LMFDB - Embedded newform 368.2.j.e.93.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(93,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, 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("368.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.j (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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			93.5
Character	$\chi$	$=$	368.93
Dual form			368.2.j.e.277.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18490 + 0.772024i) q^{2} +(-1.82824 - 1.82824i) q^{3} +(0.807958 - 1.82954i) q^{4} +(2.39711 - 2.39711i) q^{5} +(3.57771 + 0.754828i) q^{6} -3.25556i q^{7} +(0.455100 + 2.79157i) q^{8} +3.68490i q^{9} +(-0.989698 + 4.69094i) q^{10} +(3.63984 - 3.63984i) q^{11} +(-4.82197 + 1.86769i) q^{12} +(3.29801 + 3.29801i) q^{13} +(2.51337 + 3.85750i) q^{14} -8.76496 q^{15} +(-2.69441 - 2.95638i) q^{16} -2.56873 q^{17} +(-2.84483 - 4.36623i) q^{18} +(-0.481432 - 0.481432i) q^{19} +(-2.44883 - 6.32235i) q^{20} +(-5.95194 + 5.95194i) q^{21} +(-1.50279 + 7.12288i) q^{22} +1.00000i q^{23} +(4.27163 - 5.93569i) q^{24} -6.49223i q^{25} +(-6.45394 - 1.36166i) q^{26} +(1.25216 - 1.25216i) q^{27} +(-5.95617 - 2.63036i) q^{28} +(0.0920153 + 0.0920153i) q^{29} +(10.3856 - 6.76676i) q^{30} +8.50086 q^{31} +(5.47499 + 1.42285i) q^{32} -13.3090 q^{33} +(3.04368 - 1.98312i) q^{34} +(-7.80393 - 7.80393i) q^{35} +(6.74166 + 2.97725i) q^{36} +(0.196808 - 0.196808i) q^{37} +(0.942123 + 0.198770i) q^{38} -12.0591i q^{39} +(7.78262 + 5.60077i) q^{40} -4.27014i q^{41} +(2.45739 - 11.6475i) q^{42} +(-2.01239 + 2.01239i) q^{43} +(-3.71838 - 9.60006i) q^{44} +(8.83310 + 8.83310i) q^{45} +(-0.772024 - 1.18490i) q^{46} -10.0961 q^{47} +(-0.478940 + 10.3310i) q^{48} -3.59868 q^{49} +(5.01216 + 7.69262i) q^{50} +(4.69625 + 4.69625i) q^{51} +(8.69848 - 3.36918i) q^{52} +(-5.08525 + 5.08525i) q^{53} +(-0.516983 + 2.45038i) q^{54} -17.4502i q^{55} +(9.08814 - 1.48161i) q^{56} +1.76034i q^{57} +(-0.180067 - 0.0379906i) q^{58} +(-10.2860 + 10.2860i) q^{59} +(-7.08171 + 16.0358i) q^{60} +(6.92061 + 6.92061i) q^{61} +(-10.0726 + 6.56287i) q^{62} +11.9964 q^{63} +(-7.58577 + 2.54089i) q^{64} +15.8114 q^{65} +(15.7698 - 10.2749i) q^{66} +(10.3605 + 10.3605i) q^{67} +(-2.07543 + 4.69959i) q^{68} +(1.82824 - 1.82824i) q^{69} +(15.2717 + 3.22202i) q^{70} +3.95374i q^{71} +(-10.2867 + 1.67700i) q^{72} +0.262477i q^{73} +(-0.0812565 + 0.385137i) q^{74} +(-11.8693 + 11.8693i) q^{75} +(-1.26977 + 0.491820i) q^{76} +(-11.8497 - 11.8497i) q^{77} +(9.30990 + 14.2888i) q^{78} -13.6866 q^{79} +(-13.5455 - 0.627965i) q^{80} +6.47620 q^{81} +(3.29665 + 5.05967i) q^{82} +(-0.820880 - 0.820880i) q^{83} +(6.08038 + 15.6982i) q^{84} +(-6.15752 + 6.15752i) q^{85} +(0.830859 - 3.93808i) q^{86} -0.336452i q^{87} +(11.8174 + 8.50439i) q^{88} -1.90031i q^{89} +(-17.2857 - 3.64694i) q^{90} +(10.7369 - 10.7369i) q^{91} +(1.82954 + 0.807958i) q^{92} +(-15.5416 - 15.5416i) q^{93} +(11.9628 - 7.79443i) q^{94} -2.30809 q^{95} +(-7.40827 - 12.6109i) q^{96} +10.1437 q^{97} +(4.26407 - 2.77827i) q^{98} +(13.4125 + 13.4125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 2 q^{2} + 6 q^{3} + 4 q^{5} + 2 q^{8} - 10 q^{10} + 4 q^{11} - 16 q^{12} + 2 q^{13} + 28 q^{14} - 12 q^{15} - 8 q^{16} - 16 q^{17} - 34 q^{18} + 4 q^{19} + 18 q^{20} - 28 q^{22} - 30 q^{24} + 2 q^{26}+ \cdots - 28 q^{99}+O(q^{100}) $ 46 * q + 2 * q^2 + 6 * q^3 + 4 * q^5 + 2 * q^8 - 10 * q^10 + 4 * q^11 - 16 * q^12 + 2 * q^13 + 28 * q^14 - 12 * q^15 - 8 * q^16 - 16 * q^17 - 34 * q^18 + 4 * q^19 + 18 * q^20 - 28 * q^22 - 30 * q^24 + 2 * q^26 - 26 * q^28 + 2 * q^29 + 56 * q^30 + 40 * q^31 - 8 * q^32 + 60 * q^33 + 10 * q^34 + 8 * q^35 + 50 * q^36 + 24 * q^37 - 56 * q^38 + 10 * q^42 - 8 * q^43 - 50 * q^44 + 12 * q^45 - 2 * q^46 + 20 * q^47 - 110 * q^49 - 44 * q^51 + 24 * q^52 + 20 * q^53 - 64 * q^54 - 8 * q^56 - 2 * q^58 - 54 * q^59 - 90 * q^60 - 8 * q^61 + 18 * q^62 + 24 * q^63 - 6 * q^64 + 28 * q^65 + 6 * q^66 + 42 * q^68 - 6 * q^69 - 58 * q^70 + 90 * q^72 + 6 * q^74 - 30 * q^75 - 44 * q^76 - 28 * q^77 + 44 * q^78 + 16 * q^79 - 52 * q^80 - 26 * q^81 - 62 * q^82 + 28 * q^83 + 170 * q^84 - 12 * q^85 - 92 * q^86 + 64 * q^88 + 140 * q^90 + 48 * q^91 - 4 * q^92 - 48 * q^93 + 52 * q^94 - 56 * q^96 + 72 * q^97 - 44 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.18490	+	0.772024i	−0.837848	+	0.545903i
$2$	−1.18490	+	0.772024i	−0.837848	+	0.545903i
$3$	−1.82824	−	1.82824i	−1.05553	−	1.05553i	−0.998365	−	0.0571687i	$-0.981793\pi$
$3$	−1.82824	−	1.82824i	−1.05553	−	1.05553i	−0.0571687	−	0.998365i	$-0.518207\pi$
$4$	0.807958	−	1.82954i	0.403979	−	0.914768i
$5$	2.39711	−	2.39711i	1.07202	−	1.07202i	0.0748213	−	0.997197i	$-0.476161\pi$
$5$	2.39711	−	2.39711i	1.07202	−	1.07202i	0.997197	−	0.0748213i	$-0.0238386\pi$
$6$	3.57771	+	0.754828i	1.46060	+	0.308157i
$7$		−	3.25556i		−	1.23049i	−0.788337	−	0.615243i	$-0.789058\pi$
$7$		−	3.25556i		−	1.23049i	0.788337	−	0.615243i	$-0.210942\pi$
$8$	0.455100	+	2.79157i	0.160902	+	0.986970i
$9$			3.68490i			1.22830i
$10$	−0.989698	+	4.69094i	−0.312970	+	1.48341i
$11$	3.63984	−	3.63984i	1.09745	−	1.09745i	0.102745	−	0.994708i	$-0.467237\pi$
$11$	3.63984	−	3.63984i	1.09745	−	1.09745i	0.994708	−	0.102745i	$-0.0327627\pi$
$12$	−4.82197	+	1.86769i	−1.39198	+	0.539155i
$13$	3.29801	+	3.29801i	0.914703	+	0.914703i	0.996638	−	0.0819345i	$-0.0261098\pi$
$13$	3.29801	+	3.29801i	0.914703	+	0.914703i	−0.0819345	+	0.996638i	$0.526110\pi$
$14$	2.51337	+	3.85750i	0.671727	+	1.03096i
$15$	−8.76496			−2.26310
$16$	−2.69441	−	2.95638i	−0.673602	−	0.739094i
$17$	−2.56873			−0.623009			−0.311505	−	0.950245i	$-0.600833\pi$
$17$	−2.56873			−0.623009			−0.311505	+	0.950245i	$0.600833\pi$
$18$	−2.84483	−	4.36623i	−0.670534	−	1.02913i
$19$	−0.481432	−	0.481432i	−0.110448	−	0.110448i	0.649723	−	0.760171i	$-0.274885\pi$
$19$	−0.481432	−	0.481432i	−0.110448	−	0.110448i	−0.760171	+	0.649723i	$0.774885\pi$
$20$	−2.44883	−	6.32235i	−0.547576	−	1.41372i
$21$	−5.95194	+	5.95194i	−1.29882	+	1.29882i
$22$	−1.50279	+	7.12288i	−0.320396	+	1.51860i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	4.27163	−	5.93569i	0.871942	−	1.21162i
$25$		−	6.49223i		−	1.29845i
$26$	−6.45394	−	1.36166i	−1.26572	−	0.267043i
$27$	1.25216	−	1.25216i	0.240979	−	0.240979i
$28$	−5.95617	−	2.63036i	−1.12561	−	0.497091i
$29$	0.0920153	+	0.0920153i	0.0170868	+	0.0170868i	0.715599	−	0.698512i	$-0.246154\pi$
$29$	0.0920153	+	0.0920153i	0.0170868	+	0.0170868i	−0.698512	+	0.715599i	$0.746154\pi$
$30$	10.3856	−	6.76676i	1.89614	−	1.23544i
$31$	8.50086			1.52680			0.763400	−	0.645926i	$-0.223529\pi$
$31$	8.50086			1.52680			0.763400	+	0.645926i	$0.223529\pi$
$32$	5.47499	+	1.42285i	0.967850	+	0.251527i
$33$	−13.3090			−2.31680
$34$	3.04368	−	1.98312i	0.521987	−	0.340103i
$35$	−7.80393	−	7.80393i	−1.31910	−	1.31910i
$36$	6.74166	+	2.97725i	1.12361	+	0.496208i
$37$	0.196808	−	0.196808i	0.0323550	−	0.0323550i	−0.690744	−	0.723099i	$-0.742717\pi$
$37$	0.196808	−	0.196808i	0.0323550	−	0.0323550i	0.723099	+	0.690744i	$0.242717\pi$
$38$	0.942123	+	0.198770i	0.152833	+	0.0322447i
$39$		−	12.0591i		−	1.93100i
$40$	7.78262	+	5.60077i	1.23054	+	0.885560i
$41$		−	4.27014i		−	0.666883i	−0.942771	−	0.333442i	$-0.891790\pi$
$41$		−	4.27014i		−	0.666883i	0.942771	−	0.333442i	$-0.108210\pi$
$42$	2.45739	−	11.6475i	0.379183	−	1.79724i
$43$	−2.01239	+	2.01239i	−0.306886	+	0.306886i	−0.843700	−	0.536814i	$-0.819628\pi$
$43$	−2.01239	+	2.01239i	−0.306886	+	0.306886i	0.536814	+	0.843700i	$0.319628\pi$
$44$	−3.71838	−	9.60006i	−0.560567	−	1.44726i
$45$	8.83310	+	8.83310i	1.31676	+	1.31676i
$46$	−0.772024	−	1.18490i	−0.113829	−	0.174703i
$47$	−10.0961			−1.47267			−0.736334	−	0.676618i	$-0.763445\pi$
$47$	−10.0961			−1.47267			−0.736334	+	0.676618i	$0.763445\pi$
$48$	−0.478940	+	10.3310i	−0.0691290	+	1.49115i
$49$	−3.59868			−0.514098
$50$	5.01216	+	7.69262i	0.708826	+	1.08790i
$51$	4.69625	+	4.69625i	0.657607	+	0.657607i
$52$	8.69848	−	3.36918i	1.20626	−	0.467221i
$53$	−5.08525	+	5.08525i	−0.698512	+	0.698512i	−0.964090	−	0.265577i	$-0.914437\pi$
$53$	−5.08525	+	5.08525i	−0.698512	+	0.698512i	0.265577	+	0.964090i	$0.414437\pi$
$54$	−0.516983	+	2.45038i	−0.0703525	+	0.333455i
$55$		−	17.4502i		−	2.35298i
$56$	9.08814	−	1.48161i	1.21445	−	0.197988i
$57$			1.76034i			0.233163i
$58$	−0.180067	−	0.0379906i	−0.0236439	−	0.00498840i
$59$	−10.2860	+	10.2860i	−1.33912	+	1.33912i	−0.442205	+	0.896914i	$0.645804\pi$
$59$	−10.2860	+	10.2860i	−1.33912	+	1.33912i	−0.896914	+	0.442205i	$0.854196\pi$
$60$	−7.08171	+	16.0358i	−0.914245	+	2.07021i
$61$	6.92061	+	6.92061i	0.886093	+	0.886093i	0.994145	−	0.108052i	$-0.0344614\pi$
$61$	6.92061	+	6.92061i	0.886093	+	0.886093i	−0.108052	+	0.994145i	$0.534461\pi$
$62$	−10.0726	+	6.56287i	−1.27923	+	0.833485i
$63$	11.9964			1.51141
$64$	−7.58577	+	2.54089i	−0.948221	+	0.317611i
$65$	15.8114			1.96116
$66$	15.7698	−	10.2749i	1.94112	−	1.26475i
$67$	10.3605	+	10.3605i	1.26574	+	1.26574i	0.948267	+	0.317473i	$0.102834\pi$
$67$	10.3605	+	10.3605i	1.26574	+	1.26574i	0.317473	+	0.948267i	$0.397166\pi$
$68$	−2.07543	+	4.69959i	−0.251683	+	0.569909i
$69$	1.82824	−	1.82824i	0.220094	−	0.220094i
$70$	15.2717	+	3.22202i	1.82531	+	0.385105i
$71$			3.95374i			0.469222i	0.972089	+	0.234611i	$0.0753816\pi$
$71$			3.95374i			0.469222i	−0.972089	+	0.234611i	$0.924618\pi$
$72$	−10.2867	+	1.67700i	−1.21230	+	0.197636i
$73$			0.262477i			0.0307206i	0.999882	+	0.0153603i	$0.00488953\pi$
$73$			0.262477i			0.0307206i	−0.999882	+	0.0153603i	$0.995110\pi$
$74$	−0.0812565	+	0.385137i	−0.00944587	+	0.0447713i
$75$	−11.8693	+	11.8693i	−1.37055	+	1.37055i
$76$	−1.26977	+	0.491820i	−0.145653	+	0.0564157i
$77$	−11.8497	−	11.8497i	−1.35040	−	1.35040i
$78$	9.30990	+	14.2888i	1.05414	+	1.61788i
$79$	−13.6866			−1.53987			−0.769933	−	0.638125i	$-0.779710\pi$
$79$	−13.6866			−1.53987			−0.769933	+	0.638125i	$0.779710\pi$
$80$	−13.5455	−	0.627965i	−1.51444	−	0.0702086i
$81$	6.47620			0.719578
$82$	3.29665	+	5.05967i	0.364054	+	0.558747i
$83$	−0.820880	−	0.820880i	−0.0901033	−	0.0901033i	0.660619	−	0.750722i	$-0.270294\pi$
$83$	−0.820880	−	0.820880i	−0.0901033	−	0.0901033i	−0.750722	+	0.660619i	$0.770294\pi$
$84$	6.08038	+	15.6982i	0.663423	+	1.71281i
$85$	−6.15752	+	6.15752i	−0.667877	+	0.667877i
$86$	0.830859	−	3.93808i	0.0895938	−	0.424654i
$87$		−	0.336452i		−	0.0360714i
$88$	11.8174	+	8.50439i	1.25974	+	0.906571i
$89$		−	1.90031i		−	0.201433i	−0.994915	−	0.100716i	$-0.967887\pi$
$89$		−	1.90031i		−	0.201433i	0.994915	−	0.100716i	$-0.0321135\pi$
$90$	−17.2857	−	3.64694i	−1.82207	−	0.384421i
$91$	10.7369	−	10.7369i	1.12553	−	1.12553i
$92$	1.82954	+	0.807958i	0.190742	+	0.0842354i
$93$	−15.5416	−	15.5416i	−1.61159	−	1.61159i
$94$	11.9628	−	7.79443i	1.23387	−	0.803934i
$95$	−2.30809			−0.236805
$96$	−7.40827	−	12.6109i	−0.756103	−	1.28709i
$97$	10.1437			1.02993			0.514966	−	0.857210i	$-0.327804\pi$
$97$	10.1437			1.02993			0.514966	+	0.857210i	$0.327804\pi$
$98$	4.26407	−	2.77827i	0.430736	−	0.280648i
$99$	13.4125	+	13.4125i	1.34800	+	1.34800i
$100$	−11.8778	−	5.24545i	−1.18778	−	0.524545i
$101$	11.8566	−	11.8566i	1.17977	−	1.17977i	0.199969	−	0.979802i	$-0.435916\pi$
$101$	11.8566	−	11.8566i	1.17977	−	1.17977i	0.979802	−	0.199969i	$-0.0640841\pi$
$102$	−9.19019	−	1.93895i	−0.909964	−	0.191985i
$103$		−	6.70435i		−	0.660599i	−0.943876	−	0.330300i	$-0.892850\pi$
$103$		−	6.70435i		−	0.660599i	0.943876	−	0.330300i	$-0.107150\pi$
$104$	−7.70571	+	10.7076i	−0.755607	+	1.04996i
$105$			28.5349i			2.78472i
$106$	2.09956	−	9.95142i	0.203927	−	0.966568i
$107$	0.482697	−	0.482697i	0.0466641	−	0.0466641i	−0.683390	−	0.730054i	$-0.739495\pi$
$107$	0.482697	−	0.482697i	0.0466641	−	0.0466641i	0.730054	+	0.683390i	$0.239495\pi$
$108$	−1.27918	−	3.30257i	−0.123089	−	0.317790i
$109$	6.86136	+	6.86136i	0.657199	+	0.657199i	0.954716	−	0.297518i	$-0.0961587\pi$
$109$	6.86136	+	6.86136i	0.657199	+	0.657199i	−0.297518	+	0.954716i	$0.596159\pi$
$110$	13.4719	+	20.6766i	1.28450	+	1.97144i
$111$	−0.719623			−0.0683036
$112$	−9.62467	+	8.77181i	−0.909446	+	0.828859i
$113$	−8.50457			−0.800042			−0.400021	−	0.916506i	$-0.630997\pi$
$113$	−8.50457			−0.800042			−0.400021	+	0.916506i	$0.630997\pi$
$114$	−1.35903	−	2.08582i	−0.127285	−	0.195355i
$115$	2.39711	+	2.39711i	0.223531	+	0.223531i
$116$	0.242690	−	0.0940009i	0.0225332	−	0.00872777i
$117$	−12.1528	+	12.1528i	−1.12353	+	1.12353i
$118$	4.24679	−	20.1288i	0.390949	−	1.85301i
$119$			8.36267i			0.766605i
$120$	−3.98893	−	24.4680i	−0.364138	−	2.23361i
$121$		−	15.4969i		−	1.40881i
$122$	−13.5431	−	2.85733i	−1.22613	−	0.258690i
$123$	−7.80682	+	7.80682i	−0.703917	+	0.703917i
$124$	6.86833	−	15.5526i	0.616795	−	1.39667i
$125$	−3.57704	−	3.57704i	−0.319940	−	0.319940i
$126$	−14.2145	+	9.26153i	−1.26633	+	0.825083i
$127$	−1.59635			−0.141653			−0.0708266	−	0.997489i	$-0.522564\pi$
$127$	−1.59635			−0.141653			−0.0708266	+	0.997489i	$0.522564\pi$
$128$	7.02672	−	8.86709i	0.621080	−	0.783747i
$129$	7.35824			0.647857
$130$	−18.7348	+	12.2067i	−1.64315	+	1.07060i
$131$	7.27006	+	7.27006i	0.635188	+	0.635188i	0.949365	−	0.314176i	$-0.101728\pi$
$131$	7.27006	+	7.27006i	0.635188	+	0.635188i	−0.314176	+	0.949365i	$0.601728\pi$
$132$	−10.7531	+	24.3493i	−0.935937	+	2.11933i
$133$	−1.56733	+	1.56733i	−0.135905	+	0.135905i
$134$	−20.2747	−	4.27758i	−1.75147	−	0.369526i
$135$		−	6.00313i		−	0.516668i
$136$	−1.16903	−	7.17081i	−0.100244	−	0.614892i
$137$			11.3853i			0.972715i	0.873760	+	0.486357i	$0.161675\pi$
$137$			11.3853i			0.972715i	−0.873760	+	0.486357i	$0.838325\pi$
$138$	−0.754828	+	3.57771i	−0.0642552	+	0.304555i
$139$	16.3606	−	16.3606i	1.38769	−	1.38769i	0.557535	−	0.830153i	$-0.311747\pi$
$139$	16.3606	−	16.3606i	1.38769	−	1.38769i	0.830153	−	0.557535i	$-0.188253\pi$
$140$	−20.5828	+	7.97233i	−1.73957	+	0.673785i
$141$	18.4581	+	18.4581i	1.55445	+	1.55445i
$142$	−3.05238	−	4.68477i	−0.256150	−	0.393137i
$143$	24.0085			2.00769
$144$	10.8940	−	9.92863i	0.907830	−	0.827386i
$145$	0.441141			0.0366348
$146$	−0.202638	−	0.311008i	−0.0167705	−	0.0257392i
$147$	6.57925	+	6.57925i	0.542647	+	0.542647i
$148$	−0.201055	−	0.519080i	−0.0165266	−	0.0426681i
$149$	6.17590	−	6.17590i	0.505949	−	0.505949i	−0.407331	−	0.913280i	$-0.633541\pi$
$149$	6.17590	−	6.17590i	0.505949	−	0.505949i	0.913280	+	0.407331i	$0.133541\pi$
$150$	4.90052	−	23.2274i	0.400126	−	1.89651i
$151$		−	7.29289i		−	0.593487i	−0.954957	−	0.296744i	$-0.904099\pi$
$151$		−	7.29289i		−	0.593487i	0.954957	−	0.296744i	$-0.0959006\pi$
$152$	1.12485	−	1.56305i	0.0912376	−	0.126780i
$153$		−	9.46553i		−	0.765243i
$154$	23.1890	+	4.89242i	1.86862	+	0.394243i
$155$	20.3775	−	20.3775i	1.63676	−	1.63676i
$156$	−22.0625	−	9.74323i	−1.76642	−	0.780083i
$157$	−3.37778	−	3.37778i	−0.269576	−	0.269576i	0.559353	−	0.828929i	$-0.311050\pi$
$157$	−3.37778	−	3.37778i	−0.269576	−	0.269576i	−0.828929	+	0.559353i	$0.811050\pi$
$158$	16.2172	−	10.5664i	1.29017	−	0.840618i
$159$	18.5941			1.47461
$160$	16.5349	−	9.71340i	1.30719	−	0.767912i
$161$	3.25556			0.256574
$162$	−7.67363	+	4.99978i	−0.602897	+	0.392820i
$163$	5.87038	+	5.87038i	0.459803	+	0.459803i	0.898591	−	0.438788i	$-0.144592\pi$
$163$	5.87038	+	5.87038i	0.459803	+	0.459803i	−0.438788	+	0.898591i	$0.644592\pi$
$164$	−7.81237	−	3.45009i	−0.610043	−	0.269407i
$165$	−31.9030	+	31.9030i	−2.48365	+	2.48365i
$166$	1.60640	+	0.338918i	0.124681	+	0.0263052i
$167$		−	6.00128i		−	0.464393i	−0.972669	−	0.232197i	$-0.925409\pi$
$167$		−	6.00128i		−	0.464393i	0.972669	−	0.232197i	$-0.0745912\pi$
$168$	−19.3240	−	13.9065i	−1.49088	−	1.07291i
$169$			8.75373i			0.673364i
$170$	2.54227	−	12.0498i	0.194983	−	0.924176i
$171$	1.77403	−	1.77403i	0.135663	−	0.135663i
$172$	2.05581	+	5.30766i	0.156754	+	0.404705i
$173$	−17.0750	−	17.0750i	−1.29819	−	1.29819i	−0.929589	−	0.368597i	$-0.879838\pi$
$173$	−17.0750	−	17.0750i	−1.29819	−	1.29819i	−0.368597	−	0.929589i	$-0.620162\pi$
$174$	0.259749	+	0.398660i	0.0196915	+	0.0302224i
$175$	−21.1359			−1.59772
$176$	−20.5680	−	0.953522i	−1.55037	−	0.0718744i
$177$	37.6104			2.82697
$178$	1.46709	+	2.25167i	0.109963	+	0.168770i
$179$	6.86959	+	6.86959i	0.513457	+	0.513457i	0.915584	−	0.402127i	$-0.131729\pi$
$179$	6.86959	+	6.86959i	0.513457	+	0.513457i	−0.402127	+	0.915584i	$0.631729\pi$
$180$	23.2973	−	9.02371i	1.73647	−	0.672587i
$181$	−0.457775	+	0.457775i	−0.0340261	+	0.0340261i	−0.723915	−	0.689889i	$-0.757659\pi$
$181$	−0.457775	+	0.457775i	−0.0340261	+	0.0340261i	0.689889	+	0.723915i	$0.257659\pi$
$182$	−4.43296	+	21.0112i	−0.328593	+	1.55745i
$183$		−	25.3050i		−	1.87060i
$184$	−2.79157	+	0.455100i	−0.205798	+	0.0335504i
$185$		−	0.943539i		−	0.0693703i
$186$	30.4136	+	6.41669i	2.23004	+	0.470494i
$187$	−9.34978	+	9.34978i	−0.683723	+	0.683723i
$188$	−8.15722	+	18.4712i	−0.594927	+	1.34715i
$189$	−4.07649	−	4.07649i	−0.296521	−	0.296521i
$190$	2.73484	−	1.78190i	0.198406	−	0.129272i
$191$	−18.9763			−1.37308			−0.686538	−	0.727094i	$-0.740870\pi$
$191$	−18.9763			−1.37308			−0.686538	+	0.727094i	$0.740870\pi$
$192$	18.5139	+	9.22323i	1.33613	+	0.665629i
$193$	−1.22637			−0.0882761			−0.0441381	−	0.999025i	$-0.514054\pi$
$193$	−1.22637			−0.0882761			−0.0441381	+	0.999025i	$0.514054\pi$
$194$	−12.0192	+	7.83115i	−0.862927	+	0.562244i
$195$	−28.9069	−	28.9069i	−2.07007	−	2.07007i
$196$	−2.90759	+	6.58393i	−0.207685	+	0.470280i
$197$	−0.892750	+	0.892750i	−0.0636058	+	0.0636058i	−0.738194	−	0.674588i	$-0.764321\pi$
$197$	−0.892750	+	0.892750i	−0.0636058	+	0.0636058i	0.674588	+	0.738194i	$0.264321\pi$
$198$	−26.2471	−	5.53763i	−1.86530	−	0.393542i
$199$			22.4436i			1.59099i	0.605962	+	0.795494i	$0.292788\pi$
$199$			22.4436i			1.59099i	−0.605962	+	0.795494i	$0.707212\pi$
$200$	18.1235	−	2.95462i	1.28153	−	0.208923i
$201$		−	37.8830i		−	2.67206i
$202$	−4.89524	+	23.2023i	−0.344428	+	1.63251i
$203$	0.299562	−	0.299562i	0.0210251	−	0.0210251i
$204$	12.3863	−	4.79759i	0.867217	−	0.335899i
$205$	−10.2360	−	10.2360i	−0.714911	−	0.714911i
$206$	5.17592	+	7.94396i	0.360623	+	0.553482i
$207$	−3.68490			−0.256118
$208$	0.863973	−	18.6363i	0.0599058	−	1.29220i
$209$	−3.50467			−0.242423
$210$	−22.0296	−	33.8108i	−1.52019	−	2.33317i
$211$	3.50681	+	3.50681i	0.241419	+	0.241419i	0.817437	−	0.576018i	$-0.195394\pi$
$211$	3.50681	+	3.50681i	0.241419	+	0.241419i	−0.576018	+	0.817437i	$0.695394\pi$
$212$	5.19498	+	13.4123i	0.356793	+	0.921161i
$213$	7.22837	−	7.22837i	0.495279	−	0.495279i
$214$	−0.199292	+	0.944600i	−0.0136233	+	0.0645715i
$215$			9.64781i			0.657975i
$216$	4.06537	+	2.92565i	0.276613	+	0.199065i
$217$		−	27.6751i		−	1.87871i
$218$	−13.4271	−	2.83286i	−0.909400	−	0.191866i
$219$	0.479870	−	0.479870i	0.0324266	−	0.0324266i
$220$	−31.9257	−	14.0990i	−2.15243	−	0.950554i
$221$	−8.47170	−	8.47170i	−0.569868	−	0.569868i
$222$	0.852678	−	0.555566i	0.0572280	−	0.0372872i
$223$	3.25202			0.217771			0.108886	−	0.994054i	$-0.465272\pi$
$223$	3.25202			0.217771			0.108886	+	0.994054i	$0.465272\pi$
$224$	4.63218	−	17.8242i	0.309501	−	1.19093i
$225$	23.9232			1.59488
$226$	10.0770	−	6.56573i	0.670314	−	0.436746i
$227$	10.2038	+	10.2038i	0.677250	+	0.677250i	0.959377	−	0.282127i	$-0.0910399\pi$
$227$	10.2038	+	10.2038i	0.677250	+	0.677250i	−0.282127	+	0.959377i	$0.591040\pi$
$228$	3.22061	+	1.42228i	0.213290	+	0.0941930i
$229$	−11.8458	+	11.8458i	−0.782791	+	0.782791i	−0.980301	−	0.197510i	$-0.936715\pi$
$229$	−11.8458	+	11.8458i	−0.782791	+	0.782791i	0.197510	+	0.980301i	$0.436715\pi$
$230$	−4.69094	−	0.989698i	−0.309312	−	0.0652588i
$231$			43.3282i			2.85079i
$232$	−0.214991	+	0.298744i	−0.0141149	+	0.0196135i
$233$		−	10.3727i		−	0.679539i	−0.940509	−	0.339770i	$-0.889651\pi$
$233$		−	10.3727i		−	0.679539i	0.940509	−	0.339770i	$-0.110349\pi$
$234$	5.01757	−	23.7821i	0.328009	−	1.55469i
$235$	−24.2014	+	24.2014i	−1.57873	+	1.57873i
$236$	10.5079	+	27.1292i	0.684008	+	1.76596i
$237$	25.0224	+	25.0224i	1.62538	+	1.62538i
$238$	−6.45618	−	9.90889i	−0.418492	−	0.642298i
$239$	−22.0590			−1.42688			−0.713438	−	0.700718i	$-0.752863\pi$
$239$	−22.0590			−1.42688			−0.713438	+	0.700718i	$0.752863\pi$
$240$	23.6164	+	25.9125i	1.52443	+	1.67265i
$241$	10.9782			0.707170			0.353585	−	0.935402i	$-0.384963\pi$
$241$	10.9782			0.707170			0.353585	+	0.935402i	$0.384963\pi$
$242$	11.9640	+	18.3622i	0.769072	+	1.18037i
$243$	−15.5965	−	15.5965i	−1.00052	−	1.00052i
$244$	18.2531	−	7.06995i	1.16853	−	0.452607i
$245$	−8.62643	+	8.62643i	−0.551122	+	0.551122i
$246$	3.22322	−	15.2773i	0.205505	−	0.974047i
$247$		−	3.17553i		−	0.202054i
$248$	3.86874	+	23.7308i	0.245665	+	1.50691i
$249$			3.00153i			0.190214i
$250$	6.99998	+	1.47686i	0.442717	+	0.0934048i
$251$	2.93230	−	2.93230i	0.185085	−	0.185085i	−0.608482	−	0.793567i	$-0.708221\pi$
$251$	2.93230	−	2.93230i	0.185085	−	0.185085i	0.793567	+	0.608482i	$0.208221\pi$
$252$	9.69261	−	21.9479i	0.610577	−	1.38259i
$253$	3.63984	+	3.63984i	0.228835	+	0.228835i
$254$	1.89151	−	1.23242i	0.118684	−	0.0773290i
$255$	22.5148			1.40993
$256$	−1.48033	+	15.9314i	−0.0925203	+	0.995711i
$257$	0.477404			0.0297796			0.0148898	−	0.999889i	$-0.495260\pi$
$257$	0.477404			0.0297796			0.0148898	+	0.999889i	$0.495260\pi$
$258$	−8.71875	+	5.68074i	−0.542806	+	0.353667i
$259$	−0.640720	−	0.640720i	−0.0398124	−	0.0398124i
$260$	12.7749	−	28.9275i	0.792266	−	1.79400i
$261$	−0.339067	+	0.339067i	−0.0209877	+	0.0209877i
$262$	−14.2269	−	3.00161i	−0.878943	−	0.185440i
$263$		−	12.6991i		−	0.783062i	−0.920165	−	0.391531i	$-0.871946\pi$
$263$		−	12.6991i		−	0.783062i	0.920165	−	0.391531i	$-0.128054\pi$
$264$	−6.05692	−	37.1530i	−0.372778	−	2.28661i
$265$			24.3797i			1.49764i
$266$	0.647107	−	3.06714i	0.0396767	−	0.188058i
$267$	−3.47422	+	3.47422i	−0.212619	+	0.212619i
$268$	27.3258	−	10.5841i	1.66919	−	0.646527i
$269$	−4.86600	−	4.86600i	−0.296685	−	0.296685i	0.543029	−	0.839714i	$-0.317277\pi$
$269$	−4.86600	−	4.86600i	−0.296685	−	0.296685i	−0.839714	+	0.543029i	$0.817277\pi$
$270$	4.63456	+	7.11309i	0.282051	+	0.432889i
$271$	−4.07629			−0.247617			−0.123808	−	0.992306i	$-0.539511\pi$
$271$	−4.07629			−0.247617			−0.123808	+	0.992306i	$0.539511\pi$
$272$	6.92121	+	7.59414i	0.419660	+	0.460462i
$273$	−39.2591			−2.37607
$274$	−8.78975	−	13.4904i	−0.531008	−	0.814987i
$275$	−23.6307	−	23.6307i	−1.42498	−	1.42498i
$276$	−1.86769	−	4.82197i	−0.112422	−	0.290248i
$277$	5.95541	−	5.95541i	0.357826	−	0.357826i	−0.505185	−	0.863011i	$-0.668576\pi$
$277$	5.95541	−	5.95541i	0.357826	−	0.357826i	0.863011	+	0.505185i	$0.168576\pi$
$278$	−6.75484	+	32.0164i	−0.405128	+	1.92022i
$279$			31.3248i			1.87537i
$280$	18.2337	−	25.3368i	1.08967	−	1.51416i
$281$			5.02546i			0.299794i	0.988702	+	0.149897i	$0.0478942\pi$
$281$			5.02546i			0.299794i	−0.988702	+	0.149897i	$0.952106\pi$
$282$	−36.1210	−	7.62082i	−2.15097	−	0.453813i
$283$	15.9958	−	15.9958i	0.950850	−	0.950850i	−0.0479974	−	0.998847i	$-0.515284\pi$
$283$	15.9958	−	15.9958i	0.950850	−	0.950850i	0.998847	+	0.0479974i	$0.0152839\pi$
$284$	7.23350	+	3.19445i	0.429229	+	0.189556i
$285$	4.21973	+	4.21973i	0.249955	+	0.249955i
$286$	−28.4475	+	18.5351i	−1.68214	+	1.09600i
$287$	−13.9017			−0.820591
$288$	−5.24307	+	20.1748i	−0.308951	+	1.18881i
$289$	−10.4016			−0.611860
$290$	−0.522706	+	0.340571i	−0.0306944	+	0.0199990i
$291$	−18.5450	−	18.5450i	−1.08713	−	1.08713i
$292$	0.480211	+	0.212070i	0.0281022	+	0.0124105i
$293$	19.1063	−	19.1063i	1.11620	−	1.11620i	0.123911	−	0.992293i	$-0.460456\pi$
$293$	19.1063	−	19.1063i	1.11620	−	1.11620i	0.992293	−	0.123911i	$-0.0395438\pi$
$294$	−12.8751	−	2.71639i	−0.750889	−	0.158423i
$295$			49.3131i			2.87112i
$296$	0.638971	+	0.459836i	0.0371394	+	0.0267274i
$297$		−	9.11535i		−	0.528926i
$298$	−2.54986	+	12.0857i	−0.147709	+	0.700108i
$299$	−3.29801	+	3.29801i	−0.190729	+	0.190729i
$300$	12.1255	+	31.3053i	0.700064	+	1.80741i
$301$	6.55145	+	6.55145i	0.377619	+	0.377619i
$302$	5.63029	+	8.64132i	0.323987	+	0.497252i
$303$	−43.3532			−2.49057
$304$	−0.126120	+	2.72047i	−0.00723346	+	0.156029i
$305$	33.1789			1.89982
$306$	7.30761	+	11.2157i	0.417749	+	0.641157i
$307$	7.32796	+	7.32796i	0.418229	+	0.418229i	0.884593	−	0.466364i	$-0.154436\pi$
$307$	7.32796	+	7.32796i	0.418229	+	0.418229i	−0.466364	+	0.884593i	$0.654436\pi$
$308$	−31.2536	+	12.1054i	−1.78084	+	0.689771i
$309$	−12.2571	+	12.2571i	−0.697285	+	0.697285i
$310$	−8.41328	+	39.8771i	−0.477842	+	2.26486i
$311$		−	17.8115i		−	1.01000i	−0.863120	−	0.504999i	$-0.831493\pi$
$311$		−	17.8115i		−	1.01000i	0.863120	−	0.504999i	$-0.168507\pi$
$312$	33.6638	−	5.48809i	1.90584	−	0.310702i
$313$			23.5541i			1.33136i	0.746239	+	0.665678i	$0.231858\pi$
$313$			23.5541i			1.33136i	−0.746239	+	0.665678i	$0.768142\pi$
$314$	6.61004	+	1.39459i	0.373026	+	0.0787013i
$315$	28.7567	−	28.7567i	1.62026	−	1.62026i
$316$	−11.0582	+	25.0402i	−0.622073	+	1.40862i
$317$	−22.8872	−	22.8872i	−1.28547	−	1.28547i	−0.937507	−	0.347966i	$-0.886873\pi$
$317$	−22.8872	−	22.8872i	−1.28547	−	1.28547i	−0.347966	−	0.937507i	$-0.613127\pi$
$318$	−22.0320	+	14.3551i	−1.23550	+	0.804992i
$319$	0.669842			0.0375040
$320$	−12.0931	+	24.2747i	−0.676025	+	1.35700i
$321$	−1.76497			−0.0985110
$322$	−3.85750	+	2.51337i	−0.214970	+	0.140065i
$323$	1.23667	+	1.23667i	0.0688101	+	0.0688101i
$324$	5.23250	−	11.8485i	0.290694	−	0.658247i
$325$	21.4114	−	21.4114i	1.18769	−	1.18769i
$326$	−11.4879	−	2.42371i	−0.636253	−	0.134237i
$327$		−	25.0884i		−	1.38739i
$328$	11.9204	−	1.94334i	0.658194	−	0.107303i
$329$			32.8685i			1.81210i
$330$	13.1719	−	62.4317i	0.725088	−	3.43675i
$331$	−18.9952	+	18.9952i	−1.04407	+	1.04407i	−0.0450863	+	0.998983i	$0.514356\pi$
$331$	−18.9952	+	18.9952i	−1.04407	+	1.04407i	−0.998983	+	0.0450863i	$0.985644\pi$
$332$	−2.16507	+	0.838594i	−0.118823	+	0.0460238i
$333$	0.725218	+	0.725218i	0.0397417	+	0.0397417i
$334$	4.63313	+	7.11089i	0.253514	+	0.389091i
$335$	49.6706			2.71379
$336$	33.6331	+	1.55922i	1.83484	+	0.0850623i
$337$	−12.5759			−0.685051			−0.342526	−	0.939508i	$-0.611282\pi$
$337$	−12.5759			−0.685051			−0.342526	+	0.939508i	$0.611282\pi$
$338$	−6.75809	−	10.3723i	−0.367592	−	0.564177i
$339$	15.5484	+	15.5484i	0.844471	+	0.844471i
$340$	6.29040	+	16.2404i	0.341145	+	0.880761i
$341$	30.9418	−	30.9418i	1.67559	−	1.67559i
$342$	−0.732447	+	3.47163i	−0.0396062	+	0.187724i
$343$		−	11.0732i		−	0.597896i
$344$	−6.53357	−	4.70189i	−0.352266	−	0.253509i
$345$		−	8.76496i		−	0.471889i
$346$	33.4144	+	7.04978i	1.79637	+	0.378999i
$347$	−5.06848	+	5.06848i	−0.272090	+	0.272090i	−0.829941	−	0.557851i	$-0.811626\pi$
$347$	−5.06848	+	5.06848i	−0.272090	+	0.272090i	0.557851	+	0.829941i	$0.311626\pi$
$348$	−0.615551	−	0.271839i	−0.0329970	−	0.0145721i
$349$	−4.59417	−	4.59417i	−0.245920	−	0.245920i	0.573374	−	0.819294i	$-0.305634\pi$
$349$	−4.59417	−	4.59417i	−0.245920	−	0.245920i	−0.819294	+	0.573374i	$0.805634\pi$
$350$	25.0438	−	16.3174i	1.33865	−	0.872201i
$351$	8.25929			0.440848
$352$	25.1070	−	14.7491i	1.33821	−	0.786131i
$353$	29.4472			1.56732			0.783658	−	0.621192i	$-0.213351\pi$
$353$	29.4472			1.56732			0.783658	+	0.621192i	$0.213351\pi$
$354$	−44.5644	+	29.0361i	−2.36857	+	1.54325i
$355$	9.47752	+	9.47752i	0.503015	+	0.503015i
$356$	−3.47669	−	1.53537i	−0.184264	−	0.0813745i
$357$	15.2889	−	15.2889i	0.809177	−	0.809177i
$358$	−13.4432	−	2.83626i	−0.710497	−	0.149901i
$359$			27.2407i			1.43771i	0.695160	+	0.718855i	$0.255334\pi$
$359$			27.2407i			1.43771i	−0.695160	+	0.718855i	$0.744666\pi$
$360$	−20.6383	+	28.6782i	−1.08773	+	1.51147i
$361$		−	18.5364i		−	0.975602i
$362$	0.189002	−	0.895829i	0.00993375	−	0.0470837i
$363$	−28.3320	+	28.3320i	−1.48704	+	1.48704i
$364$	−10.9686	−	28.3184i	−0.574909	−	1.48429i
$365$	0.629185	+	0.629185i	0.0329330	+	0.0329330i
$366$	19.5361	+	29.9838i	1.02117	+	1.56728i
$367$	−11.8645			−0.619324			−0.309662	−	0.950847i	$-0.600216\pi$
$367$	−11.8645			−0.619324			−0.309662	+	0.950847i	$0.600216\pi$
$368$	2.95638	−	2.69441i	0.154112	−	0.140456i
$369$	15.7350			0.819133
$370$	0.728434	+	1.11800i	0.0378695	+	0.0581218i
$371$	16.5553	+	16.5553i	0.859510	+	0.859510i
$372$	−40.9908	+	15.8770i	−2.12528	+	0.823182i
$373$	−10.9819	+	10.9819i	−0.568622	+	0.568622i	−0.931742	−	0.363121i	$-0.881711\pi$
$373$	−10.9819	+	10.9819i	−0.568622	+	0.568622i	0.363121	+	0.931742i	$0.381711\pi$
$374$	3.86026	−	18.2968i	0.199609	−	0.946103i
$375$			13.0793i			0.675415i
$376$	−4.59474	−	28.1840i	−0.236956	−	1.45348i
$377$			0.606935i			0.0312587i
$378$	7.97738	+	1.68307i	0.410312	+	0.0865678i
$379$	17.0171	−	17.0171i	0.874111	−	0.874111i	−0.118806	−	0.992917i	$-0.537907\pi$
$379$	17.0171	−	17.0171i	0.874111	−	0.874111i	0.992917	+	0.118806i	$0.0379067\pi$
$380$	−1.86484	+	4.22273i	−0.0956640	+	0.216621i
$381$	2.91851	+	2.91851i	0.149520	+	0.149520i
$382$	22.4849	−	14.6502i	1.15043	−	0.749567i
$383$	18.8374			0.962544			0.481272	−	0.876571i	$-0.340175\pi$
$383$	18.8374			0.962544			0.481272	+	0.876571i	$0.340175\pi$
$384$	−29.0576	+	3.36463i	−1.48284	+	0.171701i
$385$	−56.8101			−2.89531
$386$	1.45312	−	0.946788i	0.0739620	−	0.0481902i
$387$	−7.41545	−	7.41545i	−0.376949	−	0.376949i
$388$	8.19565	−	18.5582i	0.416071	−	0.942150i
$389$	3.85585	−	3.85585i	0.195499	−	0.195499i	−0.602568	−	0.798067i	$-0.705856\pi$
$389$	3.85585	−	3.85585i	0.195499	−	0.195499i	0.798067	+	0.602568i	$0.205856\pi$
$390$	56.5685	+	11.9349i	2.86446	+	0.604345i
$391$		−	2.56873i		−	0.129906i
$392$	−1.63776	−	10.0460i	−0.0827195	−	0.507399i
$393$		−	26.5828i		−	1.34092i
$394$	0.368592	−	1.74704i	0.0185694	−	0.0880147i
$395$	−32.8083	+	32.8083i	−1.65076	+	1.65076i
$396$	35.3753	−	13.7019i	1.77767	−	0.688545i
$397$	−6.27832	−	6.27832i	−0.315100	−	0.315100i	0.531782	−	0.846882i	$-0.321523\pi$
$397$	−6.27832	−	6.27832i	−0.315100	−	0.315100i	−0.846882	+	0.531782i	$0.821523\pi$
$398$	−17.3270	−	26.5934i	−0.868525	−	1.33301i
$399$	5.73090			0.286904
$400$	−19.1935	+	17.4927i	−0.959674	+	0.874636i
$401$	13.5687			0.677587			0.338793	−	0.940861i	$-0.389981\pi$
$401$	13.5687			0.677587			0.338793	+	0.940861i	$0.389981\pi$
$402$	29.2466	+	44.8874i	1.45869	+	2.23878i
$403$	28.0359	+	28.0359i	1.39657	+	1.39657i
$404$	−12.1124	−	31.2716i	−0.602615	−	1.55582i
$405$	15.5241	−	15.5241i	0.771401	−	0.771401i
$406$	−0.123681	+	0.586218i	−0.00613817	+	0.0290935i
$407$		−	1.43270i		−	0.0710162i
$408$	−10.9727	+	15.2472i	−0.543228	+	0.754849i
$409$		−	21.7077i		−	1.07337i	−0.843781	−	0.536687i	$-0.819675\pi$
$409$		−	21.7077i		−	1.07337i	0.843781	−	0.536687i	$-0.180325\pi$
$410$	20.0310	+	4.22614i	0.989259	+	0.208714i
$411$	20.8151	−	20.8151i	1.02673	−	1.02673i
$412$	−12.2659	−	5.41683i	−0.604295	−	0.266868i
$413$	33.4866	+	33.4866i	1.64777	+	1.64777i
$414$	4.36623	−	2.84483i	0.214588	−	0.139816i
$415$	−3.93547			−0.193185
$416$	13.3640	+	22.7491i	0.655223	+	1.11537i
$417$	−59.8221			−2.92950
$418$	4.15267	−	2.70569i	0.203114	−	0.132340i
$419$	8.96791	+	8.96791i	0.438111	+	0.438111i	0.891376	−	0.453265i	$-0.149741\pi$
$419$	8.96791	+	8.96791i	0.438111	+	0.438111i	−0.453265	+	0.891376i	$0.649741\pi$
$420$	52.2056	+	23.0550i	2.54737	+	1.12497i
$421$	−19.4591	+	19.4591i	−0.948378	+	0.948378i	−0.998731	−	0.0503535i	$-0.983965\pi$
$421$	−19.4591	+	19.4591i	−0.948378	+	0.948378i	0.0503535	+	0.998731i	$0.483965\pi$
$422$	−6.86254	−	1.44786i	−0.334063	−	0.0704808i
$423$		−	37.2031i		−	1.80888i
$424$	−16.5101	−	11.8815i	−0.801803	−	0.577019i
$425$			16.6768i			0.808944i
$426$	−2.98439	+	14.1453i	−0.144594	+	0.685344i
$427$	22.5305	−	22.5305i	1.09033	−	1.09033i
$428$	−0.493113	−	1.27311i	−0.0238355	−	0.0615381i
$429$	−43.8931	−	43.8931i	−2.11918	−	2.11918i
$430$	−7.44834	−	11.4317i	−0.359191	−	0.551283i
$431$	10.5204			0.506749			0.253375	−	0.967368i	$-0.418459\pi$
$431$	10.5204			0.506749			0.253375	+	0.967368i	$0.418459\pi$
$432$	−7.07570	−	0.328027i	−0.340430	−	0.0157822i
$433$	−33.5736			−1.61344			−0.806721	−	0.590932i	$-0.798760\pi$
$433$	−33.5736			−1.61344			−0.806721	+	0.590932i	$0.798760\pi$
$434$	21.3658	+	32.7921i	1.02559	+	1.57407i
$435$	−0.806510	−	0.806510i	−0.0386692	−	0.0386692i
$436$	18.0968	−	7.00942i	0.866679	−	0.335690i
$437$	0.481432	−	0.481432i	0.0230300	−	0.0230300i
$438$	−0.198125	+	0.939067i	−0.00946677	+	0.0448704i
$439$		−	2.28055i		−	0.108845i	−0.998518	−	0.0544223i	$-0.982668\pi$
$439$		−	2.28055i		−	0.108845i	0.998518	−	0.0544223i	$-0.0173317\pi$
$440$	48.7134	−	7.94157i	2.32232	−	0.378600i
$441$		−	13.2608i		−	0.631467i
$442$	16.5784	+	3.49773i	0.788556	+	0.166370i
$443$	−20.3016	+	20.3016i	−0.964557	+	0.964557i	−0.999393	−	0.0348364i	$-0.988909\pi$
$443$	−20.3016	+	20.3016i	−0.964557	+	0.964557i	0.0348364	+	0.999393i	$0.488909\pi$
$444$	−0.581425	+	1.31658i	−0.0275932	+	0.0624820i
$445$	−4.55525	−	4.55525i	−0.215940	−	0.215940i
$446$	−3.85330	+	2.51064i	−0.182459	+	0.118882i
$447$	−22.5820			−1.06809
$448$	8.27203	+	24.6959i	0.390817	+	1.16677i
$449$	−28.1111			−1.32665			−0.663323	−	0.748333i	$-0.730855\pi$
$449$	−28.1111			−1.32665			−0.663323	+	0.748333i	$0.730855\pi$
$450$	−28.3466	+	18.4693i	−1.33627	+	0.870652i
$451$	−15.5426	−	15.5426i	−0.731873	−	0.731873i
$452$	−6.87133	+	15.5594i	−0.323200	+	0.731853i
$453$	−13.3331	+	13.3331i	−0.626445	+	0.626445i
$454$	−19.9680	−	4.21287i	−0.937146	−	0.197720i
$455$		−	51.4748i		−	2.41318i
$456$	−4.91413	+	0.801132i	−0.230125	+	0.0375165i
$457$			12.3670i			0.578505i	0.957253	+	0.289252i	$0.0934066\pi$
$457$			12.3670i			0.578505i	−0.957253	+	0.289252i	$0.906593\pi$
$458$	4.89079	−	23.1813i	0.228532	−	1.08319i
$459$	−3.21647	+	3.21647i	−0.150132	+	0.150132i
$460$	6.32235	−	2.44883i	0.294781	−	0.114177i
$461$	21.0053	+	21.0053i	0.978315	+	0.978315i	0.999770	−	0.0214550i	$-0.00682987\pi$
$461$	21.0053	+	21.0053i	0.978315	+	0.978315i	−0.0214550	+	0.999770i	$0.506830\pi$
$462$	−33.4504	−	51.3394i	−1.55625	−	2.38853i
$463$	−0.584883			−0.0271818			−0.0135909	−	0.999908i	$-0.504326\pi$
$463$	−0.584883			−0.0271818			−0.0135909	+	0.999908i	$0.504326\pi$
$464$	0.0241051	−	0.519959i	0.00111905	−	0.0241385i
$465$	−74.5096			−3.45530
$466$	8.00799	+	12.2906i	0.370963	+	0.569351i
$467$	11.5595	+	11.5595i	0.534911	+	0.534911i	0.922030	−	0.387119i	$-0.126530\pi$
$467$	11.5595	+	11.5595i	0.534911	+	0.534911i	−0.387119	+	0.922030i	$0.626530\pi$
$468$	12.4151	+	32.0530i	0.573888	+	1.48165i
$469$	33.7294	−	33.7294i	1.55748	−	1.55748i
$470$	9.99209	−	47.3603i	0.460901	−	2.18457i
$471$			12.3508i			0.569093i
$472$	−33.3952	−	24.0329i	−1.53714	−	1.10620i
$473$			14.6495i			0.673587i
$474$	−48.9668	−	10.3310i	−2.24912	−	0.474521i
$475$	−3.12557	+	3.12557i	−0.143411	+	0.143411i
$476$	15.2998	+	6.75668i	0.701266	+	0.309692i
$477$	−18.7386	−	18.7386i	−0.857983	−	0.857983i
$478$	26.1376	−	17.0301i	1.19551	−	0.778937i
$479$	−18.5624			−0.848140			−0.424070	−	0.905629i	$-0.639399\pi$
$479$	−18.5624			−0.848140			−0.424070	+	0.905629i	$0.639399\pi$
$480$	−47.9880	−	12.4712i	−2.19034	−	0.569231i
$481$	1.29815			0.0591905
$482$	−13.0081	+	8.47546i	−0.592501	+	0.386046i
$483$	−5.95194	−	5.95194i	−0.270823	−	0.270823i
$484$	−28.3521	−	12.5208i	−1.28873	−	0.569128i
$485$	24.3154	−	24.3154i	1.10411	−	1.10411i
$486$	30.5212	+	6.43937i	1.38447	+	0.292096i
$487$		−	2.57016i		−	0.116465i	−0.998303	−	0.0582325i	$-0.981454\pi$
$487$		−	2.57016i		−	0.116465i	0.998303	−	0.0582325i	$-0.0185465\pi$
$488$	−16.1698	+	22.4690i	−0.731973	+	1.01712i
$489$		−	21.4649i		−	0.970675i
$490$	3.56161	−	16.8812i	0.160897	−	0.762616i
$491$	−1.41013	+	1.41013i	−0.0636381	+	0.0636381i	−0.738210	−	0.674571i	$-0.764328\pi$
$491$	−1.41013	+	1.41013i	−0.0636381	+	0.0636381i	0.674571	+	0.738210i	$0.264328\pi$
$492$	7.97528	+	20.5904i	0.359553	+	0.928289i
$493$	−0.236363	−	0.236363i	−0.0106452	−	0.0106452i
$494$	2.45159	+	3.76268i	0.110302	+	0.169291i
$495$	64.3021			2.89017
$496$	−22.9048	−	25.1317i	−1.02846	−	1.12845i
$497$	12.8716			0.577372
$498$	−2.31725	−	3.55650i	−0.103838	−	0.159370i
$499$	11.6643	+	11.6643i	0.522164	+	0.522164i	0.918225	−	0.396060i	$-0.129623\pi$
$499$	11.6643	+	11.6643i	0.522164	+	0.522164i	−0.396060	+	0.918225i	$0.629623\pi$
$500$	−9.43442	+	3.65423i	−0.421920	+	0.163422i
$501$	−10.9718	+	10.9718i	−0.490182	+	0.490182i
$502$	−1.21067	+	5.73828i	−0.0540346	+	0.256112i
$503$		−	35.8097i		−	1.59668i	−0.602210	−	0.798338i	$-0.705713\pi$
$503$		−	35.8097i		−	1.59668i	0.602210	−	0.798338i	$-0.294287\pi$
$504$	5.45958	+	33.4889i	0.243189	+	1.49171i
$505$		−	56.8428i		−	2.52947i
$506$	−7.12288	−	1.50279i	−0.316651	−	0.0668071i
$507$	16.0039	−	16.0039i	0.710758	−	0.710758i
$508$	−1.28978	+	2.92058i	−0.0572249	+	0.129580i
$509$	8.74832	+	8.74832i	0.387762	+	0.387762i	0.873889	−	0.486126i	$-0.161590\pi$
$509$	8.74832	+	8.74832i	0.387762	+	0.387762i	−0.486126	+	0.873889i	$0.661590\pi$
$510$	−26.6777	+	17.3820i	−1.18131	+	0.769687i
$511$	0.854509			0.0378013
$512$	−10.5454	−	20.0199i	−0.466044	−	0.884762i
$513$	−1.20566			−0.0532313
$514$	−0.565674	+	0.368567i	−0.0249508	+	0.0162568i
$515$	−16.0710	−	16.0710i	−0.708175	−	0.708175i
$516$	5.94515	−	13.4622i	0.261721	−	0.592639i
$517$	−36.7482	+	36.7482i	−1.61618	+	1.61618i
$518$	1.25384	+	0.264536i	0.0550905	+	0.0116230i
$519$			62.4342i			2.74056i
$520$	7.19575	+	44.1386i	0.315555	+	1.93560i
$521$			19.7099i			0.863506i	0.901992	+	0.431753i	$0.142105\pi$
$521$			19.7099i			0.863506i	−0.901992	+	0.431753i	$0.857895\pi$
$522$	0.139991	−	0.663528i	0.00612726	−	0.0290418i
$523$	9.98534	−	9.98534i	0.436628	−	0.436628i	−0.454247	−	0.890876i	$-0.650092\pi$
$523$	9.98534	−	9.98534i	0.436628	−	0.436628i	0.890876	+	0.454247i	$0.150092\pi$
$524$	19.1747	−	7.42694i	0.837653	−	0.324447i
$525$	38.6414	+	38.6414i	1.68645	+	1.68645i
$526$	9.80404	+	15.0472i	0.427476	+	0.656087i
$527$	−21.8364			−0.951210
$528$	35.8598	+	39.3464i	1.56060	+	1.71233i
$529$	−1.00000			−0.0434783
$530$	−18.8218	−	28.8875i	−0.817565	−	1.25479i
$531$	−37.9028	−	37.9028i	−1.64484	−	1.64484i
$532$	1.60115	+	4.13383i	0.0694187	+	0.179224i
$533$	14.0829	−	14.0829i	0.610000	−	0.610000i
$534$	1.43441	−	6.79877i	0.0620729	−	0.294212i
$535$		−	2.31415i		−	0.100049i
$536$	−24.2071	+	33.6373i	−1.04559	+	1.45291i
$537$		−	25.1185i		−	1.08394i
$538$	9.52238	+	2.00904i	0.410539	+	0.0866157i
$539$	−13.0986	+	13.0986i	−0.564198	+	0.564198i
$540$	−10.9830	−	4.85028i	−0.472631	−	0.208723i
$541$	−31.2396	−	31.2396i	−1.34310	−	1.34310i	−0.892959	−	0.450137i	$-0.851375\pi$
$541$	−31.2396	−	31.2396i	−1.34310	−	1.34310i	−0.450137	−	0.892959i	$-0.648625\pi$
$542$	4.82998	−	3.14699i	0.207465	−	0.135175i
$543$	1.67384			0.0718314
$544$	−14.0638	−	3.65492i	−0.602980	−	0.156704i
$545$	32.8948			1.40906
$546$	46.5180	−	30.3090i	1.99078	−	1.29710i
$547$	4.04864	+	4.04864i	0.173107	+	0.173107i	0.788343	−	0.615236i	$-0.210939\pi$
$547$	4.04864	+	4.04864i	0.173107	+	0.173107i	−0.615236	+	0.788343i	$0.710939\pi$
$548$	20.8299	+	9.19887i	0.889809	+	0.392956i
$549$	−25.5018	+	25.5018i	−1.08839	+	1.08839i
$550$	46.2434	+	9.75645i	1.97182	+	0.416017i
$551$		−	0.0885982i		−	0.00377441i
$552$	5.93569	+	4.27163i	0.252640	+	0.181813i
$553$			44.5576i			1.89478i
$554$	−2.45882	+	11.6543i	−0.104465	+	0.495142i
$555$	−1.72501	+	1.72501i	−0.0732227	+	0.0732227i
$556$	−16.7136	−	43.1510i	−0.708817	−	1.83001i
$557$	9.72009	+	9.72009i	0.411854	+	0.411854i	0.882384	−	0.470530i	$-0.155937\pi$
$557$	9.72009	+	9.72009i	0.411854	+	0.411854i	−0.470530	+	0.882384i	$0.655937\pi$
$558$	−24.1835	−	37.1167i	−1.02377	−	1.57127i
$559$	−13.2737			−0.561420
$560$	−2.04438	+	44.0983i	−0.0863908	+	1.86349i
$561$	34.1872			1.44339
$562$	−3.87978	−	5.95465i	−0.163659	−	0.251182i
$563$	−3.53659	−	3.53659i	−0.149049	−	0.149049i	0.628644	−	0.777693i	$-0.283610\pi$
$563$	−3.53659	−	3.53659i	−0.149049	−	0.149049i	−0.777693	+	0.628644i	$0.783610\pi$
$564$	48.6831	−	18.8564i	2.04993	−	0.793996i
$565$	−20.3863	+	20.3863i	−0.857660	+	0.857660i
$566$	−6.60421	+	31.3025i	−0.277596	+	1.31574i
$567$		−	21.0837i		−	0.885431i
$568$	−11.0371	+	1.79935i	−0.463108	+	0.0754989i
$569$			23.9010i			1.00198i	0.865453	+	0.500991i	$0.167031\pi$
$569$			23.9010i			1.00198i	−0.865453	+	0.500991i	$0.832969\pi$
$570$	−8.25767	−	1.74221i	−0.345876	−	0.0729730i
$571$	−21.3154	+	21.3154i	−0.892020	+	0.892020i	−0.994713	−	0.102693i	$-0.967254\pi$
$571$	−21.3154	+	21.3154i	−0.892020	+	0.892020i	0.102693	+	0.994713i	$0.467254\pi$
$572$	19.3978	−	43.9243i	0.811063	−	1.83657i
$573$	34.6932	+	34.6932i	1.44933	+	1.44933i
$574$	16.4721	−	10.7324i	0.687530	−	0.447963i
$575$	6.49223			0.270745
$576$	−9.36294	−	27.9528i	−0.390122	−	1.16470i
$577$	12.5006			0.520407			0.260204	−	0.965554i	$-0.416210\pi$
$577$	12.5006			0.520407			0.260204	+	0.965554i	$0.416210\pi$
$578$	12.3248	−	8.03030i	0.512645	−	0.334016i
$579$	2.24210	+	2.24210i	0.0931784	+	0.0931784i
$580$	0.356423	−	0.807083i	0.0147997	−	0.0335123i
$581$	−2.67243	+	2.67243i	−0.110871	+	0.110871i
$582$	36.2911	+	7.65672i	1.50432	+	0.317381i
$583$			37.0190i			1.53317i
$584$	−0.732723	+	0.119453i	−0.0303203	+	0.00494301i
$585$			58.2633i			2.40889i
$586$	−7.88848	+	37.3896i	−0.325870	+	1.54455i
$587$	19.0629	−	19.0629i	0.786810	−	0.786810i	−0.194160	−	0.980970i	$-0.562198\pi$
$587$	19.0629	−	19.0629i	0.786810	−	0.786810i	0.980970	+	0.194160i	$0.0621980\pi$
$588$	17.3527	−	6.72122i	0.715615	−	0.277179i
$589$	−4.09258	−	4.09258i	−0.168632	−	0.168632i
$590$	−38.0709	−	58.4309i	−1.56735	−	2.40556i
$591$	3.26432			0.134276
$592$	−1.11212	−	0.0515574i	−0.0457078	−	0.00211900i
$593$	−5.60035			−0.229979			−0.114989	−	0.993367i	$-0.536683\pi$
$593$	−5.60035			−0.229979			−0.114989	+	0.993367i	$0.536683\pi$
$594$	7.03727	+	10.8007i	0.288743	+	0.443160i
$595$	20.0462	+	20.0462i	0.821814	+	0.821814i
$596$	−6.30917	−	16.2889i	−0.258434	−	0.667219i
$597$	41.0323	−	41.0323i	1.67934	−	1.67934i
$598$	1.36166	−	6.45394i	0.0556823	−	0.263921i
$599$		−	21.6901i		−	0.886235i	−0.896464	−	0.443118i	$-0.853872\pi$
$599$		−	21.6901i		−	0.886235i	0.896464	−	0.443118i	$-0.146128\pi$
$600$	−38.5359	−	27.7324i	−1.57322	−	1.13217i
$601$		−	7.80591i		−	0.318410i	−0.987246	−	0.159205i	$-0.949107\pi$
$601$		−	7.80591i		−	0.318410i	0.987246	−	0.159205i	$-0.0508930\pi$
$602$	−12.8207	−	2.70491i	−0.522532	−	0.110244i
$603$	−38.1775	+	38.1775i	−1.55471	+	1.55471i
$604$	−13.3426	−	5.89235i	−0.542903	−	0.239756i
$605$	−37.1476	−	37.1476i	−1.51027	−	1.51027i
$606$	51.3690	−	33.4697i	2.08672	−	1.35961i
$607$	6.68045			0.271151			0.135576	−	0.990767i	$-0.456712\pi$
$607$	6.68045			0.271151			0.135576	+	0.990767i	$0.456712\pi$
$608$	−1.95083	−	3.32084i	−0.0791165	−	0.134678i
$609$	−1.09534			−0.0443854
$610$	−39.3135	+	25.6149i	−1.59176	+	1.03712i
$611$	−33.2970	−	33.2970i	−1.34705	−	1.34705i
$612$	−17.3175	−	7.64775i	−0.700020	−	0.309142i
$613$	−0.352749	+	0.352749i	−0.0142474	+	0.0142474i	−0.714195	−	0.699947i	$-0.753207\pi$
$613$	−0.352749	+	0.352749i	−0.0142474	+	0.0142474i	0.699947	+	0.714195i	$0.253207\pi$
$614$	−14.3402	−	3.02551i	−0.578724	−	0.122100i
$615$			37.4275i			1.50922i
$616$	27.6866	−	38.4722i	1.11552	−	1.55009i
$617$		−	25.8830i		−	1.04201i	−0.853553	−	0.521006i	$-0.825557\pi$
$617$		−	25.8830i		−	1.04201i	0.853553	−	0.521006i	$-0.174443\pi$
$618$	5.06063	−	23.9863i	0.203569	−	0.964869i
$619$	20.0539	−	20.0539i	0.806035	−	0.806035i	−0.177996	−	0.984031i	$-0.556961\pi$
$619$	20.0539	−	20.0539i	0.806035	−	0.806035i	0.984031	+	0.177996i	$0.0569614\pi$
$620$	−20.8172	−	53.7454i	−0.836038	−	2.15847i
$621$	1.25216	+	1.25216i	0.0502476	+	0.0502476i
$622$	13.7509	+	21.1048i	0.551361	+	0.846225i
$623$	−6.18658			−0.247860
$624$	−35.6512	+	32.4921i	−1.42719	+	1.30073i
$625$	15.3121			0.612483
$626$	−18.1843	−	27.9092i	−0.726792	−	1.11547i
$627$	6.40737	+	6.40737i	0.255886	+	0.255886i
$628$	−8.90887	+	3.45067i	−0.355503	+	0.137697i
$629$	−0.505547	+	0.505547i	−0.0201575	+	0.0201575i
$630$	−11.8728	+	56.2746i	−0.473025	+	2.24203i
$631$			33.5917i			1.33727i	0.743592	+	0.668633i	$0.233120\pi$
$631$			33.5917i			1.33727i	−0.743592	+	0.668633i	$0.766880\pi$
$632$	−6.22878	−	38.2072i	−0.247768	−	1.51980i
$633$		−	12.8225i		−	0.509650i
$634$	44.7884	+	9.44948i	1.77878	+	0.375287i
$635$	−3.82662	+	3.82662i	−0.151855	+	0.151855i
$636$	15.0232	−	34.0185i	0.595710	−	1.34892i
$637$	−11.8685	−	11.8685i	−0.470247	−	0.470247i
$638$	−0.793693	+	0.517134i	−0.0314226	+	0.0204735i
$639$	−14.5691			−0.576346
$640$	−4.41156	−	38.0991i	−0.174382	−	1.50600i
$641$	−30.4283			−1.20185			−0.600923	−	0.799307i	$-0.705200\pi$
$641$	−30.4283			−1.20185			−0.600923	+	0.799307i	$0.705200\pi$
$642$	2.09131	−	1.36260i	0.0825372	−	0.0537775i
$643$	9.00717	+	9.00717i	0.355208	+	0.355208i	0.862043	−	0.506835i	$-0.169185\pi$
$643$	9.00717	+	9.00717i	0.355208	+	0.355208i	−0.506835	+	0.862043i	$0.669185\pi$
$644$	2.63036	−	5.95617i	0.103651	−	0.234706i
$645$	17.6385	−	17.6385i	0.694515	−	0.694515i
$646$	−2.42006	−	0.510586i	−0.0952161	−	0.0200887i
$647$			1.83901i			0.0722990i	0.999346	+	0.0361495i	$0.0115093\pi$
$647$			1.83901i			0.0722990i	−0.999346	+	0.0361495i	$0.988491\pi$
$648$	2.94732	+	18.0788i	0.115782	+	0.710202i
$649$			74.8786i			2.93924i
$650$	−8.84019	+	41.9005i	−0.346741	+	1.64347i
$651$	−50.5966	+	50.5966i	−1.98304	+	1.98304i
$652$	15.4831	−	5.99705i	0.606364	−	0.234863i
$653$	19.8510	+	19.8510i	0.776828	+	0.776828i	0.979290	−	0.202462i	$-0.0648942\pi$
$653$	19.8510	+	19.8510i	0.776828	+	0.776828i	−0.202462	+	0.979290i	$0.564894\pi$
$654$	19.3688	+	29.7271i	0.757381	+	1.16242i
$655$	34.8542			1.36187
$656$	−12.6241	+	11.5055i	−0.492889	+	0.449214i
$657$	−0.967201			−0.0377341
$658$	−25.3753	−	38.9457i	−0.989231	−	1.51826i
$659$	4.81572	+	4.81572i	0.187594	+	0.187594i	0.794655	−	0.607061i	$-0.207652\pi$
$659$	4.81572	+	4.81572i	0.187594	+	0.187594i	−0.607061	+	0.794655i	$0.707652\pi$
$660$	32.5915	+	84.1441i	1.26862	+	3.27530i
$661$	0.581499	−	0.581499i	0.0226177	−	0.0226177i	−0.695707	−	0.718325i	$-0.744909\pi$
$661$	0.581499	−	0.581499i	0.0226177	−	0.0226177i	0.718325	+	0.695707i	$0.244909\pi$
$662$	7.84258	−	37.1720i	0.304810	−	1.44473i
$663$			30.9766i			1.20303i
$664$	1.91796	−	2.66513i	0.0744314	−	0.103427i
$665$			7.51412i			0.291385i
$666$	−1.41919	−	0.299422i	−0.0549926	−	0.0116024i
$667$	−0.0920153	+	0.0920153i	−0.00356285	+	0.00356285i
$668$	−10.9796	−	4.84878i	−0.424812	−	0.187605i
$669$	−5.94546	−	5.94546i	−0.229865	−	0.229865i
$670$	−58.8545	+	38.3469i	−2.27375	+	1.48147i
$671$	50.3798			1.94489
$672$	−41.0555	+	24.1181i	−1.58375	+	0.930375i
$673$	42.7451			1.64770			0.823852	−	0.566806i	$-0.191821\pi$
$673$	42.7451			1.64770			0.823852	+	0.566806i	$0.191821\pi$
$674$	14.9011	−	9.70888i	0.573969	−	0.373972i
$675$	−8.12933	−	8.12933i	−0.312898	−	0.312898i
$676$	16.0153	+	7.07264i	0.615972	+	0.272025i
$677$	6.55762	−	6.55762i	0.252030	−	0.252030i	−0.569773	−	0.821802i	$-0.692969\pi$
$677$	6.55762	−	6.55762i	0.252030	−	0.252030i	0.821802	+	0.569773i	$0.192969\pi$
$678$	−30.4269	−	6.41949i	−1.16854	−	0.246539i
$679$		−	33.0233i		−	1.26732i
$680$	−19.9915	−	14.3869i	−0.766638	−	0.551712i
$681$		−	37.3099i		−	1.42972i
$682$	−12.7750	+	60.5506i	−0.489180	+	2.31860i
$683$	13.7218	−	13.7218i	0.525050	−	0.525050i	−0.394042	−	0.919092i	$-0.628924\pi$
$683$	13.7218	−	13.7218i	0.525050	−	0.525050i	0.919092	+	0.394042i	$0.128924\pi$
$684$	−1.81231	−	4.67899i	−0.0692954	−	0.178906i
$685$	27.2919	+	27.2919i	1.04277	+	1.04277i
$686$	8.54877	+	13.1206i	0.326394	+	0.500946i
$687$	43.3138			1.65252
$688$	11.3716	+	0.527181i	0.433537	+	0.0200986i
$689$	−33.5424			−1.27786
$690$	6.76676	+	10.3856i	0.257606	+	0.395372i
$691$	−17.3853	−	17.3853i	−0.661367	−	0.661367i	0.294335	−	0.955702i	$-0.404902\pi$
$691$	−17.3853	−	17.3853i	−0.661367	−	0.661367i	−0.955702	+	0.294335i	$0.904902\pi$
$692$	−45.0352	+	17.4434i	−1.71198	+	0.663100i
$693$	43.6651	−	43.6651i	1.65870	−	1.65870i
$694$	2.09263	−	9.91861i	0.0794353	−	0.376505i
$695$		−	78.4362i		−	2.97525i
$696$	0.939230	−	0.153119i	0.0356014	−	0.00580397i
$697$			10.9688i			0.415474i
$698$	8.99042	+	1.89680i	0.340292	+	0.0717951i
$699$	−18.9638	+	18.9638i	−0.717276	+	0.717276i
$700$	−17.0769	+	38.6688i	−0.645446	+	1.46154i
$701$	6.17906	+	6.17906i	0.233380	+	0.233380i	0.814102	−	0.580722i	$-0.197230\pi$
$701$	6.17906	+	6.17906i	0.233380	+	0.233380i	−0.580722	+	0.814102i	$0.697230\pi$
$702$	−9.78640	+	6.37637i	−0.369364	+	0.240661i
$703$	−0.189499			−0.00714709
$704$	−18.3625	+	36.8594i	−0.692064	+	1.38919i
$705$	88.4919			3.33280
$706$	−34.8919	+	22.7339i	−1.31317	+	0.855603i
$707$	−38.5997	−	38.5997i	−1.45169	−	1.45169i
$708$	30.3876	−	68.8096i	1.14204	−	2.58602i
$709$	10.4694	−	10.4694i	0.393186	−	0.393186i	−0.482636	−	0.875821i	$-0.660320\pi$
$709$	10.4694	−	10.4694i	0.393186	−	0.393186i	0.875821	+	0.482636i	$0.160320\pi$
$710$	−18.5468	−	3.91300i	−0.696047	−	0.146852i
$711$		−	50.4339i		−	1.89142i
$712$	5.30486	−	0.864832i	0.198808	−	0.0324110i
$713$			8.50086i			0.318360i
$714$	−6.31238	+	29.9192i	−0.236235	+	1.11970i
$715$	57.5508	−	57.5508i	2.15228	−	2.15228i
$716$	18.1185	−	7.01783i	0.677121	−	0.262269i
$717$	40.3290	+	40.3290i	1.50612	+	1.50612i
$718$	−21.0305	−	32.2774i	−0.784851	−	1.20458i
$719$	−14.4576			−0.539179			−0.269590	−	0.962975i	$-0.586888\pi$
$719$	−14.4576			−0.539179			−0.269590	+	0.962975i	$0.586888\pi$
$720$	2.31399	−	49.9139i	0.0862373	−	1.86018i
$721$	−21.8264			−0.812859
$722$	14.3106	+	21.9638i	0.532585	+	0.817407i
$723$	−20.0708	−	20.0708i	−0.746441	−	0.746441i
$724$	0.467653	+	1.20738i	0.0173802	+	0.0448719i
$725$	0.597385	−	0.597385i	0.0221863	−	0.0221863i
$726$	11.6975	−	55.4434i	0.434134	−	2.05770i
$727$			27.7945i			1.03084i	0.856937	+	0.515421i	$0.172364\pi$
$727$			27.7945i			1.03084i	−0.856937	+	0.515421i	$0.827636\pi$
$728$	34.8591	+	25.0864i	1.29197	+	0.929765i
$729$			37.5997i			1.39258i
$730$	−1.23126	−	0.259773i	−0.0455711	−	0.00961462i
$731$	5.16929	−	5.16929i	0.191193	−	0.191193i
$732$	−46.2965	−	20.4454i	−1.71117	−	0.755683i
$733$	8.67670	+	8.67670i	0.320481	+	0.320481i	0.848952	−	0.528471i	$-0.177234\pi$
$733$	8.67670	+	8.67670i	0.320481	+	0.320481i	−0.528471	+	0.848952i	$0.677234\pi$
$734$	14.0582	−	9.15971i	0.518899	−	0.338091i
$735$	31.5423			1.16346
$736$	−1.42285	+	5.47499i	−0.0524470	+	0.201811i
$737$	75.4214			2.77818
$738$	−18.6444	+	12.1478i	−0.686309	+	0.447167i
$739$	−26.3954	−	26.3954i	−0.970970	−	0.970970i	0.0286201	−	0.999590i	$-0.490889\pi$
$739$	−26.3954	−	26.3954i	−0.970970	−	0.970970i	−0.999590	+	0.0286201i	$0.990889\pi$
$740$	−1.72624	−	0.762339i	−0.0634578	−	0.0280241i
$741$	−5.80563	+	5.80563i	−0.213275	+	0.213275i
$742$	−32.3975	−	6.83524i	−1.18935	−	0.250929i
$743$			21.9196i			0.804152i	0.915606	+	0.402076i	$0.131711\pi$
$743$			21.9196i			0.804152i	−0.915606	+	0.402076i	$0.868289\pi$
$744$	36.3125	−	50.4585i	1.33128	−	1.84990i
$745$		−	29.6086i		−	1.08477i
$746$	4.53412	−	21.4907i	0.166006	−	0.786831i
$747$	3.02486	−	3.02486i	0.110674	−	0.110674i
$748$	9.55153	+	24.6600i	0.349239	+	0.901658i
$749$	−1.57145	−	1.57145i	−0.0574195	−	0.0574195i
$750$	−10.0976	−	15.4977i	−0.368711	−	0.565895i
$751$	4.61473			0.168394			0.0841969	−	0.996449i	$-0.473168\pi$
$751$	4.61473			0.168394			0.0841969	+	0.996449i	$0.473168\pi$
$752$	27.2030	+	29.8479i	0.991992	+	1.08844i
$753$	−10.7219			−0.390727
$754$	−0.468568	−	0.719155i	−0.0170642	−	0.0261901i
$755$	−17.4818	−	17.4818i	−0.636229	−	0.636229i
$756$	−10.7517	+	4.16446i	−0.391037	+	0.151460i
$757$	4.92941	−	4.92941i	0.179162	−	0.179162i	−0.611828	−	0.790991i	$-0.709566\pi$
$757$	4.92941	−	4.92941i	0.179162	−	0.179162i	0.790991	+	0.611828i	$0.209566\pi$
$758$	−7.02590	+	33.3012i	−0.255192	+	1.20955i
$759$		−	13.3090i		−	0.483085i
$760$	−1.05041	−	6.44319i	−0.0381024	−	0.233719i
$761$		−	8.12779i		−	0.294632i	−0.989089	−	0.147316i	$-0.952937\pi$
$761$		−	8.12779i		−	0.294632i	0.989089	−	0.147316i	$-0.0470635\pi$
$762$	−5.71129	−	1.20497i	−0.206898	−	0.0436515i
$763$	22.3376	−	22.3376i	0.808674	−	0.808674i
$764$	−15.3320	+	34.7178i	−0.554694	+	1.25605i
$765$	−22.6899	−	22.6899i	−0.820354	−	0.820354i
$766$	−22.3203	+	14.5429i	−0.806466	+	0.525456i
$767$	−67.8464			−2.44979
$768$	31.8327	−	26.4199i	1.14866	−	0.953348i
$769$	−39.5146			−1.42493			−0.712466	−	0.701707i	$-0.752422\pi$
$769$	−39.5146			−1.42493			−0.712466	+	0.701707i	$0.752422\pi$
$770$	67.3141	−	43.8588i	2.42583	−	1.58056i
$771$	−0.872807	−	0.872807i	−0.0314334	−	0.0314334i
$772$	−0.990856	+	2.24369i	−0.0356617	+	0.0807522i
$773$	−36.3147	+	36.3147i	−1.30615	+	1.30615i	−0.381976	+	0.924172i	$0.624756\pi$
$773$	−36.3147	+	36.3147i	−1.30615	+	1.30615i	−0.924172	+	0.381976i	$0.875244\pi$
$774$	14.5114	+	3.06163i	0.521603	+	0.110048i
$775$		−	55.1895i		−	1.98247i
$776$	4.61638	+	28.3168i	0.165718	+	1.01651i
$777$			2.34278i			0.0840467i
$778$	−1.59197	+	7.54558i	−0.0570749	+	0.270522i
$779$	−2.05578	+	2.05578i	−0.0736559	+	0.0736559i
$780$	−76.2418	+	29.5307i	−2.72989	+	1.05737i
$781$	14.3910	+	14.3910i	0.514949	+	0.514949i
$782$	1.98312	+	3.04368i	0.0709163	+	0.108842i
$783$	0.230436			0.00823512
$784$	9.69633	+	10.6391i	0.346297	+	0.379967i
$785$	−16.1938			−0.577981
$786$	20.5226	+	31.4978i	0.732015	+	1.12349i
$787$	19.7546	+	19.7546i	0.704175	+	0.704175i	0.965304	−	0.261129i	$-0.0840949\pi$
$787$	19.7546	+	19.7546i	0.704175	+	0.704175i	−0.261129	+	0.965304i	$0.584095\pi$
$788$	0.912015	+	2.35462i	0.0324892	+	0.0838800i
$789$	−23.2170	+	23.2170i	−0.826548	+	0.826548i
$790$	13.5456	−	64.2032i	0.481932	−	2.28425i
$791$			27.6871i			0.984442i
$792$	−31.3378	+	43.5459i	−1.11354	+	1.54734i
$793$			45.6485i			1.62102i
$794$	12.2862	+	2.59214i	0.436020	+	0.0919917i
$795$	44.5720	−	44.5720i	1.58080	−	1.58080i
$796$	41.0615	+	18.1335i	1.45538	+	0.642725i
$797$	0.716927	+	0.716927i	0.0253949	+	0.0253949i	0.719690	−	0.694295i	$-0.244284\pi$
$797$	0.716927	+	0.716927i	0.0253949	+	0.0253949i	−0.694295	+	0.719690i	$0.744284\pi$
$798$	−6.79053	+	4.42440i	−0.240382	+	0.156622i
$799$	25.9342			0.917485
$800$	9.23748	−	35.5449i	0.326594	−	1.25670i
$801$	7.00246			0.247420
$802$	−16.0775	+	10.4753i	−0.567715	+	0.369897i
$803$	0.955374	+	0.955374i	0.0337144	+	0.0337144i
$804$	−69.3084	−	30.6079i	−2.44432	−	1.07946i
$805$	7.80393	−	7.80393i	0.275052	−	0.275052i
$806$	−54.8640	−	11.5752i	−1.93250	−	0.407721i
$807$			17.7924i			0.626322i
$808$	38.4944	+	27.7025i	1.35423	+	0.974571i
$809$			7.97393i			0.280348i	0.990127	+	0.140174i	$0.0447663\pi$
$809$			7.97393i			0.280348i	−0.990127	+	0.140174i	$0.955234\pi$
$810$	−6.40949	+	30.3795i	−0.225206	+	1.06743i
$811$	12.8849	−	12.8849i	0.452452	−	0.452452i	−0.443716	−	0.896167i	$-0.646340\pi$
$811$	12.8849	−	12.8849i	0.452452	−	0.452452i	0.896167	+	0.443716i	$0.146340\pi$
$812$	−0.306026	−	0.790092i	−0.0107394	−	0.0277268i
$813$	7.45242	+	7.45242i	0.261368	+	0.261368i
$814$	1.10608	+	1.69760i	0.0387680	+	0.0595008i
$815$	28.1438			0.985835
$816$	1.23027	−	26.5375i	0.0430680	−	0.928999i
$817$	1.93765			0.0677899
$818$	16.7588	+	25.7213i	0.585959	+	0.899325i
$819$	39.5643	+	39.5643i	1.38249	+	1.38249i
$820$	−26.9973	+	10.4568i	−0.942787	+	0.365169i
$821$	−7.41159	+	7.41159i	−0.258666	+	0.258666i	−0.824511	−	0.565845i	$-0.808550\pi$
$821$	−7.41159	+	7.41159i	−0.258666	+	0.258666i	0.565845	+	0.824511i	$0.308550\pi$
$822$	−8.59397	+	40.7335i	−0.299749	+	1.42074i
$823$			35.2525i			1.22883i	0.788985	+	0.614413i	$0.210607\pi$
$823$			35.2525i			1.22883i	−0.788985	+	0.614413i	$0.789393\pi$
$824$	18.7157	−	3.05115i	0.651992	−	0.106292i
$825$			86.4050i			3.00824i
$826$	−65.5306	−	13.8257i	−2.28010	−	0.481057i
$827$	−12.8828	+	12.8828i	−0.447978	+	0.447978i	−0.894682	−	0.446704i	$-0.852598\pi$
$827$	−12.8828	+	12.8828i	−0.447978	+	0.447978i	0.446704	+	0.894682i	$0.352598\pi$
$828$	−2.97725	+	6.74166i	−0.103466	+	0.234289i
$829$	−10.7788	−	10.7788i	−0.374363	−	0.374363i	0.494700	−	0.869064i	$-0.335278\pi$
$829$	−10.7788	−	10.7788i	−0.374363	−	0.374363i	−0.869064	+	0.494700i	$0.835278\pi$
$830$	4.66313	−	3.03828i	0.161859	−	0.105460i
$831$	−21.7758			−0.755394
$832$	−33.3978	−	16.6380i	−1.15786	−	0.576821i
$833$	9.24406			0.320288
$834$	70.8830	−	46.1841i	2.45448	−	1.59923i
$835$	−14.3857	−	14.3857i	−0.497838	−	0.497838i
$836$	−2.83162	+	6.41192i	−0.0979338	+	0.221761i
$837$	10.6445	−	10.6445i	0.367926	−	0.367926i
$838$	−17.5495	−	3.70260i	−0.606237	−	0.127904i
$839$			33.3416i			1.15108i	0.817774	+	0.575540i	$0.195208\pi$
$839$			33.3416i			1.15108i	−0.817774	+	0.575540i	$0.804792\pi$
$840$	−79.6572	+	12.9862i	−2.74843	+	0.448067i
$841$		−	28.9831i		−	0.999416i
$842$	8.03411	−	38.0799i	0.276874	−	1.31232i
$843$	9.18774	−	9.18774i	0.316443	−	0.316443i
$844$	9.24918	−	3.58248i	0.318370	−	0.123314i
$845$	20.9836	+	20.9836i	0.721858	+	0.721858i
$846$	28.7217	+	44.0819i	0.987473	+	1.51557i
$847$	−50.4510			−1.73352
$848$	28.7356	+	1.33217i	0.986786	+	0.0457470i
$849$	−58.4881			−2.00731
$850$	−12.8749	−	19.7603i	−0.441605	−	0.677772i
$851$	0.196808	+	0.196808i	0.00674649	+	0.00674649i
$852$	−7.38435	−	19.0648i	−0.252983	−	0.653148i
$853$	−29.7296	+	29.7296i	−1.01792	+	1.01792i	−0.0180866	+	0.999836i	$0.505757\pi$
$853$	−29.7296	+	29.7296i	−1.01792	+	1.01792i	−0.999836	+	0.0180866i	$0.994243\pi$
$854$	−9.30220	+	44.0903i	−0.318315	+	1.50874i
$855$		−	8.50507i		−	0.290867i
$856$	1.56716	+	1.12781i	0.0535644	+	0.0385477i
$857$			53.3709i			1.82311i	0.411173	+	0.911557i	$0.365119\pi$
$857$			53.3709i			1.82311i	−0.411173	+	0.911557i	$0.634881\pi$
$858$	85.8954	+	18.1223i	2.93242	+	0.618684i
$859$	32.4157	−	32.4157i	1.10601	−	1.10601i	0.112339	−	0.993670i	$-0.464166\pi$
$859$	32.4157	−	32.4157i	1.10601	−	1.10601i	0.993670	−	0.112339i	$-0.0358342\pi$
$860$	17.6510	+	7.79502i	0.601895	+	0.265808i
$861$	25.4156	+	25.4156i	0.866161	+	0.866161i
$862$	−12.4656	+	8.12200i	−0.424579	+	0.276636i
$863$	7.24837			0.246737			0.123369	−	0.992361i	$-0.460630\pi$
$863$	7.24837			0.246737			0.123369	+	0.992361i	$0.460630\pi$
$864$	8.63722	−	5.07394i	0.293844	−	0.172619i
$865$	−81.8611			−2.78336
$866$	39.7812	−	25.9196i	1.35182	−	0.880784i
$867$	19.0166	+	19.0166i	0.645838	+	0.645838i
$868$	−50.6326	−	22.3603i	−1.71858	−	0.758958i
$869$	−49.8171	+	49.8171i	−1.68993	+	1.68993i
$870$	1.57828	+	0.332986i	0.0535086	+	0.0112893i
$871$			68.3383i			2.31555i
$872$	−16.0314	+	22.2766i	−0.542891	+	0.754380i
$873$			37.3784i			1.26507i
$874$	−0.198770	+	0.942123i	−0.00672349	+	0.0318678i
$875$	−11.6453	+	11.6453i	−0.393682	+	0.393682i
$876$	−0.490225	−	1.26565i	−0.0165632	−	0.0427625i
$877$	0.766861	+	0.766861i	0.0258951	+	0.0258951i	0.719936	−	0.694041i	$-0.244171\pi$
$877$	0.766861	+	0.766861i	0.0258951	+	0.0258951i	−0.694041	+	0.719936i	$0.744171\pi$
$878$	1.76064	+	2.70221i	0.0594186	+	0.0911952i
$879$	−69.8618			−2.35638
$880$	−51.5893	+	47.0179i	−1.73907	+	1.58497i
$881$	−7.81104			−0.263161			−0.131580	−	0.991306i	$-0.542005\pi$
$881$	−7.81104			−0.263161			−0.131580	+	0.991306i	$0.542005\pi$
$882$	10.2377	+	15.7127i	0.344720	+	0.529073i
$883$	5.95253	+	5.95253i	0.200319	+	0.200319i	0.800137	−	0.599818i	$-0.204760\pi$
$883$	5.95253	+	5.95253i	0.200319	+	0.200319i	−0.599818	+	0.800137i	$0.704760\pi$
$884$	−22.3441	+	8.65451i	−0.751512	+	0.291083i
$885$	90.1560	−	90.1560i	3.03056	−	3.03056i
$886$	8.38195	−	39.7286i	0.281597	−	1.33471i
$887$		−	17.0843i		−	0.573635i	−0.957985	−	0.286818i	$-0.907403\pi$
$887$		−	17.0843i		−	0.573635i	0.957985	−	0.286818i	$-0.0925974\pi$
$888$	−0.327501	−	2.00888i	−0.0109902	−	0.0674136i
$889$			5.19702i			0.174302i
$890$	8.91426	+	1.88074i	0.298807	+	0.0630424i
$891$	23.5723	−	23.5723i	0.789703	−	0.789703i
$892$	2.62749	−	5.94968i	0.0879750	−	0.199210i
$893$	4.86058	+	4.86058i	0.162653	+	0.162653i
$894$	26.7573	−	17.4339i	0.894899	−	0.583075i
$895$	32.9343			1.10087
$896$	−28.8674	−	22.8759i	−0.964391	−	0.764231i
$897$	12.0591			0.402641
$898$	33.3088	−	21.7025i	1.11153	−	0.724221i
$899$	0.782209	+	0.782209i	0.0260881	+	0.0260881i
$900$	19.3290	−	43.7684i	0.644299	−	1.45895i
$901$	13.0626	−	13.0626i	0.435180	−	0.435180i
$902$	30.4156	+	6.41711i	1.01273	+	0.213666i
$903$		−	23.9552i		−	0.797180i
$904$	−3.87043	−	23.7411i	−0.128729	−	0.789618i
$905$			2.19467i			0.0729533i
$906$	5.50488	−	26.0919i	0.182887	−	0.866845i
$907$	14.8197	−	14.8197i	0.492079	−	0.492079i	−0.416882	−	0.908961i	$-0.636877\pi$
$907$	14.8197	−	14.8197i	0.492079	−	0.492079i	0.908961	+	0.416882i	$0.136877\pi$
$908$	26.9125	−	10.4240i	0.893122	−	0.345932i
$909$	43.6902	+	43.6902i	1.44911	+	1.44911i
$910$	39.7398	+	60.9923i	1.31736	+	2.02188i
$911$	14.7021			0.487101			0.243551	−	0.969888i	$-0.421688\pi$
$911$	14.7021			0.487101			0.243551	+	0.969888i	$0.421688\pi$
$912$	5.20424	−	4.74308i	0.172329	−	0.157059i
$913$	−5.97574			−0.197768
$914$	−9.54763	−	14.6536i	−0.315808	−	0.484699i
$915$	−60.6588	−	60.6588i	−2.00532	−	2.00532i
$916$	12.1014	+	31.2432i	0.399842	+	1.03230i
$917$	23.6681	−	23.6681i	0.781591	−	0.781591i
$918$	1.32799	−	6.29438i	0.0438303	−	0.207745i
$919$			24.2710i			0.800626i	0.916379	+	0.400313i	$0.131099\pi$
$919$			24.2710i			0.800626i	−0.916379	+	0.400313i	$0.868901\pi$
$920$	−5.60077	+	7.78262i	−0.184652	+	0.256585i
$921$		−	26.7945i		−	0.882908i
$922$	−41.1057	−	8.67251i	−1.35374	−	0.285614i
$923$	−13.0395	+	13.0395i	−0.429199	+	0.429199i
$924$	79.2706	+	35.0074i	2.60781	+	1.15166i
$925$	−1.27772	−	1.27772i	−0.0420113	−	0.0420113i
$926$	0.693026	−	0.451544i	0.0227742	−	0.0148387i
$927$	24.7049			0.811415
$928$	0.372859	+	0.634707i	0.0122397	+	0.0208353i
$929$	−24.3994			−0.800518			−0.400259	−	0.916402i	$-0.631080\pi$
$929$	−24.3994			−0.800518			−0.400259	+	0.916402i	$0.631080\pi$
$930$	88.2862	−	57.5232i	2.89502	−	1.88626i
$931$	1.73252	+	1.73252i	0.0567811	+	0.0567811i
$932$	−18.9773	−	8.38072i	−0.621621	−	0.274520i
$933$	−32.5637	+	32.5637i	−1.06609	+	1.06609i
$934$	−22.6211	−	4.77260i	−0.740184	−	0.156164i
$935$			44.8248i			1.46593i
$936$	−39.4563	−	28.3948i	−1.28967	−	0.928113i
$937$			13.4591i			0.439690i	0.975535	+	0.219845i	$0.0705552\pi$
$937$			13.4591i			0.439690i	−0.975535	+	0.219845i	$0.929445\pi$
$938$	−13.9259	+	66.0057i	−0.454697	+	2.15516i
$939$	43.0625	−	43.0625i	1.40529	−	1.40529i
$940$	24.7237	+	63.8311i	0.806397	+	2.08194i
$941$	−24.4482	−	24.4482i	−0.796989	−	0.796989i	0.185631	−	0.982620i	$-0.440567\pi$
$941$	−24.4482	−	24.4482i	−0.796989	−	0.796989i	−0.982620	+	0.185631i	$0.940567\pi$
$942$	−9.53508	−	14.6344i	−0.310670	−	0.476813i
$943$	4.27014			0.139055
$944$	58.1238	+	2.69459i	1.89177	+	0.0877016i
$945$	−19.5436			−0.635753
$946$	−11.3098	−	17.3582i	−0.367713	−	0.564363i
$947$	2.95290	+	2.95290i	0.0959564	+	0.0959564i	0.753455	−	0.657499i	$-0.228386\pi$
$947$	2.95290	+	2.95290i	0.0959564	+	0.0959564i	−0.657499	+	0.753455i	$0.728386\pi$
$948$	65.9964	−	25.5623i	2.14346	−	0.830226i
$949$	−0.865651	+	0.865651i	−0.0281002	+	0.0281002i
$950$	1.29046	−	6.11648i	0.0418680	−	0.198445i
$951$			83.6864i			2.71372i
$952$	−23.3450	+	3.80585i	−0.756616	+	0.123348i
$953$		−	7.06105i		−	0.228730i	−0.993439	−	0.114365i	$-0.963517\pi$
$953$		−	7.06105i		−	0.228730i	0.993439	−	0.114365i	$-0.0364833\pi$
$954$	36.6700	+	7.73666i	1.18724	+	0.250484i
$955$	−45.4882	+	45.4882i	−1.47196	+	1.47196i
$956$	−17.8227	+	40.3577i	−0.576428	+	1.30526i
$957$	−1.22463	−	1.22463i	−0.0395867	−	0.0395867i
$958$	21.9946	−	14.3307i	0.710612	−	0.463002i
$959$	37.0657			1.19691
$960$	66.4889	−	22.2708i	2.14592	−	0.718787i
$961$	41.2646			1.33112
$962$	−1.53817	+	1.00220i	−0.0495926	+	0.0323123i
$963$	1.77869	+	1.77869i	0.0573175	+	0.0573175i
$964$	8.86995	−	20.0851i	0.285682	−	0.646897i
$965$	−2.93974	+	2.93974i	−0.0946336	+	0.0946336i
$966$	11.6475	+	2.45739i	0.374751	+	0.0790652i
$967$		−	25.3194i		−	0.814218i	−0.913379	−	0.407109i	$-0.866537\pi$
$967$		−	25.3194i		−	0.814218i	0.913379	−	0.407109i	$-0.133463\pi$
$968$	43.2607	−	7.05263i	1.39045	−	0.226680i
$969$		−	4.52185i		−	0.145263i
$970$	−10.0392	+	47.5834i	−0.322338	+	1.52781i
$971$	−14.6874	+	14.6874i	−0.471341	+	0.471341i	−0.902348	−	0.431007i	$-0.858158\pi$
$971$	−14.6874	+	14.6874i	−0.471341	+	0.471341i	0.431007	+	0.902348i	$0.358158\pi$
$972$	−41.1357	+	15.9331i	−1.31943	+	0.511054i
$973$	−53.2630	−	53.2630i	−1.70753	−	1.70753i
$974$	1.98422	+	3.04537i	0.0635786	+	0.0975800i
$975$	−78.2904			−2.50730
$976$	1.81298	−	39.1069i	0.0580320	−	1.25178i
$977$	−18.0071			−0.576097			−0.288048	−	0.957616i	$-0.593006\pi$
$977$	−18.0071			−0.576097			−0.288048	+	0.957616i	$0.593006\pi$
$978$	16.5714	+	25.4336i	0.529895	+	0.813278i
$979$	−6.91683	−	6.91683i	−0.221063	−	0.221063i
$980$	8.81258	+	22.7522i	0.281507	+	0.726791i
$981$	−25.2834	+	25.2834i	−0.807238	+	0.807238i
$982$	0.582202	−	2.75951i	0.0185788	−	0.0880593i
$983$		−	0.830366i		−	0.0264846i	−0.999912	−	0.0132423i	$-0.995785\pi$
$983$		−	0.830366i		−	0.0264846i	0.999912	−	0.0132423i	$-0.00421527\pi$
$984$	−25.3462	−	18.2404i	−0.808007	−	0.581484i
$985$			4.28003i			0.136373i
$986$	0.462543	+	0.0975876i	0.0147304	+	0.00310782i
$987$	60.0914	−	60.0914i	1.91273	−	1.91273i
$988$	−5.80975	−	2.56570i	−0.184833	−	0.0816257i
$989$	−2.01239	−	2.01239i	−0.0639902	−	0.0639902i
$990$	−76.1914	+	49.6428i	−2.42152	+	1.57775i
$991$	−9.35097			−0.297043			−0.148522	−	0.988909i	$-0.547451\pi$
$991$	−9.35097			−0.297043			−0.148522	+	0.988909i	$0.547451\pi$
$992$	46.5421	+	12.0955i	1.47771	+	0.384031i
$993$	69.4554			2.20410
$994$	−15.2515	+	9.93721i	−0.483750	+	0.315189i
$995$	53.7998	+	53.7998i	1.70557	+	1.70557i
$996$	5.49140	+	2.42511i	0.174002	+	0.0768424i
$997$	−10.9212	+	10.9212i	−0.345878	+	0.345878i	−0.858572	−	0.512694i	$-0.828648\pi$
$997$	−10.9212	+	10.9212i	−0.345878	+	0.345878i	0.512694	+	0.858572i	$0.328648\pi$
$998$	−22.8260	−	4.81585i	−0.722546	−	0.152443i
$999$		−	0.492871i		−	0.0155938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.j.e.93.5	✓	46
4.3	odd	2		1472.2.j.e.1105.20		46
16.5	even	4	inner	368.2.j.e.277.5	yes	46
16.11	odd	4		1472.2.j.e.369.20		46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.j.e.93.5	✓	46	1.1	even	1	trivial
368.2.j.e.277.5	yes	46	16.5	even	4	inner
1472.2.j.e.369.20		46	16.11	odd	4
1472.2.j.e.1105.20		46	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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18490 + 0.772024i) q^{2} +(-1.82824 - 1.82824i) q^{3} +(0.807958 - 1.82954i) q^{4} +(2.39711 - 2.39711i) q^{5} +(3.57771 + 0.754828i) q^{6} -3.25556i q^{7} +(0.455100 + 2.79157i) q^{8} +3.68490i q^{9} +(-0.989698 + 4.69094i) q^{10} +(3.63984 - 3.63984i) q^{11} +(-4.82197 + 1.86769i) q^{12} +(3.29801 + 3.29801i) q^{13} +(2.51337 + 3.85750i) q^{14} -8.76496 q^{15} +(-2.69441 - 2.95638i) q^{16} -2.56873 q^{17} +(-2.84483 - 4.36623i) q^{18} +(-0.481432 - 0.481432i) q^{19} +(-2.44883 - 6.32235i) q^{20} +(-5.95194 + 5.95194i) q^{21} +(-1.50279 + 7.12288i) q^{22} +1.00000i q^{23} +(4.27163 - 5.93569i) q^{24} -6.49223i q^{25} +(-6.45394 - 1.36166i) q^{26} +(1.25216 - 1.25216i) q^{27} +(-5.95617 - 2.63036i) q^{28} +(0.0920153 + 0.0920153i) q^{29} +(10.3856 - 6.76676i) q^{30} +8.50086 q^{31} +(5.47499 + 1.42285i) q^{32} -13.3090 q^{33} +(3.04368 - 1.98312i) q^{34} +(-7.80393 - 7.80393i) q^{35} +(6.74166 + 2.97725i) q^{36} +(0.196808 - 0.196808i) q^{37} +(0.942123 + 0.198770i) q^{38} -12.0591i q^{39} +(7.78262 + 5.60077i) q^{40} -4.27014i q^{41} +(2.45739 - 11.6475i) q^{42} +(-2.01239 + 2.01239i) q^{43} +(-3.71838 - 9.60006i) q^{44} +(8.83310 + 8.83310i) q^{45} +(-0.772024 - 1.18490i) q^{46} -10.0961 q^{47} +(-0.478940 + 10.3310i) q^{48} -3.59868 q^{49} +(5.01216 + 7.69262i) q^{50} +(4.69625 + 4.69625i) q^{51} +(8.69848 - 3.36918i) q^{52} +(-5.08525 + 5.08525i) q^{53} +(-0.516983 + 2.45038i) q^{54} -17.4502i q^{55} +(9.08814 - 1.48161i) q^{56} +1.76034i q^{57} +(-0.180067 - 0.0379906i) q^{58} +(-10.2860 + 10.2860i) q^{59} +(-7.08171 + 16.0358i) q^{60} +(6.92061 + 6.92061i) q^{61} +(-10.0726 + 6.56287i) q^{62} +11.9964 q^{63} +(-7.58577 + 2.54089i) q^{64} +15.8114 q^{65} +(15.7698 - 10.2749i) q^{66} +(10.3605 + 10.3605i) q^{67} +(-2.07543 + 4.69959i) q^{68} +(1.82824 - 1.82824i) q^{69} +(15.2717 + 3.22202i) q^{70} +3.95374i q^{71} +(-10.2867 + 1.67700i) q^{72} +0.262477i q^{73} +(-0.0812565 + 0.385137i) q^{74} +(-11.8693 + 11.8693i) q^{75} +(-1.26977 + 0.491820i) q^{76} +(-11.8497 - 11.8497i) q^{77} +(9.30990 + 14.2888i) q^{78} -13.6866 q^{79} +(-13.5455 - 0.627965i) q^{80} +6.47620 q^{81} +(3.29665 + 5.05967i) q^{82} +(-0.820880 - 0.820880i) q^{83} +(6.08038 + 15.6982i) q^{84} +(-6.15752 + 6.15752i) q^{85} +(0.830859 - 3.93808i) q^{86} -0.336452i q^{87} +(11.8174 + 8.50439i) q^{88} -1.90031i q^{89} +(-17.2857 - 3.64694i) q^{90} +(10.7369 - 10.7369i) q^{91} +(1.82954 + 0.807958i) q^{92} +(-15.5416 - 15.5416i) q^{93} +(11.9628 - 7.79443i) q^{94} -2.30809 q^{95} +(-7.40827 - 12.6109i) q^{96} +10.1437 q^{97} +(4.26407 - 2.77827i) q^{98} +(13.4125 + 13.4125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 2 q^{2} + 6 q^{3} + 4 q^{5} + 2 q^{8} - 10 q^{10} + 4 q^{11} - 16 q^{12} + 2 q^{13} + 28 q^{14} - 12 q^{15} - 8 q^{16} - 16 q^{17} - 34 q^{18} + 4 q^{19} + 18 q^{20} - 28 q^{22} - 30 q^{24} + 2 q^{26}+ \cdots - 28 q^{99}+O(q^{100}) \) 46 * q + 2 * q^2 + 6 * q^3 + 4 * q^5 + 2 * q^8 - 10 * q^10 + 4 * q^11 - 16 * q^12 + 2 * q^13 + 28 * q^14 - 12 * q^15 - 8 * q^16 - 16 * q^17 - 34 * q^18 + 4 * q^19 + 18 * q^20 - 28 * q^22 - 30 * q^24 + 2 * q^26 - 26 * q^28 + 2 * q^29 + 56 * q^30 + 40 * q^31 - 8 * q^32 + 60 * q^33 + 10 * q^34 + 8 * q^35 + 50 * q^36 + 24 * q^37 - 56 * q^38 + 10 * q^42 - 8 * q^43 - 50 * q^44 + 12 * q^45 - 2 * q^46 + 20 * q^47 - 110 * q^49 - 44 * q^51 + 24 * q^52 + 20 * q^53 - 64 * q^54 - 8 * q^56 - 2 * q^58 - 54 * q^59 - 90 * q^60 - 8 * q^61 + 18 * q^62 + 24 * q^63 - 6 * q^64 + 28 * q^65 + 6 * q^66 + 42 * q^68 - 6 * q^69 - 58 * q^70 + 90 * q^72 + 6 * q^74 - 30 * q^75 - 44 * q^76 - 28 * q^77 + 44 * q^78 + 16 * q^79 - 52 * q^80 - 26 * q^81 - 62 * q^82 + 28 * q^83 + 170 * q^84 - 12 * q^85 - 92 * q^86 + 64 * q^88 + 140 * q^90 + 48 * q^91 - 4 * q^92 - 48 * q^93 + 52 * q^94 - 56 * q^96 + 72 * q^97 - 44 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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