LMFDB - Embedded newform 245.4.l.b.117.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(68,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 10]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("245.68");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.l (of order $12$, degree $4$, not 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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			117.5
Character	$\chi$	$=$	245.117
Dual form			245.4.l.b.178.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.235661 + 0.0631451i) q^{2} +(-1.06857 + 3.98796i) q^{3} +(-6.87665 + 3.97024i) q^{4} +(9.57348 - 5.77481i) q^{5} -1.00728i q^{6} +(2.74998 - 2.74998i) q^{8} +(8.62069 + 4.97716i) q^{9} +O(q^{10})$	\(q+(-0.235661 + 0.0631451i) q^{2} +(-1.06857 + 3.98796i) q^{3} +(-6.87665 + 3.97024i) q^{4} +(9.57348 - 5.77481i) q^{5} -1.00728i q^{6} +(2.74998 - 2.74998i) q^{8} +(8.62069 + 4.97716i) q^{9} +(-1.89144 + 1.96541i) q^{10} +(7.57217 + 13.1154i) q^{11} +(-8.48496 - 31.6663i) q^{12} +(40.2848 + 40.2848i) q^{13} +(12.7998 + 44.3495i) q^{15} +(31.2875 - 54.1915i) q^{16} +(-41.0649 - 11.0033i) q^{17} +(-2.34584 - 0.628566i) q^{18} +(-32.5592 + 56.3943i) q^{19} +(-42.9061 + 77.7204i) q^{20} +(-2.61264 - 2.61264i) q^{22} +(20.7160 + 77.3131i) q^{23} +(8.02827 + 13.9054i) q^{24} +(58.3031 - 110.570i) q^{25} +(-12.0373 - 6.94976i) q^{26} +(-107.884 + 107.884i) q^{27} -104.464i q^{29} +(-5.81686 - 9.64318i) q^{30} +(-275.180 + 158.876i) q^{31} +(-12.0038 + 44.7988i) q^{32} +(-60.3951 + 16.1828i) q^{33} +10.3722 q^{34} -79.0420 q^{36} +(-260.725 + 69.8611i) q^{37} +(4.11191 - 15.3459i) q^{38} +(-203.701 + 117.607i) q^{39} +(10.4463 - 42.2075i) q^{40} +370.814i q^{41} +(10.8913 - 10.8913i) q^{43} +(-104.142 - 60.1267i) q^{44} +(111.272 - 2.13414i) q^{45} +(-9.76388 - 16.9115i) q^{46} +(-36.7767 - 137.252i) q^{47} +(182.681 + 182.681i) q^{48} +(-6.75779 + 29.7386i) q^{50} +(87.7616 - 152.008i) q^{51} +(-436.965 - 117.084i) q^{52} +(453.868 + 121.614i) q^{53} +(18.6117 - 32.2364i) q^{54} +(148.231 + 81.8320i) q^{55} +(-190.106 - 190.106i) q^{57} +(6.59639 + 24.6180i) q^{58} +(242.391 + 419.833i) q^{59} +(-264.098 - 254.158i) q^{60} +(-273.026 - 157.631i) q^{61} +(54.8170 - 54.8170i) q^{62} +489.285i q^{64} +(618.303 + 153.029i) q^{65} +(13.2109 - 7.62730i) q^{66} +(-14.6831 + 54.7982i) q^{67} +(326.075 - 87.3716i) q^{68} -330.458 q^{69} +906.887 q^{71} +(37.3938 - 10.0196i) q^{72} +(-35.3368 + 131.879i) q^{73} +(57.0313 - 32.9270i) q^{74} +(378.648 + 350.662i) q^{75} -517.072i q^{76} +(40.5781 - 40.5781i) q^{78} +(306.978 + 177.234i) q^{79} +(-13.4157 - 699.481i) q^{80} +(-180.572 - 312.761i) q^{81} +(-23.4151 - 87.3862i) q^{82} +(-522.441 - 522.441i) q^{83} +(-456.677 + 131.802i) q^{85} +(-1.87892 + 3.25438i) q^{86} +(416.598 + 111.627i) q^{87} +(56.8904 + 15.2437i) q^{88} +(-532.089 + 921.605i) q^{89} +(-26.0877 + 7.52923i) q^{90} +(-449.408 - 449.408i) q^{92} +(-339.540 - 1267.18i) q^{93} +(17.3336 + 30.0227i) q^{94} +(13.9610 + 727.913i) q^{95} +(-165.829 - 95.7414i) q^{96} +(577.458 - 577.458i) q^{97} +150.752i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} + 352 q^{8}+O(q^{10}) $ 32 * q - 4 * q^2 + 352 * q^8	$ 32 q - 4 q^{2} + 352 q^{8} + 152 q^{11} - 960 q^{15} + 504 q^{16} - 288 q^{18} + 696 q^{22} + 72 q^{23} + 160 q^{25} - 1780 q^{30} - 432 q^{32} + 688 q^{36} + 256 q^{37} - 624 q^{43} + 1856 q^{46} - 40 q^{50} - 696 q^{51} - 1768 q^{53} - 7840 q^{57} + 4764 q^{58} + 2000 q^{60} + 1000 q^{65} - 4504 q^{67} + 12736 q^{71} - 7848 q^{72} + 10680 q^{78} + 3088 q^{81} - 4560 q^{85} + 9336 q^{86} + 2048 q^{88} - 12656 q^{92} + 3960 q^{93} - 1240 q^{95}+O(q^{100}) $ 32 * q - 4 * q^2 + 352 * q^8 + 152 * q^11 - 960 * q^15 + 504 * q^16 - 288 * q^18 + 696 * q^22 + 72 * q^23 + 160 * q^25 - 1780 * q^30 - 432 * q^32 + 688 * q^36 + 256 * q^37 - 624 * q^43 + 1856 * q^46 - 40 * q^50 - 696 * q^51 - 1768 * q^53 - 7840 * q^57 + 4764 * q^58 + 2000 * q^60 + 1000 * q^65 - 4504 * q^67 + 12736 * q^71 - 7848 * q^72 + 10680 * q^78 + 3088 * q^81 - 4560 * q^85 + 9336 * q^86 + 2048 * q^88 - 12656 * q^92 + 3960 * q^93 - 1240 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.235661	+	0.0631451i	−0.0833186	+	0.0223252i	−0.300238	−	0.953864i	$-0.597066\pi$
$2$	−0.235661	+	0.0631451i	−0.0833186	+	0.0223252i	0.216919	+	0.976190i	$0.430399\pi$
$3$	−1.06857	+	3.98796i	−0.205647	+	0.767484i	0.783605	+	0.621259i	$0.213379\pi$
$3$	−1.06857	+	3.98796i	−0.205647	+	0.767484i	−0.989251	+	0.146224i	$0.953288\pi$
$4$	−6.87665	+	3.97024i	−0.859582	+	0.496280i
$5$	9.57348	−	5.77481i	0.856278	−	0.516515i
$5$	9.57348	−	5.77481i	0.856278	−	0.516515i
$6$		−	1.00728i		−	0.0685368i
$7$		0			0
$7$		0			0
$8$	2.74998	−	2.74998i	0.121533	−	0.121533i
$9$	8.62069	+	4.97716i	0.319285	+	0.184339i
$10$	−1.89144	+	1.96541i	−0.0598127	+	0.0621519i
$11$	7.57217	+	13.1154i	0.207554	+	0.359494i	0.950944	−	0.309365i	$-0.100116\pi$
$11$	7.57217	+	13.1154i	0.207554	+	0.359494i	−0.743389	+	0.668859i	$0.766783\pi$
$12$	−8.48496	−	31.6663i	−0.204117	−	0.761773i
$13$	40.2848	+	40.2848i	0.859461	+	0.859461i	0.991275	−	0.131813i	$-0.0420800\pi$
$13$	40.2848	+	40.2848i	0.859461	+	0.859461i	−0.131813	+	0.991275i	$0.542080\pi$
$14$		0			0
$15$	12.7998	+	44.3495i	0.220326	+	0.763399i
$16$	31.2875	−	54.1915i	0.488867	−	0.846743i
$17$	−41.0649	−	11.0033i	−0.585865	−	0.156982i	−0.0463025	−	0.998927i	$-0.514744\pi$
$17$	−41.0649	−	11.0033i	−0.585865	−	0.156982i	−0.539563	+	0.841945i	$0.681410\pi$
$18$	−2.34584	−	0.628566i	−0.0307178	−	0.00823081i
$19$	−32.5592	+	56.3943i	−0.393137	+	0.680933i	−0.992861	−	0.119273i	$-0.961943\pi$
$19$	−32.5592	+	56.3943i	−0.393137	+	0.680933i	0.599725	+	0.800207i	$0.295277\pi$
$20$	−42.9061	+	77.7204i	−0.479705	+	0.868940i
$21$		0			0
$22$	−2.61264	−	2.61264i	−0.0253189	−	0.0253189i
$23$	20.7160	+	77.3131i	0.187808	+	0.700908i	0.994012	+	0.109271i	$0.0348516\pi$
$23$	20.7160	+	77.3131i	0.187808	+	0.700908i	−0.806204	+	0.591637i	$0.798482\pi$
$24$	8.02827	+	13.9054i	0.0682818	+	0.118268i
$25$	58.3031	−	110.570i	0.466425	−	0.884561i
$26$	−12.0373	−	6.94976i	−0.0907967	−	0.0524215i
$27$	−107.884	+	107.884i	−0.768974	+	0.768974i
$28$		0			0
$29$		−	104.464i		−	0.668913i	−0.942411	−	0.334456i	$-0.891447\pi$
$29$		−	104.464i		−	0.668913i	0.942411	−	0.334456i	$-0.108553\pi$
$30$	−5.81686	−	9.64318i	−0.0354003	−	0.0586865i
$31$	−275.180	+	158.876i	−1.59432	+	0.920480i	−0.601765	+	0.798674i	$0.705535\pi$
$31$	−275.180	+	158.876i	−1.59432	+	0.920480i	−0.992554	+	0.121807i	$0.961131\pi$
$32$	−12.0038	+	44.7988i	−0.0663123	+	0.247481i
$33$	−60.3951	+	16.1828i	−0.318589	+	0.0853656i
$34$	10.3722			0.0523182
$35$		0			0
$36$	−79.0420			−0.365935
$37$	−260.725	+	69.8611i	−1.15846	+	0.310408i	−0.786350	−	0.617782i	$-0.788032\pi$
$37$	−260.725	+	69.8611i	−1.15846	+	0.310408i	−0.372108	+	0.928189i	$0.621365\pi$
$38$	4.11191	−	15.3459i	0.0175537	−	0.0655113i
$39$	−203.701	+	117.607i	−0.836368	+	0.482877i
$40$	10.4463	−	42.2075i	0.0412925	−	0.166840i
$41$			370.814i			1.41247i	0.707976	+	0.706236i	$0.249608\pi$
$41$			370.814i			1.41247i	−0.707976	+	0.706236i	$0.750392\pi$
$42$		0			0
$43$	10.8913	−	10.8913i	0.0386257	−	0.0386257i	−0.687530	−	0.726156i	$-0.741305\pi$
$43$	10.8913	−	10.8913i	0.0386257	−	0.0386257i	0.726156	+	0.687530i	$0.241305\pi$
$44$	−104.142	−	60.1267i	−0.356820	−	0.206010i
$45$	111.272	−	2.13414i	0.368611	−	0.00706975i
$46$	−9.76388	−	16.9115i	−0.0312958	−	0.0542059i
$47$	−36.7767	−	137.252i	−0.114137	−	0.425964i	0.885084	−	0.465431i	$-0.154101\pi$
$47$	−36.7767	−	137.252i	−0.114137	−	0.425964i	−0.999221	+	0.0394669i	$0.987434\pi$
$48$	182.681	+	182.681i	0.549327	+	0.549327i
$49$		0			0
$50$	−6.75779	+	29.7386i	−0.0191139	+	0.0841134i
$51$	87.7616	−	152.008i	0.240962	−	0.417359i
$52$	−436.965	−	117.084i	−1.16531	−	0.312244i
$53$	453.868	+	121.614i	1.17629	+	0.315187i	0.793456	−	0.608628i	$-0.208280\pi$
$53$	453.868	+	121.614i	1.17629	+	0.315187i	0.382839	+	0.923815i	$0.374946\pi$
$54$	18.6117	−	32.2364i	0.0469024	−	0.0812373i
$55$	148.231	+	81.8320i	0.363408	+	0.200622i
$56$		0			0
$57$	−190.106	−	190.106i	−0.441758	−	0.441758i
$58$	6.59639	+	24.6180i	0.0149336	+	0.0557329i
$59$	242.391	+	419.833i	0.534857	+	0.926400i	0.999170	+	0.0407290i	$0.0129680\pi$
$59$	242.391	+	419.833i	0.534857	+	0.926400i	−0.464313	+	0.885671i	$0.653699\pi$
$60$	−264.098	−	254.158i	−0.568248	−	0.546861i
$61$	−273.026	−	157.631i	−0.573071	−	0.330863i	0.185304	−	0.982681i	$-0.440673\pi$
$61$	−273.026	−	157.631i	−0.573071	−	0.330863i	−0.758375	+	0.651818i	$0.774006\pi$
$62$	54.8170	−	54.8170i	0.112287	−	0.112287i
$63$		0			0
$64$			489.285i			0.955634i
$65$	618.303	+	153.029i	1.17986	+	0.292013i
$66$	13.2109	−	7.62730i	0.0246386	−	0.0142251i
$67$	−14.6831	+	54.7982i	−0.0267736	+	0.0999204i	−0.978020	−	0.208512i	$-0.933138\pi$
$67$	−14.6831	+	54.7982i	−0.0267736	+	0.0999204i	0.951246	+	0.308433i	$0.0998045\pi$
$68$	326.075	−	87.3716i	0.581506	−	0.155814i
$69$	−330.458			−0.576558
$70$		0			0
$71$	906.887			1.51588			0.757942	−	0.652322i	$-0.226205\pi$
$71$	906.887			1.51588			0.757942	+	0.652322i	$0.226205\pi$
$72$	37.3938	−	10.0196i	0.0612070	−	0.0164004i
$73$	−35.3368	+	131.879i	−0.0566556	+	0.211442i	−0.988451	−	0.151543i	$-0.951576\pi$
$73$	−35.3368	+	131.879i	−0.0566556	+	0.211442i	0.931795	+	0.362985i	$0.118242\pi$
$74$	57.0313	−	32.9270i	0.0895912	−	0.0517255i
$75$	378.648	+	350.662i	0.582967	+	0.539880i
$76$		−	517.072i		−	0.780424i
$77$		0			0
$78$	40.5781	−	40.5781i	0.0589047	−	0.0589047i
$79$	306.978	+	177.234i	0.437187	+	0.252410i	0.702404	−	0.711779i	$-0.252110\pi$
$79$	306.978	+	177.234i	0.437187	+	0.252410i	−0.265217	+	0.964189i	$0.585444\pi$
$80$	−13.4157	−	699.481i	−0.0187490	−	0.977554i
$81$	−180.572	−	312.761i	−0.247699	−	0.429027i
$82$	−23.4151	−	87.3862i	−0.0315337	−	0.117685i
$83$	−522.441	−	522.441i	−0.690908	−	0.690908i	0.271524	−	0.962432i	$-0.412472\pi$
$83$	−522.441	−	522.441i	−0.690908	−	0.690908i	−0.962432	+	0.271524i	$0.912472\pi$
$84$		0			0
$85$	−456.677	+	131.802i	−0.582747	+	0.168188i
$86$	−1.87892	+	3.25438i	−0.00235591	+	0.00408056i
$87$	416.598	+	111.627i	0.513380	+	0.137560i
$88$	56.8904	+	15.2437i	0.0689152	+	0.0184658i
$89$	−532.089	+	921.605i	−0.633722	+	1.09764i	0.353062	+	0.935600i	$0.385141\pi$
$89$	−532.089	+	921.605i	−0.633722	+	1.09764i	−0.986784	+	0.162039i	$0.948193\pi$
$90$	−26.0877	+	7.52923i	−0.0305543	+	0.00881834i
$91$		0			0
$92$	−449.408	−	449.408i	−0.509283	−	0.509283i
$93$	−339.540	−	1267.18i	−0.378587	−	1.41291i
$94$	17.3336	+	30.0227i	0.0190194	+	0.0329426i
$95$	13.9610	+	727.913i	0.0150775	+	0.786129i
$96$	−165.829	−	95.7414i	−0.176301	−	0.101787i
$97$	577.458	−	577.458i	0.604454	−	0.604454i	−0.337037	−	0.941491i	$-0.609425\pi$
$97$	577.458	−	577.458i	0.604454	−	0.604454i	0.941491	+	0.337037i	$0.109425\pi$
$98$		0			0
$99$			150.752i			0.153041i
$100$	38.0595	+	991.830i	0.0380595	+	0.991830i
$101$	915.775	−	528.723i	0.902208	−	0.520890i	0.0242923	−	0.999705i	$-0.492267\pi$
$101$	915.775	−	528.723i	0.902208	−	0.520890i	0.877916	+	0.478815i	$0.158933\pi$
$102$	−11.0834	+	41.3639i	−0.0107591	+	0.0401533i
$103$	76.6659	−	20.5426i	0.0733409	−	0.0196516i	−0.221962	−	0.975055i	$-0.571246\pi$
$103$	76.6659	−	20.5426i	0.0733409	−	0.0196516i	0.295303	+	0.955404i	$0.404579\pi$
$104$	221.565			0.208906
$105$		0			0
$106$	−114.638			−0.105044
$107$	−1823.66	+	488.648i	−1.64766	+	0.441489i	−0.958957	−	0.283553i	$-0.908487\pi$
$107$	−1823.66	+	488.648i	−1.64766	+	0.441489i	−0.688704	+	0.725042i	$0.741820\pi$
$108$	313.556	−	1170.21i	0.279370	−	1.04262i
$109$	280.941	−	162.201i	0.246874	−	0.142533i	−0.371458	−	0.928450i	$-0.621142\pi$
$109$	280.941	−	162.201i	0.246874	−	0.142533i	0.618332	+	0.785917i	$0.287809\pi$
$110$	−40.0995	−	9.92454i	−0.0347576	−	0.00860243i
$111$		−	1114.41i		−	0.952931i
$112$		0			0
$113$	136.101	−	136.101i	0.113303	−	0.113303i	−0.648182	−	0.761485i	$-0.724470\pi$
$113$	136.101	−	136.101i	0.113303	−	0.113303i	0.761485	+	0.648182i	$0.224470\pi$
$114$	56.8048	+	32.7963i	0.0466690	+	0.0269443i
$115$	644.793	+	620.524i	0.522845	+	0.503167i
$116$	414.747	+	718.363i	0.331968	+	0.574985i
$117$	146.779	+	547.787i	0.115981	+	0.432845i
$118$	−83.6324	−	83.6324i	−0.0652456	−	0.0652456i
$119$		0			0
$120$	157.159	+	86.7610i	0.119555	+	0.0660014i
$121$	550.824	−	954.056i	0.413843	−	0.716796i
$122$	74.2951	+	19.9073i	0.0551341	+	0.0147731i
$123$	−1478.79	−	396.241i	−1.08405	−	0.290470i
$124$	1261.55	−	2185.06i	0.913631	−	1.58246i
$125$	−80.3581	−	1395.23i	−0.0574996	−	0.998346i
$126$		0			0
$127$	−731.290	−	731.290i	−0.510957	−	0.510957i	0.403863	−	0.914820i	$-0.367667\pi$
$127$	−731.290	−	731.290i	−0.510957	−	0.510957i	−0.914820	+	0.403863i	$0.867667\pi$
$128$	−126.926	−	473.696i	−0.0876470	−	0.327103i
$129$	31.7959	+	55.0721i	0.0217013	+	0.0375878i
$130$	−155.373	+	2.97997i	−0.104824	+	0.00201046i
$131$	1301.93	+	751.672i	0.868324	+	0.501327i	0.866791	−	0.498672i	$-0.166179\pi$
$131$	1301.93	+	751.672i	0.868324	+	0.501327i	0.00153311	+	0.999999i	$0.499512\pi$
$132$	351.066	−	351.066i	0.231488	−	0.231488i
$133$		0			0
$134$		−	13.8409i		−	0.00892295i
$135$	−409.816	+	1655.84i	−0.261269	+	1.05564i
$136$	−143.187	+	82.6689i	−0.0902806	+	0.0521235i
$137$	702.332	−	2621.14i	0.437987	−	1.63459i	−0.295828	−	0.955241i	$-0.595596\pi$
$137$	702.332	−	2621.14i	0.437987	−	1.63459i	0.733815	−	0.679349i	$-0.237738\pi$
$138$	77.8760	−	20.8668i	0.0480380	−	0.0128717i
$139$	658.997			0.402125			0.201063	−	0.979578i	$-0.435561\pi$
$139$	658.997			0.402125			0.201063	+	0.979578i	$0.435561\pi$
$140$		0			0
$141$	586.656			0.350392
$142$	−213.718	+	57.2655i	−0.126301	+	0.0338423i
$143$	−223.307	+	833.394i	−0.130587	+	0.487356i
$144$	539.440	−	311.446i	0.312176	−	0.180235i
$145$	−603.260	−	1000.08i	−0.345503	−	0.572775i
$146$		−	33.3100i		−	0.0188819i
$147$		0			0
$148$	1515.55	−	1515.55i	0.841740	−	0.841740i
$149$	2621.56	+	1513.56i	1.44138	+	0.832183i	0.997942	−	0.0641198i	$-0.0204240\pi$
$149$	2621.56	+	1513.56i	1.44138	+	0.832183i	0.443442	+	0.896303i	$0.353757\pi$
$150$	−111.375	−	58.7276i	−0.0606250	−	0.0319672i
$151$	1063.57	+	1842.17i	0.573195	+	0.992803i	0.996235	+	0.0866922i	$0.0276297\pi$
$151$	1063.57	+	1842.17i	0.573195	+	0.992803i	−0.423040	+	0.906111i	$0.639037\pi$
$152$	65.5458	+	244.620i	0.0349768	+	0.130535i
$153$	−299.243	−	299.243i	−0.158120	−	0.158120i
$154$		0			0
$155$	−1716.96	+	3110.11i	−0.889738	+	1.61168i
$156$	933.856	−	1617.49i	0.479284	−	0.830145i
$157$	2135.94	+	572.323i	1.08577	+	0.290932i	0.756959	−	0.653463i	$-0.226684\pi$
$157$	2135.94	+	572.323i	1.08577	+	0.290932i	0.328814	+	0.944395i	$0.393351\pi$
$158$	−83.5342	−	22.3829i	−0.0420609	−	0.0112702i
$159$	−969.981	+	1680.06i	−0.483802	+	0.837970i
$160$	143.787	+	498.200i	0.0710458	+	0.246164i
$161$		0			0
$162$	62.3031	+	62.3031i	0.0302160	+	0.0302160i
$163$	−492.240	−	1837.07i	−0.236535	−	0.882761i	−0.977451	−	0.211163i	$-0.932275\pi$
$163$	−492.240	−	1837.07i	−0.236535	−	0.882761i	0.740916	−	0.671598i	$-0.234392\pi$
$164$	−1472.22	−	2549.96i	−0.700982	−	1.21414i
$165$	−484.738	+	503.696i	−0.228708	+	0.237653i
$166$	156.108	+	90.1292i	0.0729901	+	0.0421409i
$167$	−1463.69	+	1463.69i	−0.678228	+	0.678228i	−0.959599	−	0.281371i	$-0.909211\pi$
$167$	−1463.69	+	1463.69i	−0.678228	+	0.678228i	0.281371	+	0.959599i	$0.409211\pi$
$168$		0			0
$169$			1048.73i			0.477347i
$170$	99.2980	−	59.8975i	0.0447989	−	0.0270231i
$171$	−561.366	+	324.105i	−0.251045	+	0.144941i
$172$	−31.6546	+	118.137i	−0.0140328	+	0.0523711i
$173$	−2756.52	+	738.606i	−1.21141	+	0.324597i	−0.807315	−	0.590120i	$-0.799080\pi$
$173$	−2756.52	+	738.606i	−1.21141	+	0.324597i	−0.404095	+	0.914717i	$0.632414\pi$
$174$	−105.225			−0.0458451
$175$		0			0
$176$	947.657			0.405866
$177$	−1933.29	+	518.024i	−0.820989	+	0.219983i
$178$	67.1976	−	250.785i	0.0282959	−	0.105602i
$179$	−1916.35	+	1106.41i	−0.800194	+	0.461992i	−0.843539	−	0.537068i	$-0.819532\pi$
$179$	−1916.35	+	1106.41i	−0.800194	+	0.461992i	0.0433447	+	0.999060i	$0.486199\pi$
$180$	−756.707	+	456.453i	−0.313342	+	0.189011i
$181$			2077.03i			0.852954i	0.904498	+	0.426477i	$0.140245\pi$
$181$			2077.03i			0.852954i	−0.904498	+	0.426477i	$0.859755\pi$
$182$		0			0
$183$	920.375	−	920.375i	0.371782	−	0.371782i
$184$	269.578	+	155.641i	0.108008	+	0.0623587i
$185$	−2092.61	+	2174.45i	−0.831632	+	0.864156i
$186$	160.032	+	277.184i	0.0630867	+	0.109269i
$187$	−166.638	−	621.902i	−0.0651646	−	0.243198i
$188$	797.825	+	797.825i	0.309507	+	0.309507i
$189$		0			0
$190$	−49.2542	−	170.659i	−0.0188067	−	0.0651626i
$191$	1019.63	−	1766.06i	0.386273	−	0.669044i	−0.605672	−	0.795714i	$-0.707096\pi$
$191$	1019.63	−	1766.06i	0.386273	−	0.669044i	0.991945	+	0.126670i	$0.0404290\pi$
$192$	−1951.25	−	522.835i	−0.733433	−	0.196523i
$193$	550.944	+	147.625i	0.205481	+	0.0550585i	0.360091	−	0.932917i	$-0.382746\pi$
$193$	550.944	+	147.625i	0.205481	+	0.0550585i	−0.154610	+	0.987976i	$0.549412\pi$
$194$	−99.6206	+	172.548i	−0.0368677	+	0.0638568i
$195$	−1270.97	+	2302.25i	−0.466750	+	0.845473i
$196$		0			0
$197$	−2118.02	−	2118.02i	−0.766003	−	0.766003i	0.211397	−	0.977400i	$-0.432199\pi$
$197$	−2118.02	−	2118.02i	−0.766003	−	0.766003i	−0.977400	+	0.211397i	$0.932199\pi$
$198$	−9.51923	−	35.5262i	−0.00341668	−	0.0127512i
$199$	271.835	+	470.831i	0.0968334	+	0.167720i	0.910372	−	0.413790i	$-0.135795\pi$
$199$	271.835	+	470.831i	0.0968334	+	0.167720i	−0.813539	+	0.581510i	$0.802462\pi$
$200$	−143.733	−	464.398i	−0.0508174	−	0.164190i
$201$	−202.843	−	117.112i	−0.0711813	−	0.0410966i
$202$	−182.426	+	182.426i	−0.0635418	+	0.0635418i
$203$		0			0
$204$			1393.74i			0.478339i
$205$	2141.38	+	3549.98i	0.729563	+	1.20947i
$206$	−16.7700	+	9.68214i	−0.00567194	+	0.00327469i
$207$	−206.213	+	769.599i	−0.0692407	+	0.258410i
$208$	3443.51	−	922.685i	1.14790	−	0.307580i
$209$	−986.177			−0.326389
$210$		0			0
$211$	829.151			0.270526			0.135263	−	0.990810i	$-0.456812\pi$
$211$	829.151			0.270526			0.135263	+	0.990810i	$0.456812\pi$
$212$	−3603.93	+	965.671i	−1.16754	+	0.312842i
$213$	−969.074	+	3616.63i	−0.311736	+	1.16342i
$214$	398.909	−	230.310i	0.127425	−	0.0735686i
$215$	41.3724	−	167.163i	0.0131236	−	0.0530251i
$216$			593.358i			0.186912i
$217$		0			0
$218$	−55.9645	+	55.9645i	−0.0173871	+	0.0173871i
$219$	−488.167	−	281.844i	−0.150627	−	0.0869645i
$220$	−1344.23	+	25.7815i	−0.411944	+	0.00790086i
$221$	−1211.03	−	2097.56i	−0.368608	−	0.638449i
$222$	70.3697	+	262.623i	0.0212743	+	0.0793969i
$223$	2531.23	+	2531.23i	0.760107	+	0.760107i	0.976342	−	0.216234i	$-0.0693774\pi$
$223$	2531.23	+	2531.23i	0.760107	+	0.760107i	−0.216234	+	0.976342i	$0.569377\pi$
$224$		0			0
$225$	1052.94	−	663.007i	0.311982	−	0.196447i
$226$	−23.4795	+	40.6676i	−0.00691075	+	0.0119698i
$227$	−387.403	−	103.804i	−0.113273	−	0.0303513i	0.201737	−	0.979440i	$-0.435341\pi$
$227$	−387.403	−	103.804i	−0.113273	−	0.0303513i	−0.315010	+	0.949088i	$0.602008\pi$
$228$	2062.06	+	552.528i	0.598962	+	0.160491i
$229$	2237.57	−	3875.58i	0.645688	−	1.11836i	−0.338455	−	0.940983i	$-0.609904\pi$
$229$	2237.57	−	3875.58i	0.645688	−	1.11836i	0.984142	−	0.177381i	$-0.0567625\pi$
$230$	−191.135	−	105.518i	−0.0547960	−	0.0302506i
$231$		0			0
$232$	−287.274	−	287.274i	−0.0812951	−	0.0812951i
$233$	−759.602	−	2834.87i	−0.213576	−	0.797076i	−0.986663	−	0.162776i	$-0.947955\pi$
$233$	−759.602	−	2834.87i	−0.213576	−	0.797076i	0.773087	−	0.634300i	$-0.218711\pi$
$234$	−69.1801	−	119.823i	−0.0193267	−	0.0334748i
$235$	−1144.69	−	1101.60i	−0.317750	−	0.305791i
$236$	−3333.68	−	1924.70i	−0.919508	−	0.530878i
$237$	−1034.83	+	1034.83i	−0.283626	+	0.283626i
$238$		0			0
$239$		−	561.502i		−	0.151969i	−0.997109	−	0.0759844i	$-0.975790\pi$
$239$		−	561.502i		−	0.151969i	0.997109	−	0.0759844i	$-0.0242099\pi$
$240$	2803.84	+	693.944i	0.754113	+	0.186641i
$241$	−425.848	+	245.864i	−0.113823	+	0.0657156i	−0.555831	−	0.831296i	$-0.687600\pi$
$241$	−425.848	+	245.864i	−0.113823	+	0.0657156i	0.442008	+	0.897011i	$0.354266\pi$
$242$	−69.5637	+	259.615i	−0.0184782	+	0.0689616i
$243$	−2538.82	+	680.276i	−0.670229	+	0.179587i
$244$	2503.34			0.656802
$245$		0			0
$246$	373.514			0.0968063
$247$	−3583.47	+	960.189i	−0.923122	+	0.247350i
$248$	−319.836	+	1193.65i	−0.0818937	+	0.305631i
$249$	2641.74	−	1525.21i	0.672343	−	0.388177i
$250$	107.039	+	323.727i	0.0270790	+	0.0818971i
$251$			4742.82i			1.19268i	0.802730	+	0.596342i	$0.203380\pi$
$251$			4742.82i			1.19268i	−0.802730	+	0.596342i	$0.796620\pi$
$252$		0			0
$253$	−857.126	+	857.126i	−0.212992	+	0.212992i
$254$	218.514	+	126.159i	0.0539794	+	0.0311650i
$255$	−37.6310	−	1962.05i	−0.00924136	−	0.481836i
$256$	−1897.32	−	3286.25i	−0.463212	−	0.802306i
$257$	331.895	+	1238.65i	0.0805565	+	0.300641i	0.994436	−	0.105345i	$-0.0335948\pi$
$257$	331.895	+	1238.65i	0.0805565	+	0.300641i	−0.913879	+	0.405986i	$0.866928\pi$
$258$	−10.9706	−	10.9706i	−0.00264728	−	0.00264728i
$259$		0			0
$260$	−4859.42	+	1402.49i	−1.15911	+	0.334532i
$261$	519.934	−	900.552i	0.123307	−	0.213574i
$262$	−354.279	−	94.9287i	−0.0835398	−	0.0223844i
$263$	5072.89	+	1359.28i	1.18938	+	0.318694i	0.798642	−	0.601806i	$-0.205552\pi$
$263$	5072.89	+	1359.28i	1.18938	+	0.318694i	0.390741	+	0.920501i	$0.372219\pi$
$264$	−121.583	+	210.588i	−0.0283443	+	0.0490938i
$265$	5047.40	−	1456.74i	1.17003	−	0.337686i
$266$		0			0
$267$	−3106.75	−	3106.75i	−0.712097	−	0.712097i
$268$	−116.591	−	435.124i	−0.0265744	−	0.0991769i
$269$	−70.1641	−	121.528i	−0.0159033	−	0.0275453i	0.857964	−	0.513709i	$-0.171729\pi$
$269$	−70.1641	−	121.528i	−0.0159033	−	0.0275453i	−0.873868	+	0.486164i	$0.838396\pi$
$270$	−7.98045	−	416.093i	−0.00179879	−	0.0937876i
$271$	3694.54	+	2133.04i	0.828146	+	0.478130i	0.853217	−	0.521556i	$-0.174648\pi$
$271$	3694.54	+	2133.04i	0.828146	+	0.478130i	−0.0250717	+	0.999686i	$0.507981\pi$
$272$	−1881.11	+	1881.11i	−0.419334	+	0.419334i
$273$		0			0
$274$			662.048i			0.145970i
$275$	1891.65	−	72.5884i	0.414803	−	0.0159173i
$276$	2272.45	−	1312.00i	0.495598	−	0.286134i
$277$	−558.791	+	2085.44i	−0.121208	+	0.452353i	−0.999676	−	0.0254471i	$-0.991899\pi$
$277$	−558.791	+	2085.44i	−0.121208	+	0.452353i	0.878468	+	0.477800i	$0.158566\pi$
$278$	−155.300	+	41.6124i	−0.0335045	+	0.00897751i
$279$	−3163.00			−0.678722
$280$		0			0
$281$	7194.47			1.52735			0.763676	−	0.645600i	$-0.223393\pi$
$281$	7194.47			1.52735			0.763676	+	0.645600i	$0.223393\pi$
$282$	−138.252	+	37.0444i	−0.0291942	+	0.00782257i
$283$	945.305	−	3527.93i	0.198560	−	0.741037i	−0.792756	−	0.609539i	$-0.791355\pi$
$283$	945.305	−	3527.93i	0.198560	−	0.741037i	0.991316	−	0.131498i	$-0.0419788\pi$
$284$	−6236.35	+	3600.56i	−1.30303	+	0.752302i
$285$	−2917.81	−	722.151i	−0.606442	−	0.150093i
$286$		−	210.499i		−	0.0435212i
$287$		0			0
$288$	−326.452	+	326.452i	−0.0667929	+	0.0667929i
$289$	−2689.53	−	1552.80i	−0.547431	−	0.316059i
$290$	205.315	+	197.588i	0.0415742	+	0.0400094i
$291$	1685.83	+	2919.94i	0.339605	+	0.588212i
$292$	−280.591	−	1047.18i	−0.0562341	−	0.209868i
$293$	−6367.25	−	6367.25i	−1.26955	−	1.26955i	−0.946320	−	0.323231i	$-0.895231\pi$
$293$	−6367.25	−	6367.25i	−1.26955	−	1.26955i	−0.323231	−	0.946320i	$-0.604769\pi$
$294$		0			0
$295$	4744.98	+	2619.50i	0.936486	+	0.516995i
$296$	−524.872	+	909.105i	−0.103066	+	0.178516i
$297$	−2231.86	−	598.025i	−0.436046	−	0.116838i
$298$	−713.371	−	191.147i	−0.138673	−	0.0371573i
$299$	−2280.00	+	3949.08i	−0.440990	+	0.763817i
$300$	−3996.05	−	908.061i	−0.769040	−	0.174756i
$301$		0			0
$302$	−366.966	−	366.966i	−0.0699223	−	0.0699223i
$303$	1129.96	+	4217.05i	0.214239	+	0.799549i
$304$	2037.39	+	3528.87i	0.384383	+	0.665772i
$305$	−3524.10	+	67.5903i	−0.661604	+	0.0126892i
$306$	89.4155	+	51.6241i	0.0167044	+	0.00964429i
$307$	5777.89	−	5777.89i	1.07414	−	1.07414i	0.0771200	−	0.997022i	$-0.475428\pi$
$307$	5777.89	−	5777.89i	1.07414	−	1.07414i	0.997022	−	0.0771200i	$-0.0245725\pi$
$308$		0			0
$309$			327.692i			0.0603292i
$310$	208.232	−	841.348i	0.0381509	−	0.154146i
$311$	−3225.69	+	1862.35i	−0.588142	+	0.339564i	−0.764362	−	0.644787i	$-0.776946\pi$
$311$	−3225.69	+	1862.35i	−0.588142	+	0.339564i	0.176221	+	0.984351i	$0.443613\pi$
$312$	−236.758	+	883.592i	−0.0429608	+	0.160332i
$313$	4100.23	−	1098.65i	0.740443	−	0.198401i	0.131168	−	0.991360i	$-0.458127\pi$
$313$	4100.23	−	1098.65i	0.740443	−	0.198401i	0.609275	+	0.792959i	$0.291461\pi$
$314$	−539.496			−0.0969602
$315$		0			0
$316$	−2814.64			−0.501064
$317$	3359.86	−	900.271i	0.595295	−	0.159509i	0.0514228	−	0.998677i	$-0.483624\pi$
$317$	3359.86	−	900.271i	0.595295	−	0.159509i	0.543872	+	0.839168i	$0.316958\pi$
$318$	122.499	−	457.173i	0.0216019	−	0.0806195i
$319$	1370.09	−	791.019i	0.240470	−	0.138836i
$320$	2825.53	+	4684.16i	0.493599	+	0.818289i
$321$		−	7794.83i		−	1.35534i
$322$		0			0
$323$	1957.57	−	1957.57i	0.337220	−	0.337220i
$324$	2483.47	+	1433.83i	0.425835	+	0.245856i
$325$	6803.02	−	2105.57i	1.16112	−	0.359372i
$326$	232.003	+	401.842i	0.0394156	+	0.0682698i
$327$	346.647	+	1293.71i	0.0586227	+	0.218783i
$328$	1019.73	+	1019.73i	0.171662	+	0.171662i
$329$		0			0
$330$	82.4278	−	149.310i	0.0137500	−	0.0249068i
$331$	3406.22	−	5899.74i	0.565627	−	0.979695i	−0.431364	−	0.902178i	$-0.641967\pi$
$331$	3406.22	−	5899.74i	0.565627	−	0.979695i	0.996991	−	0.0775170i	$-0.0246992\pi$
$332$	5666.86	+	1518.43i	0.936775	+	0.251008i
$333$	−2595.34	−	695.419i	−0.427098	−	0.114441i
$334$	252.510	−	437.360i	0.0413675	−	0.0716506i
$335$	175.881	+	609.402i	0.0286847	+	0.0993886i
$336$		0			0
$337$	1850.53	+	1850.53i	0.299124	+	0.299124i	0.840671	−	0.541547i	$-0.182161\pi$
$337$	1850.53	+	1850.53i	0.299124	+	0.299124i	−0.541547	+	0.840671i	$0.682161\pi$
$338$	−66.2222	−	247.145i	−0.0106569	−	0.0397719i
$339$	397.331	+	688.197i	0.0636579	+	0.110259i
$340$	2617.12	−	2719.47i	0.417451	−	0.433777i
$341$	−4167.43	−	2406.07i	−0.661815	−	0.382099i
$342$	111.826	−	111.826i	0.0176809	−	0.0176809i
$343$		0			0
$344$		−	59.9016i		−	0.00938860i
$345$	−3163.63	+	1908.33i	−0.493694	+	0.297801i
$346$	602.963	−	348.121i	0.0936864	−	0.0540899i
$347$	1483.75	−	5537.42i	0.229544	−	0.856670i	−0.750989	−	0.660315i	$-0.770423\pi$
$347$	1483.75	−	5537.42i	0.229544	−	0.856670i	0.980533	−	0.196355i	$-0.0629104\pi$
$348$	−3307.99	+	886.373i	−0.509560	+	0.136536i
$349$	1734.54			0.266039			0.133020	−	0.991113i	$-0.457533\pi$
$349$	1734.54			0.266039			0.133020	+	0.991113i	$0.457533\pi$
$350$		0			0
$351$	−8692.18			−1.32181
$352$	−678.449	+	181.790i	−0.102731	+	0.0275268i
$353$	2823.19	−	10536.3i	0.425675	−	1.58864i	−0.336769	−	0.941587i	$-0.609334\pi$
$353$	2823.19	−	10536.3i	0.425675	−	1.58864i	0.762444	−	0.647054i	$-0.223999\pi$
$354$	422.890	−	244.156i	0.0634925	−	0.0366574i
$355$	8682.07	−	5237.10i	1.29802	−	0.782977i
$356$		−	8450.08i		−	1.25801i
$357$		0			0
$358$	381.745	−	381.745i	0.0563571	−	0.0563571i
$359$	1695.47	+	978.882i	0.249258	+	0.143909i	0.619425	−	0.785056i	$-0.287366\pi$
$359$	1695.47	+	978.882i	0.249258	+	0.143909i	−0.370166	+	0.928965i	$0.620699\pi$
$360$	300.128	−	311.865i	0.0439392	−	0.0456576i
$361$	1309.29	+	2267.76i	0.190887	+	0.330626i
$362$	−131.154	−	489.475i	−0.0190423	−	0.0710670i
$363$	3216.14	+	3216.14i	0.465024	+	0.465024i
$364$		0			0
$365$	423.279	+	1466.60i	0.0606998	+	0.210316i
$366$	−158.779	+	275.014i	−0.0226763	+	0.0392765i
$367$	−2035.24	−	545.340i	−0.289478	−	0.0775655i	0.111158	−	0.993803i	$-0.464544\pi$
$367$	−2035.24	−	545.340i	−0.289478	−	0.0775655i	−0.400636	+	0.916237i	$0.631211\pi$
$368$	4837.86	+	1296.30i	0.685302	+	0.183626i
$369$	−1845.60	+	3196.67i	−0.260374	+	0.450981i
$370$	355.840	−	644.571i	0.0499980	−	0.0905666i
$371$		0			0
$372$	7365.90	+	7365.90i	1.02662	+	1.02662i
$373$	255.343	+	952.954i	0.0354455	+	0.132284i	0.981381	−	0.192069i	$-0.0615199\pi$
$373$	255.343	+	952.954i	0.0354455	+	0.132284i	−0.945936	+	0.324354i	$0.894853\pi$
$374$	78.5401	+	136.035i	0.0108589	+	0.0188081i
$375$	5649.99	+	1170.44i	0.778038	+	0.161176i
$376$	−478.577	−	276.306i	−0.0656402	−	0.0378974i
$377$	4208.31	−	4208.31i	0.574905	−	0.574905i
$378$		0			0
$379$		−	7235.49i		−	0.980639i	−0.871543	−	0.490319i	$-0.836880\pi$
$379$		−	7235.49i		−	0.980639i	0.871543	−	0.490319i	$-0.163120\pi$
$380$	−2985.99	−	4950.18i	−0.403100	−	0.668260i
$381$	3697.79	−	2134.92i	0.497228	−	0.287074i
$382$	−128.770	+	480.575i	−0.0172472	+	0.0643674i
$383$	5260.57	−	1409.57i	0.701834	−	0.188056i	0.109782	−	0.993956i	$-0.464985\pi$
$383$	5260.57	−	1409.57i	0.701834	−	0.188056i	0.592052	+	0.805900i	$0.298318\pi$
$384$	2024.71			0.269070
$385$		0			0
$386$	−139.158			−0.0183496
$387$	148.098	−	39.6827i	0.0194528	−	0.00521237i
$388$	−1678.33	+	6263.63i	−0.219599	+	0.819556i
$389$	1226.76	−	708.271i	0.159895	−	0.0923156i	−0.417917	−	0.908485i	$-0.637240\pi$
$389$	1226.76	−	708.271i	0.159895	−	0.0923156i	0.577813	+	0.816169i	$0.303906\pi$
$390$	154.143	−	622.805i	0.0200137	−	0.0808640i
$391$		−	3402.80i		−	0.440120i
$392$		0			0
$393$	−4388.85	+	4388.85i	−0.563328	+	0.563328i
$394$	632.876	+	365.391i	0.0809234	+	0.0467212i
$395$	3962.34	−	75.9956i	0.504727	−	0.00968039i
$396$	−598.520	−	1036.67i	−0.0759514	−	0.131552i
$397$	−3765.17	−	14051.8i	−0.475992	−	1.77643i	−0.617589	−	0.786501i	$-0.711891\pi$
$397$	−3765.17	−	14051.8i	−0.475992	−	1.77643i	0.141598	−	0.989924i	$-0.454776\pi$
$398$	−93.7914	−	93.7914i	−0.0118124	−	0.0118124i
$399$		0			0
$400$	−4167.81	−	6618.99i	−0.520976	−	0.827374i
$401$	−4902.45	+	8491.30i	−0.610516	+	1.05744i	0.380638	+	0.924724i	$0.375705\pi$
$401$	−4902.45	+	8491.30i	−0.610516	+	1.05744i	−0.991154	+	0.132720i	$0.957629\pi$
$402$	55.1972	+	14.7900i	0.00684822	+	0.00183497i
$403$	−17485.9	−	4685.32i	−2.16137	−	0.579138i
$404$	−4198.31	+	7271.69i	−0.517015	+	0.895496i
$405$	−3534.84	−	1951.44i	−0.433698	−	0.239426i
$406$		0			0
$407$	−2890.51	−	2890.51i	−0.352033	−	0.352033i
$408$	−176.675	−	659.361i	−0.0214380	−	0.0800079i
$409$	742.992	+	1286.90i	0.0898254	+	0.155582i	0.907437	−	0.420188i	$-0.138036\pi$
$409$	742.992	+	1286.90i	0.0898254	+	0.155582i	−0.817612	+	0.575770i	$0.804702\pi$
$410$	−728.803	−	701.373i	−0.0877878	−	0.0844838i
$411$	9702.50	+	5601.74i	1.16445	+	0.672296i
$412$	−445.646	+	445.646i	−0.0532898	+	0.0532898i
$413$		0			0
$414$		−	194.386i		−	0.0230762i
$415$	−8018.58	−	1984.58i	−0.948473	−	0.234745i
$416$	−2288.28	+	1321.14i	−0.269693	+	0.155707i
$417$	−704.185	+	2628.05i	−0.0826956	+	0.308624i
$418$	232.403	−	62.2722i	0.0271943	−	0.00728668i
$419$	−4210.27			−0.490895			−0.245447	−	0.969410i	$-0.578935\pi$
$419$	−4210.27			−0.490895			−0.245447	+	0.969410i	$0.578935\pi$
$420$		0			0
$421$	−4272.21			−0.494571			−0.247286	−	0.968943i	$-0.579539\pi$
$421$	−4272.21			−0.494571			−0.247286	+	0.968943i	$0.579539\pi$
$422$	−195.398	+	52.3568i	−0.0225399	+	0.00603955i
$423$	366.087	−	1366.25i	0.0420798	−	0.157044i
$424$	1582.56	−	913.694i	0.181264	−	0.104653i
$425$	−3610.85	+	3899.03i	−0.412122	+	0.445013i
$426$		−	913.490i		−	0.103894i
$427$		0			0
$428$	10600.6	−	10600.6i	1.19720	−	1.19720i
$429$	−3084.92	−	1781.08i	−0.347183	−	0.200446i
$430$	0.805654	+	42.0061i	9.03537e−5	+	0.00471096i
$431$	1027.70	+	1780.02i	0.114855	+	0.198934i	0.917722	−	0.397224i	$-0.130026\pi$
$431$	1027.70	+	1780.02i	0.114855	+	0.198934i	−0.802867	+	0.596158i	$0.796693\pi$
$432$	2470.98	+	9221.83i	0.275197	+	1.02705i
$433$	−1679.54	−	1679.54i	−0.186406	−	0.186406i	0.607734	−	0.794140i	$-0.292078\pi$
$433$	−1679.54	−	1679.54i	−0.186406	−	0.186406i	−0.794140	+	0.607734i	$0.792078\pi$
$434$		0			0
$435$	4632.92	−	1337.12i	0.510647	−	0.147379i
$436$	−1287.96	+	2230.80i	−0.141472	+	0.245037i
$437$	−5034.51	−	1348.99i	−0.551106	−	0.147668i
$438$	132.839	+	35.5941i	0.0144915	+	0.00388299i
$439$	4703.51	−	8146.72i	0.511359	−	0.885699i	−0.488555	−	0.872533i	$-0.662476\pi$
$439$	4703.51	−	8146.72i	0.511359	−	0.885699i	0.999913	−	0.0131659i	$-0.00419095\pi$
$440$	632.669	−	182.596i	0.0685484	−	0.0197839i
$441$		0			0
$442$	417.842	+	417.842i	0.0449654	+	0.0449654i
$443$	833.435	+	3110.42i	0.0893853	+	0.333591i	0.996108	−	0.0881358i	$-0.0280909\pi$
$443$	833.435	+	3110.42i	0.0893853	+	0.333591i	−0.906723	+	0.421726i	$0.861424\pi$
$444$	4424.48	+	7663.43i	0.472921	+	0.819123i
$445$	228.153	+	11895.7i	0.0243044	+	1.26721i
$446$	−756.347	−	436.677i	−0.0803006	−	0.0463616i
$447$	−8837.32	+	8837.32i	−0.935103	+	0.935103i
$448$		0			0
$449$			5028.95i			0.528577i	0.964444	+	0.264288i	$0.0851371\pi$
$449$			5028.95i			0.528577i	−0.964444	+	0.264288i	$0.914863\pi$
$450$	−206.270	+	222.733i	−0.0216082	+	0.0233327i
$451$	−4863.37	+	2807.87i	−0.507776	+	0.293165i
$452$	−395.565	+	1476.27i	−0.0411633	+	0.153623i
$453$	−8482.99	+	2273.01i	−0.879836	+	0.235751i
$454$	97.8505			0.0101153
$455$		0			0
$456$	−1045.58			−0.107376
$457$	17422.6	−	4668.38i	1.78336	−	0.477850i	0.792171	−	0.610300i	$-0.208951\pi$
$457$	17422.6	−	4668.38i	1.78336	−	0.477850i	0.991190	+	0.132450i	$0.0422843\pi$
$458$	−282.583	+	1054.61i	−0.0288302	+	0.107596i
$459$	5617.34	−	3243.17i	0.571231	−	0.329800i
$460$	−6897.65	−	1707.15i	−0.699140	−	0.173036i
$461$			12702.8i			1.28336i	0.766973	+	0.641680i	$0.221762\pi$
$461$			12702.8i			1.28336i	−0.766973	+	0.641680i	$0.778238\pi$
$462$		0			0
$463$	−10925.8	+	10925.8i	−1.09668	+	1.09668i	−0.101884	+	0.994796i	$0.532487\pi$
$463$	−10925.8	+	10925.8i	−1.09668	+	1.09668i	−0.994796	+	0.101884i	$0.967513\pi$
$464$	−5661.06	−	3268.42i	−0.566397	−	0.327009i
$465$	−10568.3	−	10170.5i	−1.05396	−	1.01430i
$466$	358.017	+	620.103i	0.0355897	+	0.0616432i
$467$	2608.19	+	9733.89i	0.258442	+	0.964520i	0.966143	+	0.258007i	$0.0830659\pi$
$467$	2608.19	+	9733.89i	0.258442	+	0.964520i	−0.707701	+	0.706512i	$0.750267\pi$
$468$	−3184.19	−	3184.19i	−0.314507	−	0.314507i
$469$		0			0
$470$	339.319	+	187.324i	0.0333013	+	0.0183842i
$471$	−4564.80	+	7906.47i	−0.446571	+	0.773483i
$472$	1821.10	+	487.963i	0.177591	+	0.0475854i
$473$	225.314	+	60.3727i	0.0219026	+	0.00586879i
$474$	178.524	−	309.213i	0.0172994	−	0.0299634i
$475$	4337.22	+	6888.04i	0.418958	+	0.665358i
$476$		0			0
$477$	3307.37	+	3307.37i	0.317472	+	0.317472i
$478$	35.4561	+	132.324i	0.00339273	+	0.0126618i
$479$	−6373.77	−	11039.7i	−0.607985	−	1.05306i	−0.991572	−	0.129556i	$-0.958645\pi$
$479$	−6373.77	−	11039.7i	−0.607985	−	1.05306i	0.383587	−	0.923505i	$-0.374689\pi$
$480$	−2140.45	+	41.0527i	−0.203537	+	0.00390373i
$481$	−13317.6	−	7688.92i	−1.26243	−	0.728866i
$482$	84.8306	−	84.8306i	0.00801645	−	0.00801645i
$483$		0			0
$484$			8747.62i			0.821527i
$485$	2193.57	−	8863.00i	0.205371	−	0.829790i
$486$	555.345	−	320.628i	0.0518332	−	0.0299259i
$487$	1557.58	−	5812.97i	0.144930	−	0.540885i	−0.854829	−	0.518910i	$-0.826338\pi$
$487$	1557.58	−	5812.97i	0.144930	−	0.540885i	0.999759	−	0.0219747i	$-0.00699532\pi$
$488$	−1184.30	+	317.332i	−0.109858	+	0.0294364i
$489$	7852.14			0.726147
$490$		0			0
$491$	6284.86			0.577662			0.288831	−	0.957380i	$-0.406733\pi$
$491$	6284.86			0.577662			0.288831	+	0.957380i	$0.406733\pi$
$492$	11742.3	−	3146.34i	1.07598	−	0.288309i
$493$	−1149.45	+	4289.81i	−0.105007	+	0.391893i
$494$	783.853	−	452.558i	0.0713911	−	0.0412177i
$495$	870.562	+	1443.22i	0.0790482	+	0.131046i
$496$			19883.3i			1.79997i
$497$		0			0
$498$	−526.245	+	526.245i	−0.0473526	+	0.0473526i
$499$	5773.24	+	3333.18i	0.517927	+	0.299025i	0.736086	−	0.676888i	$-0.236672\pi$
$499$	5773.24	+	3333.18i	0.517927	+	0.299025i	−0.218159	+	0.975913i	$0.570005\pi$
$500$	6091.99	+	9275.48i	0.544884	+	0.829624i
$501$	−4273.10	−	7401.22i	−0.381054	−	0.660004i
$502$	−299.486	−	1117.70i	−0.0266269	−	0.0993729i
$503$	7649.95	+	7649.95i	0.678120	+	0.678120i	0.959575	−	0.281455i	$-0.0908169\pi$
$503$	7649.95	+	7649.95i	0.678120	+	0.678120i	−0.281455	+	0.959575i	$0.590817\pi$
$504$		0			0
$505$	5713.88	−	10350.2i	0.503494	−	0.912031i
$506$	147.868	−	256.114i	0.0129911	−	0.0225013i
$507$	−4182.30	−	1120.64i	−0.366356	−	0.0981648i
$508$	7932.23	+	2125.43i	0.692787	+	0.185632i
$509$	4736.25	−	8203.43i	0.412437	−	0.714363i	−0.582718	−	0.812674i	$-0.698011\pi$
$509$	4736.25	−	8203.43i	0.412437	−	0.714363i	0.995156	+	0.0983116i	$0.0313442\pi$
$510$	132.762	+	460.002i	0.0115270	+	0.0399396i
$511$		0			0
$512$	3428.79	+	3428.79i	0.295962	+	0.295962i
$513$	−2571.42	−	9596.67i	−0.221308	−	0.825932i
$514$	−156.429	−	270.943i	−0.0134237	−	0.0232505i
$515$	615.330	−	639.395i	0.0526498	−	0.0547089i
$516$	−437.299	−	252.475i	−0.0373082	−	0.0215399i
$517$	1521.64	−	1521.64i	0.129442	−	0.129442i
$518$		0			0
$519$		−	11782.1i		−	0.996490i
$520$	2121.15	−	1279.50i	0.178882	−	0.107903i
$521$	88.6639	−	51.1901i	0.00745573	−	0.00430457i	−0.496268	−	0.868170i	$-0.665296\pi$
$521$	88.6639	−	51.1901i	0.00745573	−	0.00430457i	0.503723	+	0.863865i	$0.331963\pi$
$522$	−65.6625	+	245.056i	−0.00550569	+	0.0205475i
$523$	11521.6	−	3087.22i	0.963301	−	0.258116i	0.257304	−	0.966331i	$-0.417166\pi$
$523$	11521.6	−	3087.22i	0.963301	−	0.258116i	0.705997	+	0.708215i	$0.250499\pi$
$524$	−11937.3			−0.995194
$525$		0			0
$526$	−1281.31			−0.106213
$527$	13048.4	−	3496.32i	1.07855	−	0.288998i
$528$	−1012.64	+	3779.22i	−0.0834649	+	0.311495i
$529$	4988.77	−	2880.27i	0.410025	−	0.236728i
$530$	−1097.49	+	662.014i	−0.0899468	+	0.0542567i
$531$			4825.67i			0.394381i
$532$		0			0
$533$	−14938.2	+	14938.2i	−1.21397	+	1.21397i
$534$	928.315	+	535.963i	0.0752287	+	0.0434333i
$535$	−14636.9	+	15209.3i	−1.18282	+	1.22908i
$536$	110.316	+	191.072i	0.00888976	+	0.0153975i
$537$	−2364.55	−	8824.61i	−0.190014	−	0.709143i
$538$	24.2088	+	24.2088i	0.00193999	+	0.00193999i
$539$		0			0
$540$	−3755.90	−	13013.7i	−0.299312	−	1.03707i
$541$	−9889.63	+	17129.3i	−0.785931	+	1.36127i	0.142511	+	0.989793i	$0.454482\pi$
$541$	−9889.63	+	17129.3i	−0.785931	+	1.36127i	−0.928442	+	0.371478i	$0.878851\pi$
$542$	−1005.35	−	269.383i	−0.0796743	−	0.0213487i
$543$	−8283.13	−	2219.46i	−0.654628	−	0.175407i
$544$	985.871	−	1707.58i	0.0777001	−	0.134581i
$545$	1752.90	−	3175.21i	0.137772	−	0.249562i
$546$		0			0
$547$	11797.7	+	11797.7i	0.922180	+	0.922180i	0.997183	−	0.0750033i	$-0.0238967\pi$
$547$	11797.7	+	11797.7i	0.922180	+	0.922180i	−0.0750033	+	0.997183i	$0.523897\pi$
$548$	5576.85	+	20813.1i	0.434728	+	1.62243i
$549$	−1569.11	−	2717.78i	−0.121982	−	0.211279i
$550$	−441.204	+	136.555i	−0.0342055	+	0.0105867i
$551$	5891.17	+	3401.27i	0.455485	+	0.262974i
$552$	−908.753	+	908.753i	−0.0700709	+	0.0700709i
$553$		0			0
$554$		−	526.741i		−	0.0403954i
$555$	−6435.52	−	10668.8i	−0.492203	−	0.815974i
$556$	−4531.69	+	2616.37i	−0.345659	+	0.199567i
$557$	−2202.04	+	8218.13i	−0.167511	+	0.625159i	0.830196	+	0.557472i	$0.188229\pi$
$557$	−2202.04	+	8218.13i	−0.167511	+	0.625159i	−0.997707	+	0.0676868i	$0.978438\pi$
$558$	745.394	−	199.728i	0.0565502	−	0.0151526i
$559$	877.506			0.0663946
$560$		0			0
$561$	2658.18			0.200051
$562$	−1695.45	+	454.295i	−0.127257	+	0.0340984i
$563$	−3253.10	+	12140.7i	−0.243520	+	0.908828i	0.730602	+	0.682804i	$0.239240\pi$
$563$	−3253.10	+	12140.7i	−0.243520	+	0.908828i	−0.974122	+	0.226025i	$0.927427\pi$
$564$	−4034.23	+	2329.16i	−0.301191	+	0.173893i
$565$	517.001	−	2088.91i	0.0384963	−	0.155542i
$566$			891.085i			0.0661751i
$567$		0			0
$568$	2493.92	−	2493.92i	0.184230	−	0.184230i
$569$	−19812.9	−	11439.0i	−1.45975	−	0.842788i	−0.460753	−	0.887528i	$-0.652421\pi$
$569$	−19812.9	−	11439.0i	−1.45975	−	0.842788i	−0.998999	+	0.0447399i	$0.985754\pi$
$570$	733.213	−	14.0626i	0.0538788	−	0.00103337i
$571$	−2792.26	−	4836.33i	−0.204645	−	0.354456i	0.745375	−	0.666646i	$-0.232271\pi$
$571$	−2792.26	−	4836.33i	−0.204645	−	0.354456i	−0.950020	+	0.312190i	$0.898937\pi$
$572$	−1773.17	−	6617.55i	−0.129615	−	0.483730i
$573$	5953.42	+	5953.42i	0.434045	+	0.434045i
$574$		0			0
$575$	9756.32	+	2217.02i	0.707594	+	0.160794i
$576$	−2435.25	+	4217.97i	−0.176161	+	0.305120i
$577$	4296.66	+	1151.29i	0.310004	+	0.0830652i	0.410467	−	0.911876i	$-0.365366\pi$
$577$	4296.66	+	1151.29i	0.310004	+	0.0830652i	−0.100463	+	0.994941i	$0.532032\pi$
$578$	731.867	+	196.103i	0.0526672	+	0.0141121i
$579$	−1177.45	+	2039.40i	−0.0845129	+	0.146381i
$580$	8118.98	+	4482.15i	0.581245	+	0.320881i
$581$		0			0
$582$	−581.663	−	581.663i	−0.0414273	−	0.0414273i
$583$	1841.76	+	6873.54i	0.130837	+	0.488290i
$584$	265.488	+	459.840i	0.0188116	+	0.0325827i
$585$	4568.55	+	4396.61i	0.322883	+	0.310730i
$586$	1902.57	+	1098.45i	0.134120	+	0.0774343i
$587$	−7974.07	+	7974.07i	−0.560690	+	0.560690i	−0.929503	−	0.368813i	$-0.879764\pi$
$587$	−7974.07	+	7974.07i	−0.560690	+	0.560690i	0.368813	+	0.929503i	$0.379764\pi$
$588$		0			0
$589$		−	20691.5i		−	1.44750i
$590$	−1283.61	−	317.692i	−0.0895688	−	0.0221681i
$591$	10709.8	−	6183.32i	0.745420	−	0.430369i
$592$	−4371.55	+	16314.9i	−0.303496	+	1.13266i
$593$	−8507.63	+	2279.61i	−0.589151	+	0.157863i	−0.541065	−	0.840981i	$-0.681979\pi$
$593$	−8507.63	+	2279.61i	−0.589151	+	0.157863i	−0.0480859	+	0.998843i	$0.515312\pi$
$594$	563.724			0.0389392
$595$		0			0
$596$	−24036.7			−1.65198
$597$	−2168.13	+	580.949i	−0.148636	+	0.0398269i
$598$	287.942	−	1074.61i	0.0196903	−	0.0734854i
$599$	−5253.79	+	3033.28i	−0.358371	+	0.206906i	−0.668366	−	0.743833i	$-0.733006\pi$
$599$	−5253.79	+	3033.28i	−0.358371	+	0.206906i	0.309995	+	0.950738i	$0.399673\pi$
$600$	2005.59	−	76.9606i	0.136463	−	0.00523651i
$601$		−	14162.7i		−	0.961245i	−0.876928	−	0.480622i	$-0.840411\pi$
$601$		−	14162.7i		−	0.961245i	0.876928	−	0.480622i	$-0.159589\pi$
$602$		0			0
$603$	−399.318	+	399.318i	−0.0269676	+	0.0269676i
$604$	−14627.7	−	8445.29i	−0.985416	−	0.568930i
$605$	−236.186	−	12314.5i	−0.0158716	−	0.827533i
$606$	−532.573	−	922.443i	−0.0357001	−	0.0618344i
$607$	4812.75	+	17961.4i	0.321818	+	1.20104i	0.917472	+	0.397800i	$0.130226\pi$
$607$	4812.75	+	17961.4i	0.321818	+	1.20104i	−0.595654	+	0.803241i	$0.703107\pi$
$608$	−2135.56	−	2135.56i	−0.142448	−	0.142448i
$609$		0			0
$610$	826.223	−	238.458i	0.0548407	−	0.0158277i
$611$	4047.65	−	7010.73i	0.268004	−	0.464196i
$612$	3245.86	+	869.725i	0.214389	+	0.0574453i
$613$	9342.14	+	2503.22i	0.615539	+	0.164933i	0.553099	−	0.833115i	$-0.313445\pi$
$613$	9342.14	+	2503.22i	0.615539	+	0.164933i	0.0624401	+	0.998049i	$0.480112\pi$
$614$	−996.776	+	1726.47i	−0.0655156	+	0.113476i
$615$	−16445.4	+	4746.34i	−1.07828	+	0.311205i
$616$		0			0
$617$	−10902.0	−	10902.0i	−0.711343	−	0.711343i	0.255473	−	0.966816i	$-0.417769\pi$
$617$	−10902.0	−	10902.0i	−0.711343	−	0.711343i	−0.966816	+	0.255473i	$0.917769\pi$
$618$	−20.6921	−	77.2240i	−0.00134686	−	0.00502655i
$619$	−9945.11	−	17225.4i	−0.645764	−	1.11850i	−0.984125	−	0.177479i	$-0.943206\pi$
$619$	−9945.11	−	17225.4i	−0.645764	−	1.11850i	0.338361	−	0.941017i	$-0.390128\pi$
$620$	−540.935	−	28203.9i	−0.0350395	−	1.82693i
$621$	−10575.8	−	6105.93i	−0.683400	−	0.394561i
$622$	642.570	−	642.570i	0.0414223	−	0.0414223i
$623$		0			0
$624$			14718.5i			0.944251i
$625$	−8826.50	−	12893.2i	−0.564896	−	0.825162i
$626$	−896.888	+	517.819i	−0.0572633	+	0.0330610i
$627$	1053.80	−	3932.83i	0.0671207	−	0.250498i
$628$	−16960.4	+	4544.51i	−1.07769	+	0.288767i
$629$	11475.4			0.727429
$630$		0			0
$631$	−1793.20			−0.113132			−0.0565660	−	0.998399i	$-0.518015\pi$
$631$	−1793.20			−0.113132			−0.0565660	+	0.998399i	$0.518015\pi$
$632$	1331.57	−	356.794i	0.0838088	−	0.0224565i
$633$	−886.006	+	3306.62i	−0.0556329	+	0.207625i
$634$	−734.939	+	424.317i	−0.0460381	+	0.0265801i
$635$	−11224.1	−	2777.93i	−0.701438	−	0.173604i
$636$		−	15404.2i		−	0.960405i
$637$		0			0
$638$	−272.926	+	272.926i	−0.0169361	+	0.0169361i
$639$	7818.00	+	4513.72i	0.483999	+	0.279437i
$640$	−3950.63	−	3801.94i	−0.244004	−	0.234820i
$641$	3407.93	+	5902.71i	0.209992	+	0.363718i	0.951712	−	0.306993i	$-0.0993227\pi$
$641$	3407.93	+	5902.71i	0.209992	+	0.363718i	−0.741719	+	0.670710i	$0.765989\pi$
$642$	492.205	+	1836.94i	0.0302583	+	0.112925i
$643$	−5954.74	−	5954.74i	−0.365213	−	0.365213i	0.500515	−	0.865728i	$-0.333144\pi$
$643$	−5954.74	−	5954.74i	−0.365213	−	0.365213i	−0.865728	+	0.500515i	$0.833144\pi$
$644$		0			0
$645$	622.428	+	343.616i	0.0379971	+	0.0209766i
$646$	−337.711	+	584.932i	−0.0205682	+	0.0356252i
$647$	14057.1	+	3766.58i	0.854159	+	0.228871i	0.659226	−	0.751945i	$-0.270884\pi$
$647$	14057.1	+	3766.58i	0.854159	+	0.228871i	0.194934	+	0.980816i	$0.437551\pi$
$648$	−1356.66	−	363.515i	−0.0822446	−	0.0220374i
$649$	−3670.85	+	6358.10i	−0.222024	+	0.384556i
$650$	−1470.25	+	925.777i	−0.0887199	+	0.0558646i
$651$		0			0
$652$	10678.6	+	10678.6i	0.641418	+	0.641418i
$653$	7663.77	+	28601.6i	0.459275	+	1.71404i	0.675207	+	0.737628i	$0.264054\pi$
$653$	7663.77	+	28601.6i	0.459275	+	1.71404i	−0.215932	+	0.976408i	$0.569279\pi$
$654$	−163.382	−	282.986i	−0.00976873	−	0.0169199i
$655$	16804.8	−	322.307i	1.00247	−	0.0192268i
$656$	20095.0	+	11601.8i	1.19600	+	0.690512i
$657$	−961.009	+	961.009i	−0.0570663	+	0.0570663i
$658$		0			0
$659$		−	4483.31i		−	0.265015i	−0.991182	−	0.132508i	$-0.957697\pi$
$659$		−	4483.31i		−	0.265015i	0.991182	−	0.132508i	$-0.0423029\pi$
$660$	1333.58	−	5388.27i	0.0786511	−	0.317785i
$661$	9298.38	−	5368.42i	0.547149	−	0.315896i	−0.200823	−	0.979628i	$-0.564361\pi$
$661$	9298.38	−	5368.42i	0.547149	−	0.315896i	0.747971	+	0.663731i	$0.231028\pi$
$662$	−430.172	+	1605.42i	−0.0252554	+	0.0942546i
$663$	9659.06	−	2588.14i	0.565802	−	0.151606i
$664$	−2873.40			−0.167936
$665$		0			0
$666$	655.532			0.0381402
$667$	8076.43	−	2164.07i	0.468847	−	0.125627i
$668$	4254.11	−	15876.5i	0.246402	−	0.919583i
$669$	−12799.3	+	7389.66i	−0.739683	+	0.427056i
$670$	−79.9289	−	132.506i	−0.00460884	−	0.00764053i
$671$		−	4774.45i		−	0.274688i
$672$		0			0
$673$	1551.60	−	1551.60i	0.0888706	−	0.0888706i	−0.661274	−	0.750145i	$-0.729984\pi$
$673$	1551.60	−	1551.60i	0.0888706	−	0.0888706i	0.750145	+	0.661274i	$0.229984\pi$
$674$	−552.949	−	319.246i	−0.0316006	−	0.0182446i
$675$	5638.78	+	18218.7i	0.321536	+	1.03887i
$676$	−4163.71	−	7211.76i	−0.236898	−	0.410319i
$677$	−417.055	−	1556.47i	−0.0236761	−	0.0883605i	0.953077	−	0.302728i	$-0.0978975\pi$
$677$	−417.055	−	1556.47i	−0.0236761	−	0.0883605i	−0.976753	+	0.214368i	$0.931231\pi$
$678$	−137.091	−	137.091i	−0.00776543	−	0.00776543i
$679$		0			0
$680$	−893.398	+	1618.31i	−0.0503827	+	0.0912635i
$681$	827.936	−	1434.03i	0.0465882	−	0.0806932i
$682$	1134.03	+	303.862i	0.0636719	+	0.0170608i
$683$	8875.43	+	2378.17i	0.497231	+	0.133233i	0.498715	−	0.866766i	$-0.333806\pi$
$683$	8875.43	+	2378.17i	0.497231	+	0.133233i	−0.00148337	+	0.999999i	$0.500472\pi$
$684$	2573.55	−	4457.52i	0.143863	−	0.249178i
$685$	−8412.82	−	29149.2i	−0.469251	−	1.62589i
$686$		0			0
$687$	13064.7	+	13064.7i	0.725542	+	0.725542i
$688$	−249.454	−	930.976i	−0.0138232	−	0.0515888i
$689$	13384.8	+	23183.2i	0.740089	+	1.28187i
$690$	625.042	−	649.487i	0.0344854	−	0.0358341i
$691$	16561.3	+	9561.69i	0.911755	+	0.526402i	0.880995	−	0.473125i	$-0.156874\pi$
$691$	16561.3	+	9561.69i	0.911755	+	0.526402i	0.0307598	+	0.999527i	$0.490207\pi$
$692$	16023.2	−	16023.2i	0.880216	−	0.880216i
$693$		0			0
$694$			1398.64i			0.0765011i
$695$	6308.89	−	3805.58i	0.344331	−	0.207704i
$696$	1452.61	−	838.665i	0.0791107	−	0.0456746i
$697$	4080.18	−	15227.4i	0.221733	−	0.827519i
$698$	−408.762	+	109.528i	−0.0221660	+	0.00593937i
$699$	12117.1			0.655664
$700$		0			0
$701$	1396.73			0.0752551			0.0376275	−	0.999292i	$-0.488020\pi$
$701$	1396.73			0.0752551			0.0376275	+	0.999292i	$0.488020\pi$
$702$	2048.40	−	548.868i	0.110131	−	0.0295096i
$703$	4549.25	−	16978.0i	0.244066	−	0.910865i
$704$	−6417.16	+	3704.95i	−0.343545	+	0.198346i
$705$	5616.34	−	3387.83i	0.300033	−	0.180983i
$706$			2661.26i			0.141867i
$707$		0			0
$708$	11237.9	−	11237.9i	0.596534	−	0.596534i
$709$	20533.5	+	11855.0i	1.08766	+	0.627962i	0.932953	−	0.359998i	$-0.117223\pi$
$709$	20533.5	+	11855.0i	1.08766	+	0.627962i	0.154709	+	0.987960i	$0.450556\pi$
$710$	−1715.33	+	1782.41i	−0.0906690	+	0.0942150i
$711$	1764.24	+	3055.76i	0.0930581	+	0.161181i
$712$	1071.16	+	3997.63i	0.0563813	+	0.210418i
$713$	−17983.8	−	17983.8i	−0.944598	−	0.944598i
$714$		0			0
$715$	2674.87	+	9268.04i	0.139908	+	0.484762i
$716$	8785.39	−	15216.7i	0.458555	−	0.794241i
$717$	2239.25	+	600.005i	0.116634	+	0.0312519i
$718$	−461.368	−	123.623i	−0.0239806	−	0.00642560i
$719$	9868.04	−	17091.9i	0.511844	−	0.886540i	−0.488062	−	0.872809i	$-0.662296\pi$
$719$	9868.04	−	17091.9i	0.511844	−	0.886540i	0.999906	−	0.0137306i	$-0.00437073\pi$
$720$	3365.78	−	6096.78i	0.174215	−	0.315575i
$721$		0			0
$722$	−451.747	−	451.747i	−0.0232857	−	0.0232857i
$723$	−525.445	−	1960.99i	−0.0270284	−	0.100871i
$724$	−8246.32	−	14283.0i	−0.423304	−	0.733184i
$725$	−11550.6	−	6090.57i	−0.591694	−	0.311997i
$726$	−961.002	−	554.835i	−0.0491269	−	0.0283634i
$727$	6487.90	−	6487.90i	0.330981	−	0.330981i	−0.521978	−	0.852959i	$-0.674806\pi$
$727$	6487.90	−	6487.90i	0.330981	−	0.330981i	0.852959	+	0.521978i	$0.174806\pi$
$728$		0			0
$729$		−	20602.6i		−	1.04672i
$730$	−192.359	−	318.892i	−0.00975277	−	0.0161681i
$731$	−567.090	+	327.410i	−0.0286930	+	0.0165659i
$732$	−2674.99	+	9983.21i	−0.135069	+	0.504085i
$733$	3807.97	−	1020.34i	0.191884	−	0.0514151i	−0.161597	−	0.986857i	$-0.551665\pi$
$733$	3807.97	−	1020.34i	0.191884	−	0.0514151i	0.353481	+	0.935442i	$0.384998\pi$
$734$	514.061			0.0258506
$735$		0			0
$736$	−3712.20			−0.185915
$737$	−829.883	+	222.366i	−0.0414778	+	0.0111139i
$738$	233.081	−	869.871i	0.0116258	−	0.0433880i
$739$	8705.65	−	5026.21i	0.433346	−	0.250192i	−0.267425	−	0.963579i	$-0.586173\pi$
$739$	8705.65	−	5026.21i	0.433346	−	0.250192i	0.700771	+	0.713386i	$0.252840\pi$
$740$	5757.08	−	23261.1i	0.285992	−	1.15553i
$741$		−	15316.8i		−	0.759347i
$742$		0			0
$743$	−12894.8	+	12894.8i	−0.636697	+	0.636697i	−0.949739	−	0.313042i	$-0.898652\pi$
$743$	−12894.8	+	12894.8i	−0.636697	+	0.636697i	0.313042	+	0.949739i	$0.398652\pi$
$744$	−4418.44	−	2550.99i	−0.217726	−	0.125704i
$745$	33837.9	−	648.993i	1.66406	−	0.0319158i
$746$	−120.349	−	208.450i	−0.00590654	−	0.0102304i
$747$	−1903.53	−	7104.07i	−0.0932350	−	0.347958i
$748$	3615.01	+	3615.01i	0.176708	+	0.176708i
$749$		0			0
$750$	−1405.39	+	80.9432i	−0.0684234	+	0.00394084i
$751$	−5655.95	+	9796.39i	−0.274818	+	0.475999i	−0.970089	−	0.242748i	$-0.921951\pi$
$751$	−5655.95	+	9796.39i	−0.274818	+	0.475999i	0.695271	+	0.718748i	$0.255284\pi$
$752$	−8588.57	−	2301.30i	−0.416480	−	0.111595i
$753$	−18914.2	−	5068.04i	−0.915366	−	0.245272i
$754$	−725.999	+	1257.47i	−0.0350654	+	0.0607351i
$755$	20820.3	+	11494.0i	1.00361	+	0.554052i
$756$		0			0
$757$	−3513.21	−	3513.21i	−0.168679	−	0.168679i	0.617720	−	0.786398i	$-0.288057\pi$
$757$	−3513.21	−	3513.21i	−0.168679	−	0.168679i	−0.786398	+	0.617720i	$0.788057\pi$
$758$	456.886	+	1705.12i	0.0218929	+	0.0817055i
$759$	−2502.29	−	4334.09i	−0.119667	−	0.207269i
$760$	2040.14	+	1963.35i	0.0973732	+	0.0937083i
$761$	−20959.6	−	12101.1i	−0.998405	−	0.576430i	−0.0906292	−	0.995885i	$-0.528888\pi$
$761$	−20959.6	−	12101.1i	−0.998405	−	0.576430i	−0.907776	+	0.419455i	$0.862221\pi$
$762$	−736.615	+	736.615i	−0.0350193	+	0.0350193i
$763$		0			0
$764$			16192.8i			0.766797i
$765$	−4592.87	−	1136.73i	−0.217066	−	0.0537234i
$766$	−1150.70	+	664.358i	−0.0542775	+	0.0313371i
$767$	−7148.23	+	26677.6i	−0.336516	+	1.25589i
$768$	15132.8	−	4054.83i	0.711015	−	0.190516i
$769$	−13151.0			−0.616691			−0.308346	−	0.951274i	$-0.599775\pi$
$769$	−13151.0			−0.616691			−0.308346	+	0.951274i	$0.599775\pi$
$770$		0			0
$771$	−5294.33			−0.247303
$772$	−4374.76	+	1172.21i	−0.203952	+	0.0546488i
$773$	565.476	−	2110.38i	0.0263114	−	0.0981956i	−0.951521	−	0.307582i	$-0.900480\pi$
$773$	565.476	−	2110.38i	0.0263114	−	0.0981956i	0.977833	+	0.209387i	$0.0671467\pi$
$774$	−32.3951	+	18.7033i	−0.00150442	+	0.000868575i
$775$	1523.01	+	39689.7i	0.0705913	+	1.83961i
$776$		−	3176.00i		−	0.146922i
$777$		0			0
$778$	−244.376	+	244.376i	−0.0112613	+	0.0112613i
$779$	−20911.8	−	12073.4i	−0.961800	−	0.555295i
$780$	−400.425	−	20877.8i	−0.0183814	−	0.958392i
$781$	6867.11	+	11894.2i	0.314628	+	0.544952i
$782$	214.870	+	801.907i	0.00982576	+	0.0366702i
$783$	11270.0	+	11270.0i	0.514377	+	0.514377i
$784$		0			0
$785$	23753.4	−	6855.51i	1.07999	−	0.311699i
$786$	757.144	−	1311.41i	0.0343593	−	0.0595121i
$787$	18292.2	+	4901.39i	0.828524	+	0.222002i	0.648070	−	0.761581i	$-0.275577\pi$
$787$	18292.2	+	4901.39i	0.828524	+	0.222002i	0.180454	+	0.983583i	$0.442243\pi$
$788$	22973.9	+	6155.84i	1.03859	+	0.278290i
$789$	−10841.5	+	18778.0i	−0.489185	+	0.847294i
$790$	−928.970	+	268.112i	−0.0418370	+	0.0120747i
$791$		0			0
$792$	414.564	+	414.564i	0.0185996	+	0.0185996i
$793$	−4648.63	−	17348.9i	−0.208169	−	0.776896i
$794$	1774.61	+	3073.71i	0.0793180	+	0.137383i
$795$	415.915	+	21685.5i	0.0185547	+	0.967426i
$796$	−3738.63	−	2158.50i	−0.166472	−	0.0961129i
$797$	10313.5	−	10313.5i	0.458372	−	0.458372i	−0.439749	−	0.898121i	$-0.644933\pi$
$797$	10313.5	−	10313.5i	0.458372	−	0.458372i	0.898121	+	0.439749i	$0.144933\pi$
$798$		0			0
$799$			6040.93i			0.267475i
$800$	4253.55	+	3939.17i	0.187982	+	0.174088i
$801$	−9173.95	+	5296.58i	−0.404676	+	0.233640i
$802$	619.132	−	2310.63i	0.0272597	−	0.101735i
$803$	−1997.22	+	535.153i	−0.0877712	+	0.0235182i
$804$	1859.84			0.0815816
$805$		0			0
$806$	4416.59			0.193012
$807$	559.623	−	149.951i	0.0244110	−	0.00654091i
$808$	1064.39	−	3972.34i	0.0463428	−	0.172954i
$809$	16227.9	−	9369.19i	0.705245	−	0.407173i	−0.104053	−	0.994572i	$-0.533181\pi$
$809$	16227.9	−	9369.19i	0.705245	−	0.407173i	0.809298	+	0.587398i	$0.199848\pi$
$810$	956.247	+	236.669i	0.0414804	+	0.0102663i
$811$			3494.94i			0.151324i	0.997134	+	0.0756621i	$0.0241070\pi$
$811$			3494.94i			0.151324i	−0.997134	+	0.0756621i	$0.975893\pi$
$812$		0			0
$813$	−12454.4	+	12454.4i	−0.537262	+	0.537262i
$814$	863.701	+	498.658i	0.0371900	+	0.0214717i
$815$	−15321.2	−	14744.5i	−0.658499	−	0.633715i
$816$	−5491.68	−	9511.87i	−0.235597	−	0.408066i
$817$	259.594	+	968.817i	0.0111163	+	0.0414867i
$818$	−256.355	−	256.355i	−0.0109575	−	0.0109575i
$819$		0			0
$820$	−28819.8	−	15910.2i	−1.22735	−	0.677571i
$821$	−11659.7	+	20195.2i	−0.495648	+	0.858487i	−0.999987	−	0.00501802i	$-0.998403\pi$
$821$	−11659.7	+	20195.2i	−0.495648	+	0.858487i	0.504339	+	0.863505i	$0.331736\pi$
$822$	−2640.22	−	707.445i	−0.112030	−	0.0300182i
$823$	−25289.1	−	6776.18i	−1.07111	−	0.287002i	−0.320159	−	0.947364i	$-0.603736\pi$
$823$	−25289.1	−	6776.18i	−1.07111	−	0.287002i	−0.750948	+	0.660362i	$0.770403\pi$
$824$	154.338	−	267.321i	0.00652502	−	0.0113017i
$825$	−1731.88	+	7621.40i	−0.0730866	+	0.321628i
$826$		0			0
$827$	−17866.3	−	17866.3i	−0.751236	−	0.751236i	0.223474	−	0.974710i	$-0.428260\pi$
$827$	−17866.3	−	17866.3i	−0.751236	−	0.751236i	−0.974710	+	0.223474i	$0.928260\pi$
$828$	−1637.43	−	6110.98i	−0.0687255	−	0.256487i
$829$	15880.5	+	27505.8i	0.665321	+	1.15237i	0.979198	+	0.202907i	$0.0650389\pi$
$829$	15880.5	+	27505.8i	0.665321	+	1.15237i	−0.313877	+	0.949464i	$0.601628\pi$
$830$	2014.98	−	38.6462i	0.0842662	−	0.00161618i
$831$	−7719.54	−	4456.88i	−0.322248	−	0.186050i
$832$	−19710.7	+	19710.7i	−0.821330	+	0.821330i
$833$		0			0
$834$		−	663.795i		−	0.0275604i
$835$	−5560.09	+	22465.2i	−0.230437	+	0.931067i
$836$	6781.60	−	3915.36i	0.280558	−	0.161980i
$837$	12547.5	−	46827.7i	0.518164	−	1.93382i
$838$	992.194	−	265.858i	0.0409007	−	0.0109593i
$839$	−33411.9			−1.37486			−0.687429	−	0.726251i	$-0.741261\pi$
$839$	−33411.9			−1.37486			−0.687429	+	0.726251i	$0.741261\pi$
$840$		0			0
$841$	13476.3			0.552556
$842$	1006.79	−	269.769i	0.0412070	−	0.0110414i
$843$	−7687.80	+	28691.2i	−0.314095	+	1.17222i
$844$	−5701.78	+	3291.93i	−0.232540	+	0.134257i
$845$	6056.23	+	10040.0i	0.246557	+	0.408742i
$846$			345.089i			0.0140241i
$847$		0			0
$848$	20790.8	−	20790.8i	0.841934	−	0.841934i
$849$	13059.1	+	7539.68i	0.527901	+	0.304784i
$850$	604.731	−	1146.86i	0.0244025	−	0.0462786i
$851$	−10802.3	−	18710.2i	−0.435135	−	0.753676i
$852$	−7694.91	−	28717.8i	−0.309417	−	1.15476i
$853$	−13286.0	−	13286.0i	−0.533301	−	0.533301i	0.388252	−	0.921553i	$-0.373079\pi$
$853$	−13286.0	−	13286.0i	−0.533301	−	0.533301i	−0.921553	+	0.388252i	$0.873079\pi$
$854$		0			0
$855$	−3502.58	+	6344.60i	−0.140100	+	0.253779i
$856$	−3671.25	+	6358.80i	−0.146590	+	0.253901i
$857$	−39366.4	−	10548.2i	−1.56911	−	0.420443i	−0.633579	−	0.773678i	$-0.718415\pi$
$857$	−39366.4	−	10548.2i	−1.56911	−	0.420443i	−0.935535	+	0.353235i	$0.885082\pi$
$858$	839.462	+	224.933i	0.0334018	+	0.00894999i
$859$	−19866.7	+	34410.1i	−0.789106	+	1.36677i	0.137410	+	0.990514i	$0.456122\pi$
$859$	−19866.7	+	34410.1i	−0.789106	+	1.36677i	−0.926515	+	0.376257i	$0.877211\pi$
$860$	379.172	+	1313.78i	0.0150345	+	0.0520924i
$861$		0			0
$862$	−354.588	−	354.588i	−0.0140108	−	0.0140108i
$863$	−8404.58	−	31366.3i	−0.331513	−	1.23722i	−0.907601	−	0.419834i	$-0.862088\pi$
$863$	−8404.58	−	31366.3i	−0.331513	−	1.23722i	0.576088	−	0.817387i	$-0.304578\pi$
$864$	−3538.06	−	6128.10i	−0.139314	−	0.241299i
$865$	−22124.1	+	22989.4i	−0.869646	+	0.903657i
$866$	501.857	+	289.747i	0.0196926	+	0.0113695i
$867$	9066.45	−	9066.45i	0.355147	−	0.355147i
$868$		0			0
$869$			5368.18i			0.209555i
$870$	−1007.37	+	607.652i	−0.0392562	+	0.0236797i
$871$	−2799.04	+	1616.03i	−0.108889	+	0.0628668i
$872$	326.532	−	1218.63i	0.0126809	−	0.0473258i
$873$	7852.20	−	2103.99i	0.304418	−	0.0815684i
$874$	1271.62			0.0492141
$875$		0			0
$876$	4475.95			0.172635
$877$	−211.207	+	56.5927i	−0.00813221	+	0.00217902i	−0.262883	−	0.964828i	$-0.584673\pi$
$877$	−211.207	+	56.5927i	−0.00813221	+	0.00217902i	0.254751	+	0.967007i	$0.418007\pi$
$878$	−594.008	+	2216.87i	−0.0228323	+	0.0852114i
$879$	32196.2	−	18588.5i	1.23544	−	0.713281i
$880$	9072.38	−	5472.54i	0.347534	−	0.209636i
$881$			18280.7i			0.699082i	0.936921	+	0.349541i	$0.113662\pi$
$881$			18280.7i			0.699082i	−0.936921	+	0.349541i	$0.886338\pi$
$882$		0			0
$883$	−571.541	+	571.541i	−0.0217824	+	0.0217824i	−0.717914	−	0.696132i	$-0.754903\pi$
$883$	−571.541	+	571.541i	−0.0217824	+	0.0217824i	0.696132	+	0.717914i	$0.254903\pi$
$884$	16655.6	+	9616.13i	0.633698	+	0.365866i
$885$	−15516.8	+	16123.7i	−0.589370	+	0.612420i
$886$	−392.816	−	680.377i	−0.0148949	−	0.0257988i
$887$	3129.10	+	11678.0i	0.118450	+	0.442061i	0.999522	−	0.0309215i	$-0.00984419\pi$
$887$	3129.10	+	11678.0i	0.118450	+	0.442061i	−0.881072	+	0.472982i	$0.843178\pi$
$888$	−3064.61	−	3064.61i	−0.115813	−	0.115813i
$889$		0			0
$890$	−804.920	−	2788.94i	−0.0303157	−	0.105040i
$891$	2734.65	−	4736.55i	0.102822	−	0.178093i
$892$	−27456.0	−	7356.82i	−1.03060	−	0.276149i
$893$	8937.67	+	2394.84i	0.334925	+	0.0897428i
$894$	1524.58	−	2640.64i	0.0570352	−	0.0987878i
$895$	−11956.9	+	21658.7i	−0.446563	+	0.808906i
$896$		0			0
$897$	−13312.4	−	13312.4i	−0.495529	−	0.495529i
$898$	−317.554	−	1185.13i	−0.0118006	−	0.0440403i
$899$	16596.8	+	28746.4i	0.615721	+	1.06646i
$900$	−4608.39	+	8739.69i	−0.170681	+	0.323692i
$901$	−17299.9	−	9988.12i	−0.639672	−	0.369315i
$902$	968.801	−	968.801i	0.0357623	−	0.0357623i
$903$		0			0
$904$		−	748.548i		−	0.0275402i
$905$	11994.5	+	19884.4i	0.440563	+	0.730366i
$906$	1855.58	−	1071.32i	0.0680435	−	0.0392849i
$907$	2216.09	−	8270.55i	0.0811289	−	0.302777i	−0.913424	−	0.407009i	$-0.866572\pi$
$907$	2216.09	−	8270.55i	0.0811289	−	0.302777i	0.994553	+	0.104232i	$0.0332384\pi$
$908$	3076.17	−	824.256i	0.112430	−	0.0301255i
$909$	10526.2			0.384082
$910$		0			0
$911$	23536.9			0.855995			0.427998	−	0.903780i	$-0.359219\pi$
$911$	23536.9			0.855995			0.427998	+	0.903780i	$0.359219\pi$
$912$	−16250.1	+	4354.20i	−0.590016	+	0.158094i
$913$	2896.00	−	10808.0i	0.104977	−	0.391778i
$914$	−3811.04	+	2200.31i	−0.137919	+	0.0796276i
$915$	3496.20	−	14126.2i	0.126318	−	0.510380i
$916$			35534.7i			1.28177i
$917$		0			0
$918$	−1119.00	+	1119.00i	−0.0402313	+	0.0402313i
$919$	1740.48	+	1004.86i	0.0624734	+	0.0360690i	0.530911	−	0.847427i	$-0.321850\pi$
$919$	1740.48	+	1004.86i	0.0624734	+	0.0360690i	−0.468438	+	0.883496i	$0.655183\pi$
$920$	3479.60	−	66.7368i	0.124694	−	0.00239157i
$921$	16867.9	+	29216.1i	0.603493	+	1.04528i
$922$	−802.120	−	2993.55i	−0.0286512	−	0.106928i
$923$	36533.8	+	36533.8i	1.30284	+	1.30284i
$924$		0			0
$925$	−7476.53	+	32901.5i	−0.265759	+	1.16951i
$926$	1884.86	−	3264.68i	0.0668903	−	0.115857i
$927$	763.156	+	204.487i	0.0270392	+	0.00724513i
$928$	4679.86	+	1253.97i	0.165543	+	0.0443571i
$929$	11959.9	−	20715.2i	0.422382	−	0.731587i	−0.573790	−	0.819003i	$-0.694527\pi$
$929$	11959.9	−	20715.2i	0.422382	−	0.731587i	0.996172	+	0.0874153i	$0.0278607\pi$
$930$	3132.75	+	1729.46i	0.110459	+	0.0609798i
$931$		0			0
$932$	16478.6	+	16478.6i	0.579159	+	0.579159i
$933$	−3980.11	−	14854.0i	−0.139660	−	0.521219i
$934$	−1229.29	−	2129.20i	−0.0430661	−	0.0745927i
$935$	−5186.67	−	4991.46i	−0.181414	−	0.174586i
$936$	1910.04	+	1102.76i	0.0667005	+	0.0385096i
$937$	−31840.2	+	31840.2i	−1.11011	+	1.11011i	−0.116976	+	0.993135i	$0.537320\pi$
$937$	−31840.2	+	31840.2i	−1.11011	+	1.11011i	−0.993135	+	0.116976i	$0.962680\pi$
$938$		0			0
$939$			17525.5i			0.609078i
$940$	12245.3	+	3030.67i	0.424890	+	0.105159i
$941$	−30309.3	+	17499.1i	−1.05000	+	0.606220i	−0.922650	−	0.385637i	$-0.873982\pi$
$941$	−30309.3	+	17499.1i	−1.05000	+	0.606220i	−0.127354	+	0.991857i	$0.540648\pi$
$942$	576.489	−	2151.49i	0.0199395	−	0.0744154i
$943$	−28668.8	+	7681.77i	−0.990014	+	0.265273i
$944$	30335.2			1.04590
$945$		0			0
$946$	−56.9099			−0.00195592
$947$	−24600.1	+	6591.59i	−0.844136	+	0.226186i	−0.654871	−	0.755740i	$-0.727277\pi$
$947$	−24600.1	+	6591.59i	−0.844136	+	0.226186i	−0.189265	+	0.981926i	$0.560611\pi$
$948$	3007.65	−	11224.7i	0.103042	−	0.384558i
$949$	−6736.25	+	3889.17i	−0.230419	+	0.133033i
$950$	−1457.06	−	1349.37i	−0.0497612	−	0.0460834i
$951$			14361.0i			0.489681i
$952$		0			0
$953$	6157.51	−	6157.51i	0.209298	−	0.209298i	−0.594671	−	0.803969i	$-0.702718\pi$
$953$	6157.51	−	6157.51i	0.209298	−	0.209298i	0.803969	+	0.594671i	$0.202718\pi$
$954$	−988.261	−	570.573i	−0.0335389	−	0.0193637i
$955$	−437.206	−	22795.5i	−0.0148143	−	0.772403i
$956$	2229.30	+	3861.26i	0.0754191	+	0.130630i
$957$	1690.52	+	6309.11i	0.0571021	+	0.213108i
$958$	2199.15	+	2199.15i	0.0741662	+	0.0741662i
$959$		0			0
$960$	−21699.5	+	6262.74i	−0.729530	+	0.210551i
$961$	35587.4	−	61639.1i	1.19457	−	2.06905i
$962$	3623.95	+	971.035i	0.121456	+	0.0325441i
$963$	−18153.3	−	4864.16i	−0.607457	−	0.162768i
$964$	1952.27	−	3381.44i	0.0652267	−	0.112976i
$965$	6126.96	−	1768.31i	0.204387	−	0.0589886i
$966$		0			0
$967$	−28380.1	−	28380.1i	−0.943788	−	0.943788i	0.0547136	−	0.998502i	$-0.482575\pi$
$967$	−28380.1	−	28380.1i	−0.943788	−	0.943788i	−0.998502	+	0.0547136i	$0.982575\pi$
$968$	−1108.88	−	4138.39i	−0.0368189	−	0.137410i
$969$	5714.90	+	9898.50i	0.189462	+	0.328159i
$970$	42.7160	+	2227.17i	0.00141395	+	0.0737219i
$971$	2488.17	+	1436.55i	0.0822340	+	0.0474778i	0.540553	−	0.841310i	$-0.318215\pi$
$971$	2488.17	+	1436.55i	0.0822340	+	0.0474778i	−0.458319	+	0.888788i	$0.651548\pi$
$972$	14757.8	−	14757.8i	0.486991	−	0.486991i
$973$		0			0
$974$			1468.24i			0.0483013i
$975$	1127.41	+	29380.1i	0.0370317	+	0.965044i
$976$	−17084.6	+	9863.79i	−0.560311	+	0.323496i
$977$	−6040.06	+	22541.8i	−0.197788	+	0.738154i	0.793740	+	0.608257i	$0.208131\pi$
$977$	−6040.06	+	22541.8i	−0.197788	+	0.738154i	−0.991528	+	0.129896i	$0.958536\pi$
$978$	−1850.44	+	495.824i	−0.0605016	+	0.0162114i
$979$	−16116.3			−0.526127
$980$		0			0
$981$	3229.21			0.105098
$982$	−1481.10	+	396.858i	−0.0481300	+	0.0128964i
$983$	−9680.58	+	36128.4i	−0.314102	+	1.17225i	0.610720	+	0.791846i	$0.290880\pi$
$983$	−9680.58	+	36128.4i	−0.314102	+	1.17225i	−0.924823	+	0.380399i	$0.875787\pi$
$984$	−5156.30	+	2976.99i	−0.167050	+	0.0964462i
$985$	−32508.0	−	8045.65i	−1.05156	−	0.260260i
$986$		−	1083.52i		−	0.0349963i
$987$		0			0
$988$	20830.1	−	20830.1i	0.670744	−	0.670744i
$989$	1067.66	+	616.415i	0.0343273	+	0.0198189i
$990$	−296.289	−	285.138i	−0.00951181	−	0.00915382i
$991$	7784.70	+	13483.5i	0.249535	+	0.432207i	0.963397	−	0.268079i	$-0.0863889\pi$
$991$	7784.70	+	13483.5i	0.249535	+	0.432207i	−0.713862	+	0.700286i	$0.753056\pi$
$992$	−3814.22	−	14234.9i	−0.122078	−	0.455602i
$993$	19888.2	+	19888.2i	0.635581	+	0.635581i
$994$		0			0
$995$	5321.37	+	2937.70i	0.169546	+	0.0935994i
$996$	−12110.9	+	20976.7i	−0.385289	+	0.667341i
$997$	6867.35	+	1840.10i	0.218146	+	0.0584519i	0.366236	−	0.930522i	$-0.380646\pi$
$997$	6867.35	+	1840.10i	0.218146	+	0.0584519i	−0.148091	+	0.988974i	$0.547313\pi$
$998$	−1571.00	−	420.948i	−0.0498288	−	0.0133516i
$999$	20591.2	−	35665.0i	0.652128	−	1.12952i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.f.b.13.3	✓	16	35.33	even	12
35.4.f.b.13.4	yes	16	35.23	odd	12
35.4.f.b.27.3	yes	16	7.2	even	3
35.4.f.b.27.4	yes	16	7.5	odd	6
175.4.f.g.118.5		16	35.2	odd	12
175.4.f.g.118.6		16	35.12	even	12
175.4.f.g.132.5		16	35.19	odd	6
175.4.f.g.132.6		16	35.9	even	6
245.4.l.b.68.3		32	5.3	odd	4	inner
245.4.l.b.68.4		32	35.13	even	4	inner
245.4.l.b.117.5		32	1.1	even	1	trivial
245.4.l.b.117.6		32	7.6	odd	2	inner
245.4.l.b.178.5		32	35.3	even	12	inner
245.4.l.b.178.6		32	35.18	odd	12	inner
245.4.l.b.227.3		32	7.3	odd	6	inner
245.4.l.b.227.4		32	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.235661 + 0.0631451i) q^{2} +(-1.06857 + 3.98796i) q^{3} +(-6.87665 + 3.97024i) q^{4} +(9.57348 - 5.77481i) q^{5} -1.00728i q^{6} +(2.74998 - 2.74998i) q^{8} +(8.62069 + 4.97716i) q^{9} +O(q^{10})\)	\(q+(-0.235661 + 0.0631451i) q^{2} +(-1.06857 + 3.98796i) q^{3} +(-6.87665 + 3.97024i) q^{4} +(9.57348 - 5.77481i) q^{5} -1.00728i q^{6} +(2.74998 - 2.74998i) q^{8} +(8.62069 + 4.97716i) q^{9} +(-1.89144 + 1.96541i) q^{10} +(7.57217 + 13.1154i) q^{11} +(-8.48496 - 31.6663i) q^{12} +(40.2848 + 40.2848i) q^{13} +(12.7998 + 44.3495i) q^{15} +(31.2875 - 54.1915i) q^{16} +(-41.0649 - 11.0033i) q^{17} +(-2.34584 - 0.628566i) q^{18} +(-32.5592 + 56.3943i) q^{19} +(-42.9061 + 77.7204i) q^{20} +(-2.61264 - 2.61264i) q^{22} +(20.7160 + 77.3131i) q^{23} +(8.02827 + 13.9054i) q^{24} +(58.3031 - 110.570i) q^{25} +(-12.0373 - 6.94976i) q^{26} +(-107.884 + 107.884i) q^{27} -104.464i q^{29} +(-5.81686 - 9.64318i) q^{30} +(-275.180 + 158.876i) q^{31} +(-12.0038 + 44.7988i) q^{32} +(-60.3951 + 16.1828i) q^{33} +10.3722 q^{34} -79.0420 q^{36} +(-260.725 + 69.8611i) q^{37} +(4.11191 - 15.3459i) q^{38} +(-203.701 + 117.607i) q^{39} +(10.4463 - 42.2075i) q^{40} +370.814i q^{41} +(10.8913 - 10.8913i) q^{43} +(-104.142 - 60.1267i) q^{44} +(111.272 - 2.13414i) q^{45} +(-9.76388 - 16.9115i) q^{46} +(-36.7767 - 137.252i) q^{47} +(182.681 + 182.681i) q^{48} +(-6.75779 + 29.7386i) q^{50} +(87.7616 - 152.008i) q^{51} +(-436.965 - 117.084i) q^{52} +(453.868 + 121.614i) q^{53} +(18.6117 - 32.2364i) q^{54} +(148.231 + 81.8320i) q^{55} +(-190.106 - 190.106i) q^{57} +(6.59639 + 24.6180i) q^{58} +(242.391 + 419.833i) q^{59} +(-264.098 - 254.158i) q^{60} +(-273.026 - 157.631i) q^{61} +(54.8170 - 54.8170i) q^{62} +489.285i q^{64} +(618.303 + 153.029i) q^{65} +(13.2109 - 7.62730i) q^{66} +(-14.6831 + 54.7982i) q^{67} +(326.075 - 87.3716i) q^{68} -330.458 q^{69} +906.887 q^{71} +(37.3938 - 10.0196i) q^{72} +(-35.3368 + 131.879i) q^{73} +(57.0313 - 32.9270i) q^{74} +(378.648 + 350.662i) q^{75} -517.072i q^{76} +(40.5781 - 40.5781i) q^{78} +(306.978 + 177.234i) q^{79} +(-13.4157 - 699.481i) q^{80} +(-180.572 - 312.761i) q^{81} +(-23.4151 - 87.3862i) q^{82} +(-522.441 - 522.441i) q^{83} +(-456.677 + 131.802i) q^{85} +(-1.87892 + 3.25438i) q^{86} +(416.598 + 111.627i) q^{87} +(56.8904 + 15.2437i) q^{88} +(-532.089 + 921.605i) q^{89} +(-26.0877 + 7.52923i) q^{90} +(-449.408 - 449.408i) q^{92} +(-339.540 - 1267.18i) q^{93} +(17.3336 + 30.0227i) q^{94} +(13.9610 + 727.913i) q^{95} +(-165.829 - 95.7414i) q^{96} +(577.458 - 577.458i) q^{97} +150.752i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 352 q^{8}+O(q^{10}) \) 32 * q - 4 * q^2 + 352 * q^8	\( 32 q - 4 q^{2} + 352 q^{8} + 152 q^{11} - 960 q^{15} + 504 q^{16} - 288 q^{18} + 696 q^{22} + 72 q^{23} + 160 q^{25} - 1780 q^{30} - 432 q^{32} + 688 q^{36} + 256 q^{37} - 624 q^{43} + 1856 q^{46} - 40 q^{50} - 696 q^{51} - 1768 q^{53} - 7840 q^{57} + 4764 q^{58} + 2000 q^{60} + 1000 q^{65} - 4504 q^{67} + 12736 q^{71} - 7848 q^{72} + 10680 q^{78} + 3088 q^{81} - 4560 q^{85} + 9336 q^{86} + 2048 q^{88} - 12656 q^{92} + 3960 q^{93} - 1240 q^{95}+O(q^{100}) \) 32 * q - 4 * q^2 + 352 * q^8 + 152 * q^11 - 960 * q^15 + 504 * q^16 - 288 * q^18 + 696 * q^22 + 72 * q^23 + 160 * q^25 - 1780 * q^30 - 432 * q^32 + 688 * q^36 + 256 * q^37 - 624 * q^43 + 1856 * q^46 - 40 * q^50 - 696 * q^51 - 1768 * q^53 - 7840 * q^57 + 4764 * q^58 + 2000 * q^60 + 1000 * q^65 - 4504 * q^67 + 12736 * q^71 - 7848 * q^72 + 10680 * q^78 + 3088 * q^81 - 4560 * q^85 + 9336 * q^86 + 2048 * q^88 - 12656 * q^92 + 3960 * q^93 - 1240 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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