LMFDB - Embedded newform 49.4.e.a.8.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,4,Mod(8,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.8"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([12])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			8.3
Character	$\chi$	$=$	49.8
Dual form			49.4.e.a.43.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.45388 - 3.07706i) q^{2} +(2.79026 - 1.34372i) q^{3} +(-1.66664 + 7.30203i) q^{4} +(16.4856 - 7.93907i) q^{5} +(-10.9817 - 5.28849i) q^{6} +(-6.70370 - 17.2644i) q^{7} +(-1.80909 + 0.871210i) q^{8} +(-10.8543 + 13.6108i) q^{9} +(-64.8827 - 31.2459i) q^{10} +(6.93723 + 8.69901i) q^{11} +(5.16151 + 22.6141i) q^{12} +(-20.0311 - 25.1182i) q^{13} +(-36.6737 + 62.9925i) q^{14} +(35.3314 - 44.3041i) q^{15} +(61.1048 + 29.4265i) q^{16} +(-15.1891 - 66.5479i) q^{17} +68.5163 q^{18} +113.492 q^{19} +(30.4957 + 133.610i) q^{20} +(-41.9036 - 39.1644i) q^{21} +(9.74430 - 42.6926i) q^{22} +(-33.6662 + 147.501i) q^{23} +(-3.87716 + 4.86181i) q^{24} +(130.811 - 164.032i) q^{25} +(-28.1364 + 123.274i) q^{26} +(-30.6038 + 134.084i) q^{27} +(137.238 - 20.1770i) q^{28} +(40.8875 + 179.140i) q^{29} -223.025 q^{30} +167.796 q^{31} +(-55.8218 - 244.571i) q^{32} +(31.0457 + 14.9508i) q^{33} +(-167.500 + 210.038i) q^{34} +(-247.578 - 231.394i) q^{35} +(-81.2964 - 101.942i) q^{36} +(-56.8583 - 249.112i) q^{37} +(-278.496 - 349.223i) q^{38} +(-89.6437 - 43.1701i) q^{39} +(-22.9074 + 28.7249i) q^{40} +(214.875 - 103.478i) q^{41} +(-17.6849 + 225.044i) q^{42} +(81.3480 + 39.1751i) q^{43} +(-75.0823 + 36.1577i) q^{44} +(-70.8822 + 310.555i) q^{45} +(536.484 - 258.357i) q^{46} +(220.566 + 276.581i) q^{47} +210.039 q^{48} +(-253.121 + 231.471i) q^{49} -825.732 q^{50} +(-131.803 - 165.276i) q^{51} +(216.798 - 104.405i) q^{52} +(-51.4561 + 225.444i) q^{53} +(487.683 - 234.856i) q^{54} +(183.427 + 88.3336i) q^{55} +(27.1685 + 25.3925i) q^{56} +(316.673 - 152.502i) q^{57} +(450.891 - 565.400i) q^{58} +(-215.108 - 103.590i) q^{59} +(264.625 + 331.830i) q^{60} +(-7.36738 - 32.2786i) q^{61} +(-411.750 - 516.318i) q^{62} +(307.746 + 96.1497i) q^{63} +(-277.295 + 347.717i) q^{64} +(-529.640 - 255.061i) q^{65} +(-30.1777 - 132.217i) q^{66} -505.936 q^{67} +511.249 q^{68} +(104.263 + 456.805i) q^{69} +(-104.488 + 1329.63i) q^{70} +(-152.017 + 666.031i) q^{71} +(7.77842 - 34.0795i) q^{72} +(366.125 - 459.106i) q^{73} +(-627.011 + 786.247i) q^{74} +(144.585 - 633.466i) q^{75} +(-189.151 + 828.725i) q^{76} +(103.678 - 178.083i) q^{77} +(87.1373 + 381.774i) q^{78} -50.1378 q^{79} +1240.97 q^{80} +(-9.81499 - 43.0023i) q^{81} +(-845.684 - 407.260i) q^{82} +(348.620 - 437.156i) q^{83} +(355.818 - 240.708i) q^{84} +(-778.730 - 976.497i) q^{85} +(-79.0735 - 346.444i) q^{86} +(354.800 + 444.905i) q^{87} +(-20.1287 - 9.69348i) q^{88} +(-730.109 + 915.527i) q^{89} +(1129.53 - 543.955i) q^{90} +(-299.369 + 514.210i) q^{91} +(-1020.95 - 491.664i) q^{92} +(468.194 - 225.470i) q^{93} +(309.816 - 1357.39i) q^{94} +(1870.99 - 901.023i) q^{95} +(-484.393 - 607.409i) q^{96} +5.56045 q^{97} +(1333.38 + 210.867i) q^{98} -193.699 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19}+ \cdots + 10768 q^{99}+O(q^{100}) $ 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	−2.45388	−	3.07706i	−0.867576	−	1.08791i	−0.995371	−	0.0961052i	$-0.969361\pi$
$2$	−2.45388	−	3.07706i	−0.867576	−	1.08791i	0.127795	−	0.991801i	$-0.459210\pi$
$3$	2.79026	−	1.34372i	0.536986	−	0.258599i	−0.145677	−	0.989332i	$-0.546536\pi$
$3$	2.79026	−	1.34372i	0.536986	−	0.258599i	0.682663	+	0.730733i	$0.260822\pi$
$4$	−1.66664	+	7.30203i	−0.208330	+	0.912754i
$5$	16.4856	−	7.93907i	1.47452	−	0.710092i	0.487866	−	0.872919i	$-0.337776\pi$
$5$	16.4856	−	7.93907i	1.47452	−	0.710092i	0.986655	+	0.162827i	$0.0520612\pi$
$6$	−10.9817	−	5.28849i	−0.747207	−	0.359836i
$7$	−6.70370	−	17.2644i	−0.361966	−	0.932191i
$7$	−6.70370	−	17.2644i	−0.361966	−	0.932191i
$8$	−1.80909	+	0.871210i	−0.0799511	+	0.0385024i
$9$	−10.8543	+	13.6108i	−0.402009	+	0.504104i
$10$	−64.8827	−	31.2459i	−2.05177	−	0.988081i
$11$	6.93723	+	8.69901i	0.190150	+	0.238441i	0.867763	−	0.496978i	$-0.165557\pi$
$11$	6.93723	+	8.69901i	0.190150	+	0.238441i	−0.677613	+	0.735419i	$0.736986\pi$
$12$	5.16151	+	22.6141i	0.124167	+	0.544010i
$13$	−20.0311	−	25.1182i	−0.427356	−	0.535887i	0.520806	−	0.853675i	$-0.325631\pi$
$13$	−20.0311	−	25.1182i	−0.427356	−	0.535887i	−0.948162	+	0.317788i	$0.897060\pi$
$14$	−36.6737	+	62.9925i	−0.700104	+	1.20253i
$15$	35.3314	−	44.3041i	0.608168	−	0.762618i
$16$	61.1048	+	29.4265i	0.954762	+	0.459789i
$17$	−15.1891	−	66.5479i	−0.216700	−	0.949425i	−0.959897	−	0.280353i	$-0.909549\pi$
$17$	−15.1891	−	66.5479i	−0.216700	−	0.949425i	0.743197	−	0.669073i	$-0.233309\pi$
$18$	68.5163			0.897191
$19$	113.492			1.37036			0.685182	−	0.728372i	$-0.259722\pi$
$19$	113.492			1.37036			0.685182	+	0.728372i	$0.259722\pi$
$20$	30.4957	+	133.610i	0.340952	+	1.49381i
$21$	−41.9036	−	39.1644i	−0.435434	−	0.406970i
$22$	9.74430	−	42.6926i	0.0944314	−	0.413731i
$23$	−33.6662	+	147.501i	−0.305213	+	1.33722i	0.556930	+	0.830559i	$0.311979\pi$
$23$	−33.6662	+	147.501i	−0.305213	+	1.33722i	−0.862143	+	0.506665i	$0.830878\pi$
$24$	−3.87716	+	4.86181i	−0.0329759	+	0.0413505i
$25$	130.811	−	164.032i	1.04649	−	1.31226i
$26$	−28.1364	+	123.274i	−0.212231	+	0.929846i
$27$	−30.6038	+	134.084i	−0.218137	+	0.955722i
$28$	137.238	−	20.1770i	0.926270	−	0.136182i
$29$	40.8875	+	179.140i	0.261814	+	1.14708i	0.919282	+	0.393600i	$0.128771\pi$
$29$	40.8875	+	179.140i	0.261814	+	1.14708i	−0.657467	+	0.753483i	$0.728372\pi$
$30$	−223.025			−1.35729
$31$	167.796			0.972162			0.486081	−	0.873914i	$-0.338426\pi$
$31$	167.796			0.972162			0.486081	+	0.873914i	$0.338426\pi$
$32$	−55.8218	−	244.571i	−0.308375	−	1.35108i
$33$	31.0457	+	14.9508i	0.163768	+	0.0788667i
$34$	−167.500	+	210.038i	−0.844881	+	1.05945i
$35$	−247.578	−	231.394i	−1.19567	−	1.11751i
$36$	−81.2964	−	101.942i	−0.376372	−	0.471956i
$37$	−56.8583	−	249.112i	−0.252634	−	1.10686i	−0.928937	−	0.370237i	$-0.879276\pi$
$37$	−56.8583	−	249.112i	−0.252634	−	1.10686i	0.676304	−	0.736623i	$-0.263581\pi$
$38$	−278.496	−	349.223i	−1.18890	−	1.49083i
$39$	−89.6437	−	43.1701i	−0.368064	−	0.177250i
$40$	−22.9074	+	28.7249i	−0.0905493	+	0.113545i
$41$	214.875	−	103.478i	0.818482	−	0.394160i	0.0226994	−	0.999742i	$-0.492774\pi$
$41$	214.875	−	103.478i	0.818482	−	0.394160i	0.795783	+	0.605582i	$0.207060\pi$
$42$	−17.6849	+	225.044i	−0.0649725	+	0.826788i
$43$	81.3480	+	39.1751i	0.288499	+	0.138934i	0.572536	−	0.819880i	$-0.305960\pi$
$43$	81.3480	+	39.1751i	0.288499	+	0.138934i	−0.284037	+	0.958813i	$0.591674\pi$
$44$	−75.0823	+	36.1577i	−0.257252	+	0.123886i
$45$	−70.8822	+	310.555i	−0.234811	+	1.02877i
$46$	536.484	−	258.357i	1.71957	−	0.828101i
$47$	220.566	+	276.581i	0.684529	+	0.858373i	0.995763	−	0.0919610i	$-0.0293135\pi$
$47$	220.566	+	276.581i	0.684529	+	0.858373i	−0.311233	+	0.950334i	$0.600742\pi$
$48$	210.039			0.631595
$49$	−253.121	+	231.471i	−0.737961	+	0.674843i
$50$	−825.732			−2.33552
$51$	−131.803	−	165.276i	−0.361885	−	0.453790i
$52$	216.798	−	104.405i	0.578164	−	0.278429i
$53$	−51.4561	+	225.444i	−0.133359	+	0.584285i	0.863448	+	0.504438i	$0.168300\pi$
$53$	−51.4561	+	225.444i	−0.133359	+	0.584285i	−0.996807	+	0.0798470i	$0.974557\pi$
$54$	487.683	−	234.856i	1.22899	−	0.591848i
$55$	183.427	+	88.3336i	0.449695	+	0.216562i
$56$	27.1685	+	25.3925i	0.0648312	+	0.0605932i
$57$	316.673	−	152.502i	0.735866	−	0.354375i
$58$	450.891	−	565.400i	1.02077	−	1.28001i
$59$	−215.108	−	103.590i	−0.474655	−	0.228582i	0.181233	−	0.983440i	$-0.441991\pi$
$59$	−215.108	−	103.590i	−0.474655	−	0.228582i	−0.655888	+	0.754858i	$0.727706\pi$
$60$	264.625	+	331.830i	0.569383	+	0.713984i
$61$	−7.36738	−	32.2786i	−0.0154639	−	0.0677516i	0.966607	−	0.256262i	$-0.0824911\pi$
$61$	−7.36738	−	32.2786i	−0.0154639	−	0.0677516i	−0.982071	+	0.188511i	$0.939634\pi$
$62$	−411.750	−	516.318i	−0.843425	−	1.05762i
$63$	307.746	+	96.1497i	0.615435	+	0.192281i
$64$	−277.295	+	347.717i	−0.541592	+	0.679135i
$65$	−529.640	−	255.061i	−1.01067	−	0.486715i
$66$	−30.1777	−	132.217i	−0.0562820	−	0.246588i
$67$	−505.936			−0.922537			−0.461268	−	0.887261i	$-0.652605\pi$
$67$	−505.936			−0.922537			−0.461268	+	0.887261i	$0.652605\pi$
$68$	511.249			0.911737
$69$	104.263	+	456.805i	0.181910	+	0.796998i
$70$	−104.488	+	1329.63i	−0.178409	+	2.27029i
$71$	−152.017	+	666.031i	−0.254100	+	1.11329i	0.673345	+	0.739328i	$0.264857\pi$
$71$	−152.017	+	666.031i	−0.254100	+	1.11329i	−0.927446	+	0.373958i	$0.878000\pi$
$72$	7.77842	−	34.0795i	0.0127319	−	0.0557820i
$73$	366.125	−	459.106i	0.587009	−	0.736086i	−0.396282	−	0.918129i	$-0.629700\pi$
$73$	366.125	−	459.106i	0.587009	−	0.736086i	0.983291	+	0.182043i	$0.0582710\pi$
$74$	−627.011	+	786.247i	−0.984981	+	1.23513i
$75$	144.585	−	633.466i	0.222602	−	0.975285i
$76$	−189.151	+	828.725i	−0.285488	+	1.25081i
$77$	103.678	−	178.083i	0.153445	−	0.263564i
$78$	87.1373	+	381.774i	0.126492	+	0.554197i
$79$	−50.1378			−0.0714043			−0.0357022	−	0.999362i	$-0.511367\pi$
$79$	−50.1378			−0.0714043			−0.0357022	+	0.999362i	$0.511367\pi$
$80$	1240.97			1.73431
$81$	−9.81499	−	43.0023i	−0.0134636	−	0.0589881i
$82$	−845.684	−	407.260i	−1.13890	−	0.548468i
$83$	348.620	−	437.156i	0.461037	−	0.578122i	−0.495914	−	0.868372i	$-0.665167\pi$
$83$	348.620	−	437.156i	0.461037	−	0.578122i	0.956951	+	0.290250i	$0.0937383\pi$
$84$	355.818	−	240.708i	0.462177	−	0.312660i
$85$	−778.730	−	976.497i	−0.993708	−	1.24607i
$86$	−79.0735	−	346.444i	−0.0991479	−	0.434395i
$87$	354.800	+	444.905i	0.437225	+	0.548263i
$88$	−20.1287	−	9.69348i	−0.0243833	−	0.0117424i
$89$	−730.109	+	915.527i	−0.869566	+	1.09040i	0.125589	+	0.992082i	$0.459918\pi$
$89$	−730.109	+	915.527i	−0.869566	+	1.09040i	−0.995155	+	0.0983186i	$0.968654\pi$
$90$	1129.53	−	543.955i	1.32293	−	0.637088i
$91$	−299.369	+	514.210i	−0.344861	+	0.592350i
$92$	−1020.95	−	491.664i	−1.15697	−	0.557168i
$93$	468.194	−	225.470i	0.522037	−	0.251400i
$94$	309.816	−	1357.39i	0.339947	−	1.48941i
$95$	1870.99	−	901.023i	2.02063	−	0.973085i
$96$	−484.393	−	607.409i	−0.514980	−	0.645765i
$97$	5.56045			0.00582039			0.00291019	−	0.999996i	$-0.499074\pi$
$97$	5.56045			0.00582039			0.00291019	+	0.999996i	$0.499074\pi$
$98$	1333.38	+	210.867i	1.37440	+	0.217355i
$99$	−193.699			−0.196641
$100$	979.753	+	1228.57i	0.979753	+	1.22857i
$101$	−1405.71	+	676.954i	−1.38488	+	0.666925i	−0.970035	−	0.242966i	$-0.921880\pi$
$101$	−1405.71	+	676.954i	−1.38488	+	0.666925i	−0.414849	+	0.909890i	$0.636165\pi$
$102$	−185.136	+	811.133i	−0.179717	+	0.787394i
$103$	−863.327	+	415.757i	−0.825885	+	0.397725i	−0.798570	−	0.601901i	$-0.794410\pi$
$103$	−863.327	+	415.757i	−0.825885	+	0.397725i	−0.0273149	+	0.999627i	$0.508696\pi$
$104$	58.1212	+	27.9897i	0.0548005	+	0.0263905i
$105$	−1001.74	−	312.974i	−0.931042	−	0.290887i
$106$	819.972	−	394.878i	0.751346	−	0.361829i
$107$	−995.533	+	1248.36i	−0.899456	+	1.12788i	0.0917795	+	0.995779i	$0.470744\pi$
$107$	−995.533	+	1248.36i	−0.899456	+	1.12788i	−0.991236	+	0.132103i	$0.957827\pi$
$108$	−928.080	−	446.940i	−0.826894	−	0.398211i
$109$	−862.847	−	1081.98i	−0.758218	−	0.950775i	0.241590	−	0.970378i	$-0.422331\pi$
$109$	−862.847	−	1081.98i	−0.758218	−	0.950775i	−0.999808	+	0.0196031i	$0.993760\pi$
$110$	−178.298	−	781.175i	−0.154546	−	0.677110i
$111$	−493.386	−	618.687i	−0.421893	−	0.529038i
$112$	98.4036	−	1252.21i	0.0830202	−	1.05645i
$113$	1313.76	−	1647.40i	1.09370	−	1.37146i	0.171301	−	0.985219i	$-0.445203\pi$
$113$	1313.76	−	1647.40i	1.09370	−	1.37146i	0.922399	−	0.386238i	$-0.126226\pi$
$114$	−1246.33	−	600.203i	−1.02395	−	0.493107i
$115$	616.014	+	2698.93i	0.499509	+	2.18849i
$116$	−1376.23			−1.10155
$117$	559.301			0.441944
$118$	209.093	+	916.098i	0.163124	+	0.714692i
$119$	−1047.09	+	708.348i	−0.806608	+	0.545666i
$120$	−25.3193	+	110.931i	−0.0192610	+	0.0843881i
$121$	268.628	−	1176.94i	0.201824	−	0.884249i
$122$	−81.2446	+	101.877i	−0.0602913	+	0.0756029i
$123$	460.511	−	577.462i	0.337584	−	0.423317i
$124$	−279.655	+	1225.25i	−0.202531	+	0.887345i
$125$	345.294	−	1512.83i	0.247072	−	1.08249i
$126$	−459.313	−	1182.89i	−0.324753	−	0.836354i
$127$	456.555	+	2000.30i	0.318997	+	1.39762i	0.839315	+	0.543646i	$0.182957\pi$
$127$	456.555	+	2000.30i	0.318997	+	1.39762i	−0.520317	+	0.853973i	$0.674186\pi$
$128$	−256.493			−0.177117
$129$	279.622			0.190848
$130$	514.832	+	2255.63i	0.347336	+	1.52178i
$131$	−142.775	−	68.7569i	−0.0952239	−	0.0458574i	0.385666	−	0.922639i	$-0.373972\pi$
$131$	−142.775	−	68.7569i	−0.0952239	−	0.0458574i	−0.480889	+	0.876781i	$0.659686\pi$
$132$	−160.913	+	201.779i	−0.106104	+	0.133050i
$133$	−760.819	−	1959.38i	−0.496025	−	1.27744i
$134$	1241.50	+	1556.80i	0.800371	+	1.00363i
$135$	559.979	+	2453.43i	0.357002	+	1.56413i
$136$	85.4556	+	107.158i	0.0538806	+	0.0675641i
$137$	63.9127	+	30.7787i	0.0398572	+	0.0191942i	0.453706	−	0.891151i	$-0.350102\pi$
$137$	63.9127	+	30.7787i	0.0398572	+	0.0191942i	−0.413849	+	0.910346i	$0.635816\pi$
$138$	1149.77	−	1441.77i	0.709239	−	0.889357i
$139$	−1238.41	+	596.389i	−0.755690	+	0.363921i	−0.771730	−	0.635950i	$-0.780608\pi$
$139$	−1238.41	+	596.389i	−0.755690	+	0.363921i	0.0160398	+	0.999871i	$0.494894\pi$
$140$	2102.27	−	1422.17i	1.26910	−	0.858540i
$141$	987.084	+	475.355i	0.589557	+	0.283915i
$142$	2422.45	−	1166.59i	1.43160	−	0.689423i
$143$	79.5431	−	348.501i	0.0465156	−	0.203798i
$144$	−1063.76	+	512.282i	−0.615605	+	0.296460i
$145$	2096.26	+	2628.62i	1.20058	+	1.50549i
$146$	−2311.12			−1.31007
$147$	−395.241	+	985.988i	−0.221761	+	0.553217i
$148$	1913.79			1.06292
$149$	217.825	+	273.144i	0.119764	+	0.150180i	0.838099	−	0.545518i	$-0.183667\pi$
$149$	217.825	+	273.144i	0.119764	+	0.150180i	−0.718335	+	0.695697i	$0.755095\pi$
$150$	−2304.01	+	1109.55i	−1.25414	+	0.603963i
$151$	369.528	−	1619.01i	0.199151	−	0.872536i	−0.772293	−	0.635267i	$-0.780890\pi$
$151$	369.528	−	1619.01i	0.199151	−	0.872536i	0.971444	−	0.237270i	$-0.0762526\pi$
$152$	−205.318	+	98.8757i	−0.109562	+	0.0527624i
$153$	1070.64	+	515.591i	0.565724	+	0.272438i
$154$	−802.385	+	117.968i	−0.419857	+	0.0617284i
$155$	2766.22	−	1332.14i	1.43347	−	0.690324i
$156$	464.634	−	582.632i	0.238465	−	0.299025i
$157$	−2771.54	−	1334.71i	−1.40887	−	0.678478i	−0.433934	−	0.900944i	$-0.642875\pi$
$157$	−2771.54	−	1334.71i	−1.40887	−	0.678478i	−0.974940	+	0.222466i	$0.928589\pi$
$158$	123.032	+	154.277i	0.0619487	+	0.0776812i
$159$	159.357	+	698.190i	0.0794834	+	0.348239i
$160$	−2861.93	−	3588.74i	−1.41410	−	1.77322i
$161$	2772.21	−	407.577i	1.35703	−	0.199513i
$162$	−108.236	+	135.724i	−0.0524927	+	0.0658238i
$163$	2497.85	+	1202.90i	1.20028	+	0.578027i	0.923757	−	0.382979i	$-0.125102\pi$
$163$	2497.85	+	1202.90i	1.20028	+	0.578027i	0.276528	+	0.961006i	$0.410816\pi$
$164$	397.482	+	1741.48i	0.189257	+	0.829188i
$165$	630.503			0.297483
$166$	−2200.63			−1.02893
$167$	132.019	+	578.411i	0.0611731	+	0.268017i	0.996260	−	0.0864003i	$-0.0275364\pi$
$167$	132.019	+	578.411i	0.0611731	+	0.268017i	−0.935087	+	0.354417i	$0.884679\pi$
$168$	109.928	+	34.3449i	0.0504828	+	0.0157724i
$169$	259.199	−	1135.63i	0.117979	−	0.516899i
$170$	−1093.83	+	4792.40i	−0.493490	+	2.16212i
$171$	−1231.87	+	1544.72i	−0.550899	+	0.690806i
$172$	−421.636	+	528.715i	−0.186915	+	0.234384i
$173$	361.048	−	1581.85i	0.158670	−	0.695180i	−0.831525	−	0.555488i	$-0.812532\pi$
$173$	361.048	−	1581.85i	0.158670	−	0.695180i	0.990195	−	0.139692i	$-0.0446113\pi$
$174$	498.366	−	2183.48i	0.217132	−	0.951319i
$175$	−3708.84	−	1158.76i	−1.60207	−	0.500537i
$176$	167.916	+	735.689i	0.0719157	+	0.315083i
$177$	−739.403			−0.313994
$178$	4608.73			1.94067
$179$	−450.708	−	1974.68i	−0.188198	−	0.824551i	−0.977566	−	0.210630i	$-0.932449\pi$
$179$	−450.708	−	1974.68i	−0.188198	−	0.824551i	0.789368	−	0.613921i	$-0.210409\pi$
$180$	−2149.55	−	1035.17i	−0.890100	−	0.428650i
$181$	−1724.53	+	2162.50i	−0.708197	+	0.888050i	−0.997606	−	0.0691550i	$-0.977970\pi$
$181$	−1724.53	+	2162.50i	−0.708197	+	0.888050i	0.289409	+	0.957205i	$0.406541\pi$
$182$	2316.87	−	340.631i	0.943615	−	0.138732i
$183$	−63.9302	−	80.1660i	−0.0258244	−	0.0323827i
$184$	−67.5996	−	296.173i	−0.0270843	−	0.118664i
$185$	−2915.07	−	3655.38i	−1.15849	−	1.45270i
$186$	−1842.68	−	887.386i	−0.726406	−	0.349819i
$187$	473.530	−	593.788i	0.185176	−	0.232204i
$188$	−2387.21	+	1149.62i	−0.926091	+	0.445982i
$189$	2520.04	−	370.502i	0.969874	−	0.142593i
$190$	−7363.69	−	3546.17i	−2.81168	−	1.35403i
$191$	−879.733	+	423.657i	−0.333274	+	0.160496i	−0.593035	−	0.805177i	$-0.702070\pi$
$191$	−879.733	+	423.657i	−0.333274	+	0.160496i	0.259761	+	0.965673i	$0.416356\pi$
$192$	−306.492	+	1342.83i	−0.115204	+	0.504741i
$193$	−4125.10	+	1986.54i	−1.53850	+	0.740904i	−0.995129	−	0.0985863i	$-0.968568\pi$
$193$	−4125.10	+	1986.54i	−1.53850	+	0.740904i	−0.543375	+	0.839490i	$0.682854\pi$
$194$	−13.6446	−	17.1098i	−0.00504963	−	0.00633204i
$195$	−1820.57			−0.668581
$196$	−1268.35	−	2234.07i	−0.462226	−	0.814167i
$197$	1085.93			0.392737			0.196369	−	0.980530i	$-0.437085\pi$
$197$	1085.93			0.392737			0.196369	+	0.980530i	$0.437085\pi$
$198$	475.313	+	596.023i	0.170601	+	0.213927i
$199$	2398.39	−	1155.00i	0.854359	−	0.411437i	0.0451651	−	0.998980i	$-0.485619\pi$
$199$	2398.39	−	1155.00i	0.854359	−	0.411437i	0.809194	+	0.587542i	$0.199904\pi$
$200$	−93.7425	+	410.713i	−0.0331430	+	0.145209i
$201$	−1411.69	+	679.836i	−0.495389	+	0.238567i
$202$	5532.46	+	2664.29i	1.92704	+	0.928015i
$203$	2818.65	−	1906.80i	0.974533	−	0.659266i
$204$	1426.52	−	686.975i	0.489590	−	0.235774i
$205$	2720.83	−	3411.81i	0.926979	−	1.16239i
$206$	3397.81	+	1636.30i	1.14921	+	0.553428i
$207$	−1642.19	−	2059.24i	−0.551401	−	0.691436i
$208$	−484.855	−	2124.29i	−0.161628	−	0.708138i
$209$	787.322	+	987.271i	0.260575	+	0.326751i
$210$	1495.09	+	3850.40i	0.491292	+	1.26525i
$211$	2081.37	−	2609.96i	0.679088	−	0.851549i	−0.316182	−	0.948699i	$-0.602401\pi$
$211$	2081.37	−	2609.96i	0.679088	−	0.851549i	0.995270	+	0.0971494i	$0.0309725\pi$
$212$	−1560.44	−	751.468i	−0.505526	−	0.243448i
$213$	470.790	+	2062.67i	0.151446	+	0.663529i
$214$	6284.19			2.00738
$215$	1652.09			0.524053
$216$	−61.4505	−	269.232i	−0.0193573	−	0.0848098i
$217$	−1124.85	−	2896.90i	−0.351890	−	0.906241i
$218$	−1211.99	+	5310.07i	−0.376542	+	1.64974i
$219$	404.674	−	1772.99i	0.124865	−	0.547068i
$220$	−950.721	+	1192.17i	−0.291353	+	0.365345i
$221$	−1367.31	+	1714.55i	−0.416177	+	0.521869i
$222$	−693.030	+	3036.36i	−0.209519	+	0.917961i
$223$	60.7385	−	266.113i	0.0182392	−	0.0799113i	−0.964989	−	0.262290i	$-0.915522\pi$
$223$	60.7385	−	266.113i	0.0182392	−	0.0799113i	0.983228	+	0.182378i	$0.0583796\pi$
$224$	−3848.17	+	2603.27i	−1.14784	+	0.776509i
$225$	812.751	+	3560.89i	0.240815	+	1.05508i
$226$	−8292.96			−2.44088
$227$	3637.99			1.06371			0.531855	−	0.846836i	$-0.321495\pi$
$227$	3637.99			1.06371			0.531855	+	0.846836i	$0.321495\pi$
$228$	585.792	+	2566.52i	0.170154	+	0.745492i
$229$	769.269	+	370.461i	0.221986	+	0.106903i	0.541572	−	0.840655i	$-0.317829\pi$
$229$	769.269	+	370.461i	0.221986	+	0.106903i	−0.319586	+	0.947557i	$0.603544\pi$
$230$	6793.16	−	8518.36i	1.94751	−	2.44210i
$231$	49.9962	−	636.212i	0.0142403	−	0.181211i
$232$	−230.037	−	288.458i	−0.0650978	−	0.0816301i
$233$	1386.99	+	6076.81i	0.389978	+	1.70861i	0.664725	+	0.747088i	$0.268549\pi$
$233$	1386.99	+	6076.81i	0.389978	+	1.70861i	−0.274747	+	0.961517i	$0.588594\pi$
$234$	−1372.46	−	1721.00i	−0.383420	−	0.480793i
$235$	5831.97	+	2808.53i	1.61888	+	0.779609i
$236$	1114.93	−	1398.08i	0.307524	−	0.385623i
$237$	−139.897	+	67.3711i	−0.0383431	+	0.0184651i
$238$	4749.05	+	1483.75i	1.29343	+	0.404107i
$239$	−3939.73	−	1897.27i	−1.06628	−	0.513492i	−0.183371	−	0.983044i	$-0.558701\pi$
$239$	−3939.73	−	1897.27i	−1.06628	−	0.513492i	−0.882905	+	0.469552i	$0.844415\pi$
$240$	3462.63	−	1667.51i	0.931299	−	0.448490i
$241$	−83.4356	+	365.555i	−0.0223011	+	0.0977074i	−0.984854	−	0.173388i	$-0.944529\pi$
$241$	−83.4356	+	365.555i	−0.0223011	+	0.0977074i	0.962553	+	0.271095i	$0.0873858\pi$
$242$	−4280.68	+	2061.47i	−1.13708	+	0.547587i
$243$	−2400.42	−	3010.03i	−0.633691	−	0.794623i
$244$	247.978			0.0650621
$245$	−2335.19	+	5825.49i	−0.608939	+	1.51909i
$246$	−2906.92			−0.753409
$247$	−2273.38	−	2850.72i	−0.585633	−	0.734361i
$248$	−303.557	+	146.186i	−0.0777254	+	0.0374306i
$249$	385.327	−	1688.23i	0.0980687	−	0.429667i
$250$	−5502.38	+	2649.81i	−1.39201	+	0.670354i
$251$	4664.41	+	2246.26i	1.17297	+	0.564872i	0.915855	−	0.401509i	$-0.131514\pi$
$251$	4664.41	+	2246.26i	1.17297	+	0.564872i	0.257114	+	0.966381i	$0.417228\pi$
$252$	−1214.99	+	2086.93i	−0.303719	+	0.521683i
$253$	−1516.67	+	730.388i	−0.376885	+	0.181498i
$254$	5034.71	−	6313.32i	1.24372	−	1.55958i
$255$	−3485.00	−	1678.29i	−0.855839	−	0.412150i
$256$	2847.76	+	3570.98i	0.695255	+	0.871822i
$257$	−574.002	−	2514.87i	−0.139320	−	0.610401i	−0.995585	−	0.0938643i	$-0.970078\pi$
$257$	−574.002	−	2514.87i	−0.139320	−	0.610401i	0.856265	−	0.516537i	$-0.172779\pi$
$258$	−686.159	−	860.416i	−0.165575	−	0.207625i
$259$	−3919.62	+	2651.60i	−0.940361	+	0.636149i
$260$	2745.19	−	3442.35i	0.654805	−	0.821099i
$261$	−2882.04	−	1387.92i	−0.683501	−	0.329157i
$262$	138.783	+	608.049i	0.0327254	+	0.143379i
$263$	−3988.24			−0.935078			−0.467539	−	0.883973i	$-0.654859\pi$
$263$	−3988.24			−0.935078			−0.467539	+	0.883973i	$0.654859\pi$
$264$	−69.1897			−0.0161300
$265$	941.527	+	4125.10i	0.218255	+	0.956238i
$266$	−4162.18	+	7149.16i	−0.959397	+	1.64791i
$267$	−806.982	+	3535.62i	−0.184968	+	0.810398i
$268$	843.214	−	3694.36i	0.192192	−	0.842049i
$269$	1962.01	−	2460.28i	0.444706	−	0.557643i	−0.508071	−	0.861315i	$-0.669641\pi$
$269$	1962.01	−	2460.28i	0.444706	−	0.557643i	0.952777	+	0.303672i	$0.0982127\pi$
$270$	6175.23	−	7743.49i	1.39190	−	1.74539i
$271$	−470.843	+	2062.90i	−0.105541	+	0.462406i	0.894346	+	0.447376i	$0.147641\pi$
$271$	−470.843	+	2062.90i	−0.105541	+	0.462406i	−0.999887	+	0.0150299i	$0.995216\pi$
$272$	1030.14	−	4513.36i	0.229638	−	1.00611i
$273$	−144.363	+	1837.05i	−0.0320046	+	0.407264i
$274$	−62.1257	−	272.191i	−0.0136976	−	0.0600133i
$275$	2334.39			0.511886
$276$	−3509.37			−0.765360
$277$	706.729	+	3096.38i	0.153297	+	0.671637i	0.991914	+	0.126915i	$0.0405077\pi$
$277$	706.729	+	3096.38i	0.153297	+	0.671637i	−0.838617	+	0.544722i	$0.816635\pi$
$278$	4874.04	+	2347.21i	1.05153	+	0.506391i
$279$	−1821.30	+	2283.84i	−0.390818	+	0.490071i
$280$	649.483	+	202.919i	0.138622	+	0.0433098i
$281$	946.925	+	1187.41i	0.201028	+	0.252081i	0.872119	−	0.489294i	$-0.162745\pi$
$281$	946.925	+	1187.41i	0.201028	+	0.252081i	−0.671091	+	0.741375i	$0.734174\pi$
$282$	−959.485	−	4203.78i	−0.202612	−	0.887700i
$283$	947.021	+	1187.53i	0.198921	+	0.249439i	0.871280	−	0.490786i	$-0.163290\pi$
$283$	947.021	+	1187.53i	0.198921	+	0.249439i	−0.672359	+	0.740225i	$0.734719\pi$
$284$	−4610.02	−	2220.07i	−0.963219	−	0.463862i
$285$	4009.84	−	5028.18i	0.833412	−	1.04507i
$286$	−1267.55	+	610.419i	−0.262069	+	0.126206i
$287$	−3226.95	−	3016.00i	−0.663696	−	0.620310i
$288$	3934.72	+	1894.86i	0.805054	+	0.387693i
$289$	228.550	−	110.064i	0.0465194	−	0.0224026i
$290$	2944.49	−	12900.6i	0.596228	−	2.61225i
$291$	15.5151	−	7.47167i	0.00312547	−	0.00150515i
$292$	2742.21	+	3438.62i	0.549574	+	0.689144i
$293$	−6408.29			−1.27774			−0.638868	−	0.769317i	$-0.720597\pi$
$293$	−6408.29			−1.27774			−0.638868	+	0.769317i	$0.720597\pi$
$294$	4003.82	−	1203.31i	0.794243	−	0.238702i
$295$	−4368.60			−0.862202
$296$	319.891	+	401.131i	0.0628152	+	0.0787677i
$297$	−1378.70	+	663.949i	−0.269362	+	0.129718i
$298$	305.965	−	1340.52i	0.0594768	−	0.260585i
$299$	4379.34	−	2108.98i	0.847036	−	0.407911i
$300$	4384.62	+	2111.52i	0.843820	+	0.406362i
$301$	131.003	−	1667.04i	0.0250861	−	0.319225i
$302$	−5888.56	+	2835.78i	−1.12202	+	0.540334i
$303$	−3012.66	+	3777.75i	−0.571197	+	0.716258i
$304$	6934.92	+	3339.68i	1.30837	+	0.630079i
$305$	−377.718	−	473.643i	−0.0709116	−	0.0889204i
$306$	−1040.70	−	4559.61i	−0.194421	−	0.851816i
$307$	−2896.22	−	3631.75i	−0.538424	−	0.675163i	0.435982	−	0.899955i	$-0.356401\pi$
$307$	−2896.22	−	3631.75i	−0.538424	−	0.675163i	−0.974407	+	0.224793i	$0.927830\pi$
$308$	1127.57	+	1053.86i	0.208602	+	0.194965i
$309$	−1850.25	+	2320.14i	−0.340637	+	0.427146i
$310$	−10887.1	−	5242.93i	−1.99465	−	0.960575i
$311$	184.604	+	808.804i	0.0336590	+	0.147470i	0.988965	−	0.148149i	$-0.0473314\pi$
$311$	184.604	+	808.804i	0.0336590	+	0.147470i	−0.955306	+	0.295618i	$0.904474\pi$
$312$	199.784			0.0362517
$313$	7156.11			1.29229			0.646146	−	0.763214i	$-0.276380\pi$
$313$	7156.11			1.29229			0.646146	+	0.763214i	$0.276380\pi$
$314$	2694.05	+	11803.4i	0.484185	+	2.12135i
$315$	5836.73	−	858.130i	1.04401	−	0.153492i
$316$	83.5617	−	366.108i	0.0148757	−	0.0651746i
$317$	−693.068	+	3036.53i	−0.122797	+	0.538008i	0.875683	+	0.482887i	$0.160412\pi$
$317$	−693.068	+	3036.53i	−0.122797	+	0.538008i	−0.998480	+	0.0551214i	$0.982445\pi$
$318$	1757.33	−	2203.62i	0.309894	−	0.388594i
$319$	−1274.69	+	1598.41i	−0.223727	+	0.280545i
$320$	−1810.84	+	7933.81i	−0.316341	+	1.38598i
$321$	−1100.35	+	4820.96i	−0.191326	+	0.838255i
$322$	−8056.81	−	7530.13i	−1.39437	−	1.30322i
$323$	−1723.85	−	7552.67i	−0.296958	−	1.30106i
$324$	330.362			0.0566465
$325$	−6740.49			−1.15045
$326$	−2428.01	−	10637.8i	−0.412500	−	1.80728i
$327$	−3861.44	−	1859.57i	−0.653022	−	0.314479i
$328$	−298.576	+	374.402i	−0.0502624	+	0.0630271i
$329$	3296.41	−	5662.06i	0.552391	−	0.948814i
$330$	−1547.18	−	1940.10i	−0.258089	−	0.323633i
$331$	1863.06	+	8162.59i	0.309374	+	1.35546i	0.855521	+	0.517768i	$0.173237\pi$
$331$	1863.06	+	8162.59i	0.309374	+	1.35546i	−0.546146	+	0.837690i	$0.683906\pi$
$332$	2611.10	+	3274.22i	0.431635	+	0.541253i
$333$	4007.77	+	1930.04i	0.659534	+	0.317615i
$334$	1455.85	−	1825.58i	0.238505	−	0.299076i
$335$	−8340.68	+	4016.66i	−1.36030	+	0.655086i
$336$	−1408.04	−	3626.21i	−0.228616	−	0.588767i
$337$	−4281.88	−	2062.04i	−0.692133	−	0.333314i	0.0545339	−	0.998512i	$-0.482633\pi$
$337$	−4281.88	−	2062.04i	−0.692133	−	0.333314i	−0.746667	+	0.665198i	$0.768347\pi$
$338$	−4130.44	+	1989.11i	−0.664693	+	0.320099i
$339$	1452.09	−	6362.01i	0.232645	−	1.01928i
$340$	8428.27	−	4058.84i	1.34437	−	0.647417i
$341$	1164.04	+	1459.66i	0.184857	+	0.231803i
$342$	7776.07			1.22948
$343$	5693.06	+	2818.27i	0.896200	+	0.443651i
$344$	−181.295			−0.0284151
$345$	5345.44	+	6702.98i	0.834171	+	1.04602i
$346$	−5753.43	+	2770.71i	−0.893949	+	0.430503i
$347$	1313.57	−	5755.13i	0.203217	−	0.890351i	−0.765746	−	0.643143i	$-0.777630\pi$
$347$	1313.57	−	5755.13i	0.203217	−	0.890351i	0.968963	−	0.247207i	$-0.0795129\pi$
$348$	−3840.04	+	1849.26i	−0.591516	+	0.284859i
$349$	−402.624	−	193.894i	−0.0617535	−	0.0297389i	0.402752	−	0.915309i	$-0.368054\pi$
$349$	−402.624	−	193.894i	−0.0617535	−	0.0297389i	−0.464506	+	0.885570i	$0.653768\pi$
$350$	5535.46	+	14255.8i	0.845380	+	2.17715i
$351$	3980.98	−	1917.14i	0.605381	−	0.291536i
$352$	1740.28	−	2182.24i	0.263515	−	0.330437i
$353$	−6920.77	−	3332.86i	−1.04350	−	0.502523i	−0.168022	−	0.985783i	$-0.553738\pi$
$353$	−6920.77	−	3332.86i	−1.04350	−	0.502523i	−0.875477	+	0.483261i	$0.839452\pi$
$354$	1814.40	+	2275.19i	0.272414	+	0.341596i
$355$	2781.56	+	12186.8i	0.415859	+	1.82200i
$356$	−5468.38	−	6857.13i	−0.814111	−	1.02086i
$357$	−1969.83	+	3383.47i	−0.292029	+	0.501602i
$358$	−4970.23	+	6232.48i	−0.733757	+	0.920102i
$359$	−8474.58	−	4081.14i	−1.24588	−	0.599984i	−0.309476	−	0.950907i	$-0.600154\pi$
$359$	−8474.58	−	4081.14i	−1.24588	−	0.599984i	−0.936404	+	0.350923i	$0.885868\pi$
$360$	−142.327	−	623.575i	−0.0208369	−	0.0912925i
$361$	6021.51			0.877900
$362$	10885.9			1.58053
$363$	−831.928	−	3644.92i	−0.120289	−	0.527020i
$364$	−3255.84	−	3043.00i	−0.468825	−	0.438178i
$365$	2390.93	−	10475.3i	0.342868	−	1.50220i
$366$	−89.7989	+	393.435i	−0.0128248	+	0.0561889i
$367$	−277.598	+	348.097i	−0.0394836	+	0.0495109i	−0.801181	−	0.598422i	$-0.795795\pi$
$367$	−277.598	+	348.097i	−0.0394836	+	0.0495109i	0.761698	+	0.647933i	$0.224366\pi$
$368$	−6397.62	+	8022.36i	−0.906247	+	1.13640i
$369$	−923.883	+	4047.79i	−0.130340	+	0.571056i
$370$	−4094.61	+	17939.7i	−0.575321	+	2.52065i
$371$	4237.11	−	622.949i	0.592937	−	0.0871749i
$372$	866.080	+	3794.55i	0.120710	+	0.528866i
$373$	9545.30			1.32503			0.662516	−	0.749048i	$-0.269489\pi$
$373$	9545.30			1.32503			0.662516	+	0.749048i	$0.269489\pi$
$374$	−2989.11			−0.413270
$375$	−1069.36	−	4685.17i	−0.147257	−	0.645176i
$376$	−639.984	−	308.200i	−0.0877783	−	0.0422718i
$377$	3680.65	−	4615.38i	0.502819	−	0.630516i
$378$	−7323.93	−	6845.16i	−0.996567	−	0.931421i
$379$	200.352	+	251.234i	0.0271541	+	0.0340501i	0.795223	−	0.606317i	$-0.207354\pi$
$379$	200.352	+	251.234i	0.0271541	+	0.0340501i	−0.768069	+	0.640367i	$0.778782\pi$
$380$	3461.02	+	15163.7i	0.467228	+	2.04706i
$381$	3961.74	+	4967.87i	0.532720	+	0.668009i
$382$	3462.38	+	1667.39i	0.463745	+	0.223328i
$383$	2758.30	−	3458.79i	0.367996	−	0.461452i	−0.563013	−	0.826448i	$-0.690358\pi$
$383$	2758.30	−	3458.79i	0.367996	−	0.461452i	0.931009	+	0.364996i	$0.118930\pi$
$384$	−715.682	+	344.654i	−0.0951094	+	0.0458023i
$385$	295.392	−	3758.92i	0.0391027	−	0.497590i
$386$	16235.2	+	7818.46i	2.14080	+	1.03096i
$387$	−1416.18	+	681.995i	−0.186016	+	0.0895807i
$388$	−9.26727	+	40.6026i	−0.00121256	+	0.00531258i
$389$	8575.10	−	4129.55i	1.11767	−	0.538243i	0.218500	−	0.975837i	$-0.429884\pi$
$389$	8575.10	−	4129.55i	1.11767	−	0.538243i	0.899173	+	0.437594i	$0.144169\pi$
$390$	4467.44	+	5601.99i	0.580045	+	0.727354i
$391$	10327.3			1.33573
$392$	256.257	−	639.273i	0.0330177	−	0.0823677i
$393$	−490.770			−0.0629925
$394$	−2664.74	−	3341.47i	−0.340729	−	0.427261i
$395$	−826.554	+	398.047i	−0.105287	+	0.0507036i
$396$	322.826	−	1414.40i	0.0409663	−	0.179485i
$397$	1337.77	−	644.237i	0.169121	−	0.0814442i	−0.347408	−	0.937714i	$-0.612938\pi$
$397$	1337.77	−	644.237i	0.169121	−	0.0814442i	0.516529	+	0.856270i	$0.327224\pi$
$398$	−9439.37	−	4545.76i	−1.18883	−	0.572509i
$399$	−4755.74	−	4444.85i	−0.596703	−	0.557697i
$400$	12820.1	−	6173.83i	1.60251	−	0.771729i
$401$	3857.43	−	4837.06i	0.480376	−	0.602373i	−0.481301	−	0.876555i	$-0.659836\pi$
$401$	3857.43	−	4837.06i	0.480376	−	0.602373i	0.961678	+	0.274182i	$0.0884072\pi$
$402$	5556.02	+	2675.64i	0.689326	+	0.331962i
$403$	−3361.13	−	4214.73i	−0.415459	−	0.520969i
$404$	−2600.32	−	11392.8i	−0.320225	−	1.40300i
$405$	−503.204	−	630.998i	−0.0617393	−	0.0774187i
$406$	−12783.9	−	3994.11i	−1.56270	−	0.488237i
$407$	1772.59	−	2222.76i	0.215882	−	0.270708i
$408$	382.434	+	184.170i	0.0464051	+	0.0223475i
$409$	−2389.42	−	10468.7i	−0.288873	−	1.26564i	−0.886074	−	0.463545i	$-0.846577\pi$
$409$	−2389.42	−	10468.7i	−0.288873	−	1.26564i	0.597200	−	0.802092i	$-0.296280\pi$
$410$	−17174.9			−2.06880
$411$	219.691			0.0263663
$412$	−1597.01	−	6996.96i	−0.190969	−	0.836688i
$413$	−346.411	+	4408.15i	−0.0412731	+	0.525208i
$414$	−2306.68	+	10106.2i	−0.273834	+	1.19975i
$415$	2276.62	−	9974.52i	0.269289	−	1.17983i
$416$	−5025.02	+	6301.18i	−0.592240	+	0.742646i
$417$	−2654.12	+	3328.16i	−0.311685	+	0.390841i
$418$	1105.90	−	4845.28i	0.129405	−	0.566962i
$419$	−1094.84	+	4796.79i	−0.127652	+	0.559281i	0.870136	+	0.492811i	$0.164031\pi$
$419$	−1094.84	+	4796.79i	−0.127652	+	0.559281i	−0.997788	+	0.0664695i	$0.978827\pi$
$420$	3954.88	−	6793.09i	0.459472	−	0.789212i
$421$	2626.63	+	11508.0i	0.304071	+	1.33222i	0.863920	+	0.503628i	$0.168002\pi$
$421$	2626.63	+	11508.0i	0.304071	+	1.33222i	−0.559849	+	0.828595i	$0.689141\pi$
$422$	−13138.4			−1.51557
$423$	−6158.57			−0.707896
$424$	−103.321	−	452.677i	−0.0118342	−	0.0518489i
$425$	−12902.9	−	6213.71i	−1.47267	−	0.709198i
$426$	5191.70	−	6510.18i	0.590466	−	0.740421i
$427$	−507.883	+	343.580i	−0.0575601	+	0.0389391i
$428$	−7456.36	−	9349.98i	−0.842095	−	1.05595i
$429$	−246.341	−	1079.29i	−0.0277237	−	0.121466i
$430$	−4054.02	−	5083.58i	−0.454656	−	0.570121i
$431$	−2614.59	−	1259.12i	−0.292205	−	0.140718i	0.282039	−	0.959403i	$-0.408989\pi$
$431$	−2614.59	−	1259.12i	−0.292205	−	0.140718i	−0.574243	+	0.818685i	$0.694704\pi$
$432$	−5815.66	+	7292.61i	−0.647700	+	0.812190i
$433$	−358.890	+	172.832i	−0.0398317	+	0.0191820i	−0.453694	−	0.891158i	$-0.649894\pi$
$433$	−358.890	+	172.832i	−0.0398317	+	0.0191820i	0.413862	+	0.910340i	$0.364180\pi$
$434$	−6153.69	+	10569.9i	−0.680614	+	1.16906i
$435$	9381.24	+	4517.77i	1.03401	+	0.497955i
$436$	9338.68	−	4497.27i	1.02578	−	0.493991i
$437$	−3820.86	+	16740.3i	−0.418253	+	1.83249i
$438$	−6448.63	+	3105.50i	−0.703487	+	0.338782i
$439$	−3103.51	−	3891.67i	−0.337408	−	0.423097i	0.583963	−	0.811780i	$-0.301501\pi$
$439$	−3103.51	−	3891.67i	−0.337408	−	0.423097i	−0.921371	+	0.388684i	$0.872930\pi$
$440$	−408.792			−0.0442918
$441$	−403.071	−	5957.62i	−0.0435235	−	0.643302i
$442$	8630.98			0.928810
$443$	−1372.67	−	1721.27i	−0.147218	−	0.184605i	0.702755	−	0.711432i	$-0.251953\pi$
$443$	−1372.67	−	1721.27i	−0.147218	−	0.184605i	−0.849973	+	0.526827i	$0.823382\pi$
$444$	5339.97	−	2571.59i	0.570774	−	0.274870i
$445$	−4767.88	+	20889.4i	−0.507908	+	2.22529i
$446$	−967.889	+	466.111i	−0.102760	+	0.0494865i
$447$	974.816	+	469.447i	0.103148	+	0.0496735i
$448$	7862.04	+	2456.35i	0.829122	+	0.259044i
$449$	−16500.4	+	7946.19i	−1.73431	+	0.835198i	−0.749400	+	0.662118i	$0.769658\pi$
$449$	−16500.4	+	7946.19i	−1.73431	+	0.835198i	−0.984908	+	0.173080i	$0.944628\pi$
$450$	8962.70	−	11238.9i	0.938902	−	1.17735i
$451$	2390.79	+	1151.34i	0.249619	+	0.120210i
$452$	9839.82	+	12338.7i	1.02395	+	1.28400i
$453$	−1144.41	−	5014.00i	−0.118696	−	0.520040i
$454$	−8927.18	−	11194.3i	−0.922849	−	1.15722i
$455$	−852.937	+	10853.8i	−0.0878820	+	1.11832i
$456$	−440.028	+	551.778i	−0.0451891	+	0.0566653i
$457$	7881.58	+	3795.57i	0.806750	+	0.388510i	0.791344	−	0.611371i	$-0.209382\pi$
$457$	7881.58	+	3795.57i	0.806750	+	0.388510i	0.0154057	+	0.999881i	$0.495096\pi$
$458$	−747.761	−	3276.15i	−0.0762894	−	0.334246i
$459$	9387.85			0.954657
$460$	−20734.4			−2.10162
$461$	−2071.19	−	9074.50i	−0.209252	−	0.916793i	−0.965066	−	0.262007i	$-0.915616\pi$
$461$	−2071.19	−	9074.50i	−0.209252	−	0.916793i	0.755814	−	0.654786i	$-0.227241\pi$
$462$	−2080.35	+	1407.34i	−0.209495	+	0.141722i
$463$	3165.38	−	13868.4i	0.317727	−	1.39205i	−0.523801	−	0.851841i	$-0.675486\pi$
$463$	3165.38	−	13868.4i	0.317727	−	1.39205i	0.841528	−	0.540214i	$-0.181657\pi$
$464$	−2773.04	+	12149.5i	−0.277446	+	1.21557i
$465$	5928.46	−	7434.05i	0.591238	−	0.741389i
$466$	15295.2	−	19179.6i	1.52047	−	1.90660i
$467$	−1309.43	+	5736.99i	−0.129750	+	0.568471i	0.867699	+	0.497090i	$0.165598\pi$
$467$	−1309.43	+	5736.99i	−0.129750	+	0.568471i	−0.997449	+	0.0713816i	$0.977259\pi$
$468$	−932.154	+	4084.04i	−0.0920702	+	0.403386i
$469$	3391.65	+	8734.70i	0.333927	+	0.859981i
$470$	−5668.91	−	24837.1i	−0.556356	−	2.43755i
$471$	−9526.80			−0.931999
$472$	479.398			0.0467501
$473$	223.545	+	979.414i	0.0217307	+	0.0952082i
$474$	550.596	+	265.153i	0.0533538	+	0.0256938i
$475$	14846.1	−	18616.4i	1.43407	−	1.79827i
$476$	−3427.26	−	8826.43i	−0.330018	−	0.849913i
$477$	−2509.96	−	3147.38i	−0.240929	−	0.302115i
$478$	3829.58	+	16778.5i	0.366445	+	1.60550i
$479$	7787.25	+	9764.91i	0.742816	+	0.931461i	0.999385	−	0.0350644i	$-0.0111636\pi$
$479$	7787.25	+	9764.91i	0.742816	+	0.931461i	−0.256569	+	0.966526i	$0.582592\pi$
$480$	−12807.8	−	6167.90i	−1.21790	−	0.586510i
$481$	−5118.32	+	6418.17i	−0.485188	+	0.608406i
$482$	1329.58	−	640.290i	0.125644	−	0.0605071i
$483$	7187.53	−	4862.32i	0.677110	−	0.458061i
$484$	8146.31	+	3923.06i	0.765055	+	0.368431i
$485$	91.6675	−	44.1448i	0.00858228	−	0.00413301i
$486$	−3371.72	+	14772.5i	−0.314700	+	1.37879i
$487$	−7360.98	+	3544.86i	−0.684924	+	0.329842i	−0.743780	−	0.668425i	$-0.766969\pi$
$487$	−7360.98	+	3544.86i	−0.684924	+	0.329842i	0.0588563	+	0.998266i	$0.481255\pi$
$488$	41.4497	+	51.9762i	0.00384496	+	0.00482142i
$489$	8586.00			0.794013
$490$	23655.7	−	7109.49i	2.18093	−	0.655458i
$491$	5894.06			0.541741			0.270871	−	0.962616i	$-0.412688\pi$
$491$	5894.06			0.541741			0.270871	+	0.962616i	$0.412688\pi$
$492$	3449.14	+	4325.08i	0.316055	+	0.396321i
$493$	11300.3	−	5441.95i	1.03233	−	0.497146i
$494$	−3193.27	+	13990.6i	−0.290834	+	1.27423i
$495$	−3193.25	+	1537.79i	−0.289951	+	0.139633i
$496$	10253.1	+	4937.65i	0.928184	+	0.446990i
$497$	12517.7	−	1840.38i	1.12977	−	0.166101i
$498$	−6140.32	+	2957.02i	−0.552519	+	0.266079i
$499$	4420.01	−	5542.51i	0.396526	−	0.497228i	−0.542987	−	0.839741i	$-0.682707\pi$
$499$	4420.01	−	5542.51i	0.396526	−	0.497228i	0.939513	+	0.342513i	$0.111278\pi$
$500$	10471.3	+	5042.69i	0.936578	+	0.451032i
$501$	1145.59	+	1436.52i	0.102158	+	0.128102i
$502$	−4534.00	−	19864.7i	−0.403112	−	1.76615i
$503$	−1818.10	−	2279.83i	−0.161164	−	0.202093i	0.694692	−	0.719307i	$-0.255540\pi$
$503$	−1818.10	−	2279.83i	−0.161164	−	0.202093i	−0.855856	+	0.517214i	$0.826969\pi$
$504$	−640.507	+	94.1687i	−0.0566080	+	0.00832263i
$505$	−17799.6	+	22320.0i	−1.56846	+	1.96679i
$506$	5969.16	+	2874.59i	0.524430	+	0.252552i
$507$	−802.729	−	3516.99i	−0.0703165	−	0.308077i
$508$	−15367.1			−1.34214
$509$	11495.4			1.00104			0.500518	−	0.865726i	$-0.333143\pi$
$509$	11495.4			1.00104			0.500518	+	0.865726i	$0.333143\pi$
$510$	3387.56	+	14841.9i	0.294125	+	1.28864i
$511$	−10380.6	−	3243.22i	−0.898650	−	0.280767i
$512$	3543.48	−	15525.0i	0.305862	−	1.34007i
$513$	−3473.30	+	15217.5i	−0.298928	+	1.30969i
$514$	−6329.87	+	7937.41i	−0.543188	+	0.681137i
$515$	−10931.8	+	13708.0i	−0.935363	+	1.17291i
$516$	−466.030	+	2041.81i	−0.0397594	+	0.174197i
$517$	−875.864	+	3837.41i	−0.0745077	+	0.326439i
$518$	17777.4	+	5554.22i	1.50790	+	0.471117i
$519$	−1118.15	−	4898.93i	−0.0945689	−	0.414334i
$520$	1180.38			0.0995442
$521$	16479.2			1.38574			0.692868	−	0.721064i	$-0.256347\pi$
$521$	16479.2			1.38574			0.692868	+	0.721064i	$0.256347\pi$
$522$	2801.46	+	12274.0i	0.234897	+	1.02915i
$523$	−11139.1	−	5364.32i	−0.931320	−	0.448500i	−0.0942208	−	0.995551i	$-0.530036\pi$
$523$	−11139.1	−	5364.32i	−0.931320	−	0.448500i	−0.837099	+	0.547051i	$0.815750\pi$
$524$	740.020	−	927.956i	0.0616945	−	0.0773625i
$525$	−11905.7	+	1750.40i	−0.989727	+	0.145512i
$526$	9786.64	+	12272.1i	0.811251	+	1.01728i
$527$	−2548.67	−	11166.5i	−0.210668	−	0.922995i
$528$	1457.09	+	1827.13i	0.120098	+	0.150598i
$529$	−9661.15	−	4652.56i	−0.794045	−	0.382392i
$530$	10382.8	−	13019.6i	0.850944	−	1.06705i
$531$	3744.78	−	1803.39i	0.306045	−	0.147383i
$532$	15575.5	−	2289.94i	1.26933	−	0.186619i
$533$	−6903.36	−	3324.48i	−0.561009	−	0.270168i
$534$	12859.6	−	6192.83i	1.04211	−	0.501854i
$535$	−6501.20	+	28483.6i	−0.525367	+	2.30178i
$536$	915.283	−	440.777i	0.0737578	−	0.0355199i
$537$	−3911.01	−	4904.25i	−0.314288	−	0.394104i
$538$	−12385.0			−0.992479
$539$	−3769.52	−	596.132i	−0.301234	−	0.0476386i
$540$	−18848.3			−1.50204
$541$	−3557.64	−	4461.14i	−0.282726	−	0.354528i	0.620108	−	0.784517i	$-0.287089\pi$
$541$	−3557.64	−	4461.14i	−0.282726	−	0.354528i	−0.902834	+	0.429989i	$0.858517\pi$
$542$	7503.05	−	3613.28i	0.594619	−	0.286354i
$543$	−1906.11	+	8351.22i	−0.150643	+	0.660009i
$544$	−15427.8	+	7429.65i	−1.21592	+	0.585558i
$545$	−22814.5	−	10986.9i	−1.79315	−	0.863533i
$546$	6006.96	−	4063.67i	0.470832	−	0.318515i
$547$	−5813.34	+	2799.56i	−0.454407	+	0.218831i	−0.647065	−	0.762435i	$-0.724004\pi$
$547$	−5813.34	+	2799.56i	−0.454407	+	0.218831i	0.192658	+	0.981266i	$0.438289\pi$
$548$	−331.267	+	415.395i	−0.0258230	+	0.0323811i
$549$	519.305	+	250.084i	0.0403705	+	0.0194414i
$550$	−5728.29	−	7183.05i	−0.444100	−	0.556884i
$551$	4640.42	+	20331.0i	0.358781	+	1.57192i
$552$	−586.594	−	735.565i	−0.0452302	−	0.0567169i
$553$	336.109	+	865.600i	0.0258459	+	0.0665625i
$554$	7793.53	−	9772.78i	0.597681	−	0.749469i
$555$	−13045.6	−	6282.42i	−0.997756	−	0.480494i
$556$	−2290.86	−	10036.9i	−0.174738	−	0.765575i
$557$	8462.90			0.643778			0.321889	−	0.946777i	$-0.395682\pi$
$557$	8462.90			0.643778			0.321889	+	0.946777i	$0.395682\pi$
$558$	11496.7			0.872215
$559$	−645.481	−	2828.04i	−0.0488389	−	0.213977i
$560$	−8319.09	−	21424.6i	−0.627761	−	1.61671i
$561$	523.388	−	2293.11i	0.0393894	−	0.172576i
$562$	1330.09	−	5827.50i	0.0998334	−	0.437399i
$563$	10363.7	−	12995.6i	0.775802	−	0.972825i	−0.224197	−	0.974544i	$-0.571976\pi$
$563$	10363.7	−	12995.6i	0.775802	−	0.972825i	0.999999	+	0.00171932i	$0.000547278\pi$
$564$	−5116.17	+	6415.47i	−0.381967	+	0.478972i
$565$	8579.33	−	37588.5i	0.638824	−	2.79887i
$566$	1330.22	−	5828.08i	0.0987869	−	0.432814i
$567$	−676.613	+	457.725i	−0.0501148	+	0.0339024i
$568$	−305.241	−	1337.35i	−0.0225486	−	0.0987919i
$569$	−5553.95			−0.409198			−0.204599	−	0.978846i	$-0.565589\pi$
$569$	−5553.95			−0.409198			−0.204599	+	0.978846i	$0.565589\pi$
$570$	−25311.7			−1.85998
$571$	−3864.13	−	16929.9i	−0.283203	−	1.24079i	−0.893660	−	0.448744i	$-0.851871\pi$
$571$	−3864.13	−	16929.9i	−0.283203	−	1.24079i	0.610457	−	0.792049i	$-0.290986\pi$
$572$	2412.20	+	1161.65i	0.176327	+	0.0849146i
$573$	−1885.41	+	2364.23i	−0.137459	+	0.172368i
$574$	−1361.90	+	17330.4i	−0.0990321	+	1.26020i
$575$	19791.1	+	24817.2i	1.43538	+	1.79991i
$576$	−1722.88	−	7548.42i	−0.124629	−	0.546037i
$577$	8832.30	+	11075.4i	0.637251	+	0.799087i	0.990656	−	0.136383i	$-0.0435478\pi$
$577$	8832.30	+	11075.4i	0.637251	+	0.799087i	−0.353405	+	0.935470i	$0.614976\pi$
$578$	−899.506	−	433.179i	−0.0647310	−	0.0311728i
$579$	−8840.74	+	11085.9i	−0.634557	+	0.795710i
$580$	−22688.0	+	10926.0i	−1.62426	+	0.782200i
$581$	−9884.30	−	3088.17i	−0.705800	−	0.220514i
$582$	−61.0629	−	29.4063i	−0.00434904	−	0.00209439i
$583$	−2318.10	+	1116.34i	−0.164676	+	0.0793037i
$584$	−262.374	+	1149.53i	−0.0185909	+	0.0814522i
$585$	9220.44	−	4440.33i	0.651655	−	0.313821i
$586$	15725.1	+	19718.7i	1.10853	+	1.39006i
$587$	13013.6			0.915043			0.457521	−	0.889199i	$-0.348737\pi$
$587$	13013.6			0.915043			0.457521	+	0.889199i	$0.348737\pi$
$588$	−6540.99	−	4529.35i	−0.458751	−	0.317665i
$589$	19043.5			1.33222
$590$	10720.0	+	13442.5i	0.748026	+	0.937995i
$591$	3030.03	−	1459.18i	0.210894	−	0.101561i
$592$	3856.20	−	16895.1i	0.267717	−	1.17295i
$593$	−1342.40	+	646.467i	−0.0929609	+	0.0447676i	−0.479786	−	0.877385i	$-0.659286\pi$
$593$	−1342.40	+	646.467i	−0.0929609	+	0.0447676i	0.386826	+	0.922153i	$0.373572\pi$
$594$	5426.18	+	2613.11i	0.374813	+	0.180500i
$595$	−11638.3	+	19990.5i	−0.801887	+	1.37736i
$596$	−2357.54	+	1135.33i	−0.162028	+	0.0780285i
$597$	5140.13	−	6445.52i	0.352381	−	0.441872i
$598$	−17235.8	−	8300.33i	−1.17864	−	0.567601i
$599$	−7334.75	−	9197.48i	−0.500317	−	0.627377i	0.465984	−	0.884793i	$-0.345700\pi$
$599$	−7334.75	−	9197.48i	−0.500317	−	0.627377i	−0.966301	+	0.257416i	$0.917129\pi$
$600$	290.316	+	1271.96i	0.0197535	+	0.0865458i
$601$	7091.14	+	8892.01i	0.481287	+	0.603515i	0.961894	−	0.273421i	$-0.0881552\pi$
$601$	7091.14	+	8892.01i	0.481287	+	0.603515i	−0.480607	+	0.876936i	$0.659584\pi$
$602$	−5451.07	+	3687.61i	−0.369051	+	0.249661i
$603$	5491.56	−	6886.20i	0.370868	−	0.465054i
$604$	11206.2	+	5396.61i	0.754922	+	0.363551i
$605$	−4915.26	−	21535.2i	−0.330304	−	1.44716i
$606$	19017.1			1.27478
$607$	−20896.4			−1.39730			−0.698648	−	0.715465i	$-0.746215\pi$
$607$	−20896.4			−1.39730			−0.698648	+	0.715465i	$0.746215\pi$
$608$	−6335.35	−	27757.0i	−0.422586	−	1.85147i
$609$	5302.56	−	9107.93i	0.352825	−	0.606030i
$610$	−530.557	+	2324.52i	−0.0352158	+	0.154290i
$611$	2529.04	−	11080.4i	0.167453	−	0.733661i
$612$	−5549.23	+	6958.51i	−0.366527	+	0.459610i
$613$	−2631.12	+	3299.33i	−0.173361	+	0.217387i	−0.860919	−	0.508741i	$-0.830111\pi$
$613$	−2631.12	+	3299.33i	−0.173361	+	0.217387i	0.687559	+	0.726129i	$0.258682\pi$
$614$	−4068.15	+	17823.7i	−0.267389	+	1.17151i
$615$	3007.30	−	13175.9i	0.197181	−	0.863905i
$616$	−32.4154	+	412.493i	−0.00212022	+	0.0269802i
$617$	55.6319	+	243.739i	0.00362991	+	0.0159037i	0.976710	−	0.214562i	$-0.0688323\pi$
$617$	55.6319	+	243.739i	0.00362991	+	0.0159037i	−0.973081	+	0.230465i	$0.925975\pi$
$618$	11679.5			0.760223
$619$	−10844.4			−0.704158			−0.352079	−	0.935970i	$-0.614525\pi$
$619$	−10844.4			−0.704158			−0.352079	+	0.935970i	$0.614525\pi$
$620$	5117.05	+	22419.2i	0.331461	+	1.45222i
$621$	−18747.3	−	9028.21i	−1.21144	−	0.583397i
$622$	2035.74	−	2552.74i	0.131231	−	0.164559i
$623$	20700.5	+	6467.48i	1.33122	+	0.415914i
$624$	−4207.31	−	5275.80i	−0.269916	−	0.338463i
$625$	−482.322	−	2113.19i	−0.0308686	−	0.135244i
$626$	−17560.2	−	22019.8i	−1.12116	−	1.40589i
$627$	3523.45	+	1696.80i	0.224423	+	0.108076i
$628$	14365.2	−	18013.4i	0.912795	−	1.14461i
$629$	−15714.3	+	7567.60i	−0.996136	+	0.479714i
$630$	−16963.1	−	15854.3i	−1.07274	−	1.00262i
$631$	11468.4	+	5522.89i	0.723533	+	0.348435i	0.759137	−	0.650931i	$-0.225621\pi$
$631$	11468.4	+	5522.89i	0.723533	+	0.348435i	−0.0356039	+	0.999366i	$0.511335\pi$
$632$	90.7036	−	43.6806i	0.00570886	−	0.00274924i
$633$	2300.52	−	10079.2i	0.144451	−	0.632881i
$634$	11044.3	−	5318.65i	0.691838	−	0.333171i
$635$	23407.1	+	29351.5i	1.46281	+	1.83430i
$636$	−5363.80			−0.334416
$637$	10884.4	+	1721.32i	0.677012	+	0.107066i
$638$	8046.35			0.499307
$639$	−7415.18	−	9298.34i	−0.459061	−	0.575644i
$640$	−4228.45	+	2036.32i	−0.261163	+	0.125769i
$641$	2189.18	−	9591.42i	0.134894	−	0.591011i	−0.861617	−	0.507559i	$-0.830548\pi$
$641$	2189.18	−	9591.42i	0.134894	−	0.591011i	0.996512	−	0.0834527i	$-0.0265948\pi$
$642$	17534.5	−	8444.19i	1.07793	−	0.519105i
$643$	14826.9	+	7140.27i	0.909357	+	0.437923i	0.829259	−	0.558864i	$-0.188763\pi$
$643$	14826.9	+	7140.27i	0.909357	+	0.437923i	0.0800975	+	0.996787i	$0.474477\pi$
$644$	−1644.15	+	20922.1i	−0.100603	+	1.28019i
$645$	4609.75	−	2219.94i	0.281409	−	0.135520i
$646$	−19009.9	+	23837.7i	−1.15780	+	1.45183i
$647$	7541.85	+	3631.96i	0.458270	+	0.220691i	0.648753	−	0.760999i	$-0.275291\pi$
$647$	7541.85	+	3631.96i	0.458270	+	0.220691i	−0.190483	+	0.981691i	$0.561005\pi$
$648$	55.2202	+	69.2440i	0.00334762	+	0.00419778i
$649$	−591.117	−	2589.85i	−0.0357525	−	0.156642i
$650$	16540.3	+	20740.9i	0.998099	+	1.25158i
$651$	−7031.25	−	6571.62i	−0.423313	−	0.395640i
$652$	−12946.6	+	16234.6i	−0.777652	+	0.975144i
$653$	−8722.42	−	4200.50i	−0.522718	−	0.251728i	0.153868	−	0.988091i	$-0.450827\pi$
$653$	−8722.42	−	4200.50i	−0.522718	−	0.251728i	−0.676586	+	0.736364i	$0.736541\pi$
$654$	3753.47	+	16445.0i	0.224423	+	0.983260i
$655$	−2899.61			−0.172972
$656$	16174.9			0.962687
$657$	2274.79	+	9966.50i	0.135081	+	0.591827i
$658$	−25511.5	+	3750.76i	−1.51146	+	0.222218i
$659$	−885.394	+	3879.17i	−0.0523370	+	0.229303i	−0.994331	−	0.106325i	$-0.966092\pi$
$659$	−885.394	+	3879.17i	−0.0523370	+	0.229303i	0.941994	+	0.335629i	$0.108949\pi$
$660$	−1050.82	+	4603.96i	−0.0619746	+	0.271528i
$661$	−14825.2	+	18590.2i	−0.872363	+	1.09391i	0.122479	+	0.992471i	$0.460916\pi$
$661$	−14825.2	+	18590.2i	−0.872363	+	1.09391i	−0.994842	+	0.101437i	$0.967656\pi$
$662$	20545.1	−	25762.7i	1.20620	−	1.51253i
$663$	−1511.27	+	6621.32i	−0.0885263	+	0.387859i
$664$	−249.830	+	1094.58i	−0.0146013	+	0.0639725i
$665$	−28098.2	−	26261.4i	−1.63850	−	1.53139i
$666$	−3895.72	−	17068.3i	−0.226661	−	0.993065i
$667$	−27799.9			−1.61382
$668$	−4443.61			−0.257378
$669$	−188.104	−	824.139i	−0.0108707	−	0.0476279i
$670$	32826.5	+	15808.4i	1.89283	+	0.911541i
$671$	229.682	−	288.013i	0.0132143	−	0.0165702i
$672$	−7239.35	+	12434.6i	−0.415571	+	0.713805i
$673$	−4229.13	−	5303.16i	−0.242230	−	0.303747i	0.645823	−	0.763487i	$-0.276514\pi$
$673$	−4229.13	−	5303.16i	−0.242230	−	0.303747i	−0.888054	+	0.459740i	$0.847943\pi$
$674$	4162.16	+	18235.6i	0.237864	+	1.04215i
$675$	17990.8	+	22559.7i	1.02587	+	1.28641i
$676$	7860.39	+	3785.36i	0.447223	+	0.215371i
$677$	−12457.1	+	15620.7i	−0.707188	+	0.886786i	−0.997538	−	0.0701349i	$-0.977657\pi$
$677$	−12457.1	+	15620.7i	−0.707188	+	0.886786i	0.290349	+	0.956921i	$0.406228\pi$
$678$	−23139.5	+	11143.4i	−1.31072	+	0.631210i
$679$	−37.2756	−	95.9979i	−0.00210678	−	0.00542572i
$680$	2259.53	+	1088.13i	0.127425	+	0.0613645i
$681$	10150.9	−	4888.44i	0.571197	−	0.275074i
$682$	1635.05	−	7163.63i	0.0918027	−	0.402214i
$683$	−6358.43	+	3062.06i	−0.356221	+	0.171547i	−0.603431	−	0.797415i	$-0.706200\pi$
$683$	−6358.43	+	3062.06i	−0.356221	+	0.171547i	0.247211	+	0.968962i	$0.420486\pi$
$684$	−9226.51	−	11569.7i	−0.515767	−	0.646751i
$685$	1298.00			0.0723998
$686$	−5298.07	−	24433.6i	−0.294870	−	1.35988i
$687$	2644.26			0.146848
$688$	3817.96	+	4787.57i	0.211568	+	0.265297i
$689$	6693.47	−	3223.40i	0.370103	−	0.178232i
$690$	7508.42	−	32896.5i	0.414262	−	1.81500i
$691$	−8184.85	+	3941.61i	−0.450602	+	0.216999i	−0.645400	−	0.763845i	$-0.723309\pi$
$691$	−8184.85	+	3941.61i	−0.450602	+	0.216999i	0.194798	+	0.980843i	$0.437595\pi$
$692$	10949.0	+	5272.76i	0.601472	+	0.289654i
$693$	1298.50	+	3344.10i	0.0711774	+	0.183307i
$694$	−20932.2	+	10080.4i	−1.14492	+	0.551366i
$695$	−15681.3	+	19663.7i	−0.855864	+	1.07322i
$696$	−1029.47	−	495.767i	−0.0560660	−	0.0270000i
$697$	−10150.0	−	12727.7i	−0.551591	−	0.691673i
$698$	391.367	+	1714.69i	0.0212227	+	0.0929828i
$699$	12035.6	+	15092.2i	0.651256	+	0.816649i
$700$	14642.6	−	25150.8i	0.790626	−	1.35802i
$701$	9731.08	−	12202.4i	0.524305	−	0.657458i	−0.447212	−	0.894428i	$-0.647583\pi$
$701$	9731.08	−	12202.4i	0.524305	−	0.657458i	0.971517	+	0.236970i	$0.0761545\pi$
$702$	−15668.0	−	7545.30i	−0.842378	−	0.405668i
$703$	−6452.98	−	28272.4i	−0.346200	−	1.51680i
$704$	−4948.45			−0.264917
$705$	20046.6			1.07092
$706$	6727.26	+	29474.1i	0.358617	+	1.57121i
$707$	21110.7	+	19730.7i	1.12298	+	1.04957i
$708$	1232.32	−	5399.14i	0.0654144	−	0.286599i
$709$	3164.80	−	13865.9i	0.167640	−	0.734479i	−0.819297	−	0.573370i	$-0.805636\pi$
$709$	3164.80	−	13865.9i	0.167640	−	0.734479i	0.986937	−	0.161109i	$-0.0515070\pi$
$710$	30674.0	−	38464.0i	1.62137	−	2.03314i
$711$	544.208	−	682.416i	0.0287052	−	0.0359952i
$712$	523.213	−	2292.35i	0.0275397	−	0.120659i
$713$	−5649.05	+	24750.1i	−0.296716	+	1.30000i
$714$	15244.8	−	2241.33i	0.799053	−	0.117479i
$715$	−1455.45	−	6376.76i	−0.0761272	−	0.333535i
$716$	15170.3			0.791819
$717$	−13542.3			−0.705363
$718$	8237.63	+	36091.4i	0.428169	+	1.87593i
$719$	2102.48	+	1012.50i	0.109053	+	0.0525173i	0.487615	−	0.873059i	$-0.337867\pi$
$719$	2102.48	+	1012.50i	0.109053	+	0.0525173i	−0.378562	+	0.925576i	$0.623581\pi$
$720$	−13469.8	+	16890.6i	−0.697208	+	0.874272i
$721$	12965.3	+	12117.7i	0.669698	+	0.625920i
$722$	−14776.0	−	18528.6i	−0.761645	−	0.955072i
$723$	258.396	+	1132.11i	0.0132916	+	0.0582345i
$724$	−12916.4	−	16196.7i	−0.663033	−	0.831417i
$725$	34733.2	+	16726.6i	1.77925	+	0.856844i
$726$	−9174.18	+	11504.1i	−0.468989	+	0.588093i
$727$	19463.0	−	9372.87i	0.992904	−	0.478158i	0.134380	−	0.990930i	$-0.457096\pi$
$727$	19463.0	−	9372.87i	0.992904	−	0.478158i	0.858525	+	0.512772i	$0.171381\pi$
$728$	93.5988	−	1191.06i	0.00476512	−	0.0606371i
$729$	−9669.44	−	4656.56i	−0.491259	−	0.236578i
$730$	−38100.3	+	18348.1i	−1.93172	+	0.930268i
$731$	1371.42	−	6008.57i	0.0693895	−	0.304015i
$732$	691.923	−	333.213i	0.0349375	−	0.0168250i
$733$	−20687.2	−	25940.9i	−1.04243	−	1.30716i	−0.950274	−	0.311416i	$-0.899197\pi$
$733$	−20687.2	−	25940.9i	−1.04243	−	1.30716i	−0.0921522	−	0.995745i	$-0.529375\pi$
$734$	1752.31			0.0881183
$735$	1312.02	+	19392.5i	0.0658432	+	0.973201i
$736$	37953.9			1.90082
$737$	−3509.80	−	4401.14i	−0.175421	−	0.219970i
$738$	14722.4	−	7089.94i	0.734335	−	0.353637i
$739$	4355.52	−	19082.8i	0.216807	−	0.949894i	−0.743013	−	0.669277i	$-0.766604\pi$
$739$	4355.52	−	19082.8i	0.216807	−	0.949894i	0.959820	−	0.280617i	$-0.0905390\pi$
$740$	31550.0	−	15193.7i	1.56730	−	0.754772i
$741$	−10173.9	−	4899.48i	−0.504382	−	0.242897i
$742$	−12314.2	−	11509.2i	−0.609256	−	0.569429i
$743$	−25084.8	+	12080.2i	−1.23859	+	0.596473i	−0.934430	−	0.356148i	$-0.884090\pi$
$743$	−25084.8	+	12080.2i	−1.23859	+	0.596473i	−0.304159	+	0.952621i	$0.598376\pi$
$744$	−650.572	+	815.791i	−0.0320580	+	0.0401994i
$745$	5759.49	+	2773.62i	0.283237	+	0.136400i
$746$	−23423.0	−	29371.5i	−1.14957	−	1.44151i
$747$	2166.03	+	9490.01i	0.106092	+	0.464821i
$748$	3546.65	+	4447.36i	0.173367	+	0.217395i
$749$	28226.0	+	8818.68i	1.37698	+	0.430210i
$750$	−11792.5	+	14787.3i	−0.574134	+	0.719941i
$751$	26681.1	+	12848.9i	1.29641	+	0.624320i	0.949556	−	0.313598i	$-0.101534\pi$
$751$	26681.1	+	12848.9i	1.29641	+	0.624320i	0.346858	+	0.937918i	$0.387249\pi$
$752$	5338.82	+	23390.9i	0.258892	+	1.13428i
$753$	16033.3			0.775943
$754$	−23233.7			−1.12218
$755$	−6761.51	−	29624.1i	−0.325929	−	1.42799i
$756$	−1494.59	+	19018.9i	−0.0719016	+	0.914962i
$757$	−1640.42	+	7187.15i	−0.0787610	+	0.345074i	−0.998920	−	0.0464714i	$-0.985202\pi$
$757$	−1640.42	+	7187.15i	−0.0787610	+	0.345074i	0.920159	+	0.391546i	$0.128060\pi$
$758$	281.422	−	1232.99i	0.0134851	−	0.0590821i
$759$	−3250.46	+	4075.94i	−0.155447	+	0.194924i
$760$	−2599.81	+	3260.06i	−0.124086	+	0.155598i
$761$	−5363.05	+	23497.0i	−0.255467	+	1.11927i	0.670572	+	0.741845i	$0.266049\pi$
$761$	−5363.05	+	23497.0i	−0.255467	+	1.11927i	−0.926039	+	0.377429i	$0.876808\pi$
$762$	5564.82	−	24381.0i	0.264556	−	1.15910i
$763$	−12895.4	+	22149.8i	−0.611855	+	1.05095i
$764$	−1627.36	−	7129.92i	−0.0770625	−	0.337633i
$765$	21743.4			1.02763
$766$	−17411.4			−0.821281
$767$	1706.84	+	7478.15i	0.0803525	+	0.352047i
$768$	12744.4	+	6137.38i	0.598794	+	0.288364i
$769$	21351.9	−	26774.4i	1.00126	−	1.25554i	0.0346181	−	0.999401i	$-0.488979\pi$
$769$	21351.9	−	26774.4i	1.00126	−	1.25554i	0.966640	−	0.256138i	$-0.0824501\pi$
$770$	−12291.3	+	8314.98i	−0.575256	+	0.389157i
$771$	−4980.89	−	6245.84i	−0.232662	−	0.291749i
$772$	−7630.74	−	33432.5i	−0.355746	−	1.55863i
$773$	−13260.6	−	16628.2i	−0.617011	−	0.773707i	0.370910	−	0.928669i	$-0.379046\pi$
$773$	−13260.6	−	16628.2i	−0.617011	−	0.773707i	−0.987920	+	0.154962i	$0.950475\pi$
$774$	5573.66	+	2684.13i	0.258839	+	0.124650i
$775$	21949.6	−	27523.9i	1.01736	−	1.27573i
$776$	−10.0593	+	4.84432i	−0.000465347	+	0.000224099i
$777$	−7373.76	+	12665.5i	−0.340453	+	0.584779i
$778$	−33749.1	−	16252.7i	−1.55522	−	0.748956i
$779$	24386.6	−	11744.0i	1.12162	−	0.540143i
$780$	3034.23	−	13293.8i	0.139286	−	0.610250i
$781$	−6848.38	+	3298.01i	−0.313770	+	0.151104i
$782$	−25341.8	−	31777.6i	−1.15885	−	1.45315i
$783$	−25271.1			−1.15340
$784$	−22278.3	+	6695.53i	−1.01486	+	0.305008i
$785$	−56287.0			−2.55920
$786$	1204.29	+	1510.13i	0.0546508	+	0.0685299i
$787$	−1597.65	+	769.387i	−0.0723634	+	0.0348484i	−0.469715	−	0.882818i	$-0.655643\pi$
$787$	−1597.65	+	769.387i	−0.0723634	+	0.0348484i	0.397352	+	0.917666i	$0.369929\pi$
$788$	−1809.85	+	7929.49i	−0.0818190	+	0.358473i
$789$	−11128.2	+	5359.07i	−0.502123	+	0.241810i
$790$	3253.08	+	1566.60i	0.146505	+	0.0705533i
$791$	−37248.5	−	11637.6i	−1.67434	−	0.523117i
$792$	350.418	−	168.752i	0.0157217	−	0.00757116i
$793$	−663.203	+	831.630i	−0.0296987	+	0.0372409i
$794$	−5265.08	−	2535.53i	−0.235328	−	0.113328i
$795$	8170.08	+	10245.0i	0.364482	+	0.457046i
$796$	4436.62	+	19438.1i	0.197552	+	0.865534i
$797$	2789.25	+	3497.60i	0.123965	+	0.155447i	0.839941	−	0.542678i	$-0.182589\pi$
$797$	2789.25	+	3497.60i	0.123965	+	0.155447i	−0.715976	+	0.698125i	$0.754018\pi$
$798$	−2007.11	+	25540.8i	−0.0890360	+	1.13300i
$799$	15055.7	−	18879.2i	0.666623	−	0.835919i
$800$	−47419.7	−	22836.1i	−2.09568	−	1.00922i
$801$	−4536.28	−	19874.7i	−0.200102	−	0.876703i
$802$	−24349.6			−1.07209
$803$	6533.66			0.287133
$804$	−2611.40	−	11441.3i	−0.114548	−	0.501869i
$805$	42466.0	−	28728.0i	1.85929	−	1.25780i
$806$	−4721.18	+	20684.8i	−0.206323	+	0.903961i
$807$	2168.59	−	9501.21i	0.0945948	−	0.414447i
$808$	1953.28	−	2449.34i	0.0850447	−	0.106643i
$809$	−9511.70	+	11927.3i	−0.413367	+	0.518345i	−0.944308	−	0.329063i	$-0.893267\pi$
$809$	−9511.70	+	11927.3i	−0.413367	+	0.518345i	0.530941	+	0.847409i	$0.321838\pi$
$810$	−706.821	+	3096.78i	−0.0306607	+	0.134333i
$811$	1092.98	−	4788.65i	0.0473238	−	0.207339i	−0.945738	−	0.324929i	$-0.894660\pi$
$811$	1092.98	−	4788.65i	0.0473238	−	0.207339i	0.993062	+	0.117590i	$0.0375168\pi$
$812$	9225.83	+	23759.8i	0.398723	+	1.02685i
$813$	1458.18	+	6388.70i	0.0629035	+	0.275598i
$814$	−11189.3			−0.481799
$815$	50728.5			2.18030
$816$	−3190.31	−	13977.7i	−0.136867	−	0.599652i
$817$	9232.37	+	4446.08i	0.395349	+	0.190390i
$818$	−26349.6	+	33041.4i	−1.12627	+	1.41230i
$819$	−3749.39	−	9656.02i	−0.159969	−	0.411976i
$820$	20378.5	+	25553.8i	0.867863	+	1.08827i
$821$	−5071.74	−	22220.8i	−0.215597	−	0.944592i	−0.960688	−	0.277629i	$-0.910451\pi$
$821$	−5071.74	−	22220.8i	−0.215597	−	0.944592i	0.745091	−	0.666962i	$-0.232406\pi$
$822$	−539.094	−	676.003i	−0.0228748	−	0.0286841i
$823$	−15639.6	−	7531.61i	−0.662406	−	0.318998i	0.0723004	−	0.997383i	$-0.476966\pi$
$823$	−15639.6	−	7531.61i	−0.662406	−	0.318998i	−0.734707	+	0.678385i	$0.762680\pi$
$824$	1199.62	−	1504.28i	0.0507171	−	0.0635972i
$825$	6513.54	−	3136.76i	0.274876	−	0.132373i
$826$	14414.2	−	9751.12i	0.607184	−	0.410757i
$827$	31144.4	+	14998.4i	1.30955	+	0.630646i	0.952813	−	0.303559i	$-0.0981750\pi$
$827$	31144.4	+	14998.4i	1.30955	+	0.630646i	0.356737	+	0.934205i	$0.383889\pi$
$828$	17773.6	−	8559.31i	0.745984	−	0.359247i
$829$	126.404	−	553.812i	0.00529577	−	0.0232023i	−0.972211	−	0.234106i	$-0.924784\pi$
$829$	126.404	−	553.812i	0.00529577	−	0.0232023i	0.977507	+	0.210904i	$0.0676408\pi$
$830$	−36278.8	+	17470.9i	−1.51717	+	0.730632i
$831$	6132.62	+	7690.06i	0.256003	+	0.321017i
$832$	14288.6			0.595392
$833$	19248.6	+	13328.8i	0.800629	+	0.554401i
$834$	16753.8			0.695609
$835$	6768.46	+	8487.38i	0.280518	+	0.351758i
$836$	−8521.26	+	4103.62i	−0.352529	+	0.169769i
$837$	−5135.19	+	22498.8i	−0.212065	+	0.929117i
$838$	17446.6	−	8401.85i	0.719192	−	0.346345i
$839$	−25272.9	−	12170.8i	−1.03995	−	0.500814i	−0.165643	−	0.986186i	$-0.552970\pi$
$839$	−25272.9	−	12170.8i	−1.03995	−	0.500814i	−0.874308	+	0.485372i	$0.838684\pi$
$840$	2084.89	−	306.526i	0.0856377	−	0.0125906i
$841$	−8445.53	+	4067.15i	−0.346284	+	0.166762i
$842$	28965.4	−	36321.5i	1.18553	−	1.48661i
$843$	4237.71	+	2040.77i	0.173137	+	0.0833783i
$844$	15589.1	+	19548.1i	0.635780	+	0.797243i
$845$	−4742.75	−	20779.3i	−0.193083	−	0.845954i
$846$	15112.4	+	18950.3i	0.614154	+	0.770124i
$847$	−22119.9	+	3252.12i	−0.897342	+	0.131929i
$848$	−9778.24	+	12261.5i	−0.395974	+	0.496536i
$849$	4238.14	+	2040.98i	0.171322	+	0.0825044i
$850$	12542.1	+	54950.7i	0.506108	+	2.21740i
$851$	38658.6			1.55723
$852$	−15846.3			−0.637189
$853$	1834.18	+	8036.05i	0.0736237	+	0.322566i	0.998307	−	0.0581717i	$-0.0185271\pi$
$853$	1834.18	+	8036.05i	0.0736237	+	0.322566i	−0.924683	+	0.380738i	$0.875670\pi$
$854$	2303.50	+	719.685i	0.0922998	+	0.0288374i
$855$	−8044.59	+	35245.7i	−0.321777	+	1.40980i
$856$	713.423	−	3125.71i	0.0284863	−	0.124807i
$857$	−13580.3	+	17029.1i	−0.541298	+	0.678766i	−0.974978	−	0.222301i	$-0.928643\pi$
$857$	−13580.3	+	17029.1i	−0.541298	+	0.678766i	0.433680	+	0.901067i	$0.357215\pi$
$858$	−2716.56	+	3406.46i	−0.108091	+	0.135541i
$859$	10403.1	−	45579.0i	0.413212	−	1.81040i	−0.155466	−	0.987841i	$-0.549688\pi$
$859$	10403.1	−	45579.0i	0.413212	−	1.81040i	0.568678	−	0.822560i	$-0.307455\pi$
$860$	−2753.44	+	12063.6i	−0.109176	+	0.478332i
$861$	−13056.7	−	4079.32i	−0.516806	−	0.161467i
$862$	2541.48	+	11135.0i	0.100421	+	0.439975i
$863$	−20805.6			−0.820663			−0.410331	−	0.911936i	$-0.634587\pi$
$863$	−20805.6			−0.820663			−0.410331	+	0.911936i	$0.634587\pi$
$864$	34501.5			1.35852
$865$	−6606.34	−	28944.3i	−0.259679	−	1.13773i
$866$	1412.49	+	680.217i	0.0554252	+	0.0266914i
$867$	489.819	−	614.213i	0.0191870	−	0.0240597i
$868$	23028.0	−	3385.62i	0.900484	−	0.132391i
$869$	−347.817	−	436.149i	−0.0135776	−	0.0170257i
$870$	−9118.94	−	39952.7i	−0.355357	−	1.55692i
$871$	10134.5	+	12708.2i	0.394251	+	0.494376i
$872$	2503.59	+	1205.67i	0.0972275	+	0.0468223i
$873$	−60.3545	+	75.6821i	−0.00233985	+	0.00293408i
$874$	60886.8	−	29321.5i	2.35644	−	1.13480i
$875$	−28432.9	+	4180.27i	−1.09852	+	0.161507i
$876$	12272.0	+	5909.89i	0.473325	+	0.227941i
$877$	−3160.56	+	1522.05i	−0.121693	+	0.0586042i	−0.493740	−	0.869610i	$-0.664370\pi$
$877$	−3160.56	+	1522.05i	−0.121693	+	0.0586042i	0.372047	+	0.928214i	$0.378656\pi$
$878$	−4359.31	+	19099.4i	−0.167562	+	0.734137i
$879$	−17880.8	+	8610.94i	−0.686126	+	0.330421i
$880$	8608.89	+	10795.2i	0.329779	+	0.413530i
$881$	29531.8			1.12934			0.564671	−	0.825316i	$-0.309003\pi$
$881$	29531.8			1.12934			0.564671	+	0.825316i	$0.309003\pi$
$882$	−17342.9	+	15859.5i	−0.662092	+	0.605463i
$883$	−41514.5			−1.58219			−0.791096	−	0.611692i	$-0.790489\pi$
$883$	−41514.5			−1.58219			−0.791096	+	0.611692i	$0.790489\pi$
$884$	−10240.9	−	12841.7i	−0.389636	−	0.488588i
$885$	−12189.5	+	5870.17i	−0.462990	+	0.222964i
$886$	−1928.10	+	8447.57i	−0.0731105	+	0.320318i
$887$	−33209.6	+	15992.9i	−1.25713	+	0.605400i	−0.939413	−	0.342787i	$-0.888629\pi$
$887$	−33209.6	+	15992.9i	−1.25713	+	0.605400i	−0.317713	+	0.948187i	$0.602915\pi$
$888$	1431.59	+	689.415i	0.0541001	+	0.0260532i
$889$	31473.4	−	21291.5i	1.18738	−	0.803257i
$890$	75977.9	−	36589.0i	2.86155	−	1.37805i
$891$	305.988	−	383.697i	0.0115050	−	0.0144269i
$892$	1841.93	+	887.028i	0.0691395	+	0.0332958i
$893$	25032.6	+	31389.8i	0.938055	+	1.17628i
$894$	−947.560	−	4151.53i	−0.0354487	−	0.155311i
$895$	−23107.3	−	28975.7i	−0.863009	−	1.08218i
$896$	1719.45	+	4428.21i	0.0641104	+	0.165107i
$897$	9385.62	−	11769.2i	0.349361	−	0.438085i
$898$	64941.0	+	31273.9i	2.41326	+	1.16216i
$899$	6860.75	+	30058.9i	0.254526	+	1.11515i
$900$	−27356.3			−1.01320
$901$	15784.4			0.583634
$902$	−2323.95	−	10181.9i	−0.0857859	−	0.375853i
$903$	−1874.51	−	4827.52i	−0.0690804	−	0.177907i
$904$	−941.472	+	4124.86i	−0.0346381	+	0.151760i
$905$	−11261.8	+	49341.3i	−0.413653	+	1.81233i
$906$	−12620.1	+	15825.1i	−0.462777	+	0.580304i
$907$	−10866.3	+	13625.9i	−0.397806	+	0.498833i	−0.939883	−	0.341496i	$-0.889067\pi$
$907$	−10866.3	+	13625.9i	−0.397806	+	0.498833i	0.542077	+	0.840329i	$0.317638\pi$
$908$	−6063.23	+	26564.7i	−0.221603	+	0.970905i
$909$	6044.03	−	26480.6i	0.220537	−	0.966235i
$910$	35490.8	−	24009.3i	1.29287	−	0.874616i
$911$	3336.65	+	14618.8i	0.121348	+	0.531660i	0.998661	+	0.0517408i	$0.0164770\pi$
$911$	3336.65	+	14618.8i	0.121348	+	0.531660i	−0.877313	+	0.479919i	$0.840666\pi$
$912$	23837.8			0.865515
$913$	6221.28			0.225514
$914$	−7661.21	−	33566.0i	−0.277254	−	1.21473i
$915$	−1690.37	−	814.041i	−0.0610733	−	0.0294113i
$916$	−3987.21	+	4999.80i	−0.143822	+	0.180347i
$917$	−229.926	+	2925.86i	−0.00828008	+	0.105366i
$918$	−23036.6	−	28887.0i	−0.828237	−	1.03858i
$919$	−5500.53	−	24099.4i	−0.197438	−	0.865034i	−0.972455	−	0.233093i	$-0.925115\pi$
$919$	−5500.53	−	24099.4i	−0.197438	−	0.865034i	0.775016	−	0.631941i	$-0.217742\pi$
$920$	−3465.76	−	4345.93i	−0.124199	−	0.155740i
$921$	−12961.3	−	6241.82i	−0.463722	−	0.223317i
$922$	−22840.3	+	28640.9i	−0.815842	+	1.02303i
$923$	19774.6	−	9522.93i	0.705187	−	0.339600i
$924$	4562.31	+	1425.41i	0.162434	+	0.0507495i
$925$	−48300.2	−	23260.1i	−1.71686	−	0.826799i
$926$	−50441.5	+	24291.4i	−1.79008	+	0.862055i
$927$	3711.99	−	16263.3i	0.131519	−	0.576221i
$928$	41530.0	−	19999.8i	1.46906	−	0.707464i
$929$	−25722.1	−	32254.5i	−0.908412	−	1.13911i	−0.989805	−	0.142431i	$-0.954508\pi$
$929$	−25722.1	−	32254.5i	−0.908412	−	1.13911i	0.0813926	−	0.996682i	$-0.474063\pi$
$930$	−37422.7			−1.31950
$931$	−28727.3	+	26270.2i	−1.01128	+	0.924781i
$932$	−46684.7			−1.64078
$933$	1601.90	+	2008.72i	0.0562099	+	0.0704849i
$934$	20866.2	−	10048.7i	0.731011	−	0.352036i
$935$	3092.32	−	13548.4i	0.108160	−	0.473881i
$936$	−1011.82	+	487.269i	−0.0353339	+	0.0170159i
$937$	27273.8	+	13134.4i	0.950902	+	0.457930i	0.844002	−	0.536339i	$-0.180193\pi$
$937$	27273.8	+	13134.4i	0.950902	+	0.457930i	0.106900	+	0.994270i	$0.465908\pi$
$938$	18554.5	−	31870.2i	0.645871	−	1.10938i
$939$	19967.4	−	9615.80i	0.693942	−	0.334185i
$940$	−30227.8	+	37904.4i	−1.04885	+	1.31522i
$941$	−44612.0	−	21484.0i	−1.54550	−	0.744271i	−0.549655	−	0.835392i	$-0.685241\pi$
$941$	−44612.0	−	21484.0i	−1.54550	−	0.744271i	−0.995840	+	0.0911203i	$0.970955\pi$
$942$	23377.6	+	29314.6i	0.808580	+	1.01393i
$943$	8029.15	+	35178.0i	0.277270	+	1.21480i
$944$	−10095.8	−	12659.7i	−0.348083	−	0.436482i
$945$	38603.1	−	26114.8i	1.32884	−	0.898956i
$946$	2465.17	−	3091.22i	0.0847246	−	0.106241i
$947$	43942.3	+	21161.5i	1.50785	+	0.726142i	0.991484	−	0.130226i	$-0.0415701\pi$
$947$	43942.3	+	21161.5i	1.50785	+	0.726142i	0.516366	+	0.856368i	$0.327284\pi$
$948$	−258.787	−	1133.82i	−0.00886604	−	0.0388447i
$949$	−18865.8			−0.645321
$950$	−93714.3			−3.20052
$951$	2146.40	+	9404.00i	0.0731881	+	0.320658i
$952$	1277.15	−	2193.70i	0.0434798	−	0.0746829i
$953$	9644.32	−	42254.5i	0.327818	−	1.43626i	−0.495463	−	0.868629i	$-0.665002\pi$
$953$	9644.32	−	42254.5i	0.327818	−	1.43626i	0.823281	−	0.567634i	$-0.192141\pi$
$954$	−3525.58	+	15446.6i	−0.119649	+	0.524215i
$955$	−11139.5	+	13968.5i	−0.377452	+	0.473310i
$956$	20420.1	−	25606.0i	0.690829	−	0.866272i
$957$	−1408.91	+	6172.82i	−0.0475898	+	0.208505i
$958$	10938.3	−	47923.7i	0.368893	−	1.61623i
$959$	102.926	−	1309.75i	0.00346573	−	0.0441021i
$960$	5608.09	+	24570.6i	0.188542	+	0.826056i
$961$	−1635.54			−0.0549006
$962$	32308.8			1.08283
$963$	−6185.40	−	27100.0i	−0.206980	−	0.906839i
$964$	−2530.24	−	1218.50i	−0.0845368	−	0.0407108i
$965$	−52233.6	+	65498.9i	−1.74244	+	2.18496i
$966$	−32599.0	−	10184.9i	−1.08577	−	0.339229i
$967$	−397.038	−	497.870i	−0.0132036	−	0.0165568i	0.775186	−	0.631733i	$-0.217656\pi$
$967$	−397.038	−	497.870i	−0.0132036	−	0.0165568i	−0.788389	+	0.615176i	$0.789085\pi$
$968$	539.387	+	2363.21i	0.0179097	+	0.0784674i
$969$	−14958.7	−	18757.6i	−0.495915	−	0.621857i
$970$	−360.777	−	173.741i	−0.0119421	−	0.00575102i
$971$	−12322.6	+	15452.0i	−0.407261	+	0.510689i	−0.942589	−	0.333956i	$-0.891616\pi$
$971$	−12322.6	+	15452.0i	−0.407261	+	0.510689i	0.535328	+	0.844644i	$0.320188\pi$
$972$	25980.0	−	12511.3i	0.857313	−	0.412860i
$973$	18598.3	+	17382.5i	0.612778	+	0.572721i
$974$	28970.7	+	13951.5i	0.953060	+	0.458970i
$975$	−18807.7	+	9057.32i	−0.617773	+	0.297504i
$976$	499.664	−	2189.17i	0.0163872	−	0.0717968i
$977$	−36922.2	+	17780.8i	−1.20905	+	0.582250i	−0.926243	−	0.376926i	$-0.876981\pi$
$977$	−36922.2	+	17780.8i	−1.20905	+	0.582250i	−0.282811	+	0.959176i	$0.591267\pi$
$978$	−21069.0	−	26419.7i	−0.688867	−	0.863811i
$979$	−13029.1			−0.425344
$980$	−38646.0	−	26760.7i	−1.25969	−	0.872284i
$981$	24092.1			0.784100
$982$	−14463.3	−	18136.4i	−0.470002	−	0.589364i
$983$	−8376.16	+	4033.75i	−0.271778	+	0.130882i	−0.564809	−	0.825221i	$-0.691050\pi$
$983$	−8376.16	+	4033.75i	−0.271778	+	0.130882i	0.293031	+	0.956103i	$0.405336\pi$
$984$	−330.013	+	1445.88i	−0.0106915	+	0.0468425i
$985$	17902.2	−	8621.26i	0.579099	−	0.278880i
$986$	−44474.8	−	21417.9i	−1.43648	−	0.691771i
$987$	1589.61	−	20228.1i	0.0512642	−	0.652347i
$988$	24605.0	−	11849.1i	0.792296	−	0.381550i
$989$	−8517.06	+	10680.1i	−0.273839	+	0.343383i
$990$	12567.7	+	6052.29i	0.403463	+	0.194297i
$991$	4099.74	+	5140.91i	0.131415	+	0.164789i	0.843185	−	0.537623i	$-0.180678\pi$
$991$	4099.74	+	5140.91i	0.131415	+	0.164789i	−0.711770	+	0.702412i	$0.752106\pi$
$992$	−9366.67	−	41038.1i	−0.299791	−	1.31347i
$993$	16166.6	+	20272.3i	0.516649	+	0.647858i
$994$	−36379.9	−	34001.7i	−1.16087	−	1.08498i
$995$	30369.3	−	38082.0i	0.967611	−	1.21335i
$996$	11685.3	+	5627.34i	0.371749	+	0.179025i
$997$	1197.28	+	5245.61i	0.0380322	+	0.166630i	0.990378	−	0.138392i	$-0.0441933\pi$
$997$	1197.28	+	5245.61i	0.0380322	+	0.166630i	−0.952345	+	0.305022i	$0.901336\pi$
$998$	−27900.8			−0.884954
$999$	35142.1			1.11296

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.4.e.a.8.3	✓	78
49.22	even	7		2401.4.a.d.1.7		39
49.27	odd	14		2401.4.a.c.1.7		39
49.43	even	7	inner	49.4.e.a.43.3	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.8.3	✓	78	1.1	even	1	trivial
49.4.e.a.43.3	yes	78	49.43	even	7	inner
2401.4.a.c.1.7		39	49.27	odd	14
2401.4.a.d.1.7		39	49.22	even	7

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.45388 - 3.07706i) q^{2} +(2.79026 - 1.34372i) q^{3} +(-1.66664 + 7.30203i) q^{4} +(16.4856 - 7.93907i) q^{5} +(-10.9817 - 5.28849i) q^{6} +(-6.70370 - 17.2644i) q^{7} +(-1.80909 + 0.871210i) q^{8} +(-10.8543 + 13.6108i) q^{9} +(-64.8827 - 31.2459i) q^{10} +(6.93723 + 8.69901i) q^{11} +(5.16151 + 22.6141i) q^{12} +(-20.0311 - 25.1182i) q^{13} +(-36.6737 + 62.9925i) q^{14} +(35.3314 - 44.3041i) q^{15} +(61.1048 + 29.4265i) q^{16} +(-15.1891 - 66.5479i) q^{17} +68.5163 q^{18} +113.492 q^{19} +(30.4957 + 133.610i) q^{20} +(-41.9036 - 39.1644i) q^{21} +(9.74430 - 42.6926i) q^{22} +(-33.6662 + 147.501i) q^{23} +(-3.87716 + 4.86181i) q^{24} +(130.811 - 164.032i) q^{25} +(-28.1364 + 123.274i) q^{26} +(-30.6038 + 134.084i) q^{27} +(137.238 - 20.1770i) q^{28} +(40.8875 + 179.140i) q^{29} -223.025 q^{30} +167.796 q^{31} +(-55.8218 - 244.571i) q^{32} +(31.0457 + 14.9508i) q^{33} +(-167.500 + 210.038i) q^{34} +(-247.578 - 231.394i) q^{35} +(-81.2964 - 101.942i) q^{36} +(-56.8583 - 249.112i) q^{37} +(-278.496 - 349.223i) q^{38} +(-89.6437 - 43.1701i) q^{39} +(-22.9074 + 28.7249i) q^{40} +(214.875 - 103.478i) q^{41} +(-17.6849 + 225.044i) q^{42} +(81.3480 + 39.1751i) q^{43} +(-75.0823 + 36.1577i) q^{44} +(-70.8822 + 310.555i) q^{45} +(536.484 - 258.357i) q^{46} +(220.566 + 276.581i) q^{47} +210.039 q^{48} +(-253.121 + 231.471i) q^{49} -825.732 q^{50} +(-131.803 - 165.276i) q^{51} +(216.798 - 104.405i) q^{52} +(-51.4561 + 225.444i) q^{53} +(487.683 - 234.856i) q^{54} +(183.427 + 88.3336i) q^{55} +(27.1685 + 25.3925i) q^{56} +(316.673 - 152.502i) q^{57} +(450.891 - 565.400i) q^{58} +(-215.108 - 103.590i) q^{59} +(264.625 + 331.830i) q^{60} +(-7.36738 - 32.2786i) q^{61} +(-411.750 - 516.318i) q^{62} +(307.746 + 96.1497i) q^{63} +(-277.295 + 347.717i) q^{64} +(-529.640 - 255.061i) q^{65} +(-30.1777 - 132.217i) q^{66} -505.936 q^{67} +511.249 q^{68} +(104.263 + 456.805i) q^{69} +(-104.488 + 1329.63i) q^{70} +(-152.017 + 666.031i) q^{71} +(7.77842 - 34.0795i) q^{72} +(366.125 - 459.106i) q^{73} +(-627.011 + 786.247i) q^{74} +(144.585 - 633.466i) q^{75} +(-189.151 + 828.725i) q^{76} +(103.678 - 178.083i) q^{77} +(87.1373 + 381.774i) q^{78} -50.1378 q^{79} +1240.97 q^{80} +(-9.81499 - 43.0023i) q^{81} +(-845.684 - 407.260i) q^{82} +(348.620 - 437.156i) q^{83} +(355.818 - 240.708i) q^{84} +(-778.730 - 976.497i) q^{85} +(-79.0735 - 346.444i) q^{86} +(354.800 + 444.905i) q^{87} +(-20.1287 - 9.69348i) q^{88} +(-730.109 + 915.527i) q^{89} +(1129.53 - 543.955i) q^{90} +(-299.369 + 514.210i) q^{91} +(-1020.95 - 491.664i) q^{92} +(468.194 - 225.470i) q^{93} +(309.816 - 1357.39i) q^{94} +(1870.99 - 901.023i) q^{95} +(-484.393 - 607.409i) q^{96} +5.56045 q^{97} +(1333.38 + 210.867i) q^{98} -193.699 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19}+ \cdots + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

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