LMFDB - Embedded newform 363.3.h.q.245.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, 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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			245.5
Character	$\chi$	$=$	363.245
Dual form			363.3.h.q.323.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.69141 + 2.32802i) q^{2} +(-1.38470 + 2.66132i) q^{3} +(-1.32276 + 4.07105i) q^{4} +(-2.90829 + 4.00292i) q^{5} +(-8.53770 + 1.27775i) q^{6} +(-3.45484 + 10.6329i) q^{7} +(-0.767802 + 0.249474i) q^{8} +(-5.16520 - 7.37026i) q^{9} -14.2380 q^{10} +(-9.00271 - 9.15748i) q^{12} +(13.6720 - 9.93330i) q^{13} +(-30.5972 + 9.94163i) q^{14} +(-6.62591 - 13.2827i) q^{15} +(11.9727 + 8.69868i) q^{16} +(-0.0367864 + 0.0506321i) q^{17} +(8.42167 - 24.4908i) q^{18} +(1.66282 + 5.11764i) q^{19} +(-12.4491 - 17.1347i) q^{20} +(-23.5136 - 23.9178i) q^{21} -8.69537i q^{23} +(0.399248 - 2.38881i) q^{24} +(0.160235 + 0.493153i) q^{25} +(46.2499 + 15.0275i) q^{26} +(26.7668 - 3.54062i) q^{27} +(-38.7171 - 28.1296i) q^{28} +(-47.5106 - 15.4371i) q^{29} +(19.7154 - 37.8918i) q^{30} +(19.8827 - 14.4457i) q^{31} +45.8150i q^{32} -0.180094 q^{34} +(-32.5149 - 44.7530i) q^{35} +(36.8370 - 11.2787i) q^{36} +(-12.1319 + 37.3382i) q^{37} +(-9.10148 + 12.5271i) q^{38} +(7.50398 + 50.1402i) q^{39} +(1.23437 - 3.79899i) q^{40} +(-41.7596 + 13.5685i) q^{41} +(15.9102 - 95.1949i) q^{42} +0.201842 q^{43} +(44.5244 + 0.758975i) q^{45} +(20.2430 - 14.7074i) q^{46} +(14.1766 - 4.60627i) q^{47} +(-39.7286 + 19.8181i) q^{48} +(-61.4808 - 44.6684i) q^{49} +(-0.877048 + 1.20715i) q^{50} +(-0.0838099 - 0.168011i) q^{51} +(22.3541 + 68.7988i) q^{52} +(57.5690 + 79.2369i) q^{53} +(53.5163 + 56.3252i) q^{54} -9.02585i q^{56} +(-15.9222 - 2.66112i) q^{57} +(-44.4218 - 136.716i) q^{58} +(-13.7827 - 4.47826i) q^{59} +(62.8391 - 9.40449i) q^{60} +(-23.7229 - 17.2357i) q^{61} +(67.2596 + 21.8540i) q^{62} +(96.2122 - 29.4580i) q^{63} +(-58.7676 + 42.6972i) q^{64} +83.6168i q^{65} +82.8515 q^{67} +(-0.157466 - 0.216733i) q^{68} +(23.1411 + 12.0405i) q^{69} +(49.1899 - 151.391i) q^{70} +(15.6972 - 21.6053i) q^{71} +(5.80454 + 4.37031i) q^{72} +(4.31706 - 13.2865i) q^{73} +(-107.444 + 34.9108i) q^{74} +(-1.53431 - 0.256434i) q^{75} -23.0337 q^{76} +(-104.035 + 102.277i) q^{78} +(-40.6025 + 29.4994i) q^{79} +(-69.6402 + 22.6275i) q^{80} +(-27.6414 + 76.1377i) q^{81} +(-102.220 - 74.2674i) q^{82} +(-35.4092 + 48.7366i) q^{83} +(128.473 - 64.0873i) q^{84} +(-0.0956907 - 0.294506i) q^{85} +(0.341398 + 0.469894i) q^{86} +(106.871 - 105.065i) q^{87} +40.3489i q^{89} +(73.5420 + 104.938i) q^{90} +(58.3852 + 179.691i) q^{91} +(35.3993 + 11.5019i) q^{92} +(10.9128 + 72.9172i) q^{93} +(34.7020 + 25.2125i) q^{94} +(-25.3215 - 8.22744i) q^{95} +(-121.928 - 63.4402i) q^{96} +(24.9281 - 18.1114i) q^{97} -218.681i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) $ 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	1.69141	+	2.32802i	0.845704	+	1.16401i	0.984793	+	0.173732i	$0.0555825\pi$
$2$	1.69141	+	2.32802i	0.845704	+	1.16401i	−0.139089	+	0.990280i	$0.544417\pi$
$3$	−1.38470	+	2.66132i	−0.461567	+	0.887105i
$3$	−1.38470	+	2.66132i	−0.461567	+	0.887105i
$4$	−1.32276	+	4.07105i	−0.330691	+	1.01776i
$5$	−2.90829	+	4.00292i	−0.581658	+	0.800583i	−0.993876	−	0.110502i	$-0.964754\pi$
$5$	−2.90829	+	4.00292i	−0.581658	+	0.800583i	0.412218	+	0.911085i	$0.364754\pi$
$6$	−8.53770	+	1.27775i	−1.42295	+	0.212959i
$7$	−3.45484	+	10.6329i	−0.493548	+	1.51899i	0.325658	+	0.945488i	$0.394414\pi$
$7$	−3.45484	+	10.6329i	−0.493548	+	1.51899i	−0.819207	+	0.573498i	$0.805586\pi$
$8$	−0.767802	+	0.249474i	−0.0959752	+	0.0311842i
$9$	−5.16520	−	7.37026i	−0.573911	−	0.818918i
$10$	−14.2380			−1.42380
$11$		0			0
$11$		0			0
$12$	−9.00271	−	9.15748i	−0.750226	−	0.763123i
$13$	13.6720	−	9.93330i	1.05169	−	0.764100i	0.0791598	−	0.996862i	$-0.474776\pi$
$13$	13.6720	−	9.93330i	1.05169	−	0.764100i	0.972534	+	0.232762i	$0.0747763\pi$
$14$	−30.5972	+	9.94163i	−2.18551	+	0.710116i
$15$	−6.62591	−	13.2827i	−0.441727	−	0.885514i
$16$	11.9727	+	8.69868i	0.748294	+	0.543668i
$17$	−0.0367864	+	0.0506321i	−0.00216391	+	0.00297836i	−0.810098	−	0.586295i	$-0.800586\pi$
$17$	−0.0367864	+	0.0506321i	−0.00216391	+	0.00297836i	0.807934	+	0.589273i	$0.200586\pi$
$18$	8.42167	−	24.4908i	0.467871	−	1.36060i
$19$	1.66282	+	5.11764i	0.0875170	+	0.269350i	0.985231	−	0.171228i	$-0.0547735\pi$
$19$	1.66282	+	5.11764i	0.0875170	+	0.269350i	−0.897714	+	0.440578i	$0.854774\pi$
$20$	−12.4491	−	17.1347i	−0.622454	−	0.856734i
$21$	−23.5136	−	23.9178i	−1.11969	−	1.13894i
$22$		0			0
$23$		−	8.69537i		−	0.378060i	−0.981971	−	0.189030i	$-0.939466\pi$
$23$		−	8.69537i		−	0.378060i	0.981971	−	0.189030i	$-0.0605343\pi$
$24$	0.399248	−	2.38881i	0.0166353	−	0.0995337i
$25$	0.160235	+	0.493153i	0.00640940	+	0.0197261i
$26$	46.2499	+	15.0275i	1.77884	+	0.577981i
$27$	26.7668	−	3.54062i	0.991365	−	0.131134i
$28$	−38.7171	−	28.1296i	−1.38275	−	1.00463i
$29$	−47.5106	−	15.4371i	−1.63830	−	0.532315i	−0.662139	−	0.749381i	$-0.730351\pi$
$29$	−47.5106	−	15.4371i	−1.63830	−	0.532315i	−0.976157	+	0.217066i	$0.930351\pi$
$30$	19.7154	−	37.8918i	0.657179	−	1.26306i
$31$	19.8827	−	14.4457i	0.641379	−	0.465989i	−0.218945	−	0.975737i	$-0.570261\pi$
$31$	19.8827	−	14.4457i	0.641379	−	0.465989i	0.860324	+	0.509748i	$0.170261\pi$
$32$			45.8150i			1.43172i
$33$		0			0
$34$	−0.180094			−0.00529687
$35$	−32.5149	−	44.7530i	−0.928998	−	1.27866i
$36$	36.8370	−	11.2787i	1.02325	−	0.313296i
$37$	−12.1319	+	37.3382i	−0.327890	+	1.00914i	0.642229	+	0.766512i	$0.278010\pi$
$37$	−12.1319	+	37.3382i	−0.327890	+	1.00914i	−0.970119	+	0.242629i	$0.921990\pi$
$38$	−9.10148	+	12.5271i	−0.239513	+	0.329661i
$39$	7.50398	+	50.1402i	0.192410	+	1.28565i
$40$	1.23437	−	3.79899i	0.0308591	−	0.0949747i
$41$	−41.7596	+	13.5685i	−1.01853	+	0.330940i	−0.770245	−	0.637748i	$-0.779866\pi$
$41$	−41.7596	+	13.5685i	−1.01853	+	0.330940i	−0.248282	+	0.968688i	$0.579866\pi$
$42$	15.9102	−	95.1949i	0.378814	−	2.26655i
$43$	0.201842			0.00469401			0.00234701	−	0.999997i	$-0.499253\pi$
$43$	0.201842			0.00469401			0.00234701	+	0.999997i	$0.499253\pi$
$44$		0			0
$45$	44.5244	+	0.758975i	0.989431	+	0.0168661i
$46$	20.2430	−	14.7074i	0.440066	−	0.319726i
$47$	14.1766	−	4.60627i	0.301631	−	0.0980058i	−0.154291	−	0.988025i	$-0.549309\pi$
$47$	14.1766	−	4.60627i	0.301631	−	0.0980058i	0.455922	+	0.890020i	$0.349309\pi$
$48$	−39.7286	+	19.8181i	−0.827679	+	0.412877i
$49$	−61.4808	−	44.6684i	−1.25471	−	0.911601i
$50$	−0.877048	+	1.20715i	−0.0175410	+	0.0241431i
$51$	−0.0838099	−	0.168011i	−0.00164333	−	0.00329433i
$52$	22.3541	+	68.7988i	0.429886	+	1.32305i
$53$	57.5690	+	79.2369i	1.08621	+	1.49504i	0.852499	+	0.522729i	$0.175086\pi$
$53$	57.5690	+	79.2369i	1.08621	+	1.49504i	0.233709	+	0.972307i	$0.424914\pi$
$54$	53.5163	+	56.3252i	0.991042	+	1.04306i
$55$		0			0
$56$		−	9.02585i		−	0.161176i
$57$	−15.9222	−	2.66112i	−0.279337	−	0.0466862i
$58$	−44.4218	−	136.716i	−0.765893	−	2.35718i
$59$	−13.7827	−	4.47826i	−0.233605	−	0.0759028i	0.189875	−	0.981808i	$-0.439192\pi$
$59$	−13.7827	−	4.47826i	−0.233605	−	0.0759028i	−0.423480	+	0.905905i	$0.639192\pi$
$60$	62.8391	−	9.40449i	1.04732	−	0.156741i
$61$	−23.7229	−	17.2357i	−0.388900	−	0.282552i	0.376105	−	0.926577i	$-0.377263\pi$
$61$	−23.7229	−	17.2357i	−0.388900	−	0.282552i	−0.765005	+	0.644025i	$0.777263\pi$
$62$	67.2596	+	21.8540i	1.08483	+	0.352484i
$63$	96.2122	−	29.4580i	1.52718	−	0.467587i
$64$	−58.7676	+	42.6972i	−0.918244	+	0.667143i
$65$			83.6168i			1.28641i
$66$		0			0
$67$	82.8515			1.23659			0.618294	−	0.785947i	$-0.287824\pi$
$67$	82.8515			1.23659			0.618294	+	0.785947i	$0.287824\pi$
$68$	−0.157466	−	0.216733i	−0.00231568	−	0.00318726i
$69$	23.1411	+	12.0405i	0.335379	+	0.174500i
$70$	49.1899	−	151.391i	0.702713	−	2.16273i
$71$	15.6972	−	21.6053i	0.221087	−	0.304301i	−0.684037	−	0.729447i	$-0.739777\pi$
$71$	15.6972	−	21.6053i	0.221087	−	0.304301i	0.905125	+	0.425147i	$0.139777\pi$
$72$	5.80454	+	4.37031i	0.0806186	+	0.0606988i
$73$	4.31706	−	13.2865i	0.0591378	−	0.182007i	−0.917124	−	0.398603i	$-0.869495\pi$
$73$	4.31706	−	13.2865i	0.0591378	−	0.182007i	0.976261	+	0.216595i	$0.0694952\pi$
$74$	−107.444	+	34.9108i	−1.45195	+	0.471767i
$75$	−1.53431	−	0.256434i	−0.0204575	−	0.00341912i
$76$	−23.0337			−0.303075
$77$		0			0
$78$	−104.035	+	102.277i	−1.33379	+	1.31124i
$79$	−40.6025	+	29.4994i	−0.513956	+	0.373411i	−0.814322	−	0.580413i	$-0.802891\pi$
$79$	−40.6025	+	29.4994i	−0.513956	+	0.373411i	0.300366	+	0.953824i	$0.402891\pi$
$80$	−69.6402	+	22.6275i	−0.870502	+	0.282843i
$81$	−27.6414	+	76.1377i	−0.341252	+	0.939972i
$82$	−102.220	−	74.2674i	−1.24659	−	0.905700i
$83$	−35.4092	+	48.7366i	−0.426617	+	0.587188i	−0.967173	−	0.254120i	$-0.918214\pi$
$83$	−35.4092	+	48.7366i	−0.426617	+	0.587188i	0.540556	+	0.841308i	$0.318214\pi$
$84$	128.473	−	64.0873i	1.52945	−	0.762944i
$85$	−0.0956907	−	0.294506i	−0.00112577	−	0.00346477i
$86$	0.341398	+	0.469894i	0.00396974	+	0.00546388i
$87$	106.871	−	105.065i	1.22840	−	1.20764i
$88$		0			0
$89$			40.3489i			0.453359i	0.973969	+	0.226679i	$0.0727869\pi$
$89$			40.3489i			0.453359i	−0.973969	+	0.226679i	$0.927213\pi$
$90$	73.5420	+	104.938i	0.817134	+	1.16597i
$91$	58.3852	+	179.691i	0.641596	+	1.97463i
$92$	35.3993	+	11.5019i	0.384774	+	0.125021i
$93$	10.9128	+	72.9172i	0.117342	+	0.784056i
$94$	34.7020	+	25.2125i	0.369170	+	0.268218i
$95$	−25.3215	−	8.22744i	−0.266542	−	0.0866047i
$96$	−121.928	−	63.4402i	−1.27009	−	0.660835i
$97$	24.9281	−	18.1114i	0.256991	−	0.186715i	−0.451828	−	0.892105i	$-0.649228\pi$
$97$	24.9281	−	18.1114i	0.256991	−	0.186715i	0.708820	+	0.705390i	$0.249228\pi$
$98$		−	218.681i		−	2.23144i
$99$		0			0
$100$	−2.21960			−0.0221960
$101$	30.5189	+	42.0057i	0.302167	+	0.415898i	0.932919	−	0.360087i	$-0.117253\pi$
$101$	30.5189	+	42.0057i	0.302167	+	0.415898i	−0.630751	+	0.775985i	$0.717253\pi$
$102$	0.249376	−	0.479286i	0.00244486	−	0.00469888i
$103$	−15.8074	+	48.6501i	−0.153470	+	0.472331i	−0.998003	−	0.0631724i	$-0.979878\pi$
$103$	−15.8074	+	48.6501i	−0.153470	+	0.472331i	0.844533	+	0.535504i	$0.179878\pi$
$104$	−8.01930	+	11.0376i	−0.0771086	+	0.106131i
$105$	164.125	−	24.5630i	1.56310	−	0.233933i
$106$	−87.0927	+	268.044i	−0.821630	+	2.52872i
$107$	65.0929	−	21.1500i	0.608345	−	0.197663i	0.0113861	−	0.999935i	$-0.496376\pi$
$107$	65.0929	−	21.1500i	0.608345	−	0.197663i	0.596959	+	0.802272i	$0.296376\pi$
$108$	−20.9922	+	113.652i	−0.194372	+	1.05234i
$109$	−125.737			−1.15355			−0.576773	−	0.816904i	$-0.695688\pi$
$109$	−125.737			−1.15355			−0.576773	+	0.816904i	$0.695688\pi$
$110$		0			0
$111$	−82.5697	−	83.9892i	−0.743871	−	0.756659i
$112$	−133.856	+	97.2521i	−1.19514	+	0.868322i
$113$	93.8997	−	30.5099i	0.830971	−	0.269999i	0.137516	−	0.990499i	$-0.456088\pi$
$113$	93.8997	−	30.5099i	0.830971	−	0.269999i	0.693454	+	0.720501i	$0.256088\pi$
$114$	−20.7358	−	41.5682i	−0.181893	−	0.364634i
$115$	34.8068	+	25.2886i	0.302668	+	0.219901i
$116$	125.691	−	172.998i	1.08354	−	1.49136i
$117$	−143.830	−	49.4588i	−1.22931	−	0.422725i
$118$	−12.8866	−	39.6610i	−0.109209	−	0.336110i
$119$	−0.411275	−	0.566072i	−0.00345609	−	0.00475691i
$120$	8.40107	+	8.54550i	0.0700089	+	0.0712125i
$121$		0			0
$122$		−	84.3801i		−	0.691640i
$123$	21.7145	−	129.924i	0.176541	−	1.05629i
$124$	32.5088	+	100.052i	0.262168	+	0.806869i
$125$	−120.083	−	39.0173i	−0.960662	−	0.312138i
$126$	231.313	+	174.159i	1.83582	+	1.38221i
$127$	16.8672	+	12.2547i	0.132813	+	0.0964940i	0.652208	−	0.758040i	$-0.273843\pi$
$127$	16.8672	+	12.2547i	0.132813	+	0.0964940i	−0.519395	+	0.854534i	$0.673843\pi$
$128$	−24.5092	−	7.96353i	−0.191478	−	0.0622151i
$129$	−0.279492	+	0.537167i	−0.00216660	+	0.00416408i
$130$	−194.662	+	141.430i	−1.49740	+	1.08792i
$131$		−	29.0290i		−	0.221595i	−0.993843	−	0.110798i	$-0.964659\pi$
$131$		−	29.0290i		−	0.221595i	0.993843	−	0.110798i	$-0.0353405\pi$
$132$		0			0
$133$	−60.1602			−0.452332
$134$	140.136	+	192.880i	1.04579	+	1.43940i
$135$	−63.6729	+	117.443i	−0.471651	+	0.869945i
$136$	0.0156133	−	0.0480527i	0.000114803	−	0.000353328i
$137$	−89.1732	+	122.736i	−0.650899	+	0.895886i	−0.999138	−	0.0415199i	$-0.986780\pi$
$137$	−89.1732	+	122.736i	−0.650899	+	0.895886i	0.348238	+	0.937406i	$0.386780\pi$
$138$	11.1105	+	74.2385i	0.0805110	+	0.537960i
$139$	−5.94013	+	18.2818i	−0.0427348	+	0.131524i	−0.970148	−	0.242515i	$-0.922028\pi$
$139$	−5.94013	+	18.2818i	−0.0427348	+	0.131524i	0.927413	+	0.374039i	$0.122028\pi$
$140$	225.201	−	73.1722i	1.60858	−	0.522659i
$141$	−7.37169	+	44.1068i	−0.0522815	+	0.312815i
$142$	76.8481			0.541184
$143$		0			0
$144$	2.27009	−	133.172i	0.0157645	−	0.924808i
$145$	199.968	−	145.285i	1.37909	−	1.00197i
$146$	38.2333	−	12.4227i	0.261872	−	0.0850873i
$147$	204.009	−	101.767i	1.38782	−	0.692295i
$148$	−135.958	−	98.7793i	−0.918635	−	0.667427i
$149$	106.781	−	146.971i	0.716651	−	0.986385i	−0.282978	−	0.959127i	$-0.591322\pi$
$149$	106.781	−	146.971i	0.716651	−	0.986385i	0.999628	−	0.0272587i	$-0.00867780\pi$
$150$	−1.99817	−	4.00565i	−0.0133211	−	0.0267043i
$151$	43.3216	+	133.330i	0.286898	+	0.882982i	0.985823	+	0.167787i	$0.0536621\pi$
$151$	43.3216	+	133.330i	0.286898	+	0.882982i	−0.698925	+	0.715195i	$0.746338\pi$
$152$	−2.55344	−	3.51451i	−0.0167989	−	0.0231217i
$153$	0.563181	+	0.00960013i	0.00368092	+	6.27460e-5i
$154$		0			0
$155$			121.601i			0.784523i
$156$	−214.049	−	35.7746i	−1.37211	−	0.229324i
$157$	−55.5031	−	170.821i	−0.353523	−	1.08803i	−0.956861	−	0.290547i	$-0.906163\pi$
$157$	−55.5031	−	170.821i	−0.353523	−	1.08803i	0.603338	−	0.797486i	$-0.293837\pi$
$158$	−137.351	−	44.6280i	−0.869309	−	0.282456i
$159$	−290.590	+	43.4897i	−1.82761	+	0.273520i
$160$	−183.394	−	133.243i	−1.14621	−	0.832771i
$161$	92.4570	+	30.0411i	0.574267	+	0.186591i
$162$	−224.003	+	64.4301i	−1.38274	+	0.397717i
$163$	−179.001	+	130.052i	−1.09816	+	0.797863i	−0.980759	−	0.195222i	$-0.937457\pi$
$163$	−179.001	+	130.052i	−1.09816	+	0.797863i	−0.117404	+	0.993084i	$0.537457\pi$
$164$		−	187.953i		−	1.14606i
$165$		0			0
$166$	−173.351			−1.04428
$167$	−108.399	−	149.198i	−0.649095	−	0.893402i	0.349965	−	0.936763i	$-0.386194\pi$
$167$	−108.399	−	149.198i	−0.649095	−	0.893402i	−0.999059	+	0.0433607i	$0.986194\pi$
$168$	24.0206	+	12.4981i	0.142980	+	0.0743935i
$169$	36.0297	−	110.888i	0.213193	−	0.656142i
$170$	0.523764	−	0.720899i	0.00308096	−	0.00424058i
$171$	29.1295	−	38.6891i	0.170348	−	0.226252i
$172$	−0.266990	+	0.821710i	−0.00155227	+	0.00477739i
$173$	231.626	−	75.2598i	1.33888	−	0.435028i	0.449941	−	0.893058i	$-0.351445\pi$
$173$	231.626	−	75.2598i	1.33888	−	0.435028i	0.888937	+	0.458030i	$0.151445\pi$
$174$	425.356	+	71.0908i	2.44457	+	0.408568i
$175$	−5.79723			−0.0331270
$176$		0			0
$177$	31.0030	−	30.4790i	0.175158	−	0.172198i
$178$	−93.9332	+	68.2465i	−0.527715	+	0.383407i
$179$	301.127	−	97.8421i	1.68227	−	0.546604i	0.696923	−	0.717146i	$-0.254552\pi$
$179$	301.127	−	97.8421i	1.68227	−	0.546604i	0.985350	+	0.170542i	$0.0545520\pi$
$180$	−61.9851	+	180.257i	−0.344362	+	1.00143i
$181$	24.9975	+	18.1618i	0.138108	+	0.100341i	0.654694	−	0.755894i	$-0.272797\pi$
$181$	24.9975	+	18.1618i	0.138108	+	0.100341i	−0.516586	+	0.856235i	$0.672797\pi$
$182$	−319.572	+	439.853i	−1.75589	+	2.41678i
$183$	78.7188	−	39.2678i	0.430157	−	0.214578i
$184$	2.16927	+	6.67632i	0.0117895	+	0.0362843i
$185$	−114.179	−	157.153i	−0.617182	−	0.849478i
$186$	−151.295	+	148.738i	−0.813413	+	0.799666i
$187$		0			0
$188$			63.8068i			0.339398i
$189$	−54.8281	+	296.841i	−0.290096	+	1.57059i
$190$	−23.6752	−	72.8649i	−0.124607	−	0.383500i
$191$	281.437	+	91.4445i	1.47349	+	0.478767i	0.932162	−	0.362042i	$-0.117920\pi$
$191$	281.437	+	91.4445i	1.47349	+	0.478767i	0.541332	+	0.840809i	$0.317920\pi$
$192$	−32.2550	−	215.522i	−0.167995	−	1.12251i
$193$	64.3229	+	46.7333i	0.333279	+	0.242142i	0.741821	−	0.670598i	$-0.233962\pi$
$193$	64.3229	+	46.7333i	0.333279	+	0.242142i	−0.408541	+	0.912740i	$0.633962\pi$
$194$	84.3273	+	27.3996i	0.434677	+	0.141235i
$195$	−222.531	−	115.784i	−1.14118	−	0.593766i
$196$	263.172	−	191.206i	1.34271	−	0.975539i
$197$			360.331i			1.82909i	0.404485	+	0.914544i	$0.367451\pi$
$197$			360.331i			1.82909i	−0.404485	+	0.914544i	$0.632549\pi$
$198$		0			0
$199$	369.874			1.85866			0.929332	−	0.369245i	$-0.120384\pi$
$199$	369.874			1.85866			0.929332	+	0.369245i	$0.120384\pi$
$200$	−0.246058	−	0.338669i	−0.00123029	−	0.00169335i
$201$	−114.725	+	220.494i	−0.570769	+	1.09698i
$202$	−46.1703	+	142.097i	−0.228566	+	0.703453i
$203$	328.283	−	451.843i	1.61716	−	2.22583i
$204$	0.794840	−	0.118956i	0.00389627	−	0.000583116i
$205$	67.1353	−	206.621i	0.327489	−	1.00791i
$206$	−139.995	+	45.4872i	−0.679589	+	0.220812i
$207$	−64.0871	+	44.9133i	−0.309600	+	0.216973i
$208$	250.098			1.20239
$209$		0			0
$210$	334.786	+	340.541i	1.59422	+	1.62163i
$211$	125.195	−	90.9598i	0.593343	−	0.431089i	−0.250167	−	0.968203i	$-0.580485\pi$
$211$	125.195	−	90.9598i	0.593343	−	0.431089i	0.843510	+	0.537114i	$0.180485\pi$
$212$	−398.727	+	129.554i	−1.88079	+	0.611105i
$213$	35.7627	+	71.6922i	0.167900	+	0.336583i
$214$	159.336	+	115.765i	0.744562	+	0.540956i
$215$	−0.587016	+	0.807958i	−0.00273031	+	0.00375795i
$216$	−19.6683	+	9.39612i	−0.0910571	+	0.0435006i
$217$	84.9076	+	261.319i	0.391279	+	1.20423i
$218$	−212.672	−	292.718i	−0.975559	−	1.34274i
$219$	29.3818	+	29.8870i	0.134164	+	0.136470i
$220$		0			0
$221$			1.05765i			0.00478576i
$222$	55.8698	−	334.284i	0.251666	−	1.50578i
$223$	−110.417	−	339.829i	−0.495145	−	1.52390i	−0.816731	−	0.577018i	$-0.804216\pi$
$223$	−110.417	−	339.829i	−0.495145	−	1.52390i	0.321587	−	0.946880i	$-0.395784\pi$
$224$	−487.147	−	158.284i	−2.17476	−	0.706623i
$225$	2.80702	−	3.72821i	0.0124756	−	0.0165698i
$226$	229.850	+	166.996i	1.01704	+	0.738920i
$227$	97.5400	+	31.6927i	0.429692	+	0.139615i	0.515875	−	0.856664i	$-0.327467\pi$
$227$	97.5400	+	31.6927i	0.429692	+	0.139615i	−0.0861831	+	0.996279i	$0.527467\pi$
$228$	31.8948	−	61.2999i	0.139889	−	0.268859i
$229$	298.821	−	217.106i	1.30490	−	0.948063i	0.304906	−	0.952382i	$-0.401375\pi$
$229$	298.821	−	217.106i	1.30490	−	0.948063i	0.999991	+	0.00431926i	$0.00137487\pi$
$230$			123.804i			0.538280i
$231$		0			0
$232$	40.3299			0.173836
$233$	10.1837	+	14.0166i	0.0437067	+	0.0601571i	0.830311	−	0.557300i	$-0.188163\pi$
$233$	10.1837	+	14.0166i	0.0437067	+	0.0601571i	−0.786604	+	0.617457i	$0.788163\pi$
$234$	−128.133	−	418.494i	−0.547579	−	1.78844i
$235$	−22.7913	+	70.1443i	−0.0969841	+	0.298486i
$236$	36.4624	−	50.1862i	0.154502	−	0.212654i
$237$	−22.2850	−	148.904i	−0.0940294	−	0.628287i
$238$	0.622194	−	1.91492i	0.00261426	−	0.00804587i
$239$	−208.117	+	67.6212i	−0.870781	+	0.282934i	−0.710124	−	0.704077i	$-0.751361\pi$
$239$	−208.117	+	67.6212i	−0.870781	+	0.282934i	−0.160657	+	0.987010i	$0.551361\pi$
$240$	36.2121	−	216.667i	0.150884	−	0.902778i
$241$	118.033			0.489765			0.244883	−	0.969553i	$-0.421251\pi$
$241$	118.033			0.489765			0.244883	+	0.969553i	$0.421251\pi$
$242$		0			0
$243$	−164.351	−	178.991i	−0.676343	−	0.736587i
$244$	101.547	−	73.7783i	0.416177	−	0.302370i
$245$	357.608	−	116.194i	1.45962	−	0.474261i
$246$	339.194	−	169.202i	1.37884	−	0.687814i
$247$	73.5693	+	53.4512i	0.297851	+	0.216402i
$248$	−11.6622	+	16.0516i	−0.0470249	+	0.0647243i
$249$	−80.6722	−	161.721i	−0.323985	−	0.649481i
$250$	−112.276	−	345.550i	−0.449103	−	1.38220i
$251$	94.3753	+	129.896i	0.375997	+	0.517516i	0.954519	−	0.298151i	$-0.0963700\pi$
$251$	94.3753	+	129.896i	0.375997	+	0.517516i	−0.578521	+	0.815667i	$0.696370\pi$
$252$	−7.34098	+	430.650i	−0.0291309	+	1.70893i
$253$		0			0
$254$			59.9950i			0.236201i
$255$	0.916275	+	0.153139i	0.00359324	+	0.000600547i
$256$	66.8731	+	205.814i	0.261223	+	0.803962i
$257$	−24.9007	−	8.09071i	−0.0968897	−	0.0314814i	0.260171	−	0.965563i	$-0.416221\pi$
$257$	−24.9007	−	8.09071i	−0.0968897	−	0.0314814i	−0.357061	+	0.934081i	$0.616221\pi$
$258$	−1.72327	+	0.257905i	−0.00667934	+	0.000999630i
$259$	−355.100	−	257.995i	−1.37104	−	0.996120i
$260$	−340.408	−	110.605i	−1.30926	−	0.425405i
$261$	131.626	+	429.901i	0.504315	+	1.64713i
$262$	67.5801	−	49.0998i	0.257939	−	0.187404i
$263$		−	221.020i		−	0.840378i	−0.907437	−	0.420189i	$-0.861964\pi$
$263$		−	221.020i		−	0.840378i	0.907437	−	0.420189i	$-0.138036\pi$
$264$		0			0
$265$	−484.606			−1.82870
$266$	−101.755	−	140.054i	−0.382539	−	0.526520i
$267$	−107.381	−	55.8712i	−0.402177	−	0.209256i
$268$	−109.593	+	337.292i	−0.408929	+	1.25855i
$269$	−73.7314	+	101.483i	−0.274094	+	0.377259i	−0.923767	−	0.382956i	$-0.874906\pi$
$269$	−73.7314	+	101.483i	−0.274094	+	0.377259i	0.649672	+	0.760214i	$0.274906\pi$
$270$	−381.106	+	50.4112i	−1.41150	+	0.186708i
$271$	123.585	−	380.355i	0.456032	−	1.40352i	−0.413887	−	0.910328i	$-0.635829\pi$
$271$	123.585	−	380.355i	0.456032	−	1.40352i	0.869919	−	0.493195i	$-0.164171\pi$
$272$	−0.880865	+	0.286211i	−0.00323848	+	0.00105224i
$273$	−559.061	−	93.4373i	−2.04784	−	0.342261i
$274$	−436.561			−1.59329
$275$		0			0
$276$	−79.6276	+	78.2819i	−0.288506	+	0.283630i
$277$	−59.5551	+	43.2693i	−0.215000	+	0.156207i	−0.690073	−	0.723740i	$-0.742422\pi$
$277$	−59.5551	+	43.2693i	−0.215000	+	0.156207i	0.475073	+	0.879946i	$0.342422\pi$
$278$	−52.6077	+	17.0933i	−0.189236	+	0.0614866i
$279$	−209.167	−	71.9262i	−0.749701	−	0.257800i
$280$	36.1297	+	26.2498i	0.129035	+	0.0937492i
$281$	−246.506	+	339.286i	−0.877244	+	1.20742i	0.0999321	+	0.994994i	$0.468137\pi$
$281$	−246.506	+	339.286i	−0.877244	+	1.20742i	−0.977176	+	0.212429i	$0.931863\pi$
$282$	−115.150	+	57.4412i	−0.408334	+	0.203692i
$283$	−81.9963	−	252.359i	−0.289739	−	0.891726i	−0.984938	−	0.172909i	$-0.944683\pi$
$283$	−81.9963	−	252.359i	−0.289739	−	0.891726i	0.695198	−	0.718818i	$-0.255317\pi$
$284$	67.1927	+	92.4828i	0.236594	+	0.325644i
$285$	56.9585	−	55.9959i	0.199854	−	0.196477i
$286$		0			0
$287$		−	490.903i		−	1.71046i
$288$	337.669	−	236.644i	1.17246	−	0.821680i
$289$	89.3047	+	274.852i	0.309013	+	0.951044i
$290$	676.455	+	219.793i	2.33260	+	0.757908i
$291$	13.6820	+	91.4205i	0.0470171	+	0.314160i
$292$	48.3797	+	35.1499i	0.165684	+	0.120376i
$293$	181.199	+	58.8752i	0.618427	+	0.200939i	0.601442	−	0.798917i	$-0.294593\pi$
$293$	181.199	+	58.8752i	0.618427	+	0.200939i	0.0169852	+	0.999856i	$0.494593\pi$
$294$	581.980	+	302.809i	1.97952	+	1.02996i
$295$	58.0101	−	42.1468i	0.196644	−	0.142871i
$296$		−	31.6949i		−	0.107078i
$297$		0			0
$298$	522.763			1.75424
$299$	−86.3737	−	118.883i	−0.288875	−	0.397603i
$300$	3.07349	−	5.90706i	0.0102450	−	0.0196902i
$301$	−0.697333	+	2.14617i	−0.00231672	+	0.00713014i
$302$	−237.121	+	326.370i	−0.785170	+	1.08069i
$303$	−154.050	+	23.0551i	−0.508416	+	0.0760895i
$304$	−24.6083	+	75.7365i	−0.0809482	+	0.249133i
$305$	137.986	−	44.8344i	0.452413	−	0.146998i
$306$	0.930219	+	1.32734i	0.00303993	+	0.00433770i
$307$	−285.254			−0.929166			−0.464583	−	0.885530i	$-0.653796\pi$
$307$	−285.254			−0.929166			−0.464583	+	0.885530i	$0.653796\pi$
$308$		0			0
$309$	−107.585	−	109.434i	−0.348171	−	0.354156i
$310$	−283.090	+	205.677i	−0.913194	+	0.663474i
$311$	−480.177	+	156.019i	−1.54398	+	0.501669i	−0.952470	−	0.304631i	$-0.901467\pi$
$311$	−480.177	+	156.019i	−1.54398	+	0.501669i	−0.591507	+	0.806300i	$0.701467\pi$
$312$	−18.2702	−	36.6257i	−0.0585585	−	0.117390i
$313$	−64.8592	−	47.1229i	−0.207218	−	0.150553i	0.479336	−	0.877631i	$-0.340877\pi$
$313$	−64.8592	−	47.1229i	−0.207218	−	0.150553i	−0.686554	+	0.727079i	$0.740877\pi$
$314$	303.797	−	418.141i	0.967507	−	1.33166i
$315$	−161.895	+	470.801i	−0.513952	+	1.49461i
$316$	−66.3861	−	204.315i	−0.210083	−	0.646568i
$317$	−5.08824	−	7.00336i	−0.0160512	−	0.0220926i	0.800916	−	0.598777i	$-0.204346\pi$
$317$	−5.08824	−	7.00336i	−0.0160512	−	0.0220926i	−0.816967	+	0.576684i	$0.804346\pi$
$318$	−592.752	−	602.942i	−1.86400	−	1.89604i
$319$		0			0
$320$		−	359.417i		−	1.12318i
$321$	−33.8475	+	202.519i	−0.105444	+	0.630901i
$322$	86.4461	+	266.054i	0.268466	+	0.826254i
$323$	−0.320286	−	0.104067i	−0.000991599	−	0.000322190i
$324$	−273.397	−	213.242i	−0.843818	−	0.658153i
$325$	7.08937	+	5.15073i	0.0218135	+	0.0158484i
$326$	−605.526	−	196.747i	−1.85744	−	0.603520i
$327$	174.108	−	334.625i	0.532440	−	1.02332i
$328$	28.6781	−	20.8359i	0.0874333	−	0.0635240i
$329$			166.653i			0.506544i
$330$		0			0
$331$	28.2554			0.0853638			0.0426819	−	0.999089i	$-0.486410\pi$
$331$	28.2554			0.0853638			0.0426819	+	0.999089i	$0.486410\pi$
$332$	−151.571	−	208.619i	−0.456539	−	0.628372i
$333$	337.856	−	103.444i	1.01458	−	0.310643i
$334$	163.990	−	504.710i	0.490989	−	1.51111i
$335$	−240.956	+	331.647i	−0.719271	+	0.989992i
$336$	−73.4678	−	490.898i	−0.218654	−	1.46101i
$337$	−89.1584	+	274.401i	−0.264565	+	0.814247i	0.727228	+	0.686396i	$0.240808\pi$
$337$	−89.1584	+	274.401i	−0.264565	+	0.814247i	−0.991793	+	0.127851i	$0.959192\pi$
$338$	319.091	−	103.679i	0.944055	−	0.306742i
$339$	−48.8267	+	292.144i	−0.144032	+	0.861781i
$340$	1.32552			0.00389859
$341$		0			0
$342$	139.339	+	2.37521i	0.407424	+	0.00694506i
$343$	244.162	−	177.394i	0.711843	−	0.517184i
$344$	−0.154975	+	0.0503544i	−0.000450509	+	0.000146379i
$345$	−115.498	+	57.6147i	−0.334777	+	0.166999i
$346$	566.980	+	411.935i	1.63867	+	1.19056i
$347$	154.947	−	213.267i	0.446534	−	0.614602i	−0.525114	−	0.851032i	$-0.675977\pi$
$347$	154.947	−	213.267i	0.446534	−	0.614602i	0.971648	+	0.236430i	$0.0759774\pi$
$348$	286.359	+	574.053i	0.822870	+	1.64958i
$349$	−150.777	−	464.043i	−0.432025	−	1.32964i	−0.896105	−	0.443842i	$-0.853615\pi$
$349$	−150.777	−	464.043i	−0.432025	−	1.32964i	0.464080	−	0.885793i	$-0.346385\pi$
$350$	−9.80548	−	13.4961i	−0.0280157	−	0.0385603i
$351$	330.787	−	314.291i	0.942412	−	0.895415i
$352$		0			0
$353$			437.345i			1.23894i	0.785021	+	0.619469i	$0.212652\pi$
$353$			437.345i			1.23894i	−0.785021	+	0.619469i	$0.787348\pi$
$354$	123.394	+	20.6232i	0.348572	+	0.0582577i
$355$	40.8324	+	125.669i	0.115021	+	0.353997i
$356$	−164.262	−	53.3721i	−0.461411	−	0.149922i
$357$	2.07599	−	0.310692i	0.00581510	−	0.000870287i
$358$	737.107	+	535.540i	2.05896	+	1.49592i
$359$	233.007	+	75.7087i	0.649046	+	0.210888i	0.614993	−	0.788532i	$-0.289159\pi$
$359$	233.007	+	75.7087i	0.649046	+	0.210888i	0.0340525	+	0.999420i	$0.489159\pi$
$360$	−34.3753	+	10.5249i	−0.0954868	+	0.0292359i
$361$	268.630	−	195.171i	0.744127	−	0.540640i
$362$			88.9137i			0.245618i
$363$		0			0
$364$	−808.761			−2.22187
$365$	40.6296	+	55.9219i	0.111314	+	0.153211i
$366$	224.562	+	116.841i	0.613557	+	0.319238i
$367$	69.5602	−	214.084i	0.189537	−	0.583336i	−0.810460	−	0.585795i	$-0.800783\pi$
$367$	69.5602	−	214.084i	0.189537	−	0.583336i	0.999997	+	0.00245833i	$0.000782511\pi$
$368$	75.6383	−	104.107i	0.205539	−	0.282900i
$369$	315.700	+	237.695i	0.855556	+	0.644160i
$370$	172.734	−	531.621i	0.466849	−	1.43681i
$371$	−1041.41	+	338.375i	−2.80703	+	0.912061i
$372$	−311.284	−	52.0257i	−0.836786	−	0.139854i
$373$	−283.156			−0.759131			−0.379566	−	0.925165i	$-0.623927\pi$
$373$	−283.156			−0.759131			−0.379566	+	0.925165i	$0.623927\pi$
$374$		0			0
$375$	270.116	−	265.551i	0.720310	−	0.708136i
$376$	−9.73571	+	7.07341i	−0.0258928	+	0.0188123i
$377$	−802.907	+	260.880i	−2.12973	+	0.691990i
$378$	−783.791	+	374.439i	−2.07352	+	0.990579i
$379$	369.384	+	268.373i	0.974627	+	0.708108i	0.956501	−	0.291727i	$-0.0942300\pi$
$379$	369.384	+	268.373i	0.974627	+	0.708108i	0.0181260	+	0.999836i	$0.494230\pi$
$380$	66.9886	−	92.2019i	0.176286	−	0.242637i
$381$	−55.9698	+	27.9198i	−0.146902	+	0.0732803i
$382$	263.140	+	809.863i	0.688849	+	2.12006i
$383$	188.834	+	259.908i	0.493040	+	0.678611i	0.980945	−	0.194285i	$-0.0622388\pi$
$383$	188.834	+	259.908i	0.493040	+	0.678611i	−0.487905	+	0.872897i	$0.662239\pi$
$384$	55.1314	−	54.1997i	0.143571	−	0.141145i
$385$		0			0
$386$			228.790i			0.592721i
$387$	−1.04256	−	1.48763i	−0.00269395	−	0.00384401i
$388$	40.7581	+	125.441i	0.105047	+	0.323301i
$389$	299.994	+	97.4741i	0.771194	+	0.250576i	0.668076	−	0.744093i	$-0.267118\pi$
$389$	299.994	+	97.4741i	0.771194	+	0.250576i	0.103118	+	0.994669i	$0.467118\pi$
$390$	−106.842	−	713.895i	−0.273953	−	1.83050i
$391$	0.440265	+	0.319871i	0.00112600	+	0.000818085i
$392$	58.3487	+	18.9586i	0.148849	+	0.0483639i
$393$	77.2552	+	40.1964i	0.196578	+	0.102281i
$394$	−838.858	+	609.466i	−2.12908	+	1.54687i
$395$		−	248.321i		−	0.628661i
$396$		0			0
$397$	−338.199			−0.851885			−0.425943	−	0.904750i	$-0.640057\pi$
$397$	−338.199			−0.851885			−0.425943	+	0.904750i	$0.640057\pi$
$398$	625.608	+	861.076i	1.57188	+	2.16351i
$399$	83.3039	−	160.105i	0.208782	−	0.401266i
$400$	−2.37133	+	7.29821i	−0.00592833	+	0.0182455i
$401$	212.161	−	292.015i	0.529080	−	0.728216i	−0.457910	−	0.888999i	$-0.651402\pi$
$401$	212.161	−	292.015i	0.529080	−	0.728216i	0.986990	+	0.160782i	$0.0514017\pi$
$402$	−707.361	+	105.864i	−1.75960	+	0.263342i
$403$	128.344	−	395.002i	0.318472	−	0.980155i
$404$	−211.376	+	68.6803i	−0.523209	+	0.170001i
$405$	−224.384	−	332.077i	−0.554034	−	0.819942i
$406$	1607.16			3.95852
$407$		0			0
$408$	0.106264	+	0.108090i	0.000260450	+	0.000264928i
$409$	−356.891	+	259.297i	−0.872595	+	0.633978i	−0.931282	−	0.364299i	$-0.881309\pi$
$409$	−356.891	+	259.297i	−0.872595	+	0.633978i	0.0586868	+	0.998276i	$0.481309\pi$
$410$	594.572	−	193.188i	1.45018	−	0.471191i
$411$	−203.162	−	407.271i	−0.494311	−	0.990928i
$412$	−177.147	−	128.705i	−0.429970	−	0.312391i
$413$	95.2338	−	131.078i	0.230590	−	0.317380i
$414$	−212.957	−	73.2295i	−0.514388	−	0.176883i
$415$	−92.1083	−	283.480i	−0.221948	−	0.683085i
$416$	455.094	+	626.384i	1.09398	+	1.50573i
$417$	−40.4284	−	41.1235i	−0.0969507	−	0.0986174i
$418$		0			0
$419$			393.180i			0.938377i	0.883098	+	0.469188i	$0.155453\pi$
$419$			393.180i			0.938377i	−0.883098	+	0.469188i	$0.844547\pi$
$420$	−117.102	+	700.653i	−0.278814	+	1.66822i
$421$	−217.358	−	668.959i	−0.516289	−	1.58898i	−0.780924	−	0.624627i	$-0.785251\pi$
$421$	−217.358	−	668.959i	−0.516289	−	1.58898i	0.264634	−	0.964349i	$-0.414749\pi$
$422$	423.513	+	137.608i	1.00359	+	0.326085i
$423$	−107.175	−	80.6932i	−0.253368	−	0.190764i
$424$	−63.9691	−	46.4763i	−0.150871	−	0.109614i
$425$	−0.0308638	−	0.0100283i	−7.26208e−5	−	2.35959e-5i
$426$	−106.412	+	204.517i	−0.249793	+	0.480087i
$427$	265.224	−	192.697i	0.621134	−	0.451280i
$428$			292.973i			0.684515i
$429$		0			0
$430$	−2.87383			−0.00668332
$431$	88.9050	+	122.367i	0.206276	+	0.283915i	0.899603	−	0.436708i	$-0.143856\pi$
$431$	88.9050	+	122.367i	0.206276	+	0.283915i	−0.693327	+	0.720623i	$0.743856\pi$
$432$	351.270	+	190.446i	0.813126	+	0.440846i
$433$	−145.735	+	448.525i	−0.336569	+	1.03585i	0.629375	+	0.777102i	$0.283311\pi$
$433$	−145.735	+	448.525i	−0.336569	+	1.03585i	−0.965944	+	0.258752i	$0.916689\pi$
$434$	−464.742	+	639.663i	−1.07084	+	1.47388i
$435$	109.754	+	733.355i	0.252308	+	1.68587i
$436$	166.320	−	511.880i	0.381467	−	1.17404i
$437$	44.4998	−	14.4589i	0.101830	−	0.0330866i
$438$	−19.8809	+	118.953i	−0.0453901	+	0.271581i
$439$	506.417			1.15357			0.576784	−	0.816897i	$-0.304307\pi$
$439$	506.417			1.15357			0.576784	+	0.816897i	$0.304307\pi$
$440$		0			0
$441$	−11.6571	+	683.851i	−0.0264334	+	1.55068i
$442$	−2.46224	+	1.78892i	−0.00557068	+	0.00404734i
$443$	607.289	−	197.320i	1.37086	−	0.445418i	0.471203	−	0.882025i	$-0.343820\pi$
$443$	607.289	−	197.320i	1.37086	−	0.445418i	0.899652	+	0.436607i	$0.143820\pi$
$444$	451.144	−	225.047i	1.01609	−	0.506863i
$445$	−161.513	−	117.346i	−0.362951	−	0.263699i
$446$	604.370	−	831.844i	1.35509	−	1.86512i
$447$	243.277	+	487.689i	0.544245	+	1.09103i
$448$	−250.962	−	772.382i	−0.560183	−	1.72407i
$449$	194.835	+	268.168i	0.433931	+	0.597255i	0.968850	−	0.247648i	$-0.0796577\pi$
$449$	194.835	+	268.168i	0.433931	+	0.597255i	−0.534919	+	0.844904i	$0.679658\pi$
$450$	13.4272	+	0.228883i	0.0298381	+	0.000508629i
$451$		0			0
$452$			422.627i			0.935016i
$453$	−414.821	−	69.3302i	−0.915721	−	0.153047i
$454$	91.1986	+	280.681i	0.200878	+	0.618239i
$455$	−889.089	−	288.883i	−1.95404	−	0.634907i
$456$	12.8890	−	1.92896i	0.0282653	−	0.00423018i
$457$	69.5244	+	50.5125i	0.152132	+	0.110531i	0.661248	−	0.750168i	$-0.270027\pi$
$457$	69.5244	+	50.5125i	0.152132	+	0.110531i	−0.509115	+	0.860698i	$0.670027\pi$
$458$	1010.86	+	328.448i	2.20711	+	0.717134i
$459$	−0.805387	+	1.48551i	−0.00175465	+	0.00323640i
$460$	−148.992	+	108.249i	−0.323897	+	0.235325i
$461$			65.3245i			0.141702i	0.997487	+	0.0708508i	$0.0225714\pi$
$461$			65.3245i			0.141702i	−0.997487	+	0.0708508i	$0.977429\pi$
$462$		0			0
$463$	535.374			1.15632			0.578158	−	0.815925i	$-0.303772\pi$
$463$	535.374			1.15632			0.578158	+	0.815925i	$0.303772\pi$
$464$	−434.548	−	598.104i	−0.936525	−	1.28902i
$465$	−323.619	−	168.381i	−0.695954	−	0.362110i
$466$	−15.4063	+	47.4156i	−0.0330607	+	0.101750i
$467$	292.723	−	402.899i	0.626817	−	0.862739i	−0.371010	−	0.928629i	$-0.620989\pi$
$467$	292.723	−	402.899i	0.626817	−	0.862739i	0.997827	+	0.0658897i	$0.0209886\pi$
$468$	391.602	−	520.115i	0.836756	−	1.11136i
$469$	−286.238	+	880.951i	−0.610317	+	1.87836i
$470$	−201.847	+	65.5840i	−0.429461	+	0.139540i
$471$	531.464	+	88.8250i	1.12837	+	0.188588i
$472$	11.6996			0.0247872
$473$		0			0
$474$	308.959	−	303.737i	0.651812	−	0.640796i
$475$	−2.25734	+	1.64005i	−0.00475229	+	0.00345274i
$476$	2.84852	−	0.925542i	0.00598430	−	0.00194442i
$477$	286.641	−	833.573i	0.600925	−	1.74753i
$478$	−509.434	−	370.125i	−1.06576	−	0.774321i
$479$	−510.599	+	702.779i	−1.06597	+	1.46718i	−0.191875	+	0.981419i	$0.561457\pi$
$479$	−510.599	+	702.779i	−1.06597	+	1.46718i	−0.874093	+	0.485759i	$0.838543\pi$
$480$	608.548	−	303.566i	1.26781	−	0.632429i
$481$	205.024	+	630.999i	0.426245	+	1.31185i
$482$	199.643	+	274.784i	0.414196	+	0.570092i
$483$	−207.974	+	204.459i	−0.430588	+	0.423311i
$484$		0			0
$485$			152.458i			0.314347i
$486$	138.709	−	685.360i	0.285409	−	1.41021i
$487$	74.5091	+	229.315i	0.152996	+	0.470873i	0.997952	−	0.0639620i	$-0.0203736\pi$
$487$	74.5091	+	229.315i	0.152996	+	0.470873i	−0.844956	+	0.534835i	$0.820374\pi$
$488$	22.5143	+	7.31535i	0.0461359	+	0.0149905i
$489$	−98.2457	−	656.460i	−0.200912	−	1.34245i
$490$	875.363	+	635.988i	1.78645	+	1.29794i
$491$	−475.575	−	154.524i	−0.968585	−	0.314712i	−0.218340	−	0.975873i	$-0.570064\pi$
$491$	−475.575	−	154.524i	−0.968585	−	0.314712i	−0.750245	+	0.661160i	$0.770064\pi$
$492$	500.203	+	260.259i	1.01667	+	0.528982i
$493$	2.52936	−	1.83769i	0.00513054	−	0.00372756i
$494$			261.679i			0.529714i
$495$		0			0
$496$	363.708			0.733283
$497$	175.496	+	241.550i	0.353111	+	0.486016i
$498$	240.040	−	461.343i	0.482008	−	0.926391i
$499$	−171.447	+	527.660i	−0.343582	+	1.05744i	0.618757	+	0.785582i	$0.287637\pi$
$499$	−171.447	+	527.660i	−0.343582	+	1.05744i	−0.962339	+	0.271853i	$0.912363\pi$
$500$	317.682	−	437.252i	0.635364	−	0.874504i
$501$	547.163	−	81.8884i	1.09214	−	0.163450i
$502$	−142.775	+	439.416i	−0.284412	+	0.875330i
$503$	639.571	−	207.809i	1.27151	−	0.413140i	0.405929	−	0.913904i	$-0.366948\pi$
$503$	639.571	−	207.809i	1.27151	−	0.413140i	0.865583	+	0.500765i	$0.166948\pi$
$504$	−66.5229	+	46.6203i	−0.131990	+	0.0925007i
$505$	−256.903			−0.508719
$506$		0			0
$507$	245.217	+	249.433i	0.483664	+	0.491979i
$508$	−72.2010	+	52.4571i	−0.142128	+	0.103262i
$509$	−612.141	+	198.897i	−1.20264	+	0.390760i	−0.840730	−	0.541455i	$-0.817874\pi$
$509$	−612.141	+	198.897i	−1.20264	+	0.390760i	−0.361906	+	0.932215i	$0.617874\pi$
$510$	1.19328	+	2.39213i	0.00233977	+	0.00469045i
$511$	126.360	+	91.8057i	0.247279	+	0.179659i
$512$	−426.621	+	587.193i	−0.833243	+	1.14686i
$513$	62.6282	+	131.096i	0.122082	+	0.255547i
$514$	−23.2818	−	71.6540i	−0.0452953	−	0.139405i
$515$	−148.770	−	204.764i	−0.288874	−	0.397600i
$516$	−1.81713	−	1.84837i	−0.00352157	−	0.00358211i
$517$		0			0
$518$		−	1263.06i		−	2.43833i
$519$	−120.443	+	720.642i	−0.232067	+	1.38852i
$520$	−20.8602	−	64.2011i	−0.0401158	−	0.123464i
$521$	507.873	+	165.018i	0.974803	+	0.316733i	0.752753	−	0.658303i	$-0.228725\pi$
$521$	507.873	+	165.018i	0.974803	+	0.316733i	0.222050	+	0.975035i	$0.428725\pi$
$522$	−778.186	+	1033.57i	−1.49078	+	1.98001i
$523$	−805.063	−	584.913i	−1.53932	−	1.11838i	−0.950761	−	0.309924i	$-0.899696\pi$
$523$	−805.063	−	584.913i	−1.53932	−	1.11838i	−0.588557	−	0.808456i	$-0.700304\pi$
$524$	118.178	+	38.3984i	0.225531	+	0.0732794i
$525$	8.02744	−	15.4283i	0.0152904	−	0.0293872i
$526$	514.539	−	373.834i	0.978210	−	0.710711i
$527$			1.53811i			0.00291861i
$528$		0			0
$529$	453.391			0.857071
$530$	−819.666	−	1128.17i	−1.54654	−	2.12863i
$531$	38.1843	+	124.713i	0.0719102	+	0.234864i
$532$	79.5777	−	244.915i	0.149582	−	0.460366i
$533$	−436.158	+	600.320i	−0.818307	+	1.12630i
$534$	−51.5559	−	344.487i	−0.0965466	−	0.645107i
$535$	−104.647	+	322.071i	−0.195603	+	0.602003i
$536$	−63.6135	+	20.6693i	−0.118682	+	0.0385621i
$537$	−156.582	+	936.876i	−0.291587	+	1.74465i
$538$	−360.964			−0.670936
$539$		0			0
$540$	−393.890	−	414.564i	−0.729426	−	0.767711i
$541$	−558.792	+	405.986i	−1.03289	+	0.750436i	−0.968884	−	0.247513i	$-0.920387\pi$
$541$	−558.792	+	405.986i	−1.03289	+	0.750436i	−0.0640026	+	0.997950i	$0.520387\pi$
$542$	1094.51	−	355.627i	2.01939	−	0.656138i
$543$	−82.9482	+	41.3776i	−0.152759	+	0.0762019i
$544$	−2.31971	−	1.68537i	−0.00426418	−	0.00309811i
$545$	365.678	−	503.313i	0.670969	−	0.923510i
$546$	−728.076	−	1459.55i	−1.33347	−	2.67316i
$547$	26.8715	+	82.7020i	0.0491253	+	0.151192i	0.972610	−	0.232443i	$-0.0746720\pi$
$547$	26.8715	+	82.7020i	0.0491253	+	0.151192i	−0.923485	+	0.383635i	$0.874672\pi$
$548$	−381.711	−	525.380i	−0.696552	−	0.958722i
$549$	−4.49800	+	263.870i	−0.00819307	+	0.480637i
$550$		0			0
$551$		−	268.812i		−	0.487861i
$552$	−20.7716	−	3.47161i	−0.0376297	−	0.00628914i
$553$	−173.390	−	533.638i	−0.313544	−	0.964988i
$554$	−201.464	−	65.4595i	−0.363653	−	0.118158i
$555$	576.338	−	86.2547i	1.03845	−	0.155414i
$556$	−66.5688	−	48.3651i	−0.119728	−	0.0869876i
$557$	−699.473	−	227.272i	−1.25579	−	0.408029i	−0.395795	−	0.918339i	$-0.629531\pi$
$557$	−699.473	−	227.272i	−1.25579	−	0.408029i	−0.859991	+	0.510309i	$0.829531\pi$
$558$	−186.340	−	608.601i	−0.333943	−	1.09068i
$559$	2.75959	−	2.00496i	0.00493666	−	0.00358669i
$560$		−	818.651i		−	1.46188i
$561$		0			0
$562$	−1206.81			−2.14734
$563$	335.019	+	461.115i	0.595061	+	0.819031i	0.995245	−	0.0974037i	$-0.0310538\pi$
$563$	335.019	+	461.115i	0.595061	+	0.819031i	−0.400184	+	0.916435i	$0.631054\pi$
$564$	−169.810	−	88.3534i	−0.301082	−	0.156655i
$565$	−150.959	+	464.604i	−0.267184	+	0.822308i
$566$	448.807	−	617.730i	0.792946	−	1.09140i
$567$	−714.068	−	556.952i	−1.25938	−	0.982279i
$568$	−6.66237	+	20.5047i	−0.0117295	+	0.0360997i
$569$	540.055	−	175.474i	0.949130	−	0.308391i	0.206768	−	0.978390i	$-0.433706\pi$
$569$	540.055	−	175.474i	0.949130	−	0.308391i	0.742362	+	0.669999i	$0.233706\pi$
$570$	226.700	+	37.8889i	0.397719	+	0.0664718i
$571$	229.442			0.401825			0.200912	−	0.979609i	$-0.435609\pi$
$571$	229.442			0.401825			0.200912	+	0.979609i	$0.435609\pi$
$572$		0			0
$573$	−633.070	+	622.370i	−1.10483	+	1.08616i
$574$	1142.83	−	830.317i	1.99100	−	1.44655i
$575$	4.28815	−	1.39330i	0.00745765	−	0.00242314i
$576$	618.235	+	212.593i	1.07333	+	0.369085i
$577$	581.714	+	422.640i	1.00817	+	0.732479i	0.963825	−	0.266538i	$-0.0858797\pi$
$577$	581.714	+	422.640i	1.00817	+	0.732479i	0.0443458	+	0.999016i	$0.485880\pi$
$578$	−488.810	+	672.790i	−0.845692	+	1.16400i
$579$	−213.440	+	106.472i	−0.368636	+	0.183889i
$580$	326.953	+	1006.26i	0.563712	+	1.73493i
$581$	−395.878	−	544.880i	−0.681374	−	0.937831i
$582$	−189.687	+	186.481i	−0.325923	+	0.320415i
$583$		0			0
$584$			11.2784i			0.0193124i
$585$	616.278	−	431.898i	1.05347	−	0.738287i
$586$	169.419	+	521.418i	0.289111	+	0.889791i
$587$	−486.604	−	158.107i	−0.828968	−	0.269348i	−0.136358	−	0.990660i	$-0.543540\pi$
$587$	−486.604	−	158.107i	−0.828968	−	0.269348i	−0.692611	+	0.721312i	$0.743540\pi$
$588$	144.444	+	965.146i	0.245653	+	1.64141i
$589$	106.989	+	77.7322i	0.181646	+	0.131973i
$590$	196.237	+	63.7614i	0.332606	+	0.108070i
$591$	−958.953	−	498.950i	−1.62259	−	0.844248i
$592$	−470.045	+	341.508i	−0.793996	+	0.576872i
$593$		−	241.775i		−	0.407715i	−0.979001	−	0.203858i	$-0.934652\pi$
$593$		−	241.775i		−	0.407715i	0.979001	−	0.203858i	$-0.0653480\pi$
$594$		0			0
$595$	3.46204			0.00581856
$596$	457.081	+	629.119i	0.766915	+	1.05557i
$597$	−512.165	+	984.352i	−0.857899	+	1.64883i
$598$	130.670	−	402.160i	0.218511	−	0.672508i
$599$	−284.669	+	391.813i	−0.475240	+	0.654112i	−0.977582	−	0.210557i	$-0.932472\pi$
$599$	−284.669	+	391.813i	−0.475240	+	0.654112i	0.502341	+	0.864669i	$0.332472\pi$
$600$	1.24202	−	0.185881i	0.00207004	−	0.000309801i
$601$	149.380	−	459.745i	0.248553	−	0.764966i	−0.746479	−	0.665409i	$-0.768257\pi$
$601$	149.380	−	459.745i	0.248553	−	0.764966i	0.995032	−	0.0995576i	$-0.0317428\pi$
$602$	−6.17581	+	2.00664i	−0.0102588	+	0.00333329i
$603$	−427.944	−	610.637i	−0.709692	−	1.01266i
$604$	−600.098			−0.993540
$605$		0			0
$606$	−314.234	−	319.636i	−0.518538	−	0.527453i
$607$	402.569	−	292.483i	0.663211	−	0.481851i	−0.204535	−	0.978859i	$-0.565568\pi$
$607$	402.569	−	292.483i	0.663211	−	0.481851i	0.867746	+	0.497009i	$0.165568\pi$
$608$	−234.465	+	76.1823i	−0.385633	+	0.125300i
$609$	747.922	+	1499.33i	1.22811	+	2.46196i
$610$	337.766	+	245.402i	0.553715	+	0.402298i
$611$	148.068	−	203.798i	0.242337	−	0.333548i
$612$	−0.784038	+	2.28004i	−0.00128111	+	0.00372555i
$613$	−323.828	−	996.640i	−0.528267	−	1.62584i	−0.757763	−	0.652530i	$-0.773708\pi$
$613$	−323.828	−	996.640i	−0.528267	−	1.62584i	0.229496	−	0.973310i	$-0.426292\pi$
$614$	−482.481	−	664.078i	−0.785799	−	1.08156i
$615$	456.922	+	464.777i	0.742963	+	0.755735i
$616$		0			0
$617$			322.739i			0.523078i	0.965193	+	0.261539i	$0.0842301\pi$
$617$			322.739i			0.523078i	−0.965193	+	0.261539i	$0.915770\pi$
$618$	72.7959	−	435.558i	0.117793	−	0.704786i
$619$	166.334	+	511.925i	0.268715	+	0.827019i	0.990814	+	0.135230i	$0.0431773\pi$
$619$	166.334	+	511.925i	0.268715	+	0.827019i	−0.722099	+	0.691789i	$0.756823\pi$
$620$	−495.044	−	160.849i	−0.798457	−	0.259435i
$621$	−30.7870	−	232.748i	−0.0495764	−	0.374795i
$622$	−1175.39	−	853.971i	−1.88970	−	1.37294i
$623$	−429.026	−	139.399i	−0.688645	−	0.223754i
$624$	−346.311	+	665.589i	−0.554985	+	1.06665i
$625$	494.931	−	359.588i	0.791889	−	0.575341i
$626$		−	230.698i		−	0.368527i
$627$		0			0
$628$	768.838			1.22426
$629$	−1.44422	−	1.98780i	−0.00229606	−	0.00316026i
$630$	−1369.87	+	419.423i	−2.17439	+	0.665750i
$631$	272.965	−	840.101i	0.432591	−	1.33138i	−0.462943	−	0.886388i	$-0.653207\pi$
$631$	272.965	−	840.101i	0.432591	−	1.33138i	0.895535	−	0.444992i	$-0.146793\pi$
$632$	23.8153	−	32.7790i	0.0376825	−	0.0518655i
$633$	68.7144	+	459.137i	0.108554	+	0.725335i
$634$	7.69770	−	23.6911i	0.0121415	−	0.0373676i
$635$	−98.1094	+	31.8777i	−0.154503	+	0.0502011i
$636$	207.334	−	1240.53i	0.325996	−	1.95052i
$637$	−1284.27			−2.01613
$638$		0			0
$639$	−240.316	−	4.09649i	−0.376082	−	0.00641079i
$640$	103.157	−	74.9481i	0.161183	−	0.117106i
$641$	−280.561	+	91.1597i	−0.437692	+	0.142215i	−0.519571	−	0.854427i	$-0.673908\pi$
$641$	−280.561	+	91.1597i	−0.437692	+	0.142215i	0.0818783	+	0.996642i	$0.473908\pi$
$642$	−528.719	+	263.745i	−0.823550	+	0.410817i
$643$	−675.938	−	491.098i	−1.05123	−	0.763760i	−0.0787805	−	0.996892i	$-0.525103\pi$
$643$	−675.938	−	491.098i	−1.05123	−	0.763760i	−0.972445	+	0.233132i	$0.925103\pi$
$644$	−244.597	+	336.659i	−0.379810	+	0.522763i
$645$	−1.33739	−	2.68102i	−0.00207347	−	0.00415662i
$646$	−0.299464	−	0.921655i	−0.000463566	−	0.00142671i
$647$	−480.606	−	661.498i	−0.742823	−	1.02241i	−0.998451	−	0.0556327i	$-0.982282\pi$
$647$	−480.606	−	661.498i	−0.742823	−	1.02241i	0.255629	−	0.966775i	$-0.417718\pi$
$648$	2.22875	−	65.3545i	0.00343943	−	0.100856i
$649$		0			0
$650$			25.2162i			0.0387942i
$651$	−813.023	−	135.883i	−1.24888	−	0.208729i
$652$	−292.671	−	900.748i	−0.448881	−	1.38151i
$653$	−262.841	−	85.4023i	−0.402514	−	0.130785i	0.100762	−	0.994911i	$-0.467872\pi$
$653$	−262.841	−	85.4023i	−0.402514	−	0.130785i	−0.503276	+	0.864126i	$0.667872\pi$
$654$	1073.50	−	160.660i	1.64144	−	0.245658i
$655$	116.200	+	84.4246i	0.177405	+	0.128892i
$656$	−618.004	−	200.802i	−0.942079	−	0.306100i
$657$	−120.224	+	36.8098i	−0.182989	+	0.0560271i
$658$	−387.972	+	281.878i	−0.589623	+	0.428386i
$659$		−	881.372i		−	1.33744i	−0.743515	−	0.668719i	$-0.766843\pi$
$659$		−	881.372i		−	1.33744i	0.743515	−	0.668719i	$-0.233157\pi$
$660$		0			0
$661$	−501.036			−0.757997			−0.378999	−	0.925397i	$-0.623731\pi$
$661$	−501.036			−0.757997			−0.378999	+	0.925397i	$0.623731\pi$
$662$	47.7915	+	65.7793i	0.0721925	+	0.0993645i
$663$	−2.81475	−	1.46453i	−0.00424547	−	0.00220895i
$664$	15.0287	−	46.2537i	0.0226336	−	0.0696592i
$665$	174.963	−	240.816i	0.263103	−	0.362130i
$666$	812.272	+	611.571i	1.21963	+	0.918275i
$667$	−134.231	+	413.122i	−0.201247	+	0.619373i
$668$	750.779	−	243.943i	1.12392	−	0.365184i
$669$	1057.29	+	176.707i	1.58040	+	0.264136i
$670$	−1179.64			−1.76065
$671$		0			0
$672$	1095.80	−	1077.28i	1.63065	−	1.60309i
$673$	3.60405	−	2.61850i	0.00535520	−	0.00389078i	−0.585104	−	0.810958i	$-0.698946\pi$
$673$	3.60405	−	2.61850i	0.00535520	−	0.00389078i	0.590460	+	0.807067i	$0.298946\pi$
$674$	−789.616	+	256.562i	−1.17154	+	0.380655i
$675$	6.03505	+	12.6328i	0.00894082	+	0.0187153i
$676$	403.771	+	293.357i	0.597295	+	0.433960i
$677$	10.1571	−	13.9800i	0.0150031	−	0.0206500i	−0.801450	−	0.598062i	$-0.795938\pi$
$677$	10.1571	−	13.9800i	0.0150031	−	0.0206500i	0.816453	+	0.577412i	$0.195938\pi$
$678$	−762.703	+	380.464i	−1.12493	+	0.561157i
$679$	106.454	+	327.630i	0.156780	+	0.482519i
$680$	0.146943	+	0.202250i	0.000216092	+	0.000297426i
$681$	−219.408	+	215.700i	−0.322185	+	0.316740i
$682$		0			0
$683$		−	1085.69i		−	1.58958i	−0.606882	−	0.794792i	$-0.707580\pi$
$683$		−	1085.69i		−	1.58958i	0.606882	−	0.794792i	$-0.292420\pi$
$684$	118.974	+	169.764i	0.173938	+	0.248193i
$685$	−231.962	−	713.906i	−0.338631	−	1.04220i
$686$	825.955	+	268.369i	1.20402	+	0.391209i
$687$	164.010	+	1095.89i	0.238734	+	1.59518i
$688$	2.41660	+	1.75576i	0.00351250	+	0.00255198i
$689$	1574.17	+	511.478i	2.28471	+	0.742349i
$690$	−329.483	−	171.432i	−0.477511	−	0.248453i
$691$	163.068	−	118.476i	0.235988	−	0.171456i	−0.463506	−	0.886094i	$-0.653409\pi$
$691$	163.068	−	118.476i	0.235988	−	0.171456i	0.699494	+	0.714638i	$0.253409\pi$
$692$			1042.51i			1.50652i
$693$		0			0
$694$	758.569			1.09304
$695$	−55.9050	−	76.9467i	−0.0804389	−	0.110715i
$696$	−55.8448	+	107.330i	−0.0802368	+	0.154210i
$697$	0.849182	−	2.61351i	0.00121834	−	0.00374966i
$698$	825.278	−	1135.90i	1.18235	−	1.62736i
$699$	−51.4040	+	7.69311i	−0.0735393	+	0.0110059i
$700$	7.66836	−	23.6008i	0.0109548	−	0.0337154i
$701$	408.672	−	132.785i	0.582984	−	0.189423i	−0.00265309	−	0.999996i	$-0.500845\pi$
$701$	408.672	−	132.785i	0.582984	−	0.189423i	0.585637	+	0.810574i	$0.300845\pi$
$702$	1291.17	+	238.486i	1.83927	+	0.339723i
$703$	−211.257			−0.300508
$704$		0			0
$705$	−155.117	−	157.784i	−0.220024	−	0.223807i
$706$	−1018.15	+	739.729i	−1.44214	+	1.04777i
$707$	−552.080	+	179.382i	−0.780877	+	0.253722i
$708$	83.0718	+	166.531i	0.117333	+	0.235213i
$709$	−606.394	−	440.571i	−0.855281	−	0.621398i	0.0713162	−	0.997454i	$-0.477280\pi$
$709$	−606.394	−	440.571i	−0.855281	−	0.621398i	−0.926597	+	0.376056i	$0.877280\pi$
$710$	−223.496	+	307.616i	−0.314784	+	0.433263i
$711$	427.139	+	146.880i	0.600758	+	0.206583i
$712$	−10.0660	−	30.9800i	−0.0141376	−	0.0435112i
$713$	−125.610	−	172.888i	−0.176172	−	0.242479i
$714$	4.23464	+	4.30744i	0.00593087	+	0.00603283i
$715$		0			0
$716$			1355.32i			1.89291i
$717$	108.218	−	647.499i	0.150932	−	0.903067i
$718$	217.859	+	670.501i	0.303425	+	0.933845i
$719$	−429.113	−	139.427i	−0.596820	−	0.193919i	−0.00499824	−	0.999988i	$-0.501591\pi$
$719$	−429.113	−	139.427i	−0.596820	−	0.193919i	−0.591822	+	0.806069i	$0.701591\pi$
$720$	526.476	+	396.391i	0.731216	+	0.550543i
$721$	−462.680	−	336.157i	−0.641720	−	0.466237i
$722$	908.725	+	295.263i	1.25862	+	0.408951i
$723$	−163.441	+	314.124i	−0.226060	+	0.434473i
$724$	−107.003	+	77.7423i	−0.147794	+	0.107379i
$725$		−	25.9035i		−	0.0357290i
$726$		0			0
$727$	300.631			0.413523			0.206761	−	0.978391i	$-0.433708\pi$
$727$	300.631			0.413523			0.206761	+	0.978391i	$0.433708\pi$
$728$	−89.6565	−	123.402i	−0.123155	−	0.169508i
$729$	703.928	−	189.542i	0.965608	−	0.260003i
$730$	−61.4662	+	189.174i	−0.0842003	+	0.259142i
$731$	−0.00742506	+	0.0102197i	−1.01574e−5	+	1.39805e-5i
$732$	55.7348	+	372.410i	0.0761405	+	0.508757i
$733$	412.036	−	1268.12i	0.562122	−	1.73003i	−0.114228	−	0.993455i	$-0.536439\pi$
$733$	412.036	−	1268.12i	0.562122	−	1.73003i	0.676350	−	0.736580i	$-0.263561\pi$
$734$	616.048	−	200.166i	0.839303	−	0.272706i
$735$	−185.952	+	1112.60i	−0.252996	+	1.51374i
$736$	398.379			0.541275
$737$		0			0
$738$	−19.3815	+	1137.00i	−0.0262623	+	1.54065i
$739$	854.307	−	620.691i	1.15603	−	0.839906i	0.166760	−	0.985997i	$-0.446669\pi$
$739$	854.307	−	620.691i	1.15603	−	0.839906i	0.989271	+	0.146091i	$0.0466693\pi$
$740$	790.810	−	256.950i	1.06866	−	0.347229i
$741$	−244.122	+	121.777i	−0.329449	+	0.164341i
$742$	−2549.19	−	1852.10i	−3.43557	−	2.49609i
$743$	−593.078	+	816.301i	−0.798220	+	1.09866i	0.194815	+	0.980840i	$0.437589\pi$
$743$	−593.078	+	816.301i	−0.798220	+	1.09866i	−0.993035	+	0.117816i	$0.962411\pi$
$744$	−26.5698	−	53.2635i	−0.0357121	−	0.0715907i
$745$	277.764	+	854.870i	0.372838	+	1.14748i
$746$	−478.932	−	659.193i	−0.642000	−	0.883637i
$747$	542.097	+	9.24073i	0.725699	+	0.0123705i
$748$		0			0
$749$			765.196i			1.02162i
$750$	1075.09	+	179.682i	1.43345	+	0.239576i
$751$	−15.5397	−	47.8263i	−0.0206920	−	0.0636836i	0.940177	−	0.340686i	$-0.110659\pi$
$751$	−15.5397	−	47.8263i	−0.0206920	−	0.0636836i	−0.960869	+	0.277002i	$0.910659\pi$
$752$	209.801	+	68.1686i	0.278991	+	0.0906497i
$753$	−476.377	+	71.2946i	−0.632639	+	0.0946807i
$754$	−1965.38	−	1427.93i	−2.60660	−	1.89381i
$755$	−659.702	−	214.350i	−0.873777	−	0.283907i
$756$	−1135.93	−	615.859i	−1.50255	−	0.814628i
$757$	−256.265	+	186.187i	−0.338527	+	0.245954i	−0.744040	−	0.668135i	$-0.767093\pi$
$757$	−256.265	+	186.187i	−0.338527	+	0.245954i	0.405513	+	0.914089i	$0.367093\pi$
$758$			1313.86i			1.73333i
$759$		0			0
$760$	21.4944			0.0282821
$761$	−41.9533	−	57.7438i	−0.0551292	−	0.0758788i	0.780562	−	0.625078i	$-0.214933\pi$
$761$	−41.9533	−	57.7438i	−0.0551292	−	0.0758788i	−0.835692	+	0.549199i	$0.814933\pi$
$762$	−159.666	−	83.0752i	−0.209535	−	0.109023i
$763$	434.400	−	1336.94i	0.569331	−	1.75222i
$764$	−744.550	+	1024.79i	−0.974542	+	1.34134i
$765$	−1.67632	+	2.22645i	−0.00219127	+	0.00291039i
$766$	−285.676	+	879.221i	−0.372945	+	1.14781i
$767$	−232.921	+	75.6806i	−0.303678	+	0.0986709i
$768$	−640.336	−	107.021i	−0.833771	−	0.139350i
$769$	634.282			0.824814			0.412407	−	0.911000i	$-0.364688\pi$
$769$	634.282			0.824814			0.412407	+	0.911000i	$0.364688\pi$
$770$		0			0
$771$	56.0119	−	55.0653i	0.0726484	−	0.0714206i
$772$	−275.338	+	200.045i	−0.356655	+	0.259125i
$773$	821.374	−	266.881i	1.06258	−	0.345253i	0.274986	−	0.961448i	$-0.411327\pi$
$773$	821.374	−	266.881i	1.06258	−	0.345253i	0.787593	+	0.616195i	$0.211327\pi$
$774$	1.69985	−	4.94329i	0.00219619	−	0.00638668i
$775$	10.3098	+	7.49053i	0.0133030	+	0.00966520i
$776$	−14.6216	+	20.1248i	−0.0188422	+	0.0259341i
$777$	1178.31	−	587.786i	1.51649	−	0.756482i
$778$	280.491	+	863.262i	0.360528	+	1.10959i
$779$	−138.878	−	191.149i	−0.178277	−	0.245377i
$780$	765.719	−	752.778i	0.981691	−	0.965100i
$781$		0			0
$782$			1.56598i			0.00200253i
$783$	−1326.37	−	244.986i	−1.69395	−	0.312882i
$784$	−347.536	−	1069.60i	−0.443285	−	1.36429i
$785$	845.202	+	274.623i	1.07669	+	0.349838i
$786$	37.0918	+	247.840i	0.0471906	+	0.315319i
$787$	973.760	+	707.478i	1.23731	+	0.898956i	0.997416	−	0.0718441i	$-0.0228884\pi$
$787$	973.760	+	707.478i	1.23731	+	0.898956i	0.239891	+	0.970800i	$0.422888\pi$
$788$	−1466.92	−	476.632i	−1.86158	−	0.604863i
$789$	588.203	+	306.046i	0.745504	+	0.387891i
$790$	578.098	−	420.013i	0.731769	−	0.531661i
$791$			1103.83i			1.39549i
$792$		0			0
$793$	−495.547			−0.624902
$794$	−572.032	−	787.334i	−0.720443	−	0.991604i
$795$	671.035	−	1289.69i	0.844069	−	1.62225i
$796$	−489.256	+	1505.77i	−0.614643	+	1.89168i
$797$	−368.331	+	506.965i	−0.462147	+	0.636091i	−0.974952	−	0.222414i	$-0.928606\pi$
$797$	−368.331	+	506.965i	−0.462147	+	0.636091i	0.512805	+	0.858505i	$0.328606\pi$
$798$	513.630	−	76.8698i	0.643646	−	0.0963280i
$799$	−0.288282	+	0.887242i	−0.000360804	+	0.00111044i
$800$	−22.5938	+	7.34117i	−0.0282423	+	0.00917647i
$801$	297.382	−	208.410i	0.371263	−	0.260188i
$802$	1038.67			1.29510
$803$		0			0
$804$	−745.887	−	758.710i	−0.927721	−	0.943670i
$805$	−389.144	+	282.729i	−0.483408	+	0.351217i
$806$	1136.66	−	369.322i	1.41024	−	0.458216i
$807$	−167.981	−	336.746i	−0.208155	−	0.417281i
$808$	−33.9118	−	24.6384i	−0.0419700	−	0.0304930i
$809$	236.367	−	325.331i	0.292171	−	0.402139i	−0.637547	−	0.770412i	$-0.720051\pi$
$809$	236.367	−	325.331i	0.292171	−	0.402139i	0.929718	+	0.368272i	$0.120051\pi$
$810$	393.558	−	1084.05i	0.485874	−	1.33833i
$811$	−171.141	−	526.717i	−0.211024	−	0.649466i	−0.999412	−	0.0342874i	$-0.989084\pi$
$811$	−171.141	−	526.717i	−0.211024	−	0.649466i	0.788388	−	0.615179i	$-0.210916\pi$
$812$	1405.23	+	1934.14i	1.73058	+	2.38194i
$813$	841.116	+	855.576i	1.03458	+	1.05237i
$814$		0			0
$815$		−	1094.75i		−	1.34325i
$816$	0.458040	−	2.74058i	0.000561323	−	0.00335855i
$817$	0.335628	+	1.03296i	0.000410806	+	0.00126433i
$818$	−1207.30	−	392.275i	−1.47591	−	0.479554i
$819$	1022.80	−	1358.45i	1.24884	−	1.65867i
$820$	752.361	+	546.622i	0.917513	+	0.666612i
$821$	−210.185	−	68.2932i	−0.256011	−	0.0831829i	0.178200	−	0.983994i	$-0.442973\pi$
$821$	−210.185	−	68.2932i	−0.256011	−	0.0831829i	−0.434211	+	0.900811i	$0.642973\pi$
$822$	604.508	−	1161.83i	0.735411	−	1.41342i
$823$	−581.483	+	422.472i	−0.706541	+	0.513332i	−0.882056	−	0.471145i	$-0.843841\pi$
$823$	−581.483	+	422.472i	−0.706541	+	0.513332i	0.175515	+	0.984477i	$0.443841\pi$
$824$		−	41.2972i		−	0.0501179i
$825$		0			0
$826$	466.232			0.564446
$827$	377.587	+	519.704i	0.456574	+	0.628421i	0.973794	−	0.227432i	$-0.0730329\pi$
$827$	377.587	+	519.704i	0.456574	+	0.628421i	−0.517220	+	0.855853i	$0.673033\pi$
$828$	−98.0722	−	320.311i	−0.118445	−	0.386849i
$829$	253.712	−	780.846i	0.306046	−	0.941913i	−0.673239	−	0.739425i	$-0.735097\pi$
$829$	253.712	−	780.846i	0.306046	−	0.941913i	0.979285	−	0.202488i	$-0.0649027\pi$
$830$	504.156	−	693.911i	0.607416	−	0.836037i
$831$	−32.6872	−	218.410i	−0.0393348	−	0.262828i
$832$	−379.348	+	1167.51i	−0.455947	+	1.40326i
$833$	4.52332	−	1.46971i	0.00543015	−	0.00176436i
$834$	27.3554	−	163.675i	0.0328002	−	0.196253i
$835$	912.483			1.09279
$836$		0			0
$837$	481.052	−	457.062i	0.574733	−	0.546071i
$838$	−915.332	+	665.027i	−1.09228	+	0.793589i
$839$	327.020	−	106.255i	0.389774	−	0.126645i	−0.107573	−	0.994197i	$-0.534308\pi$
$839$	327.020	−	106.255i	0.389774	−	0.126645i	0.497346	+	0.867552i	$0.334308\pi$
$840$	−119.888	+	59.8045i	−0.142724	+	0.0711958i
$841$	1338.57	+	972.526i	1.59164	+	1.15639i
$842$	1189.71	−	1637.50i	1.41296	−	1.94477i
$843$	−561.610	−	1125.84i	−0.666204	−	1.33552i
$844$	204.698	+	629.995i	0.242533	+	0.746439i
$845$	339.090	+	466.718i	0.401290	+	0.552329i
$846$	6.57969	−	385.990i	0.00777741	−	0.456253i
$847$		0			0
$848$			1449.45i			1.70926i
$849$	785.146	+	131.223i	0.924789	+	0.154562i
$850$	−0.0288573	−	0.0888136i	−3.39498e−5	−	0.000104487i
$851$	324.670	+	105.492i	0.381515	+	0.123962i
$852$	−339.168	+	50.7598i	−0.398084	+	0.0595772i
$853$	276.697	+	201.032i	0.324381	+	0.235677i	0.738043	−	0.674754i	$-0.235750\pi$
$853$	276.697	+	201.032i	0.324381	+	0.235677i	−0.413661	+	0.910431i	$0.635750\pi$
$854$	897.205	+	291.520i	1.05059	+	0.341358i
$855$	70.1521	+	229.122i	0.0820492	+	0.267979i
$856$	−44.7021	+	32.4780i	−0.0522220	+	0.0379415i
$857$		−	1404.79i		−	1.63920i	−0.572937	−	0.819600i	$-0.694196\pi$
$857$		−	1404.79i		−	1.63920i	0.572937	−	0.819600i	$-0.305804\pi$
$858$		0			0
$859$	759.128			0.883735			0.441867	−	0.897080i	$-0.354316\pi$
$859$	759.128			0.883735			0.441867	+	0.897080i	$0.354316\pi$
$860$	−2.51275	−	3.45851i	−0.00292181	−	0.00402152i
$861$	1306.45	+	679.754i	1.51736	+	0.789494i
$862$	−134.499	+	413.946i	−0.156031	+	0.480215i
$863$	232.529	−	320.049i	0.269443	−	0.370856i	−0.652759	−	0.757566i	$-0.726388\pi$
$863$	232.529	−	320.049i	0.269443	−	0.370856i	0.922202	+	0.386710i	$0.126388\pi$
$864$	162.213	+	1226.32i	0.187747	+	1.41936i
$865$	−372.376	+	1146.06i	−0.430493	+	1.32492i
$866$	−1290.67	+	419.365i	−1.49038	+	0.484255i
$867$	−855.127	−	142.920i	−0.986306	−	0.164844i
$868$	−1176.15			−1.35501
$869$		0			0
$870$	−1521.63	+	1495.91i	−1.74900	+	1.71944i
$871$	1132.75	−	822.989i	1.30051	−	0.944878i
$872$	96.5408	−	31.3680i	0.110712	−	0.0359725i
$873$	−262.244	−	90.1781i	−0.300394	−	0.103297i
$874$	108.928	+	79.1407i	0.124631	+	0.0905501i
$875$	829.733	−	1142.03i	0.948267	−	1.30518i
$876$	−160.536	+	80.0815i	−0.183261	+	0.0914172i
$877$	350.305	+	1078.13i	0.399436	+	1.22934i	0.925453	+	0.378863i	$0.123685\pi$
$877$	350.305	+	1078.13i	0.399436	+	1.22934i	−0.526017	+	0.850474i	$0.676315\pi$
$878$	856.557	+	1178.95i	0.975577	+	1.34277i
$879$	−407.592	+	400.703i	−0.463700	+	0.455863i
$880$		0			0
$881$		−	894.628i		−	1.01547i	−0.861514	−	0.507735i	$-0.830483\pi$
$881$		−	894.628i		−	1.01547i	0.861514	−	0.507735i	$-0.169517\pi$
$882$	−1611.74	+	1129.53i	−1.82737	+	1.28065i
$883$	9.80769	+	30.1850i	0.0111072	+	0.0341846i	0.956457	−	0.291875i	$-0.0942791\pi$
$883$	9.80769	+	30.1850i	0.0111072	+	0.0341846i	−0.945349	+	0.326059i	$0.894279\pi$
$884$	−4.30576	−	1.39903i	−0.00487077	−	0.00158261i
$885$	31.8392	+	212.744i	0.0359765	+	0.240389i
$886$	1486.54	+	1080.03i	1.67781	+	1.21900i
$887$	1289.18	+	418.881i	1.45342	+	0.472244i	0.926053	−	0.377394i	$-0.123180\pi$
$887$	1289.18	+	418.881i	1.45342	+	0.472244i	0.527366	+	0.849638i	$0.323180\pi$
$888$	84.3503	+	43.8881i	0.0949890	+	0.0494235i
$889$	−188.577	+	137.009i	−0.212123	+	0.154116i
$890$		−	574.487i		−	0.645491i
$891$		0			0
$892$	1529.52			1.71470
$893$	47.1465	+	64.8916i	0.0527957	+	0.0726670i
$894$	−723.871	+	1391.24i	−0.809699	+	1.55619i
$895$	−484.110	+	1489.94i	−0.540905	+	1.66474i
$896$	169.351	−	233.091i	0.189008	−	0.260147i
$897$	435.988	−	65.2499i	0.486051	−	0.0727423i
$898$	−294.755	+	907.162i	−0.328235	+	1.01020i
$899$	−1167.64	+	379.389i	−1.29882	+	0.422012i
$900$	11.4647	+	16.3590i	0.0127385	+	0.0181767i
$901$	−6.12969			−0.00680321
$902$		0			0
$903$	−4.74604	−	4.82763i	−0.00525586	−	0.00534621i
$904$	−64.4849	+	46.8510i	−0.0713329	+	0.0518264i
$905$	−145.400	+	47.2433i	−0.160663	+	0.0522025i
$906$	−540.230	−	1082.98i	−0.596280	−	1.19534i
$907$	−728.063	−	528.968i	−0.802715	−	0.583207i	0.108994	−	0.994042i	$-0.465237\pi$
$907$	−728.063	−	528.968i	−0.802715	−	0.583207i	−0.911709	+	0.410836i	$0.865237\pi$
$908$	−258.045	+	355.168i	−0.284190	+	0.391154i
$909$	151.956	−	441.900i	0.167169	−	0.486139i
$910$	−831.287	−	2558.44i	−0.913502	−	2.81147i
$911$	188.025	+	258.794i	0.206394	+	0.284077i	0.899648	−	0.436617i	$-0.143823\pi$
$911$	188.025	+	258.794i	0.206394	+	0.284077i	−0.693254	+	0.720694i	$0.743823\pi$
$912$	−167.483	−	170.363i	−0.183644	−	0.186801i
$913$		0			0
$914$			247.292i			0.270560i
$915$	−71.7511	+	429.307i	−0.0784165	+	0.469188i
$916$	488.581	+	1503.70i	0.533385	+	1.64159i
$917$	308.662	+	100.290i	0.336600	+	0.109368i
$918$	−4.82054	+	0.637642i	−0.00525113	+	0.000694599i
$919$	362.706	+	263.522i	0.394675	+	0.286748i	0.767369	−	0.641206i	$-0.221566\pi$
$919$	362.706	+	263.522i	0.394675	+	0.286748i	−0.372693	+	0.927955i	$0.621566\pi$
$920$	−33.0336	−	10.7333i	−0.0359061	−	0.0116666i
$921$	394.992	−	759.151i	0.428873	−	0.824268i
$922$	−152.077	+	110.490i	−0.164942	+	0.119838i
$923$		−	451.314i		−	0.488964i
$924$		0			0
$925$	−20.3574			−0.0220080
$926$	905.536	+	1246.36i	0.977901	+	1.34597i
$927$	440.212	−	134.783i	0.474878	−	0.145397i
$928$	707.252	−	2176.70i	0.762125	−	2.34558i
$929$	−172.146	+	236.939i	−0.185303	+	0.255047i	−0.891554	−	0.452914i	$-0.850385\pi$
$929$	−172.146	+	236.939i	−0.185303	+	0.255047i	0.706252	+	0.707961i	$0.250385\pi$
$930$	−155.376	−	1038.19i	−0.167071	−	1.11634i
$931$	126.365	−	388.913i	0.135731	−	0.417737i
$932$	−70.5329	+	22.9175i	−0.0756791	+	0.0245896i
$933$	249.686	−	1493.94i	0.267617	−	1.60122i
$934$	1433.07			1.53434
$935$		0			0
$936$	122.771	+	2.09279i	0.131166	+	0.00223589i
$937$	−119.433	+	86.7730i	−0.127463	+	0.0926073i	−0.649690	−	0.760199i	$-0.725101\pi$
$937$	−119.433	+	86.7730i	−0.127463	+	0.0926073i	0.522227	+	0.852806i	$0.325101\pi$
$938$	−2535.02	+	823.678i	−2.70258	+	0.878122i
$939$	215.220	−	107.359i	0.229201	−	0.114334i
$940$	−255.413	−	185.569i	−0.271716	−	0.197413i
$941$	20.5137	−	28.2347i	0.0217999	−	0.0300049i	−0.797978	−	0.602687i	$-0.794097\pi$
$941$	20.5137	−	28.2347i	0.0217999	−	0.0300049i	0.819778	+	0.572682i	$0.194097\pi$
$942$	692.136	+	1387.50i	0.734752	+	1.47293i
$943$	117.983	+	363.115i	0.125115	+	0.385064i
$944$	−126.061	−	173.508i	−0.133539	−	0.183801i
$945$	−1028.78	−	1082.77i	−1.08865	−	1.14579i
$946$		0			0
$947$		−	867.513i		−	0.916064i	−0.888936	−	0.458032i	$-0.848554\pi$
$947$		−	867.513i		−	0.916064i	0.888936	−	0.458032i	$-0.151446\pi$
$948$	635.673	+	106.242i	0.670541	+	0.112069i
$949$	−72.9563	−	224.536i	−0.0768771	−	0.236603i
$950$	−7.63616	−	2.48114i	−0.00803806	−	0.00261172i
$951$	25.6838	−	3.84384i	0.0270072	−	0.00404190i
$952$	0.456998	+	0.332028i	0.000480040	+	0.000348769i
$953$	−1236.76	−	401.847i	−1.29775	−	0.421666i	−0.422954	−	0.906151i	$-0.639007\pi$
$953$	−1236.76	−	401.847i	−1.29775	−	0.421666i	−0.874799	+	0.484485i	$0.839007\pi$
$954$	2425.40	−	742.604i	2.54235	−	0.778411i
$955$	−1184.55	+	860.623i	−1.24036	+	0.901176i
$956$		−	936.699i		−	0.979811i
$957$		0			0
$958$	−2499.72			−2.60931
$959$	−996.965	−	1372.20i	−1.03959	−	1.43087i
$960$	956.523	+	497.686i	0.996378	+	0.518423i
$961$	−110.319	+	339.527i	−0.114796	+	0.353306i
$962$	−1122.20	+	1544.58i	−1.16653	+	1.60559i
$963$	−492.099	−	370.508i	−0.511006	−	0.384743i
$964$	−156.130	+	480.520i	−0.161961	+	0.498464i
$965$	−374.139	+	121.565i	−0.387709	+	0.125974i
$966$	−827.755	−	138.345i	−0.856889	−	0.143214i
$967$	−1422.62			−1.47117			−0.735585	−	0.677433i	$-0.763093\pi$
$967$	−1422.62			−1.47117			−0.735585	+	0.677433i	$0.763093\pi$
$968$		0			0
$969$	0.720457	−	0.708281i	0.000743506	−	0.000730940i
$970$	−354.926	+	257.869i	−0.365903	+	0.265844i
$971$	−330.282	+	107.315i	−0.340146	+	0.110520i	−0.474109	−	0.880466i	$-0.657230\pi$
$971$	−330.282	+	107.315i	−0.340146	+	0.110520i	0.133963	+	0.990986i	$0.457230\pi$
$972$	946.077	−	432.320i	0.973330	−	0.444774i
$973$	−173.867	−	126.322i	−0.178691	−	0.129827i
$974$	−407.826	+	561.325i	−0.418713	+	0.576309i
$975$	−23.5244	+	11.7348i	−0.0241276	+	0.0120357i
$976$	−134.100	−	412.716i	−0.137397	−	0.422865i
$977$	274.257	+	377.482i	0.280713	+	0.386369i	0.925970	−	0.377597i	$-0.123250\pi$
$977$	274.257	+	377.482i	0.280713	+	0.386369i	−0.645257	+	0.763966i	$0.723250\pi$
$978$	1362.08	−	1339.06i	1.39272	−	1.36918i
$979$		0			0
$980$			1609.54i			1.64238i
$981$	649.455	+	926.711i	0.662033	+	0.944660i
$982$	−444.657	−	1368.51i	−0.452807	−	1.39360i
$983$	963.856	+	313.176i	0.980525	+	0.318592i	0.755057	−	0.655659i	$-0.227609\pi$
$983$	963.856	+	313.176i	0.980525	+	0.318592i	0.225467	+	0.974251i	$0.427609\pi$
$984$	15.7402	+	105.173i	0.0159961	+	0.106883i
$985$	−1442.37	−	1047.94i	−1.46434	−	1.06390i
$986$	8.55635	+	2.78013i	0.00867784	+	0.00281960i
$987$	−443.516	−	230.765i	−0.449357	−	0.233804i
$988$	−314.917	+	228.801i	−0.318742	+	0.231580i
$989$		−	1.75510i		−	0.00177462i
$990$		0			0
$991$	−1208.63			−1.21960			−0.609802	−	0.792554i	$-0.708751\pi$
$991$	−1208.63			−1.21960			−0.609802	+	0.792554i	$0.708751\pi$
$992$	661.828	+	910.928i	0.667165	+	0.918274i
$993$	−39.1254	+	75.1966i	−0.0394012	+	0.0757267i
$994$	−265.498	+	817.118i	−0.267100	+	0.822050i
$995$	−1075.70	+	1480.57i	−1.08111	+	1.48801i
$996$	765.083	−	114.502i	0.768155	−	0.114962i
$997$	44.6144	−	137.309i	0.0447486	−	0.137722i	−0.926186	−	0.377067i	$-0.876933\pi$
$997$	44.6144	−	137.309i	0.0447486	−	0.137722i	0.970935	+	0.239345i	$0.0769326\pi$
$998$	−1518.39	+	493.356i	−1.52144	+	0.494344i
$999$	−192.533	+	1042.38i	−0.192726	+	1.04342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.q.245.5		24
3.2	odd	2	inner	363.3.h.q.245.2		24
11.2	odd	10		363.3.b.k.122.5	yes	6
11.3	even	5	inner	363.3.h.q.269.5		24
11.4	even	5	inner	363.3.h.q.323.2		24
11.5	even	5	inner	363.3.h.q.251.2		24
11.6	odd	10		363.3.h.p.251.5		24
11.7	odd	10		363.3.h.p.323.5		24
11.8	odd	10		363.3.h.p.269.2		24
11.9	even	5		363.3.b.j.122.2	✓	6
11.10	odd	2		363.3.h.p.245.2		24
33.2	even	10		363.3.b.k.122.2	yes	6
33.5	odd	10	inner	363.3.h.q.251.5		24
33.8	even	10		363.3.h.p.269.5		24
33.14	odd	10	inner	363.3.h.q.269.2		24
33.17	even	10		363.3.h.p.251.2		24
33.20	odd	10		363.3.b.j.122.5	yes	6
33.26	odd	10	inner	363.3.h.q.323.5		24
33.29	even	10		363.3.h.p.323.2		24
33.32	even	2		363.3.h.p.245.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.j.122.2	✓	6	11.9	even	5
363.3.b.j.122.5	yes	6	33.20	odd	10
363.3.b.k.122.2	yes	6	33.2	even	10
363.3.b.k.122.5	yes	6	11.2	odd	10
363.3.h.p.245.2		24	11.10	odd	2
363.3.h.p.245.5		24	33.32	even	2
363.3.h.p.251.2		24	33.17	even	10
363.3.h.p.251.5		24	11.6	odd	10
363.3.h.p.269.2		24	11.8	odd	10
363.3.h.p.269.5		24	33.8	even	10
363.3.h.p.323.2		24	33.29	even	10
363.3.h.p.323.5		24	11.7	odd	10
363.3.h.q.245.2		24	3.2	odd	2	inner
363.3.h.q.245.5		24	1.1	even	1	trivial
363.3.h.q.251.2		24	11.5	even	5	inner
363.3.h.q.251.5		24	33.5	odd	10	inner
363.3.h.q.269.2		24	33.14	odd	10	inner
363.3.h.q.269.5		24	11.3	even	5	inner
363.3.h.q.323.2		24	11.4	even	5	inner
363.3.h.q.323.5		24	33.26	odd	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.69141 + 2.32802i) q^{2} +(-1.38470 + 2.66132i) q^{3} +(-1.32276 + 4.07105i) q^{4} +(-2.90829 + 4.00292i) q^{5} +(-8.53770 + 1.27775i) q^{6} +(-3.45484 + 10.6329i) q^{7} +(-0.767802 + 0.249474i) q^{8} +(-5.16520 - 7.37026i) q^{9} -14.2380 q^{10} +(-9.00271 - 9.15748i) q^{12} +(13.6720 - 9.93330i) q^{13} +(-30.5972 + 9.94163i) q^{14} +(-6.62591 - 13.2827i) q^{15} +(11.9727 + 8.69868i) q^{16} +(-0.0367864 + 0.0506321i) q^{17} +(8.42167 - 24.4908i) q^{18} +(1.66282 + 5.11764i) q^{19} +(-12.4491 - 17.1347i) q^{20} +(-23.5136 - 23.9178i) q^{21} -8.69537i q^{23} +(0.399248 - 2.38881i) q^{24} +(0.160235 + 0.493153i) q^{25} +(46.2499 + 15.0275i) q^{26} +(26.7668 - 3.54062i) q^{27} +(-38.7171 - 28.1296i) q^{28} +(-47.5106 - 15.4371i) q^{29} +(19.7154 - 37.8918i) q^{30} +(19.8827 - 14.4457i) q^{31} +45.8150i q^{32} -0.180094 q^{34} +(-32.5149 - 44.7530i) q^{35} +(36.8370 - 11.2787i) q^{36} +(-12.1319 + 37.3382i) q^{37} +(-9.10148 + 12.5271i) q^{38} +(7.50398 + 50.1402i) q^{39} +(1.23437 - 3.79899i) q^{40} +(-41.7596 + 13.5685i) q^{41} +(15.9102 - 95.1949i) q^{42} +0.201842 q^{43} +(44.5244 + 0.758975i) q^{45} +(20.2430 - 14.7074i) q^{46} +(14.1766 - 4.60627i) q^{47} +(-39.7286 + 19.8181i) q^{48} +(-61.4808 - 44.6684i) q^{49} +(-0.877048 + 1.20715i) q^{50} +(-0.0838099 - 0.168011i) q^{51} +(22.3541 + 68.7988i) q^{52} +(57.5690 + 79.2369i) q^{53} +(53.5163 + 56.3252i) q^{54} -9.02585i q^{56} +(-15.9222 - 2.66112i) q^{57} +(-44.4218 - 136.716i) q^{58} +(-13.7827 - 4.47826i) q^{59} +(62.8391 - 9.40449i) q^{60} +(-23.7229 - 17.2357i) q^{61} +(67.2596 + 21.8540i) q^{62} +(96.2122 - 29.4580i) q^{63} +(-58.7676 + 42.6972i) q^{64} +83.6168i q^{65} +82.8515 q^{67} +(-0.157466 - 0.216733i) q^{68} +(23.1411 + 12.0405i) q^{69} +(49.1899 - 151.391i) q^{70} +(15.6972 - 21.6053i) q^{71} +(5.80454 + 4.37031i) q^{72} +(4.31706 - 13.2865i) q^{73} +(-107.444 + 34.9108i) q^{74} +(-1.53431 - 0.256434i) q^{75} -23.0337 q^{76} +(-104.035 + 102.277i) q^{78} +(-40.6025 + 29.4994i) q^{79} +(-69.6402 + 22.6275i) q^{80} +(-27.6414 + 76.1377i) q^{81} +(-102.220 - 74.2674i) q^{82} +(-35.4092 + 48.7366i) q^{83} +(128.473 - 64.0873i) q^{84} +(-0.0956907 - 0.294506i) q^{85} +(0.341398 + 0.469894i) q^{86} +(106.871 - 105.065i) q^{87} +40.3489i q^{89} +(73.5420 + 104.938i) q^{90} +(58.3852 + 179.691i) q^{91} +(35.3993 + 11.5019i) q^{92} +(10.9128 + 72.9172i) q^{93} +(34.7020 + 25.2125i) q^{94} +(-25.3215 - 8.22744i) q^{95} +(-121.928 - 63.4402i) q^{96} +(24.9281 - 18.1114i) q^{97} -218.681i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) \) 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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