LMFDB - Embedded newform 38.4.c.b.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,4,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.24207258022$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	38.11
Dual form			38.4.c.b.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(2.50000 - 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.00000 - 10.3923i) q^{5} +(5.00000 + 8.66025i) q^{6} +8.00000 q^{7} +8.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(2.50000 - 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.00000 - 10.3923i) q^{5} +(5.00000 + 8.66025i) q^{6} +8.00000 q^{7} +8.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(12.0000 + 20.7846i) q^{10} +9.00000 q^{11} -20.0000 q^{12} +(-13.0000 - 22.5167i) q^{13} +(-8.00000 + 13.8564i) q^{14} +(-30.0000 - 51.9615i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-57.0000 + 98.7269i) q^{17} -4.00000 q^{18} +(-66.5000 - 49.3634i) q^{19} -48.0000 q^{20} +(20.0000 - 34.6410i) q^{21} +(-9.00000 + 15.5885i) q^{22} +(39.0000 + 67.5500i) q^{23} +(20.0000 - 34.6410i) q^{24} +(-9.50000 - 16.4545i) q^{25} +52.0000 q^{26} +145.000 q^{27} +(-16.0000 - 27.7128i) q^{28} +(102.000 + 176.669i) q^{29} +120.000 q^{30} +98.0000 q^{31} +(-16.0000 - 27.7128i) q^{32} +(22.5000 - 38.9711i) q^{33} +(-114.000 - 197.454i) q^{34} +(48.0000 - 83.1384i) q^{35} +(4.00000 - 6.92820i) q^{36} -334.000 q^{37} +(152.000 - 65.8179i) q^{38} -130.000 q^{39} +(48.0000 - 83.1384i) q^{40} +(-88.5000 + 153.286i) q^{41} +(40.0000 + 69.2820i) q^{42} +(158.000 - 273.664i) q^{43} +(-18.0000 - 31.1769i) q^{44} +24.0000 q^{45} -156.000 q^{46} +(246.000 + 426.084i) q^{47} +(40.0000 + 69.2820i) q^{48} -279.000 q^{49} +38.0000 q^{50} +(285.000 + 493.634i) q^{51} +(-52.0000 + 90.0666i) q^{52} +(-339.000 - 587.165i) q^{53} +(-145.000 + 251.147i) q^{54} +(54.0000 - 93.5307i) q^{55} +64.0000 q^{56} +(-380.000 + 164.545i) q^{57} -408.000 q^{58} +(289.500 - 501.429i) q^{59} +(-120.000 + 207.846i) q^{60} +(176.000 + 304.841i) q^{61} +(-98.0000 + 169.741i) q^{62} +(8.00000 + 13.8564i) q^{63} +64.0000 q^{64} -312.000 q^{65} +(45.0000 + 77.9423i) q^{66} +(-377.500 - 653.849i) q^{67} +456.000 q^{68} +390.000 q^{69} +(96.0000 + 166.277i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(8.00000 + 13.8564i) q^{72} +(72.5000 - 125.574i) q^{73} +(334.000 - 578.505i) q^{74} -95.0000 q^{75} +(-38.0000 + 329.090i) q^{76} +72.0000 q^{77} +(130.000 - 225.167i) q^{78} +(158.000 - 273.664i) q^{79} +(96.0000 + 166.277i) q^{80} +(335.500 - 581.103i) q^{81} +(-177.000 - 306.573i) q^{82} -567.000 q^{83} -160.000 q^{84} +(684.000 + 1184.72i) q^{85} +(316.000 + 547.328i) q^{86} +1020.00 q^{87} +72.0000 q^{88} +(57.0000 + 98.7269i) q^{89} +(-24.0000 + 41.5692i) q^{90} +(-104.000 - 180.133i) q^{91} +(156.000 - 270.200i) q^{92} +(245.000 - 424.352i) q^{93} -984.000 q^{94} +(-912.000 + 394.908i) q^{95} -160.000 q^{96} +(471.500 - 816.662i) q^{97} +(279.000 - 483.242i) q^{98} +(9.00000 + 15.5885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 5 q^{3} - 4 q^{4} + 12 q^{5} + 10 q^{6} + 16 q^{7} + 16 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 5 * q^3 - 4 * q^4 + 12 * q^5 + 10 * q^6 + 16 * q^7 + 16 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 5 q^{3} - 4 q^{4} + 12 q^{5} + 10 q^{6} + 16 q^{7} + 16 q^{8} + 2 q^{9} + 24 q^{10} + 18 q^{11} - 40 q^{12} - 26 q^{13} - 16 q^{14} - 60 q^{15} - 16 q^{16} - 114 q^{17} - 8 q^{18} - 133 q^{19} - 96 q^{20} + 40 q^{21} - 18 q^{22} + 78 q^{23} + 40 q^{24} - 19 q^{25} + 104 q^{26} + 290 q^{27} - 32 q^{28} + 204 q^{29} + 240 q^{30} + 196 q^{31} - 32 q^{32} + 45 q^{33} - 228 q^{34} + 96 q^{35} + 8 q^{36} - 668 q^{37} + 304 q^{38} - 260 q^{39} + 96 q^{40} - 177 q^{41} + 80 q^{42} + 316 q^{43} - 36 q^{44} + 48 q^{45} - 312 q^{46} + 492 q^{47} + 80 q^{48} - 558 q^{49} + 76 q^{50} + 570 q^{51} - 104 q^{52} - 678 q^{53} - 290 q^{54} + 108 q^{55} + 128 q^{56} - 760 q^{57} - 816 q^{58} + 579 q^{59} - 240 q^{60} + 352 q^{61} - 196 q^{62} + 16 q^{63} + 128 q^{64} - 624 q^{65} + 90 q^{66} - 755 q^{67} + 912 q^{68} + 780 q^{69} + 192 q^{70} - 6 q^{71} + 16 q^{72} + 145 q^{73} + 668 q^{74} - 190 q^{75} - 76 q^{76} + 144 q^{77} + 260 q^{78} + 316 q^{79} + 192 q^{80} + 671 q^{81} - 354 q^{82} - 1134 q^{83} - 320 q^{84} + 1368 q^{85} + 632 q^{86} + 2040 q^{87} + 144 q^{88} + 114 q^{89} - 48 q^{90} - 208 q^{91} + 312 q^{92} + 490 q^{93} - 1968 q^{94} - 1824 q^{95} - 320 q^{96} + 943 q^{97} + 558 q^{98} + 18 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 5 * q^3 - 4 * q^4 + 12 * q^5 + 10 * q^6 + 16 * q^7 + 16 * q^8 + 2 * q^9 + 24 * q^10 + 18 * q^11 - 40 * q^12 - 26 * q^13 - 16 * q^14 - 60 * q^15 - 16 * q^16 - 114 * q^17 - 8 * q^18 - 133 * q^19 - 96 * q^20 + 40 * q^21 - 18 * q^22 + 78 * q^23 + 40 * q^24 - 19 * q^25 + 104 * q^26 + 290 * q^27 - 32 * q^28 + 204 * q^29 + 240 * q^30 + 196 * q^31 - 32 * q^32 + 45 * q^33 - 228 * q^34 + 96 * q^35 + 8 * q^36 - 668 * q^37 + 304 * q^38 - 260 * q^39 + 96 * q^40 - 177 * q^41 + 80 * q^42 + 316 * q^43 - 36 * q^44 + 48 * q^45 - 312 * q^46 + 492 * q^47 + 80 * q^48 - 558 * q^49 + 76 * q^50 + 570 * q^51 - 104 * q^52 - 678 * q^53 - 290 * q^54 + 108 * q^55 + 128 * q^56 - 760 * q^57 - 816 * q^58 + 579 * q^59 - 240 * q^60 + 352 * q^61 - 196 * q^62 + 16 * q^63 + 128 * q^64 - 624 * q^65 + 90 * q^66 - 755 * q^67 + 912 * q^68 + 780 * q^69 + 192 * q^70 - 6 * q^71 + 16 * q^72 + 145 * q^73 + 668 * q^74 - 190 * q^75 - 76 * q^76 + 144 * q^77 + 260 * q^78 + 316 * q^79 + 192 * q^80 + 671 * q^81 - 354 * q^82 - 1134 * q^83 - 320 * q^84 + 1368 * q^85 + 632 * q^86 + 2040 * q^87 + 144 * q^88 + 114 * q^89 - 48 * q^90 - 208 * q^91 + 312 * q^92 + 490 * q^93 - 1968 * q^94 - 1824 * q^95 - 320 * q^96 + 943 * q^97 + 558 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	2.50000	−	4.33013i	0.481125	−	0.833333i	−0.518640	−	0.854993i	$-0.673562\pi$
$3$	2.50000	−	4.33013i	0.481125	−	0.833333i	0.999765	+	0.0216593i	$0.00689490\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	6.00000	−	10.3923i	0.536656	−	0.929516i	−0.462425	−	0.886658i	$-0.653021\pi$
$5$	6.00000	−	10.3923i	0.536656	−	0.929516i	0.999081	−	0.0428575i	$-0.0136462\pi$
$6$	5.00000	+	8.66025i	0.340207	+	0.589256i
$7$	8.00000			0.431959			0.215980	−	0.976398i	$-0.430705\pi$
$7$	8.00000			0.431959			0.215980	+	0.976398i	$0.430705\pi$
$8$	8.00000			0.353553
$9$	1.00000	+	1.73205i	0.0370370	+	0.0641500i
$10$	12.0000	+	20.7846i	0.379473	+	0.657267i
$11$	9.00000			0.246691			0.123346	−	0.992364i	$-0.460638\pi$
$11$	9.00000			0.246691			0.123346	+	0.992364i	$0.460638\pi$
$12$	−20.0000			−0.481125
$13$	−13.0000	−	22.5167i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−13.0000	−	22.5167i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−8.00000	+	13.8564i	−0.152721	+	0.264520i
$15$	−30.0000	−	51.9615i	−0.516398	−	0.894427i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−57.0000	+	98.7269i	−0.813208	+	1.40852i	0.0974001	+	0.995245i	$0.468947\pi$
$17$	−57.0000	+	98.7269i	−0.813208	+	1.40852i	−0.910608	+	0.413272i	$0.864386\pi$
$18$	−4.00000			−0.0523783
$19$	−66.5000	−	49.3634i	−0.802955	−	0.596040i
$19$	−66.5000	−	49.3634i	−0.802955	−	0.596040i
$20$	−48.0000			−0.536656
$21$	20.0000	−	34.6410i	0.207827	−	0.359966i
$22$	−9.00000	+	15.5885i	−0.0872185	+	0.151067i
$23$	39.0000	+	67.5500i	0.353568	+	0.612398i	0.986872	−	0.161506i	$-0.0516350\pi$
$23$	39.0000	+	67.5500i	0.353568	+	0.612398i	−0.633304	+	0.773903i	$0.718302\pi$
$24$	20.0000	−	34.6410i	0.170103	−	0.294628i
$25$	−9.50000	−	16.4545i	−0.0760000	−	0.131636i
$26$	52.0000			0.392232
$27$	145.000			1.03353
$28$	−16.0000	−	27.7128i	−0.107990	−	0.187044i
$29$	102.000	+	176.669i	0.653135	+	1.13126i	0.982358	+	0.187011i	$0.0598801\pi$
$29$	102.000	+	176.669i	0.653135	+	1.13126i	−0.329222	+	0.944252i	$0.606787\pi$
$30$	120.000			0.730297
$31$	98.0000			0.567785			0.283892	−	0.958856i	$-0.408374\pi$
$31$	98.0000			0.567785			0.283892	+	0.958856i	$0.408374\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	22.5000	−	38.9711i	0.118689	−	0.205576i
$34$	−114.000	−	197.454i	−0.575025	−	0.995972i
$35$	48.0000	−	83.1384i	0.231814	−	0.401513i
$36$	4.00000	−	6.92820i	0.0185185	−	0.0320750i
$37$	−334.000			−1.48403			−0.742017	−	0.670381i	$-0.766131\pi$
$37$	−334.000			−1.48403			−0.742017	+	0.670381i	$0.766131\pi$
$38$	152.000	−	65.8179i	0.648886	−	0.280976i
$39$	−130.000			−0.533761
$40$	48.0000	−	83.1384i	0.189737	−	0.328634i
$41$	−88.5000	+	153.286i	−0.337107	+	0.583886i	−0.983887	−	0.178790i	$-0.942782\pi$
$41$	−88.5000	+	153.286i	−0.337107	+	0.583886i	0.646780	+	0.762676i	$0.276115\pi$
$42$	40.0000	+	69.2820i	0.146956	+	0.254535i
$43$	158.000	−	273.664i	0.560344	−	0.970544i	−0.437123	−	0.899402i	$-0.644002\pi$
$43$	158.000	−	273.664i	0.560344	−	0.970544i	0.997466	−	0.0711416i	$-0.0226642\pi$
$44$	−18.0000	−	31.1769i	−0.0616728	−	0.106820i
$45$	24.0000			0.0795046
$46$	−156.000			−0.500021
$47$	246.000	+	426.084i	0.763464	+	1.32236i	0.941055	+	0.338253i	$0.109836\pi$
$47$	246.000	+	426.084i	0.763464	+	1.32236i	−0.177591	+	0.984104i	$0.556831\pi$
$48$	40.0000	+	69.2820i	0.120281	+	0.208333i
$49$	−279.000			−0.813411
$50$	38.0000			0.107480
$51$	285.000	+	493.634i	0.782509	+	1.35535i
$52$	−52.0000	+	90.0666i	−0.138675	+	0.240192i
$53$	−339.000	−	587.165i	−0.878589	−	1.52176i	−0.852889	−	0.522092i	$-0.825152\pi$
$53$	−339.000	−	587.165i	−0.878589	−	1.52176i	−0.0256998	−	0.999670i	$-0.508181\pi$
$54$	−145.000	+	251.147i	−0.365407	+	0.632904i
$55$	54.0000	−	93.5307i	0.132388	−	0.229303i
$56$	64.0000			0.152721
$57$	−380.000	+	164.545i	−0.883022	+	0.382360i
$58$	−408.000			−0.923673
$59$	289.500	−	501.429i	0.638808	−	1.10645i	−0.346886	−	0.937907i	$-0.612761\pi$
$59$	289.500	−	501.429i	0.638808	−	1.10645i	0.985695	−	0.168541i	$-0.0539056\pi$
$60$	−120.000	+	207.846i	−0.258199	+	0.447214i
$61$	176.000	+	304.841i	0.369418	+	0.639851i	0.989475	−	0.144706i	$-0.0462238\pi$
$61$	176.000	+	304.841i	0.369418	+	0.639851i	−0.620057	+	0.784557i	$0.712890\pi$
$62$	−98.0000	+	169.741i	−0.200742	+	0.347696i
$63$	8.00000	+	13.8564i	0.0159985	+	0.0277102i
$64$	64.0000			0.125000
$65$	−312.000			−0.595367
$66$	45.0000	+	77.9423i	0.0839260	+	0.145364i
$67$	−377.500	−	653.849i	−0.688343	−	1.19224i	−0.972374	−	0.233430i	$-0.925005\pi$
$67$	−377.500	−	653.849i	−0.688343	−	1.19224i	0.284031	−	0.958815i	$-0.408328\pi$
$68$	456.000			0.813208
$69$	390.000			0.680442
$70$	96.0000	+	166.277i	0.163917	+	0.283913i
$71$	−3.00000	+	5.19615i	−0.00501457	+	0.00868549i	−0.868522	−	0.495651i	$-0.834930\pi$
$71$	−3.00000	+	5.19615i	−0.00501457	+	0.00868549i	0.863507	+	0.504336i	$0.168263\pi$
$72$	8.00000	+	13.8564i	0.0130946	+	0.0226805i
$73$	72.5000	−	125.574i	0.116239	−	0.201333i	−0.802035	−	0.597277i	$-0.796249\pi$
$73$	72.5000	−	125.574i	0.116239	−	0.201333i	0.918275	+	0.395944i	$0.129583\pi$
$74$	334.000	−	578.505i	0.524685	−	0.908782i
$75$	−95.0000			−0.146262
$76$	−38.0000	+	329.090i	−0.0573539	+	0.496700i
$77$	72.0000			0.106561
$78$	130.000	−	225.167i	0.188713	−	0.326860i
$79$	158.000	−	273.664i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	158.000	−	273.664i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$	96.0000	+	166.277i	0.134164	+	0.232379i
$81$	335.500	−	581.103i	0.460219	−	0.797124i
$82$	−177.000	−	306.573i	−0.238370	−	0.412870i
$83$	−567.000			−0.749835			−0.374918	−	0.927058i	$-0.622329\pi$
$83$	−567.000			−0.749835			−0.374918	+	0.927058i	$0.622329\pi$
$84$	−160.000			−0.207827
$85$	684.000	+	1184.72i	0.872826	+	1.51178i
$86$	316.000	+	547.328i	0.396223	+	0.686278i
$87$	1020.00			1.25696
$88$	72.0000			0.0872185
$89$	57.0000	+	98.7269i	0.0678875	+	0.117585i	0.897971	−	0.440054i	$-0.145041\pi$
$89$	57.0000	+	98.7269i	0.0678875	+	0.117585i	−0.830084	+	0.557639i	$0.811707\pi$
$90$	−24.0000	+	41.5692i	−0.0281091	+	0.0486864i
$91$	−104.000	−	180.133i	−0.119804	−	0.207507i
$92$	156.000	−	270.200i	0.176784	−	0.306199i
$93$	245.000	−	424.352i	0.273175	−	0.473154i
$94$	−984.000			−1.07970
$95$	−912.000	+	394.908i	−0.984939	+	0.426491i
$96$	−160.000			−0.170103
$97$	471.500	−	816.662i	0.493542	−	0.854840i	−0.506430	−	0.862281i	$-0.669035\pi$
$97$	471.500	−	816.662i	0.493542	−	0.854840i	0.999972	+	0.00744110i	$0.00236860\pi$
$98$	279.000	−	483.242i	0.287584	−	0.498111i
$99$	9.00000	+	15.5885i	0.00913671	+	0.0158252i
$100$	−38.0000	+	65.8179i	−0.0380000	+	0.0658179i
$101$	750.000	+	1299.04i	0.738889	+	1.27979i	0.952996	+	0.302983i	$0.0979826\pi$
$101$	750.000	+	1299.04i	0.738889	+	1.27979i	−0.214107	+	0.976810i	$0.568684\pi$
$102$	−1140.00			−1.10664
$103$	−658.000			−0.629463			−0.314731	−	0.949181i	$-0.601914\pi$
$103$	−658.000			−0.629463			−0.314731	+	0.949181i	$0.601914\pi$
$104$	−104.000	−	180.133i	−0.0980581	−	0.169842i
$105$	−240.000	−	415.692i	−0.223063	−	0.386356i
$106$	1356.00			1.24251
$107$	−1440.00			−1.30103			−0.650514	−	0.759494i	$-0.725447\pi$
$107$	−1440.00			−1.30103			−0.650514	+	0.759494i	$0.725447\pi$
$108$	−290.000	−	502.295i	−0.258382	−	0.447531i
$109$	−640.000	+	1108.51i	−0.562393	+	0.974094i	0.434894	+	0.900482i	$0.356786\pi$
$109$	−640.000	+	1108.51i	−0.562393	+	0.974094i	−0.997287	+	0.0736121i	$0.976547\pi$
$110$	108.000	+	187.061i	0.0936127	+	0.162142i
$111$	−835.000	+	1446.26i	−0.714006	+	1.23670i
$112$	−64.0000	+	110.851i	−0.0539949	+	0.0935220i
$113$	−369.000			−0.307191			−0.153596	−	0.988134i	$-0.549085\pi$
$113$	−369.000			−0.307191			−0.153596	+	0.988134i	$0.549085\pi$
$114$	95.0000	−	822.724i	0.0780488	−	0.675923i
$115$	936.000			0.758978
$116$	408.000	−	706.677i	0.326568	−	0.565632i
$117$	26.0000	−	45.0333i	0.0205445	−	0.0355840i
$118$	579.000	+	1002.86i	0.451706	+	0.782377i
$119$	−456.000	+	789.815i	−0.351273	+	0.608422i
$120$	−240.000	−	415.692i	−0.182574	−	0.316228i
$121$	−1250.00			−0.939144
$122$	−704.000			−0.522436
$123$	442.500	+	766.432i	0.324381	+	0.561845i
$124$	−196.000	−	339.482i	−0.141946	−	0.245858i
$125$	1272.00			0.910169
$126$	−32.0000			−0.0226253
$127$	−451.000	−	781.155i	−0.315116	−	0.545798i	0.664346	−	0.747425i	$-0.268710\pi$
$127$	−451.000	−	781.155i	−0.315116	−	0.545798i	−0.979462	+	0.201628i	$0.935377\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	−790.000	−	1368.32i	−0.539191	−	0.933906i
$130$	312.000	−	540.400i	0.210494	−	0.364586i
$131$	226.500	−	392.310i	0.151064	−	0.261651i	−0.780555	−	0.625087i	$-0.785063\pi$
$131$	226.500	−	392.310i	0.151064	−	0.261651i	0.931619	+	0.363437i	$0.118397\pi$
$132$	−180.000			−0.118689
$133$	−532.000	−	394.908i	−0.346844	−	0.257465i
$134$	1510.00			0.973464
$135$	870.000	−	1506.88i	0.554649	−	0.960681i
$136$	−456.000	+	789.815i	−0.287512	+	0.497986i
$137$	−1000.50	−	1732.92i	−0.623931	−	1.08068i	−0.988747	−	0.149600i	$-0.952201\pi$
$137$	−1000.50	−	1732.92i	−0.623931	−	1.08068i	0.364816	−	0.931080i	$-0.381132\pi$
$138$	−390.000	+	675.500i	−0.240572	+	0.416684i
$139$	1467.50	+	2541.78i	0.895480	+	1.55102i	0.833209	+	0.552958i	$0.186501\pi$
$139$	1467.50	+	2541.78i	0.895480	+	1.55102i	0.0622707	+	0.998059i	$0.480166\pi$
$140$	−384.000			−0.231814
$141$	2460.00			1.46929
$142$	−6.00000	−	10.3923i	−0.00354584	−	0.00614157i
$143$	−117.000	−	202.650i	−0.0684198	−	0.118507i
$144$	−32.0000			−0.0185185
$145$	2448.00			1.40204
$146$	145.000	+	251.147i	0.0821937	+	0.142364i
$147$	−697.500	+	1208.11i	−0.391353	+	0.677843i
$148$	668.000	+	1157.01i	0.371009	+	0.642606i
$149$	−3.00000	+	5.19615i	−0.00164946	+	0.00285695i	−0.866849	−	0.498571i	$-0.833858\pi$
$149$	−3.00000	+	5.19615i	−0.00164946	+	0.00285695i	0.865199	+	0.501428i	$0.167192\pi$
$150$	95.0000	−	164.545i	0.0517115	−	0.0895669i
$151$	2774.00			1.49500			0.747500	−	0.664262i	$-0.231254\pi$
$151$	2774.00			1.49500			0.747500	+	0.664262i	$0.231254\pi$
$152$	−532.000	−	394.908i	−0.283887	−	0.210732i
$153$	−228.000			−0.120475
$154$	−72.0000	+	124.708i	−0.0376748	+	0.0652547i
$155$	588.000	−	1018.45i	0.304705	−	0.527765i
$156$	260.000	+	450.333i	0.133440	+	0.231125i
$157$	1364.00	−	2362.52i	0.693370	−	1.20095i	−0.277357	−	0.960767i	$-0.589459\pi$
$157$	1364.00	−	2362.52i	0.693370	−	1.20095i	0.970727	−	0.240185i	$-0.0772081\pi$
$158$	316.000	+	547.328i	0.159111	+	0.275589i
$159$	−3390.00			−1.69085
$160$	−384.000			−0.189737
$161$	312.000	+	540.400i	0.152727	+	0.264531i
$162$	671.000	+	1162.21i	0.325424	+	0.563651i
$163$	−1657.00			−0.796235			−0.398117	−	0.917334i	$-0.630336\pi$
$163$	−1657.00			−0.796235			−0.398117	+	0.917334i	$0.630336\pi$
$164$	708.000			0.337107
$165$	−270.000	−	467.654i	−0.127391	−	0.220647i
$166$	567.000	−	982.073i	0.265107	−	0.459179i
$167$	−1392.00	−	2411.01i	−0.645007	−	1.11719i	−0.984300	−	0.176504i	$-0.943521\pi$
$167$	−1392.00	−	2411.01i	−0.645007	−	1.11719i	0.339293	−	0.940681i	$-0.389812\pi$
$168$	160.000	−	277.128i	0.0734778	−	0.127267i
$169$	760.500	−	1317.22i	0.346154	−	0.599556i
$170$	−2736.00			−1.23436
$171$	19.0000	−	164.545i	0.00849688	−	0.0735851i
$172$	−1264.00			−0.560344
$173$	−1191.00	+	2062.87i	−0.523411	+	0.906574i	0.476218	+	0.879327i	$0.342007\pi$
$173$	−1191.00	+	2062.87i	−0.523411	+	0.906574i	−0.999629	+	0.0272467i	$0.991326\pi$
$174$	−1020.00	+	1766.69i	−0.444402	+	0.769727i
$175$	−76.0000	−	131.636i	−0.0328289	−	0.0568613i
$176$	−72.0000	+	124.708i	−0.0308364	+	0.0534102i
$177$	−1447.50	−	2507.14i	−0.614694	−	1.06468i
$178$	−228.000			−0.0960074
$179$	−3645.00			−1.52201			−0.761006	−	0.648745i	$-0.775294\pi$
$179$	−3645.00			−1.52201			−0.761006	+	0.648745i	$0.775294\pi$
$180$	−48.0000	−	83.1384i	−0.0198762	−	0.0344265i
$181$	953.000	+	1650.64i	0.391359	+	0.677853i	0.992629	−	0.121192i	$-0.0386718\pi$
$181$	953.000	+	1650.64i	0.391359	+	0.677853i	−0.601270	+	0.799046i	$0.705338\pi$
$182$	416.000			0.169428
$183$	1760.00			0.710945
$184$	312.000	+	540.400i	0.125005	+	0.216515i
$185$	−2004.00	+	3471.03i	−0.796416	+	1.37943i
$186$	490.000	+	848.705i	0.193164	+	0.334570i
$187$	−513.000	+	888.542i	−0.200611	+	0.347469i
$188$	984.000	−	1704.34i	0.381732	−	0.661179i
$189$	1160.00			0.446442
$190$	228.000	−	1974.54i	0.0870572	−	0.753937i
$191$	1332.00			0.504608			0.252304	−	0.967648i	$-0.418812\pi$
$191$	1332.00			0.504608			0.252304	+	0.967648i	$0.418812\pi$
$192$	160.000	−	277.128i	0.0601407	−	0.104167i
$193$	−661.000	+	1144.89i	−0.246528	+	0.426998i	−0.962560	−	0.271069i	$-0.912623\pi$
$193$	−661.000	+	1144.89i	−0.246528	+	0.426998i	0.716032	+	0.698067i	$0.245956\pi$
$194$	943.000	+	1633.32i	0.348987	+	0.604463i
$195$	−780.000	+	1351.00i	−0.286446	+	0.496139i
$196$	558.000	+	966.484i	0.203353	+	0.352217i
$197$	3726.00			1.34755			0.673773	−	0.738939i	$-0.264673\pi$
$197$	3726.00			1.34755			0.673773	+	0.738939i	$0.264673\pi$
$198$	−36.0000			−0.0129213
$199$	239.000	+	413.960i	0.0851370	+	0.147462i	0.905450	−	0.424454i	$-0.139534\pi$
$199$	239.000	+	413.960i	0.0851370	+	0.147462i	−0.820313	+	0.571915i	$0.806201\pi$
$200$	−76.0000	−	131.636i	−0.0268701	−	0.0465403i
$201$	−3775.00			−1.32472
$202$	−3000.00			−1.04495
$203$	816.000	+	1413.35i	0.282128	+	0.488660i
$204$	1140.00	−	1974.54i	0.391255	−	0.677673i
$205$	1062.00	+	1839.44i	0.361821	+	0.626692i
$206$	658.000	−	1139.69i	0.222549	−	0.385466i
$207$	−78.0000	+	135.100i	−0.0261902	+	0.0453628i
$208$	416.000			0.138675
$209$	−598.500	−	444.271i	−0.198082	−	0.147038i
$210$	960.000			0.315459
$211$	410.000	−	710.141i	0.133770	−	0.231697i	−0.791357	−	0.611355i	$-0.790625\pi$
$211$	410.000	−	710.141i	0.133770	−	0.231697i	0.925127	+	0.379658i	$0.123958\pi$
$212$	−1356.00	+	2348.66i	−0.439295	+	0.760881i
$213$	15.0000	+	25.9808i	0.00482527	+	0.00835762i
$214$	1440.00	−	2494.15i	0.459983	−	0.796714i
$215$	−1896.00	−	3283.97i	−0.601424	−	1.04170i
$216$	1160.00			0.365407
$217$	784.000			0.245260
$218$	−1280.00	−	2217.03i	−0.397672	−	0.688788i
$219$	−362.500	−	627.868i	−0.111852	−	0.193732i
$220$	−432.000			−0.132388
$221$	2964.00			0.902173
$222$	−1670.00	−	2892.52i	−0.504879	−	0.874475i
$223$	−463.000	+	801.940i	−0.139035	+	0.240815i	−0.927132	−	0.374736i	$-0.877733\pi$
$223$	−463.000	+	801.940i	−0.139035	+	0.240815i	0.788097	+	0.615551i	$0.211067\pi$
$224$	−128.000	−	221.703i	−0.0381802	−	0.0661300i
$225$	19.0000	−	32.9090i	0.00562963	−	0.00975080i
$226$	369.000	−	639.127i	0.108608	−	0.188115i
$227$	4977.00			1.45522			0.727610	−	0.685991i	$-0.240631\pi$
$227$	4977.00			1.45522			0.727610	+	0.685991i	$0.240631\pi$
$228$	1330.00	+	987.269i	0.386322	+	0.286770i
$229$	−4312.00			−1.24430			−0.622151	−	0.782898i	$-0.713741\pi$
$229$	−4312.00			−1.24430			−0.622151	+	0.782898i	$0.713741\pi$
$230$	−936.000	+	1621.20i	−0.268339	+	0.464777i
$231$	180.000	−	311.769i	0.0512690	−	0.0888004i
$232$	816.000	+	1413.35i	0.230918	+	0.399962i
$233$	910.500	−	1577.03i	0.256004	−	0.443411i	−0.709164	−	0.705044i	$-0.750927\pi$
$233$	910.500	−	1577.03i	0.256004	−	0.443411i	0.965168	+	0.261632i	$0.0842608\pi$
$234$	52.0000	+	90.0666i	0.0145271	+	0.0251617i
$235$	5904.00			1.63887
$236$	−2316.00			−0.638808
$237$	−790.000	−	1368.32i	−0.216523	−	0.375029i
$238$	−912.000	−	1579.63i	−0.248387	−	0.430219i
$239$	324.000			0.0876896			0.0438448	−	0.999038i	$-0.486039\pi$
$239$	324.000			0.0876896			0.0438448	+	0.999038i	$0.486039\pi$
$240$	960.000			0.258199
$241$	−170.500	−	295.315i	−0.0455721	−	0.0789332i	0.842340	−	0.538947i	$-0.181178\pi$
$241$	−170.500	−	295.315i	−0.0455721	−	0.0789332i	−0.887912	+	0.460014i	$0.847844\pi$
$242$	1250.00	−	2165.06i	0.332037	−	0.575106i
$243$	280.000	+	484.974i	0.0739177	+	0.128029i
$244$	704.000	−	1219.36i	0.184709	−	0.319925i
$245$	−1674.00	+	2899.45i	−0.436522	+	0.756079i
$246$	−1770.00			−0.458744
$247$	−247.000	+	2139.08i	−0.0636285	+	0.551039i
$248$	784.000			0.200742
$249$	−1417.50	+	2455.18i	−0.360765	+	0.624863i
$250$	−1272.00	+	2203.17i	−0.321793	+	0.557362i
$251$	−2431.50	−	4211.48i	−0.611454	−	1.05907i	−0.990996	−	0.133895i	$-0.957252\pi$
$251$	−2431.50	−	4211.48i	−0.611454	−	1.05907i	0.379542	−	0.925175i	$-0.376082\pi$
$252$	32.0000	−	55.4256i	0.00799925	−	0.0138551i
$253$	351.000	+	607.950i	0.0872221	+	0.151073i
$254$	1804.00			0.445642
$255$	6840.00			1.67975
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	1726.50	+	2990.39i	0.419051	+	0.725818i	0.995844	−	0.0910725i	$-0.0290295\pi$
$257$	1726.50	+	2990.39i	0.419051	+	0.725818i	−0.576793	+	0.816890i	$0.695696\pi$
$258$	3160.00			0.762531
$259$	−2672.00			−0.641042
$260$	624.000	+	1080.80i	0.148842	+	0.257801i
$261$	−204.000	+	353.338i	−0.0483804	+	0.0837973i
$262$	453.000	+	784.619i	0.106818	+	0.185015i
$263$	60.0000	−	103.923i	0.0140675	−	0.0243657i	−0.858906	−	0.512133i	$-0.828855\pi$
$263$	60.0000	−	103.923i	0.0140675	−	0.0243657i	0.872973	+	0.487768i	$0.162189\pi$
$264$	180.000	−	311.769i	0.0419630	−	0.0726821i
$265$	−8136.00			−1.88600
$266$	1216.00	−	526.543i	0.280292	−	0.121370i
$267$	570.000			0.130650
$268$	−1510.00	+	2615.40i	−0.344171	+	0.596122i
$269$	3534.00	−	6121.07i	0.801010	−	1.38739i	−0.117941	−	0.993021i	$-0.537629\pi$
$269$	3534.00	−	6121.07i	0.801010	−	1.38739i	0.918952	−	0.394370i	$-0.129037\pi$
$270$	1740.00	+	3013.77i	0.392196	+	0.679304i
$271$	−694.000	+	1202.04i	−0.155563	+	0.269443i	−0.933264	−	0.359192i	$-0.883052\pi$
$271$	−694.000	+	1202.04i	−0.155563	+	0.269443i	0.777701	+	0.628634i	$0.216386\pi$
$272$	−912.000	−	1579.63i	−0.203302	−	0.352129i
$273$	−1040.00			−0.230563
$274$	4002.00			0.882371
$275$	−85.5000	−	148.090i	−0.0187485	−	0.0324734i
$276$	−780.000	−	1351.00i	−0.170110	−	0.294640i
$277$	−5164.00			−1.12013			−0.560063	−	0.828450i	$-0.689223\pi$
$277$	−5164.00			−1.12013			−0.560063	+	0.828450i	$0.689223\pi$
$278$	−5870.00			−1.26640
$279$	98.0000	+	169.741i	0.0210291	+	0.0364234i
$280$	384.000	−	665.108i	0.0819585	−	0.141956i
$281$	322.500	+	558.586i	0.0684653	+	0.118585i	0.898226	−	0.439534i	$-0.144856\pi$
$281$	322.500	+	558.586i	0.0684653	+	0.118585i	−0.829761	+	0.558119i	$0.811523\pi$
$282$	−2460.00	+	4260.84i	−0.519471	+	0.899750i
$283$	−3371.50	+	5839.61i	−0.708180	+	1.22660i	0.257352	+	0.966318i	$0.417150\pi$
$283$	−3371.50	+	5839.61i	−0.708180	+	1.22660i	−0.965532	+	0.260286i	$0.916183\pi$
$284$	24.0000			0.00501457
$285$	−570.000	+	4936.34i	−0.118470	+	1.02598i
$286$	468.000			0.0967602
$287$	−708.000	+	1226.29i	−0.145616	+	0.252215i
$288$	32.0000	−	55.4256i	0.00654729	−	0.0113402i
$289$	−4041.50	−	7000.08i	−0.822613	−	1.42481i
$290$	−2448.00	+	4240.06i	−0.495695	+	0.858569i
$291$	−2357.50	−	4083.31i	−0.474911	−	0.822570i
$292$	−580.000			−0.116239
$293$	−252.000			−0.0502457			−0.0251229	−	0.999684i	$-0.507998\pi$
$293$	−252.000			−0.0502457			−0.0251229	+	0.999684i	$0.507998\pi$
$294$	−1395.00	−	2416.21i	−0.276728	−	0.479307i
$295$	−3474.00	−	6017.14i	−0.685641	−	1.18757i
$296$	−2672.00			−0.524685
$297$	1305.00			0.254962
$298$	−6.00000	−	10.3923i	−0.00116634	−	0.00202017i
$299$	1014.00	−	1756.30i	0.196124	−	0.339697i
$300$	190.000	+	329.090i	0.0365655	+	0.0633333i
$301$	1264.00	−	2189.31i	0.242046	−	0.419235i
$302$	−2774.00	+	4804.71i	−0.528562	+	0.915496i
$303$	7500.00			1.42199
$304$	1216.00	−	526.543i	0.229416	−	0.0993399i
$305$	4224.00			0.793002
$306$	228.000	−	394.908i	0.0425944	−	0.0737757i
$307$	3558.50	−	6163.50i	0.661545	−	1.14583i	−0.318665	−	0.947868i	$-0.603234\pi$
$307$	3558.50	−	6163.50i	0.661545	−	1.14583i	0.980210	−	0.197962i	$-0.0634323\pi$
$308$	−144.000	−	249.415i	−0.0266401	−	0.0461421i
$309$	−1645.00	+	2849.22i	−0.302850	+	0.524552i
$310$	1176.00	+	2036.89i	0.215459	+	0.373186i
$311$	4410.00			0.804078			0.402039	−	0.915623i	$-0.368302\pi$
$311$	4410.00			0.804078			0.402039	+	0.915623i	$0.368302\pi$
$312$	−1040.00			−0.188713
$313$	−3362.50	−	5824.02i	−0.607220	−	1.05174i	−0.991696	−	0.128601i	$-0.958951\pi$
$313$	−3362.50	−	5824.02i	−0.607220	−	1.05174i	0.384477	−	0.923135i	$-0.374382\pi$
$314$	2728.00	+	4725.03i	0.490286	+	0.849201i
$315$	192.000			0.0343428
$316$	−1264.00			−0.225018
$317$	2433.00	+	4214.08i	0.431075	+	0.746644i	0.996966	−	0.0778357i	$-0.0248010\pi$
$317$	2433.00	+	4214.08i	0.431075	+	0.746644i	−0.565891	+	0.824480i	$0.691468\pi$
$318$	3390.00	−	5871.65i	0.597804	−	1.03543i
$319$	918.000	+	1590.02i	0.161123	+	0.279073i
$320$	384.000	−	665.108i	0.0670820	−	0.116190i
$321$	−3600.00	+	6235.38i	−0.625958	+	1.08419i
$322$	−1248.00			−0.215989
$323$	8664.00	−	3751.62i	1.49250	−	0.646272i
$324$	−2684.00			−0.460219
$325$	−247.000	+	427.817i	−0.0421572	+	0.0730184i
$326$	1657.00	−	2870.01i	0.281511	−	0.487592i
$327$	3200.00	+	5542.56i	0.541163	+	0.937322i
$328$	−708.000	+	1226.29i	−0.119185	+	0.206435i
$329$	1968.00	+	3408.68i	0.329785	+	0.571205i
$330$	1080.00			0.180158
$331$	2375.00			0.394386			0.197193	−	0.980365i	$-0.436817\pi$
$331$	2375.00			0.394386			0.197193	+	0.980365i	$0.436817\pi$
$332$	1134.00	+	1964.15i	0.187459	+	0.324688i
$333$	−334.000	−	578.505i	−0.0549642	−	0.0952008i
$334$	5568.00			0.912178
$335$	−9060.00			−1.47761
$336$	320.000	+	554.256i	0.0519566	+	0.0899915i
$337$	5166.50	−	8948.64i	0.835125	−	1.44648i	−0.0588033	−	0.998270i	$-0.518728\pi$
$337$	5166.50	−	8948.64i	0.835125	−	1.44648i	0.893928	−	0.448210i	$-0.147938\pi$
$338$	1521.00	+	2634.45i	0.244768	+	0.423950i
$339$	−922.500	+	1597.82i	−0.147797	+	0.255993i
$340$	2736.00	−	4738.89i	0.436413	−	0.755890i
$341$	882.000			0.140067
$342$	266.000	+	197.454i	0.0420574	+	0.0312195i
$343$	−4976.00			−0.783320
$344$	1264.00	−	2189.31i	0.198111	−	0.343139i
$345$	2340.00	−	4053.00i	0.365163	−	0.632482i
$346$	−2382.00	−	4125.75i	−0.370107	−	0.641045i
$347$	−2554.50	+	4424.52i	−0.395195	+	0.684498i	−0.993126	−	0.117049i	$-0.962656\pi$
$347$	−2554.50	+	4424.52i	−0.395195	+	0.684498i	0.597931	+	0.801548i	$0.295990\pi$
$348$	−2040.00	−	3533.38i	−0.314240	−	0.544279i
$349$	−2044.00			−0.313504			−0.156752	−	0.987638i	$-0.550102\pi$
$349$	−2044.00			−0.313504			−0.156752	+	0.987638i	$0.550102\pi$
$350$	304.000			0.0464271
$351$	−1885.00	−	3264.92i	−0.286649	−	0.496491i
$352$	−144.000	−	249.415i	−0.0218046	−	0.0377667i
$353$	−1701.00			−0.256473			−0.128237	−	0.991744i	$-0.540932\pi$
$353$	−1701.00			−0.256473			−0.128237	+	0.991744i	$0.540932\pi$
$354$	5790.00			0.869308
$355$	36.0000	+	62.3538i	0.00538220	+	0.00932225i
$356$	228.000	−	394.908i	0.0339438	−	0.0587923i
$357$	2280.00	+	3949.08i	0.338012	+	0.585455i
$358$	3645.00	−	6313.33i	0.538112	−	0.932038i
$359$	−885.000	+	1532.86i	−0.130107	+	0.225352i	−0.923718	−	0.383074i	$-0.874866\pi$
$359$	−885.000	+	1532.86i	−0.130107	+	0.225352i	0.793610	+	0.608426i	$0.208199\pi$
$360$	192.000			0.0281091
$361$	1985.50	+	6565.34i	0.289474	+	0.957186i
$362$	−3812.00			−0.553465
$363$	−3125.00	+	5412.66i	−0.451846	+	0.782620i
$364$	−416.000	+	720.533i	−0.0599020	+	0.103753i
$365$	−870.000	−	1506.88i	−0.124761	−	0.216093i
$366$	−1760.00	+	3048.41i	−0.251357	+	0.435363i
$367$	5279.00	+	9143.50i	0.750849	+	1.30051i	0.947412	+	0.320017i	$0.103689\pi$
$367$	5279.00	+	9143.50i	0.750849	+	1.30051i	−0.196563	+	0.980491i	$0.562978\pi$
$368$	−1248.00			−0.176784
$369$	−354.000			−0.0499417
$370$	−4008.00	−	6942.06i	−0.563151	−	0.975407i
$371$	−2712.00	−	4697.32i	−0.379515	−	0.657339i
$372$	−1960.00			−0.273175
$373$	−124.000			−0.0172131			−0.00860654	−	0.999963i	$-0.502740\pi$
$373$	−124.000			−0.0172131			−0.00860654	+	0.999963i	$0.502740\pi$
$374$	−1026.00	−	1777.08i	−0.141853	−	0.245697i
$375$	3180.00	−	5507.92i	0.437905	−	0.758474i
$376$	1968.00	+	3408.68i	0.269925	+	0.467524i
$377$	2652.00	−	4593.40i	0.362294	−	0.627512i
$378$	−1160.00	+	2009.18i	−0.157841	+	0.273389i
$379$	44.0000			0.00596340			0.00298170	−	0.999996i	$-0.499051\pi$
$379$	44.0000			0.00596340			0.00298170	+	0.999996i	$0.499051\pi$
$380$	3192.00	+	2369.45i	0.430911	+	0.319868i
$381$	−4510.00			−0.606442
$382$	−1332.00	+	2307.09i	−0.178406	+	0.309008i
$383$	−4656.00	+	8064.43i	−0.621176	+	1.07591i	0.368091	+	0.929790i	$0.380012\pi$
$383$	−4656.00	+	8064.43i	−0.621176	+	1.07591i	−0.989267	+	0.146119i	$0.953322\pi$
$384$	320.000	+	554.256i	0.0425259	+	0.0736570i
$385$	432.000	−	748.246i	0.0571864	−	0.0990497i
$386$	−1322.00	−	2289.77i	−0.174321	−	0.301933i
$387$	632.000			0.0830139
$388$	−3772.00			−0.493542
$389$	5646.00	+	9779.16i	0.735896	+	1.27461i	0.954329	+	0.298757i	$0.0965721\pi$
$389$	5646.00	+	9779.16i	0.735896	+	1.27461i	−0.218433	+	0.975852i	$0.570095\pi$
$390$	−1560.00	−	2702.00i	−0.202548	−	0.350823i
$391$	−8892.00			−1.15010
$392$	−2232.00			−0.287584
$393$	−1132.50	−	1961.55i	−0.145361	−	0.251773i
$394$	−3726.00	+	6453.62i	−0.476429	+	0.825200i
$395$	−1896.00	−	3283.97i	−0.241514	−	0.418315i
$396$	36.0000	−	62.3538i	0.00456835	−	0.00791262i
$397$	167.000	−	289.252i	0.0211121	−	0.0365672i	−0.855276	−	0.518172i	$-0.826613\pi$
$397$	167.000	−	289.252i	0.0211121	−	0.0365672i	0.876388	+	0.481605i	$0.159946\pi$
$398$	−956.000			−0.120402
$399$	−3040.00	+	1316.36i	−0.381429	+	0.165164i
$400$	304.000			0.0380000
$401$	−2806.50	+	4861.00i	−0.349501	+	0.605354i	−0.986161	−	0.165791i	$-0.946982\pi$
$401$	−2806.50	+	4861.00i	−0.349501	+	0.605354i	0.636660	+	0.771145i	$0.280316\pi$
$402$	3775.00	−	6538.49i	0.468358	−	0.811220i
$403$	−1274.00	−	2206.63i	−0.157475	−	0.272755i
$404$	3000.00	−	5196.15i	0.369445	−	0.639897i
$405$	−4026.00	−	6973.24i	−0.493959	−	0.855563i
$406$	−3264.00			−0.398989
$407$	−3006.00			−0.366098
$408$	2280.00	+	3949.08i	0.276659	+	0.479187i
$409$	1677.50	+	2905.52i	0.202804	+	0.351268i	0.949431	−	0.313976i	$-0.101661\pi$
$409$	1677.50	+	2905.52i	0.202804	+	0.351268i	−0.746627	+	0.665243i	$0.768328\pi$
$410$	−4248.00			−0.511692
$411$	−10005.0			−1.20075
$412$	1316.00	+	2279.38i	0.157366	+	0.272565i
$413$	2316.00	−	4011.43i	0.275939	−	0.477941i
$414$	−156.000	−	270.200i	−0.0185193	−	0.0320763i
$415$	−3402.00	+	5892.44i	−0.402404	+	0.696984i
$416$	−416.000	+	720.533i	−0.0490290	+	0.0849208i
$417$	14675.0			1.72335
$418$	1368.00	−	592.361i	0.160074	−	0.0693142i
$419$	5796.00			0.675783			0.337892	−	0.941185i	$-0.390286\pi$
$419$	5796.00			0.675783			0.337892	+	0.941185i	$0.390286\pi$
$420$	−960.000	+	1662.77i	−0.111531	+	0.193178i
$421$	−325.000	+	562.917i	−0.0376236	+	0.0651660i	−0.884224	−	0.467063i	$-0.845312\pi$
$421$	−325.000	+	562.917i	−0.0376236	+	0.0651660i	0.846600	+	0.532229i	$0.178645\pi$
$422$	820.000	+	1420.28i	0.0945900	+	0.163835i
$423$	−492.000	+	852.169i	−0.0565529	+	0.0979524i
$424$	−2712.00	−	4697.32i	−0.310628	−	0.538024i
$425$	2166.00			0.247215
$426$	−60.0000			−0.00682397
$427$	1408.00	+	2438.73i	0.159574	+	0.276389i
$428$	2880.00	+	4988.31i	0.325257	+	0.563362i
$429$	−1170.00			−0.131674
$430$	7584.00			0.850542
$431$	−2103.00	−	3642.50i	−0.235030	−	0.407084i	0.724251	−	0.689536i	$-0.242186\pi$
$431$	−2103.00	−	3642.50i	−0.235030	−	0.407084i	−0.959281	+	0.282452i	$0.908852\pi$
$432$	−1160.00	+	2009.18i	−0.129191	+	0.223765i
$433$	6539.00	+	11325.9i	0.725737	+	1.25701i	0.958670	+	0.284521i	$0.0918346\pi$
$433$	6539.00	+	11325.9i	0.725737	+	1.25701i	−0.232932	+	0.972493i	$0.574832\pi$
$434$	−784.000	+	1357.93i	−0.0867125	+	0.150190i
$435$	6120.00	−	10600.2i	0.674555	−	1.16836i
$436$	5120.00			0.562393
$437$	741.000	−	6417.25i	0.0811140	−	0.702468i
$438$	1450.00			0.158182
$439$	1301.00	−	2253.40i	0.141443	−	0.244986i	−0.786597	−	0.617466i	$-0.788159\pi$
$439$	1301.00	−	2253.40i	0.141443	−	0.244986i	0.928040	+	0.372480i	$0.121493\pi$
$440$	432.000	−	748.246i	0.0468063	−	0.0810710i
$441$	−279.000	−	483.242i	−0.0301263	−	0.0521803i
$442$	−2964.00	+	5133.80i	−0.318966	+	0.552466i
$443$	−3961.50	−	6861.52i	−0.424868	−	0.735893i	0.571540	−	0.820574i	$-0.306346\pi$
$443$	−3961.50	−	6861.52i	−0.424868	−	0.735893i	−0.996408	+	0.0846811i	$0.973013\pi$
$444$	6680.00			0.714006
$445$	1368.00			0.145729
$446$	−926.000	−	1603.88i	−0.0983125	−	0.170282i
$447$	15.0000	+	25.9808i	0.00158719	+	0.00274910i
$448$	512.000			0.0539949
$449$	2529.00			0.265815			0.132907	−	0.991128i	$-0.457569\pi$
$449$	2529.00			0.265815			0.132907	+	0.991128i	$0.457569\pi$
$450$	38.0000	+	65.8179i	0.00398075	+	0.00689486i
$451$	−796.500	+	1379.58i	−0.0831612	+	0.144039i
$452$	738.000	+	1278.25i	0.0767978	+	0.133018i
$453$	6935.00	−	12011.8i	0.719282	−	1.24583i
$454$	−4977.00	+	8620.42i	−0.514498	+	0.891137i
$455$	−2496.00			−0.257174
$456$	−3040.00	+	1316.36i	−0.312195	+	0.135185i
$457$	7037.00			0.720300			0.360150	−	0.932894i	$-0.382726\pi$
$457$	7037.00			0.720300			0.360150	+	0.932894i	$0.382726\pi$
$458$	4312.00	−	7468.60i	0.439927	−	0.761976i
$459$	−8265.00	+	14315.4i	−0.840473	+	1.45574i
$460$	−1872.00	−	3242.40i	−0.189744	−	0.328647i
$461$	5865.00	−	10158.5i	0.592539	−	1.02631i	−0.401351	−	0.915924i	$-0.631459\pi$
$461$	5865.00	−	10158.5i	0.592539	−	1.02631i	0.993889	−	0.110382i	$-0.0352076\pi$
$462$	360.000	+	623.538i	0.0362526	+	0.0627914i
$463$	11762.0			1.18062			0.590309	−	0.807177i	$-0.299006\pi$
$463$	11762.0			1.18062			0.590309	+	0.807177i	$0.299006\pi$
$464$	−3264.00			−0.326568
$465$	−2940.00	−	5092.23i	−0.293203	−	0.507842i
$466$	1821.00	+	3154.06i	0.181022	+	0.313539i
$467$	−3465.00			−0.343343			−0.171671	−	0.985154i	$-0.554917\pi$
$467$	−3465.00			−0.343343			−0.171671	+	0.985154i	$0.554917\pi$
$468$	−208.000			−0.0205445
$469$	−3020.00	−	5230.79i	−0.297336	−	0.515001i
$470$	−5904.00	+	10226.0i	−0.579428	+	1.00360i
$471$	−6820.00	−	11812.6i	−0.667195	−	1.15562i
$472$	2316.00	−	4011.43i	0.225853	−	0.391189i
$473$	1422.00	−	2462.98i	0.138232	−	0.239424i
$474$	3160.00			0.306210
$475$	−180.500	+	1563.18i	−0.0174356	+	0.150997i
$476$	3648.00			0.351273
$477$	678.000	−	1174.33i	0.0650807	−	0.112723i
$478$	−324.000	+	561.184i	−0.0310030	+	0.0536987i
$479$	2010.00	+	3481.42i	0.191731	+	0.332088i	0.945824	−	0.324680i	$-0.105256\pi$
$479$	2010.00	+	3481.42i	0.191731	+	0.332088i	−0.754093	+	0.656768i	$0.771923\pi$
$480$	−960.000	+	1662.77i	−0.0912871	+	0.158114i
$481$	4342.00	+	7520.56i	0.411597	+	0.712907i
$482$	682.000			0.0644486
$483$	3120.00			0.293923
$484$	2500.00	+	4330.13i	0.234786	+	0.406661i
$485$	−5658.00	−	9799.94i	−0.529725	−	0.917510i
$486$	−1120.00			−0.104535
$487$	18146.0			1.68845			0.844224	−	0.535991i	$-0.180062\pi$
$487$	18146.0			1.68845			0.844224	+	0.535991i	$0.180062\pi$
$488$	1408.00	+	2438.73i	0.130609	+	0.226221i
$489$	−4142.50	+	7175.02i	−0.383089	+	0.663529i
$490$	−3348.00	−	5798.91i	−0.308668	−	0.534628i
$491$	−9264.00	+	16045.7i	−0.851484	+	1.47481i	0.0283856	+	0.999597i	$0.490963\pi$
$491$	−9264.00	+	16045.7i	−0.851484	+	1.47481i	−0.879869	+	0.475216i	$0.842370\pi$
$492$	1770.00	−	3065.73i	0.162191	−	0.280922i
$493$	−23256.0			−2.12454
$494$	−3458.00	−	2566.90i	−0.314945	−	0.233786i
$495$	216.000			0.0196131
$496$	−784.000	+	1357.93i	−0.0709731	+	0.122929i
$497$	−24.0000	+	41.5692i	−0.00216609	+	0.00375178i
$498$	−2835.00	−	4910.36i	−0.255099	−	0.441845i
$499$	8001.50	−	13859.0i	0.717828	−	1.24332i	−0.244030	−	0.969768i	$-0.578470\pi$
$499$	8001.50	−	13859.0i	0.717828	−	1.24332i	0.961858	−	0.273547i	$-0.0881971\pi$
$500$	−2544.00	−	4406.34i	−0.227542	−	0.394115i
$501$	−13920.0			−1.24132
$502$	9726.00			0.864726
$503$	−6999.00	−	12122.6i	−0.620417	−	1.07459i	−0.989408	−	0.145161i	$-0.953630\pi$
$503$	−6999.00	−	12122.6i	−0.620417	−	1.07459i	0.368991	−	0.929433i	$-0.379703\pi$
$504$	64.0000	+	110.851i	0.00565632	+	0.00979704i
$505$	18000.0			1.58612
$506$	−1404.00			−0.123351
$507$	−3802.50	−	6586.12i	−0.333087	−	0.576923i
$508$	−1804.00	+	3124.62i	−0.157558	+	0.272899i
$509$	5664.00	+	9810.34i	0.493227	+	0.854294i	0.999970	−	0.00780356i	$-0.00248398\pi$
$509$	5664.00	+	9810.34i	0.493227	+	0.854294i	−0.506743	+	0.862097i	$0.669151\pi$
$510$	−6840.00	+	11847.2i	−0.593883	+	1.02864i
$511$	580.000	−	1004.59i	0.0502107	−	0.0869676i
$512$	512.000			0.0441942
$513$	−9642.50	−	7157.70i	−0.829877	−	0.616024i
$514$	−6906.00			−0.592628
$515$	−3948.00	+	6838.14i	−0.337805	+	0.585096i
$516$	−3160.00	+	5473.28i	−0.269595	+	0.466953i
$517$	2214.00	+	3834.76i	0.188340	+	0.326214i
$518$	2672.00	−	4628.04i	0.226643	−	0.392557i
$519$	5955.00	+	10314.4i	0.503652	+	0.872351i
$520$	−2496.00			−0.210494
$521$	−1575.00			−0.132441			−0.0662207	−	0.997805i	$-0.521094\pi$
$521$	−1575.00			−0.132441			−0.0662207	+	0.997805i	$0.521094\pi$
$522$	−408.000	−	706.677i	−0.0342101	−	0.0592536i
$523$	10634.0	+	18418.6i	0.889087	+	1.53994i	0.840957	+	0.541102i	$0.181993\pi$
$523$	10634.0	+	18418.6i	0.889087	+	1.53994i	0.0481299	+	0.998841i	$0.484674\pi$
$524$	−1812.00			−0.151064
$525$	−760.000			−0.0631793
$526$	120.000	+	207.846i	0.00994724	+	0.0172291i
$527$	−5586.00	+	9675.24i	−0.461727	+	0.799734i
$528$	360.000	+	623.538i	0.0296723	+	0.0513940i
$529$	3041.50	−	5268.03i	0.249979	−	0.432977i
$530$	8136.00	−	14092.0i	0.666802	−	1.15494i
$531$	1158.00			0.0946383
$532$	−304.000	+	2632.72i	−0.0247746	+	0.214554i
$533$	4602.00			0.373986
$534$	−570.000	+	987.269i	−0.0461916	+	0.0800062i
$535$	−8640.00	+	14964.9i	−0.698205	+	1.20933i
$536$	−3020.00	−	5230.79i	−0.243366	−	0.421522i
$537$	−9112.50	+	15783.3i	−0.732278	+	1.26834i
$538$	7068.00	+	12242.1i	0.566400	+	0.981033i
$539$	−2511.00			−0.200661
$540$	−6960.00			−0.554649
$541$	−3874.00	−	6709.96i	−0.307867	−	0.533242i	0.670028	−	0.742336i	$-0.266282\pi$
$541$	−3874.00	−	6709.96i	−0.307867	−	0.533242i	−0.977896	+	0.209094i	$0.932949\pi$
$542$	−1388.00	−	2404.09i	−0.109999	−	0.190525i
$543$	9530.00			0.753170
$544$	3648.00			0.287512
$545$	7680.00	+	13302.2i	0.603624	+	1.04551i
$546$	1040.00	−	1801.33i	0.0815163	−	0.141190i
$547$	−6898.00	−	11947.7i	−0.539190	−	0.933905i	−0.998948	−	0.0458607i	$-0.985397\pi$
$547$	−6898.00	−	11947.7i	−0.539190	−	0.933905i	0.459757	−	0.888045i	$-0.347936\pi$
$548$	−4002.00	+	6931.67i	−0.311965	+	0.540340i
$549$	−352.000	+	609.682i	−0.0273643	+	0.0473963i
$550$	342.000			0.0265144
$551$	1938.00	−	16783.6i	0.149840	−	1.29765i
$552$	3120.00			0.240572
$553$	1264.00	−	2189.31i	0.0971985	−	0.168353i
$554$	5164.00	−	8944.31i	0.396024	−	0.685934i
$555$	10020.0	+	17355.1i	0.766352	+	1.32736i
$556$	5870.00	−	10167.1i	0.447740	−	0.775508i
$557$	−7836.00	−	13572.4i	−0.596090	−	1.03246i	−0.993392	−	0.114770i	$-0.963387\pi$
$557$	−7836.00	−	13572.4i	−0.596090	−	1.03246i	0.397302	−	0.917688i	$-0.369946\pi$
$558$	−392.000			−0.0297396
$559$	−8216.00			−0.621645
$560$	768.000	+	1330.22i	0.0579534	+	0.100378i
$561$	2565.00	+	4442.71i	0.193038	+	0.334352i
$562$	−1290.00			−0.0968245
$563$	−12663.0			−0.947925			−0.473963	−	0.880545i	$-0.657177\pi$
$563$	−12663.0			−0.947925			−0.473963	+	0.880545i	$0.657177\pi$
$564$	−4920.00	−	8521.69i	−0.367322	−	0.636220i
$565$	−2214.00	+	3834.76i	−0.164856	+	0.285539i
$566$	−6743.00	−	11679.2i	−0.500759	−	0.867340i
$567$	2684.00	−	4648.82i	0.198796	−	0.344325i
$568$	−24.0000	+	41.5692i	−0.00177292	+	0.00307078i
$569$	−14670.0			−1.08084			−0.540420	−	0.841395i	$-0.681735\pi$
$569$	−14670.0			−1.08084			−0.540420	+	0.841395i	$0.681735\pi$
$570$	−7980.00	−	5923.61i	−0.586395	−	0.435286i
$571$	4643.00			0.340286			0.170143	−	0.985419i	$-0.445577\pi$
$571$	4643.00			0.340286			0.170143	+	0.985419i	$0.445577\pi$
$572$	−468.000	+	810.600i	−0.0342099	+	0.0592533i
$573$	3330.00	−	5767.73i	0.242780	−	0.420507i
$574$	−1416.00	−	2452.58i	−0.102966	−	0.178343i
$575$	741.000	−	1283.45i	0.0537423	−	0.0930844i
$576$	64.0000	+	110.851i	0.00462963	+	0.00801875i
$577$	−18277.0			−1.31869			−0.659343	−	0.751843i	$-0.729165\pi$
$577$	−18277.0			−1.31869			−0.659343	+	0.751843i	$0.729165\pi$
$578$	16166.0			1.16335
$579$	3305.00	+	5724.43i	0.237221	+	0.410879i
$580$	−4896.00	−	8480.12i	−0.350509	−	0.607100i
$581$	−4536.00			−0.323898
$582$	9430.00			0.671626
$583$	−3051.00	−	5284.49i	−0.216740	−	0.375405i
$584$	580.000	−	1004.59i	0.0410969	−	0.0711819i
$585$	−312.000	−	540.400i	−0.0220506	−	0.0381928i
$586$	252.000	−	436.477i	0.0177645	−	0.0307691i
$587$	6306.00	−	10922.3i	0.443401	−	0.767993i	−0.554538	−	0.832158i	$-0.687105\pi$
$587$	6306.00	−	10922.3i	0.443401	−	0.767993i	0.997939	+	0.0641650i	$0.0204384\pi$
$588$	5580.00			0.391353
$589$	−6517.00	−	4837.62i	−0.455905	−	0.338422i
$590$	13896.0			0.969643
$591$	9315.00	−	16134.1i	0.648338	−	1.12295i
$592$	2672.00	−	4628.04i	0.185504	−	0.321303i
$593$	11554.5	+	20013.0i	0.800146	+	1.38589i	0.919520	+	0.393044i	$0.128578\pi$
$593$	11554.5	+	20013.0i	0.800146	+	1.38589i	−0.119374	+	0.992849i	$0.538089\pi$
$594$	−1305.00	+	2260.33i	−0.0901428	+	0.156132i
$595$	5472.00	+	9477.78i	0.377025	+	0.653027i
$596$	24.0000			0.00164946
$597$	2390.00			0.163846
$598$	2028.00	+	3512.60i	0.138681	+	0.240202i
$599$	39.0000	+	67.5500i	0.00266026	+	0.00460771i	0.867352	−	0.497694i	$-0.165820\pi$
$599$	39.0000	+	67.5500i	0.00266026	+	0.00460771i	−0.864692	+	0.502302i	$0.832487\pi$
$600$	−760.000			−0.0517115
$601$	21707.0			1.47329			0.736645	−	0.676280i	$-0.236409\pi$
$601$	21707.0			1.47329			0.736645	+	0.676280i	$0.236409\pi$
$602$	2528.00	+	4378.62i	0.171152	+	0.296444i
$603$	755.000	−	1307.70i	0.0509884	−	0.0883144i
$604$	−5548.00	−	9609.42i	−0.373750	−	0.647354i
$605$	−7500.00	+	12990.4i	−0.503997	+	0.872949i
$606$	−7500.00	+	12990.4i	−0.502750	+	0.870789i
$607$	728.000			0.0486798			0.0243399	−	0.999704i	$-0.492252\pi$
$607$	728.000			0.0486798			0.0243399	+	0.999704i	$0.492252\pi$
$608$	−304.000	+	2632.72i	−0.0202777	+	0.175610i
$609$	8160.00			0.542955
$610$	−4224.00	+	7316.18i	−0.280368	+	0.485612i
$611$	6396.00	−	11078.2i	0.423493	−	0.733512i
$612$	456.000	+	789.815i	0.0301188	+	0.0521673i
$613$	−4609.00	+	7983.02i	−0.303680	+	0.525989i	−0.976967	−	0.213393i	$-0.931549\pi$
$613$	−4609.00	+	7983.02i	−0.303680	+	0.525989i	0.673287	+	0.739382i	$0.264882\pi$
$614$	7117.00	+	12327.0i	0.467783	+	0.810224i
$615$	10620.0			0.696325
$616$	576.000			0.0376748
$617$	13930.5	+	24128.3i	0.908948	+	1.57434i	0.815528	+	0.578717i	$0.196446\pi$
$617$	13930.5	+	24128.3i	0.908948	+	1.57434i	0.0934194	+	0.995627i	$0.470220\pi$
$618$	−3290.00	−	5698.45i	−0.214148	−	0.370915i
$619$	23156.0			1.50358			0.751792	−	0.659401i	$-0.229190\pi$
$619$	23156.0			1.50358			0.751792	+	0.659401i	$0.229190\pi$
$620$	−4704.00			−0.304705
$621$	5655.00	+	9794.75i	0.365422	+	0.632930i
$622$	−4410.00	+	7638.34i	−0.284284	+	0.492395i
$623$	456.000	+	789.815i	0.0293246	+	0.0507918i
$624$	1040.00	−	1801.33i	0.0667201	−	0.115563i
$625$	8819.50	−	15275.8i	0.564448	−	0.977653i
$626$	13450.0			0.858738
$627$	−3420.00	+	1480.90i	−0.217834	+	0.0943247i
$628$	−10912.0			−0.693370
$629$	19038.0	−	32974.8i	1.20683	−	2.09029i
$630$	−192.000	+	332.554i	−0.0121420	+	0.0210306i
$631$	−12568.0	−	21768.4i	−0.792907	−	1.37335i	−0.924160	−	0.382006i	$-0.875233\pi$
$631$	−12568.0	−	21768.4i	−0.792907	−	1.37335i	0.131253	−	0.991349i	$-0.458100\pi$
$632$	1264.00	−	2189.31i	0.0795557	−	0.137795i
$633$	−2050.00	−	3550.70i	−0.128721	−	0.222951i
$634$	−9732.00			−0.609633
$635$	−10824.0			−0.676437
$636$	6780.00	+	11743.3i	0.422711	+	0.732158i
$637$	3627.00	+	6282.15i	0.225600	+	0.390750i
$638$	−3672.00			−0.227862
$639$	−12.0000			−0.000742899
$640$	768.000	+	1330.22i	0.0474342	+	0.0821584i
$641$	−5200.50	+	9007.53i	−0.320448	+	0.555033i	−0.980581	−	0.196117i	$-0.937167\pi$
$641$	−5200.50	+	9007.53i	−0.320448	+	0.555033i	0.660132	+	0.751149i	$0.270500\pi$
$642$	−7200.00	−	12470.8i	−0.442619	−	0.766638i
$643$	5868.50	−	10164.5i	0.359924	−	0.623406i	−0.628024	−	0.778194i	$-0.716136\pi$
$643$	5868.50	−	10164.5i	0.359924	−	0.623406i	0.987948	+	0.154788i	$0.0494693\pi$
$644$	1248.00	−	2161.60i	0.0763635	−	0.132265i
$645$	−18960.0			−1.15744
$646$	−2166.00	+	18758.1i	−0.131920	+	1.14246i
$647$	−23058.0			−1.40109			−0.700544	−	0.713610i	$-0.747059\pi$
$647$	−23058.0			−1.40109			−0.700544	+	0.713610i	$0.747059\pi$
$648$	2684.00	−	4648.82i	0.162712	−	0.281826i
$649$	2605.50	−	4512.86i	0.157588	−	0.272951i
$650$	−494.000	−	855.633i	−0.0298097	−	0.0516318i
$651$	1960.00	−	3394.82i	0.118001	−	0.204383i
$652$	3314.00	+	5740.02i	0.199059	+	0.344780i
$653$	−22860.0			−1.36996			−0.684978	−	0.728564i	$-0.740188\pi$
$653$	−22860.0			−1.36996			−0.684978	+	0.728564i	$0.740188\pi$
$654$	−12800.0			−0.765321
$655$	−2718.00	−	4707.71i	−0.162139	−	0.280833i
$656$	−1416.00	−	2452.58i	−0.0842767	−	0.145972i
$657$	290.000			0.0172207
$658$	−7872.00			−0.466387
$659$	−1410.00	−	2442.19i	−0.0833472	−	0.144362i	0.821339	−	0.570441i	$-0.193228\pi$
$659$	−1410.00	−	2442.19i	−0.0833472	−	0.144362i	−0.904686	+	0.426079i	$0.859894\pi$
$660$	−1080.00	+	1870.61i	−0.0636954	+	0.110324i
$661$	5930.00	+	10271.1i	0.348941	+	0.604384i	0.986062	−	0.166380i	$-0.0532079\pi$
$661$	5930.00	+	10271.1i	0.348941	+	0.604384i	−0.637120	+	0.770764i	$0.719875\pi$
$662$	−2375.00	+	4113.62i	−0.139437	+	0.241511i
$663$	7410.00	−	12834.5i	0.434058	−	0.751811i
$664$	−4536.00			−0.265107
$665$	−7296.00	+	3159.26i	−0.425454	+	0.184227i
$666$	1336.00			0.0777312
$667$	−7956.00	+	13780.2i	−0.461855	+	0.799957i
$668$	−5568.00	+	9644.06i	−0.322504	+	0.558593i
$669$	2315.00	+	4009.70i	0.133786	+	0.231725i
$670$	9060.00	−	15692.4i	0.522415	−	0.904850i
$671$	1584.00	+	2743.57i	0.0911321	+	0.157845i
$672$	−1280.00			−0.0734778
$673$	−31330.0			−1.79448			−0.897238	−	0.441547i	$-0.854430\pi$
$673$	−31330.0			−1.79448			−0.897238	+	0.441547i	$0.854430\pi$
$674$	10333.0	+	17897.3i	0.590523	+	1.02282i
$675$	−1377.50	−	2385.90i	−0.0785481	−	0.136049i
$676$	−6084.00			−0.346154
$677$	−4410.00			−0.250355			−0.125177	−	0.992134i	$-0.539950\pi$
$677$	−4410.00			−0.250355			−0.125177	+	0.992134i	$0.539950\pi$
$678$	−1845.00	−	3195.63i	−0.104509	−	0.181014i
$679$	3772.00	−	6533.30i	0.213190	−	0.369256i
$680$	5472.00	+	9477.78i	0.308591	+	0.534495i
$681$	12442.5	−	21551.0i	0.700143	−	1.21268i
$682$	−882.000	+	1527.67i	−0.0495213	+	0.0857734i
$683$	−180.000			−0.0100842			−0.00504210	−	0.999987i	$-0.501605\pi$
$683$	−180.000			−0.0100842			−0.00504210	+	0.999987i	$0.501605\pi$
$684$	−608.000	+	263.272i	−0.0339875	+	0.0147170i
$685$	−24012.0			−1.33935
$686$	4976.00	−	8618.68i	0.276945	−	0.479684i
$687$	−10780.0	+	18671.5i	−0.598665	+	1.03692i
$688$	2528.00	+	4378.62i	0.140086	+	0.242636i
$689$	−8814.00	+	15266.3i	−0.487354	+	0.844121i
$690$	4680.00	+	8106.00i	0.258210	+	0.447232i
$691$	−27412.0			−1.50912			−0.754560	−	0.656231i	$-0.772150\pi$
$691$	−27412.0			−1.50912			−0.754560	+	0.656231i	$0.772150\pi$
$692$	9528.00			0.523411
$693$	72.0000	+	124.708i	0.00394669	+	0.00683586i
$694$	−5109.00	−	8849.05i	−0.279445	−	0.484013i
$695$	35220.0			1.92226
$696$	8160.00			0.444402
$697$	−10089.0	−	17474.7i	−0.548276	−	0.949641i
$698$	2044.00	−	3540.31i	0.110840	−	0.191981i
$699$	−4552.50	−	7885.16i	−0.246340	−	0.426673i
$700$	−304.000	+	526.543i	−0.0164145	+	0.0284307i
$701$	−12918.0	+	22374.6i	−0.696014	+	1.20553i	0.273823	+	0.961780i	$0.411712\pi$
$701$	−12918.0	+	22374.6i	−0.696014	+	1.20553i	−0.969838	+	0.243752i	$0.921622\pi$
$702$	7540.00			0.405383
$703$	22211.0	+	16487.4i	1.19161	+	0.884543i
$704$	576.000			0.0308364
$705$	14760.0	−	25565.1i	0.788502	−	1.36573i
$706$	1701.00	−	2946.22i	0.0906770	−	0.157057i
$707$	6000.00	+	10392.3i	0.319170	+	0.552819i
$708$	−5790.00	+	10028.6i	−0.307347	+	0.532340i
$709$	−7465.00	−	12929.8i	−0.395422	−	0.684890i	0.597733	−	0.801695i	$-0.296068\pi$
$709$	−7465.00	−	12929.8i	−0.395422	−	0.684890i	−0.993155	+	0.116805i	$0.962735\pi$
$710$	−144.000			−0.00761158
$711$	632.000			0.0333359
$712$	456.000	+	789.815i	0.0240019	+	0.0415724i
$713$	3822.00	+	6619.90i	0.200750	+	0.347710i
$714$	−9120.00			−0.478022
$715$	−2808.00			−0.146872
$716$	7290.00	+	12626.7i	0.380503	+	0.659050i
$717$	810.000	−	1402.96i	0.0421897	−	0.0730747i
$718$	−1770.00	−	3065.73i	−0.0919997	−	0.159348i
$719$	−2073.00	+	3590.54i	−0.107524	+	0.186237i	−0.914767	−	0.403983i	$-0.867626\pi$
$719$	−2073.00	+	3590.54i	−0.107524	+	0.186237i	0.807243	+	0.590220i	$0.200959\pi$
$720$	−192.000	+	332.554i	−0.00993808	+	0.0172133i
$721$	−5264.00			−0.271902
$722$	−13357.0	−	3126.35i	−0.688499	−	0.161151i
$723$	−1705.00			−0.0877035
$724$	3812.00	−	6602.58i	0.195679	−	0.338927i
$725$	1938.00	−	3356.71i	0.0992766	−	0.171952i
$726$	−6250.00	−	10825.3i	−0.319503	−	0.553396i
$727$	9428.00	−	16329.8i	0.480970	−	0.833064i	−0.518792	−	0.854901i	$-0.673618\pi$
$727$	9428.00	−	16329.8i	0.480970	−	0.833064i	0.999762	+	0.0218363i	$0.00695127\pi$
$728$	−832.000	−	1441.07i	−0.0423571	−	0.0733647i
$729$	20917.0			1.06269
$730$	3480.00			0.176439
$731$	18012.0	+	31197.7i	0.911351	+	1.57851i
$732$	−3520.00	−	6096.82i	−0.177736	−	0.307848i
$733$	17318.0			0.872653			0.436327	−	0.899788i	$-0.356279\pi$
$733$	17318.0			0.872653			0.436327	+	0.899788i	$0.356279\pi$
$734$	−21116.0			−1.06186
$735$	8370.00	+	14497.3i	0.420044	+	0.727537i
$736$	1248.00	−	2161.60i	0.0625026	−	0.108258i
$737$	−3397.50	−	5884.64i	−0.169808	−	0.294116i
$738$	354.000	−	613.146i	0.0176571	−	0.0305829i
$739$	12915.5	−	22370.3i	0.642902	−	1.11354i	−0.341880	−	0.939744i	$-0.611064\pi$
$739$	12915.5	−	22370.3i	0.642902	−	1.11354i	0.984782	−	0.173795i	$-0.0556030\pi$
$740$	16032.0			0.796416
$741$	8645.00	+	6417.25i	0.428586	+	0.318142i
$742$	10848.0			0.536715
$743$	−255.000	+	441.673i	−0.0125909	+	0.0218081i	−0.872252	−	0.489056i	$-0.837341\pi$
$743$	−255.000	+	441.673i	−0.0125909	+	0.0218081i	0.859661	+	0.510864i	$0.170675\pi$
$744$	1960.00	−	3394.82i	0.0965821	−	0.167285i
$745$	36.0000	+	62.3538i	0.00177039	+	0.00306640i
$746$	124.000	−	214.774i	0.00608574	−	0.0105408i
$747$	−567.000	−	982.073i	−0.0277717	−	0.0481020i
$748$	4104.00			0.200611
$749$	−11520.0			−0.561992
$750$	6360.00	+	11015.8i	0.309646	+	0.536322i
$751$	347.000	+	601.022i	0.0168605	+	0.0292032i	0.874333	−	0.485327i	$-0.161300\pi$
$751$	347.000	+	601.022i	0.0168605	+	0.0292032i	−0.857472	+	0.514531i	$0.827966\pi$
$752$	−7872.00			−0.381732
$753$	−24315.0			−1.17674
$754$	5304.00	+	9186.80i	0.256181	+	0.443718i
$755$	16644.0	−	28828.3i	0.802301	−	1.38963i
$756$	−2320.00	−	4018.36i	−0.111611	−	0.193315i
$757$	−2299.00	+	3981.98i	−0.110381	+	0.191186i	−0.915924	−	0.401352i	$-0.868541\pi$
$757$	−2299.00	+	3981.98i	−0.110381	+	0.191186i	0.805543	+	0.592538i	$0.201874\pi$
$758$	−44.0000	+	76.2102i	−0.00210838	+	0.00365182i
$759$	3510.00			0.167859
$760$	−7296.00	+	3159.26i	−0.348229	+	0.150787i
$761$	32697.0			1.55751			0.778755	−	0.627328i	$-0.215851\pi$
$761$	32697.0			1.55751			0.778755	+	0.627328i	$0.215851\pi$
$762$	4510.00	−	7811.55i	0.214410	−	0.371368i
$763$	−5120.00	+	8868.10i	−0.242931	+	0.420769i
$764$	−2664.00	−	4614.18i	−0.126152	−	0.218502i
$765$	−1368.00	+	2369.45i	−0.0646538	+	0.111984i
$766$	−9312.00	−	16128.9i	−0.439238	−	0.760782i
$767$	−15054.0			−0.708694
$768$	−1280.00			−0.0601407
$769$	2255.00	+	3905.77i	0.105744	+	0.183155i	0.914042	−	0.405619i	$-0.132944\pi$
$769$	2255.00	+	3905.77i	0.105744	+	0.183155i	−0.808298	+	0.588774i	$0.799611\pi$
$770$	864.000	+	1496.49i	0.0404369	+	0.0700387i
$771$	17265.0			0.806464
$772$	5288.00			0.246528
$773$	1506.00	+	2608.47i	0.0700738	+	0.121371i	0.898933	−	0.438085i	$-0.144343\pi$
$773$	1506.00	+	2608.47i	0.0700738	+	0.121371i	−0.828860	+	0.559457i	$0.811010\pi$
$774$	−632.000	+	1094.66i	−0.0293498	+	0.0508354i
$775$	−931.000	−	1612.54i	−0.0431516	−	0.0747408i
$776$	3772.00	−	6533.30i	0.174493	−	0.302232i
$777$	−6680.00	+	11570.1i	−0.308422	+	0.534202i
$778$	−22584.0			−1.04071
$779$	13452.0	−	5824.89i	0.618701	−	0.267905i
$780$	6240.00			0.286446
$781$	−27.0000	+	46.7654i	−0.00123705	+	0.00214263i
$782$	8892.00	−	15401.4i	0.406621	−	0.704287i
$783$	14790.0	+	25617.0i	0.675034	+	1.16919i
$784$	2232.00	−	3865.94i	0.101676	−	0.176109i
$785$	−16368.0	−	28350.2i	−0.744203	−	1.28900i
$786$	4530.00			0.205572
$787$	12131.0			0.549458			0.274729	−	0.961522i	$-0.411412\pi$
$787$	12131.0			0.549458			0.274729	+	0.961522i	$0.411412\pi$
$788$	−7452.00	−	12907.2i	−0.336886	−	0.583504i
$789$	−300.000	−	519.615i	−0.0135365	−	0.0234459i
$790$	7584.00			0.341553
$791$	−2952.00			−0.132694
$792$	72.0000	+	124.708i	0.00323031	+	0.00559507i
$793$	4576.00	−	7925.86i	0.204916	−	0.354925i
$794$	334.000	+	578.505i	0.0149285	+	0.0258569i
$795$	−20340.0	+	35229.9i	−0.907403	+	1.57167i
$796$	956.000	−	1655.84i	0.0425685	−	0.0737308i
$797$	8442.00			0.375196			0.187598	−	0.982246i	$-0.439930\pi$
$797$	8442.00			0.375196			0.187598	+	0.982246i	$0.439930\pi$
$798$	760.000	−	6581.79i	0.0337139	−	0.291971i
$799$	−56088.0			−2.48342
$800$	−304.000	+	526.543i	−0.0134350	+	0.0232702i
$801$	−114.000	+	197.454i	−0.00502870	+	0.00870997i
$802$	−5613.00	−	9722.00i	−0.247135	−	0.428050i
$803$	652.500	−	1130.16i	0.0286752	−	0.0496670i
$804$	7550.00	+	13077.0i	0.331179	+	0.573619i
$805$	7488.00			0.327848
$806$	5096.00			0.222703
$807$	−17670.0	−	30605.3i	−0.770773	−	1.33502i
$808$	6000.00	+	10392.3i	0.261237	+	0.452475i
$809$	−8307.00			−0.361012			−0.180506	−	0.983574i	$-0.557773\pi$
$809$	−8307.00			−0.361012			−0.180506	+	0.983574i	$0.557773\pi$
$810$	16104.0			0.698564
$811$	8.00000	+	13.8564i	0.000346385	+	0.000599956i	0.866199	−	0.499700i	$-0.166556\pi$
$811$	8.00000	+	13.8564i	0.000346385	+	0.000599956i	−0.865852	+	0.500300i	$0.833223\pi$
$812$	3264.00	−	5653.41i	0.141064	−	0.244330i
$813$	3470.00	+	6010.22i	0.149690	+	0.259271i
$814$	3006.00	−	5206.54i	0.129435	−	0.224188i
$815$	−9942.00	+	17220.0i	−0.427304	+	0.740113i
$816$	−9120.00			−0.391255
$817$	−24016.0	+	10399.2i	−1.02841	+	0.445316i
$818$	−6710.00			−0.286809
$819$	208.000	−	360.267i	0.00887437	−	0.0153709i
$820$	4248.00	−	7357.75i	0.180910	−	0.313346i
$821$	11127.0	+	19272.5i	0.473002	+	0.819264i	0.999523	−	0.0308985i	$-0.00983685\pi$
$821$	11127.0	+	19272.5i	0.473002	+	0.819264i	−0.526520	+	0.850163i	$0.676504\pi$
$822$	10005.0	−	17329.2i	0.424531	−	0.735309i
$823$	19835.0	+	34355.2i	0.840103	+	1.45510i	0.889807	+	0.456337i	$0.150839\pi$
$823$	19835.0	+	34355.2i	0.840103	+	1.45510i	−0.0497043	+	0.998764i	$0.515828\pi$
$824$	−5264.00			−0.222549
$825$	−855.000			−0.0360816
$826$	4632.00	+	8022.86i	0.195119	+	0.337955i
$827$	−7741.50	−	13408.7i	−0.325512	−	0.563803i	0.656104	−	0.754671i	$-0.272203\pi$
$827$	−7741.50	−	13408.7i	−0.325512	−	0.563803i	−0.981616	+	0.190867i	$0.938870\pi$
$828$	624.000			0.0261902
$829$	27188.0			1.13906			0.569529	−	0.821972i	$-0.307126\pi$
$829$	27188.0			1.13906			0.569529	+	0.821972i	$0.307126\pi$
$830$	−6804.00	−	11784.9i	−0.284543	−	0.492842i
$831$	−12910.0	+	22360.8i	−0.538921	+	0.933438i
$832$	−832.000	−	1441.07i	−0.0346688	−	0.0600481i
$833$	15903.0	−	27544.8i	0.661472	−	1.14570i
$834$	−14675.0	+	25417.8i	−0.609297	+	1.05533i
$835$	−33408.0			−1.38459
$836$	−342.000	+	2961.81i	−0.0141487	+	0.122531i
$837$	14210.0			0.586821
$838$	−5796.00	+	10039.0i	−0.238925	+	0.413831i
$839$	−876.000	+	1517.28i	−0.0360463	+	0.0624341i	−0.883486	−	0.468458i	$-0.844810\pi$
$839$	−876.000	+	1517.28i	−0.0360463	+	0.0624341i	0.847439	+	0.530892i	$0.178143\pi$
$840$	−1920.00	−	3325.54i	−0.0788646	−	0.136598i
$841$	−8613.50	+	14919.0i	−0.353172	+	0.611711i
$842$	−650.000	−	1125.83i	−0.0266039	−	0.0460793i
$843$	3225.00			0.131761
$844$	−3280.00			−0.133770
$845$	−9126.00	−	15806.7i	−0.371531	−	0.643511i
$846$	−984.000	−	1704.34i	−0.0399889	−	0.0692628i
$847$	−10000.0			−0.405672
$848$	10848.0			0.439295
$849$	16857.5	+	29198.0i	0.681446	+	1.18030i
$850$	−2166.00	+	3751.62i	−0.0874037	+	0.151388i
$851$	−13026.0	−	22561.7i	−0.524707	−	0.908819i
$852$	60.0000	−	103.923i	0.00241264	−	0.00417881i
$853$	8231.00	−	14256.5i	0.330392	−	0.572255i	−0.652197	−	0.758050i	$-0.726153\pi$
$853$	8231.00	−	14256.5i	0.330392	−	0.572255i	0.982589	+	0.185794i	$0.0594858\pi$
$854$	−5632.00			−0.225671
$855$	−1596.00	−	1184.72i	−0.0638387	−	0.0473879i
$856$	−11520.0			−0.459983
$857$	−11050.5	+	19140.0i	−0.440464	+	0.762907i	−0.997724	−	0.0674318i	$-0.978519\pi$
$857$	−11050.5	+	19140.0i	−0.440464	+	0.762907i	0.557260	+	0.830338i	$0.311853\pi$
$858$	1170.00	−	2026.50i	0.0465538	−	0.0806335i
$859$	−21779.5	−	37723.2i	−0.865084	−	1.49837i	−0.866964	−	0.498371i	$-0.833932\pi$
$859$	−21779.5	−	37723.2i	−0.865084	−	1.49837i	0.00188022	−	0.999998i	$-0.499402\pi$
$860$	−7584.00	+	13135.9i	−0.300712	+	0.520848i
$861$	3540.00	+	6131.46i	0.140119	+	0.242694i
$862$	8412.00			0.332383
$863$	15570.0			0.614147			0.307074	−	0.951686i	$-0.400650\pi$
$863$	15570.0			0.614147			0.307074	+	0.951686i	$0.400650\pi$
$864$	−2320.00	−	4018.36i	−0.0913519	−	0.158226i
$865$	14292.0	+	24754.5i	0.561783	+	0.973037i
$866$	−26156.0			−1.02635
$867$	−40415.0			−1.58312
$868$	−1568.00	−	2715.86i	−0.0613150	−	0.106201i
$869$	1422.00	−	2462.98i	0.0555098	−	0.0961459i
$870$	12240.0	+	21200.3i	0.476983	+	0.826158i
$871$	−9815.00	+	17000.1i	−0.381824	+	0.661338i
$872$	−5120.00	+	8868.10i	−0.198836	+	0.344394i
$873$	1886.00			0.0731173
$874$	10374.0	+	7700.70i	0.401494	+	0.298032i
$875$	10176.0			0.393156
$876$	−1450.00	+	2511.47i	−0.0559258	+	0.0968662i
$877$	5072.00	−	8784.96i	0.195290	−	0.338252i	−0.751706	−	0.659499i	$-0.770769\pi$
$877$	5072.00	−	8784.96i	0.195290	−	0.338252i	0.946996	+	0.321247i	$0.104102\pi$
$878$	2602.00	+	4506.80i	0.100015	+	0.173231i
$879$	−630.000	+	1091.19i	−0.0241745	+	0.0418714i
$880$	864.000	+	1496.49i	0.0330971	+	0.0573258i
$881$	40887.0			1.56358			0.781792	−	0.623539i	$-0.214306\pi$
$881$	40887.0			1.56358			0.781792	+	0.623539i	$0.214306\pi$
$882$	1116.00			0.0426051
$883$	−6299.50	−	10911.1i	−0.240085	−	0.415839i	0.720653	−	0.693296i	$-0.243842\pi$
$883$	−6299.50	−	10911.1i	−0.240085	−	0.415839i	−0.960738	+	0.277456i	$0.910509\pi$
$884$	−5928.00	−	10267.6i	−0.225543	−	0.390652i
$885$	−34740.0			−1.31952
$886$	15846.0			0.600854
$887$	−24576.0	−	42566.9i	−0.930306	−	1.61134i	−0.782798	−	0.622276i	$-0.786208\pi$
$887$	−24576.0	−	42566.9i	−0.930306	−	1.61134i	−0.147508	−	0.989061i	$-0.547125\pi$
$888$	−6680.00	+	11570.1i	−0.252439	+	0.437238i
$889$	−3608.00	−	6249.24i	−0.136117	−	0.235762i
$890$	−1368.00	+	2369.45i	−0.0515230	+	0.0892404i
$891$	3019.50	−	5229.93i	0.113532	−	0.196643i
$892$	3704.00			0.139035
$893$	4674.00	−	40478.0i	0.175151	−	1.51685i
$894$	−60.0000			−0.00224463
$895$	−21870.0	+	37880.0i	−0.816797	+	1.41473i
$896$	−512.000	+	886.810i	−0.0190901	+	0.0330650i
$897$	−5070.00	−	8781.50i	−0.188721	−	0.326874i
$898$	−2529.00	+	4380.36i	−0.0939798	+	0.162778i
$899$	9996.00	+	17313.6i	0.370840	+	0.642314i
$900$	−152.000			−0.00562963
$901$	77292.0			2.85790
$902$	−1593.00	−	2759.16i	−0.0588039	−	0.101851i
$903$	−6320.00	−	10946.6i	−0.232909	−	0.403409i
$904$	−2952.00			−0.108608
$905$	22872.0			0.840101
$906$	13870.0	+	24023.5i	0.508609	+	0.880937i
$907$	4494.50	−	7784.70i	0.164540	−	0.284991i	−0.771952	−	0.635681i	$-0.780719\pi$
$907$	4494.50	−	7784.70i	0.164540	−	0.284991i	0.936492	+	0.350690i	$0.114053\pi$
$908$	−9954.00	−	17240.8i	−0.363805	−	0.630129i
$909$	−1500.00	+	2598.08i	−0.0547325	+	0.0947995i
$910$	2496.00	−	4323.20i	0.0909248	−	0.157486i
$911$	26406.0			0.960340			0.480170	−	0.877175i	$-0.340575\pi$
$911$	26406.0			0.960340			0.480170	+	0.877175i	$0.340575\pi$
$912$	760.000	−	6581.79i	0.0275944	−	0.238975i
$913$	−5103.00			−0.184978
$914$	−7037.00	+	12188.4i	−0.254664	+	0.441092i
$915$	10560.0	−	18290.5i	0.381533	−	0.660835i
$916$	8624.00	+	14937.2i	0.311075	+	0.538798i
$917$	1812.00	−	3138.48i	0.0652536	−	0.113022i
$918$	−16530.0	−	28630.8i	−0.594304	−	1.02937i
$919$	43514.0			1.56191			0.780955	−	0.624588i	$-0.214733\pi$
$919$	43514.0			1.56191			0.780955	+	0.624588i	$0.214733\pi$
$920$	7488.00			0.268339
$921$	−17792.5	−	30817.5i	−0.636572	−	1.10258i
$922$	11730.0	+	20317.0i	0.418988	+	0.725709i
$923$	156.000			0.00556317
$924$	−1440.00			−0.0512690
$925$	3173.00	+	5495.80i	0.112787	+	0.195352i
$926$	−11762.0	+	20372.4i	−0.417412	+	0.722978i
$927$	−658.000	−	1139.69i	−0.0233134	−	0.0403801i
$928$	3264.00	−	5653.41i	0.115459	−	0.199981i
$929$	−14074.5	+	24377.7i	−0.497061	+	0.860934i	−0.999994	−	0.00339072i	$-0.998921\pi$
$929$	−14074.5	+	24377.7i	−0.497061	+	0.860934i	0.502934	+	0.864325i	$0.332254\pi$
$930$	11760.0			0.414651
$931$	18553.5	+	13772.4i	0.653133	+	0.484825i
$932$	−7284.00			−0.256004
$933$	11025.0	−	19095.9i	0.386862	−	0.670065i
$934$	3465.00	−	6001.56i	0.121390	−	0.210254i
$935$	6156.00	+	10662.5i	0.215318	+	0.372942i
$936$	208.000	−	360.267i	0.00726356	−	0.0125809i
$937$	−17873.5	−	30957.8i	−0.623161	−	1.07935i	−0.988893	−	0.148626i	$-0.952515\pi$
$937$	−17873.5	−	30957.8i	−0.623161	−	1.07935i	0.365732	−	0.930720i	$-0.380819\pi$
$938$	12080.0			0.420497
$939$	−33625.0			−1.16859
$940$	−11808.0	−	20452.1i	−0.409718	−	0.709652i
$941$	−6495.00	−	11249.7i	−0.225006	−	0.389722i	0.731315	−	0.682040i	$-0.238907\pi$
$941$	−6495.00	−	11249.7i	−0.225006	−	0.389722i	−0.956321	+	0.292317i	$0.905574\pi$
$942$	27280.0			0.943557
$943$	−13806.0			−0.476761
$944$	4632.00	+	8022.86i	0.159702	+	0.276612i
$945$	6960.00	−	12055.1i	0.239586	−	0.414975i
$946$	2844.00	+	4925.95i	0.0977446	+	0.169299i
$947$	−5862.00	+	10153.3i	−0.201150	+	0.348403i	−0.948899	−	0.315579i	$-0.897801\pi$
$947$	−5862.00	+	10153.3i	−0.201150	+	0.348403i	0.747749	+	0.663982i	$0.231135\pi$
$948$	−3160.00	+	5473.28i	−0.108262	+	0.187515i
$949$	−3770.00			−0.128956
$950$	−2527.00	−	1875.81i	−0.0863018	−	0.0640625i
$951$	24330.0			0.829605
$952$	−3648.00	+	6318.52i	−0.124194	+	0.215110i
$953$	−12508.5	+	21665.4i	−0.425173	+	0.736422i	−0.996437	−	0.0843452i	$-0.973120\pi$
$953$	−12508.5	+	21665.4i	−0.425173	+	0.736422i	0.571263	+	0.820767i	$0.306453\pi$
$954$	1356.00	+	2348.66i	0.0460190	+	0.0797072i
$955$	7992.00	−	13842.6i	0.270801	−	0.469041i
$956$	−648.000	−	1122.37i	−0.0219224	−	0.0379707i
$957$	9180.00			0.310081
$958$	−8040.00			−0.271149
$959$	−8004.00	−	13863.3i	−0.269513	−	0.466810i
$960$	−1920.00	−	3325.54i	−0.0645497	−	0.111803i
$961$	−20187.0			−0.677621
$962$	−17368.0			−0.582086
$963$	−1440.00	−	2494.15i	−0.0481862	−	0.0834610i
$964$	−682.000	+	1181.26i	−0.0227860	+	0.0394666i
$965$	7932.00	+	13738.6i	0.264601	+	0.458303i
$966$	−3120.00	+	5404.00i	−0.103918	+	0.179990i
$967$	12947.0	−	22424.9i	0.430556	−	0.745745i	−0.566365	−	0.824154i	$-0.691651\pi$
$967$	12947.0	−	22424.9i	0.430556	−	0.745745i	0.996921	+	0.0784097i	$0.0249842\pi$
$968$	−10000.0			−0.332037
$969$	5415.00	−	46895.3i	0.179520	−	1.55469i
$970$	22632.0			0.749144
$971$	−18295.5	+	31688.7i	−0.604666	+	1.04731i	0.387438	+	0.921896i	$0.373360\pi$
$971$	−18295.5	+	31688.7i	−0.604666	+	1.04731i	−0.992104	+	0.125416i	$0.959973\pi$
$972$	1120.00	−	1939.90i	0.0369589	−	0.0640146i
$973$	11740.0	+	20334.3i	0.386811	+	0.669976i
$974$	−18146.0	+	31429.8i	−0.596956	+	1.03396i
$975$	1235.00	+	2139.08i	0.0405658	+	0.0702620i
$976$	−5632.00			−0.184709
$977$	−24687.0			−0.808400			−0.404200	−	0.914671i	$-0.632450\pi$
$977$	−24687.0			−0.808400			−0.404200	+	0.914671i	$0.632450\pi$
$978$	−8285.00	−	14350.0i	−0.270885	−	0.469186i
$979$	513.000	+	888.542i	0.0167472	+	0.0290071i
$980$	13392.0			0.436522
$981$	−2560.00			−0.0833175
$982$	−18528.0	−	32091.4i	−0.602090	−	1.04285i
$983$	12984.0	−	22488.9i	0.421287	−	0.729691i	−0.574778	−	0.818309i	$-0.694912\pi$
$983$	12984.0	−	22488.9i	0.421287	−	0.729691i	0.996066	+	0.0886183i	$0.0282451\pi$
$984$	3540.00	+	6131.46i	0.114686	+	0.198642i
$985$	22356.0	−	38721.7i	0.723169	−	1.25257i
$986$	23256.0	−	40280.6i	0.751138	−	1.30101i
$987$	19680.0			0.634672
$988$	7904.00	−	3422.53i	0.254514	−	0.110208i
$989$	24648.0			0.792478
$990$	−216.000	+	374.123i	−0.00693427	+	0.0120105i
$991$	−9292.00	+	16094.2i	−0.297851	+	0.515893i	−0.975644	−	0.219360i	$-0.929603\pi$
$991$	−9292.00	+	16094.2i	−0.297851	+	0.515893i	0.677793	+	0.735253i	$0.262936\pi$
$992$	−1568.00	−	2715.86i	−0.0501855	−	0.0869239i
$993$	5937.50	−	10284.1i	0.189749	−	0.328655i
$994$	−48.0000	−	83.1384i	−0.00153166	−	0.00265291i
$995$	5736.00			0.182757
$996$	11340.0			0.360765
$997$	24116.0	+	41770.1i	0.766060	+	1.32685i	0.939685	+	0.342042i	$0.111119\pi$
$997$	24116.0	+	41770.1i	0.766060	+	1.32685i	−0.173625	+	0.984812i	$0.555548\pi$
$998$	16003.0	+	27718.0i	0.507581	+	0.879157i
$999$	−48430.0			−1.53379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.4.c.b.11.1	yes	2
3.2	odd	2		342.4.g.c.163.1		2
4.3	odd	2		304.4.i.a.49.1		2
19.7	even	3	inner	38.4.c.b.7.1	✓	2
19.8	odd	6		722.4.a.b.1.1		1
19.11	even	3		722.4.a.c.1.1		1
57.26	odd	6		342.4.g.c.235.1		2
76.7	odd	6		304.4.i.a.273.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.c.b.7.1	✓	2	19.7	even	3	inner
38.4.c.b.11.1	yes	2	1.1	even	1	trivial
304.4.i.a.49.1		2	4.3	odd	2
304.4.i.a.273.1		2	76.7	odd	6
342.4.g.c.163.1		2	3.2	odd	2
342.4.g.c.235.1		2	57.26	odd	6
722.4.a.b.1.1		1	19.8	odd	6
722.4.a.c.1.1		1	19.11	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(2.50000 - 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.00000 - 10.3923i) q^{5} +(5.00000 + 8.66025i) q^{6} +8.00000 q^{7} +8.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(2.50000 - 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.00000 - 10.3923i) q^{5} +(5.00000 + 8.66025i) q^{6} +8.00000 q^{7} +8.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(12.0000 + 20.7846i) q^{10} +9.00000 q^{11} -20.0000 q^{12} +(-13.0000 - 22.5167i) q^{13} +(-8.00000 + 13.8564i) q^{14} +(-30.0000 - 51.9615i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-57.0000 + 98.7269i) q^{17} -4.00000 q^{18} +(-66.5000 - 49.3634i) q^{19} -48.0000 q^{20} +(20.0000 - 34.6410i) q^{21} +(-9.00000 + 15.5885i) q^{22} +(39.0000 + 67.5500i) q^{23} +(20.0000 - 34.6410i) q^{24} +(-9.50000 - 16.4545i) q^{25} +52.0000 q^{26} +145.000 q^{27} +(-16.0000 - 27.7128i) q^{28} +(102.000 + 176.669i) q^{29} +120.000 q^{30} +98.0000 q^{31} +(-16.0000 - 27.7128i) q^{32} +(22.5000 - 38.9711i) q^{33} +(-114.000 - 197.454i) q^{34} +(48.0000 - 83.1384i) q^{35} +(4.00000 - 6.92820i) q^{36} -334.000 q^{37} +(152.000 - 65.8179i) q^{38} -130.000 q^{39} +(48.0000 - 83.1384i) q^{40} +(-88.5000 + 153.286i) q^{41} +(40.0000 + 69.2820i) q^{42} +(158.000 - 273.664i) q^{43} +(-18.0000 - 31.1769i) q^{44} +24.0000 q^{45} -156.000 q^{46} +(246.000 + 426.084i) q^{47} +(40.0000 + 69.2820i) q^{48} -279.000 q^{49} +38.0000 q^{50} +(285.000 + 493.634i) q^{51} +(-52.0000 + 90.0666i) q^{52} +(-339.000 - 587.165i) q^{53} +(-145.000 + 251.147i) q^{54} +(54.0000 - 93.5307i) q^{55} +64.0000 q^{56} +(-380.000 + 164.545i) q^{57} -408.000 q^{58} +(289.500 - 501.429i) q^{59} +(-120.000 + 207.846i) q^{60} +(176.000 + 304.841i) q^{61} +(-98.0000 + 169.741i) q^{62} +(8.00000 + 13.8564i) q^{63} +64.0000 q^{64} -312.000 q^{65} +(45.0000 + 77.9423i) q^{66} +(-377.500 - 653.849i) q^{67} +456.000 q^{68} +390.000 q^{69} +(96.0000 + 166.277i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(8.00000 + 13.8564i) q^{72} +(72.5000 - 125.574i) q^{73} +(334.000 - 578.505i) q^{74} -95.0000 q^{75} +(-38.0000 + 329.090i) q^{76} +72.0000 q^{77} +(130.000 - 225.167i) q^{78} +(158.000 - 273.664i) q^{79} +(96.0000 + 166.277i) q^{80} +(335.500 - 581.103i) q^{81} +(-177.000 - 306.573i) q^{82} -567.000 q^{83} -160.000 q^{84} +(684.000 + 1184.72i) q^{85} +(316.000 + 547.328i) q^{86} +1020.00 q^{87} +72.0000 q^{88} +(57.0000 + 98.7269i) q^{89} +(-24.0000 + 41.5692i) q^{90} +(-104.000 - 180.133i) q^{91} +(156.000 - 270.200i) q^{92} +(245.000 - 424.352i) q^{93} -984.000 q^{94} +(-912.000 + 394.908i) q^{95} -160.000 q^{96} +(471.500 - 816.662i) q^{97} +(279.000 - 483.242i) q^{98} +(9.00000 + 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 5 q^{3} - 4 q^{4} + 12 q^{5} + 10 q^{6} + 16 q^{7} + 16 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 5 * q^3 - 4 * q^4 + 12 * q^5 + 10 * q^6 + 16 * q^7 + 16 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 5 q^{3} - 4 q^{4} + 12 q^{5} + 10 q^{6} + 16 q^{7} + 16 q^{8} + 2 q^{9} + 24 q^{10} + 18 q^{11} - 40 q^{12} - 26 q^{13} - 16 q^{14} - 60 q^{15} - 16 q^{16} - 114 q^{17} - 8 q^{18} - 133 q^{19} - 96 q^{20} + 40 q^{21} - 18 q^{22} + 78 q^{23} + 40 q^{24} - 19 q^{25} + 104 q^{26} + 290 q^{27} - 32 q^{28} + 204 q^{29} + 240 q^{30} + 196 q^{31} - 32 q^{32} + 45 q^{33} - 228 q^{34} + 96 q^{35} + 8 q^{36} - 668 q^{37} + 304 q^{38} - 260 q^{39} + 96 q^{40} - 177 q^{41} + 80 q^{42} + 316 q^{43} - 36 q^{44} + 48 q^{45} - 312 q^{46} + 492 q^{47} + 80 q^{48} - 558 q^{49} + 76 q^{50} + 570 q^{51} - 104 q^{52} - 678 q^{53} - 290 q^{54} + 108 q^{55} + 128 q^{56} - 760 q^{57} - 816 q^{58} + 579 q^{59} - 240 q^{60} + 352 q^{61} - 196 q^{62} + 16 q^{63} + 128 q^{64} - 624 q^{65} + 90 q^{66} - 755 q^{67} + 912 q^{68} + 780 q^{69} + 192 q^{70} - 6 q^{71} + 16 q^{72} + 145 q^{73} + 668 q^{74} - 190 q^{75} - 76 q^{76} + 144 q^{77} + 260 q^{78} + 316 q^{79} + 192 q^{80} + 671 q^{81} - 354 q^{82} - 1134 q^{83} - 320 q^{84} + 1368 q^{85} + 632 q^{86} + 2040 q^{87} + 144 q^{88} + 114 q^{89} - 48 q^{90} - 208 q^{91} + 312 q^{92} + 490 q^{93} - 1968 q^{94} - 1824 q^{95} - 320 q^{96} + 943 q^{97} + 558 q^{98} + 18 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 5 * q^3 - 4 * q^4 + 12 * q^5 + 10 * q^6 + 16 * q^7 + 16 * q^8 + 2 * q^9 + 24 * q^10 + 18 * q^11 - 40 * q^12 - 26 * q^13 - 16 * q^14 - 60 * q^15 - 16 * q^16 - 114 * q^17 - 8 * q^18 - 133 * q^19 - 96 * q^20 + 40 * q^21 - 18 * q^22 + 78 * q^23 + 40 * q^24 - 19 * q^25 + 104 * q^26 + 290 * q^27 - 32 * q^28 + 204 * q^29 + 240 * q^30 + 196 * q^31 - 32 * q^32 + 45 * q^33 - 228 * q^34 + 96 * q^35 + 8 * q^36 - 668 * q^37 + 304 * q^38 - 260 * q^39 + 96 * q^40 - 177 * q^41 + 80 * q^42 + 316 * q^43 - 36 * q^44 + 48 * q^45 - 312 * q^46 + 492 * q^47 + 80 * q^48 - 558 * q^49 + 76 * q^50 + 570 * q^51 - 104 * q^52 - 678 * q^53 - 290 * q^54 + 108 * q^55 + 128 * q^56 - 760 * q^57 - 816 * q^58 + 579 * q^59 - 240 * q^60 + 352 * q^61 - 196 * q^62 + 16 * q^63 + 128 * q^64 - 624 * q^65 + 90 * q^66 - 755 * q^67 + 912 * q^68 + 780 * q^69 + 192 * q^70 - 6 * q^71 + 16 * q^72 + 145 * q^73 + 668 * q^74 - 190 * q^75 - 76 * q^76 + 144 * q^77 + 260 * q^78 + 316 * q^79 + 192 * q^80 + 671 * q^81 - 354 * q^82 - 1134 * q^83 - 320 * q^84 + 1368 * q^85 + 632 * q^86 + 2040 * q^87 + 144 * q^88 + 114 * q^89 - 48 * q^90 - 208 * q^91 + 312 * q^92 + 490 * q^93 - 1968 * q^94 - 1824 * q^95 - 320 * q^96 + 943 * q^97 + 558 * q^98 + 18 * q^99

Introduction

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