LMFDB - Embedded newform 35.4.f.b.13.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [35,4,Mod(13,35)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("35.13"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	35.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.06506685020$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10654x^{12} + 22102125x^{8} + 5700572500x^{4} + 44626562500 $ x^16 + 10654x^12 + 22102125x^8 + 5700572500*x^4 + 44626562500
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.3
Root			$-2.91939 - 2.91939i$ of defining polynomial
Character	$\chi$	$=$	35.13
Dual form			35.4.f.b.27.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.172516 - 0.172516i) q^{2} +(-2.91939 + 2.91939i) q^{3} +7.94048i q^{4} +(-9.78787 + 5.40347i) q^{5} +1.00728i q^{6} +(18.1737 - 3.56610i) q^{7} +(2.74998 + 2.74998i) q^{8} +9.95432i q^{9} +(-0.756378 + 2.62074i) q^{10} -15.1443 q^{11} +(-23.1814 - 23.1814i) q^{12} +(40.2848 - 40.2848i) q^{13} +(2.52004 - 3.75045i) q^{14} +(12.7998 - 44.3495i) q^{15} -62.5750 q^{16} +(30.0616 + 30.0616i) q^{17} +(1.71728 + 1.71728i) q^{18} +65.1185 q^{19} +(-42.9061 - 77.7204i) q^{20} +(-42.6452 + 63.4669i) q^{21} +(-2.61264 + 2.61264i) q^{22} +(56.5971 + 56.5971i) q^{23} -16.0565 q^{24} +(66.6050 - 105.777i) q^{25} -13.8995i q^{26} +(-107.884 - 107.884i) q^{27} +(28.3165 + 144.308i) q^{28} +104.464i q^{29} +(-5.44281 - 9.85914i) q^{30} +317.751i q^{31} +(-32.7950 + 32.7950i) q^{32} +(44.2123 - 44.2123i) q^{33} +10.3722 q^{34} +(-158.612 + 133.106i) q^{35} -79.0420 q^{36} +(190.864 - 190.864i) q^{37} +(11.2340 - 11.2340i) q^{38} +235.214i q^{39} +(-41.7759 - 12.0570i) q^{40} -370.814i q^{41} +(3.59207 + 18.3060i) q^{42} +(10.8913 + 10.8913i) q^{43} -120.253i q^{44} +(-53.7879 - 97.4316i) q^{45} +19.5278 q^{46} +(-100.476 - 100.476i) q^{47} +(182.681 - 182.681i) q^{48} +(317.566 - 129.618i) q^{49} +(-6.75779 - 29.7386i) q^{50} -175.523 q^{51} +(319.881 + 319.881i) q^{52} +(-332.255 - 332.255i) q^{53} -37.2234 q^{54} +(148.231 - 81.8320i) q^{55} +(59.7840 + 40.1706i) q^{56} +(-190.106 + 190.106i) q^{57} +(18.0217 + 18.0217i) q^{58} -484.782 q^{59} +(352.156 + 101.636i) q^{60} -315.263i q^{61} +(54.8170 + 54.8170i) q^{62} +(35.4981 + 180.907i) q^{63} -489.285i q^{64} +(-176.625 + 611.980i) q^{65} -15.2546i q^{66} +(-40.1151 + 40.1151i) q^{67} +(-238.704 + 238.704i) q^{68} -330.458 q^{69} +(-4.40034 + 50.3259i) q^{70} +906.887 q^{71} +(-27.3742 + 27.3742i) q^{72} +(-96.5419 + 96.5419i) q^{73} -65.8540i q^{74} +(114.358 + 503.250i) q^{75} +517.072i q^{76} +(-275.229 + 54.0063i) q^{77} +(40.5781 + 40.5781i) q^{78} +354.468i q^{79} +(612.476 - 338.122i) q^{80} +361.145 q^{81} +(-63.9712 - 63.9712i) q^{82} +(-522.441 + 522.441i) q^{83} +(-503.958 - 338.624i) q^{84} +(-456.677 - 131.802i) q^{85} +3.75783 q^{86} +(-304.971 - 304.971i) q^{87} +(-41.6467 - 41.6467i) q^{88} +1064.18 q^{89} +(-26.0877 - 7.52923i) q^{90} +(588.464 - 875.783i) q^{91} +(-449.408 + 449.408i) q^{92} +(-927.639 - 927.639i) q^{93} -34.6673 q^{94} +(-637.371 + 351.866i) q^{95} -191.483i q^{96} +(577.458 + 577.458i) q^{97} +(32.4239 - 77.1463i) q^{98} -150.752i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 32 q^{7} + 176 q^{8} - 152 q^{11} - 480 q^{15} - 504 q^{16} + 288 q^{18} + 328 q^{21} + 348 q^{22} - 72 q^{23} - 160 q^{25} - 528 q^{28} + 1780 q^{30} + 432 q^{32} + 160 q^{35} + 344 q^{36}+ \cdots + 3308 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 + 32 * q^7 + 176 * q^8 - 152 * q^11 - 480 * q^15 - 504 * q^16 + 288 * q^18 + 328 * q^21 + 348 * q^22 - 72 * q^23 - 160 * q^25 - 528 * q^28 + 1780 * q^30 + 432 * q^32 + 160 * q^35 + 344 * q^36 - 256 * q^37 - 1300 * q^42 - 312 * q^43 - 1856 * q^46 - 20 * q^50 + 696 * q^51 + 1768 * q^53 + 1304 * q^56 - 3920 * q^57 - 4764 * q^58 - 2000 * q^60 + 2544 * q^63 - 1000 * q^65 + 4504 * q^67 - 180 * q^70 + 6368 * q^71 + 7848 * q^72 - 3016 * q^77 + 5340 * q^78 - 3088 * q^81 - 2280 * q^85 - 9336 * q^86 - 2048 * q^88 + 1608 * q^91 - 6328 * q^92 - 3960 * q^93 + 1240 * q^95 + 3308 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.172516	−	0.172516i	0.0609935	−	0.0609935i	−0.675952	−	0.736946i	$-0.736267\pi$
$2$	0.172516	−	0.172516i	0.0609935	−	0.0609935i	0.736946	+	0.675952i	$0.236267\pi$
$3$	−2.91939	+	2.91939i	−0.561837	+	0.561837i	−0.929829	−	0.367992i	$-0.880045\pi$
$3$	−2.91939	+	2.91939i	−0.561837	+	0.561837i	0.367992	+	0.929829i	$0.380045\pi$
$4$			7.94048i			0.992560i
$5$	−9.78787	+	5.40347i	−0.875454	+	0.483301i
$5$	−9.78787	+	5.40347i	−0.875454	+	0.483301i
$6$			1.00728i			0.0685368i
$7$	18.1737	−	3.56610i	0.981287	−	0.192551i
$7$	18.1737	−	3.56610i	0.981287	−	0.192551i
$8$	2.74998	+	2.74998i	0.121533	+	0.121533i
$9$			9.95432i			0.368678i
$10$	−0.756378	+	2.62074i	−0.0239188	+	0.0828752i
$11$	−15.1443			−0.415108			−0.207554	−	0.978224i	$-0.566550\pi$
$11$	−15.1443			−0.415108			−0.207554	+	0.978224i	$0.566550\pi$
$12$	−23.1814	−	23.1814i	−0.557657	−	0.557657i
$13$	40.2848	−	40.2848i	0.859461	−	0.859461i	−0.131813	−	0.991275i	$-0.542080\pi$
$13$	40.2848	−	40.2848i	0.859461	−	0.859461i	0.991275	+	0.131813i	$0.0420800\pi$
$14$	2.52004	−	3.75045i	0.0481077	−	0.0715965i
$15$	12.7998	−	44.3495i	0.220326	−	0.763399i
$16$	−62.5750			−0.977734
$17$	30.0616	+	30.0616i	0.428883	+	0.428883i	0.888248	−	0.459365i	$-0.151923\pi$
$17$	30.0616	+	30.0616i	0.428883	+	0.428883i	−0.459365	+	0.888248i	$0.651923\pi$
$18$	1.71728	+	1.71728i	0.0224870	+	0.0224870i
$19$	65.1185			0.786274			0.393137	−	0.919480i	$-0.371390\pi$
$19$	65.1185			0.786274			0.393137	+	0.919480i	$0.371390\pi$
$20$	−42.9061	−	77.7204i	−0.479705	−	0.868940i
$21$	−42.6452	+	63.4669i	−0.443141	+	0.659506i
$22$	−2.61264	+	2.61264i	−0.0253189	+	0.0253189i
$23$	56.5971	+	56.5971i	0.513101	+	0.513101i	0.915475	−	0.402375i	$-0.131815\pi$
$23$	56.5971	+	56.5971i	0.513101	+	0.513101i	−0.402375	+	0.915475i	$0.631815\pi$
$24$	−16.0565			−0.136564
$25$	66.6050	−	105.777i	0.532840	−	0.846216i
$26$		−	13.8995i		−	0.104843i
$27$	−107.884	−	107.884i	−0.768974	−	0.768974i
$28$	28.3165	+	144.308i	0.191119	+	0.973986i
$29$			104.464i			0.668913i	0.942411	+	0.334456i	$0.108553\pi$
$29$			104.464i			0.668913i	−0.942411	+	0.334456i	$0.891447\pi$
$30$	−5.44281	−	9.85914i	−0.0331239	−	0.0600008i
$31$			317.751i			1.84096i	0.390789	+	0.920480i	$0.372202\pi$
$31$			317.751i			1.84096i	−0.390789	+	0.920480i	$0.627798\pi$
$32$	−32.7950	+	32.7950i	−0.181169	+	0.181169i
$33$	44.2123	−	44.2123i	0.233223	−	0.233223i
$34$	10.3722			0.0523182
$35$	−158.612	+	133.106i	−0.766011	+	0.642827i
$36$	−79.0420			−0.365935
$37$	190.864	−	190.864i	0.848050	−	0.848050i	−0.141840	−	0.989890i	$-0.545302\pi$
$37$	190.864	−	190.864i	0.848050	−	0.848050i	0.989890	+	0.141840i	$0.0453018\pi$
$38$	11.2340	−	11.2340i	0.0479576	−	0.0479576i
$39$			235.214i			0.965754i
$40$	−41.7759	−	12.0570i	−0.165134	−	0.0476596i
$41$		−	370.814i		−	1.41247i	−0.707976	−	0.706236i	$-0.750392\pi$
$41$		−	370.814i		−	1.41247i	0.707976	−	0.706236i	$-0.249608\pi$
$42$	3.59207	+	18.3060i	0.0131968	+	0.0672542i
$43$	10.8913	+	10.8913i	0.0386257	+	0.0386257i	0.726156	−	0.687530i	$-0.241305\pi$
$43$	10.8913	+	10.8913i	0.0386257	+	0.0386257i	−0.687530	+	0.726156i	$0.741305\pi$
$44$		−	120.253i		−	0.412020i
$45$	−53.7879	−	97.4316i	−0.178183	−	0.322761i
$46$	19.5278			0.0625916
$47$	−100.476	−	100.476i	−0.311827	−	0.311827i	0.533790	−	0.845617i	$-0.320767\pi$
$47$	−100.476	−	100.476i	−0.311827	−	0.311827i	−0.845617	+	0.533790i	$0.820767\pi$
$48$	182.681	−	182.681i	0.549327	−	0.549327i
$49$	317.566	−	129.618i	0.925848	−	0.377896i
$50$	−6.75779	−	29.7386i	−0.0191139	−	0.0841134i
$51$	−175.523			−0.481925
$52$	319.881	+	319.881i	0.853066	+	0.853066i
$53$	−332.255	−	332.255i	−0.861108	−	0.861108i	0.130359	−	0.991467i	$-0.458387\pi$
$53$	−332.255	−	332.255i	−0.861108	−	0.861108i	−0.991467	+	0.130359i	$0.958387\pi$
$54$	−37.2234			−0.0938048
$55$	148.231	−	81.8320i	0.363408	−	0.200622i
$56$	59.7840	+	40.1706i	0.142660	+	0.0958575i
$57$	−190.106	+	190.106i	−0.441758	+	0.441758i
$58$	18.0217	+	18.0217i	0.0407993	+	0.0407993i
$59$	−484.782			−1.06971			−0.534857	−	0.844942i	$-0.679635\pi$
$59$	−484.782			−1.06971			−0.534857	+	0.844942i	$0.679635\pi$
$60$	352.156	+	101.636i	0.757719	+	0.218687i
$61$		−	315.263i		−	0.661726i	−0.943679	−	0.330863i	$-0.892660\pi$
$61$		−	315.263i		−	0.661726i	0.943679	−	0.330863i	$-0.107340\pi$
$62$	54.8170	+	54.8170i	0.112287	+	0.112287i
$63$	35.4981	+	180.907i	0.0709895	+	0.361779i
$64$		−	489.285i		−	0.955634i
$65$	−176.625	+	611.980i	−0.337040	+	1.16780i
$66$		−	15.2546i		−	0.0284502i
$67$	−40.1151	+	40.1151i	−0.0731468	+	0.0731468i	−0.742734	−	0.669587i	$-0.766471\pi$
$67$	−40.1151	+	40.1151i	−0.0731468	+	0.0731468i	0.669587	+	0.742734i	$0.266471\pi$
$68$	−238.704	+	238.704i	−0.425692	+	0.425692i
$69$	−330.458			−0.576558
$70$	−4.40034	+	50.3259i	−0.00751344	+	0.0859299i
$71$	906.887			1.51588			0.757942	−	0.652322i	$-0.226205\pi$
$71$	906.887			1.51588			0.757942	+	0.652322i	$0.226205\pi$
$72$	−27.3742	+	27.3742i	−0.0448067	+	0.0448067i
$73$	−96.5419	+	96.5419i	−0.154786	+	0.154786i	−0.780252	−	0.625466i	$-0.784909\pi$
$73$	−96.5419	+	96.5419i	−0.154786	+	0.154786i	0.625466	+	0.780252i	$0.284909\pi$
$74$		−	65.8540i		−	0.103451i
$75$	114.358	+	503.250i	0.176066	+	0.774805i
$76$			517.072i			0.780424i
$77$	−275.229	+	54.0063i	−0.407340	+	0.0799297i
$78$	40.5781	+	40.5781i	0.0589047	+	0.0589047i
$79$			354.468i			0.504820i	0.967620	+	0.252410i	$0.0812231\pi$
$79$			354.468i			0.504820i	−0.967620	+	0.252410i	$0.918777\pi$
$80$	612.476	−	338.122i	0.855961	−	0.472540i
$81$	361.145			0.495398
$82$	−63.9712	−	63.9712i	−0.0861516	−	0.0861516i
$83$	−522.441	+	522.441i	−0.690908	+	0.690908i	−0.962432	−	0.271524i	$-0.912472\pi$
$83$	−522.441	+	522.441i	−0.690908	+	0.690908i	0.271524	+	0.962432i	$0.412472\pi$
$84$	−503.958	−	338.624i	−0.654599	−	0.439844i
$85$	−456.677	−	131.802i	−0.582747	−	0.168188i
$86$	3.75783			0.00471183
$87$	−304.971	−	304.971i	−0.375820	−	0.375820i
$88$	−41.6467	−	41.6467i	−0.0504494	−	0.0504494i
$89$	1064.18			1.26744			0.633722	−	0.773561i	$-0.281526\pi$
$89$	1064.18			1.26744			0.633722	+	0.773561i	$0.281526\pi$
$90$	−26.0877	−	7.52923i	−0.0305543	−	0.00881834i
$91$	588.464	−	875.783i	0.677888	−	1.00887i
$92$	−449.408	+	449.408i	−0.509283	+	0.509283i
$93$	−927.639	−	927.639i	−1.03432	−	1.03432i
$94$	−34.6673			−0.0380389
$95$	−637.371	+	351.866i	−0.688347	+	0.380007i
$96$		−	191.483i		−	0.203574i
$97$	577.458	+	577.458i	0.604454	+	0.604454i	0.941491	−	0.337037i	$-0.109425\pi$
$97$	577.458	+	577.458i	0.604454	+	0.604454i	−0.337037	+	0.941491i	$0.609425\pi$
$98$	32.4239	−	77.1463i	0.0334215	−	0.0795199i
$99$		−	150.752i		−	0.153041i
$100$	839.920	+	528.875i	0.839920	+	0.528875i
$101$		−	1057.45i		−	1.04178i	−0.853624	−	0.520890i	$-0.825600\pi$
$101$		−	1057.45i		−	1.04178i	0.853624	−	0.520890i	$-0.174400\pi$
$102$	−30.2805	+	30.2805i	−0.0293943	+	0.0293943i
$103$	−56.1233	+	56.1233i	−0.0536893	+	0.0536893i	−0.733442	−	0.679752i	$-0.762087\pi$
$103$	−56.1233	+	56.1233i	−0.0536893	+	0.0536893i	0.679752	+	0.733442i	$0.262087\pi$
$104$	221.565			0.208906
$105$	74.4646	−	851.639i	0.0692095	−	0.791537i
$106$	−114.638			−0.105044
$107$	1335.01	−	1335.01i	1.20617	−	1.20617i	0.233914	−	0.972257i	$-0.424847\pi$
$107$	1335.01	−	1335.01i	1.20617	−	1.20617i	0.972257	−	0.233914i	$-0.0751534\pi$
$108$	856.651	−	856.651i	0.763253	−	0.763253i
$109$		−	324.403i		−	0.285065i	−0.989790	−	0.142533i	$-0.954475\pi$
$109$		−	324.403i		−	0.285065i	0.989790	−	0.142533i	$-0.0455246\pi$
$110$	11.4548	−	39.6894i	0.00992888	−	0.0344022i
$111$			1114.41i			0.952931i
$112$	−1137.22	+	223.149i	−0.959438	+	0.188264i
$113$	136.101	+	136.101i	0.113303	+	0.113303i	0.761485	−	0.648182i	$-0.224470\pi$
$113$	136.101	+	136.101i	0.113303	+	0.113303i	−0.648182	+	0.761485i	$0.724470\pi$
$114$			65.5926i			0.0538887i
$115$	−859.786	−	248.145i	−0.697178	−	0.201214i
$116$	−829.494			−0.663936
$117$	401.008	+	401.008i	0.316865	+	0.316865i
$118$	−83.6324	+	83.6324i	−0.0652456	+	0.0652456i
$119$	653.533	+	439.128i	0.503440	+	0.338275i
$120$	157.159	−	86.7610i	0.119555	−	0.0660014i
$121$	−1101.65			−0.827685
$122$	−54.3878	−	54.3878i	−0.0403610	−	0.0403610i
$123$	1082.55	+	1082.55i	0.793580	+	0.793580i
$124$	−2523.09			−1.82726
$125$	−80.3581	+	1395.23i	−0.0574996	+	0.998346i
$126$	37.3332	+	25.0852i	0.0263961	+	0.0177363i
$127$	−731.290	+	731.290i	−0.510957	+	0.510957i	−0.914820	−	0.403863i	$-0.867667\pi$
$127$	−731.290	+	731.290i	−0.510957	+	0.510957i	0.403863	+	0.914820i	$0.367667\pi$
$128$	−346.769	−	346.769i	−0.239456	−	0.239456i
$129$	−63.5918			−0.0434027
$130$	75.1056	+	136.047i	0.0506708	+	0.0917853i
$131$			1503.34i			1.00265i	0.865258	+	0.501327i	$0.167155\pi$
$131$			1503.34i			1.00265i	−0.865258	+	0.501327i	$0.832845\pi$
$132$	351.066	+	351.066i	0.231488	+	0.231488i
$133$	1183.44	−	232.219i	0.771560	−	0.151398i
$134$			13.8409i			0.00892295i
$135$	1638.90	+	473.007i	1.04485	+	0.301555i
$136$			165.338i			0.104247i
$137$	1918.81	−	1918.81i	1.19660	−	1.19660i	0.221426	−	0.975177i	$-0.428929\pi$
$137$	1918.81	−	1918.81i	1.19660	−	1.19660i	0.975177	−	0.221426i	$-0.0710711\pi$
$138$	−57.0092	+	57.0092i	−0.0351663	+	0.0351663i
$139$	658.997			0.402125			0.201063	−	0.979578i	$-0.435561\pi$
$139$	658.997			0.402125			0.201063	+	0.979578i	$0.435561\pi$
$140$	−1056.92	−	1259.46i	−0.638044	−	0.760312i
$141$	586.656			0.350392
$142$	156.452	−	156.452i	0.0924590	−	0.0924590i
$143$	−610.087	+	610.087i	−0.356769	+	0.356769i
$144$		−	622.891i		−	0.360470i
$145$	−564.468	−	1022.48i	−0.323286	−	0.585602i
$146$			33.3100i			0.0188819i
$147$	−548.692	+	1305.51i	−0.307860	+	0.732492i
$148$	1515.55	+	1515.55i	0.841740	+	0.841740i
$149$			3027.11i			1.66437i	0.554500	+	0.832183i	$0.312909\pi$
$149$			3027.11i			1.66437i	−0.554500	+	0.832183i	$0.687091\pi$
$150$	106.547	+	67.0899i	0.0579969	+	0.0365191i
$151$	−2127.15			−1.14639			−0.573195	−	0.819419i	$-0.694296\pi$
$151$	−2127.15			−1.14639			−0.573195	+	0.819419i	$0.694296\pi$
$152$	179.075	+	179.075i	0.0955583	+	0.0955583i
$153$	−299.243	+	299.243i	−0.158120	+	0.158120i
$154$	−38.1643	+	56.7981i	−0.0199699	+	0.0297203i
$155$	−1716.96	−	3110.11i	−0.889738	−	1.61168i
$156$	−1867.71			−0.958569
$157$	−1563.61	−	1563.61i	−0.794841	−	0.794841i	0.187436	−	0.982277i	$-0.439982\pi$
$157$	−1563.61	−	1563.61i	−0.794841	−	0.794841i	−0.982277	+	0.187436i	$0.939982\pi$
$158$	61.1512	+	61.1512i	0.0307907	+	0.0307907i
$159$	1939.96			0.967604
$160$	143.787	−	498.200i	0.0710458	−	0.246164i
$161$	1230.41	+	826.747i	0.602297	+	0.404701i
$162$	62.3031	−	62.3031i	0.0302160	−	0.0302160i
$163$	−1344.83	−	1344.83i	−0.646226	−	0.646226i	0.305853	−	0.952079i	$-0.401058\pi$
$163$	−1344.83	−	1344.83i	−0.646226	−	0.646226i	−0.952079	+	0.305853i	$0.901058\pi$
$164$	2944.44			1.40196
$165$	−193.844	+	671.644i	−0.0914591	+	0.316893i
$166$			180.258i			0.0842817i
$167$	−1463.69	−	1463.69i	−0.678228	−	0.678228i	0.281371	−	0.959599i	$-0.409211\pi$
$167$	−1463.69	−	1463.69i	−0.678228	−	0.678228i	−0.959599	+	0.281371i	$0.909211\pi$
$168$	−291.806	+	57.2592i	−0.134008	+	0.0262955i
$169$		−	1048.73i		−	0.477347i
$170$	−101.522	+	56.0459i	−0.0458021	+	0.0252854i
$171$			648.210i			0.289882i
$172$	−86.4819	+	86.4819i	−0.0383383	+	0.0383383i
$173$	2017.91	−	2017.91i	0.886814	−	0.886814i	−0.107401	−	0.994216i	$-0.534253\pi$
$173$	2017.91	−	2017.91i	0.886814	−	0.886814i	0.994216	+	0.107401i	$0.0342530\pi$
$174$	−105.225			−0.0458451
$175$	833.247	−	2159.88i	0.359929	−	0.932980i
$176$	947.657			0.405866
$177$	1415.27	−	1415.27i	0.601005	−	0.601005i
$178$	183.587	−	183.587i	0.0773059	−	0.0773059i
$179$			2212.81i			0.923985i	0.886884	+	0.461992i	$0.152865\pi$
$179$			2212.81i			0.923985i	−0.886884	+	0.461992i	$0.847135\pi$
$180$	773.654	−	427.101i	0.320360	−	0.176857i
$181$		−	2077.03i		−	0.852954i	−0.904498	−	0.426477i	$-0.859755\pi$
$181$		−	2077.03i		−	0.852954i	0.904498	−	0.426477i	$-0.140245\pi$
$182$	−49.5671	−	252.605i	−0.0201877	−	0.102881i
$183$	920.375	+	920.375i	0.371782	+	0.371782i
$184$			311.282i			0.124717i
$185$	−836.824	+	2899.48i	−0.332565	+	1.15229i
$186$	−320.064			−0.126173
$187$	−455.264	−	455.264i	−0.178033	−	0.178033i
$188$	797.825	−	797.825i	0.309507	−	0.309507i
$189$	−2345.38	−	1575.93i	−0.902651	−	0.606517i
$190$	−49.2542	+	170.659i	−0.0188067	+	0.0651626i
$191$	−2039.27			−0.772546			−0.386273	−	0.922385i	$-0.626238\pi$
$191$	−2039.27			−0.772546			−0.386273	+	0.922385i	$0.626238\pi$
$192$	1428.41	+	1428.41i	0.536910	+	0.536910i
$193$	−403.319	−	403.319i	−0.150423	−	0.150423i	0.627884	−	0.778307i	$-0.283921\pi$
$193$	−403.319	−	403.319i	−0.150423	−	0.150423i	−0.778307	+	0.627884i	$0.783921\pi$
$194$	199.241			0.0737355
$195$	−1270.97	−	2302.25i	−0.466750	−	0.845473i
$196$	1029.23	+	2521.62i	0.375085	+	0.918959i
$197$	−2118.02	+	2118.02i	−0.766003	+	0.766003i	−0.977400	−	0.211397i	$-0.932199\pi$
$197$	−2118.02	+	2118.02i	−0.766003	+	0.766003i	0.211397	+	0.977400i	$0.432199\pi$
$198$	−26.0070	−	26.0070i	−0.00933453	−	0.00933453i
$199$	−543.669			−0.193667			−0.0968334	−	0.995301i	$-0.530871\pi$
$199$	−543.669			−0.193667			−0.0968334	+	0.995301i	$0.530871\pi$
$200$	474.047	−	107.722i	0.167601	−	0.0380856i
$201$		−	234.223i		−	0.0821931i
$202$	−182.426	−	182.426i	−0.0635418	−	0.0635418i
$203$	372.529	+	1898.50i	0.128800	+	0.656395i
$204$		−	1393.74i		−	0.478339i
$205$	2003.68	+	3629.48i	0.682650	+	1.23656i
$206$			19.3643i			0.00654939i
$207$	−563.386	+	563.386i	−0.189169	+	0.189169i
$208$	−2520.82	+	2520.82i	−0.840325	+	0.840325i
$209$	−986.177			−0.326389
$210$	−134.075	−	159.767i	−0.0440573	−	0.0524999i
$211$	829.151			0.270526			0.135263	−	0.990810i	$-0.456812\pi$
$211$	829.151			0.270526			0.135263	+	0.990810i	$0.456812\pi$
$212$	2638.26	−	2638.26i	0.854701	−	0.854701i
$213$	−2647.56	+	2647.56i	−0.851679	+	0.851679i
$214$		−	460.620i		−	0.147137i
$215$	−165.453	−	47.7518i	−0.0524829	−	0.0151472i
$216$		−	593.358i		−	0.186912i
$217$	1133.13	+	5774.71i	0.354479	+	1.80651i
$218$	−55.9645	−	55.9645i	−0.0173871	−	0.0173871i
$219$		−	563.687i		−	0.173929i
$220$	649.785	+	1177.02i	0.199130	+	0.360704i
$221$	2422.05			0.737217
$222$	192.254	+	192.254i	0.0581226	+	0.0581226i
$223$	2531.23	−	2531.23i	0.760107	−	0.760107i	−0.216234	−	0.976342i	$-0.569377\pi$
$223$	2531.23	−	2531.23i	0.760107	−	0.760107i	0.976342	+	0.216234i	$0.0693774\pi$
$224$	−479.056	+	712.957i	−0.142894	+	0.212663i
$225$	1052.94	+	663.007i	0.311982	+	0.196447i
$226$	46.9589			0.0138215
$227$	283.599	+	283.599i	0.0829212	+	0.0829212i	0.747351	−	0.664430i	$-0.231325\pi$
$227$	283.599	+	283.599i	0.0829212	+	0.0829212i	−0.664430	+	0.747351i	$0.731325\pi$
$228$	−1509.53	−	1509.53i	−0.438471	−	0.438471i
$229$	−4475.13			−1.29138			−0.645688	−	0.763602i	$-0.723429\pi$
$229$	−4475.13			−1.29138			−0.645688	+	0.763602i	$0.723429\pi$
$230$	−191.135	+	105.518i	−0.0547960	+	0.0302506i
$231$	645.834	−	961.165i	0.183951	−	0.273766i
$232$	−287.274	+	287.274i	−0.0812951	+	0.0812951i
$233$	−2075.27	−	2075.27i	−0.583500	−	0.583500i	0.352363	−	0.935863i	$-0.385378\pi$
$233$	−2075.27	−	2075.27i	−0.583500	−	0.583500i	−0.935863	+	0.352363i	$0.885378\pi$
$234$	138.360			0.0386534
$235$	1526.36	+	440.526i	0.423697	+	0.122284i
$236$		−	3849.40i		−	1.06176i
$237$	−1034.83	−	1034.83i	−0.283626	−	0.283626i
$238$	188.501	−	36.9883i	0.0513391	−	0.0100739i
$239$			561.502i			0.151969i	0.997109	+	0.0759844i	$0.0242099\pi$
$239$			561.502i			0.151969i	−0.997109	+	0.0759844i	$0.975790\pi$
$240$	−800.946	+	2775.17i	−0.215420	+	0.746401i
$241$			491.727i			0.131431i	0.997838	+	0.0657156i	$0.0209330\pi$
$241$			491.727i			0.131431i	−0.997838	+	0.0657156i	$0.979067\pi$
$242$	−190.052	+	190.052i	−0.0504834	+	0.0504834i
$243$	1858.55	−	1858.55i	0.490641	−	0.490641i
$244$	2503.34			0.656802
$245$	−2407.91	+	2984.65i	−0.627900	+	0.778294i
$246$	373.514			0.0968063
$247$	2623.29	−	2623.29i	0.675772	−	0.675772i
$248$	−873.809	+	873.809i	−0.223738	+	0.223738i
$249$		−	3050.42i		−	0.776355i
$250$	226.836	+	254.562i	0.0573855	+	0.0643997i
$251$		−	4742.82i		−	1.19268i	−0.802730	−	0.596342i	$-0.796620\pi$
$251$		−	4742.82i		−	1.19268i	0.802730	−	0.596342i	$-0.203380\pi$
$252$	−1436.49	+	281.872i	−0.359088	+	0.0704614i
$253$	−857.126	−	857.126i	−0.212992	−	0.212992i
$254$			252.318i			0.0623301i
$255$	1718.00	−	948.435i	0.421903	−	0.232915i
$256$	3794.63			0.926423
$257$	906.753	+	906.753i	0.220084	+	0.220084i	0.808534	−	0.588450i	$-0.200261\pi$
$257$	906.753	+	906.753i	0.220084	+	0.220084i	−0.588450	+	0.808534i	$0.700261\pi$
$258$	−10.9706	+	10.9706i	−0.00264728	+	0.00264728i
$259$	2788.06	−	4149.34i	0.668887	−	0.995473i
$260$	−4859.42	−	1402.49i	−1.15911	−	0.334532i
$261$	−1039.87			−0.246614
$262$	259.350	+	259.350i	0.0611554	+	0.0611554i
$263$	−3713.61	−	3713.61i	−0.870689	−	0.870689i	0.121858	−	0.992547i	$-0.461115\pi$
$263$	−3713.61	−	3713.61i	−0.870689	−	0.870689i	−0.992547	+	0.121858i	$0.961115\pi$
$264$	243.166			0.0566887
$265$	5047.40	+	1456.74i	1.17003	+	0.337686i
$266$	164.101	−	244.224i	0.0378258	−	0.0562944i
$267$	−3106.75	+	3106.75i	−0.712097	+	0.712097i
$268$	−318.533	−	318.533i	−0.0726025	−	0.0726025i
$269$	140.328			0.0318065			0.0159033	−	0.999874i	$-0.494938\pi$
$269$	140.328			0.0318065			0.0159033	+	0.999874i	$0.494938\pi$
$270$	364.338	−	201.135i	0.0821218	−	0.0453360i
$271$			4266.09i			0.956260i	0.878289	+	0.478130i	$0.158685\pi$
$271$			4266.09i			0.956260i	−0.878289	+	0.478130i	$0.841315\pi$
$272$	−1881.11	−	1881.11i	−0.419334	−	0.419334i
$273$	838.797	+	4274.71i	0.185957	+	0.947682i
$274$		−	662.048i		−	0.145970i
$275$	−1008.69	+	1601.92i	−0.221186	+	0.351271i
$276$		−	2623.99i		−	0.572268i
$277$	−1526.65	+	1526.65i	−0.331146	+	0.331146i	−0.853021	−	0.521876i	$-0.825232\pi$
$277$	−1526.65	+	1526.65i	−0.331146	+	0.331146i	0.521876	+	0.853021i	$0.325232\pi$
$278$	113.687	−	113.687i	0.0245270	−	0.0245270i
$279$	−3163.00			−0.678722
$280$	−802.219	−	70.1435i	−0.171221	−	0.0149710i
$281$	7194.47			1.52735			0.763676	−	0.645600i	$-0.223393\pi$
$281$	7194.47			1.52735			0.763676	+	0.645600i	$0.223393\pi$
$282$	101.207	−	101.207i	0.0213716	−	0.0213716i
$283$	2582.62	−	2582.62i	0.542477	−	0.542477i	−0.381777	−	0.924254i	$-0.624688\pi$
$283$	2582.62	−	2582.62i	0.542477	−	0.542477i	0.924254	+	0.381777i	$0.124688\pi$
$284$			7201.12i			1.50460i
$285$	833.502	−	2887.97i	0.173237	−	0.600241i
$286$			210.499i			0.0435212i
$287$	−1322.36	−	6739.05i	−0.271974	−	1.38604i
$288$	−326.452	−	326.452i	−0.0667929	−	0.0667929i
$289$		−	3105.60i		−	0.632118i
$290$	−273.773	−	79.0142i	−0.0554363	−	0.0159996i
$291$	−3371.65			−0.679209
$292$	−766.589	−	766.589i	−0.153634	−	0.153634i
$293$	−6367.25	+	6367.25i	−1.26955	+	1.26955i	−0.323231	+	0.946320i	$0.604769\pi$
$293$	−6367.25	+	6367.25i	−1.26955	+	1.26955i	−0.946320	+	0.323231i	$0.895231\pi$
$294$	130.562	+	319.878i	0.0258998	+	0.0634546i
$295$	4744.98	−	2619.50i	0.936486	−	0.516995i
$296$	1049.74			0.206132
$297$	1633.83	+	1633.83i	0.319208	+	0.319208i
$298$	522.224	+	522.224i	0.101516	+	0.101516i
$299$	4560.01			0.881980
$300$	−3996.05	+	908.061i	−0.769040	+	0.174756i
$301$	236.774	+	159.095i	0.0453403	+	0.0304655i
$302$	−366.966	+	366.966i	−0.0699223	+	0.0699223i
$303$	3087.10	+	3087.10i	0.585311	+	0.585311i
$304$	−4074.79			−0.768767
$305$	1703.51	+	3085.75i	0.319813	+	0.579311i
$306$			103.248i			0.0192886i
$307$	5777.89	+	5777.89i	1.07414	+	1.07414i	0.997022	+	0.0771200i	$0.0245725\pi$
$307$	5777.89	+	5777.89i	1.07414	+	1.07414i	0.0771200	+	0.997022i	$0.475428\pi$
$308$	−428.835	−	2185.45i	−0.0793350	−	0.404310i
$309$		−	327.692i		−	0.0603292i
$310$	−832.744	−	240.340i	−0.152570	−	0.0440335i
$311$			3724.71i			0.679128i	0.940583	+	0.339564i	$0.110279\pi$
$311$			3724.71i			0.679128i	−0.940583	+	0.339564i	$0.889721\pi$
$312$	−646.834	+	646.834i	−0.117371	+	0.117371i
$313$	−3001.58	+	3001.58i	−0.542042	+	0.542042i	−0.924127	−	0.382085i	$-0.875206\pi$
$313$	−3001.58	+	3001.58i	−0.542042	+	0.542042i	0.382085	+	0.924127i	$0.375206\pi$
$314$	−539.496			−0.0969602
$315$	−1324.98	−	1578.88i	−0.236996	−	0.282412i
$316$	−2814.64			−0.501064
$317$	−2459.59	+	2459.59i	−0.435786	+	0.435786i	−0.890591	−	0.454805i	$-0.849709\pi$
$317$	−2459.59	+	2459.59i	−0.435786	+	0.435786i	0.454805	+	0.890591i	$0.349709\pi$
$318$	334.674	−	334.674i	0.0590175	−	0.0590175i
$319$		−	1582.04i		−	0.277671i
$320$	2643.84	+	4789.06i	0.461859	+	0.836614i
$321$			7794.83i			1.35534i
$322$	354.892	−	69.6380i	0.0614203	−	0.0120521i
$323$	1957.57	+	1957.57i	0.337220	+	0.337220i
$324$			2867.66i			0.491712i
$325$	−1578.04	−	6944.38i	−0.269335	−	1.18525i
$326$	−464.007			−0.0788311
$327$	947.058	+	947.058i	0.160160	+	0.160160i
$328$	1019.73	−	1019.73i	0.171662	−	0.171662i
$329$	−2184.32	−	1467.71i	−0.366035	−	0.245949i
$330$	82.4278	+	149.310i	0.0137500	+	0.0249068i
$331$	−6812.43			−1.13125			−0.565627	−	0.824661i	$-0.691366\pi$
$331$	−6812.43			−1.13125			−0.565627	+	0.824661i	$0.691366\pi$
$332$	−4148.43	−	4148.43i	−0.685767	−	0.685767i
$333$	1899.92	+	1899.92i	0.312658	+	0.312658i
$334$	−505.020			−0.0827350
$335$	175.881	−	609.402i	0.0286847	−	0.0993886i
$336$	2668.53	−	3971.44i	0.433274	−	0.644821i
$337$	1850.53	−	1850.53i	0.299124	−	0.299124i	−0.541547	−	0.840671i	$-0.682161\pi$
$337$	1850.53	−	1850.53i	0.299124	−	0.299124i	0.840671	+	0.541547i	$0.182161\pi$
$338$	−180.923	−	180.923i	−0.0291151	−	0.0291151i
$339$	−794.661			−0.127316
$340$	1046.57	−	3626.23i	0.166936	−	0.578411i
$341$		−	4812.13i		−	0.764198i
$342$	111.826	+	111.826i	0.0176809	+	0.0176809i
$343$	5309.11	−	3488.12i	0.835758	−	0.549098i
$344$			59.9016i			0.00938860i
$345$	3234.48	−	1785.62i	0.504750	−	0.278651i
$346$		−	696.242i		−	0.108180i
$347$	4053.67	−	4053.67i	0.627126	−	0.627126i	−0.320218	−	0.947344i	$-0.603756\pi$
$347$	4053.67	−	4053.67i	0.627126	−	0.627126i	0.947344	+	0.320218i	$0.103756\pi$
$348$	2421.62	−	2421.62i	0.373024	−	0.373024i
$349$	1734.54			0.266039			0.133020	−	0.991113i	$-0.457533\pi$
$349$	1734.54			0.266039			0.133020	+	0.991113i	$0.457533\pi$
$350$	−228.865	−	516.361i	−0.0349524	−	0.0788590i
$351$	−8692.18			−1.32181
$352$	496.659	−	496.659i	0.0752046	−	0.0752046i
$353$	7713.10	−	7713.10i	1.16297	−	1.16297i	0.179143	−	0.983823i	$-0.442667\pi$
$353$	7713.10	−	7713.10i	1.16297	−	1.16297i	0.983823	−	0.179143i	$-0.0573326\pi$
$354$		−	488.311i		−	0.0733148i
$355$	−8876.50	+	4900.34i	−1.32709	+	0.732628i
$356$			8450.08i			1.25801i
$357$	−3189.90	+	625.934i	−0.472907	+	0.0927953i
$358$	381.745	+	381.745i	0.0563571	+	0.0563571i
$359$			1957.76i			0.287819i	0.989591	+	0.143909i	$0.0459673\pi$
$359$			1957.76i			0.287819i	−0.989591	+	0.143909i	$0.954033\pi$
$360$	120.019	−	415.851i	0.0175711	−	0.0608813i
$361$	−2618.58			−0.381773
$362$	−358.321	−	358.321i	−0.0520246	−	0.0520246i
$363$	3216.14	−	3216.14i	0.465024	−	0.465024i
$364$	6954.14	+	4672.68i	1.00136	+	0.672844i
$365$	423.279	−	1466.60i	0.0606998	−	0.210316i
$366$	317.558			0.0453526
$367$	1489.90	+	1489.90i	0.211913	+	0.211913i	0.805080	−	0.593167i	$-0.202123\pi$
$367$	1489.90	+	1489.90i	0.211913	+	0.211913i	−0.593167	+	0.805080i	$0.702123\pi$
$368$	−3541.56	−	3541.56i	−0.501676	−	0.501676i
$369$	3691.20			0.520748
$370$	355.840	+	644.571i	0.0499980	+	0.0905666i
$371$	−7223.15	−	4853.44i	−1.01080	−	0.679186i
$372$	7365.90	−	7365.90i	1.02662	−	1.02662i
$373$	697.611	+	697.611i	0.0968389	+	0.0968389i	0.753867	−	0.657028i	$-0.228187\pi$
$373$	697.611	+	697.611i	0.0968389	+	0.0968389i	−0.657028	+	0.753867i	$0.728187\pi$
$374$	−157.080			−0.0217177
$375$	−3838.63	−	4307.82i	−0.528602	−	0.593213i
$376$		−	552.613i		−	0.0757947i
$377$	4208.31	+	4208.31i	0.574905	+	0.574905i
$378$	−676.486	+	132.742i	−0.0920494	+	0.0180622i
$379$			7235.49i			0.980639i	0.871543	+	0.490319i	$0.163120\pi$
$379$			7235.49i			0.980639i	−0.871543	+	0.490319i	$0.836880\pi$
$380$	−2793.98	−	5061.03i	−0.377180	−	0.683225i
$381$		−	4269.84i		−	0.574149i
$382$	−351.805	+	351.805i	−0.0471202	+	0.0471202i
$383$	−3851.00	+	3851.00i	−0.513778	+	0.513778i	−0.915682	−	0.401904i	$-0.868349\pi$
$383$	−3851.00	+	3851.00i	−0.513778	+	0.513778i	0.401904	+	0.915682i	$0.368349\pi$
$384$	2024.71			0.269070
$385$	2402.08	−	2015.80i	0.317978	−	0.266843i
$386$	−139.158			−0.0183496
$387$	−108.415	+	108.415i	−0.0142405	+	0.0142405i
$388$	−4585.30	+	4585.30i	−0.599956	+	0.599956i
$389$		−	1416.54i		−	0.184631i	−0.995730	−	0.0923156i	$-0.970573\pi$
$389$		−	1416.54i		−	0.184631i	0.995730	−	0.0923156i	$-0.0294269\pi$
$390$	−616.436	−	177.911i	−0.0800371	−	0.0230996i
$391$			3402.80i			0.440120i
$392$	1229.75	+	516.852i	0.158448	+	0.0665943i
$393$	−4388.85	−	4388.85i	−0.563328	−	0.563328i
$394$			730.782i			0.0934423i
$395$	−1915.36	−	3469.49i	−0.243980	−	0.441946i
$396$	1197.04			0.151903
$397$	−10286.6	−	10286.6i	−1.30043	−	1.30043i	−0.928098	−	0.372335i	$-0.878557\pi$
$397$	−10286.6	−	10286.6i	−1.30043	−	1.30043i	−0.372335	−	0.928098i	$-0.621443\pi$
$398$	−93.7914	+	93.7914i	−0.0118124	+	0.0118124i
$399$	−2776.99	+	4132.87i	−0.348430	+	0.518552i
$400$	−4167.81	+	6618.99i	−0.520976	+	0.827374i
$401$	9804.91			1.22103			0.610516	−	0.792004i	$-0.290962\pi$
$401$	9804.91			1.22103			0.610516	+	0.792004i	$0.290962\pi$
$402$	−40.4071	−	40.4071i	−0.00501324	−	0.00501324i
$403$	12800.5	+	12800.5i	1.58223	+	1.58223i
$404$	8396.63			1.03403
$405$	−3534.84	+	1951.44i	−0.433698	+	0.239426i
$406$	391.787	+	263.253i	0.0478918	+	0.0321799i
$407$	−2890.51	+	2890.51i	−0.352033	+	0.352033i
$408$	−482.686	−	482.686i	−0.0585698	−	0.0585698i
$409$	−1485.98			−0.179651			−0.0898254	−	0.995958i	$-0.528631\pi$
$409$	−1485.98			−0.179651			−0.0898254	+	0.995958i	$0.528631\pi$
$410$	971.808	+	280.475i	0.117059	+	0.0337846i
$411$			11203.5i			1.34459i
$412$	−445.646	−	445.646i	−0.0532898	−	0.0532898i
$413$	−8810.27	+	1728.78i	−1.04970	+	0.205975i
$414$			194.386i			0.0230762i
$415$	2290.59	−	7936.58i	0.270941	−	0.938774i
$416$			2642.28i			0.311415i
$417$	−1923.87	+	1923.87i	−0.225929	+	0.225929i
$418$	−170.131	+	170.131i	−0.0199076	+	0.0199076i
$419$	−4210.27			−0.490895			−0.245447	−	0.969410i	$-0.578935\pi$
$419$	−4210.27			−0.490895			−0.245447	+	0.969410i	$0.578935\pi$
$420$	6762.42	+	591.284i	0.785648	+	0.0686946i
$421$	−4272.21			−0.494571			−0.247286	−	0.968943i	$-0.579539\pi$
$421$	−4272.21			−0.494571			−0.247286	+	0.968943i	$0.579539\pi$
$422$	143.041	−	143.041i	0.0165004	−	0.0165004i
$423$	1000.17	−	1000.17i	0.114964	−	0.114964i
$424$		−	1827.39i		−	0.209306i
$425$	5182.08	−	1177.57i	0.591454	−	0.134402i
$426$			913.490i			0.103894i
$427$	−1124.26	−	5729.49i	−0.127416	−	0.649343i
$428$	10600.6	+	10600.6i	1.19720	+	1.19720i
$429$		−	3562.16i		−	0.400893i
$430$	−36.7812	+	20.3053i	−0.00412499	+	0.00227723i
$431$	−2055.39			−0.229710			−0.114855	−	0.993382i	$-0.536640\pi$
$431$	−2055.39			−0.229710			−0.114855	+	0.993382i	$0.536640\pi$
$432$	6750.84	+	6750.84i	0.751852	+	0.751852i
$433$	−1679.54	+	1679.54i	−0.186406	+	0.186406i	−0.794140	−	0.607734i	$-0.792078\pi$
$433$	−1679.54	+	1679.54i	−0.186406	+	0.186406i	0.607734	+	0.794140i	$0.292078\pi$
$434$	1191.71	+	800.744i	0.131806	+	0.0885644i
$435$	4632.92	+	1337.12i	0.510647	+	0.147379i
$436$	2575.91			0.282944
$437$	3685.52	+	3685.52i	0.403438	+	0.403438i
$438$	−97.2448	−	97.2448i	−0.0106085	−	0.0106085i
$439$	−9407.03			−1.02272			−0.511359	−	0.859367i	$-0.670858\pi$
$439$	−9407.03			−1.02272			−0.511359	+	0.859367i	$0.670858\pi$
$440$	632.669	+	182.596i	0.0685484	+	0.0197839i
$441$	1290.26	+	3161.15i	0.139322	+	0.341340i
$442$	417.842	−	417.842i	0.0449654	−	0.0449654i
$443$	2276.99	+	2276.99i	0.244205	+	0.244205i	0.818587	−	0.574382i	$-0.194758\pi$
$443$	2276.99	+	2276.99i	0.244205	+	0.244205i	−0.574382	+	0.818587i	$0.694758\pi$
$444$	−8848.97			−0.945841
$445$	−10416.0	+	5750.25i	−1.10959	+	0.612558i
$446$		−	873.355i		−	0.0927232i
$447$	−8837.32	−	8837.32i	−0.935103	−	0.935103i
$448$	−1744.84	−	8892.11i	−0.184009	−	0.937751i
$449$		−	5028.95i		−	0.528577i	−0.964444	−	0.264288i	$-0.914863\pi$
$449$		−	5028.95i		−	0.528577i	0.964444	−	0.264288i	$-0.0851371\pi$
$450$	296.027	−	67.2692i	0.0310108	−	0.00704689i
$451$			5615.73i			0.586329i
$452$	−1080.70	+	1080.70i	−0.112460	+	0.112460i
$453$	6209.98	−	6209.98i	0.644084	−	0.644084i
$454$	97.8505			0.0101153
$455$	−1027.54	+	11751.8i	−0.105872	+	1.21084i
$456$	−1045.58			−0.107376
$457$	−12754.2	+	12754.2i	−1.30551	+	1.30551i	−0.380890	+	0.924620i	$0.624382\pi$
$457$	−12754.2	+	12754.2i	−1.30551	+	1.30551i	−0.924620	+	0.380890i	$0.875618\pi$
$458$	−772.030	+	772.030i	−0.0787655	+	0.0787655i
$459$		−	6486.34i		−	0.659600i
$460$	1970.39	−	6827.11i	0.199717	−	0.691991i
$461$		−	12702.8i		−	1.28336i	−0.766973	−	0.641680i	$-0.778238\pi$
$461$		−	12702.8i		−	1.28336i	0.766973	−	0.641680i	$-0.221762\pi$
$462$	−54.3995	−	277.232i	−0.00547812	−	0.0279178i
$463$	−10925.8	−	10925.8i	−1.09668	−	1.09668i	−0.994796	−	0.101884i	$-0.967513\pi$
$463$	−10925.8	−	10925.8i	−1.09668	−	1.09668i	−0.101884	−	0.994796i	$-0.532487\pi$
$464$		−	6536.83i		−	0.654019i
$465$	14092.1	+	4067.14i	1.40539	+	0.405611i
$466$	−716.033			−0.0711794
$467$	7125.70	+	7125.70i	0.706077	+	0.706077i	0.965708	−	0.259631i	$-0.0836008\pi$
$467$	7125.70	+	7125.70i	0.706077	+	0.706077i	−0.259631	+	0.965708i	$0.583601\pi$
$468$	−3184.19	+	3184.19i	−0.314507	+	0.314507i
$469$	−585.984	+	872.093i	−0.0576935	+	0.0858625i
$470$	339.319	−	187.324i	0.0333013	−	0.0183842i
$471$	9129.60			0.893142
$472$	−1333.14	−	1333.14i	−0.130006	−	0.130006i
$473$	−164.941	−	164.941i	−0.0160338	−	0.0160338i
$474$	−357.049			−0.0345987
$475$	4337.22	−	6888.04i	0.418958	−	0.665358i
$476$	−3486.88	+	5189.37i	−0.335759	+	0.499694i
$477$	3307.37	−	3307.37i	0.317472	−	0.317472i
$478$	96.8679	+	96.8679i	0.00926911	+	0.00926911i
$479$	12747.5			1.21597			0.607985	−	0.793949i	$-0.291978\pi$
$479$	12747.5			1.21597			0.607985	+	0.793949i	$0.291978\pi$
$480$	1034.67	+	1874.21i	0.0983877	+	0.178220i
$481$		−	15377.8i		−	1.45773i
$482$	84.8306	+	84.8306i	0.00801645	+	0.00801645i
$483$	−6005.64	+	1178.45i	−0.565768	+	0.111017i
$484$		−	8747.62i		−	0.821527i
$485$	−8772.37	−	2531.81i	−0.821305	−	0.237038i
$486$		−	641.257i		−	0.0598518i
$487$	4255.39	−	4255.39i	0.395955	−	0.395955i	−0.480849	−	0.876804i	$-0.659671\pi$
$487$	4255.39	−	4255.39i	0.395955	−	0.395955i	0.876804	+	0.480849i	$0.159671\pi$
$488$	866.967	−	866.967i	0.0804216	−	0.0804216i
$489$	7852.14			0.726147
$490$	99.4969	+	930.299i	0.00917309	+	0.0857687i
$491$	6284.86			0.577662			0.288831	−	0.957380i	$-0.406733\pi$
$491$	6284.86			0.577662			0.288831	+	0.957380i	$0.406733\pi$
$492$	−8595.97	+	8595.97i	−0.787675	+	0.787675i
$493$	−3140.36	+	3140.36i	−0.286885	+	0.286885i
$494$		−	905.115i		−	0.0824353i
$495$	814.582	+	1475.54i	0.0739651	+	0.133981i
$496$		−	19883.3i		−	1.79997i
$497$	16481.5	−	3234.05i	1.48752	−	0.291885i
$498$	−526.245	−	526.245i	−0.0473526	−	0.0473526i
$499$			6666.36i			0.598051i	0.954245	+	0.299025i	$0.0966615\pi$
$499$			6666.36i			0.598051i	−0.954245	+	0.299025i	$0.903338\pi$
$500$	−11078.8	−	638.082i	−0.990917	−	0.0570718i
$501$	8546.19			0.762107
$502$	−818.210	−	818.210i	−0.0727460	−	0.0727460i
$503$	7649.95	−	7649.95i	0.678120	−	0.678120i	−0.281455	−	0.959575i	$-0.590817\pi$
$503$	7649.95	−	7649.95i	0.678120	−	0.678120i	0.959575	+	0.281455i	$0.0908169\pi$
$504$	−399.871	+	595.109i	−0.0353406	+	0.0525958i
$505$	5713.88	+	10350.2i	0.503494	+	0.912031i
$506$	−295.735			−0.0259823
$507$	3061.66	+	3061.66i	0.268191	+	0.268191i
$508$	−5806.79	−	5806.79i	−0.507155	−	0.507155i
$509$	−9472.50			−0.824875			−0.412437	−	0.910986i	$-0.635322\pi$
$509$	−9472.50			−0.824875			−0.412437	+	0.910986i	$0.635322\pi$
$510$	132.762	−	460.002i	0.0115270	−	0.0399396i
$511$	−1410.24	+	2098.80i	−0.122085	+	0.181694i
$512$	3428.79	−	3428.79i	0.295962	−	0.295962i
$513$	−7025.25	−	7025.25i	−0.604624	−	0.604624i
$514$	312.858			0.0268474
$515$	246.067	−	852.589i	0.0210544	−	0.0729506i
$516$		−	504.949i		−	0.0430797i
$517$	1521.64	+	1521.64i	0.129442	+	0.129442i
$518$	−234.842	−	1196.81i	−0.0199196	−	0.101515i
$519$			11782.1i			0.996490i
$520$	−2168.65	+	1197.22i	−0.182888	+	0.100965i
$521$		−	102.380i		−	0.00860914i	−0.999991	−	0.00430457i	$-0.998630\pi$
$521$		−	102.380i		−	0.00860914i	0.999991	−	0.00430457i	$-0.00137019\pi$
$522$	−179.393	+	179.393i	−0.0150418	+	0.0150418i
$523$	−8434.43	+	8434.43i	−0.705185	+	0.705185i	−0.965519	−	0.260333i	$-0.916168\pi$
$523$	−8434.43	+	8434.43i	−0.705185	+	0.705185i	0.260333	+	0.965519i	$0.416168\pi$
$524$	−11937.3			−0.995194
$525$	3872.96	+	8738.10i	0.321961	+	0.726404i
$526$	−1281.31			−0.106213
$527$	−9552.11	+	9552.11i	−0.789557	+	0.789557i
$528$	−2766.58	+	2766.58i	−0.228030	+	0.228030i
$529$		−	5760.54i		−	0.473456i
$530$	1122.06	−	619.445i	0.0919611	−	0.0507678i
$531$		−	4825.67i		−	0.394381i
$532$	1843.93	+	9397.10i	0.150272	+	0.765819i
$533$	−14938.2	−	14938.2i	−1.21397	−	1.21397i
$534$			1071.93i			0.0868666i
$535$	−5853.22	+	20280.6i	−0.473004	+	1.63889i
$536$	−220.631			−0.0177795
$537$	−6460.06	−	6460.06i	−0.519129	−	0.519129i
$538$	24.2088	−	24.2088i	0.00193999	−	0.00193999i
$539$	−4809.33	+	1962.99i	−0.384327	+	0.156868i
$540$	−3755.90	+	13013.7i	−0.299312	+	1.03707i
$541$	19779.3			1.57186			0.785931	−	0.618315i	$-0.212184\pi$
$541$	19779.3			1.57186			0.785931	+	0.618315i	$0.212184\pi$
$542$	735.967	+	735.967i	0.0583256	+	0.0583256i
$543$	6063.67	+	6063.67i	0.479221	+	0.479221i
$544$	−1971.74			−0.155400
$545$	1752.90	+	3175.21i	0.137772	+	0.249562i
$546$	882.160	+	592.748i	0.0691446	+	0.0464602i
$547$	11797.7	−	11797.7i	0.922180	−	0.922180i	−0.0750033	−	0.997183i	$-0.523897\pi$
$547$	11797.7	−	11797.7i	0.922180	−	0.922180i	0.997183	+	0.0750033i	$0.0238967\pi$
$548$	15236.2	+	15236.2i	1.18770	+	1.18770i
$549$	3138.23			0.243964
$550$	102.342	+	450.371i	0.00793434	+	0.0349162i
$551$			6802.53i			0.525949i
$552$	−908.753	−	908.753i	−0.0700709	−	0.0700709i
$553$	1264.07	+	6441.99i	0.0972037	+	0.495373i
$554$			526.741i			0.0403954i
$555$	−6021.70	−	10907.7i	−0.460553	−	0.834248i
$556$			5232.75i			0.399133i
$557$	−6016.09	+	6016.09i	−0.457648	+	0.457648i	−0.897883	−	0.440235i	$-0.854895\pi$
$557$	−6016.09	+	6016.09i	−0.457648	+	0.457648i	0.440235	+	0.897883i	$0.354895\pi$
$558$	−545.666	+	545.666i	−0.0413976	+	0.0413976i
$559$	877.506			0.0663946
$560$	9925.17	−	8329.08i	0.748955	−	0.628514i
$561$	2658.18			0.200051
$562$	1241.16	−	1241.16i	0.0931585	−	0.0931585i
$563$	−8887.62	+	8887.62i	−0.665309	+	0.665309i	−0.956626	−	0.291318i	$-0.905906\pi$
$563$	−8887.62	+	8887.62i	−0.665309	+	0.665309i	0.291318	+	0.956626i	$0.405906\pi$
$564$			4658.33i			0.347785i
$565$	−2067.55	−	596.720i	−0.153951	−	0.0444322i
$566$		−	891.085i		−	0.0661751i
$567$	6563.33	−	1287.88i	0.486127	−	0.0953895i
$568$	2493.92	+	2493.92i	0.184230	+	0.184230i
$569$		−	22877.9i		−	1.68558i	−0.538245	−	0.842788i	$-0.680913\pi$
$569$		−	22877.9i		−	1.68558i	0.538245	−	0.842788i	$-0.319087\pi$
$570$	−354.428	−	642.012i	−0.0260445	−	0.0471771i
$571$	5584.51			0.409290			0.204645	−	0.978836i	$-0.434396\pi$
$571$	5584.51			0.409290			0.204645	+	0.978836i	$0.434396\pi$
$572$	−4844.38	−	4844.38i	−0.354115	−	0.354115i
$573$	5953.42	−	5953.42i	0.434045	−	0.434045i
$574$	−1390.72	−	934.464i	−0.101128	−	0.0679509i
$575$	9756.32	−	2217.02i	0.707594	−	0.160794i
$576$	4870.49			0.352322
$577$	−3145.37	−	3145.37i	−0.226938	−	0.226938i	0.584474	−	0.811412i	$-0.301301\pi$
$577$	−3145.37	−	3145.37i	−0.226938	−	0.226938i	−0.811412	+	0.584474i	$0.801301\pi$
$578$	−535.764	−	535.764i	−0.0385551	−	0.0385551i
$579$	2354.89			0.169026
$580$	8118.98	−	4482.15i	0.581245	−	0.320881i
$581$	−7631.60	+	11357.8i	−0.544943	+	0.811014i
$582$	−581.663	+	581.663i	−0.0414273	+	0.0414273i
$583$	5031.78	+	5031.78i	0.357453	+	0.357453i
$584$	−530.977			−0.0376233
$585$	−6091.85	−	1758.18i	−0.430542	−	0.124259i
$586$			2196.90i			0.154869i
$587$	−7974.07	−	7974.07i	−0.560690	−	0.560690i	0.368813	−	0.929503i	$-0.379764\pi$
$587$	−7974.07	−	7974.07i	−0.560690	−	0.560690i	−0.929503	+	0.368813i	$0.879764\pi$
$588$	−10366.3	−	4356.88i	−0.727042	−	0.305569i
$589$			20691.5i			1.44750i
$590$	366.678	−	1270.49i	0.0255863	−	0.0886529i
$591$		−	12366.6i		−	0.860737i
$592$	−11943.3	+	11943.3i	−0.829167	+	0.829167i
$593$	6228.02	−	6228.02i	0.431289	−	0.431289i	−0.457778	−	0.889067i	$-0.651355\pi$
$593$	6228.02	−	6228.02i	0.431289	−	0.431289i	0.889067	+	0.457778i	$0.151355\pi$
$594$	563.724			0.0389392
$595$	−8769.52	−	766.779i	−0.604227	−	0.0528317i
$596$	−24036.7			−1.65198
$597$	1587.18	−	1587.18i	0.108809	−	0.108809i
$598$	786.672	−	786.672i	0.0537950	−	0.0537950i
$599$			6066.56i			0.413811i	0.978361	+	0.206906i	$0.0663393\pi$
$599$			6066.56i			0.413811i	−0.978361	+	0.206906i	$0.933661\pi$
$600$	−1069.45	+	1698.41i	−0.0727665	+	0.115562i
$601$			14162.7i			0.961245i	0.876928	+	0.480622i	$0.159589\pi$
$601$			14162.7i			0.961245i	−0.876928	+	0.480622i	$0.840411\pi$
$602$	68.2936	−	13.4008i	0.00462366	−	0.000907269i
$603$	−399.318	−	399.318i	−0.0269676	−	0.0269676i
$604$		−	16890.6i		−	1.13786i
$605$	10782.8	−	5952.73i	0.724600	−	0.400021i
$606$	1065.15			0.0714003
$607$	13148.7	+	13148.7i	0.879223	+	0.879223i	0.993454	−	0.114231i	$-0.0364405\pi$
$607$	13148.7	+	13148.7i	0.879223	+	0.879223i	−0.114231	+	0.993454i	$0.536440\pi$
$608$	−2135.56	+	2135.56i	−0.142448	+	0.142448i
$609$	−6630.01	−	4454.89i	−0.441152	−	0.296422i
$610$	826.223	+	238.458i	0.0548407	+	0.0158277i
$611$	−8095.29			−0.536007
$612$	−2376.13	−	2376.13i	−0.156944	−	0.156944i
$613$	−6838.92	−	6838.92i	−0.450606	−	0.450606i	0.444950	−	0.895556i	$-0.353222\pi$
$613$	−6838.92	−	6838.92i	−0.450606	−	0.450606i	−0.895556	+	0.444950i	$0.853222\pi$
$614$	1993.55			0.131031
$615$	−16445.4	−	4746.34i	−1.07828	−	0.311205i
$616$	−905.389	−	608.357i	−0.0592194	−	0.0397912i
$617$	−10902.0	+	10902.0i	−0.711343	+	0.711343i	−0.966816	−	0.255473i	$-0.917769\pi$
$617$	−10902.0	+	10902.0i	−0.711343	+	0.711343i	0.255473	+	0.966816i	$0.417769\pi$
$618$	−56.5319	−	56.5319i	−0.00367969	−	0.00367969i
$619$	19890.2			1.29153			0.645764	−	0.763537i	$-0.276539\pi$
$619$	19890.2			1.29153			0.645764	+	0.763537i	$0.276539\pi$
$620$	24695.7	−	13633.5i	1.59968	−	0.883118i
$621$		−	12211.9i		−	0.789122i
$622$	642.570	+	642.570i	0.0414223	+	0.0414223i
$623$	19340.0	−	3794.96i	1.24373	−	0.244048i
$624$		−	14718.5i		−	0.944251i
$625$	−6752.55	−	14090.6i	−0.432163	−	0.901795i
$626$			1035.64i			0.0661220i
$627$	2879.03	−	2879.03i	0.183377	−	0.183377i
$628$	12415.8	−	12415.8i	0.788927	−	0.788927i
$629$	11475.4			0.727429
$630$	−500.960	−	43.8024i	−0.0316805	−	0.00277004i
$631$	−1793.20			−0.113132			−0.0565660	−	0.998399i	$-0.518015\pi$
$631$	−1793.20			−0.113132			−0.0565660	+	0.998399i	$0.518015\pi$
$632$	−974.780	+	974.780i	−0.0613523	+	0.0613523i
$633$	−2420.61	+	2420.61i	−0.151992	+	0.151992i
$634$			848.634i			0.0531602i
$635$	3206.27	−	11109.3i	0.200373	−	0.694265i
$636$			15404.2i			0.960405i
$637$	7571.43	−	18014.7i	0.470943	−	1.12052i
$638$	−272.926	−	272.926i	−0.0169361	−	0.0169361i
$639$			9027.45i			0.558874i
$640$	5267.89	+	1520.38i	0.325362	+	0.0939034i
$641$	−6815.86			−0.419985			−0.209992	−	0.977703i	$-0.567344\pi$
$641$	−6815.86			−0.419985			−0.209992	+	0.977703i	$0.567344\pi$
$642$	1344.73	+	1344.73i	0.0826671	+	0.0826671i
$643$	−5954.74	+	5954.74i	−0.365213	+	0.365213i	−0.865728	−	0.500515i	$-0.833144\pi$
$643$	−5954.74	+	5954.74i	−0.365213	+	0.365213i	0.500515	+	0.865728i	$0.333144\pi$
$644$	−6564.77	+	9770.03i	−0.401689	+	0.597816i
$645$	622.428	−	343.616i	0.0379971	−	0.0209766i
$646$	675.422			0.0411364
$647$	−10290.5	−	10290.5i	−0.625288	−	0.625288i	0.321591	−	0.946879i	$-0.395782\pi$
$647$	−10290.5	−	10290.5i	−0.625288	−	0.625288i	−0.946879	+	0.321591i	$0.895782\pi$
$648$	993.142	+	993.142i	0.0602072	+	0.0602072i
$649$	7341.70			0.444048
$650$	−1470.25	−	925.777i	−0.0887199	−	0.0558646i
$651$	−20166.7	−	13550.6i	−1.21412	−	0.815805i
$652$	10678.6	−	10678.6i	0.641418	−	0.641418i
$653$	20937.8	+	20937.8i	1.25476	+	1.25476i	0.953561	+	0.301202i	$0.0973877\pi$
$653$	20937.8	+	20937.8i	1.25476	+	1.25476i	0.301202	+	0.953561i	$0.402612\pi$
$654$	326.765			0.0195375
$655$	−8123.27	−	14714.5i	−0.484584	−	0.877778i
$656$			23203.7i			1.38102i
$657$	−961.009	−	961.009i	−0.0570663	−	0.0570663i
$658$	−630.032	+	123.627i	−0.0373271	+	0.00732444i
$659$			4483.31i			0.265015i	0.991182	+	0.132508i	$0.0423029\pi$
$659$			4483.31i			0.265015i	−0.991182	+	0.132508i	$0.957697\pi$
$660$	−5333.17	−	1539.22i	−0.314535	−	0.0907787i
$661$		−	10736.8i		−	0.631793i	−0.948794	−	0.315896i	$-0.897695\pi$
$661$		−	10736.8i		−	0.631793i	0.948794	−	0.315896i	$-0.102305\pi$
$662$	−1175.25	+	1175.25i	−0.0689991	+	0.0689991i
$663$	−7070.92	+	7070.92i	−0.414196	+	0.414196i
$664$	−2873.40			−0.167936
$665$	−10328.6	+	8667.63i	−0.602295	+	0.505438i
$666$	655.532			0.0381402
$667$	−5912.36	+	5912.36i	−0.343219	+	0.343219i
$668$	11622.4	−	11622.4i	0.673182	−	0.673182i
$669$			14779.3i			0.854113i
$670$	−74.7892	−	135.473i	−0.00431247	−	0.00781164i
$671$			4774.45i			0.274688i
$672$	−682.847	−	3479.95i	−0.0391985	−	0.199765i
$673$	1551.60	+	1551.60i	0.0888706	+	0.0888706i	0.750145	−	0.661274i	$-0.229984\pi$
$673$	1551.60	+	1551.60i	0.0888706	+	0.0888706i	−0.661274	+	0.750145i	$0.729984\pi$
$674$		−	638.491i		−	0.0364893i
$675$	−18597.3	+	4226.04i	−1.06046	+	0.240978i
$676$	8327.43			0.473795
$677$	−1139.42	−	1139.42i	−0.0646844	−	0.0646844i	0.674025	−	0.738709i	$-0.264564\pi$
$677$	−1139.42	−	1139.42i	−0.0646844	−	0.0646844i	−0.738709	+	0.674025i	$0.764564\pi$
$678$	−137.091	+	137.091i	−0.00776543	+	0.00776543i
$679$	12553.8	+	8435.27i	0.709531	+	0.476754i
$680$	−893.398	−	1618.31i	−0.0503827	−	0.0912635i
$681$	−1655.87			−0.0931764
$682$	−830.168	−	830.168i	−0.0466111	−	0.0466111i
$683$	−6497.27	−	6497.27i	−0.363999	−	0.363999i	0.501284	−	0.865283i	$-0.332861\pi$
$683$	−6497.27	−	6497.27i	−0.363999	−	0.363999i	−0.865283	+	0.501284i	$0.832861\pi$
$684$	−5147.10			−0.287725
$685$	−8412.82	+	29149.2i	−0.469251	+	1.62589i
$686$	314.150	−	1517.66i	0.0174844	−	0.0844672i
$687$	13064.7	−	13064.7i	0.725542	−	0.725542i
$688$	−681.522	−	681.522i	−0.0377657	−	0.0377657i
$689$	−26769.6			−1.48018
$690$	249.951	−	866.046i	0.0137905	−	0.0477823i
$691$			19123.4i			1.05280i	0.850236	+	0.526402i	$0.176459\pi$
$691$			19123.4i			1.05280i	−0.850236	+	0.526402i	$0.823541\pi$
$692$	16023.2	+	16023.2i	0.880216	+	0.880216i
$693$	−537.596	−	2739.71i	−0.0294683	−	0.150178i
$694$		−	1398.64i		−	0.0765011i
$695$	−6450.18	+	3560.87i	−0.352042	+	0.194348i
$696$		−	1677.33i		−	0.0913491i
$697$	11147.3	−	11147.3i	0.605786	−	0.605786i
$698$	299.235	−	299.235i	0.0162267	−	0.0162267i
$699$	12117.1			0.655664
$700$	17150.5	+	6616.38i	0.926038	+	0.357251i
$701$	1396.73			0.0752551			0.0376275	−	0.999292i	$-0.488020\pi$
$701$	1396.73			0.0752551			0.0376275	+	0.999292i	$0.488020\pi$
$702$	−1499.54	+	1499.54i	−0.0806216	+	0.0806216i
$703$	12428.8	−	12428.8i	0.666799	−	0.666799i
$704$			7409.89i			0.396692i
$705$	−5742.11	+	3169.98i	−0.306752	+	0.169345i
$706$		−	2661.26i		−	0.141867i
$707$	−3770.96	−	19217.7i	−0.200596	−	1.02229i
$708$	11237.9	+	11237.9i	0.596534	+	0.596534i
$709$			23710.1i			1.25592i	0.778244	+	0.627962i	$0.216111\pi$
$709$			23710.1i			1.25592i	−0.778244	+	0.627962i	$0.783889\pi$
$710$	−685.950	+	2376.72i	−0.0362581	+	0.125629i
$711$	−3528.49			−0.186116
$712$	2926.47	+	2926.47i	0.154037	+	0.154037i
$713$	−17983.8	+	17983.8i	−0.944598	+	0.944598i
$714$	−442.325	+	658.292i	−0.0231843	+	0.0345041i
$715$	2674.87	−	9268.04i	0.139908	−	0.484762i
$716$	−17570.8			−0.917110
$717$	−1639.24	−	1639.24i	−0.0853817	−	0.0853817i
$718$	337.745	+	337.745i	0.0175551	+	0.0175551i
$719$	−19736.1			−1.02369			−0.511844	−	0.859078i	$-0.671037\pi$
$719$	−19736.1			−1.02369			−0.511844	+	0.859078i	$0.671037\pi$
$720$	3365.78	+	6096.78i	0.174215	+	0.315575i
$721$	−819.826	+	1220.11i	−0.0423466	+	0.0630225i
$722$	−451.747	+	451.747i	−0.0232857	+	0.0232857i
$723$	−1435.54	−	1435.54i	−0.0738429	−	0.0738429i
$724$	16492.6			0.846608
$725$	11049.9	+	6957.82i	0.566045	+	0.356423i
$726$		−	1109.67i		−	0.0567269i
$727$	6487.90	+	6487.90i	0.330981	+	0.330981i	0.852959	−	0.521978i	$-0.174806\pi$
$727$	6487.90	+	6487.90i	0.330981	+	0.330981i	−0.521978	+	0.852959i	$0.674806\pi$
$728$	4026.65	−	790.123i	0.204997	−	0.0402251i
$729$			20602.6i			1.04672i
$730$	−179.990	−	326.034i	−0.00912563	−	0.0165302i
$731$			654.819i			0.0331318i
$732$	−7308.22	+	7308.22i	−0.369016	+	0.369016i
$733$	−2787.63	+	2787.63i	−0.140469	+	0.140469i	−0.773844	−	0.633376i	$-0.781669\pi$
$733$	−2787.63	+	2787.63i	−0.140469	+	0.140469i	0.633376	+	0.773844i	$0.281669\pi$
$734$	514.061			0.0258506
$735$	−1683.73	−	15743.0i	−0.0844972	−	0.790052i
$736$	−3712.20			−0.185915
$737$	607.516	−	607.516i	0.0303638	−	0.0303638i
$738$	636.789	−	636.789i	0.0317623	−	0.0317623i
$739$		−	10052.4i		−	0.500384i	−0.968196	−	0.250192i	$-0.919506\pi$
$739$		−	10052.4i		−	0.500384i	0.968196	−	0.250192i	$-0.0804938\pi$
$740$	−23023.3	−	6644.79i	−1.14372	−	0.330091i
$741$			15316.8i			0.759347i
$742$	−2083.40	+	408.812i	−0.103078	+	0.0202263i
$743$	−12894.8	−	12894.8i	−0.636697	−	0.636697i	0.313042	−	0.949739i	$-0.398652\pi$
$743$	−12894.8	−	12894.8i	−0.636697	−	0.636697i	−0.949739	+	0.313042i	$0.898652\pi$
$744$		−	5101.98i		−	0.251408i
$745$	−16356.9	−	29629.0i	−0.804391	−	1.45708i
$746$	240.697			0.0118131
$747$	−5200.54	−	5200.54i	−0.254723	−	0.254723i
$748$	3615.01	−	3615.01i	0.176708	−	0.176708i
$749$	19501.3	−	29022.8i	0.951350	−	1.41585i
$750$	−1405.39	−	80.9432i	−0.0684234	−	0.00394084i
$751$	11311.9			0.549637			0.274818	−	0.961496i	$-0.411382\pi$
$751$	11311.9			0.549637			0.274818	+	0.961496i	$0.411382\pi$
$752$	6287.27	+	6287.27i	0.304884	+	0.304884i
$753$	13846.1	+	13846.1i	0.670094	+	0.670094i
$754$	1452.00			0.0701308
$755$	20820.3	−	11494.0i	1.00361	−	0.554052i
$756$	12513.6	−	18623.4i	0.602005	−	0.895935i
$757$	−3513.21	+	3513.21i	−0.168679	+	0.168679i	−0.786398	−	0.617720i	$-0.788057\pi$
$757$	−3513.21	+	3513.21i	−0.168679	+	0.168679i	0.617720	+	0.786398i	$0.288057\pi$
$758$	1248.23	+	1248.23i	0.0598126	+	0.0598126i
$759$	5004.57			0.239334
$760$	−2720.38	−	785.135i	−0.129840	−	0.0374735i
$761$		−	24202.1i		−	1.15286i	−0.817147	−	0.576430i	$-0.804446\pi$
$761$		−	24202.1i		−	1.15286i	0.817147	−	0.576430i	$-0.195554\pi$
$762$	−736.615	−	736.615i	−0.0350193	−	0.0350193i
$763$	−1156.85	−	5895.59i	−0.0548897	−	0.279731i
$764$		−	16192.8i		−	0.766797i
$765$	1312.00	−	4545.90i	0.0620072	−	0.214846i
$766$			1328.72i			0.0626743i
$767$	−19529.3	+	19529.3i	−0.919379	+	0.919379i
$768$	−11078.0	+	11078.0i	−0.520499	+	0.520499i
$769$	−13151.0			−0.616691			−0.308346	−	0.951274i	$-0.599775\pi$
$769$	−13151.0			−0.616691			−0.308346	+	0.951274i	$0.599775\pi$
$770$	66.6402	−	762.153i	0.00311889	−	0.0356702i
$771$	−5294.33			−0.247303
$772$	3202.55	−	3202.55i	0.149303	−	0.149303i
$773$	1544.91	−	1544.91i	0.0718842	−	0.0718842i	−0.670251	−	0.742135i	$-0.733813\pi$
$773$	1544.91	−	1544.91i	0.0718842	−	0.0718842i	0.742135	+	0.670251i	$0.233813\pi$
$774$			37.4066i			0.00173715i
$775$	33610.8	+	21163.8i	1.55785	+	0.980937i
$776$			3176.00i			0.146922i
$777$	3974.11	+	20253.0i	0.183488	+	0.935099i
$778$	−244.376	−	244.376i	−0.0112613	−	0.0112613i
$779$		−	24146.8i		−	1.11059i
$780$	18280.9	−	10092.1i	0.839183	−	0.463277i
$781$	−13734.2			−0.629256
$782$	587.036	+	587.036i	0.0268445	+	0.0268445i
$783$	11270.0	−	11270.0i	0.514377	−	0.514377i
$784$	−19871.7	+	8110.87i	−0.905233	+	0.369482i
$785$	23753.4	+	6855.51i	1.07999	+	0.311699i
$786$	−1514.29			−0.0687187
$787$	−13390.9	−	13390.9i	−0.606522	−	0.606522i	0.335514	−	0.942035i	$-0.391090\pi$
$787$	−13390.9	−	13390.9i	−0.606522	−	0.606522i	−0.942035	+	0.335514i	$0.891090\pi$
$788$	−16818.1	−	16818.1i	−0.760303	−	0.760303i
$789$	21683.0			0.978371
$790$	−928.970	−	268.112i	−0.0418370	−	0.0120747i
$791$	2958.80	+	1988.10i	0.133000	+	0.0893662i
$792$	414.564	−	414.564i	0.0185996	−	0.0185996i
$793$	−12700.3	−	12700.3i	−0.568728	−	0.568728i
$794$	−3549.21			−0.158636
$795$	−18988.1	+	10482.5i	−0.847093	+	0.467644i
$796$		−	4316.99i		−	0.192226i
$797$	10313.5	+	10313.5i	0.458372	+	0.458372i	0.898121	−	0.439749i	$-0.144933\pi$
$797$	10313.5	+	10313.5i	0.458372	+	0.458372i	−0.439749	+	0.898121i	$0.644933\pi$
$798$	233.910	+	1192.06i	0.0103763	+	0.0528802i
$799$		−	6040.93i		−	0.267475i
$800$	1284.65	+	5653.27i	0.0567739	+	0.249842i
$801$			10593.2i			0.467280i
$802$	1691.50	−	1691.50i	0.0744750	−	0.0744750i
$803$	1462.06	−	1462.06i	0.0642530	−	0.0642530i
$804$	1859.84			0.0815816
$805$	−16510.4	−	1443.62i	−0.722876	−	0.0632059i
$806$	4416.59			0.193012
$807$	−409.673	+	409.673i	−0.0178701	+	0.0178701i
$808$	2907.96	−	2907.96i	0.126611	−	0.126611i
$809$		−	18738.4i		−	0.814347i	−0.913351	−	0.407173i	$-0.866514\pi$
$809$		−	18738.4i		−	0.814347i	0.913351	−	0.407173i	$-0.133486\pi$
$810$	−273.162	+	946.468i	−0.0118493	+	0.0410562i
$811$		−	3494.94i		−	0.151324i	−0.997134	−	0.0756621i	$-0.975893\pi$
$811$		−	3494.94i		−	0.151324i	0.997134	−	0.0756621i	$-0.0241070\pi$
$812$	−15075.0	+	2958.06i	−0.651511	+	0.127842i
$813$	−12454.4	−	12454.4i	−0.537262	−	0.537262i
$814$			997.316i			0.0429434i
$815$	20429.7	+	5896.26i	0.878063	+	0.253419i
$816$	10983.4			0.471194
$817$	709.224	+	709.224i	0.0303704	+	0.0303704i
$818$	−256.355	+	256.355i	−0.0109575	+	0.0109575i
$819$	8717.83	+	5857.76i	0.371948	+	0.249923i
$820$	−28819.8	+	15910.2i	−1.22735	+	0.677571i
$821$	23319.4			0.991296			0.495648	−	0.868524i	$-0.334931\pi$
$821$	23319.4			0.991296			0.495648	+	0.868524i	$0.334931\pi$
$822$	1932.78	+	1932.78i	0.0820113	+	0.0820113i
$823$	18512.9	+	18512.9i	0.784105	+	0.784105i	0.980521	−	0.196416i	$-0.0629303\pi$
$823$	18512.9	+	18512.9i	0.784105	+	0.784105i	−0.196416	+	0.980521i	$0.562930\pi$
$824$	−308.676			−0.0130500
$825$	−1731.88	−	7621.40i	−0.0730866	−	0.321628i
$826$	−1221.67	+	1818.15i	−0.0514616	+	0.0765878i
$827$	−17866.3	+	17866.3i	−0.751236	+	0.751236i	−0.974710	−	0.223474i	$-0.928260\pi$
$827$	−17866.3	+	17866.3i	−0.751236	+	0.751236i	0.223474	+	0.974710i	$0.428260\pi$
$828$	−4473.55	−	4473.55i	−0.187762	−	0.187762i
$829$	−31760.9			−1.33064			−0.665321	−	0.746557i	$-0.731706\pi$
$829$	−31760.9			−1.33064			−0.665321	+	0.746557i	$0.731706\pi$
$830$	−974.021	−	1764.35i	−0.0407335	−	0.0737848i
$831$		−	8913.76i		−	0.372100i
$832$	−19710.7	−	19710.7i	−0.821330	−	0.821330i
$833$	13443.1	+	5650.01i	0.559154	+	0.235007i
$834$			663.795i			0.0275604i
$835$	22235.5	+	6417.43i	0.921546	+	0.265969i
$836$		−	7830.71i		−	0.323960i
$837$	34280.3	−	34280.3i	1.41565	−	1.41565i
$838$	−726.336	+	726.336i	−0.0299414	+	0.0299414i
$839$	−33411.9			−1.37486			−0.687429	−	0.726251i	$-0.741261\pi$
$839$	−33411.9			−1.37486			−0.687429	+	0.726251i	$0.741261\pi$
$840$	2546.77	−	2137.21i	0.104609	−	0.0877868i
$841$	13476.3			0.552556
$842$	−737.022	+	737.022i	−0.0301656	+	0.0301656i
$843$	−21003.5	+	21003.5i	−0.858123	+	0.858123i
$844$			6583.85i			0.268514i
$845$	5666.79	+	10264.9i	0.230702	+	0.417895i
$846$		−	345.089i		−	0.0140241i
$847$	−20021.0	+	3928.59i	−0.812197	+	0.159372i
$848$	20790.8	+	20790.8i	0.841934	+	0.841934i
$849$			15079.4i			0.609567i
$850$	690.840	−	1097.14i	0.0278772	−	0.0442725i
$851$	21604.7			0.870270
$852$	−21022.9	−	21022.9i	−0.845343	−	0.845343i
$853$	−13286.0	+	13286.0i	−0.533301	+	0.533301i	−0.921553	−	0.388252i	$-0.873079\pi$
$853$	−13286.0	+	13286.0i	−0.533301	+	0.533301i	0.388252	+	0.921553i	$0.373079\pi$
$854$	−1182.38	−	794.474i	−0.0473772	−	0.0318341i
$855$	−3502.58	−	6344.60i	−0.140100	−	0.253779i
$856$	7342.51			0.293180
$857$	28818.2	+	28818.2i	1.14867	+	1.14867i	0.986814	+	0.161857i	$0.0517483\pi$
$857$	28818.2	+	28818.2i	1.14867	+	1.14867i	0.161857	+	0.986814i	$0.448252\pi$
$858$	−614.529	−	614.529i	−0.0244518	−	0.0244518i
$859$	39733.3			1.57821			0.789106	−	0.614258i	$-0.210544\pi$
$859$	39733.3			1.57821			0.789106	+	0.614258i	$0.210544\pi$
$860$	379.172	−	1313.78i	0.0150345	−	0.0520924i
$861$	23534.4	+	15813.4i	0.931534	+	0.625924i
$862$	−354.588	+	354.588i	−0.0140108	+	0.0140108i
$863$	−22961.7	−	22961.7i	−0.905709	−	0.905709i	0.0902133	−	0.995922i	$-0.471245\pi$
$863$	−22961.7	−	22961.7i	−0.905709	−	0.905709i	−0.995922	+	0.0902133i	$0.971245\pi$
$864$	7076.12			0.278628
$865$	−8847.33	+	30654.8i	−0.347767	+	1.20496i
$866$			579.495i			0.0227391i
$867$	9066.45	+	9066.45i	0.355147	+	0.355147i
$868$	−45853.9	+	8997.61i	−1.79307	+	0.351842i
$869$		−	5368.18i		−	0.209555i
$870$	1029.92	−	568.578i	0.0401353	−	0.0221570i
$871$			3232.05i			0.125734i
$872$	892.101	−	892.101i	0.0346449	−	0.0346449i
$873$	−5748.21	+	5748.21i	−0.222849	+	0.222849i
$874$	1271.62			0.0492141
$875$	3515.13	+	25643.0i	0.135809	+	0.990735i
$876$	4475.95			0.172635
$877$	154.614	−	154.614i	0.00595319	−	0.00595319i	−0.704124	−	0.710077i	$-0.748660\pi$
$877$	154.614	−	154.614i	0.00595319	−	0.00595319i	0.710077	+	0.704124i	$0.248660\pi$
$878$	−1622.86	+	1622.86i	−0.0623791	+	0.0623791i
$879$		−	37177.0i		−	1.42656i
$880$	−9275.55	+	5120.64i	−0.355317	+	0.196155i
$881$		−	18280.7i		−	0.699082i	−0.936921	−	0.349541i	$-0.886338\pi$
$881$		−	18280.7i		−	0.699082i	0.936921	−	0.349541i	$-0.113662\pi$
$882$	767.938	+	322.757i	0.0293173	+	0.0123218i
$883$	−571.541	−	571.541i	−0.0217824	−	0.0217824i	0.696132	−	0.717914i	$-0.254903\pi$
$883$	−571.541	−	571.541i	−0.0217824	−	0.0217824i	−0.717914	+	0.696132i	$0.754903\pi$
$884$			19232.3i			0.731732i
$885$	−6205.10	+	21499.8i	−0.235686	+	0.816619i
$886$	785.632			0.0297899
$887$	8548.86	+	8548.86i	0.323611	+	0.323611i	0.850151	−	0.526540i	$-0.176511\pi$
$887$	8548.86	+	8548.86i	0.323611	+	0.323611i	−0.526540	+	0.850151i	$0.676511\pi$
$888$	−3064.61	+	3064.61i	−0.115813	+	0.115813i
$889$	−10682.4	+	15898.1i	−0.403010	+	0.599781i
$890$	−804.920	+	2788.94i	−0.0303157	+	0.105040i
$891$	−5469.30			−0.205644
$892$	20099.2	+	20099.2i	0.754452	+	0.754452i
$893$	−6542.83	−	6542.83i	−0.245182	−	0.245182i
$894$	−3049.15			−0.114070
$895$	−11956.9	−	21658.7i	−0.446563	−	0.808906i
$896$	−7538.69	−	5065.46i	−0.281083	−	0.188867i
$897$	−13312.4	+	13312.4i	−0.495529	+	0.495529i
$898$	−867.573	−	867.573i	−0.0322397	−	0.0322397i
$899$	−33193.5			−1.23144
$900$	−5264.59	+	8360.83i	−0.194985	+	0.309660i
$901$		−	19976.2i		−	0.738629i
$902$	968.801	+	968.801i	0.0357623	+	0.0357623i
$903$	−1155.70	+	226.775i	−0.0425905	+	0.00835724i
$904$			748.548i			0.0275402i
$905$	11223.2	+	20329.7i	0.412234	+	0.746722i
$906$		−	2142.64i		−	0.0785699i
$907$	6054.46	−	6054.46i	0.221648	−	0.221648i	−0.587544	−	0.809192i	$-0.699905\pi$
$907$	6054.46	−	6054.46i	0.221648	−	0.221648i	0.809192	+	0.587544i	$0.199905\pi$
$908$	−2251.91	+	2251.91i	−0.0823043	+	0.0823043i
$909$	10526.2			0.384082
$910$	1850.10	+	2204.64i	0.0673959	+	0.0803110i
$911$	23536.9			0.855995			0.427998	−	0.903780i	$-0.359219\pi$
$911$	23536.9			0.855995			0.427998	+	0.903780i	$0.359219\pi$
$912$	11895.9	−	11895.9i	0.431922	−	0.431922i
$913$	7912.02	−	7912.02i	0.286801	−	0.286801i
$914$			4400.61i			0.159255i
$915$	−13981.7	−	4035.30i	−0.505161	−	0.145795i
$916$		−	35534.7i		−	1.28177i
$917$	5361.07	+	27321.3i	0.193062	+	0.983891i
$918$	−1119.00	−	1119.00i	−0.0402313	−	0.0402313i
$919$			2009.73i			0.0721380i	0.999349	+	0.0360690i	$0.0114836\pi$
$919$			2009.73i			0.0721380i	−0.999349	+	0.0360690i	$0.988516\pi$
$920$	−1682.00	−	3046.79i	−0.0602761	−	0.109184i
$921$	−33735.8			−1.20699
$922$	−2191.43	−	2191.43i	−0.0782766	−	0.0782766i
$923$	36533.8	−	36533.8i	1.30284	−	1.30284i
$924$	7632.11	+	5128.23i	0.271729	+	0.182583i
$925$	−7476.53	−	32901.5i	−0.265759	−	1.16951i
$926$	−3769.73			−0.133781
$927$	−558.669	−	558.669i	−0.0197941	−	0.0197941i
$928$	−3425.90	−	3425.90i	−0.121186	−	0.121186i
$929$	−23919.9			−0.844764			−0.422382	−	0.906418i	$-0.638806\pi$
$929$	−23919.9			−0.844764			−0.422382	+	0.906418i	$0.638806\pi$
$930$	3132.75	−	1729.46i	0.110459	−	0.0609798i
$931$	20679.4	−	8440.55i	0.727970	−	0.297130i
$932$	16478.6	−	16478.6i	0.579159	−	0.579159i
$933$	−10873.9	−	10873.9i	−0.381559	−	0.381559i
$934$	2458.59			0.0861322
$935$	6916.07	+	1996.06i	0.241903	+	0.0698162i
$936$			2205.53i			0.0770192i
$937$	−31840.2	−	31840.2i	−1.11011	−	1.11011i	−0.993135	−	0.116976i	$-0.962680\pi$
$937$	−31840.2	−	31840.2i	−1.11011	−	1.11011i	−0.116976	−	0.993135i	$-0.537320\pi$
$938$	49.3582	+	251.541i	0.00171813	+	0.00875598i
$939$		−	17525.5i		−	0.609078i
$940$	−3497.99	+	12120.0i	−0.121374	+	0.420545i
$941$			34998.1i			1.21244i	0.795297	+	0.606220i	$0.207315\pi$
$941$			34998.1i			1.21244i	−0.795297	+	0.606220i	$0.792685\pi$
$942$	1575.00	−	1575.00i	0.0544758	−	0.0544758i
$943$	20987.0	−	20987.0i	0.724741	−	0.724741i
$944$	30335.2			1.04590
$945$	31471.7	+	2751.79i	1.08336	+	0.0947256i
$946$	−56.9099			−0.00195592
$947$	18008.6	−	18008.6i	0.617951	−	0.617951i	−0.327055	−	0.945005i	$-0.606056\pi$
$947$	18008.6	−	18008.6i	0.617951	−	0.617951i	0.945005	+	0.327055i	$0.106056\pi$
$948$	8217.05	−	8217.05i	0.281516	−	0.281516i
$949$			7778.35i			0.266065i
$950$	−440.057	−	1936.53i	−0.0150288	−	0.0661362i
$951$		−	14361.0i		−	0.489681i
$952$	589.611	+	3004.80i	0.0200729	+	0.102296i
$953$	6157.51	+	6157.51i	0.209298	+	0.209298i	0.803969	−	0.594671i	$-0.202718\pi$
$953$	6157.51	+	6157.51i	0.209298	+	0.209298i	−0.594671	+	0.803969i	$0.702718\pi$
$954$		−	1141.15i		−	0.0387274i
$955$	19960.1	−	11019.1i	0.676328	−	0.373372i
$956$	−4458.59			−0.150838
$957$	4618.59	+	4618.59i	0.156006	+	0.156006i
$958$	2199.15	−	2199.15i	0.0741662	−	0.0741662i
$959$	28029.1	−	41714.4i	0.943803	−	1.40462i
$960$	−21699.5	−	6262.74i	−0.729530	−	0.210551i
$961$	−71174.7			−2.38913
$962$	−2652.92	−	2652.92i	−0.0889121	−	0.0889121i
$963$	13289.1	+	13289.1i	0.444689	+	0.444689i
$964$	−3904.55			−0.130453
$965$	6126.96	+	1768.31i	0.204387	+	0.0589886i
$966$	−832.766	+	1239.37i	−0.0277369	+	0.0412795i
$967$	−28380.1	+	28380.1i	−0.943788	+	0.943788i	−0.998502	−	0.0547136i	$-0.982575\pi$
$967$	−28380.1	+	28380.1i	−0.943788	+	0.943788i	0.0547136	+	0.998502i	$0.482575\pi$
$968$	−3029.51	−	3029.51i	−0.100591	−	0.100591i
$969$	−11429.8			−0.378925
$970$	−1950.15	+	1076.59i	−0.0645520	+	0.0356364i
$971$			2873.09i			0.0949557i	0.998872	+	0.0474778i	$0.0151183\pi$
$971$			2873.09i			0.0949557i	−0.998872	+	0.0474778i	$0.984882\pi$
$972$	14757.8	+	14757.8i	0.486991	+	0.486991i
$973$	11976.4	−	2350.05i	0.394600	−	0.0774297i
$974$		−	1468.24i		−	0.0483013i
$975$	24880.3	+	15666.4i	0.817237	+	0.514592i
$976$			19727.6i			0.646992i
$977$	−16501.7	+	16501.7i	−0.540366	+	0.540366i	−0.923636	−	0.383270i	$-0.874798\pi$
$977$	−16501.7	+	16501.7i	−0.540366	+	0.540366i	0.383270	+	0.923636i	$0.374798\pi$
$978$	1354.62	−	1354.62i	0.0442903	−	0.0442903i
$979$	−16116.3			−0.526127
$980$	−23699.5	−	19119.9i	−0.772503	−	0.623228i
$981$	3229.21			0.105098
$982$	1084.24	−	1084.24i	0.0352336	−	0.0352336i
$983$	−26447.8	+	26447.8i	−0.858143	+	0.858143i	−0.991119	−	0.132976i	$-0.957547\pi$
$983$	−26447.8	+	26447.8i	−0.858143	+	0.858143i	0.132976	+	0.991119i	$0.457547\pi$
$984$			5953.99i			0.192892i
$985$	9286.24	−	32175.5i	0.300390	−	1.04081i
$986$			1083.52i			0.0349963i
$987$	10661.7	−	2092.07i	0.343835	−	0.0674685i
$988$	20830.1	+	20830.1i	0.670744	+	0.670744i
$989$			1232.83i			0.0396377i
$990$	395.081	+	114.025i	0.0126833	+	0.00366056i
$991$	−15569.4			−0.499070			−0.249535	−	0.968366i	$-0.580278\pi$
$991$	−15569.4			−0.499070			−0.249535	+	0.968366i	$0.580278\pi$
$992$	−10420.6	−	10420.6i	−0.333524	−	0.333524i
$993$	19888.2	−	19888.2i	0.635581	−	0.635581i
$994$	2285.39	−	3401.24i	0.0729257	−	0.108532i
$995$	5321.37	−	2937.70i	0.169546	−	0.0935994i
$996$	24221.8			0.770578
$997$	−5027.25	−	5027.25i	−0.159694	−	0.159694i	0.622737	−	0.782431i	$-0.286021\pi$
$997$	−5027.25	−	5027.25i	−0.159694	−	0.159694i	−0.782431	+	0.622737i	$0.786021\pi$
$998$	1150.05	+	1150.05i	0.0364772	+	0.0364772i
$999$	−41182.4			−1.30426

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.4.f.b.13.3	✓	16
5.2	odd	4	inner	35.4.f.b.27.4	yes	16
5.3	odd	4		175.4.f.g.132.5		16
5.4	even	2		175.4.f.g.118.6		16
7.2	even	3		245.4.l.b.178.5		32
7.3	odd	6		245.4.l.b.68.3		32
7.4	even	3		245.4.l.b.68.4		32
7.5	odd	6		245.4.l.b.178.6		32
7.6	odd	2	inner	35.4.f.b.13.4	yes	16
35.2	odd	12		245.4.l.b.227.3		32
35.12	even	12		245.4.l.b.227.4		32
35.13	even	4		175.4.f.g.132.6		16
35.17	even	12		245.4.l.b.117.5		32
35.27	even	4	inner	35.4.f.b.27.3	yes	16
35.32	odd	12		245.4.l.b.117.6		32
35.34	odd	2		175.4.f.g.118.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.f.b.13.3	✓	16	1.1	even	1	trivial
35.4.f.b.13.4	yes	16	7.6	odd	2	inner
35.4.f.b.27.3	yes	16	35.27	even	4	inner
35.4.f.b.27.4	yes	16	5.2	odd	4	inner
175.4.f.g.118.5		16	35.34	odd	2
175.4.f.g.118.6		16	5.4	even	2
175.4.f.g.132.5		16	5.3	odd	4
175.4.f.g.132.6		16	35.13	even	4
245.4.l.b.68.3		32	7.3	odd	6
245.4.l.b.68.4		32	7.4	even	3
245.4.l.b.117.5		32	35.17	even	12
245.4.l.b.117.6		32	35.32	odd	12
245.4.l.b.178.5		32	7.2	even	3
245.4.l.b.178.6		32	7.5	odd	6
245.4.l.b.227.3		32	35.2	odd	12
245.4.l.b.227.4		32	35.12	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	35.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.172516 - 0.172516i) q^{2} +(-2.91939 + 2.91939i) q^{3} +7.94048i q^{4} +(-9.78787 + 5.40347i) q^{5} +1.00728i q^{6} +(18.1737 - 3.56610i) q^{7} +(2.74998 + 2.74998i) q^{8} +9.95432i q^{9} +(-0.756378 + 2.62074i) q^{10} -15.1443 q^{11} +(-23.1814 - 23.1814i) q^{12} +(40.2848 - 40.2848i) q^{13} +(2.52004 - 3.75045i) q^{14} +(12.7998 - 44.3495i) q^{15} -62.5750 q^{16} +(30.0616 + 30.0616i) q^{17} +(1.71728 + 1.71728i) q^{18} +65.1185 q^{19} +(-42.9061 - 77.7204i) q^{20} +(-42.6452 + 63.4669i) q^{21} +(-2.61264 + 2.61264i) q^{22} +(56.5971 + 56.5971i) q^{23} -16.0565 q^{24} +(66.6050 - 105.777i) q^{25} -13.8995i q^{26} +(-107.884 - 107.884i) q^{27} +(28.3165 + 144.308i) q^{28} +104.464i q^{29} +(-5.44281 - 9.85914i) q^{30} +317.751i q^{31} +(-32.7950 + 32.7950i) q^{32} +(44.2123 - 44.2123i) q^{33} +10.3722 q^{34} +(-158.612 + 133.106i) q^{35} -79.0420 q^{36} +(190.864 - 190.864i) q^{37} +(11.2340 - 11.2340i) q^{38} +235.214i q^{39} +(-41.7759 - 12.0570i) q^{40} -370.814i q^{41} +(3.59207 + 18.3060i) q^{42} +(10.8913 + 10.8913i) q^{43} -120.253i q^{44} +(-53.7879 - 97.4316i) q^{45} +19.5278 q^{46} +(-100.476 - 100.476i) q^{47} +(182.681 - 182.681i) q^{48} +(317.566 - 129.618i) q^{49} +(-6.75779 - 29.7386i) q^{50} -175.523 q^{51} +(319.881 + 319.881i) q^{52} +(-332.255 - 332.255i) q^{53} -37.2234 q^{54} +(148.231 - 81.8320i) q^{55} +(59.7840 + 40.1706i) q^{56} +(-190.106 + 190.106i) q^{57} +(18.0217 + 18.0217i) q^{58} -484.782 q^{59} +(352.156 + 101.636i) q^{60} -315.263i q^{61} +(54.8170 + 54.8170i) q^{62} +(35.4981 + 180.907i) q^{63} -489.285i q^{64} +(-176.625 + 611.980i) q^{65} -15.2546i q^{66} +(-40.1151 + 40.1151i) q^{67} +(-238.704 + 238.704i) q^{68} -330.458 q^{69} +(-4.40034 + 50.3259i) q^{70} +906.887 q^{71} +(-27.3742 + 27.3742i) q^{72} +(-96.5419 + 96.5419i) q^{73} -65.8540i q^{74} +(114.358 + 503.250i) q^{75} +517.072i q^{76} +(-275.229 + 54.0063i) q^{77} +(40.5781 + 40.5781i) q^{78} +354.468i q^{79} +(612.476 - 338.122i) q^{80} +361.145 q^{81} +(-63.9712 - 63.9712i) q^{82} +(-522.441 + 522.441i) q^{83} +(-503.958 - 338.624i) q^{84} +(-456.677 - 131.802i) q^{85} +3.75783 q^{86} +(-304.971 - 304.971i) q^{87} +(-41.6467 - 41.6467i) q^{88} +1064.18 q^{89} +(-26.0877 - 7.52923i) q^{90} +(588.464 - 875.783i) q^{91} +(-449.408 + 449.408i) q^{92} +(-927.639 - 927.639i) q^{93} -34.6673 q^{94} +(-637.371 + 351.866i) q^{95} -191.483i q^{96} +(577.458 + 577.458i) q^{97} +(32.4239 - 77.1463i) q^{98} -150.752i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 32 q^{7} + 176 q^{8} - 152 q^{11} - 480 q^{15} - 504 q^{16} + 288 q^{18} + 328 q^{21} + 348 q^{22} - 72 q^{23} - 160 q^{25} - 528 q^{28} + 1780 q^{30} + 432 q^{32} + 160 q^{35} + 344 q^{36}+ \cdots + 3308 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 + 32 * q^7 + 176 * q^8 - 152 * q^11 - 480 * q^15 - 504 * q^16 + 288 * q^18 + 328 * q^21 + 348 * q^22 - 72 * q^23 - 160 * q^25 - 528 * q^28 + 1780 * q^30 + 432 * q^32 + 160 * q^35 + 344 * q^36 - 256 * q^37 - 1300 * q^42 - 312 * q^43 - 1856 * q^46 - 20 * q^50 + 696 * q^51 + 1768 * q^53 + 1304 * q^56 - 3920 * q^57 - 4764 * q^58 - 2000 * q^60 + 2544 * q^63 - 1000 * q^65 + 4504 * q^67 - 180 * q^70 + 6368 * q^71 + 7848 * q^72 - 3016 * q^77 + 5340 * q^78 - 3088 * q^81 - 2280 * q^85 - 9336 * q^86 - 2048 * q^88 + 1608 * q^91 - 6328 * q^92 - 3960 * q^93 + 1240 * q^95 + 3308 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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