	1.67640	+	34.1240i	0.0637734	+	1.29814i	−0.727259	+	0.686363i	$0.759206\pi$
$692$	4.85219	−	23.9436i	0.184453	−	0.910197i
$693$	5.00186	−	19.9686i	0.190005	−	0.758543i
$694$	2.60428	+	5.90377i	0.0988570	+	0.224104i
$695$	−23.8862	+	12.7674i	−0.906055	+	0.484297i
$696$	−6.18766	+	2.00719i	−0.234543	+	0.0760824i
$697$	0.908016	+	2.99333i	0.0343935	+	0.113380i
$698$	1.44212	+	0.729154i	0.0545851	+	0.0275989i
$699$	24.9026	−	22.5704i	0.941902	−	0.853690i
$700$	−7.70694	−	3.67907i	−0.291295	−	0.139056i
$701$	−1.32291	+	0.981134i	−0.0499655	+	0.0370569i	−0.620394	−	0.784290i	$-0.713027\pi$
$701$	−1.32291	+	0.981134i	−0.0499655	+	0.0370569i	0.570428	+	0.821347i	$0.306777\pi$
$702$	−0.266258	+	0.133424i	−0.0100493	+	0.00503575i
$703$	11.1186	−	11.1186i	0.419345	−	0.419345i
$704$	21.3716	+	14.6158i	0.805473	+	0.550854i
$705$	−38.4288	−	38.4288i	−1.44731	−	1.44731i
$706$	−18.4196	−	6.12176i	−0.693232	−	0.230396i
$707$	11.1441	+	15.0260i	0.419116	+	0.565112i
$708$	38.5456	−	34.6842i	1.44863	−	1.30351i
$709$	−6.05421	−	6.67980i	−0.227371	−	0.250865i	0.616572	−	0.787299i	$-0.288521\pi$
$709$	−6.05421	−	6.67980i	−0.227371	−	0.250865i	−0.843942	+	0.536434i	$0.819771\pi$
$710$	−19.9503	+	6.55095i	−0.748722	+	0.245853i
$711$	13.5575	−	4.11261i	0.508445	−	0.154235i
$712$	1.15450	+	0.911037i	0.0432667	+	0.0341425i
$713$	−13.1239	−	24.5531i	−0.491494	−	0.919521i
$714$	3.20264	−	8.25830i	0.119856	−	0.309059i
$715$	−1.10419	−	0.276586i	−0.0412944	−	0.0103437i
$716$	−1.18868	−	6.09023i	−0.0444232	−	0.227603i
$717$	18.4456	−	0.906172i	0.688862	−	0.0338416i
$718$	−28.1037	−	0.740444i	−1.04882	−	0.0276331i
$719$	16.7567	+	25.0782i	0.624921	+	0.935260i	0.999966	+	0.00825332i	$0.00262714\pi$
$719$	16.7567	+	25.0782i	0.624921	+	0.935260i	−0.375045	+	0.927006i	$0.622373\pi$
$720$	18.4026	+	1.03671i	0.685823	+	0.0386359i
$721$	−10.4925	+	15.7032i	−0.390762	+	0.584817i
$722$	−0.977658	−	0.691176i	−0.0363847	−	0.0257229i
$723$	16.9106	+	6.05071i	0.628912	+	0.225028i
$724$	−2.87039	+	28.1076i	−0.106677	+	1.04461i
$725$	−1.64719	+	0.244337i	−0.0611750	+	0.00907445i
$726$	0.938342	−	1.47593i	0.0348251	−	0.0547769i
$727$	−11.1561	+	1.09878i	−0.413756	+	0.0407514i	−0.302754	−	0.953069i	$-0.597906\pi$
$727$	−11.1561	+	1.09878i	−0.413756	+	0.0407514i	−0.111002	+	0.993820i	$0.535406\pi$
$728$	−0.728379	−	1.16407i	−0.0269955	−	0.0431435i
$729$	11.5104	+	14.0255i	0.426311	+	0.519462i
$730$	−8.15255	−	14.4518i	−0.301739	−	0.534884i
$731$	4.22071	+	11.7961i	0.156108	+	0.436294i
$732$	39.1201	−	28.7961i	1.44592	−	1.06433i
$733$	−20.5427	−	12.3128i	−0.758763	−	0.454785i	0.0816978	−	0.996657i	$-0.473966\pi$
$733$	−20.5427	−	12.3128i	−0.758763	−	0.454785i	−0.840461	+	0.541872i	$0.817716\pi$
$734$	12.4010	+	45.1267i	0.457729	+	1.66566i
$735$	2.84103	−	1.17679i	0.104793	−	0.0434066i
$736$	5.29204	−	15.5488i	0.195067	−	0.573135i
$737$	−40.9812	−	16.9750i	−1.50956	−	0.625281i
$738$	1.31299	−	10.4902i	0.0483317	−	0.386150i
$739$	18.4071	−	4.61074i	0.677116	−	0.169609i	0.110858	−	0.993836i	$-0.464640\pi$
$739$	18.4071	−	4.61074i	0.677116	−	0.169609i	0.566259	+	0.824227i	$0.308390\pi$
$740$	5.43787	+	11.6051i	0.199900	+	0.426613i
$741$	0.868374	−	1.83602i	0.0319005	−	0.0674480i
$742$	−4.19165	+	5.35125i	−0.153880	+	0.196451i
$743$	−18.4998	−	1.82207i	−0.678693	−	0.0668454i	−0.247204	−	0.968964i	$-0.579512\pi$
$743$	−18.4998	−	1.82207i	−0.678693	−	0.0668454i	−0.431489	+	0.902118i	$0.642012\pi$
$744$	−60.4932	−	20.3466i	−2.21779	−	0.745944i
$745$	−20.8623	−	17.1212i	−0.764334	−	0.627273i
$746$	−7.91537	−	11.2820i	−0.289802	−	0.413062i
$747$	5.19965	−	7.01092i	0.190245	−	0.256516i
$748$	−4.38007	+	5.29818i	−0.160151	+	0.193721i
$749$	−7.21400	−	15.2527i	−0.263594	−	0.557322i
$750$	39.5061	+	8.94599i	1.44256	+	0.326661i
$751$	−1.81699	−	9.13463i	−0.0663030	−	0.333328i	0.933370	−	0.358917i	$-0.116854\pi$
$751$	−1.81699	−	9.13463i	−0.0663030	−	0.333328i	−0.999673	+	0.0255892i	$0.991854\pi$
$752$	−15.1194	+	48.5821i	−0.551349	+	1.77161i
$753$	8.29441	−	41.6988i	0.302265	−	1.51959i
$754$	−0.244587	−	0.108944i	−0.00890732	−	0.00396751i
$755$	−1.70660	+	1.88294i	−0.0621094	+	0.0685272i
$756$	3.86636	−	3.83866i	0.140618	−	0.139611i
$757$	−6.37009	−	10.6279i	−0.231525	−	0.386276i	0.719938	−	0.694038i	$-0.244170\pi$
$757$	−6.37009	−	10.6279i	−0.231525	−	0.386276i	−0.951463	+	0.307762i	$0.900420\pi$
$758$	−13.4721	+	0.306499i	−0.489330	+	0.0111325i
$759$	21.1618	+	6.41936i	0.768125	+	0.233008i
$760$	18.7742	−	13.0714i	0.681012	−	0.474151i
$761$	5.85494	+	3.12953i	0.212242	+	0.113445i	0.574092	−	0.818791i	$-0.305355\pi$
$761$	5.85494	+	3.12953i	0.212242	+	0.113445i	−0.361851	+	0.932236i	$0.617855\pi$
$762$	5.51760	−	73.0116i	0.199881	−	2.64493i
$763$	−27.1124	−	1.33195i	−0.981536	−	0.0482198i
$764$	−23.7918	+	31.8397i	−0.860757	+	1.15192i
$765$	−0.718055	+	4.84073i	−0.0259613	+	0.175017i
$766$	21.7053	−	1.56187i	0.784245	−	0.0564326i
$767$	2.13431			0.0770656
$768$	−15.6077	−	34.2658i	−0.563196	−	1.23646i
$769$	9.68231			0.349153			0.174577	−	0.984644i	$-0.444144\pi$
$769$	9.68231			0.349153			0.174577	+	0.984644i	$0.444144\pi$
$770$	20.7706	−	1.49461i	0.748521	−	0.0538619i
$771$	6.69957	−	45.1648i	0.241279	−	1.62657i
$772$	−43.2862	−	32.3451i	−1.55791	−	1.16412i
$773$	33.0181	+	1.62207i	1.18758	+	0.0583420i	0.633244	−	0.773952i	$-0.281723\pi$
$773$	33.0181	+	1.62207i	1.18758	+	0.0583420i	0.554334	+	0.832294i	$0.312973\pi$
$774$	3.19087	−	42.2232i	0.114693	−	1.51768i
$775$	−14.4088	−	7.70164i	−0.517578	−	0.276651i
$776$	36.8261	+	6.59464i	1.32198	+	0.236734i
$777$	−19.9193	−	6.04246i	−0.714602	−	0.216772i
$778$	−9.21551	+	0.209658i	−0.330392	+	0.00751660i
$779$	−6.74577	−	11.2546i	−0.241692	−	0.403239i
$780$	1.16633	+	1.17474i	0.0417612	+	0.0420625i
$781$	−17.7754	+	19.6121i	−0.636054	+	0.701778i
$782$	3.98351	+	1.77434i	0.142450	+	0.0634504i
$783$	0.207255	−	1.04194i	0.00740671	−	0.0372360i
$784$	−2.21230	−	1.84236i	−0.0790107	−	0.0657985i
$785$	0.505914	+	2.54340i	0.0180569	+	0.0907779i
$786$	−60.7176	−	13.7493i	−2.16572	−	0.490420i
$787$	11.8782	+	25.1144i	0.423413	+	0.895231i	0.997096	+	0.0761538i	$0.0242640\pi$
$787$	11.8782	+	25.1144i	0.423413	+	0.895231i	−0.573683	+	0.819077i	$0.694486\pi$
$788$	−11.1778	−	9.24080i	−0.398192	−	0.329190i
$789$	−16.5814	+	22.3574i	−0.590313	+	0.795945i
$790$	8.23135	+	11.7324i	0.292858	+	0.417418i
$791$	−2.01688	−	1.65521i	−0.0717119	−	0.0588525i
$792$	20.8089	−	10.3341i	0.739411	−	0.367205i
$793$	1.98978	+	0.195976i	0.0706590	+	0.00695931i
$794$	−5.51917	+	7.04602i	−0.195868	+	0.250054i
$795$	3.50362	−	7.40779i	0.124261	−	0.262727i
$796$	6.27784	−	2.94163i	0.222512	−	0.104263i
$797$	51.6405	−	12.9353i	1.82920	−	0.458191i	0.833640	−	0.552308i	$-0.186253\pi$
$797$	51.6405	−	12.9353i	1.82920	−	0.458191i	0.995561	+	0.0941175i	$0.0300029\pi$
$798$	−4.61453	+	36.8681i	−0.163353	+	1.30512i
$799$	−12.4806	−	5.16965i	−0.441533	−	0.182889i
$800$	−2.48718	−	9.31224i	−0.0879352	−	0.329237i
$801$	1.21924	−	0.505027i	0.0430798	−	0.0178442i
$802$	11.5479	+	42.0225i	0.407772	+	1.48387i
$803$	−17.9398	−	10.7527i	−0.633082	−	0.379454i
$804$	38.2408	+	51.9510i	1.34865	+	1.83217i
$805$	−4.45040	−	12.4380i	−0.156856	−	0.438383i
$806$	−1.29074	−	2.28805i	−0.0454643	−	0.0805931i
$807$	−17.3855	−	21.1843i	−0.611998	−	0.745722i
$808$	−4.73713	+	20.5759i	−0.166652	+	0.723856i
$809$	53.3089	−	5.25047i	1.87424	−	0.184597i	0.904130	−	0.427258i	$-0.140520\pi$
$809$	53.3089	−	5.25047i	1.87424	−	0.184597i	0.970111	+	0.242662i	$0.0780205\pi$
$810$	−14.0126	+	22.0407i	−0.492354	+	0.774430i
$811$	−29.5410	+	4.38200i	−1.03733	+	0.153873i	−0.643605	−	0.765357i	$-0.722562\pi$
$811$	−29.5410	+	4.38200i	−1.03733	+	0.153873i	−0.393720	+	0.919230i	$0.628812\pi$
$812$	4.87296	+	0.497635i	0.171007	+	0.0174636i
$813$	−6.88593	−	2.46382i	−0.241500	−	0.0864101i
$814$	13.1912	+	9.32581i	0.462352	+	0.326869i
$815$	13.1160	−	19.6295i	0.459435	−	0.687593i
$816$	9.43660	−	3.30015i	0.330347	−	0.115528i
$817$	−29.1977	−	43.6975i	−1.02150	−	1.52878i
$818$	−8.18601	−	0.215675i	−0.286217	−	0.00754091i
$819$	−1.23073	+	0.0604619i	−0.0430052	+	0.00211271i
$820$	10.4967	−	2.04872i	0.366559	−	0.0715445i
$821$	−15.4313	−	3.86534i	−0.538556	−	0.134901i	−0.0358473	−	0.999357i	$-0.511413\pi$
$821$	−15.4313	−	3.86534i	−0.538556	−	0.134901i	−0.502708	+	0.864456i	$0.667663\pi$
$822$	7.98024	−	20.5778i	0.278343	−	0.717733i
$823$	18.9689	+	35.4882i	0.661213	+	1.23704i	0.959269	+	0.282494i	$0.0911618\pi$
$823$	18.9689	+	35.4882i	0.661213	+	1.23704i	−0.298056	+	0.954548i	$0.596338\pi$
$824$	−21.1690	+	2.49517i	−0.737459	+	0.0869233i
$825$	12.4186	−	3.76714i	0.432361	−	0.131155i
$826$	−37.0967	+	12.1812i	−1.29076	+	0.423838i
$827$	−4.11800	−	4.54351i	−0.143197	−	0.157993i	0.665129	−	0.746728i	$-0.268376\pi$
$827$	−4.11800	−	4.54351i	−0.143197	−	0.157993i	−0.808326	+	0.588735i	$0.799626\pi$
$828$	−9.85856	−	10.9561i	−0.342609	−	0.380752i
$829$	−14.2397	−	19.2000i	−0.494564	−	0.666842i	0.483452	−	0.875371i	$-0.339383\pi$
$829$	−14.2397	−	19.2000i	−0.494564	−	0.666842i	−0.978016	+	0.208528i	$0.933133\pi$
$830$	8.37927	+	2.78485i	0.290849	+	0.0966635i
$831$	37.0157	+	37.0157i	1.28406	+	1.28406i
$832$	0.465854	−	1.47815i	0.0161506	−	0.0512456i
$833$	0.540499	−	0.540499i	0.0187272	−	0.0187272i
$834$	44.3878	−	22.2431i	1.53702	−	0.770214i
$835$	11.4706	−	8.50714i	0.396955	−	0.294402i
$836$	12.4227	−	26.0232i	0.429649	−	0.900032i
$837$	7.72302	−	6.99974i	0.266947	−	0.241946i
$838$	41.5610	+	21.0137i	1.43570	+	0.725908i
$839$	−1.33787	−	4.41036i	−0.0461883	−	0.152262i	0.930813	−	0.365496i	$-0.119101\pi$
$839$	−1.33787	−	4.41036i	−0.0461883	−	0.152262i	−0.977001	+	0.213233i	$0.931601\pi$
$840$	−26.9767	−	13.7617i	−0.930783	−	0.474823i
$841$	−24.7334	+	13.2203i	−0.852875	+	0.455871i
$842$	−7.23034	−	16.3908i	−0.249174	−	0.564865i
$843$	−12.7286	+	50.8153i	−0.438395	+	1.75017i
$844$	26.1354	+	5.29638i	0.899618	+	0.182309i
$845$	−1.15474	−	23.5053i	−0.0397242	−	0.808605i
$846$	31.4232	+	33.1238i	1.08035	+	1.13882i
$847$	−1.09501	+	0.731665i	−0.0376251	+	0.0251403i
$848$	−7.66520	+	0.321354i	−0.263224	+	0.0110353i
$849$	27.4384	+	18.3337i	0.941683	+	0.629212i
$850$	2.52221	−	0.432977i	0.0865110	−	0.0148510i
$851$	3.45248	−	9.64903i	0.118349	−	0.330765i
$852$	36.8752	−	11.0414i	1.26332	−	0.378272i
$853$	−3.64206	−	24.5528i	−0.124702	−	0.840670i	−0.957777	−	0.287511i	$-0.907172\pi$
$853$	−3.64206	−	24.5528i	−0.124702	−	0.840670i	0.833076	−	0.553159i	$-0.186578\pi$
$854$	−35.7030	+	7.95000i	−1.22173	+	0.272043i
$855$	−2.01211	−	20.4293i	−0.0688128	−	0.698668i
$856$	7.81084	−	17.3676i	0.266969	−	0.593614i
$857$	20.8858	−	17.1405i	0.713444	−	0.585508i	−0.206083	−	0.978534i	$-0.566072\pi$
$857$	20.8858	−	17.1405i	0.713444	−	0.585508i	0.919527	+	0.393026i	$0.128572\pi$
$858$	2.01008	+	0.560153i	0.0686228	+	0.0191233i
$859$	−53.6867	+	19.2094i	−1.83177	+	0.655417i	−0.837768	+	0.546026i	$0.816140\pi$
$859$	−53.6867	+	19.2094i	−1.83177	+	0.655417i	−0.993999	+	0.109391i	$0.965110\pi$
$860$	41.5883	−	10.2586i	1.41815	−	0.349816i
$861$	−8.93011	+	14.8990i	−0.304337	+	0.507756i
$862$	8.20347	−	14.4207i	0.279411	−	0.491170i
$863$	−2.85660	−	6.89645i	−0.0972399	−	0.234758i	0.867773	−	0.496961i	$-0.165551\pi$
$863$	−2.85660	−	6.89645i	−0.0972399	−	0.234758i	−0.965013	+	0.262203i	$0.915551\pi$
$864$	6.12822	+	0.507446i	0.208486	+	0.0172637i
$865$	8.48669	−	20.4887i	0.288556	−	0.696636i
$866$	26.9609	+	34.6755i	0.916168	+	1.17832i
$867$	−9.07582	−	36.2327i	−0.308231	−	1.23053i
$868$	35.4930	+	32.4021i	1.20471	+	1.09980i
$869$	16.3312	+	7.72407i	0.553997	+	0.262021i
$870$	−5.86192	+	0.712307i	−0.198738	+	0.0241495i
$871$	−0.260254	+	2.64240i	−0.00881836	+	0.0895343i
$872$	−18.7185	−	24.2539i	−0.633887	−	0.821342i
$873$	21.2975	−	25.9511i	0.720812	−	0.878312i
$874$	−18.0178	−	3.15975i	−0.609462	−	0.106880i
$875$	−24.4988	−	18.1695i	−0.828209	−	0.614242i
$876$	14.2418	+	26.8764i	0.481186	+	0.908070i
$877$	−48.1117	+	22.7552i	−1.62462	+	0.768387i	−0.999922	−	0.0124816i	$-0.996027\pi$
$877$	−48.1117	+	22.7552i	−1.62462	+	0.768387i	−0.624695	+	0.780868i	$0.714777\pi$
$878$	10.6372	+	16.8650i	0.358989	+	0.569166i
$879$	−68.9347	+	13.7120i	−2.32511	+	0.462493i
$880$	16.4994	+	16.7383i	0.556194	+	0.564248i
$881$	−16.9777	−	3.37707i	−0.571992	−	0.113776i	−0.0993844	−	0.995049i	$-0.531687\pi$
$881$	−16.9777	−	3.37707i	−0.571992	−	0.113776i	−0.472608	+	0.881273i	$0.656687\pi$
$882$	−2.41201	+	0.925438i	−0.0812166	+	0.0311611i
$883$	−35.1558	−	31.8634i	−1.18309	−	1.07229i	−0.995946	−	0.0899556i	$-0.971327\pi$
$883$	−35.1558	−	31.8634i	−1.18309	−	1.07229i	−0.187142	−	0.982333i	$-0.559923\pi$
$884$	0.379593	+	0.158833i	0.0127671	+	0.00534214i
$885$	40.3735	−	24.1990i	1.35714	−	0.813439i
$886$	32.8188	+	31.3587i	1.10257	+	1.05352i
$887$	−7.88408	+	25.9903i	−0.264721	+	0.872670i	0.719312	+	0.694687i	$0.244457\pi$
$887$	−7.88408	+	25.9903i	−0.264721	+	0.872670i	−0.984034	+	0.177983i	$0.943043\pi$
$888$	−9.40457	−	21.5289i	−0.315597	−	0.722463i
$889$	−25.9902	+	48.6242i	−0.871682	+	1.63080i
$890$	0.870174	+	1.01245i	0.0291683	+	0.0339373i
$891$	−1.61542	+	32.8826i	−0.0541185	+	1.10161i
$892$	24.9457	−	14.8303i	0.835244	−	0.496555i
$893$	56.0542	+	8.31485i	1.87578	+	0.278246i
$894$	37.4034	+	32.3818i	1.25096	+	1.08301i
$895$		−	5.63278i		−	0.188283i
$896$	0.339212	+	28.3506i	0.0113323	+	0.947128i
$897$		−	1.32371i		−	0.0441974i
$898$	−6.52939	+	7.54194i	−0.217889	+	0.251678i
$899$	9.26949	+	1.37500i	0.309155	+	0.0458588i
$900$	−8.38243	−	2.13174i	−0.279414	−	0.0710578i
$901$	0.0999472	−	2.03447i	0.00332973	−	0.0677781i
$902$	10.2237	−	8.78702i	0.340412	−	0.292576i
$903$	−32.7960	+	61.3571i	−1.09138	+	2.04184i
$904$	−0.0563963	−	2.94423i	−0.00187571	−	0.0979235i
$905$	−7.44511	+	24.5432i	−0.247484	+	0.815844i
$906$	3.21824	−	3.36809i	0.106919	−	0.111897i
$907$	10.9605	−	6.56946i	0.363937	−	0.218135i	−0.320432	−	0.947272i	$-0.603828\pi$
$907$	10.9605	−	6.56946i	0.363937	−	0.218135i	0.684368	+	0.729136i	$0.260078\pi$
$908$	28.2822	−	11.5959i	0.938577	−	0.384825i
$909$	14.0386	+	12.7238i	0.465631	+	0.422023i
$910$	−0.446522	−	1.16379i	−0.0148021	−	0.0385793i
$911$	5.17706	+	1.02978i	0.171524	+	0.0341182i	0.280105	−	0.959969i	$-0.409631\pi$
$911$	5.17706	+	1.02978i	0.171524	+	0.0341182i	−0.108581	+	0.994088i	$0.534631\pi$
$912$	−35.0348	+	23.0469i	−1.16012	+	0.763160i
$913$	10.9164	−	2.17142i	0.361282	−	0.0718634i
$914$	−19.3054	+	12.1764i	−0.638564	+	0.402761i
$915$	39.8614	−	18.8530i	1.31778	−	0.623262i
$916$	−14.5172	+	47.2448i	−0.479662	+	1.56101i
$917$	37.6526	+	27.9251i	1.24340	+	0.922167i
$918$	−0.282008	+	1.60809i	−0.00930767	+	0.0530750i
$919$	−5.55175	+	6.76483i	−0.183135	+	0.223151i	−0.856483	−	0.516175i	$-0.827356\pi$
$919$	−5.55175	+	6.76483i	−0.183135	+	0.223151i	0.673348	+	0.739326i	$0.264856\pi$
$920$	7.41877	−	12.9329i	0.244590	−	0.426385i
$921$	−6.07405	+	61.6709i	−0.200147	+	2.03212i
$922$	−2.80126	−	23.0529i	−0.0922546	−	0.759208i
$923$	1.43227	+	0.677412i	0.0471437	+	0.0222973i
$924$	−38.1342	+	1.73605i	−1.25452	+	0.0571118i
$925$	−1.46128	−	5.83377i	−0.0480467	−	0.191813i
$926$	6.75825	−	5.25468i	0.222090	−	0.172679i
$927$	−7.31978	+	17.6715i	−0.240413	+	0.580409i
$928$	3.14258	+	4.54838i	0.103160	+	0.149308i
$929$	−13.3826	−	32.3085i	−0.439069	−	1.06001i	−0.976271	−	0.216553i	$-0.930519\pi$
$929$	−13.3826	−	32.3085i	−0.439069	−	1.06001i	0.537202	−	0.843454i	$-0.319481\pi$
$930$	−50.3582	−	28.6472i	−1.65131	−	0.939379i
$931$	−1.64844	+	2.75025i	−0.0540254	+	0.0901359i
$932$	−24.4464	−	14.7723i	−0.800770	−	0.483883i
$933$	39.3998	−	14.0975i	1.28989	−	0.461531i
$934$	6.04921	−	21.7072i	0.197936	−	0.710282i
$935$	−4.82373	+	3.95873i	−0.157753	+	0.129464i
$936$	−0.953520	−	1.01239i	−0.0311668	−	0.0330909i
$937$	0.0392200	+	0.398207i	0.00128126	+	0.0130089i	0.995804	−	0.0915106i	$-0.0291695\pi$
$937$	0.0392200	+	0.398207i	0.00128126	+	0.0130089i	−0.994523	+	0.104519i	$0.966670\pi$
$938$	−10.5575	−	47.4131i	−0.344715	−	1.54809i
$939$	−0.421763	−	2.84330i	−0.0137637	−	0.0927875i
$940$	−21.9188	+	40.6550i	−0.714911	+	1.32602i
$941$	−8.07307	+	22.5627i	−0.263175	+	0.735524i	0.735163	+	0.677890i	$0.237106\pi$
$941$	−8.07307	+	22.5627i	−0.263175	+	0.735524i	−0.998338	+	0.0576337i	$0.981644\pi$
$942$	−0.804290	−	4.68520i	−0.0262052	−	0.152652i
$943$	−7.11061	−	4.75116i	−0.231553	−	0.154719i
$944$	−37.6348	−	22.9267i	−1.22491	−	0.746202i
$945$	4.11224	−	2.74771i	0.133771	−	0.0893831i
$946$	39.1721	−	37.1609i	1.27359	−	1.20821i
$947$	−0.174661	−	3.55531i	−0.00567572	−	0.115532i	−0.999961	−	0.00878047i	$-0.997205\pi$
$947$	−0.174661	−	3.55531i	−0.00567572	−	0.115532i	0.994286	−	0.106752i	$-0.0340449\pi$
$948$	−14.5175	−	21.8969i	−0.471506	−	0.711179i
$949$	−0.304203	+	1.21445i	−0.00987485	+	0.0394226i
$950$	−9.82181	+	4.33261i	−0.318661	+	0.140568i
$951$	−26.0280	+	13.9123i	−0.844017	+	0.451137i
$952$	−7.50424	−	0.594239i	−0.243214	−	0.0192594i
$953$	−6.91651	−	22.8007i	−0.224048	−	0.738587i	−0.994836	−	0.101495i	$-0.967637\pi$
$953$	−6.91651	−	22.8007i	−0.224048	−	0.738587i	0.770788	−	0.637091i	$-0.219863\pi$
$954$	−3.10635	+	6.14373i	−0.100572	+	0.198911i
$955$	−26.7340	+	24.2303i	−0.865091	+	0.784073i
$956$	−5.23439	−	14.7966i	−0.169292	−	0.478556i
$957$	−5.97862	+	4.43405i	−0.193261	+	0.143332i
$958$	6.82949	+	13.6288i	0.220651	+	0.440326i
$959$	−11.7517	+	11.7517i	−0.379483	+	0.379483i
$960$	−7.94706	−	33.2432i	−0.256490	−	1.07292i
$961$	43.0918	+	43.0918i	1.39006	+	1.39006i
$962$	0.304981	−	0.917651i	0.00983298	−	0.0295862i
$963$	−10.1795	−	13.7255i	−0.328031	−	0.442299i
$964$	0.803759	−	15.2428i	0.0258873	−	0.490939i
$965$	−32.9412	−	36.3450i	−1.06041	−	1.16999i
$966$	7.55483	+	23.0075i	0.243073	+	0.740255i
$967$	9.81595	−	2.97764i	0.315660	−	0.0957543i	−0.128479	−	0.991712i	$-0.541010\pi$
$967$	9.81595	−	2.97764i	0.315660	−	0.0957543i	0.444139	+	0.895958i	$0.353510\pi$
$968$	−1.43038	−	0.404154i	−0.0459741	−	0.0129900i
$969$	−5.24856	−	9.81937i	−0.168608	−	0.315444i
$970$	31.6633	+	12.2793i	1.01665	+	0.394265i
$971$	51.6551	+	12.9389i	1.65769	+	0.415230i	0.955081	−	0.296344i	$-0.0957676\pi$
$971$	51.6551	+	12.9389i	1.65769	+	0.415230i	0.702611	+	0.711575i	$0.252018\pi$
$972$	23.0993	−	34.3030i	0.740909	−	1.10027i
$973$	−37.3406	+	1.83443i	−1.19709	+	0.0588090i
$974$	−1.47915	+	56.1415i	−0.0473950	+	1.79889i
$975$	−0.431571	−	0.645892i	−0.0138213	−	0.0206851i
$976$	−32.9810	−	24.8298i	−1.05570	−	0.794784i
$977$	3.98350	−	5.96172i	0.127443	−	0.190732i	−0.762261	−	0.647270i	$-0.775911\pi$
$977$	3.98350	−	5.96172i	0.127443	−	0.190732i	0.889704	+	0.456538i	$0.150911\pi$
$978$	−24.9828	+	35.3378i	−0.798863	+	1.12998i
$979$	1.58444	+	0.566922i	0.0506389	+	0.0181189i
$980$	−1.65067	−	2.02615i	−0.0527287	−	0.0647230i
$981$	−27.1946	+	4.03394i	−0.868257	+	0.128794i
$982$	15.2265	+	9.68043i	0.485896	+	0.308915i
$983$	60.9856	−	6.00656i	1.94514	−	0.191580i	0.951793	−	0.306741i	$-0.0992384\pi$
$983$	60.9856	−	6.00656i	1.94514	−	0.191580i	0.993347	+	0.115161i	$0.0367384\pi$
$984$	−19.3340	+	3.24750i	−0.616345	+	0.103526i
$985$	−8.35190	−	10.1768i	−0.266114	−	0.324260i
$986$	−1.27843	+	0.721190i	−0.0407135	+	0.0229674i
$987$	−25.2724	−	70.6318i	−0.804431	−	2.24823i
$988$	−1.70649	−	0.259406i	−0.0542908	−	0.00825280i
$989$	−29.3791	−	17.6091i	−0.934200	−	0.559938i
$990$	20.3366	−	5.58858i	0.646341	−	0.177617i
$991$	−41.0925	+	17.0211i	−1.30535	+	0.540692i	−0.923523	−	0.383544i	$-0.874703\pi$
$991$	−41.0925	+	17.0211i	−1.30535	+	0.540692i	−0.381823	+	0.924236i	$0.624703\pi$
$992$	−1.81831	+	54.2108i	−0.0577315	+	1.72119i
$993$	68.9096	+	28.5433i	2.18678	+	0.905794i
$994$	−28.7606	−	3.59976i	−0.912229	−	0.114177i
$995$	6.10476	−	1.52916i	0.193534	−	0.0484777i
$996$	−15.2205	−	5.50778i	−0.482281	−	0.174521i
$997$	−13.5059	+	28.5558i	−0.427735	+	0.904371i	0.568900	+	0.822407i	$0.307369\pi$
$997$	−13.5059	+	28.5558i	−0.427735	+	0.904371i	−0.996635	+	0.0819638i	$0.973881\pi$
$998$	15.2297	+	11.9295i	0.482087	+	0.377620i
$999$	3.81828	+	0.376068i	0.120805	+	0.0118983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.5.17	✓	992
256.205	even	64	inner	256.2.m.a.205.17	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.5.17	✓	992	1.1	even	1	trivial
256.2.m.a.205.17	yes	992	256.205	even	64	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(0.101501 + 1.41057i) q^{2} +(0.345303 - 2.32784i) q^{3} +(-1.97939 + 0.286349i) q^{4} +(-1.81333 - 0.0890833i) q^{5} +(3.31862 + 0.250793i) q^{6} +(-2.21013 - 1.18134i) q^{7} +(-0.604825 - 2.76300i) q^{8} +(-2.42879 - 0.736767i) q^{9} +O(q^{10})\)	\(q+(0.101501 + 1.41057i) q^{2} +(0.345303 - 2.32784i) q^{3} +(-1.97939 + 0.286349i) q^{4} +(-1.81333 - 0.0890833i) q^{5} +(3.31862 + 0.250793i) q^{6} +(-2.21013 - 1.18134i) q^{7} +(-0.604825 - 2.76300i) q^{8} +(-2.42879 - 0.736767i) q^{9} +(-0.0583977 - 2.56687i) q^{10} +(-1.66386 - 2.77598i) q^{11} +(-0.0169161 + 4.70660i) q^{12} +(-0.130100 + 0.143543i) q^{13} +(1.44203 - 3.23745i) q^{14} +(-0.833520 + 4.19039i) q^{15} +(3.83601 - 1.13359i) q^{16} +(0.207189 + 1.04161i) q^{17} +(0.792733 - 3.50076i) q^{18} +(-1.90474 - 4.02723i) q^{19} +(3.61481 - 0.342914i) q^{20} +(-3.51314 + 4.73692i) q^{21} +(3.74682 - 2.62875i) q^{22} +(-2.24444 - 1.84196i) q^{23} +(-6.64068 + 0.453864i) q^{24} +(-1.69569 - 0.167011i) q^{25} +(-0.215682 - 0.168944i) q^{26} +(0.464767 - 0.982667i) q^{27} +(4.71300 + 1.70547i) q^{28} +(0.948010 - 0.237464i) q^{29} +(-5.99543 - 0.750406i) q^{30} +(8.85870 + 3.66939i) q^{31} +(1.98837 + 5.29588i) q^{32} +(-7.03658 + 2.91465i) q^{33} +(-1.44823 + 0.397978i) q^{34} +(3.90247 + 2.33905i) q^{35} +(5.01852 + 0.762870i) q^{36} +(1.18907 + 3.32324i) q^{37} +(5.48734 - 3.09553i) q^{38} +(0.289221 + 0.352417i) q^{39} +(0.850611 + 5.06412i) q^{40} +(2.93118 - 0.288696i) q^{41} +(-7.03833 - 4.47471i) q^{42} +(11.6692 - 1.73096i) q^{43} +(4.08833 + 5.01832i) q^{44} +(4.33858 + 1.55237i) q^{45} +(2.37039 - 3.35289i) q^{46} +(-7.06692 + 10.5764i) q^{47} +(-1.31424 - 9.32106i) q^{48} +(-0.399870 - 0.598447i) q^{49} +(0.0634651 - 2.40883i) q^{50} +(2.49624 - 0.122633i) q^{51} +(0.216415 - 0.321382i) q^{52} +(-1.86050 - 0.466032i) q^{53} +(1.43329 + 0.555843i) q^{54} +(2.76983 + 5.18199i) q^{55} +(-1.92730 + 6.82111i) q^{56} +(-10.0325 + 3.04332i) q^{57} +(0.431183 + 1.31313i) q^{58} +(-7.39861 - 8.16311i) q^{59} +(0.449953 - 8.53311i) q^{60} +(-6.14803 - 8.28966i) q^{61} +(-4.27675 + 12.8682i) q^{62} +(4.49759 + 4.49759i) q^{63} +(-7.26837 + 3.34227i) q^{64} +(0.248701 - 0.248701i) q^{65} +(-4.82552 - 9.62972i) q^{66} +(11.0086 - 8.16451i) q^{67} +(-0.708372 - 2.00243i) q^{68} +(-5.06280 + 4.58866i) q^{69} +(-2.90328 + 5.74210i) q^{70} +(-2.37407 - 7.82625i) q^{71} +(-0.566693 + 7.15638i) q^{72} +(5.69942 - 3.04641i) q^{73} +(-4.56696 + 2.01458i) q^{74} +(-0.974300 + 3.88962i) q^{75} +(4.92342 + 7.42606i) q^{76} +(0.397970 + 8.10087i) q^{77} +(-0.467751 + 0.443736i) q^{78} +(-4.64124 + 3.10118i) q^{79} +(-7.05694 + 1.71386i) q^{80} +(-8.45803 - 5.65147i) q^{81} +(0.704743 + 4.10532i) q^{82} +(-1.15859 + 3.23804i) q^{83} +(5.59748 - 10.3822i) q^{84} +(-0.282912 - 1.90724i) q^{85} +(3.62607 + 16.2845i) q^{86} +(-0.225429 - 2.28881i) q^{87} +(-6.66370 + 6.27623i) q^{88} +(-0.401933 + 0.329858i) q^{89} +(-1.74935 + 6.27742i) q^{90} +(0.457110 - 0.163557i) q^{91} +(4.97007 + 3.00328i) q^{92} +(11.6007 - 19.3546i) q^{93} +(-15.6360 - 8.89484i) q^{94} +(3.09516 + 7.47239i) q^{95} +(13.0146 - 2.79993i) q^{96} +(-5.06179 + 12.2202i) q^{97} +(0.803562 - 0.624786i) q^{98} +(1.99592 + 7.96816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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