LMFDB - Embedded newform 304.2.k.b.77.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (of order $4$, degree $2$, 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.25
Character	$\chi$	$=$	304.77
Dual form			304.2.k.b.229.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987457 - 1.01239i) q^{2} +(-0.0665185 - 0.0665185i) q^{3} +(-0.0498557 - 1.99938i) q^{4} +(-0.733023 + 0.733023i) q^{5} +(-0.133027 + 0.00165829i) q^{6} -2.20223i q^{7} +(-2.07338 - 1.92383i) q^{8} -2.99115i q^{9} +O(q^{10})$	\(q+(0.987457 - 1.01239i) q^{2} +(-0.0665185 - 0.0665185i) q^{3} +(-0.0498557 - 1.99938i) q^{4} +(-0.733023 + 0.733023i) q^{5} +(-0.133027 + 0.00165829i) q^{6} -2.20223i q^{7} +(-2.07338 - 1.92383i) q^{8} -2.99115i q^{9} +(0.0182741 + 1.46593i) q^{10} +(0.374733 - 0.374733i) q^{11} +(-0.129679 + 0.136312i) q^{12} +(0.108769 + 0.108769i) q^{13} +(-2.22951 - 2.17461i) q^{14} +0.0975191 q^{15} +(-3.99503 + 0.199361i) q^{16} +5.30079 q^{17} +(-3.02820 - 2.95363i) q^{18} +(0.707107 + 0.707107i) q^{19} +(1.50214 + 1.42904i) q^{20} +(-0.146489 + 0.146489i) q^{21} +(-0.00934201 - 0.749408i) q^{22} -2.96407i q^{23} +(0.00994768 + 0.265888i) q^{24} +3.92535i q^{25} +(0.217520 - 0.00271158i) q^{26} +(-0.398522 + 0.398522i) q^{27} +(-4.40310 + 0.109794i) q^{28} +(5.18039 + 5.18039i) q^{29} +(0.0962960 - 0.0987271i) q^{30} -2.99298 q^{31} +(-3.74309 + 4.24138i) q^{32} -0.0498533 q^{33} +(5.23430 - 5.36645i) q^{34} +(1.61429 + 1.61429i) q^{35} +(-5.98044 + 0.149126i) q^{36} +(-5.95722 + 5.95722i) q^{37} +(1.41410 - 0.0176280i) q^{38} -0.0144703i q^{39} +(2.93004 - 0.109622i) q^{40} +3.65123i q^{41} +(0.00365195 + 0.292956i) q^{42} +(2.17232 - 2.17232i) q^{43} +(-0.767916 - 0.730551i) q^{44} +(2.19258 + 2.19258i) q^{45} +(-3.00078 - 2.92689i) q^{46} +3.00996 q^{47} +(0.279004 + 0.252482i) q^{48} +2.15016 q^{49} +(3.97398 + 3.87612i) q^{50} +(-0.352600 - 0.352600i) q^{51} +(0.212047 - 0.222893i) q^{52} +(-0.619445 + 0.619445i) q^{53} +(0.00993507 + 0.796983i) q^{54} +0.549376i q^{55} +(-4.23672 + 4.56606i) q^{56} -0.0940713i q^{57} +(10.3600 - 0.129146i) q^{58} +(7.96783 - 7.96783i) q^{59} +(-0.00486188 - 0.194978i) q^{60} +(7.39165 + 7.39165i) q^{61} +(-2.95544 + 3.03006i) q^{62} -6.58722 q^{63} +(0.597772 + 7.97764i) q^{64} -0.159460 q^{65} +(-0.0492281 + 0.0504709i) q^{66} +(3.76872 + 3.76872i) q^{67} +(-0.264274 - 10.5983i) q^{68} +(-0.197165 + 0.197165i) q^{69} +(3.22833 - 0.0402439i) q^{70} -9.60500i q^{71} +(-5.75446 + 6.20178i) q^{72} -7.61653i q^{73} +(0.148512 + 11.9135i) q^{74} +(0.261109 - 0.261109i) q^{75} +(1.37852 - 1.44903i) q^{76} +(-0.825250 - 0.825250i) q^{77} +(-0.0146495 - 0.0142888i) q^{78} -16.7295 q^{79} +(2.78231 - 3.07458i) q^{80} -8.92043 q^{81} +(3.69646 + 3.60544i) q^{82} +(2.91902 + 2.91902i) q^{83} +(0.300191 + 0.285584i) q^{84} +(-3.88560 + 3.88560i) q^{85} +(-0.0541554 - 4.34430i) q^{86} -0.689183i q^{87} +(-1.49788 + 0.0560405i) q^{88} -1.61152i q^{89} +(4.38482 - 0.0546606i) q^{90} +(0.239534 - 0.239534i) q^{91} +(-5.92629 + 0.147776i) q^{92} +(0.199089 + 0.199089i) q^{93} +(2.97220 - 3.04724i) q^{94} -1.03665 q^{95} +(0.531115 - 0.0331452i) q^{96} +14.5732 q^{97} +(2.12319 - 2.17680i) q^{98} +(-1.12088 - 1.12088i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.987457	−	1.01239i	0.698238	−	0.715866i
$2$	0.987457	−	1.01239i	0.698238	−	0.715866i
$3$	−0.0665185	−	0.0665185i	−0.0384045	−	0.0384045i	0.687644	−	0.726048i	$-0.258645\pi$
$3$	−0.0665185	−	0.0665185i	−0.0384045	−	0.0384045i	−0.726048	+	0.687644i	$0.758645\pi$
$4$	−0.0498557	−	1.99938i	−0.0249278	−	0.999689i
$5$	−0.733023	+	0.733023i	−0.327818	+	0.327818i	−0.851756	−	0.523938i	$-0.824462\pi$
$5$	−0.733023	+	0.733023i	−0.327818	+	0.327818i	0.523938	+	0.851756i	$0.324462\pi$
$6$	−0.133027	+	0.00165829i	−0.0543079	+	0.000676994i
$7$		−	2.20223i		−	0.832366i	−0.909281	−	0.416183i	$-0.863367\pi$
$7$		−	2.20223i		−	0.832366i	0.909281	−	0.416183i	$-0.136633\pi$
$8$	−2.07338	−	1.92383i	−0.733049	−	0.680176i
$9$		−	2.99115i		−	0.997050i
$10$	0.0182741	+	1.46593i	0.00577878	+	0.463568i
$11$	0.374733	−	0.374733i	0.112986	−	0.112986i	−0.648353	−	0.761340i	$-0.724542\pi$
$11$	0.374733	−	0.374733i	0.112986	−	0.112986i	0.761340	+	0.648353i	$0.224542\pi$
$12$	−0.129679	+	0.136312i	−0.0374352	+	0.0393499i
$13$	0.108769	+	0.108769i	0.0301670	+	0.0301670i	0.722029	−	0.691862i	$-0.243210\pi$
$13$	0.108769	+	0.108769i	0.0301670	+	0.0301670i	−0.691862	+	0.722029i	$0.743210\pi$
$14$	−2.22951	−	2.17461i	−0.595863	−	0.581190i
$15$	0.0975191			0.0251793
$16$	−3.99503	+	0.199361i	−0.998757	+	0.0498402i
$17$	5.30079			1.28563			0.642815	−	0.766022i	$-0.277766\pi$
$17$	5.30079			1.28563			0.642815	+	0.766022i	$0.277766\pi$
$18$	−3.02820	−	2.95363i	−0.713754	−	0.696178i
$19$	0.707107	+	0.707107i	0.162221	+	0.162221i
$19$	0.707107	+	0.707107i	0.162221	+	0.162221i
$20$	1.50214	+	1.42904i	0.335888	+	0.319544i
$21$	−0.146489	+	0.146489i	−0.0319666	+	0.0319666i
$22$	−0.00934201	−	0.749408i	−0.00199172	−	0.159774i
$23$		−	2.96407i		−	0.618051i	−0.951054	−	0.309025i	$-0.899997\pi$
$23$		−	2.96407i		−	0.618051i	0.951054	−	0.309025i	$-0.100003\pi$
$24$	0.00994768	+	0.265888i	0.00203056	+	0.0542741i
$25$			3.92535i			0.785071i
$26$	0.217520	−	0.00271158i	0.0426593	−	0.000531784i
$27$	−0.398522	+	0.398522i	−0.0766956	+	0.0766956i
$28$	−4.40310	+	0.109794i	−0.832108	+	0.0207491i
$29$	5.18039	+	5.18039i	0.961974	+	0.961974i	0.999303	−	0.0373288i	$-0.0118849\pi$
$29$	5.18039	+	5.18039i	0.961974	+	0.961974i	−0.0373288	+	0.999303i	$0.511885\pi$
$30$	0.0962960	−	0.0987271i	0.0175812	−	0.0180250i
$31$	−2.99298			−0.537555			−0.268778	−	0.963202i	$-0.586620\pi$
$31$	−2.99298			−0.537555			−0.268778	+	0.963202i	$0.586620\pi$
$32$	−3.74309	+	4.24138i	−0.661691	+	0.749776i
$33$	−0.0498533			−0.00867835
$34$	5.23430	−	5.36645i	0.897675	−	0.920338i
$35$	1.61429	+	1.61429i	0.272865	+	0.272865i
$36$	−5.98044	+	0.149126i	−0.996740	+	0.0248543i
$37$	−5.95722	+	5.95722i	−0.979360	+	0.979360i	−0.999791	−	0.0204311i	$-0.993496\pi$
$37$	−5.95722	+	5.95722i	−0.979360	+	0.979360i	0.0204311	+	0.999791i	$0.493496\pi$
$38$	1.41410	−	0.0176280i	0.229398	−	0.00285964i
$39$		−	0.0144703i		−	0.00231710i
$40$	2.93004	−	0.109622i	0.463280	−	0.0173327i
$41$			3.65123i			0.570227i	0.958494	+	0.285113i	$0.0920313\pi$
$41$			3.65123i			0.570227i	−0.958494	+	0.285113i	$0.907969\pi$
$42$	0.00365195	+	0.292956i	0.000563507	+	0.0452041i
$43$	2.17232	−	2.17232i	0.331276	−	0.331276i	−0.521795	−	0.853071i	$-0.674737\pi$
$43$	2.17232	−	2.17232i	0.331276	−	0.331276i	0.853071	+	0.521795i	$0.174737\pi$
$44$	−0.767916	−	0.730551i	−0.115768	−	0.110135i
$45$	2.19258	+	2.19258i	0.326851	+	0.326851i
$46$	−3.00078	−	2.92689i	−0.442441	−	0.431546i
$47$	3.00996			0.439047			0.219524	−	0.975607i	$-0.429550\pi$
$47$	3.00996			0.439047			0.219524	+	0.975607i	$0.429550\pi$
$48$	0.279004	+	0.252482i	0.0402708	+	0.0364426i
$49$	2.15016			0.307166
$50$	3.97398	+	3.87612i	0.562005	+	0.548166i
$51$	−0.352600	−	0.352600i	−0.0493739	−	0.0493739i
$52$	0.212047	−	0.222893i	0.0294056	−	0.0309096i
$53$	−0.619445	+	0.619445i	−0.0850873	+	0.0850873i	−0.748369	−	0.663282i	$-0.769163\pi$
$53$	−0.619445	+	0.619445i	−0.0850873	+	0.0850873i	0.663282	+	0.748369i	$0.269163\pi$
$54$	0.00993507	+	0.796983i	0.00135199	+	0.108456i
$55$			0.549376i			0.0740778i
$56$	−4.23672	+	4.56606i	−0.566156	+	0.610165i
$57$		−	0.0940713i		−	0.0124601i
$58$	10.3600	−	0.129146i	1.36033	−	0.0169577i
$59$	7.96783	−	7.96783i	1.03732	−	1.03732i	0.0380472	−	0.999276i	$-0.487886\pi$
$59$	7.96783	−	7.96783i	1.03732	−	1.03732i	0.999276	−	0.0380472i	$-0.0121137\pi$
$60$	−0.00486188	−	0.194978i	−0.000627666	−	0.0251715i
$61$	7.39165	+	7.39165i	0.946404	+	0.946404i	0.998635	−	0.0522312i	$-0.0166333\pi$
$61$	7.39165	+	7.39165i	0.946404	+	0.946404i	−0.0522312	+	0.998635i	$0.516633\pi$
$62$	−2.95544	+	3.03006i	−0.375342	+	0.384818i
$63$	−6.58722			−0.829911
$64$	0.597772	+	7.97764i	0.0747216	+	0.997204i
$65$	−0.159460			−0.0197786
$66$	−0.0492281	+	0.0504709i	−0.00605956	+	0.00621254i
$67$	3.76872	+	3.76872i	0.460423	+	0.460423i	0.898794	−	0.438371i	$-0.144445\pi$
$67$	3.76872	+	3.76872i	0.460423	+	0.460423i	−0.438371	+	0.898794i	$0.644445\pi$
$68$	−0.264274	−	10.5983i	−0.0320480	−	1.28523i
$69$	−0.197165	+	0.197165i	−0.0237359	+	0.0237359i
$70$	3.22833	−	0.0402439i	0.385859	−	0.00481006i
$71$		−	9.60500i		−	1.13990i	−0.821678	−	0.569952i	$-0.806962\pi$
$71$		−	9.60500i		−	1.13990i	0.821678	−	0.569952i	$-0.193038\pi$
$72$	−5.75446	+	6.20178i	−0.678169	+	0.730887i
$73$		−	7.61653i		−	0.891447i	−0.895171	−	0.445724i	$-0.852946\pi$
$73$		−	7.61653i		−	0.891447i	0.895171	−	0.445724i	$-0.147054\pi$
$74$	0.148512	+	11.9135i	0.0172642	+	1.38492i
$75$	0.261109	−	0.261109i	0.0301502	−	0.0301502i
$76$	1.37852	−	1.44903i	0.158127	−	0.166215i
$77$	−0.825250	−	0.825250i	−0.0940460	−	0.0940460i
$78$	−0.0146495	−	0.0142888i	−0.00165873	−	0.00161788i
$79$	−16.7295			−1.88221			−0.941106	−	0.338111i	$-0.890212\pi$
$79$	−16.7295			−1.88221			−0.941106	+	0.338111i	$0.890212\pi$
$80$	2.78231	−	3.07458i	0.311072	−	0.343749i
$81$	−8.92043			−0.991159
$82$	3.69646	+	3.60544i	0.408206	+	0.398154i
$83$	2.91902	+	2.91902i	0.320404	+	0.320404i	0.848922	−	0.528518i	$-0.177252\pi$
$83$	2.91902	+	2.91902i	0.320404	+	0.320404i	−0.528518	+	0.848922i	$0.677252\pi$
$84$	0.300191	+	0.285584i	0.0327535	+	0.0311598i
$85$	−3.88560	+	3.88560i	−0.421452	+	0.421452i
$86$	−0.0541554	−	4.34430i	−0.00583973	−	0.468458i
$87$		−	0.689183i		−	0.0738882i
$88$	−1.49788	+	0.0560405i	−0.159675	+	0.00597393i
$89$		−	1.61152i		−	0.170820i	−0.996346	−	0.0854102i	$-0.972780\pi$
$89$		−	1.61152i		−	0.170820i	0.996346	−	0.0854102i	$-0.0272201\pi$
$90$	4.38482	−	0.0546606i	0.462201	−	0.00576173i
$91$	0.239534	−	0.239534i	0.0251100	−	0.0251100i
$92$	−5.92629	+	0.147776i	−0.617858	+	0.0154067i
$93$	0.199089	+	0.199089i	0.0206445	+	0.0206445i
$94$	2.97220	−	3.04724i	0.306559	−	0.314299i
$95$	−1.03665			−0.106358
$96$	0.531115	−	0.0331452i	0.0542067	−	0.00338287i
$97$	14.5732			1.47968			0.739842	−	0.672780i	$-0.234900\pi$
$97$	14.5732			1.47968			0.739842	+	0.672780i	$0.234900\pi$
$98$	2.12319	−	2.17680i	0.214475	−	0.219890i
$99$	−1.12088	−	1.12088i	−0.112653	−	0.112653i
$100$	7.84827	−	0.195701i	0.784827	−	0.0195701i
$101$	−2.14007	+	2.14007i	−0.212945	+	0.212945i	−0.805517	−	0.592572i	$-0.798113\pi$
$101$	−2.14007	+	2.14007i	−0.212945	+	0.212945i	0.592572	+	0.805517i	$0.298113\pi$
$102$	−0.705146	+	0.00879025i	−0.0698198	+	0.000870364i
$103$			3.62530i			0.357212i	0.983921	+	0.178606i	$0.0571587\pi$
$103$			3.62530i			0.357212i	−0.983921	+	0.178606i	$0.942841\pi$
$104$	−0.0162661	−	0.434771i	−0.00159502	−	0.0426328i
$105$		−	0.214760i		−	0.0209584i
$106$	0.0154426	+	1.23879i	0.00149992	+	0.120322i
$107$	−1.36615	+	1.36615i	−0.132071	+	0.132071i	−0.770052	−	0.637981i	$-0.779770\pi$
$107$	−1.36615	+	1.36615i	−0.132071	+	0.132071i	0.637981	+	0.770052i	$0.279770\pi$
$108$	0.816665	+	0.776928i	0.0785837	+	0.0747600i
$109$	−0.676339	−	0.676339i	−0.0647815	−	0.0647815i	0.673974	−	0.738755i	$-0.264586\pi$
$109$	−0.676339	−	0.676339i	−0.0647815	−	0.0647815i	−0.738755	+	0.673974i	$0.764586\pi$
$110$	0.556181	+	0.542485i	0.0530298	+	0.0517239i
$111$	0.792530			0.0752236
$112$	0.439039	+	8.79799i	0.0414853	+	0.831332i
$113$	−1.51650			−0.142660			−0.0713302	−	0.997453i	$-0.522724\pi$
$113$	−1.51650			−0.142660			−0.0713302	+	0.997453i	$0.522724\pi$
$114$	−0.0952366	−	0.0928914i	−0.00891973	−	0.00870008i
$115$	2.17273	+	2.17273i	0.202608	+	0.202608i
$116$	10.0993	−	10.6158i	0.937695	−	0.985655i
$117$	0.325344	−	0.325344i	0.0300780	−	0.0300780i
$118$	−0.198636	−	15.9344i	−0.0182859	−	1.46688i
$119$		−	11.6736i		−	1.07011i
$120$	−0.202194	−	0.187610i	−0.0184577	−	0.0171264i
$121$			10.7192i			0.974468i
$122$	14.7822	−	0.184272i	1.33831	−	0.0166832i
$123$	0.242875	−	0.242875i	0.0218993	−	0.0218993i
$124$	0.149217	+	5.98410i	0.0134001	+	0.537388i
$125$	−6.54249	−	6.54249i	−0.585178	−	0.585178i
$126$	−6.50459	+	6.66881i	−0.579475	+	0.594105i
$127$	−11.0291			−0.978672			−0.489336	−	0.872095i	$-0.662761\pi$
$127$	−11.0291			−0.978672			−0.489336	+	0.872095i	$0.662761\pi$
$128$	8.66673	+	7.27240i	0.766038	+	0.642795i
$129$	−0.288999			−0.0254449
$130$	−0.157460	+	0.161435i	−0.0138101	+	0.0141588i
$131$	−8.79691	−	8.79691i	−0.768590	−	0.768590i	0.209268	−	0.977858i	$-0.432892\pi$
$131$	−8.79691	−	8.79691i	−0.768590	−	0.768590i	−0.977858	+	0.209268i	$0.932892\pi$
$132$	0.00248547	+	0.0996757i	0.000216333	+	0.00867566i
$133$	1.55722	−	1.55722i	0.135028	−	0.135028i
$134$	7.53686	−	0.0939534i	0.651085	−	0.00811634i
$135$		−	0.584252i		−	0.0502844i
$136$	−10.9905	−	10.1978i	−0.942429	−	0.874454i
$137$		−	12.6300i		−	1.07905i	−0.841968	−	0.539527i	$-0.818603\pi$
$137$		−	12.6300i		−	1.07905i	0.841968	−	0.539527i	$-0.181397\pi$
$138$	0.00491528	+	0.394300i	0.000418417	+	0.0335650i
$139$	−12.0800	+	12.0800i	−1.02461	+	1.02461i	−0.0249247	+	0.999689i	$0.507935\pi$
$139$	−12.0800	+	12.0800i	−1.02461	+	1.02461i	−0.999689	+	0.0249247i	$0.992065\pi$
$140$	3.14709	−	3.30806i	0.265978	−	0.279582i
$141$	−0.200218	−	0.200218i	−0.0168614	−	0.0168614i
$142$	−9.72398	−	9.48453i	−0.816018	−	0.795924i
$143$	0.0815185			0.00681692
$144$	0.596318	+	11.9497i	0.0496932	+	0.995811i
$145$	−7.59469			−0.630705
$146$	−7.71088	−	7.52100i	−0.638157	−	0.622442i
$147$	−0.143026	−	0.143026i	−0.0117965	−	0.0117965i
$148$	12.2077	+	11.6137i	1.00347	+	0.954642i
$149$	−3.03478	+	3.03478i	−0.248619	+	0.248619i	−0.820404	−	0.571785i	$-0.806251\pi$
$149$	−3.03478	+	3.03478i	−0.248619	+	0.248619i	0.571785	+	0.820404i	$0.306251\pi$
$150$	−0.00650938	−	0.522177i	−0.000531489	−	0.0426356i
$151$			18.2004i			1.48113i	0.671987	+	0.740563i	$0.265441\pi$
$151$			18.2004i			1.48113i	−0.671987	+	0.740563i	$0.734559\pi$
$152$	−0.105746	−	2.82645i	−0.00857715	−	0.229255i
$153$		−	15.8555i		−	1.28184i
$154$	−1.65037	+	0.0205733i	−0.132991	+	0.00165784i
$155$	2.19392	−	2.19392i	0.176220	−	0.176220i
$156$	−0.0289315		0.000721425i	−0.00231638		5.77602e-5i
$157$	−7.40195	−	7.40195i	−0.590740	−	0.590740i	0.347091	−	0.937831i	$-0.387169\pi$
$157$	−7.40195	−	7.40195i	−0.590740	−	0.590740i	−0.937831	+	0.347091i	$0.887169\pi$
$158$	−16.5196	+	16.9367i	−1.31423	+	1.34741i
$159$	0.0824091			0.00653547
$160$	−0.365255	−	5.85280i	−0.0288759	−	0.462704i
$161$	−6.52757			−0.514445
$162$	−8.80855	+	9.03093i	−0.692065	+	0.709537i
$163$	−3.33454	−	3.33454i	−0.261182	−	0.261182i	0.564352	−	0.825534i	$-0.309126\pi$
$163$	−3.33454	−	3.33454i	−0.261182	−	0.261182i	−0.825534	+	0.564352i	$0.809126\pi$
$164$	7.30020	−	0.182035i	0.570050	−	0.0142145i
$165$	0.0365436	−	0.0365436i	0.00284492	−	0.00284492i
$166$	5.83759	−	0.0727705i	0.453085	−	0.00564809i
$167$		−	13.6049i		−	1.05278i	−0.850244	−	0.526389i	$-0.823545\pi$
$167$		−	13.6049i		−	1.05278i	0.850244	−	0.526389i	$-0.176455\pi$
$168$	0.585548	−	0.0219071i	0.0451760	−	0.00169017i
$169$		−	12.9763i		−	0.998180i
$170$	0.0968671	+	7.77059i	0.00742937	+	0.595977i
$171$	2.11506	−	2.11506i	0.161743	−	0.161743i
$172$	−4.45159	−	4.23499i	−0.339431	−	0.322915i
$173$	−1.66878	−	1.66878i	−0.126875	−	0.126875i	0.640818	−	0.767693i	$-0.278595\pi$
$173$	−1.66878	−	1.66878i	−0.126875	−	0.126875i	−0.767693	+	0.640818i	$0.778595\pi$
$174$	−0.697720	−	0.680539i	−0.0528940	−	0.0515915i
$175$	8.64455			0.653467
$176$	−1.42236	+	1.57178i	−0.107215	+	0.118477i
$177$	−1.06002			−0.0796757
$178$	−1.63148	−	1.59130i	−0.122284	−	0.119273i
$179$	14.1012	+	14.1012i	1.05397	+	1.05397i	0.998458	+	0.0555132i	$0.0176795\pi$
$179$	14.1012	+	14.1012i	1.05397	+	1.05397i	0.0555132	+	0.998458i	$0.482321\pi$
$180$	4.27449	−	4.49311i	0.318602	−	0.334897i
$181$	−17.3950	+	17.3950i	−1.29296	+	1.29296i	−0.360013	+	0.932947i	$0.617228\pi$
$181$	−17.3950	+	17.3950i	−1.29296	+	1.29296i	−0.932947	+	0.360013i	$0.882772\pi$
$182$	−0.00597153	−	0.479031i	−0.000442640	−	0.0355082i
$183$		−	0.983363i		−	0.0726923i
$184$	−5.70235	+	6.14562i	−0.420383	+	0.453061i
$185$		−	8.73355i		−	0.642103i
$186$	0.398146	−	0.00496323i	0.0291935	−	0.000363922i
$187$	1.98638	−	1.98638i	0.145258	−	0.145258i
$188$	−0.150063	−	6.01804i	−0.0109445	−	0.438911i
$189$	0.877640	+	0.877640i	0.0638389	+	0.0638389i
$190$	−1.02365	+	1.04949i	−0.0742633	+	0.0761382i
$191$	−2.68053			−0.193956			−0.0969780	−	0.995287i	$-0.530918\pi$
$191$	−2.68053			−0.193956			−0.0969780	+	0.995287i	$0.530918\pi$
$192$	0.490897	−	0.570423i	0.0354275	−	0.0411667i
$193$	5.86634			0.422268			0.211134	−	0.977457i	$-0.432284\pi$
$193$	5.86634			0.422268			0.211134	+	0.977457i	$0.432284\pi$
$194$	14.3904	−	14.7537i	1.03317	−	1.05926i
$195$	0.0106070	+	0.0106070i	0.000759585	+	0.000759585i
$196$	−0.107198	−	4.29899i	−0.00765699	−	0.307071i
$197$	−3.61113	+	3.61113i	−0.257282	+	0.257282i	−0.823948	−	0.566666i	$-0.808233\pi$
$197$	−3.61113	+	3.61113i	−0.257282	+	0.257282i	0.566666	+	0.823948i	$0.308233\pi$
$198$	−2.24159	+	0.0279434i	−0.159303	+	0.00198585i
$199$		−	6.85221i		−	0.485740i	−0.970059	−	0.242870i	$-0.921911\pi$
$199$		−	6.85221i		−	0.485740i	0.970059	−	0.242870i	$-0.0780889\pi$
$200$	7.55171	−	8.13873i	0.533986	−	0.575495i
$201$		−	0.501379i		−	0.0353646i
$202$	0.0533515	+	4.27981i	0.00375380	+	0.301127i
$203$	11.4084	−	11.4084i	0.800715	−	0.800715i
$204$	−0.687402	+	0.722561i	−0.0481278	+	0.0505894i
$205$	−2.67644	−	2.67644i	−0.186931	−	0.186931i
$206$	3.67021	+	3.57983i	0.255716	+	0.249419i
$207$	−8.86597			−0.616227
$208$	−0.456218	−	0.412850i	−0.0316330	−	0.0286260i
$209$	0.529953			0.0366576
$210$	−0.217420	−	0.212066i	−0.0150034	−	0.0146340i
$211$	−5.15969	−	5.15969i	−0.355208	−	0.355208i	0.506835	−	0.862043i	$-0.330815\pi$
$211$	−5.15969	−	5.15969i	−0.355208	−	0.355208i	−0.862043	+	0.506835i	$0.830815\pi$
$212$	1.26939	+	1.20762i	0.0871819	+	0.0829398i
$213$	−0.638910	+	0.638910i	−0.0437774	+	0.0437774i
$214$	0.0340579	+	2.73209i	0.00232815	+	0.186762i
$215$			3.18472i			0.217196i
$216$	1.59297	−	0.0595981i	0.108388	−	0.00405514i
$217$			6.59125i			0.447443i
$218$	−1.35257	+	0.0168610i	−0.0916078	+	0.00114197i
$219$	−0.506640	+	0.506640i	−0.0342356	+	0.0342356i
$220$	1.09841	−	0.0273895i	0.0740548	−	0.00184660i
$221$	0.576560	+	0.576560i	0.0387836	+	0.0387836i
$222$	0.782589	−	0.802347i	0.0525240	−	0.0538500i
$223$	−1.43142			−0.0958548			−0.0479274	−	0.998851i	$-0.515262\pi$
$223$	−1.43142			−0.0958548			−0.0479274	+	0.998851i	$0.515262\pi$
$224$	9.34051	+	8.24316i	0.624089	+	0.550770i
$225$	11.7413			0.782755
$226$	−1.49748	+	1.53529i	−0.0996108	+	0.102126i
$227$	11.7034	+	11.7034i	0.776784	+	0.776784i	0.979283	−	0.202499i	$-0.0649062\pi$
$227$	11.7034	+	11.7034i	0.776784	+	0.776784i	−0.202499	+	0.979283i	$0.564906\pi$
$228$	−0.188084	+	0.00468999i	−0.0124562	+	0.000310602i
$229$	11.2284	−	11.2284i	0.741997	−	0.741997i	−0.230965	−	0.972962i	$-0.574188\pi$
$229$	11.2284	−	11.2284i	0.741997	−	0.741997i	0.972962	+	0.230965i	$0.0741884\pi$
$230$	4.34512	−	0.0541656i	0.286509	−	0.00357158i
$231$			0.109789i			0.00722357i
$232$	−0.774715	−	20.7071i	−0.0508625	−	1.35949i
$233$		−	18.3277i		−	1.20069i	−0.799742	−	0.600344i	$-0.795030\pi$
$233$		−	18.3277i		−	1.20069i	0.799742	−	0.600344i	$-0.204970\pi$
$234$	−0.00811074	−	0.650637i	−0.000530216	−	0.0425334i
$235$	−2.20637	+	2.20637i	−0.143927	+	0.143927i
$236$	−16.3280	−	15.5335i	−1.06286	−	1.01114i
$237$	1.11282	+	1.11282i	0.0722854	+	0.0722854i
$238$	−11.8182	−	11.5272i	−0.766059	−	0.747195i
$239$	22.4859			1.45449			0.727245	−	0.686378i	$-0.240800\pi$
$239$	22.4859			1.45449			0.727245	+	0.686378i	$0.240800\pi$
$240$	−0.389592	+	0.0194415i	−0.0251480	+	0.00125494i
$241$	5.28961			0.340734			0.170367	−	0.985381i	$-0.445505\pi$
$241$	5.28961			0.340734			0.170367	+	0.985381i	$0.445505\pi$
$242$	10.8519	+	10.5847i	0.697589	+	0.680411i
$243$	1.78894	+	1.78894i	0.114761	+	0.114761i
$244$	14.4102	−	15.1472i	0.922518	−	0.969702i
$245$	−1.57612	+	1.57612i	−0.100694	+	0.100694i
$246$	−0.00605481	−	0.485711i	−0.000386040	−	0.0309678i
$247$			0.153822i			0.00978747i
$248$	6.20558	+	5.75798i	0.394054	+	0.365632i
$249$		−	0.388338i		−	0.0246099i
$250$	−13.0840	+	0.163103i	−0.827502	+	0.0103155i
$251$	−5.95521	+	5.95521i	−0.375890	+	0.375890i	−0.869617	−	0.493727i	$-0.835634\pi$
$251$	−5.95521	+	5.95521i	−0.375890	+	0.375890i	0.493727	+	0.869617i	$0.335634\pi$
$252$	0.328410	+	13.1703i	0.0206879	+	0.829653i
$253$	−1.11073	−	1.11073i	−0.0698312	−	0.0698312i
$254$	−10.8907	+	11.1657i	−0.683346	+	0.700598i
$255$	0.516928			0.0323713
$256$	15.9205	−	1.59290i	0.995032	−	0.0995565i
$257$	−14.5488			−0.907527			−0.453763	−	0.891122i	$-0.649919\pi$
$257$	−14.5488			−0.907527			−0.453763	+	0.891122i	$0.649919\pi$
$258$	−0.285374	+	0.292579i	−0.0177666	+	0.0182152i
$259$	13.1192	+	13.1192i	0.815187	+	0.815187i
$260$	0.00794998	+	0.318821i	0.000493037	+	0.0197724i
$261$	15.4953	−	15.4953i	0.959137	−	0.959137i
$262$	−17.5925	+	0.219305i	−1.08687	+	0.0135487i
$263$			31.0876i			1.91695i	0.285183	+	0.958473i	$0.407946\pi$
$263$			31.0876i			1.91695i	−0.285183	+	0.958473i	$0.592054\pi$
$264$	0.103365	+	0.0959093i	0.00636166	+	0.00590281i
$265$		−	0.908135i		−	0.0557863i
$266$	−0.0388210	−	3.11419i	−0.00238027	−	0.190943i
$267$	−0.107196	+	0.107196i	−0.00656026	+	0.00656026i
$268$	7.34721	−	7.72299i	0.448802	−	0.471757i
$269$	15.0697	+	15.0697i	0.918813	+	0.918813i	0.996943	−	0.0781301i	$-0.0248950\pi$
$269$	15.0697	+	15.0697i	0.918813	+	0.918813i	−0.0781301	+	0.996943i	$0.524895\pi$
$270$	−0.591489	−	0.576924i	−0.0359969	−	0.0351105i
$271$	−7.50983			−0.456190			−0.228095	−	0.973639i	$-0.573250\pi$
$271$	−7.50983			−0.456190			−0.228095	+	0.973639i	$0.573250\pi$
$272$	−21.1768	+	1.05677i	−1.28403	+	0.0640760i
$273$	−0.0318669			−0.00192867
$274$	−12.7865	−	12.4716i	−0.772458	−	0.753437i
$275$	1.47096	+	1.47096i	0.0887022	+	0.0887022i
$276$	0.404038	+	0.384378i	0.0243202	+	0.0231368i
$277$	−7.31732	+	7.31732i	−0.439655	+	0.439655i	−0.891896	−	0.452241i	$-0.850625\pi$
$277$	−7.31732	+	7.31732i	−0.439655	+	0.439655i	0.452241	+	0.891896i	$0.350625\pi$
$278$	0.301152	+	24.1582i	0.0180619	+	1.44891i
$279$			8.95246i			0.535970i
$280$	−0.241413	−	6.45264i	−0.0144272	−	0.385619i
$281$			23.6607i			1.41148i	0.708471	+	0.705740i	$0.249385\pi$
$281$			23.6607i			1.41148i	−0.708471	+	0.705740i	$0.750615\pi$
$282$	−0.400404	+	0.00499138i	−0.0238437	+	0.000297232i
$283$	−9.50523	+	9.50523i	−0.565027	+	0.565027i	−0.930731	−	0.365704i	$-0.880828\pi$
$283$	−9.50523	+	9.50523i	−0.565027	+	0.565027i	0.365704	+	0.930731i	$0.380828\pi$
$284$	−19.2040	+	0.478864i	−1.13955	+	0.0284153i
$285$	0.0689564	+	0.0689564i	0.00408463	+	0.00408463i
$286$	0.0804960	−	0.0825282i	0.00475983	−	0.00488000i
$287$	8.04087			0.474638
$288$	12.6866	+	11.1961i	0.747565	+	0.659739i
$289$	11.0983			0.652843
$290$	−7.49943	+	7.68877i	−0.440382	+	0.451500i
$291$	−0.969387	−	0.969387i	−0.0568265	−	0.0568265i
$292$	−15.2283	+	0.379727i	−0.891170	+	0.0222219i
$293$	18.1299	−	18.1299i	1.05916	−	1.05916i	0.0610257	−	0.998136i	$-0.480563\pi$
$293$	18.1299	−	18.1299i	1.05916	−	1.05916i	0.998136	−	0.0610257i	$-0.0194372\pi$
$294$	−0.286029	+	0.00356559i	−0.0166815	+	0.000207950i
$295$			11.6812i			0.680106i
$296$	23.8122	−	0.890888i	1.38406	−	0.0517818i
$297$			0.298679i			0.0173311i
$298$	0.0756563	+	6.06909i	0.00438265	+	0.351573i
$299$	0.322398	−	0.322398i	0.0186447	−	0.0186447i
$300$	−0.535073	−	0.509037i	−0.0308924	−	0.0293893i
$301$	−4.78396	−	4.78396i	−0.275743	−	0.275743i
$302$	18.4258	+	17.9721i	1.06029	+	1.03418i
$303$	0.284709			0.0163561
$304$	−2.96588	−	2.68394i	−0.170105	−	0.153935i
$305$	−10.8365			−0.620496
$306$	−16.0519	−	15.6566i	−0.917624	−	0.895027i
$307$	5.99964	+	5.99964i	0.342418	+	0.342418i	0.857276	−	0.514858i	$-0.172155\pi$
$307$	5.99964	+	5.99964i	0.342418	+	0.342418i	−0.514858	+	0.857276i	$0.672155\pi$
$308$	−1.60884	+	1.69113i	−0.0916724	+	0.0963611i
$309$	0.241150	−	0.241150i	0.0137185	−	0.0137185i
$310$	−0.0546940	−	4.38751i	−0.00310641	−	0.249194i
$311$			16.5114i			0.936274i	0.883656	+	0.468137i	$0.155075\pi$
$311$			16.5114i			0.936274i	−0.883656	+	0.468137i	$0.844925\pi$
$312$	−0.0278383	+	0.0300023i	−0.00157603	+	0.00169854i
$313$			17.4341i			0.985434i	0.870190	+	0.492717i	$0.163996\pi$
$313$			17.4341i			0.985434i	−0.870190	+	0.492717i	$0.836004\pi$
$314$	−14.8027	+	0.184529i	−0.835367	+	0.0104136i
$315$	4.82858	−	4.82858i	0.272060	−	0.272060i
$316$	0.834059	+	33.4485i	0.0469195	+	1.88163i
$317$	−12.2446	−	12.2446i	−0.687727	−	0.687727i	0.274002	−	0.961729i	$-0.411653\pi$
$317$	−12.2446	−	12.2446i	−0.687727	−	0.687727i	−0.961729	+	0.274002i	$0.911653\pi$
$318$	0.0813755	−	0.0834299i	0.00456331	−	0.00467852i
$319$	3.88253			0.217380
$320$	−6.28597	−	5.40961i	−0.351396	−	0.302406i
$321$	0.181749			0.0101442
$322$	−6.44570	+	6.60843i	−0.359205	+	0.368273i
$323$	3.74822	+	3.74822i	0.208557	+	0.208557i
$324$	0.444734	+	17.8353i	0.0247075	+	0.990851i
$325$	−0.426956	+	0.426956i	−0.0236832	+	0.0236832i
$326$	−6.66857	+	0.0831294i	−0.369338	+	0.00460411i
$327$			0.0899781i			0.00497580i
$328$	7.02434	−	7.57038i	0.387855	−	0.418004i
$329$		−	6.62863i		−	0.365448i
$330$	−0.000911025	−	0.0730816i	−5.01503e−5	−	0.00402301i
$331$	−21.5045	+	21.5045i	−1.18199	+	1.18199i	−0.202765	+	0.979227i	$0.564993\pi$
$331$	−21.5045	+	21.5045i	−1.18199	+	1.18199i	−0.979227	+	0.202765i	$0.935007\pi$
$332$	5.69070	−	5.98176i	0.312318	−	0.328292i
$333$	17.8189	+	17.8189i	0.976471	+	0.976471i
$334$	−13.7734	−	13.4343i	−0.753648	−	0.735090i
$335$	−5.52512			−0.301869
$336$	0.556025	−	0.614433i	0.0303336	−	0.0335201i
$337$	−2.66513			−0.145179			−0.0725894	−	0.997362i	$-0.523126\pi$
$337$	−2.66513			−0.145179			−0.0725894	+	0.997362i	$0.523126\pi$
$338$	−13.1371	−	12.8136i	−0.714563	−	0.696967i
$339$	0.100875	+	0.100875i	0.00547879	+	0.00547879i
$340$	7.96250	+	7.57506i	0.431827	+	0.410815i
$341$	−1.12157	+	1.12157i	−0.0607364	+	0.0607364i
$342$	−0.0527280	−	4.22980i	−0.00285121	−	0.228721i
$343$		−	20.1508i		−	1.08804i
$344$	−8.68320	+	0.324865i	−0.468167	+	0.0175156i
$345$		−	0.289053i		−	0.0155621i
$346$	−3.33729	+	0.0416022i	−0.179414	+	0.00223655i
$347$	22.8571	−	22.8571i	1.22703	−	1.22703i	0.261952	−	0.965081i	$-0.415634\pi$
$347$	22.8571	−	22.8571i	1.22703	−	1.22703i	0.965081	−	0.261952i	$-0.0843662\pi$
$348$	−1.37794	+	0.0343597i	−0.0738652	+	0.00184187i
$349$	−15.8490	−	15.8490i	−0.848377	−	0.848377i	0.141554	−	0.989931i	$-0.454790\pi$
$349$	−15.8490	−	15.8490i	−0.848377	−	0.848377i	−0.989931	+	0.141554i	$0.954790\pi$
$350$	8.53613	−	8.75163i	0.456275	−	0.467795i
$351$	−0.0866935			−0.00462736
$352$	0.186724	+	2.99204i	0.00995243	+	0.159476i
$353$	4.51652			0.240390			0.120195	−	0.992750i	$-0.461648\pi$
$353$	4.51652			0.240390			0.120195	+	0.992750i	$0.461648\pi$
$354$	−1.04672	+	1.07315i	−0.0556326	+	0.0570371i
$355$	7.04068	+	7.04068i	0.373681	+	0.373681i
$356$	−3.22203	+	0.0803432i	−0.170767	+	0.00425818i
$357$	−0.776509	+	0.776509i	−0.0410972	+	0.0410972i
$358$	28.2002	−	0.351539i	1.49042	−	0.0185794i
$359$			10.9825i			0.579636i	0.957082	+	0.289818i	$0.0935947\pi$
$359$			10.9825i			0.579636i	−0.957082	+	0.289818i	$0.906405\pi$
$360$	−0.327896	−	8.76420i	−0.0172816	−	0.461914i
$361$			1.00000i			0.0526316i
$362$	0.433653	+	34.7873i	0.0227923	+	1.82838i
$363$	0.713022	−	0.713022i	0.0374239	−	0.0374239i
$364$	−0.490862	−	0.466977i	−0.0257281	−	0.0244763i
$365$	5.58309	+	5.58309i	0.292232	+	0.292232i
$366$	−0.995544	−	0.971029i	−0.0520379	−	0.0507565i
$367$	27.0610			1.41257			0.706286	−	0.707926i	$-0.250369\pi$
$367$	27.0610			1.41257			0.706286	+	0.707926i	$0.250369\pi$
$368$	0.590918	+	11.8415i	0.0308038	+	0.617282i
$369$	10.9214			0.568545
$370$	−8.84173	−	8.62401i	−0.459660	−	0.448341i
$371$	1.36416	+	1.36416i	0.0708238	+	0.0708238i
$372$	0.388128	−	0.407979i	0.0201235	−	0.0211527i
$373$	7.12450	−	7.12450i	0.368893	−	0.368893i	−0.498181	−	0.867073i	$-0.665998\pi$
$373$	7.12450	−	7.12450i	0.368893	−	0.368893i	0.867073	+	0.498181i	$0.165998\pi$
$374$	−0.0495200	−	3.97245i	−0.00256062	−	0.205411i
$375$			0.870393i			0.0449469i
$376$	−6.24077	−	5.79064i	−0.321843	−	0.298629i
$377$			1.12693i			0.0580398i
$378$	1.75514	−	0.0218794i	0.0902748	−	0.00112535i
$379$	−21.5128	+	21.5128i	−1.10504	+	1.10504i	−0.111243	+	0.993793i	$0.535483\pi$
$379$	−21.5128	+	21.5128i	−1.10504	+	1.10504i	−0.993793	+	0.111243i	$0.964517\pi$
$380$	0.0516829	+	2.07266i	0.00265128	+	0.106325i
$381$	0.733637	+	0.733637i	0.0375854	+	0.0375854i
$382$	−2.64691	+	2.71373i	−0.135427	+	0.138847i
$383$	30.8910			1.57846			0.789229	−	0.614100i	$-0.210481\pi$
$383$	30.8910			1.57846			0.789229	+	0.614100i	$0.210481\pi$
$384$	−0.0927489	−	1.06025i	−0.00473307	−	0.0541055i
$385$	1.20985			0.0616599
$386$	5.79276	−	5.93901i	0.294844	−	0.302288i
$387$	−6.49774	−	6.49774i	−0.330298	−	0.330298i
$388$	−0.726557	−	29.1373i	−0.0368853	−	1.47922i
$389$	7.02095	−	7.02095i	0.355976	−	0.355976i	−0.506351	−	0.862327i	$-0.669006\pi$
$389$	7.02095	−	7.02095i	0.355976	−	0.355976i	0.862327	+	0.506351i	$0.169006\pi$
$390$	0.0212124		0.000264431i	0.00107413		1.33900e-5i
$391$		−	15.7119i		−	0.794584i
$392$	−4.45809	−	4.13654i	−0.225168	−	0.208927i
$393$			1.17031i			0.0590346i
$394$	0.0900245	+	7.22169i	0.00453537	+	0.363823i
$395$	12.2631	−	12.2631i	0.617023	−	0.617023i
$396$	−2.18519	+	2.29695i	−0.109810	+	0.115426i
$397$	−18.9996	−	18.9996i	−0.953562	−	0.953562i	0.0454070	−	0.998969i	$-0.485542\pi$
$397$	−18.9996	−	18.9996i	−0.953562	−	0.953562i	−0.998969	+	0.0454070i	$0.985542\pi$
$398$	−6.93709	−	6.76626i	−0.347725	−	0.339162i
$399$	−0.207167			−0.0103713
$400$	−0.782562	−	15.6819i	−0.0391281	−	0.784095i
$401$	−17.7571			−0.886746			−0.443373	−	0.896337i	$-0.646218\pi$
$401$	−17.7571			−0.886746			−0.443373	+	0.896337i	$0.646218\pi$
$402$	−0.507590	−	0.495091i	−0.0253163	−	0.0246929i
$403$	−0.325543	−	0.325543i	−0.0162164	−	0.0162164i
$404$	4.38551	+	4.17212i	0.218187	+	0.207571i
$405$	6.53888	−	6.53888i	0.324920	−	0.324920i
$406$	−0.284410	−	22.8151i	−0.0141150	−	1.13229i
$407$			4.46473i			0.221309i
$408$	0.0527306	+	1.40942i	0.00261055	+	0.0697764i
$409$			31.7861i			1.57172i	0.618403	+	0.785861i	$0.287780\pi$
$409$			31.7861i			1.57172i	−0.618403	+	0.785861i	$0.712220\pi$
$410$	−5.35246	+	0.0667230i	−0.264339	+	0.00329521i
$411$	−0.840129	+	0.840129i	−0.0414405	+	0.0414405i
$412$	7.24835	−	0.180742i	0.357101	−	0.00890451i
$413$	−17.5470	−	17.5470i	−0.863433	−	0.863433i
$414$	−8.75477	+	8.97579i	−0.430273	+	0.441136i
$415$	−4.27942			−0.210068
$416$	−0.868460	+	0.0541979i	−0.0425798	+	0.00265727i
$417$	1.60709			0.0786995
$418$	0.523306	−	0.536517i	0.0255957	−	0.0262419i
$419$	−23.0815	−	23.0815i	−1.12760	−	1.12760i	−0.990566	−	0.137038i	$-0.956242\pi$
$419$	−23.0815	−	23.0815i	−1.12760	−	1.12760i	−0.137038	−	0.990566i	$-0.543758\pi$
$420$	−0.429387	+	0.0107070i	−0.0209519	+	0.000522448i
$421$	2.49543	−	2.49543i	0.121620	−	0.121620i	−0.643677	−	0.765297i	$-0.722592\pi$
$421$	2.49543	−	2.49543i	0.121620	−	0.121620i	0.765297	+	0.643677i	$0.222592\pi$
$422$	−10.3186	+	0.128630i	−0.502301	+	0.00626161i
$423$		−	9.00323i		−	0.437752i
$424$	2.47605	−	0.0926366i	0.120248	−	0.00449883i
$425$			20.8075i			1.00931i
$426$	0.0159279	+	1.27772i	0.000771708	+	0.0619058i
$427$	16.2781	−	16.2781i	0.787755	−	0.787755i
$428$	2.79957	+	2.66334i	0.135322	+	0.128738i
$429$	−0.00542248	−	0.00542248i	−0.000261800	−	0.000261800i
$430$	3.22417	+	3.14478i	0.155483	+	0.151655i
$431$	−14.7359			−0.709804			−0.354902	−	0.934904i	$-0.615486\pi$
$431$	−14.7359			−0.709804			−0.354902	+	0.934904i	$0.615486\pi$
$432$	1.51266	−	1.67156i	0.0727778	−	0.0804229i
$433$	−7.51233			−0.361019			−0.180510	−	0.983573i	$-0.557775\pi$
$433$	−7.51233			−0.361019			−0.180510	+	0.983573i	$0.557775\pi$
$434$	6.67290	+	6.50858i	0.320309	+	0.312422i
$435$	0.505187	+	0.505187i	0.0242219	+	0.0242219i
$436$	−1.31854	+	1.38598i	−0.0631465	+	0.0663762i
$437$	2.09591	−	2.09591i	0.100261	−	0.100261i
$438$	0.0126304	+	1.01320i	0.000603505	+	0.0484126i
$439$		−	4.36345i		−	0.208256i	−0.994564	−	0.104128i	$-0.966795\pi$
$439$		−	4.36345i		−	0.208256i	0.994564	−	0.104128i	$-0.0332052\pi$
$440$	1.05690	−	1.13906i	0.0503859	−	0.0543027i
$441$		−	6.43146i		−	0.306260i
$442$	1.15303	−	0.0143735i	0.0548440	−	0.000683678i
$443$	−10.1677	+	10.1677i	−0.483081	+	0.483081i	−0.906114	−	0.423033i	$-0.860965\pi$
$443$	−10.1677	+	10.1677i	−0.483081	+	0.483081i	0.423033	+	0.906114i	$0.360965\pi$
$444$	−0.0395121	−	1.58457i	−0.00187516	−	0.0752002i
$445$	1.18128	+	1.18128i	0.0559979	+	0.0559979i
$446$	−1.41346	+	1.44915i	−0.0669295	+	0.0686192i
$447$	0.403738			0.0190961
$448$	17.5686	−	1.31644i	0.830040	−	0.0621957i
$449$	−6.21631			−0.293366			−0.146683	−	0.989184i	$-0.546860\pi$
$449$	−6.21631			−0.293366			−0.146683	+	0.989184i	$0.546860\pi$
$450$	11.5941	−	11.8868i	0.546549	−	0.560348i
$451$	1.36824	+	1.36824i	0.0644278	+	0.0644278i
$452$	0.0756061	+	3.03206i	0.00355621	+	0.142616i
$453$	1.21066	−	1.21066i	0.0568819	−	0.0568819i
$454$	23.4050	−	0.291764i	1.09845	−	0.0136932i
$455$			0.351168i			0.0164630i
$456$	−0.180977	+	0.195045i	−0.00847503	+	0.00913383i
$457$		−	39.6023i		−	1.85252i	−0.376887	−	0.926259i	$-0.623005\pi$
$457$		−	39.6023i		−	1.85252i	0.376887	−	0.926259i	$-0.376995\pi$
$458$	−0.279923	−	22.4552i	−0.0130799	−	1.04926i
$459$	−2.11248	+	2.11248i	−0.0986022	+	0.0986022i
$460$	4.23578	−	4.45243i	0.197494	−	0.207596i
$461$	1.56146	+	1.56146i	0.0727246	+	0.0727246i	0.742534	−	0.669809i	$-0.233624\pi$
$461$	1.56146	+	1.56146i	0.0727246	+	0.0727246i	−0.669809	+	0.742534i	$0.733624\pi$
$462$	0.111149	+	0.108412i	0.00517111	+	0.00504377i
$463$	1.80980			0.0841087			0.0420544	−	0.999115i	$-0.486610\pi$
$463$	1.80980			0.0841087			0.0420544	+	0.999115i	$0.486610\pi$
$464$	−21.7286	−	19.6630i	−1.00872	−	0.912834i
$465$	−0.291873			−0.0135353
$466$	−18.5547	−	18.0978i	−0.859531	−	0.838366i
$467$	−18.0310	−	18.0310i	−0.834377	−	0.834377i	0.153735	−	0.988112i	$-0.450870\pi$
$467$	−18.0310	−	18.0310i	−0.834377	−	0.834377i	−0.988112	+	0.153735i	$0.950870\pi$
$468$	−0.666705	−	0.634265i	−0.0308185	−	0.0293189i
$469$	8.29961	−	8.29961i	0.383240	−	0.383240i
$470$	0.0550042	+	4.41239i	0.00253716	+	0.203528i
$471$			0.984733i			0.0453741i
$472$	−31.8490	+	1.19157i	−1.46597	+	0.0548465i
$473$		−	1.62808i		−	0.0748592i
$474$	2.22546	−	0.0277423i	0.102219	−	0.00127425i
$475$	−2.77565	+	2.77565i	−0.127355	+	0.127355i
$476$	−23.3399	+	0.581994i	−1.06978	+	0.0266757i
$477$	1.85285	+	1.85285i	0.0848363	+	0.0848363i
$478$	22.2038	−	22.7644i	1.01558	−	1.04122i
$479$	31.4957			1.43908			0.719539	−	0.694452i	$-0.244353\pi$
$479$	31.4957			1.43908			0.719539	+	0.694452i	$0.244353\pi$
$480$	−0.365023	+	0.413615i	−0.0166609	+	0.0188789i
$481$	−1.29592			−0.0590887
$482$	5.22327	−	5.35514i	0.237913	−	0.243920i
$483$	0.434204	+	0.434204i	0.0197570	+	0.0197570i
$484$	21.4316	−	0.534411i	0.974165	−	0.0242914i
$485$	−10.6825	+	10.6825i	−0.485067	+	0.485067i
$486$	3.57760	−	0.0445979i	0.162283	−	0.00202300i
$487$			1.63167i			0.0739379i	0.999316	+	0.0369689i	$0.0117703\pi$
$487$			1.63167i			0.0739379i	−0.999316	+	0.0369689i	$0.988230\pi$
$488$	−1.10540	−	29.5459i	−0.0500393	−	1.33748i
$489$			0.443618i			0.0200611i
$490$	0.0392923	+	3.15199i	0.00177504	+	0.142392i
$491$	−15.3887	+	15.3887i	−0.694481	+	0.694481i	−0.963215	−	0.268734i	$-0.913395\pi$
$491$	−15.3887	+	15.3887i	−0.694481	+	0.694481i	0.268734	+	0.963215i	$0.413395\pi$
$492$	−0.497707	−	0.473489i	−0.0224384	−	0.0213466i
$493$	27.4601	+	27.4601i	1.23674	+	1.23674i
$494$	0.155728	+	0.151893i	0.00700652	+	0.00683398i
$495$	1.64327			0.0738593
$496$	11.9570	−	0.596683i	0.536887	−	0.0267919i
$497$	−21.1525			−0.948817
$498$	−0.393148	−	0.383467i	−0.0176174	−	0.0171836i
$499$	−27.6397	−	27.6397i	−1.23732	−	1.23732i	−0.961091	−	0.276233i	$-0.910914\pi$
$499$	−27.6397	−	27.6397i	−1.23732	−	1.23732i	−0.276233	−	0.961091i	$-0.589086\pi$
$500$	−12.7547	+	13.4071i	−0.570409	+	0.599583i
$501$	−0.904977	+	0.904977i	−0.0404314	+	0.0404314i
$502$	0.148462	+	11.9095i	0.00662619	+	0.531547i
$503$		−	8.78907i		−	0.391885i	−0.980615	−	0.195943i	$-0.937223\pi$
$503$		−	8.78907i		−	0.391885i	0.980615	−	0.195943i	$-0.0627767\pi$
$504$	13.6578	+	12.6727i	0.608366	+	0.564486i
$505$		−	3.13745i		−	0.139614i
$506$	−2.22129	+	0.0276903i	−0.0987486	+	0.00123099i
$507$	−0.863166	+	0.863166i	−0.0383346	+	0.0383346i
$508$	0.549862	+	22.0513i	0.0243962	+	0.978368i
$509$	−3.43493	−	3.43493i	−0.152250	−	0.152250i	0.626872	−	0.779122i	$-0.284335\pi$
$509$	−3.43493	−	3.43493i	−0.152250	−	0.152250i	−0.779122	+	0.626872i	$0.784335\pi$
$510$	0.510445	−	0.523331i	0.0226029	−	0.0231735i
$511$	−16.7734			−0.742011
$512$	14.1082	−	17.6906i	0.623500	−	0.781823i
$513$	−0.563596			−0.0248834
$514$	−14.3663	+	14.7290i	−0.633670	+	0.649668i
$515$	−2.65743	−	2.65743i	−0.117100	−	0.117100i
$516$	0.0144082	+	0.577818i	0.000634287	+	0.0254370i
$517$	1.12793	−	1.12793i	0.0496063	−	0.0496063i
$518$	26.2363	−	0.327058i	1.15276	−	0.0143701i
$519$			0.222009i			0.00974511i
$520$	0.330620	+	0.306773i	0.0144987	+	0.0134529i
$521$			29.0214i			1.27145i	0.771916	+	0.635725i	$0.219299\pi$
$521$			29.0214i			1.27145i	−0.771916	+	0.635725i	$0.780701\pi$
$522$	−0.386295	−	30.9882i	−0.0169077	−	1.35632i
$523$	13.9000	−	13.9000i	0.607805	−	0.607805i	−0.334567	−	0.942372i	$-0.608590\pi$
$523$	13.9000	−	13.9000i	0.607805	−	0.607805i	0.942372	+	0.334567i	$0.108590\pi$
$524$	−17.1498	+	18.0269i	−0.749192	+	0.787510i
$525$	−0.575023	−	0.575023i	−0.0250960	−	0.0250960i
$526$	31.4727	+	30.6977i	1.37228	+	1.33848i
$527$	−15.8652			−0.691097
$528$	0.199166	−	0.00993880i	0.00866757	−	0.000432531i
$529$	14.2143			0.618014
$530$	−0.919384	−	0.896744i	−0.0399355	−	0.0389521i
$531$	−23.8330	−	23.8330i	−1.03426	−	1.03426i
$532$	−3.19110	−	3.03583i	−0.138352	−	0.131620i
$533$	−0.397140	+	0.397140i	−0.0172020	+	0.0172020i
$534$	0.00267236	+	0.214375i	0.000115644	+	0.00927689i
$535$		−	2.00284i		−	0.0865904i
$536$	−0.563603	−	15.0643i	−0.0243440	−	0.650681i
$537$		−	1.87598i		−	0.0809544i
$538$	30.1370	−	0.375683i	1.29930	−	0.0161969i
$539$	0.805737	−	0.805737i	0.0347055	−	0.0347055i
$540$	−1.16814	+	0.0291283i	−0.0502688	+	0.00125348i
$541$	−1.87980	−	1.87980i	−0.0808190	−	0.0808190i	0.665542	−	0.746361i	$-0.268201\pi$
$541$	−1.87980	−	1.87980i	−0.0808190	−	0.0808190i	−0.746361	+	0.665542i	$0.768201\pi$
$542$	−7.41564	+	7.60286i	−0.318529	+	0.326571i
$543$	2.31418			0.0993109
$544$	−19.8413	+	22.4826i	−0.850690	+	0.963935i
$545$	0.991544			0.0424731
$546$	−0.0314672	+	0.0322616i	−0.00134667	+	0.00138067i
$547$	−26.2568	−	26.2568i	−1.12266	−	1.12266i	−0.991340	−	0.131322i	$-0.958078\pi$
$547$	−26.2568	−	26.2568i	−1.12266	−	1.12266i	−0.131322	−	0.991340i	$-0.541922\pi$
$548$	−25.2522	+	0.629678i	−1.07872	+	0.0268985i
$549$	22.1095	−	22.1095i	0.943612	−	0.943612i
$550$	2.94169	−	0.0366707i	0.125434	−	0.00156364i
$551$			7.32618i			0.312106i
$552$	0.788109	−	0.0294856i	0.0335442	−	0.00125499i
$553$			36.8422i			1.56669i
$554$	0.182419	+	14.6335i	0.00775025	+	0.621718i
$555$	−0.580943	+	0.580943i	−0.0246596	+	0.0246596i
$556$	24.7548	+	23.5503i	1.04984	+	0.998754i
$557$	2.69945	+	2.69945i	0.114379	+	0.114379i	0.761980	−	0.647601i	$-0.224227\pi$
$557$	2.69945	+	2.69945i	0.114379	+	0.114379i	−0.647601	+	0.761980i	$0.724227\pi$
$558$	9.06336	+	8.84017i	0.383682	+	0.374234i
$559$	0.472561			0.0199872
$560$	−6.77095	−	6.12730i	−0.286125	−	0.258926i
$561$	−0.264262			−0.0111571
$562$	23.9538	+	23.3639i	1.01043	+	0.985548i
$563$	−25.0025	−	25.0025i	−1.05373	−	1.05373i	−0.998472	−	0.0552581i	$-0.982402\pi$
$563$	−25.0025	−	25.0025i	−1.05373	−	1.05373i	−0.0552581	−	0.998472i	$-0.517598\pi$
$564$	−0.390329	+	0.410293i	−0.0164358	+	0.0172764i
$565$	1.11163	−	1.11163i	0.0467666	−	0.0467666i
$566$	0.236963	+	19.0090i	0.00996031	+	0.799007i
$567$			19.6449i			0.825008i
$568$	−18.4784	+	19.9148i	−0.775335	+	0.835605i
$569$		−	3.66861i		−	0.153796i	−0.997039	−	0.0768981i	$-0.975498\pi$
$569$		−	3.66861i		−	0.153796i	0.997039	−	0.0768981i	$-0.0245016\pi$
$570$	0.137902	−	0.00171907i	0.00577609	−	7.20039e-5i
$571$	−28.3952	+	28.3952i	−1.18830	+	1.18830i	−0.210765	+	0.977537i	$0.567595\pi$
$571$	−28.3952	+	28.3952i	−1.18830	+	1.18830i	−0.977537	+	0.210765i	$0.932405\pi$
$572$	−0.00406416	−	0.162986i	−0.000169931	−	0.00681480i
$573$	0.178305	+	0.178305i	0.00744878	+	0.00744878i
$574$	7.94002	−	8.14048i	0.331410	−	0.339777i
$575$	11.6350			0.485214
$576$	23.8623	−	1.78803i	0.994263	−	0.0745011i
$577$	1.69688			0.0706421			0.0353210	−	0.999376i	$-0.488755\pi$
$577$	1.69688			0.0706421			0.0353210	+	0.999376i	$0.488755\pi$
$578$	10.9591	−	11.2358i	0.455840	−	0.467348i
$579$	−0.390220	−	0.390220i	−0.0162170	−	0.0162170i
$580$	0.378638	+	15.1847i	0.0157221	+	0.630509i
$581$	6.42837	−	6.42837i	0.266694	−	0.266694i
$582$	−1.93862	+	0.0241666i	−0.0803585	+	0.00100174i
$583$			0.464253i			0.0192274i
$584$	−14.6529	+	15.7919i	−0.606341	+	0.653475i
$585$			0.476969i			0.0197202i
$586$	−0.451975	−	36.2570i	−0.0186709	−	1.49776i
$587$	25.4959	−	25.4959i	1.05233	−	1.05233i	0.0537739	−	0.998553i	$-0.482875\pi$
$587$	25.4959	−	25.4959i	1.05233	−	1.05233i	0.998553	−	0.0537739i	$-0.0171250\pi$
$588$	−0.278832	+	0.293093i	−0.0114988	+	0.0120869i
$589$	−2.11636	−	2.11636i	−0.0872030	−	0.0872030i
$590$	11.8259	+	11.5347i	0.486865	+	0.474876i
$591$	0.480413			0.0197616
$592$	22.6116	−	24.9869i	0.929332	−	1.02695i
$593$	−19.5748			−0.803840			−0.401920	−	0.915675i	$-0.631657\pi$
$593$	−19.5748			−0.803840			−0.401920	+	0.915675i	$0.631657\pi$
$594$	0.302379	+	0.294933i	0.0124067	+	0.0121012i
$595$	8.55700	+	8.55700i	0.350803	+	0.350803i
$596$	6.21897	+	5.91637i	0.254739	+	0.242344i
$597$	−0.455798	+	0.455798i	−0.0186546	+	0.0186546i
$598$	−0.00803730	−	0.644745i	−0.000328670	−	0.0263656i
$599$		−	33.8132i		−	1.38157i	−0.723061	−	0.690784i	$-0.757265\pi$
$599$		−	33.8132i		−	1.38157i	0.723061	−	0.690784i	$-0.242735\pi$
$600$	−1.04370	+	0.0390482i	−0.0426091	+	0.00159414i
$601$			13.0421i			0.532000i	0.963973	+	0.266000i	$0.0857021\pi$
$601$			13.0421i			0.532000i	−0.963973	+	0.266000i	$0.914298\pi$
$602$	−9.56717	+	0.119263i	−0.389929	+	0.00486080i
$603$	11.2728	−	11.2728i	0.459064	−	0.459064i
$604$	36.3895	−	0.907393i	1.48067	−	0.0369213i
$605$	−7.85738	−	7.85738i	−0.319448	−	0.319448i
$606$	0.281138	−	0.288236i	0.0114204	−	0.0117088i
$607$	25.2159			1.02348			0.511740	−	0.859140i	$-0.329001\pi$
$607$	25.2159			1.02348			0.511740	+	0.859140i	$0.329001\pi$
$608$	−5.64587	+	0.352341i	−0.228970	+	0.0142893i
$609$	−1.51774			−0.0615021
$610$	−10.7006	+	10.9707i	−0.433254	+	0.444192i
$611$	0.327389	+	0.327389i	0.0132447	+	0.0132447i
$612$	−31.7010	+	0.790484i	−1.28144	+	0.0319534i
$613$	9.82549	−	9.82549i	0.396848	−	0.396848i	−0.480272	−	0.877120i	$-0.659462\pi$
$613$	9.82549	−	9.82549i	0.396848	−	0.396848i	0.877120	+	0.480272i	$0.159462\pi$
$614$	11.9984	−	0.149570i	0.484214	−	0.00603614i
$615$			0.356065i			0.0143579i
$616$	0.123414	+	3.29869i	0.00497250	+	0.132908i
$617$			42.2303i			1.70013i	0.526679	+	0.850064i	$0.323437\pi$
$617$			42.2303i			1.70013i	−0.526679	+	0.850064i	$0.676563\pi$
$618$	−0.00601180	−	0.482262i	−0.000241830	−	0.0193994i
$619$	−29.8531	+	29.8531i	−1.19990	+	1.19990i	−0.225701	+	0.974197i	$0.572467\pi$
$619$	−29.8531	+	29.8531i	−1.19990	+	1.19990i	−0.974197	+	0.225701i	$0.927533\pi$
$620$	−4.49586	−	4.27711i	−0.180558	−	0.171773i
$621$	1.18125	+	1.18125i	0.0474018	+	0.0474018i
$622$	16.7159	+	16.3043i	0.670247	+	0.653742i
$623$	−3.54894			−0.142185
$624$	0.00288480	+	0.0578091i	0.000115484	+	0.00231422i
$625$	−10.0352			−0.401407
$626$	17.6501	+	17.2154i	0.705438	+	0.688067i
$627$	−0.0352516	−	0.0352516i	−0.00140781	−	0.00140781i
$628$	−14.4303	+	15.1683i	−0.575830	+	0.605282i
$629$	−31.5779	+	31.5779i	−1.25909	+	1.25909i
$630$	−0.120375	−	9.65641i	−0.00479587	−	0.384721i
$631$			24.0295i			0.956599i	0.878197	+	0.478300i	$0.158747\pi$
$631$			24.0295i			0.956599i	−0.878197	+	0.478300i	$0.841253\pi$
$632$	34.6865	+	32.1846i	1.37975	+	1.28024i
$633$			0.686430i			0.0272831i
$634$	−24.4874	+	0.305256i	−0.972518	+	0.0121233i
$635$	8.08456	−	8.08456i	0.320826	−	0.320826i
$636$	−0.00410856	−	0.164767i	−0.000162915	−	0.00653344i
$637$	0.233870	+	0.233870i	0.00926628	+	0.00926628i
$638$	3.83383	−	3.93062i	0.151783	−	0.155615i
$639$	−28.7300			−1.13654
$640$	−11.6837	+	1.02208i	−0.461841	+	0.0404012i
$641$	−17.6714			−0.697980			−0.348990	−	0.937127i	$-0.613475\pi$
$641$	−17.6714			−0.697980			−0.348990	+	0.937127i	$0.613475\pi$
$642$	0.179469	−	0.184000i	0.00708308	−	0.00726190i
$643$	−1.32146	−	1.32146i	−0.0521134	−	0.0521134i	0.680570	−	0.732683i	$-0.261732\pi$
$643$	−1.32146	−	1.32146i	−0.0521134	−	0.0521134i	−0.732683	+	0.680570i	$0.761732\pi$
$644$	0.325436	+	13.0511i	0.0128240	+	0.514285i
$645$	0.211843	−	0.211843i	0.00834130	−	0.00834130i
$646$	7.49586	−	0.0934423i	0.294921	−	0.00367644i
$647$			11.5047i			0.452296i	0.974093	+	0.226148i	$0.0726133\pi$
$647$			11.5047i			0.452296i	−0.974093	+	0.226148i	$0.927387\pi$
$648$	18.4954	+	17.1614i	0.726568	+	0.674163i
$649$		−	5.97162i		−	0.234407i
$650$	0.0106439	+	0.853845i	0.000417489	+	0.0334906i
$651$	0.438440	−	0.438440i	0.0171838	−	0.0171838i
$652$	−6.50077	+	6.83326i	−0.254590	+	0.267611i
$653$	10.0700	+	10.0700i	0.394071	+	0.394071i	0.876136	−	0.482065i	$-0.160113\pi$
$653$	10.0700	+	10.0700i	0.394071	+	0.394071i	−0.482065	+	0.876136i	$0.660113\pi$
$654$	0.0910926	+	0.0888495i	0.00356200	+	0.00347429i
$655$	12.8967			0.503915
$656$	−0.727913	−	14.5868i	−0.0284202	−	0.569518i
$657$	−22.7822			−0.888818
$658$	−6.71074	−	6.54549i	−0.261612	−	0.255170i
$659$	5.82941	+	5.82941i	0.227082	+	0.227082i	0.811472	−	0.584391i	$-0.198666\pi$
$659$	5.82941	+	5.82941i	0.227082	+	0.227082i	−0.584391	+	0.811472i	$0.698666\pi$
$660$	−0.0748865	−	0.0712427i	−0.00291495	−	0.00277312i
$661$	−18.7946	+	18.7946i	−0.731023	+	0.731023i	−0.970823	−	0.239799i	$-0.922918\pi$
$661$	−18.7946	+	18.7946i	−0.731023	+	0.731023i	0.239799	+	0.970823i	$0.422918\pi$
$662$	0.536102	+	43.0056i	0.0208362	+	1.67146i
$663$		−	0.0767037i		−	0.00297893i
$664$	−0.436533	−	11.6679i	−0.0169408	−	0.452803i
$665$			2.28295i			0.0885290i
$666$	35.6351	−	0.444222i	1.38083	−	0.0172132i
$667$	15.3550	−	15.3550i	0.594549	−	0.594549i
$668$	−27.2013	+	0.678281i	−1.05245	+	0.0262435i
$669$	0.0952158	+	0.0952158i	0.00368125	+	0.00368125i
$670$	−5.45582	+	5.59356i	−0.210777	+	0.216098i
$671$	5.53979			0.213861
$672$	−0.0729935	−	1.16964i	−0.00281579	−	0.0451198i
$673$	32.5576			1.25500			0.627502	−	0.778615i	$-0.284077\pi$
$673$	32.5576			1.25500			0.627502	+	0.778615i	$0.284077\pi$
$674$	−2.63170	+	2.69814i	−0.101369	+	0.103928i
$675$	−1.56434	−	1.56434i	−0.0602115	−	0.0602115i
$676$	−25.9446	+	0.646944i	−0.997870	+	0.0248825i
$677$	−3.63087	+	3.63087i	−0.139546	+	0.139546i	−0.773429	−	0.633883i	$-0.781460\pi$
$677$	−3.63087	+	3.63087i	−0.139546	+	0.139546i	0.633883	+	0.773429i	$0.281460\pi$
$678$	0.201735	−	0.00251480i	0.00774758	−	9.65802e-5i
$679$		−	32.0936i		−	1.23164i
$680$	15.5315	−	0.581082i	0.595607	−	0.0222835i
$681$		−	1.55699i		−	0.0596639i
$682$	0.0279605	+	2.24296i	0.00107066	+	0.0858875i
$683$	−13.2932	+	13.2932i	−0.508651	+	0.508651i	−0.914112	−	0.405461i	$-0.867111\pi$
$683$	−13.2932	+	13.2932i	−0.508651	+	0.508651i	0.405461	+	0.914112i	$0.367111\pi$
$684$	−4.33426	−	4.12336i	−0.165725	−	0.157661i
$685$	9.25808	+	9.25808i	0.353733	+	0.353733i
$686$	−20.4004	−	19.8981i	−0.778892	−	0.759712i
$687$	−1.49380			−0.0569920
$688$	−8.24540	+	9.11156i	−0.314353	+	0.347375i
$689$	−0.134752			−0.00513366
$690$	−0.292634	−	0.285428i	−0.0111404	−	0.0108660i
$691$	15.8971	+	15.8971i	0.604756	+	0.604756i	0.941571	−	0.336815i	$-0.109350\pi$
$691$	15.8971	+	15.8971i	0.604756	+	0.604756i	−0.336815	+	0.941571i	$0.609350\pi$
$692$	−3.25332	+	3.41971i	−0.123673	+	0.129998i
$693$	−2.46845	+	2.46845i	−0.0937686	+	0.0937686i
$694$	−0.569822	−	45.7106i	−0.0216302	−	1.73515i
$695$		−	17.7099i		−	0.671773i
$696$	−1.32587	+	1.42894i	−0.0502570	+	0.0541637i
$697$			19.3544i			0.733101i
$698$	−31.6955	+	0.395112i	−1.19969	+	0.0149552i
$699$	−1.21913	+	1.21913i	−0.0461118	+	0.0461118i
$700$	−0.430980	−	17.2837i	−0.0162895	−	0.653264i
$701$	−20.5172	−	20.5172i	−0.774922	−	0.774922i	0.204040	−	0.978962i	$-0.434593\pi$
$701$	−20.5172	−	20.5172i	−0.774922	−	0.774922i	−0.978962	+	0.204040i	$0.934593\pi$
$702$	−0.0856061	+	0.0877674i	−0.00323100	+	0.00331257i
$703$	−8.42477			−0.317746
$704$	3.21349	+	2.76548i	0.121113	+	0.104228i
$705$	0.293528			0.0110549
$706$	4.45987	−	4.57247i	0.167850	−	0.172087i
$707$	4.71294	+	4.71294i	0.177248	+	0.177248i
$708$	0.0528478	+	2.11937i	0.00198614	+	0.0796509i
$709$	9.35449	−	9.35449i	0.351315	−	0.351315i	−0.509283	−	0.860599i	$-0.670090\pi$
$709$	9.35449	−	9.35449i	0.351315	−	0.351315i	0.860599	+	0.509283i	$0.170090\pi$
$710$	14.0803	−	0.175523i	0.528423	−	0.00658725i
$711$			50.0404i			1.87666i
$712$	−3.10028	+	3.34128i	−0.116188	+	0.125220i
$713$			8.87140i			0.332236i
$714$	0.0193582	+	1.55290i	0.000724462	+	0.0581157i
$715$	−0.0597549	+	0.0597549i	−0.00223471	+	0.00223471i
$716$	27.4906	−	28.8966i	1.02737	−	1.07992i
$717$	−1.49573	−	1.49573i	−0.0558589	−	0.0558589i
$718$	11.1186	+	10.8448i	0.414941	+	0.404723i
$719$	−46.7189			−1.74232			−0.871161	−	0.490998i	$-0.836632\pi$
$719$	−46.7189			−1.74232			−0.871161	+	0.490998i	$0.836632\pi$
$720$	−9.19654	−	8.32231i	−0.342735	−	0.310154i
$721$	7.98376			0.297331
$722$	1.01239	+	0.987457i	0.0376772	+	0.0367494i
$723$	−0.351857	−	0.351857i	−0.0130857	−	0.0130857i
$724$	35.6464	+	33.9120i	1.32479	+	1.26033i
$725$	−20.3349	+	20.3349i	−0.755218	+	0.755218i
$726$	−0.0177755	−	1.42593i	−0.000659710	−	0.0529213i
$727$		−	53.3053i		−	1.97698i	−0.151273	−	0.988492i	$-0.548337\pi$
$727$		−	53.3053i		−	1.97698i	0.151273	−	0.988492i	$-0.451663\pi$
$728$	−0.957467	+	0.0358218i	−0.0354861	+	0.00132764i
$729$			26.5233i			0.982345i
$730$	11.1653	−	0.139185i	0.413247	−	0.00515148i
$731$	11.5150	−	11.5150i	0.425898	−	0.425898i
$732$	−1.96611	+	0.0490262i	−0.0726697	+	0.00181206i
$733$	20.0646	+	20.0646i	0.741104	+	0.741104i	0.972791	−	0.231686i	$-0.0744243\pi$
$733$	20.0646	+	20.0646i	0.741104	+	0.741104i	−0.231686	+	0.972791i	$0.574424\pi$
$734$	26.7216	−	27.3962i	0.986311	−	1.01121i
$735$	0.209682			0.00773424
$736$	12.5717	+	11.0948i	0.463400	+	0.408959i
$737$	2.82453			0.104043
$738$	10.7844	−	11.0567i	0.396979	−	0.407002i
$739$	13.6203	+	13.6203i	0.501031	+	0.501031i	0.911758	−	0.410727i	$-0.134725\pi$
$739$	13.6203	+	13.6203i	0.501031	+	0.501031i	−0.410727	+	0.911758i	$0.634725\pi$
$740$	−17.4617	+	0.435417i	−0.641904	+	0.0160063i
$741$	0.0102320	−	0.0102320i	0.000375883	−	0.000375883i
$742$	2.72811	−	0.0340083i	0.100152	−	0.00124848i
$743$		−	16.1126i		−	0.591114i	−0.955325	−	0.295557i	$-0.904495\pi$
$743$		−	16.1126i		−	0.591114i	0.955325	−	0.295557i	$-0.0955053\pi$
$744$	−0.0297732	−	0.795798i	−0.00109154	−	0.0291754i
$745$		−	4.44912i		−	0.163003i
$746$	−0.177612	−	14.2479i	−0.00650285	−	0.521653i
$747$	8.73123	−	8.73123i	0.319459	−	0.319459i
$748$	−4.07056	−	3.87249i	−0.148834	−	0.141592i
$749$	3.00859	+	3.00859i	0.109931	+	0.109931i
$750$	0.881175	+	0.859476i	0.0321760	+	0.0313836i
$751$	33.5770			1.22524			0.612622	−	0.790376i	$-0.290115\pi$
$751$	33.5770			1.22524			0.612622	+	0.790376i	$0.290115\pi$
$752$	−12.0249	+	0.600067i	−0.438501	+	0.0218822i
$753$	0.792264			0.0288717
$754$	1.14089	+	1.11279i	0.0415487	+	0.0405256i
$755$	−13.3413	−	13.3413i	−0.485540	−	0.485540i
$756$	1.71098	−	1.79849i	0.0622277	−	0.0654104i
$757$	31.3525	−	31.3525i	1.13953	−	1.13953i	0.150993	−	0.988535i	$-0.451753\pi$
$757$	31.3525	−	31.3525i	1.13953	−	1.13953i	0.988535	−	0.150993i	$-0.0482470\pi$
$758$	0.536308	+	43.0222i	0.0194796	+	1.56264i
$759$			0.147769i			0.00536366i
$760$	2.14937	+	1.99434i	0.0779657	+	0.0723422i
$761$		−	35.9431i		−	1.30294i	−0.758676	−	0.651468i	$-0.774153\pi$
$761$		−	35.9431i		−	1.30294i	0.758676	−	0.651468i	$-0.225847\pi$
$762$	1.46716	−	0.0182894i	0.0531496	−	0.000662555i
$763$	−1.48946	+	1.48946i	−0.0539220	+	0.0539220i
$764$	0.133639	+	5.35939i	0.00483491	+	0.193896i
$765$	11.6224	+	11.6224i	0.420209	+	0.420209i
$766$	30.5036	−	31.2737i	1.10214	−	1.12996i
$767$	1.73330			0.0625859
$768$	−1.16497	−	0.953051i	−0.0420371	−	0.0343903i
$769$	51.0126			1.83956			0.919780	−	0.392434i	$-0.128367\pi$
$769$	51.0126			1.83956			0.919780	+	0.392434i	$0.128367\pi$
$770$	1.19468	−	1.22484i	0.0430533	−	0.0441402i
$771$	0.967762	+	0.967762i	0.0348531	+	0.0348531i
$772$	−0.292470	−	11.7290i	−0.0105262	−	0.422137i
$773$	21.8399	−	21.8399i	0.785527	−	0.785527i	−0.195230	−	0.980757i	$-0.562545\pi$
$773$	21.8399	−	21.8399i	0.785527	−	0.785527i	0.980757	+	0.195230i	$0.0625455\pi$
$774$	−12.9945	+	0.161987i	−0.467076	+	0.00582251i
$775$		−	11.7485i		−	0.422019i
$776$	−30.2157	−	28.0363i	−1.08468	−	1.00645i
$777$		−	1.74534i		−	0.0626136i
$778$	−0.175031	−	14.0408i	−0.00627516	−	0.503387i
$779$	−2.58181	+	2.58181i	−0.0925030	+	0.0925030i
$780$	0.0206786	−	0.0217363i	0.000740414	−	0.000778284i
$781$	−3.59931	−	3.59931i	−0.128793	−	0.128793i
$782$	−15.9065	−	15.5148i	−0.568816	−	0.554809i
$783$	−4.12900			−0.147558
$784$	−8.58996	+	0.428658i	−0.306784	+	0.0153092i
$785$	10.8516			0.387310
$786$	1.18481	+	1.15564i	0.0422608	+	0.0412202i
$787$	−1.35256	−	1.35256i	−0.0482135	−	0.0482135i	0.682589	−	0.730802i	$-0.260854\pi$
$787$	−1.35256	−	1.35256i	−0.0482135	−	0.0482135i	−0.730802	+	0.682589i	$0.760854\pi$
$788$	7.40004	+	7.03997i	0.263616	+	0.250789i
$789$	2.06790	−	2.06790i	0.0736193	−	0.0736193i
$790$	−0.305716	−	24.5243i	−0.0108769	−	0.872534i
$791$			3.33969i			0.118746i
$792$	0.167625	+	4.48040i	0.00595631	+	0.159204i
$793$			1.60796i			0.0571003i
$794$	−37.9962	+	0.473655i	−1.34843	+	0.0168094i
$795$	−0.0604078	+	0.0604078i	−0.00214244	+	0.00214244i
$796$	−13.7002	+	0.341621i	−0.485589	+	0.0121085i
$797$	9.29408	+	9.29408i	0.329213	+	0.329213i	0.852287	−	0.523074i	$-0.175215\pi$
$797$	9.29408	+	9.29408i	0.329213	+	0.329213i	−0.523074	+	0.852287i	$0.675215\pi$
$798$	−0.204569	+	0.209733i	−0.00724166	+	0.00742448i
$799$	15.9551			0.564452
$800$	−16.6489	−	14.6930i	−0.588628	−	0.519475i
$801$	−4.82029			−0.170316
$802$	−17.5344	+	17.9770i	−0.619159	+	0.634791i
$803$	−2.85417	−	2.85417i	−0.100721	−	0.100721i
$804$	−1.00245	+	0.0249966i	−0.0353536	+	0.000881562i
$805$	4.78486	−	4.78486i	0.168644	−	0.168644i
$806$	−0.651035	+	0.00811571i	−0.0229317	+	0.000285864i
$807$		−	2.00482i		−	0.0705730i
$808$	8.55431	−	0.320043i	0.300940	−	0.0112591i
$809$		−	31.2755i		−	1.09959i	−0.835300	−	0.549795i	$-0.814706\pi$
$809$		−	31.2755i		−	1.09959i	0.835300	−	0.549795i	$-0.185294\pi$
$810$	−0.163013	−	13.0767i	−0.00572769	−	0.459470i
$811$	15.1481	−	15.1481i	0.531923	−	0.531923i	−0.389222	−	0.921144i	$-0.627256\pi$
$811$	15.1481	−	15.1481i	0.531923	−	0.531923i	0.921144	+	0.389222i	$0.127256\pi$
$812$	−23.3786	−	22.2410i	−0.820426	−	0.780506i
$813$	0.499543	+	0.499543i	0.0175197	+	0.0175197i
$814$	4.52004	+	4.40873i	0.158427	+	0.154526i
$815$	4.88859			0.171240
$816$	1.47894	+	1.33835i	0.0517734	+	0.0468517i
$817$	3.07212			0.107480
$818$	32.1799	+	31.3874i	1.12514	+	1.09744i
$819$	−0.716483	−	0.716483i	−0.0250359	−	0.0250359i
$820$	−5.21778	+	5.48465i	−0.182213	+	0.191532i
$821$	−12.5687	+	12.5687i	−0.438652	+	0.438652i	−0.891558	−	0.452906i	$-0.850387\pi$
$821$	−12.5687	+	12.5687i	−0.438652	+	0.438652i	0.452906	+	0.891558i	$0.350387\pi$
$822$	0.0209442	+	1.68013i	0.000730514	+	0.0586012i
$823$			22.2997i			0.777318i	0.921382	+	0.388659i	$0.127062\pi$
$823$			22.2997i			0.777318i	−0.921382	+	0.388659i	$0.872938\pi$
$824$	6.97446	−	7.51661i	0.242967	−	0.261854i
$825$		−	0.195692i		−	0.00681312i
$826$	−35.0913	+	0.437444i	−1.22098	+	0.0152206i
$827$	2.77394	−	2.77394i	0.0964594	−	0.0964594i	−0.657230	−	0.753690i	$-0.728272\pi$
$827$	2.77394	−	2.77394i	0.0964594	−	0.0964594i	0.753690	+	0.657230i	$0.228272\pi$
$828$	0.442019	+	17.7264i	0.0153612	+	0.616036i
$829$	−39.8947	−	39.8947i	−1.38560	−	1.38560i	−0.834324	−	0.551275i	$-0.814141\pi$
$829$	−39.8947	−	39.8947i	−1.38560	−	1.38560i	−0.551275	−	0.834324i	$-0.685859\pi$
$830$	−4.22574	+	4.33243i	−0.146678	+	0.150381i
$831$	0.973474			0.0337695
$832$	−0.802698	+	0.932736i	−0.0278285	+	0.0323368i
$833$	11.3976			0.394902
$834$	1.58693	−	1.62700i	0.0549510	−	0.0563383i
$835$	9.97270	+	9.97270i	0.345120	+	0.345120i
$836$	−0.0264211	−	1.05958i	−0.000913794	−	0.0366462i
$837$	1.19277	−	1.19277i	0.0412282	−	0.0412282i
$838$	−46.1593	+	0.575416i	−1.59455	+	0.0198774i
$839$		−	11.1851i		−	0.386153i	−0.981184	−	0.193076i	$-0.938153\pi$
$839$		−	11.1851i		−	0.386153i	0.981184	−	0.193076i	$-0.0618465\pi$
$840$	−0.413161	+	0.445278i	−0.0142554	+	0.0153636i
$841$			24.6729i			0.850789i
$842$	−0.0622105	−	4.99047i	−0.00214392	−	0.171983i
$843$	1.57387	−	1.57387i	0.0542071	−	0.0542071i
$844$	−10.0589	+	10.5734i	−0.346243	+	0.363952i
$845$	9.51195	+	9.51195i	0.327221	+	0.327221i
$846$	−9.11475	−	8.89031i	−0.313372	−	0.305655i
$847$	23.6061			0.811115
$848$	2.35121	−	2.59819i	0.0807408	−	0.0892223i
$849$	1.26455			0.0433991
$850$	21.0652	+	20.5465i	0.722531	+	0.704739i
$851$	17.6576	+	17.6576i	0.605294	+	0.605294i
$852$	1.30928	+	1.24557i	0.0448550	+	0.0426725i
$853$	22.7440	−	22.7440i	0.778741	−	0.778741i	−0.200876	−	0.979617i	$-0.564379\pi$
$853$	22.7440	−	22.7440i	0.778741	−	0.778741i	0.979617	+	0.200876i	$0.0643788\pi$
$854$	−0.405811	−	32.5538i	−0.0138866	−	1.11397i
$855$			3.10078i			0.106044i
$856$	5.46079	−	0.204305i	0.186646	−	0.00698300i
$857$			51.9578i			1.77484i	0.460957	+	0.887422i	$0.347506\pi$
$857$			51.9578i			1.77484i	−0.460957	+	0.887422i	$0.652494\pi$
$858$	−0.0108441		0.000135181i	−0.000370212		4.61501e-6i
$859$	−34.0606	+	34.0606i	−1.16213	+	1.16213i	−0.178125	+	0.984008i	$0.557003\pi$
$859$	−34.0606	+	34.0606i	−1.16213	+	1.16213i	−0.984008	+	0.178125i	$0.942997\pi$
$860$	6.36746	−	0.158776i	0.217129	−	0.00541423i
$861$	−0.534867	−	0.534867i	−0.0182282	−	0.0182282i
$862$	−14.5511	+	14.9184i	−0.495612	+	0.508124i
$863$	−26.7788			−0.911560			−0.455780	−	0.890092i	$-0.650640\pi$
$863$	−26.7788			−0.911560			−0.455780	+	0.890092i	$0.650640\pi$
$864$	−0.198578	−	3.18199i	−0.00675576	−	0.108253i
$865$	2.44650			0.0831836
$866$	−7.41811	+	7.60539i	−0.252077	+	0.258442i
$867$	−0.738245	−	0.738245i	−0.0250721	−	0.0250721i
$868$	13.1784	−	0.328611i	0.447304	−	0.0111538i
$869$	−6.26909	+	6.26909i	−0.212664	+	0.212664i
$870$	1.01030	−	0.0125942i	0.0342522	−	0.000426983i
$871$			0.819838i			0.0277791i
$872$	0.101145	+	2.70346i	0.00342520	+	0.0915508i
$873$		−	43.5906i		−	1.47532i
$874$	−0.0522506	−	4.19150i	−0.00176740	−	0.141780i
$875$	−14.4081	+	14.4081i	−0.487083	+	0.487083i
$876$	1.03822	+	0.987706i	0.0350783	+	0.0333715i
$877$	−16.1864	−	16.1864i	−0.546576	−	0.546576i	0.378873	−	0.925449i	$-0.376312\pi$
$877$	−16.1864	−	16.1864i	−0.546576	−	0.546576i	−0.925449	+	0.378873i	$0.876312\pi$
$878$	−4.41750	−	4.30872i	−0.149083	−	0.145412i
$879$	−2.41195			−0.0813531
$880$	−0.109524	−	2.19477i	−0.00369205	−	0.0739858i
$881$	−8.61613			−0.290285			−0.145142	−	0.989411i	$-0.546364\pi$
$881$	−8.61613			−0.290285			−0.145142	+	0.989411i	$0.546364\pi$
$882$	−6.51113	−	6.35079i	−0.219241	−	0.213842i
$883$	−2.50438	−	2.50438i	−0.0842792	−	0.0842792i	0.663710	−	0.747990i	$-0.268981\pi$
$883$	−2.50438	−	2.50438i	−0.0842792	−	0.0842792i	−0.747990	+	0.663710i	$0.768981\pi$
$884$	1.12402	−	1.18151i	0.0378048	−	0.0397383i
$885$	0.777016	−	0.777016i	0.0261191	−	0.0261191i
$886$	0.253478	+	20.3338i	0.00851575	+	0.683126i
$887$			26.7175i			0.897087i	0.893761	+	0.448544i	$0.148057\pi$
$887$			26.7175i			0.897087i	−0.893761	+	0.448544i	$0.851943\pi$
$888$	−1.64321	−	1.52469i	−0.0551426	−	0.0511653i
$889$			24.2886i			0.814613i
$890$	2.36237	−	0.0294490i	0.0791869	−	0.000987133i
$891$	−3.34278	+	3.34278i	−0.111987	+	0.111987i
$892$	0.0713643	+	2.86195i	0.00238945	+	0.0958251i
$893$	2.12836	+	2.12836i	0.0712228	+	0.0712228i
$894$	0.398674	−	0.408739i	0.0133336	−	0.0136703i
$895$	−20.6730			−0.691021
$896$	16.0155	−	19.0862i	0.535041	−	0.637624i
$897$	−0.0428908			−0.00143208
$898$	−6.13835	+	6.29332i	−0.204839	+	0.210011i
$899$	−15.5048	−	15.5048i	−0.517114	−	0.517114i
$900$	−0.585372	−	23.4754i	−0.0195124	−	0.782512i
$901$	−3.28355	+	3.28355i	−0.109391	+	0.109391i
$902$	2.73626	−	0.0341099i	0.0911076	−	0.00113573i
$903$			0.636443i			0.0211795i
$904$	3.14427	+	2.91749i	0.104577	+	0.0970341i
$905$		−	25.5019i		−	0.847711i
$906$	−0.0301815	−	2.42114i	−0.00100271	−	0.0804369i
$907$	−23.0537	+	23.0537i	−0.765485	+	0.765485i	−0.977308	−	0.211823i	$-0.932060\pi$
$907$	−23.0537	+	23.0537i	−0.765485	+	0.765485i	0.211823	+	0.977308i	$0.432060\pi$
$908$	22.8161	−	23.9831i	0.757179	−	0.795906i
$909$	6.40128	+	6.40128i	0.212317	+	0.212317i
$910$	0.355518	+	0.346764i	0.0117853	+	0.0114951i
$911$	20.2595			0.671227			0.335614	−	0.942000i	$-0.391056\pi$
$911$	20.2595			0.671227			0.335614	+	0.942000i	$0.391056\pi$
$912$	0.0187541	+	0.375818i	0.000621011	+	0.0124446i
$913$	2.18771			0.0724025
$914$	−40.0929	−	39.1056i	−1.32615	−	1.29350i
$915$	0.720827	+	0.720827i	0.0238298	+	0.0238298i
$916$	−23.0097	−	21.8901i	−0.760263	−	0.723270i
$917$	−19.3729	+	19.3729i	−0.639748	+	0.639748i
$918$	0.0526637	+	4.22463i	0.00173816	+	0.139434i
$919$		−	47.2146i		−	1.55747i	−0.627356	−	0.778733i	$-0.715863\pi$
$919$		−	47.2146i		−	1.55747i	0.627356	−	0.778733i	$-0.284137\pi$
$920$	−0.324926	−	8.68484i	−0.0107125	−	0.286331i
$921$		−	0.798174i		−	0.0263007i
$922$	3.12269	−	0.0389270i	0.102840	−	0.00128199i
$923$	1.04472	−	1.04472i	0.0343875	−	0.0343875i
$924$	0.219509	−	0.00547359i	0.00722133	−	0.000180068i
$925$	−23.3842	−	23.3842i	−0.768867	−	0.768867i
$926$	1.78710	−	1.83222i	0.0587279	−	0.0602106i
$927$	10.8438			0.356158
$928$	−41.3626	+	2.58131i	−1.35780	+	0.0847358i
$929$	25.1806			0.826149			0.413075	−	0.910697i	$-0.364455\pi$
$929$	25.1806			0.826149			0.413075	+	0.910697i	$0.364455\pi$
$930$	−0.288212	+	0.295489i	−0.00945085	+	0.00968945i
$931$	1.52039	+	1.52039i	0.0498289	+	0.0498289i
$932$	−36.6440	+	0.913740i	−1.20031	+	0.0299306i
$933$	1.09831	−	1.09831i	0.0359571	−	0.0359571i
$934$	−36.0593	+	0.449510i	−1.17990	+	0.0147084i
$935$			2.91212i			0.0952366i
$936$	−1.30046	+	0.0486544i	−0.0425070	+	0.00159032i
$937$		−	42.0901i		−	1.37502i	−0.726173	−	0.687512i	$-0.758703\pi$
$937$		−	42.0901i		−	1.37502i	0.726173	−	0.687512i	$-0.241297\pi$
$938$	−0.206907	−	16.5979i	−0.00675577	−	0.541942i
$939$	1.15969	−	1.15969i	0.0378451	−	0.0378451i
$940$	4.52136	+	4.30136i	0.147471	+	0.140295i
$941$	28.4457	+	28.4457i	0.927304	+	0.927304i	0.997531	−	0.0702272i	$-0.0223724\pi$
$941$	28.4457	+	28.4457i	0.927304	+	0.927304i	−0.0702272	+	0.997531i	$0.522372\pi$
$942$	0.996931	+	0.972382i	0.0324818	+	0.0316819i
$943$	10.8225			0.352429
$944$	−30.2432	+	33.4202i	−0.984334	+	1.08773i
$945$	−1.28666			−0.0418550
$946$	−1.64825	−	1.60766i	−0.0535891	−	0.0522695i
$947$	28.4422	+	28.4422i	0.924246	+	0.924246i	0.997326	−	0.0730797i	$-0.0232827\pi$
$947$	28.4422	+	28.4422i	0.924246	+	0.924246i	−0.0730797	+	0.997326i	$0.523283\pi$
$948$	2.16947	−	2.28043i	0.0704610	−	0.0740648i
$949$	0.828440	−	0.828440i	0.0268923	−	0.0268923i
$950$	0.0691962	+	5.55086i	0.00224502	+	0.180094i
$951$			1.62899i			0.0528236i
$952$	−22.4580	+	24.2037i	−0.727866	+	0.784447i
$953$			15.0965i			0.489025i	0.969646	+	0.244512i	$0.0786279\pi$
$953$			15.0965i			0.489025i	−0.969646	+	0.244512i	$0.921372\pi$
$954$	3.70542	−	0.0461912i	0.119967	−	0.00149550i
$955$	1.96489	−	1.96489i	0.0635823	−	0.0635823i
$956$	−1.12105	−	44.9578i	−0.0362573	−	1.45404i
$957$	−0.258260	−	0.258260i	−0.00834835	−	0.00834835i
$958$	31.1007	−	31.8859i	1.00482	−	1.03019i
$959$	−27.8142			−0.898169
$960$	0.0582943	+	0.777972i	0.00188144	+	0.0251089i
$961$	−22.0421			−0.711034
$962$	−1.27966	+	1.31197i	−0.0412580	+	0.0422996i
$963$	4.08637	+	4.08637i	0.131681	+	0.131681i
$964$	−0.263717	−	10.5759i	−0.00849376	−	0.340628i
$965$	−4.30016	+	4.30016i	−0.138427	+	0.138427i
$966$	0.868341	−	0.0108246i	0.0279384	−	0.000348276i
$967$			0.250748i			0.00806352i	0.999992	+	0.00403176i	$0.00128335\pi$
$967$			0.250748i			0.00806352i	−0.999992	+	0.00403176i	$0.998717\pi$
$968$	20.6218	−	22.2248i	0.662810	−	0.714333i
$969$		−	0.498652i		−	0.0160190i
$970$	0.266312	+	21.3633i	0.00855077	+	0.685935i
$971$	37.0140	−	37.0140i	1.18784	−	1.18784i	0.210173	−	0.977664i	$-0.432597\pi$
$971$	37.0140	−	37.0140i	1.18784	−	1.18784i	0.977664	−	0.210173i	$-0.0674027\pi$
$972$	3.48758	−	3.66596i	0.111864	−	0.117586i
$973$	26.6030	+	26.6030i	0.852854	+	0.852854i
$974$	1.65188	+	1.61120i	0.0529296	+	0.0516262i
$975$	0.0568009			0.00181908
$976$	−31.0035	−	28.0563i	−0.992397	−	0.898059i
$977$	−28.2790			−0.904726			−0.452363	−	0.891834i	$-0.649419\pi$
$977$	−28.2790			−0.904726			−0.452363	+	0.891834i	$0.649419\pi$
$978$	0.449113	+	0.438053i	0.0143610	+	0.0140074i
$979$	−0.603888	−	0.603888i	−0.0193004	−	0.0193004i
$980$	3.22984	+	3.07268i	0.103173	+	0.0981531i
$981$	−2.02303	+	2.02303i	−0.0645904	+	0.0645904i
$982$	0.383636	+	30.7749i	0.0122423	+	0.982068i
$983$			51.7389i			1.65021i	0.564976	+	0.825107i	$0.308886\pi$
$983$			51.7389i			1.65021i	−0.564976	+	0.825107i	$0.691114\pi$
$984$	−0.970819	+	0.0363213i	−0.0309486	+	0.00115788i
$985$		−	5.29408i		−	0.168683i
$986$	54.9160	−	0.684575i	1.74888	−	0.0218013i
$987$	−0.440926	+	0.440926i	−0.0140348	+	0.0140348i
$988$	0.307549	−	0.00766891i	0.00978443	−	0.000243980i
$989$	−6.43890	−	6.43890i	−0.204745	−	0.204745i
$990$	1.62266	−	1.66362i	0.0515714	−	0.0528734i
$991$	33.8140			1.07414			0.537068	−	0.843539i	$-0.319532\pi$
$991$	33.8140			1.07414			0.537068	+	0.843539i	$0.319532\pi$
$992$	11.2030	−	12.6944i	0.355696	−	0.403046i
$993$	2.86089			0.0907876
$994$	−20.8872	+	21.4145i	−0.662500	+	0.679226i
$995$	5.02283	+	5.02283i	0.159234	+	0.159234i
$996$	−0.776434	+	0.0193608i	−0.0246023	+	0.000613472i
$997$	−24.4783	+	24.4783i	−0.775237	+	0.775237i	−0.979017	−	0.203780i	$-0.934677\pi$
$997$	−24.4783	+	24.4783i	−0.775237	+	0.775237i	0.203780	+	0.979017i	$0.434677\pi$
$998$	−55.2752	+	0.689052i	−1.74970	+	0.0218116i
$999$		−	4.74817i		−	0.150225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.77.25	✓	68
4.3	odd	2		1216.2.k.b.913.20		68
16.5	even	4	inner	304.2.k.b.229.25	yes	68
16.11	odd	4		1216.2.k.b.305.20		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.25	✓	68	1.1	even	1	trivial
304.2.k.b.229.25	yes	68	16.5	even	4	inner
1216.2.k.b.305.20		68	16.11	odd	4
1216.2.k.b.913.20		68	4.3	odd	2

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987457 - 1.01239i) q^{2} +(-0.0665185 - 0.0665185i) q^{3} +(-0.0498557 - 1.99938i) q^{4} +(-0.733023 + 0.733023i) q^{5} +(-0.133027 + 0.00165829i) q^{6} -2.20223i q^{7} +(-2.07338 - 1.92383i) q^{8} -2.99115i q^{9} +O(q^{10})\)	\(q+(0.987457 - 1.01239i) q^{2} +(-0.0665185 - 0.0665185i) q^{3} +(-0.0498557 - 1.99938i) q^{4} +(-0.733023 + 0.733023i) q^{5} +(-0.133027 + 0.00165829i) q^{6} -2.20223i q^{7} +(-2.07338 - 1.92383i) q^{8} -2.99115i q^{9} +(0.0182741 + 1.46593i) q^{10} +(0.374733 - 0.374733i) q^{11} +(-0.129679 + 0.136312i) q^{12} +(0.108769 + 0.108769i) q^{13} +(-2.22951 - 2.17461i) q^{14} +0.0975191 q^{15} +(-3.99503 + 0.199361i) q^{16} +5.30079 q^{17} +(-3.02820 - 2.95363i) q^{18} +(0.707107 + 0.707107i) q^{19} +(1.50214 + 1.42904i) q^{20} +(-0.146489 + 0.146489i) q^{21} +(-0.00934201 - 0.749408i) q^{22} -2.96407i q^{23} +(0.00994768 + 0.265888i) q^{24} +3.92535i q^{25} +(0.217520 - 0.00271158i) q^{26} +(-0.398522 + 0.398522i) q^{27} +(-4.40310 + 0.109794i) q^{28} +(5.18039 + 5.18039i) q^{29} +(0.0962960 - 0.0987271i) q^{30} -2.99298 q^{31} +(-3.74309 + 4.24138i) q^{32} -0.0498533 q^{33} +(5.23430 - 5.36645i) q^{34} +(1.61429 + 1.61429i) q^{35} +(-5.98044 + 0.149126i) q^{36} +(-5.95722 + 5.95722i) q^{37} +(1.41410 - 0.0176280i) q^{38} -0.0144703i q^{39} +(2.93004 - 0.109622i) q^{40} +3.65123i q^{41} +(0.00365195 + 0.292956i) q^{42} +(2.17232 - 2.17232i) q^{43} +(-0.767916 - 0.730551i) q^{44} +(2.19258 + 2.19258i) q^{45} +(-3.00078 - 2.92689i) q^{46} +3.00996 q^{47} +(0.279004 + 0.252482i) q^{48} +2.15016 q^{49} +(3.97398 + 3.87612i) q^{50} +(-0.352600 - 0.352600i) q^{51} +(0.212047 - 0.222893i) q^{52} +(-0.619445 + 0.619445i) q^{53} +(0.00993507 + 0.796983i) q^{54} +0.549376i q^{55} +(-4.23672 + 4.56606i) q^{56} -0.0940713i q^{57} +(10.3600 - 0.129146i) q^{58} +(7.96783 - 7.96783i) q^{59} +(-0.00486188 - 0.194978i) q^{60} +(7.39165 + 7.39165i) q^{61} +(-2.95544 + 3.03006i) q^{62} -6.58722 q^{63} +(0.597772 + 7.97764i) q^{64} -0.159460 q^{65} +(-0.0492281 + 0.0504709i) q^{66} +(3.76872 + 3.76872i) q^{67} +(-0.264274 - 10.5983i) q^{68} +(-0.197165 + 0.197165i) q^{69} +(3.22833 - 0.0402439i) q^{70} -9.60500i q^{71} +(-5.75446 + 6.20178i) q^{72} -7.61653i q^{73} +(0.148512 + 11.9135i) q^{74} +(0.261109 - 0.261109i) q^{75} +(1.37852 - 1.44903i) q^{76} +(-0.825250 - 0.825250i) q^{77} +(-0.0146495 - 0.0142888i) q^{78} -16.7295 q^{79} +(2.78231 - 3.07458i) q^{80} -8.92043 q^{81} +(3.69646 + 3.60544i) q^{82} +(2.91902 + 2.91902i) q^{83} +(0.300191 + 0.285584i) q^{84} +(-3.88560 + 3.88560i) q^{85} +(-0.0541554 - 4.34430i) q^{86} -0.689183i q^{87} +(-1.49788 + 0.0560405i) q^{88} -1.61152i q^{89} +(4.38482 - 0.0546606i) q^{90} +(0.239534 - 0.239534i) q^{91} +(-5.92629 + 0.147776i) q^{92} +(0.199089 + 0.199089i) q^{93} +(2.97220 - 3.04724i) q^{94} -1.03665 q^{95} +(0.531115 - 0.0331452i) q^{96} +14.5732 q^{97} +(2.12319 - 2.17680i) q^{98} +(-1.12088 - 1.12088i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

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