LMFDB - Embedded newform 35.5.i.a.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(19,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("35.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	35.19
Dual form			35.5.i.a.24.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.575938 - 0.332518i) q^{2} +(2.14828 + 3.72093i) q^{3} +(-7.77886 - 13.4734i) q^{4} +(-2.48237 - 24.8765i) q^{5} -2.85737i q^{6} +(47.2932 - 12.8202i) q^{7} +20.9870i q^{8} +(31.2698 - 54.1608i) q^{9} +O(q^{10})$	\(q+(-0.575938 - 0.332518i) q^{2} +(2.14828 + 3.72093i) q^{3} +(-7.77886 - 13.4734i) q^{4} +(-2.48237 - 24.8765i) q^{5} -2.85737i q^{6} +(47.2932 - 12.8202i) q^{7} +20.9870i q^{8} +(31.2698 - 54.1608i) q^{9} +(-6.84217 + 15.1527i) q^{10} +(-47.5799 - 82.4108i) q^{11} +(33.4224 - 57.8893i) q^{12} -113.514 q^{13} +(-31.5009 - 8.34220i) q^{14} +(87.2308 - 62.6784i) q^{15} +(-117.483 + 203.487i) q^{16} +(105.857 + 183.350i) q^{17} +(-36.0189 + 20.7955i) q^{18} +(287.370 + 165.913i) q^{19} +(-315.860 + 226.957i) q^{20} +(149.302 + 148.433i) q^{21} +63.2847i q^{22} +(103.936 + 60.0075i) q^{23} +(-78.0913 + 45.0860i) q^{24} +(-612.676 + 123.505i) q^{25} +(65.3772 + 37.7455i) q^{26} +616.727 q^{27} +(-540.618 - 537.473i) q^{28} -450.921 q^{29} +(-71.0812 + 7.09306i) q^{30} +(511.698 - 295.429i) q^{31} +(426.131 - 246.027i) q^{32} +(204.430 - 354.083i) q^{33} -140.798i q^{34} +(-436.320 - 1144.66i) q^{35} -972.973 q^{36} +(2325.01 + 1342.35i) q^{37} +(-110.338 - 191.111i) q^{38} +(-243.861 - 422.379i) q^{39} +(522.083 - 52.0976i) q^{40} -1521.13i q^{41} +(-36.6320 - 135.134i) q^{42} +1378.04i q^{43} +(-740.235 + 1282.12i) q^{44} +(-1424.95 - 643.434i) q^{45} +(-39.9071 - 69.1212i) q^{46} +(1741.18 - 3015.81i) q^{47} -1009.55 q^{48} +(2072.29 - 1212.61i) q^{49} +(393.931 + 132.594i) q^{50} +(-454.822 + 787.775i) q^{51} +(883.012 + 1529.42i) q^{52} +(-3308.05 + 1909.90i) q^{53} +(-355.196 - 205.073i) q^{54} +(-1931.98 + 1388.19i) q^{55} +(269.057 + 992.543i) q^{56} +1425.71i q^{57} +(259.703 + 149.940i) q^{58} +(-2163.23 + 1248.94i) q^{59} +(-1523.05 - 687.727i) q^{60} +(5768.17 + 3330.25i) q^{61} -392.942 q^{62} +(784.495 - 2962.32i) q^{63} +3432.23 q^{64} +(281.785 + 2823.83i) q^{65} +(-235.478 + 135.953i) q^{66} +(-2850.27 + 1645.60i) q^{67} +(1646.90 - 2852.51i) q^{68} +515.652i q^{69} +(-129.327 + 804.338i) q^{70} -6058.46 q^{71} +(1136.67 + 656.260i) q^{72} +(688.721 + 1192.90i) q^{73} +(-892.709 - 1546.22i) q^{74} +(-1775.75 - 2014.40i) q^{75} -5162.46i q^{76} +(-3306.72 - 3287.49i) q^{77} +324.352i q^{78} +(-9.97798 + 17.2824i) q^{79} +(5353.67 + 2417.44i) q^{80} +(-1207.95 - 2092.23i) q^{81} +(-505.805 + 876.080i) q^{82} +7245.35 q^{83} +(838.500 - 3166.25i) q^{84} +(4298.32 - 3088.49i) q^{85} +(458.222 - 793.664i) q^{86} +(-968.706 - 1677.85i) q^{87} +(1729.56 - 998.561i) q^{88} +(-818.419 - 472.514i) q^{89} +(606.731 + 844.400i) q^{90} +(-5368.45 + 1455.27i) q^{91} -1867.16i q^{92} +(2198.54 + 1269.33i) q^{93} +(-2005.62 + 1157.95i) q^{94} +(3413.97 - 7560.60i) q^{95} +(1830.90 + 1057.07i) q^{96} -8583.56 q^{97} +(-1596.72 + 9.31735i) q^{98} -5951.25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) $ 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9	$ 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) $ 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$22$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.575938	−	0.332518i	−0.143985	−	0.0831295i	0.426277	−	0.904593i	$-0.359825\pi$
$2$	−0.575938	−	0.332518i	−0.143985	−	0.0831295i	−0.570262	+	0.821463i	$0.693158\pi$
$3$	2.14828	+	3.72093i	0.238698	+	0.413437i	0.960341	−	0.278828i	$-0.0899461\pi$
$3$	2.14828	+	3.72093i	0.238698	+	0.413437i	−0.721643	+	0.692265i	$0.756613\pi$
$4$	−7.77886	−	13.4734i	−0.486179	−	0.842087i
$5$	−2.48237	−	24.8765i	−0.0992950	−	0.995058i
$5$	−2.48237	−	24.8765i	−0.0992950	−	0.995058i
$6$		−	2.85737i		−	0.0793714i
$7$	47.2932	−	12.8202i	0.965167	−	0.261636i
$7$	47.2932	−	12.8202i	0.965167	−	0.261636i
$8$			20.9870i			0.327922i
$9$	31.2698	−	54.1608i	0.386047	−	0.668652i
$10$	−6.84217	+	15.1527i	−0.0684217	+	0.151527i
$11$	−47.5799	−	82.4108i	−0.393222	−	0.681081i	0.599650	−	0.800262i	$-0.295306\pi$
$11$	−47.5799	−	82.4108i	−0.393222	−	0.681081i	−0.992873	+	0.119181i	$0.961973\pi$
$12$	33.4224	−	57.8893i	0.232100	−	0.402009i
$13$	−113.514			−0.671682			−0.335841	−	0.941919i	$-0.609020\pi$
$13$	−113.514			−0.671682			−0.335841	+	0.941919i	$0.609020\pi$
$14$	−31.5009	−	8.34220i	−0.160719	−	0.0425623i
$15$	87.2308	−	62.6784i	0.387692	−	0.278571i
$16$	−117.483	+	203.487i	−0.458919	+	0.794871i
$17$	105.857	+	183.350i	0.366288	+	0.634429i	0.988982	−	0.148036i	$-0.0472953\pi$
$17$	105.857	+	183.350i	0.366288	+	0.634429i	−0.622694	+	0.782465i	$0.713962\pi$
$18$	−36.0189	+	20.7955i	−0.111169	+	0.0641837i
$19$	287.370	+	165.913i	0.796038	+	0.459593i	0.842084	−	0.539346i	$-0.181329\pi$
$19$	287.370	+	165.913i	0.796038	+	0.459593i	−0.0460456	+	0.998939i	$0.514662\pi$
$20$	−315.860	+	226.957i	−0.789650	+	0.567391i
$21$	149.302	+	148.433i	0.338553	+	0.336584i
$22$			63.2847i			0.130754i
$23$	103.936	+	60.0075i	0.196476	+	0.113436i	0.595011	−	0.803718i	$-0.297148\pi$
$23$	103.936	+	60.0075i	0.196476	+	0.113436i	−0.398535	+	0.917153i	$0.630481\pi$
$24$	−78.0913	+	45.0860i	−0.135575	+	0.0782744i
$25$	−612.676	+	123.505i	−0.980281	+	0.197608i
$26$	65.3772	+	37.7455i	0.0967118	+	0.0558366i
$27$	616.727			0.845990
$28$	−540.618	−	537.473i	−0.689564	−	0.685552i
$29$	−450.921			−0.536173			−0.268086	−	0.963395i	$-0.586391\pi$
$29$	−450.921			−0.536173			−0.268086	+	0.963395i	$0.586391\pi$
$30$	−71.0812	+	7.09306i	−0.0789791	+	0.00788118i
$31$	511.698	−	295.429i	0.532465	−	0.307419i	−0.209555	−	0.977797i	$-0.567201\pi$
$31$	511.698	−	295.429i	0.532465	−	0.307419i	0.742019	+	0.670378i	$0.233868\pi$
$32$	426.131	−	246.027i	0.416143	−	0.240261i
$33$	204.430	−	354.083i	0.187723	−	0.325145i
$34$		−	140.798i		−	0.121797i
$35$	−436.320	−	1144.66i	−0.356179	−	0.934418i
$36$	−972.973			−0.750751
$37$	2325.01	+	1342.35i	1.69833	+	0.980530i	0.947348	+	0.320207i	$0.103752\pi$
$37$	2325.01	+	1342.35i	1.69833	+	0.980530i	0.750981	+	0.660324i	$0.229581\pi$
$38$	−110.338	−	191.111i	−0.0764115	−	0.132349i
$39$	−243.861	−	422.379i	−0.160329	−	0.277698i
$40$	522.083	−	52.0976i	0.326302	−	0.0325610i
$41$		−	1521.13i		−	0.904899i	−0.891790	−	0.452449i	$-0.850550\pi$
$41$		−	1521.13i		−	0.904899i	0.891790	−	0.452449i	$-0.149450\pi$
$42$	−36.6320	−	135.134i	−0.0207664	−	0.0766066i
$43$			1378.04i			0.745288i	0.927974	+	0.372644i	$0.121549\pi$
$43$			1378.04i			0.745288i	−0.927974	+	0.372644i	$0.878451\pi$
$44$	−740.235	+	1282.12i	−0.382353	+	0.662255i
$45$	−1424.95	−	643.434i	−0.703680	−	0.317745i
$46$	−39.9071	−	69.1212i	−0.0188597	−	0.0326660i
$47$	1741.18	−	3015.81i	0.788221	−	1.36524i	−0.138834	−	0.990316i	$-0.544336\pi$
$47$	1741.18	−	3015.81i	0.788221	−	1.36524i	0.927056	−	0.374924i	$-0.122331\pi$
$48$	−1009.55			−0.438172
$49$	2072.29	−	1212.61i	0.863093	−	0.505045i
$50$	393.931	+	132.594i	0.157572	+	0.0530377i
$51$	−454.822	+	787.775i	−0.174864	+	0.302874i
$52$	883.012	+	1529.42i	0.326558	+	0.565614i
$53$	−3308.05	+	1909.90i	−1.17766	+	0.679923i	−0.955472	−	0.295081i	$-0.904653\pi$
$53$	−3308.05	+	1909.90i	−1.17766	+	0.679923i	−0.222188	+	0.975004i	$0.571320\pi$
$54$	−355.196	−	205.073i	−0.121809	−	0.0703267i
$55$	−1931.98	+	1388.19i	−0.638670	+	0.458907i
$56$	269.057	+	992.543i	0.0857963	+	0.316500i
$57$			1425.71i			0.438816i
$58$	259.703	+	149.940i	0.0772006	+	0.0445718i
$59$	−2163.23	+	1248.94i	−0.621440	+	0.358789i	−0.777429	−	0.628970i	$-0.783477\pi$
$59$	−2163.23	+	1248.94i	−0.621440	+	0.358789i	0.155989	+	0.987759i	$0.450143\pi$
$60$	−1523.05	−	687.727i	−0.423068	−	0.191035i
$61$	5768.17	+	3330.25i	1.55017	+	0.894989i	0.998127	+	0.0611711i	$0.0194835\pi$
$61$	5768.17	+	3330.25i	1.55017	+	0.894989i	0.552039	+	0.833818i	$0.313850\pi$
$62$	−392.942			−0.102222
$63$	784.495	−	2962.32i	0.197656	−	0.746365i
$64$	3432.23			0.837947
$65$	281.785	+	2823.83i	0.0666946	+	0.668363i
$66$	−235.478	+	135.953i	−0.0540583	+	0.0312106i
$67$	−2850.27	+	1645.60i	−0.634945	+	0.366585i	−0.782665	−	0.622444i	$-0.786140\pi$
$67$	−2850.27	+	1645.60i	−0.634945	+	0.366585i	0.147720	+	0.989029i	$0.452807\pi$
$68$	1646.90	−	2852.51i	0.356163	−	0.616892i
$69$			515.652i			0.108307i
$70$	−129.327	+	804.338i	−0.0263934	+	0.164151i
$71$	−6058.46			−1.20184			−0.600919	−	0.799310i	$-0.705199\pi$
$71$	−6058.46			−1.20184			−0.600919	+	0.799310i	$0.705199\pi$
$72$	1136.67	+	656.260i	0.219266	+	0.126593i
$73$	688.721	+	1192.90i	0.129240	+	0.223851i	0.923382	−	0.383881i	$-0.125413\pi$
$73$	688.721	+	1192.90i	0.129240	+	0.223851i	−0.794142	+	0.607732i	$0.792079\pi$
$74$	−892.709	−	1546.22i	−0.163022	−	0.282362i
$75$	−1775.75	−	2014.40i	−0.315690	−	0.358116i
$76$		−	5162.46i		−	0.893778i
$77$	−3306.72	−	3287.49i	−0.557720	−	0.554475i
$78$			324.352i			0.0533123i
$79$	−9.97798	+	17.2824i	−0.00159878	+	0.00276917i	−0.866824	−	0.498615i	$-0.833842\pi$
$79$	−9.97798	+	17.2824i	−0.00159878	+	0.00276917i	0.865225	+	0.501384i	$0.167176\pi$
$80$	5353.67	+	2417.44i	0.836511	+	0.377724i
$81$	−1207.95	−	2092.23i	−0.184111	−	0.318889i
$82$	−505.805	+	876.080i	−0.0752238	+	0.130291i
$83$	7245.35			1.05173			0.525864	−	0.850569i	$-0.323742\pi$
$83$	7245.35			1.05173			0.525864	+	0.850569i	$0.323742\pi$
$84$	838.500	−	3166.25i	0.118835	−	0.448731i
$85$	4298.32	−	3088.49i	0.594923	−	0.427473i
$86$	458.222	−	793.664i	0.0619554	−	0.107310i
$87$	−968.706	−	1677.85i	−0.127983	−	0.221674i
$88$	1729.56	−	998.561i	0.223342	−	0.128946i
$89$	−818.419	−	472.514i	−0.103323	−	0.0596534i	0.447448	−	0.894310i	$-0.352333\pi$
$89$	−818.419	−	472.514i	−0.103323	−	0.0596534i	−0.550771	+	0.834656i	$0.685666\pi$
$90$	606.731	+	844.400i	0.0749051	+	0.104247i
$91$	−5368.45	+	1455.27i	−0.648285	+	0.175736i
$92$		−	1867.16i		−	0.220600i
$93$	2198.54	+	1269.33i	0.254196	+	0.146760i
$94$	−2005.62	+	1157.95i	−0.226983	+	0.131049i
$95$	3413.97	−	7560.60i	0.378279	−	0.837740i
$96$	1830.90	+	1057.07i	0.198665	+	0.114699i
$97$	−8583.56			−0.912271			−0.456136	−	0.889910i	$-0.650767\pi$
$97$	−8583.56			−0.912271			−0.456136	+	0.889910i	$0.650767\pi$
$98$	−1596.72	+	9.31735i	−0.166256	+	0.000970153i
$99$	−5951.25			−0.607209
$100$	6429.95	+	7294.09i	0.642995	+	0.729409i
$101$	5645.64	−	3259.51i	0.553440	−	0.319529i	−0.197068	−	0.980390i	$-0.563142\pi$
$101$	5645.64	−	3259.51i	0.553440	−	0.319529i	0.750508	+	0.660861i	$0.229809\pi$
$102$	523.898	−	302.473i	0.0503555	−	0.0290728i
$103$	−3725.85	+	6453.36i	−0.351197	+	0.608291i	−0.986459	−	0.164005i	$-0.947559\pi$
$103$	−3725.85	+	6453.36i	−0.351197	+	0.608291i	0.635263	+	0.772296i	$0.280892\pi$
$104$		−	2382.33i		−	0.220259i
$105$	3321.87	−	4082.57i	0.301304	−	0.370301i
$106$	2540.31			0.226087
$107$	−16671.1	−	9625.07i	−1.45612	−	0.840691i	−0.457302	−	0.889311i	$-0.651184\pi$
$107$	−16671.1	−	9625.07i	−1.45612	−	0.840691i	−0.998817	+	0.0486206i	$0.984517\pi$
$108$	−4797.43	−	8309.40i	−0.411303	−	0.712397i
$109$	7518.67	+	13022.7i	0.632831	+	1.09610i	0.986970	+	0.160903i	$0.0514406\pi$
$109$	7518.67	+	13022.7i	0.632831	+	1.09610i	−0.354139	+	0.935193i	$0.615226\pi$
$110$	1574.30	−	157.096i	0.130107	−	0.0129832i
$111$			11535.0i			0.936202i
$112$	−2947.42	+	11129.7i	−0.234966	+	0.887253i
$113$			15948.8i			1.24903i	0.781014	+	0.624513i	$0.214703\pi$
$113$			15948.8i			1.24903i	−0.781014	+	0.624513i	$0.785297\pi$
$114$	474.075	−	821.122i	0.0364785	−	0.0631827i
$115$	1234.76	−	2734.52i	0.0933660	−	0.206769i
$116$	3507.66	+	6075.44i	0.260676	+	0.451504i
$117$	−3549.57	+	6148.03i	−0.259301	+	0.449122i
$118$	1661.18			0.119304
$119$	7356.90	+	7314.09i	0.519518	+	0.516495i
$120$	1315.43	+	1830.71i	0.0913495	+	0.127133i
$121$	2792.81	−	4837.28i	0.190752	−	0.330393i
$122$	−2214.74	−	3836.04i	−0.148800	−	0.257729i
$123$	5660.04	−	3267.83i	0.374119	−	0.215997i
$124$	−7960.87	−	4596.21i	−0.517746	−	0.298921i
$125$	4593.26	+	14934.6i	0.293969	+	0.955815i
$126$	−1436.85	+	1445.25i	−0.0905043	+	0.0910339i
$127$		−	9430.98i		−	0.584722i	−0.956308	−	0.292361i	$-0.905559\pi$
$127$		−	9430.98i		−	0.584722i	0.956308	−	0.292361i	$-0.0944409\pi$
$128$	−8794.85	−	5077.71i	−0.536795	−	0.309919i
$129$	−5127.58	+	2960.41i	−0.308130	+	0.177899i
$130$	776.684	−	1720.05i	0.0459577	−	0.101778i
$131$	−16941.7	−	9781.32i	−0.987223	−	0.569973i	−0.0827800	−	0.996568i	$-0.526380\pi$
$131$	−16941.7	−	9781.32i	−0.987223	−	0.569973i	−0.904443	+	0.426594i	$0.859713\pi$
$132$	−6360.93			−0.365067
$133$	15717.7	+	4162.42i	0.888556	+	0.235311i
$134$	2188.77			0.121896
$135$	−1530.95	−	15342.0i	−0.0840025	−	0.841809i
$136$	−3847.97	+	2221.63i	−0.208043	+	0.120114i
$137$	3981.85	−	2298.92i	0.212151	−	0.122485i	−0.390160	−	0.920747i	$-0.627580\pi$
$137$	3981.85	−	2298.92i	0.212151	−	0.122485i	0.602310	+	0.798262i	$0.294247\pi$
$138$	171.463	−	296.983i	0.00900354	−	0.0155946i
$139$		−	23930.7i		−	1.23858i	−0.785161	−	0.619292i	$-0.787420\pi$
$139$		−	23930.7i		−	1.23858i	0.785161	−	0.619292i	$-0.212580\pi$
$140$	−12028.4	+	14782.9i	−0.613694	+	0.754228i
$141$	14962.2			0.752587
$142$	3489.30	+	2014.55i	0.173046	+	0.0999082i
$143$	5401.00	+	9354.80i	0.264120	+	0.457470i
$144$	7347.35	+	12726.0i	0.354328	+	0.613714i
$145$	1119.36	+	11217.3i	0.0532393	+	0.533523i
$146$		−	916.049i		−	0.0429747i
$147$	8963.91	+	5105.80i	0.414823	+	0.236281i
$148$		−	41767.7i		−	1.90685i
$149$	16060.3	−	27817.2i	0.723404	−	1.25297i	−0.236224	−	0.971699i	$-0.575910\pi$
$149$	16060.3	−	27817.2i	0.723404	−	1.25297i	0.959628	−	0.281274i	$-0.0907569\pi$
$150$	352.900	+	1750.64i	0.0156845	+	0.0778062i
$151$	−9721.02	−	16837.3i	−0.426342	−	0.738445i	0.570203	−	0.821504i	$-0.306865\pi$
$151$	−9721.02	−	16837.3i	−0.426342	−	0.738445i	−0.996545	+	0.0830585i	$0.973531\pi$
$152$	−3482.02	+	6031.04i	−0.150711	+	0.261039i
$153$	13240.5			0.565616
$154$	811.321	+	2992.93i	0.0342098	+	0.126199i
$155$	−8619.46	−	11995.9i	−0.358770	−	0.499308i
$156$	−3793.92	+	6571.26i	−0.155897	+	0.270022i
$157$	3911.89	+	6775.58i	0.158704	+	0.274883i	0.934401	−	0.356222i	$-0.115935\pi$
$157$	3911.89	+	6775.58i	0.158704	+	0.274883i	−0.775698	+	0.631104i	$0.782602\pi$
$158$	11.4934	−	6.63572i	0.000460399	−	0.000265811i
$159$	−14213.2	−	8206.02i	−0.562210	−	0.324592i
$160$	−7178.09	−	9989.89i	−0.280394	−	0.390230i
$161$	5684.77	+	1505.47i	0.219311	+	0.0580790i
$162$			1606.66i			0.0612201i
$163$	−16301.0	−	9411.41i	−0.613536	−	0.354225i	0.160812	−	0.986985i	$-0.448589\pi$
$163$	−16301.0	−	9411.41i	−0.613536	−	0.354225i	−0.774348	+	0.632760i	$0.781922\pi$
$164$	−20494.8	+	11832.7i	−0.762003	+	0.439943i
$165$	−9315.81	−	4206.53i	−0.342178	−	0.154510i
$166$	−4172.87	−	2409.21i	−0.151432	−	0.0874296i
$167$	49227.7			1.76513			0.882565	−	0.470190i	$-0.155815\pi$
$167$	49227.7			1.76513			0.882565	+	0.470190i	$0.155815\pi$
$168$	−3115.17	+	3133.41i	−0.110373	+	0.111019i
$169$	−15675.5			−0.548843
$170$	−3502.55	+	349.512i	−0.121195	+	0.0120939i
$171$	17972.0	−	10376.1i	0.614616	−	0.354849i
$172$	18566.8	−	10719.6i	0.627597	−	0.362343i
$173$	−18824.5	+	32604.9i	−0.628971	+	1.08941i	0.358788	+	0.933419i	$0.383190\pi$
$173$	−18824.5	+	32604.9i	−0.628971	+	1.08941i	−0.987759	+	0.155990i	$0.950143\pi$
$174$			1288.45i			0.0425568i
$175$	−27392.0	+	13695.6i	−0.894433	+	0.447202i
$176$	22359.4			0.721829
$177$	−9294.47	−	5366.16i	−0.296673	−	0.171284i
$178$	314.239	+	544.278i	0.00991791	+	0.0171783i
$179$	23762.0	+	41157.0i	0.741612	+	1.28451i	0.951761	+	0.306840i	$0.0992718\pi$
$179$	23762.0	+	41157.0i	0.741612	+	1.28451i	−0.210149	+	0.977669i	$0.567395\pi$
$180$	2415.28	+	24204.1i	0.0745458	+	0.747041i
$181$			44252.3i			1.35076i	0.737469	+	0.675381i	$0.236021\pi$
$181$			44252.3i			1.35076i	−0.737469	+	0.675381i	$0.763979\pi$
$182$	3575.80	+	946.959i	0.107952	+	0.0285883i
$183$			28617.3i			0.854528i
$184$	−1259.38	+	2181.31i	−0.0371981	+	0.0644290i
$185$	27621.3	−	61170.3i	0.807049	−	1.78730i
$186$	−844.150	−	1462.11i	−0.0244002	−	0.0422624i
$187$	10073.3	−	17447.5i	0.288065	−	0.498943i
$188$	−54177.6			−1.53287
$189$	29167.0	−	7906.54i	0.816521	−	0.221342i
$190$	−4480.27	+	3219.23i	−0.124107	+	0.0891754i
$191$	−4874.46	+	8442.81i	−0.133616	+	0.231430i	−0.925068	−	0.379801i	$-0.875992\pi$
$191$	−4874.46	+	8442.81i	−0.133616	+	0.231430i	0.791452	+	0.611232i	$0.209326\pi$
$192$	7373.40	+	12771.1i	0.200016	+	0.346438i
$193$	2463.98	−	1422.58i	0.0661488	−	0.0381910i	−0.466561	−	0.884489i	$-0.654507\pi$
$193$	2463.98	−	1422.58i	0.0661488	−	0.0381910i	0.532710	+	0.846298i	$0.321174\pi$
$194$	4943.60	+	2854.19i	0.131353	+	0.0758367i
$195$	−9901.94	+	7114.89i	−0.260406	+	0.187111i
$196$	−32458.0	−	18488.0i	−0.844909	−	0.481257i
$197$			27992.2i			0.721281i	0.932705	+	0.360641i	$0.117442\pi$
$197$			27992.2i			0.721281i	−0.932705	+	0.360641i	$0.882558\pi$
$198$	3427.55	+	1978.90i	0.0874286	+	0.0504769i
$199$	−42998.8	+	24825.4i	−1.08580	+	0.626888i	−0.932456	−	0.361285i	$-0.882338\pi$
$199$	−42998.8	+	24825.4i	−1.08580	+	0.626888i	−0.153346	+	0.988173i	$0.549005\pi$
$200$	−2592.01	−	12858.2i	−0.0648002	−	0.321456i
$201$	−12246.4	−	7070.43i	−0.303120	−	0.175006i
$202$	−4335.39			−0.106249
$203$	−21325.5	+	5780.89i	−0.517496	+	0.140282i
$204$	14152.0			0.340061
$205$	−37840.4	+	3776.03i	−0.900427	+	0.0898519i
$206$	4291.71	−	2477.82i	0.101134	−	0.0583896i
$207$	6500.11	−	3752.84i	0.151698	−	0.0875829i
$208$	13336.0	−	23098.7i	0.308248	−	0.533900i
$209$		−	31576.5i		−	0.722889i
$210$	−3270.72	+	1246.73i	−0.0741660	+	0.0282704i
$211$	5229.81			0.117468			0.0587342	−	0.998274i	$-0.481294\pi$
$211$	5229.81			0.117468			0.0587342	+	0.998274i	$0.481294\pi$
$212$	51465.7	+	29713.7i	1.14511	+	0.661128i
$213$	−13015.3	−	22543.1i	−0.286876	−	0.496884i
$214$	6401.02	+	11086.9i	0.139772	+	0.242093i
$215$	34280.7	−	3420.80i	0.741605	−	0.0740033i
$216$			12943.3i			0.277419i
$217$	20412.4	−	20531.8i	0.433485	−	0.436022i
$218$		−	10000.4i		−	0.210428i
$219$	−2959.13	+	5125.37i	−0.0616988	+	0.106865i
$220$	33732.3	+	15231.7i	0.696947	+	0.314705i
$221$	−12016.3	−	20812.8i	−0.246029	−	0.426134i
$222$	3835.58	−	6643.42i	0.0778260	−	0.134799i
$223$	14277.7			0.287111			0.143555	−	0.989642i	$-0.454147\pi$
$223$	14277.7			0.287111			0.143555	+	0.989642i	$0.454147\pi$
$224$	16999.0	−	17098.5i	0.338787	−	0.340770i
$225$	−12469.1	+	37045.0i	−0.246303	+	0.731753i
$226$	5303.27	−	9185.53i	0.103831	−	0.179840i
$227$	−500.209	−	866.388i	−0.00970733	−	0.0168136i	0.861131	−	0.508383i	$-0.169757\pi$
$227$	−500.209	−	866.388i	−0.00970733	−	0.0168136i	−0.870838	+	0.491570i	$0.836423\pi$
$228$	19209.2	−	11090.4i	0.369521	−	0.213343i
$229$	−26598.0	−	15356.3i	−0.507198	−	0.292831i	0.224483	−	0.974478i	$-0.427931\pi$
$229$	−26598.0	−	15356.3i	−0.507198	−	0.292831i	−0.731681	+	0.681647i	$0.761264\pi$
$230$	−1620.42	+	1164.33i	−0.0306319	+	0.0220101i
$231$	5128.74	−	19366.5i	0.0961139	−	0.362934i
$232$		−	9463.50i		−	0.175823i
$233$	46288.6	+	26724.8i	0.852634	+	0.492268i	0.861539	−	0.507692i	$-0.169501\pi$
$233$	46288.6	+	26724.8i	0.852634	+	0.492268i	−0.00890483	+	0.999960i	$0.502835\pi$
$234$	4088.66	−	2360.59i	0.0746705	−	0.0431111i
$235$	−79345.0	−	35828.0i	−1.43676	−	0.648765i
$236$	33655.0	+	19430.7i	0.604262	+	0.348871i
$237$	−85.7420			−0.00152650
$238$	−1805.05	−	6658.76i	−0.0318666	−	0.117555i
$239$	−46246.2			−0.809618			−0.404809	−	0.914401i	$-0.632662\pi$
$239$	−46246.2			−0.809618			−0.404809	+	0.914401i	$0.632662\pi$
$240$	2506.08	+	25114.0i	0.0435083	+	0.436007i
$241$	−19499.1	+	11257.8i	−0.335723	+	0.193830i	−0.658379	−	0.752687i	$-0.728758\pi$
$241$	−19499.1	+	11257.8i	−0.335723	+	0.193830i	0.322656	+	0.946516i	$0.395424\pi$
$242$	−3216.97	+	1857.32i	−0.0549308	+	0.0317143i
$243$	30167.5	−	52251.6i	0.510889	−	0.884885i
$244$		−	103622.i		−	1.74050i
$245$	−35309.7	−	48541.0i	−0.588250	−	0.808679i
$246$	−4346.44			−0.0718231
$247$	−32620.6	−	18833.5i	−0.534685	−	0.308700i
$248$	6200.18	+	10739.0i	0.100809	+	0.174607i
$249$	15565.1	+	26959.5i	0.251045	+	0.434823i
$250$	2320.59	−	10128.8i	0.0371295	−	0.162060i
$251$			9332.95i			0.148140i	0.997253	+	0.0740698i	$0.0235988\pi$
$251$			9332.95i			0.148140i	−0.997253	+	0.0740698i	$0.976401\pi$
$252$	−46015.0	+	12473.7i	−0.724600	+	0.196424i
$253$		−	11420.6i		−	0.178422i
$254$	−3135.97	+	5431.66i	−0.0486076	+	0.0841909i
$255$	20726.1	+	9358.80i	0.318740	+	0.143926i
$256$	−24081.0	−	41709.5i	−0.367447	−	0.636436i
$257$	4375.77	−	7579.05i	0.0662503	−	0.114749i	−0.830998	−	0.556276i	$-0.812230\pi$
$257$	4375.77	−	7579.05i	0.0662503	−	0.114749i	0.897248	+	0.441527i	$0.145563\pi$
$258$	3937.56			0.0591545
$259$	127166.	+	33676.7i	1.89571	+	0.502031i
$260$	35854.6	−	25762.8i	0.530394	−	0.381106i
$261$	−14100.2	+	24422.3i	−0.206988	+	0.358513i
$262$	6504.93	+	11266.9i	0.0947632	+	0.164135i
$263$	−75319.2	+	43485.6i	−1.08892	+	0.628686i	−0.933288	−	0.359130i	$-0.883074\pi$
$263$	−75319.2	+	43485.6i	−1.08892	+	0.628686i	−0.155628	+	0.987816i	$0.549740\pi$
$264$	7431.15	+	4290.38i	0.106622	+	0.0615585i
$265$	55723.4	+	77551.4i	0.793498	+	1.10433i
$266$	−7668.32	−	7623.70i	−0.108377	−	0.107746i
$267$		−	4060.37i		−	0.0569565i
$268$	44343.7	+	25601.8i	0.617394	+	0.356452i
$269$	−95568.2	+	55176.3i	−1.32071	+	0.762514i	−0.983842	−	0.179036i	$-0.942702\pi$
$269$	−95568.2	+	55176.3i	−1.32071	+	0.762514i	−0.336871	+	0.941551i	$0.609369\pi$
$270$	−4219.75	+	9345.09i	−0.0578841	+	0.128191i
$271$	88667.4	+	51192.2i	1.20733	+	0.697052i	0.962175	−	0.272433i	$-0.0878282\pi$
$271$	88667.4	+	51192.2i	1.20733	+	0.697052i	0.245154	+	0.969484i	$0.421162\pi$
$272$	−49745.8			−0.672385
$273$	−16947.9	−	16849.3i	−0.227400	−	0.226077i
$274$	−3057.73			−0.0407285
$275$	39329.2	+	44614.7i	0.520056	+	0.589947i
$276$	6947.57	−	4011.18i	0.0912042	−	0.0526568i
$277$	−127091.	+	73376.1i	−1.65636	+	0.956302i	−0.681990	+	0.731361i	$0.738885\pi$
$277$	−127091.	+	73376.1i	−1.65636	+	0.956302i	−0.974373	+	0.224940i	$0.927781\pi$
$278$	−7957.38	+	13782.6i	−0.102963	+	0.178337i
$279$		−	36952.0i		−	0.474712i
$280$	24023.0	−	9157.05i	0.306416	−	0.116799i
$281$	−52692.9			−0.667328			−0.333664	−	0.942692i	$-0.608285\pi$
$281$	−52692.9			−0.667328			−0.333664	+	0.942692i	$0.608285\pi$
$282$	−8617.29	−	4975.20i	−0.108361	−	0.0625622i
$283$	30272.2	+	52433.0i	0.377982	+	0.654684i	0.990769	−	0.135564i	$-0.0432848\pi$
$283$	30272.2	+	52433.0i	0.377982	+	0.654684i	−0.612787	+	0.790249i	$0.709951\pi$
$284$	47128.0	+	81628.0i	0.584308	+	1.01205i
$285$	35466.7	−	3539.15i	0.436647	−	0.0435722i
$286$		−	7183.72i		−	0.0878248i
$287$	−19501.2	−	71939.3i	−0.236754	−	0.873378i
$288$		−	30772.8i		−	0.371007i
$289$	19349.0	−	33513.5i	0.231667	−	0.401259i
$290$	3085.28	−	6832.69i	0.0366859	−	0.0812448i
$291$	−18439.9	−	31938.9i	−0.217757	−	0.377167i
$292$	10714.9	−	18558.8i	0.125668	−	0.217663i
$293$	−41915.4			−0.488246			−0.244123	−	0.969744i	$-0.578500\pi$
$293$	−41915.4			−0.488246			−0.244123	+	0.969744i	$0.578500\pi$
$294$	−3464.88	−	5921.29i	−0.0400861	−	0.0685049i
$295$	36439.2	+	50713.2i	0.418721	+	0.582743i
$296$	−28171.9	+	48795.1i	−0.321538	+	0.556920i
$297$	−29343.8	−	50824.9i	−0.332662	−	0.576188i
$298$	−18499.5	+	10680.7i	−0.208318	+	0.120272i
$299$	−11798.2	−	6811.70i	−0.131970	−	0.0761927i
$300$	−13327.4	+	39595.2i	−0.148083	+	0.439946i
$301$	17666.7	+	65171.7i	0.194994	+	0.719327i
$302$			12929.7i			0.141766i
$303$	24256.9	+	14004.7i	0.264210	+	0.152542i
$304$	−67522.3	+	38984.0i	−0.730634	+	0.421832i
$305$	68526.2	−	151759.i	0.736642	−	1.63137i
$306$	−7625.72	−	4402.71i	−0.0814400	−	0.0470194i
$307$	−59190.6			−0.628023			−0.314012	−	0.949419i	$-0.601673\pi$
$307$	−59190.6			−0.628023			−0.314012	+	0.949419i	$0.601673\pi$
$308$	−18571.0	+	70125.7i	−0.195764	+	0.739223i
$309$	−32016.7			−0.335320
$310$	975.429	+	9775.01i	0.0101502	+	0.101717i
$311$	135878.	−	78449.0i	1.40484	−	0.811085i	0.409956	−	0.912105i	$-0.365544\pi$
$311$	135878.	−	78449.0i	1.40484	−	0.811085i	0.994884	+	0.101020i	$0.0322106\pi$
$312$	8864.48	−	5117.91i	0.0910634	−	0.0525755i
$313$	46303.4	−	80199.9i	0.472633	−	0.818625i	−0.526876	−	0.849942i	$-0.676637\pi$
$313$	46303.4	−	80199.9i	0.472633	−	0.818625i	0.999509	+	0.0313172i	$0.00997021\pi$
$314$		−	5203.09i		−	0.0527718i
$315$	−75639.4	−	12161.9i	−0.762302	−	0.122569i
$316$	310.469			0.00310917
$317$	17266.6	+	9968.90i	0.171826	+	0.0992039i	0.583447	−	0.812151i	$-0.301704\pi$
$317$	17266.6	+	9968.90i	0.171826	+	0.0992039i	−0.411620	+	0.911355i	$0.635037\pi$
$318$	5457.30	+	9452.32i	0.0539664	+	0.0934725i
$319$	21454.8	+	37160.8i	0.210835	+	0.365177i
$320$	−8520.08	−	85381.7i	−0.0832039	−	0.833806i
$321$		−	82709.4i		−	0.802685i
$322$	−2773.48	−	2757.34i	−0.0267493	−	0.0265937i
$323$			70252.3i			0.673373i
$324$	−18792.9	+	32550.3i	−0.179021	+	0.310074i
$325$	69547.4	−	14019.6i	0.658437	−	0.132730i
$326$	6258.93	+	10840.8i	0.0588931	+	0.102006i
$327$	−32304.4	+	55952.9i	−0.302111	+	0.523272i
$328$	31924.1			0.296736
$329$	43682.7	−	164950.i	0.403569	−	1.52391i
$330$	3966.58	+	5520.37i	0.0364241	+	0.0506921i
$331$	11425.9	−	19790.2i	0.104288	−	0.180632i	−0.809159	−	0.587590i	$-0.800077\pi$
$331$	11425.9	−	19790.2i	0.104288	−	0.180632i	0.913447	+	0.406958i	$0.133410\pi$
$332$	−56360.6	−	97619.4i	−0.511328	−	0.885646i
$333$	145405.	−	83949.7i	1.31127	−	0.757061i
$334$	−28352.1	−	16369.1i	−0.254151	−	0.146734i
$335$	48012.2	+	66819.5i	0.427821	+	0.595407i
$336$	−47744.7	+	12942.6i	−0.422909	+	0.114642i
$337$			64755.6i			0.570187i	0.958500	+	0.285093i	$0.0920247\pi$
$337$			64755.6i			0.570187i	−0.958500	+	0.285093i	$0.907975\pi$
$338$	9028.13	+	5212.39i	0.0790249	+	0.0456251i
$339$	−59344.5	+	34262.5i	−0.516394	+	0.298140i
$340$	−75048.5	−	33887.9i	−0.649208	−	0.293148i
$341$	−48693.1	−	28113.0i	−0.418754	−	0.241768i
$342$	−13801.0			−0.117994
$343$	82459.1	−	83915.4i	0.700891	−	0.713269i
$344$	−28920.9			−0.244396
$345$	12827.6	−	1280.04i	0.107772	−	0.0107544i
$346$	21683.5	−	12518.9i	0.181124	−	0.104572i
$347$	68381.1	−	39479.9i	0.567907	−	0.327881i	−0.188406	−	0.982091i	$-0.560332\pi$
$347$	68381.1	−	39479.9i	0.567907	−	0.327881i	0.756313	+	0.654210i	$0.226999\pi$
$348$	−15070.9	+	26103.5i	−0.124446	+	0.215546i
$349$			47202.6i			0.387539i	0.981047	+	0.193769i	$0.0620713\pi$
$349$			47202.6i			0.387539i	−0.981047	+	0.193769i	$0.937929\pi$
$350$	20330.1	+	1220.54i	0.165960	+	0.00996359i
$351$	−70007.3			−0.568236
$352$	−40550.5	−	23411.9i	−0.327274	−	0.188952i
$353$	−41463.3	−	71816.5i	−0.332747	−	0.576334i	0.650303	−	0.759675i	$-0.274642\pi$
$353$	−41463.3	−	71816.5i	−0.332747	−	0.576334i	−0.983049	+	0.183341i	$0.941309\pi$
$354$	3568.69	+	6181.16i	0.0284775	+	0.0493245i
$355$	15039.4	+	150713.i	0.119336	+	1.19590i
$356$			14702.5i			0.116009i
$357$	−11410.6	+	43087.2i	−0.0895304	+	0.338074i
$358$		−	31605.2i		−	0.246599i
$359$	63632.1	−	110214.i	0.493728	−	0.855161i	−0.506246	−	0.862389i	$-0.668967\pi$
$359$	63632.1	−	110214.i	0.493728	−	0.855161i	0.999974	+	0.00722775i	$0.00230068\pi$
$360$	13503.8	−	29905.5i	0.104196	−	0.230752i
$361$	−10106.2	−	17504.5i	−0.0775485	−	0.134318i
$362$	14714.7	−	25486.6i	0.112288	−	0.194489i
$363$	23998.9			0.182129
$364$	61367.9	+	61010.8i	0.463168	+	0.460473i
$365$	27965.5	−	20094.2i	0.209912	−	0.150829i
$366$	9515.77	−	16481.8i	0.0710365	−	0.123039i
$367$	75701.7	+	131119.i	0.562048	+	0.973495i	0.997318	+	0.0731953i	$0.0233196\pi$
$367$	75701.7	+	131119.i	0.562048	+	0.973495i	−0.435270	+	0.900300i	$0.643347\pi$
$368$	−24421.5	+	14099.7i	−0.180333	+	0.104116i
$369$	−82385.9	−	47565.5i	−0.605063	−	0.349333i
$370$	−36248.3	+	26045.7i	−0.264780	+	0.190254i
$371$	−131963.	+	132735.i	−0.958746	+	0.964357i
$372$		−	39495.8i		−	0.285407i
$373$	−181074.	−	104543.i	−1.30149	−	0.751414i	−0.320827	−	0.947138i	$-0.603961\pi$
$373$	−181074.	−	104543.i	−1.30149	−	0.751414i	−0.980659	+	0.195724i	$0.937294\pi$
$374$	−11603.2	+	6699.14i	−0.0829538	+	0.0478934i
$375$	−45703.1	+	49175.0i	−0.324999	+	0.349689i
$376$	63293.0	+	36542.2i	0.447692	+	0.258475i
$377$	51186.0			0.360138
$378$	−19427.4	−	5144.86i	−0.135966	−	0.0360073i
$379$	189978.			1.32259			0.661295	−	0.750126i	$-0.270007\pi$
$379$	189978.			1.32259			0.661295	+	0.750126i	$0.270007\pi$
$380$	−128424.	+	12815.2i	−0.889361	+	0.0887476i
$381$	35092.0	−	20260.4i	0.241746	−	0.139572i
$382$	5614.78	−	3241.69i	0.0384774	−	0.0222149i
$383$	−111113.	+	192454.i	−0.757475	+	1.31198i	0.186660	+	0.982425i	$0.440234\pi$
$383$	−111113.	+	192454.i	−0.757475	+	1.31198i	−0.944135	+	0.329560i	$0.893100\pi$
$384$		−	43633.4i		−	0.295908i
$385$	−73572.4	+	90420.3i	−0.496356	+	0.610021i
$386$	−1892.13			−0.0126992
$387$	74635.6	+	43090.9i	0.498338	+	0.287716i
$388$	66770.4	+	115650.i	0.443527	+	0.768212i
$389$	101323.	+	175496.i	0.669587	+	1.15976i	0.978020	+	0.208512i	$0.0668620\pi$
$389$	101323.	+	175496.i	0.669587	+	1.15976i	−0.308433	+	0.951246i	$0.599805\pi$
$390$	8068.73	−	805.163i	0.0530489	−	0.00529364i
$391$			25408.9i			0.166200i
$392$	25449.1	+	43491.1i	0.165615	+	0.283027i
$393$		−	84052.1i		−	0.544206i
$394$	9307.91	−	16121.8i	0.0599597	−	0.103853i
$395$	454.693	+	205.315i	0.00291423	+	0.00131591i
$396$	46294.0	+	80183.5i	0.295212	+	0.511322i
$397$	−42330.6	+	73318.7i	−0.268580	+	0.465194i	−0.968495	−	0.249032i	$-0.919888\pi$
$397$	−42330.6	+	73318.7i	−0.268580	+	0.465194i	0.699916	+	0.714226i	$0.253221\pi$
$398$	33019.6			0.208452
$399$	18277.9	+	67426.4i	0.114810	+	0.423530i
$400$	46847.4	−	139181.i	0.292796	−	0.869883i
$401$	−11744.1	+	20341.5i	−0.0730353	+	0.126501i	−0.900230	−	0.435414i	$-0.856602\pi$
$401$	−11744.1	+	20341.5i	−0.0730353	+	0.126501i	0.827195	+	0.561915i	$0.189935\pi$
$402$	4702.09	+	8144.26i	0.0290964	+	0.0503964i
$403$	−58085.1	+	33535.4i	−0.357647	+	0.206488i
$404$	−87833.4	−	50710.6i	−0.538142	−	0.310696i
$405$	−49048.7	+	35243.2i	−0.299032	+	0.214865i
$406$	14204.4	+	3761.68i	0.0861730	+	0.0228207i
$407$		−	255475.i		−	1.54227i
$408$	−16533.0	−	9545.36i	−0.0993190	−	0.0573419i
$409$	−92846.7	+	53605.0i	−0.555034	+	0.320449i	−0.751150	−	0.660132i	$-0.770500\pi$
$409$	−92846.7	+	53605.0i	−0.555034	+	0.320449i	0.196116	+	0.980581i	$0.437167\pi$
$410$	23049.3	+	10407.9i	0.137117	+	0.0619148i
$411$	17108.3	+	9877.47i	0.101280	+	0.0584739i
$412$	115931.			0.682978
$413$	−86294.5	+	86799.5i	−0.505921	+	0.508882i
$414$	−4991.55			−0.0291229
$415$	−17985.7	−	180239.i	−0.104431	−	1.04653i
$416$	−48371.9	+	27927.5i	−0.279516	+	0.161379i
$417$	89044.4	−	51409.8i	0.512076	−	0.295647i
$418$	−10499.8	+	18186.1i	−0.0600934	+	0.104085i
$419$		−	117730.i		−	0.670596i	−0.942112	−	0.335298i	$-0.891163\pi$
$419$		−	117730.i		−	0.670596i	0.942112	−	0.335298i	$-0.108837\pi$
$420$	−80846.4	−	12999.1i	−0.458313	−	0.0736910i
$421$	96464.0			0.544253			0.272127	−	0.962261i	$-0.412273\pi$
$421$	96464.0			0.544253			0.272127	+	0.962261i	$0.412273\pi$
$422$	−3012.05	−	1739.01i	−0.0169136	−	0.00976510i
$423$	−108893.	−	188608.i	−0.608580	−	1.05409i
$424$	−40083.2	−	69426.1i	−0.222962	−	0.386181i
$425$	−87500.8	−	99260.1i	−0.484433	−	0.549537i
$426$			17311.3i			0.0953915i
$427$	315489.	+	83549.3i	1.73033	+	0.458234i
$428$			299488.i			1.63490i
$429$	−23205.7	+	40193.5i	−0.126090	+	0.218394i
$430$	−20881.0	−	9428.77i	−0.112931	−	0.0509939i
$431$	−29089.6	−	50384.7i	−0.156597	−	0.271234i	0.777042	−	0.629448i	$-0.216719\pi$
$431$	−29089.6	−	50384.7i	−0.156597	−	0.271234i	−0.933639	+	0.358214i	$0.883386\pi$
$432$	−72455.1	+	125496.i	−0.388241	+	0.672453i
$433$	16430.5			0.0876343			0.0438172	−	0.999040i	$-0.486048\pi$
$433$	16430.5			0.0876343			0.0438172	+	0.999040i	$0.486048\pi$
$434$	−18583.5	+	5037.59i	−0.0986615	+	0.0267450i
$435$	−39334.2	+	28263.0i	−0.207870	+	0.149362i
$436$	116973.	−	202604.i	0.615338	−	1.06580i
$437$	19912.0	+	34488.7i	0.104268	+	0.180598i
$438$	3408.56	−	1967.93i	0.0177673	−	0.0102580i
$439$	−78291.5	−	45201.6i	−0.406243	−	0.234544i	0.282931	−	0.959140i	$-0.408693\pi$
$439$	−78291.5	−	45201.6i	−0.406243	−	0.234544i	−0.689174	+	0.724596i	$0.742026\pi$
$440$	−29134.1	−	40546.5i	−0.150486	−	0.209434i
$441$	−876.197	−	150155.i	−0.00450531	−	0.772080i
$442$			15982.5i			0.0818090i
$443$	−194715.	−	112419.i	−0.992186	−	0.572839i	−0.0862588	−	0.996273i	$-0.527491\pi$
$443$	−194715.	−	112419.i	−0.992186	−	0.572839i	−0.905927	+	0.423434i	$0.860825\pi$
$444$	155415.	−	89728.8i	0.788364	−	0.455162i
$445$	−9722.86	+	21532.3i	−0.0490991	+	0.108735i
$446$	−8223.08	−	4747.60i	−0.0413395	−	0.0238674i
$447$	138008.			0.690700
$448$	162321.	−	44001.8i	0.808758	−	0.219237i
$449$	−105537.			−0.523496			−0.261748	−	0.965136i	$-0.584299\pi$
$449$	−105537.			−0.523496			−0.261748	+	0.965136i	$0.584299\pi$
$450$	19499.5	−	17189.4i	0.0962941	−	0.0848861i
$451$	−125358.	+	72375.4i	−0.616309	+	0.355826i
$452$	214885.	−	124064.i	1.05179	−	0.607250i
$453$	41767.0	−	72342.5i	0.203534	−	0.352531i
$454$			665.314i			0.00322786i
$455$	49528.5	+	129935.i	0.239239	+	0.627631i
$456$	−29921.5			−0.143897
$457$	22106.5	+	12763.2i	0.105849	+	0.0611121i	0.551990	−	0.833851i	$-0.313869\pi$
$457$	22106.5	+	12763.2i	0.105849	+	0.0611121i	−0.446141	+	0.894963i	$0.647202\pi$
$458$	10212.5	+	17688.6i	0.0486858	+	0.0843262i
$459$	65284.9	+	113077.i	0.309876	+	0.536720i
$460$	−46448.3	+	4634.99i	−0.219510	+	0.0219045i
$461$			92915.4i			0.437206i	0.975814	+	0.218603i	$0.0701499\pi$
$461$			92915.4i			0.437206i	−0.975814	+	0.218603i	$0.929850\pi$
$462$	−9393.56	+	9448.53i	−0.0440095	+	0.0442670i
$463$		−	215653.i		−	1.00599i	−0.864289	−	0.502996i	$-0.832231\pi$
$463$		−	215653.i		−	1.00599i	0.864289	−	0.502996i	$-0.167769\pi$
$464$	52975.7	−	91756.6i	0.246060	−	0.426188i
$465$	26118.8	−	57842.9i	0.120795	−	0.267513i
$466$	−17772.9	−	30783.6i	−0.0818441	−	0.141758i
$467$	85447.4	−	147999.i	0.391801	−	0.678619i	−0.600886	−	0.799334i	$-0.705186\pi$
$467$	85447.4	−	147999.i	0.391801	−	0.678619i	0.992687	+	0.120716i	$0.0385189\pi$
$468$	110446.			0.504266
$469$	−113701.	+	114367.i	−0.516915	+	0.519941i
$470$	33784.3	+	47018.4i	0.152940	+	0.212849i
$471$	−16807.7	+	29111.7i	−0.0757645	+	0.131228i
$472$	−26211.6	−	45399.8i	−0.117655	−	0.203784i
$473$	113565.	−	65566.9i	0.507601	−	0.293064i
$474$	49.3821	+	28.5108i	0.000219793	+	0.000126897i
$475$	−196556.	−	66159.2i	−0.871161	−	0.293226i
$476$	41317.3	−	156018.i	0.182355	−	0.688588i
$477$			238889.i			1.04993i
$478$	26634.9	+	15377.7i	0.116572	+	0.0673031i
$479$	−60743.0	+	35070.0i	−0.264744	+	0.152850i	−0.626497	−	0.779424i	$-0.715512\pi$
$479$	−60743.0	+	35070.0i	−0.264744	+	0.152850i	0.361753	+	0.932274i	$0.382178\pi$
$480$	21751.2	−	48170.3i	0.0944061	−	0.209072i
$481$	−263922.	−	152375.i	−1.14074	−	0.658605i
$482$	14973.7			0.0644518
$483$	6610.74	+	24386.8i	0.0283371	+	0.104535i
$484$	−86899.4			−0.370959
$485$	21307.6	+	213529.i	0.0905839	+	0.907763i
$486$	−34749.2	+	20062.4i	−0.147120	+	0.0849398i
$487$	−103456.	+	59730.4i	−0.436212	+	0.251847i	−0.701990	−	0.712187i	$-0.747705\pi$
$487$	−103456.	+	59730.4i	−0.436212	+	0.251847i	0.265777	+	0.964034i	$0.414371\pi$
$488$	−69892.1	+	121057.i	−0.293487	+	0.508334i
$489$		−	80873.4i		−	0.338211i
$490$	4195.45	+	39697.7i	0.0174738	+	0.165338i
$491$	244965.			1.01611			0.508055	−	0.861325i	$-0.330365\pi$
$491$	244965.			1.01611			0.508055	+	0.861325i	$0.330365\pi$
$492$	−88057.4	−	50839.9i	−0.363777	−	0.210027i
$493$	−47733.2	−	82676.4i	−0.196394	−	0.340164i
$494$	12525.0	+	21693.9i	0.0513242	+	0.0888961i
$495$	14773.2	+	148046.i	0.0602927	+	0.604208i
$496$			138832.i			0.564321i
$497$	−286524.	+	77670.5i	−1.15997	+	0.314444i
$498$		−	20702.6i		−	0.0834770i
$499$	−31262.0	+	54147.3i	−0.125550	+	0.217458i	−0.921948	−	0.387315i	$-0.873403\pi$
$499$	−31262.0	+	54147.3i	−0.125550	+	0.217458i	0.796398	+	0.604773i	$0.206736\pi$
$500$	165489.	−	178061.i	0.661958	−	0.712244i
$501$	105755.	+	183173.i	0.421333	+	0.729770i
$502$	3103.37	−	5375.20i	0.0123148	−	0.0213298i
$503$	−69780.9			−0.275804			−0.137902	−	0.990446i	$-0.544036\pi$
$503$	−69780.9			−0.275804			−0.137902	+	0.990446i	$0.544036\pi$
$504$	62170.3	+	16464.2i	0.244750	+	0.0648157i
$505$	−95099.7	−	132352.i	−0.372904	−	0.518978i
$506$	−3797.55	+	6577.56i	−0.0148321	+	0.0256900i
$507$	−33675.4	−	58327.5i	−0.131008	−	0.226912i
$508$	−127067.	+	73362.3i	−0.492387	+	0.284279i
$509$	371065.	+	214235.i	1.43224	+	0.826903i	0.997291	−	0.0735539i	$-0.0234341\pi$
$509$	371065.	+	214235.i	1.43224	+	0.826903i	0.434946	+	0.900456i	$0.356767\pi$
$510$	−8824.96	−	12281.9i	−0.0339291	−	0.0472199i
$511$	47865.0	+	47586.5i	0.183306	+	0.182239i
$512$			194516.i			0.742020i
$513$	177229.	+	102323.i	0.673441	+	0.388811i
$514$	−5040.34	+	2910.04i	−0.0190780	+	0.0110147i
$515$	169786.	+	76666.2i	0.640157	+	0.289061i
$516$	79773.5	+	46057.3i	0.299612	+	0.172981i
$517$	−331381.			−1.23978
$518$	−62041.8	−	61680.8i	−0.231220	−	0.229874i
$519$	−161761.			−0.600536
$520$	−59263.8	+	5913.83i	−0.219171	+	0.0218707i
$521$	258422.	−	149200.i	0.952037	−	0.549659i	0.0583238	−	0.998298i	$-0.481424\pi$
$521$	258422.	−	149200.i	0.952037	−	0.549659i	0.893713	+	0.448639i	$0.148091\pi$
$522$	16241.7	−	9377.15i	0.0596061	−	0.0344136i
$523$	102410.	−	177379.i	0.374403	−	0.648485i	−0.615835	−	0.787876i	$-0.711181\pi$
$523$	102410.	−	177379.i	0.374403	−	0.648485i	0.990237	+	0.139391i	$0.0445144\pi$
$524$			304350.i			1.10844i
$525$	−109806.	−	72501.9i	−0.398389	−	0.263045i
$526$	57838.9			0.209049
$527$	108334.	+	62546.6i	0.390070	+	0.225207i
$528$	48034.2	+	83197.7i	0.172299	+	0.298431i
$529$	−132719.	−	229876.i	−0.474265	−	0.821451i
$530$	−6306.00	−	63193.9i	−0.0224493	−	0.224969i
$531$			156217.i			0.554036i
$532$	−66183.6	−	244149.i	−0.233845	−	0.862644i
$533$			172671.i			0.607804i
$534$	−1350.15	+	2338.52i	−0.00473477	+	0.00820086i
$535$	−198054.	+	438611.i	−0.691951	+	1.53240i
$536$	−34536.3	−	59818.6i	−0.120212	−	0.208213i
$537$	−102095.	+	176834.i	−0.354043	+	0.613220i
$538$	73388.5			0.253550
$539$	−198532.	−	113083.i	−0.683364	−	0.389241i
$540$	−194799.	+	139970.i	−0.668036	+	0.480007i
$541$	−182333.	+	315811.i	−0.622976	+	1.07903i	0.365952	+	0.930634i	$0.380743\pi$
$541$	−182333.	+	315811.i	−0.622976	+	1.07903i	−0.988928	+	0.148393i	$0.952590\pi$
$542$	−34044.6	−	58967.0i	−0.115891	−	0.200729i
$543$	−164660.	+	95066.4i	−0.558455	+	0.322424i
$544$	90218.0	+	52087.4i	0.304856	+	0.176009i
$545$	305295.	−	219365.i	1.02784	−	0.738541i
$546$	4158.25	+	15339.6i	0.0139484	+	0.0514553i
$547$		−	537341.i		−	1.79587i	−0.440126	−	0.897936i	$-0.645066\pi$
$547$		−	537341.i		−	1.79587i	0.440126	−	0.897936i	$-0.354934\pi$
$548$	−61948.6	−	35766.0i	−0.206286	−	0.119099i
$549$	360739.	−	208273.i	1.19687	−	0.691015i
$550$	−7816.00	−	38773.0i	−0.0258380	−	0.128175i
$551$	−129581.	−	74813.8i	−0.426814	−	0.246421i
$552$	−10822.0			−0.0355164
$553$	−250.327	+	945.257i	−0.000818574	+	0.00309101i
$554$	97595.4			0.317987
$555$	286949.	−	28634.1i	0.931576	−	0.0929602i
$556$	−322427.	+	186153.i	−1.04299	+	0.602173i
$557$	−202385.	+	116847.i	−0.652332	+	0.376624i	−0.789349	−	0.613945i	$-0.789582\pi$
$557$	−202385.	+	116847.i	−0.652332	+	0.376624i	0.137017	+	0.990569i	$0.456248\pi$
$558$	−12287.2	+	21282.1i	−0.0394625	+	0.0683511i
$559$		−	156427.i		−	0.500596i
$560$	284184.	+	45693.2i	0.906199	+	0.145705i
$561$	86561.5			0.275042
$562$	30347.8	+	17521.3i	0.0960849	+	0.0554746i
$563$	130697.	+	226374.i	0.412335	+	0.714185i	0.995145	−	0.0984240i	$-0.0313801\pi$
$563$	130697.	+	226374.i	0.412335	+	0.714185i	−0.582810	+	0.812609i	$0.698047\pi$
$564$	−116389.	−	201591.i	−0.365892	−	0.633744i
$565$	396750.	−	39590.9i	1.24285	−	0.124022i
$566$		−	40264.2i		−	0.125686i
$567$	−83950.5	−	83462.0i	−0.261130	−	0.259611i
$568$		−	127149.i		−	0.394109i
$569$	−5416.87	+	9382.29i	−0.0167311	+	0.0289791i	−0.874270	−	0.485440i	$-0.838659\pi$
$569$	−5416.87	+	9382.29i	−0.0167311	+	0.0289791i	0.857539	+	0.514420i	$0.171993\pi$
$570$	−21603.4	−	9754.97i	−0.0664925	−	0.0300245i
$571$	−220481.	−	381884.i	−0.676237	−	1.17128i	−0.976106	−	0.217297i	$-0.930276\pi$
$571$	−220481.	−	381884.i	−0.676237	−	1.17128i	0.299868	−	0.953981i	$-0.403057\pi$
$572$	84027.2	−	145539.i	0.256820	−	0.444824i
$573$	−41886.9			−0.127576
$574$	−12689.6	+	47917.1i	−0.0385145	+	0.145434i
$575$	−71090.3	−	23928.5i	−0.215018	−	0.0723734i
$576$	107325.	−	185892.i	0.323487	−	0.560295i
$577$	166668.	+	288677.i	0.500610	+	0.867083i	1.00000		0.000705086i	$0.000224436\pi$
$577$	166668.	+	288677.i	0.500610	+	0.867083i	−0.499389	+	0.866378i	$0.666442\pi$
$578$	−22287.7	+	12867.8i	−0.0667128	+	0.0385167i
$579$	10586.6	+	6112.20i	0.0315792	+	0.0182322i
$580$	142428.	−	102340.i	0.423389	−	0.304220i
$581$	342655.	−	92886.6i	1.01509	−	0.275170i
$582$			24526.4i			0.0724082i
$583$	314793.	+	181746.i	0.926165	+	0.534722i
$584$	−25035.4	+	14454.2i	−0.0734056	+	0.0423808i
$585$	161752.	+	73038.9i	0.472649	+	0.213424i
$586$	24140.7	+	13937.6i	0.0702999	+	0.0405877i
$587$	−309306.			−0.897659			−0.448830	−	0.893617i	$-0.648159\pi$
$587$	−309306.			−0.897659			−0.448830	+	0.893617i	$0.648159\pi$
$588$	−936.514	−	160492.i	−0.00270869	−	0.464192i
$589$	196062.			0.565150
$590$	−4123.68	−	41324.4i	−0.0118463	−	0.118714i
$591$	−104157.	+	60135.1i	−0.298204	+	0.172168i
$592$	−546300.	+	315406.i	−1.55879	+	0.899968i
$593$	118891.	−	205926.i	0.338097	−	0.585601i	−0.645978	−	0.763356i	$-0.723550\pi$
$593$	118891.	−	205926.i	0.338097	−	0.585601i	0.984075	+	0.177755i	$0.0568836\pi$
$594$			39029.4i			0.110616i
$595$	163686.	−	201170.i	0.462357	−	0.568236i
$596$	−499723.			−1.40682
$597$	−184747.	−	106664.i	−0.518357	−	0.299274i
$598$	4530.03	+	7846.24i	0.0126677	+	0.0219411i
$599$	−280699.	−	486185.i	−0.782325	−	1.35503i	−0.930584	−	0.366078i	$-0.880700\pi$
$599$	−280699.	−	486185.i	−0.782325	−	1.35503i	0.148259	−	0.988949i	$-0.452633\pi$
$600$	42276.3	−	37267.8i	0.117434	−	0.103522i
$601$		−	512891.i		−	1.41996i	−0.704222	−	0.709980i	$-0.748704\pi$
$601$		−	512891.i		−	1.41996i	0.704222	−	0.709980i	$-0.251296\pi$
$602$	11495.9	−	43409.4i	0.0317211	−	0.119782i
$603$			205830.i			0.566076i
$604$	−151237.	+	261950.i	−0.414557	+	0.718033i
$605$	−127267.	−	57467.2i	−0.347701	−	0.157003i
$606$	−9313.63	−	16131.7i	−0.0253614	−	0.0439273i
$607$	321335.	−	556568.i	0.872128	−	1.51057i	0.0123369	−	0.999924i	$-0.496073\pi$
$607$	321335.	−	556568.i	0.872128	−	1.51057i	0.859791	−	0.510646i	$-0.170594\pi$
$608$	163276.			0.441688
$609$	−67323.5	−	66931.8i	−0.181523	−	0.180467i
$610$	−89929.3	+	64617.3i	−0.241680	+	0.173656i
$611$	−197649.	+	342338.i	−0.529434	+	0.917007i
$612$	−102996.	−	178395.i	−0.274991	−	0.476298i
$613$	230007.	−	132795.i	0.612097	−	0.353394i	−0.161689	−	0.986842i	$-0.551694\pi$
$613$	230007.	−	132795.i	0.612097	−	0.353394i	0.773786	+	0.633447i	$0.218361\pi$
$614$	34090.1	+	19681.9i	0.0904256	+	0.0522073i
$615$	−95342.3	−	132690.i	−0.252078	−	0.350822i
$616$	68994.5	−	69398.3i	0.181825	−	0.182889i
$617$			389675.i			1.02360i	0.859103	+	0.511802i	$0.171022\pi$
$617$			389675.i			1.02360i	−0.859103	+	0.511802i	$0.828978\pi$
$618$	18439.6	+	10646.1i	0.0482809	+	0.0278750i
$619$	135142.	−	78024.5i	0.352704	−	0.203634i	−0.313171	−	0.949697i	$-0.601391\pi$
$619$	135142.	−	78024.5i	0.352704	−	0.203634i	0.665876	+	0.746063i	$0.268058\pi$
$620$	−94575.5	+	209448.i	−0.246034	+	0.544869i
$621$	64100.1	+	37008.2i	0.166217	+	0.0959654i
$622$	−104343.			−0.269700
$623$	−44763.3	−	11854.4i	−0.115331	−	0.0305425i
$624$	114598.			0.294312
$625$	360118.	−	151337.i	0.921902	−	0.387424i
$626$	−53335.8	+	30793.4i	−0.136104	+	0.0785795i
$627$	117494.	−	67835.2i	0.298869	−	0.172552i
$628$	60860.0	−	105413.i	0.154317	−	0.267284i
$629$			568388.i			1.43662i
$630$	39519.6	+	32156.0i	0.0995707	+	0.0810178i
$631$	404761.			1.01658			0.508288	−	0.861187i	$-0.330278\pi$
$631$	404761.			1.01658			0.508288	+	0.861187i	$0.330278\pi$
$632$	−362.706	−	209.408i	−0.000908071	−	0.000524275i
$633$	11235.1	+	19459.8i	0.0280395	+	0.0485658i
$634$	−6629.68	−	11482.9i	−0.0164935	−	0.0285677i
$635$	−234609.	+	23411.2i	−0.581832	+	0.0580599i
$636$			255334.i			0.631240i
$637$	−235234.	+	137649.i	−0.579724	+	0.339230i
$638$		−	28536.4i		−	0.0701065i
$639$	−189447.	+	328131.i	−0.463965	+	0.803611i
$640$	−104483.	+	231389.i	−0.255086	+	0.564915i
$641$	279499.	+	484107.i	0.680243	+	1.17822i	0.974906	+	0.222615i	$0.0714592\pi$
$641$	279499.	+	484107.i	0.680243	+	1.17822i	−0.294663	+	0.955601i	$0.595207\pi$
$642$	−27502.4	+	47635.5i	−0.0667268	+	0.115574i
$643$	−580893.			−1.40499			−0.702497	−	0.711687i	$-0.747931\pi$
$643$	−580893.			−1.40499			−0.702497	+	0.711687i	$0.747931\pi$
$644$	−23937.3	−	88303.9i	−0.0577170	−	0.212916i
$645$	86373.1	+	120207.i	0.207615	+	0.288942i
$646$	23360.2	−	40461.0i	0.0559772	−	0.0969553i
$647$	−83049.5	−	143846.i	−0.198394	−	0.343628i	0.749614	−	0.661875i	$-0.230239\pi$
$647$	−83049.5	−	143846.i	−0.198394	−	0.343628i	−0.948008	+	0.318247i	$0.896906\pi$
$648$	43909.7	−	25351.3i	0.104571	−	0.0603739i
$649$	205853.	+	118849.i	0.488728	+	0.282167i
$650$	−44716.8	−	15051.3i	−0.105839	−	0.0356245i
$651$	120249.	+	31844.9i	0.283740	+	0.0751412i
$652$			292840.i			0.688868i
$653$	496304.	+	286541.i	1.16392	+	0.671987i	0.952239	−	0.305353i	$-0.0987745\pi$
$653$	496304.	+	286541.i	1.16392	+	0.671987i	0.211676	+	0.977340i	$0.432108\pi$
$654$	37210.7	−	21483.6i	0.0869986	−	0.0502287i
$655$	−201269.	+	445731.i	−0.469130	+	1.03894i
$656$	309531.	+	178708.i	0.719278	+	0.415275i
$657$	86144.6			0.199571
$658$	−80007.2	+	80475.5i	−0.184790	+	0.185871i
$659$	−90012.4			−0.207268			−0.103634	−	0.994616i	$-0.533047\pi$
$659$	−90012.4			−0.207268			−0.103634	+	0.994616i	$0.533047\pi$
$660$	15790.2	+	158237.i	0.0362493	+	0.363263i
$661$	13094.0	−	7559.83i	0.0299688	−	0.0173025i	−0.484941	−	0.874547i	$-0.661159\pi$
$661$	13094.0	−	7559.83i	0.0299688	−	0.0173025i	0.514910	+	0.857245i	$0.327825\pi$
$662$	−13161.2	+	7598.62i	−0.0300317	+	0.0173388i
$663$	51628.8	−	89423.6i	0.117453	−	0.203435i
$664$			152058.i			0.344885i
$665$	64529.2	−	401332.i	0.145919	−	0.907530i
$666$	−111659.			−0.251736
$667$	−46867.0	−	27058.7i	−0.105345	−	0.0608211i
$668$	−382936.	−	663264.i	−0.858169	−	1.48639i
$669$	30672.6	+	53126.4i	0.0685327	+	0.118702i
$670$	−5433.34	−	54448.8i	−0.0121037	−	0.121294i
$671$		−	633813.i		−	1.40772i
$672$	100141.	+	26519.7i	0.221755	+	0.0587260i
$673$		−	191645.i		−	0.423123i	−0.977365	−	0.211561i	$-0.932145\pi$
$673$		−	191645.i		−	0.423123i	0.977365	−	0.211561i	$-0.0678548\pi$
$674$	21532.4	−	37295.2i	0.0473994	−	0.0820981i
$675$	−377853.	+	76169.0i	−0.829308	+	0.167175i
$676$	121938.	+	211202.i	0.266836	+	0.462174i
$677$	−285374.	+	494283.i	−0.622641	+	1.07845i	0.366351	+	0.930477i	$0.380607\pi$
$677$	−285374.	+	494283.i	−0.622641	+	1.07845i	−0.988992	+	0.147969i	$0.952726\pi$
$678$	45571.7			0.0991369
$679$	−405944.	+	110043.i	−0.880494	+	0.238683i
$680$	64818.3	+	90208.9i	0.140178	+	0.195089i
$681$	2149.18	−	3722.49i	0.00463424	−	0.00802674i
$682$	18696.2	+	32382.7i	0.0401961	+	0.0696216i
$683$	−88543.5	+	51120.6i	−0.189808	+	0.109586i	−0.591893	−	0.806017i	$-0.701619\pi$
$683$	−88543.5	+	51120.6i	−0.189808	+	0.109586i	0.402085	+	0.915603i	$0.368286\pi$
$684$	−279603.	−	161429.i	−0.597627	−	0.345040i
$685$	−67073.5	−	93347.6i	−0.142945	−	0.198940i
$686$	−75394.7	+	20910.9i	−0.160211	+	0.0444350i
$687$		−	131959.i		−	0.279592i
$688$	−280413.	−	161896.i	−0.592408	−	0.342027i
$689$	375511.	−	216801.i	0.791014	−	0.456692i
$690$	−7813.53	−	3528.18i	−0.0164115	−	0.00741058i
$691$	−127015.	−	73331.9i	−0.266010	−	0.153581i	0.361063	−	0.932541i	$-0.382414\pi$
$691$	−127015.	−	73331.9i	−0.266010	−	0.153581i	−0.627073	+	0.778961i	$0.715747\pi$
$692$	585732.			1.22317
$693$	−281453.	+	76296.1i	−0.586057	+	0.158868i
$694$	−52511.1			−0.109026
$695$	−595310.	+	59404.9i	−1.23246	+	0.122985i
$696$	35213.0	−	20330.3i	0.0726917	−	0.0419686i
$697$	278900.	−	161023.i	0.574094	−	0.331453i
$698$	15695.7	−	27185.8i	0.0322159	−	0.0557996i
$699$			229649.i			0.470014i
$700$	397604.	+	262527.i	0.811437	+	0.535770i
$701$	−665857.			−1.35502			−0.677509	−	0.735515i	$-0.736940\pi$
$701$	−665857.			−1.35502			−0.677509	+	0.735515i	$0.736940\pi$
$702$	40319.9	+	23278.7i	0.0818172	+	0.0472372i
$703$	445426.	+	771500.i	0.901290	+	1.56108i
$704$	−163305.	−	282853.i	−0.329499	−	0.570710i
$705$	−37141.7	−	372206.i	−0.0747281	−	0.748868i
$706$			55149.1i			0.110644i
$707$	225213.	−	226531.i	0.450562	−	0.453199i
$708$			166971.i			0.333099i
$709$	−1254.60	+	2173.03i	−0.00249581	+	0.00432288i	−0.867271	−	0.497837i	$-0.834128\pi$
$709$	−1254.60	+	2173.03i	−0.00249581	+	0.00432288i	0.864775	+	0.502160i	$0.167461\pi$
$710$	41453.1	−	91802.3i	0.0822318	−	0.182111i
$711$	624.018	+	1080.83i	0.00123441	+	0.00213805i
$712$	9916.67	−	17176.2i	0.0195617	−	0.0338818i
$713$	70911.8			0.139489
$714$	20899.1	−	21021.4i	0.0409949	−	0.0412349i
$715$	219307.	−	157580.i	0.428983	−	0.308240i
$716$	369683.	−	640309.i	0.721112	−	1.24900i
$717$	−99349.8	−	172079.i	−0.193254	−	0.334726i
$718$	−73296.3	+	42317.6i	−0.142178	+	0.0820867i
$719$	631609.	+	364660.i	1.22177	+	0.705391i	0.965296	−	0.261159i	$-0.0841048\pi$
$719$	631609.	+	364660.i	1.22177	+	0.705391i	0.256477	+	0.966550i	$0.417438\pi$
$720$	298338.	−	214367.i	0.575498	−	0.413516i
$721$	−93474.0	+	352966.i	−0.179813	+	0.678988i
$722$			13442.0i			0.0257863i
$723$	−83779.2	−	48369.9i	−0.160273	−	0.0925334i
$724$	596229.	−	344233.i	1.13746	−	0.656712i
$725$	276269.	−	55691.2i	0.525600	−	0.105952i
$726$	−13821.9	−	7980.08i	−0.0262237	−	0.0151403i
$727$	786936.			1.48892			0.744458	−	0.667669i	$-0.232708\pi$
$727$	786936.			1.48892			0.744458	+	0.667669i	$0.232708\pi$
$728$	−30541.8	−	112668.i	−0.0576278	−	0.212587i
$729$	63545.1			0.119571
$730$	−22788.0	+	2273.98i	−0.0427623	+	0.00426717i
$731$	−252663.	+	145875.i	−0.472832	+	0.272990i
$732$	385572.	−	222610.i	0.719587	−	0.415454i
$733$	−467180.	+	809180.i	−0.869514	+	1.50604i	−0.00701978	+	0.999975i	$0.502234\pi$
$733$	−467180.	+	809180.i	−0.869514	+	1.50604i	−0.862494	+	0.506067i	$0.831099\pi$
$734$		−	100689.i		−	0.186891i
$735$	104763.	−	235665.i	0.193924	−	0.436234i
$736$	59053.8			0.109016
$737$	271231.	+	156595.i	0.499349	+	0.288299i
$738$	31632.8	+	54789.6i	0.0580798	+	0.100597i
$739$	−392715.	−	680202.i	−0.719098	−	1.24551i	−0.961358	−	0.275303i	$-0.911222\pi$
$739$	−392715.	−	680202.i	−0.719098	−	1.24551i	0.242259	−	0.970212i	$-0.422111\pi$
$740$	−1.03903e6	+	103683.i	−1.89743	+	0.189341i
$741$		−	161839.i		−	0.294745i
$742$	120139.	−	32567.2i	0.218211	−	0.0591524i
$743$		−	735260.i		−	1.33187i	−0.746008	−	0.665937i	$-0.768032\pi$
$743$		−	735260.i		−	1.33187i	0.746008	−	0.665937i	$-0.231968\pi$
$744$	−26639.5	+	46140.9i	−0.0481260	+	0.0833567i
$745$	−731862.	−	330470.i	−1.31861	−	0.595415i
$746$	69525.1	+	120421.i	0.124929	+	0.216384i
$747$	226560.	−	392414.i	0.406016	−	0.703240i
$748$	−313437.			−0.560205
$749$	−911825.	−	241474.i	−1.62535	−	0.430433i
$750$	42673.7	−	13124.7i	0.0758643	−	0.0233327i
$751$	154880.	−	268260.i	0.274609	−	0.475637i	−0.695427	−	0.718596i	$-0.744785\pi$
$751$	154880.	−	268260.i	0.274609	−	0.475637i	0.970036	+	0.242960i	$0.0781182\pi$
$752$	409119.	+	708615.i	0.723459	+	1.25307i
$753$	−34727.3	+	20049.8i	−0.0612464	+	0.0353606i
$754$	−29480.0	−	17020.3i	−0.0518543	−	0.0299381i
$755$	−394721.	+	283621.i	−0.692462	+	0.497559i
$756$	−333414.	−	331474.i	−0.583364	−	0.579970i
$757$		−	270922.i		−	0.472773i	−0.971659	−	0.236387i	$-0.924037\pi$
$757$		−	270922.i		−	0.472773i	0.971659	−	0.236387i	$-0.0759632\pi$
$758$	−109416.	−	63171.1i	−0.190432	−	0.109946i
$759$	42495.3	−	24534.7i	0.0737661	−	0.0425889i
$760$	158675.	+	71649.1i	0.274714	+	0.124046i
$761$	−243116.	−	140363.i	−0.419802	−	0.242373i	0.275190	−	0.961390i	$-0.411259\pi$
$761$	−243116.	−	140363.i	−0.419802	−	0.242373i	−0.694993	+	0.719017i	$0.744592\pi$
$762$	−26947.8			−0.0464102
$763$	522535.	+	519495.i	0.897566	+	0.892344i
$764$	151671.			0.259846
$765$	−32867.9	−	329377.i	−0.0561629	−	0.562821i
$766$	127989.	−	73894.3i	0.218129	−	0.125937i
$767$	245558.	−	141773.i	0.417410	−	0.240992i
$768$	103465.	−	179207.i	0.175418	−	0.303832i
$769$			477319.i			0.807154i	0.914946	+	0.403577i	$0.132233\pi$
$769$			477319.i			0.807154i	−0.914946	+	0.403577i	$0.867767\pi$
$770$	72439.6	−	27612.4i	0.122178	−	0.0465717i
$771$	37601.5			0.0632552
$772$	−38333.9	−	22132.1i	−0.0643203	−	0.0371354i
$773$	−247892.	−	429361.i	−0.414861	−	0.718561i	0.580553	−	0.814223i	$-0.302837\pi$
$773$	−247892.	−	429361.i	−0.414861	−	0.718561i	−0.995414	+	0.0956621i	$0.969503\pi$
$774$	−28657.0	−	49635.4i	−0.0478353	−	0.0828532i
$775$	−277018.	+	244200.i	−0.461216	+	0.406576i
$776$		−	180143.i		−	0.299154i
$777$	147880.	+	545524.i	0.244944	+	0.903591i
$778$		−	134766.i		−	0.222650i
$779$	252376.	−	437128.i	0.415885	−	0.720334i
$780$	172887.	+	78066.9i	0.284167	+	0.128315i
$781$	288261.	+	499283.i	0.472589	+	0.818549i
$782$	8448.91	−	14633.9i	0.0138162	−	0.0239303i
$783$	−278095.			−0.453597
$784$	3291.95	+	564145.i	0.00535576	+	0.917822i
$785$	158842.	−	114133.i	0.257766	−	0.185214i
$786$	−27948.8	+	48408.8i	−0.0452396	+	0.0783572i
$787$	194428.	+	336759.i	0.313913	+	0.543712i	0.979206	−	0.202870i	$-0.0650268\pi$
$787$	194428.	+	336759.i	0.313913	+	0.543712i	−0.665293	+	0.746582i	$0.731693\pi$
$788$	377150.	−	217748.i	0.607381	−	0.350672i
$789$	−323614.	−	186838.i	−0.519844	−	0.300132i
$790$	−193.604	−	269.443i	−0.000310213	−	0.000431730i
$791$	204467.	+	754270.i	0.326790	+	1.20552i
$792$		−	124899.i		−	0.199117i
$793$	−654770.	−	378031.i	−1.04122	−	0.601148i
$794$	48759.6	−	28151.4i	0.0773427	−	0.0446538i
$795$	−168854.	+	373945.i	−0.267164	+	0.591662i
$796$	668964.	+	386227.i	1.05579	+	0.609559i
$797$	−418101.			−0.658211			−0.329105	−	0.944293i	$-0.606747\pi$
$797$	−418101.			−0.658211			−0.329105	+	0.944293i	$0.606747\pi$
$798$	11893.6	−	44911.2i	0.0186770	−	0.0705259i
$799$	737266.			1.15486
$800$	−230694.	+	203364.i	−0.360460	+	0.317756i
$801$	−51183.5	+	29550.8i	−0.0797747	+	0.0460579i
$802$	13527.8	−	7810.28i	0.0210319	−	0.0121428i
$803$	65538.6	−	113516.i	0.101640	−	0.176046i
$804$			220000.i			0.340338i
$805$	23338.9	−	145154.i	0.0360155	−	0.223994i
$806$	44604.5			0.0686608
$807$	−410615.	−	237068.i	−0.630503	−	0.364021i
$808$	68407.5	+	118485.i	0.104781	+	0.181485i
$809$	−46869.0	−	81179.5i	−0.0716125	−	0.124036i	0.827996	−	0.560735i	$-0.189481\pi$
$809$	−46869.0	−	81179.5i	−0.0716125	−	0.124036i	−0.899608	+	0.436698i	$0.856148\pi$
$810$	39968.0	−	3988.33i	0.0609175	−	0.00607884i
$811$			19252.2i			0.0292711i	0.999893	+	0.0146355i	$0.00465880\pi$
$811$			19252.2i			0.0292711i	−0.999893	+	0.0146355i	$0.995341\pi$
$812$	243776.	+	242358.i	0.369726	+	0.367574i
$813$			439901.i			0.665539i
$814$	−84950.0	+	147138.i	−0.128208	+	0.222062i
$815$	−193657.	+	428875.i	−0.291554	+	0.645677i
$816$	−106868.	−	185101.i	−0.160497	−	0.277989i
$817$	−228634.	+	396006.i	−0.342529	+	0.593278i
$818$	71298.6			0.106555
$819$	−89051.4	+	336266.i	−0.132762	+	0.501320i
$820$	345231.	+	480466.i	0.513432	+	0.714553i
$821$	−79476.0	+	137656.i	−0.117910	+	0.204226i	−0.918939	−	0.394399i	$-0.870953\pi$
$821$	−79476.0	+	137656.i	−0.117910	+	0.204226i	0.801029	+	0.598625i	$0.204286\pi$
$822$	−6568.88	−	11377.6i	−0.00972182	−	0.0168387i
$823$	−268716.	+	155143.i	−0.396729	+	0.229051i	−0.685071	−	0.728476i	$-0.740229\pi$
$823$	−268716.	+	155143.i	−0.396729	+	0.229051i	0.288343	+	0.957527i	$0.406896\pi$
$824$	−135437.	−	78194.4i	−0.199472	−	0.115165i
$825$	−81518.2	+	242186.i	−0.119770	+	0.355829i
$826$	78562.7	−	21296.7i	0.115148	−	0.0312142i
$827$			208368.i			0.304663i	0.988329	+	0.152331i	$0.0486781\pi$
$827$			208368.i			0.304663i	−0.988329	+	0.152331i	$0.951322\pi$
$828$	−101127.	−	58385.7i	−0.147505	−	0.0851619i
$829$	533400.	−	307959.i	0.776147	−	0.448109i	−0.0589161	−	0.998263i	$-0.518764\pi$
$829$	533400.	−	307959.i	0.776147	−	0.448109i	0.835063	+	0.550154i	$0.185431\pi$
$830$	−49573.9	+	109787.i	−0.0719610	+	0.159365i
$831$	−546055.	−	315265.i	−0.790741	−	0.456534i
$832$	−389607.			−0.562834
$833$	441699.	+	251590.i	0.636555	+	0.362579i
$834$	−68378.8			−0.0983080
$835$	−122202.	−	1.22461e6i	−0.175269	−	1.75641i
$836$	−425443.	+	245629.i	−0.608735	+	0.351453i
$837$	315578.	−	182199.i	0.450460	−	0.260073i
$838$	−39147.5	+	67805.5i	−0.0557463	+	0.0965554i
$839$			1.15962e6i			1.64738i	0.567041	+	0.823690i	$0.308088\pi$
$839$			1.15962e6i			1.64738i	−0.567041	+	0.823690i	$0.691912\pi$
$840$	85681.0	+	69716.2i	0.121430	+	0.0988041i
$841$	−503951.			−0.712519
$842$	−55557.3	−	32076.0i	−0.0783640	−	0.0452435i
$843$	−113199.	−	196067.i	−0.159290	−	0.275898i
$844$	−40682.0	−	70463.3i	−0.0571107	−	0.0989186i
$845$	38912.5	+	389951.i	0.0544974	+	0.546131i
$846$			144835.i			0.202364i
$847$	70065.8	−	264575.i	0.0976651	−	0.368792i
$848$		−	897526.i		−	1.24812i
$849$	−130066.	+	225282.i	−0.180447	+	0.312543i
$850$	17389.3	+	86263.3i	0.0240682	+	0.119396i
$851$	161102.	+	279036.i	0.222454	+	0.385302i
$852$	−202488.	+	350720.i	−0.278946	+	0.483149i
$853$	932240.			1.28124			0.640619	−	0.767859i	$-0.278678\pi$
$853$	932240.			1.28124			0.640619	+	0.767859i	$0.278678\pi$
$854$	−153921.	−	153025.i	−0.211048	−	0.209820i
$855$	−302734.	−	421322.i	−0.414123	−	0.576344i
$856$	202002.	−	349877.i	0.275681	−	0.477494i
$857$	−609219.	−	1.05520e6i	−0.829491	−	1.43672i	−0.898438	−	0.439100i	$-0.855298\pi$
$857$	−609219.	−	1.05520e6i	−0.829491	−	1.43672i	0.0689479	−	0.997620i	$-0.478036\pi$
$858$	26730.1	−	15432.6i	0.0363100	−	0.0209636i
$859$	−161473.	−	93226.5i	−0.218834	−	0.126344i	0.386577	−	0.922257i	$-0.373658\pi$
$859$	−161473.	−	93226.5i	−0.218834	−	0.126344i	−0.605410	+	0.795914i	$0.706991\pi$
$860$	−312754.	−	435267.i	−0.422870	−	0.588517i
$861$	225787.	−	227109.i	0.304574	−	0.306357i
$862$			38691.3i			0.0520713i
$863$	140628.	+	81191.6i	0.188821	+	0.109016i	0.591430	−	0.806356i	$-0.298563\pi$
$863$	140628.	+	81191.6i	0.188821	+	0.109016i	−0.402610	+	0.915372i	$0.631897\pi$
$864$	262806.	−	151731.i	0.352053	−	0.203258i
$865$	857824.	+	387348.i	1.14648	+	0.517690i
$866$	−9462.93	−	5463.43i	−0.0126180	−	0.00728500i
$867$	166269.			0.221193
$868$	−435419.	−	115310.i	−0.577920	−	0.153047i
$869$	1899.01			0.00251470
$870$	32052.0	−	3198.41i	0.0423465	−	0.00422567i
$871$	323546.	−	186799.i	0.426481	−	0.246229i
$872$	−273308.	+	157794.i	−0.359434	+	0.207519i
$873$	−268406.	+	464893.i	−0.352179	+	0.609992i
$874$		−	26484.5i		−	0.0346711i
$875$	408694.	+	647418.i	0.533805	+	0.845608i
$876$	92074.8			0.119987
$877$	336914.	+	194518.i	0.438047	+	0.252906i	0.702769	−	0.711418i	$-0.251947\pi$
$877$	336914.	+	194518.i	0.438047	+	0.252906i	−0.264722	+	0.964325i	$0.585280\pi$
$878$	30060.7	+	52066.7i	0.0389951	+	0.0675415i
$879$	−90046.2	−	155965.i	−0.116543	−	0.201859i
$880$	−55504.3	−	556222.i	−0.0716739	−	0.718261i
$881$		−	821070.i		−	1.05786i	−0.848665	−	0.528930i	$-0.822593\pi$
$881$		−	821070.i		−	1.05786i	0.848665	−	0.528930i	$-0.177407\pi$
$882$	−49424.6	+	86771.3i	−0.0635339	+	0.111542i
$883$			1.11465e6i			1.42961i	0.699326	+	0.714803i	$0.253484\pi$
$883$			1.11465e6i			1.42961i	−0.699326	+	0.714803i	$0.746516\pi$
$884$	−186946.	+	323800.i	−0.239228	+	0.414355i
$885$	−110419.	+	244534.i	−0.140980	+	0.312214i
$886$	74762.7	+	129493.i	0.0952396	+	0.164960i
$887$	−56971.7	+	98677.9i	−0.0724123	+	0.125422i	−0.899958	−	0.435977i	$-0.856403\pi$
$887$	−56971.7	+	98677.9i	−0.0724123	+	0.125422i	0.827546	+	0.561398i	$0.189736\pi$
$888$	−242084.			−0.307002
$889$	−120907.	−	446021.i	−0.152984	−	0.564354i
$890$	12759.6	−	9168.25i	0.0161086	−	0.0115746i
$891$	−114948.	+	199096.i	−0.144793	+	0.250788i
$892$	−111064.	−	192369.i	−0.139587	−	0.241772i
$893$	1.00073e6	−	577769.i	1.25491	−	0.724522i
$894$	−79484.1	−	45890.2i	−0.0994501	−	0.0574176i
$895$	964853.	−	693281.i	1.20452	−	0.865492i
$896$	−481033.	−	127389.i	−0.599182	−	0.158678i
$897$		−	58533.8i		−	0.0727482i
$898$	60782.9	+	35093.0i	0.0753753	+	0.0435179i
$899$	−230736.	+	133215.i	−0.285493	+	0.164830i
$900$	596117.	−	120167.i	0.735947	−	0.148355i
$901$	−700361.	−	404354.i	−0.862725	−	0.498095i
$902$	96264.6			0.118319
$903$	−204547.	+	205744.i	−0.250852	+	0.252320i
$904$	−334718.			−0.409584
$905$	1.10084e6	−	109851.i	1.34409	−	0.134124i
$906$	−48110.4	+	27776.5i	−0.0586114	+	0.0338393i
$907$	−282112.	+	162877.i	−0.342931	+	0.197991i	−0.661567	−	0.749886i	$-0.730108\pi$
$907$	−282112.	+	162877.i	−0.342931	+	0.197991i	0.318637	+	0.947877i	$0.396775\pi$
$908$	−7782.12	+	13479.0i	−0.00943900	+	0.0163488i
$909$		−	407697.i		−	0.493412i
$910$	14680.5	−	91303.9i	0.0177279	−	0.110257i
$911$	507497.			0.611500			0.305750	−	0.952112i	$-0.401093\pi$
$911$	507497.			0.611500			0.305750	+	0.952112i	$0.401093\pi$
$912$	−290114.	−	167497.i	−0.348802	−	0.201381i
$913$	−344733.	−	597095.i	−0.413563	−	0.716312i
$914$	−8487.99	−	14701.6i	−0.0101604	−	0.0175984i
$915$	711897.	−	71038.8i	0.850305	−	0.0848503i
$916$			477820.i			0.569473i
$917$	−926626.	−	245393.i	−1.10196	−	0.291826i
$918$		−	86833.7i		−	0.103039i
$919$	285733.	−	494905.i	0.338322	−	0.585991i	−0.645795	−	0.763511i	$-0.723474\pi$
$919$	285733.	−	494905.i	0.338322	−	0.585991i	0.984117	+	0.177520i	$0.0568074\pi$
$920$	57389.4	+	25914.0i	0.0678041	+	0.0306168i
$921$	−127158.	−	220244.i	−0.149908	−	0.259648i
$922$	30896.0	−	53513.5i	0.0363447	−	0.0629508i
$923$	687722.			0.807253
$924$	−300829.	+	81548.3i	−0.352351	+	0.0955148i
$925$	−1.59027e6	−	535272.i	−1.85860	−	0.625591i
$926$	−71708.7	+	124203.i	−0.0836276	+	0.144847i
$927$	233013.	+	403590.i	0.271157	+	0.469657i
$928$	−192152.	+	110939.i	−0.223125	+	0.128821i
$929$	203307.	+	117380.i	0.235571	+	0.136007i	0.613139	−	0.789975i	$-0.289906\pi$
$929$	203307.	+	117380.i	0.235571	+	0.136007i	−0.377569	+	0.925982i	$0.623240\pi$
$930$	−34276.6	+	24629.0i	−0.0396308	+	0.0284761i
$931$	796701.	−	4648.98i	0.919170	−	0.00536362i
$932$		−	831553.i		−	0.957322i
$933$	583807.	+	337061.i	0.670665	+	0.387209i
$934$	−98424.9	+	56825.6i	−0.112827	+	0.0651404i
$935$	−459039.	−	207278.i	−0.525081	−	0.237099i
$936$	−129029.	−	74494.8i	−0.147277	−	0.0850304i
$937$	123634.			0.140818			0.0704092	−	0.997518i	$-0.477569\pi$
$937$	123634.			0.140818			0.0704092	+	0.997518i	$0.477569\pi$
$938$	103514.	−	28060.4i	0.117650	−	0.0318925i
$939$	397891.			0.451266
$940$	134489.	+	1.34775e6i	0.152206	+	1.52529i
$941$	973539.	−	562073.i	1.09945	−	0.634766i	0.163371	−	0.986565i	$-0.447763\pi$
$941$	973539.	−	562073.i	1.09945	−	0.634766i	0.936076	+	0.351799i	$0.114430\pi$
$942$	19360.3	−	11177.7i	0.0218178	−	0.0125965i
$943$	91279.4	−	158101.i	0.102648	−	0.177791i
$944$		−	586920.i		−	0.658620i
$945$	−269090.	−	705943.i	−0.301324	−	0.790508i
$946$	−87208.7			−0.0974490
$947$	−1.01739e6	−	587388.i	−1.13445	−	0.654975i	−0.189400	−	0.981900i	$-0.560654\pi$
$947$	−1.01739e6	−	587388.i	−1.13445	−	0.654975i	−0.945050	+	0.326925i	$0.893988\pi$
$948$	666.976	+	1155.24i	0.000742153	+	0.00128545i
$949$	−78179.7	−	135411.i	−0.0868083	−	0.150356i
$950$	91204.8	+	103462.i	0.101058	+	0.114639i
$951$			85664.0i			0.0947191i
$952$	−153501.	+	154399.i	−0.169370	+	0.170362i
$953$			327215.i			0.360286i	0.983640	+	0.180143i	$0.0576561\pi$
$953$			327215.i			0.360286i	−0.983640	+	0.180143i	$0.942344\pi$
$954$	79434.9	−	137585.i	0.0872799	−	0.151173i
$955$	222127.	+	100301.i	0.243554	+	0.109976i
$956$	359743.	+	623093.i	0.393619	+	0.681768i
$957$	−92181.9	+	159664.i	−0.100652	+	0.174334i
$958$	46645.6			0.0508253
$959$	158842.	−	159771.i	0.172714	−	0.173725i
$960$	299396.	−	215127.i	0.324866	−	0.233427i
$961$	−287204.	+	497451.i	−0.310988	+	0.538646i
$962$	101335.	+	175518.i	0.109499	+	0.189658i
$963$	−1.04260e6	+	601947.i	−1.12426	+	0.649092i
$964$	303362.	+	175146.i	0.326443	+	0.188472i
$965$	−41505.2	−	57763.6i	−0.0445705	−	0.0620297i
$966$	4301.67	−	16243.5i	0.00460981	−	0.0174070i
$967$			317565.i			0.339610i	0.985478	+	0.169805i	$0.0543137\pi$
$967$			317565.i			0.339610i	−0.985478	+	0.169805i	$0.945686\pi$
$968$	101520.	+	58612.7i	0.108343	+	0.0625520i
$969$	−261404.	+	150922.i	−0.278397	+	0.160733i
$970$	58730.2	−	130064.i	0.0624192	−	0.138234i
$971$	−201536.	−	116357.i	−0.213754	−	0.123411i	0.389301	−	0.921111i	$-0.372717\pi$
$971$	−201536.	−	116357.i	−0.213754	−	0.123411i	−0.603055	+	0.797700i	$0.706050\pi$
$972$	−938674.			−0.993533
$973$	−306795.	−	1.13176e6i	−0.324058	−	1.19544i
$974$	79445.7			0.0837437
$975$	201573.	+	228663.i	0.212043	+	0.240540i
$976$	−1.35533e6	+	782498.i	−1.42280	+	0.821455i
$977$	−1.11662e6	+	644682.i	−1.16982	+	0.675393i	−0.953637	−	0.300961i	$-0.902693\pi$
$977$	−1.11662e6	+	644682.i	−1.16982	+	0.675393i	−0.216179	+	0.976354i	$0.569359\pi$
$978$	−26891.9	+	46578.1i	−0.0281153	+	0.0486972i
$979$			89928.7i			0.0938281i
$980$	−379342.	+	853335.i	−0.394983	+	0.888520i
$981$	940428.			0.977209
$982$	−141085.	−	81455.2i	−0.146304	−	0.0844687i
$983$	732173.	+	1.26816e6i	0.757717	+	1.31240i	0.944012	+	0.329910i	$0.107018\pi$
$983$	732173.	+	1.26816e6i	0.757717	+	1.31240i	−0.186296	+	0.982494i	$0.559648\pi$
$984$	68582.0	+	118787.i	0.0708304	+	0.122682i
$985$	696347.	−	69487.1i	0.717717	−	0.0716196i
$986$			63488.7i			0.0653044i
$987$	707609.	−	191818.i	0.726372	−	0.196904i
$988$			586013.i			0.600334i
$989$	−82692.5	+	143228.i	−0.0845422	+	0.146431i
$990$	40719.5	−	90177.7i	0.0415463	−	0.0920087i
$991$	−476293.	−	824964.i	−0.484984	−	0.840017i	0.514867	−	0.857270i	$-0.327841\pi$
$991$	−476293.	−	824964.i	−0.484984	−	0.840017i	−0.999851	+	0.0172533i	$0.994508\pi$
$992$	145367.	−	251783.i	0.147721	−	0.255860i
$993$	98184.0			0.0995732
$994$	190847.	+	50540.9i	0.193158	+	0.0511529i
$995$	724307.	+	1.00803e6i	0.731604	+	1.01819i
$996$	242157.	−	419428.i	0.244106	−	0.422804i
$997$	−511400.	−	885771.i	−0.514482	−	0.891109i	−0.999859	−	0.0168042i	$-0.994651\pi$
$997$	−511400.	−	885771.i	−0.514482	−	0.891109i	0.485377	−	0.874305i	$-0.338683\pi$
$998$	36009.9	−	20790.3i	0.0361544	−	0.0208737i
$999$	1.43390e6	+	827861.i	1.43677	+	0.829519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.i.a.19.7	✓	28
5.2	odd	4		175.5.i.e.26.8		28
5.3	odd	4		175.5.i.e.26.7		28
5.4	even	2	inner	35.5.i.a.19.8	yes	28
7.2	even	3		245.5.c.a.244.16		28
7.3	odd	6	inner	35.5.i.a.24.8	yes	28
7.5	odd	6		245.5.c.a.244.14		28
35.3	even	12		175.5.i.e.101.7		28
35.9	even	6		245.5.c.a.244.13		28
35.17	even	12		175.5.i.e.101.8		28
35.19	odd	6		245.5.c.a.244.15		28
35.24	odd	6	inner	35.5.i.a.24.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.i.a.19.7	✓	28	1.1	even	1	trivial
35.5.i.a.19.8	yes	28	5.4	even	2	inner
35.5.i.a.24.7	yes	28	35.24	odd	6	inner
35.5.i.a.24.8	yes	28	7.3	odd	6	inner
175.5.i.e.26.7		28	5.3	odd	4
175.5.i.e.26.8		28	5.2	odd	4
175.5.i.e.101.7		28	35.3	even	12
175.5.i.e.101.8		28	35.17	even	12
245.5.c.a.244.13		28	35.9	even	6
245.5.c.a.244.14		28	7.5	odd	6
245.5.c.a.244.15		28	35.19	odd	6
245.5.c.a.244.16		28	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.575938 - 0.332518i) q^{2} +(2.14828 + 3.72093i) q^{3} +(-7.77886 - 13.4734i) q^{4} +(-2.48237 - 24.8765i) q^{5} -2.85737i q^{6} +(47.2932 - 12.8202i) q^{7} +20.9870i q^{8} +(31.2698 - 54.1608i) q^{9} +O(q^{10})\)	\(q+(-0.575938 - 0.332518i) q^{2} +(2.14828 + 3.72093i) q^{3} +(-7.77886 - 13.4734i) q^{4} +(-2.48237 - 24.8765i) q^{5} -2.85737i q^{6} +(47.2932 - 12.8202i) q^{7} +20.9870i q^{8} +(31.2698 - 54.1608i) q^{9} +(-6.84217 + 15.1527i) q^{10} +(-47.5799 - 82.4108i) q^{11} +(33.4224 - 57.8893i) q^{12} -113.514 q^{13} +(-31.5009 - 8.34220i) q^{14} +(87.2308 - 62.6784i) q^{15} +(-117.483 + 203.487i) q^{16} +(105.857 + 183.350i) q^{17} +(-36.0189 + 20.7955i) q^{18} +(287.370 + 165.913i) q^{19} +(-315.860 + 226.957i) q^{20} +(149.302 + 148.433i) q^{21} +63.2847i q^{22} +(103.936 + 60.0075i) q^{23} +(-78.0913 + 45.0860i) q^{24} +(-612.676 + 123.505i) q^{25} +(65.3772 + 37.7455i) q^{26} +616.727 q^{27} +(-540.618 - 537.473i) q^{28} -450.921 q^{29} +(-71.0812 + 7.09306i) q^{30} +(511.698 - 295.429i) q^{31} +(426.131 - 246.027i) q^{32} +(204.430 - 354.083i) q^{33} -140.798i q^{34} +(-436.320 - 1144.66i) q^{35} -972.973 q^{36} +(2325.01 + 1342.35i) q^{37} +(-110.338 - 191.111i) q^{38} +(-243.861 - 422.379i) q^{39} +(522.083 - 52.0976i) q^{40} -1521.13i q^{41} +(-36.6320 - 135.134i) q^{42} +1378.04i q^{43} +(-740.235 + 1282.12i) q^{44} +(-1424.95 - 643.434i) q^{45} +(-39.9071 - 69.1212i) q^{46} +(1741.18 - 3015.81i) q^{47} -1009.55 q^{48} +(2072.29 - 1212.61i) q^{49} +(393.931 + 132.594i) q^{50} +(-454.822 + 787.775i) q^{51} +(883.012 + 1529.42i) q^{52} +(-3308.05 + 1909.90i) q^{53} +(-355.196 - 205.073i) q^{54} +(-1931.98 + 1388.19i) q^{55} +(269.057 + 992.543i) q^{56} +1425.71i q^{57} +(259.703 + 149.940i) q^{58} +(-2163.23 + 1248.94i) q^{59} +(-1523.05 - 687.727i) q^{60} +(5768.17 + 3330.25i) q^{61} -392.942 q^{62} +(784.495 - 2962.32i) q^{63} +3432.23 q^{64} +(281.785 + 2823.83i) q^{65} +(-235.478 + 135.953i) q^{66} +(-2850.27 + 1645.60i) q^{67} +(1646.90 - 2852.51i) q^{68} +515.652i q^{69} +(-129.327 + 804.338i) q^{70} -6058.46 q^{71} +(1136.67 + 656.260i) q^{72} +(688.721 + 1192.90i) q^{73} +(-892.709 - 1546.22i) q^{74} +(-1775.75 - 2014.40i) q^{75} -5162.46i q^{76} +(-3306.72 - 3287.49i) q^{77} +324.352i q^{78} +(-9.97798 + 17.2824i) q^{79} +(5353.67 + 2417.44i) q^{80} +(-1207.95 - 2092.23i) q^{81} +(-505.805 + 876.080i) q^{82} +7245.35 q^{83} +(838.500 - 3166.25i) q^{84} +(4298.32 - 3088.49i) q^{85} +(458.222 - 793.664i) q^{86} +(-968.706 - 1677.85i) q^{87} +(1729.56 - 998.561i) q^{88} +(-818.419 - 472.514i) q^{89} +(606.731 + 844.400i) q^{90} +(-5368.45 + 1455.27i) q^{91} -1867.16i q^{92} +(2198.54 + 1269.33i) q^{93} +(-2005.62 + 1157.95i) q^{94} +(3413.97 - 7560.60i) q^{95} +(1830.90 + 1057.07i) q^{96} -8583.56 q^{97} +(-1596.72 + 9.31735i) q^{98} -5951.25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) \) 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9	\( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9} + 390 q^{10} + 34 q^{11} - 258 q^{14} + 60 q^{15} - 206 q^{16} + 366 q^{19} - 1116 q^{21} - 288 q^{24} + 40 q^{25} + 474 q^{26} + 856 q^{29} - 1620 q^{30} - 5520 q^{31} - 2620 q^{35} + 11892 q^{36} + 1656 q^{39} + 6510 q^{40} - 1082 q^{44} + 7920 q^{45} - 5442 q^{46} + 8356 q^{49} - 15960 q^{50} - 2976 q^{51} + 4392 q^{54} + 11640 q^{56} - 13920 q^{59} - 5700 q^{60} - 24960 q^{61} - 45596 q^{64} + 5290 q^{65} + 10332 q^{66} - 26400 q^{70} + 38272 q^{71} + 31806 q^{74} + 41310 q^{75} + 22028 q^{79} + 48000 q^{80} - 29238 q^{81} + 62784 q^{84} - 33820 q^{85} - 21180 q^{86} - 12516 q^{89} + 4448 q^{91} - 89418 q^{94} - 28890 q^{95} - 27900 q^{96} - 3108 q^{99}+O(q^{100}) \) 28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more