LMFDB - Embedded newform 20.4.e.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,4,Mod(3,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("20.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	20.e (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:	$1.18003820011$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 44x^{8} - 156x^{6} + 704x^{4} - 1792x^{2} + 4096 $ x^12 - 7x^10 + 44x^8 - 156x^6 + 704x^4 - 1792*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$-1.13579 + 1.64620i$ of defining polynomial
Character	$\chi$	$=$	20.7
Dual form			20.4.e.b.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.78199 - 0.510409i) q^{2} +(4.02923 + 4.02923i) q^{3} +(7.47897 + 2.83991i) q^{4} +(10.9349 - 2.32970i) q^{5} +(-9.15273 - 13.2658i) q^{6} +(-14.4440 + 14.4440i) q^{7} +(-19.3569 - 11.7179i) q^{8} +5.46937i q^{9} +O(q^{10})$	\(q+(-2.78199 - 0.510409i) q^{2} +(4.02923 + 4.02923i) q^{3} +(7.47897 + 2.83991i) q^{4} +(10.9349 - 2.32970i) q^{5} +(-9.15273 - 13.2658i) q^{6} +(-14.4440 + 14.4440i) q^{7} +(-19.3569 - 11.7179i) q^{8} +5.46937i q^{9} +(-31.6100 + 0.899920i) q^{10} -47.0607i q^{11} +(18.6918 + 41.5771i) q^{12} +(-8.79525 + 8.79525i) q^{13} +(47.5554 - 32.8107i) q^{14} +(53.4462 + 34.6724i) q^{15} +(47.8698 + 42.4791i) q^{16} +(-26.4898 - 26.4898i) q^{17} +(2.79162 - 15.2157i) q^{18} -49.8054 q^{19} +(88.3980 + 13.6304i) q^{20} -116.396 q^{21} +(-24.0202 + 130.922i) q^{22} +(-41.2762 - 41.2762i) q^{23} +(-30.7792 - 125.208i) q^{24} +(114.145 - 50.9501i) q^{25} +(28.9575 - 19.9791i) q^{26} +(86.7518 - 86.7518i) q^{27} +(-149.046 + 67.0065i) q^{28} +247.406i q^{29} +(-130.990 - 123.738i) q^{30} +62.3240i q^{31} +(-111.492 - 142.610i) q^{32} +(189.618 - 189.618i) q^{33} +(60.1738 + 87.2150i) q^{34} +(-124.294 + 191.594i) q^{35} +(-15.5325 + 40.9052i) q^{36} +(-73.2182 - 73.2182i) q^{37} +(138.558 + 25.4211i) q^{38} -70.8761 q^{39} +(-238.966 - 83.0389i) q^{40} +118.624 q^{41} +(323.814 + 59.4097i) q^{42} +(245.335 + 245.335i) q^{43} +(133.648 - 351.965i) q^{44} +(12.7420 + 59.8071i) q^{45} +(93.7624 + 135.898i) q^{46} +(125.525 - 125.525i) q^{47} +(21.7203 + 364.037i) q^{48} -74.2578i q^{49} +(-343.556 + 83.4822i) q^{50} -213.467i q^{51} +(-90.7571 + 40.8017i) q^{52} +(-326.574 + 326.574i) q^{53} +(-285.622 + 197.064i) q^{54} +(-109.637 - 514.605i) q^{55} +(448.845 - 110.337i) q^{56} +(-200.677 - 200.677i) q^{57} +(126.278 - 688.282i) q^{58} -365.123 q^{59} +(301.256 + 411.096i) q^{60} -268.160 q^{61} +(31.8107 - 173.385i) q^{62} +(-78.9995 - 78.9995i) q^{63} +(237.380 + 453.646i) q^{64} +(-75.6851 + 116.666i) q^{65} +(-624.299 + 430.733i) q^{66} +(-112.617 + 112.617i) q^{67} +(-122.888 - 273.345i) q^{68} -332.623i q^{69} +(443.576 - 469.573i) q^{70} +559.873i q^{71} +(64.0897 - 105.870i) q^{72} +(215.825 - 215.825i) q^{73} +(166.321 + 241.064i) q^{74} +(665.206 + 254.627i) q^{75} +(-372.493 - 141.443i) q^{76} +(679.744 + 679.744i) q^{77} +(197.177 + 36.1758i) q^{78} +1172.36 q^{79} +(622.417 + 352.984i) q^{80} +846.759 q^{81} +(-330.012 - 60.5470i) q^{82} +(-592.561 - 592.561i) q^{83} +(-870.524 - 330.555i) q^{84} +(-351.377 - 227.951i) q^{85} +(-557.299 - 807.742i) q^{86} +(-996.857 + 996.857i) q^{87} +(-551.454 + 910.949i) q^{88} -552.071i q^{89} +(-4.92200 - 172.887i) q^{90} -254.077i q^{91} +(-191.483 - 425.924i) q^{92} +(-251.118 + 251.118i) q^{93} +(-413.277 + 285.139i) q^{94} +(-544.618 + 116.032i) q^{95} +(125.382 - 1023.83i) q^{96} +(460.651 + 460.651i) q^{97} +(-37.9019 + 206.585i) q^{98} +257.392 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 8 q^{6} - 12 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 + 8 * q^6 - 12 * q^8	$ 12 q - 6 q^{2} + 8 q^{6} - 12 q^{8} - 110 q^{10} - 80 q^{12} + 116 q^{13} + 312 q^{16} - 332 q^{17} + 198 q^{18} + 140 q^{20} - 144 q^{21} + 360 q^{22} + 340 q^{25} - 164 q^{26} - 880 q^{28} - 1240 q^{30} - 376 q^{32} + 80 q^{33} + 460 q^{36} + 508 q^{37} + 1600 q^{38} + 1420 q^{40} - 656 q^{41} + 1160 q^{42} + 1180 q^{45} - 1432 q^{46} - 2720 q^{48} - 1570 q^{50} - 932 q^{52} - 644 q^{53} + 2048 q^{56} - 960 q^{57} + 1576 q^{58} + 3280 q^{60} - 896 q^{61} + 2440 q^{62} - 2740 q^{65} - 1680 q^{66} - 844 q^{68} - 3040 q^{70} - 3036 q^{72} + 1436 q^{73} + 800 q^{76} + 3120 q^{77} + 3720 q^{78} + 1840 q^{80} + 5988 q^{81} - 1352 q^{82} + 500 q^{85} - 2552 q^{86} - 2400 q^{88} - 750 q^{90} - 1840 q^{92} - 3280 q^{93} + 1088 q^{96} - 4772 q^{97} + 1698 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 + 8 * q^6 - 12 * q^8 - 110 * q^10 - 80 * q^12 + 116 * q^13 + 312 * q^16 - 332 * q^17 + 198 * q^18 + 140 * q^20 - 144 * q^21 + 360 * q^22 + 340 * q^25 - 164 * q^26 - 880 * q^28 - 1240 * q^30 - 376 * q^32 + 80 * q^33 + 460 * q^36 + 508 * q^37 + 1600 * q^38 + 1420 * q^40 - 656 * q^41 + 1160 * q^42 + 1180 * q^45 - 1432 * q^46 - 2720 * q^48 - 1570 * q^50 - 932 * q^52 - 644 * q^53 + 2048 * q^56 - 960 * q^57 + 1576 * q^58 + 3280 * q^60 - 896 * q^61 + 2440 * q^62 - 2740 * q^65 - 1680 * q^66 - 844 * q^68 - 3040 * q^70 - 3036 * q^72 + 1436 * q^73 + 800 * q^76 + 3120 * q^77 + 3720 * q^78 + 1840 * q^80 + 5988 * q^81 - 1352 * q^82 + 500 * q^85 - 2552 * q^86 - 2400 * q^88 - 750 * q^90 - 1840 * q^92 - 3280 * q^93 + 1088 * q^96 - 4772 * q^97 + 1698 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−2.78199	−	0.510409i	−0.983583	−	0.180457i
$2$	−2.78199	−	0.510409i	−0.983583	−	0.180457i
$3$	4.02923	+	4.02923i	0.775425	+	0.775425i	0.979049	−	0.203624i	$-0.0652719\pi$
$3$	4.02923	+	4.02923i	0.775425	+	0.775425i	−0.203624	+	0.979049i	$0.565272\pi$
$4$	7.47897	+	2.83991i	0.934871	+	0.354989i
$5$	10.9349	−	2.32970i	0.978049	−	0.208375i
$5$	10.9349	−	2.32970i	0.978049	−	0.208375i
$6$	−9.15273	−	13.2658i	−0.622764	−	0.902626i
$7$	−14.4440	+	14.4440i	−0.779902	+	0.779902i	−0.979814	−	0.199912i	$-0.935934\pi$
$7$	−14.4440	+	14.4440i	−0.779902	+	0.779902i	0.199912	+	0.979814i	$0.435934\pi$
$8$	−19.3569	−	11.7179i	−0.855463	−	0.517864i
$9$			5.46937i			0.202569i
$10$	−31.6100	+	0.899920i	−0.999595	+	0.0284580i
$11$		−	47.0607i		−	1.28994i	−0.764209	−	0.644969i	$-0.776870\pi$
$11$		−	47.0607i		−	1.28994i	0.764209	−	0.644969i	$-0.223130\pi$
$12$	18.6918	+	41.5771i	0.449655	+	1.00019i
$13$	−8.79525	+	8.79525i	−0.187643	+	0.187643i	−0.794676	−	0.607033i	$-0.792360\pi$
$13$	−8.79525	+	8.79525i	−0.187643	+	0.187643i	0.607033	+	0.794676i	$0.292360\pi$
$14$	47.5554	−	32.8107i	0.907837	−	0.626360i
$15$	53.4462	+	34.6724i	0.919983	+	0.596825i
$16$	47.8698	+	42.4791i	0.747966	+	0.663737i
$17$	−26.4898	−	26.4898i	−0.377925	−	0.377925i	0.492428	−	0.870353i	$-0.336109\pi$
$17$	−26.4898	−	26.4898i	−0.377925	−	0.377925i	−0.870353	+	0.492428i	$0.836109\pi$
$18$	2.79162	−	15.2157i	0.0365550	−	0.199244i
$19$	−49.8054			−0.601376			−0.300688	−	0.953723i	$-0.597216\pi$
$19$	−49.8054			−0.601376			−0.300688	+	0.953723i	$0.597216\pi$
$20$	88.3980	+	13.6304i	0.988320	+	0.152393i
$21$	−116.396			−1.20951
$22$	−24.0202	+	130.922i	−0.232778	+	1.26876i
$23$	−41.2762	−	41.2762i	−0.374204	−	0.374204i	0.494802	−	0.869006i	$-0.335241\pi$
$23$	−41.2762	−	41.2762i	−0.374204	−	0.374204i	−0.869006	+	0.494802i	$0.835241\pi$
$24$	−30.7792	−	125.208i	−0.261782	−	1.06491i
$25$	114.145	−	50.9501i	0.913160	−	0.407601i
$26$	28.9575	−	19.9791i	0.218424	−	0.150701i
$27$	86.7518	−	86.7518i	0.618348	−	0.618348i
$28$	−149.046	+	67.0065i	−1.00596	+	0.452251i
$29$			247.406i			1.58421i	0.610382	+	0.792107i	$0.291016\pi$
$29$			247.406i			1.58421i	−0.610382	+	0.792107i	$0.708984\pi$
$30$	−130.990	−	123.738i	−0.797178	−	0.753044i
$31$			62.3240i			0.361088i	0.983567	+	0.180544i	$0.0577858\pi$
$31$			62.3240i			0.361088i	−0.983567	+	0.180544i	$0.942214\pi$
$32$	−111.492	−	142.610i	−0.615911	−	0.787816i
$33$	189.618	−	189.618i	1.00025	−	1.00025i
$34$	60.1738	+	87.2150i	0.303521	+	0.439919i
$35$	−124.294	+	191.594i	−0.600271	+	0.925294i
$36$	−15.5325	+	40.9052i	−0.0719098	+	0.189376i
$37$	−73.2182	−	73.2182i	−0.325324	−	0.325324i	0.525481	−	0.850805i	$-0.323885\pi$
$37$	−73.2182	−	73.2182i	−0.325324	−	0.325324i	−0.850805	+	0.525481i	$0.823885\pi$
$38$	138.558	+	25.4211i	0.591503	+	0.108522i
$39$	−70.8761			−0.291007
$40$	−238.966	−	83.0389i	−0.944594	−	0.328240i
$41$	118.624			0.451854			0.225927	−	0.974144i	$-0.427459\pi$
$41$	118.624			0.451854			0.225927	+	0.974144i	$0.427459\pi$
$42$	323.814	+	59.4097i	1.18966	+	0.218265i
$43$	245.335	+	245.335i	0.870076	+	0.870076i	0.992480	−	0.122404i	$-0.0390605\pi$
$43$	245.335	+	245.335i	0.870076	+	0.870076i	−0.122404	+	0.992480i	$0.539060\pi$
$44$	133.648	−	351.965i	0.457913	−	1.20593i
$45$	12.7420	+	59.8071i	0.0422103	+	0.198123i
$46$	93.7624	+	135.898i	0.300533	+	0.435588i
$47$	125.525	−	125.525i	0.389567	−	0.389567i	−0.484966	−	0.874533i	$-0.661168\pi$
$47$	125.525	−	125.525i	0.389567	−	0.389567i	0.874533	+	0.484966i	$0.161168\pi$
$48$	21.7203	+	364.037i	0.0653138	+	1.09467i
$49$		−	74.2578i		−	0.216495i
$50$	−343.556	+	83.4822i	−0.971723	+	0.236123i
$51$		−	213.467i		−	0.586105i
$52$	−90.7571	+	40.8017i	−0.242033	+	0.108811i
$53$	−326.574	+	326.574i	−0.846385	+	0.846385i	−0.989680	−	0.143295i	$-0.954230\pi$
$53$	−326.574	+	326.574i	−0.846385	+	0.846385i	0.143295	+	0.989680i	$0.454230\pi$
$54$	−285.622	+	197.064i	−0.719782	+	0.496611i
$55$	−109.637	−	514.605i	−0.268790	−	1.26162i
$56$	448.845	−	110.337i	1.07106	−	0.263294i
$57$	−200.677	−	200.677i	−0.466322	−	0.466322i
$58$	126.278	−	688.282i	0.285882	−	1.55821i
$59$	−365.123			−0.805677			−0.402839	−	0.915271i	$-0.631976\pi$
$59$	−365.123			−0.805677			−0.402839	+	0.915271i	$0.631976\pi$
$60$	301.256	+	411.096i	0.648199	+	0.884538i
$61$	−268.160			−0.562858			−0.281429	−	0.959582i	$-0.590808\pi$
$61$	−268.160			−0.562858			−0.281429	+	0.959582i	$0.590808\pi$
$62$	31.8107	−	173.385i	0.0651608	−	0.355160i
$63$	−78.9995	−	78.9995i	−0.157984	−	0.157984i
$64$	237.380	+	453.646i	0.463633	+	0.886027i
$65$	−75.6851	+	116.666i	−0.144424	+	0.222624i
$66$	−624.299	+	430.733i	−1.16433	+	0.803328i
$67$	−112.617	+	112.617i	−0.205349	+	0.205349i	−0.802287	−	0.596938i	$-0.796384\pi$
$67$	−112.617	+	112.617i	−0.205349	+	0.205349i	0.596938	+	0.802287i	$0.296384\pi$
$68$	−122.888	−	273.345i	−0.219152	−	0.487469i
$69$		−	332.623i		−	0.580334i
$70$	443.576	−	469.573i	0.757392	−	0.801781i
$71$			559.873i			0.935841i	0.883771	+	0.467921i	$0.154997\pi$
$71$			559.873i			0.935841i	−0.883771	+	0.467921i	$0.845003\pi$
$72$	64.0897	−	105.870i	0.104903	−	0.173290i
$73$	215.825	−	215.825i	0.346033	−	0.346033i	−0.512597	−	0.858629i	$-0.671316\pi$
$73$	215.825	−	215.825i	0.346033	−	0.346033i	0.858629	+	0.512597i	$0.171316\pi$
$74$	166.321	+	241.064i	0.261276	+	0.378690i
$75$	665.206	+	254.627i	1.02415	+	0.392023i
$76$	−372.493	−	141.443i	−0.562209	−	0.213482i
$77$	679.744	+	679.744i	1.00603	+	1.00603i
$78$	197.177	+	36.1758i	0.286229	+	0.0525142i
$79$	1172.36			1.66963			0.834816	−	0.550528i	$-0.185574\pi$
$79$	1172.36			1.66963			0.834816	+	0.550528i	$0.185574\pi$
$80$	622.417	+	352.984i	0.869854	+	0.493310i
$81$	846.759			1.16153
$82$	−330.012	−	60.5470i	−0.444436	−	0.0815402i
$83$	−592.561	−	592.561i	−0.783639	−	0.783639i	0.196804	−	0.980443i	$-0.436944\pi$
$83$	−592.561	−	592.561i	−0.783639	−	0.783639i	−0.980443	+	0.196804i	$0.936944\pi$
$84$	−870.524	−	330.555i	−1.13074	−	0.429363i
$85$	−351.377	−	227.951i	−0.448379	−	0.290879i
$86$	−557.299	−	807.742i	−0.698781	−	1.01280i
$87$	−996.857	+	996.857i	−1.22844	+	1.22844i
$88$	−551.454	+	910.949i	−0.668013	+	1.10349i
$89$		−	552.071i		−	0.657522i	−0.944413	−	0.328761i	$-0.893369\pi$
$89$		−	552.071i		−	0.657522i	0.944413	−	0.328761i	$-0.106631\pi$
$90$	−4.92200	−	172.887i	−0.00576471	−	0.202487i
$91$		−	254.077i		−	0.292687i
$92$	−191.483	−	425.924i	−0.216994	−	0.482670i
$93$	−251.118	+	251.118i	−0.279997	+	0.279997i
$94$	−413.277	+	285.139i	−0.453471	+	0.312871i
$95$	−544.618	+	116.032i	−0.588175	+	0.125311i
$96$	125.382	−	1023.83i	0.133299	−	1.08849i
$97$	460.651	+	460.651i	0.482186	+	0.482186i	0.905829	−	0.423643i	$-0.139249\pi$
$97$	460.651	+	460.651i	0.482186	+	0.482186i	−0.423643	+	0.905829i	$0.639249\pi$
$98$	−37.9019	+	206.585i	−0.0390680	+	0.212941i
$99$	257.392			0.261302
$100$	998.380	−	56.8929i	0.998380	−	0.0568929i
$101$	−5.97644			−0.00588790			−0.00294395	−	0.999996i	$-0.500937\pi$
$101$	−5.97644			−0.00588790			−0.00294395	+	0.999996i	$0.500937\pi$
$102$	−108.955	+	593.863i	−0.105767	+	0.576483i
$103$	−137.824	−	137.824i	−0.131847	−	0.131847i	0.638104	−	0.769951i	$-0.279719\pi$
$103$	−137.824	−	137.824i	−0.131847	−	0.131847i	−0.769951	+	0.638104i	$0.779719\pi$
$104$	273.311	−	67.1867i	0.257696	−	0.0633481i
$105$	−1272.78	+	271.168i	−1.18296	+	0.252032i
$106$	1075.21	−	741.840i	0.985225	−	0.679754i
$107$	723.943	−	723.943i	0.654077	−	0.654077i	−0.299895	−	0.953972i	$-0.596952\pi$
$107$	723.943	−	723.943i	0.654077	−	0.654077i	0.953972	+	0.299895i	$0.0969518\pi$
$108$	895.181	−	402.447i	0.797582	−	0.358569i
$109$		−	896.758i		−	0.788017i	−0.919107	−	0.394009i	$-0.871088\pi$
$109$		−	896.758i		−	0.788017i	0.919107	−	0.394009i	$-0.128912\pi$
$110$	42.3508	+	1487.59i	0.0367090	+	1.28942i
$111$		−	590.026i		−	0.504530i
$112$	−1305.00	+	77.8631i	−1.10099	+	0.0656908i
$113$	−525.727	+	525.727i	−0.437665	+	0.437665i	−0.891226	−	0.453560i	$-0.850154\pi$
$113$	−525.727	+	525.727i	−0.437665	+	0.437665i	0.453560	+	0.891226i	$0.350154\pi$
$114$	455.855	+	660.710i	0.374515	+	0.542817i
$115$	−547.513	−	355.191i	−0.443964	−	0.288015i
$116$	−702.611	+	1850.34i	−0.562378	+	1.48103i
$117$	−48.1045	−	48.1045i	−0.0380108	−	0.0380108i
$118$	1015.77	+	186.362i	0.792450	+	0.145390i
$119$	765.237			0.589488
$120$	−628.264	−	1297.43i	−0.477937	−	0.986988i
$121$	−883.705			−0.663941
$122$	746.019	+	136.871i	0.553618	+	0.101572i
$123$	477.965	+	477.965i	0.350379	+	0.350379i
$124$	−176.995	+	466.119i	−0.128182	+	0.337571i
$125$	1129.47	−	823.059i	0.808182	−	0.588933i
$126$	179.454	+	260.098i	0.126881	+	0.183900i
$127$	−75.4237	+	75.4237i	−0.0526990	+	0.0526990i	−0.732965	−	0.680266i	$-0.761864\pi$
$127$	−75.4237	+	75.4237i	−0.0526990	+	0.0526990i	0.680266	+	0.732965i	$0.261864\pi$
$128$	−428.844	−	1383.20i	−0.296132	−	0.955147i
$129$			1977.02i			1.34936i
$130$	270.103	−	285.933i	0.182227	−	0.192907i
$131$			1374.47i			0.916701i	0.888771	+	0.458351i	$0.151560\pi$
$131$			1374.47i			0.916701i	−0.888771	+	0.458351i	$0.848440\pi$
$132$	1956.65	−	879.649i	1.29018	−	0.580028i
$133$	719.389	−	719.389i	0.469014	−	0.469014i
$134$	370.782	−	255.820i	0.239035	−	0.164922i
$135$	746.519	−	1150.73i	0.475927	−	0.733623i
$136$	202.355	+	823.166i	0.127587	+	0.519014i
$137$	−2002.37	−	2002.37i	−1.24871	−	1.24871i	−0.956289	−	0.292424i	$-0.905538\pi$
$137$	−2002.37	−	2002.37i	−1.24871	−	1.24871i	−0.292424	−	0.956289i	$-0.594462\pi$
$138$	−169.774	+	925.354i	−0.104725	+	0.570807i
$139$	−2575.00			−1.57129			−0.785643	−	0.618679i	$-0.787668\pi$
$139$	−2575.00			−1.57129			−0.785643	+	0.618679i	$0.787668\pi$
$140$	−1473.70	+	1079.94i	−0.889645	+	0.651941i
$141$	1011.53			0.604160
$142$	285.764	−	1557.56i	0.168879	−	0.920477i
$143$	413.910	+	413.910i	0.242048	+	0.242048i
$144$	−232.334	+	261.818i	−0.134453	+	0.151515i
$145$	576.382	+	2705.37i	0.330110	+	1.54944i
$146$	−710.582	+	490.264i	−0.402796	+	0.277908i
$147$	299.202	−	299.202i	0.167876	−	0.167876i
$148$	−339.663	−	755.529i	−0.188650	−	0.419623i
$149$		−	1322.91i		−	0.727364i	−0.931523	−	0.363682i	$-0.881519\pi$
$149$		−	1322.91i		−	0.727364i	0.931523	−	0.363682i	$-0.118481\pi$
$150$	−1720.63	−	1047.90i	−0.936595	−	0.570403i
$151$			57.2419i			0.0308495i	0.999881	+	0.0154248i	$0.00491005\pi$
$151$			57.2419i			0.0308495i	−0.999881	+	0.0154248i	$0.995090\pi$
$152$	964.079	+	583.616i	0.514455	+	0.311431i
$153$	144.882	−	144.882i	0.0765559	−	0.0765559i
$154$	−1544.09	−	2237.99i	−0.807966	−	1.17105i
$155$	145.196	+	681.508i	0.0752415	+	0.353162i
$156$	−530.080	−	201.282i	−0.272054	−	0.103304i
$157$	1622.22	+	1622.22i	0.824634	+	0.824634i	0.986769	−	0.162134i	$-0.0518378\pi$
$157$	1622.22	+	1622.22i	0.824634	+	0.824634i	−0.162134	+	0.986769i	$0.551838\pi$
$158$	−3261.50	−	598.384i	−1.64222	−	0.301297i
$159$	−2631.68			−1.31262
$160$	−1551.39	−	1299.69i	−0.766552	−	0.642182i
$161$	1192.39			0.583685
$162$	−2355.68	−	432.193i	−1.14247	−	0.209607i
$163$	1696.16	+	1696.16i	0.815052	+	0.815052i	0.985386	−	0.170334i	$-0.0544847\pi$
$163$	1696.16	+	1696.16i	0.815052	+	0.815052i	−0.170334	+	0.985386i	$0.554485\pi$
$164$	887.188	+	336.882i	0.422425	+	0.160403i
$165$	1631.71	−	2515.21i	0.769868	−	1.18672i
$166$	1346.05	+	1950.95i	0.629361	+	0.912187i
$167$	2015.29	−	2015.29i	0.933819	−	0.933819i	−0.0641235	−	0.997942i	$-0.520425\pi$
$167$	2015.29	−	2015.29i	0.933819	−	0.933819i	0.997942	+	0.0641235i	$0.0204251\pi$
$168$	2253.07	+	1363.92i	1.03469	+	0.626363i
$169$			2042.29i			0.929580i
$170$	861.180	+	813.503i	0.388526	+	0.367017i
$171$		−	272.404i		−	0.121820i
$172$	1138.12	+	2531.58i	0.504542	+	1.12228i
$173$	317.896	−	317.896i	0.139706	−	0.139706i	−0.633795	−	0.773501i	$-0.718504\pi$
$173$	317.896	−	317.896i	0.139706	−	0.139706i	0.773501	+	0.633795i	$0.218504\pi$
$174$	3282.05	−	2264.44i	1.42995	−	0.986592i
$175$	−912.786	+	2384.63i	−0.394287	+	1.03006i
$176$	1999.10	−	2252.79i	0.856179	−	0.964830i
$177$	−1471.16	−	1471.16i	−0.624743	−	0.624743i
$178$	−281.782	+	1535.86i	−0.118654	+	0.646727i
$179$	3518.04			1.46900			0.734499	−	0.678610i	$-0.237417\pi$
$179$	3518.04			1.46900			0.734499	+	0.678610i	$0.237417\pi$
$180$	−74.5499	+	483.481i	−0.0308701	+	0.200203i
$181$	−4769.86			−1.95879			−0.979395	−	0.201955i	$-0.935271\pi$
$181$	−4769.86			−1.95879			−0.979395	+	0.201955i	$0.935271\pi$
$182$	−129.683	+	706.840i	−0.0528174	+	0.287882i
$183$	−1080.48	−	1080.48i	−0.436455	−	0.436455i
$184$	315.308	+	1282.65i	0.126331	+	0.513904i
$185$	−971.212	−	630.059i	−0.385972	−	0.250394i
$186$	826.781	−	570.435i	0.325927	−	0.224873i
$187$	−1246.63	+	1246.63i	−0.487499	+	0.487499i
$188$	1295.27	−	582.316i	0.502486	−	0.225903i
$189$			2506.09i			0.964502i
$190$	1574.35	−	44.8209i	0.601132	−	0.0171139i
$191$		−	1728.42i		−	0.654787i	−0.944888	−	0.327393i	$-0.893830\pi$
$191$		−	1728.42i		−	0.654787i	0.944888	−	0.327393i	$-0.106170\pi$
$192$	−871.385	+	2784.30i	−0.327536	+	1.04656i
$193$	1439.32	−	1439.32i	0.536813	−	0.536813i	−0.385779	−	0.922591i	$-0.626067\pi$
$193$	1439.32	−	1439.32i	0.536813	−	0.536813i	0.922591	+	0.385779i	$0.126067\pi$
$194$	−1046.41	−	1516.65i	−0.387256	−	0.561283i
$195$	−775.025	+	165.120i	−0.284619	+	0.0606384i
$196$	210.885	−	555.372i	0.0768533	−	0.202395i
$197$	−658.673	−	658.673i	−0.238216	−	0.238216i	0.577895	−	0.816111i	$-0.303874\pi$
$197$	−658.673	−	658.673i	−0.238216	−	0.238216i	−0.816111	+	0.577895i	$0.803874\pi$
$198$	−716.063	−	131.375i	−0.257012	−	0.0471537i
$199$	−658.733			−0.234655			−0.117327	−	0.993093i	$-0.537433\pi$
$199$	−658.733			−0.234655			−0.117327	+	0.993093i	$0.537433\pi$
$200$	−2806.53	−	351.307i	−0.992256	−	0.124206i
$201$	−907.523			−0.318466
$202$	16.6264	+	3.05043i	0.00579124	+	0.00106251i
$203$	−3573.53	−	3573.53i	−1.23553	−	1.23553i
$204$	606.226	−	1596.51i	0.208060	−	0.547932i
$205$	1297.15	−	276.359i	0.441935	−	0.0941549i
$206$	313.080	+	453.773i	0.105890	+	0.153475i
$207$	225.755	−	225.755i	0.0758022	−	0.0758022i
$208$	−794.642	+	47.4125i	−0.264897	+	0.0158051i
$209$			2343.87i			0.775738i
$210$	3679.28	−	104.747i	1.20902	−	0.0344203i
$211$		−	5821.53i		−	1.89939i	−0.313182	−	0.949693i	$-0.601395\pi$
$211$		−	5821.53i		−	1.89939i	0.313182	−	0.949693i	$-0.398605\pi$
$212$	−3369.88	+	1515.00i	−1.09172	+	0.490803i
$213$	−2255.86	+	2255.86i	−0.725675	+	0.725675i
$214$	−2383.51	+	1644.50i	−0.761371	+	0.525306i
$215$	3254.28	+	2111.16i	1.03228	+	0.669675i
$216$	−2695.80	+	662.695i	−0.849194	+	0.208753i
$217$	−900.208	−	900.208i	−0.281613	−	0.281613i
$218$	−457.714	+	2494.77i	−0.142203	+	0.775080i
$219$	1739.22			0.536645
$220$	641.457	−	4160.07i	0.196578	−	1.27487i
$221$	465.969			0.141830
$222$	−301.155	+	1641.45i	−0.0910458	+	0.496247i
$223$	2315.57	+	2315.57i	0.695347	+	0.695347i	0.963403	−	0.268056i	$-0.0863814\pi$
$223$	2315.57	+	2315.57i	0.695347	+	0.695347i	−0.268056	+	0.963403i	$0.586381\pi$
$224$	3670.24	+	449.469i	1.09477	+	0.134069i
$225$	278.665	+	624.301i	0.0825674	+	0.184978i
$226$	1730.90	−	1194.23i	0.509460	−	0.351501i
$227$	−2970.19	+	2970.19i	−0.868450	+	0.868450i	−0.992301	−	0.123851i	$-0.960476\pi$
$227$	−2970.19	+	2970.19i	−0.868450	+	0.868450i	0.123851	+	0.992301i	$0.460476\pi$
$228$	−930.954	−	2070.76i	−0.270412	−	0.601490i
$229$		−	4981.25i		−	1.43742i	−0.695308	−	0.718712i	$-0.744732\pi$
$229$		−	4981.25i		−	1.43742i	0.695308	−	0.718712i	$-0.255268\pi$
$230$	1341.89	+	1267.59i	0.384701	+	0.363403i
$231$			5477.69i			1.56020i
$232$	2899.09	−	4789.02i	0.820408	−	1.35524i
$233$	1649.04	−	1649.04i	0.463659	−	0.463659i	−0.436194	−	0.899853i	$-0.643674\pi$
$233$	1649.04	−	1649.04i	0.463659	−	0.463659i	0.899853	+	0.436194i	$0.143674\pi$
$234$	109.273	+	158.379i	0.0305274	+	0.0442460i
$235$	1080.17	−	1665.04i	0.299840	−	0.462191i
$236$	−2730.74	−	1036.92i	−0.753204	−	0.286006i
$237$	4723.71	+	4723.71i	1.29468	+	1.29468i
$238$	−2128.88	−	390.584i	−0.579811	−	0.106377i
$239$	−3574.98			−0.967558			−0.483779	−	0.875190i	$-0.660736\pi$
$239$	−3574.98			−0.967558			−0.483779	+	0.875190i	$0.660736\pi$
$240$	1085.61	+	3930.11i	0.291982	+	1.05703i
$241$	5135.22			1.37257			0.686283	−	0.727334i	$-0.259241\pi$
$241$	5135.22			1.37257			0.686283	+	0.727334i	$0.259241\pi$
$242$	2458.46	+	451.051i	0.653041	+	0.119813i
$243$	1069.49	+	1069.49i	0.282336	+	0.282336i
$244$	−2005.56	−	761.549i	−0.526200	−	0.199808i
$245$	−172.998	−	812.003i	−0.0451121	−	0.211743i
$246$	−1085.74	−	1573.65i	−0.281399	−	0.407855i
$247$	438.051	−	438.051i	0.112844	−	0.112844i
$248$	730.309	−	1206.40i	0.186995	−	0.308897i
$249$		−	4775.13i		−	1.21531i
$250$	−3562.27	+	1713.25i	−0.901191	+	0.433423i
$251$			6648.06i			1.67180i	0.548882	+	0.835900i	$0.315054\pi$
$251$			6648.06i			1.67180i	−0.548882	+	0.835900i	$0.684946\pi$
$252$	−366.483	−	815.186i	−0.0916122	−	0.203777i
$253$	−1942.49	+	1942.49i	−0.482700	+	0.482700i
$254$	248.325	−	171.331i	0.0613437	−	0.0423239i
$255$	−497.313	−	2334.24i	−0.122129	−	0.573239i
$256$	487.044	+	4066.94i	0.118907	+	0.992905i
$257$	−448.260	−	448.260i	−0.108800	−	0.108800i	0.650611	−	0.759411i	$-0.274513\pi$
$257$	−448.260	−	448.260i	−0.108800	−	0.108800i	−0.759411	+	0.650611i	$0.774513\pi$
$258$	1009.09	−	5500.06i	0.243501	−	1.32721i
$259$	2115.13			0.507442
$260$	−897.366	+	657.600i	−0.214047	+	0.156856i
$261$	−1353.16			−0.320913
$262$	701.541	−	3823.76i	0.165425	−	0.901652i
$263$	−145.529	−	145.529i	−0.0341205	−	0.0341205i	0.689841	−	0.723961i	$-0.257681\pi$
$263$	−145.529	−	145.529i	−0.0341205	−	0.0341205i	−0.723961	+	0.689841i	$0.757681\pi$
$264$	−5892.35	+	1448.49i	−1.37367	+	0.337683i
$265$	−2810.24	+	4331.88i	−0.651441	+	1.00417i
$266$	−2368.52	+	1634.15i	−0.545951	+	0.376678i
$267$	2224.42	−	2224.42i	0.509859	−	0.509859i
$268$	−1162.09	+	522.439i	−0.264872	+	0.119078i
$269$			2764.90i			0.626687i	0.949640	+	0.313344i	$0.101449\pi$
$269$			2764.90i			0.626687i	−0.949640	+	0.313344i	$0.898551\pi$
$270$	−2664.15	+	2820.29i	−0.600501	+	0.635695i
$271$		−	6372.29i		−	1.42837i	−0.699955	−	0.714187i	$-0.746797\pi$
$271$		−	6372.29i		−	1.42837i	0.699955	−	0.714187i	$-0.253203\pi$
$272$	−142.798	−	2393.33i	−0.0318324	−	0.533517i
$273$	1023.73	−	1023.73i	0.226957	−	0.226957i
$274$	4548.54	+	6592.59i	1.00287	+	1.45355i
$275$	−2397.75	−	5371.74i	−0.525780	−	1.17792i
$276$	944.618	−	2487.67i	0.206012	−	0.542538i
$277$	−387.343	−	387.343i	−0.0840187	−	0.0840187i	0.663848	−	0.747867i	$-0.268922\pi$
$277$	−387.343	−	387.343i	−0.0840187	−	0.0840187i	−0.747867	+	0.663848i	$0.768922\pi$
$278$	7163.64	+	1314.30i	1.54549	+	0.283549i
$279$	−340.873			−0.0731453
$280$	4651.03	−	2252.20i	0.992687	−	0.480696i
$281$	5284.49			1.12187			0.560936	−	0.827859i	$-0.310441\pi$
$281$	5284.49			1.12187			0.560936	+	0.827859i	$0.310441\pi$
$282$	−2814.08	−	516.296i	−0.594241	−	0.109025i
$283$	−341.577	−	341.577i	−0.0717479	−	0.0717479i	0.670322	−	0.742070i	$-0.266156\pi$
$283$	−341.577	−	341.577i	−0.0717479	−	0.0717479i	−0.742070	+	0.670322i	$0.766156\pi$
$284$	−1589.99	+	4187.27i	−0.332213	+	0.874890i
$285$	−2661.91	−	1726.87i	−0.553256	−	0.358916i
$286$	−940.232	−	1362.76i	−0.194395	−	0.281754i
$287$	−1713.41	+	1713.41i	−0.352402	+	0.352402i
$288$	779.986	−	609.790i	0.159587	−	0.124765i
$289$		−	3509.58i		−	0.714346i
$290$	−222.646	−	7820.51i	−0.0450835	−	1.58357i
$291$			3712.13i			0.747798i
$292$	2227.07	−	1001.22i	0.446333	−	0.200658i
$293$	−6655.74	+	6655.74i	−1.32707	+	1.32707i	−0.419161	+	0.907912i	$0.637676\pi$
$293$	−6655.74	+	6655.74i	−1.32707	+	1.32707i	−0.907912	+	0.419161i	$0.862324\pi$
$294$	−985.092	+	679.662i	−0.195414	+	0.134825i
$295$	−3992.59	+	850.626i	−0.787992	+	0.167883i
$296$	559.312	+	2275.24i	0.109829	+	0.446777i
$297$	−4082.60	−	4082.60i	−0.797631	−	0.797631i
$298$	−675.227	+	3680.33i	−0.131258	+	0.715423i
$299$	726.069			0.140434
$300$	4251.94	+	3793.47i	0.818286	+	0.730053i
$301$	−7087.24			−1.35715
$302$	29.2168	−	159.247i	0.00556701	−	0.0303431i
$303$	−24.0804	−	24.0804i	−0.00456563	−	0.00456563i
$304$	−2384.18	−	2115.69i	−0.449809	−	0.399155i
$305$	−2932.31	+	624.732i	−0.550503	+	0.117285i
$306$	−477.011	+	329.113i	−0.0891141	+	0.0614840i
$307$	−535.672	+	535.672i	−0.0995844	+	0.0995844i	−0.755144	−	0.655559i	$-0.772433\pi$
$307$	−535.672	+	535.672i	−0.0995844	+	0.0995844i	0.655559	+	0.755144i	$0.272433\pi$
$308$	3153.37	+	7014.19i	0.583376	+	1.29763i
$309$		−	1110.65i		−	0.204475i
$310$	−56.0867	−	1970.06i	−0.0102758	−	0.360942i
$311$		−	3579.61i		−	0.652672i	−0.945254	−	0.326336i	$-0.894186\pi$
$311$		−	3579.61i		−	0.652672i	0.945254	−	0.326336i	$-0.105814\pi$
$312$	1371.94	+	830.522i	0.248945	+	0.150702i
$313$	6740.52	−	6740.52i	1.21724	−	1.21724i	0.248648	−	0.968594i	$-0.420014\pi$
$313$	6740.52	−	6740.52i	1.21724	−	1.21724i	0.968594	−	0.248648i	$-0.0799861\pi$
$314$	−3685.02	−	5341.01i	−0.662285	−	0.959907i
$315$	−1047.90	−	679.809i	−0.187436	−	0.121596i
$316$	8768.05	+	3329.40i	1.56089	+	0.592701i
$317$	4163.19	+	4163.19i	0.737628	+	0.737628i	0.972118	−	0.234490i	$-0.0753421\pi$
$317$	4163.19	+	4163.19i	0.737628	+	0.737628i	−0.234490	+	0.972118i	$0.575342\pi$
$318$	7321.32	+	1343.23i	1.29107	+	0.236871i
$319$	11643.1			2.04354
$320$	3652.59	+	4407.56i	0.638081	+	0.769969i
$321$	5833.86			1.01438
$322$	−3317.21	−	608.605i	−0.574102	−	0.105330i
$323$	1319.33	+	1319.33i	0.227275	+	0.227275i
$324$	6332.88	+	2404.72i	1.08588	+	0.412332i
$325$	−555.815	+	1452.05i	−0.0948648	+	0.247832i
$326$	−3852.97	−	5584.44i	−0.654590	−	0.948753i
$327$	3613.24	−	3613.24i	0.611049	−	0.611049i
$328$	−2296.20	−	1390.03i	−0.386544	−	0.233999i
$329$			3626.15i			0.607648i
$330$	−5823.18	+	6164.46i	−0.971381	+	1.02831i
$331$			8821.65i			1.46490i	0.680821	+	0.732450i	$0.261623\pi$
$331$			8821.65i			1.46490i	−0.680821	+	0.732450i	$0.738377\pi$
$332$	−2748.93	−	6114.57i	−0.454418	−	1.01078i
$333$	400.457	−	400.457i	0.0659007	−	0.0659007i
$334$	−6635.14	+	4577.90i	−1.08700	+	0.749974i
$335$	−969.099	+	1493.83i	−0.158052	+	0.243631i
$336$	−5571.87	−	4944.42i	−0.904674	−	0.802798i
$337$	3165.30	+	3165.30i	0.511647	+	0.511647i	0.915031	−	0.403384i	$-0.132166\pi$
$337$	3165.30	+	3165.30i	0.511647	+	0.511647i	−0.403384	+	0.915031i	$0.632166\pi$
$338$	1042.40	−	5681.63i	0.167749	−	0.914319i
$339$	−4236.55			−0.678754
$340$	−1980.58	−	2702.71i	−0.315917	−	0.431103i
$341$	2933.01			0.465781
$342$	−139.038	+	757.826i	−0.0219833	+	0.119820i
$343$	−3881.71	−	3881.71i	−0.611057	−	0.611057i
$344$	−1874.11	−	7623.75i	−0.293736	−	1.19490i
$345$	−774.910	−	3637.20i	−0.120927	−	0.567595i
$346$	−1046.64	+	722.128i	−0.162624	+	0.112202i
$347$	856.765	−	856.765i	0.132546	−	0.132546i	−0.637721	−	0.770267i	$-0.720123\pi$
$347$	856.765	−	856.765i	0.132546	−	0.132546i	0.770267	+	0.637721i	$0.220123\pi$
$348$	−10286.4	+	4624.47i	−1.58451	+	0.712350i
$349$		−	3731.17i		−	0.572278i	−0.958188	−	0.286139i	$-0.907628\pi$
$349$		−	3731.17i		−	0.572278i	0.958188	−	0.286139i	$-0.0923720\pi$
$350$	3756.50	−	6168.14i	0.573696	−	0.942002i
$351$			1526.01i			0.232058i
$352$	−6711.31	+	5246.88i	−1.01623	+	0.794487i
$353$	−1774.39	+	1774.39i	−0.267539	+	0.267539i	−0.828108	−	0.560569i	$-0.810583\pi$
$353$	−1774.39	+	1774.39i	−0.267539	+	0.267539i	0.560569	+	0.828108i	$0.310583\pi$
$354$	3341.87	+	4843.66i	0.501747	+	0.727225i
$355$	1304.34	+	6122.17i	0.195005	+	0.915298i
$356$	1567.83	−	4128.92i	0.233413	−	0.614698i
$357$	3083.31	+	3083.31i	0.457104	+	0.457104i
$358$	−9787.16	−	1795.64i	−1.44488	−	0.265091i
$359$	−10477.6			−1.54036			−0.770178	−	0.637829i	$-0.779832\pi$
$359$	−10477.6			−1.54036			−0.770178	+	0.637829i	$0.779832\pi$
$360$	454.171	−	1306.99i	0.0664914	−	0.191346i
$361$	−4378.42			−0.638347
$362$	13269.7	+	2434.58i	1.92663	+	0.353477i
$363$	−3560.65	−	3560.65i	−0.514837	−	0.514837i
$364$	721.555	−	1900.23i	0.103901	−	0.273624i
$365$	1857.22	−	2862.83i	0.266333	−	0.410541i
$366$	2454.39	+	3557.37i	0.350528	+	0.508051i
$367$	−5250.87	+	5250.87i	−0.746848	+	0.746848i	−0.973886	−	0.227038i	$-0.927096\pi$
$367$	−5250.87	+	5250.87i	−0.746848	+	0.746848i	0.227038	+	0.973886i	$0.427096\pi$
$368$	−222.507	−	3729.27i	−0.0315190	−	0.528265i
$369$			648.801i			0.0915317i
$370$	2380.32	+	2248.53i	0.334451	+	0.315935i
$371$		−	9434.06i		−	1.32019i
$372$	−2591.25	+	1164.95i	−0.361156	+	0.162365i
$373$	3349.09	−	3349.09i	0.464904	−	0.464904i	−0.435355	−	0.900259i	$-0.643377\pi$
$373$	3349.09	−	3349.09i	0.464904	−	0.464904i	0.900259	+	0.435355i	$0.143377\pi$
$374$	4104.40	−	2831.82i	0.567469	−	0.391523i
$375$	7867.18	+	1234.59i	1.08336	+	0.170011i
$376$	−3900.66	+	958.879i	−0.535003	+	0.131517i
$377$	−2176.00	−	2176.00i	−0.297267	−	0.297267i
$378$	1279.13	−	6971.91i	0.174051	−	0.948668i
$379$	1701.61			0.230622			0.115311	−	0.993329i	$-0.463213\pi$
$379$	1701.61			0.230622			0.115311	+	0.993329i	$0.463213\pi$
$380$	−4402.70	−	678.870i	−0.594352	−	0.0916454i
$381$	−607.798			−0.0817282
$382$	−882.202	+	4808.46i	−0.118161	+	0.644037i
$383$	5674.07	+	5674.07i	0.757001	+	0.757001i	0.975775	−	0.218775i	$-0.0702060\pi$
$383$	5674.07	+	5674.07i	0.757001	+	0.757001i	−0.218775	+	0.975775i	$0.570206\pi$
$384$	3845.32	−	7301.14i	0.511017	−	0.970273i
$385$	9016.54	+	5849.35i	1.19357	+	0.774312i
$386$	−4738.83	+	3269.55i	−0.624871	+	0.431128i
$387$	−1341.83	+	1341.83i	−0.176251	+	0.176251i
$388$	2136.99	+	4753.40i	0.279611	+	0.621951i
$389$			2301.42i			0.299965i	0.988689	+	0.149983i	$0.0479218\pi$
$389$			2301.42i			0.299965i	−0.988689	+	0.149983i	$0.952078\pi$
$390$	2240.39	−	63.7829i	0.290889	−	0.00828147i
$391$			2186.80i			0.282842i
$392$	−870.148	+	1437.40i	−0.112115	+	0.185203i
$393$	−5538.05	+	5538.05i	−0.710833	+	0.710833i
$394$	1496.23	+	2168.62i	0.191317	+	0.277293i
$395$	12819.7	−	2731.25i	1.63298	−	0.347909i
$396$	1925.03	+	730.970i	0.244283	+	0.0927592i
$397$	−7499.18	−	7499.18i	−0.948043	−	0.948043i	0.0506721	−	0.998715i	$-0.483864\pi$
$397$	−7499.18	−	7499.18i	−0.948043	−	0.948043i	−0.998715	+	0.0506721i	$0.983864\pi$
$398$	1832.59	+	336.223i	0.230803	+	0.0423451i
$399$	5797.16			0.727371
$400$	7628.42	+	2409.81i	0.953553	+	0.301226i
$401$	−9495.99			−1.18256			−0.591280	−	0.806466i	$-0.701377\pi$
$401$	−9495.99			−1.18256			−0.591280	+	0.806466i	$0.701377\pi$
$402$	2524.72	+	463.208i	0.313238	+	0.0574694i
$403$	−548.155	−	548.155i	−0.0677557	−	0.0677557i
$404$	−44.6976	−	16.9725i	−0.00550442	−	0.00209014i
$405$	9259.24	−	1972.69i	1.13604	−	0.242034i
$406$	8117.58	+	11765.5i	0.992288	+	1.43821i
$407$	−3445.70	+	3445.70i	−0.419648	+	0.419648i
$408$	−2501.39	+	4132.06i	−0.303523	+	0.501391i
$409$			10456.4i			1.26415i	0.774909	+	0.632073i	$0.217796\pi$
$409$			10456.4i			1.26415i	−0.774909	+	0.632073i	$0.782204\pi$
$410$	−3749.71	+	106.753i	−0.451671	+	0.0128589i
$411$		−	16136.0i		−	1.93657i
$412$	−639.375	−	1422.19i	−0.0764557	−	0.170064i
$413$	5273.83	−	5273.83i	0.628349	−	0.628349i
$414$	−743.276	+	512.821i	−0.0882368	+	0.0608787i
$415$	−7860.10	−	5099.12i	−0.929728	−	0.603147i
$416$	2234.89	+	273.691i	0.263400	+	0.0322568i
$417$	−10375.3	−	10375.3i	−1.21842	−	1.21842i
$418$	1196.33	−	6520.64i	0.139987	−	0.763002i
$419$	−8542.91			−0.996058			−0.498029	−	0.867160i	$-0.665943\pi$
$419$	−8542.91			−0.996058			−0.498029	+	0.867160i	$0.665943\pi$
$420$	−10289.2	−	1586.53i	−1.19539	−	0.184321i
$421$	−3112.71			−0.360342			−0.180171	−	0.983635i	$-0.557665\pi$
$421$	−3112.71			−0.360342			−0.180171	+	0.983635i	$0.557665\pi$
$422$	−2971.36	+	16195.4i	−0.342757	+	1.86820i
$423$	686.540	+	686.540i	0.0789142	+	0.0789142i
$424$	10148.2	−	2494.69i	1.16236	−	0.285738i
$425$	−4373.34	−	1674.02i	−0.499148	−	0.191063i
$426$	7427.19	−	5124.37i	0.844714	−	0.582808i
$427$	3873.30	−	3873.30i	0.438974	−	0.438974i
$428$	7470.28	−	3358.41i	0.843667	−	0.379287i
$429$			3335.48i			0.375381i
$430$	−7975.82	−	7534.26i	−0.894484	−	0.844963i
$431$			1474.93i			0.164837i	0.996598	+	0.0824187i	$0.0262645\pi$
$431$			1474.93i			0.164837i	−0.996598	+	0.0824187i	$0.973736\pi$
$432$	7837.94	−	467.653i	0.872924	−	0.0520832i
$433$	−6196.57	+	6196.57i	−0.687733	+	0.687733i	−0.961730	−	0.273998i	$-0.911654\pi$
$433$	−6196.57	+	6196.57i	−0.687733	+	0.687733i	0.273998	+	0.961730i	$0.411654\pi$
$434$	2044.90	+	2963.85i	0.226171	+	0.327809i
$435$	−8578.17	+	13222.9i	−0.945499	+	1.45745i
$436$	2546.71	−	6706.82i	0.279737	−	0.736694i
$437$	2055.78	+	2055.78i	0.225037	+	0.225037i
$438$	−4838.48	−	887.711i	−0.527835	−	0.0968413i
$439$	−4661.49			−0.506790			−0.253395	−	0.967363i	$-0.581547\pi$
$439$	−4661.49			−0.506790			−0.253395	+	0.967363i	$0.581547\pi$
$440$	−3907.87	+	11245.9i	−0.423410	+	1.21847i
$441$	406.144			0.0438553
$442$	−1296.32	−	237.835i	−0.139502	−	0.0255942i
$443$	5250.61	+	5250.61i	0.563124	+	0.563124i	0.930194	−	0.367069i	$-0.119639\pi$
$443$	5250.61	+	5250.61i	0.563124	+	0.563124i	−0.367069	+	0.930194i	$0.619639\pi$
$444$	1675.62	−	4412.78i	0.179102	−	0.471670i
$445$	−1286.16	−	6036.85i	−0.137011	−	0.643088i
$446$	−5260.02	−	7623.80i	−0.558451	−	0.809411i
$447$	5330.32	−	5330.32i	0.564017	−	0.564017i
$448$	−9981.17	−	3123.74i	−1.05260	−	0.329427i
$449$		−	2992.06i		−	0.314485i	−0.987560	−	0.157243i	$-0.949740\pi$
$449$		−	2992.06i		−	0.314485i	0.987560	−	0.157243i	$-0.0502605\pi$
$450$	−456.595	−	1879.03i	−0.0478314	−	0.196841i
$451$		−	5582.54i		−	0.582864i
$452$	−5424.91	+	2438.88i	−0.564527	+	0.253794i
$453$	−230.641	+	230.641i	−0.0239215	+	0.0239215i
$454$	9779.05	−	6747.03i	1.01091	−	0.697475i
$455$	−591.923	−	2778.31i	−0.0609885	−	0.286262i
$456$	1532.97	+	6236.02i	0.157430	+	0.640413i
$457$	13147.8	+	13147.8i	1.34579	+	1.34579i	0.890175	+	0.455619i	$0.150582\pi$
$457$	13147.8	+	13147.8i	1.34579	+	1.34579i	0.455619	+	0.890175i	$0.349418\pi$
$458$	−2542.47	+	13857.8i	−0.259393	+	1.41383i
$459$	−4596.08			−0.467378
$460$	−3086.12	−	4211.35i	−0.312807	−	0.426859i
$461$	3239.67			0.327302			0.163651	−	0.986518i	$-0.447673\pi$
$461$	3239.67			0.327302			0.163651	+	0.986518i	$0.447673\pi$
$462$	2795.86	−	15238.9i	0.281548	−	1.53458i
$463$	−1552.82	−	1552.82i	−0.155865	−	0.155865i	0.624867	−	0.780732i	$-0.285153\pi$
$463$	−1552.82	−	1552.82i	−0.155865	−	0.155865i	−0.780732	+	0.624867i	$0.785153\pi$
$464$	−10509.6	+	11843.3i	−1.05150	+	1.18494i
$465$	−2160.92	+	3330.98i	−0.215506	+	0.332195i
$466$	−5429.32	+	3745.94i	−0.539717	+	0.372377i
$467$	6322.16	−	6322.16i	0.626456	−	0.626456i	−0.320719	−	0.947174i	$-0.603924\pi$
$467$	6322.16	−	6322.16i	0.626456	−	0.626456i	0.947174	+	0.320719i	$0.103924\pi$
$468$	−223.159	−	496.384i	−0.0220418	−	0.0490285i
$469$		−	3253.29i		−	0.320305i
$470$	−3854.86	+	4080.79i	−0.378323	+	0.400495i
$471$			13072.6i			1.27888i
$472$	7067.65	+	4278.49i	0.689227	+	0.417232i
$473$	11545.6	−	11545.6i	1.12234	−	1.12234i
$474$	−10730.3	−	15552.4i	−1.03979	−	1.50705i
$475$	−5685.04	+	2537.59i	−0.549152	+	0.245121i
$476$	5723.18	+	2173.20i	0.551095	+	0.209262i
$477$	−1786.15	−	1786.15i	−0.171451	−	0.171451i
$478$	9945.57	+	1824.70i	0.951673	+	0.174602i
$479$	7141.64			0.681232			0.340616	−	0.940203i	$-0.389364\pi$
$479$	7141.64			0.681232			0.340616	+	0.940203i	$0.389364\pi$
$480$	−1014.18	−	11487.6i	−0.0964394	−	1.09237i
$481$	1287.94			0.122090
$482$	−14286.1	−	2621.06i	−1.35003	−	0.247689i
$483$	4804.40	+	4804.40i	0.452604	+	0.452604i
$484$	−6609.20	−	2509.64i	−0.620699	−	0.235691i
$485$	6110.36	+	3964.00i	0.572076	+	0.371126i
$486$	−2429.43	−	3521.18i	−0.226751	−	0.328650i
$487$	3827.76	−	3827.76i	0.356165	−	0.356165i	−0.506232	−	0.862397i	$-0.668962\pi$
$487$	3827.76	−	3827.76i	0.356165	−	0.356165i	0.862397	+	0.506232i	$0.168962\pi$
$488$	5190.75	+	3142.28i	0.481504	+	0.291484i
$489$			13668.4i			1.26402i
$490$	66.8261	+	2347.29i	0.00616101	+	0.216407i
$491$			14943.2i			1.37348i	0.726904	+	0.686739i	$0.240959\pi$
$491$			14943.2i			1.37348i	−0.726904	+	0.686739i	$0.759041\pi$
$492$	2217.31	+	4932.06i	0.203179	+	0.451940i
$493$	6553.74	−	6553.74i	0.598713	−	0.598713i
$494$	−1442.24	+	995.069i	−0.131355	+	0.0906281i
$495$	2814.56	−	599.646i	0.255566	−	0.0544486i
$496$	−2647.47	+	2983.44i	−0.239667	+	0.270082i
$497$	−8086.80	−	8086.80i	−0.729865	−	0.729865i
$498$	−2437.27	+	13284.4i	−0.219311	+	1.19536i
$499$	2324.51			0.208535			0.104268	−	0.994549i	$-0.466750\pi$
$499$	2324.51			0.208535			0.104268	+	0.994549i	$0.466750\pi$
$500$	10784.7	−	2948.04i	0.964610	−	0.263681i
$501$	16240.1			1.44821
$502$	3393.23	−	18494.8i	0.301688	−	1.64435i
$503$	−4791.06	−	4791.06i	−0.424697	−	0.424697i	0.462120	−	0.886817i	$-0.347089\pi$
$503$	−4791.06	−	4791.06i	−0.424697	−	0.424697i	−0.886817	+	0.462120i	$0.847089\pi$
$504$	603.476	+	2454.90i	0.0533352	+	0.216964i
$505$	−65.3519	+	13.9233i	−0.00575865	+	0.00122689i
$506$	6395.44	−	4412.52i	0.561882	−	0.387669i
$507$	−8228.84	+	8228.84i	−0.720820	+	0.720820i
$508$	−778.287	+	349.895i	−0.0679742	+	0.0305592i
$509$		−	3391.52i		−	0.295337i	−0.989037	−	0.147668i	$-0.952823\pi$
$509$		−	3391.52i		−	0.295337i	0.989037	−	0.147668i	$-0.0471768\pi$
$510$	192.103	+	6747.68i	0.0166794	+	0.585867i
$511$			6234.74i			0.539743i
$512$	720.851	−	11562.8i	0.0622215	−	0.998062i
$513$	−4320.71	+	4320.71i	−0.371860	+	0.371860i
$514$	1018.26	+	1475.85i	0.0873804	+	0.126648i
$515$	−1828.19	−	1186.01i	−0.156426	−	0.101479i
$516$	−5614.56	+	14786.1i	−0.479007	+	1.26148i
$517$	−5907.27	−	5907.27i	−0.502517	−	0.502517i
$518$	−5884.27	−	1079.58i	−0.499112	−	0.0915714i
$519$	2561.75			0.216664
$520$	2832.11	−	1371.41i	0.238839	−	0.115655i
$521$	−10835.4			−0.911146			−0.455573	−	0.890198i	$-0.650566\pi$
$521$	−10835.4			−0.911146			−0.455573	+	0.890198i	$0.650566\pi$
$522$	3764.47	+	690.663i	0.315645	+	0.0579109i
$523$	1210.80	+	1210.80i	0.101233	+	0.101233i	0.755909	−	0.654676i	$-0.227195\pi$
$523$	1210.80	+	1210.80i	0.101233	+	0.101233i	−0.654676	+	0.755909i	$0.727195\pi$
$524$	−3903.36	+	10279.6i	−0.325418	+	0.856997i
$525$	−13286.1	+	5930.41i	−1.10448	+	0.492998i
$526$	330.581	+	479.139i	0.0274030	+	0.0397176i
$527$	1650.95	−	1650.95i	0.136464	−	0.136464i
$528$	17131.8	−	1022.17i	1.41206	−	0.0842507i
$529$		−	8759.55i		−	0.719943i
$530$	10029.1	−	10616.9i	0.821955	−	0.870128i
$531$		−	1996.99i		−	0.163205i
$532$	7423.28	−	3337.29i	0.604963	−	0.271973i
$533$	−1043.33	+	1043.33i	−0.0847874	+	0.0847874i
$534$	−7323.69	+	5052.96i	−0.593496	+	0.409481i
$535$	6229.69	−	9602.83i	0.503426	−	0.776012i
$536$	3499.57	−	860.282i	0.282012	−	0.0693256i
$537$	14175.0	+	14175.0i	1.13910	+	1.13910i
$538$	1411.23	−	7691.93i	0.113090	−	0.616399i
$539$	−3494.62			−0.279265
$540$	8851.16	−	6486.23i	0.705358	−	0.516894i
$541$	−7014.81			−0.557468			−0.278734	−	0.960368i	$-0.589915\pi$
$541$	−7014.81			−0.557468			−0.278734	+	0.960368i	$0.589915\pi$
$542$	−3252.47	+	17727.7i	−0.257760	+	1.40492i
$543$	−19218.9	−	19218.9i	−1.51890	−	1.51890i
$544$	−824.311	+	6731.10i	−0.0649670	+	0.530503i
$545$	−2089.18	−	9805.98i	−0.164203	−	0.770719i
$546$	−3370.55	+	2325.50i	−0.264187	+	0.182275i
$547$	10104.9	−	10104.9i	0.789860	−	0.789860i	−0.191611	−	0.981471i	$-0.561371\pi$
$547$	10104.9	−	10104.9i	0.789860	−	0.789860i	0.981471	+	0.191611i	$0.0613711\pi$
$548$	−9289.09	−	20662.2i	−0.724106	−	1.61066i
$549$		−	1466.67i		−	0.114018i
$550$	3928.73	+	16168.0i	0.304585	+	1.25346i
$551$		−	12322.2i		−	0.952708i
$552$	−3897.65	+	6438.55i	−0.300535	+	0.496454i
$553$	−16933.6	+	16933.6i	−1.30215	+	1.30215i
$554$	879.882	+	1275.29i	0.0674776	+	0.0978011i
$555$	−1374.58	−	6451.89i	−0.105131	−	0.493455i
$556$	−19258.4	−	7312.77i	−1.46895	−	0.557789i
$557$	1950.22	+	1950.22i	0.148355	+	0.148355i	0.777383	−	0.629028i	$-0.216547\pi$
$557$	1950.22	+	1950.22i	0.148355	+	0.148355i	−0.629028	+	0.777383i	$0.716547\pi$
$558$	948.307	+	173.985i	0.0719445	+	0.0131996i
$559$	−4315.57			−0.326528
$560$	−14088.7	+	3891.68i	−1.06313	+	0.293667i
$561$	−10045.9			−0.756039
$562$	−14701.4	−	2697.25i	−1.10346	−	0.202450i
$563$	4425.60	+	4425.60i	0.331291	+	0.331291i	0.853077	−	0.521786i	$-0.174734\pi$
$563$	4425.60	+	4425.60i	0.331291	+	0.331291i	−0.521786	+	0.853077i	$0.674734\pi$
$564$	7565.23	+	2872.66i	0.564811	+	0.214470i
$565$	−4523.99	+	6973.56i	−0.336860	+	0.519257i
$566$	775.921	+	1124.61i	0.0576226	+	0.0835174i
$567$	−12230.6	+	12230.6i	−0.905884	+	0.905884i
$568$	6560.56	−	10837.4i	0.484639	−	0.800577i
$569$		−	14666.9i		−	1.08061i	−0.841469	−	0.540305i	$-0.818309\pi$
$569$		−	14666.9i		−	1.08061i	0.841469	−	0.540305i	$-0.181691\pi$
$570$	6524.00	+	6162.81i	0.479404	+	0.452863i
$571$		−	664.054i		−	0.0486686i	−0.999704	−	0.0243343i	$-0.992253\pi$
$571$		−	664.054i		−	0.0486686i	0.999704	−	0.0243343i	$-0.00774662\pi$
$572$	1920.15	+	4271.09i	0.140359	+	0.312208i
$573$	6964.21	−	6964.21i	0.507738	−	0.507738i
$574$	5641.23	−	3892.15i	0.410210	−	0.283023i
$575$	−6814.50	−	2608.45i	−0.494234	−	0.189182i
$576$	−2481.16	+	1298.32i	−0.179482	+	0.0939178i
$577$	583.058	+	583.058i	0.0420676	+	0.0420676i	0.727828	−	0.685760i	$-0.240530\pi$
$577$	583.058	+	583.058i	0.0420676	+	0.0420676i	−0.685760	+	0.727828i	$0.740530\pi$
$578$	−1791.32	+	9763.63i	−0.128909	+	0.702619i
$579$	11598.7			0.832516
$580$	−3372.26	+	21870.2i	−0.241423	+	1.56571i
$581$	17117.9			1.22232
$582$	1894.71	−	10327.1i	0.134945	−	0.735521i
$583$	15368.8	+	15368.8i	1.09178	+	1.09178i
$584$	−6706.72	+	1648.68i	−0.475216	+	0.116820i
$585$	−638.088	−	413.950i	−0.0450969	−	0.0292559i
$586$	21913.4	−	15119.1i	1.54477	−	1.06581i
$587$	−6911.99	+	6911.99i	−0.486011	+	0.486011i	−0.907045	−	0.421034i	$-0.861667\pi$
$587$	−6911.99	+	6911.99i	−0.486011	+	0.486011i	0.421034	+	0.907045i	$0.361667\pi$
$588$	3087.43	−	1388.01i	0.216536	−	0.0973482i
$589$		−	3104.07i		−	0.217150i
$590$	11541.5	−	328.582i	0.805351	−	0.0229279i
$591$		−	5307.89i		−	0.369437i
$592$	−394.697	−	6615.19i	−0.0274019	−	0.459261i
$593$	−11384.8	+	11384.8i	−0.788396	+	0.788396i	−0.981231	−	0.192835i	$-0.938232\pi$
$593$	−11384.8	+	11384.8i	−0.788396	+	0.788396i	0.192835	+	0.981231i	$0.438232\pi$
$594$	9273.96	+	13441.6i	0.640598	+	0.928474i
$595$	8367.80	−	1782.77i	0.576549	−	0.122834i
$596$	3756.95	−	9894.02i	0.258206	−	0.679991i
$597$	−2654.19	−	2654.19i	−0.181957	−	0.181957i
$598$	−2019.92	−	370.592i	−0.138128	−	0.0253422i
$599$	25321.6			1.72723			0.863616	−	0.504151i	$-0.168194\pi$
$599$	25321.6			1.72723			0.863616	+	0.504151i	$0.168194\pi$
$600$	−9892.64	−	12723.6i	−0.673109	−	0.865733i
$601$	27777.8			1.88533			0.942663	−	0.333746i	$-0.108313\pi$
$601$	27777.8			1.88533			0.942663	+	0.333746i	$0.108313\pi$
$602$	19716.6	+	3617.39i	1.33487	+	0.244907i
$603$	−615.947	−	615.947i	−0.0415975	−	0.0415975i
$604$	−162.562	+	428.110i	−0.0109512	+	0.0288403i
$605$	−9663.25	+	2058.77i	−0.649367	+	0.138348i
$606$	54.7007	+	79.2825i	0.00366677	+	0.00531457i
$607$	−19575.7	+	19575.7i	−1.30898	+	1.30898i	−0.386833	+	0.922150i	$0.626431\pi$
$607$	−19575.7	+	19575.7i	−1.30898	+	1.30898i	−0.922150	+	0.386833i	$0.873569\pi$
$608$	5552.89	+	7102.74i	0.370394	+	0.473773i
$609$		−	28797.2i		−	1.91613i
$610$	8476.53	−	241.323i	0.562630	−	0.0160178i
$611$			2208.04i			0.146199i
$612$	1495.02	−	672.118i	0.0987463	−	0.0443934i
$613$	−12841.3	+	12841.3i	−0.846091	+	0.846091i	−0.989643	−	0.143552i	$-0.954147\pi$
$613$	−12841.3	+	12841.3i	−0.846091	+	0.846091i	0.143552	+	0.989643i	$0.454147\pi$
$614$	1763.65	−	1216.82i	0.115920	−	0.0799788i
$615$	6340.02	+	4112.99i	0.415698	+	0.269678i
$616$	−5192.55	−	21122.9i	−0.339633	−	1.38160i
$617$	15254.6	+	15254.6i	0.995346	+	0.995346i	0.999989	−	0.00464336i	$-0.00147803\pi$
$617$	15254.6	+	15254.6i	0.995346	+	0.995346i	−0.00464336	+	0.999989i	$0.501478\pi$
$618$	−566.887	+	3089.83i	−0.0368989	+	0.201118i
$619$	−13042.3			−0.846874			−0.423437	−	0.905926i	$-0.639176\pi$
$619$	−13042.3			−0.846874			−0.423437	+	0.905926i	$0.639176\pi$
$620$	−849.504	+	5509.32i	−0.0550273	+	0.356870i
$621$	−7161.58			−0.462776
$622$	−1827.07	+	9958.45i	−0.117779	+	0.641957i
$623$	7974.11	+	7974.11i	0.512803	+	0.512803i
$624$	−3392.83	−	3010.76i	−0.217663	−	0.193152i
$625$	10433.2	−	11631.4i	0.667723	−	0.744410i
$626$	−22192.5	+	15311.7i	−1.41692	+	0.977599i
$627$	−9444.01	+	9444.01i	−0.601527	+	0.601527i
$628$	7525.59	+	16739.5i	0.478191	+	1.06366i
$629$			3879.07i			0.245896i
$630$	2568.27	+	2426.08i	0.162416	+	0.153424i
$631$		−	6843.39i		−	0.431745i	−0.976422	−	0.215872i	$-0.930740\pi$
$631$		−	6843.39i		−	0.431745i	0.976422	−	0.215872i	$-0.0692595\pi$
$632$	−22693.3	−	13737.7i	−1.42831	−	0.864644i
$633$	23456.3	−	23456.3i	1.47283	−	1.47283i
$634$	−9457.04	−	13706.9i	−0.592409	−	0.858629i
$635$	−649.038	+	1000.47i	−0.0405611	+	0.0625233i
$636$	−19682.3	−	7473.74i	−1.22713	−	0.465964i
$637$	653.116	+	653.116i	0.0406239	+	0.0406239i
$638$	−32391.0	−	5942.74i	−2.00999	−	0.368770i
$639$	−3062.15			−0.189573
$640$	−7911.82	−	14126.1i	−0.488660	−	0.872475i
$641$	−2449.97			−0.150964			−0.0754820	−	0.997147i	$-0.524050\pi$
$641$	−2449.97			−0.150964			−0.0754820	+	0.997147i	$0.524050\pi$
$642$	−16229.8	−	2977.66i	−0.997723	−	0.183051i
$643$	−22279.7	−	22279.7i	−1.36645	−	1.36645i	−0.865448	−	0.500999i	$-0.832966\pi$
$643$	−22279.7	−	22279.7i	−1.36645	−	1.36645i	−0.500999	−	0.865448i	$-0.667034\pi$
$644$	8917.82	+	3386.27i	0.545670	+	0.207201i
$645$	4605.87	+	21618.6i	0.281172	+	1.31974i
$646$	−2996.98	−	4343.78i	−0.182530	−	0.264557i
$647$	5040.77	−	5040.77i	0.306295	−	0.306295i	−0.537175	−	0.843471i	$-0.680509\pi$
$647$	5040.77	−	5040.77i	0.306295	−	0.306295i	0.843471	+	0.537175i	$0.180509\pi$
$648$	−16390.6	−	9922.27i	−0.993650	−	0.601518i
$649$			17182.9i			1.03927i
$650$	2287.41	−	3755.91i	0.138030	−	0.226644i
$651$		−	7254.29i		−	0.436740i
$652$	7868.58	+	17502.5i	0.472634	+	1.05130i
$653$	−4532.72	+	4532.72i	−0.271637	+	0.271637i	−0.829759	−	0.558122i	$-0.811522\pi$
$653$	−4532.72	+	4532.72i	−0.271637	+	0.271637i	0.558122	+	0.829759i	$0.311522\pi$
$654$	−11896.3	+	8207.79i	−0.711285	+	0.490749i
$655$	3202.10	+	15029.7i	0.191017	+	0.896579i
$656$	5678.53	+	5039.06i	0.337972	+	0.299912i
$657$	1180.43	+	1180.43i	0.0700956	+	0.0700956i
$658$	1850.82	−	10087.9i	0.109654	−	0.597672i
$659$	12951.7			0.765595			0.382797	−	0.923832i	$-0.374961\pi$
$659$	12951.7			0.765595			0.382797	+	0.923832i	$0.374961\pi$
$660$	19346.4	−	14177.3i	1.14100	−	0.836137i
$661$	6827.08			0.401729			0.200864	−	0.979619i	$-0.435625\pi$
$661$	6827.08			0.401729			0.200864	+	0.979619i	$0.435625\pi$
$662$	4502.65	−	24541.8i	0.264351	−	1.44085i
$663$	1877.49	+	1877.49i	0.109979	+	0.109979i
$664$	4526.56	+	18413.8i	0.264555	+	1.07619i
$665$	6190.50	−	9542.42i	0.360988	−	0.556450i
$666$	−1318.47	+	909.673i	−0.0767110	+	0.0529266i
$667$	10212.0	−	10212.0i	0.592819	−	0.592819i
$668$	20795.5	−	9349.04i	1.20449	−	0.541505i
$669$			18660.0i			1.07838i
$670$	3458.49	−	3661.18i	0.199422	−	0.211110i
$671$			12619.8i			0.726052i
$672$	12977.2	+	16599.3i	0.744952	+	0.952873i
$673$	9731.89	−	9731.89i	0.557410	−	0.557410i	−0.371159	−	0.928569i	$-0.621040\pi$
$673$	9731.89	−	9731.89i	0.557410	−	0.557410i	0.928569	+	0.371159i	$0.121040\pi$
$674$	−7190.25	−	10421.5i	−0.410917	−	0.595578i
$675$	5482.27	−	14322.3i	0.312611	−	0.816690i
$676$	−5799.91	+	15274.2i	−0.329990	+	0.869037i
$677$	−7885.88	−	7885.88i	−0.447679	−	0.447679i	0.446903	−	0.894582i	$-0.352527\pi$
$677$	−7885.88	−	7885.88i	−0.447679	−	0.447679i	−0.894582	+	0.446903i	$0.852527\pi$
$678$	11786.0	+	2162.37i	0.667611	+	0.122486i
$679$	−13307.3			−0.752115
$680$	4130.46	+	8529.83i	0.232935	+	0.481035i
$681$	−23935.1			−1.34684
$682$	−8159.61	−	1497.03i	−0.458134	−	0.0840534i
$683$	−15861.8	−	15861.8i	−0.888629	−	0.888629i	0.105763	−	0.994391i	$-0.466272\pi$
$683$	−15861.8	−	15861.8i	−0.888629	−	0.888629i	−0.994391	+	0.105763i	$0.966272\pi$
$684$	773.603	−	2037.30i	0.0432448	−	0.113886i
$685$	−26560.6	−	17230.8i	−1.48150	−	0.961102i
$686$	8817.63	+	12780.1i	0.490756	+	0.711295i
$687$	20070.6	−	20070.6i	1.11462	−	1.11462i
$688$	1322.53	+	22165.8i	0.0732861	+	1.22829i
$689$		−	5744.60i		−	0.317637i
$690$	299.334	+	10514.2i	0.0165151	+	0.580099i
$691$			30100.7i			1.65714i	0.559883	+	0.828572i	$0.310846\pi$
$691$			30100.7i			1.65714i	−0.559883	+	0.828572i	$0.689154\pi$
$692$	3280.33	−	1474.74i	0.180201	−	0.0810132i
$693$	−3717.77	+	3717.77i	−0.203790	+	0.203790i
$694$	−2820.81	+	1946.21i	−0.154289	+	0.106451i
$695$	−28157.5	+	5998.98i	−1.53680	+	0.327416i
$696$	30977.2	−	7614.96i	1.68705	−	0.414719i
$697$	−3142.34	−	3142.34i	−0.170767	−	0.170767i
$698$	−1904.43	+	10380.1i	−0.103272	+	0.562883i
$699$	13288.8			0.719066
$700$	−13598.8	+	15242.4i	−0.734268	+	0.823010i
$701$	−20267.4			−1.09199			−0.545997	−	0.837787i	$-0.683849\pi$
$701$	−20267.4			−1.09199			−0.545997	+	0.837787i	$0.683849\pi$
$702$	778.888	−	4245.34i	0.0418764	−	0.228248i
$703$	3646.66	+	3646.66i	0.195642	+	0.195642i
$704$	21348.9	−	11171.3i	1.14292	−	0.598058i
$705$	11061.0	−	2356.57i	0.590898	−	0.125892i
$706$	5842.01	−	4030.68i	0.311426	−	0.214868i
$707$	86.3236	−	86.3236i	0.00459199	−	0.00459199i
$708$	−6824.81	−	15180.8i	−0.362277	−	0.805830i
$709$			18499.1i			0.979900i	0.871750	+	0.489950i	$0.162985\pi$
$709$			18499.1i			0.979900i	−0.871750	+	0.489950i	$0.837015\pi$
$710$	−503.841	−	17697.6i	−0.0266321	−	0.935462i
$711$			6412.08i			0.338216i
$712$	−6469.13	+	10686.4i	−0.340507	+	0.562485i
$713$	2572.50	−	2572.50i	0.135120	−	0.135120i
$714$	−7004.00	−	10151.5i	−0.367112	−	0.532088i
$715$	5490.36	+	3561.79i	0.287172	+	0.186298i
$716$	26311.3	+	9990.91i	1.37332	+	0.521478i
$717$	−14404.4	−	14404.4i	−0.750269	−	0.750269i
$718$	29148.7	+	5347.87i	1.51507	+	0.277968i
$719$	−25990.9			−1.34812			−0.674060	−	0.738676i	$-0.735451\pi$
$719$	−25990.9			−1.34812			−0.674060	+	0.738676i	$0.735451\pi$
$720$	−1930.60	+	3404.23i	−0.0999294	+	0.176206i
$721$	3981.47			0.205656
$722$	12180.7	+	2234.79i	0.627867	+	0.115194i
$723$	20691.0	+	20691.0i	1.06432	+	1.06432i
$724$	−35673.6	−	13546.0i	−1.83122	−	0.695348i
$725$	12605.4	+	28240.2i	0.645727	+	1.44664i
$726$	8088.31	+	11723.1i	0.413479	+	0.599290i
$727$	23543.5	−	23543.5i	1.20107	−	1.20107i	0.227232	−	0.973841i	$-0.427033\pi$
$727$	23543.5	−	23543.5i	1.20107	−	1.20107i	0.973841	−	0.227232i	$-0.0729675\pi$
$728$	−2977.26	+	4918.15i	−0.151572	+	0.250383i
$729$		−	14244.1i		−	0.723674i
$730$	−6627.99	+	7016.44i	−0.336045	+	0.355740i
$731$		−	12997.8i		−	0.657646i
$732$	−5012.40	−	11149.3i	−0.253092	−	0.562965i
$733$	16546.7	−	16546.7i	0.833789	−	0.833789i	−0.154244	−	0.988033i	$-0.549294\pi$
$733$	16546.7	−	16546.7i	0.833789	−	0.833789i	0.988033	+	0.154244i	$0.0492942\pi$
$734$	17288.0	−	11927.8i	0.869361	−	0.599813i
$735$	2574.70	−	3968.80i	0.129210	−	0.199172i
$736$	−1284.44	+	10488.4i	−0.0643274	+	0.525280i
$737$	5299.85	+	5299.85i	0.264888	+	0.264888i
$738$	331.154	−	1804.96i	0.0165175	−	0.0900291i
$739$	−8124.95			−0.404440			−0.202220	−	0.979340i	$-0.564816\pi$
$739$	−8124.95			−0.404440			−0.202220	+	0.979340i	$0.564816\pi$
$740$	−5474.35	−	7470.34i	−0.271947	−	0.371102i
$741$	3530.01			0.175004
$742$	−4815.23	+	26245.5i	−0.238238	+	1.29852i
$743$	−5222.62	−	5222.62i	−0.257873	−	0.257873i	0.566316	−	0.824188i	$-0.308368\pi$
$743$	−5222.62	−	5222.62i	−0.257873	−	0.257873i	−0.824188	+	0.566316i	$0.808368\pi$
$744$	7803.45	−	1918.28i	0.384527	−	0.0945264i
$745$	−3081.99	−	14465.9i	−0.151564	−	0.711398i
$746$	−11026.5	+	7607.73i	−0.541167	+	0.373376i
$747$	3240.94	−	3240.94i	0.158741	−	0.158741i
$748$	−12863.8	+	5783.17i	−0.628806	+	0.282692i
$749$			20913.3i			1.02023i
$750$	−21256.3	−	7450.11i	−1.03489	−	0.362719i
$751$		−	27086.9i		−	1.31613i	−0.752961	−	0.658066i	$-0.771375\pi$
$751$		−	27086.9i		−	1.31613i	0.752961	−	0.658066i	$-0.228625\pi$
$752$	11341.0	−	676.664i	0.549953	−	0.0328130i
$753$	−26786.5	+	26786.5i	−1.29636	+	1.29636i
$754$	4942.97	+	7164.27i	0.238743	+	0.346031i
$755$	133.356	+	625.936i	0.00642826	+	0.0301724i
$756$	−7117.05	+	18742.9i	−0.342387	+	0.901685i
$757$	−11094.6	−	11094.6i	−0.532684	−	0.532684i	0.388686	−	0.921370i	$-0.372929\pi$
$757$	−11094.6	−	11094.6i	−0.532684	−	0.532684i	−0.921370	+	0.388686i	$0.872929\pi$
$758$	−4733.87	−	868.517i	−0.226836	−	0.0416174i
$759$	−15653.4			−0.748595
$760$	11901.8	+	4135.79i	0.568056	+	0.197396i
$761$	−8006.53			−0.381388			−0.190694	−	0.981649i	$-0.561074\pi$
$761$	−8006.53			−0.381388			−0.190694	+	0.981649i	$0.561074\pi$
$762$	1690.89	+	310.226i	0.0803865	+	0.0147484i
$763$	12952.8	+	12952.8i	0.614576	+	0.614576i
$764$	4908.56	−	12926.8i	0.232442	−	0.612141i
$765$	1246.75	−	1921.81i	0.0589231	−	0.0908277i
$766$	−12889.1	−	18681.3i	−0.607967	−	0.881179i
$767$	3211.35	−	3211.35i	0.151180	−	0.151180i
$768$	−14424.2	+	18349.0i	−0.677720	+	0.862128i
$769$		−	5515.54i		−	0.258642i	−0.991603	−	0.129321i	$-0.958720\pi$
$769$		−	5515.54i		−	0.258642i	0.991603	−	0.129321i	$-0.0412797\pi$
$770$	−22098.4	−	20875.0i	−1.03425	−	0.976989i
$771$		−	3612.28i		−	0.168733i
$772$	14852.2	−	6677.11i	0.692413	−	0.311288i
$773$	7904.07	−	7904.07i	0.367774	−	0.367774i	−0.498891	−	0.866665i	$-0.666259\pi$
$773$	7904.07	−	7904.07i	0.367774	−	0.367774i	0.866665	+	0.498891i	$0.166259\pi$
$774$	4417.84	−	3048.08i	0.205163	−	0.141551i
$775$	3175.42	+	7113.98i	0.147180	+	0.329731i
$776$	−3518.90	−	14314.7i	−0.162785	−	0.662199i
$777$	8522.33	+	8522.33i	0.393484	+	0.393484i
$778$	1174.66	−	6402.52i	0.0541308	−	0.295041i
$779$	−5908.13			−0.271734
$780$	−6265.31	−	966.073i	−0.287608	−	0.0443474i
$781$	26348.0			1.20718
$782$	1116.16	−	6083.65i	0.0510407	−	0.278198i
$783$	21463.0	+	21463.0i	0.979596	+	0.979596i
$784$	3154.41	−	3554.71i	0.143696	−	0.161931i
$785$	21518.2	+	13959.6i	0.978366	+	0.634700i
$786$	18233.5	−	12580.1i	0.827438	−	0.570889i
$787$	−27606.7	+	27606.7i	−1.25041	+	1.25041i	−0.294870	+	0.955537i	$0.595276\pi$
$787$	−27606.7	+	27606.7i	−1.25041	+	1.25041i	−0.955537	+	0.294870i	$0.904724\pi$
$788$	−3055.62	−	6796.76i	−0.138137	−	0.307265i
$789$		−	1172.74i		−	0.0529158i
$790$	−37058.3	+	1055.03i	−1.66896	+	0.0475144i
$791$		−	15187.2i		−	0.682673i
$792$	−4982.32	−	3016.10i	−0.223534	−	0.135319i
$793$	2358.53	−	2358.53i	0.105617	−	0.105617i
$794$	17035.0	+	24690.3i	0.761398	+	1.10356i
$795$	−28777.2	+	6131.03i	−1.28380	+	0.273516i
$796$	−4926.64	−	1870.74i	−0.219372	−	0.0832998i
$797$	−19000.5	−	19000.5i	−0.844456	−	0.844456i	0.144979	−	0.989435i	$-0.453689\pi$
$797$	−19000.5	−	19000.5i	−0.844456	−	0.844456i	−0.989435	+	0.144979i	$0.953689\pi$
$798$	−16127.7	−	2958.92i	−0.715430	−	0.131259i
$799$	−6650.24			−0.294454
$800$	−19992.2	−	10597.7i	−0.883540	−	0.468356i
$801$	3019.48			0.133194
$802$	26417.8	+	4846.84i	1.16315	+	0.213401i
$803$	−10156.9	−	10156.9i	−0.446361	−	0.446361i
$804$	−6787.33	−	2577.28i	−0.297725	−	0.113052i
$805$	13038.7	−	2777.90i	0.570872	−	0.121625i
$806$	1245.18	+	1804.75i	0.0544164	+	0.0788704i
$807$	−11140.4	+	11140.4i	−0.485949	+	0.485949i
$808$	115.685	+	70.0315i	0.00503688	+	0.00304913i
$809$			33025.1i			1.43523i	0.696440	+	0.717615i	$0.254766\pi$
$809$			33025.1i			1.43523i	−0.696440	+	0.717615i	$0.745234\pi$
$810$	−26766.0	+	762.016i	−1.16106	+	0.0330549i
$811$			19125.0i			0.828075i	0.910260	+	0.414037i	$0.135882\pi$
$811$			19125.0i			0.828075i	−0.910260	+	0.414037i	$0.864118\pi$
$812$	−16577.8	−	36874.9i	−0.716463	−	1.59366i
$813$	25675.4	−	25675.4i	1.10760	−	1.10760i
$814$	11344.6	−	7827.19i	0.488487	−	0.337030i
$815$	22498.9	+	14595.8i	0.966997	+	0.627325i
$816$	9067.89	−	10218.6i	0.389019	−	0.438387i
$817$	−12219.0	−	12219.0i	−0.523243	−	0.523243i
$818$	5337.04	−	29089.6i	0.228124	−	1.24339i
$819$	1389.64			0.0592894
$820$	10486.2	+	1616.90i	0.446576	+	0.0688594i
$821$	8022.85			0.341047			0.170523	−	0.985354i	$-0.445454\pi$
$821$	8022.85			0.341047			0.170523	+	0.985354i	$0.445454\pi$
$822$	−8235.95	+	44890.2i	−0.349467	+	1.90477i
$823$	−941.682	−	941.682i	−0.0398845	−	0.0398845i	0.686883	−	0.726768i	$-0.258978\pi$
$823$	−941.682	−	941.682i	−0.0398845	−	0.0398845i	−0.726768	+	0.686883i	$0.758978\pi$
$824$	1052.84	+	4282.87i	0.0445113	+	0.181069i
$825$	11982.9	−	31305.0i	0.505686	−	1.32109i
$826$	−17363.6	+	11980.0i	−0.731424	+	0.504644i
$827$	−413.194	+	413.194i	−0.0173739	+	0.0173739i	−0.715740	−	0.698366i	$-0.753911\pi$
$827$	−413.194	+	413.194i	−0.0173739	+	0.0173739i	0.698366	+	0.715740i	$0.253911\pi$
$828$	2329.54	−	1047.29i	0.0977741	−	0.0439563i
$829$			13830.1i			0.579418i	0.957115	+	0.289709i	$0.0935585\pi$
$829$			13830.1i			0.579418i	−0.957115	+	0.289709i	$0.906441\pi$
$830$	19264.1	+	18197.6i	0.805623	+	0.761021i
$831$		−	3121.39i		−	0.130301i
$832$	−6077.75	−	1902.11i	−0.253255	−	0.0792595i
$833$	−1967.07	+	1967.07i	−0.0818188	+	0.0818188i
$834$	23568.3	+	34159.6i	0.978542	+	1.41828i
$835$	17342.0	−	26732.0i	0.718736	−	1.10790i
$836$	−6656.39	+	17529.8i	−0.275378	+	0.725214i
$837$	5406.72	+	5406.72i	0.223278	+	0.223278i
$838$	23766.3	+	4360.38i	0.979705	+	0.179745i
$839$	29230.2			1.20279			0.601393	−	0.798954i	$-0.294613\pi$
$839$	29230.2			1.20279			0.601393	+	0.798954i	$0.294613\pi$
$840$	27814.7	+	9665.43i	1.14250	+	0.397011i
$841$	−36820.9			−1.50973
$842$	8659.53	+	1588.75i	0.354426	+	0.0650262i
$843$	21292.4	+	21292.4i	0.869929	+	0.869929i
$844$	16532.6	−	43539.0i	0.674260	−	1.77568i
$845$	4757.91	+	22332.2i	0.193701	+	0.909175i
$846$	−1559.53	−	2260.37i	−0.0633781	−	0.0918593i
$847$	12764.2	−	12764.2i	0.517809	−	0.517809i
$848$	−29505.6	+	1760.46i	−1.19484	+	0.0712906i
$849$		−	2752.59i		−	0.111270i
$850$	11312.2	+	6889.30i	0.456475	+	0.278001i
$851$			6044.34i			0.243475i
$852$	−23277.9	+	10465.0i	−0.936018	+	0.420806i
$853$	−20858.3	+	20858.3i	−0.837251	+	0.837251i	−0.988496	−	0.151245i	$-0.951672\pi$
$853$	−20858.3	+	20858.3i	−0.837251	+	0.837251i	0.151245	+	0.988496i	$0.451672\pi$
$854$	−12752.5	+	8798.52i	−0.510984	+	0.352552i
$855$	−634.619	−	2978.72i	−0.0253842	−	0.119146i
$856$	−22496.4	+	5530.18i	−0.898261	+	0.220815i
$857$	24905.5	+	24905.5i	0.992714	+	0.992714i	0.999974	−	0.00725972i	$-0.00231086\pi$
$857$	24905.5	+	24905.5i	0.992714	+	0.992714i	−0.00725972	+	0.999974i	$0.502311\pi$
$858$	1702.46	−	9279.27i	0.0677400	−	0.369218i
$859$	26939.2			1.07003			0.535013	−	0.844844i	$-0.320307\pi$
$859$	26939.2			1.07003			0.535013	+	0.844844i	$0.320307\pi$
$860$	18343.1	+	25031.2i	0.727320	+	0.992507i
$861$	−13807.4			−0.546523
$862$	752.818	−	4103.25i	0.0297460	−	0.162131i
$863$	−17233.1	−	17233.1i	−0.679747	−	0.679747i	0.280196	−	0.959943i	$-0.409601\pi$
$863$	−17233.1	−	17233.1i	−0.679747	−	0.679747i	−0.959943	+	0.280196i	$0.909601\pi$
$864$	−22043.8	−	2699.55i	−0.867992	−	0.106297i
$865$	2735.57	−	4216.77i	0.107528	−	0.165751i
$866$	20401.6	−	14076.0i	0.800548	−	0.552336i
$867$	14140.9	−	14140.9i	0.553922	−	0.553922i
$868$	−4176.12	−	9289.13i	−0.163303	−	0.363241i
$869$		−	55172.1i		−	2.15372i
$870$	30613.5	−	32407.7i	1.19298	−	1.26290i
$871$		−	1981.00i		−	0.0770649i
$872$	−10508.2	+	17358.5i	−0.408086	+	0.674119i
$873$	−2519.47	+	2519.47i	−0.0976760	+	0.0976760i
$874$	−4669.87	−	6768.45i	−0.180733	−	0.261952i
$875$	−4425.77	+	28202.3i	−0.170992	+	1.08961i
$876$	13007.5	+	4939.21i	0.501694	+	0.190503i
$877$	8676.94	+	8676.94i	0.334093	+	0.334093i	0.854138	−	0.520046i	$-0.174085\pi$
$877$	8676.94	+	8676.94i	0.334093	+	0.334093i	−0.520046	+	0.854138i	$0.674085\pi$
$878$	12968.2	+	2379.26i	0.498470	+	0.0914536i
$879$	−53635.0			−2.05809
$880$	16611.7	−	29291.3i	0.636339	−	1.12206i
$881$	−9480.93			−0.362566			−0.181283	−	0.983431i	$-0.558025\pi$
$881$	−9480.93			−0.362566			−0.181283	+	0.983431i	$0.558025\pi$
$882$	−1129.89	−	207.299i	−0.0431353	−	0.00791398i
$883$	−27861.7	−	27861.7i	−1.06186	−	1.06186i	−0.997956	−	0.0639013i	$-0.979646\pi$
$883$	−27861.7	−	27861.7i	−1.06186	−	1.06186i	−0.0639013	−	0.997956i	$-0.520354\pi$
$884$	3484.96	+	1323.31i	0.132593	+	0.0503480i
$885$	−19514.4	−	12659.7i	−0.741209	−	0.480848i
$886$	−11927.2	−	17287.1i	−0.452260	−	0.655499i
$887$	−27498.7	+	27498.7i	−1.04094	+	1.04094i	−0.0418178	+	0.999125i	$0.513315\pi$
$887$	−27498.7	+	27498.7i	−1.04094	+	1.04094i	−0.999125	+	0.0418178i	$0.986685\pi$
$888$	−6913.88	+	11421.1i	−0.261278	+	0.431606i
$889$		−	2178.84i		−	0.0822001i
$890$	496.820	+	17450.9i	0.0187117	+	0.657255i
$891$		−	39849.0i		−	1.49831i
$892$	10742.1	+	23894.1i	0.403219	+	0.896899i
$893$	−6251.80	+	6251.80i	−0.234276	+	0.234276i
$894$	−17549.5	+	12108.3i	−0.656538	+	0.452976i
$895$	38469.5	−	8195.97i	1.43675	−	0.306102i
$896$	26173.2	+	13784.7i	0.975875	+	0.513968i
$897$	2925.50	+	2925.50i	0.108896	+	0.108896i
$898$	−1527.17	+	8323.88i	−0.0567510	+	0.309322i
$899$	−15419.4			−0.572040
$900$	311.168	+	5460.51i	0.0115248	+	0.202241i
$901$	17301.8			0.639739
$902$	−2849.38	+	15530.6i	−0.105182	+	0.573295i
$903$	−28556.1	−	28556.1i	−1.05237	−	1.05237i
$904$	16336.9	−	4016.01i	0.601058	−	0.147755i
$905$	−52158.0	+	11112.3i	−1.91579	+	0.408162i
$906$	759.362	−	523.920i	0.0278456	−	0.0192120i
$907$	−1450.80	+	1450.80i	−0.0531127	+	0.0531127i	−0.733164	−	0.680052i	$-0.761957\pi$
$907$	−1450.80	+	1450.80i	−0.0531127	+	0.0531127i	0.680052	+	0.733164i	$0.261957\pi$
$908$	−30649.0	+	13778.9i	−1.12018	+	0.503599i
$909$		−	32.6873i		−	0.00119271i
$910$	228.649	+	8031.37i	0.00832928	+	0.292568i
$911$			20370.8i			0.740850i	0.928862	+	0.370425i	$0.120788\pi$
$911$			20370.8i			0.740850i	−0.928862	+	0.370425i	$0.879212\pi$
$912$	−1081.79	−	18131.0i	−0.0392781	−	0.658308i
$913$	−27886.3	+	27886.3i	−1.01085	+	1.01085i
$914$	−29866.3	−	43287.8i	−1.08084	−	1.56656i
$915$	−14332.1	−	9297.75i	−0.517820	−	0.335928i
$916$	14146.3	−	37254.6i	0.510269	−	1.34381i
$917$	−19852.8	−	19852.8i	−0.714937	−	0.714937i
$918$	12786.2	+	2345.88i	0.459705	+	0.0843415i
$919$	21825.1			0.783399			0.391699	−	0.920093i	$-0.371887\pi$
$919$	21825.1			0.783399			0.391699	+	0.920093i	$0.371887\pi$
$920$	6436.06	+	13291.1i	0.230642	+	0.476300i
$921$	−4316.69			−0.154440
$922$	−9012.73	−	1653.56i	−0.321929	−	0.0590639i
$923$	−4924.22	−	4924.22i	−0.175604	−	0.175604i
$924$	−15556.1	+	40967.4i	−0.553852	+	1.45858i
$925$	−12088.0	−	4627.02i	−0.429676	−	0.164471i
$926$	3527.35	+	5112.49i	0.125179	+	0.181433i
$927$	753.812	−	753.812i	0.0267081	−	0.0267081i
$928$	35282.6	−	27583.8i	1.24807	−	0.975735i
$929$		−	9339.19i		−	0.329827i	−0.986308	−	0.164913i	$-0.947266\pi$
$929$		−	9339.19i		−	0.329827i	0.986308	−	0.164913i	$-0.0527345\pi$
$930$	7711.84	−	8163.81i	0.271915	−	0.287852i
$931$			3698.44i			0.130195i
$932$	17016.3	−	7650.01i	0.598055	−	0.268867i
$933$	14423.1	−	14423.1i	0.506099	−	0.506099i
$934$	−20815.1	+	14361.3i	−0.729219	+	0.503123i
$935$	−10727.5	+	16536.0i	−0.375216	+	0.578381i
$936$	367.469	+	1494.84i	0.0128324	+	0.0522012i
$937$	431.639	+	431.639i	0.0150491	+	0.0150491i	0.714591	−	0.699542i	$-0.246613\pi$
$937$	431.639	+	431.639i	0.0150491	+	0.0150491i	−0.699542	+	0.714591i	$0.746613\pi$
$938$	−1660.51	+	9050.63i	−0.0578012	+	0.315047i
$939$	54318.2			1.88776
$940$	12807.1	−	9385.17i	0.444384	−	0.325649i
$941$	21225.1			0.735300			0.367650	−	0.929964i	$-0.380162\pi$
$941$	21225.1			0.735300			0.367650	+	0.929964i	$0.380162\pi$
$942$	6672.38	−	36367.9i	0.230783	−	1.25789i
$943$	−4896.37	−	4896.37i	−0.169086	−	0.169086i
$944$	−17478.4	−	15510.1i	−0.602619	−	0.534758i
$945$	5838.42	+	27403.9i	0.200978	+	0.943330i
$946$	−38012.9	+	26226.9i	−1.30645	+	0.901384i
$947$	11052.1	−	11052.1i	0.379244	−	0.379244i	−0.491585	−	0.870830i	$-0.663582\pi$
$947$	11052.1	−	11052.1i	0.379244	−	0.379244i	0.870830	+	0.491585i	$0.163582\pi$
$948$	21913.6	+	48743.4i	0.750759	+	1.66995i
$949$			3796.47i			0.129861i
$950$	17110.9	−	4157.87i	0.584371	−	0.141999i
$951$			33548.9i			1.14395i
$952$	−14812.6	−	8966.99i	−0.504285	−	0.305275i
$953$	22553.2	−	22553.2i	0.766600	−	0.766600i	−0.210906	−	0.977506i	$-0.567641\pi$
$953$	22553.2	−	22553.2i	0.766600	−	0.766600i	0.977506	+	0.210906i	$0.0676414\pi$
$954$	4057.40	+	5880.74i	0.137697	+	0.199576i
$955$	−4026.70	−	18900.2i	−0.136441	−	0.640413i
$956$	−26737.2	−	10152.6i	−0.904541	−	0.343472i
$957$	46912.7	+	46912.7i	1.58461	+	1.58461i
$958$	−19868.0	−	3645.16i	−0.670048	−	0.122933i
$959$	57844.3			1.94775
$960$	−3041.95	+	32476.2i	−0.102269	+	1.09184i
$961$	25906.7			0.869616
$962$	−3583.05	−	657.379i	−0.120086	−	0.0220320i
$963$	3959.51	+	3959.51i	0.132496	+	0.132496i
$964$	38406.1	+	14583.6i	1.28317	+	0.487246i
$965$	12385.7	−	19092.1i	0.413171	−	0.636887i
$966$	−10913.6	−	15818.0i	−0.363498	−	0.526849i
$967$	−18695.9	+	18695.9i	−0.621739	+	0.621739i	−0.945976	−	0.324237i	$-0.894892\pi$
$967$	−18695.9	+	18695.9i	−0.621739	+	0.621739i	0.324237	+	0.945976i	$0.394892\pi$
$968$	17105.8	+	10355.2i	0.567976	+	0.343831i
$969$			10631.8i			0.352469i
$970$	−14975.7	−	14146.6i	−0.495712	−	0.468268i
$971$		−	11285.7i		−	0.372993i	−0.982456	−	0.186496i	$-0.940287\pi$
$971$		−	11285.7i		−	0.372993i	0.982456	−	0.186496i	$-0.0597133\pi$
$972$	4961.41	+	11035.9i	0.163721	+	0.364173i
$973$	37193.3	−	37193.3i	1.22545	−	1.22545i
$974$	−12602.5	+	8695.07i	−0.414590	+	0.286045i
$975$	−8090.16	+	3611.15i	−0.265736	+	0.118615i
$976$	−12836.8	−	11391.2i	−0.420999	−	0.373590i
$977$	9765.98	+	9765.98i	0.319797	+	0.319797i	0.848689	−	0.528892i	$-0.177392\pi$
$977$	9765.98	+	9765.98i	0.319797	+	0.319797i	−0.528892	+	0.848689i	$0.677392\pi$
$978$	6976.49	−	38025.5i	0.228102	−	1.24327i
$979$	−25980.8			−0.848162
$980$	1012.17	−	6564.25i	0.0329923	−	0.213966i
$981$	4904.70			0.159628
$982$	7627.15	−	41571.9i	0.247854	−	1.35093i
$983$	33483.4	+	33483.4i	1.08642	+	1.08642i	0.995894	+	0.0905295i	$0.0288559\pi$
$983$	33483.4	+	33483.4i	1.08642	+	1.08642i	0.0905295	+	0.995894i	$0.471144\pi$
$984$	−3651.16	−	14852.7i	−0.118287	−	0.481185i
$985$	−8737.05	−	5668.03i	−0.282625	−	0.183349i
$986$	−21577.5	+	14887.4i	−0.696926	+	0.480842i
$987$	−14610.6	+	14610.6i	−0.471186	+	0.471186i
$988$	4520.19	−	2032.14i	0.145553	−	0.0654363i
$989$		−	20253.0i		−	0.651171i
$990$	−8136.16	+	231.632i	−0.261196	+	0.00743612i
$991$			35651.6i			1.14280i	0.820673	+	0.571398i	$0.193599\pi$
$991$			35651.6i			1.14280i	−0.820673	+	0.571398i	$0.806401\pi$
$992$	8888.02	−	6948.62i	0.284471	−	0.222398i
$993$	−35544.4	+	35544.4i	−1.13592	+	1.13592i
$994$	18369.8	+	26625.0i	0.586173	+	0.849591i
$995$	−7203.19	+	1534.65i	−0.229504	+	0.0488961i
$996$	13560.9	−	35713.0i	0.431420	−	1.13616i
$997$	−19421.9	−	19421.9i	−0.616949	−	0.616949i	0.327799	−	0.944748i	$-0.393693\pi$
$997$	−19421.9	−	19421.9i	−0.616949	−	0.616949i	−0.944748	+	0.327799i	$0.893693\pi$
$998$	−6466.76	−	1186.45i	−0.205112	−	0.0376316i
$999$	−12703.6			−0.402327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.4.e.b.7.1	yes	12
3.2	odd	2		180.4.k.e.127.6		12
4.3	odd	2	inner	20.4.e.b.7.4	yes	12
5.2	odd	4		100.4.e.e.43.3		12
5.3	odd	4	inner	20.4.e.b.3.4	yes	12
5.4	even	2		100.4.e.e.7.6		12
8.3	odd	2		320.4.n.k.127.5		12
8.5	even	2		320.4.n.k.127.2		12
12.11	even	2		180.4.k.e.127.3		12
15.8	even	4		180.4.k.e.163.3		12
20.3	even	4	inner	20.4.e.b.3.1	✓	12
20.7	even	4		100.4.e.e.43.6		12
20.19	odd	2		100.4.e.e.7.3		12
40.3	even	4		320.4.n.k.63.2		12
40.13	odd	4		320.4.n.k.63.5		12
60.23	odd	4		180.4.k.e.163.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.4.e.b.3.1	✓	12	20.3	even	4	inner
20.4.e.b.3.4	yes	12	5.3	odd	4	inner
20.4.e.b.7.1	yes	12	1.1	even	1	trivial
20.4.e.b.7.4	yes	12	4.3	odd	2	inner
100.4.e.e.7.3		12	20.19	odd	2
100.4.e.e.7.6		12	5.4	even	2
100.4.e.e.43.3		12	5.2	odd	4
100.4.e.e.43.6		12	20.7	even	4
180.4.k.e.127.3		12	12.11	even	2
180.4.k.e.127.6		12	3.2	odd	2
180.4.k.e.163.3		12	15.8	even	4
180.4.k.e.163.6		12	60.23	odd	4
320.4.n.k.63.2		12	40.3	even	4
320.4.n.k.63.5		12	40.13	odd	4
320.4.n.k.127.2		12	8.5	even	2
320.4.n.k.127.5		12	8.3	odd	2

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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	20.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.78199 - 0.510409i) q^{2} +(4.02923 + 4.02923i) q^{3} +(7.47897 + 2.83991i) q^{4} +(10.9349 - 2.32970i) q^{5} +(-9.15273 - 13.2658i) q^{6} +(-14.4440 + 14.4440i) q^{7} +(-19.3569 - 11.7179i) q^{8} +5.46937i q^{9} +O(q^{10})\)	\(q+(-2.78199 - 0.510409i) q^{2} +(4.02923 + 4.02923i) q^{3} +(7.47897 + 2.83991i) q^{4} +(10.9349 - 2.32970i) q^{5} +(-9.15273 - 13.2658i) q^{6} +(-14.4440 + 14.4440i) q^{7} +(-19.3569 - 11.7179i) q^{8} +5.46937i q^{9} +(-31.6100 + 0.899920i) q^{10} -47.0607i q^{11} +(18.6918 + 41.5771i) q^{12} +(-8.79525 + 8.79525i) q^{13} +(47.5554 - 32.8107i) q^{14} +(53.4462 + 34.6724i) q^{15} +(47.8698 + 42.4791i) q^{16} +(-26.4898 - 26.4898i) q^{17} +(2.79162 - 15.2157i) q^{18} -49.8054 q^{19} +(88.3980 + 13.6304i) q^{20} -116.396 q^{21} +(-24.0202 + 130.922i) q^{22} +(-41.2762 - 41.2762i) q^{23} +(-30.7792 - 125.208i) q^{24} +(114.145 - 50.9501i) q^{25} +(28.9575 - 19.9791i) q^{26} +(86.7518 - 86.7518i) q^{27} +(-149.046 + 67.0065i) q^{28} +247.406i q^{29} +(-130.990 - 123.738i) q^{30} +62.3240i q^{31} +(-111.492 - 142.610i) q^{32} +(189.618 - 189.618i) q^{33} +(60.1738 + 87.2150i) q^{34} +(-124.294 + 191.594i) q^{35} +(-15.5325 + 40.9052i) q^{36} +(-73.2182 - 73.2182i) q^{37} +(138.558 + 25.4211i) q^{38} -70.8761 q^{39} +(-238.966 - 83.0389i) q^{40} +118.624 q^{41} +(323.814 + 59.4097i) q^{42} +(245.335 + 245.335i) q^{43} +(133.648 - 351.965i) q^{44} +(12.7420 + 59.8071i) q^{45} +(93.7624 + 135.898i) q^{46} +(125.525 - 125.525i) q^{47} +(21.7203 + 364.037i) q^{48} -74.2578i q^{49} +(-343.556 + 83.4822i) q^{50} -213.467i q^{51} +(-90.7571 + 40.8017i) q^{52} +(-326.574 + 326.574i) q^{53} +(-285.622 + 197.064i) q^{54} +(-109.637 - 514.605i) q^{55} +(448.845 - 110.337i) q^{56} +(-200.677 - 200.677i) q^{57} +(126.278 - 688.282i) q^{58} -365.123 q^{59} +(301.256 + 411.096i) q^{60} -268.160 q^{61} +(31.8107 - 173.385i) q^{62} +(-78.9995 - 78.9995i) q^{63} +(237.380 + 453.646i) q^{64} +(-75.6851 + 116.666i) q^{65} +(-624.299 + 430.733i) q^{66} +(-112.617 + 112.617i) q^{67} +(-122.888 - 273.345i) q^{68} -332.623i q^{69} +(443.576 - 469.573i) q^{70} +559.873i q^{71} +(64.0897 - 105.870i) q^{72} +(215.825 - 215.825i) q^{73} +(166.321 + 241.064i) q^{74} +(665.206 + 254.627i) q^{75} +(-372.493 - 141.443i) q^{76} +(679.744 + 679.744i) q^{77} +(197.177 + 36.1758i) q^{78} +1172.36 q^{79} +(622.417 + 352.984i) q^{80} +846.759 q^{81} +(-330.012 - 60.5470i) q^{82} +(-592.561 - 592.561i) q^{83} +(-870.524 - 330.555i) q^{84} +(-351.377 - 227.951i) q^{85} +(-557.299 - 807.742i) q^{86} +(-996.857 + 996.857i) q^{87} +(-551.454 + 910.949i) q^{88} -552.071i q^{89} +(-4.92200 - 172.887i) q^{90} -254.077i q^{91} +(-191.483 - 425.924i) q^{92} +(-251.118 + 251.118i) q^{93} +(-413.277 + 285.139i) q^{94} +(-544.618 + 116.032i) q^{95} +(125.382 - 1023.83i) q^{96} +(460.651 + 460.651i) q^{97} +(-37.9019 + 206.585i) q^{98} +257.392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 8 q^{6} - 12 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 + 8 * q^6 - 12 * q^8	\( 12 q - 6 q^{2} + 8 q^{6} - 12 q^{8} - 110 q^{10} - 80 q^{12} + 116 q^{13} + 312 q^{16} - 332 q^{17} + 198 q^{18} + 140 q^{20} - 144 q^{21} + 360 q^{22} + 340 q^{25} - 164 q^{26} - 880 q^{28} - 1240 q^{30} - 376 q^{32} + 80 q^{33} + 460 q^{36} + 508 q^{37} + 1600 q^{38} + 1420 q^{40} - 656 q^{41} + 1160 q^{42} + 1180 q^{45} - 1432 q^{46} - 2720 q^{48} - 1570 q^{50} - 932 q^{52} - 644 q^{53} + 2048 q^{56} - 960 q^{57} + 1576 q^{58} + 3280 q^{60} - 896 q^{61} + 2440 q^{62} - 2740 q^{65} - 1680 q^{66} - 844 q^{68} - 3040 q^{70} - 3036 q^{72} + 1436 q^{73} + 800 q^{76} + 3120 q^{77} + 3720 q^{78} + 1840 q^{80} + 5988 q^{81} - 1352 q^{82} + 500 q^{85} - 2552 q^{86} - 2400 q^{88} - 750 q^{90} - 1840 q^{92} - 3280 q^{93} + 1088 q^{96} - 4772 q^{97} + 1698 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 + 8 * q^6 - 12 * q^8 - 110 * q^10 - 80 * q^12 + 116 * q^13 + 312 * q^16 - 332 * q^17 + 198 * q^18 + 140 * q^20 - 144 * q^21 + 360 * q^22 + 340 * q^25 - 164 * q^26 - 880 * q^28 - 1240 * q^30 - 376 * q^32 + 80 * q^33 + 460 * q^36 + 508 * q^37 + 1600 * q^38 + 1420 * q^40 - 656 * q^41 + 1160 * q^42 + 1180 * q^45 - 1432 * q^46 - 2720 * q^48 - 1570 * q^50 - 932 * q^52 - 644 * q^53 + 2048 * q^56 - 960 * q^57 + 1576 * q^58 + 3280 * q^60 - 896 * q^61 + 2440 * q^62 - 2740 * q^65 - 1680 * q^66 - 844 * q^68 - 3040 * q^70 - 3036 * q^72 + 1436 * q^73 + 800 * q^76 + 3120 * q^77 + 3720 * q^78 + 1840 * q^80 + 5988 * q^81 - 1352 * q^82 + 500 * q^85 - 2552 * q^86 - 2400 * q^88 - 750 * q^90 - 1840 * q^92 - 3280 * q^93 + 1088 * q^96 - 4772 * q^97 + 1698 * q^98

Introduction

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