LMFDB - Embedded newform 40.4.k.a.3.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,4,Mod(3,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("40.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	40.k (of order $4$, 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:	$2.36007640023$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.7
Character	$\chi$	$=$	40.3
Dual form			40.4.k.a.27.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.607409 - 2.76244i) q^{2} +(-2.02737 - 2.02737i) q^{3} +(-7.26211 + 3.35586i) q^{4} +(-10.8122 - 2.84559i) q^{5} +(-4.36904 + 6.83193i) q^{6} +(1.63237 + 1.63237i) q^{7} +(13.6814 + 18.0227i) q^{8} -18.7795i q^{9} +O(q^{10})$	\(q+(-0.607409 - 2.76244i) q^{2} +(-2.02737 - 2.02737i) q^{3} +(-7.26211 + 3.35586i) q^{4} +(-10.8122 - 2.84559i) q^{5} +(-4.36904 + 6.83193i) q^{6} +(1.63237 + 1.63237i) q^{7} +(13.6814 + 18.0227i) q^{8} -18.7795i q^{9} +(-1.29335 + 31.5963i) q^{10} -62.3878 q^{11} +(21.5266 + 7.91943i) q^{12} +(47.3701 - 47.3701i) q^{13} +(3.51780 - 5.50083i) q^{14} +(16.1512 + 27.6893i) q^{15} +(41.4765 - 48.7412i) q^{16} +(26.6151 - 26.6151i) q^{17} +(-51.8773 + 11.4068i) q^{18} -59.7713i q^{19} +(88.0684 - 15.6191i) q^{20} -6.61884i q^{21} +(37.8949 + 172.342i) q^{22} +(6.56082 - 6.56082i) q^{23} +(8.80150 - 64.2761i) q^{24} +(108.805 + 61.5338i) q^{25} +(-159.630 - 102.084i) q^{26} +(-92.8121 + 92.8121i) q^{27} +(-17.3324 - 6.37645i) q^{28} -73.0449 q^{29} +(66.6796 - 61.4354i) q^{30} +168.579i q^{31} +(-159.838 - 84.9703i) q^{32} +(126.483 + 126.483i) q^{33} +(-89.6887 - 57.3562i) q^{34} +(-13.0044 - 22.2945i) q^{35} +(63.0214 + 136.379i) q^{36} +(-97.0101 - 97.0101i) q^{37} +(-165.114 + 36.3056i) q^{38} -192.074 q^{39} +(-96.6402 - 233.796i) q^{40} +27.5126 q^{41} +(-18.2841 + 4.02034i) q^{42} +(204.855 + 204.855i) q^{43} +(453.067 - 209.364i) q^{44} +(-53.4388 + 203.047i) q^{45} +(-22.1089 - 14.1387i) q^{46} +(-165.258 - 165.258i) q^{47} +(-182.905 + 14.7283i) q^{48} -337.671i q^{49} +(103.894 - 337.944i) q^{50} -107.917 q^{51} +(-185.040 + 502.974i) q^{52} +(372.552 - 372.552i) q^{53} +(312.762 + 200.013i) q^{54} +(674.546 + 177.530i) q^{55} +(-7.08666 + 51.7529i) q^{56} +(-121.179 + 121.179i) q^{57} +(44.3681 + 201.782i) q^{58} -67.1632i q^{59} +(-210.213 - 146.882i) q^{60} +659.080i q^{61} +(465.688 - 102.396i) q^{62} +(30.6551 - 30.6551i) q^{63} +(-137.638 + 493.153i) q^{64} +(-646.969 + 377.377i) q^{65} +(272.575 - 426.229i) q^{66} +(506.483 - 506.483i) q^{67} +(-103.965 + 282.598i) q^{68} -26.6024 q^{69} +(-53.6881 + 49.4656i) q^{70} -1147.99i q^{71} +(338.459 - 256.930i) q^{72} +(-685.459 - 685.459i) q^{73} +(-209.060 + 326.909i) q^{74} +(-95.8369 - 345.341i) q^{75} +(200.584 + 434.066i) q^{76} +(-101.840 - 101.840i) q^{77} +(116.667 + 530.591i) q^{78} -751.180 q^{79} +(-587.147 + 408.972i) q^{80} -130.718 q^{81} +(-16.7114 - 76.0018i) q^{82} +(251.518 + 251.518i) q^{83} +(22.2119 + 48.0667i) q^{84} +(-363.502 + 212.031i) q^{85} +(441.468 - 690.329i) q^{86} +(148.089 + 148.089i) q^{87} +(-853.553 - 1124.40i) q^{88} +497.545i q^{89} +(593.364 + 24.2886i) q^{90} +154.651 q^{91} +(-25.6282 + 69.6625i) q^{92} +(341.772 - 341.772i) q^{93} +(-356.135 + 556.893i) q^{94} +(-170.084 + 646.257i) q^{95} +(151.784 + 496.316i) q^{96} +(305.299 - 305.299i) q^{97} +(-932.794 + 205.104i) q^{98} +1171.61i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 44 q^{8}+O(q^{10}) $ 32 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 44 * q^8	$ 32 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 44 q^{8} + 70 q^{10} - 8 q^{11} + 28 q^{12} + 72 q^{16} + 48 q^{17} - 278 q^{18} - 320 q^{20} + 68 q^{22} + 40 q^{25} - 92 q^{26} + 104 q^{27} + 620 q^{28} - 740 q^{30} + 288 q^{32} - 112 q^{33} - 460 q^{35} + 476 q^{36} + 636 q^{38} + 540 q^{40} - 8 q^{41} + 1020 q^{42} - 868 q^{43} + 1328 q^{46} - 784 q^{48} + 790 q^{50} + 1480 q^{51} - 1900 q^{52} - 2392 q^{56} + 104 q^{57} - 700 q^{58} - 1100 q^{60} - 2880 q^{62} + 520 q^{65} - 4360 q^{66} - 1852 q^{67} + 1196 q^{68} - 1500 q^{70} + 5596 q^{72} - 744 q^{73} + 3300 q^{75} + 4312 q^{76} + 2240 q^{78} + 1120 q^{80} - 1240 q^{81} + 5828 q^{82} + 2676 q^{83} + 6976 q^{86} - 2864 q^{88} + 4070 q^{90} - 1704 q^{91} - 7500 q^{92} - 10656 q^{96} - 584 q^{97} - 3814 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 44 * q^8 + 70 * q^10 - 8 * q^11 + 28 * q^12 + 72 * q^16 + 48 * q^17 - 278 * q^18 - 320 * q^20 + 68 * q^22 + 40 * q^25 - 92 * q^26 + 104 * q^27 + 620 * q^28 - 740 * q^30 + 288 * q^32 - 112 * q^33 - 460 * q^35 + 476 * q^36 + 636 * q^38 + 540 * q^40 - 8 * q^41 + 1020 * q^42 - 868 * q^43 + 1328 * q^46 - 784 * q^48 + 790 * q^50 + 1480 * q^51 - 1900 * q^52 - 2392 * q^56 + 104 * q^57 - 700 * q^58 - 1100 * q^60 - 2880 * q^62 + 520 * q^65 - 4360 * q^66 - 1852 * q^67 + 1196 * q^68 - 1500 * q^70 + 5596 * q^72 - 744 * q^73 + 3300 * q^75 + 4312 * q^76 + 2240 * q^78 + 1120 * q^80 - 1240 * q^81 + 5828 * q^82 + 2676 * q^83 + 6976 * q^86 - 2864 * q^88 + 4070 * q^90 - 1704 * q^91 - 7500 * q^92 - 10656 * q^96 - 584 * q^97 - 3814 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.607409	−	2.76244i	−0.214751	−	0.976669i
$2$	−0.607409	−	2.76244i	−0.214751	−	0.976669i
$3$	−2.02737	−	2.02737i	−0.390168	−	0.390168i	0.484579	−	0.874747i	$-0.338973\pi$
$3$	−2.02737	−	2.02737i	−0.390168	−	0.390168i	−0.874747	+	0.484579i	$0.838973\pi$
$4$	−7.26211	+	3.35586i	−0.907764	+	0.419482i
$5$	−10.8122	−	2.84559i	−0.967068	−	0.254517i
$5$	−10.8122	−	2.84559i	−0.967068	−	0.254517i
$6$	−4.36904	+	6.83193i	−0.297276	+	0.464854i
$7$	1.63237	+	1.63237i	0.0881396	+	0.0881396i	0.749802	−	0.661662i	$-0.230149\pi$
$7$	1.63237	+	1.63237i	0.0881396	+	0.0881396i	−0.661662	+	0.749802i	$0.730149\pi$
$8$	13.6814	+	18.0227i	0.604638	+	0.796500i
$9$		−	18.7795i		−	0.695538i
$10$	−1.29335	+	31.5963i	−0.0408994	+	0.999163i
$11$	−62.3878			−1.71006			−0.855028	−	0.518581i	$-0.826460\pi$
$11$	−62.3878			−1.71006			−0.855028	+	0.518581i	$0.826460\pi$
$12$	21.5266	+	7.91943i	0.517849	+	0.190512i
$13$	47.3701	−	47.3701i	1.01062	−	1.01062i	0.0106811	−	0.999943i	$-0.496600\pi$
$13$	47.3701	−	47.3701i	1.01062	−	1.01062i	0.999943	−	0.0106811i	$-0.00339997\pi$
$14$	3.51780	−	5.50083i	0.0671551	−	0.105011i
$15$	16.1512	+	27.6893i	0.278015	+	0.476623i
$16$	41.4765	−	48.7412i	0.648070	−	0.761581i
$17$	26.6151	−	26.6151i	0.379712	−	0.379712i	−0.491286	−	0.870998i	$-0.663473\pi$
$17$	26.6151	−	26.6151i	0.379712	−	0.379712i	0.870998	+	0.491286i	$0.163473\pi$
$18$	−51.8773	+	11.4068i	−0.679310	+	0.149368i
$19$		−	59.7713i		−	0.721710i	−0.932622	−	0.360855i	$-0.882485\pi$
$19$		−	59.7713i		−	0.721710i	0.932622	−	0.360855i	$-0.117515\pi$
$20$	88.0684	−	15.6191i	0.984635	−	0.174627i
$21$		−	6.61884i		−	0.0687785i
$22$	37.8949	+	172.342i	0.367237	+	1.67016i
$23$	6.56082	−	6.56082i	0.0594793	−	0.0594793i	−0.676741	−	0.736221i	$-0.736608\pi$
$23$	6.56082	−	6.56082i	0.0594793	−	0.0594793i	0.736221	+	0.676741i	$0.236608\pi$
$24$	8.80150	−	64.2761i	0.0748583	−	0.546679i
$25$	108.805	+	61.5338i	0.870442	+	0.492270i
$26$	−159.630	−	102.084i	−1.20408	−	0.770012i
$27$	−92.8121	+	92.8121i	−0.661544	+	0.661544i
$28$	−17.3324	−	6.37645i	−0.116983	−	0.0430370i
$29$	−73.0449			−0.467728			−0.233864	−	0.972269i	$-0.575137\pi$
$29$	−73.0449			−0.467728			−0.233864	+	0.972269i	$0.575137\pi$
$30$	66.6796	−	61.4354i	0.405799	−	0.373884i
$31$			168.579i			0.976699i	0.872648	+	0.488349i	$0.162401\pi$
$31$			168.579i			0.976699i	−0.872648	+	0.488349i	$0.837599\pi$
$32$	−159.838	−	84.9703i	−0.882986	−	0.469399i
$33$	126.483	+	126.483i	0.667209	+	0.667209i
$34$	−89.6887	−	57.3562i	−0.452397	−	0.289309i
$35$	−13.0044	−	22.2945i	−0.0628040	−	0.107670i
$36$	63.0214	+	136.379i	0.291766	+	0.631384i
$37$	−97.0101	−	97.0101i	−0.431037	−	0.431037i	0.457944	−	0.888981i	$-0.348586\pi$
$37$	−97.0101	−	97.0101i	−0.431037	−	0.431037i	−0.888981	+	0.457944i	$0.848586\pi$
$38$	−165.114	+	36.3056i	−0.704871	+	0.154988i
$39$	−192.074			−0.788626
$40$	−96.6402	−	233.796i	−0.382004	−	0.924161i
$41$	27.5126			0.104799			0.0523993	−	0.998626i	$-0.483313\pi$
$41$	27.5126			0.104799			0.0523993	+	0.998626i	$0.483313\pi$
$42$	−18.2841	+	4.02034i	−0.0671738	+	0.0147703i
$43$	204.855	+	204.855i	0.726513	+	0.726513i	0.969923	−	0.243411i	$-0.0782662\pi$
$43$	204.855	+	204.855i	0.726513	+	0.726513i	−0.243411	+	0.969923i	$0.578266\pi$
$44$	453.067	−	209.364i	1.55233	−	0.717338i
$45$	−53.4388	+	203.047i	−0.177026	+	0.672633i
$46$	−22.1089	−	14.1387i	−0.0708649	−	0.0453183i
$47$	−165.258	−	165.258i	−0.512879	−	0.512879i	0.402529	−	0.915407i	$-0.368131\pi$
$47$	−165.258	−	165.258i	−0.512879	−	0.512879i	−0.915407	+	0.402529i	$0.868131\pi$
$48$	−182.905	+	14.7283i	−0.550000	+	0.0442884i
$49$		−	337.671i		−	0.984463i
$50$	103.894	−	337.944i	0.293856	−	0.955850i
$51$	−107.917			−0.296303
$52$	−185.040	+	502.974i	−0.493469	+	1.34135i
$53$	372.552	−	372.552i	0.965546	−	0.965546i	−0.0338796	−	0.999426i	$-0.510786\pi$
$53$	372.552	−	372.552i	0.965546	−	0.965546i	0.999426	+	0.0338796i	$0.0107863\pi$
$54$	312.762	+	200.013i	0.788177	+	0.504042i
$55$	674.546	+	177.530i	1.65374	+	0.435238i
$56$	−7.08666	+	51.7529i	−0.0169106	+	0.123496i
$57$	−121.179	+	121.179i	−0.281588	+	0.281588i
$58$	44.3681	+	201.782i	0.100445	+	0.456815i
$59$		−	67.1632i		−	0.148202i	−0.997251	−	0.0741009i	$-0.976391\pi$
$59$		−	67.1632i		−	0.148202i	0.997251	−	0.0741009i	$-0.0236087\pi$
$60$	−210.213	−	146.882i	−0.452306	−	0.316039i
$61$			659.080i			1.38339i	0.722192	+	0.691693i	$0.243135\pi$
$61$			659.080i			1.38339i	−0.722192	+	0.691693i	$0.756865\pi$
$62$	465.688	−	102.396i	0.953911	−	0.209747i
$63$	30.6551	−	30.6551i	0.0613045	−	0.0613045i
$64$	−137.638	+	493.153i	−0.268825	+	0.963189i
$65$	−646.969	+	377.377i	−1.23456	+	0.720122i
$66$	272.575	−	426.229i	0.508358	−	0.794926i
$67$	506.483	−	506.483i	0.923533	−	0.923533i	−0.0737437	−	0.997277i	$-0.523495\pi$
$67$	506.483	−	506.483i	0.923533	−	0.923533i	0.997277	+	0.0737437i	$0.0234947\pi$
$68$	−103.965	+	282.598i	−0.185406	+	0.503971i
$69$	−26.6024			−0.0464139
$70$	−53.6881	+	49.4656i	−0.0916708	+	0.0844610i
$71$		−	1147.99i		−	1.91889i	−0.281902	−	0.959443i	$-0.590965\pi$
$71$		−	1147.99i		−	1.91889i	0.281902	−	0.959443i	$-0.409035\pi$
$72$	338.459	−	256.930i	0.553996	−	0.420549i
$73$	−685.459	−	685.459i	−1.09900	−	1.09900i	−0.994528	−	0.104470i	$-0.966685\pi$
$73$	−685.459	−	685.459i	−1.09900	−	1.09900i	−0.104470	−	0.994528i	$-0.533315\pi$
$74$	−209.060	+	326.909i	−0.328415	+	0.513546i
$75$	−95.8369	−	345.341i	−0.147550	−	0.531687i
$76$	200.584	+	434.066i	0.302744	+	0.655142i
$77$	−101.840	−	101.840i	−0.150724	−	0.150724i
$78$	116.667	+	530.591i	0.169359	+	0.770226i
$79$	−751.180			−1.06980			−0.534901	−	0.844915i	$-0.679651\pi$
$79$	−751.180			−1.06980			−0.534901	+	0.844915i	$0.679651\pi$
$80$	−587.147	+	408.972i	−0.820563	+	0.571556i
$81$	−130.718			−0.179311
$82$	−16.7114	−	76.0018i	−0.0225056	−	0.102354i
$83$	251.518	+	251.518i	0.332622	+	0.332622i	0.853582	−	0.520959i	$-0.174426\pi$
$83$	251.518	+	251.518i	0.332622	+	0.332622i	−0.520959	+	0.853582i	$0.674426\pi$
$84$	22.2119	+	48.0667i	0.0288513	+	0.0624346i
$85$	−363.502	+	212.031i	−0.463851	+	0.270564i
$86$	441.468	−	690.329i	0.553543	−	0.865582i
$87$	148.089	+	148.089i	0.182492	+	0.182492i
$88$	−853.553	−	1124.40i	−1.03397	−	1.36206i
$89$			497.545i			0.592581i	0.955098	+	0.296291i	$0.0957497\pi$
$89$			497.545i			0.592581i	−0.955098	+	0.296291i	$0.904250\pi$
$90$	593.364	+	24.2886i	0.694956	+	0.0284471i
$91$	154.651			0.178152
$92$	−25.6282	+	69.6625i	−0.0290427	+	0.0789437i
$93$	341.772	−	341.772i	0.381076	−	0.381076i
$94$	−356.135	+	556.893i	−0.390771	+	0.611054i
$95$	−170.084	+	646.257i	−0.183687	+	0.697942i
$96$	151.784	+	496.316i	0.161368	+	0.527657i
$97$	305.299	−	305.299i	0.319572	−	0.319572i	−0.529031	−	0.848603i	$-0.677444\pi$
$97$	305.299	−	305.299i	0.319572	−	0.319572i	0.848603	+	0.529031i	$0.177444\pi$
$98$	−932.794	+	205.104i	−0.961494	+	0.211415i
$99$			1171.61i			1.18941i
$100$	−996.654	−	81.7304i	−0.996654	−	0.0817304i
$101$			942.824i			0.928857i	0.885611	+	0.464428i	$0.153740\pi$
$101$			942.824i			0.928857i	−0.885611	+	0.464428i	$0.846260\pi$
$102$	65.5499	+	298.115i	0.0636315	+	0.289390i
$103$	250.655	−	250.655i	0.239784	−	0.239784i	−0.576977	−	0.816761i	$-0.695768\pi$
$103$	250.655	−	250.655i	0.239784	−	0.239784i	0.816761	+	0.576977i	$0.195768\pi$
$104$	1501.83	+	205.650i	1.41602	+	0.193900i
$105$	−18.8345	+	71.5639i	−0.0175053	+	0.0665135i
$106$	−1255.44	−	802.860i	−1.15037	−	0.735666i
$107$	347.839	−	347.839i	0.314270	−	0.314270i	−0.532292	−	0.846561i	$-0.678669\pi$
$107$	347.839	−	347.839i	0.314270	−	0.314270i	0.846561	+	0.532292i	$0.178669\pi$
$108$	362.548	−	985.476i	0.323020	−	0.878032i
$109$	822.067			0.722383			0.361191	−	0.932492i	$-0.382370\pi$
$109$	822.067			0.722383			0.361191	+	0.932492i	$0.382370\pi$
$110$	80.6894	−	1971.22i	0.0699403	−	1.70863i
$111$			393.351i			0.336354i
$112$	147.268	−	11.8587i	0.124246	−	0.0100048i
$113$	698.411	+	698.411i	0.581425	+	0.581425i	0.935295	−	0.353870i	$-0.115134\pi$
$113$	698.411	+	698.411i	0.581425	+	0.581425i	−0.353870	+	0.935295i	$0.615134\pi$
$114$	408.353	+	261.143i	0.335489	+	0.214547i
$115$	−89.6059	+	52.2672i	−0.0726591	+	0.0423821i
$116$	530.460	−	245.128i	0.424586	−	0.196203i
$117$	−889.589	−	889.589i	−0.702928	−	0.702928i
$118$	−185.534	+	40.7955i	−0.144744	+	0.0318266i
$119$	86.8913			0.0669354
$120$	−278.066	+	669.917i	−0.211532	+	0.509623i
$121$	2561.24			1.92429
$122$	1820.67	−	400.331i	1.35111	−	0.297084i
$123$	−55.7782	−	55.7782i	−0.0408890	−	0.0408890i
$124$	−565.726	−	1224.24i	−0.409707	−	0.886611i
$125$	−1001.32	−	974.928i	−0.716486	−	0.697601i
$126$	−103.303	−	66.0626i	−0.0730394	−	0.0467090i
$127$	952.133	+	952.133i	0.665261	+	0.665261i	0.956615	−	0.291354i	$-0.0941058\pi$
$127$	952.133	+	952.133i	0.665261	+	0.665261i	−0.291354	+	0.956615i	$0.594106\pi$
$128$	1445.91	+	80.6717i	0.998447	+	0.0557066i
$129$		−	830.633i		−	0.566924i
$130$	1435.46	+	1557.99i	0.968444	+	1.05111i
$131$	−2296.26			−1.53149			−0.765744	−	0.643146i	$-0.777629\pi$
$131$	−2296.26			−1.53149			−0.765744	+	0.643146i	$0.777629\pi$
$132$	−1342.99	−	494.076i	−0.885550	−	0.325786i
$133$	97.5689	−	97.5689i	0.0636112	−	0.0636112i
$134$	−1706.77	−	1091.48i	−1.10032	−	0.703656i
$135$	1267.60	−	739.394i	0.808133	−	0.471384i
$136$	843.808	+	115.545i	0.532029	+	0.0728522i
$137$	−1005.61	+	1005.61i	−0.627119	+	0.627119i	−0.947342	−	0.320223i	$-0.896242\pi$
$137$	−1005.61	+	1005.61i	−0.627119	+	0.627119i	0.320223	+	0.947342i	$0.396242\pi$
$138$	16.1585	+	73.4875i	0.00996744	+	0.0453310i
$139$			407.100i			0.248416i	0.992256	+	0.124208i	$0.0396389\pi$
$139$			407.100i			0.248416i	−0.992256	+	0.124208i	$0.960361\pi$
$140$	169.256	+	118.264i	0.102177	+	0.0713938i
$141$			670.077i			0.400218i
$142$	−3171.24	+	697.297i	−1.87412	+	0.412084i
$143$	−2955.32	+	2955.32i	−1.72822	+	1.72822i
$144$	−915.336	−	778.909i	−0.529709	−	0.450757i
$145$	789.773	+	207.856i	0.452325	+	0.119045i
$146$	−1477.18	+	2309.89i	−0.837346	+	1.30937i
$147$	−684.584	+	684.584i	−0.384106	+	0.384106i
$148$	1030.05	+	378.946i	0.572092	+	0.210467i
$149$	2180.37			1.19881			0.599405	−	0.800446i	$-0.295404\pi$
$149$	2180.37			1.19881			0.599405	+	0.800446i	$0.295404\pi$
$150$	−895.769	+	474.506i	−0.487595	+	0.258288i
$151$		−	2581.10i		−	1.39104i	−0.718506	−	0.695520i	$-0.755174\pi$
$151$		−	2581.10i		−	1.39104i	0.718506	−	0.695520i	$-0.244826\pi$
$152$	1077.24	−	817.756i	0.574842	−	0.436373i
$153$	−499.819	−	499.819i	−0.264104	−	0.264104i
$154$	−219.468	+	343.185i	−0.114839	+	0.179575i
$155$	479.705	−	1822.70i	0.248586	−	0.944534i
$156$	1394.86	−	644.572i	0.715886	−	0.330814i
$157$	−549.008	−	549.008i	−0.279080	−	0.279080i	0.553662	−	0.832742i	$-0.313230\pi$
$157$	−549.008	−	549.008i	−0.279080	−	0.279080i	−0.832742	+	0.553662i	$0.813230\pi$
$158$	456.274	+	2075.09i	0.229742	+	1.04484i
$159$	−1510.60			−0.753450
$160$	1486.40	+	1373.54i	0.734438	+	0.678676i
$161$	21.4194			0.0104850
$162$	79.3993	+	361.100i	0.0385074	+	0.175128i
$163$	−317.555	−	317.555i	−0.152594	−	0.152594i	0.626681	−	0.779276i	$-0.284413\pi$
$163$	−317.555	−	317.555i	−0.152594	−	0.152594i	−0.779276	+	0.626681i	$0.784413\pi$
$164$	−199.799	+	92.3282i	−0.0951324	+	0.0439611i
$165$	−1007.64	−	1727.47i	−0.475421	−	0.815053i
$166$	542.028	−	847.576i	0.253431	−	0.396293i
$167$	1146.69	+	1146.69i	0.531338	+	0.531338i	0.920970	−	0.389633i	$-0.127398\pi$
$167$	1146.69	+	1146.69i	0.531338	+	0.531338i	−0.389633	+	0.920970i	$0.627398\pi$
$168$	119.290	−	90.5550i	0.0547821	−	0.0415861i
$169$		−	2290.86i		−	1.04272i
$170$	806.516	+	875.361i	0.363864	+	0.394924i
$171$	−1122.48			−0.501977
$172$	−2175.14	−	800.215i	−0.964261	−	0.354743i
$173$	186.798	−	186.798i	0.0820922	−	0.0820922i	−0.664868	−	0.746961i	$-0.731512\pi$
$173$	186.798	−	186.798i	0.0820922	−	0.0820922i	0.746961	+	0.664868i	$0.231512\pi$
$174$	319.136	−	499.038i	0.139044	−	0.217425i
$175$	77.1645	+	278.056i	0.0333319	+	0.120109i
$176$	−2587.63	+	3040.85i	−1.10824	+	1.30235i
$177$	−136.165	+	136.165i	−0.0578236	+	0.0578236i
$178$	1374.44	−	302.213i	0.578755	−	0.127258i
$179$		−	2285.01i		−	0.954134i	−0.878867	−	0.477067i	$-0.841700\pi$
$179$		−	2285.01i		−	0.954134i	0.878867	−	0.477067i	$-0.158300\pi$
$180$	−293.319	−	1653.88i	−0.121459	−	0.684851i
$181$		−	32.6132i		−	0.0133929i	−0.999978	−	0.00669646i	$-0.997868\pi$
$181$		−	32.6132i		−	0.0133929i	0.999978	−	0.00669646i	$-0.00213157\pi$
$182$	−93.9364	−	427.214i	−0.0382584	−	0.173996i
$183$	1336.20	−	1336.20i	0.539753	−	0.539753i
$184$	208.005	+	28.4827i	0.0833388	+	0.0114118i
$185$	772.838	+	1324.94i	0.307136	+	0.526548i
$186$	−1151.72	−	736.528i	−0.454022	−	0.290349i
$187$	−1660.46	+	1660.46i	−0.649329	+	0.649329i
$188$	1754.70	+	645.538i	0.680716	+	0.250429i
$189$	−303.007			−0.116617
$190$	1888.55	+	77.3054i	0.721106	+	0.0295175i
$191$		−	896.187i		−	0.339507i	−0.985487	−	0.169753i	$-0.945703\pi$
$191$		−	896.187i		−	0.339507i	0.985487	−	0.169753i	$-0.0542972\pi$
$192$	1278.85	−	720.760i	0.480692	−	0.270919i
$193$	−2046.33	−	2046.33i	−0.763202	−	0.763202i	0.213698	−	0.976900i	$-0.431449\pi$
$193$	−2046.33	−	2046.33i	−0.763202	−	0.763202i	−0.976900	+	0.213698i	$0.931449\pi$
$194$	−1028.81	−	657.928i	−0.380744	−	0.243487i
$195$	2076.73	+	546.562i	0.762655	+	0.200719i
$196$	1133.17	+	2452.20i	0.412964	+	0.893660i
$197$	2980.13	+	2980.13i	1.07779	+	1.07779i	0.996707	+	0.0810878i	$0.0258394\pi$
$197$	2980.13	+	2980.13i	1.07779	+	1.07779i	0.0810878	+	0.996707i	$0.474161\pi$
$198$	3236.51	−	711.648i	1.16166	−	0.255427i
$199$	4534.78			1.61539			0.807693	−	0.589603i	$-0.200716\pi$
$199$	4534.78			1.61539			0.807693	+	0.589603i	$0.200716\pi$
$200$	379.602	+	2802.84i	0.134209	+	0.990953i
$201$	−2053.66			−0.720666
$202$	2604.49	−	572.680i	0.907185	−	0.199473i
$203$	−119.236	−	119.236i	−0.0412254	−	0.0412254i
$204$	783.707	−	362.155i	0.268973	−	0.124294i
$205$	−297.470	−	78.2894i	−0.101347	−	0.0266730i
$206$	−844.668	−	540.168i	−0.285683	−	0.182696i
$207$	−123.209	−	123.209i	−0.0413702	−	0.0413702i
$208$	−344.130	−	4273.62i	−0.114717	−	1.42463i
$209$			3729.00i			1.23416i
$210$	209.131	+	8.56049i	0.0687210	+	0.00281300i
$211$	3171.97			1.03492			0.517459	−	0.855708i	$-0.326878\pi$
$211$	3171.97			1.03492			0.517459	+	0.855708i	$0.326878\pi$
$212$	−1455.28	+	3955.74i	−0.471459	+	1.28152i
$213$	−2327.40	+	2327.40i	−0.748688	+	0.748688i
$214$	−1172.16	−	749.602i	−0.374427	−	0.239447i
$215$	−1631.99	−	2797.85i	−0.517678	−	0.887497i
$216$	−2942.53	−	402.928i	−0.926915	−	0.126925i
$217$	−275.183	+	275.183i	−0.0860859	+	0.0860859i
$218$	−499.330	−	2270.91i	−0.155133	−	0.705529i
$219$			2779.36i			0.857587i
$220$	−5494.39	+	974.439i	−1.68378	+	0.298621i
$221$		−	2521.52i		−	0.767492i
$222$	1086.61	−	238.925i	0.328506	−	0.0722324i
$223$	−3221.86	+	3221.86i	−0.967497	+	0.967497i	−0.999488	−	0.0319913i	$-0.989815\pi$
$223$	−3221.86	+	3221.86i	−0.967497	+	0.967497i	0.0319913	+	0.999488i	$0.489815\pi$
$224$	−122.211	−	399.617i	−0.0364534	−	0.119199i
$225$	1155.58	−	2043.31i	0.342393	−	0.605426i
$226$	1505.09	−	2353.54i	0.442997	−	0.692721i
$227$	2709.11	−	2709.11i	0.792113	−	0.792113i	−0.189724	−	0.981837i	$-0.560759\pi$
$227$	2709.11	−	2709.11i	0.792113	−	0.792113i	0.981837	+	0.189724i	$0.0607594\pi$
$228$	473.355	−	1286.67i	0.137494	−	0.373736i
$229$	−1946.36			−0.561657			−0.280828	−	0.959758i	$-0.590609\pi$
$229$	−1946.36			−0.561657			−0.280828	+	0.959758i	$0.590609\pi$
$230$	198.812	+	215.783i	0.0569969	+	0.0618623i
$231$			412.935i			0.117615i
$232$	−999.358	−	1316.47i	−0.282806	−	0.372545i
$233$	1215.55	+	1215.55i	0.341774	+	0.341774i	0.857034	−	0.515260i	$-0.172305\pi$
$233$	1215.55	+	1215.55i	0.341774	+	0.341774i	−0.515260	+	0.857034i	$0.672305\pi$
$234$	−1917.09	+	2997.78i	−0.535573	+	0.837482i
$235$	1316.54	+	2257.05i	0.365452	+	0.626525i
$236$	225.390	+	487.747i	0.0621680	+	0.134532i
$237$	1522.92	+	1522.92i	0.417403	+	0.417403i
$238$	−52.7785	−	240.032i	−0.0143745	−	0.0653737i
$239$	−4078.95			−1.10396			−0.551978	−	0.833859i	$-0.686127\pi$
$239$	−4078.95			−1.10396			−0.551978	+	0.833859i	$0.686127\pi$
$240$	2019.50	+	361.227i	0.543160	+	0.0971545i
$241$	−1100.86			−0.294242			−0.147121	−	0.989118i	$-0.547001\pi$
$241$	−1100.86			−0.294242			−0.147121	+	0.989118i	$0.547001\pi$
$242$	−1555.72	−	7075.25i	−0.413245	−	1.87940i
$243$	2770.94	+	2770.94i	0.731506	+	0.731506i
$244$	−2211.78	−	4786.31i	−0.580306	−	1.25579i
$245$	−960.871	+	3650.95i	−0.250562	+	0.952043i
$246$	−120.204	+	187.964i	−0.0311541	+	0.0487160i
$247$	−2831.38	−	2831.38i	−0.729377	−	0.729377i
$248$	−3038.25	+	2306.40i	−0.777940	+	0.590549i
$249$		−	1019.84i		−	0.259557i
$250$	−2084.97	+	3358.26i	−0.527459	+	0.849580i
$251$	3914.44			0.984372			0.492186	−	0.870490i	$-0.336198\pi$
$251$	3914.44			0.984372			0.492186	+	0.870490i	$0.336198\pi$
$252$	−119.747	+	325.495i	−0.0299339	+	0.0813661i
$253$	−409.315	+	409.315i	−0.101713	+	0.101713i
$254$	2051.87	−	3208.54i	0.506874	−	0.792606i
$255$	1166.82	+	307.088i	0.286545	+	0.0754141i
$256$	−655.405	−	4043.22i	−0.160011	−	0.987115i
$257$	−1389.39	+	1389.39i	−0.337229	+	0.337229i	−0.855324	−	0.518094i	$-0.826642\pi$
$257$	−1389.39	+	1389.39i	−0.337229	+	0.337229i	0.518094	+	0.855324i	$0.326642\pi$
$258$	−2294.57	+	504.534i	−0.553697	+	0.121748i
$259$		−	316.713i		−	0.0759829i
$260$	3431.94	−	4911.69i	0.818614	−	1.17158i
$261$			1371.75i			0.325323i
$262$	1394.77	+	6343.26i	0.328889	+	1.49576i
$263$	4340.69	−	4340.69i	1.01771	−	1.01771i	0.0178731	−	0.999840i	$-0.494311\pi$
$263$	4340.69	−	4340.69i	1.01771	−	1.01771i	0.999840	−	0.0178731i	$-0.00568950\pi$
$264$	−549.106	+	4010.04i	−0.128012	+	0.934852i
$265$	−5088.22	+	2967.96i	−1.17950	+	0.688001i
$266$	−328.792	−	210.264i	−0.0757877	−	0.0484665i
$267$	1008.71	−	1008.71i	0.231206	−	0.231206i
$268$	−1978.45	+	5377.82i	−0.450945	+	1.22576i
$269$	2033.97			0.461017			0.230508	−	0.973070i	$-0.425961\pi$
$269$	2033.97			0.461017			0.230508	+	0.973070i	$0.425961\pi$
$270$	−2812.48	−	3052.56i	−0.633934	−	0.688048i
$271$			3331.79i			0.746833i	0.927664	+	0.373416i	$0.121814\pi$
$271$			3331.79i			0.746833i	−0.927664	+	0.373416i	$0.878186\pi$
$272$	−193.351	−	2401.15i	−0.0431015	−	0.535261i
$273$	−313.535	−	313.535i	−0.0695092	−	0.0695092i
$274$	3388.76	+	2167.12i	0.747162	+	0.477813i
$275$	−6788.12	−	3838.96i	−1.48851	−	0.841810i
$276$	193.190	−	89.2739i	0.0421328	−	0.0194698i
$277$	−2835.89	−	2835.89i	−0.615134	−	0.615134i	0.329145	−	0.944279i	$-0.393239\pi$
$277$	−2835.89	−	2835.89i	−0.615134	−	0.615134i	−0.944279	+	0.329145i	$0.893239\pi$
$278$	1124.59	−	247.276i	0.242620	−	0.0533476i
$279$	3165.83			0.679331
$280$	223.889	−	539.394i	0.0477855	−	0.115125i
$281$	480.154			0.101935			0.0509673	−	0.998700i	$-0.483770\pi$
$281$	480.154			0.101935			0.0509673	+	0.998700i	$0.483770\pi$
$282$	1851.05	−	407.011i	0.390880	−	0.0859473i
$283$	−3181.67	−	3181.67i	−0.668305	−	0.668305i	0.289018	−	0.957324i	$-0.406671\pi$
$283$	−3181.67	−	3181.67i	−0.668305	−	0.668305i	−0.957324	+	0.289018i	$0.906671\pi$
$284$	3852.48	+	8336.80i	0.804938	+	1.74190i
$285$	1655.03	−	965.378i	0.343984	−	0.200646i
$286$	9958.96	+	6368.79i	2.05904	+	1.31676i
$287$	44.9107	+	44.9107i	0.00923691	+	0.00923691i
$288$	−1595.70	+	3001.67i	−0.326485	+	0.614151i
$289$			3496.27i			0.711637i
$290$	94.4729	−	2307.95i	0.0191298	−	0.467336i
$291$	−1237.91			−0.249373
$292$	7278.17	+	2677.58i	1.45864	+	0.536621i
$293$	3468.44	−	3468.44i	0.691564	−	0.691564i	−0.271012	−	0.962576i	$-0.587358\pi$
$293$	3468.44	−	3468.44i	0.691564	−	0.691564i	0.962576	+	0.271012i	$0.0873583\pi$
$294$	2306.94	+	1475.30i	0.457631	+	0.292657i
$295$	−191.119	+	726.179i	−0.0377199	+	0.143321i
$296$	421.153	−	3075.62i	0.0826995	−	0.603943i
$297$	5790.34	−	5790.34i	1.13128	−	1.13128i
$298$	−1324.37	−	6023.13i	−0.257446	−	1.17084i
$299$		−	621.574i		−	0.120223i
$300$	1854.89	+	2186.29i	0.356974	+	0.420751i
$301$			668.797i			0.128069i
$302$	−7130.13	+	1567.78i	−1.35859	+	0.298728i
$303$	1911.46	−	1911.46i	0.362410	−	0.362410i
$304$	−2913.32	−	2479.10i	−0.549640	−	0.467718i
$305$	1875.47	−	7126.08i	0.352095	−	1.33783i
$306$	−1077.12	+	1684.31i	−0.201226	+	0.314659i
$307$	−4035.38	+	4035.38i	−0.750201	+	0.750201i	−0.974516	−	0.224316i	$-0.927985\pi$
$307$	−4035.38	+	4035.38i	−0.750201	+	0.750201i	0.224316	+	0.974516i	$0.427985\pi$
$308$	1081.33	+	397.812i	0.200048	+	0.0735957i
$309$	−1016.34			−0.187112
$310$	−5326.47	−	218.032i	−0.975881	−	0.0399464i
$311$			4519.57i			0.824055i	0.911171	+	0.412027i	$0.135179\pi$
$311$			4519.57i			0.824055i	−0.911171	+	0.412027i	$0.864821\pi$
$312$	−2627.84	−	3461.70i	−0.476834	−	0.628141i
$313$	36.2445	+	36.2445i	0.00654525	+	0.00654525i	0.710372	−	0.703827i	$-0.248527\pi$
$313$	36.2445	+	36.2445i	0.00654525	+	0.00654525i	−0.703827	+	0.710372i	$0.748527\pi$
$314$	−1183.13	+	1850.07i	−0.212636	+	0.332502i
$315$	−418.680	+	244.216i	−0.0748887	+	0.0436826i
$316$	5455.15	−	2520.85i	0.971128	−	0.448763i
$317$	−1598.38	−	1598.38i	−0.283199	−	0.283199i	0.551184	−	0.834383i	$-0.314176\pi$
$317$	−1598.38	−	1598.38i	−0.283199	−	0.283199i	−0.834383	+	0.551184i	$0.814176\pi$
$318$	917.553	+	4172.94i	0.161804	+	0.735871i
$319$	4557.11			0.799841
$320$	2891.47	−	4940.38i	0.505120	−	0.863049i
$321$	−1410.40			−0.245236
$322$	−13.0103	−	59.1696i	−0.00225166	−	0.0102403i
$323$	−1590.82	−	1590.82i	−0.274042	−	0.274042i
$324$	949.289	−	438.671i	0.162772	−	0.0752179i
$325$	8068.99	−	2239.26i	1.37719	−	0.382190i
$326$	−684.340	+	1070.11i	−0.116264	+	0.181804i
$327$	−1666.63	−	1666.63i	−0.281850	−	0.281850i
$328$	376.411	+	495.852i	0.0633653	+	0.0834721i
$329$		−	539.523i		−	0.0904099i
$330$	−4159.99	+	3832.82i	−0.693939	+	0.639362i
$331$	−2971.73			−0.493477			−0.246739	−	0.969082i	$-0.579359\pi$
$331$	−2971.73			−0.493477			−0.246739	+	0.969082i	$0.579359\pi$
$332$	−2670.61	−	982.492i	−0.441471	−	0.162413i
$333$	−1821.80	+	1821.80i	−0.299803	+	0.299803i
$334$	2471.14	−	3864.16i	0.404835	−	0.633046i
$335$	−6917.41	+	4034.93i	−1.12817	+	0.658065i
$336$	−322.610	−	274.526i	−0.0523804	−	0.0445733i
$337$	2602.78	−	2602.78i	0.420719	−	0.420719i	−0.464732	−	0.885451i	$-0.653849\pi$
$337$	2602.78	−	2602.78i	0.420719	−	0.420719i	0.885451	+	0.464732i	$0.153849\pi$
$338$	−6328.36	+	1391.49i	−1.01839	+	0.223926i
$339$		−	2831.88i		−	0.453706i
$340$	1928.25	−	2759.65i	0.307570	−	0.440186i
$341$		−	10517.3i		−	1.67021i
$342$	681.802	+	3100.77i	0.107800	+	0.490265i
$343$	1111.11	−	1111.11i	0.174910	−	0.174910i
$344$	−889.343	+	6494.74i	−0.139390	+	1.01795i
$345$	287.630	+	75.6995i	0.0448854	+	0.0118131i
$346$	−629.479	−	402.554i	−0.0978063	−	0.0625475i
$347$	−771.195	+	771.195i	−0.119308	+	0.119308i	−0.764240	−	0.644932i	$-0.776886\pi$
$347$	−771.195	+	771.195i	−0.119308	+	0.119308i	0.644932	+	0.764240i	$0.276886\pi$
$348$	−1572.41	−	578.474i	−0.242212	−	0.0891077i
$349$	−12180.8			−1.86826			−0.934130	−	0.356933i	$-0.883822\pi$
$349$	−12180.8			−1.86826			−0.934130	+	0.356933i	$0.883822\pi$
$350$	721.242	−	382.056i	0.110149	−	0.0583478i
$351$			8793.05i			1.33715i
$352$	9971.91	+	5301.11i	1.50996	+	0.802699i
$353$	7908.15	+	7908.15i	1.19238	+	1.19238i	0.976398	+	0.215977i	$0.0692936\pi$
$353$	7908.15	+	7908.15i	1.19238	+	1.19238i	0.215977	+	0.976398i	$0.430706\pi$
$354$	458.854	+	293.439i	0.0688922	+	0.0440568i
$355$	−3266.69	+	12412.2i	−0.488389	+	1.85569i
$356$	−1669.69	−	3613.23i	−0.248577	−	0.537924i
$357$	−176.161	−	176.161i	−0.0261160	−	0.0261160i
$358$	−6312.21	+	1387.94i	−0.931873	+	0.204902i
$359$	−6142.68			−0.903060			−0.451530	−	0.892256i	$-0.649122\pi$
$359$	−6142.68			−0.903060			−0.451530	+	0.892256i	$0.649122\pi$
$360$	−4390.58	+	1814.86i	−0.642789	+	0.265698i
$361$	3286.39			0.479135
$362$	−90.0919	+	19.8095i	−0.0130805	+	0.00287615i
$363$	−5192.58	−	5192.58i	−0.750798	−	0.750798i
$364$	−1123.09	+	518.987i	−0.161720	+	0.0747316i
$365$	5460.75	+	9361.81i	0.783093	+	1.34252i
$366$	−4502.79	−	2879.55i	−0.643072	−	0.411247i
$367$	−2826.77	−	2826.77i	−0.402061	−	0.402061i	0.476898	−	0.878959i	$-0.341761\pi$
$367$	−2826.77	−	2826.77i	−0.402061	−	0.402061i	−0.878959	+	0.476898i	$0.841761\pi$
$368$	−47.6624	−	591.902i	−0.00675157	−	0.0838451i
$369$		−	516.673i		−	0.0728914i
$370$	3190.63	−	2939.69i	0.448305	−	0.413047i
$371$	1216.28			0.170206
$372$	−1335.05	+	3628.92i	−0.186073	+	0.505782i
$373$	−765.331	+	765.331i	−0.106240	+	0.106240i	−0.758228	−	0.651989i	$-0.773935\pi$
$373$	−765.331	+	765.331i	−0.106240	+	0.106240i	0.651989	+	0.758228i	$0.273935\pi$
$374$	5595.48	+	3578.33i	0.773624	+	0.494735i
$375$	53.5066	+	4006.59i	0.00736818	+	0.551731i
$376$	717.439	−	5239.35i	0.0984018	−	0.718614i
$377$	−3460.15	+	3460.15i	−0.472697	+	0.472697i
$378$	184.049	+	837.038i	0.0250436	+	0.113896i
$379$		−	3482.43i		−	0.471980i	−0.971755	−	0.235990i	$-0.924167\pi$
$379$		−	3482.43i		−	0.471980i	0.971755	−	0.235990i	$-0.0758333\pi$
$380$	−933.572	−	5263.97i	−0.126030	−	0.710620i
$381$		−	3860.66i		−	0.519127i
$382$	−2475.66	+	544.352i	−0.331586	+	0.0729096i
$383$	9322.29	−	9322.29i	1.24373	−	1.24373i	0.285282	−	0.958444i	$-0.407913\pi$
$383$	9322.29	−	9322.29i	1.24373	−	1.24373i	0.958444	−	0.285282i	$-0.0920874\pi$
$384$	−2767.84	−	3094.94i	−0.367827	−	0.411297i
$385$	811.314	+	1390.90i	0.107398	+	0.184122i
$386$	−4409.89	+	6895.81i	−0.581496	+	0.909294i
$387$	3847.07	−	3847.07i	0.505317	−	0.505317i
$388$	−1192.58	+	3241.66i	−0.156041	+	0.424150i
$389$	−7236.20			−0.943161			−0.471581	−	0.881823i	$-0.656316\pi$
$389$	−7236.20			−0.943161			−0.471581	+	0.881823i	$0.656316\pi$
$390$	248.419	−	6068.82i	0.0322543	−	0.787966i
$391$		−	349.233i		−	0.0451701i
$392$	6085.75	−	4619.81i	0.784125	−	0.595244i
$393$	4655.36	+	4655.36i	0.597537	+	0.597537i
$394$	6422.27	−	10042.6i	0.821191	−	1.28411i
$395$	8121.88	+	2137.55i	1.03457	+	0.272283i
$396$	−3931.76	−	8508.38i	−0.498936	−	1.07970i
$397$	3899.18	+	3899.18i	0.492933	+	0.492933i	0.909229	−	0.416296i	$-0.136672\pi$
$397$	3899.18	+	3899.18i	0.492933	+	0.492933i	−0.416296	+	0.909229i	$0.636672\pi$
$398$	−2754.46	−	12527.0i	−0.346906	−	1.57770i
$399$	−395.617			−0.0496381
$400$	7512.09	−	2751.09i	0.939011	−	0.343887i
$401$	−7856.60			−0.978403			−0.489202	−	0.872171i	$-0.662712\pi$
$401$	−7856.60			−0.978403			−0.489202	+	0.872171i	$0.662712\pi$
$402$	1247.41	+	5673.10i	0.154764	+	0.703852i
$403$	7985.60	+	7985.60i	0.987075	+	0.987075i
$404$	−3163.98	−	6846.89i	−0.389639	−	0.843182i
$405$	1413.34	+	371.969i	0.173406	+	0.0456378i
$406$	−256.958	+	401.808i	−0.0314103	+	0.0491167i
$407$	6052.25	+	6052.25i	0.737098	+	0.737098i
$408$	−1476.46	−	1944.97i	−0.179156	−	0.236005i
$409$		−	278.474i		−	0.0336666i	−0.999858	−	0.0168333i	$-0.994642\pi$
$409$		−	278.474i		−	0.0336666i	0.999858	−	0.0168333i	$-0.00535846\pi$
$410$	−35.5835	+	869.296i	−0.00428620	+	0.104711i
$411$	4077.50			0.489363
$412$	−979.121	+	2661.44i	−0.117082	+	0.318252i
$413$	109.635	−	109.635i	0.0130625	−	0.0130625i
$414$	−265.519	+	415.195i	−0.0315206	+	0.0492892i
$415$	−2003.73	−	3435.16i	−0.237010	−	0.406326i
$416$	−11596.6	+	3546.47i	−1.36675	+	0.417981i
$417$	825.343	−	825.343i	0.0969238	−	0.0969238i
$418$	10301.1	−	2265.03i	1.20537	−	0.265039i
$419$		−	4588.99i		−	0.535052i	−0.963551	−	0.267526i	$-0.913794\pi$
$419$		−	4588.99i		−	0.535052i	0.963551	−	0.267526i	$-0.0862062\pi$
$420$	−103.380	−	582.910i	−0.0120106	−	0.0677217i
$421$			5953.12i			0.689162i	0.938757	+	0.344581i	$0.111979\pi$
$421$			5953.12i			0.689162i	−0.938757	+	0.344581i	$0.888021\pi$
$422$	−1926.68	−	8762.38i	−0.222250	−	1.01077i
$423$	−3103.46	+	3103.46i	−0.356727	+	0.356727i
$424$	11811.4	+	1617.37i	1.35286	+	0.185251i
$425$	4533.59	−	1258.13i	0.517439	−	0.143596i
$426$	7842.96	+	5015.60i	0.892002	+	0.570438i
$427$	−1075.86	+	1075.86i	−0.121931	+	0.121931i
$428$	−1358.75	+	3693.34i	−0.153452	+	0.417113i
$429$	11983.1			1.34860
$430$	−6737.60	+	6207.70i	−0.755619	+	0.696191i
$431$		−	4163.99i		−	0.465365i	−0.972553	−	0.232683i	$-0.925250\pi$
$431$		−	4163.99i		−	0.465365i	0.972553	−	0.232683i	$-0.0747504\pi$
$432$	674.253	+	8373.29i	0.0750927	+	0.932547i
$433$	−2024.70	−	2024.70i	−0.224713	−	0.224713i	0.585767	−	0.810480i	$-0.300793\pi$
$433$	−2024.70	−	2024.70i	−0.224713	−	0.224713i	−0.810480	+	0.585767i	$0.800793\pi$
$434$	927.324	+	593.027i	0.102564	+	0.0655903i
$435$	−1179.76	−	2022.56i	−0.130035	−	0.222930i
$436$	−5969.94	+	2758.74i	−0.655753	+	0.303026i
$437$	−392.149	−	392.149i	−0.0429268	−	0.0429268i
$438$	7677.80	−	1688.21i	0.837579	−	0.184168i
$439$	−3583.38			−0.389580			−0.194790	−	0.980845i	$-0.562403\pi$
$439$	−3583.38			−0.389580			−0.194790	+	0.980845i	$0.562403\pi$
$440$	6029.17	+	14586.0i	0.653248	+	1.58037i
$441$	−6341.30			−0.684731
$442$	−6965.54	+	1531.59i	−0.749586	+	0.164820i
$443$	1001.91	+	1001.91i	0.107454	+	0.107454i	0.758790	−	0.651336i	$-0.225791\pi$
$443$	1001.91	+	1001.91i	0.107454	+	0.107454i	−0.651336	+	0.758790i	$0.725791\pi$
$444$	−1320.03	−	2856.56i	−0.141094	−	0.305330i
$445$	1415.81	−	5379.54i	0.150822	−	0.573066i
$446$	10857.2	+	6943.20i	1.15270	+	0.737153i
$447$	−4420.41	−	4420.41i	−0.467737	−	0.467737i
$448$	−1029.68	+	580.331i	−0.108589	+	0.0612010i
$449$		−	7881.21i		−	0.828368i	−0.910193	−	0.414184i	$-0.864067\pi$
$449$		−	7881.21i		−	0.828368i	0.910193	−	0.414184i	$-0.135933\pi$
$450$	−6346.43	−	1951.08i	−0.664830	−	0.204388i
$451$	−1716.45			−0.179212
$452$	−7415.70	−	2728.17i	−0.771693	−	0.283899i
$453$	−5232.85	+	5232.85i	−0.542739	+	0.542739i
$454$	−9129.27	−	5838.20i	−0.943739	−	0.603525i
$455$	−1672.11	−	440.073i	−0.172285	−	0.0453427i
$456$	−3841.87	−	526.077i	−0.394544	−	0.0540259i
$457$	−7151.43	+	7151.43i	−0.732013	+	0.732013i	−0.971018	−	0.239006i	$-0.923179\pi$
$457$	−7151.43	+	7151.43i	−0.732013	+	0.732013i	0.239006	+	0.971018i	$0.423179\pi$
$458$	1182.24	+	5376.71i	0.120617	+	0.548552i
$459$			4940.40i			0.502393i
$460$	475.327	−	680.275i	0.0481788	−	0.0689521i
$461$			5918.81i			0.597975i	0.954257	+	0.298987i	$0.0966488\pi$
$461$			5918.81i			0.597975i	−0.954257	+	0.298987i	$0.903351\pi$
$462$	1140.71	−	250.820i	0.114871	−	0.0252580i
$463$	4849.09	−	4849.09i	0.486731	−	0.486731i	−0.420542	−	0.907273i	$-0.638160\pi$
$463$	4849.09	−	4849.09i	0.486731	−	0.486731i	0.907273	+	0.420542i	$0.138160\pi$
$464$	−3029.65	+	3560.30i	−0.303120	+	0.356213i
$465$	−4667.83	+	2722.75i	−0.465517	+	0.271537i
$466$	2619.54	−	4096.21i	0.260403	−	0.407196i
$467$	−2370.31	+	2370.31i	−0.234871	+	0.234871i	−0.814722	−	0.579851i	$-0.803111\pi$
$467$	−2370.31	+	2370.31i	−0.234871	+	0.234871i	0.579851	+	0.814722i	$0.303111\pi$
$468$	9445.62	+	3474.96i	0.932958	+	0.343227i
$469$	1653.53			0.162800
$470$	5435.27	−	5007.80i	0.533426	−	0.491473i
$471$			2226.09i			0.217776i
$472$	1210.47	−	918.887i	0.118043	−	0.0896085i
$473$	−12780.4	−	12780.4i	−1.24238	−	1.24238i
$474$	3281.94	−	5132.01i	0.318026	−	0.497302i
$475$	3677.96	−	6503.44i	0.355276	−	0.628207i
$476$	−631.014	+	291.595i	−0.0607615	+	0.0280782i
$477$	−6996.35	−	6996.35i	−0.671574	−	0.671574i
$478$	2477.59	+	11267.8i	0.237076	+	1.07820i
$479$	11996.7			1.14435			0.572174	−	0.820132i	$-0.306100\pi$
$479$	11996.7			1.14435			0.572174	+	0.820132i	$0.306100\pi$
$480$	−228.799	−	5798.16i	−0.0217566	−	0.551352i
$481$	−9190.77			−0.871233
$482$	668.669	+	3041.04i	0.0631889	+	0.287377i
$483$	−43.4250	−	43.4250i	−0.00409090	−	0.00409090i
$484$	−18600.0	+	8595.14i	−1.74680	+	0.807207i
$485$	−4169.70	+	2432.19i	−0.390384	+	0.227711i
$486$	5971.45	−	9337.64i	0.557347	−	0.871531i
$487$	−6021.08	−	6021.08i	−0.560249	−	0.560249i	0.369129	−	0.929378i	$-0.379656\pi$
$487$	−6021.08	−	6021.08i	−0.560249	−	0.560249i	−0.929378	+	0.369129i	$0.879656\pi$
$488$	−11878.4	+	9017.14i	−1.10187	+	0.836449i
$489$			1287.60i			0.119075i
$490$	10669.2	+	436.728i	0.983639	+	0.0402640i
$491$	9946.16			0.914183			0.457092	−	0.889420i	$-0.348891\pi$
$491$	9946.16			0.914183			0.457092	+	0.889420i	$0.348891\pi$
$492$	592.251	+	217.884i	0.0542698	+	0.0199654i
$493$	−1944.10	+	1944.10i	−0.177602	+	0.177602i
$494$	−6101.69	+	9541.30i	−0.555725	+	0.868995i
$495$	3333.93	−	12667.7i	0.302725	−	1.15024i
$496$	8216.73	+	6992.06i	0.743835	+	0.632969i
$497$	1873.94	−	1873.94i	0.169130	−	0.169130i
$498$	−2817.24	+	619.459i	−0.253501	+	0.0557402i
$499$		−	15650.8i		−	1.40406i	−0.712148	−	0.702029i	$-0.752278\pi$
$499$		−	15650.8i		−	1.40406i	0.712148	−	0.702029i	$-0.247722\pi$
$500$	10543.4	+	3719.75i	0.943031	+	0.332704i
$501$		−	4649.52i		−	0.414622i
$502$	−2377.67	−	10813.4i	−0.211395	−	0.961405i
$503$	−6492.90	+	6492.90i	−0.575555	+	0.575555i	−0.933675	−	0.358120i	$-0.883418\pi$
$503$	−6492.90	+	6492.90i	−0.575555	+	0.575555i	0.358120	+	0.933675i	$0.383418\pi$
$504$	971.894	+	133.084i	0.0858961	+	0.0117620i
$505$	2682.89	−	10194.0i	0.236410	−	0.898268i
$506$	1379.33	+	882.085i	0.121183	+	0.0774970i
$507$	−4644.42	+	4644.42i	−0.406837	+	0.406837i
$508$	−10109.7	−	3719.27i	−0.882965	−	0.324835i
$509$	−9155.78			−0.797294			−0.398647	−	0.917104i	$-0.630520\pi$
$509$	−9155.78			−0.797294			−0.398647	+	0.917104i	$0.630520\pi$
$510$	139.575	−	3409.79i	0.0121186	−	0.296055i
$511$		−	2237.84i		−	0.193731i
$512$	−10771.1	+	4266.40i	−0.929722	+	0.368262i
$513$	5547.50	+	5547.50i	0.477443	+	0.477443i
$514$	4682.04	+	2994.18i	0.401782	+	0.256941i
$515$	−3423.38	+	1996.86i	−0.292916	+	0.170858i
$516$	2787.48	+	6032.15i	0.237814	+	0.514633i
$517$	10310.1	+	10310.1i	0.877052	+	0.877052i
$518$	−874.899	+	192.374i	−0.0742101	+	0.0163174i
$519$	−757.416			−0.0640595
$520$	−15652.8	−	6497.10i	−1.32004	−	0.547917i
$521$	8890.03			0.747561			0.373781	−	0.927517i	$-0.378061\pi$
$521$	8890.03			0.747561			0.373781	+	0.927517i	$0.378061\pi$
$522$	3789.37	−	833.213i	0.317732	−	0.0698635i
$523$	−9129.71	−	9129.71i	−0.763316	−	0.763316i	0.213604	−	0.976920i	$-0.431480\pi$
$523$	−9129.71	−	9129.71i	−0.763316	−	0.763316i	−0.976920	+	0.213604i	$0.931480\pi$
$524$	16675.7	−	7705.90i	1.39023	−	0.642431i
$525$	407.282	−	720.164i	0.0338576	−	0.0598677i
$526$	−14627.5	−	9354.31i	−1.21252	−	0.775413i
$527$	4486.74	+	4486.74i	0.370864	+	0.370864i
$528$	11411.0	−	918.864i	0.940532	−	0.0757357i
$529$			12080.9i			0.992924i
$530$	11289.4	+	12253.1i	0.925248	+	1.00423i
$531$	−1261.29			−0.103080
$532$	−381.129	+	1035.98i	−0.0310602	+	0.0844277i
$533$	1303.27	−	1303.27i	0.105912	−	0.105912i
$534$	−3399.19	−	2173.80i	−0.275464	−	0.176160i
$535$	−4750.69	+	2771.08i	−0.383907	+	0.223933i
$536$	16057.6	+	2198.81i	1.29400	+	0.177191i
$537$	−4632.57	+	4632.57i	−0.372272	+	0.372272i
$538$	−1235.45	−	5618.72i	−0.0990040	−	0.450261i
$539$			21066.5i			1.68349i
$540$	−6724.18	+	9623.45i	−0.535856	+	0.766903i
$541$		−	8774.26i		−	0.697292i	−0.937254	−	0.348646i	$-0.886642\pi$
$541$		−	8774.26i		−	0.697292i	0.937254	−	0.348646i	$-0.113358\pi$
$542$	9203.85	−	2023.76i	0.729408	−	0.160383i
$543$	−66.1191	+	66.1191i	−0.00522549	+	0.00522549i
$544$	−6515.58	+	1992.60i	−0.513517	+	0.157044i
$545$	−8888.31	−	2339.26i	−0.698593	−	0.183859i
$546$	−675.677	+	1056.57i	−0.0529603	+	0.0828147i
$547$	14817.9	−	14817.9i	1.15826	−	1.15826i	0.173406	−	0.984850i	$-0.444523\pi$
$547$	14817.9	−	14817.9i	1.15826	−	1.15826i	0.984850	−	0.173406i	$-0.0554774\pi$
$548$	3928.18	−	10677.6i	0.306211	−	0.832341i
$549$	12377.2			0.962198
$550$	−6481.71	+	21083.6i	−0.502511	+	1.63456i
$551$			4365.99i			0.337564i
$552$	−363.959	−	479.449i	−0.0280636	−	0.0369686i
$553$	−1226.20	−	1226.20i	−0.0942920	−	0.0942920i
$554$	−6111.42	+	9556.51i	−0.468681	+	0.732883i
$555$	1119.31	−	4252.97i	0.0856077	−	0.325277i
$556$	−1366.17	−	2956.40i	−0.104206	−	0.225503i
$557$	13934.8	+	13934.8i	1.06003	+	1.06003i	0.998079	+	0.0619489i	$0.0197316\pi$
$557$	13934.8	+	13934.8i	1.06003	+	1.06003i	0.0619489	+	0.998079i	$0.480268\pi$
$558$	−1922.95	−	8745.41i	−0.145887	−	0.663481i
$559$	19408.0			1.46846
$560$	−1626.03	−	290.847i	−0.122701	−	0.0219474i
$561$	6732.72			0.506695
$562$	−291.650	−	1326.40i	−0.0218906	−	0.0995563i
$563$	7373.79	+	7373.79i	0.551986	+	0.551986i	0.927014	−	0.375027i	$-0.122367\pi$
$563$	7373.79	+	7373.79i	0.551986	+	0.551986i	−0.375027	+	0.927014i	$0.622367\pi$
$564$	−2248.68	−	4866.17i	−0.167884	−	0.363303i
$565$	−5563.94	−	9538.71i	−0.414295	−	0.710260i
$566$	−6856.58	+	10721.7i	−0.509194	+	0.796233i
$567$	−213.380	−	213.380i	−0.0158044	−	0.0158044i
$568$	20689.9	−	15706.1i	1.52839	−	1.16023i
$569$			8066.19i			0.594292i	0.954832	+	0.297146i	$0.0960349\pi$
$569$			8066.19i			0.594292i	−0.954832	+	0.297146i	$0.903965\pi$
$570$	−3672.07	−	3985.53i	−0.269835	−	0.292869i
$571$	1577.74			0.115633			0.0578164	−	0.998327i	$-0.481586\pi$
$571$	1577.74			0.115633			0.0578164	+	0.998327i	$0.481586\pi$
$572$	11544.2	−	31379.5i	0.843861	−	2.29378i
$573$	−1816.90	+	1816.90i	−0.132465	+	0.132465i
$574$	96.7838	−	151.342i	0.00703776	−	0.0110050i
$575$	1117.56	−	310.140i	0.0810533	−	0.0224934i
$576$	9261.18	+	2584.78i	0.669935	+	0.186978i
$577$	14468.0	−	14468.0i	1.04387	−	1.04387i	0.0448739	−	0.998993i	$-0.485711\pi$
$577$	14468.0	−	14468.0i	1.04387	−	1.04387i	0.998993	−	0.0448739i	$-0.0142886\pi$
$578$	9658.24	−	2123.67i	0.695034	−	0.152825i
$579$			8297.33i			0.595553i
$580$	−6432.95	+	1140.89i	−0.460541	+	0.0816777i
$581$			821.139i			0.0586344i
$582$	751.917	+	3419.65i	0.0535532	+	0.243555i
$583$	−23242.7	+	23242.7i	−1.65114	+	1.65114i
$584$	2975.80	−	21731.9i	0.210856	−	1.53985i
$585$	7086.97	+	12149.8i	0.500872	+	0.858686i
$586$	−11688.1	−	7474.58i	−0.823943	−	0.526915i
$587$	−16990.1	+	16990.1i	−1.19465	+	1.19465i	−0.218898	+	0.975748i	$0.570246\pi$
$587$	−16990.1	+	16990.1i	−1.19465	+	1.19465i	−0.975748	+	0.218898i	$0.929754\pi$
$588$	2674.16	−	7268.89i	0.187552	−	0.509803i
$589$	10076.2			0.704893
$590$	2122.11	+	86.8658i	0.148078	+	0.00606137i
$591$		−	12083.7i		−	0.841042i
$592$	−8752.03	+	704.751i	−0.607612	+	0.0489275i
$593$	−67.7222	−	67.7222i	−0.00468974	−	0.00468974i	0.704758	−	0.709448i	$-0.251056\pi$
$593$	−67.7222	−	67.7222i	−0.00468974	−	0.00468974i	−0.709448	+	0.704758i	$0.751056\pi$
$594$	−19512.6	−	12478.3i	−1.34783	−	0.861941i
$595$	−939.482	−	247.257i	−0.0647311	−	0.0170362i
$596$	−15834.1	+	7317.00i	−1.08824	+	0.502879i
$597$	−9193.68	−	9193.68i	−0.630272	−	0.630272i
$598$	−1717.06	+	377.549i	−0.117418	+	0.0258180i
$599$	−12494.2			−0.852252			−0.426126	−	0.904664i	$-0.640122\pi$
$599$	−12494.2			−0.852252			−0.426126	+	0.904664i	$0.640122\pi$
$600$	4912.80	−	6451.99i	0.334274	−	0.439002i
$601$	19551.9			1.32702			0.663508	−	0.748169i	$-0.269067\pi$
$601$	19551.9			1.32702			0.663508	+	0.748169i	$0.269067\pi$
$602$	1847.51	−	406.233i	0.125081	−	0.0275030i
$603$	−9511.51	−	9511.51i	−0.642353	−	0.642353i
$604$	8661.81	+	18744.2i	0.583516	+	1.26274i
$605$	−27692.5	−	7288.22i	−1.86092	−	0.489765i
$606$	−6441.31	−	4119.24i	−0.431783	−	0.276126i
$607$	6194.33	+	6194.33i	0.414201	+	0.414201i	0.883199	−	0.468998i	$-0.155385\pi$
$607$	6194.33	+	6194.33i	0.414201	+	0.414201i	−0.468998	+	0.883199i	$0.655385\pi$
$608$	−5078.79	+	9553.70i	−0.338770	+	0.637260i
$609$			483.473i			0.0321696i
$610$	−20824.5	−	852.423i	−1.38223	−	0.0565797i
$611$	−15656.6			−1.03666
$612$	5307.06	+	1952.42i	0.350531	+	0.128957i
$613$	4151.90	−	4151.90i	0.273562	−	0.273562i	−0.556970	−	0.830532i	$-0.688036\pi$
$613$	4151.90	−	4151.90i	0.273562	−	0.273562i	0.830532	+	0.556970i	$0.188036\pi$
$614$	13598.6	+	8696.37i	0.893804	+	0.571591i
$615$	444.361	+	761.804i	0.0291356	+	0.0499495i
$616$	442.121	−	3228.75i	0.0289181	−	0.211185i
$617$	9127.15	−	9127.15i	0.595535	−	0.595535i	−0.343586	−	0.939121i	$-0.611642\pi$
$617$	9127.15	−	9127.15i	0.595535	−	0.595535i	0.939121	+	0.343586i	$0.111642\pi$
$618$	617.334	+	2807.58i	0.0401825	+	0.182746i
$619$			9443.78i			0.613211i	0.951837	+	0.306605i	$0.0991932\pi$
$619$			9443.78i			0.613211i	−0.951837	+	0.306605i	$0.900807\pi$
$620$	2633.04	+	14846.5i	0.170557	+	0.961691i
$621$			1217.85i			0.0786965i
$622$	12485.0	−	2745.22i	0.804829	−	0.176967i
$623$	−812.178	+	812.178i	−0.0522299	+	0.0522299i
$624$	−7966.54	+	9361.90i	−0.511085	+	0.600603i
$625$	8052.18	+	13390.4i	0.515340	+	0.856986i
$626$	78.1080	−	122.138i	0.00498694	−	0.00779814i
$627$	7560.07	−	7560.07i	0.481531	−	0.481531i
$628$	5829.35	+	2144.56i	0.370408	+	0.136270i
$629$	−5163.87			−0.327340
$630$	928.941	+	1008.24i	0.0587459	+	0.0637605i
$631$			3283.13i			0.207130i	0.994623	+	0.103565i	$0.0330251\pi$
$631$			3283.13i			0.207130i	−0.994623	+	0.103565i	$0.966975\pi$
$632$	−10277.2	−	13538.3i	−0.646844	−	0.852098i
$633$	−6430.77	−	6430.77i	−0.403792	−	0.403792i
$634$	−3444.56	+	5386.30i	−0.215774	+	0.337409i
$635$	−7585.23	−	13004.0i	−0.474033	−	0.812673i
$636$	10970.2	−	5069.36i	0.683955	−	0.316059i
$637$	−15995.5	−	15995.5i	−0.994922	−	0.994922i
$638$	−2768.03	−	12588.7i	−0.171767	−	0.781180i
$639$	−21558.6			−1.33466
$640$	−15403.8	−	4986.68i	−0.951388	−	0.307994i
$641$	17569.8			1.08263			0.541316	−	0.840819i	$-0.317926\pi$
$641$	17569.8			1.08263			0.541316	+	0.840819i	$0.317926\pi$
$642$	856.687	+	3896.13i	0.0526647	+	0.239514i
$643$	6841.79	+	6841.79i	0.419617	+	0.419617i	0.885072	−	0.465455i	$-0.154109\pi$
$643$	6841.79	+	6841.79i	0.419617	+	0.419617i	−0.465455	+	0.885072i	$0.654109\pi$
$644$	−155.550	+	71.8802i	−0.00951788	+	0.00439826i
$645$	−2363.64	+	8980.93i	−0.144292	+	0.548254i
$646$	−3428.26	+	5360.81i	−0.208797	+	0.326499i
$647$	20801.5	+	20801.5i	1.26398	+	1.26398i	0.949149	+	0.314827i	$0.101946\pi$
$647$	20801.5	+	20801.5i	1.26398	+	1.26398i	0.314827	+	0.949149i	$0.398054\pi$
$648$	−1788.41	−	2355.90i	−0.108419	−	0.142822i
$649$			4190.17i			0.253434i
$650$	−11087.0	−	20929.9i	−0.669026	−	1.26298i
$651$	1115.80			0.0671759
$652$	3371.79	+	1240.45i	0.202530	+	0.0745089i
$653$	6791.66	−	6791.66i	0.407011	−	0.407011i	−0.473684	−	0.880695i	$-0.657076\pi$
$653$	6791.66	−	6791.66i	0.407011	−	0.407011i	0.880695	+	0.473684i	$0.157076\pi$
$654$	−3591.64	+	5616.30i	−0.214747	+	0.335802i
$655$	24827.5	+	6534.19i	1.48105	+	0.389789i
$656$	1141.12	−	1341.00i	0.0679168	−	0.0798126i
$657$	−12872.6	+	12872.6i	−0.764395	+	0.764395i
$658$	−1490.40	+	327.711i	−0.0883005	+	0.0194157i
$659$			2846.76i			0.168276i	0.996454	+	0.0841381i	$0.0268137\pi$
$659$			2846.76i			0.168276i	−0.996454	+	0.0841381i	$0.973186\pi$
$660$	13114.7	+	9163.63i	0.773470	+	0.540445i
$661$			20101.9i			1.18286i	0.806355	+	0.591432i	$0.201437\pi$
$661$			20101.9i			1.18286i	−0.806355	+	0.591432i	$0.798563\pi$
$662$	1805.05	+	8209.21i	0.105975	+	0.481964i
$663$	−5112.06	+	5112.06i	−0.299451	+	0.299451i
$664$	−1091.92	+	7974.15i	−0.0638175	+	0.466050i
$665$	−1332.57	+	777.289i	−0.0777065	+	0.0453263i
$666$	6139.20	+	3926.04i	0.357191	+	0.228425i
$667$	−479.235	+	479.235i	−0.0278201	+	0.0278201i
$668$	−12175.5	−	4479.25i	−0.705215	−	0.259442i
$669$	13063.8			0.754972
$670$	15347.9	+	16658.1i	0.884989	+	0.960533i
$671$		−	41118.6i		−	2.36567i
$672$	−562.405	+	1057.94i	−0.0322846	+	0.0607305i
$673$	−7942.65	−	7942.65i	−0.454928	−	0.454928i	0.442058	−	0.896986i	$-0.354248\pi$
$673$	−7942.65	−	7942.65i	−0.454928	−	0.454928i	−0.896986	+	0.442058i	$0.854248\pi$
$674$	−8770.95	−	5609.05i	−0.501253	−	0.320553i
$675$	−15809.5	+	4387.37i	−0.901495	+	0.250177i
$676$	7687.80	+	16636.5i	0.437403	+	0.946545i
$677$	1214.74	+	1214.74i	0.0689604	+	0.0689604i	0.740746	−	0.671785i	$-0.234472\pi$
$677$	1214.74	+	1214.74i	0.0689604	+	0.0689604i	−0.671785	+	0.740746i	$0.734472\pi$
$678$	−7822.88	+	1720.11i	−0.443121	+	0.0974341i
$679$	996.722			0.0563339
$680$	−8794.59	−	3650.42i	−0.495967	−	0.205863i
$681$	−10984.7			−0.618114
$682$	−29053.3	+	6388.28i	−1.63124	+	0.358680i
$683$	−2979.54	−	2979.54i	−0.166924	−	0.166924i	0.618702	−	0.785626i	$-0.287659\pi$
$683$	−2979.54	−	2979.54i	−0.166924	−	0.166924i	−0.785626	+	0.618702i	$0.787659\pi$
$684$	8151.55	−	3766.87i	0.455676	−	0.210570i
$685$	13734.4	−	8011.28i	0.766079	−	0.446855i
$686$	−3744.25	−	2394.46i	−0.208391	−	0.133267i
$687$	3946.00	+	3946.00i	0.219140	+	0.219140i
$688$	18481.5	−	1488.21i	1.02413	−	0.0824673i
$689$		−	35295.7i		−	1.95161i
$690$	34.4063	−	840.539i	0.00189830	−	0.0463750i
$691$	−24835.3			−1.36726			−0.683631	−	0.729827i	$-0.739600\pi$
$691$	−24835.3			−1.36726			−0.683631	+	0.729827i	$0.739600\pi$
$692$	−729.679	+	1983.41i	−0.0400841	+	0.108957i
$693$	−1912.51	+	1912.51i	−0.104834	+	0.104834i
$694$	2598.81	+	1661.95i	0.142146	+	0.0909030i
$695$	1158.44	−	4401.63i	0.0632260	−	0.240235i
$696$	−642.905	+	4695.04i	−0.0350133	+	0.255697i
$697$	732.250	−	732.250i	0.0397933	−	0.0397933i
$698$	7398.72	+	33648.7i	0.401211	+	1.82467i
$699$		−	4928.74i		−	0.266698i
$700$	−1493.49	−	1760.32i	−0.0806411	−	0.0950485i
$701$		−	16050.4i		−	0.864787i	−0.901685	−	0.432394i	$-0.857669\pi$
$701$		−	16050.4i		−	0.864787i	0.901685	−	0.432394i	$-0.142331\pi$
$702$	24290.2	−	5340.97i	1.30595	−	0.287154i
$703$	−5798.42	+	5798.42i	−0.311084	+	0.311084i
$704$	8586.95	−	30766.7i	0.459706	−	1.64711i
$705$	1906.76	−	7244.98i	0.101862	−	0.387038i
$706$	17042.3	−	26649.2i	0.908491	−	1.42062i
$707$	−1539.04	+	1539.04i	−0.0818691	+	0.0818691i
$708$	531.894	−	1445.79i	0.0282342	−	0.0767461i
$709$	13000.2			0.688620			0.344310	−	0.938856i	$-0.388113\pi$
$709$	13000.2			0.688620			0.344310	+	0.938856i	$0.388113\pi$
$710$	36272.1	+	1484.75i	1.91728	+	0.0784813i
$711$			14106.8i			0.744088i
$712$	−8967.13	+	6807.12i	−0.471991	+	0.358297i
$713$	1106.02	+	1106.02i	0.0580934	+	0.0580934i
$714$	−379.632	+	593.635i	−0.0198983	+	0.0311152i
$715$	40363.0	−	23543.7i	2.11117	−	1.23145i
$716$	7668.18	+	16594.0i	0.400242	+	0.866128i
$717$	8269.55	+	8269.55i	0.430728	+	0.430728i
$718$	3731.12	+	16968.8i	0.193933	+	0.881990i
$719$	−724.797			−0.0375944			−0.0187972	−	0.999823i	$-0.505984\pi$
$719$	−724.797			−0.0375944			−0.0187972	+	0.999823i	$0.505984\pi$
$720$	7680.31	+	11026.3i	0.397539	+	0.570733i
$721$	818.322			0.0422689
$722$	−1996.18	−	9078.44i	−0.102895	−	0.467956i
$723$	2231.84	+	2231.84i	0.114804	+	0.114804i
$724$	109.445	+	236.841i	0.00561809	+	0.0121576i
$725$	−7947.68	−	4494.73i	−0.407130	−	0.230249i
$726$	−11190.1	+	17498.2i	−0.572046	+	0.894516i
$727$	−22261.1	−	22261.1i	−1.13565	−	1.13565i	−0.989221	−	0.146430i	$-0.953222\pi$
$727$	−22261.1	−	22261.1i	−1.13565	−	1.13565i	−0.146430	−	0.989221i	$-0.546778\pi$
$728$	2115.84	+	2787.24i	0.107718	+	0.141898i
$729$		−	7706.07i		−	0.391509i
$730$	22544.5	−	20771.4i	1.14303	−	1.05313i
$731$	10904.4			0.551731
$732$	−5219.54	+	14187.7i	−0.263551	+	0.716385i
$733$	8886.09	−	8886.09i	0.447770	−	0.447770i	−0.446843	−	0.894613i	$-0.647452\pi$
$733$	8886.09	−	8886.09i	0.447770	−	0.447770i	0.894613	+	0.446843i	$0.147452\pi$
$734$	−6091.77	+	9525.78i	−0.306337	+	0.479023i
$735$	9349.87	−	5453.78i	0.469218	−	0.273695i
$736$	−1606.14	+	491.191i	−0.0804390	+	0.0245999i
$737$	−31598.4	+	31598.4i	−1.57929	+	1.57929i
$738$	−1427.28	+	313.832i	−0.0711908	+	0.0156535i
$739$		−	21372.7i		−	1.06388i	−0.846783	−	0.531939i	$-0.821464\pi$
$739$		−	21372.7i		−	1.06388i	0.846783	−	0.531939i	$-0.178536\pi$
$740$	−10058.7	−	7028.32i	−0.499684	−	0.349144i
$741$			11480.5i			0.569159i
$742$	−738.782	−	3359.91i	−0.0365519	−	0.166235i
$743$	17304.4	−	17304.4i	0.854421	−	0.854421i	−0.136253	−	0.990674i	$-0.543506\pi$
$743$	17304.4	−	17304.4i	0.854421	−	0.854421i	0.990674	+	0.136253i	$0.0435059\pi$
$744$	10835.6	+	1483.75i	0.533941	+	0.0731140i
$745$	−23574.5	−	6204.42i	−1.15933	−	0.305117i
$746$	2579.05	+	1649.31i	0.126576	+	0.0809458i
$747$	4723.38	−	4723.38i	0.231351	−	0.231351i
$748$	6486.16	−	17630.7i	0.317056	−	0.861819i
$749$	1135.60			0.0553992
$750$	11035.4	−	2581.44i	0.537277	−	0.125681i
$751$		−	9428.24i		−	0.458111i	−0.973413	−	0.229055i	$-0.926436\pi$
$751$		−	9428.24i		−	0.458111i	0.973413	−	0.229055i	$-0.0735637\pi$
$752$	−14909.2	+	1200.55i	−0.722980	+	0.0582174i
$753$	−7936.03	−	7936.03i	−0.384070	−	0.384070i
$754$	11660.2	+	7456.72i	0.563181	+	0.360156i
$755$	−7344.75	+	27907.3i	−0.354043	+	1.34523i
$756$	2200.47	−	1016.85i	0.105860	−	0.0489185i
$757$	642.402	+	642.402i	0.0308435	+	0.0308435i	0.722360	−	0.691517i	$-0.243057\pi$
$757$	642.402	+	642.402i	0.0308435	+	0.0308435i	−0.691517	+	0.722360i	$0.743057\pi$
$758$	−9619.99	+	2115.26i	−0.460968	+	0.101358i
$759$	1659.67			0.0793703
$760$	−13974.3	+	5776.31i	−0.666976	+	0.275696i
$761$	−20575.9			−0.980124			−0.490062	−	0.871688i	$-0.663026\pi$
$761$	−20575.9			−0.980124			−0.490062	+	0.871688i	$0.663026\pi$
$762$	−10664.8	+	2345.00i	−0.507015	+	0.111483i
$763$	1341.92	+	1341.92i	0.0636705	+	0.0636705i
$764$	3007.48	+	6508.21i	0.142417	+	0.308192i
$765$	3981.84	+	6826.39i	0.188188	+	0.322626i
$766$	−31414.7	−	20089.8i	−1.48180	−	0.947616i
$767$	−3181.53	−	3181.53i	−0.149776	−	0.149776i
$768$	−6868.37	+	9525.87i	−0.322709	+	0.447572i
$769$			14159.5i			0.663987i	0.943282	+	0.331994i	$0.107721\pi$
$769$			14159.5i			0.663987i	−0.943282	+	0.331994i	$0.892279\pi$
$770$	3349.48	−	3086.05i	0.156762	−	0.144433i
$771$	5633.63			0.263152
$772$	21727.8	+	7993.48i	1.01296	+	0.372657i
$773$	−4651.93	+	4651.93i	−0.216453	+	0.216453i	−0.807002	−	0.590549i	$-0.798911\pi$
$773$	−4651.93	+	4651.93i	−0.216453	+	0.216453i	0.590549	+	0.807002i	$0.298911\pi$
$774$	−12964.0	−	8290.55i	−0.602045	−	0.385010i
$775$	−10373.3	+	18342.3i	−0.480800	+	0.850160i
$776$	9679.25	+	1325.41i	0.447764	+	0.0613135i
$777$	−642.094	+	642.094i	−0.0296461	+	0.0296461i
$778$	4395.33	+	19989.5i	0.202545	+	0.921156i
$779$		−	1644.46i		−	0.0756342i
$780$	−16915.6	+	3000.01i	−0.776509	+	0.137715i
$781$			71620.3i			3.28140i
$782$	−964.735	+	212.127i	−0.0441162	+	0.00970033i
$783$	6779.46	−	6779.46i	0.309423	−	0.309423i
$784$	−16458.5	−	14005.4i	−0.749748	−	0.638001i
$785$	4373.71	+	7498.21i	0.198859	+	0.340920i
$786$	10032.4	−	15687.9i	0.455274	−	0.711918i
$787$	11118.1	−	11118.1i	0.503581	−	0.503581i	−0.408968	−	0.912549i	$-0.634111\pi$
$787$	11118.1	−	11118.1i	0.503581	−	0.503581i	0.912549	+	0.408968i	$0.134111\pi$
$788$	−31642.9	−	11641.2i	−1.43050	−	0.526268i
$789$	−17600.4			−0.794158
$790$	971.542	−	23734.5i	0.0437543	−	1.06891i
$791$			2280.13i			0.102493i
$792$	−21115.7	+	16029.3i	−0.947365	+	0.719163i
$793$	31220.7	+	31220.7i	1.39808	+	1.39808i
$794$	8402.85	−	13139.6i	0.375574	−	0.587290i
$795$	16332.9	+	4298.55i	0.728638	+	0.191766i
$796$	−32932.1	+	15218.1i	−1.46639	+	0.677625i
$797$	−26274.8	−	26274.8i	−1.16776	−	1.16776i	−0.982734	−	0.185021i	$-0.940765\pi$
$797$	−26274.8	−	26274.8i	−1.16776	−	1.16776i	−0.185021	−	0.982734i	$-0.559235\pi$
$798$	240.301	+	1092.87i	0.0106599	+	0.0484800i
$799$	−8796.69			−0.389493
$800$	−12162.6	−	19080.6i	−0.537517	−	0.843253i
$801$	9343.67			0.412163
$802$	4772.16	+	21703.3i	0.210113	+	0.955576i
$803$	42764.2	+	42764.2i	1.87935	+	1.87935i
$804$	14913.9	−	6891.78i	0.654195	−	0.302306i
$805$	−231.589	−	60.9506i	−0.0101397	−	0.00266860i
$806$	17209.2	−	26910.2i	0.752070	−	1.17602i
$807$	−4123.62	−	4123.62i	−0.179874	−	0.179874i
$808$	−16992.3	+	12899.2i	−0.739834	+	0.561622i
$809$		−	29424.6i		−	1.27876i	−0.768892	−	0.639379i	$-0.779192\pi$
$809$		−	29424.6i		−	1.27876i	0.768892	−	0.639379i	$-0.220808\pi$
$810$	169.065	−	4130.21i	0.00733373	−	0.179161i
$811$	−15648.6			−0.677554			−0.338777	−	0.940867i	$-0.610013\pi$
$811$	−15648.6			−0.677554			−0.338777	+	0.940867i	$0.610013\pi$
$812$	1266.05	+	465.767i	0.0547162	+	0.0201296i
$813$	6754.77	−	6754.77i	0.291390	−	0.291390i
$814$	13042.8	−	20395.1i	0.561608	−	0.878193i
$815$	2529.82	+	4337.08i	0.108731	+	0.186407i
$816$	−4476.03	+	5260.02i	−0.192025	+	0.225659i
$817$	12244.4	−	12244.4i	0.524331	−	0.524331i
$818$	−769.266	+	169.147i	−0.0328811	+	0.00722995i
$819$		−	2904.27i		−	0.123912i
$820$	2422.99	−	429.721i	0.103188	−	0.0183006i
$821$		−	3218.41i		−	0.136813i	−0.997658	−	0.0684064i	$-0.978209\pi$
$821$		−	3218.41i		−	0.136813i	0.997658	−	0.0684064i	$-0.0217915\pi$
$822$	−2476.71	−	11263.8i	−0.105091	−	0.477946i
$823$	4720.16	−	4720.16i	0.199920	−	0.199920i	−0.600046	−	0.799966i	$-0.704851\pi$
$823$	4720.16	−	4720.16i	0.199920	−	0.199920i	0.799966	+	0.600046i	$0.204851\pi$
$824$	7946.79	+	1088.18i	0.335970	+	0.0460053i
$825$	5979.05	+	21545.0i	0.252320	+	0.909214i
$826$	−369.454	−	236.267i	−0.0155629	−	0.00995251i
$827$	4751.81	−	4751.81i	0.199802	−	0.199802i	−0.600113	−	0.799915i	$-0.704878\pi$
$827$	4751.81	−	4751.81i	0.199802	−	0.199802i	0.799915	+	0.600113i	$0.204878\pi$
$828$	1308.23	+	481.286i	0.0549084	+	0.0202003i
$829$	−35341.2			−1.48064			−0.740319	−	0.672255i	$-0.765326\pi$
$829$	−35341.2			−1.48064			−0.740319	+	0.672255i	$0.765326\pi$
$830$	−8272.33	+	7621.73i	−0.345948	+	0.318740i
$831$			11498.8i			0.480011i
$832$	16840.8	+	29880.7i	0.701741	+	1.24510i
$833$	−8987.13	−	8987.13i	−0.373812	−	0.373812i
$834$	−2781.28	−	1778.64i	−0.115477	−	0.0738479i
$835$	−9135.17	−	15661.2i	−0.378605	−	0.649074i
$836$	−12514.0	−	27080.4i	−0.517710	−	1.12033i
$837$	−15646.2	−	15646.2i	−0.646129	−	0.646129i
$838$	−12676.8	+	2787.39i	−0.522569	+	0.114903i
$839$	−33758.3			−1.38911			−0.694557	−	0.719438i	$-0.744400\pi$
$839$	−33758.3			−1.38911			−0.694557	+	0.719438i	$0.744400\pi$
$840$	−1547.46	+	639.646i	−0.0635624	+	0.0262737i
$841$	−19053.4			−0.781231
$842$	16445.1	−	3615.97i	0.673083	−	0.147998i
$843$	−973.451	−	973.451i	−0.0397716	−	0.0397716i
$844$	−23035.2	+	10644.7i	−0.939461	+	0.434129i
$845$	−6518.84	+	24769.1i	−0.265390	+	1.00838i
$846$	10458.2	+	6688.04i	0.425011	+	0.271796i
$847$	4180.88	+	4180.88i	0.169607	+	0.169607i
$848$	−2706.48	−	33610.8i	−0.109600	−	1.36108i
$849$			12900.8i			0.521503i
$850$	−6229.26	−	11759.5i	−0.251367	−	0.474528i
$851$	−1272.93			−0.0512756
$852$	9091.40	−	24712.2i	0.365571	−	0.993693i
$853$	27284.0	−	27284.0i	1.09518	−	1.09518i	0.100210	−	0.994966i	$-0.468049\pi$
$853$	27284.0	−	27284.0i	1.09518	−	1.09518i	0.994966	−	0.100210i	$-0.0319514\pi$
$854$	3625.49	+	2318.51i	0.145271	+	0.0929015i
$855$	12136.4	+	3194.10i	0.485446	+	0.127761i
$856$	11027.9	+	1510.08i	0.440335	+	0.0602963i
$857$	8957.01	−	8957.01i	0.357019	−	0.357019i	−0.505694	−	0.862713i	$-0.668763\pi$
$857$	8957.01	−	8957.01i	0.357019	−	0.357019i	0.862713	+	0.505694i	$0.168763\pi$
$858$	−7278.61	−	33102.4i	−0.289613	−	1.31713i
$859$			34133.2i			1.35578i	0.735166	+	0.677888i	$0.237104\pi$
$859$			34133.2i			1.35578i	−0.735166	+	0.677888i	$0.762896\pi$
$860$	21240.9	+	14841.6i	0.842218	+	0.588481i
$861$		−	182.101i		−	0.00720789i
$862$	−11502.8	+	2529.25i	−0.454508	+	0.0999379i
$863$	2289.06	−	2289.06i	0.0902901	−	0.0902901i	−0.660519	−	0.750809i	$-0.729664\pi$
$863$	2289.06	−	2289.06i	0.0902901	−	0.0902901i	0.750809	+	0.660519i	$0.229664\pi$
$864$	22721.1	−	6948.59i	0.894663	−	0.273606i
$865$	−2551.23	+	1488.14i	−0.100283	+	0.0584949i
$866$	−4363.28	+	6822.91i	−0.171213	+	0.267727i
$867$	7088.25	−	7088.25i	0.277658	−	0.277658i
$868$	1074.93	−	2921.88i	0.0420342	−	0.114257i
$869$	46864.5			1.82942
$870$	−4870.61	+	4487.54i	−0.189803	+	0.174876i
$871$		−	47984.3i		−	1.86669i
$872$	11247.0	+	14815.9i	0.436780	+	0.575378i
$873$	−5733.38	−	5733.38i	−0.222274	−	0.222274i
$874$	−845.091	+	1321.48i	−0.0327067	+	0.0511439i
$875$	−43.0816	−	3225.96i	−0.00166449	−	0.124637i
$876$	−9327.12	−	20184.0i	−0.359742	−	0.778487i
$877$	26605.5	+	26605.5i	1.02441	+	1.02441i	0.999695	+	0.0247110i	$0.00786655\pi$
$877$	26605.5	+	26605.5i	1.02441	+	1.02441i	0.0247110	+	0.999695i	$0.492133\pi$
$878$	2176.58	+	9898.87i	0.0836628	+	0.380491i
$879$	−14063.6			−0.539652
$880$	36630.8	−	25514.9i	1.40321	−	0.977393i
$881$	17574.1			0.672061			0.336031	−	0.941851i	$-0.390915\pi$
$881$	17574.1			0.672061			0.336031	+	0.941851i	$0.390915\pi$
$882$	3851.76	+	17517.4i	0.147047	+	0.668756i
$883$	7230.39	+	7230.39i	0.275563	+	0.275563i	0.831335	−	0.555772i	$-0.187577\pi$
$883$	7230.39	+	7230.39i	0.275563	+	0.275563i	−0.555772	+	0.831335i	$0.687577\pi$
$884$	8461.86	+	18311.6i	0.321949	+	0.696702i
$885$	1859.70	−	1084.77i	0.0706364	−	0.0412023i
$886$	2159.14	−	3376.27i	0.0818709	−	0.128023i
$887$	27480.2	+	27480.2i	1.04024	+	1.04024i	0.999156	+	0.0410876i	$0.0130823\pi$
$887$	27480.2	+	27480.2i	1.04024	+	1.04024i	0.0410876	+	0.999156i	$0.486918\pi$
$888$	−7089.27	+	5381.60i	−0.267906	+	0.203372i
$889$			3108.47i			0.117272i
$890$	−15720.6	−	643.502i	−0.592085	−	0.0242362i
$891$	8155.21			0.306633
$892$	12585.4	−	34209.6i	0.472411	−	1.28411i
$893$	−9877.67	+	9877.67i	−0.370149	+	0.370149i
$894$	−9526.12	+	14896.1i	−0.356377	+	0.557271i
$895$	−6502.20	+	24705.9i	−0.242843	+	0.922713i
$896$	2228.57	+	2491.94i	0.0830928	+	0.0929127i
$897$	−1260.16	+	1260.16i	−0.0469070	+	0.0469070i
$898$	−21771.4	+	4787.12i	−0.809042	+	0.177893i
$899$		−	12313.8i		−	0.456829i
$900$	−1534.86	+	18716.7i	−0.0568466	+	0.693211i
$901$		−	19831.0i		−	0.733259i
$902$	1042.59	+	4741.58i	0.0384859	+	0.175030i
$903$	1355.90	−	1355.90i	0.0499685	−	0.0499685i
$904$	−3032.04	+	22142.5i	−0.111553	+	0.814656i
$905$	−92.8036	+	352.619i	−0.00340873	+	0.0129519i
$906$	17633.9	+	11276.9i	0.646631	+	0.413522i
$907$	−32472.3	+	32472.3i	−1.18878	+	1.18878i	−0.211377	+	0.977405i	$0.567795\pi$
$907$	−32472.3	+	32472.3i	−1.18878	+	1.18878i	−0.977405	+	0.211377i	$0.932205\pi$
$908$	−10582.5	+	28765.2i	−0.386774	+	1.05133i
$909$	17705.8			0.646055
$910$	−200.019	+	4886.41i	−0.00728632	+	0.178003i
$911$			33425.7i			1.21564i	0.794077	+	0.607818i	$0.207955\pi$
$911$			33425.7i			1.21564i	−0.794077	+	0.607818i	$0.792045\pi$
$912$	880.328	+	10932.5i	0.0319634	+	0.396941i
$913$	−15691.6	−	15691.6i	−0.568803	−	0.568803i
$914$	24099.2	+	15411.5i	0.872135	+	0.557733i
$915$	−18249.5	+	10644.9i	−0.659354	+	0.384602i
$916$	14134.7	−	6531.72i	0.509851	−	0.235605i
$917$	−3748.34	−	3748.34i	−0.134985	−	0.134985i
$918$	13647.6	−	3000.84i	0.490671	−	0.107890i
$919$	27640.7			0.992145			0.496072	−	0.868281i	$-0.334775\pi$
$919$	27640.7			0.992145			0.496072	+	0.868281i	$0.334775\pi$
$920$	−2167.93	−	899.856i	−0.0776898	−	0.0322471i
$921$	16362.4			0.585408
$922$	16350.3	−	3595.13i	0.584023	−	0.128416i
$923$	−54380.3	−	54380.3i	−1.93927	−	1.93927i
$924$	−1385.75	−	2998.78i	−0.0493374	−	0.106767i
$925$	−4585.81	−	16524.6i	−0.163006	−	0.587380i
$926$	−16340.7	−	10449.9i	−0.579901	−	0.370849i
$927$	−4707.18	−	4707.18i	−0.166779	−	0.166779i
$928$	11675.3	+	6206.65i	0.412997	+	0.219551i
$929$		−	4275.33i		−	0.150989i	−0.997146	−	0.0754946i	$-0.975946\pi$
$929$		−	4275.33i		−	0.150989i	0.997146	−	0.0754946i	$-0.0240536\pi$
$930$	10356.7	+	11240.8i	0.365172	+	0.396343i
$931$	−20183.0			−0.710496
$932$	−12906.7	−	4748.25i	−0.453618	−	0.166882i
$933$	9162.84	−	9162.84i	0.321520	−	0.321520i
$934$	7987.58	+	5108.08i	0.279830	+	0.178952i
$935$	22678.1	−	13228.1i	0.793211	−	0.462681i
$936$	3862.00	−	28203.7i	0.134865	−	0.984899i
$937$	4338.96	−	4338.96i	0.151278	−	0.151278i	−0.627410	−	0.778689i	$-0.715885\pi$
$937$	4338.96	−	4338.96i	0.151278	−	0.151278i	0.778689	+	0.627410i	$0.215885\pi$
$938$	−1004.37	−	4567.78i	−0.0349615	−	0.159002i
$939$		−	146.962i		−	0.00510749i
$940$	−17135.1	−	11972.8i	−0.594560	−	0.415436i
$941$		−	29214.9i		−	1.01209i	−0.862506	−	0.506047i	$-0.831106\pi$
$941$		−	29214.9i		−	1.01209i	0.862506	−	0.506047i	$-0.168894\pi$
$942$	6149.42	−	1352.14i	0.212695	−	0.0467678i
$943$	180.505	−	180.505i	0.00623335	−	0.00623335i
$944$	−3273.62	−	2785.69i	−0.112868	−	0.0960451i
$945$	3276.16	+	862.233i	0.112776	+	0.0296809i
$946$	−27542.2	+	43068.1i	−0.946589	+	1.48019i
$947$	35030.7	−	35030.7i	1.20205	−	1.20205i	0.228512	−	0.973541i	$-0.426614\pi$
$947$	35030.7	−	35030.7i	1.20205	−	1.20205i	0.973541	−	0.228512i	$-0.0733860\pi$
$948$	−16170.3	−	5948.92i	−0.553996	−	0.203810i
$949$	−64940.5			−2.22135
$950$	−20199.4	−	6209.88i	−0.689846	−	0.212079i
$951$			6481.03i			0.220990i
$952$	1188.79	+	1566.02i	0.0404717	+	0.0533140i
$953$	25184.3	+	25184.3i	0.856035	+	0.856035i	0.990868	−	0.134834i	$-0.0430500\pi$
$953$	25184.3	+	25184.3i	0.856035	+	0.856035i	−0.134834	+	0.990868i	$0.543050\pi$
$954$	−15077.3	+	23576.6i	−0.511684	+	0.800127i
$955$	−2550.18	+	9689.71i	−0.0864103	+	0.328326i
$956$	29621.8	−	13688.4i	1.00213	−	0.463090i
$957$	−9238.96	−	9238.96i	−0.312072	−	0.312072i
$958$	−7286.89	−	33140.1i	−0.245750	−	1.11765i
$959$	−3283.06			−0.110548
$960$	−15878.1	+	4153.90i	−0.533816	+	0.139653i
$961$	1372.17			0.0460599
$962$	5582.55	+	25388.9i	0.187098	+	0.850906i
$963$	−6532.25	−	6532.25i	−0.218586	−	0.218586i
$964$	7994.53	−	3694.31i	0.267102	−	0.123429i
$965$	16302.2	+	27948.2i	0.543820	+	0.932316i
$966$	−93.5820	+	146.335i	−0.00311693	+	0.00487398i
$967$	−35241.6	−	35241.6i	−1.17197	−	1.17197i	−0.981740	−	0.190228i	$-0.939077\pi$
$967$	−35241.6	−	35241.6i	−1.17197	−	1.17197i	−0.190228	−	0.981740i	$-0.560923\pi$
$968$	35041.3	+	46160.5i	1.16350	+	1.53270i
$969$			6450.36i			0.213845i
$970$	9251.47	+	10041.2i	0.306234	+	0.332374i
$971$	16611.5			0.549010			0.274505	−	0.961586i	$-0.411486\pi$
$971$	16611.5			0.549010			0.274505	+	0.961586i	$0.411486\pi$
$972$	−29421.8	−	10824.0i	−0.970888	−	0.357181i
$973$	−664.537	+	664.537i	−0.0218953	+	0.0218953i
$974$	−12975.6	+	20290.1i	−0.426863	+	0.667492i
$975$	−20898.6	−	11819.0i	−0.686453	−	0.388217i
$976$	32124.3	+	27336.3i	1.05356	+	0.896531i
$977$	17592.3	−	17592.3i	0.576076	−	0.576076i	−0.357744	−	0.933820i	$-0.616454\pi$
$977$	17592.3	−	17592.3i	0.576076	−	0.576076i	0.933820	+	0.357744i	$0.116454\pi$
$978$	3556.92	−	782.102i	0.116296	−	0.0255714i
$979$		−	31040.8i		−	1.01335i
$980$	−5274.10	−	29738.1i	−0.171913	−	0.969336i
$981$		−	15438.0i		−	0.502445i
$982$	−6041.39	−	27475.6i	−0.196322	−	0.892854i
$983$	10007.4	−	10007.4i	0.324705	−	0.324705i	−0.525864	−	0.850569i	$-0.676258\pi$
$983$	10007.4	−	10007.4i	0.324705	−	0.324705i	0.850569	+	0.525864i	$0.176258\pi$
$984$	242.152	−	1768.40i	0.00784504	−	0.0572912i
$985$	−23741.4	−	40701.9i	−0.767984	−	1.31662i
$986$	6551.31	+	4189.58i	0.211598	+	0.135318i
$987$	−1093.81	+	1093.81i	−0.0352750	+	0.0352750i
$988$	30063.4	+	11060.1i	0.968062	+	0.356142i
$989$	2688.03			0.0864250
$990$	−37018.7	−	1515.31i	−1.18841	−	0.0486462i
$991$			54042.7i			1.73231i	0.499772	+	0.866157i	$0.333417\pi$
$991$			54042.7i			1.73231i	−0.499772	+	0.866157i	$0.666583\pi$
$992$	14324.2	−	26945.2i	0.458461	−	0.862411i
$993$	6024.80	+	6024.80i	0.192539	+	0.192539i
$994$	−6314.88	−	4038.39i	−0.201505	−	0.128863i
$995$	−49030.7	−	12904.1i	−1.56219	−	0.411143i
$996$	3422.43	+	7406.19i	0.108879	+	0.235616i
$997$	2684.64	+	2684.64i	0.0852791	+	0.0852791i	0.748460	−	0.663180i	$-0.230794\pi$
$997$	2684.64	+	2684.64i	0.0852791	+	0.0852791i	−0.663180	+	0.748460i	$0.730794\pi$
$998$	−43234.3	+	9506.42i	−1.37130	+	0.301523i
$999$	18007.4			0.570300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.4.k.a.3.7	✓	32
4.3	odd	2		160.4.o.a.143.11		32
5.2	odd	4	inner	40.4.k.a.27.16	yes	32
5.3	odd	4		200.4.k.j.107.1		32
5.4	even	2		200.4.k.j.43.10		32
8.3	odd	2	inner	40.4.k.a.3.16	yes	32
8.5	even	2		160.4.o.a.143.12		32
20.7	even	4		160.4.o.a.47.12		32
40.3	even	4		200.4.k.j.107.10		32
40.19	odd	2		200.4.k.j.43.1		32
40.27	even	4	inner	40.4.k.a.27.7	yes	32
40.37	odd	4		160.4.o.a.47.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.k.a.3.7	✓	32	1.1	even	1	trivial
40.4.k.a.3.16	yes	32	8.3	odd	2	inner
40.4.k.a.27.7	yes	32	40.27	even	4	inner
40.4.k.a.27.16	yes	32	5.2	odd	4	inner
160.4.o.a.47.11		32	40.37	odd	4
160.4.o.a.47.12		32	20.7	even	4
160.4.o.a.143.11		32	4.3	odd	2
160.4.o.a.143.12		32	8.5	even	2
200.4.k.j.43.1		32	40.19	odd	2
200.4.k.j.43.10		32	5.4	even	2
200.4.k.j.107.1		32	5.3	odd	4
200.4.k.j.107.10		32	40.3	even	4

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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.607409 - 2.76244i) q^{2} +(-2.02737 - 2.02737i) q^{3} +(-7.26211 + 3.35586i) q^{4} +(-10.8122 - 2.84559i) q^{5} +(-4.36904 + 6.83193i) q^{6} +(1.63237 + 1.63237i) q^{7} +(13.6814 + 18.0227i) q^{8} -18.7795i q^{9} +O(q^{10})\)	\(q+(-0.607409 - 2.76244i) q^{2} +(-2.02737 - 2.02737i) q^{3} +(-7.26211 + 3.35586i) q^{4} +(-10.8122 - 2.84559i) q^{5} +(-4.36904 + 6.83193i) q^{6} +(1.63237 + 1.63237i) q^{7} +(13.6814 + 18.0227i) q^{8} -18.7795i q^{9} +(-1.29335 + 31.5963i) q^{10} -62.3878 q^{11} +(21.5266 + 7.91943i) q^{12} +(47.3701 - 47.3701i) q^{13} +(3.51780 - 5.50083i) q^{14} +(16.1512 + 27.6893i) q^{15} +(41.4765 - 48.7412i) q^{16} +(26.6151 - 26.6151i) q^{17} +(-51.8773 + 11.4068i) q^{18} -59.7713i q^{19} +(88.0684 - 15.6191i) q^{20} -6.61884i q^{21} +(37.8949 + 172.342i) q^{22} +(6.56082 - 6.56082i) q^{23} +(8.80150 - 64.2761i) q^{24} +(108.805 + 61.5338i) q^{25} +(-159.630 - 102.084i) q^{26} +(-92.8121 + 92.8121i) q^{27} +(-17.3324 - 6.37645i) q^{28} -73.0449 q^{29} +(66.6796 - 61.4354i) q^{30} +168.579i q^{31} +(-159.838 - 84.9703i) q^{32} +(126.483 + 126.483i) q^{33} +(-89.6887 - 57.3562i) q^{34} +(-13.0044 - 22.2945i) q^{35} +(63.0214 + 136.379i) q^{36} +(-97.0101 - 97.0101i) q^{37} +(-165.114 + 36.3056i) q^{38} -192.074 q^{39} +(-96.6402 - 233.796i) q^{40} +27.5126 q^{41} +(-18.2841 + 4.02034i) q^{42} +(204.855 + 204.855i) q^{43} +(453.067 - 209.364i) q^{44} +(-53.4388 + 203.047i) q^{45} +(-22.1089 - 14.1387i) q^{46} +(-165.258 - 165.258i) q^{47} +(-182.905 + 14.7283i) q^{48} -337.671i q^{49} +(103.894 - 337.944i) q^{50} -107.917 q^{51} +(-185.040 + 502.974i) q^{52} +(372.552 - 372.552i) q^{53} +(312.762 + 200.013i) q^{54} +(674.546 + 177.530i) q^{55} +(-7.08666 + 51.7529i) q^{56} +(-121.179 + 121.179i) q^{57} +(44.3681 + 201.782i) q^{58} -67.1632i q^{59} +(-210.213 - 146.882i) q^{60} +659.080i q^{61} +(465.688 - 102.396i) q^{62} +(30.6551 - 30.6551i) q^{63} +(-137.638 + 493.153i) q^{64} +(-646.969 + 377.377i) q^{65} +(272.575 - 426.229i) q^{66} +(506.483 - 506.483i) q^{67} +(-103.965 + 282.598i) q^{68} -26.6024 q^{69} +(-53.6881 + 49.4656i) q^{70} -1147.99i q^{71} +(338.459 - 256.930i) q^{72} +(-685.459 - 685.459i) q^{73} +(-209.060 + 326.909i) q^{74} +(-95.8369 - 345.341i) q^{75} +(200.584 + 434.066i) q^{76} +(-101.840 - 101.840i) q^{77} +(116.667 + 530.591i) q^{78} -751.180 q^{79} +(-587.147 + 408.972i) q^{80} -130.718 q^{81} +(-16.7114 - 76.0018i) q^{82} +(251.518 + 251.518i) q^{83} +(22.2119 + 48.0667i) q^{84} +(-363.502 + 212.031i) q^{85} +(441.468 - 690.329i) q^{86} +(148.089 + 148.089i) q^{87} +(-853.553 - 1124.40i) q^{88} +497.545i q^{89} +(593.364 + 24.2886i) q^{90} +154.651 q^{91} +(-25.6282 + 69.6625i) q^{92} +(341.772 - 341.772i) q^{93} +(-356.135 + 556.893i) q^{94} +(-170.084 + 646.257i) q^{95} +(151.784 + 496.316i) q^{96} +(305.299 - 305.299i) q^{97} +(-932.794 + 205.104i) q^{98} +1171.61i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 44 q^{8}+O(q^{10}) \) 32 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 44 * q^8	\( 32 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 44 q^{8} + 70 q^{10} - 8 q^{11} + 28 q^{12} + 72 q^{16} + 48 q^{17} - 278 q^{18} - 320 q^{20} + 68 q^{22} + 40 q^{25} - 92 q^{26} + 104 q^{27} + 620 q^{28} - 740 q^{30} + 288 q^{32} - 112 q^{33} - 460 q^{35} + 476 q^{36} + 636 q^{38} + 540 q^{40} - 8 q^{41} + 1020 q^{42} - 868 q^{43} + 1328 q^{46} - 784 q^{48} + 790 q^{50} + 1480 q^{51} - 1900 q^{52} - 2392 q^{56} + 104 q^{57} - 700 q^{58} - 1100 q^{60} - 2880 q^{62} + 520 q^{65} - 4360 q^{66} - 1852 q^{67} + 1196 q^{68} - 1500 q^{70} + 5596 q^{72} - 744 q^{73} + 3300 q^{75} + 4312 q^{76} + 2240 q^{78} + 1120 q^{80} - 1240 q^{81} + 5828 q^{82} + 2676 q^{83} + 6976 q^{86} - 2864 q^{88} + 4070 q^{90} - 1704 q^{91} - 7500 q^{92} - 10656 q^{96} - 584 q^{97} - 3814 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 44 * q^8 + 70 * q^10 - 8 * q^11 + 28 * q^12 + 72 * q^16 + 48 * q^17 - 278 * q^18 - 320 * q^20 + 68 * q^22 + 40 * q^25 - 92 * q^26 + 104 * q^27 + 620 * q^28 - 740 * q^30 + 288 * q^32 - 112 * q^33 - 460 * q^35 + 476 * q^36 + 636 * q^38 + 540 * q^40 - 8 * q^41 + 1020 * q^42 - 868 * q^43 + 1328 * q^46 - 784 * q^48 + 790 * q^50 + 1480 * q^51 - 1900 * q^52 - 2392 * q^56 + 104 * q^57 - 700 * q^58 - 1100 * q^60 - 2880 * q^62 + 520 * q^65 - 4360 * q^66 - 1852 * q^67 + 1196 * q^68 - 1500 * q^70 + 5596 * q^72 - 744 * q^73 + 3300 * q^75 + 4312 * q^76 + 2240 * q^78 + 1120 * q^80 - 1240 * q^81 + 5828 * q^82 + 2676 * q^83 + 6976 * q^86 - 2864 * q^88 + 4070 * q^90 - 1704 * q^91 - 7500 * q^92 - 10656 * q^96 - 584 * q^97 - 3814 * q^98

Introduction

L-functions

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