LMFDB - Embedded newform 28.4.f.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,4,Mod(3,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("28.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	28.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.65205348016$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + \cdots + 1073741824 $ x^20 - 2x^18 - 24x^17 + 28x^16 + 56x^15 - 192x^14 + 352x^13 - 448x^12 + 5376x^11 - 41472x^10 + 43008x^9 - 28672x^8 + 180224x^7 - 786432x^6 + 1835008x^5 + 7340032x^4 - 50331648x^3 - 33554432*x^2 + 1073741824
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$2.59951 - 1.11469i$ of defining polynomial
Character	$\chi$	$=$	28.19
Dual form			28.4.f.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.26510 - 1.69390i) q^{2} +(-1.67134 - 2.89484i) q^{3} +(2.26140 + 7.67373i) q^{4} +(-15.9583 - 9.21354i) q^{5} +(-1.11782 + 9.38820i) q^{6} +(-15.4841 + 10.1609i) q^{7} +(7.87623 - 21.2124i) q^{8} +(7.91327 - 13.7062i) q^{9} +O(q^{10})$	\(q+(-2.26510 - 1.69390i) q^{2} +(-1.67134 - 2.89484i) q^{3} +(2.26140 + 7.67373i) q^{4} +(-15.9583 - 9.21354i) q^{5} +(-1.11782 + 9.38820i) q^{6} +(-15.4841 + 10.1609i) q^{7} +(7.87623 - 21.2124i) q^{8} +(7.91327 - 13.7062i) q^{9} +(20.5404 + 47.9014i) q^{10} +(35.6274 - 20.5695i) q^{11} +(18.4347 - 19.3718i) q^{12} -24.8455i q^{13} +(52.2846 + 3.21300i) q^{14} +61.5957i q^{15} +(-53.7722 + 34.7067i) q^{16} +(-41.3826 + 23.8923i) q^{17} +(-41.1413 + 17.6416i) q^{18} +(30.9150 - 53.5464i) q^{19} +(34.6141 - 143.295i) q^{20} +(55.2933 + 27.8416i) q^{21} +(-115.542 - 13.7572i) q^{22} +(-64.3994 - 37.1810i) q^{23} +(-74.5703 + 12.6526i) q^{24} +(107.279 + 185.812i) q^{25} +(-42.0858 + 56.2776i) q^{26} -143.155 q^{27} +(-112.988 - 95.8427i) q^{28} +28.8513 q^{29} +(104.337 - 139.521i) q^{30} +(11.5660 + 20.0328i) q^{31} +(180.589 + 12.4705i) q^{32} +(-119.091 - 68.7571i) q^{33} +(134.207 + 15.9796i) q^{34} +(340.717 - 19.4877i) q^{35} +(123.072 + 29.7291i) q^{36} +(51.8900 - 89.8761i) q^{37} +(-160.728 + 68.9212i) q^{38} +(-71.9237 + 41.5252i) q^{39} +(-321.133 + 265.946i) q^{40} -96.1780i q^{41} +(-78.0840 - 156.726i) q^{42} +195.747i q^{43} +(238.412 + 226.879i) q^{44} +(-252.565 + 145.818i) q^{45} +(82.8904 + 193.305i) q^{46} +(89.8186 - 155.570i) q^{47} +(190.342 + 97.6553i) q^{48} +(136.513 - 314.664i) q^{49} +(71.7499 - 602.603i) q^{50} +(138.329 + 79.8641i) q^{51} +(190.657 - 56.1855i) q^{52} +(-218.681 - 378.767i) q^{53} +(324.261 + 242.491i) q^{54} -758.071 q^{55} +(93.5805 + 408.483i) q^{56} -206.678 q^{57} +(-65.3511 - 48.8712i) q^{58} +(-286.640 - 496.475i) q^{59} +(-472.669 + 139.292i) q^{60} +(368.470 + 212.736i) q^{61} +(7.73553 - 64.9681i) q^{62} +(16.7374 + 292.633i) q^{63} +(-387.930 - 334.147i) q^{64} +(-228.915 + 396.492i) q^{65} +(153.285 + 357.470i) q^{66} +(728.093 - 420.365i) q^{67} +(-276.925 - 263.529i) q^{68} +248.568i q^{69} +(-804.771 - 533.000i) q^{70} +1179.04i q^{71} +(-228.414 - 275.812i) q^{72} +(716.185 - 413.489i) q^{73} +(-269.777 + 115.682i) q^{74} +(358.597 - 621.109i) q^{75} +(480.812 + 116.144i) q^{76} +(-342.652 + 680.505i) q^{77} +(233.254 + 27.7728i) q^{78} +(-282.007 - 162.817i) q^{79} +(1177.88 - 58.4284i) q^{80} +(25.6023 + 44.3445i) q^{81} +(-162.916 + 217.853i) q^{82} +507.854 q^{83} +(-88.6091 + 487.266i) q^{84} +880.530 q^{85} +(331.577 - 443.388i) q^{86} +(-48.2202 - 83.5198i) q^{87} +(-155.718 - 917.751i) q^{88} +(-176.826 - 102.090i) q^{89} +(819.088 + 97.5260i) q^{90} +(252.452 + 384.709i) q^{91} +(139.684 - 578.264i) q^{92} +(38.6612 - 66.9632i) q^{93} +(-466.970 + 200.239i) q^{94} +(-986.704 + 569.674i) q^{95} +(-265.726 - 543.620i) q^{96} +1116.33i q^{97} +(-842.225 + 481.507i) q^{98} -651.087i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9}+O(q^{10}) $ 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9	$ 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9} - 12 q^{10} - 168 q^{12} - 56 q^{14} - 104 q^{16} - 6 q^{17} + 68 q^{18} + 238 q^{21} - 184 q^{22} + 348 q^{24} - 36 q^{25} + 396 q^{26} + 448 q^{28} - 352 q^{29} + 644 q^{30} - 40 q^{32} + 30 q^{33} + 208 q^{36} + 258 q^{37} - 1620 q^{38} - 1548 q^{40} - 980 q^{42} - 1248 q^{44} - 504 q^{45} + 232 q^{46} - 644 q^{49} - 864 q^{50} + 2592 q^{52} + 570 q^{53} + 4572 q^{54} + 1904 q^{56} + 1452 q^{57} + 2244 q^{58} - 736 q^{60} + 294 q^{61} + 2560 q^{64} - 124 q^{65} - 4272 q^{66} - 6084 q^{68} - 4144 q^{70} - 4672 q^{72} + 966 q^{73} + 832 q^{74} - 378 q^{77} - 4056 q^{78} + 7032 q^{80} - 1262 q^{81} + 7692 q^{82} + 6188 q^{84} - 2980 q^{85} + 5696 q^{86} - 1396 q^{88} - 3186 q^{89} + 3312 q^{92} - 306 q^{93} - 6780 q^{94} - 11784 q^{96} - 4900 q^{98}+O(q^{100}) $ 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9 - 12 * q^10 - 168 * q^12 - 56 * q^14 - 104 * q^16 - 6 * q^17 + 68 * q^18 + 238 * q^21 - 184 * q^22 + 348 * q^24 - 36 * q^25 + 396 * q^26 + 448 * q^28 - 352 * q^29 + 644 * q^30 - 40 * q^32 + 30 * q^33 + 208 * q^36 + 258 * q^37 - 1620 * q^38 - 1548 * q^40 - 980 * q^42 - 1248 * q^44 - 504 * q^45 + 232 * q^46 - 644 * q^49 - 864 * q^50 + 2592 * q^52 + 570 * q^53 + 4572 * q^54 + 1904 * q^56 + 1452 * q^57 + 2244 * q^58 - 736 * q^60 + 294 * q^61 + 2560 * q^64 - 124 * q^65 - 4272 * q^66 - 6084 * q^68 - 4144 * q^70 - 4672 * q^72 + 966 * q^73 + 832 * q^74 - 378 * q^77 - 4056 * q^78 + 7032 * q^80 - 1262 * q^81 + 7692 * q^82 + 6188 * q^84 - 2980 * q^85 + 5696 * q^86 - 1396 * q^88 - 3186 * q^89 + 3312 * q^92 - 306 * q^93 - 6780 * q^94 - 11784 * q^96 - 4900 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−2.26510	−	1.69390i	−0.800835	−	0.598885i
$2$	−2.26510	−	1.69390i	−0.800835	−	0.598885i
$3$	−1.67134	−	2.89484i	−0.321649	−	0.557112i	0.659179	−	0.751986i	$-0.270904\pi$
$3$	−1.67134	−	2.89484i	−0.321649	−	0.557112i	−0.980828	+	0.194873i	$0.937570\pi$
$4$	2.26140	+	7.67373i	0.282675	+	0.959216i
$5$	−15.9583	−	9.21354i	−1.42736	−	0.824084i	−0.430444	−	0.902617i	$-0.641643\pi$
$5$	−15.9583	−	9.21354i	−1.42736	−	0.824084i	−0.996911	+	0.0785333i	$0.974976\pi$
$6$	−1.11782	+	9.38820i	−0.0760581	+	0.638786i
$7$	−15.4841	+	10.1609i	−0.836061	+	0.548636i
$7$	−15.4841	+	10.1609i	−0.836061	+	0.548636i
$8$	7.87623	−	21.2124i	0.348084	−	0.937463i
$9$	7.91327	−	13.7062i	0.293084	−	0.507636i
$10$	20.5404	+	47.9014i	0.649546	+	1.51478i
$11$	35.6274	−	20.5695i	0.976551	−	0.563812i	0.0753237	−	0.997159i	$-0.476001\pi$
$11$	35.6274	−	20.5695i	0.976551	−	0.563812i	0.901227	+	0.433347i	$0.142668\pi$
$12$	18.4347	−	19.3718i	0.443469	−	0.466012i
$13$		−	24.8455i		−	0.530069i	−0.964239	−	0.265035i	$-0.914617\pi$
$13$		−	24.8455i		−	0.530069i	0.964239	−	0.265035i	$-0.0853834\pi$
$14$	52.2846	+	3.21300i	0.998117	+	0.0613365i
$15$			61.5957i			1.06026i
$16$	−53.7722	+	34.7067i	−0.840190	+	0.542292i
$17$	−41.3826	+	23.8923i	−0.590398	+	0.340866i	−0.765255	−	0.643728i	$-0.777387\pi$
$17$	−41.3826	+	23.8923i	−0.590398	+	0.340866i	0.174857	+	0.984594i	$0.444054\pi$
$18$	−41.1413	+	17.6416i	−0.538727	+	0.231010i
$19$	30.9150	−	53.5464i	0.373284	−	0.646547i	−0.616785	−	0.787132i	$-0.711565\pi$
$19$	30.9150	−	53.5464i	0.373284	−	0.646547i	0.990069	+	0.140585i	$0.0448984\pi$
$20$	34.6141	−	143.295i	0.386997	−	1.60209i
$21$	55.2933	+	27.8416i	0.574570	+	0.289312i
$22$	−115.542	−	13.7572i	−1.11971	−	0.133321i
$23$	−64.3994	−	37.1810i	−0.583835	−	0.337077i	0.178821	−	0.983882i	$-0.442772\pi$
$23$	−64.3994	−	37.1810i	−0.583835	−	0.337077i	−0.762656	+	0.646804i	$0.776105\pi$
$24$	−74.5703	+	12.6526i	−0.634233	+	0.107612i
$25$	107.279	+	185.812i	0.858229	+	1.48650i
$26$	−42.0858	+	56.2776i	−0.317450	+	0.424498i
$27$	−143.155			−1.02038
$28$	−112.988	−	95.8427i	−0.762594	−	0.646877i
$29$	28.8513			0.184743			0.0923715	−	0.995725i	$-0.470555\pi$
$29$	28.8513			0.184743			0.0923715	+	0.995725i	$0.470555\pi$
$30$	104.337	−	139.521i	0.634975	−	0.849096i
$31$	11.5660	+	20.0328i	0.0670099	+	0.116065i	0.897584	−	0.440844i	$-0.145321\pi$
$31$	11.5660	+	20.0328i	0.0670099	+	0.116065i	−0.830574	+	0.556908i	$0.811987\pi$
$32$	180.589	+	12.4705i	0.997624	+	0.0688903i
$33$	−119.091	−	68.7571i	−0.628213	−	0.362699i
$34$	134.207	+	15.9796i	0.676951	+	0.0806023i
$35$	340.717	−	19.4877i	1.64548	−	0.0941147i
$36$	123.072	+	29.7291i	0.569780	+	0.137635i
$37$	51.8900	−	89.8761i	0.230558	−	0.399339i	−0.727414	−	0.686199i	$-0.759278\pi$
$37$	51.8900	−	89.8761i	0.230558	−	0.399339i	0.957973	+	0.286860i	$0.0926114\pi$
$38$	−160.728	+	68.9212i	−0.686146	+	0.294224i
$39$	−71.9237	+	41.5252i	−0.295308	+	0.170496i
$40$	−321.133	+	265.946i	−1.26939	+	1.05124i
$41$		−	96.1780i		−	0.366353i	−0.983080	−	0.183177i	$-0.941362\pi$
$41$		−	96.1780i		−	0.366353i	0.983080	−	0.183177i	$-0.0586380\pi$
$42$	−78.0840	−	156.726i	−0.286872	−	0.575792i
$43$			195.747i			0.694213i	0.937826	+	0.347107i	$0.112836\pi$
$43$			195.747i			0.694213i	−0.937826	+	0.347107i	$0.887164\pi$
$44$	238.412	+	226.879i	0.816863	+	0.777348i
$45$	−252.565	+	145.818i	−0.836670	+	0.483052i
$46$	82.8904	+	193.305i	0.265685	+	0.619593i
$47$	89.8186	−	155.570i	0.278753	−	0.482815i	−0.692322	−	0.721589i	$-0.743412\pi$
$47$	89.8186	−	155.570i	0.278753	−	0.482815i	0.971075	+	0.238774i	$0.0767456\pi$
$48$	190.342	+	97.6553i	0.572364	+	0.293653i
$49$	136.513	−	314.664i	0.397996	−	0.917387i
$50$	71.7499	−	602.603i	0.202939	−	1.70442i
$51$	138.329	+	79.8641i	0.379802	+	0.219279i
$52$	190.657	−	56.1855i	0.508451	−	0.149837i
$53$	−218.681	−	378.767i	−0.566758	−	0.981654i	−0.996884	−	0.0788851i	$-0.974864\pi$
$53$	−218.681	−	378.767i	−0.566758	−	0.981654i	0.430125	−	0.902769i	$-0.358469\pi$
$54$	324.261	+	242.491i	0.817155	+	0.611089i
$55$	−758.071			−1.85851
$56$	93.5805	+	408.483i	0.223307	+	0.974748i
$57$	−206.678			−0.480266
$58$	−65.3511	−	48.8712i	−0.147949	−	0.110640i
$59$	−286.640	−	496.475i	−0.632497	−	1.09552i	−0.987040	−	0.160477i	$-0.948697\pi$
$59$	−286.640	−	496.475i	−0.632497	−	1.09552i	0.354542	−	0.935040i	$-0.384637\pi$
$60$	−472.669	+	139.292i	−1.01702	+	0.299709i
$61$	368.470	+	212.736i	0.773405	+	0.446526i	0.834088	−	0.551632i	$-0.185995\pi$
$61$	368.470	+	212.736i	0.773405	+	0.446526i	−0.0606829	+	0.998157i	$0.519328\pi$
$62$	7.73553	−	64.9681i	0.0158454	−	0.133080i
$63$	16.7374	+	292.633i	0.0334717	+	0.585211i
$64$	−387.930	−	334.147i	−0.757675	−	0.652631i
$65$	−228.915	+	396.492i	−0.436822	+	0.756597i
$66$	153.285	+	357.470i	0.285880	+	0.666689i
$67$	728.093	−	420.365i	1.32762	−	0.766504i	0.342692	−	0.939448i	$-0.388661\pi$
$67$	728.093	−	420.365i	1.32762	−	0.766504i	0.984932	+	0.172944i	$0.0553281\pi$
$68$	−276.925	−	263.529i	−0.493855	−	0.469965i
$69$			248.568i			0.433682i
$70$	−804.771	−	533.000i	−1.37412	−	0.910081i
$71$			1179.04i			1.97079i	0.170279	+	0.985396i	$0.445533\pi$
$71$			1179.04i			1.97079i	−0.170279	+	0.985396i	$0.554467\pi$
$72$	−228.414	−	275.812i	−0.373873	−	0.451455i
$73$	716.185	−	413.489i	1.14826	−	0.662949i	0.199798	−	0.979837i	$-0.435971\pi$
$73$	716.185	−	413.489i	1.14826	−	0.662949i	0.948463	+	0.316888i	$0.102638\pi$
$74$	−269.777	+	115.682i	−0.423797	+	0.181727i
$75$	358.597	−	621.109i	0.552097	−	0.956260i
$76$	480.812	+	116.144i	0.725696	+	0.175297i
$77$	−342.652	+	680.505i	−0.507128	+	1.00715i
$78$	233.254	+	27.7728i	0.338601	+	0.0403160i
$79$	−282.007	−	162.817i	−0.401623	−	0.231877i	0.285561	−	0.958361i	$-0.407820\pi$
$79$	−282.007	−	162.817i	−0.401623	−	0.231877i	−0.687184	+	0.726483i	$0.741153\pi$
$80$	1177.88	−	58.4284i	1.64614	−	0.0816561i
$81$	25.6023	+	44.3445i	0.0351198	+	0.0608292i
$82$	−162.916	+	217.853i	−0.219403	+	0.293389i
$83$	507.854			0.671617			0.335808	−	0.941930i	$-0.390991\pi$
$83$	507.854			0.671617			0.335808	+	0.941930i	$0.390991\pi$
$84$	−88.6091	+	487.266i	−0.115096	+	0.632918i
$85$	880.530			1.12361
$86$	331.577	−	443.388i	0.415754	−	0.555951i
$87$	−48.2202	−	83.5198i	−0.0594224	−	0.102923i
$88$	−155.718	−	917.751i	−0.188632	−	1.11173i
$89$	−176.826	−	102.090i	−0.210601	−	0.121590i	0.390990	−	0.920395i	$-0.372133\pi$
$89$	−176.826	−	102.090i	−0.210601	−	0.121590i	−0.601591	+	0.798805i	$0.705466\pi$
$90$	819.088	+	97.5260i	0.959327	+	0.114224i
$91$	252.452	+	384.709i	0.290815	+	0.443170i
$92$	139.684	−	578.264i	0.158295	−	0.655307i
$93$	38.6612	−	66.9632i	0.0431074	−	0.0746641i
$94$	−466.970	+	200.239i	−0.512385	+	0.219714i
$95$	−986.704	+	569.674i	−1.06562	+	0.615235i
$96$	−265.726	−	543.620i	−0.282505	−	0.577947i
$97$			1116.33i			1.16852i	0.811566	+	0.584261i	$0.198615\pi$
$97$			1116.33i			1.16852i	−0.811566	+	0.584261i	$0.801385\pi$
$98$	−842.225	+	481.507i	−0.868138	+	0.496322i
$99$		−	651.087i		−	0.660977i
$100$	−1183.27	+	1243.42i	−1.18327	+	1.24342i
$101$	−3.43081	+	1.98078i	−0.00337999	+	0.00195144i	−0.501689	−	0.865048i	$-0.667288\pi$
$101$	−3.43081	+	1.98078i	−0.00337999	+	0.00195144i	0.498309	+	0.866999i	$0.333954\pi$
$102$	−178.047	−	415.216i	−0.172836	−	0.403063i
$103$	179.406	−	310.741i	0.171626	−	0.297264i	−0.767363	−	0.641213i	$-0.778431\pi$
$103$	179.406	−	310.741i	0.171626	−	0.297264i	0.938988	+	0.343949i	$0.111765\pi$
$104$	−527.032	−	195.689i	−0.496920	−	0.184508i
$105$	−625.867	−	953.752i	−0.581699	−	0.886445i
$106$	−146.258	+	1228.37i	−0.134017	+	1.12557i
$107$	−803.472	−	463.885i	−0.725931	−	0.419116i	0.0910010	−	0.995851i	$-0.470993\pi$
$107$	−803.472	−	463.885i	−0.725931	−	0.419116i	−0.816932	+	0.576735i	$0.804327\pi$
$108$	−323.731	−	1098.53i	−0.288435	−	0.978763i
$109$	−594.270	−	1029.31i	−0.522209	−	0.904492i	−0.999666	−	0.0258371i	$-0.991775\pi$
$109$	−594.270	−	1029.31i	−0.522209	−	0.904492i	0.477458	−	0.878655i	$-0.341558\pi$
$110$	1717.11	+	1284.10i	1.48836	+	1.11303i
$111$	−346.903			−0.296635
$112$	479.961	−	1083.77i	0.404929	−	0.914348i
$113$	−662.367			−0.551418			−0.275709	−	0.961241i	$-0.588913\pi$
$113$	−662.367			−0.551418			−0.275709	+	0.961241i	$0.588913\pi$
$114$	468.147	+	350.092i	0.384614	+	0.287624i
$115$	685.137	+	1186.69i	0.555560	+	0.962258i
$116$	65.2442	+	221.397i	0.0522222	+	0.177208i
$117$	−340.537	−	196.609i	−0.269082	−	0.155355i
$118$	−191.710	+	1610.11i	−0.149562	+	1.25612i
$119$	398.005	−	790.434i	0.306597	−	0.608899i
$120$	1306.59	+	485.142i	0.993958	+	0.369060i
$121$	180.707	−	312.993i	0.135768	−	0.235156i
$122$	−474.268	−	1106.02i	−0.351953	−	0.820774i
$123$	−278.420	+	160.746i	−0.204100	+	0.117837i
$124$	−127.571	+	134.056i	−0.0923890	+	0.0970855i
$125$		−	1650.28i		−	1.18084i
$126$	457.780	−	691.196i	0.323669	−	0.488704i
$127$		−	1496.04i		−	1.04529i	−0.852549	−	0.522647i	$-0.824945\pi$
$127$		−	1496.04i		−	1.04529i	0.852549	−	0.522647i	$-0.175055\pi$
$128$	312.689	+	1413.99i	0.215922	+	0.976411i
$129$	566.657	−	327.160i	0.386755	−	0.223293i
$130$	1190.13	−	510.337i	0.802936	−	0.344304i
$131$	−984.794	+	1705.71i	−0.656808	+	1.13762i	0.324630	+	0.945841i	$0.394760\pi$
$131$	−984.794	+	1705.71i	−0.656808	+	1.13762i	−0.981437	+	0.191783i	$0.938573\pi$
$132$	258.311	−	1069.36i	0.170327	−	0.705118i
$133$	65.3887	+	1143.24i	0.0426310	+	0.745350i
$134$	−2361.26	−	281.148i	−1.52225	−	0.181250i
$135$	2284.52	+	1318.97i	1.45644	+	0.840878i
$136$	180.873	+	1066.01i	0.114042	+	0.672126i
$137$	896.791	+	1553.29i	0.559256	+	0.968660i	0.997559	+	0.0698322i	$0.0222464\pi$
$137$	896.791	+	1553.29i	0.559256	+	0.968660i	−0.438303	+	0.898827i	$0.644420\pi$
$138$	421.050	−	563.032i	0.259726	−	0.347308i
$139$	306.409			0.186973			0.0934867	−	0.995621i	$-0.470199\pi$
$139$	306.409			0.186973			0.0934867	+	0.995621i	$0.470199\pi$
$140$	920.040	+	2570.50i	0.555411	+	1.55177i
$141$	−600.469			−0.358643
$142$	1997.18	−	2670.65i	1.18028	−	1.57828i
$143$	−511.059	−	885.180i	−0.298859	−	0.517639i
$144$	50.1826	+	1011.65i	0.0290408	+	0.585448i
$145$	−460.418	−	265.822i	−0.263694	−	0.152244i
$146$	−2322.64	−	276.549i	−1.31660	−	0.156763i
$147$	−1139.06	+	130.727i	−0.639103	+	0.0733481i
$148$	807.028	+	194.944i	0.448225	+	0.108272i
$149$	714.928	−	1238.29i	0.393082	−	0.680838i	−0.599773	−	0.800171i	$-0.704742\pi$
$149$	714.928	−	1238.29i	0.393082	−	0.680838i	0.992854	+	0.119333i	$0.0380756\pi$
$150$	−1864.36	+	799.448i	−1.01483	+	0.435164i
$151$	1079.16	−	623.054i	0.581595	−	0.335784i	−0.180172	−	0.983635i	$-0.557665\pi$
$151$	1079.16	−	623.054i	0.581595	−	0.335784i	0.761767	+	0.647851i	$0.224332\pi$
$152$	−892.352	−	1077.53i	−0.476180	−	0.574992i
$153$			756.264i			0.399610i
$154$	1928.85	−	960.995i	1.00929	−	0.502852i
$155$		−	426.254i		−	0.220887i
$156$	−481.301	−	458.018i	−0.247019	−	0.235069i
$157$	−2201.64	+	1271.12i	−1.11917	+	0.646154i	−0.941189	−	0.337880i	$-0.890290\pi$
$157$	−2201.64	+	1271.12i	−1.11917	+	0.646154i	−0.177982	+	0.984034i	$0.556957\pi$
$158$	362.980	+	846.489i	0.182766	+	0.426222i
$159$	−730.980	+	1266.10i	−0.364594	+	0.631496i
$160$	−2767.00	−	1862.87i	−1.36719	−	0.920457i
$161$	1374.96	−	78.6420i	0.673054	−	0.0384960i
$162$	17.1233	−	143.813i	0.00830453	−	0.0697469i
$163$	−637.434	−	368.022i	−0.306305	−	0.176845i	0.338967	−	0.940798i	$-0.389922\pi$
$163$	−637.434	−	368.022i	−0.306305	−	0.176845i	−0.645272	+	0.763953i	$0.723256\pi$
$164$	738.044	−	217.497i	0.351412	−	0.103559i
$165$	1266.99	+	2194.49i	0.597789	+	1.03540i
$166$	−1150.34	−	860.254i	−0.537855	−	0.402221i
$167$	3110.82			1.44145			0.720726	−	0.693220i	$-0.243809\pi$
$167$	3110.82			1.44145			0.720726	+	0.693220i	$0.243809\pi$
$168$	1026.09	−	953.614i	0.471218	−	0.437934i
$169$	1579.70			0.719027
$170$	−1994.49	−	1491.53i	−0.899827	−	0.672913i
$171$	−489.278	−	847.454i	−0.218807	−	0.378985i
$172$	−1502.11	+	442.662i	−0.665901	+	0.196237i
$173$	2719.50	+	1570.10i	1.19514	+	0.690015i	0.959468	−	0.281817i	$-0.0909370\pi$
$173$	2719.50	+	1570.10i	1.19514	+	0.690015i	0.235674	+	0.971832i	$0.424270\pi$
$174$	−32.2506	+	270.861i	−0.0140512	+	0.118011i
$175$	−3549.12	−	1787.08i	−1.53308	−	0.771946i
$176$	−1201.86	+	2342.57i	−0.514738	+	1.00328i
$177$	−958.144	+	1659.55i	−0.406884	+	0.704744i
$178$	227.598	+	530.770i	0.0958380	+	0.223500i
$179$	−206.742	+	119.362i	−0.0863274	+	0.0498411i	−0.542542	−	0.840028i	$-0.682538\pi$
$179$	−206.742	+	119.362i	−0.0863274	+	0.0498411i	0.456215	+	0.889870i	$0.349205\pi$
$180$	−1690.12	−	1608.36i	−0.699856	−	0.666000i
$181$		−	1947.09i		−	0.799591i	−0.916604	−	0.399796i	$-0.869081\pi$
$181$		−	1947.09i		−	0.799591i	0.916604	−	0.399796i	$-0.130919\pi$
$182$	79.8286	−	1299.04i	0.0325126	−	0.529071i
$183$		−	1422.21i		−	0.574498i
$184$	−1295.92	+	1073.22i	−0.519221	+	0.429993i
$185$	−1656.15	+	956.181i	−0.658177	+	0.379999i
$186$	−201.001	+	86.1904i	−0.0792371	+	0.0339773i
$187$	−982.903	+	1702.44i	−0.384369	+	0.665746i
$188$	1396.92	+	337.437i	0.541920	+	0.130905i
$189$	2216.62	−	1454.58i	0.853099	−	0.559817i
$190$	3199.96	+	381.008i	1.22184	+	0.145480i
$191$	393.391	+	227.124i	0.149030	+	0.0860427i	0.572661	−	0.819792i	$-0.305911\pi$
$191$	393.391	+	227.124i	0.149030	+	0.0860427i	−0.423631	+	0.905835i	$0.639245\pi$
$192$	−318.942	+	1681.47i	−0.119884	+	0.632029i
$193$	−1605.08	−	2780.08i	−0.598634	−	1.03686i	−0.993023	−	0.117921i	$-0.962377\pi$
$193$	−1605.08	−	2780.08i	−0.598634	−	1.03686i	0.394389	−	0.918944i	$-0.370956\pi$
$194$	1890.96	−	2528.61i	0.699809	−	0.935793i
$195$	1530.38			0.562013
$196$	2723.35	+	335.981i	0.992476	+	0.122442i
$197$	−4173.52			−1.50940			−0.754698	−	0.656073i	$-0.772216\pi$
$197$	−4173.52			−1.50940			−0.754698	+	0.656073i	$0.772216\pi$
$198$	−1102.88	+	1474.78i	−0.395849	+	0.529333i
$199$	2639.30	+	4571.40i	0.940176	+	1.62843i	0.765134	+	0.643871i	$0.222673\pi$
$199$	2639.30	+	4571.40i	0.940176	+	1.62843i	0.175042	+	0.984561i	$0.443994\pi$
$200$	4786.47	−	812.135i	1.69227	−	0.287133i
$201$	−2433.78	−	1405.14i	−0.854057	−	0.493090i
$202$	11.1264	+	1.32478i	0.00387550	+	0.000461443i
$203$	−446.735	+	293.155i	−0.154456	+	0.101357i
$204$	−300.039	+	1242.10i	−0.102975	+	0.426296i
$205$	−886.140	+	1534.84i	−0.301906	+	0.522916i
$206$	−932.738	+	399.964i	−0.315471	+	0.135276i
$207$	−1019.22	+	588.446i	−0.342225	+	0.197584i
$208$	862.305	+	1336.00i	0.287452	+	0.445359i
$209$		−	2543.62i		−	0.841848i
$210$	−197.907	+	3220.51i	−0.0650328	+	1.05827i
$211$		−	871.583i		−	0.284371i	−0.989840	−	0.142185i	$-0.954587\pi$
$211$		−	871.583i		−	0.284371i	0.989840	−	0.142185i	$-0.0454130\pi$
$212$	2412.03	−	2534.64i	0.781410	−	0.821132i
$213$	3413.13	−	1970.57i	1.09795	−	0.633903i
$214$	1034.17	+	2411.75i	0.330349	+	0.770392i
$215$	1803.53	−	3123.80i	0.572090	−	0.990889i
$216$	−1127.52	+	3036.66i	−0.355177	+	0.956568i
$217$	−382.640	−	192.669i	−0.119702	−	0.0602730i
$218$	−397.459	+	3338.12i	−0.123483	+	1.03709i
$219$	−2393.97	−	1382.16i	−0.738674	−	0.426474i
$220$	−1714.30	−	5817.23i	−0.525355	−	1.78272i
$221$	593.615	+	1028.17i	0.180683	+	0.312952i
$222$	785.771	+	587.619i	0.237556	+	0.177650i
$223$	1930.21			0.579624			0.289812	−	0.957084i	$-0.406407\pi$
$223$	1930.21			0.579624			0.289812	+	0.957084i	$0.406407\pi$
$224$	−2922.97	+	1641.85i	−0.871870	+	0.489737i
$225$	3395.70			1.00613
$226$	1500.33	+	1121.98i	0.441595	+	0.330236i
$227$	988.231	+	1711.67i	0.288948	+	0.500473i	0.973559	−	0.228436i	$-0.0733612\pi$
$227$	988.231	+	1711.67i	0.288948	+	0.500473i	−0.684611	+	0.728909i	$0.740028\pi$
$228$	−467.380	−	1585.99i	−0.135759	−	0.460678i
$229$	−2237.66	−	1291.92i	−0.645716	−	0.372804i	0.141097	−	0.989996i	$-0.454937\pi$
$229$	−2237.66	−	1291.92i	−0.645716	−	0.372804i	−0.786813	+	0.617192i	$0.788270\pi$
$230$	458.233	−	3848.54i	0.131369	−	1.10333i
$231$	2542.64	−	145.429i	0.724214	−	0.0414221i
$232$	227.239	−	612.004i	0.0643060	−	0.173190i
$233$	1724.22	−	2986.43i	0.484795	−	0.839690i	−0.515052	−	0.857159i	$-0.672227\pi$
$233$	1724.22	−	2986.43i	0.484795	−	0.839690i	0.999847	+	0.0174686i	$0.00556071\pi$
$234$	438.315	+	1022.18i	0.122451	+	0.285563i
$235$	−2866.71	+	1655.10i	−0.795759	+	0.459432i
$236$	3161.61	−	3322.32i	0.872047	−	0.916376i
$237$			1088.49i			0.298333i
$238$	−2240.44	+	1116.23i	−0.610194	+	0.304012i
$239$		−	3647.94i		−	0.987304i	−0.869659	−	0.493652i	$-0.835662\pi$
$239$		−	3647.94i		−	0.987304i	0.869659	−	0.493652i	$-0.164338\pi$
$240$	−2137.78	−	3312.14i	−0.574972	−	0.890823i
$241$	−2194.49	+	1266.99i	−0.586553	+	0.338646i	−0.763733	−	0.645532i	$-0.776636\pi$
$241$	−2194.49	+	1266.99i	−0.586553	+	0.338646i	0.177180	+	0.984178i	$0.443302\pi$
$242$	−939.499	+	402.863i	−0.249559	+	0.107012i
$243$	−1847.01	+	3199.12i	−0.487597	+	0.844542i
$244$	−799.222	+	3308.62i	−0.209692	+	0.868084i
$245$	−5077.68	+	3763.74i	−1.32409	+	0.981455i
$246$	902.938	+	107.510i	0.234021	+	0.0278641i
$247$	−1330.39	−	768.099i	−0.342714	−	0.197866i
$248$	516.040	−	87.5582i	0.132131	−	0.0224192i
$249$	−848.795	−	1470.16i	−0.216025	−	0.374166i
$250$	−2795.41	+	3738.05i	−0.707189	+	0.945661i
$251$	−5658.23			−1.42289			−0.711443	−	0.702744i	$-0.751958\pi$
$251$	−5658.23			−1.42289			−0.711443	+	0.702744i	$0.751958\pi$
$252$	−2207.74	+	790.198i	−0.551882	+	0.197531i
$253$	−3059.18			−0.760193
$254$	−2534.15	+	3388.69i	−0.626010	+	0.837108i
$255$	−1471.66	−	2548.99i	−0.361408	−	0.625977i
$256$	1686.89	−	3732.51i	0.411839	−	0.911257i
$257$	4328.82	+	2499.25i	1.05068	+	0.606610i	0.922840	−	0.385185i	$-0.125862\pi$
$257$	4328.82	+	2499.25i	1.05068	+	0.606610i	0.127840	+	0.991795i	$0.459196\pi$
$258$	−1837.71	−	218.810i	−0.443454	−	0.0528006i
$259$	109.753	+	1918.90i	0.0263310	+	0.460364i
$260$	−3560.24	−	860.004i	−0.849218	−	0.205135i
$261$	228.308	−	395.441i	0.0541452	−	0.0937822i
$262$	5119.97	−	2195.47i	1.20730	−	0.517698i
$263$	1646.99	−	950.892i	0.386152	−	0.222945i	−0.294340	−	0.955701i	$-0.595100\pi$
$263$	1646.99	−	950.892i	0.386152	−	0.222945i	0.680491	+	0.732756i	$0.261766\pi$
$264$	−2396.49	+	1984.65i	−0.558688	+	0.462677i
$265$			8059.32i			1.86823i
$266$	1788.42	−	2700.32i	0.412238	−	0.622433i
$267$			682.509i			0.156438i
$268$	4872.27	+	4636.58i	1.11053	+	1.05681i
$269$	6976.20	−	4027.71i	1.58121	−	0.912913i	0.586530	−	0.809928i	$-0.300494\pi$
$269$	6976.20	−	4027.71i	1.58121	−	0.912913i	0.994683	−	0.102986i	$-0.0328395\pi$
$270$	−2940.47	−	6857.34i	−0.662782	−	1.54565i
$271$	2189.04	−	3791.53i	0.490682	−	0.849886i	−0.509261	−	0.860612i	$-0.670081\pi$
$271$	2189.04	−	3791.53i	0.490682	−	0.849886i	0.999942	+	0.0107264i	$0.00341438\pi$
$272$	1396.01	−	2720.99i	0.311197	−	0.606560i
$273$	691.739	−	1373.79i	0.153355	−	0.304562i
$274$	599.791	−	5037.44i	0.132243	−	1.11067i
$275$	7644.11	+	4413.33i	1.67621	+	0.967759i
$276$	−1907.44	+	562.111i	−0.415995	+	0.122591i
$277$	1602.26	+	2775.19i	0.347547	+	0.601968i	0.985813	−	0.167847i	$-0.0536815\pi$
$277$	1602.26	+	2775.19i	0.347547	+	0.601968i	−0.638266	+	0.769815i	$0.720348\pi$
$278$	−694.049	−	519.027i	−0.149735	−	0.111975i
$279$	366.098			0.0785581
$280$	2270.19	−	7380.92i	0.484535	−	1.57534i
$281$	6258.33			1.32861			0.664307	−	0.747460i	$-0.268727\pi$
$281$	6258.33			1.32861			0.664307	+	0.747460i	$0.268727\pi$
$282$	1360.12	+	1017.13i	0.287214	+	0.214785i
$283$	−3029.37	−	5247.02i	−0.636316	−	1.10213i	−0.986235	−	0.165351i	$-0.947124\pi$
$283$	−3029.37	−	5247.02i	−0.636316	−	1.10213i	0.349919	−	0.936780i	$-0.386209\pi$
$284$	−9047.62	+	2666.28i	−1.89041	+	0.557093i
$285$	3298.23	+	1904.23i	0.685510	+	0.395779i
$286$	−341.806	+	2870.71i	−0.0706692	+	0.593526i
$287$	977.254	+	1489.23i	0.200995	+	0.306294i
$288$	1599.97	−	2376.51i	0.327359	−	0.486240i
$289$	−1314.82	+	2277.33i	−0.267620	+	0.463532i
$290$	592.618	+	1382.02i	0.119999	+	0.279844i
$291$	3231.61	−	1865.77i	0.650998	−	0.375854i
$292$	4792.58	+	4560.74i	0.960495	+	0.914032i
$293$		−	457.644i		−	0.0912486i	−0.998959	−	0.0456243i	$-0.985472\pi$
$293$		−	457.644i		−	0.0912486i	0.998959	−	0.0456243i	$-0.0145277\pi$
$294$	2801.53	+	1633.35i	0.555743	+	0.324009i
$295$			10563.9i			2.08492i
$296$	−1497.79	−	1808.59i	−0.294112	−	0.355143i
$297$	−5100.24	+	2944.63i	−0.996451	+	0.575301i
$298$	−3716.93	+	1593.84i	−0.722537	+	0.309828i
$299$	−923.780	+	1600.03i	−0.178674	+	0.309473i
$300$	5577.15	+	1347.20i	1.07332	+	0.259270i
$301$	−1988.97	−	3030.96i	−0.380871	−	0.580405i
$302$	−3499.80	−	416.710i	−0.666858	−	0.0794005i
$303$	11.4681	+	6.62110i	0.00217434	+	0.00125535i
$304$	196.050	+	3952.26i	0.0369876	+	0.745651i
$305$	−3920.10	−	6789.82i	−0.735949	−	1.27470i
$306$	1281.04	−	1713.02i	0.239320	−	0.320022i
$307$	4195.62			0.779989			0.389995	−	0.920817i	$-0.372477\pi$
$307$	4195.62			0.779989			0.389995	+	0.920817i	$0.372477\pi$
$308$	−5996.88	−	1090.53i	−1.10943	−	0.201749i
$309$	−1199.39			−0.220813
$310$	−722.032	+	965.509i	−0.132286	+	0.176894i
$311$	−3254.20	−	5636.44i	−0.593341	−	1.02770i	−0.993779	−	0.111372i	$-0.964475\pi$
$311$	−3254.20	−	5636.44i	−0.593341	−	1.02770i	0.400438	−	0.916324i	$-0.368858\pi$
$312$	314.360	+	1852.74i	0.0570420	+	0.336187i
$313$	−7481.59	−	4319.50i	−1.35107	−	0.780040i	−0.362670	−	0.931918i	$-0.618135\pi$
$313$	−7481.59	−	4319.50i	−1.35107	−	0.780040i	−0.988399	+	0.151878i	$0.951468\pi$
$314$	7140.09	+	850.146i	1.28324	+	0.152792i
$315$	2429.09	−	4824.14i	0.434487	−	0.862888i
$316$	611.682	−	2532.24i	0.108892	−	0.450789i
$317$	−463.165	+	802.226i	−0.0820629	+	0.142137i	−0.904136	−	0.427245i	$-0.859484\pi$
$317$	−463.165	+	802.226i	−0.0820629	+	0.142137i	0.822073	+	0.569382i	$0.192818\pi$
$318$	3800.39	−	1629.63i	0.670173	−	0.287374i
$319$	1027.90	−	593.455i	0.180411	−	0.104160i
$320$	3112.03	+	8906.64i	0.543649	+	1.55593i
$321$			3101.23i			0.539233i
$322$	−3247.63	−	2150.91i	−0.562060	−	0.372253i
$323$			2954.52i			0.508960i
$324$	−282.391	+	296.746i	−0.0484209	+	0.0508823i
$325$	4616.59	−	2665.39i	0.787946	−	0.454921i
$326$	820.460	+	1913.36i	0.139390	+	0.325065i
$327$	−1986.45	+	3440.63i	−0.335936	+	0.581858i
$328$	−2040.16	−	757.520i	−0.343443	−	0.127522i
$329$	189.976	+	3321.50i	0.0318351	+	0.556596i
$330$	847.387	−	7116.92i	0.141355	−	1.18719i
$331$	−8260.72	−	4769.33i	−1.37175	−	0.791982i	−0.380604	−	0.924738i	$-0.624284\pi$
$331$	−8260.72	−	4769.33i	−1.37175	−	0.791982i	−0.991149	+	0.132756i	$0.957617\pi$
$332$	1148.46	+	3897.13i	0.189849	+	0.644225i
$333$	−821.238	−	1422.43i	−0.135146	−	0.234080i
$334$	−7046.33	−	5269.42i	−1.15437	−	0.863263i
$335$	−15492.2			−2.52665
$336$	−3939.53	+	421.941i	−0.639640	+	0.0685082i
$337$	4736.32			0.765589			0.382795	−	0.923833i	$-0.374962\pi$
$337$	4736.32			0.765589			0.382795	+	0.923833i	$0.374962\pi$
$338$	−3578.19	−	2675.86i	−0.575822	−	0.430614i
$339$	1107.04	+	1917.45i	0.177363	+	0.307202i
$340$	1991.23	+	6756.94i	0.317616	+	1.07778i
$341$	824.130	+	475.812i	0.130877	+	0.0755620i
$342$	−327.238	+	2748.36i	−0.0517398	+	0.434545i
$343$	1083.49	+	6259.36i	0.170563	+	0.985347i
$344$	4152.26	+	1541.75i	0.650800	+	0.241644i
$345$	2290.19	−	3966.73i	0.357391	−	0.619019i
$346$	−3500.35	−	8163.01i	−0.543872	−	1.26834i
$347$	1694.40	−	978.260i	0.262133	−	0.151342i	−0.363174	−	0.931721i	$-0.618307\pi$
$347$	1694.40	−	978.260i	0.262133	−	0.151342i	0.625307	+	0.780379i	$0.284974\pi$
$348$	531.863	−	558.900i	0.0819278	−	0.0860925i
$349$		−	9739.50i		−	1.49382i	−0.664924	−	0.746911i	$-0.731536\pi$
$349$		−	9739.50i		−	1.49382i	0.664924	−	0.746911i	$-0.268464\pi$
$350$	5012.00	+	10059.8i	0.765437	+	1.53634i
$351$			3556.76i			0.540871i
$352$	6690.43	−	3270.34i	1.01307	−	0.495198i
$353$	−2590.09	+	1495.39i	−0.390528	+	0.225471i	−0.682389	−	0.730989i	$-0.739059\pi$
$353$	−2590.09	+	1495.39i	−0.390528	+	0.225471i	0.291861	+	0.956461i	$0.405726\pi$
$354$	4981.42	−	2136.06i	0.747908	−	0.320707i
$355$	10863.1	−	18815.5i	1.62410	−	2.81302i
$356$	383.540	−	1587.78i	0.0571000	−	0.236382i
$357$	−2953.38	+	168.921i	−0.437842	+	0.0250428i
$358$	670.480	+	79.8318i	0.0989831	+	0.0117856i
$359$	−1144.24	−	660.628i	−0.168219	−	0.0971215i	0.413527	−	0.910492i	$-0.364297\pi$
$359$	−1144.24	−	660.628i	−0.168219	−	0.0971215i	−0.581746	+	0.813371i	$0.697630\pi$
$360$	1103.89	+	6506.00i	0.161612	+	0.952490i
$361$	1518.02	+	2629.29i	0.221318	+	0.383334i
$362$	−3298.18	+	4410.36i	−0.478863	+	0.640341i
$363$	−1208.09			−0.174678
$364$	−2381.26	+	2807.23i	−0.342890	+	0.404228i
$365$	−15238.8			−2.18530
$366$	−2409.09	+	3221.46i	−0.344058	+	0.460078i
$367$	3367.76	+	5833.14i	0.479008	+	0.829666i	0.999710	−	0.0240726i	$-0.00766327\pi$
$367$	3367.76	+	5833.14i	0.479008	+	0.829666i	−0.520703	+	0.853738i	$0.674330\pi$
$368$	4753.32	−	235.786i	0.673327	−	0.0334000i
$369$	−1318.23	−	761.082i	−0.185974	−	0.107372i
$370$	5371.04	+	639.511i	0.754667	+	0.0898557i
$371$	7234.69	+	3642.86i	1.01242	+	0.509779i
$372$	601.286	+	145.245i	0.0838044	+	0.0202436i
$373$	−104.742	+	181.419i	−0.0145398	+	0.0251837i	−0.873204	−	0.487355i	$-0.837962\pi$
$373$	−104.742	+	181.419i	−0.0145398	+	0.0251837i	0.858664	+	0.512539i	$0.171295\pi$
$374$	5110.14	−	2191.26i	0.706521	−	0.302961i
$375$	−4777.29	+	2758.17i	−0.657862	+	0.379817i
$376$	−2592.59	−	3130.58i	−0.355592	−	0.429381i
$377$		−	716.824i		−	0.0979265i
$378$	−7484.80	−	459.958i	−1.01846	−	0.0625864i
$379$			1205.99i			0.163450i	0.996655	+	0.0817250i	$0.0260429\pi$
$379$			1205.99i			0.163450i	−0.996655	+	0.0817250i	$0.973957\pi$
$380$	−6602.85	−	6283.44i	−0.891366	−	0.848246i
$381$	−4330.81	+	2500.39i	−0.582346	+	0.336218i
$382$	−506.346	−	1180.83i	−0.0678191	−	0.158158i
$383$	−1590.45	+	2754.73i	−0.212188	+	0.367520i	−0.952399	−	0.304854i	$-0.901392\pi$
$383$	−1590.45	+	2754.73i	−0.212188	+	0.367520i	0.740211	+	0.672375i	$0.234726\pi$
$384$	3570.68	−	3268.44i	0.474519	−	0.434354i
$385$	11738.0	−	7702.67i	1.55383	−	1.01965i
$386$	−1073.51	+	9016.03i	−0.141555	+	1.18887i
$387$	2682.95	+	1549.00i	0.352408	+	0.203463i
$388$	−8566.44	+	2524.47i	−1.12086	+	0.330311i
$389$	4006.02	+	6938.63i	0.522142	+	0.904377i	0.999668	+	0.0257595i	$0.00820040\pi$
$389$	4006.02	+	6938.63i	0.522142	+	0.904377i	−0.477526	+	0.878618i	$0.658466\pi$
$390$	−3466.46	−	2592.31i	−0.450080	−	0.336581i
$391$	3553.36			0.459593
$392$	−5599.56	−	5374.12i	−0.721481	−	0.692434i
$393$	6583.69			0.845046
$394$	9453.46	+	7069.53i	1.20878	+	0.903954i
$395$	3000.24	+	5196.56i	0.382173	+	0.661943i
$396$	4996.26	−	1472.37i	0.634019	−	0.186841i
$397$	10496.5	+	6060.15i	1.32696	+	0.766121i	0.984828	−	0.173531i	$-0.0555177\pi$
$397$	10496.5	+	6060.15i	1.32696	+	0.766121i	0.342132	+	0.939652i	$0.388851\pi$
$398$	1765.21	−	14825.4i	0.222317	−	1.86716i
$399$	3200.21	−	2100.03i	0.401531	−	0.263491i
$400$	−12217.5	−	6268.23i	−1.52719	−	0.783529i
$401$	−5497.13	+	9521.31i	−0.684573	+	1.18571i	0.288998	+	0.957330i	$0.406678\pi$
$401$	−5497.13	+	9521.31i	−0.684573	+	1.18571i	−0.973571	+	0.228385i	$0.926655\pi$
$402$	3132.59	+	7305.38i	0.388655	+	0.906366i
$403$	497.726	−	287.362i	0.0615223	−	0.0355199i
$404$	−22.9584	−	21.8478i	−0.00282728	−	0.00269052i
$405$		−	943.552i		−	0.115767i
$406$	1508.48	+	92.6992i	0.184395	+	0.0113315i
$407$		−	4269.40i		−	0.519966i
$408$	2783.62	−	2305.25i	0.337768	−	0.279723i
$409$	−1739.78	+	1004.46i	−0.210333	+	0.121436i	−0.601466	−	0.798898i	$-0.705417\pi$
$409$	−1739.78	+	1004.46i	−0.210333	+	0.121436i	0.391133	+	0.920334i	$0.372083\pi$
$410$	4607.06	−	1975.54i	0.554943	−	0.237963i
$411$	2997.68	−	5192.14i	0.359768	−	0.623137i
$412$	2790.25	+	674.007i	0.333655	+	0.0805969i
$413$	9482.98	+	4774.93i	1.12985	+	0.568908i
$414$	3305.41	+	393.564i	0.392396	+	0.0467213i
$415$	−8104.49	−	4679.13i	−0.958636	−	0.553469i
$416$	309.835	−	4486.83i	0.0365166	−	0.528810i
$417$	−512.113	−	887.006i	−0.0601398	−	0.104165i
$418$	−4308.65	+	5761.57i	−0.504169	+	0.674181i
$419$	−6662.83			−0.776850			−0.388425	−	0.921480i	$-0.626981\pi$
$419$	−6662.83			−0.776850			−0.388425	+	0.921480i	$0.626981\pi$
$420$	5903.50	−	6959.55i	0.685860	−	0.808550i
$421$	5859.67			0.678344			0.339172	−	0.940724i	$-0.389853\pi$
$421$	5859.67			0.678344			0.339172	+	0.940724i	$0.389853\pi$
$422$	−1476.38	+	1974.23i	−0.170305	+	0.227734i
$423$	−1421.52	−	2462.14i	−0.163396	−	0.283010i
$424$	−9756.94	+	1655.49i	−1.11754	+	0.189617i
$425$	−8878.94	−	5126.26i	−1.01339	−	0.585083i
$426$	−11069.1	−	1317.95i	−1.25891	−	0.149895i
$427$	−7867.00	+	449.960i	−0.891594	+	0.0509956i
$428$	1742.76	−	7214.65i	0.196821	−	0.814798i
$429$	−1708.30	+	2958.87i	−0.192256	+	0.332996i
$430$	−9376.58	+	4020.73i	−1.05158	+	0.450923i
$431$	3178.02	−	1834.83i	0.355174	−	0.205060i	−0.311788	−	0.950152i	$-0.600928\pi$
$431$	3178.02	−	1834.83i	0.355174	−	0.205060i	0.666962	+	0.745092i	$0.267594\pi$
$432$	7697.76	−	4968.44i	0.857312	−	0.553343i
$433$			8282.34i			0.919224i	0.888120	+	0.459612i	$0.152011\pi$
$433$			8282.34i			0.919224i	−0.888120	+	0.459612i	$0.847989\pi$
$434$	540.356	+	1084.57i	0.0597648	+	0.119956i
$435$			1777.11i			0.195876i
$436$	6554.73	−	6887.93i	0.719988	−	0.756588i
$437$	−3981.82	+	2298.90i	−0.435872	+	0.251651i
$438$	3081.35	+	7185.89i	0.336148	+	0.783916i
$439$	−4840.93	+	8384.73i	−0.526298	+	0.911575i	0.473233	+	0.880938i	$0.343087\pi$
$439$	−4840.93	+	8384.73i	−0.526298	+	0.911575i	−0.999531	+	0.0306374i	$0.990246\pi$
$440$	−5970.74	+	16080.5i	−0.646918	+	1.74229i
$441$	−3232.58	−	4361.08i	−0.349053	−	0.470909i
$442$	397.021	−	3334.44i	0.0427248	−	0.358831i
$443$	7154.34	+	4130.56i	0.767298	+	0.443000i	0.831910	−	0.554911i	$-0.187248\pi$
$443$	7154.34	+	4130.56i	0.767298	+	0.443000i	−0.0646117	+	0.997910i	$0.520581\pi$
$444$	−784.484	−	2662.04i	−0.0838513	−	0.284537i
$445$	1881.23	+	3258.38i	0.200402	+	0.347106i
$446$	−4372.12	−	3269.58i	−0.464184	−	0.347128i
$447$	−4779.54			−0.505737
$448$	9401.97	+	1232.25i	0.991520	+	0.129951i
$449$	−73.1562			−0.00768921			−0.00384461	−	0.999993i	$-0.501224\pi$
$449$	−73.1562			−0.00768921			−0.00384461	+	0.999993i	$0.501224\pi$
$450$	−7691.61	−	5751.97i	−0.805746	−	0.602557i
$451$	−1978.33	−	3426.57i	−0.206554	−	0.357762i
$452$	−1497.88	−	5082.83i	−0.155872	−	0.528929i
$453$	−3607.28	−	2082.67i	−0.374139	−	0.216009i
$454$	660.948	−	5551.07i	0.0683256	−	0.573843i
$455$	−484.180	−	8465.29i	−0.0498873	−	0.872217i
$456$	−1627.84	+	4384.13i	−0.167173	+	0.450231i
$457$	6586.17	−	11407.6i	0.674153	−	1.16767i	−0.302563	−	0.953129i	$-0.597842\pi$
$457$	6586.17	−	11407.6i	0.674153	−	1.16767i	0.976716	−	0.214538i	$-0.0688245\pi$
$458$	2880.16	+	6716.70i	0.293845	+	0.685264i
$459$	5924.14	−	3420.30i	0.602429	−	0.347813i
$460$	−7556.99	+	7941.14i	−0.765970	+	0.804908i
$461$		−	12655.0i		−	1.27853i	−0.768985	−	0.639267i	$-0.779238\pi$
$461$		−	12655.0i		−	1.27853i	0.768985	−	0.639267i	$-0.220762\pi$
$462$	−6005.69	−	3977.57i	−0.604784	−	0.400548i
$463$		−	852.596i		−	0.0855799i	−0.999084	−	0.0427899i	$-0.986375\pi$
$463$		−	852.596i		−	0.0855799i	0.999084	−	0.0427899i	$-0.0136246\pi$
$464$	−1551.40	+	1001.33i	−0.155219	+	0.100185i
$465$	−1233.94	+	712.414i	−0.123059	+	0.0710482i
$466$	−8964.26	+	3843.93i	−0.891119	+	0.382117i
$467$	−5462.60	+	9461.49i	−0.541282	+	0.937528i	0.457549	+	0.889185i	$0.348728\pi$
$467$	−5462.60	+	9461.49i	−0.541282	+	0.937528i	−0.998831	+	0.0483436i	$0.984606\pi$
$468$	738.635	−	3057.80i	0.0729560	−	0.302023i
$469$	−7002.56	+	13907.0i	−0.689442	+	1.36923i
$470$	9296.96	+	1106.96i	0.912419	+	0.108639i
$471$	7359.36	+	4248.93i	0.719961	+	0.415669i
$472$	−12789.1	+	2169.96i	−1.24717	+	0.211611i
$473$	4026.42	+	6973.96i	0.391406	+	0.677935i
$474$	1843.79	−	2465.54i	0.178667	−	0.238915i
$475$	13266.1			1.28145
$476$	6965.62	+	1266.69i	0.670733	+	0.121972i
$477$	−6921.93			−0.664431
$478$	−6179.25	+	8262.97i	−0.591281	+	0.790668i
$479$	−5330.56	−	9232.81i	−0.508475	−	0.880705i	−0.999952	−	0.00981425i	$-0.996876\pi$
$479$	−5330.56	−	9232.81i	−0.508475	−	0.880705i	0.491477	−	0.870891i	$-0.336457\pi$
$480$	−768.128	+	11123.5i	−0.0730418	+	1.05774i
$481$	−2233.01	−	1289.23i	−0.211677	−	0.122212i
$482$	7116.89	+	847.384i	0.672542	+	0.0800774i
$483$	−2525.67	−	3848.84i	−0.237934	−	0.362585i
$484$	2810.47	+	678.892i	0.263944	+	0.0637577i
$485$	10285.4	−	17814.8i	0.962960	−	1.66789i
$486$	9602.68	−	4117.69i	0.896268	−	0.384325i
$487$	−46.9282	+	27.0940i	−0.00436657	+	0.00252104i	−0.502182	−	0.864762i	$-0.667469\pi$
$487$	−46.9282	+	27.0940i	−0.00436657	+	0.00252104i	0.497815	+	0.867283i	$0.334136\pi$
$488$	7414.79	−	6140.56i	0.687811	−	0.569611i
$489$			2460.36i			0.227528i
$490$	17876.9	+	75.8217i	1.64815	+	0.00699036i
$491$			5628.07i			0.517294i	0.965972	+	0.258647i	$0.0832766\pi$
$491$			5628.07i			0.517294i	−0.965972	+	0.258647i	$0.916723\pi$
$492$	−1863.14	−	1773.01i	−0.170725	−	0.162466i
$493$	−1193.94	+	689.322i	−0.109072	+	0.0629727i
$494$	1712.38	+	3993.37i	0.155959	+	0.363705i
$495$	−5998.81	+	10390.3i	−0.544700	+	0.943449i
$496$	−1317.20	−	675.793i	−0.119242	−	0.0611774i
$497$	−11980.1	−	18256.3i	−1.08125	−	1.64770i
$498$	−567.690	+	4767.83i	−0.0510819	+	0.429019i
$499$	536.728	+	309.880i	0.0481508	+	0.0277999i	0.523882	−	0.851791i	$-0.324483\pi$
$499$	536.728	+	309.880i	0.0481508	+	0.0277999i	−0.475731	+	0.879591i	$0.657817\pi$
$500$	12663.8	−	3731.93i	1.13268	−	0.333794i
$501$	−5199.23	−	9005.33i	−0.463641	−	0.803050i
$502$	12816.5	+	9584.49i	1.13950	+	0.852144i
$503$	18680.1			1.65587			0.827935	−	0.560823i	$-0.189515\pi$
$503$	18680.1			1.65587			0.827935	+	0.560823i	$0.189515\pi$
$504$	6339.27	+	1949.81i	0.560265	+	0.172324i
$505$	73.0000			0.00643259
$506$	6929.35	+	5181.94i	0.608789	+	0.455268i
$507$	−2640.21	−	4572.98i	−0.231274	−	0.400579i
$508$	11480.2	−	3383.15i	1.00266	−	0.295478i
$509$	3084.16	+	1780.64i	0.268572	+	0.155060i	0.628238	−	0.778021i	$-0.283776\pi$
$509$	3084.16	+	1780.64i	0.268572	+	0.155060i	−0.359667	+	0.933081i	$0.617110\pi$
$510$	−984.275	+	8266.58i	−0.0854596	+	0.717746i
$511$	−6888.03	+	13679.6i	−0.596298	+	1.18424i
$512$	−10143.5	+	5597.09i	−0.875553	+	0.483123i
$513$	−4425.65	+	7665.44i	−0.380891	+	0.659722i
$514$	−5571.76	−	12993.7i	−0.478132	−	1.11503i
$515$	−5726.05	+	3305.93i	−0.489941	+	0.282868i
$516$	3791.97	+	3608.53i	0.323512	+	0.307862i
$517$		−	7390.09i		−	0.628657i
$518$	3001.82	−	4532.41i	0.254618	−	0.384445i
$519$		−	10496.7i		−	0.887771i
$520$	6607.55	+	7978.69i	0.557232	+	0.672863i
$521$	10004.0	−	5775.82i	0.841235	−	0.485687i	−0.0164486	−	0.999865i	$-0.505236\pi$
$521$	10004.0	−	5775.82i	0.841235	−	0.485687i	0.857684	+	0.514177i	$0.171903\pi$
$522$	−1186.98	+	508.984i	−0.0995261	+	0.0426774i
$523$	2135.62	−	3699.00i	0.178554	−	0.309265i	−0.762831	−	0.646598i	$-0.776191\pi$
$523$	2135.62	−	3699.00i	0.178554	−	0.309265i	0.941386	+	0.337332i	$0.109525\pi$
$524$	−15316.2	−	3699.74i	−1.27689	−	0.308443i
$525$	758.474	+	13261.0i	0.0630524	+	1.10239i
$526$	−5341.33	−	635.974i	−0.442762	−	0.0527182i
$527$	−957.260	−	552.674i	−0.0791250	−	0.0456829i
$528$	8790.09	−	436.028i	0.724507	−	0.0359388i
$529$	−3318.65	−	5748.06i	−0.272758	−	0.472431i
$530$	13651.7	−	18255.2i	1.11885	−	1.49614i
$531$	−9073.03			−0.741499
$532$	−8625.04	+	3087.10i	−0.702900	+	0.251584i
$533$	−2389.59			−0.194192
$534$	1156.10	−	1545.96i	0.0936882	−	0.125281i
$535$	8548.04	+	14805.6i	0.690774	+	1.19646i
$536$	−3182.30	−	18755.5i	−0.256445	−	1.51141i
$537$	691.070	+	398.990i	0.0555342	+	0.0320627i
$538$	−22624.4	−	2693.81i	−1.81302	−	0.215870i
$539$	−1608.88	−	14018.6i	−0.128570	−	1.12027i
$540$	−4955.18	+	20513.5i	−0.394884	+	1.63474i
$541$	−4878.48	+	8449.78i	−0.387694	+	0.671505i	−0.992139	−	0.125142i	$-0.960061\pi$
$541$	−4878.48	+	8449.78i	−0.387694	+	0.671505i	0.604445	+	0.796647i	$0.293395\pi$
$542$	−11380.9	+	4880.19i	−0.901939	+	0.386757i
$543$	−5636.51	+	3254.24i	−0.445462	+	0.257188i
$544$	−7771.21	+	3798.63i	−0.612477	+	0.299384i
$545$			21901.3i			1.72138i
$546$	−3893.92	+	1940.04i	−0.305210	+	0.152062i
$547$		−	19891.0i		−	1.55480i	−0.629005	−	0.777401i	$-0.716537\pi$
$547$		−	19891.0i		−	1.55480i	0.629005	−	0.777401i	$-0.283463\pi$
$548$	−9891.51	+	10394.3i	−0.771066	+	0.810263i
$549$	5831.60	−	3366.87i	0.453345	−	0.261739i
$550$	−9838.97	−	22945.0i	−0.762791	−	1.77887i
$551$	891.938	−	1544.88i	0.0689616	−	0.119445i
$552$	5272.72	+	1957.78i	0.406561	+	0.150958i
$553$	6020.98	−	344.376i	0.462998	−	0.0264816i
$554$	1071.62	−	9000.17i	0.0821819	−	0.690218i
$555$	5535.98	+	3196.20i	0.423404	+	0.244453i
$556$	692.913	+	2351.30i	0.0528526	+	0.179348i
$557$	−3043.39	−	5271.30i	−0.231513	−	0.400992i	0.726741	−	0.686912i	$-0.241034\pi$
$557$	−3043.39	−	5271.30i	−0.231513	−	0.400992i	−0.958253	+	0.285920i	$0.907701\pi$
$558$	−829.250	−	620.134i	−0.0629121	−	0.0470472i
$559$	4863.44			0.367981
$560$	−17644.8	+	12873.1i	−1.33148	+	0.971404i
$561$	6571.05			0.494527
$562$	−14175.8	−	10601.0i	−1.06400	−	0.795686i
$563$	4067.94	+	7045.87i	0.304517	+	0.527439i	0.977154	−	0.212534i	$-0.0681716\pi$
$563$	4067.94	+	7045.87i	0.304517	+	0.527439i	−0.672637	+	0.739973i	$0.734838\pi$
$564$	−1357.90	−	4607.83i	−0.101379	−	0.344016i
$565$	10570.3	+	6102.75i	0.787070	+	0.454415i
$566$	−2026.10	+	17016.5i	−0.150465	+	1.26371i
$567$	−847.008	−	426.491i	−0.0627354	−	0.0315890i
$568$	25010.2	+	9286.39i	1.84755	+	0.686000i
$569$	−11495.9	+	19911.5i	−0.846985	+	1.46702i	0.0369008	+	0.999319i	$0.488251\pi$
$569$	−11495.9	+	19911.5i	−0.846985	+	1.46702i	−0.883886	+	0.467702i	$0.845082\pi$
$570$	−4245.25	−	9900.16i	−0.311954	−	0.727495i
$571$	−16493.6	+	9522.59i	−1.20882	+	0.697912i	−0.962501	−	0.271277i	$-0.912554\pi$
$571$	−16493.6	+	9522.59i	−1.20882	+	0.697912i	−0.246318	+	0.969189i	$0.579221\pi$
$572$	5636.92	−	5923.47i	0.412048	−	0.432994i
$573$		−	1518.41i		−	0.110702i
$574$	309.020	−	5028.62i	0.0224708	−	0.365663i
$575$		−	15954.9i		−	1.15716i
$576$	−7649.67	+	2672.84i	−0.553362	+	0.193348i
$577$	13902.1	−	8026.36i	1.00303	−	0.579102i	0.0938892	−	0.995583i	$-0.470070\pi$
$577$	13902.1	−	8026.36i	1.00303	−	0.579102i	0.909144	+	0.416481i	$0.136737\pi$
$578$	6835.78	−	2931.22i	0.491922	−	0.210939i
$579$	−5365.27	+	9292.92i	−0.385100	+	0.667013i
$580$	998.660	−	4134.25i	0.0714950	−	0.295975i
$581$	−7863.64	+	5160.25i	−0.561513	+	0.368473i
$582$	−10480.4	−	1247.86i	−0.746435	−	0.0888755i
$583$	−15582.1	−	8996.32i	−1.10694	−	0.639090i
$584$	−3130.25	−	18448.7i	−0.221799	−	1.30721i
$585$	3622.93	+	6275.10i	0.256051	+	0.443493i
$586$	−775.203	+	1036.61i	−0.0546474	+	0.0730751i
$587$	21155.6			1.48754			0.743770	−	0.668436i	$-0.233036\pi$
$587$	21155.6			1.48754			0.743770	+	0.668436i	$0.233036\pi$
$588$	−3579.03	−	8445.21i	−0.251015	−	0.592304i
$589$	1430.25			0.100055
$590$	17894.2	−	23928.3i	1.24863	−	1.66968i
$591$	6975.36	+	12081.7i	0.485495	+	0.840903i
$592$	329.064	+	6633.76i	0.0228454	+	0.460550i
$593$	−1240.18	−	716.018i	−0.0858821	−	0.0495840i	0.456444	−	0.889752i	$-0.349123\pi$
$593$	−1240.18	−	716.018i	−0.0858821	−	0.0495840i	−0.542326	+	0.840168i	$0.682456\pi$
$594$	16540.5	+	1969.42i	1.14253	+	0.136038i
$595$	−13634.2	+	8946.96i	−0.939406	+	0.616453i
$596$	11119.0	+	2685.89i	0.764184	+	0.184595i
$597$	8822.32	−	15280.7i	0.604813	−	1.04757i
$598$	4802.76	−	2059.45i	0.328427	−	0.140832i
$599$	4611.09	−	2662.21i	0.314531	−	0.181595i	−0.334421	−	0.942424i	$-0.608541\pi$
$599$	4611.09	−	2662.21i	0.314531	−	0.181595i	0.648952	+	0.760829i	$0.275207\pi$
$600$	−10350.8	−	12498.7i	−0.704283	−	0.850429i
$601$			8711.39i			0.591256i	0.955303	+	0.295628i	$0.0955289\pi$
$601$			8711.39i			0.591256i	−0.955303	+	0.295628i	$0.904471\pi$
$602$	−628.936	+	10234.6i	−0.0425806	+	0.692906i
$603$		−	13305.8i		−	0.898599i
$604$	7221.55	+	6872.21i	0.486491	+	0.462957i
$605$	−5767.55	+	3329.90i	−0.387577	+	0.223768i
$606$	−14.7609	−	34.4233i	−0.000989475	−	0.00230751i
$607$	12379.6	−	21442.1i	0.827796	−	1.43378i	−0.0719681	−	0.997407i	$-0.522928\pi$
$607$	12379.6	−	21442.1i	0.827796	−	1.43378i	0.899764	−	0.436377i	$-0.143739\pi$
$608$	6250.67	−	9284.38i	0.416938	−	0.619295i
$609$	1595.28	+	803.266i	0.106148	+	0.0534483i
$610$	−2621.84	+	22019.9i	−0.174025	+	1.46157i
$611$	−3865.22	−	2231.59i	−0.255925	−	0.147758i
$612$	−5803.36	+	1710.21i	−0.383312	+	0.112960i
$613$	−3167.74	−	5486.69i	−0.208717	−	0.361509i	0.742593	−	0.669743i	$-0.233596\pi$
$613$	−3167.74	−	5486.69i	−0.208717	−	0.361509i	−0.951311	+	0.308233i	$0.900262\pi$
$614$	−9503.52	−	7106.97i	−0.624643	−	0.467123i
$615$	5924.15			0.388431
$616$	11736.3	+	12628.3i	0.767646	+	0.825988i
$617$	12720.7			0.830013			0.415006	−	0.909819i	$-0.363779\pi$
$617$	12720.7			0.830013			0.415006	+	0.909819i	$0.363779\pi$
$618$	2716.75	+	2031.65i	0.176835	+	0.132241i
$619$	11135.8	+	19287.7i	0.723077	+	1.25241i	0.959761	+	0.280820i	$0.0906063\pi$
$619$	11135.8	+	19287.7i	0.723077	+	1.25241i	−0.236683	+	0.971587i	$0.576060\pi$
$620$	3270.95	−	963.929i	0.211879	−	0.0624392i
$621$	9219.10	+	5322.65i	0.595733	+	0.343946i
$622$	−2176.47	+	18279.4i	−0.140303	+	1.17836i
$623$	3775.31	−	215.932i	0.242784	−	0.0138863i
$624$	2426.29	−	4729.13i	0.155656	−	0.303392i
$625$	−1795.08	+	3109.16i	−0.114885	+	0.198987i
$626$	9629.78	+	22457.2i	0.614830	+	1.43382i
$627$	−7363.39	+	4251.25i	−0.469004	+	0.270779i
$628$	−14733.0	−	14020.3i	−0.936162	−	0.890876i
$629$			4959.08i			0.314358i
$630$	−13673.8	+	6812.56i	−0.864723	+	0.430824i
$631$			7895.30i			0.498110i	0.968489	+	0.249055i	$0.0801199\pi$
$631$			7895.30i			0.498110i	−0.968489	+	0.249055i	$0.919880\pi$
$632$	−5674.88	+	4699.65i	−0.357175	+	0.295795i
$633$	−2523.10	+	1456.71i	−0.158427	+	0.0914676i
$634$	2408.01	−	1032.57i	0.150843	−	0.0646822i
$635$	−13783.8	+	23874.3i	−0.861410	+	1.49201i
$636$	−11368.7	−	2746.20i	−0.708803	−	0.171217i
$637$	−7817.98	−	3391.72i	−0.486279	−	0.210965i
$638$	−3333.54	−	396.914i	−0.206859	−	0.0246301i
$639$	16160.1	+	9330.05i	1.00045	+	0.577607i
$640$	8037.89	−	25445.9i	0.496446	−	1.57162i
$641$	−4213.92	−	7298.73i	−0.259657	−	0.449739i	0.706493	−	0.707720i	$-0.250276\pi$
$641$	−4213.92	−	7298.73i	−0.259657	−	0.449739i	−0.966150	+	0.257981i	$0.916943\pi$
$642$	5253.18	−	7024.61i	0.322938	−	0.431837i
$643$	−12838.8			−0.787424			−0.393712	−	0.919234i	$-0.628809\pi$
$643$	−12838.8			−0.787424			−0.393712	+	0.919234i	$0.628809\pi$
$644$	3712.80	+	10373.2i	0.227181	+	0.634723i
$645$	−12057.2			−0.736049
$646$	5004.67	−	6692.30i	0.304808	−	0.407593i
$647$	−11376.3	−	19704.4i	−0.691267	−	1.19731i	−0.971423	−	0.237355i	$-0.923719\pi$
$647$	−11376.3	−	19704.4i	−0.691267	−	1.19731i	0.280156	−	0.959955i	$-0.409614\pi$
$648$	1142.30	−	193.818i	0.0692498	−	0.0117498i
$649$	−20424.5	−	11792.1i	−1.23533	−	0.713219i
$650$	−14972.0	−	1782.66i	−0.903460	−	0.107572i
$651$	81.7728	+	1429.70i	0.00492309	+	0.0860740i
$652$	1382.61	−	5723.74i	0.0830480	−	0.343802i
$653$	−430.103	+	744.961i	−0.0257753	+	0.0446441i	−0.878625	−	0.477512i	$-0.841539\pi$
$653$	−430.103	+	744.961i	−0.0257753	+	0.0446441i	0.852850	+	0.522156i	$0.174872\pi$
$654$	10327.6	−	4428.54i	0.617495	−	0.264786i
$655$	31431.3	−	18146.9i	1.87500	−	1.08253i
$656$	3338.02	+	5171.70i	0.198670	+	0.307806i
$657$		−	13088.2i		−	0.777199i
$658$	5195.98	−	7845.35i	0.307842	−	0.464808i
$659$			19262.8i			1.13865i	0.822111	+	0.569327i	$0.192796\pi$
$659$			19262.8i			1.13865i	−0.822111	+	0.569327i	$0.807204\pi$
$660$	−13974.8	+	14685.2i	−0.824193	+	0.866090i
$661$	3499.64	−	2020.52i	0.205931	−	0.118894i	−0.393488	−	0.919330i	$-0.628732\pi$
$661$	3499.64	−	2020.52i	0.205931	−	0.118894i	0.599419	+	0.800436i	$0.295398\pi$
$662$	10632.6	+	24795.9i	0.624242	+	1.45577i
$663$	1984.26	−	3436.84i	0.116233	−	0.201321i
$664$	3999.98	−	10772.8i	0.233779	−	0.629616i
$665$	9489.80	−	18846.7i	0.553381	−	1.09901i
$666$	−549.259	+	4613.04i	−0.0319570	+	0.268396i
$667$	−1858.00	−	1072.72i	−0.107859	−	0.0622727i
$668$	7034.80	+	23871.6i	0.407462	+	1.38266i
$669$	−3226.03	−	5587.64i	−0.186435	−	0.322916i
$670$	35091.4	+	26242.2i	2.02343	+	1.51317i
$671$	17503.5			1.00703
$672$	9638.17	+	5717.43i	0.553275	+	0.328207i
$673$	−30094.8			−1.72373			−0.861863	−	0.507141i	$-0.830702\pi$
$673$	−30094.8			−1.72373			−0.861863	+	0.507141i	$0.830702\pi$
$674$	−10728.3	−	8022.85i	−0.613111	−	0.458500i
$675$	−15357.5	−	26599.9i	−0.875718	−	1.51679i
$676$	3572.33	+	12122.2i	0.203251	+	0.689702i
$677$	16898.8	+	9756.55i	0.959343	+	0.553877i	0.895971	−	0.444113i	$-0.146481\pi$
$677$	16898.8	+	9756.55i	0.959343	+	0.553877i	0.0633724	+	0.997990i	$0.479814\pi$
$678$	740.408	−	6218.43i	0.0419398	−	0.352238i
$679$	−11342.9	−	17285.4i	−0.641093	−	0.976955i
$680$	6935.26	−	18678.1i	0.391110	−	1.05334i
$681$	3303.34	−	5721.55i	0.185880	−	0.321953i
$682$	−1060.76	−	2473.76i	−0.0595582	−	0.138893i
$683$	−19594.6	+	11312.9i	−1.09775	+	0.633788i	−0.935630	−	0.352982i	$-0.885168\pi$
$683$	−19594.6	+	11312.9i	−1.09775	+	0.633788i	−0.162123	+	0.986771i	$0.551834\pi$
$684$	5396.68	−	5671.01i	0.301677	−	0.317013i
$685$		−	33050.5i		−	1.84350i
$686$	8148.52	−	16013.4i	0.453516	−	0.891248i
$687$			8636.90i			0.479648i
$688$	−6793.74	−	10525.8i	−0.376466	−	0.583271i
$689$	−9410.66	+	5433.24i	−0.520345	+	0.300421i
$690$	−11906.8	+	5105.69i	−0.656932	+	0.281696i
$691$	−102.478	+	177.498i	−0.00564177	+	0.00977182i	−0.868833	−	0.495106i	$-0.835129\pi$
$691$	−102.478	+	177.498i	−0.00564177	+	0.00977182i	0.863191	+	0.504878i	$0.168463\pi$
$692$	−5898.67	+	24419.3i	−0.324037	+	1.34145i
$693$	6615.62	+	10081.5i	0.362636	+	0.552617i
$694$	−5495.06	−	654.279i	−0.300562	−	0.0357869i
$695$	−4889.78	−	2823.11i	−0.266877	−	0.154082i
$696$	−2151.45	+	365.043i	−0.117170	+	0.0198806i
$697$	2297.91	+	3980.10i	0.124877	+	0.216294i
$698$	−16497.8	+	22061.0i	−0.894627	+	1.19631i
$699$	−11527.0			−0.623736
$700$	5687.58	−	31276.3i	0.307100	−	1.68876i
$701$	9946.71			0.535923			0.267962	−	0.963430i	$-0.413650\pi$
$701$	9946.71			0.535923			0.267962	+	0.963430i	$0.413650\pi$
$702$	6024.80	−	8056.43i	0.323919	−	0.433149i
$703$	−3208.36	−	5557.04i	−0.172127	−	0.298133i
$704$	−20694.2	−	3925.28i	−1.10787	−	0.210141i
$705$	9582.47	+	5532.44i	0.511910	+	0.295552i
$706$	8399.85	+	1000.14i	0.447780	+	0.0533157i
$707$	32.9964	−	65.5307i	0.00175525	−	0.00348590i
$708$	−14901.7	−	3599.62i	−0.791018	−	0.191076i
$709$	−14432.4	+	24997.6i	−0.764484	+	1.32412i	0.176035	+	0.984384i	$0.443673\pi$
$709$	−14432.4	+	24997.6i	−0.764484	+	1.32412i	−0.940519	+	0.339741i	$0.889661\pi$
$710$	−56477.7	+	24218.0i	−2.98531	+	1.28012i
$711$	−4463.19	+	2576.82i	−0.235419	+	0.135919i
$712$	−3558.30	+	2946.80i	−0.187293	+	0.155107i
$713$		−	1720.14i		−	0.0903501i
$714$	6975.85	+	4620.11i	0.365637	+	0.242161i
$715$			18834.6i			0.985141i
$716$	−1383.48	−	1316.55i	−0.0722110	−	0.0687178i
$717$	−10560.2	+	6096.94i	−0.550039	+	0.317565i
$718$	1472.79	+	3434.63i	0.0765515	+	0.178522i
$719$	−3063.07	+	5305.39i	−0.158878	+	0.275185i	−0.934464	−	0.356057i	$-0.884121\pi$
$719$	−3063.07	+	5305.39i	−0.158878	+	0.275185i	0.775586	+	0.631241i	$0.217454\pi$
$720$	8520.09	−	16606.7i	0.441007	−	0.859574i
$721$	379.464	+	6634.46i	0.0196005	+	0.342691i
$722$	1015.28	−	8527.00i	0.0523336	−	0.439532i
$723$	7335.45	+	4235.12i	0.377328	+	0.217851i
$724$	14941.4	−	4403.14i	0.766981	−	0.226024i
$725$	3095.12	+	5360.91i	0.158552	+	0.274620i
$726$	2736.44	+	2046.38i	0.139888	+	0.104612i
$727$	−20742.9			−1.05820			−0.529101	−	0.848559i	$-0.677471\pi$
$727$	−20742.9			−1.05820			−0.529101	+	0.848559i	$0.677471\pi$
$728$	10149.0	−	2325.05i	0.516684	−	0.118368i
$729$	13730.5			0.697579
$730$	34517.5	+	25813.0i	1.75007	+	1.30874i
$731$	−4676.85	−	8100.54i	−0.236634	−	0.409862i
$732$	10913.7	−	3216.19i	0.551068	−	0.162396i
$733$	−15694.9	−	9061.44i	−0.790864	−	0.456606i	0.0494026	−	0.998779i	$-0.484268\pi$
$733$	−15694.9	−	9061.44i	−0.790864	−	0.456606i	−0.840267	+	0.542173i	$0.817602\pi$
$734$	2252.42	−	18917.3i	0.113268	−	0.951296i
$735$	19381.9	+	8408.59i	0.972672	+	0.421980i
$736$	−11166.2	−	7517.58i	−0.559227	−	0.376497i
$737$	17293.4	−	29953.0i	0.864328	−	1.49706i
$738$	1696.74	+	3956.89i	0.0846311	+	0.197364i
$739$	32754.4	−	18910.8i	1.63043	−	0.941332i	0.646476	−	0.762934i	$-0.276242\pi$
$739$	32754.4	−	18910.8i	1.63043	−	0.941332i	0.983958	−	0.178398i	$-0.0570913\pi$
$740$	−11082.7	−	10546.6i	−0.550551	−	0.523918i
$741$			5135.01i			0.254574i
$742$	−10216.7	−	20506.3i	−0.505480	−	1.01457i
$743$		−	4974.35i		−	0.245614i	−0.992431	−	0.122807i	$-0.960810\pi$
$743$		−	4974.35i		−	0.245614i	0.992431	−	0.122807i	$-0.0391896\pi$
$744$	−1115.94	−	1347.51i	−0.0549899	−	0.0664009i
$745$	−22818.1	+	13174.0i	−1.12213	+	0.647865i
$746$	544.557	−	233.509i	0.0267261	−	0.0114603i
$747$	4018.78	−	6960.73i	0.196840	−	0.340937i
$748$	−15286.8	−	3692.64i	−0.747246	−	0.180503i
$749$	17154.5	−	981.168i	0.836865	−	0.0478653i
$750$	15493.1	+	1844.72i	0.754306	+	0.0898127i
$751$	19034.7	+	10989.7i	0.924884	+	0.533982i	0.885190	−	0.465230i	$-0.154028\pi$
$751$	19034.7	+	10989.7i	0.924884	+	0.533982i	0.0396939	+	0.999212i	$0.487362\pi$
$752$	569.592	+	11482.7i	0.0276208	+	0.556822i
$753$	9456.81	+	16379.7i	0.457670	+	0.792707i
$754$	−1214.23	+	1623.68i	−0.0586467	+	0.0784230i
$755$	−22962.1			−1.10686
$756$	16174.7	+	13720.4i	0.778135	+	0.660060i
$757$	−10241.5			−0.491722			−0.245861	−	0.969305i	$-0.579071\pi$
$757$	−10241.5			−0.491722			−0.245861	+	0.969305i	$0.579071\pi$
$758$	2042.83	−	2731.69i	0.0978877	−	0.130897i
$759$	5112.91	+	8855.83i	0.244515	+	0.423513i
$760$	4312.62	+	25417.2i	0.205836	+	1.21313i
$761$	−18578.2	−	10726.2i	−0.884968	−	0.510937i	−0.0126751	−	0.999920i	$-0.504035\pi$
$761$	−18578.2	−	10726.2i	−0.884968	−	0.510937i	−0.872293	+	0.488983i	$0.837368\pi$
$762$	14045.1	+	1672.31i	0.667719	+	0.0795031i
$763$	19660.4	+	9899.53i	0.932836	+	0.469708i
$764$	−853.278	+	3532.39i	−0.0404064	+	0.167274i
$765$	6967.86	−	12068.7i	0.329312	−	0.570385i
$766$	8268.77	−	3545.70i	0.390030	−	0.167247i
$767$	−12335.2	+	7121.71i	−0.580700	+	0.335267i
$768$	−13624.4	+	1354.99i	−0.640140	+	0.0636643i
$769$			26466.5i			1.24110i	0.784166	+	0.620551i	$0.213091\pi$
$769$			26466.5i			1.24110i	−0.784166	+	0.620551i	$0.786909\pi$
$770$	−39635.4	−	2435.68i	−1.85501	−	0.113995i
$771$		−	16708.3i		−	0.780462i
$772$	17703.9	−	18603.8i	0.825358	−	0.867315i
$773$	9692.09	−	5595.73i	0.450971	−	0.260368i	−0.257269	−	0.966340i	$-0.582823\pi$
$773$	9692.09	−	5595.73i	0.450971	−	0.260368i	0.708240	+	0.705972i	$0.249489\pi$
$774$	−3453.30	−	8053.29i	−0.160370	−	0.373992i
$775$	−2481.56	+	4298.19i	−0.115020	+	0.199220i
$776$	23680.1	+	8792.51i	1.09545	+	0.406743i
$777$	5371.46	−	3524.84i	0.248005	−	0.162745i
$778$	2679.30	−	22502.5i	0.123467	−	1.03696i
$779$	−5149.99	−	2973.35i	−0.236864	−	0.136754i
$780$	3460.79	+	11743.7i	0.158867	+	0.539092i
$781$	24252.2	+	42006.1i	1.11116	+	1.92458i
$782$	−8048.72	−	6019.03i	−0.368058	−	0.275243i
$783$	−4130.21			−0.188508
$784$	3580.36	+	21658.1i	0.163099	+	0.986610i
$785$	46845.9			2.12994
$786$	−14912.7	−	11152.1i	−0.676743	−	0.506085i
$787$	15026.0	+	26025.7i	0.680582	+	1.17880i	0.974804	+	0.223065i	$0.0716062\pi$
$787$	15026.0	+	26025.7i	0.680582	+	1.17880i	−0.294222	+	0.955737i	$0.595061\pi$
$788$	−9437.98	−	32026.4i	−0.426668	−	1.44784i
$789$	−5505.36	−	3178.52i	−0.248411	−	0.143420i
$790$	2006.61	−	16852.9i	0.0903698	−	0.758985i
$791$	10256.1	−	6730.24i	0.461019	−	0.302528i
$792$	−13811.1	−	5128.11i	−0.619641	−	0.230075i
$793$	5285.53	−	9154.81i	0.236689	−	0.409958i
$794$	−13510.3	−	31506.9i	−0.603859	−	1.40823i
$795$	23330.4	−	13469.8i	1.04081	−	0.600913i
$796$	−29111.2	+	30591.0i	−1.29625	+	1.36215i
$797$			26567.8i			1.18078i	0.807119	+	0.590389i	$0.201026\pi$
$797$			26567.8i			1.18078i	−0.807119	+	0.590389i	$0.798974\pi$
$798$	−10806.1	−	664.056i	−0.479361	−	0.0294578i
$799$			8583.89i			0.380070i
$800$	17056.2	+	34893.5i	0.753785	+	1.54209i
$801$	−2798.54	+	1615.74i	−0.123447	+	0.0712724i
$802$	28579.7	−	12255.2i	1.25834	−	0.539582i
$803$	17010.5	−	29463.1i	0.747557	−	1.29481i
$804$	5278.94	−	21853.7i	0.231560	−	0.958609i
$805$	−22666.6	−	11413.2i	−0.992412	−	0.499706i
$806$	−1614.16	−	192.193i	−0.0705415	−	0.00839914i
$807$	−23319.1	−	13463.3i	−1.01719	−	0.587275i
$808$	14.9952	+	88.3768i	0.000652882	+	0.00384788i
$809$	980.413	+	1698.13i	0.0426075	+	0.0737984i	0.886543	−	0.462647i	$-0.153100\pi$
$809$	980.413	+	1698.13i	0.0426075	+	0.0737984i	−0.843935	+	0.536445i	$0.819767\pi$
$810$	−1598.28	+	2137.24i	−0.0693308	+	0.0927100i
$811$	2633.82			0.114040			0.0570198	−	0.998373i	$-0.481840\pi$
$811$	2633.82			0.114040			0.0570198	+	0.998373i	$0.481840\pi$
$812$	−3259.83	−	2765.18i	−0.140884	−	0.119506i
$813$	−14634.5			−0.631309
$814$	−7231.94	+	9670.63i	−0.311400	+	0.416407i
$815$	6781.58	+	11746.0i	0.291470	+	0.504841i
$816$	−10210.0	+	506.464i	−0.438019	+	0.0217277i
$817$	10481.6	+	6051.53i	0.448841	+	0.259139i
$818$	5642.23	+	671.801i	0.241169	+	0.0287151i
$819$	7270.61	−	415.850i	0.310202	−	0.0177423i
$820$	−13781.8	−	3329.11i	−0.586931	−	0.141778i
$821$	−5333.16	+	9237.30i	−0.226710	+	0.392672i	−0.956831	−	0.290645i	$-0.906130\pi$
$821$	−5333.16	+	9237.30i	−0.226710	+	0.392672i	0.730121	+	0.683317i	$0.239463\pi$
$822$	−15585.0	+	6682.95i	−0.661302	+	0.283570i
$823$	−32943.1	+	19019.7i	−1.39529	+	0.805571i	−0.993895	−	0.110334i	$-0.964808\pi$
$823$	−32943.1	+	19019.7i	−1.39529	+	0.805571i	−0.401395	+	0.915905i	$0.631475\pi$
$824$	−5178.51	−	6253.10i	−0.218934	−	0.264365i
$825$		−	29504.6i		−	1.24512i
$826$	−13391.7	−	26879.0i	−0.564111	−	1.13225i
$827$			22277.0i			0.936697i	0.883544	+	0.468349i	$0.155151\pi$
$827$			22277.0i			0.936697i	−0.883544	+	0.468349i	$0.844849\pi$
$828$	−6820.44	−	6490.50i	−0.286264	−	0.272416i
$829$	18752.2	−	10826.6i	0.785633	−	0.453585i	−0.0527901	−	0.998606i	$-0.516811\pi$
$829$	18752.2	−	10826.6i	0.785633	−	0.453585i	0.838423	+	0.545020i	$0.183478\pi$
$830$	10431.5	+	24326.9i	0.436246	+	1.01735i
$831$	5355.83	−	9276.57i	0.223576	−	0.387245i
$832$	−8302.05	+	9638.31i	−0.345940	+	0.401620i
$833$	1868.78	+	16283.2i	0.0777304	+	0.677287i
$834$	−342.511	+	2876.63i	−0.0142208	+	0.119436i
$835$	−49643.4	−	28661.7i	−2.05746	−	1.18788i
$836$	19519.1	−	5752.14i	0.807513	−	0.237969i
$837$	−1655.73	−	2867.80i	−0.0683755	−	0.118430i
$838$	15092.0	+	11286.2i	0.622129	+	0.465244i
$839$	−47337.4			−1.94788			−0.973939	−	0.226811i	$-0.927170\pi$
$839$	−47337.4			−1.94788			−0.973939	+	0.226811i	$0.927170\pi$
$840$	−25160.8	+	5764.16i	−1.03349	+	0.236765i
$841$	−23556.6			−0.965870
$842$	−13272.8	−	9925.70i	−0.543242	−	0.406250i
$843$	−10459.8	−	18116.9i	−0.427347	−	0.740187i
$844$	6688.29	−	1971.00i	0.272773	−	0.0803845i
$845$	−25209.4	−	14554.6i	−1.02631	−	0.592538i
$846$	−950.737	+	7984.92i	−0.0386371	+	0.324500i
$847$	382.215	+	6682.55i	0.0155054	+	0.271092i
$848$	24904.7	+	12777.4i	1.00853	+	0.517428i
$849$	−10126.2	+	17539.1i	−0.409341	+	0.708999i
$850$	11428.4	+	26651.6i	0.461164	+	1.07546i
$851$	−6683.37	+	3858.64i	−0.269216	+	0.155432i
$852$	22840.1	+	21735.2i	0.918413	+	0.873985i
$853$		−	16562.9i		−	0.664833i	−0.943133	−	0.332417i	$-0.892136\pi$
$853$		−	16562.9i		−	0.664833i	0.943133	−	0.332417i	$-0.107864\pi$
$854$	18581.8	+	12306.7i	0.744560	+	0.493123i
$855$			18031.9i			0.721261i
$856$	−16168.4	+	13389.9i	−0.645591	+	0.534646i
$857$	−28076.8	+	16210.2i	−1.11912	+	0.646124i	−0.941176	−	0.337917i	$-0.890278\pi$
$857$	−28076.8	+	16210.2i	−1.11912	+	0.646124i	−0.177944	+	0.984041i	$0.556944\pi$
$858$	8881.51	−	3808.45i	0.353391	−	0.151536i
$859$	16065.2	−	27825.8i	0.638112	−	1.10524i	−0.347735	−	0.937593i	$-0.613049\pi$
$859$	16065.2	−	27825.8i	0.638112	−	1.10524i	0.985847	−	0.167649i	$-0.0536177\pi$
$860$	28049.7	+	6775.61i	1.11219	+	0.268659i
$861$	2677.75	−	5317.99i	0.105990	−	0.210496i
$862$	−10306.6	−	1227.17i	−0.407243	−	0.0484891i
$863$	33292.7	+	19221.5i	1.31320	+	0.758179i	0.982625	−	0.185600i	$-0.0594228\pi$
$863$	33292.7	+	19221.5i	1.31320	+	0.758179i	0.330579	+	0.943778i	$0.392756\pi$
$864$	−25852.3	−	1785.21i	−1.01795	−	0.0702941i
$865$	−28932.4	−	50112.4i	−1.13726	−	1.96979i
$866$	14029.5	−	18760.4i	0.550509	−	0.736147i
$867$	8790.02			0.344319
$868$	613.191	−	3371.97i	0.0239782	−	0.131857i
$869$	−13396.2			−0.522941
$870$	3010.26	−	4025.35i	0.117307	−	0.156865i
$871$	−10444.2	−	18089.8i	−0.406300	−	0.703732i
$872$	−26514.6	+	4498.82i	−1.02970	+	0.174713i
$873$	15300.7	+	8833.85i	0.593184	+	0.342475i
$874$	12913.4	+	1537.55i	0.499772	+	0.0595062i
$875$	16768.3	+	25553.0i	0.647854	+	0.987257i
$876$	5192.60	−	21496.3i	0.200276	−	0.829101i
$877$	10742.3	−	18606.2i	0.413616	−	0.716404i	−0.581666	−	0.813428i	$-0.697599\pi$
$877$	10742.3	−	18606.2i	0.413616	−	0.716404i	0.995282	+	0.0970237i	$0.0309323\pi$
$878$	25168.1	−	10792.2i	0.967406	−	0.414830i
$879$	−1324.81	+	764.877i	−0.0508357	+	0.0293500i
$880$	40763.1	−	26310.1i	1.56150	−	1.00786i
$881$		−	17193.8i		−	0.657517i	−0.944414	−	0.328759i	$-0.893370\pi$
$881$		−	17193.8i		−	0.657517i	0.944414	−	0.328759i	$-0.106630\pi$
$882$	−65.1213	+	15354.0i	−0.00248611	+	0.586163i
$883$			16514.2i			0.629384i	0.949194	+	0.314692i	$0.101901\pi$
$883$			16514.2i			0.629384i	−0.949194	+	0.314692i	$0.898099\pi$
$884$	−6547.51	+	6880.35i	−0.249114	+	0.261777i
$885$	30580.7	−	17655.8i	1.16154	−	0.670614i
$886$	−9208.57	−	21474.9i	−0.349174	−	0.814293i
$887$	10239.6	−	17735.5i	0.387612	−	0.671364i	−0.604516	−	0.796593i	$-0.706633\pi$
$887$	10239.6	−	17735.5i	0.387612	−	0.671364i	0.992128	+	0.125229i	$0.0399667\pi$
$888$	−2732.29	+	7358.63i	−0.103254	+	0.278085i
$889$	15201.1	+	23164.8i	0.573486	+	0.873929i
$890$	1258.20	−	10567.2i	0.0473876	−	0.397992i
$891$	1824.29	+	1053.25i	0.0685925	+	0.0396019i
$892$	4364.96	+	14811.9i	0.163845	+	0.555985i
$893$	−5553.49	−	9618.93i	−0.208108	−	0.360454i
$894$	10826.2	+	8096.07i	0.405012	+	0.302878i
$895$	4399.00			0.164293
$896$	−19209.1	−	18717.2i	−0.716219	−	0.697876i
$897$	6175.79			0.229882
$898$	165.706	+	123.919i	0.00615779	+	0.00460495i
$899$	333.693	+	577.973i	0.0123796	+	0.0214421i
$900$	7679.02	+	26057.6i	0.284408	+	0.965098i
$901$	18099.2	+	10449.6i	0.669226	+	0.386378i
$902$	−1323.14	+	11112.6i	−0.0488424	+	0.410211i
$903$	−5449.92	+	10823.5i	−0.200844	+	0.398874i
$904$	−5216.96	+	14050.4i	−0.191940	+	0.516935i
$905$	−17939.6	+	31072.3i	−0.658930	+	1.14130i
$906$	4643.04	+	10827.8i	0.170259	+	0.397054i
$907$	26983.7	−	15579.0i	0.987848	−	0.570334i	0.0832177	−	0.996531i	$-0.473480\pi$
$907$	26983.7	−	15579.0i	0.987848	−	0.570334i	0.904630	+	0.426197i	$0.140147\pi$
$908$	−10900.1	+	11454.2i	−0.398383	+	0.418635i
$909$			62.6978i			0.00228774i
$910$	−13242.6	+	19994.9i	−0.482406	+	0.728379i
$911$		−	412.348i		−	0.0149964i	−0.999972	−	0.00749818i	$-0.997613\pi$
$911$		−	412.348i		−	0.0149964i	0.999972	−	0.00749818i	$-0.00238677\pi$
$912$	11113.5	−	7173.10i	0.403514	−	0.260444i
$913$	18093.5	−	10446.3i	0.655868	−	0.378666i
$914$	−34241.7	+	14683.0i	−1.23918	+	0.531369i
$915$	−13103.6	+	22696.2i	−0.473435	+	0.820013i
$916$	4853.56	−	20092.7i	0.175072	−	0.724763i
$917$	−2082.95	−	36417.7i	−0.0750109	−	1.31147i
$918$	−19212.4	−	2287.56i	−0.690746	−	0.0822448i
$919$	−8444.08	−	4875.19i	−0.303095	−	0.174992i	0.340737	−	0.940159i	$-0.389323\pi$
$919$	−8444.08	−	4875.19i	−0.303095	−	0.174992i	−0.643832	+	0.765166i	$0.722657\pi$
$920$	30568.9	−	5186.72i	1.09546	−	0.185871i
$921$	−7012.30	−	12145.7i	−0.250883	−	0.434542i
$922$	−21436.4	+	28665.0i	−0.765694	+	1.02390i
$923$	29293.8			1.04466
$924$	6865.90	+	19182.7i	0.244450	+	0.682969i
$925$	22266.7			0.791487
$926$	−1444.21	+	1931.22i	−0.0512525	+	0.0685354i
$927$	−2839.38	−	4917.95i	−0.100601	−	0.174247i
$928$	5210.23	+	359.789i	0.184304	+	0.0127270i
$929$	−19036.4	−	10990.7i	−0.672297	−	0.388151i	0.124650	−	0.992201i	$-0.460219\pi$
$929$	−19036.4	−	10990.7i	−0.672297	−	0.388151i	−0.796946	+	0.604050i	$0.793553\pi$
$930$	4001.75	+	476.475i	0.141100	+	0.0168003i
$931$	−12628.8	−	17037.6i	−0.444568	−	0.599769i
$932$	26816.2	+	6477.67i	0.942484	+	0.227664i
$933$	−10877.7	+	18840.8i	−0.381695	+	0.661115i
$934$	28400.2	−	12178.2i	0.994949	−	0.426640i
$935$	31371.0	−	18112.0i	1.09726	−	0.633505i
$936$	−6852.69	+	5675.05i	−0.239303	+	0.198178i
$937$			19723.5i			0.687662i	0.939032	+	0.343831i	$0.111725\pi$
$937$			19723.5i			0.687662i	−0.939032	+	0.343831i	$0.888275\pi$
$938$	39418.7	−	19639.2i	1.37214	−	0.683629i
$939$			28877.4i			1.00360i
$940$	−19183.5	−	18255.5i	−0.665635	−	0.633435i
$941$	−9773.15	+	5642.53i	−0.338571	+	0.195474i	−0.659640	−	0.751582i	$-0.729291\pi$
$941$	−9773.15	+	5642.53i	−0.338571	+	0.195474i	0.321069	+	0.947056i	$0.395958\pi$
$942$	−9472.46	−	22090.3i	−0.327632	−	0.764056i
$943$	−3575.99	+	6193.80i	−0.123489	+	0.213890i
$944$	32644.2	+	16748.2i	1.12551	+	0.577445i
$945$	−48775.4	+	2789.76i	−1.67901	+	0.0960327i
$946$	2692.94	−	22617.1i	0.0925530	−	0.777321i
$947$	26386.0	+	15234.0i	0.905417	+	0.522743i	0.878954	−	0.476907i	$-0.158242\pi$
$947$	26386.0	+	15234.0i	0.905417	+	0.522743i	0.0264635	+	0.999650i	$0.491575\pi$
$948$	−8352.75	+	2461.50i	−0.286165	+	0.0843310i
$949$	−10273.3	−	17794.0i	−0.351409	−	0.608658i
$950$	−30049.1	−	22471.4i	−1.02623	−	0.767442i
$951$	3096.42			0.105582
$952$	−13632.2	−	14668.3i	−0.464099	−	0.499371i
$953$	11791.2			0.400791			0.200395	−	0.979715i	$-0.435777\pi$
$953$	11791.2			0.400791			0.200395	+	0.979715i	$0.435777\pi$
$954$	15678.9	+	11725.1i	0.532100	+	0.397917i
$955$	−4185.24	−	7249.05i	−0.141813	−	0.245627i
$956$	27993.3	−	8249.45i	0.947038	−	0.279086i
$957$	−3435.92	−	1983.73i	−0.116058	−	0.0670061i
$958$	−3565.18	+	29942.7i	−0.120236	+	1.00982i
$959$	−29668.8	−	14939.0i	−0.999014	−	0.503030i
$960$	20582.0	−	23894.8i	0.691961	−	0.803335i
$961$	14628.0	−	25336.4i	0.491019	−	0.850470i
$962$	2874.18	+	6702.75i	0.0963278	+	0.224642i
$963$	−12716.2	+	7341.69i	−0.425517	+	0.245672i
$964$	−14685.1	−	13974.7i	−0.490639	−	0.466904i
$965$			59154.0i			1.97330i
$966$	−798.649	+	12996.3i	−0.0266005	+	0.432866i
$967$			40914.1i			1.36061i	0.732929	+	0.680305i	$0.238153\pi$
$967$			40914.1i			1.36061i	−0.732929	+	0.680305i	$0.761847\pi$
$968$	−5216.04	−	6298.42i	−0.173192	−	0.209131i
$969$	8552.87	−	4938.00i	0.283548	−	0.163706i
$970$	−53474.0	+	22930.0i	−1.77005	+	0.759008i
$971$	−9276.00	+	16066.5i	−0.306572	+	0.530997i	−0.977610	−	0.210425i	$-0.932515\pi$
$971$	−9276.00	+	16066.5i	−0.306572	+	0.530997i	0.671038	+	0.741423i	$0.265849\pi$
$972$	−28726.0	−	6939.00i	−0.947930	−	0.228980i
$973$	−4744.46	+	3113.39i	−0.156321	+	0.102580i
$974$	152.192	+	18.1210i	0.00500671	+	0.000596133i
$975$	−15431.8	−	8909.53i	−0.506884	−	0.292650i
$976$	−27196.8	+	1349.08i	−0.891954	+	0.0442449i
$977$	1455.74	+	2521.42i	0.0476697	+	0.0825664i	0.888876	−	0.458148i	$-0.151487\pi$
$977$	1455.74	+	2521.42i	0.0476697	+	0.0825664i	−0.841206	+	0.540715i	$0.818154\pi$
$978$	4167.60	−	5572.97i	0.136263	−	0.182213i
$979$	−8399.78			−0.274217
$980$	−40364.6	−	30453.4i	−1.31571	−	0.992652i
$981$	−18810.5			−0.612204
$982$	9533.40	−	12748.2i	0.309799	−	0.414267i
$983$	−18251.1	−	31611.8i	−0.592186	−	1.02570i	−0.993937	−	0.109947i	$-0.964932\pi$
$983$	−18251.1	−	31611.8i	−0.592186	−	1.02570i	0.401752	−	0.915749i	$-0.368402\pi$
$984$	1216.90	+	7172.02i	0.0394241	+	0.232353i
$985$	66602.3	+	38452.9i	2.15444	+	1.24387i
$986$	3872.05	+	461.032i	0.125062	+	0.0148907i
$987$	9297.70	−	6101.30i	0.299847	−	0.196764i
$988$	2885.65	−	11946.0i	0.0929198	−	0.384669i
$989$	7278.08	−	12606.0i	0.234004	−	0.405306i
$990$	31188.0	−	13373.6i	1.00123	−	0.429334i
$991$	−31879.7	+	18405.7i	−1.02189	+	0.589987i	−0.914650	−	0.404246i	$-0.867534\pi$
$991$	−31879.7	+	18405.7i	−1.02189	+	0.589987i	−0.107238	+	0.994233i	$0.534201\pi$
$992$	1838.87	+	3761.95i	0.0588550	+	0.120405i
$993$			31884.6i			1.01896i
$994$	−3788.26	+	61645.6i	−0.120881	+	1.96708i
$995$		−	97269.2i		−	3.09914i
$996$	9362.11	−	9838.03i	0.297841	−	0.312982i
$997$	−10060.1	+	5808.18i	−0.319564	+	0.184500i	−0.651198	−	0.758908i	$-0.725733\pi$
$997$	−10060.1	+	5808.18i	−0.319564	+	0.184500i	0.331634	+	0.943408i	$0.392400\pi$
$998$	−690.838	−	1611.07i	−0.0219119	−	0.0510998i
$999$	−7428.32	+	12866.2i	−0.235257	+	0.407477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.4.f.a.19.2	yes	20
4.3	odd	2	inner	28.4.f.a.19.9	yes	20
7.2	even	3		196.4.d.b.195.12		20
7.3	odd	6	inner	28.4.f.a.3.9	yes	20
7.4	even	3		196.4.f.d.31.9		20
7.5	odd	6		196.4.d.b.195.11		20
7.6	odd	2		196.4.f.d.19.2		20
8.3	odd	2		448.4.p.h.383.4		20
8.5	even	2		448.4.p.h.383.7		20
28.3	even	6	inner	28.4.f.a.3.2	✓	20
28.11	odd	6		196.4.f.d.31.2		20
28.19	even	6		196.4.d.b.195.10		20
28.23	odd	6		196.4.d.b.195.9		20
28.27	even	2		196.4.f.d.19.9		20
56.3	even	6		448.4.p.h.255.7		20
56.45	odd	6		448.4.p.h.255.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.f.a.3.2	✓	20	28.3	even	6	inner
28.4.f.a.3.9	yes	20	7.3	odd	6	inner
28.4.f.a.19.2	yes	20	1.1	even	1	trivial
28.4.f.a.19.9	yes	20	4.3	odd	2	inner
196.4.d.b.195.9		20	28.23	odd	6
196.4.d.b.195.10		20	28.19	even	6
196.4.d.b.195.11		20	7.5	odd	6
196.4.d.b.195.12		20	7.2	even	3
196.4.f.d.19.2		20	7.6	odd	2
196.4.f.d.19.9		20	28.27	even	2
196.4.f.d.31.2		20	28.11	odd	6
196.4.f.d.31.9		20	7.4	even	3
448.4.p.h.255.4		20	56.45	odd	6
448.4.p.h.255.7		20	56.3	even	6
448.4.p.h.383.4		20	8.3	odd	2
448.4.p.h.383.7		20	8.5	even	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:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	28.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.26510 - 1.69390i) q^{2} +(-1.67134 - 2.89484i) q^{3} +(2.26140 + 7.67373i) q^{4} +(-15.9583 - 9.21354i) q^{5} +(-1.11782 + 9.38820i) q^{6} +(-15.4841 + 10.1609i) q^{7} +(7.87623 - 21.2124i) q^{8} +(7.91327 - 13.7062i) q^{9} +O(q^{10})\)	\(q+(-2.26510 - 1.69390i) q^{2} +(-1.67134 - 2.89484i) q^{3} +(2.26140 + 7.67373i) q^{4} +(-15.9583 - 9.21354i) q^{5} +(-1.11782 + 9.38820i) q^{6} +(-15.4841 + 10.1609i) q^{7} +(7.87623 - 21.2124i) q^{8} +(7.91327 - 13.7062i) q^{9} +(20.5404 + 47.9014i) q^{10} +(35.6274 - 20.5695i) q^{11} +(18.4347 - 19.3718i) q^{12} -24.8455i q^{13} +(52.2846 + 3.21300i) q^{14} +61.5957i q^{15} +(-53.7722 + 34.7067i) q^{16} +(-41.3826 + 23.8923i) q^{17} +(-41.1413 + 17.6416i) q^{18} +(30.9150 - 53.5464i) q^{19} +(34.6141 - 143.295i) q^{20} +(55.2933 + 27.8416i) q^{21} +(-115.542 - 13.7572i) q^{22} +(-64.3994 - 37.1810i) q^{23} +(-74.5703 + 12.6526i) q^{24} +(107.279 + 185.812i) q^{25} +(-42.0858 + 56.2776i) q^{26} -143.155 q^{27} +(-112.988 - 95.8427i) q^{28} +28.8513 q^{29} +(104.337 - 139.521i) q^{30} +(11.5660 + 20.0328i) q^{31} +(180.589 + 12.4705i) q^{32} +(-119.091 - 68.7571i) q^{33} +(134.207 + 15.9796i) q^{34} +(340.717 - 19.4877i) q^{35} +(123.072 + 29.7291i) q^{36} +(51.8900 - 89.8761i) q^{37} +(-160.728 + 68.9212i) q^{38} +(-71.9237 + 41.5252i) q^{39} +(-321.133 + 265.946i) q^{40} -96.1780i q^{41} +(-78.0840 - 156.726i) q^{42} +195.747i q^{43} +(238.412 + 226.879i) q^{44} +(-252.565 + 145.818i) q^{45} +(82.8904 + 193.305i) q^{46} +(89.8186 - 155.570i) q^{47} +(190.342 + 97.6553i) q^{48} +(136.513 - 314.664i) q^{49} +(71.7499 - 602.603i) q^{50} +(138.329 + 79.8641i) q^{51} +(190.657 - 56.1855i) q^{52} +(-218.681 - 378.767i) q^{53} +(324.261 + 242.491i) q^{54} -758.071 q^{55} +(93.5805 + 408.483i) q^{56} -206.678 q^{57} +(-65.3511 - 48.8712i) q^{58} +(-286.640 - 496.475i) q^{59} +(-472.669 + 139.292i) q^{60} +(368.470 + 212.736i) q^{61} +(7.73553 - 64.9681i) q^{62} +(16.7374 + 292.633i) q^{63} +(-387.930 - 334.147i) q^{64} +(-228.915 + 396.492i) q^{65} +(153.285 + 357.470i) q^{66} +(728.093 - 420.365i) q^{67} +(-276.925 - 263.529i) q^{68} +248.568i q^{69} +(-804.771 - 533.000i) q^{70} +1179.04i q^{71} +(-228.414 - 275.812i) q^{72} +(716.185 - 413.489i) q^{73} +(-269.777 + 115.682i) q^{74} +(358.597 - 621.109i) q^{75} +(480.812 + 116.144i) q^{76} +(-342.652 + 680.505i) q^{77} +(233.254 + 27.7728i) q^{78} +(-282.007 - 162.817i) q^{79} +(1177.88 - 58.4284i) q^{80} +(25.6023 + 44.3445i) q^{81} +(-162.916 + 217.853i) q^{82} +507.854 q^{83} +(-88.6091 + 487.266i) q^{84} +880.530 q^{85} +(331.577 - 443.388i) q^{86} +(-48.2202 - 83.5198i) q^{87} +(-155.718 - 917.751i) q^{88} +(-176.826 - 102.090i) q^{89} +(819.088 + 97.5260i) q^{90} +(252.452 + 384.709i) q^{91} +(139.684 - 578.264i) q^{92} +(38.6612 - 66.9632i) q^{93} +(-466.970 + 200.239i) q^{94} +(-986.704 + 569.674i) q^{95} +(-265.726 - 543.620i) q^{96} +1116.33i q^{97} +(-842.225 + 481.507i) q^{98} -651.087i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9}+O(q^{10}) \) 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9	\( 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9} - 12 q^{10} - 168 q^{12} - 56 q^{14} - 104 q^{16} - 6 q^{17} + 68 q^{18} + 238 q^{21} - 184 q^{22} + 348 q^{24} - 36 q^{25} + 396 q^{26} + 448 q^{28} - 352 q^{29} + 644 q^{30} - 40 q^{32} + 30 q^{33} + 208 q^{36} + 258 q^{37} - 1620 q^{38} - 1548 q^{40} - 980 q^{42} - 1248 q^{44} - 504 q^{45} + 232 q^{46} - 644 q^{49} - 864 q^{50} + 2592 q^{52} + 570 q^{53} + 4572 q^{54} + 1904 q^{56} + 1452 q^{57} + 2244 q^{58} - 736 q^{60} + 294 q^{61} + 2560 q^{64} - 124 q^{65} - 4272 q^{66} - 6084 q^{68} - 4144 q^{70} - 4672 q^{72} + 966 q^{73} + 832 q^{74} - 378 q^{77} - 4056 q^{78} + 7032 q^{80} - 1262 q^{81} + 7692 q^{82} + 6188 q^{84} - 2980 q^{85} + 5696 q^{86} - 1396 q^{88} - 3186 q^{89} + 3312 q^{92} - 306 q^{93} - 6780 q^{94} - 11784 q^{96} - 4900 q^{98}+O(q^{100}) \) 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9 - 12 * q^10 - 168 * q^12 - 56 * q^14 - 104 * q^16 - 6 * q^17 + 68 * q^18 + 238 * q^21 - 184 * q^22 + 348 * q^24 - 36 * q^25 + 396 * q^26 + 448 * q^28 - 352 * q^29 + 644 * q^30 - 40 * q^32 + 30 * q^33 + 208 * q^36 + 258 * q^37 - 1620 * q^38 - 1548 * q^40 - 980 * q^42 - 1248 * q^44 - 504 * q^45 + 232 * q^46 - 644 * q^49 - 864 * q^50 + 2592 * q^52 + 570 * q^53 + 4572 * q^54 + 1904 * q^56 + 1452 * q^57 + 2244 * q^58 - 736 * q^60 + 294 * q^61 + 2560 * q^64 - 124 * q^65 - 4272 * q^66 - 6084 * q^68 - 4144 * q^70 - 4672 * q^72 + 966 * q^73 + 832 * q^74 - 378 * q^77 - 4056 * q^78 + 7032 * q^80 - 1262 * q^81 + 7692 * q^82 + 6188 * q^84 - 2980 * q^85 + 5696 * q^86 - 1396 * q^88 - 3186 * q^89 + 3312 * q^92 - 306 * q^93 - 6780 * q^94 - 11784 * q^96 - 4900 * q^98

Introduction

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