LMFDB - Embedded newform 74.5.g.a.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,5,Mod(23,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("74.23");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	74.g (of order $12$, degree $4$, 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:	$7.64937726820$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	74.29
Dual form			74.5.g.a.23.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.732051 - 2.73205i) q^{2} +(-5.46714 - 3.15645i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(-2.29270 - 8.55648i) q^{5} +(-12.6258 + 12.6258i) q^{6} +(-24.9782 + 43.2636i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(-20.5736 - 35.6345i) q^{9} +O(q^{10})$	\(q+(0.732051 - 2.73205i) q^{2} +(-5.46714 - 3.15645i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(-2.29270 - 8.55648i) q^{5} +(-12.6258 + 12.6258i) q^{6} +(-24.9782 + 43.2636i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(-20.5736 - 35.6345i) q^{9} -25.0551 q^{10} +34.8004i q^{11} +(25.2516 + 43.7371i) q^{12} +(75.5865 + 282.093i) q^{13} +(99.9129 + 99.9129i) q^{14} +(-14.4736 + 54.0163i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-363.714 - 97.4570i) q^{17} +(-112.416 + 30.1218i) q^{18} +(37.1161 + 138.519i) q^{19} +(-18.3416 + 68.4519i) q^{20} +(273.119 - 157.685i) q^{21} +(95.0766 + 25.4757i) q^{22} +(-392.476 + 392.476i) q^{23} +(137.978 - 36.9710i) q^{24} +(473.309 - 273.265i) q^{25} +826.025 q^{26} +771.104i q^{27} +(346.109 - 199.826i) q^{28} +(-925.323 - 925.323i) q^{29} +(136.980 + 79.0854i) q^{30} +(-920.330 - 920.330i) q^{31} +(174.851 - 46.8513i) q^{32} +(109.846 - 190.259i) q^{33} +(-532.515 + 922.343i) q^{34} +(427.452 + 114.535i) q^{35} +329.177i q^{36} +(-1238.32 + 583.724i) q^{37} +405.612 q^{38} +(477.171 - 1780.83i) q^{39} +(173.587 + 100.220i) q^{40} +(-1112.69 - 642.414i) q^{41} +(-230.867 - 861.609i) q^{42} +(1246.22 - 1246.22i) q^{43} +(139.202 - 241.105i) q^{44} +(-257.737 + 257.737i) q^{45} +(784.951 + 1359.58i) q^{46} -621.711 q^{47} -404.026i q^{48} +(-47.3247 - 81.9687i) q^{49} +(-400.088 - 1493.15i) q^{50} +(1680.86 + 1680.86i) q^{51} +(604.692 - 2256.74i) q^{52} +(-1513.75 - 2621.90i) q^{53} +(2106.70 + 564.487i) q^{54} +(297.769 - 79.7870i) q^{55} +(-292.565 - 1091.87i) q^{56} +(234.310 - 874.459i) q^{57} +(-3205.41 + 1850.65i) q^{58} +(3933.61 + 1054.01i) q^{59} +(316.341 - 316.341i) q^{60} +(-3076.17 + 824.256i) q^{61} +(-3188.12 + 1840.66i) q^{62} +2055.57 q^{63} -512.000i q^{64} +(2240.42 - 1293.51i) q^{65} +(-439.384 - 439.384i) q^{66} +(216.911 + 125.234i) q^{67} +(2130.06 + 2130.06i) q^{68} +(3384.55 - 906.887i) q^{69} +(625.833 - 1083.97i) q^{70} +(-1951.90 + 3380.79i) q^{71} +(899.329 + 240.975i) q^{72} +3555.50i q^{73} +(688.255 + 3810.46i) q^{74} -3450.20 q^{75} +(296.929 - 1108.15i) q^{76} +(-1505.59 - 869.254i) q^{77} +(-4516.00 - 2607.31i) q^{78} +(2275.94 + 8493.93i) q^{79} +(400.882 - 400.882i) q^{80} +(767.495 - 1329.34i) q^{81} +(-2569.66 + 2569.66i) q^{82} +(1400.71 + 2426.10i) q^{83} -2522.97 q^{84} +3335.56i q^{85} +(-2492.45 - 4317.05i) q^{86} +(2138.13 + 7979.61i) q^{87} +(-556.807 - 556.807i) q^{88} +(-177.640 + 662.961i) q^{89} +(515.474 + 892.827i) q^{90} +(-14092.4 - 3776.04i) q^{91} +(4289.05 - 1149.25i) q^{92} +(2126.59 + 7936.55i) q^{93} +(-455.124 + 1698.55i) q^{94} +(1100.14 - 635.166i) q^{95} +(-1103.82 - 295.768i) q^{96} +(999.805 - 999.805i) q^{97} +(-258.587 + 69.2881i) q^{98} +(1240.10 - 715.970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9}+O(q^{10}) $ 28 * q - 28 * q^2 + 42 * q^5 - 40 * q^6 + 48 * q^7 - 448 * q^8 + 556 * q^9	\( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9} - 72 q^{10} + 80 q^{12} + 248 q^{13} - 192 q^{14} - 852 q^{15} + 896 q^{16} + 1092 q^{17} + 1112 q^{18} - 320 q^{19} + 336 q^{20} - 858 q^{21} - 112 q^{22} + 2348 q^{23} + 160 q^{24} - 162 q^{25} - 184 q^{26} + 1584 q^{28} - 1308 q^{29} + 2652 q^{30} - 3444 q^{31} + 1792 q^{32} + 1052 q^{33} + 1428 q^{34} - 580 q^{35} - 5694 q^{37} - 824 q^{38} - 6514 q^{39} - 1056 q^{40} - 12186 q^{41} - 1276 q^{42} - 6220 q^{43} + 1280 q^{44} + 12804 q^{45} - 4696 q^{46} + 15928 q^{47} - 4892 q^{49} - 10792 q^{50} - 6218 q^{51} + 1984 q^{52} - 9662 q^{53} - 9836 q^{54} + 1744 q^{55} - 3936 q^{56} + 16046 q^{57} + 13800 q^{58} - 9356 q^{59} - 3024 q^{60} - 6682 q^{61} + 16128 q^{62} + 60268 q^{63} - 28086 q^{65} - 4208 q^{66} + 28086 q^{67} - 5712 q^{68} + 19878 q^{69} - 6028 q^{70} + 680 q^{71} - 8896 q^{72} - 2420 q^{74} + 11076 q^{75} - 2560 q^{76} - 32208 q^{77} + 23436 q^{78} - 15136 q^{79} + 1152 q^{80} - 21274 q^{81} - 2608 q^{82} - 19732 q^{83} + 23936 q^{84} + 12440 q^{86} - 31624 q^{87} - 5120 q^{88} + 45940 q^{89} - 25608 q^{90} - 13106 q^{91} - 6944 q^{92} - 37734 q^{93} - 16960 q^{94} - 37458 q^{95} - 1280 q^{96} + 31792 q^{97} + 5216 q^{98} + 141456 q^{99}+O(q^{100}) \) 28 * q - 28 * q^2 + 42 * q^5 - 40 * q^6 + 48 * q^7 - 448 * q^8 + 556 * q^9 - 72 * q^10 + 80 * q^12 + 248 * q^13 - 192 * q^14 - 852 * q^15 + 896 * q^16 + 1092 * q^17 + 1112 * q^18 - 320 * q^19 + 336 * q^20 - 858 * q^21 - 112 * q^22 + 2348 * q^23 + 160 * q^24 - 162 * q^25 - 184 * q^26 + 1584 * q^28 - 1308 * q^29 + 2652 * q^30 - 3444 * q^31 + 1792 * q^32 + 1052 * q^33 + 1428 * q^34 - 580 * q^35 - 5694 * q^37 - 824 * q^38 - 6514 * q^39 - 1056 * q^40 - 12186 * q^41 - 1276 * q^42 - 6220 * q^43 + 1280 * q^44 + 12804 * q^45 - 4696 * q^46 + 15928 * q^47 - 4892 * q^49 - 10792 * q^50 - 6218 * q^51 + 1984 * q^52 - 9662 * q^53 - 9836 * q^54 + 1744 * q^55 - 3936 * q^56 + 16046 * q^57 + 13800 * q^58 - 9356 * q^59 - 3024 * q^60 - 6682 * q^61 + 16128 * q^62 + 60268 * q^63 - 28086 * q^65 - 4208 * q^66 + 28086 * q^67 - 5712 * q^68 + 19878 * q^69 - 6028 * q^70 + 680 * q^71 - 8896 * q^72 - 2420 * q^74 + 11076 * q^75 - 2560 * q^76 - 32208 * q^77 + 23436 * q^78 - 15136 * q^79 + 1152 * q^80 - 21274 * q^81 - 2608 * q^82 - 19732 * q^83 + 23936 * q^84 + 12440 * q^86 - 31624 * q^87 - 5120 * q^88 + 45940 * q^89 - 25608 * q^90 - 13106 * q^91 - 6944 * q^92 - 37734 * q^93 - 16960 * q^94 - 37458 * q^95 - 1280 * q^96 + 31792 * q^97 + 5216 * q^98 + 141456 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.732051	−	2.73205i	0.183013	−	0.683013i
$2$	0.732051	−	2.73205i	0.183013	−	0.683013i
$3$	−5.46714	−	3.15645i	−0.607460	−	0.350717i	0.164511	−	0.986375i	$-0.447395\pi$
$3$	−5.46714	−	3.15645i	−0.607460	−	0.350717i	−0.771971	+	0.635658i	$0.780729\pi$
$4$	−6.92820	−	4.00000i	−0.433013	−	0.250000i
$5$	−2.29270	−	8.55648i	−0.0917081	−	0.342259i	0.904792	−	0.425854i	$-0.140026\pi$
$5$	−2.29270	−	8.55648i	−0.0917081	−	0.342259i	−0.996500	+	0.0835951i	$0.973360\pi$
$6$	−12.6258	+	12.6258i	−0.350717	+	0.350717i
$7$	−24.9782	+	43.2636i	−0.509760	+	0.882930i	0.490176	+	0.871623i	$0.336932\pi$
$7$	−24.9782	+	43.2636i	−0.509760	+	0.882930i	−0.999936	+	0.0113067i	$0.996401\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$	−20.5736	−	35.6345i	−0.253995	−	0.439932i
$10$	−25.0551			−0.250551
$11$			34.8004i			0.287607i	0.989606	+	0.143803i	$0.0459333\pi$
$11$			34.8004i			0.287607i	−0.989606	+	0.143803i	$0.954067\pi$
$12$	25.2516	+	43.7371i	0.175359	+	0.303730i
$13$	75.5865	+	282.093i	0.447258	+	1.66919i	0.709906	+	0.704297i	$0.248738\pi$
$13$	75.5865	+	282.093i	0.447258	+	1.66919i	−0.262648	+	0.964892i	$0.584596\pi$
$14$	99.9129	+	99.9129i	0.509760	+	0.509760i
$15$	−14.4736	+	54.0163i	−0.0643272	+	0.240072i
$16$	32.0000	+	55.4256i	0.125000	+	0.216506i
$17$	−363.714	−	97.4570i	−1.25853	−	0.337221i	−0.432903	−	0.901441i	$-0.642511\pi$
$17$	−363.714	−	97.4570i	−1.25853	−	0.337221i	−0.825625	+	0.564219i	$0.809177\pi$
$18$	−112.416	+	30.1218i	−0.346963	+	0.0929686i
$19$	37.1161	+	138.519i	0.102815	+	0.383709i	0.998088	−	0.0618076i	$-0.0196865\pi$
$19$	37.1161	+	138.519i	0.102815	+	0.383709i	−0.895273	+	0.445517i	$0.853020\pi$
$20$	−18.3416	+	68.4519i	−0.0458541	+	0.171130i
$21$	273.119	−	157.685i	0.619318	−	0.357563i
$22$	95.0766	+	25.4757i	0.196439	+	0.0526357i
$23$	−392.476	+	392.476i	−0.741920	+	0.741920i	−0.972947	−	0.231027i	$-0.925791\pi$
$23$	−392.476	+	392.476i	−0.741920	+	0.741920i	0.231027	+	0.972947i	$0.425791\pi$
$24$	137.978	−	36.9710i	0.239544	−	0.0641857i
$25$	473.309	−	273.265i	0.757294	−	0.437224i
$26$	826.025			1.22193
$27$			771.104i			1.05776i
$28$	346.109	−	199.826i	0.441465	−	0.254880i
$29$	−925.323	−	925.323i	−1.10027	−	1.10027i	−0.994378	−	0.105887i	$-0.966232\pi$
$29$	−925.323	−	925.323i	−1.10027	−	1.10027i	−0.105887	−	0.994378i	$-0.533768\pi$
$30$	136.980	+	79.0854i	0.152200	+	0.0878726i
$31$	−920.330	−	920.330i	−0.957679	−	0.957679i	0.0414608	−	0.999140i	$-0.486799\pi$
$31$	−920.330	−	920.330i	−0.957679	−	0.957679i	−0.999140	+	0.0414608i	$0.986799\pi$
$32$	174.851	−	46.8513i	0.170753	−	0.0457532i
$33$	109.846	−	190.259i	0.100869	−	0.174710i
$34$	−532.515	+	922.343i	−0.460653	+	0.797875i
$35$	427.452	+	114.535i	0.348940	+	0.0934982i
$36$			329.177i			0.253995i
$37$	−1238.32	+	583.724i	−0.904541	+	0.426387i
$37$	−1238.32	+	583.724i	−0.904541	+	0.426387i
$38$	405.612			0.280895
$39$	477.171	−	1780.83i	0.313722	−	1.17083i
$40$	173.587	+	100.220i	0.108492	+	0.0626378i
$41$	−1112.69	−	642.414i	−0.661924	−	0.382162i	0.131086	−	0.991371i	$-0.458154\pi$
$41$	−1112.69	−	642.414i	−0.661924	−	0.382162i	−0.793010	+	0.609209i	$0.791487\pi$
$42$	−230.867	−	861.609i	−0.130877	−	0.488440i
$43$	1246.22	−	1246.22i	0.673999	−	0.673999i	−0.284637	−	0.958636i	$-0.591873\pi$
$43$	1246.22	−	1246.22i	0.673999	−	0.673999i	0.958636	+	0.284637i	$0.0918729\pi$
$44$	139.202	−	241.105i	0.0719017	−	0.124537i
$45$	−257.737	+	257.737i	−0.127277	+	0.127277i
$46$	784.951	+	1359.58i	0.370960	+	0.642521i
$47$	−621.711			−0.281444			−0.140722	−	0.990049i	$-0.544942\pi$
$47$	−621.711			−0.281444			−0.140722	+	0.990049i	$0.544942\pi$
$48$		−	404.026i		−	0.175359i
$49$	−47.3247	−	81.9687i	−0.0197104	−	0.0341394i
$50$	−400.088	−	1493.15i	−0.160035	−	0.597259i
$51$	1680.86	+	1680.86i	0.646236	+	0.646236i
$52$	604.692	−	2256.74i	0.223629	−	0.834594i
$53$	−1513.75	−	2621.90i	−0.538894	−	0.933392i	−0.998964	−	0.0455091i	$-0.985509\pi$
$53$	−1513.75	−	2621.90i	−0.538894	−	0.933392i	0.460070	−	0.887883i	$-0.347824\pi$
$54$	2106.70	+	564.487i	0.722461	+	0.193583i
$55$	297.769	−	79.7870i	0.0984361	−	0.0263759i
$56$	−292.565	−	1091.87i	−0.0932925	−	0.348173i
$57$	234.310	−	874.459i	0.0721177	−	0.269147i
$58$	−3205.41	+	1850.65i	−0.952858	+	0.550133i
$59$	3933.61	+	1054.01i	1.13002	+	0.302788i	0.774933	−	0.632044i	$-0.217784\pi$
$59$	3933.61	+	1054.01i	1.13002	+	0.302788i	0.355089	+	0.934832i	$0.384450\pi$
$60$	316.341	−	316.341i	0.0878726	−	0.0878726i
$61$	−3076.17	+	824.256i	−0.826704	+	0.221515i	−0.647275	−	0.762256i	$-0.724092\pi$
$61$	−3076.17	+	824.256i	−0.826704	+	0.221515i	−0.179429	+	0.983771i	$0.557425\pi$
$62$	−3188.12	+	1840.66i	−0.829375	+	0.478840i
$63$	2055.57			0.517906
$64$		−	512.000i		−	0.125000i
$65$	2240.42	−	1293.51i	0.530278	−	0.306156i
$66$	−439.384	−	439.384i	−0.100869	−	0.100869i
$67$	216.911	+	125.234i	0.0483207	+	0.0278979i	0.523966	−	0.851739i	$-0.324452\pi$
$67$	216.911	+	125.234i	0.0483207	+	0.0278979i	−0.475645	+	0.879637i	$0.657785\pi$
$68$	2130.06	+	2130.06i	0.460653	+	0.460653i
$69$	3384.55	−	906.887i	0.710891	−	0.190483i
$70$	625.833	−	1083.97i	0.127721	−	0.221219i
$71$	−1951.90	+	3380.79i	−0.387205	+	0.670658i	−0.992072	−	0.125668i	$-0.959893\pi$
$71$	−1951.90	+	3380.79i	−0.387205	+	0.670658i	0.604868	+	0.796326i	$0.293226\pi$
$72$	899.329	+	240.975i	0.173482	+	0.0464843i
$73$			3555.50i			0.667198i	0.942715	+	0.333599i	$0.108263\pi$
$73$			3555.50i			0.667198i	−0.942715	+	0.333599i	$0.891737\pi$
$74$	688.255	+	3810.46i	0.125686	+	0.695847i
$75$	−3450.20			−0.613368
$76$	296.929	−	1108.15i	0.0514073	−	0.191855i
$77$	−1505.59	−	869.254i	−0.253937	−	0.146610i
$78$	−4516.00	−	2607.31i	−0.742274	−	0.428552i
$79$	2275.94	+	8493.93i	0.364676	+	1.36099i	0.867860	+	0.496810i	$0.165495\pi$
$79$	2275.94	+	8493.93i	0.364676	+	1.36099i	−0.503184	+	0.864179i	$0.667838\pi$
$80$	400.882	−	400.882i	0.0626378	−	0.0626378i
$81$	767.495	−	1329.34i	0.116978	−	0.202612i
$82$	−2569.66	+	2569.66i	−0.382162	+	0.382162i
$83$	1400.71	+	2426.10i	0.203326	+	0.352171i	0.949598	−	0.313470i	$-0.101492\pi$
$83$	1400.71	+	2426.10i	0.203326	+	0.352171i	−0.746272	+	0.665641i	$0.768158\pi$
$84$	−2522.97			−0.357563
$85$			3335.56i			0.461669i
$86$	−2492.45	−	4317.05i	−0.336999	−	0.583700i
$87$	2138.13	+	7979.61i	0.282485	+	1.05425i
$88$	−556.807	−	556.807i	−0.0719017	−	0.0719017i
$89$	−177.640	+	662.961i	−0.0224264	+	0.0836966i	−0.976232	−	0.216728i	$-0.930462\pi$
$89$	−177.640	+	662.961i	−0.0224264	+	0.0836966i	0.953806	+	0.300424i	$0.0971283\pi$
$90$	515.474	+	892.827i	0.0636387	+	0.110226i
$91$	−14092.4	−	3776.04i	−1.70177	−	0.455988i
$92$	4289.05	−	1149.25i	0.506741	−	0.135781i
$93$	2126.59	+	7936.55i	0.245877	+	0.917627i
$94$	−455.124	+	1698.55i	−0.0515079	+	0.192230i
$95$	1100.14	−	635.166i	0.121899	−	0.0703785i
$96$	−1103.82	−	295.768i	−0.119772	−	0.0320929i
$97$	999.805	−	999.805i	0.106260	−	0.106260i	−0.651978	−	0.758238i	$-0.726060\pi$
$97$	999.805	−	999.805i	0.106260	−	0.106260i	0.758238	+	0.651978i	$0.226060\pi$
$98$	−258.587	+	69.2881i	−0.0269249	+	0.00721450i
$99$	1240.10	−	715.970i	0.126528	−	0.0730507i
$100$	−4372.24			−0.437224
$101$		−	10937.5i		−	1.07220i	−0.844154	−	0.536101i	$-0.819896\pi$
$101$		−	10937.5i		−	1.07220i	0.844154	−	0.536101i	$-0.180104\pi$
$102$	5822.67	−	3361.72i	0.559657	−	0.323118i
$103$	11643.2	+	11643.2i	1.09748	+	1.09748i	0.994704	+	0.102778i	$0.0327730\pi$
$103$	11643.2	+	11643.2i	1.09748	+	1.09748i	0.102778	+	0.994704i	$0.467227\pi$
$104$	−5722.87	−	3304.10i	−0.529112	−	0.305483i
$105$	−1975.41	−	1975.41i	−0.179176	−	0.179176i
$106$	−8271.30	+	2216.29i	−0.736143	+	0.197249i
$107$	1367.68	−	2368.89i	0.119458	−	0.206908i	−0.800095	−	0.599874i	$-0.795218\pi$
$107$	1367.68	−	2368.89i	0.119458	−	0.206908i	0.919553	+	0.392966i	$0.128551\pi$
$108$	3084.42	−	5342.37i	0.264439	−	0.458022i
$109$	−17982.4	−	4818.37i	−1.51354	−	0.405553i	−0.595933	−	0.803034i	$-0.703218\pi$
$109$	−17982.4	−	4818.37i	−1.51354	−	0.405553i	−0.917610	+	0.397481i	$0.869884\pi$
$110$		−	871.929i		−	0.0720603i
$111$	8612.55	+	717.385i	0.699014	+	0.0582246i
$112$	−3197.21			−0.254880
$113$	3948.12	−	14734.6i	0.309196	−	1.15394i	−0.620077	−	0.784541i	$-0.712899\pi$
$113$	3948.12	−	14734.6i	0.309196	−	1.15394i	0.929273	−	0.369394i	$-0.120435\pi$
$114$	−2217.54	−	1280.30i	−0.170632	−	0.0985146i
$115$	4258.04	+	2458.38i	0.321969	+	0.185889i
$116$	2709.53	+	10112.1i	0.201363	+	0.751495i
$117$	8497.15	−	8497.15i	0.620728	−	0.620728i
$118$	5759.20	−	9975.23i	0.413617	−	0.716405i
$119$	13301.3	−	13301.3i	0.939290	−	0.939290i
$120$	−632.683	−	1095.84i	−0.0439363	−	0.0760999i
$121$	13429.9			0.917282
$122$			9007.64i			0.605190i
$123$	4055.50	+	7024.34i	0.268062	+	0.464296i
$124$	2694.91	+	10057.6i	0.175267	+	0.654107i
$125$	−7338.21	−	7338.21i	−0.469645	−	0.469645i
$126$	1504.78	−	5615.92i	0.0947833	−	0.353736i
$127$	−3823.16	−	6621.90i	−0.237036	−	0.410559i	0.722826	−	0.691030i	$-0.242843\pi$
$127$	−3823.16	−	6621.90i	−0.237036	−	0.410559i	−0.959862	+	0.280471i	$0.909509\pi$
$128$	−1398.81	−	374.810i	−0.0853766	−	0.0228766i
$129$	−10746.9	+	2879.63i	−0.645810	+	0.173044i
$130$	−1893.83	−	7067.87i	−0.112061	−	0.418217i
$131$	2501.82	−	9336.92i	0.145785	−	0.544078i	−0.853934	−	0.520381i	$-0.825790\pi$
$131$	2501.82	−	9336.92i	0.145785	−	0.544078i	0.999719	−	0.0236966i	$-0.00754358\pi$
$132$	−1522.07	+	878.768i	−0.0873549	+	0.0504343i
$133$	−6919.93	−	1854.19i	−0.391199	−	0.104822i
$134$	500.935	−	500.935i	0.0278979	−	0.0278979i
$135$	6597.94	−	1767.91i	0.362027	−	0.0970048i
$136$	7378.74	−	4260.12i	0.398937	−	0.230327i
$137$	22667.5			1.20771			0.603856	−	0.797094i	$-0.293630\pi$
$137$	22667.5			1.20771			0.603856	+	0.797094i	$0.293630\pi$
$138$		−	9910.65i		−	0.520408i
$139$	−22523.2	+	13003.7i	−1.16573	+	0.673037i	−0.952672	−	0.304002i	$-0.901677\pi$
$139$	−22523.2	+	13003.7i	−1.16573	+	0.673037i	−0.213063	+	0.977039i	$0.568344\pi$
$140$	−2503.33	−	2503.33i	−0.127721	−	0.127721i
$141$	3398.98	+	1962.40i	0.170966	+	0.0987074i
$142$	7807.59	+	7807.59i	0.387205	+	0.387205i
$143$	−9816.95	+	2630.44i	−0.480070	+	0.128634i
$144$	1316.71	−	2280.61i	0.0634987	−	0.109983i
$145$	−5796.02	+	10039.0i	−0.275673	+	0.477479i
$146$	9713.79	+	2602.80i	0.455704	+	0.122106i
$147$			597.513i			0.0276511i
$148$	10914.2	+	909.103i	0.498274	+	0.0415040i
$149$	4492.31			0.202347			0.101174	−	0.994869i	$-0.467740\pi$
$149$	4492.31			0.202347			0.101174	+	0.994869i	$0.467740\pi$
$150$	−2525.72	+	9426.11i	−0.112254	+	0.418938i
$151$	−32582.1	−	18811.3i	−1.42898	−	0.825020i	−0.431937	−	0.901904i	$-0.642170\pi$
$151$	−32582.1	−	18811.3i	−1.42898	−	0.825020i	−0.997040	+	0.0768840i	$0.975503\pi$
$152$	−2810.16	−	1622.45i	−0.121631	−	0.0702237i
$153$	4010.08	+	14965.8i	0.171305	+	0.639319i
$154$	−3477.01	+	3477.01i	−0.146610	+	0.146610i
$155$	−5764.74	+	9984.83i	−0.239948	+	0.415602i
$156$	−10429.2	+	10429.2i	−0.428552	+	0.428552i
$157$	−19242.0	−	33328.1i	−0.780639	−	1.35211i	−0.931570	−	0.363562i	$-0.881561\pi$
$157$	−19242.0	−	33328.1i	−0.780639	−	1.35211i	0.150931	−	0.988544i	$-0.451773\pi$
$158$	24872.0			0.996313
$159$			19112.4i			0.755998i
$160$	−801.764	−	1388.70i	−0.0313189	−	0.0542459i
$161$	−7176.55	−	26783.2i	−0.276862	−	1.03326i
$162$	−3069.98	−	3069.98i	−0.116978	−	0.116978i
$163$	2512.76	−	9377.76i	0.0945750	−	0.352959i	−0.902380	−	0.430942i	$-0.858181\pi$
$163$	2512.76	−	9377.76i	0.0945750	−	0.352959i	0.996955	+	0.0779832i	$0.0248480\pi$
$164$	5139.32	+	8901.56i	0.191081	+	0.330962i
$165$	−1879.79	−	503.688i	−0.0690465	−	0.0185010i
$166$	7653.63	−	2050.78i	0.277748	−	0.0744224i
$167$	806.055	+	3008.24i	0.0289023	+	0.107865i	0.978870	−	0.204483i	$-0.0655513\pi$
$167$	806.055	+	3008.24i	0.0289023	+	0.107865i	−0.949968	+	0.312348i	$0.898885\pi$
$168$	−1846.94	+	6892.87i	−0.0654386	+	0.244220i
$169$	−49128.5	+	28364.3i	−1.72013	+	0.993115i
$170$	9112.91	+	2441.80i	0.315326	+	0.0844912i
$171$	4172.45	−	4172.45i	0.142692	−	0.142692i
$172$	−13619.0	+	3649.20i	−0.460350	+	0.123350i
$173$	−10681.2	+	6166.81i	−0.356886	+	0.206048i	−0.667714	−	0.744418i	$-0.732727\pi$
$173$	−10681.2	+	6166.81i	−0.356886	+	0.206048i	0.310828	+	0.950466i	$0.399394\pi$
$174$	23365.9			0.771764
$175$			27302.7i			0.891517i
$176$	−1928.84	+	1113.61i	−0.0622687	+	0.0359509i
$177$	−18178.7	−	18178.7i	−0.580250	−	0.580250i
$178$	1681.20	+	970.642i	0.0530615	+	0.0306351i
$179$	28897.6	+	28897.6i	0.901894	+	0.901894i	0.995600	−	0.0937057i	$-0.0298713\pi$
$179$	28897.6	+	28897.6i	0.901894	+	0.901894i	−0.0937057	+	0.995600i	$0.529871\pi$
$180$	2816.60	−	754.706i	0.0869321	−	0.0232934i
$181$	18824.7	−	32605.4i	0.574608	−	0.995250i	−0.421476	−	0.906839i	$-0.638488\pi$
$181$	18824.7	−	32605.4i	0.574608	−	0.995250i	0.996084	−	0.0884107i	$-0.0281788\pi$
$182$	−20632.7	+	35736.8i	−0.622891	+	1.07888i
$183$	19419.6	+	5203.46i	0.579879	+	0.155378i
$184$		−	12559.2i		−	0.370960i
$185$	7833.72	+	9257.32i	0.228889	+	0.270484i
$186$	23239.8			0.671749
$187$	3391.55	−	12657.4i	0.0969872	−	0.361961i
$188$	4307.34	+	2486.84i	0.121869	+	0.0703611i
$189$	−33360.7	−	19260.8i	−0.933925	−	0.539202i
$190$	−929.948	−	3470.61i	−0.0257603	−	0.0961389i
$191$	−25989.8	+	25989.8i	−0.712421	+	0.712421i	−0.967041	−	0.254620i	$-0.918050\pi$
$191$	−25989.8	+	25989.8i	−0.712421	+	0.712421i	0.254620	+	0.967041i	$0.418050\pi$
$192$	−1616.10	+	2799.18i	−0.0438396	+	0.0759325i
$193$	−27268.2	+	27268.2i	−0.732053	+	0.732053i	−0.971026	−	0.238973i	$-0.923189\pi$
$193$	−27268.2	+	27268.2i	−0.732053	+	0.732053i	0.238973	+	0.971026i	$0.423189\pi$
$194$	−1999.61	−	3463.42i	−0.0531302	−	0.0920243i
$195$	−16331.6			−0.429497
$196$			757.194i			0.0197104i
$197$	29401.0	+	50924.0i	0.757582	+	1.31217i	0.944080	+	0.329716i	$0.106953\pi$
$197$	29401.0	+	50924.0i	0.757582	+	1.31217i	−0.186498	+	0.982455i	$0.559714\pi$
$198$	−1048.25	−	3912.13i	−0.0267384	−	0.0997891i
$199$	43333.1	+	43333.1i	1.09424	+	1.09424i	0.995070	+	0.0991725i	$0.0316196\pi$
$199$	43333.1	+	43333.1i	1.09424	+	1.09424i	0.0991725	+	0.995070i	$0.468380\pi$
$200$	−3200.70	+	11945.2i	−0.0800176	+	0.298630i
$201$	−790.590	−	1369.34i	−0.0195686	−	0.0338938i
$202$	−29881.9	−	8006.83i	−0.732328	−	0.196227i
$203$	63145.7	−	16919.8i	1.53233	−	0.410586i
$204$	−4921.90	−	18368.8i	−0.118269	−	0.441387i
$205$	−2945.73	+	10993.6i	−0.0700947	+	0.261597i
$206$	40333.2	−	23286.4i	0.950447	−	0.548741i
$207$	22060.3	+	5911.04i	0.514838	+	0.137950i
$208$	−13216.4	+	13216.4i	−0.305483	+	0.305483i
$209$	−4820.53	+	1291.66i	−0.110357	+	0.0295702i
$210$	−6843.03	+	3950.83i	−0.155171	+	0.0895879i
$211$	−20963.7			−0.470873			−0.235437	−	0.971890i	$-0.575652\pi$
$211$	−20963.7			−0.470873			−0.235437	+	0.971890i	$0.575652\pi$
$212$			24220.1i			0.538894i
$213$	21342.6	−	12322.2i	0.470423	−	0.271599i
$214$	−5470.71	−	5470.71i	−0.119458	−	0.119458i
$215$	−13520.5	−	7806.07i	−0.292494	−	0.168871i
$216$	−12337.7	−	12337.7i	−0.264439	−	0.264439i
$217$	62805.0	−	16828.5i	1.33375	−	0.357377i
$218$	−26328.1	+	45601.6i	−0.553995	+	0.959548i
$219$	11222.8	−	19438.4i	0.233998	−	0.405296i
$220$	−2382.15	−	638.296i	−0.0492181	−	0.0131879i
$221$		−	109968.i		−	2.25154i
$222$	8264.76	−	23004.8i	0.167697	−	0.466779i
$223$	35862.5			0.721159			0.360580	−	0.932728i	$-0.382579\pi$
$223$	35862.5			0.721159			0.360580	+	0.932728i	$0.382579\pi$
$224$	−2340.52	+	8734.95i	−0.0466463	+	0.174086i
$225$	−19475.3	−	11244.1i	−0.384698	−	0.222105i
$226$	−37365.4	−	21572.9i	−0.731566	−	0.422370i
$227$	−3567.67	−	13314.7i	−0.0692362	−	0.258393i	0.922628	−	0.385690i	$-0.126037\pi$
$227$	−3567.67	−	13314.7i	−0.0692362	−	0.258393i	−0.991865	+	0.127297i	$0.959370\pi$
$228$	−5121.18	+	5121.18i	−0.0985146	+	0.0985146i
$229$	−30742.8	+	53248.1i	−0.586236	+	1.01539i	0.408484	+	0.912765i	$0.366057\pi$
$229$	−30742.8	+	53248.1i	−0.586236	+	1.01539i	−0.994720	+	0.102625i	$0.967276\pi$
$230$	9833.52	−	9833.52i	0.185889	−	0.185889i
$231$	5487.52	+	9504.66i	0.102838	+	0.178120i
$232$	29610.3			0.550133
$233$			38214.1i			0.703901i	0.936019	+	0.351951i	$0.114481\pi$
$233$			38214.1i			0.703901i	−0.936019	+	0.351951i	$0.885519\pi$
$234$	−16994.3	−	29435.0i	−0.310364	−	0.537567i
$235$	1425.40	+	5319.66i	0.0258107	+	0.0963270i
$236$	−23036.8	−	23036.8i	−0.413617	−	0.413617i
$237$	14367.8	−	53621.4i	0.255796	−	0.954644i
$238$	−26602.6	−	46077.0i	−0.469645	−	0.813449i
$239$	−99900.3	−	26768.2i	−1.74892	−	0.468623i	−0.764528	−	0.644590i	$-0.777028\pi$
$239$	−99900.3	−	26768.2i	−1.74892	−	0.468623i	−0.984396	+	0.175967i	$0.943695\pi$
$240$	−3457.04	+	926.312i	−0.0600181	+	0.0160818i
$241$	−5241.10	−	19560.1i	−0.0902378	−	0.336772i	0.906017	−	0.423242i	$-0.139108\pi$
$241$	−5241.10	−	19560.1i	−0.0902378	−	0.336772i	−0.996254	+	0.0864700i	$0.972441\pi$
$242$	9831.39	−	36691.2i	0.167874	−	0.626515i
$243$	45699.5	−	26384.6i	0.773924	−	0.446825i
$244$	24609.3	+	6594.05i	0.413352	+	0.110757i
$245$	−592.862	+	592.862i	−0.00987692	+	0.00987692i
$246$	22159.7	−	5937.67i	0.366179	−	0.0981174i
$247$	−36269.8	+	20940.4i	−0.594499	+	0.343234i
$248$	29450.6			0.478840
$249$		−	17685.1i		−	0.285239i
$250$	−25420.3	+	14676.4i	−0.406725	+	0.234823i
$251$	−10322.6	−	10322.6i	−0.163848	−	0.163848i	0.620421	−	0.784269i	$-0.286962\pi$
$251$	−10322.6	−	10322.6i	−0.163848	−	0.163848i	−0.784269	+	0.620421i	$0.786962\pi$
$252$	−14241.4	−	8222.27i	−0.224260	−	0.129476i
$253$	−13658.3	−	13658.3i	−0.213381	−	0.213381i
$254$	−20890.1	+	5597.49i	−0.323797	+	0.0867613i
$255$	10528.5	−	18236.0i	0.161915	−	0.280445i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	23342.9	+	6254.71i	0.353418	+	0.0946980i	0.431160	−	0.902275i	$-0.358104\pi$
$257$	23342.9	+	6254.71i	0.353418	+	0.0946980i	−0.0777422	+	0.996973i	$0.524771\pi$
$258$			31469.2i			0.472766i
$259$	5676.94	−	68154.4i	0.0846282	−	1.01600i
$260$	−20696.2			−0.306156
$261$	−13936.2	+	52010.6i	−0.204580	+	0.763504i
$262$	−23677.5	−	13670.2i	−0.344932	−	0.199146i
$263$	−4483.18	−	2588.36i	−0.0648148	−	0.0374209i	0.467242	−	0.884129i	$-0.345248\pi$
$263$	−4483.18	−	2588.36i	−0.0648148	−	0.0374209i	−0.532057	+	0.846708i	$0.678581\pi$
$264$	1286.61	+	4801.68i	0.0184603	+	0.0688946i
$265$	−18963.6	+	18963.6i	−0.270041	+	0.270041i
$266$	−10131.5	+	17548.2i	−0.143189	+	0.248010i
$267$	3063.79	−	3063.79i	0.0429770	−	0.0429770i
$268$	−1001.87	−	1735.29i	−0.0139490	−	0.0241603i
$269$	123122.			1.70149			0.850747	−	0.525575i	$-0.176150\pi$
$269$	123122.			1.70149			0.850747	+	0.525575i	$0.176150\pi$
$270$		−	19320.1i		−	0.265022i
$271$	25819.3	+	44720.3i	0.351565	+	0.608929i	0.986524	−	0.163617i	$-0.0523162\pi$
$271$	25819.3	+	44720.3i	0.351565	+	0.608929i	−0.634959	+	0.772546i	$0.718983\pi$
$272$	−6237.25	−	23277.7i	−0.0843054	−	0.314632i
$273$	65126.0	+	65126.0i	0.873835	+	0.873835i
$274$	16593.8	−	61928.9i	0.221027	−	0.824882i
$275$	9509.74	+	16471.4i	0.125749	+	0.217803i
$276$	−27076.4	−	7255.10i	−0.355445	−	0.0952413i
$277$	−5933.89	+	1589.98i	−0.0773357	+	0.0207220i	−0.297279	−	0.954791i	$-0.596079\pi$
$277$	−5933.89	+	1589.98i	−0.0773357	+	0.0207220i	0.219944	+	0.975513i	$0.429413\pi$
$278$	19038.8	+	71053.8i	0.246349	+	0.919386i
$279$	−13861.0	+	51730.0i	−0.178068	+	0.664560i
$280$	−8671.79	+	5006.66i	−0.110610	+	0.0638605i
$281$	930.468	+	249.318i	0.0117839	+	0.00315749i	0.264706	−	0.964329i	$-0.414725\pi$
$281$	930.468	+	249.318i	0.0117839	+	0.00315749i	−0.252922	+	0.967487i	$0.581392\pi$
$282$	7849.61	−	7849.61i	0.0987074	−	0.0987074i
$283$	23063.8	−	6179.93i	0.287977	−	0.0771632i	−0.111939	−	0.993715i	$-0.535706\pi$
$283$	23063.8	−	6179.93i	0.287977	−	0.0771632i	0.399916	+	0.916552i	$0.369039\pi$
$284$	27046.3	−	15615.2i	0.335329	−	0.193602i
$285$	−8019.49			−0.0987318
$286$			28746.0i			0.351436i
$287$	55586.3	−	32092.8i	0.674845	−	0.389622i
$288$	−5266.84	−	5266.84i	−0.0634987	−	0.0634987i
$289$	50459.0	+	29132.5i	0.604148	+	0.348805i
$290$	23184.1	+	23184.1i	0.275673	+	0.275673i
$291$	−8621.91	+	2310.23i	−0.101816	+	0.0272816i
$292$	14222.0	−	24633.2i	0.166799	−	0.288905i
$293$	−58312.1	+	101000.i	−0.679241	+	1.17648i	0.295969	+	0.955197i	$0.404357\pi$
$293$	−58312.1	+	101000.i	−0.679241	+	1.17648i	−0.975210	+	0.221282i	$0.928976\pi$
$294$	1632.43	+	437.410i	0.0188860	+	0.00506050i
$295$		−	36074.4i		−	0.414529i
$296$	10473.5	−	29152.6i	0.119538	−	0.332732i
$297$	−26834.8			−0.304218
$298$	3288.60	−	12273.2i	0.0370321	−	0.138206i
$299$	−140380.	−	81048.7i	−1.57023	−	0.906575i
$300$	23903.7	+	13800.8i	0.265596	+	0.153342i
$301$	22787.6	+	85044.6i	0.251516	+	0.938672i
$302$	−75245.1	+	75245.1i	−0.825020	+	0.825020i
$303$	−34523.8	+	59797.1i	−0.376040	+	0.651320i
$304$	−6489.79	+	6489.79i	−0.0702237	+	0.0702237i
$305$	14105.5	+	24431.4i	0.151631	+	0.262633i
$306$	43823.0			0.468014
$307$			39278.9i			0.416756i	0.978048	+	0.208378i	$0.0668185\pi$
$307$			39278.9i			0.416756i	−0.978048	+	0.208378i	$0.933182\pi$
$308$	6954.03	+	12044.7i	0.0733052	+	0.126968i
$309$	−26903.7	−	100406.i	−0.281771	−	1.05158i
$310$	23059.0	+	23059.0i	0.239948	+	0.239948i
$311$	36651.9	−	136787.i	0.378944	−	1.41424i	−0.468551	−	0.883436i	$-0.655224\pi$
$311$	36651.9	−	136787.i	0.378944	−	1.41424i	0.847495	−	0.530803i	$-0.178110\pi$
$312$	20858.5	+	36128.0i	0.214276	+	0.371137i
$313$	−44808.0	−	12006.3i	−0.457369	−	0.122552i	0.0227764	−	0.999741i	$-0.492749\pi$
$313$	−44808.0	−	12006.3i	−0.457369	−	0.122552i	−0.480145	+	0.877189i	$0.659416\pi$
$314$	−105140.	+	28172.2i	−1.06637	+	0.285734i
$315$	−4712.81	−	17588.4i	−0.0474961	−	0.177258i
$316$	18207.5	−	67951.5i	0.182338	−	0.680494i
$317$	−65857.3	+	38022.7i	−0.655368	+	0.378377i	−0.790510	−	0.612449i	$-0.790184\pi$
$317$	−65857.3	+	38022.7i	−0.655368	+	0.378377i	0.135142	+	0.990826i	$0.456851\pi$
$318$	52216.0	+	13991.2i	0.516356	+	0.138357i
$319$	32201.6	−	32201.6i	0.316444	−	0.316444i
$320$	−4380.92	+	1173.86i	−0.0427824	+	0.0114635i
$321$	−14954.6	+	8634.03i	−0.145132	+	0.0837922i
$322$	−78426.8			−0.756402
$323$		−	53998.6i		−	0.517580i
$324$	−10634.7	+	6139.96i	−0.101306	+	0.0584891i
$325$	112862.	+	112862.i	1.06852	+	1.06852i
$326$	−23781.0	−	13730.0i	−0.223767	−	0.129192i
$327$	83103.4	+	83103.4i	0.777183	+	0.777183i
$328$	28081.7	−	7524.48i	0.261022	−	0.0699405i
$329$	15529.2	−	26897.4i	0.143469	−	0.248496i
$330$	−2752.20	+	4766.96i	−0.0252728	+	0.0437737i
$331$	−50456.9	−	13519.9i	−0.460537	−	0.123401i	0.0210885	−	0.999778i	$-0.493287\pi$
$331$	−50456.9	−	13519.9i	−0.460537	−	0.123401i	−0.481626	+	0.876377i	$0.659953\pi$
$332$		−	22411.4i		−	0.203326i
$333$	46277.3	+	32117.5i	0.417330	+	0.289636i
$334$	8808.74			0.0789625
$335$	574.248	−	2143.12i	0.00511693	−	0.0190967i
$336$	17479.6	+	10091.9i	0.154829	+	0.0893908i
$337$	73434.6	+	42397.5i	0.646608	+	0.373319i	0.787155	−	0.616755i	$-0.211553\pi$
$337$	73434.6	+	42397.5i	0.646608	+	0.373319i	−0.140548	+	0.990074i	$0.544886\pi$
$338$	41528.3	+	154986.i	0.363505	+	1.35662i
$339$	−68094.0	+	68094.0i	−0.592529	+	0.592529i
$340$	13342.2	−	23109.4i	0.115417	−	0.199908i
$341$	32027.9	−	32027.9i	0.275435	−	0.275435i
$342$	−8344.90	−	14453.8i	−0.0713458	−	0.123575i
$343$	−115217.			−0.979330
$344$			39879.2i			0.336999i
$345$	−15519.5	−	26880.6i	−0.130389	−	0.225840i
$346$	9028.84	+	33696.1i	0.0754188	+	0.281467i
$347$	−124696.	−	124696.i	−1.03560	−	1.03560i	−0.999342	−	0.0362599i	$-0.988456\pi$
$347$	−124696.	−	124696.i	−1.03560	−	1.03560i	−0.0362599	−	0.999342i	$-0.511544\pi$
$348$	17105.0	−	63836.9i	0.141243	−	0.527125i
$349$	43272.5	+	74950.2i	0.355272	+	0.615350i	0.987165	−	0.159707i	$-0.0510548\pi$
$349$	43272.5	+	74950.2i	0.355272	+	0.615350i	−0.631892	+	0.775056i	$0.717721\pi$
$350$	74592.4	+	19987.0i	0.608918	+	0.163159i
$351$	−217523.	+	58285.1i	−1.76559	+	0.473089i
$352$	1630.44	+	6084.90i	0.0131589	+	0.0491098i
$353$	−39384.0	+	146983.i	−0.316061	+	1.17956i	0.606937	+	0.794750i	$0.292398\pi$
$353$	−39384.0	+	146983.i	−0.316061	+	1.17956i	−0.922998	+	0.384805i	$0.874269\pi$
$354$	−62972.7	+	36357.3i	−0.502511	+	0.290125i
$355$	33402.8	+	8950.24i	0.265049	+	0.0710196i
$356$	3882.57	−	3882.57i	0.0306351	−	0.0306351i
$357$	−114705.	+	30735.1i	−0.900006	+	0.241156i
$358$	100104.	−	57795.2i	0.781063	−	0.450947i
$359$	−108376.			−0.840901			−0.420451	−	0.907315i	$-0.638128\pi$
$359$	−108376.			−0.840901			−0.420451	+	0.907315i	$0.638128\pi$
$360$		−	8247.58i		−	0.0636387i
$361$	95051.4	−	54877.9i	0.729363	−	0.421098i
$362$	−75298.9	−	75298.9i	−0.574608	−	0.574608i
$363$	−73423.3	−	42391.0i	−0.557212	−	0.321707i
$364$	82530.6	+	82530.6i	0.622891	+	0.622891i
$365$	30422.5	−	8151.69i	0.228355	−	0.0611874i
$366$	28432.2	−	49246.0i	0.212250	−	0.367628i
$367$	−37513.7	+	64975.7i	−0.278521	+	0.482413i	−0.971017	−	0.239009i	$-0.923178\pi$
$367$	−37513.7	+	64975.7i	−0.278521	+	0.482413i	0.692496	+	0.721421i	$0.256511\pi$
$368$	−34312.4	−	9193.98i	−0.253370	−	0.0678904i
$369$			52867.1i			0.388269i
$370$	31026.2	−	14625.3i	0.226634	−	0.106832i
$371$	151244.			1.09883
$372$	17012.7	−	63492.4i	0.122939	−	0.458813i
$373$	−37457.5	−	21626.1i	−0.269229	−	0.155439i	0.359308	−	0.933219i	$-0.383013\pi$
$373$	−37457.5	−	21626.1i	−0.269229	−	0.155439i	−0.628537	+	0.777780i	$0.716346\pi$
$374$	−32097.9	−	18531.8i	−0.229474	−	0.132487i
$375$	16956.3	+	63281.7i	0.120578	+	0.450003i
$376$	9947.37	−	9947.37i	0.0703611	−	0.0703611i
$377$	191085.	−	330969.i	1.34445	−	2.32865i
$378$	−77043.3	+	77043.3i	−0.539202	+	0.539202i
$379$	−105021.	−	181902.i	−0.731136	−	1.26636i	−0.956398	−	0.292066i	$-0.905657\pi$
$379$	−105021.	−	181902.i	−0.731136	−	1.26636i	0.225262	−	0.974298i	$-0.427676\pi$
$380$	−10162.7			−0.0703785
$381$			48270.5i			0.332531i
$382$	51979.7	+	90031.4i	0.356211	+	0.616975i
$383$	12178.7	+	45451.4i	0.0830238	+	0.309849i	0.994933	−	0.100544i	$-0.0320583\pi$
$383$	12178.7	+	45451.4i	0.0830238	+	0.309849i	−0.911909	+	0.410393i	$0.865392\pi$
$384$	6464.42	+	6464.42i	0.0438396	+	0.0438396i
$385$	−3985.88	+	14875.5i	−0.0268907	+	0.100358i
$386$	54536.5	+	94460.0i	0.366027	+	0.633977i
$387$	−70047.9	−	18769.3i	−0.467706	−	0.125321i
$388$	−10926.1	+	2927.63i	−0.0725772	+	0.0194470i
$389$	−51479.7	−	192125.i	−0.340202	−	1.26965i	−0.898118	−	0.439754i	$-0.855066\pi$
$389$	−51479.7	−	192125.i	−0.340202	−	1.26965i	0.557917	−	0.829897i	$-0.311601\pi$
$390$	−11955.6	+	44618.8i	−0.0786034	+	0.293352i
$391$	180999.	−	104500.i	1.18392	−	0.683535i
$392$	2068.69	+	554.305i	0.0134624	+	0.00360725i
$393$	−43149.4	+	43149.4i	−0.279376	+	0.279376i
$394$	160650.	−	43046.1i	1.03488	−	0.277294i
$395$	67460.1	−	38948.1i	0.432367	−	0.249627i
$396$	−11455.5			−0.0730507
$397$		−	70764.8i		−	0.448990i	−0.974475	−	0.224495i	$-0.927927\pi$
$397$		−	70764.8i		−	0.448990i	0.974475	−	0.224495i	$-0.0720732\pi$
$398$	150110.	−	86666.2i	0.947642	−	0.547121i
$399$	31979.5	+	31979.5i	0.200875	+	0.200875i
$400$	30291.8	+	17489.0i	0.189324	+	0.109306i
$401$	−207048.	−	207048.i	−1.28760	−	1.28760i	−0.936240	−	0.351362i	$-0.885719\pi$
$401$	−207048.	−	207048.i	−1.28760	−	1.28760i	−0.351362	−	0.936240i	$-0.614281\pi$
$402$	−4319.86	+	1157.50i	−0.0267312	+	0.00716260i
$403$	190054.	−	329183.i	1.17022	−	2.02688i
$404$	−43750.2	+	75777.5i	−0.268051	+	0.464277i
$405$	−13134.1	−	3519.27i	−0.0800738	−	0.0214557i
$406$		−	184904.i		−	1.12174i
$407$	−20313.9	−	43093.9i	−0.122632	−	0.260152i
$408$	−53787.5			−0.323118
$409$	−32779.9	+	122336.i	−0.195957	+	0.731322i	0.796060	+	0.605218i	$0.206914\pi$
$409$	−32779.9	+	122336.i	−0.195957	+	0.731322i	−0.992017	+	0.126104i	$0.959753\pi$
$410$	27878.7	+	16095.8i	0.165846	+	0.0957512i
$411$	−123927.	−	71549.0i	−0.733636	−	0.423565i
$412$	−34093.6	−	127239.i	−0.200853	−	0.749594i
$413$	−143855.	+	143855.i	−0.843381	+	0.843381i
$414$	32298.5	−	55942.7i	0.188444	−	0.326394i
$415$	17547.5	−	17547.5i	0.101887	−	0.101887i
$416$	26432.8	+	45783.0i	0.152741	+	0.264556i
$417$	164183.			0.944183
$418$			14115.5i			0.0807873i
$419$	55813.0	+	96670.9i	0.317912	+	0.550640i	0.980052	−	0.198740i	$-0.0636850\pi$
$419$	55813.0	+	96670.9i	0.317912	+	0.550640i	−0.662140	+	0.749380i	$0.730352\pi$
$420$	5784.41	+	21587.7i	0.0327914	+	0.122379i
$421$	208995.	+	208995.i	1.17916	+	1.17916i	0.979960	+	0.199196i	$0.0638329\pi$
$421$	208995.	+	208995.i	1.17916	+	1.17916i	0.199196	+	0.979960i	$0.436167\pi$
$422$	−15346.5	+	57274.0i	−0.0861757	+	0.321612i
$423$	12790.8	+	22154.3i	0.0714854	+	0.123816i
$424$	66170.4	+	17730.3i	0.368071	+	0.0986244i
$425$	−198781.	+	53263.2i	−1.10052	+	0.294883i
$426$	−18040.9	−	67329.5i	−0.0994120	−	0.371011i
$427$	41176.9	−	153674.i	0.225839	−	0.842841i
$428$	−18951.1	+	10941.4i	−0.103454	+	0.0597292i
$429$	61973.5	+	16605.8i	0.336738	+	0.0902286i
$430$	−31224.3	+	31224.3i	−0.168871	+	0.168871i
$431$	−330292.	+	88501.4i	−1.77805	+	0.476426i	−0.990225	−	0.139479i	$-0.955457\pi$
$431$	−330292.	+	88501.4i	−1.77805	+	0.476426i	−0.787821	+	0.615905i	$0.788791\pi$
$432$	−42738.9	+	24675.3i	−0.229011	+	0.132219i
$433$	246660.			1.31560			0.657798	−	0.753195i	$-0.271488\pi$
$433$	246660.			1.31560			0.657798	+	0.753195i	$0.271488\pi$
$434$		−	183906.i		−	0.976373i
$435$	63375.3	−	36589.7i	0.334920	−	0.193366i
$436$	105312.	+	105312.i	0.553995	+	0.553995i
$437$	−68932.5	−	39798.2i	−0.360962	−	0.208401i
$438$	−44891.0	−	44891.0i	−0.233998	−	0.233998i
$439$	182191.	−	48818.0i	0.945362	−	0.253309i	0.246969	−	0.969023i	$-0.420565\pi$
$439$	182191.	−	48818.0i	0.945362	−	0.253309i	0.698393	+	0.715714i	$0.253899\pi$
$440$	−3487.72	+	6040.90i	−0.0180151	+	0.0312030i
$441$	−1947.28	+	3372.78i	−0.0100127	+	0.0173425i
$442$	−300437.	−	80501.9i	−1.53783	−	0.412061i
$443$			171934.i			0.876099i	0.898951	+	0.438049i	$0.144331\pi$
$443$			171934.i			0.876099i	−0.898951	+	0.438049i	$0.855669\pi$
$444$	−56799.9	−	39420.4i	−0.288126	−	0.199965i
$445$	6079.88			0.0307026
$446$	26253.2	−	97978.3i	0.131981	−	0.492561i
$447$	−24560.1	−	14179.8i	−0.122918	−	0.0709666i
$448$	22151.0	+	12788.9i	0.110366	+	0.0637200i
$449$	75141.8	+	280433.i	0.372726	+	1.39103i	0.856640	+	0.515915i	$0.172548\pi$
$449$	75141.8	+	280433.i	0.372726	+	1.39103i	−0.483914	+	0.875115i	$0.660785\pi$
$450$	−44976.3	+	44976.3i	−0.222105	+	0.222105i
$451$	22356.3	−	38722.3i	0.109912	−	0.190374i
$452$	−86291.8	+	86291.8i	−0.422370	+	0.422370i
$453$	118754.	+	205688.i	0.578697	+	1.00233i
$454$	−38988.2			−0.189157
$455$			129238.i			0.624265i
$456$	10242.4	+	17740.3i	0.0492573	+	0.0853162i
$457$	−20509.6	−	76542.7i	−0.0982028	−	0.366498i	0.899283	−	0.437368i	$-0.144089\pi$
$457$	−20509.6	−	76542.7i	−0.0982028	−	0.366498i	−0.997486	+	0.0708699i	$0.977422\pi$
$458$	122971.	+	122971.i	0.586236	+	0.586236i
$459$	75149.5	−	280462.i	0.356698	−	1.33122i
$460$	−19667.0	−	34064.3i	−0.0929444	−	0.160984i
$461$	−277474.	−	74349.1i	−1.30563	−	0.349843i	−0.462056	−	0.886851i	$-0.652888\pi$
$461$	−277474.	−	74349.1i	−1.30563	−	0.349843i	−0.843577	+	0.537007i	$0.819555\pi$
$462$	29984.4	−	8034.29i	0.140479	−	0.0376412i
$463$	53463.4	+	199528.i	0.249399	+	0.930770i	0.971121	+	0.238587i	$0.0766843\pi$
$463$	53463.4	+	199528.i	0.249399	+	0.930770i	−0.721722	+	0.692183i	$0.756649\pi$
$464$	21676.3	−	80896.9i	0.100681	−	0.375748i
$465$	63033.3	−	36392.3i	0.291517	−	0.168308i
$466$	104403.	+	27974.7i	0.480773	+	0.128823i
$467$	147478.	−	147478.i	0.676227	−	0.676227i	−0.282917	−	0.959144i	$-0.591302\pi$
$467$	147478.	−	147478.i	0.676227	−	0.676227i	0.959144	+	0.282917i	$0.0913022\pi$
$468$	−92858.6	+	24881.4i	−0.423965	+	0.113601i
$469$	−10836.1	+	6256.24i	−0.0492639	+	0.0284425i
$470$	15577.0			0.0705162
$471$			242946.i			1.09513i
$472$	−79801.8	+	46073.6i	−0.358203	+	0.206808i
$473$	43369.1	+	43369.1i	0.193847	+	0.193847i
$474$	−135978.	−	78507.2i	−0.605220	−	0.349424i
$475$	55419.8	+	55419.8i	0.245628	+	0.245628i
$476$	−145359.	+	38948.9i	−0.641547	+	0.171902i
$477$	−62286.7	+	107884.i	−0.273753	+	0.474153i
$478$	−146264.	+	253337.i	−0.640151	+	1.10877i
$479$	291347.	+	78066.2i	1.26981	+	0.340245i	0.829959	−	0.557825i	$-0.188364\pi$
$479$	291347.	+	78066.2i	1.26981	+	0.340245i	0.439853	+	0.898070i	$0.355031\pi$
$480$			10122.9i			0.0439363i
$481$	−258265.	−	305198.i	−1.11628	−	1.31914i
$482$	−57275.8			−0.246534
$483$	−45304.9	+	169080.i	−0.194201	+	0.724767i
$484$	−93045.3	−	53719.7i	−0.397195	−	0.229321i
$485$	−10847.1	−	6262.56i	−0.0461136	−	0.0266237i
$486$	−38629.7	−	144168.i	−0.163549	−	0.610375i
$487$	−140157.	+	140157.i	−0.590960	+	0.590960i	−0.937891	−	0.346931i	$-0.887224\pi$
$487$	−140157.	+	140157.i	−0.590960	+	0.590960i	0.346931	+	0.937891i	$0.387224\pi$
$488$	36030.6	−	62406.8i	0.151297	−	0.262055i
$489$	−43338.1	+	43338.1i	−0.181239	+	0.181239i
$490$	1185.72	+	2053.74i	0.00493846	+	0.00855367i
$491$	−273630.			−1.13501			−0.567507	−	0.823369i	$-0.692092\pi$
$491$	−273630.			−1.13501			−0.567507	+	0.823369i	$0.692092\pi$
$492$		−	64888.1i		−	0.268062i
$493$	246374.	+	426733.i	1.01368	+	1.75575i
$494$	30658.8	+	114420.i	0.125632	+	0.468866i
$495$	−8969.35	−	8969.35i	−0.0366059	−	0.0366059i
$496$	21559.3	−	80460.4i	0.0876337	−	0.327054i
$497$	−97509.9	−	168892.i	−0.394763	−	0.683749i
$498$	−48316.7	−	12946.4i	−0.194822	−	0.0522024i
$499$	−373101.	+	99972.0i	−1.49839	+	0.401493i	−0.912561	−	0.408942i	$-0.865898\pi$
$499$	−373101.	+	99972.0i	−1.49839	+	0.401493i	−0.585830	+	0.810434i	$0.699231\pi$
$500$	21487.8	+	80193.4i	0.0859510	+	0.320774i
$501$	5088.55	−	18990.7i	0.0202730	−	0.0756600i
$502$	−35758.4	+	20645.1i	−0.141896	+	0.0819239i
$503$	207535.	+	55608.7i	0.820265	+	0.219789i	0.644463	−	0.764636i	$-0.277081\pi$
$503$	207535.	+	55608.7i	0.820265	+	0.219789i	0.175803	+	0.984425i	$0.443748\pi$
$504$	−32889.1	+	32889.1i	−0.129476	+	0.129476i
$505$	−93586.9	+	25076.5i	−0.366971	+	0.0983297i
$506$	−47313.8	+	27316.6i	−0.184794	+	0.106691i
$507$	358123.			1.39321
$508$			61170.5i			0.237036i
$509$	118584.	−	68464.4i	0.457709	−	0.264259i	−0.253371	−	0.967369i	$-0.581539\pi$
$509$	118584.	−	68464.4i	0.457709	−	0.264259i	0.711081	+	0.703110i	$0.248206\pi$
$510$	−42114.1	−	42114.1i	−0.161915	−	0.161915i
$511$	−153823.	−	88810.0i	−0.589089	−	0.340111i
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	−106813.	+	28620.4i	−0.405871	+	0.108753i
$514$	34176.4	−	59195.2i	0.129360	−	0.224058i
$515$	72930.4	−	126319.i	0.274975	−	0.476271i
$516$	85975.5	+	23037.1i	0.322905	+	0.0865222i
$517$		−	21635.8i		−	0.0809454i
$518$	−182045.	−	65402.2i	−0.678454	−	0.243743i
$519$	77861.1			0.289058
$520$	−15150.6	+	56543.0i	−0.0560305	+	0.209109i
$521$	265052.	+	153028.i	0.976464	+	0.563762i	0.901201	−	0.433402i	$-0.142687\pi$
$521$	265052.	+	153028.i	0.976464	+	0.563762i	0.0752633	+	0.997164i	$0.476020\pi$
$522$	131894.	+	76148.9i	0.484042	+	0.279462i
$523$	105622.	+	394187.i	0.386146	+	1.44111i	0.836353	+	0.548191i	$0.184683\pi$
$523$	105622.	+	394187.i	0.386146	+	1.44111i	−0.450208	+	0.892924i	$0.648650\pi$
$524$	−54680.8	+	54680.8i	−0.199146	+	0.199146i
$525$	86179.8	−	149268.i	0.312670	−	0.541561i
$526$	−10353.5	+	10353.5i	−0.0374209	+	0.0374209i
$527$	245045.	+	424430.i	0.882316	+	1.52822i
$528$	14060.3			0.0504343
$529$		−	28233.1i		−	0.100890i
$530$	37927.3	+	65692.0i	0.135021	+	0.233862i
$531$	−43369.4	−	161857.i	−0.153813	−	0.574040i
$532$	40525.9	+	40525.9i	0.143189	+	0.143189i
$533$	97115.8	−	362441.i	0.341850	−	1.27580i
$534$	−6127.57	−	10613.3i	−0.0214885	−	0.0372192i
$535$	−23405.0	−	6271.36i	−0.0817714	−	0.0219106i
$536$	−5474.32	+	1466.84i	−0.0190546	+	0.00510568i
$537$	−66773.2	−	249201.i	−0.231555	−	0.864175i
$538$	90131.4	−	336375.i	0.311395	−	1.16214i
$539$	2852.55	−	1646.92i	0.00981873	−	0.00566885i
$540$	−52783.5	−	14143.3i	−0.181013	−	0.0485024i
$541$	327048.	−	327048.i	1.11742	−	1.11742i	0.125302	−	0.992119i	$-0.460010\pi$
$541$	327048.	−	327048.i	1.11742	−	1.11742i	0.992119	−	0.125302i	$-0.0399899\pi$
$542$	141079.	−	37802.1i	0.480247	−	0.128682i
$543$	−205835.	+	118839.i	−0.698103	+	0.403050i
$544$	−68161.9			−0.230327
$545$			164913.i			0.555217i
$546$	225603.	−	130252.i	0.756763	−	0.436917i
$547$	−323631.	−	323631.i	−1.08162	−	1.08162i	−0.996359	−	0.0852624i	$-0.972827\pi$
$547$	−323631.	−	323631.i	−1.08162	−	1.08162i	−0.0852624	−	0.996359i	$-0.527173\pi$
$548$	−157045.	−	90670.1i	−0.522954	−	0.301928i
$549$	92659.7	+	92659.7i	0.307430	+	0.307430i
$550$	51962.2	−	13923.2i	0.171776	−	0.0460272i
$551$	93830.6	−	162519.i	0.309059	−	0.535305i
$552$	−39642.6	+	68663.0i	−0.130102	+	0.225343i
$553$	−424327.	−	113698.i	−1.38756	−	0.371794i
$554$			17375.6i			0.0566136i
$555$	−13607.7	−	75337.9i	−0.0441773	−	0.244584i
$556$	208060.			0.673037
$557$	−47229.0	+	176261.i	−0.152229	+	0.568127i	0.847097	+	0.531438i	$0.178348\pi$
$557$	−47229.0	+	176261.i	−0.152229	+	0.568127i	−0.999327	+	0.0366897i	$0.988319\pi$
$558$	131182.	+	75737.9i	0.421314	+	0.243246i
$559$	445749.	+	257353.i	1.42648	+	0.823580i
$560$	7330.26	+	27356.9i	0.0233746	+	0.0872350i
$561$	−58494.6	+	58494.6i	−0.185862	+	0.185862i
$562$	1362.30	−	2359.57i	0.00431321	−	0.00747069i
$563$	−334345.	+	334345.i	−1.05482	+	1.05482i	−0.0564116	+	0.998408i	$0.517966\pi$
$563$	−334345.	+	334345.i	−1.05482	+	1.05482i	−0.998408	+	0.0564116i	$0.982034\pi$
$564$	−15699.2	−	27191.8i	−0.0493537	−	0.0854831i
$565$	−135128.			−0.423301
$566$		−	67535.5i		−	0.210814i
$567$	38341.3	+	66409.1i	0.119262	+	0.206567i
$568$	−22862.2	−	85322.9i	−0.0708633	−	0.264466i
$569$	111911.	+	111911.i	0.345658	+	0.345658i	0.858489	−	0.512831i	$-0.171403\pi$
$569$	111911.	+	111911.i	0.345658	+	0.345658i	−0.512831	+	0.858489i	$0.671403\pi$
$570$	−5870.68	+	21909.7i	−0.0180692	+	0.0674351i
$571$	−113217.	−	196098.i	−0.347249	−	0.601453i	0.638511	−	0.769613i	$-0.279551\pi$
$571$	−113217.	−	196098.i	−0.347249	−	0.601453i	−0.985760	+	0.168160i	$0.946217\pi$
$572$	78535.6	+	21043.6i	0.240035	+	0.0643172i
$573$	224126.	−	60054.3i	0.682626	−	0.182909i
$574$	−46987.1	−	175358.i	−0.142611	−	0.532233i
$575$	−78512.3	+	293012.i	−0.237466	+	0.886237i
$576$	−18244.9	+	10533.7i	−0.0549915	+	0.0317494i
$577$	−511709.	−	137112.i	−1.53699	−	0.411835i	−0.611698	−	0.791091i	$-0.709513\pi$
$577$	−511709.	−	137112.i	−1.53699	−	0.411835i	−0.925292	+	0.379256i	$0.876180\pi$
$578$	116530.	−	116530.i	0.348805	−	0.348805i
$579$	235150.	−	63008.3i	0.701437	−	0.187949i
$580$	80312.0	−	46368.2i	0.238740	−	0.137836i
$581$	−139949.			−0.414589
$582$			25246.7i			0.0745347i
$583$	91243.2	−	52679.3i	0.268450	−	0.154990i
$584$	−56887.9	−	56887.9i	−0.166799	−	0.166799i
$585$	−92187.2	−	53224.3i	−0.269376	−	0.155524i
$586$	233249.	+	233249.i	0.679241	+	0.679241i
$587$	419697.	−	112458.i	1.21804	−	0.326372i	0.408126	−	0.912926i	$-0.366182\pi$
$587$	419697.	−	112458.i	1.21804	−	0.326372i	0.809910	+	0.586554i	$0.199516\pi$
$588$	2390.05	−	4139.69i	0.00691277	−	0.0119733i
$589$	93324.2	−	161642.i	0.269007	−	0.465934i
$590$	−98557.0	−	26408.3i	−0.283128	−	0.0758640i
$591$		−	371212.i		−	1.06279i
$592$	−71979.4	−	49955.3i	−0.205383	−	0.142540i
$593$	−59607.0			−0.169507			−0.0847535	−	0.996402i	$-0.527010\pi$
$593$	−59607.0			−0.169507			−0.0847535	+	0.996402i	$0.527010\pi$
$594$	−19644.4	+	73313.9i	−0.0556757	+	0.207785i
$595$	−144308.	−	83316.3i	−0.407621	−	0.235340i
$596$	−31123.6	−	17969.2i	−0.0876189	−	0.0505868i
$597$	−100129.	−	373687.i	−0.280939	−	1.04848i
$598$	−324195.	+	324195.i	−0.906575	+	0.906575i
$599$	212519.	−	368094.i	0.592304	−	1.02590i	−0.401617	−	0.915808i	$-0.631552\pi$
$599$	212519.	−	368094.i	0.592304	−	1.02590i	0.993921	−	0.110093i	$-0.0351150\pi$
$600$	55203.1	−	55203.1i	0.153342	−	0.153342i
$601$	−3819.60	−	6615.74i	−0.0105747	−	0.0183160i	0.860690	−	0.509130i	$-0.170033\pi$
$601$	−3819.60	−	6615.74i	−0.0105747	−	0.0183160i	−0.871264	+	0.490814i	$0.836699\pi$
$602$	249028.			0.687155
$603$		−	10306.0i		−	0.0283437i
$604$	150490.	+	260657.i	0.412510	+	0.714488i
$605$	−30790.8	−	114913.i	−0.0841222	−	0.313948i
$606$	138095.	+	138095.i	0.376040	+	0.376040i
$607$	−141971.	+	529842.i	−0.385320	+	1.43803i	0.452342	+	0.891844i	$0.350589\pi$
$607$	−141971.	+	529842.i	−0.385320	+	1.43803i	−0.837662	+	0.546189i	$0.816078\pi$
$608$	12979.6	+	22481.3i	0.0351118	+	0.0608155i
$609$	−398633.	−	106813.i	−1.07483	−	0.287999i
$610$	77073.7	−	20651.8i	0.207132	−	0.0555008i
$611$	−46993.0	−	175380.i	−0.125878	−	0.469784i
$612$	32080.6	−	119727.i	0.0856525	−	0.319660i
$613$	−1129.98	+	652.395i	−0.00300712	+	0.00173616i	−0.501503	−	0.865156i	$-0.667219\pi$
$613$	−1129.98	+	652.395i	−0.00300712	+	0.00173616i	0.498496	+	0.866892i	$0.333886\pi$
$614$	107312.	+	28754.1i	0.284650	+	0.0762717i
$615$	50805.6	−	50805.6i	0.134326	−	0.134326i
$616$	37997.5	−	10181.4i	0.100137	−	0.0268316i
$617$	153779.	−	88784.1i	0.403948	−	0.233219i	−0.284238	−	0.958754i	$-0.591741\pi$
$617$	153779.	−	88784.1i	0.403948	−	0.233219i	0.688186	+	0.725534i	$0.258407\pi$
$618$	−294010.			−0.769812
$619$		−	631194.i		−	1.64733i	−0.567074	−	0.823667i	$-0.691925\pi$
$619$		−	631194.i		−	1.64733i	0.567074	−	0.823667i	$-0.308075\pi$
$620$	79878.6	−	46117.9i	0.207801	−	0.119974i
$621$	−302639.	−	302639.i	−0.784770	−	0.784770i
$622$	−346877.	−	200270.i	−0.896592	−	0.517647i
$623$	−24244.9	−	24244.9i	−0.0624661	−	0.0624661i
$624$	113973.	−	30538.9i	0.292707	−	0.0784305i
$625$	124826.	−	216205.i	0.319554	−	0.553484i
$626$	−65603.4	+	113628.i	−0.167409	+	0.289960i
$627$	30431.5	+	8154.11i	0.0774085	+	0.0207416i
$628$			307871.i			0.780639i
$629$	507282.	−	91626.5i	1.28218	−	0.231590i
$630$	−51502.5			−0.129762
$631$	−103320.	+	385595.i	−0.259493	+	0.968440i	0.706043	+	0.708169i	$0.250479\pi$
$631$	−103320.	+	385595.i	−0.259493	+	0.968440i	−0.965536	+	0.260271i	$0.916188\pi$
$632$	−172318.	−	99487.8i	−0.431416	−	0.249078i
$633$	114612.	+	66171.1i	0.286037	+	0.165143i
$634$	55669.1	+	207760.i	0.138496	+	0.516873i
$635$	−47894.8	+	47894.8i	−0.118779	+	0.118779i
$636$	76449.5	−	132414.i	0.188999	−	0.327357i
$637$	19545.7	−	19545.7i	0.0481695	−	0.0481695i
$638$	−64403.3	−	111550.i	−0.158222	−	0.274048i
$639$	160630.			0.393392
$640$			12828.2i			0.0313189i
$641$	69568.3	+	120496.i	0.169315	+	0.293262i	0.938179	−	0.346150i	$-0.112511\pi$
$641$	69568.3	+	120496.i	0.169315	+	0.293262i	−0.768864	+	0.639412i	$0.779178\pi$
$642$	12641.1	+	47177.2i	0.0306701	+	0.114462i
$643$	233125.	+	233125.i	0.563853	+	0.563853i	0.930400	−	0.366547i	$-0.119460\pi$
$643$	233125.	+	233125.i	0.563853	+	0.563853i	−0.366547	+	0.930400i	$0.619460\pi$
$644$	−57412.4	+	214266.i	−0.138431	+	0.516632i
$645$	49279.0	+	85353.8i	0.118452	+	0.205165i
$646$	−147527.	−	39529.7i	−0.353514	−	0.0947238i
$647$	−771379.	+	206690.i	−1.84272	+	0.493755i	−0.999069	−	0.0431360i	$-0.986265\pi$
$647$	−771379.	+	206690.i	−1.84272	+	0.493755i	−0.843651	+	0.536892i	$0.819598\pi$
$648$	8989.52	+	33549.3i	0.0214085	+	0.0798977i
$649$	−36679.9	+	136891.i	−0.0870841	+	0.325002i
$650$	390965.	−	225724.i	0.925361	−	0.534258i
$651$	−396482.	−	106237.i	−0.935538	−	0.250677i
$652$	−54920.0	+	54920.0i	−0.129192	+	0.129192i
$653$	−384668.	+	103071.i	−0.902110	+	0.241720i	−0.679922	−	0.733284i	$-0.737986\pi$
$653$	−384668.	+	103071.i	−0.902110	+	0.241720i	−0.222188	+	0.975004i	$0.571320\pi$
$654$	287879.	−	166207.i	0.673060	−	0.388591i
$655$	−85627.2			−0.199585
$656$		−	82229.1i		−	0.191081i
$657$	126698.	−	73149.3i	0.293522	−	0.169465i
$658$	−62116.9	−	62116.9i	−0.143469	−	0.143469i
$659$	−413986.	−	239015.i	−0.953267	−	0.550369i	−0.0591730	−	0.998248i	$-0.518846\pi$
$659$	−413986.	−	239015.i	−0.953267	−	0.550369i	−0.894094	+	0.447879i	$0.852180\pi$
$660$	11008.8	+	11008.8i	0.0252728	+	0.0252728i
$661$	−524982.	+	140668.i	−1.20155	+	0.321954i	−0.803441	−	0.595385i	$-0.797000\pi$
$661$	−524982.	+	140668.i	−1.20155	+	0.321954i	−0.398108	+	0.917339i	$0.630333\pi$
$662$	−73874.0	+	127954.i	−0.168568	+	0.291969i
$663$	−347108.	+	601209.i	−0.789655	+	1.36772i
$664$	−61229.0	−	16406.3i	−0.138874	−	0.0372112i
$665$			63461.3i			0.143505i
$666$	121624.	−	102920.i	0.274202	−	0.232035i
$667$	726333.			1.63262
$668$	6448.44	−	24065.9i	0.0144511	−	0.0539324i
$669$	−196066.	−	113198.i	−0.438076	−	0.252923i
$670$	−5434.74	−	3137.75i	−0.0121068	−	0.00698986i
$671$	−28684.5	−	107052.i	−0.0637092	−	0.237766i
$672$	40367.5	−	40367.5i	0.0893908	−	0.0893908i
$673$	76530.8	−	132555.i	0.168969	−	0.292662i	−0.769089	−	0.639142i	$-0.779290\pi$
$673$	76530.8	−	132555.i	0.168969	−	0.292662i	0.938058	+	0.346480i	$0.112623\pi$
$674$	169590.	−	169590.i	0.373319	−	0.373319i
$675$	210716.	+	364970.i	0.462476	+	0.801033i
$676$	453830.			0.993115
$677$			421114.i			0.918802i	0.888229	+	0.459401i	$0.151936\pi$
$677$			421114.i			0.918802i	−0.888229	+	0.459401i	$0.848064\pi$
$678$	136188.	+	235885.i	0.296265	+	0.513145i
$679$	18281.8	+	68228.5i	0.0396532	+	0.147988i
$680$	−53368.9	−	53368.9i	−0.115417	−	0.115417i
$681$	−22522.4	+	84054.7i	−0.0485646	+	0.181246i
$682$	−64055.8	−	110948.i	−0.137718	−	0.238534i
$683$	104742.	+	28065.6i	0.224533	+	0.0601636i	0.369332	−	0.929298i	$-0.379587\pi$
$683$	104742.	+	28065.6i	0.224533	+	0.0601636i	−0.144798	+	0.989461i	$0.546253\pi$
$684$	−45597.4	+	12217.8i	−0.0974602	+	0.0261144i
$685$	−51969.9	−	193954.i	−0.110757	−	0.413350i
$686$	−84344.8	+	314779.i	−0.179230	+	0.668895i
$687$	336150.	−	194076.i	0.712230	−	0.411206i
$688$	108952.	+	29193.6i	0.230175	+	0.0616752i
$689$	625199.	−	625199.i	1.31698	−	1.31698i
$690$	−84800.3	+	22722.2i	−0.178114	+	0.0477256i
$691$	−429158.	+	247774.i	−0.898795	+	0.518920i	−0.876809	−	0.480839i	$-0.840332\pi$
$691$	−429158.	+	247774.i	−0.898795	+	0.518920i	−0.0219860	+	0.999758i	$0.506999\pi$
$692$	98669.0			0.206048
$693$			71534.7i			0.148953i
$694$	−431959.	+	249392.i	−0.896858	+	0.517801i
$695$	162905.	+	162905.i	0.337260	+	0.337260i
$696$	−161884.	−	93463.7i	−0.334184	−	0.192941i
$697$	342095.	+	342095.i	0.704177	+	0.704177i
$698$	236445.	−	63355.4i	0.485311	−	0.130039i
$699$	120621.	−	208922.i	0.246870	−	0.427592i
$700$	109211.	−	189159.i	0.222879	−	0.386038i
$701$	−48720.8	−	13054.7i	−0.0991467	−	0.0265663i	0.208905	−	0.977936i	$-0.433010\pi$
$701$	−48720.8	−	13054.7i	−0.0991467	−	0.0265663i	−0.308051	+	0.951370i	$0.599677\pi$
$702$			636951.i			1.29250i
$703$	−126818.	−	149865.i	−0.256609	−	0.303242i
$704$	17817.8			0.0359509
$705$	8998.41	−	33582.5i	0.0181045	−	0.0675670i
$706$	372735.	+	215198.i	0.747808	+	0.431747i
$707$	473197.	+	273200.i	0.946680	+	0.546566i
$708$	53230.8	+	198660.i	0.106193	+	0.396318i
$709$	−488802.	+	488802.i	−0.972389	+	0.972389i	−0.999629	−	0.0272395i	$-0.991328\pi$
$709$	−488802.	+	488802.i	−0.972389	+	0.972389i	0.0272395	+	0.999629i	$0.491328\pi$
$710$	48905.0	−	84706.0i	0.0970145	−	0.168034i
$711$	255853.	−	255853.i	0.506117	−	0.506117i
$712$	−7765.13	−	13449.6i	−0.0153175	−	0.0265307i
$713$	722414.			1.42104
$714$			335879.i			0.658850i
$715$	45014.7	+	77967.8i	0.0880526	+	0.152512i
$716$	−84618.0	−	315799.i	−0.165058	−	0.616005i
$717$	461676.	+	461676.i	0.898048	+	0.898048i
$718$	−79336.9	+	296089.i	−0.153896	+	0.574346i
$719$	394421.	+	683158.i	0.762961	+	1.32149i	0.941318	+	0.337522i	$0.109589\pi$
$719$	394421.	+	683158.i	0.762961	+	1.32149i	−0.178356	+	0.983966i	$0.557078\pi$
$720$	−22532.8	−	6037.65i	−0.0434661	−	0.0116467i
$721$	−794552.	+	212900.i	−1.52845	+	0.409548i
$722$	−80346.9	−	299859.i	−0.154133	−	0.575231i
$723$	−33086.6	+	123481.i	−0.0632959	+	0.236223i
$724$	−260843.	+	150598.i	−0.497625	+	0.287304i
$725$	−690822.	−	185105.i	−1.31429	−	0.352162i
$726$	−169564.	+	169564.i	−0.321707	+	0.321707i
$727$	161544.	−	43285.7i	0.305649	−	0.0818984i	−0.102735	−	0.994709i	$-0.532759\pi$
$727$	161544.	−	43285.7i	0.305649	−	0.0818984i	0.408384	+	0.912810i	$0.366093\pi$
$728$	285894.	−	165061.i	0.539440	−	0.311446i
$729$	−457461.			−0.860794
$730$		−	89083.4i		−	0.167167i
$731$	−574723.	+	331816.i	−1.07553	+	0.620959i
$732$	−113729.	−	113729.i	−0.212250	−	0.212250i
$733$	−407497.	−	235269.i	−0.758432	−	0.437881i	0.0703002	−	0.997526i	$-0.477604\pi$
$733$	−407497.	−	235269.i	−0.758432	−	0.437881i	−0.828733	+	0.559645i	$0.810938\pi$
$734$	150055.	+	150055.i	0.278521	+	0.278521i
$735$	5112.61	−	1369.92i	0.00946384	−	0.00253583i
$736$	−50236.9	+	87012.8i	−0.0927400	+	0.160630i
$737$	−4358.19	+	7548.61i	−0.00802364	+	0.0138974i
$738$	144436.	+	38701.4i	0.265193	+	0.0710581i
$739$		−	349337.i		−	0.639669i	−0.947473	−	0.319835i	$-0.896373\pi$
$739$		−	349337.i		−	0.639669i	0.947473	−	0.319835i	$-0.103627\pi$
$740$	−17244.3	−	95471.5i	−0.0314907	−	0.174345i
$741$	264389.			0.481512
$742$	110718.	−	413205.i	0.201099	−	0.750512i
$743$	−596554.	−	344421.i	−1.08062	−	0.623895i	−0.149555	−	0.988753i	$-0.547784\pi$
$743$	−596554.	−	344421.i	−1.08062	−	0.623895i	−0.931063	+	0.364858i	$0.881117\pi$
$744$	−161010.	−	92959.3i	−0.290876	−	0.167937i
$745$	−10299.5	−	38438.4i	−0.0185569	−	0.0692552i
$746$	−86504.5	+	86504.5i	−0.155439	+	0.155439i
$747$	57635.3	−	99827.3i	0.103287	−	0.178899i
$748$	−74127.0	+	74127.0i	−0.132487	+	0.132487i
$749$	68324.4	+	118341.i	0.121790	+	0.210947i
$750$	185302.			0.329425
$751$			25968.9i			0.0460441i	0.999735	+	0.0230221i	$0.00732880\pi$
$751$			25968.9i			0.0460441i	−0.999735	+	0.0230221i	$0.992671\pi$
$752$	−19894.7	−	34458.7i	−0.0351805	−	0.0609345i
$753$	23852.2	+	89017.7i	0.0420667	+	0.156995i
$754$	−764340.	−	764340.i	−1.34445	−	1.34445i
$755$	−86257.3	+	321917.i	−0.151322	+	0.564742i
$756$	154087.	+	266886.i	0.269601	+	0.466962i
$757$	28240.5	+	7567.02i	0.0492812	+	0.0132048i	0.283375	−	0.959009i	$-0.408546\pi$
$757$	28240.5	+	7567.02i	0.0492812	+	0.0132048i	−0.234094	+	0.972214i	$0.575212\pi$
$758$	−573846.	+	153762.i	−0.998750	+	0.267614i
$759$	31560.1	+	117784.i	0.0547841	+	0.204457i
$760$	−7439.58	+	27764.9i	−0.0128802	+	0.0480694i
$761$	122741.	−	70864.3i	0.211943	−	0.122365i	−0.390271	−	0.920700i	$-0.627619\pi$
$761$	122741.	−	70864.3i	0.211943	−	0.122365i	0.602214	+	0.798335i	$0.294285\pi$
$762$	131877.	+	35336.4i	0.227123	+	0.0608573i
$763$	657629.	−	657629.i	1.12962	−	1.12962i
$764$	284022.	−	76103.5i	0.486593	−	0.130382i
$765$	118861.	−	68624.4i	0.203103	−	0.117261i
$766$	133091.			0.226825
$767$			1.18931e6i			2.02164i
$768$	22393.4	−	12928.8i	0.0379663	−	0.0219198i
$769$	138526.	+	138526.i	0.234249	+	0.234249i	0.814464	−	0.580214i	$-0.197031\pi$
$769$	138526.	+	138526.i	0.234249	+	0.234249i	−0.580214	+	0.814464i	$0.697031\pi$
$770$	37722.8	+	21779.3i	0.0636242	+	0.0367334i
$771$	−107876.	−	107876.i	−0.181475	−	0.181475i
$772$	297993.	−	79847.0i	0.500002	−	0.133975i
$773$	470794.	−	815439.i	0.787902	−	1.36469i	−0.139349	−	0.990243i	$-0.544501\pi$
$773$	470794.	−	815439.i	0.787902	−	1.36469i	0.927250	−	0.374442i	$-0.122166\pi$
$774$	−102557.	+	177634.i	−0.171192	+	0.296514i
$775$	−687094.	−	184106.i	−1.14397	−	0.306525i
$776$			31993.7i			0.0531302i
$777$	−246163.	+	354691.i	−0.407737	+	0.587500i
$778$	−562580.			−0.929449
$779$	47687.8	−	177973.i	0.0785837	−	0.293278i
$780$	113149.	+	65326.5i	0.185978	+	0.107374i
$781$	−117653.	−	67926.9i	−0.192886	−	0.111363i
$782$	−152998.	−	570996.i	−0.250191	−	0.933726i
$783$	713520.	−	713520.i	1.16381	−	1.16381i
$784$	3028.78	−	5246.00i	0.00492760	−	0.00853485i
$785$	−241055.	+	241055.i	−0.391180	+	0.391180i
$786$	86298.8	+	149474.i	0.139688	+	0.241947i
$787$	287818.			0.464695			0.232348	−	0.972633i	$-0.425359\pi$
$787$	287818.			0.464695			0.232348	+	0.972633i	$0.425359\pi$
$788$		−	470416.i		−	0.757582i
$789$	16340.1	+	28301.9i	0.0262483	+	0.0454634i
$790$	−57024.0	−	212816.i	−0.0913700	−	0.340997i
$791$	538854.	+	538854.i	0.861228	+	0.861228i
$792$	−8386.02	+	31297.1i	−0.0133692	+	0.0498945i
$793$	−465034.	−	805462.i	−0.739500	−	1.28085i
$794$	−193333.	−	51803.4i	−0.306666	−	0.0821708i
$795$	163535.	−	43819.0i	0.258747	−	0.0693311i
$796$	−126888.	−	473553.i	−0.200260	−	0.747382i
$797$	70378.0	−	262654.i	0.110795	−	0.413492i	−0.888143	−	0.459567i	$-0.848005\pi$
$797$	70378.0	−	262654.i	0.110795	−	0.413492i	0.998938	+	0.0460747i	$0.0146712\pi$
$798$	110780.	−	63959.1i	0.173963	−	0.100438i
$799$	226125.	+	60590.1i	0.354206	+	0.0949091i
$800$	69955.9	−	69955.9i	0.109306	−	0.109306i
$801$	27279.0	−	7309.37i	0.0425170	−	0.0113924i
$802$	−717234.	+	414095.i	−1.11510	+	0.643801i
$803$	−123733.			−0.191891
$804$			12649.4i			0.0195686i
$805$	−212717.	+	122812.i	−0.328254	+	0.189517i
$806$	−760216.	−	760216.i	−1.17022	−	1.17022i
$807$	−673124.	−	388629.i	−1.03359	−	0.596743i
$808$	175001.	+	175001.i	0.268051	+	0.268051i
$809$	1.06096e6	−	284283.i	1.62107	−	0.434364i	0.669752	−	0.742585i	$-0.266400\pi$
$809$	1.06096e6	−	284283.i	1.62107	−	0.434364i	0.951315	+	0.308221i	$0.0997337\pi$
$810$	−19229.7	+	33306.8i	−0.0293091	+	0.0507648i
$811$	340731.	−	590163.i	0.518048	−	0.897285i	−0.481732	−	0.876318i	$-0.659992\pi$
$811$	340731.	−	590163.i	0.518048	−	0.897285i	0.999780	−	0.0209667i	$-0.00667441\pi$
$812$	−505166.	−	135359.i	−0.766164	−	0.205293i
$813$		−	325990.i		−	0.493200i
$814$	−132606.	+	23951.6i	−0.200130	+	0.0361481i
$815$	−86001.7			−0.129477
$816$	−39375.2	+	146950.i	−0.0591347	+	0.220694i
$817$	218881.	+	126371.i	0.327917	+	0.189323i
$818$	310233.	+	179113.i	0.463640	+	0.267683i
$819$	155373.	+	579861.i	0.231637	+	0.864482i
$820$	64383.1	−	64383.1i	0.0957512	−	0.0957512i
$821$	19881.9	−	34436.4i	0.0294965	−	0.0510895i	−0.850900	−	0.525327i	$-0.823943\pi$
$821$	19881.9	−	34436.4i	0.0294965	−	0.0510895i	0.880397	+	0.474238i	$0.157276\pi$
$822$	−286196.	+	286196.i	−0.423565	+	0.423565i
$823$	396196.	+	686232.i	0.584939	+	1.01314i	0.994883	+	0.101034i	$0.0322149\pi$
$823$	396196.	+	686232.i	0.584939	+	1.01314i	−0.409944	+	0.912111i	$0.634452\pi$
$824$	−372582.			−0.548741
$825$		−	120068.i		−	0.176409i
$826$	287709.	+	498327.i	0.421690	+	0.730389i
$827$	−16983.0	−	63381.5i	−0.0248315	−	0.0926726i	0.952398	−	0.304857i	$-0.0986088\pi$
$827$	−16983.0	−	63381.5i	−0.0248315	−	0.0926726i	−0.977230	+	0.212185i	$0.931942\pi$
$828$	−129194.	−	129194.i	−0.188444	−	0.188444i
$829$	208687.	−	778830.i	0.303659	−	1.13327i	−0.630435	−	0.776242i	$-0.717123\pi$
$829$	208687.	−	778830.i	0.303659	−	1.13327i	0.934094	−	0.357028i	$-0.116210\pi$
$830$	−35095.0	−	60786.3i	−0.0509435	−	0.0882367i
$831$	37460.1	+	10037.4i	0.0542459	+	0.0145351i
$832$	144432.	−	38700.3i	0.208649	−	0.0559072i
$833$	9224.24	+	34425.3i	0.0132935	+	0.0496121i
$834$	120190.	−	448556.i	0.172797	−	0.644889i
$835$	23891.9	−	13794.0i	0.0342671	−	0.0197841i
$836$	38564.2	+	10333.2i	0.0551787	+	0.0147851i
$837$	709670.	−	709670.i	1.01299	−	1.01299i
$838$	304968.	−	81715.8i	0.434276	−	0.116364i
$839$	−263237.	+	151980.i	−0.373957	+	0.215904i	−0.675186	−	0.737648i	$-0.735937\pi$
$839$	−263237.	+	151980.i	−0.373957	+	0.215904i	0.301229	+	0.953552i	$0.402603\pi$
$840$	63213.2			0.0895879
$841$			1.00516e6i			1.42117i
$842$	723979.	−	417989.i	1.02118	−	0.589578i
$843$	−4300.04	−	4300.04i	−0.00605086	−	0.00605086i
$844$	145241.	+	83855.0i	0.203894	+	0.117718i
$845$	355336.	+	355336.i	0.497652	+	0.497652i
$846$	69890.3	−	18727.1i	0.0976509	−	0.0261655i
$847$	−335456.	+	581027.i	−0.467594	+	0.809896i
$848$	96880.2	−	167801.i	0.134723	−	0.233348i
$849$	−145600.	−	39013.3i	−0.201997	−	0.0541249i
$850$			582071.i			0.805635i
$851$	256911.	−	715106.i	0.354751	−	0.987442i
$852$	−197154.			−0.271599
$853$	−81031.4	+	302413.i	−0.111367	+	0.415626i	−0.998989	−	0.0449450i	$-0.985689\pi$
$853$	−81031.4	+	302413.i	−0.111367	+	0.415626i	0.887623	+	0.460571i	$0.152355\pi$
$854$	−389703.	−	224995.i	−0.534340	−	0.308501i
$855$	−45267.7	−	26135.3i	−0.0619235	−	0.0357516i
$856$	16019.4	+	59785.1i	0.0218624	+	0.0815915i
$857$	779781.	−	779781.i	1.06172	−	1.06172i	0.0637575	−	0.997965i	$-0.479692\pi$
$857$	779781.	−	779781.i	1.06172	−	1.06172i	0.997965	−	0.0637575i	$-0.0203084\pi$
$858$	90735.6	−	157159.i	0.123255	−	0.213483i
$859$	−696027.	+	696027.i	−0.943278	+	0.943278i	−0.998475	−	0.0551977i	$-0.982421\pi$
$859$	−696027.	+	696027.i	−0.943278	+	0.943278i	0.0551977	+	0.998475i	$0.482421\pi$
$860$	62448.6	+	108164.i	0.0844356	+	0.146247i
$861$	−405197.			−0.546588
$862$			967161.i			1.30162i
$863$	−276848.	−	479516.i	−0.371724	−	0.643845i	0.618107	−	0.786094i	$-0.287900\pi$
$863$	−276848.	−	479516.i	−0.371724	−	0.643845i	−0.989831	+	0.142249i	$0.954567\pi$
$864$	36127.2	+	134829.i	0.0483957	+	0.180615i
$865$	77255.1	+	77255.1i	0.103251	+	0.103251i
$866$	180567.	−	673887.i	0.240771	−	0.898568i
$867$	−183911.	−	318543.i	−0.244664	−	0.423770i
$868$	−502440.	−	134628.i	−0.666875	−	0.178689i
$869$	−295593.	+	79203.8i	−0.391430	+	0.104883i
$870$	−53571.1	−	199930.i	−0.0707770	−	0.264143i
$871$	−18932.0	+	70655.2i	−0.0249551	+	0.0931338i
$872$	364813.	−	210625.i	0.479774	−	0.276998i
$873$	−56197.1	−	15058.0i	−0.0737370	−	0.0197578i
$874$	−159193.	+	159193.i	−0.208401	+	0.208401i
$875$	500773.	−	134182.i	0.654070	−	0.175258i
$876$	−155507.	+	89782.1i	−0.202648	+	0.116999i
$877$	−61299.3			−0.0796996			−0.0398498	−	0.999206i	$-0.512688\pi$
$877$	−61299.3			−0.0796996			−0.0398498	+	0.999206i	$0.512688\pi$
$878$		−	533493.i		−	0.692053i
$879$	637601.	−	368119.i	0.825223	−	0.476443i
$880$	13950.9	+	13950.9i	0.0180151	+	0.0180151i
$881$	227514.	+	131355.i	0.293128	+	0.169237i	0.639352	−	0.768915i	$-0.279203\pi$
$881$	227514.	+	131355.i	0.293128	+	0.169237i	−0.346224	+	0.938152i	$0.612536\pi$
$882$	7789.10	+	7789.10i	0.0100127	+	0.0100127i
$883$	758987.	−	203370.i	0.973449	−	0.260835i	0.263166	−	0.964751i	$-0.415233\pi$
$883$	758987.	−	203370.i	0.973449	−	0.260835i	0.710283	+	0.703916i	$0.248567\pi$
$884$	−439871.	+	761878.i	−0.562886	+	0.974947i
$885$	−113867.	+	197224.i	−0.145382	+	0.251810i
$886$	469731.	+	125864.i	0.598387	+	0.160337i
$887$		−	652917.i		−	0.829871i	−0.909851	−	0.414935i	$-0.863804\pi$
$887$		−	652917.i		−	0.829871i	0.909851	−	0.414935i	$-0.136196\pi$
$888$	−149279.	+	126323.i	−0.189310	+	0.160197i
$889$	381983.			0.483326
$890$	4450.78	−	16610.6i	0.00561897	−	0.0209703i
$891$	46261.6	+	26709.1i	0.0582727	+	0.0336438i
$892$	−248463.	−	143450.i	−0.312271	−	0.180290i
$893$	−23075.5	−	86118.8i	−0.0289366	−	0.107993i
$894$	−56719.1	+	56719.1i	−0.0709666	+	0.0709666i
$895$	181008.	−	313515.i	0.225971	−	0.391393i
$896$	51155.4	−	51155.4i	0.0637200	−	0.0637200i
$897$	511653.	+	886209.i	0.635903	+	1.10142i
$898$	821165.			1.01831
$899$			1.70320e6i			2.10740i
$900$	89952.7	+	155803.i	0.111053	+	0.192349i
$901$	295052.	+	1.10115e6i	0.363453	+	1.35643i
$902$	−89425.2	−	89425.2i	−0.109912	−	0.109912i
$903$	143856.	−	536879.i	0.176422	−	0.658417i
$904$	172584.	+	298924.i	0.211185	+	0.365783i
$905$	−322147.	−	86319.0i	−0.393330	−	0.105392i
$906$	648883.	−	173868.i	0.790515	−	0.211818i
$907$	−300998.	−	1.12334e6i	−0.365889	−	1.36552i	−0.866212	−	0.499676i	$-0.833452\pi$
$907$	−300998.	−	1.12334e6i	−0.365889	−	1.36552i	0.500323	−	0.865839i	$-0.333214\pi$
$908$	−28541.4	+	106518.i	−0.0346181	+	0.129196i
$909$	−389754.	+	225024.i	−0.471696	+	0.272334i
$910$	353086.	+	94609.1i	0.426381	+	0.114248i
$911$	−1.10652e6	+	1.10652e6i	−1.33328	+	1.33328i	−0.430865	+	0.902417i	$0.641791\pi$
$911$	−1.10652e6	+	1.10652e6i	−1.33328	+	1.33328i	−0.902417	+	0.430865i	$0.858209\pi$
$912$	55965.3	−	14995.9i	0.0672867	−	0.0180294i
$913$	−84429.4	+	48745.4i	−0.101287	+	0.0584779i
$914$	−224133.			−0.268295
$915$		−	178093.i		−	0.212718i
$916$	425985.	−	245942.i	0.507695	−	0.293118i
$917$	341458.	+	341458.i	0.406067	+	0.406067i
$918$	−711222.	−	410624.i	−0.843956	−	0.487259i
$919$	−1.08124e6	−	1.08124e6i	−1.28024	−	1.28024i	−0.940529	−	0.339715i	$-0.889669\pi$
$919$	−1.08124e6	−	1.08124e6i	−1.28024	−	1.28024i	−0.339715	−	0.940529i	$-0.610331\pi$
$920$	−107463.	+	28794.5i	−0.126964	+	0.0340200i
$921$	123982.	−	214743.i	0.146164	−	0.253163i
$922$	−406251.	+	703647.i	−0.477895	+	0.827738i
$923$	−1.10123e6	−	295074.i	−1.29263	−	0.346360i
$924$		−	87800.3i		−	0.102838i
$925$	−426595.	+	614671.i	−0.498577	+	0.718388i
$926$	584259.			0.681371
$927$	175357.	−	654441.i	0.204063	−	0.761572i
$928$	−205146.	−	118441.i	−0.238214	−	0.137533i
$929$	−808566.	−	466826.i	−0.936880	−	0.540908i	−0.0478993	−	0.998852i	$-0.515253\pi$
$929$	−808566.	−	466826.i	−0.936880	−	0.540908i	−0.888981	+	0.457944i	$0.848586\pi$
$930$	−53282.0	−	198851.i	−0.0616048	−	0.229912i
$931$	9597.73	−	9597.73i	0.0110731	−	0.0110731i
$932$	152856.	−	264755.i	0.175975	−	0.304798i
$933$	−632142.	+	632142.i	−0.726192	+	0.726192i
$934$	−294955.	−	510877.i	−0.338113	−	0.585630i
$935$	−116079.			−0.132779
$936$			271909.i			0.310364i
$937$	194721.	+	337267.i	0.221786	+	0.384144i	0.955350	−	0.295476i	$-0.0954781\pi$
$937$	194721.	+	337267.i	0.221786	+	0.384144i	−0.733564	+	0.679620i	$0.762145\pi$
$938$	9159.77	+	34184.7i	0.0104107	+	0.0388532i
$939$	207074.	+	207074.i	0.234852	+	0.234852i
$940$	11403.2	−	42557.2i	0.0129054	−	0.0481635i
$941$	−705880.	−	1.22262e6i	−0.797171	−	1.38074i	−0.921451	−	0.388494i	$-0.872996\pi$
$941$	−705880.	−	1.22262e6i	−0.797171	−	1.38074i	0.124280	−	0.992247i	$-0.460338\pi$
$942$	663740.	+	177849.i	0.747990	+	0.200423i
$943$	688837.	−	184573.i	0.774628	−	0.207561i
$944$	67456.4	+	251751.i	0.0756971	+	0.282505i
$945$	−88318.7	+	329610.i	−0.0988983	+	0.369094i
$946$	150235.	−	86738.3i	0.167876	−	0.0969234i
$947$	−711456.	−	190634.i	−0.793320	−	0.212569i	−0.160671	−	0.987008i	$-0.551366\pi$
$947$	−711456.	−	190634.i	−0.793320	−	0.212569i	−0.632649	+	0.774439i	$0.718032\pi$
$948$	−314029.	+	314029.i	−0.349424	+	0.349424i
$949$	−1.00298e6	+	268748.i	−1.11368	+	0.298409i
$950$	191980.	−	110840.i	0.212720	−	0.122814i
$951$	480068.			0.530813
$952$			425641.i			0.469645i
$953$	−585197.	+	337864.i	−0.644342	+	0.372011i	−0.786285	−	0.617864i	$-0.787998\pi$
$953$	−585197.	+	337864.i	−0.644342	+	0.372011i	0.141943	+	0.989875i	$0.454665\pi$
$954$	249147.	+	249147.i	0.273753	+	0.273753i
$955$	281969.	+	162795.i	0.309168	+	0.178498i
$956$	585057.	+	585057.i	0.640151	+	0.640151i
$957$	−277694.	+	74407.9i	−0.303209	+	0.0812447i
$958$	426561.	−	738826.i	0.464783	−	0.805028i
$959$	−566195.	+	980679.i	−0.615643	+	1.06632i
$960$	27656.3	+	7410.50i	0.0300091	+	0.00804090i
$961$			770493.i			0.834299i
$962$	−1.02288e6	+	482171.i	−1.10529	+	0.521016i
$963$	−112552.			−0.121367
$964$	−41928.8	+	156480.i	−0.0451189	+	0.168386i
$965$	295838.	+	170802.i	0.317687	+	0.183417i
$966$	428770.	+	247551.i	0.459484	+	0.265283i
$967$	126287.	+	471309.i	0.135053	+	0.504025i	0.999998	+	0.00215787i	$0.000686871\pi$
$967$	126287.	+	471309.i	0.135053	+	0.504025i	−0.864944	+	0.501868i	$0.832646\pi$
$968$	−214879.	+	214879.i	−0.229321	+	0.229321i
$969$	−170444.	+	295218.i	−0.181524	+	0.314409i
$970$	−25050.2	+	25050.2i	−0.0266237	+	0.0266237i
$971$	269128.	+	466143.i	0.285444	+	0.494403i	0.972717	−	0.231996i	$-0.0745257\pi$
$971$	269128.	+	466143.i	0.285444	+	0.494403i	−0.687273	+	0.726399i	$0.741192\pi$
$972$	−422153.			−0.446825
$973$		−	1.29924e6i		−	1.37235i
$974$	280315.	+	485520.i	0.295480	+	0.511787i
$975$	−260788.	−	973275.i	−0.274334	−	1.02383i
$976$	−144122.	−	144122.i	−0.151297	−	0.151297i
$977$	−408124.	+	1.52314e6i	−0.427566	+	1.59570i	0.330689	+	0.943740i	$0.392719\pi$
$977$	−408124.	+	1.52314e6i	−0.427566	+	1.59570i	−0.758255	+	0.651958i	$0.773948\pi$
$978$	86676.2	+	150128.i	0.0906196	+	0.156958i
$979$	−23071.3	−	6181.94i	−0.0240717	−	0.00645000i
$980$	6478.92	−	1736.02i	0.00674606	−	0.00180760i
$981$	198262.	+	739925.i	0.206017	+	0.768865i
$982$	−200311.	+	747572.i	−0.207722	+	0.775229i
$983$	1.06795e6	−	616579.i	1.10520	−	0.638089i	0.167620	−	0.985852i	$-0.446392\pi$
$983$	1.06795e6	−	616579.i	1.10520	−	0.638089i	0.937583	+	0.347762i	$0.113058\pi$
$984$	−177278.	−	47501.4i	−0.183090	−	0.0490587i
$985$	368323.	−	368323.i	0.379626	−	0.379626i
$986$	1.34621e6	−	360717.i	1.38471	−	0.371033i
$987$	−169801.	+	98034.7i	−0.174303	+	0.100634i
$988$	335046.			0.343234
$989$			978225.i			1.00011i
$990$	−31070.8	+	17938.7i	−0.0317016	+	0.0183029i
$991$	948783.	+	948783.i	0.966094	+	0.966094i	0.999444	−	0.0333495i	$-0.0106174\pi$
$991$	948783.	+	948783.i	0.966094	+	0.966094i	−0.0333495	+	0.999444i	$0.510617\pi$
$992$	−204039.	−	117802.i	−0.207344	−	0.119710i
$993$	233180.	+	233180.i	0.236479	+	0.236479i
$994$	−532804.	+	142764.i	−0.539256	+	0.144493i
$995$	271429.	−	470129.i	0.274164	−	0.474866i
$996$	−70740.5	+	122526.i	−0.0713098	+	0.123512i
$997$	−356800.	−	95604.1i	−0.358950	−	0.0961804i	0.0748371	−	0.997196i	$-0.476156\pi$
$997$	−356800.	−	95604.1i	−0.358950	−	0.0961804i	−0.433787	+	0.901015i	$0.642823\pi$
$998$			1.09251e6i			1.09690i
$999$	−450112.	−	954871.i	−0.451014	−	0.956783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.g.a.29.3	yes	28
37.23	odd	12	inner	74.5.g.a.23.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.g.a.23.3	✓	28	37.23	odd	12	inner
74.5.g.a.29.3	yes	28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	74.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.732051 - 2.73205i) q^{2} +(-5.46714 - 3.15645i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(-2.29270 - 8.55648i) q^{5} +(-12.6258 + 12.6258i) q^{6} +(-24.9782 + 43.2636i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(-20.5736 - 35.6345i) q^{9} +O(q^{10})\)	\(q+(0.732051 - 2.73205i) q^{2} +(-5.46714 - 3.15645i) q^{3} +(-6.92820 - 4.00000i) q^{4} +(-2.29270 - 8.55648i) q^{5} +(-12.6258 + 12.6258i) q^{6} +(-24.9782 + 43.2636i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(-20.5736 - 35.6345i) q^{9} -25.0551 q^{10} +34.8004i q^{11} +(25.2516 + 43.7371i) q^{12} +(75.5865 + 282.093i) q^{13} +(99.9129 + 99.9129i) q^{14} +(-14.4736 + 54.0163i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-363.714 - 97.4570i) q^{17} +(-112.416 + 30.1218i) q^{18} +(37.1161 + 138.519i) q^{19} +(-18.3416 + 68.4519i) q^{20} +(273.119 - 157.685i) q^{21} +(95.0766 + 25.4757i) q^{22} +(-392.476 + 392.476i) q^{23} +(137.978 - 36.9710i) q^{24} +(473.309 - 273.265i) q^{25} +826.025 q^{26} +771.104i q^{27} +(346.109 - 199.826i) q^{28} +(-925.323 - 925.323i) q^{29} +(136.980 + 79.0854i) q^{30} +(-920.330 - 920.330i) q^{31} +(174.851 - 46.8513i) q^{32} +(109.846 - 190.259i) q^{33} +(-532.515 + 922.343i) q^{34} +(427.452 + 114.535i) q^{35} +329.177i q^{36} +(-1238.32 + 583.724i) q^{37} +405.612 q^{38} +(477.171 - 1780.83i) q^{39} +(173.587 + 100.220i) q^{40} +(-1112.69 - 642.414i) q^{41} +(-230.867 - 861.609i) q^{42} +(1246.22 - 1246.22i) q^{43} +(139.202 - 241.105i) q^{44} +(-257.737 + 257.737i) q^{45} +(784.951 + 1359.58i) q^{46} -621.711 q^{47} -404.026i q^{48} +(-47.3247 - 81.9687i) q^{49} +(-400.088 - 1493.15i) q^{50} +(1680.86 + 1680.86i) q^{51} +(604.692 - 2256.74i) q^{52} +(-1513.75 - 2621.90i) q^{53} +(2106.70 + 564.487i) q^{54} +(297.769 - 79.7870i) q^{55} +(-292.565 - 1091.87i) q^{56} +(234.310 - 874.459i) q^{57} +(-3205.41 + 1850.65i) q^{58} +(3933.61 + 1054.01i) q^{59} +(316.341 - 316.341i) q^{60} +(-3076.17 + 824.256i) q^{61} +(-3188.12 + 1840.66i) q^{62} +2055.57 q^{63} -512.000i q^{64} +(2240.42 - 1293.51i) q^{65} +(-439.384 - 439.384i) q^{66} +(216.911 + 125.234i) q^{67} +(2130.06 + 2130.06i) q^{68} +(3384.55 - 906.887i) q^{69} +(625.833 - 1083.97i) q^{70} +(-1951.90 + 3380.79i) q^{71} +(899.329 + 240.975i) q^{72} +3555.50i q^{73} +(688.255 + 3810.46i) q^{74} -3450.20 q^{75} +(296.929 - 1108.15i) q^{76} +(-1505.59 - 869.254i) q^{77} +(-4516.00 - 2607.31i) q^{78} +(2275.94 + 8493.93i) q^{79} +(400.882 - 400.882i) q^{80} +(767.495 - 1329.34i) q^{81} +(-2569.66 + 2569.66i) q^{82} +(1400.71 + 2426.10i) q^{83} -2522.97 q^{84} +3335.56i q^{85} +(-2492.45 - 4317.05i) q^{86} +(2138.13 + 7979.61i) q^{87} +(-556.807 - 556.807i) q^{88} +(-177.640 + 662.961i) q^{89} +(515.474 + 892.827i) q^{90} +(-14092.4 - 3776.04i) q^{91} +(4289.05 - 1149.25i) q^{92} +(2126.59 + 7936.55i) q^{93} +(-455.124 + 1698.55i) q^{94} +(1100.14 - 635.166i) q^{95} +(-1103.82 - 295.768i) q^{96} +(999.805 - 999.805i) q^{97} +(-258.587 + 69.2881i) q^{98} +(1240.10 - 715.970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9}+O(q^{10}) \) 28 * q - 28 * q^2 + 42 * q^5 - 40 * q^6 + 48 * q^7 - 448 * q^8 + 556 * q^9	\( 28 q - 28 q^{2} + 42 q^{5} - 40 q^{6} + 48 q^{7} - 448 q^{8} + 556 q^{9} - 72 q^{10} + 80 q^{12} + 248 q^{13} - 192 q^{14} - 852 q^{15} + 896 q^{16} + 1092 q^{17} + 1112 q^{18} - 320 q^{19} + 336 q^{20} - 858 q^{21} - 112 q^{22} + 2348 q^{23} + 160 q^{24} - 162 q^{25} - 184 q^{26} + 1584 q^{28} - 1308 q^{29} + 2652 q^{30} - 3444 q^{31} + 1792 q^{32} + 1052 q^{33} + 1428 q^{34} - 580 q^{35} - 5694 q^{37} - 824 q^{38} - 6514 q^{39} - 1056 q^{40} - 12186 q^{41} - 1276 q^{42} - 6220 q^{43} + 1280 q^{44} + 12804 q^{45} - 4696 q^{46} + 15928 q^{47} - 4892 q^{49} - 10792 q^{50} - 6218 q^{51} + 1984 q^{52} - 9662 q^{53} - 9836 q^{54} + 1744 q^{55} - 3936 q^{56} + 16046 q^{57} + 13800 q^{58} - 9356 q^{59} - 3024 q^{60} - 6682 q^{61} + 16128 q^{62} + 60268 q^{63} - 28086 q^{65} - 4208 q^{66} + 28086 q^{67} - 5712 q^{68} + 19878 q^{69} - 6028 q^{70} + 680 q^{71} - 8896 q^{72} - 2420 q^{74} + 11076 q^{75} - 2560 q^{76} - 32208 q^{77} + 23436 q^{78} - 15136 q^{79} + 1152 q^{80} - 21274 q^{81} - 2608 q^{82} - 19732 q^{83} + 23936 q^{84} + 12440 q^{86} - 31624 q^{87} - 5120 q^{88} + 45940 q^{89} - 25608 q^{90} - 13106 q^{91} - 6944 q^{92} - 37734 q^{93} - 16960 q^{94} - 37458 q^{95} - 1280 q^{96} + 31792 q^{97} + 5216 q^{98} + 141456 q^{99}+O(q^{100}) \) 28 * q - 28 * q^2 + 42 * q^5 - 40 * q^6 + 48 * q^7 - 448 * q^8 + 556 * q^9 - 72 * q^10 + 80 * q^12 + 248 * q^13 - 192 * q^14 - 852 * q^15 + 896 * q^16 + 1092 * q^17 + 1112 * q^18 - 320 * q^19 + 336 * q^20 - 858 * q^21 - 112 * q^22 + 2348 * q^23 + 160 * q^24 - 162 * q^25 - 184 * q^26 + 1584 * q^28 - 1308 * q^29 + 2652 * q^30 - 3444 * q^31 + 1792 * q^32 + 1052 * q^33 + 1428 * q^34 - 580 * q^35 - 5694 * q^37 - 824 * q^38 - 6514 * q^39 - 1056 * q^40 - 12186 * q^41 - 1276 * q^42 - 6220 * q^43 + 1280 * q^44 + 12804 * q^45 - 4696 * q^46 + 15928 * q^47 - 4892 * q^49 - 10792 * q^50 - 6218 * q^51 + 1984 * q^52 - 9662 * q^53 - 9836 * q^54 + 1744 * q^55 - 3936 * q^56 + 16046 * q^57 + 13800 * q^58 - 9356 * q^59 - 3024 * q^60 - 6682 * q^61 + 16128 * q^62 + 60268 * q^63 - 28086 * q^65 - 4208 * q^66 + 28086 * q^67 - 5712 * q^68 + 19878 * q^69 - 6028 * q^70 + 680 * q^71 - 8896 * q^72 - 2420 * q^74 + 11076 * q^75 - 2560 * q^76 - 32208 * q^77 + 23436 * q^78 - 15136 * q^79 + 1152 * q^80 - 21274 * q^81 - 2608 * q^82 - 19732 * q^83 + 23936 * q^84 + 12440 * q^86 - 31624 * q^87 - 5120 * q^88 + 45940 * q^89 - 25608 * q^90 - 13106 * q^91 - 6944 * q^92 - 37734 * q^93 - 16960 * q^94 - 37458 * q^95 - 1280 * q^96 + 31792 * q^97 + 5216 * q^98 + 141456 * q^99

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