LMFDB - Embedded newform 15.4.e.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,4,Mod(2,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("15.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	15.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.885028650086$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.28356903014400.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 209x^{4} + 1600 $ x^8 + 209*x^4 + 1600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.2
Root			$-1.18766 - 1.18766i$ of defining polynomial
Character	$\chi$	$=$	15.2
Dual form			15.4.e.a.8.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18766 + 1.18766i) q^{2} +(5.11173 + 0.932827i) q^{3} +5.17891i q^{4} +(-2.48157 - 10.9015i) q^{5} +(-7.17891 + 4.96314i) q^{6} +(-13.3578 - 13.3578i) q^{7} +(-15.6521 - 15.6521i) q^{8} +(25.2597 + 9.53673i) q^{9} +O(q^{10})$	\(q+(-1.18766 + 1.18766i) q^{2} +(5.11173 + 0.932827i) q^{3} +5.17891i q^{4} +(-2.48157 - 10.9015i) q^{5} +(-7.17891 + 4.96314i) q^{6} +(-13.3578 - 13.3578i) q^{7} +(-15.6521 - 15.6521i) q^{8} +(25.2597 + 9.53673i) q^{9} +(15.8945 + 10.0000i) q^{10} +28.7164i q^{11} +(-4.83102 + 26.4732i) q^{12} +(14.1789 - 14.1789i) q^{13} +31.7292 q^{14} +(-2.51595 - 58.0402i) q^{15} -4.25236 q^{16} +(-18.5587 + 18.5587i) q^{17} +(-41.3264 + 18.6736i) q^{18} +49.0735i q^{19} +(56.4577 - 12.8518i) q^{20} +(-55.8211 - 80.7421i) q^{21} +(-34.1055 - 34.1055i) q^{22} +(37.7738 + 37.7738i) q^{23} +(-65.4088 - 94.6102i) q^{24} +(-112.684 + 54.1055i) q^{25} +33.6796i q^{26} +(120.225 + 72.3121i) q^{27} +(69.1789 - 69.1789i) q^{28} -125.854 q^{29} +(71.9204 + 65.9442i) q^{30} +247.367 q^{31} +(130.267 - 130.267i) q^{32} +(-26.7874 + 146.791i) q^{33} -44.0829i q^{34} +(-112.471 + 178.768i) q^{35} +(-49.3898 + 130.818i) q^{36} +(-127.463 - 127.463i) q^{37} +(-58.2828 - 58.2828i) q^{38} +(85.7053 - 59.2524i) q^{39} +(-131.789 + 209.473i) q^{40} -390.328i q^{41} +(162.191 + 29.5978i) q^{42} +(-39.3993 + 39.3993i) q^{43} -148.720 q^{44} +(41.2806 - 299.033i) q^{45} -89.7251 q^{46} +(-124.560 + 124.560i) q^{47} +(-21.7369 - 3.96671i) q^{48} +13.8625i q^{49} +(69.5712 - 198.089i) q^{50} +(-112.179 + 77.5549i) q^{51} +(73.4313 + 73.4313i) q^{52} +(160.441 + 160.441i) q^{53} +(-228.669 + 56.9040i) q^{54} +(313.051 - 71.2618i) q^{55} +418.156i q^{56} +(-45.7770 + 250.850i) q^{57} +(149.473 - 149.473i) q^{58} +729.423 q^{59} +(300.585 - 13.0299i) q^{60} +2.00000 q^{61} +(-293.789 + 293.789i) q^{62} +(-210.024 - 464.804i) q^{63} +275.409i q^{64} +(-189.757 - 119.385i) q^{65} +(-142.524 - 206.153i) q^{66} +(-329.987 - 329.987i) q^{67} +(-96.1136 - 96.1136i) q^{68} +(157.853 + 228.326i) q^{69} +(-78.7382 - 345.895i) q^{70} +171.760i q^{71} +(-246.097 - 544.637i) q^{72} +(-279.927 + 279.927i) q^{73} +302.767 q^{74} +(-626.480 + 171.458i) q^{75} -254.147 q^{76} +(383.589 - 383.589i) q^{77} +(-31.4172 + 172.161i) q^{78} +48.0189i q^{79} +(10.5525 + 46.3569i) q^{80} +(547.102 + 481.789i) q^{81} +(463.578 + 463.578i) q^{82} +(-144.451 - 144.451i) q^{83} +(418.156 - 289.092i) q^{84} +(248.371 + 156.262i) q^{85} -93.5862i q^{86} +(-643.334 - 117.400i) q^{87} +(449.473 - 449.473i) q^{88} -1417.21 q^{89} +(306.124 + 404.179i) q^{90} -378.799 q^{91} +(-195.627 + 195.627i) q^{92} +(1264.48 + 230.751i) q^{93} -295.872i q^{94} +(534.972 - 121.779i) q^{95} +(787.409 - 544.375i) q^{96} +(908.111 + 908.111i) q^{97} +(-16.4640 - 16.4640i) q^{98} +(-273.861 + 725.367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7}+O(q^{10}) $ 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7	$ 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7} - 100 q^{10} + 132 q^{12} + 68 q^{13} + 90 q^{15} + 284 q^{16} - 240 q^{18} - 492 q^{21} - 500 q^{22} - 220 q^{25} + 702 q^{27} + 508 q^{28} + 660 q^{30} + 616 q^{31} - 240 q^{33} - 804 q^{36} - 1156 q^{37} - 600 q^{40} + 540 q^{42} + 548 q^{43} + 180 q^{45} + 736 q^{46} - 1116 q^{48} - 852 q^{51} + 224 q^{52} + 460 q^{55} + 684 q^{57} + 60 q^{58} + 540 q^{60} + 16 q^{61} + 1428 q^{63} + 2040 q^{66} + 404 q^{67} - 2220 q^{70} - 1800 q^{72} - 2512 q^{73} - 2910 q^{75} - 1488 q^{76} - 360 q^{78} + 288 q^{81} + 2800 q^{82} + 4940 q^{85} - 1680 q^{87} + 2460 q^{88} + 600 q^{90} - 1304 q^{91} + 3408 q^{93} + 4164 q^{96} + 1904 q^{97}+O(q^{100}) $ 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7 - 100 * q^10 + 132 * q^12 + 68 * q^13 + 90 * q^15 + 284 * q^16 - 240 * q^18 - 492 * q^21 - 500 * q^22 - 220 * q^25 + 702 * q^27 + 508 * q^28 + 660 * q^30 + 616 * q^31 - 240 * q^33 - 804 * q^36 - 1156 * q^37 - 600 * q^40 + 540 * q^42 + 548 * q^43 + 180 * q^45 + 736 * q^46 - 1116 * q^48 - 852 * q^51 + 224 * q^52 + 460 * q^55 + 684 * q^57 + 60 * q^58 + 540 * q^60 + 16 * q^61 + 1428 * q^63 + 2040 * q^66 + 404 * q^67 - 2220 * q^70 - 1800 * q^72 - 2512 * q^73 - 2910 * q^75 - 1488 * q^76 - 360 * q^78 + 288 * q^81 + 2800 * q^82 + 4940 * q^85 - 1680 * q^87 + 2460 * q^88 + 600 * q^90 - 1304 * q^91 + 3408 * q^93 + 4164 * q^96 + 1904 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.18766	+	1.18766i	−0.419903	+	0.419903i	−0.885170	−	0.465267i	$-0.845958\pi$
$2$	−1.18766	+	1.18766i	−0.419903	+	0.419903i	0.465267	+	0.885170i	$0.345958\pi$
$3$	5.11173	+	0.932827i	0.983754	+	0.179523i
$3$	5.11173	+	0.932827i	0.983754	+	0.179523i
$4$			5.17891i			0.647364i
$5$	−2.48157	−	10.9015i	−0.221958	−	0.975056i
$5$	−2.48157	−	10.9015i	−0.221958	−	0.975056i
$6$	−7.17891	+	4.96314i	−0.488463	+	0.337699i
$7$	−13.3578	−	13.3578i	−0.721254	−	0.721254i	0.247606	−	0.968861i	$-0.420356\pi$
$7$	−13.3578	−	13.3578i	−0.721254	−	0.721254i	−0.968861	+	0.247606i	$0.920356\pi$
$8$	−15.6521	−	15.6521i	−0.691732	−	0.691732i
$9$	25.2597	+	9.53673i	0.935543	+	0.353212i
$10$	15.8945	+	10.0000i	0.502630	+	0.316228i
$11$			28.7164i			0.787121i	0.919299	+	0.393560i	$0.128757\pi$
$11$			28.7164i			0.787121i	−0.919299	+	0.393560i	$0.871243\pi$
$12$	−4.83102	+	26.4732i	−0.116216	+	0.636846i
$13$	14.1789	−	14.1789i	0.302502	−	0.302502i	−0.539490	−	0.841992i	$-0.681383\pi$
$13$	14.1789	−	14.1789i	0.302502	−	0.302502i	0.841992	+	0.539490i	$0.181383\pi$
$14$	31.7292			0.605713
$15$	−2.51595	−	58.0402i	−0.0433078	−	0.999062i
$16$	−4.25236			−0.0664431
$17$	−18.5587	+	18.5587i	−0.264773	+	0.264773i	−0.826990	−	0.562217i	$-0.809949\pi$
$17$	−18.5587	+	18.5587i	−0.264773	+	0.264773i	0.562217	+	0.826990i	$0.309949\pi$
$18$	−41.3264	+	18.6736i	−0.541152	+	0.244522i
$19$			49.0735i			0.592538i	0.955105	+	0.296269i	$0.0957425\pi$
$19$			49.0735i			0.592538i	−0.955105	+	0.296269i	$0.904258\pi$
$20$	56.4577	−	12.8518i	0.631216	−	0.143688i
$21$	−55.8211	−	80.7421i	−0.580055	−	0.839018i
$22$	−34.1055	−	34.1055i	−0.330514	−	0.330514i
$23$	37.7738	+	37.7738i	0.342451	+	0.342451i	0.857288	−	0.514837i	$-0.172148\pi$
$23$	37.7738	+	37.7738i	0.342451	+	0.342451i	−0.514837	+	0.857288i	$0.672148\pi$
$24$	−65.4088	−	94.6102i	−0.556313	−	0.804676i
$25$	−112.684	+	54.1055i	−0.901469	+	0.432844i
$26$			33.6796i			0.254042i
$27$	120.225	+	72.3121i	0.856935	+	0.515425i
$28$	69.1789	−	69.1789i	0.466914	−	0.466914i
$29$	−125.854			−0.805882			−0.402941	−	0.915226i	$-0.632012\pi$
$29$	−125.854			−0.805882			−0.402941	+	0.915226i	$0.632012\pi$
$30$	71.9204	+	65.9442i	0.437694	+	0.401324i
$31$	247.367			1.43318			0.716588	−	0.697496i	$-0.245703\pi$
$31$	247.367			1.43318			0.716588	+	0.697496i	$0.245703\pi$
$32$	130.267	−	130.267i	0.719632	−	0.719632i
$33$	−26.7874	+	146.791i	−0.141306	+	0.774333i
$34$		−	44.0829i		−	0.222357i
$35$	−112.471	+	178.768i	−0.543175	+	0.863352i
$36$	−49.3898	+	130.818i	−0.228657	+	0.605637i
$37$	−127.463	−	127.463i	−0.566347	−	0.566347i	0.364756	−	0.931103i	$-0.381152\pi$
$37$	−127.463	−	127.463i	−0.566347	−	0.566347i	−0.931103	+	0.364756i	$0.881152\pi$
$38$	−58.2828	−	58.2828i	−0.248808	−	0.248808i
$39$	85.7053	−	59.2524i	0.351893	−	0.243281i
$40$	−131.789	+	209.473i	−0.520942	+	0.828014i
$41$		−	390.328i		−	1.48680i	−0.668845	−	0.743402i	$-0.733211\pi$
$41$		−	390.328i		−	1.48680i	0.668845	−	0.743402i	$-0.266789\pi$
$42$	162.191	+	29.5978i	0.595873	+	0.108739i
$43$	−39.3993	+	39.3993i	−0.139729	+	0.139729i	−0.773511	−	0.633783i	$-0.781501\pi$
$43$	−39.3993	+	39.3993i	−0.139729	+	0.139729i	0.633783	+	0.773511i	$0.281501\pi$
$44$	−148.720			−0.509553
$45$	41.2806	−	299.033i	0.136750	−	0.990606i
$46$	−89.7251			−0.287592
$47$	−124.560	+	124.560i	−0.386575	+	0.386575i	−0.873464	−	0.486889i	$-0.838132\pi$
$47$	−124.560	+	124.560i	−0.386575	+	0.386575i	0.486889	+	0.873464i	$0.338132\pi$
$48$	−21.7369	−	3.96671i	−0.0653637	−	0.0119280i
$49$			13.8625i			0.0404155i
$50$	69.5712	−	198.089i	0.196777	−	0.560281i
$51$	−112.179	+	77.5549i	−0.308004	+	0.212938i
$52$	73.4313	+	73.4313i	0.195829	+	0.195829i
$53$	160.441	+	160.441i	0.415816	+	0.415816i	0.883759	−	0.467943i	$-0.155005\pi$
$53$	160.441	+	160.441i	0.415816	+	0.415816i	−0.467943	+	0.883759i	$0.655005\pi$
$54$	−228.669	+	56.9040i	−0.576257	+	0.143401i
$55$	313.051	−	71.2618i	0.767487	−	0.174708i
$56$			418.156i			0.997830i
$57$	−45.7770	+	250.850i	−0.106374	+	0.582912i
$58$	149.473	−	149.473i	0.338392	−	0.338392i
$59$	729.423			1.60954			0.804769	−	0.593588i	$-0.202289\pi$
$59$	729.423			1.60954			0.804769	+	0.593588i	$0.202289\pi$
$60$	300.585	−	13.0299i	0.646756	−	0.0280359i
$61$	2.00000			0.00419793			0.00209897	−	0.999998i	$-0.499332\pi$
$61$	2.00000			0.00419793			0.00209897	+	0.999998i	$0.499332\pi$
$62$	−293.789	+	293.789i	−0.601795	+	0.601795i
$63$	−210.024	−	464.804i	−0.420009	−	0.929520i
$64$			275.409i			0.537908i
$65$	−189.757	−	119.385i	−0.362099	−	0.227813i
$66$	−142.524	−	206.153i	−0.265810	−	0.384479i
$67$	−329.987	−	329.987i	−0.601706	−	0.601706i	0.339059	−	0.940765i	$-0.389891\pi$
$67$	−329.987	−	329.987i	−0.601706	−	0.601706i	−0.940765	+	0.339059i	$0.889891\pi$
$68$	−96.1136	−	96.1136i	−0.171404	−	0.171404i
$69$	157.853	+	228.326i	0.275410	+	0.398365i
$70$	−78.7382	−	345.895i	−0.134443	−	0.590604i
$71$			171.760i			0.287100i	0.989643	+	0.143550i	$0.0458518\pi$
$71$			171.760i			0.287100i	−0.989643	+	0.143550i	$0.954148\pi$
$72$	−246.097	−	544.637i	−0.402817	−	0.891474i
$73$	−279.927	+	279.927i	−0.448807	+	0.448807i	−0.894958	−	0.446151i	$-0.852795\pi$
$73$	−279.927	+	279.927i	−0.448807	+	0.448807i	0.446151	+	0.894958i	$0.352795\pi$
$74$	302.767			0.475621
$75$	−626.480	+	171.458i	−0.964529	+	0.263978i
$76$	−254.147			−0.383587
$77$	383.589	−	383.589i	0.567714	−	0.567714i
$78$	−31.4172	+	172.161i	−0.0456064	+	0.249915i
$79$			48.0189i			0.0683866i	0.999415	+	0.0341933i	$0.0108862\pi$
$79$			48.0189i			0.0683866i	−0.999415	+	0.0341933i	$0.989114\pi$
$80$	10.5525	+	46.3569i	0.0147476	+	0.0647858i
$81$	547.102	+	481.789i	0.750483	+	0.660890i
$82$	463.578	+	463.578i	0.624313	+	0.624313i
$83$	−144.451	−	144.451i	−0.191031	−	0.191031i	0.605111	−	0.796141i	$-0.293129\pi$
$83$	−144.451	−	144.451i	−0.191031	−	0.191031i	−0.796141	+	0.605111i	$0.793129\pi$
$84$	418.156	−	289.092i	0.543150	−	0.375507i
$85$	248.371	+	156.262i	0.316937	+	0.199400i
$86$		−	93.5862i		−	0.117345i
$87$	−643.334	−	117.400i	−0.792789	−	0.144674i
$88$	449.473	−	449.473i	0.544477	−	0.544477i
$89$	−1417.21			−1.68790			−0.843952	−	0.536419i	$-0.819777\pi$
$89$	−1417.21			−1.68790			−0.843952	+	0.536419i	$0.819777\pi$
$90$	306.124	+	404.179i	0.358536	+	0.473380i
$91$	−378.799			−0.436361
$92$	−195.627	+	195.627i	−0.221690	+	0.221690i
$93$	1264.48	+	230.751i	1.40989	+	0.257288i
$94$		−	295.872i		−	0.324647i
$95$	534.972	−	121.779i	0.577758	−	0.131519i
$96$	787.409	−	544.375i	0.837131	−	0.578751i
$97$	908.111	+	908.111i	0.950564	+	0.950564i	0.998834	−	0.0482702i	$-0.0153708\pi$
$97$	908.111	+	908.111i	0.950564	+	0.950564i	−0.0482702	+	0.998834i	$0.515371\pi$
$98$	−16.4640	−	16.4640i	−0.0169706	−	0.0169706i
$99$	−273.861	+	725.367i	−0.278020	+	0.736385i
$100$	−280.207	−	583.578i	−0.280207	−	0.583578i
$101$		−	337.668i		−	0.332665i	−0.986070	−	0.166333i	$-0.946807\pi$
$101$		−	337.668i		−	0.332665i	0.986070	−	0.166333i	$-0.0531926\pi$
$102$	41.1217	−	225.340i	0.0399182	−	0.218745i
$103$	−933.505	+	933.505i	−0.893019	+	0.893019i	−0.994806	−	0.101787i	$-0.967544\pi$
$103$	−933.505	+	933.505i	−0.893019	+	0.893019i	0.101787	+	0.994806i	$0.467544\pi$
$104$	−443.860			−0.418500
$105$	−741.683	+	808.899i	−0.689342	+	0.751814i
$106$	−381.100			−0.349205
$107$	596.188	−	596.188i	0.538651	−	0.538651i	−0.384481	−	0.923133i	$-0.625620\pi$
$107$	596.188	−	596.188i	0.538651	−	0.538651i	0.923133	+	0.384481i	$0.125620\pi$
$108$	−374.498	+	622.632i	−0.333667	+	0.554748i
$109$		−	2074.60i		−	1.82303i	−0.411264	−	0.911516i	$-0.634913\pi$
$109$		−	2074.60i		−	1.82303i	0.411264	−	0.911516i	$-0.365087\pi$
$110$	−287.164	+	456.434i	−0.248909	+	0.395630i
$111$	−532.657	−	770.460i	−0.455474	−	0.658818i
$112$	56.8022	+	56.8022i	0.0479224	+	0.0479224i
$113$	−271.193	−	271.193i	−0.225767	−	0.225767i	0.585154	−	0.810922i	$-0.301034\pi$
$113$	−271.193	−	271.193i	−0.225767	−	0.225767i	−0.810922	+	0.585154i	$0.801034\pi$
$114$	−243.558	−	352.294i	−0.200099	−	0.289433i
$115$	318.051	−	505.527i	0.257899	−	0.409919i
$116$		−	651.788i		−	0.521698i
$117$	493.375	−	222.934i	0.389851	−	0.176156i
$118$	−866.309	+	866.309i	−0.675849	+	0.675849i
$119$	495.806			0.381937
$120$	−869.073	+	947.833i	−0.661126	+	0.721041i
$121$	506.367			0.380441
$122$	−2.37533	+	2.37533i	−0.00176272	+	0.00176272i
$123$	364.108	−	1995.25i	0.266915	−	1.46265i
$124$			1281.09i			0.927786i
$125$	869.461	+	1094.15i	0.622135	+	0.782910i
$126$	801.469	+	302.593i	0.566671	+	0.213945i
$127$	105.588	+	105.588i	0.0737747	+	0.0737747i	0.743031	−	0.669257i	$-0.233387\pi$
$127$	105.588	+	105.588i	0.0737747	+	0.0737747i	−0.669257	+	0.743031i	$0.733387\pi$
$128$	715.045	+	715.045i	0.493763	+	0.493763i
$129$	−238.151	+	164.646i	−0.162543	+	0.112374i
$130$	367.156	−	83.5782i	0.247706	−	0.0563868i
$131$			1979.28i			1.32008i	0.751231	+	0.660039i	$0.229460\pi$
$131$			1979.28i			1.32008i	−0.751231	+	0.660039i	$0.770540\pi$
$132$	−760.216	−	138.730i	−0.501275	−	0.0914763i
$133$	655.514	−	655.514i	0.427371	−	0.427371i
$134$	783.827			0.505316
$135$	489.962	−	1490.07i	0.312364	−	0.949962i
$136$	580.964			0.366304
$137$	−507.451	+	507.451i	−0.316456	+	0.316456i	−0.847404	−	0.530948i	$-0.821836\pi$
$137$	−507.451	+	507.451i	−0.316456	+	0.316456i	0.530948	+	0.847404i	$0.321836\pi$
$138$	−458.651	−	83.6979i	−0.282920	−	0.0516293i
$139$			68.4333i			0.0417585i	0.999782	+	0.0208793i	$0.00664656\pi$
$139$			68.4333i			0.0417585i	−0.999782	+	0.0208793i	$0.993353\pi$
$140$	−925.823	−	582.479i	−0.558903	−	0.351632i
$141$	−752.913	+	520.527i	−0.449693	+	0.310895i
$142$	−203.993	−	203.993i	−0.120554	−	0.120554i
$143$	407.167	+	407.167i	0.238105	+	0.238105i
$144$	−107.413	−	40.5536i	−0.0621604	−	0.0234685i
$145$	312.316	+	1372.00i	0.178872	+	0.785780i
$146$		−	664.917i		−	0.376911i
$147$	−12.9313	+	70.8616i	−0.00725550	+	0.0397590i
$148$	660.121	−	660.121i	0.366632	−	0.366632i
$149$	−363.356			−0.199780			−0.0998902	−	0.994998i	$-0.531849\pi$
$149$	−363.356			−0.199780			−0.0998902	+	0.994998i	$0.531849\pi$
$150$	540.413	−	947.683i	0.294163	−	0.515853i
$151$	−2083.14			−1.12267			−0.561337	−	0.827588i	$-0.689713\pi$
$151$	−2083.14			−1.12267			−0.561337	+	0.827588i	$0.689713\pi$
$152$	768.103	−	768.103i	0.409878	−	0.409878i
$153$	−645.774	+	291.797i	−0.341227	+	0.154185i
$154$			911.149i			0.476769i
$155$	−613.859	−	2696.66i	−0.318105	−	1.39743i
$156$	306.863	+	443.860i	0.157491	+	0.227803i
$157$	−1208.52	−	1208.52i	−0.614333	−	0.614333i	0.329739	−	0.944072i	$-0.393039\pi$
$157$	−1208.52	−	1208.52i	−0.614333	−	0.614333i	−0.944072	+	0.329739i	$0.893039\pi$
$158$	−57.0303	−	57.0303i	−0.0287157	−	0.0287157i
$159$	670.468	+	969.795i	0.334412	+	0.483709i
$160$	−1743.37	−	1096.84i	−0.861410	−	0.541953i
$161$		−	1009.15i		−	0.493989i
$162$	−1221.98	+	77.5696i	−0.592639	+	0.0376200i
$163$	626.062	−	626.062i	0.300840	−	0.300840i	−0.540502	−	0.841343i	$-0.681766\pi$
$163$	626.062	−	626.062i	0.300840	−	0.300840i	0.841343	+	0.540502i	$0.181766\pi$
$164$	2021.47			0.962502
$165$	1666.71	−	72.2492i	0.786382	−	0.0340884i
$166$	343.119			0.160429
$167$	−3009.65	+	3009.65i	−1.39457	+	1.39457i	−0.579848	+	0.814724i	$0.696888\pi$
$167$	−3009.65	+	3009.65i	−1.39457	+	1.39457i	−0.814724	+	0.579848i	$0.803112\pi$
$168$	−390.067	+	2137.50i	−0.179133	+	0.981619i
$169$			1794.92i			0.816985i
$170$	−480.568	+	109.395i	−0.216811	+	0.0493541i
$171$	−468.000	+	1239.58i	−0.209292	+	0.554345i
$172$	−204.045	−	204.045i	−0.0904552	−	0.0904552i
$173$	−1839.23	−	1839.23i	−0.808288	−	0.808288i	0.176086	−	0.984375i	$-0.443656\pi$
$173$	−1839.23	−	1839.23i	−0.808288	−	0.808288i	−0.984375	+	0.176086i	$0.943656\pi$
$174$	903.497	−	624.633i	0.393643	−	0.272145i
$175$	2227.94	+	782.476i	0.962379	+	0.337998i
$176$		−	122.113i		−	0.0522987i
$177$	3728.61	+	680.425i	1.58339	+	0.288948i
$178$	1683.16	−	1683.16i	0.708755	−	0.708755i
$179$	821.582			0.343061			0.171530	−	0.985179i	$-0.445129\pi$
$179$	821.582			0.343061			0.171530	+	0.985179i	$0.445129\pi$
$180$	1548.67	+	213.788i	0.641282	+	0.0885269i
$181$	2314.20			0.950350			0.475175	−	0.879891i	$-0.342385\pi$
$181$	2314.20			0.950350			0.475175	+	0.879891i	$0.342385\pi$
$182$	449.885	−	449.885i	0.183229	−	0.183229i
$183$	10.2235	+	1.86565i	0.00412973	+	0.000753623i
$184$		−	1182.48i		−	0.473769i
$185$	−1073.23	+	1705.84i	−0.426515	+	0.677925i
$186$	−1775.83	+	1227.72i	−0.700053	+	0.483982i
$187$	−532.938	−	532.938i	−0.208408	−	0.208408i
$188$	−645.087	−	645.087i	−0.250254	−	0.250254i
$189$	−640.007	−	2571.87i	−0.246316	−	0.989820i
$190$	−490.735	+	780.000i	−0.187377	+	0.297827i
$191$			931.167i			0.352758i	0.984322	+	0.176379i	$0.0564385\pi$
$191$			931.167i			0.352758i	−0.984322	+	0.176379i	$0.943562\pi$
$192$	−256.909	+	1407.82i	−0.0965666	+	0.529169i
$193$	−2623.28	+	2623.28i	−0.978382	+	0.978382i	−0.999771	−	0.0213891i	$-0.993191\pi$
$193$	−2623.28	+	2623.28i	−0.978382	+	0.978382i	0.0213891	+	0.999771i	$0.493191\pi$
$194$	−2157.06			−0.798289
$195$	−858.621	−	787.274i	−0.315319	−	0.289117i
$196$	−71.7928			−0.0261636
$197$	2995.05	−	2995.05i	1.08319	−	1.08319i	0.0869796	−	0.996210i	$-0.472279\pi$
$197$	2995.05	−	2995.05i	1.08319	−	1.08319i	0.996210	−	0.0869796i	$-0.0277215\pi$
$198$	−536.238	−	1186.75i	−0.192469	−	0.425952i
$199$		−	109.458i		−	0.0389912i	−0.999810	−	0.0194956i	$-0.993794\pi$
$199$		−	109.458i		−	0.0389912i	0.999810	−	0.0194956i	$-0.00620603\pi$
$200$	2610.60	+	916.872i	0.922987	+	0.324163i
$201$	−1378.98	−	1994.63i	−0.483911	−	0.699951i
$202$	401.036	+	401.036i	0.139687	+	0.139687i
$203$	1681.14	+	1681.14i	0.581246	+	0.581246i
$204$	−401.650	−	580.964i	−0.137849	−	0.199390i
$205$	−4255.14	+	968.625i	−1.44972	+	0.330008i
$206$		−	2217.38i		−	0.749962i
$207$	593.915	+	1314.39i	0.199420	+	0.441336i
$208$	−60.2938	+	60.2938i	−0.0200991	+	0.0200991i
$209$	−1409.21			−0.466399
$210$	−79.8292	−	1841.57i	−0.0262321	−	0.605145i
$211$	2714.94			0.885801			0.442901	−	0.896571i	$-0.353949\pi$
$211$	2714.94			0.885801			0.442901	+	0.896571i	$0.353949\pi$
$212$	−830.909	+	830.909i	−0.269184	+	0.269184i
$213$	−160.222	+	877.989i	−0.0515409	+	0.282436i
$214$			1416.14i			0.452362i
$215$	527.281	+	331.737i	0.167257	+	0.105229i
$216$	−749.932	−	3013.61i	−0.236233	−	0.949305i
$217$	−3304.29	−	3304.29i	−1.03368	−	1.03368i
$218$	2463.93	+	2463.93i	0.765496	+	0.765496i
$219$	−1692.03	+	1169.79i	−0.522087	+	0.360945i
$220$	369.058	+	1621.26i	0.113100	+	0.496843i
$221$			526.283i			0.160188i
$222$	1547.67	+	282.429i	0.467894	+	0.0853847i
$223$	2830.49	−	2830.49i	0.849971	−	0.849971i	−0.140158	−	0.990129i	$-0.544761\pi$
$223$	2830.49	−	2830.49i	0.849971	−	0.849971i	0.990129	+	0.140158i	$0.0447612\pi$
$224$	−3480.17			−1.03808
$225$	−3362.34	+	292.053i	−0.996249	+	0.0865343i
$226$	644.173			0.189601
$227$	1398.96	−	1398.96i	0.409042	−	0.409042i	−0.472362	−	0.881404i	$-0.656599\pi$
$227$	1398.96	−	1398.96i	0.409042	−	0.409042i	0.881404	+	0.472362i	$0.156599\pi$
$228$	−1299.13	−	237.075i	−0.377356	−	0.0688626i
$229$		−	3930.38i		−	1.13418i	−0.823656	−	0.567089i	$-0.808069\pi$
$229$		−	3930.38i		−	1.13418i	0.823656	−	0.567089i	$-0.191931\pi$
$230$	222.659	+	978.134i	0.0638335	+	0.280419i
$231$	2318.63	−	1602.98i	0.660408	−	0.456573i
$232$	1969.89	+	1969.89i	0.557454	+	0.557454i
$233$	1980.71	+	1980.71i	0.556912	+	0.556912i	0.928427	−	0.371515i	$-0.121162\pi$
$233$	1980.71	+	1980.71i	0.556912	+	0.556912i	−0.371515	+	0.928427i	$0.621162\pi$
$234$	−321.193	+	850.735i	−0.0897309	+	0.237668i
$235$	1667.00	+	1048.79i	0.462736	+	0.291129i
$236$			3777.61i			1.04196i
$237$	−44.7933	+	245.460i	−0.0122769	+	0.0672756i
$238$	−588.851	+	588.851i	−0.160376	+	0.160376i
$239$	2976.20			0.805500			0.402750	−	0.915310i	$-0.368054\pi$
$239$	2976.20			0.805500			0.402750	+	0.915310i	$0.368054\pi$
$240$	10.6987	+	246.808i	0.00287750	+	0.0663808i
$241$	1835.45			0.490587			0.245294	−	0.969449i	$-0.421116\pi$
$241$	1835.45			0.490587			0.245294	+	0.969449i	$0.421116\pi$
$242$	−601.394	+	601.394i	−0.159748	+	0.159748i
$243$	2347.21	+	2973.13i	0.619645	+	0.784882i
$244$			10.3578i			0.00271759i
$245$	151.122	−	34.4008i	0.0394074	−	0.00897057i
$246$	1937.25	+	2802.13i	0.502092	+	0.726248i
$247$	695.808	+	695.808i	0.179244	+	0.179244i
$248$	−3871.82	−	3871.82i	−0.991374	−	0.991374i
$249$	−603.648	−	873.143i	−0.153633	−	0.222222i
$250$	−2332.11	−	266.855i	−0.589982	−	0.0675095i
$251$		−	1542.14i		−	0.387805i	−0.981021	−	0.193902i	$-0.937885\pi$
$251$		−	1542.14i		−	0.387805i	0.981021	−	0.193902i	$-0.0621145\pi$
$252$	2407.18	−	1087.70i	0.601738	−	0.271898i
$253$	−1084.73	+	1084.73i	−0.269550	+	0.269550i
$254$	−250.805			−0.0619564
$255$	1123.84	+	1030.46i	0.275991	+	0.253057i
$256$	−3901.74			−0.952572
$257$	428.853	−	428.853i	0.104090	−	0.104090i	−0.653144	−	0.757234i	$-0.726550\pi$
$257$	428.853	−	428.853i	0.104090	−	0.104090i	0.757234	+	0.653144i	$0.226550\pi$
$258$	87.2997	−	478.388i	0.0210660	−	0.115438i
$259$			3405.26i			0.816960i
$260$	618.283	−	982.733i	0.147478	−	0.234410i
$261$	−3179.04	−	1200.24i	−0.753937	−	0.284647i
$262$	−2350.72	−	2350.72i	−0.554304	−	0.554304i
$263$	−5256.99	−	5256.99i	−1.23255	−	1.23255i	−0.962982	−	0.269565i	$-0.913120\pi$
$263$	−5256.99	−	5256.99i	−1.23255	−	1.23255i	−0.269565	−	0.962982i	$-0.586880\pi$
$264$	2716.87	−	1878.31i	0.633377	−	0.437885i
$265$	1350.89	−	2147.18i	0.313150	−	0.497738i
$266$			1557.06i			0.358908i
$267$	−7244.38	−	1322.01i	−1.66048	−	0.303017i
$268$	1708.97	−	1708.97i	0.389523	−	0.389523i
$269$	1930.34			0.437528			0.218764	−	0.975778i	$-0.429797\pi$
$269$	1930.34			0.437528			0.218764	+	0.975778i	$0.429797\pi$
$270$	1187.79	+	2351.61i	0.267729	+	0.530054i
$271$	−3261.67			−0.731116			−0.365558	−	0.930789i	$-0.619122\pi$
$271$	−3261.67			−0.731116			−0.365558	+	0.930789i	$0.619122\pi$
$272$	78.9180	−	78.9180i	0.0175923	−	0.0175923i
$273$	−1936.32	−	353.353i	−0.429272	−	0.0783367i
$274$		−	1205.36i		−	0.265762i
$275$	−1553.72	−	3235.87i	−0.340700	−	0.709565i
$276$	−1182.48	+	817.507i	−0.257887	+	0.178290i
$277$	4865.57	+	4865.57i	1.05539	+	1.05539i	0.998373	+	0.0570194i	$0.0181597\pi$
$277$	4865.57	+	4865.57i	1.05539	+	1.05539i	0.0570194	+	0.998373i	$0.481840\pi$
$278$	−81.2758	−	81.2758i	−0.0175345	−	0.0175345i
$279$	6248.41	+	2359.07i	1.34080	+	0.506215i
$280$	4558.51	−	1037.68i	0.972940	−	0.221477i
$281$		−	3981.96i		−	0.845351i	−0.906281	−	0.422676i	$-0.861091\pi$
$281$		−	3981.96i		−	0.845351i	0.906281	−	0.422676i	$-0.138909\pi$
$282$	275.997	−	1512.42i	0.0582815	−	0.319373i
$283$	−4092.66	+	4092.66i	−0.859658	+	0.859658i	−0.991298	−	0.131640i	$-0.957976\pi$
$283$	−4092.66	+	4092.66i	−0.859658	+	0.859658i	0.131640	+	0.991298i	$0.457976\pi$
$284$	−889.527			−0.185858
$285$	2848.24	−	123.467i	0.591982	−	0.0256615i
$286$	−967.156			−0.199962
$287$	−5213.93	+	5213.93i	−1.07236	+	1.07236i
$288$	4532.83	−	2048.19i	0.927429	−	0.419064i
$289$			4224.15i			0.859791i
$290$	−2000.40	−	1258.54i	−0.405060	−	0.254842i
$291$	3794.91	+	5489.13i	0.764473	+	1.10577i
$292$	−1449.71	−	1449.71i	−0.290541	−	0.290541i
$293$	4515.35	+	4515.35i	0.900305	+	0.900305i	0.995462	−	0.0951570i	$-0.0303353\pi$
$293$	4515.35	+	4515.35i	0.900305	+	0.900305i	−0.0951570	+	0.995462i	$0.530335\pi$
$294$	−68.8017	−	99.5179i	−0.0136483	−	0.0197415i
$295$	−1810.11	−	7951.77i	−0.357250	−	1.56939i
$296$			3990.14i			0.783521i
$297$	−2076.54	+	3452.42i	−0.405701	+	0.674511i
$298$	431.545	−	431.545i	0.0838883	−	0.0838883i
$299$	1071.18			0.207184
$300$	−887.968	−	3244.48i	−0.170889	−	0.624401i
$301$	1052.58			0.201560
$302$	2474.07	−	2474.07i	0.471413	−	0.471413i
$303$	314.986	−	1726.07i	0.0597210	−	0.327261i
$304$		−	208.678i		−	0.0393701i
$305$	−4.96314	−	21.8029i	−0.000931766	−	0.00409322i
$306$	420.406	−	1113.52i	0.0785393	−	0.208025i
$307$	1831.07	+	1831.07i	0.340406	+	0.340406i	0.856520	−	0.516114i	$-0.172622\pi$
$307$	1831.07	+	1831.07i	0.340406	+	0.340406i	−0.516114	+	0.856520i	$0.672622\pi$
$308$	1986.57	+	1986.57i	0.367517	+	0.367517i
$309$	−5642.63	+	3901.03i	−1.03883	+	0.718194i
$310$	3931.79	+	2473.67i	0.720357	+	0.453210i
$311$		−	4010.21i		−	0.731184i	−0.930775	−	0.365592i	$-0.880866\pi$
$311$		−	4010.21i		−	0.731184i	0.930775	−	0.365592i	$-0.119134\pi$
$312$	−2268.89	−	414.044i	−0.411701	−	0.0751303i
$313$	6072.69	−	6072.69i	1.09664	−	1.09664i	0.101841	−	0.994801i	$-0.467527\pi$
$313$	6072.69	−	6072.69i	1.09664	−	1.09664i	0.994801	−	0.101841i	$-0.0324733\pi$
$314$	2870.63			0.515920
$315$	−4545.85	+	3443.01i	−0.813110	+	0.615847i
$316$	−248.685			−0.0442710
$317$	−3112.10	+	3112.10i	−0.551397	+	0.551397i	−0.926844	−	0.375447i	$-0.877489\pi$
$317$	−3112.10	+	3112.10i	−0.551397	+	0.551397i	0.375447	+	0.926844i	$0.377489\pi$
$318$	−1948.08	−	355.500i	−0.343531	−	0.0626901i
$319$		−	3614.09i		−	0.634326i
$320$	3002.36	−	683.446i	0.524490	−	0.119393i
$321$	3603.70	−	2491.42i	0.626600	−	0.433200i
$322$	1198.53	+	1198.53i	0.207427	+	0.207427i
$323$	−910.737	−	910.737i	−0.156888	−	0.156888i
$324$	−2495.14	+	2833.39i	−0.427836	+	0.485835i
$325$	−830.574	+	2364.89i	−0.141760	+	0.403632i
$326$			1487.10i			0.252647i
$327$	1935.24	−	10604.8i	0.327275	−	1.79342i
$328$	−6109.45	+	6109.45i	−1.02847	+	1.02847i
$329$	3327.71			0.557637
$330$	−1893.68	+	2065.30i	−0.315890	+	0.344518i
$331$	−9589.47			−1.59240			−0.796201	−	0.605033i	$-0.793160\pi$
$331$	−9589.47			−1.59240			−0.796201	+	0.605033i	$0.793160\pi$
$332$	748.099	−	748.099i	0.123666	−	0.123666i
$333$	−2004.10	−	4435.26i	−0.329801	−	0.729883i
$334$		−	7148.90i		−	1.17117i
$335$	−2778.45	+	4416.22i	−0.453144	+	0.720251i
$336$	237.371	+	343.345i	0.0385407	+	0.0557470i
$337$	−2561.34	−	2561.34i	−0.414021	−	0.414021i	0.469115	−	0.883137i	$-0.344573\pi$
$337$	−2561.34	−	2561.34i	−0.414021	−	0.414021i	−0.883137	+	0.469115i	$0.844573\pi$
$338$	−2131.76	−	2131.76i	−0.343054	−	0.343054i
$339$	−1133.29	−	1639.24i	−0.181569	−	0.262630i
$340$	−809.265	+	1286.29i	−0.129084	+	0.205173i
$341$			7103.50i			1.12808i
$342$	−916.377	−	2028.03i	−0.144889	−	0.320653i
$343$	−4396.56	+	4396.56i	−0.692104	+	0.692104i
$344$	1233.36			0.193310
$345$	2097.36	−	2287.44i	0.327299	−	0.356960i
$346$	4368.77			0.678805
$347$	8177.44	−	8177.44i	1.26509	−	1.26509i	0.316503	−	0.948592i	$-0.397491\pi$
$347$	8177.44	−	8177.44i	1.26509	−	1.26509i	0.948592	−	0.316503i	$-0.102509\pi$
$348$	608.005	−	3331.77i	0.0936566	−	0.513223i
$349$			2766.04i			0.424249i	0.977243	+	0.212124i	$0.0680382\pi$
$349$			2766.04i			0.424249i	−0.977243	+	0.212124i	$0.931962\pi$
$350$	−3575.36	+	1716.72i	−0.546032	+	0.262179i
$351$	2729.96	−	679.347i	0.415141	−	0.103307i
$352$	3740.81	+	3740.81i	0.566437	+	0.566437i
$353$	6338.53	+	6338.53i	0.955711	+	0.955711i	0.999060	−	0.0433491i	$-0.0138028\pi$
$353$	6338.53	+	6338.53i	0.955711	+	0.955711i	−0.0433491	+	0.999060i	$0.513803\pi$
$354$	−5236.46	+	3620.23i	−0.786199	+	0.543539i
$355$	1872.43	−	426.233i	0.279939	−	0.0637242i
$356$		−	7339.58i		−	1.09269i
$357$	2534.43	+	462.501i	0.375732	+	0.0685663i
$358$	−975.763	+	975.763i	−0.144052	+	0.144052i
$359$	−8827.47			−1.29776			−0.648880	−	0.760890i	$-0.724762\pi$
$359$	−8827.47			−1.29776			−0.648880	+	0.760890i	$0.724762\pi$
$360$	−5326.63	+	4034.38i	−0.779828	+	0.590640i
$361$	4450.80			0.648899
$362$	−2748.50	+	2748.50i	−0.399055	+	0.399055i
$363$	2588.42	+	472.353i	0.374261	+	0.0682978i
$364$		−	1961.76i		−	0.282484i
$365$	3746.27	+	2356.95i	0.537229	+	0.337996i
$366$	−14.3578	+	9.92628i	−0.00205053	+	0.00141764i
$367$	6191.27	+	6191.27i	0.880605	+	0.880605i	0.993596	−	0.112991i	$-0.0360432\pi$
$367$	6191.27	+	6191.27i	0.880605	+	0.880605i	−0.112991	+	0.993596i	$0.536043\pi$
$368$	−160.628	−	160.628i	−0.0227535	−	0.0227535i
$369$	3722.45	−	9859.55i	0.525157	−	1.39097i
$370$	−751.338	−	3300.60i	−0.105568	−	0.463757i
$371$		−	4286.28i		−	0.599818i
$372$	−1195.04	+	6548.60i	−0.166559	+	0.912713i
$373$	3584.46	−	3584.46i	0.497577	−	0.497577i	−0.413106	−	0.910683i	$-0.635556\pi$
$373$	3584.46	−	3584.46i	0.497577	−	0.497577i	0.910683	+	0.413106i	$0.135556\pi$
$374$	1265.90			0.175022
$375$	3423.80	+	6404.06i	0.471478	+	0.881878i
$376$	3899.27			0.534812
$377$	−1784.48	+	1784.48i	−0.243781	+	0.243781i
$378$	3814.63	+	2294.40i	0.519057	+	0.312200i
$379$		−	7110.48i		−	0.963695i	−0.876255	−	0.481848i	$-0.839966\pi$
$379$		−	7110.48i		−	0.963695i	0.876255	−	0.481848i	$-0.160034\pi$
$380$	630.683	+	2770.57i	0.0851404	+	0.374019i
$381$	441.241	+	638.231i	0.0593319	+	0.0858203i
$382$	−1105.91	−	1105.91i	−0.148124	−	0.148124i
$383$	−1695.77	−	1695.77i	−0.226240	−	0.226240i	0.584880	−	0.811120i	$-0.301142\pi$
$383$	−1695.77	−	1695.77i	−0.226240	−	0.226240i	−0.811120	+	0.584880i	$0.801142\pi$
$384$	2988.11	+	4322.14i	0.397100	+	0.574383i
$385$	−5133.58	−	3229.77i	−0.679562	−	0.427544i
$386$		−	6231.15i		−	0.821650i
$387$	−1370.95	+	619.472i	−0.180076	+	0.0813683i
$388$	−4703.02	+	4703.02i	−0.615361	+	0.615361i
$389$	−12362.2			−1.61128			−0.805640	−	0.592405i	$-0.798178\pi$
$389$	−12362.2			−1.61128			−0.805640	+	0.592405i	$0.798178\pi$
$390$	1954.77	−	84.7362i	0.253804	−	0.0110020i
$391$	−1402.06			−0.181343
$392$	216.978	−	216.978i	0.0279567	−	0.0279567i
$393$	−1846.32	+	10117.5i	−0.236984	+	1.29863i
$394$			7114.22i			0.909668i
$395$	523.476	−	119.162i	0.0666808	−	0.0151790i
$396$	−3756.61	−	1418.30i	−0.476709	−	0.179980i
$397$	−1340.12	−	1340.12i	−0.169417	−	0.169417i	0.617306	−	0.786723i	$-0.288224\pi$
$397$	−1340.12	−	1340.12i	−0.169417	−	0.169417i	−0.786723	+	0.617306i	$0.788224\pi$
$398$	129.999	+	129.999i	0.0163725	+	0.0163725i
$399$	3962.30	−	2739.33i	0.497150	−	0.343705i
$400$	479.171	−	230.076i	0.0598964	−	0.0287595i
$401$			2281.30i			0.284096i	0.989860	+	0.142048i	$0.0453688\pi$
$401$			2281.30i			0.284096i	−0.989860	+	0.142048i	$0.954631\pi$
$402$	4006.72	+	731.175i	0.497107	+	0.0907156i
$403$	3507.40	−	3507.40i	0.433538	−	0.433538i
$404$	1748.75			0.215356
$405$	3894.53	−	7159.80i	0.477829	−	0.878453i
$406$	−3993.26			−0.488133
$407$	3660.29	−	3660.29i	0.445783	−	0.445783i
$408$	2969.74	+	541.939i	0.360352	+	0.0657597i
$409$			4614.82i			0.557917i	0.960303	+	0.278959i	$0.0899892\pi$
$409$			4614.82i			0.557917i	−0.960303	+	0.278959i	$0.910011\pi$
$410$	3903.28	−	6204.08i	0.470169	−	0.747311i
$411$	−3067.32	+	2120.59i	−0.368126	+	0.254504i
$412$	−4834.54	−	4834.54i	−0.578108	−	0.578108i
$413$	−9743.49	−	9743.49i	−1.16089	−	1.16089i
$414$	−2266.43	−	855.683i	−0.269055	−	0.101581i
$415$	−1216.26	+	1933.19i	−0.143865	+	0.228667i
$416$		−	3694.10i		−	0.435380i
$417$	−63.8364	+	349.813i	−0.00749660	+	0.0410801i
$418$	1673.67	−	1673.67i	0.195842	−	0.195842i
$419$	−2142.28			−0.249779			−0.124889	−	0.992171i	$-0.539858\pi$
$419$	−2142.28			−0.249779			−0.124889	+	0.992171i	$0.539858\pi$
$420$	−4189.21	−	3841.11i	−0.486697	−	0.446255i
$421$	−8889.30			−1.02907			−0.514534	−	0.857470i	$-0.672035\pi$
$421$	−8889.30			−1.02907			−0.514534	+	0.857470i	$0.672035\pi$
$422$	−3224.43	+	3224.43i	−0.371950	+	0.371950i
$423$	−4334.26	+	1958.46i	−0.498200	+	0.225115i
$424$		−	5022.48i		−	0.575267i
$425$	1087.13	−	3095.38i	0.124079	−	0.353289i
$426$	−852.466	−	1233.05i	−0.0969534	−	0.140238i
$427$	−26.7156	−	26.7156i	−0.00302778	−	0.00302778i
$428$	3087.60	+	3087.60i	0.348703	+	0.348703i
$429$	1701.52	+	2461.15i	0.191492	+	0.276982i
$430$	−1020.23	+	232.241i	−0.114418	+	0.0260457i
$431$			15707.3i			1.75543i	0.479179	+	0.877717i	$0.340935\pi$
$431$			15707.3i			1.75543i	−0.479179	+	0.877717i	$0.659065\pi$
$432$	−511.238	−	307.497i	−0.0569374	−	0.0342464i
$433$	5430.81	−	5430.81i	0.602744	−	0.602744i	−0.338296	−	0.941040i	$-0.609851\pi$
$433$	5430.81	−	5430.81i	0.602744	−	0.602744i	0.941040	+	0.338296i	$0.109851\pi$
$434$	7848.76			0.868094
$435$	316.644	+	7304.62i	0.0349009	+	0.805126i
$436$	10744.2			1.18016
$437$	−1853.69	+	1853.69i	−0.202915	+	0.202915i
$438$	620.253	−	3398.88i	0.0676640	−	0.370787i
$439$			8221.92i			0.893874i	0.894565	+	0.446937i	$0.147485\pi$
$439$			8221.92i			0.893874i	−0.894565	+	0.446937i	$0.852515\pi$
$440$	−6015.31	−	3784.51i	−0.651747	−	0.410044i
$441$	−132.203	+	350.163i	−0.0142753	+	0.0378105i
$442$	−625.047	−	625.047i	−0.0672635	−	0.0672635i
$443$	−1960.53	−	1960.53i	−0.210265	−	0.210265i	0.594115	−	0.804380i	$-0.297502\pi$
$443$	−1960.53	−	1960.53i	−0.210265	−	0.210265i	−0.804380	+	0.594115i	$0.797502\pi$
$444$	3990.14	−	2758.58i	0.426495	−	0.294857i
$445$	3516.89	+	15449.6i	0.374644	+	1.64580i
$446$			6723.34i			0.713810i
$447$	−1857.38	−	338.948i	−0.196535	−	0.0358651i
$448$	3678.86	−	3678.86i	0.387968	−	0.387968i
$449$	17849.2			1.87607			0.938036	−	0.346537i	$-0.112643\pi$
$449$	17849.2			1.87607			0.938036	+	0.346537i	$0.112643\pi$
$450$	3646.47	−	4340.19i	0.381992	−	0.454664i
$451$	11208.8			1.17029
$452$	1404.49	−	1404.49i	0.146154	−	0.146154i
$453$	−10648.5	−	1943.21i	−1.10443	−	0.201545i
$454$			3323.00i			0.343516i
$455$	940.015	+	4129.46i	0.0968540	+	0.425477i
$456$	4642.85	−	3209.83i	0.476801	−	0.329636i
$457$	−6346.80	−	6346.80i	−0.649652	−	0.649652i	0.303257	−	0.952909i	$-0.401926\pi$
$457$	−6346.80	−	6346.80i	−0.649652	−	0.649652i	−0.952909	+	0.303257i	$0.901926\pi$
$458$	4667.97	+	4667.97i	0.476245	+	0.476245i
$459$	−3573.22	+	889.192i	−0.363363	+	0.0904225i
$460$	2618.08	+	1647.16i	0.265366	+	0.166954i
$461$			8848.20i			0.893930i	0.894552	+	0.446965i	$0.147495\pi$
$461$			8848.20i			0.893930i	−0.894552	+	0.446965i	$0.852505\pi$
$462$	−849.944	+	4657.55i	−0.0855908	+	0.469024i
$463$	1329.43	−	1329.43i	0.133443	−	0.133443i	−0.637230	−	0.770673i	$-0.719920\pi$
$463$	1329.43	−	1329.43i	0.133443	−	0.133443i	0.770673	+	0.637230i	$0.219920\pi$
$464$	535.178			0.0535453
$465$	−622.365	−	14357.3i	−0.0620677	−	1.43183i
$466$	−4704.83			−0.467697
$467$	−1479.96	+	1479.96i	−0.146647	+	0.146647i	−0.776618	−	0.629971i	$-0.783067\pi$
$467$	−1479.96	+	1479.96i	−0.146647	+	0.146647i	0.629971	+	0.776618i	$0.283067\pi$
$468$	1154.56	+	2555.14i	0.114037	+	0.252375i
$469$			8815.81i			0.867966i
$470$	−3225.44	+	734.227i	−0.316550	+	0.0720582i
$471$	−5050.29	−	7304.96i	−0.494066	−	0.714639i
$472$	−11417.0	−	11417.0i	−1.11337	−	1.11337i
$473$	−1131.41	−	1131.41i	−0.109983	−	0.109983i
$474$	−238.324	−	344.723i	−0.0230941	−	0.0334043i
$475$	−2655.14	−	5529.77i	−0.256476	−	0.534155i
$476$			2567.73i			0.247252i
$477$	2522.60	+	5582.76i	0.242143	+	0.535885i
$478$	−3534.73	+	3534.73i	−0.338231	+	0.338231i
$479$	−5039.60			−0.480720			−0.240360	−	0.970684i	$-0.577266\pi$
$479$	−5039.60			−0.480720			−0.240360	+	0.970684i	$0.577266\pi$
$480$	−7888.49	−	7233.00i	−0.750122	−	0.687791i
$481$	−3614.58			−0.342642
$482$	−2179.89	+	2179.89i	−0.205999	+	0.205999i
$483$	941.362	−	5158.51i	0.0886821	−	0.485963i
$484$			2622.43i			0.246284i
$485$	7646.20	−	12153.3i	0.715868	−	1.13784i
$486$	−6318.78	−	743.377i	−0.589765	−	0.0693833i
$487$	1292.93	+	1292.93i	0.120305	+	0.120305i	0.764696	−	0.644391i	$-0.222889\pi$
$487$	1292.93	+	1292.93i	0.120305	+	0.120305i	−0.644391	+	0.764696i	$0.722889\pi$
$488$	−31.3042	−	31.3042i	−0.00290384	−	0.00290384i
$489$	3784.27	−	2616.26i	0.349961	−	0.241945i
$490$	−138.625	+	220.339i	−0.0127805	+	0.0203140i
$491$		−	13865.7i		−	1.27444i	−0.770681	−	0.637221i	$-0.780084\pi$
$491$		−	13865.7i		−	1.27444i	0.770681	−	0.637221i	$-0.219916\pi$
$492$	10333.2	+	1885.68i	0.946865	+	0.172791i
$493$	2335.69	−	2335.69i	0.213375	−	0.213375i
$494$	−1652.77			−0.150530
$495$	8587.17	+	1185.43i	0.779726	+	0.107639i
$496$	−1051.89			−0.0952247
$497$	2294.33	−	2294.33i	0.207072	−	0.207072i
$498$	1753.93	+	320.070i	0.157822	+	0.0288006i
$499$		−	10884.3i		−	0.976453i	−0.872717	−	0.488226i	$-0.837644\pi$
$499$		−	10884.3i		−	0.976453i	0.872717	−	0.488226i	$-0.162356\pi$
$500$	−5666.50	+	4502.86i	−0.506827	+	0.402748i
$501$	−18192.0	+	12577.0i	−1.62227	+	1.12156i
$502$	1831.54	+	1831.54i	0.162840	+	0.162840i
$503$	7880.86	+	7880.86i	0.698589	+	0.698589i	0.964106	−	0.265517i	$-0.0855427\pi$
$503$	7880.86	+	7880.86i	0.698589	+	0.698589i	−0.265517	+	0.964106i	$0.585543\pi$
$504$	−3987.84	+	10562.5i	−0.352445	+	0.933513i
$505$	−3681.07	+	837.946i	−0.324368	+	0.0738379i
$506$		−	2576.58i		−	0.226370i
$507$	−1674.35	+	9175.14i	−0.146667	+	0.803713i
$508$	−546.829	+	546.829i	−0.0477590	+	0.0477590i
$509$	−1788.46			−0.155741			−0.0778704	−	0.996963i	$-0.524812\pi$
$509$	−1788.46			−0.155741			−0.0778704	+	0.996963i	$0.524812\pi$
$510$	−2558.58	+	110.911i	−0.222149	+	0.00962981i
$511$	7478.42			0.647408
$512$	−1086.41	+	1086.41i	−0.0937754	+	0.0937754i
$513$	−3548.60	+	5899.84i	−0.305409	+	0.507766i
$514$			1018.67i			0.0874153i
$515$	12493.1	+	7860.01i	1.06896	+	0.672531i
$516$	−852.686	−	1233.36i	−0.0727469	−	0.105224i
$517$	−3576.93	−	3576.93i	−0.304281	−	0.304281i
$518$	−4044.31	−	4044.31i	−0.343044	−	0.343044i
$519$	−7685.96	−	11117.3i	−0.650051	−	0.940263i
$520$	1101.47	+	4838.72i	0.0928896	+	0.408061i
$521$		−	18251.6i		−	1.53478i	−0.641183	−	0.767388i	$-0.721556\pi$
$521$		−	18251.6i		−	1.53478i	0.641183	−	0.767388i	$-0.278444\pi$
$522$	5201.11	−	2350.15i	0.436104	−	0.197056i
$523$	−2125.69	+	2125.69i	−0.177725	+	0.177725i	−0.790363	−	0.612639i	$-0.790108\pi$
$523$	−2125.69	+	2125.69i	−0.177725	+	0.177725i	0.612639	+	0.790363i	$0.290108\pi$
$524$	−10250.5			−0.854570
$525$	10658.7	+	6078.09i	0.886066	+	0.505276i
$526$	12487.1			1.03510
$527$	−4590.80	+	4590.80i	−0.379466	+	0.379466i
$528$	113.910	−	624.207i	0.00938880	−	0.0514491i
$529$		−	9313.29i		−	0.765455i
$530$	945.725	+	4154.54i	0.0775088	+	0.340494i
$531$	18425.0	+	6956.30i	1.50579	+	0.568508i
$532$	3394.85	+	3394.85i	0.276664	+	0.276664i
$533$	−5534.42	−	5534.42i	−0.449761	−	0.449761i
$534$	10174.0	−	7033.79i	0.824478	−	0.570003i
$535$	−7978.81	−	5019.84i	−0.644774	−	0.405657i
$536$			10330.0i			0.832439i
$537$	4199.71	+	766.393i	0.337488	+	0.0615872i
$538$	−2292.60	+	2292.60i	−0.183719	+	0.183719i
$539$	−398.082			−0.0318119
$540$	7716.94	+	2537.47i	0.614971	+	0.202213i
$541$	−2214.16			−0.175960			−0.0879798	−	0.996122i	$-0.528041\pi$
$541$	−2214.16			−0.175960			−0.0879798	+	0.996122i	$0.528041\pi$
$542$	3873.77	−	3873.77i	0.306998	−	0.306998i
$543$	11829.6	+	2158.75i	0.934911	+	0.170609i
$544$			4835.17i			0.381078i
$545$	−22616.2	+	5148.26i	−1.77756	+	0.404637i
$546$	2719.36	−	1880.03i	0.213146	−	0.147359i
$547$	12385.1	+	12385.1i	0.968098	+	0.968098i	0.999507	−	0.0314090i	$-0.00999944\pi$
$547$	12385.1	+	12385.1i	0.968098	+	0.968098i	−0.0314090	+	0.999507i	$0.509999\pi$
$548$	−2628.04	−	2628.04i	−0.204862	−	0.204862i
$549$	50.5193	+	19.0735i	0.00392735	+	0.00148276i
$550$	5688.42	+	1997.84i	0.441009	+	0.154887i
$551$		−	6176.11i		−	0.477516i
$552$	1103.05	−	6044.52i	0.0850522	−	0.466072i
$553$	641.427	−	641.427i	0.0493242	−	0.0493242i
$554$	−11557.3			−0.886324
$555$	−7077.31	+	7718.69i	−0.541288	+	0.590343i
$556$	−354.410			−0.0270329
$557$	8716.96	−	8716.96i	0.663105	−	0.663105i	−0.293006	−	0.956111i	$-0.594656\pi$
$557$	8716.96	−	8716.96i	0.663105	−	0.663105i	0.956111	+	0.293006i	$0.0946555\pi$
$558$	−10222.8	+	4619.23i	−0.775566	+	0.350444i
$559$			1117.28i			0.0845363i
$560$	478.268	−	760.186i	0.0360902	−	0.0573638i
$561$	−2227.10	−	3221.38i	−0.167608	−	0.242436i
$562$	4729.23	+	4729.23i	0.354965	+	0.354965i
$563$	11697.0	+	11697.0i	0.875615	+	0.875615i	0.993077	−	0.117462i	$-0.0374759\pi$
$563$	11697.0	+	11697.0i	0.875615	+	0.875615i	−0.117462	+	0.993077i	$0.537476\pi$
$564$	−2695.76	−	3899.27i	−0.201262	−	0.291115i
$565$	−2283.42	+	3629.39i	−0.170025	+	0.270247i
$566$		−	9721.40i		−	0.721945i
$567$	−872.435	−	13743.7i	−0.0646188	−	1.01796i
$568$	2688.40	−	2688.40i	0.198596	−	0.198596i
$569$	11517.5			0.848576			0.424288	−	0.905527i	$-0.360524\pi$
$569$	11517.5			0.848576			0.424288	+	0.905527i	$0.360524\pi$
$570$	−3236.11	+	3529.38i	−0.237799	+	0.259350i
$571$	−11093.9			−0.813072			−0.406536	−	0.913635i	$-0.633263\pi$
$571$	−11093.9			−0.813072			−0.406536	+	0.913635i	$0.633263\pi$
$572$	−2108.68	+	2108.68i	−0.154141	+	0.154141i
$573$	−868.617	+	4759.88i	−0.0633281	+	0.347027i
$574$		−	12384.8i		−	0.900577i
$575$	−6300.25	−	2212.72i	−0.456937	−	0.160481i
$576$	−2626.50	+	6956.73i	−0.189995	+	0.503236i
$577$	−14119.4	−	14119.4i	−1.01871	−	1.01871i	−0.999822	−	0.0188920i	$-0.993986\pi$
$577$	−14119.4	−	14119.4i	−1.01871	−	1.01871i	−0.0188920	−	0.999822i	$-0.506014\pi$
$578$	−5016.87	−	5016.87i	−0.361028	−	0.361028i
$579$	−15856.6	+	10962.4i	−1.13813	+	0.786846i
$580$	−7105.44	+	1617.46i	−0.508685	+	0.115795i
$581$			3859.10i			0.275564i
$582$	−11026.3	−	2012.16i	−0.785320	−	0.143311i
$583$	−4607.29	+	4607.29i	−0.327297	+	0.327297i
$584$	8762.89			0.620909
$585$	−3654.65	−	4825.28i	−0.258293	−	0.341027i
$586$	−10725.4			−0.756081
$587$	8524.33	−	8524.33i	0.599381	−	0.599381i	−0.340767	−	0.940148i	$-0.610687\pi$
$587$	8524.33	−	8524.33i	0.599381	−	0.599381i	0.940148	+	0.340767i	$0.110687\pi$
$588$	−366.986	−	66.9702i	−0.0257385	−	0.00469695i
$589$			12139.2i			0.849211i
$590$	11593.8	+	7294.23i	0.809001	+	0.508981i
$591$	18103.8	−	12516.0i	1.26005	−	0.871135i
$592$	542.020	+	542.020i	0.0376298	+	0.0376298i
$593$	−4580.53	−	4580.53i	−0.317200	−	0.317200i	0.530491	−	0.847691i	$-0.322008\pi$
$593$	−4580.53	−	4580.53i	−0.317200	−	0.317200i	−0.847691	+	0.530491i	$0.822008\pi$
$594$	−1634.08	−	6566.55i	−0.112874	−	0.453584i
$595$	−1230.38	−	5405.01i	−0.0847740	−	0.372410i
$596$		−	1881.79i		−	0.129331i
$597$	102.105	−	559.518i	0.00699979	−	0.0383577i
$598$	−1272.20	+	1272.20i	−0.0869971	+	0.0869971i
$599$	−10195.8			−0.695477			−0.347738	−	0.937592i	$-0.613050\pi$
$599$	−10195.8			−0.695477			−0.347738	+	0.937592i	$0.613050\pi$
$600$	12489.4	+	7122.05i	0.849798	+	0.484594i
$601$	18915.8			1.28385			0.641923	−	0.766769i	$-0.278137\pi$
$601$	18915.8			1.28385			0.641923	+	0.766769i	$0.278137\pi$
$602$	−1250.11	+	1250.11i	−0.0846355	+	0.0846355i
$603$	−5188.36	−	11482.4i	−0.350392	−	0.775452i
$604$		−	10788.4i		−	0.726778i
$605$	−1256.59	−	5520.14i	−0.0844421	−	0.370952i
$606$	1675.89	+	2424.09i	0.112341	+	0.162495i
$607$	12758.2	+	12758.2i	0.853113	+	0.853113i	0.990515	−	0.137402i	$-0.0438753\pi$
$607$	12758.2	+	12758.2i	0.853113	+	0.853113i	−0.137402	+	0.990515i	$0.543875\pi$
$608$	6392.67	+	6392.67i	0.426409	+	0.426409i
$609$	7025.33	+	10161.8i	0.467456	+	0.676149i
$610$	31.7891	+	20.0000i	0.00211000	+	0.00132750i
$611$			3532.26i			0.233879i
$612$	−1511.19	−	3344.41i	−0.0998140	−	0.220898i
$613$	7340.02	−	7340.02i	0.483622	−	0.483622i	−0.422664	−	0.906286i	$-0.638905\pi$
$613$	7340.02	−	7340.02i	0.483622	−	0.483622i	0.906286	+	0.422664i	$0.138905\pi$
$614$	−4349.39			−0.285875
$615$	−22654.7	+	982.047i	−1.48541	+	0.0643902i
$616$	−12007.9			−0.785412
$617$	−17118.9	+	17118.9i	−1.11698	+	1.11698i	−0.124803	+	0.992182i	$0.539830\pi$
$617$	−17118.9	+	17118.9i	−1.11698	+	1.11698i	−0.992182	+	0.124803i	$0.960170\pi$
$618$	2068.43	−	11334.7i	0.134635	−	0.737778i
$619$			3176.16i			0.206237i	0.994669	+	0.103118i	$0.0328820\pi$
$619$			3176.16i			0.206237i	−0.994669	+	0.103118i	$0.967118\pi$
$620$	13965.8	−	3179.12i	0.904644	−	0.205930i
$621$	1809.84	+	7272.84i	0.116950	+	0.469966i
$622$	4762.79	+	4762.79i	0.307026	+	0.307026i
$623$	18930.8	+	18930.8i	1.21741	+	1.21741i
$624$	−364.450	+	251.962i	−0.0233809	+	0.0161644i
$625$	9770.20	−	12193.6i	0.625293	−	0.780390i
$626$			14424.6i			0.920965i
$627$	−7203.53	−	1314.55i	−0.458822	−	0.0837291i
$628$	6258.80	−	6258.80i	0.397697	−	0.397697i
$629$	4731.09			0.299906
$630$	1309.80	−	9488.09i	0.0828312	−	0.600023i
$631$	−11467.2			−0.723459			−0.361729	−	0.932283i	$-0.617814\pi$
$631$	−11467.2			−0.723459			−0.361729	+	0.932283i	$0.617814\pi$
$632$	751.597	−	751.597i	0.0473052	−	0.0473052i
$633$	13878.0	+	2532.57i	0.871410	+	0.159021i
$634$		−	7392.26i		−	0.463066i
$635$	889.036	−	1413.08i	0.0555596	−	0.0883094i
$636$	−5022.48	+	3472.29i	−0.313136	+	0.216486i
$637$	196.556	+	196.556i	0.0122258	+	0.0122258i
$638$	4292.32	+	4292.32i	0.266355	+	0.266355i
$639$	−1638.02	+	4338.59i	−0.101407	+	0.268595i
$640$	6020.60	−	9569.47i	0.371852	−	0.591042i
$641$			12383.2i			0.763035i	0.924362	+	0.381518i	$0.124598\pi$
$641$			12383.2i			0.763035i	−0.924362	+	0.381518i	$0.875402\pi$
$642$	−1321.02	+	7238.95i	−0.0812092	+	0.445013i
$643$	−11142.9	+	11142.9i	−0.683413	+	0.683413i	−0.960768	−	0.277354i	$-0.910542\pi$
$643$	−11142.9	+	11142.9i	−0.683413	+	0.683413i	0.277354	+	0.960768i	$0.410542\pi$
$644$	5226.29			0.319790
$645$	2385.87	+	2187.62i	0.145649	+	0.133546i
$646$	2163.30			0.131755
$647$	−2391.21	+	2391.21i	−0.145299	+	0.145299i	−0.776014	−	0.630716i	$-0.782761\pi$
$647$	−2391.21	+	2391.21i	−0.145299	+	0.145299i	0.630716	+	0.776014i	$0.282761\pi$
$648$	−1022.28	−	16104.3i	−0.0619738	−	0.976292i
$649$			20946.4i			1.26690i
$650$	−1822.25	−	3795.13i	−0.109961	−	0.229011i
$651$	−13808.3	−	19973.0i	−0.831322	−	1.20246i
$652$	3242.32	+	3242.32i	0.194753	+	0.194753i
$653$	−16623.3	−	16623.3i	−0.996201	−	0.996201i	0.00379136	−	0.999993i	$-0.498793\pi$
$653$	−16623.3	−	16623.3i	−0.996201	−	0.996201i	−0.999993	+	0.00379136i	$0.998793\pi$
$654$	10296.5	+	14893.4i	0.615636	+	0.890484i
$655$	21577.0	−	4911.71i	1.28715	−	0.293002i
$656$			1659.81i			0.0987878i
$657$	−9740.43	+	4401.27i	−0.578403	+	0.261354i
$658$	−3952.20	+	3952.20i	−0.234153	+	0.234153i
$659$	20089.8			1.18754			0.593768	−	0.804636i	$-0.297640\pi$
$659$	20089.8			1.18754			0.593768	+	0.804636i	$0.297640\pi$
$660$	374.172	+	8631.73i	0.0220676	+	0.509075i
$661$	541.434			0.0318598			0.0159299	−	0.999873i	$-0.494929\pi$
$661$	541.434			0.0318598			0.0159299	+	0.999873i	$0.494929\pi$
$662$	11389.1	−	11389.1i	0.668654	−	0.668654i
$663$	−490.931	+	2690.22i	−0.0287574	+	0.157586i
$664$			4521.93i			0.264284i
$665$	−8772.76	−	5519.36i	−0.511569	−	0.321852i
$666$	7647.80	+	2887.41i	0.444964	+	0.167995i
$667$	−4753.99	−	4753.99i	−0.275975	−	0.275975i
$668$	−15586.7	−	15586.7i	−0.902796	−	0.902796i
$669$	17109.1	−	11828.3i	0.988751	−	0.683573i
$670$	−1945.12	−	8544.86i	−0.112159	−	0.492711i
$671$			57.4328i			0.00330428i
$672$	−17789.7	−	3246.40i	−1.02121	−	0.186358i
$673$	−24314.3	+	24314.3i	−1.39264	+	1.39264i	−0.573288	+	0.819354i	$0.694332\pi$
$673$	−24314.3	+	24314.3i	−1.39264	+	1.39264i	−0.819354	+	0.573288i	$0.805668\pi$
$674$	6084.03			0.347697
$675$	−17459.8	−	1643.58i	−0.995599	−	0.0937207i
$676$	−9295.71			−0.528887
$677$	−14662.4	+	14662.4i	−0.832380	+	0.832380i	−0.987842	−	0.155462i	$-0.950313\pi$
$677$	−14662.4	+	14662.4i	−0.832380	+	0.832380i	0.155462	+	0.987842i	$0.450313\pi$
$678$	3292.84	+	600.902i	0.186520	+	0.0340376i
$679$		−	24260.8i		−	1.37120i
$680$	−1441.70	−	6333.36i	−0.0813041	−	0.357166i
$681$	8456.13	−	5846.14i	0.475829	−	0.328964i
$682$	−8436.57	−	8436.57i	−0.473685	−	0.473685i
$683$	−15981.2	−	15981.2i	−0.895320	−	0.895320i	0.0996976	−	0.995018i	$-0.468212\pi$
$683$	−15981.2	−	15981.2i	−0.895320	−	0.895320i	−0.995018	+	0.0996976i	$0.968212\pi$
$684$	−6419.67	−	2423.73i	−0.358863	−	0.135488i
$685$	6791.23	+	4272.68i	0.378803	+	0.238322i
$686$		−	10443.3i		−	0.581233i
$687$	3666.36	−	20091.1i	0.203611	−	1.11575i
$688$	167.540	−	167.540i	0.00928400	−	0.00928400i
$689$	4549.75			0.251570
$690$	225.744	+	5207.66i	0.0124550	+	0.287322i
$691$	−16714.9			−0.920209			−0.460105	−	0.887865i	$-0.652188\pi$
$691$	−16714.9			−0.920209			−0.460105	+	0.887865i	$0.652188\pi$
$692$	9525.19	−	9525.19i	0.523256	−	0.523256i
$693$	13347.5	−	6031.14i	0.731645	−	0.330598i
$694$			19424.1i			1.06243i
$695$	746.023	−	169.822i	0.0407169	−	0.00926865i
$696$	8231.98	+	11907.1i	0.448322	+	0.648474i
$697$	7243.96	+	7243.96i	0.393665	+	0.393665i
$698$	−3285.13	−	3285.13i	−0.178143	−	0.178143i
$699$	8277.19	+	11972.5i	0.447886	+	0.647842i
$700$	−4052.37	+	11538.3i	−0.218808	+	0.623009i
$701$			6990.49i			0.376643i	0.982107	+	0.188322i	$0.0603048\pi$
$701$			6990.49i			0.376643i	−0.982107	+	0.188322i	$0.939695\pi$
$702$	−2435.44	+	4049.11i	−0.130940	+	0.217698i
$703$	6255.06	−	6255.06i	0.335582	−	0.335582i
$704$	−7908.75			−0.423398
$705$	7542.91	+	6916.13i	0.402954	+	0.369470i
$706$	−15056.1			−0.802611
$707$	−4510.51	+	4510.51i	−0.239936	+	0.239936i
$708$	−3523.86	+	19310.2i	−0.187055	+	1.02503i
$709$		−	28175.0i		−	1.49243i	−0.665705	−	0.746215i	$-0.731869\pi$
$709$		−	28175.0i		−	1.49243i	0.665705	−	0.746215i	$-0.268131\pi$
$710$	−1717.60	+	2730.04i	−0.0907890	+	0.144305i
$711$	−457.943	+	1212.94i	−0.0241550	+	0.0639787i
$712$	22182.3	+	22182.3i	1.16758	+	1.16758i
$713$	9343.99	+	9343.99i	0.490793	+	0.490793i
$714$	−3559.35	+	2460.75i	−0.186562	+	0.128980i
$715$	3428.31	−	5449.13i	0.179317	−	0.285015i
$716$			4254.90i			0.222085i
$717$	15213.6	+	2776.28i	0.792414	+	0.144605i
$718$	10484.1	−	10484.1i	0.544933	−	0.544933i
$719$	−20143.8			−1.04484			−0.522418	−	0.852690i	$-0.674970\pi$
$719$	−20143.8			−1.04484			−0.522418	+	0.852690i	$0.674970\pi$
$720$	−175.540	+	1271.60i	−0.00908609	+	0.0658189i
$721$	24939.2			1.28819
$722$	−5286.05	+	5286.05i	−0.272474	+	0.272474i
$723$	9382.32	+	1712.15i	0.482617	+	0.0880715i
$724$			11985.0i			0.615222i
$725$	14181.7	−	6809.41i	0.726477	−	0.348821i
$726$	−3635.16	+	2513.17i	−0.185831	+	0.128475i
$727$	−9805.90	−	9805.90i	−0.500249	−	0.500249i	0.411267	−	0.911515i	$-0.365087\pi$
$727$	−9805.90	−	9805.90i	−0.500249	−	0.500249i	−0.911515	+	0.411267i	$0.865087\pi$
$728$	5929.00	+	5929.00i	0.301845	+	0.301845i
$729$	9224.92	+	17387.4i	0.468674	+	0.883371i
$730$	−7248.57	+	1650.04i	−0.367509	+	0.0836585i
$731$		−	1462.39i		−	0.0739926i
$732$	−9.66205	+	52.9464i	−0.000487868	+	0.00267344i
$733$	16533.1	−	16533.1i	0.833100	−	0.833100i	−0.154840	−	0.987940i	$-0.549486\pi$
$733$	16533.1	−	16533.1i	0.833100	−	0.833100i	0.987940	+	0.154840i	$0.0494861\pi$
$734$	−14706.3			−0.739536
$735$	804.585	−	34.8775i	0.0403776	−	0.00175031i
$736$	9841.37			0.492877
$737$	9476.04	−	9476.04i	0.473615	−	0.473615i
$738$	7288.81	+	16130.8i	0.363557	+	0.804586i
$739$		−	15250.1i		−	0.759114i	−0.925168	−	0.379557i	$-0.876076\pi$
$739$		−	15250.1i		−	0.759114i	0.925168	−	0.379557i	$-0.123924\pi$
$740$	−8834.41	−	5558.14i	−0.438864	−	0.276110i
$741$	2907.72	+	4205.85i	0.144153	+	0.208510i
$742$	5090.66	+	5090.66i	0.251865	+	0.251865i
$743$	−5438.49	−	5438.49i	−0.268531	−	0.268531i	0.559977	−	0.828508i	$-0.310810\pi$
$743$	−5438.49	−	5438.49i	−0.268531	−	0.268531i	−0.828508	+	0.559977i	$0.810810\pi$
$744$	−16180.0	−	23403.5i	−0.797294	−	1.15324i
$745$	901.693	+	3961.11i	0.0443429	+	0.194797i
$746$			8514.27i			0.417868i
$747$	−2271.20	−	5026.38i	−0.111243	−	0.246192i
$748$	2760.04	−	2760.04i	0.134916	−	0.134916i
$749$	−15927.5			−0.777009
$750$	−11672.2	−	3539.54i	−0.568278	−	0.172328i
$751$	2087.82			0.101446			0.0507228	−	0.998713i	$-0.483848\pi$
$751$	2087.82			0.101446			0.0507228	+	0.998713i	$0.483848\pi$
$752$	529.676	−	529.676i	0.0256852	−	0.0256852i
$753$	1438.55	−	7883.01i	0.0696197	−	0.381505i
$754$		−	4238.72i		−	0.204728i
$755$	5169.46	+	22709.3i	0.249187	+	1.09467i
$756$	13319.5	−	3314.54i	0.640774	−	0.159456i
$757$	−10258.6	−	10258.6i	−0.492546	−	0.492546i	0.416562	−	0.909107i	$-0.363235\pi$
$757$	−10258.6	−	10258.6i	−0.492546	−	0.492546i	−0.909107	+	0.416562i	$0.863235\pi$
$758$	8444.86	+	8444.86i	0.404658	+	0.404658i
$759$	−6556.70	+	4532.98i	−0.313561	+	0.216781i
$760$	−10279.5	−	6467.35i	−0.490629	−	0.308678i
$761$		−	26879.5i		−	1.28040i	−0.768210	−	0.640198i	$-0.778852\pi$
$761$		−	26879.5i		−	1.28040i	0.768210	−	0.640198i	$-0.221148\pi$
$762$	−1282.05	−	233.958i	−0.0609498	−	0.0111226i
$763$	−27712.1	+	27712.1i	−1.31487	+	1.31487i
$764$	−4822.43			−0.228363
$765$	4783.54	+	6315.77i	0.226078	+	0.298493i
$766$	4028.02			0.189998
$767$	10342.4	−	10342.4i	0.486888	−	0.486888i
$768$	−19944.6	−	3639.64i	−0.937097	−	0.171008i
$769$			25180.9i			1.18082i	0.807105	+	0.590408i	$0.201033\pi$
$769$			25180.9i			1.18082i	−0.807105	+	0.590408i	$0.798967\pi$
$770$	9932.85	−	2261.08i	0.464877	−	0.105823i
$771$	2592.23	−	1792.14i	0.121085	−	0.0837124i
$772$	−13585.7	−	13585.7i	−0.633369	−	0.633369i
$773$	18871.2	+	18871.2i	0.878072	+	0.878072i	0.993335	−	0.115263i	$-0.0367711\pi$
$773$	18871.2	+	18871.2i	0.878072	+	0.878072i	−0.115263	+	0.993335i	$0.536771\pi$
$774$	892.506	−	2363.96i	0.0414476	−	0.109781i
$775$	−27874.2	+	13383.9i	−1.29196	+	0.620341i
$776$		−	28427.7i		−	1.31507i
$777$	−3176.52	+	17406.8i	−0.146663	+	0.803688i
$778$	14682.1	−	14682.1i	0.676581	−	0.676581i
$779$	19154.7			0.880988
$780$	4077.22	−	4446.72i	0.187164	−	0.204126i
$781$	−4932.32			−0.225982
$782$	1665.18	−	1665.18i	0.0761465	−	0.0761465i
$783$	−15130.8	−	9100.79i	−0.690588	−	0.415371i
$784$		−	58.9485i		−	0.00268533i
$785$	−10175.6	+	16173.6i	−0.462653	+	0.735365i
$786$	−9823.43	−	14209.0i	−0.445789	−	0.644809i
$787$	14716.0	+	14716.0i	0.666542	+	0.666542i	0.956914	−	0.290372i	$-0.0937789\pi$
$787$	14716.0	+	14716.0i	0.666542	+	0.666542i	−0.290372	+	0.956914i	$0.593779\pi$
$788$	15511.1	+	15511.1i	0.701217	+	0.701217i
$789$	−21968.5	−	31776.2i	−0.991253	−	1.43379i
$790$	−480.189	+	763.238i	−0.0216258	+	0.0343731i
$791$			7245.10i			0.325672i
$792$	15640.0	−	7067.03i	0.701697	−	0.317066i
$793$	28.3578	−	28.3578i	0.00126988	−	0.00126988i
$794$	3183.22			0.142277
$795$	8908.37	−	9715.69i	0.397418	−	0.433434i
$796$	566.871			0.0252415
$797$	17463.9	−	17463.9i	0.776163	−	0.776163i	−0.203013	−	0.979176i	$-0.565073\pi$
$797$	17463.9	−	17463.9i	0.776163	−	0.776163i	0.979176	+	0.203013i	$0.0650735\pi$
$798$	−1452.47	+	7959.28i	−0.0644321	+	0.353077i
$799$		−	4623.35i		−	0.204709i
$800$	−7630.82	+	21727.2i	−0.337238	+	0.960214i
$801$	−35798.1	−	13515.5i	−1.57911	−	0.596188i
$802$	−2709.42	−	2709.42i	−0.119293	−	0.119293i
$803$	−8038.49	−	8038.49i	−0.353265	−	0.353265i
$804$	10330.0	−	7141.64i	0.453122	−	0.313266i
$805$	−11001.2	+	2504.28i	−0.481667	+	0.109645i
$806$			8331.22i			0.364088i
$807$	9867.40	+	1800.68i	0.430420	+	0.0785462i
$808$	−5285.22	+	5285.22i	−0.230115	+	0.230115i
$809$	−24097.9			−1.04727			−0.523633	−	0.851944i	$-0.675424\pi$
$809$	−24097.9			−1.04727			−0.523633	+	0.851944i	$0.675424\pi$
$810$	3878.04	+	13128.8i	0.168223	+	0.569506i
$811$	25302.7			1.09556			0.547780	−	0.836622i	$-0.315473\pi$
$811$	25302.7			1.09556			0.547780	+	0.836622i	$0.315473\pi$
$812$	−8706.47	+	8706.47i	−0.376277	+	0.376277i
$813$	−16672.8	−	3042.57i	−0.719238	−	0.131252i
$814$			8694.39i			0.374371i
$815$	−8378.61	−	5271.38i	−0.360110	−	0.226562i
$816$	477.025	−	329.791i	0.0204647	−	0.0141483i
$817$	−1933.46	−	1933.46i	−0.0827945	−	0.0827945i
$818$	−5480.85	−	5480.85i	−0.234271	−	0.234271i
$819$	−9568.33	−	3612.50i	−0.408235	−	0.154128i
$820$	−5016.42	−	22037.0i	−0.213635	−	0.938494i
$821$			27925.3i			1.18709i	0.804802	+	0.593544i	$0.202272\pi$
$821$			27925.3i			1.18709i	−0.804802	+	0.593544i	$0.797728\pi$
$822$	1124.39	−	6161.50i	0.0477102	−	0.261444i
$823$	997.907	−	997.907i	0.0422659	−	0.0422659i	−0.685658	−	0.727924i	$-0.740485\pi$
$823$	997.907	−	997.907i	0.0422659	−	0.0422659i	0.727924	+	0.685658i	$0.240485\pi$
$824$	29222.6			1.23546
$825$	−4923.67	−	17990.3i	−0.207782	−	0.759200i
$826$	23144.0			0.974918
$827$	−18683.3	+	18683.3i	−0.785590	+	0.785590i	−0.980768	−	0.195178i	$-0.937471\pi$
$827$	−18683.3	+	18683.3i	−0.785590	+	0.785590i	0.195178	+	0.980768i	$0.437471\pi$
$828$	−6807.11	+	3075.83i	−0.285705	+	0.129097i
$829$		−	21146.9i		−	0.885962i	−0.896531	−	0.442981i	$-0.853921\pi$
$829$		−	21146.9i		−	0.885962i	0.896531	−	0.442981i	$-0.146079\pi$
$830$	−851.473	−	3740.49i	−0.0356085	−	0.156427i
$831$	20332.8	+	29410.2i	0.848780	+	1.22771i
$832$	3904.99	+	3904.99i	0.162718	+	0.162718i
$833$	−257.270	−	257.270i	−0.0107009	−	0.0107009i
$834$	−339.644	−	491.276i	−0.0141018	−	0.0203975i
$835$	40278.2	+	25340.9i	1.66932	+	1.05025i
$836$		−	7298.19i		−	0.301930i
$837$	29739.6	+	17887.6i	1.22814	+	0.738695i
$838$	2544.31	−	2544.31i	0.104883	−	0.104883i
$839$	30903.4			1.27164			0.635820	−	0.771838i	$-0.280662\pi$
$839$	30903.4			1.27164			0.635820	+	0.771838i	$0.280662\pi$
$840$	24269.9	−	1052.06i	0.996894	−	0.0432138i
$841$	−8549.68			−0.350555
$842$	10557.5	−	10557.5i	0.432109	−	0.432109i
$843$	3714.48	−	20354.7i	0.151760	−	0.831618i
$844$			14060.4i			0.573435i
$845$	19567.2	−	4454.21i	0.796607	−	0.181337i
$846$	2821.65	−	7473.63i	0.114669	−	0.303722i
$847$	−6763.96	−	6763.96i	−0.274395	−	0.274395i
$848$	−682.252	−	682.252i	−0.0276281	−	0.0276281i
$849$	−24738.3	+	17102.8i	−1.00002	+	0.691364i
$850$	2385.12	+	4967.42i	0.0962460	+	0.200448i
$851$		−	9629.53i		−	0.387892i
$852$	−4547.02	−	829.774i	−0.182839	−	0.0333657i
$853$	181.224	−	181.224i	0.00727432	−	0.00727432i	−0.703460	−	0.710735i	$-0.748363\pi$
$853$	181.224	−	181.224i	0.00727432	−	0.00727432i	0.710735	+	0.703460i	$0.248363\pi$
$854$	63.4584			0.00254274
$855$	14674.6	+	2025.78i	0.586971	+	0.0810295i
$856$	−18663.2			−0.745205
$857$	−13852.9	+	13852.9i	−0.552167	+	0.552167i	−0.927066	−	0.374899i	$-0.877677\pi$
$857$	−13852.9	+	13852.9i	−0.552167	+	0.552167i	0.374899	+	0.927066i	$0.377677\pi$
$858$	−4943.85	−	902.189i	−0.196713	−	0.0358977i
$859$			8910.47i			0.353925i	0.984218	+	0.176962i	$0.0566271\pi$
$859$			8910.47i			0.353925i	−0.984218	+	0.176962i	$0.943373\pi$
$860$	−1718.04	+	2730.74i	−0.0681216	+	0.108276i
$861$	−31515.9	+	21788.5i	−1.24746	+	0.862428i
$862$	−18655.0	−	18655.0i	−0.737112	−	0.737112i
$863$	−6487.75	−	6487.75i	−0.255905	−	0.255905i	0.567481	−	0.823386i	$-0.307918\pi$
$863$	−6487.75	−	6487.75i	−0.255905	−	0.255905i	−0.823386	+	0.567481i	$0.807918\pi$
$864$	25081.2	−	6241.43i	0.987594	−	0.245761i
$865$	−15486.1	+	24614.4i	−0.608720	+	0.967533i
$866$			12900.0i			0.506187i
$867$	−3940.40	+	21592.8i	−0.154352	+	0.845823i
$868$	17112.6	−	17112.6i	0.669170	−	0.669170i
$869$	−1378.93			−0.0538285
$870$	−9051.50	−	8299.37i	−0.352729	−	0.323419i
$871$	−9357.71			−0.364034
$872$	−32471.9	+	32471.9i	−1.26105	+	1.26105i
$873$	14278.2	+	31599.0i	0.553543	+	1.22504i
$874$		−	4403.12i		−	0.170409i
$875$	3001.35	−	26229.5i	0.115959	−	1.01339i
$876$	−6058.22	−	8762.89i	−0.233662	−	0.337980i
$877$	−20231.6	−	20231.6i	−0.778987	−	0.778987i	0.200672	−	0.979659i	$-0.435688\pi$
$877$	−20231.6	−	20231.6i	−0.778987	−	0.778987i	−0.979659	+	0.200672i	$0.935688\pi$
$878$	−9764.88	−	9764.88i	−0.375340	−	0.375340i
$879$	18869.2	+	27293.3i	0.724054	+	1.04730i
$880$	−1331.20	+	303.031i	−0.0509942	+	0.0116081i
$881$		−	33209.0i		−	1.26996i	−0.772527	−	0.634982i	$-0.781007\pi$
$881$		−	33209.0i		−	1.26996i	0.772527	−	0.634982i	$-0.218993\pi$
$882$	−258.863	−	572.889i	−0.00988251	−	0.0218709i
$883$	26984.3	−	26984.3i	1.02842	−	1.02842i	0.0288331	−	0.999584i	$-0.490821\pi$
$883$	26984.3	−	26984.3i	1.02842	−	1.02842i	0.999584	−	0.0288331i	$-0.00917914\pi$
$884$	−2725.57			−0.103700
$885$	−1835.19	−	42335.9i	−0.0697055	−	1.60803i
$886$	4656.90			0.176582
$887$	24008.9	−	24008.9i	0.908838	−	0.908838i	−0.0873406	−	0.996179i	$-0.527837\pi$
$887$	24008.9	−	24008.9i	0.908838	−	0.908838i	0.996179	+	0.0873406i	$0.0278369\pi$
$888$	−3722.11	+	20396.5i	−0.140660	+	0.770792i
$889$		−	2820.84i		−	0.106421i
$890$	−22525.8	−	14172.1i	−0.848390	−	0.533762i
$891$	−13835.3	+	15710.8i	−0.520200	+	0.590720i
$892$	14658.8	+	14658.8i	0.550240	+	0.550240i
$893$	−6112.61	−	6112.61i	−0.229060	−	0.229060i
$894$	2608.50	−	1803.39i	0.0975853	−	0.0674656i
$895$	−2038.81	−	8956.44i	−0.0761452	−	0.334504i
$896$		−	19102.9i		−	0.712258i
$897$	5475.59	+	999.226i	0.203818	+	0.0371942i
$898$	−21198.9	+	21198.9i	−0.787768	+	0.787768i
$899$	−31132.2			−1.15497
$900$	−1512.52	−	17413.3i	−0.0560191	−	0.644935i
$901$	−5955.13			−0.220193
$902$	−13312.3	+	13312.3i	−0.491409	+	0.491409i
$903$	5380.49	+	981.871i	0.198285	+	0.0361845i
$904$			8489.50i			0.312341i
$905$	−5742.86	−	25228.2i	−0.210938	−	0.926645i
$906$	14954.7	−	10338.9i	0.548384	−	0.379125i
$907$	−23026.7	−	23026.7i	−0.842989	−	0.842989i	0.146258	−	0.989246i	$-0.453277\pi$
$907$	−23026.7	−	23026.7i	−0.842989	−	0.842989i	−0.989246	+	0.146258i	$0.953277\pi$
$908$	7245.11	+	7245.11i	0.264799	+	0.264799i
$909$	3220.25	−	8529.38i	0.117501	−	0.311223i
$910$	−6020.83	−	3787.99i	−0.219328	−	0.137990i
$911$			33422.1i			1.21550i	0.794127	+	0.607752i	$0.207929\pi$
$911$			33422.1i			1.21550i	−0.794127	+	0.607752i	$0.792071\pi$
$912$	194.660	−	1066.71i	0.00706781	−	0.0387304i
$913$	4148.12	−	4148.12i	0.150364	−	0.150364i
$914$	15075.7			0.545581
$915$	−5.03191	−	116.080i	−0.000181803	−	0.00419399i
$916$	20355.1			0.734226
$917$	26438.8	−	26438.8i	0.952112	−	0.952112i
$918$	3187.73	−	5299.85i	0.114609	−	0.190546i
$919$			42542.2i			1.52703i	0.645792	+	0.763513i	$0.276527\pi$
$919$			42542.2i			1.52703i	−0.645792	+	0.763513i	$0.723473\pi$
$920$	−12890.7	+	2934.40i	−0.461951	+	0.105157i
$921$	7651.86	+	11068.0i	0.273765	+	0.395986i
$922$	−10508.7	−	10508.7i	−0.375363	−	0.375363i
$923$	2435.36	+	2435.36i	0.0868482	+	0.0868482i
$924$	8301.70	+	12007.9i	0.295569	+	0.427524i
$925$	21259.5	+	7466.56i	0.755684	+	0.265404i
$926$			3157.84i			0.112066i
$927$	−32482.6	+	14677.4i	−1.15088	+	0.520033i
$928$	−16394.7	+	16394.7i	−0.579938	+	0.579938i
$929$	5721.21			0.202053			0.101026	−	0.994884i	$-0.467787\pi$
$929$	5721.21			0.202053			0.101026	+	0.994884i	$0.467787\pi$
$930$	17790.8	+	16312.4i	0.627292	+	0.575168i
$931$	−680.282			−0.0239477
$932$	−10257.9	+	10257.9i	−0.360524	+	0.360524i
$933$	3740.83	−	20499.1i	0.131264	−	0.719305i
$934$		−	3515.38i		−	0.123155i
$935$	−4487.28	+	7132.32i	−0.156952	+	0.249467i
$936$	−11211.8	−	4232.97i	−0.391525	−	0.147819i
$937$	1344.01	+	1344.01i	0.0468589	+	0.0468589i	0.730148	−	0.683289i	$-0.239451\pi$
$937$	1344.01	+	1344.01i	0.0468589	+	0.0468589i	−0.683289	+	0.730148i	$0.739451\pi$
$938$	−10470.2	−	10470.2i	−0.364461	−	0.364461i
$939$	36706.8	−	25377.2i	1.27570	−	0.881953i
$940$	−5431.56	+	8633.22i	−0.188466	+	0.299558i
$941$			9625.77i			0.333466i	0.986002	+	0.166733i	$0.0533217\pi$
$941$			9625.77i			0.333466i	−0.986002	+	0.166733i	$0.946678\pi$
$942$	14673.9	+	2677.80i	0.507538	+	0.0926192i
$943$	14744.1	−	14744.1i	0.509157	−	0.509157i
$944$	−3101.77			−0.106943
$945$	−26448.9	+	13359.3i	−0.910459	+	0.459870i
$946$	2687.46			0.0923645
$947$	−2234.24	+	2234.24i	−0.0766664	+	0.0766664i	−0.744400	−	0.667734i	$-0.767264\pi$
$947$	−2234.24	+	2234.24i	−0.0766664	+	0.0766664i	0.667734	+	0.744400i	$0.267264\pi$
$948$	−1271.21	−	231.980i	−0.0435518	−	0.00794765i
$949$			7938.11i			0.271530i
$950$	9720.93	+	3414.10i	0.331988	+	0.116598i
$951$	−18811.3	+	13005.2i	−0.641427	+	0.443451i
$952$	−7760.41	−	7760.41i	−0.264198	−	0.264198i
$953$	6457.14	+	6457.14i	0.219483	+	0.219483i	0.808281	−	0.588798i	$-0.200398\pi$
$953$	6457.14	+	6457.14i	0.219483	+	0.219483i	−0.588798	+	0.808281i	$0.700398\pi$
$954$	−9626.45	−	3634.44i	−0.326696	−	0.123343i
$955$	10151.1	−	2310.75i	0.343959	−	0.0782977i
$956$			15413.5i			0.521451i
$957$	3371.32	−	18474.3i	0.113876	−	0.624021i
$958$	5985.35	−	5985.35i	0.201856	−	0.201856i
$959$	13556.9			0.456491
$960$	15984.8	−	692.916i	0.537403	−	0.0232956i
$961$	31399.6			1.05399
$962$	4292.91	−	4292.91i	0.143876	−	0.143876i
$963$	20745.2	−	9373.84i	0.694190	−	0.313674i
$964$			9505.61i			0.317588i
$965$	35107.4	+	22087.7i	1.17114	+	0.736817i
$966$	5008.55	+	7244.59i	0.166819	+	0.241295i
$967$	13166.9	+	13166.9i	0.437869	+	0.437869i	0.891294	−	0.453425i	$-0.149798\pi$
$967$	13166.9	+	13166.9i	0.437869	+	0.437869i	−0.453425	+	0.891294i	$0.649798\pi$
$968$	−7925.72	−	7925.72i	−0.263163	−	0.263163i
$969$	−3805.89	−	5505.01i	−0.126174	−	0.182504i
$970$	5352.90	+	23515.1i	0.177187	+	0.778376i
$971$			21504.3i			0.710716i	0.934730	+	0.355358i	$0.115641\pi$
$971$			21504.3i			0.710716i	−0.934730	+	0.355358i	$0.884359\pi$
$972$	−15397.6	+	12156.0i	−0.508104	+	0.401136i
$973$	914.119	−	914.119i	0.0301185	−	0.0301185i
$974$	−3071.14			−0.101032
$975$	−6451.71	+	11313.9i	−0.211918	+	0.371625i
$976$	−8.50472			−0.000278924
$977$	−8996.19	+	8996.19i	−0.294589	+	0.294589i	−0.838890	−	0.544301i	$-0.816795\pi$
$977$	−8996.19	+	8996.19i	−0.294589	+	0.294589i	0.544301	+	0.838890i	$0.316795\pi$
$978$	−1387.21	+	7601.68i	−0.0453559	+	0.248543i
$979$		−	40697.1i		−	1.32858i
$980$	178.159	+	782.646i	0.00580722	+	0.0255109i
$981$	19784.9	−	52403.7i	0.643917	−	1.70553i
$982$	16467.8	+	16467.8i	0.535142	+	0.535142i
$983$	−16337.3	−	16337.3i	−0.530090	−	0.530090i	0.390509	−	0.920599i	$-0.372299\pi$
$983$	−16337.3	−	16337.3i	−0.530090	−	0.530090i	−0.920599	+	0.390509i	$0.872299\pi$
$984$	−36929.0	+	25530.8i	−1.19639	+	0.827128i
$985$	−40082.8	−	25218.0i	−1.29659	−	0.815748i
$986$			5548.02i			0.179194i
$987$	17010.4	+	3104.18i	0.548578	+	0.100108i
$988$	−3603.53	+	3603.53i	−0.116036	+	0.116036i
$989$	−2976.52			−0.0957004
$990$	−11606.6	+	8790.77i	−0.372607	+	0.282211i
$991$	−18296.9			−0.586500			−0.293250	−	0.956036i	$-0.594737\pi$
$991$	−18296.9			−0.586500			−0.293250	+	0.956036i	$0.594737\pi$
$992$	32223.9	−	32223.9i	1.03136	−	1.03136i
$993$	−49018.8	−	8945.31i	−1.56653	−	0.285872i
$994$			5449.79i			0.173900i
$995$	−1193.25	+	271.627i	−0.0380186	+	0.00865441i
$996$	4521.93	−	3126.24i	0.143858	−	0.0994564i
$997$	20406.0	+	20406.0i	0.648210	+	0.648210i	0.952560	−	0.304350i	$-0.0984393\pi$
$997$	20406.0	+	20406.0i	0.648210	+	0.648210i	−0.304350	+	0.952560i	$0.598439\pi$
$998$	12926.9	+	12926.9i	0.410015	+	0.410015i
$999$	−6107.09	−	24541.4i	−0.193413	−	0.777232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.4.e.a.2.2	✓	8
3.2	odd	2	inner	15.4.e.a.2.3	yes	8
4.3	odd	2		240.4.v.c.17.1		8
5.2	odd	4		75.4.e.c.68.2		8
5.3	odd	4	inner	15.4.e.a.8.3	yes	8
5.4	even	2		75.4.e.c.32.3		8
12.11	even	2		240.4.v.c.17.2		8
15.2	even	4		75.4.e.c.68.3		8
15.8	even	4	inner	15.4.e.a.8.2	yes	8
15.14	odd	2		75.4.e.c.32.2		8
20.3	even	4		240.4.v.c.113.2		8
60.23	odd	4		240.4.v.c.113.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.4.e.a.2.2	✓	8	1.1	even	1	trivial
15.4.e.a.2.3	yes	8	3.2	odd	2	inner
15.4.e.a.8.2	yes	8	15.8	even	4	inner
15.4.e.a.8.3	yes	8	5.3	odd	4	inner
75.4.e.c.32.2		8	15.14	odd	2
75.4.e.c.32.3		8	5.4	even	2
75.4.e.c.68.2		8	5.2	odd	4
75.4.e.c.68.3		8	15.2	even	4
240.4.v.c.17.1		8	4.3	odd	2
240.4.v.c.17.2		8	12.11	even	2
240.4.v.c.113.1		8	60.23	odd	4
240.4.v.c.113.2		8	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	15.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18766 + 1.18766i) q^{2} +(5.11173 + 0.932827i) q^{3} +5.17891i q^{4} +(-2.48157 - 10.9015i) q^{5} +(-7.17891 + 4.96314i) q^{6} +(-13.3578 - 13.3578i) q^{7} +(-15.6521 - 15.6521i) q^{8} +(25.2597 + 9.53673i) q^{9} +O(q^{10})\)	\(q+(-1.18766 + 1.18766i) q^{2} +(5.11173 + 0.932827i) q^{3} +5.17891i q^{4} +(-2.48157 - 10.9015i) q^{5} +(-7.17891 + 4.96314i) q^{6} +(-13.3578 - 13.3578i) q^{7} +(-15.6521 - 15.6521i) q^{8} +(25.2597 + 9.53673i) q^{9} +(15.8945 + 10.0000i) q^{10} +28.7164i q^{11} +(-4.83102 + 26.4732i) q^{12} +(14.1789 - 14.1789i) q^{13} +31.7292 q^{14} +(-2.51595 - 58.0402i) q^{15} -4.25236 q^{16} +(-18.5587 + 18.5587i) q^{17} +(-41.3264 + 18.6736i) q^{18} +49.0735i q^{19} +(56.4577 - 12.8518i) q^{20} +(-55.8211 - 80.7421i) q^{21} +(-34.1055 - 34.1055i) q^{22} +(37.7738 + 37.7738i) q^{23} +(-65.4088 - 94.6102i) q^{24} +(-112.684 + 54.1055i) q^{25} +33.6796i q^{26} +(120.225 + 72.3121i) q^{27} +(69.1789 - 69.1789i) q^{28} -125.854 q^{29} +(71.9204 + 65.9442i) q^{30} +247.367 q^{31} +(130.267 - 130.267i) q^{32} +(-26.7874 + 146.791i) q^{33} -44.0829i q^{34} +(-112.471 + 178.768i) q^{35} +(-49.3898 + 130.818i) q^{36} +(-127.463 - 127.463i) q^{37} +(-58.2828 - 58.2828i) q^{38} +(85.7053 - 59.2524i) q^{39} +(-131.789 + 209.473i) q^{40} -390.328i q^{41} +(162.191 + 29.5978i) q^{42} +(-39.3993 + 39.3993i) q^{43} -148.720 q^{44} +(41.2806 - 299.033i) q^{45} -89.7251 q^{46} +(-124.560 + 124.560i) q^{47} +(-21.7369 - 3.96671i) q^{48} +13.8625i q^{49} +(69.5712 - 198.089i) q^{50} +(-112.179 + 77.5549i) q^{51} +(73.4313 + 73.4313i) q^{52} +(160.441 + 160.441i) q^{53} +(-228.669 + 56.9040i) q^{54} +(313.051 - 71.2618i) q^{55} +418.156i q^{56} +(-45.7770 + 250.850i) q^{57} +(149.473 - 149.473i) q^{58} +729.423 q^{59} +(300.585 - 13.0299i) q^{60} +2.00000 q^{61} +(-293.789 + 293.789i) q^{62} +(-210.024 - 464.804i) q^{63} +275.409i q^{64} +(-189.757 - 119.385i) q^{65} +(-142.524 - 206.153i) q^{66} +(-329.987 - 329.987i) q^{67} +(-96.1136 - 96.1136i) q^{68} +(157.853 + 228.326i) q^{69} +(-78.7382 - 345.895i) q^{70} +171.760i q^{71} +(-246.097 - 544.637i) q^{72} +(-279.927 + 279.927i) q^{73} +302.767 q^{74} +(-626.480 + 171.458i) q^{75} -254.147 q^{76} +(383.589 - 383.589i) q^{77} +(-31.4172 + 172.161i) q^{78} +48.0189i q^{79} +(10.5525 + 46.3569i) q^{80} +(547.102 + 481.789i) q^{81} +(463.578 + 463.578i) q^{82} +(-144.451 - 144.451i) q^{83} +(418.156 - 289.092i) q^{84} +(248.371 + 156.262i) q^{85} -93.5862i q^{86} +(-643.334 - 117.400i) q^{87} +(449.473 - 449.473i) q^{88} -1417.21 q^{89} +(306.124 + 404.179i) q^{90} -378.799 q^{91} +(-195.627 + 195.627i) q^{92} +(1264.48 + 230.751i) q^{93} -295.872i q^{94} +(534.972 - 121.779i) q^{95} +(787.409 - 544.375i) q^{96} +(908.111 + 908.111i) q^{97} +(-16.4640 - 16.4640i) q^{98} +(-273.861 + 725.367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7}+O(q^{10}) \) 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7	\( 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7} - 100 q^{10} + 132 q^{12} + 68 q^{13} + 90 q^{15} + 284 q^{16} - 240 q^{18} - 492 q^{21} - 500 q^{22} - 220 q^{25} + 702 q^{27} + 508 q^{28} + 660 q^{30} + 616 q^{31} - 240 q^{33} - 804 q^{36} - 1156 q^{37} - 600 q^{40} + 540 q^{42} + 548 q^{43} + 180 q^{45} + 736 q^{46} - 1116 q^{48} - 852 q^{51} + 224 q^{52} + 460 q^{55} + 684 q^{57} + 60 q^{58} + 540 q^{60} + 16 q^{61} + 1428 q^{63} + 2040 q^{66} + 404 q^{67} - 2220 q^{70} - 1800 q^{72} - 2512 q^{73} - 2910 q^{75} - 1488 q^{76} - 360 q^{78} + 288 q^{81} + 2800 q^{82} + 4940 q^{85} - 1680 q^{87} + 2460 q^{88} + 600 q^{90} - 1304 q^{91} + 3408 q^{93} + 4164 q^{96} + 1904 q^{97}+O(q^{100}) \) 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7 - 100 * q^10 + 132 * q^12 + 68 * q^13 + 90 * q^15 + 284 * q^16 - 240 * q^18 - 492 * q^21 - 500 * q^22 - 220 * q^25 + 702 * q^27 + 508 * q^28 + 660 * q^30 + 616 * q^31 - 240 * q^33 - 804 * q^36 - 1156 * q^37 - 600 * q^40 + 540 * q^42 + 548 * q^43 + 180 * q^45 + 736 * q^46 - 1116 * q^48 - 852 * q^51 + 224 * q^52 + 460 * q^55 + 684 * q^57 + 60 * q^58 + 540 * q^60 + 16 * q^61 + 1428 * q^63 + 2040 * q^66 + 404 * q^67 - 2220 * q^70 - 1800 * q^72 - 2512 * q^73 - 2910 * q^75 - 1488 * q^76 - 360 * q^78 + 288 * q^81 + 2800 * q^82 + 4940 * q^85 - 1680 * q^87 + 2460 * q^88 + 600 * q^90 - 1304 * q^91 + 3408 * q^93 + 4164 * q^96 + 1904 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more