LMFDB - Embedded newform 120.4.b.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(11,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("120.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	120.11
Dual form			120.4.b.a.11.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54070 - 2.37197i) q^{2} +(3.91264 - 3.41925i) q^{3} +(-3.25251 + 7.30898i) q^{4} +5.00000 q^{5} +(-14.1386 - 4.01264i) q^{6} -2.12151i q^{7} +(22.3478 - 3.54604i) q^{8} +(3.61744 - 26.7566i) q^{9} +O(q^{10})$	\(q+(-1.54070 - 2.37197i) q^{2} +(3.91264 - 3.41925i) q^{3} +(-3.25251 + 7.30898i) q^{4} +5.00000 q^{5} +(-14.1386 - 4.01264i) q^{6} -2.12151i q^{7} +(22.3478 - 3.54604i) q^{8} +(3.61744 - 26.7566i) q^{9} +(-7.70348 - 11.8599i) q^{10} -49.3562i q^{11} +(12.2653 + 39.7185i) q^{12} -20.7644i q^{13} +(-5.03217 + 3.26860i) q^{14} +(19.5632 - 17.0963i) q^{15} +(-42.8423 - 47.5451i) q^{16} +22.7248i q^{17} +(-69.0392 + 32.6433i) q^{18} +63.4396 q^{19} +(-16.2626 + 36.5449i) q^{20} +(-7.25398 - 8.30070i) q^{21} +(-117.072 + 76.0429i) q^{22} -147.260 q^{23} +(75.3141 - 90.2872i) q^{24} +25.0000 q^{25} +(-49.2526 + 31.9916i) q^{26} +(-77.3337 - 117.058i) q^{27} +(15.5061 + 6.90024i) q^{28} -3.23196 q^{29} +(-70.6928 - 20.0632i) q^{30} -133.195i q^{31} +(-46.7687 + 174.873i) q^{32} +(-168.761 - 193.113i) q^{33} +(53.9027 - 35.0120i) q^{34} -10.6076i q^{35} +(183.797 + 113.466i) q^{36} +257.214i q^{37} +(-97.7412 - 150.477i) q^{38} +(-70.9987 - 81.2436i) q^{39} +(111.739 - 17.7302i) q^{40} -73.9667i q^{41} +(-8.51286 + 29.9951i) q^{42} +378.483 q^{43} +(360.744 + 160.532i) q^{44} +(18.0872 - 133.783i) q^{45} +(226.883 + 349.296i) q^{46} +469.412 q^{47} +(-330.195 - 39.5380i) q^{48} +338.499 q^{49} +(-38.5174 - 59.2993i) q^{50} +(77.7019 + 88.9139i) q^{51} +(151.767 + 67.5365i) q^{52} -602.609 q^{53} +(-158.510 + 363.784i) q^{54} -246.781i q^{55} +(-7.52295 - 47.4112i) q^{56} +(248.216 - 216.916i) q^{57} +(4.97946 + 7.66611i) q^{58} +637.883i q^{59} +(61.3267 + 198.593i) q^{60} +336.736i q^{61} +(-315.936 + 205.214i) q^{62} +(-56.7643 - 7.67444i) q^{63} +(486.851 - 158.493i) q^{64} -103.822i q^{65} +(-198.049 + 697.826i) q^{66} +684.370 q^{67} +(-166.095 - 73.9128i) q^{68} +(-576.174 + 503.518i) q^{69} +(-25.1608 + 16.3430i) q^{70} +898.776 q^{71} +(-14.0378 - 610.779i) q^{72} -335.058 q^{73} +(610.105 - 396.289i) q^{74} +(97.8159 - 85.4813i) q^{75} +(-206.338 + 463.679i) q^{76} -104.710 q^{77} +(-83.3201 + 293.579i) q^{78} -814.207i q^{79} +(-214.212 - 237.725i) q^{80} +(-702.828 - 193.581i) q^{81} +(-175.447 + 113.960i) q^{82} +371.223i q^{83} +(84.2633 - 26.0210i) q^{84} +113.624i q^{85} +(-583.128 - 897.753i) q^{86} +(-12.6455 + 11.0509i) q^{87} +(-175.019 - 1103.00i) q^{88} +223.909i q^{89} +(-345.196 + 163.216i) q^{90} -44.0519 q^{91} +(478.964 - 1076.32i) q^{92} +(-455.428 - 521.145i) q^{93} +(-723.221 - 1113.43i) q^{94} +317.198 q^{95} +(414.947 + 844.130i) q^{96} -1632.64 q^{97} +(-521.524 - 802.911i) q^{98} +(-1320.60 - 178.543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8}+O(q^{10}) $ 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8	$ 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8} - 15 q^{10} + 65 q^{12} - 54 q^{14} + 153 q^{16} - 175 q^{18} + 12 q^{19} - 15 q^{20} - 4 q^{21} - 102 q^{22} + 228 q^{23} - 407 q^{24} + 600 q^{25} + 336 q^{26} + 132 q^{27} - 186 q^{28} + 95 q^{30} + 177 q^{32} + 116 q^{33} + 408 q^{34} + 673 q^{36} + 312 q^{38} - 656 q^{39} + 105 q^{40} - 990 q^{42} - 450 q^{44} - 1104 q^{46} - 924 q^{47} - 535 q^{48} - 816 q^{49} - 75 q^{50} - 700 q^{51} - 1548 q^{52} + 528 q^{53} + 1331 q^{54} - 390 q^{56} - 172 q^{57} + 1410 q^{58} + 325 q^{60} - 978 q^{62} + 476 q^{63} + 1137 q^{64} - 2794 q^{66} + 1632 q^{67} - 1608 q^{68} + 980 q^{69} - 270 q^{70} + 216 q^{71} - 3699 q^{72} - 216 q^{73} + 768 q^{74} - 1812 q^{76} + 4140 q^{78} + 765 q^{80} + 152 q^{81} + 2244 q^{82} + 5086 q^{84} - 2808 q^{86} + 252 q^{87} + 2622 q^{88} - 875 q^{90} - 1800 q^{91} - 1836 q^{92} - 1968 q^{94} + 60 q^{95} - 5455 q^{96} + 792 q^{97} + 4851 q^{98} - 1328 q^{99}+O(q^{100}) $ 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8 - 15 * q^10 + 65 * q^12 - 54 * q^14 + 153 * q^16 - 175 * q^18 + 12 * q^19 - 15 * q^20 - 4 * q^21 - 102 * q^22 + 228 * q^23 - 407 * q^24 + 600 * q^25 + 336 * q^26 + 132 * q^27 - 186 * q^28 + 95 * q^30 + 177 * q^32 + 116 * q^33 + 408 * q^34 + 673 * q^36 + 312 * q^38 - 656 * q^39 + 105 * q^40 - 990 * q^42 - 450 * q^44 - 1104 * q^46 - 924 * q^47 - 535 * q^48 - 816 * q^49 - 75 * q^50 - 700 * q^51 - 1548 * q^52 + 528 * q^53 + 1331 * q^54 - 390 * q^56 - 172 * q^57 + 1410 * q^58 + 325 * q^60 - 978 * q^62 + 476 * q^63 + 1137 * q^64 - 2794 * q^66 + 1632 * q^67 - 1608 * q^68 + 980 * q^69 - 270 * q^70 + 216 * q^71 - 3699 * q^72 - 216 * q^73 + 768 * q^74 - 1812 * q^76 + 4140 * q^78 + 765 * q^80 + 152 * q^81 + 2244 * q^82 + 5086 * q^84 - 2808 * q^86 + 252 * q^87 + 2622 * q^88 - 875 * q^90 - 1800 * q^91 - 1836 * q^92 - 1968 * q^94 + 60 * q^95 - 5455 * q^96 + 792 * q^97 + 4851 * q^98 - 1328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.54070	−	2.37197i	−0.544718	−	0.838619i
$2$	−1.54070	−	2.37197i	−0.544718	−	0.838619i
$3$	3.91264	−	3.41925i	0.752987	−	0.658035i
$3$	3.91264	−	3.41925i	0.752987	−	0.658035i
$4$	−3.25251	+	7.30898i	−0.406564	+	0.913622i
$5$	5.00000			0.447214
$5$	5.00000			0.447214
$6$	−14.1386	−	4.01264i	−0.962007	−	0.273026i
$7$		−	2.12151i		−	0.114551i	−0.998358	−	0.0572754i	$-0.981759\pi$
$7$		−	2.12151i		−	0.114551i	0.998358	−	0.0572754i	$-0.0182413\pi$
$8$	22.3478	−	3.54604i	0.987644	−	0.156714i
$9$	3.61744	−	26.7566i	0.133979	−	0.990984i
$10$	−7.70348	−	11.8599i	−0.243605	−	0.375042i
$11$		−	49.3562i		−	1.35286i	−0.736507	−	0.676430i	$-0.763526\pi$
$11$		−	49.3562i		−	1.35286i	0.736507	−	0.676430i	$-0.236474\pi$
$12$	12.2653	+	39.7185i	0.295058	+	0.955479i
$13$		−	20.7644i		−	0.443001i	−0.975160	−	0.221500i	$-0.928905\pi$
$13$		−	20.7644i		−	0.443001i	0.975160	−	0.221500i	$-0.0710954\pi$
$14$	−5.03217	+	3.26860i	−0.0960645	+	0.0623979i
$15$	19.5632	−	17.0963i	0.336746	−	0.294282i
$16$	−42.8423	−	47.5451i	−0.669411	−	0.742892i
$17$			22.7248i			0.324210i	0.986773	+	0.162105i	$0.0518284\pi$
$17$			22.7248i			0.324210i	−0.986773	+	0.162105i	$0.948172\pi$
$18$	−69.0392	+	32.6433i	−0.904039	+	0.427449i
$19$	63.4396			0.766003			0.383001	−	0.923748i	$-0.374890\pi$
$19$	63.4396			0.766003			0.383001	+	0.923748i	$0.374890\pi$
$20$	−16.2626	+	36.5449i	−0.181821	+	0.408584i
$21$	−7.25398	−	8.30070i	−0.0753784	−	0.0862553i
$22$	−117.072	+	76.0429i	−1.13453	+	0.736927i
$23$	−147.260			−1.33503			−0.667517	−	0.744594i	$-0.732643\pi$
$23$	−147.260			−1.33503			−0.667517	+	0.744594i	$0.732643\pi$
$24$	75.3141	−	90.2872i	0.640560	−	0.767908i
$25$	25.0000			0.200000
$26$	−49.2526	+	31.9916i	−0.371509	+	0.241311i
$27$	−77.3337	−	117.058i	−0.551218	−	0.834361i
$28$	15.5061	+	6.90024i	0.104656	+	0.0465722i
$29$	−3.23196			−0.0206951			−0.0103476	−	0.999946i	$-0.503294\pi$
$29$	−3.23196			−0.0206951			−0.0103476	+	0.999946i	$0.503294\pi$
$30$	−70.6928	−	20.0632i	−0.430222	−	0.122101i
$31$		−	133.195i		−	0.771697i	−0.922562	−	0.385848i	$-0.873909\pi$
$31$		−	133.195i		−	0.771697i	0.922562	−	0.385848i	$-0.126091\pi$
$32$	−46.7687	+	174.873i	−0.258363	+	0.966048i
$33$	−168.761	−	193.113i	−0.890229	−	1.01869i
$34$	53.9027	−	35.0120i	0.271889	−	0.176603i
$35$		−	10.6076i		−	0.0512287i
$36$	183.797	+	113.466i	0.850914	+	0.525305i
$37$			257.214i			1.14286i	0.820651	+	0.571429i	$0.193611\pi$
$37$			257.214i			1.14286i	−0.820651	+	0.571429i	$0.806389\pi$
$38$	−97.7412	−	150.477i	−0.417256	−	0.642384i
$39$	−70.9987	−	81.2436i	−0.291510	−	0.333574i
$40$	111.739	−	17.7302i	0.441688	−	0.0700847i
$41$		−	73.9667i		−	0.281748i	−0.990028	−	0.140874i	$-0.955009\pi$
$41$		−	73.9667i		−	0.281748i	0.990028	−	0.140874i	$-0.0449912\pi$
$42$	−8.51286	+	29.9951i	−0.0312753	+	0.110199i
$43$	378.483			1.34228			0.671142	−	0.741329i	$-0.265804\pi$
$43$	378.483			1.34228			0.671142	+	0.741329i	$0.265804\pi$
$44$	360.744	+	160.532i	1.23600	+	0.550024i
$45$	18.0872	−	133.783i	0.0599174	−	0.443182i
$46$	226.883	+	349.296i	0.727218	+	1.11959i
$47$	469.412			1.45682			0.728412	−	0.685139i	$-0.240259\pi$
$47$	469.412			1.45682			0.728412	+	0.685139i	$0.240259\pi$
$48$	−330.195	−	39.5380i	−0.992907	−	0.118892i
$49$	338.499			0.986878
$50$	−38.5174	−	59.2993i	−0.108944	−	0.167724i
$51$	77.7019	+	88.9139i	0.213342	+	0.244126i
$52$	151.767	+	67.5365i	0.404735	+	0.180108i
$53$	−602.609			−1.56179			−0.780894	−	0.624664i	$-0.785236\pi$
$53$	−602.609			−1.56179			−0.780894	+	0.624664i	$0.785236\pi$
$54$	−158.510	+	363.784i	−0.399453	+	0.916754i
$55$		−	246.781i		−	0.605017i
$56$	−7.52295	−	47.4112i	−0.0179517	−	0.113135i
$57$	248.216	−	216.916i	0.576790	−	0.504057i
$58$	4.97946	+	7.66611i	0.0112730	+	0.0173553i
$59$			637.883i			1.40755i	0.710425	+	0.703773i	$0.248503\pi$
$59$			637.883i			1.40755i	−0.710425	+	0.703773i	$0.751497\pi$
$60$	61.3267	+	198.593i	0.131954	+	0.427303i
$61$			336.736i			0.706798i	0.935473	+	0.353399i	$0.114974\pi$
$61$			336.736i			0.706798i	−0.935473	+	0.353399i	$0.885026\pi$
$62$	−315.936	+	205.214i	−0.647160	+	0.420357i
$63$	−56.7643	−	7.67444i	−0.113518	−	0.0153474i
$64$	486.851	−	158.493i	0.950881	−	0.309556i
$65$		−	103.822i		−	0.198116i
$66$	−198.049	+	697.826i	−0.369366	+	1.30146i
$67$	684.370			1.24790			0.623948	−	0.781465i	$-0.285528\pi$
$67$	684.370			1.24790			0.623948	+	0.781465i	$0.285528\pi$
$68$	−166.095	−	73.9128i	−0.296206	−	0.131812i
$69$	−576.174	+	503.518i	−1.00526	+	0.878500i
$70$	−25.1608	+	16.3430i	−0.0429613	+	0.0279052i
$71$	898.776			1.50233			0.751163	−	0.660117i	$-0.229493\pi$
$71$	898.776			1.50233			0.751163	+	0.660117i	$0.229493\pi$
$72$	−14.0378	−	610.779i	−0.0229774	−	0.999736i
$73$	−335.058			−0.537200			−0.268600	−	0.963252i	$-0.586561\pi$
$73$	−335.058			−0.537200			−0.268600	+	0.963252i	$0.586561\pi$
$74$	610.105	−	396.289i	0.958423	−	0.622536i
$75$	97.8159	−	85.4813i	0.150597	−	0.131607i
$76$	−206.338	+	463.679i	−0.311429	+	0.699837i
$77$	−104.710			−0.154971
$78$	−83.3201	+	293.579i	−0.120951	+	0.426170i
$79$		−	814.207i		−	1.15956i	−0.814772	−	0.579781i	$-0.803138\pi$
$79$		−	814.207i		−	1.15956i	0.814772	−	0.579781i	$-0.196862\pi$
$80$	−214.212	−	237.725i	−0.299370	−	0.332231i
$81$	−702.828	−	193.581i	−0.964099	−	0.265543i
$82$	−175.447	+	113.960i	−0.236279	+	0.153473i
$83$			371.223i			0.490928i	0.969406	+	0.245464i	$0.0789404\pi$
$83$			371.223i			0.490928i	−0.969406	+	0.245464i	$0.921060\pi$
$84$	84.2633	−	26.0210i	0.109451	−	0.0337991i
$85$			113.624i			0.144991i
$86$	−583.128	−	897.753i	−0.731166	−	1.12566i
$87$	−12.6455	+	11.0509i	−0.0155832	+	0.0136181i
$88$	−175.019	−	1103.00i	−0.212012	−	1.33614i
$89$			223.909i			0.266677i	0.991071	+	0.133339i	$0.0425698\pi$
$89$			223.909i			0.266677i	−0.991071	+	0.133339i	$0.957430\pi$
$90$	−345.196	+	163.216i	−0.404299	+	0.191161i
$91$	−44.0519			−0.0507461
$92$	478.964	−	1076.32i	0.542777	−	1.21972i
$93$	−455.428	−	521.145i	−0.507804	−	0.581078i
$94$	−723.221	−	1113.43i	−0.793559	−	1.22172i
$95$	317.198			0.342567
$96$	414.947	+	844.130i	0.441149	+	0.897434i
$97$	−1632.64			−1.70897			−0.854484	−	0.519478i	$-0.826126\pi$
$97$	−1632.64			−1.70897			−0.854484	+	0.519478i	$0.826126\pi$
$98$	−521.524	−	802.911i	−0.537570	−	0.827615i
$99$	−1320.60	−	178.543i	−1.34066	−	0.181255i
$100$	−81.3128	+	182.724i	−0.0813128	+	0.182724i
$101$	908.215			0.894760			0.447380	−	0.894344i	$-0.352357\pi$
$101$	908.215			0.894760			0.447380	+	0.894344i	$0.352357\pi$
$102$	91.1866	−	321.296i	0.0885178	−	0.311893i
$103$		−	883.164i		−	0.844862i	−0.906395	−	0.422431i	$-0.861177\pi$
$103$		−	883.164i		−	0.844862i	0.906395	−	0.422431i	$-0.138823\pi$
$104$	−73.6314	−	464.039i	−0.0694245	−	0.437527i
$105$	−36.2699	−	41.5035i	−0.0337103	−	0.0385745i
$106$	928.437	+	1429.37i	0.850734	+	1.30974i
$107$			959.725i			0.867104i	0.901129	+	0.433552i	$0.142740\pi$
$107$			959.725i			0.867104i	−0.901129	+	0.433552i	$0.857260\pi$
$108$	1107.10	−	184.499i	0.986397	−	0.164383i
$109$			1859.97i			1.63443i	0.576333	+	0.817215i	$0.304483\pi$
$109$			1859.97i			1.63443i	−0.576333	+	0.817215i	$0.695517\pi$
$110$	−585.358	+	380.215i	−0.507379	+	0.329564i
$111$	879.480	+	1006.39i	0.752041	+	0.860558i
$112$	−100.867	+	90.8904i	−0.0850989	+	0.0766816i
$113$			496.790i			0.413575i	0.978386	+	0.206788i	$0.0663010\pi$
$113$			496.790i			0.413575i	−0.978386	+	0.206788i	$0.933699\pi$
$114$	−896.945	−	254.561i	−0.736900	−	0.209138i
$115$	−736.299			−0.597046
$116$	10.5120	−	23.6223i	0.00841390	−	0.0189075i
$117$	−555.584	−	75.1140i	−0.439007	−	0.0593530i
$118$	1513.04	−	982.783i	1.18040	−	0.766716i
$119$	48.2109			0.0371386
$120$	376.571	−	451.436i	0.286467	−	0.343419i
$121$	−1105.04			−0.830230
$122$	798.730	−	518.808i	0.592734	−	0.385006i
$123$	−252.911	−	289.405i	−0.185400	−	0.212152i
$124$	973.522	+	433.220i	0.705039	+	0.313744i
$125$	125.000			0.0894427
$126$	69.2530	+	146.467i	0.0489647	+	0.103558i
$127$			2388.53i			1.66888i	0.551101	+	0.834439i	$0.314208\pi$
$127$			2388.53i			1.66888i	−0.551101	+	0.834439i	$0.685792\pi$
$128$	−1126.03	−	910.609i	−0.777562	−	0.628807i
$129$	1480.87	−	1294.13i	1.01072	−	0.883270i
$130$	−246.263	+	159.958i	−0.166144	+	0.107917i
$131$			616.517i			0.411185i	0.978638	+	0.205593i	$0.0659122\pi$
$131$			616.517i			0.411185i	−0.978638	+	0.205593i	$0.934088\pi$
$132$	1960.36	−	605.370i	1.29263	−	0.399172i
$133$		−	134.588i		−	0.0877462i
$134$	−1054.41	−	1623.31i	−0.679752	−	1.04651i
$135$	−386.668	−	585.288i	−0.246512	−	0.373138i
$136$	80.5831	+	507.850i	0.0508084	+	0.320205i
$137$			2020.31i			1.25990i	0.776636	+	0.629950i	$0.216925\pi$
$137$			2020.31i			1.25990i	−0.776636	+	0.629950i	$0.783075\pi$
$138$	2082.04	+	590.901i	1.28431	+	0.364499i
$139$	−1204.39			−0.734927			−0.367463	−	0.930038i	$-0.619774\pi$
$139$	−1204.39			−0.734927			−0.367463	+	0.930038i	$0.619774\pi$
$140$	77.5304	+	34.5012i	0.0468037	+	0.0208277i
$141$	1836.64	−	1605.04i	1.09697	−	0.958642i
$142$	−1384.74	−	2131.87i	−0.818344	−	1.25988i
$143$	−1024.85			−0.599318
$144$	−1427.12	+	974.322i	−0.825882	+	0.563844i
$145$	−16.1598			−0.00925515
$146$	516.222	+	794.749i	0.292622	+	0.450506i
$147$	1324.42	−	1157.41i	0.743107	−	0.649401i
$148$	−1879.97	−	836.593i	−1.04414	−	0.464645i
$149$	1891.19			1.03982			0.519908	−	0.854223i	$-0.325966\pi$
$149$	1891.19			1.03982			0.519908	+	0.854223i	$0.325966\pi$
$150$	−353.464	−	100.316i	−0.192401	−	0.0546051i
$151$		−	3264.06i		−	1.75911i	−0.475797	−	0.879555i	$-0.657840\pi$
$151$		−	3264.06i		−	1.75911i	0.475797	−	0.879555i	$-0.342160\pi$
$152$	1417.74	−	224.959i	0.756538	−	0.120043i
$153$	608.038	+	82.2057i	0.321287	+	0.0434375i
$154$	161.326	+	248.369i	0.0844156	+	0.129962i
$155$		−	665.977i		−	0.345113i
$156$	824.732	−	254.682i	0.423278	−	0.130711i
$157$			1816.28i			0.923277i	0.887068	+	0.461639i	$0.152738\pi$
$157$			1816.28i			0.923277i	−0.887068	+	0.461639i	$0.847262\pi$
$158$	−1931.28	+	1254.44i	−0.972431	+	0.631635i
$159$	−2357.79	+	2060.47i	−1.17601	+	1.02771i
$160$	−233.844	+	874.367i	−0.115543	+	0.432030i
$161$			312.413i			0.152929i
$162$	623.676	+	1965.34i	0.302473	+	0.953158i
$163$	2092.71			1.00560			0.502802	−	0.864401i	$-0.332302\pi$
$163$	2092.71			1.00560			0.502802	+	0.864401i	$0.332302\pi$
$164$	540.621	+	240.578i	0.257411	+	0.114549i
$165$	−843.807	−	965.565i	−0.398123	−	0.455570i
$166$	880.532	−	571.942i	0.411702	−	0.267418i
$167$	−2377.09			−1.10146			−0.550732	−	0.834682i	$-0.685651\pi$
$167$	−2377.09			−1.10146			−0.550732	+	0.834682i	$0.685651\pi$
$168$	−191.545	−	159.780i	−0.0879645	−	0.0733766i
$169$	1765.84			0.803750
$170$	269.513	−	175.060i	0.121592	−	0.0789794i
$171$	229.489	−	1697.43i	0.102629	−	0.759096i
$172$	−1231.02	+	2766.33i	−0.545724	+	1.22634i
$173$	1359.12			0.597293			0.298646	−	0.954364i	$-0.403465\pi$
$173$	1359.12			0.597293			0.298646	+	0.954364i	$0.403465\pi$
$174$	45.6952	+	12.9687i	0.0199089	+	0.00565031i
$175$		−	53.0378i		−	0.0229102i
$176$	−2346.65	+	2114.53i	−1.00503	+	0.905620i
$177$	2181.08	+	2495.80i	0.926215	+	1.05986i
$178$	531.105	−	344.975i	0.223641	−	0.145264i
$179$			1413.86i			0.590374i	0.955439	+	0.295187i	$0.0953820\pi$
$179$			1413.86i			0.590374i	−0.955439	+	0.295187i	$0.904618\pi$
$180$	918.987	+	567.330i	0.380540	+	0.234924i
$181$		−	3775.62i		−	1.55050i	−0.631657	−	0.775248i	$-0.717625\pi$
$181$		−	3775.62i		−	1.55050i	0.631657	−	0.775248i	$-0.282375\pi$
$182$	67.8706	+	104.490i	0.0276423	+	0.0425566i
$183$	1151.39	+	1317.53i	0.465098	+	0.532210i
$184$	−3290.94	+	522.189i	−1.31854	+	0.209219i
$185$			1286.07i			0.511102i
$186$	−534.465	+	1883.19i	−0.210693	+	0.742377i
$187$	1121.61			0.438611
$188$	−1526.77	+	3430.92i	−0.592292	+	1.33099i
$189$	−248.339	+	164.064i	−0.0955768	+	0.0631424i
$190$	−488.706	−	752.386i	−0.186602	−	0.287283i
$191$	279.033			0.105707			0.0528537	−	0.998602i	$-0.483168\pi$
$191$	279.033			0.105707			0.0528537	+	0.998602i	$0.483168\pi$
$192$	1362.95	−	2284.79i	0.512303	−	0.858805i
$193$	−310.876			−0.115945			−0.0579725	−	0.998318i	$-0.518464\pi$
$193$	−310.876			−0.115945			−0.0579725	+	0.998318i	$0.518464\pi$
$194$	2515.41	+	3872.59i	0.930906	+	1.43317i
$195$	−354.994	−	406.218i	−0.130367	−	0.149179i
$196$	−1100.97	+	2474.08i	−0.401229	+	0.901634i
$197$	−5428.22			−1.96317			−0.981585	−	0.191028i	$-0.938818\pi$
$197$	−5428.22			−1.96317			−0.981585	+	0.191028i	$0.938818\pi$
$198$	1611.15	+	3407.52i	0.578279	+	1.22304i
$199$		−	2297.00i		−	0.818242i	−0.912480	−	0.409121i	$-0.865835\pi$
$199$		−	2297.00i		−	0.818242i	0.912480	−	0.409121i	$-0.134165\pi$
$200$	558.696	−	88.6509i	0.197529	−	0.0313428i
$201$	2677.69	−	2340.03i	0.939650	−	0.821160i
$202$	−1399.28	−	2154.26i	−0.487392	−	0.750363i
$203$			6.85663i			0.00237064i
$204$	−902.596	+	278.727i	−0.309776	+	0.0956609i
$205$		−	369.834i		−	0.126001i
$206$	−2094.84	+	1360.69i	−0.708517	+	0.460212i
$207$	−532.704	+	3940.17i	−0.178867	+	1.32300i
$208$	−987.246	+	889.595i	−0.329102	+	0.296550i
$209$		−	3131.14i		−	1.03629i
$210$	−42.5643	+	149.975i	−0.0139867	+	0.0492823i
$211$	−2045.57			−0.667405			−0.333703	−	0.942678i	$-0.608298\pi$
$211$	−2045.57			−0.667405			−0.333703	+	0.942678i	$0.608298\pi$
$212$	1959.99	−	4404.46i	0.634967	−	1.42688i
$213$	3516.58	−	3073.14i	1.13123	−	0.988583i
$214$	2276.44	−	1478.64i	0.727170	−	0.472327i
$215$	1892.42			0.600287
$216$	−2143.33	−	2341.76i	−0.675163	−	0.737668i
$217$	−282.575			−0.0883985
$218$	4411.80	−	2865.65i	1.37066	−	0.890304i
$219$	−1310.96	+	1145.65i	−0.404504	+	0.353496i
$220$	1803.72	+	802.659i	0.552757	+	0.245978i
$221$	471.867			0.143625
$222$	1032.11	−	3636.64i	0.312030	−	1.09944i
$223$			3925.34i			1.17874i	0.807862	+	0.589372i	$0.200625\pi$
$223$			3925.34i			1.17874i	−0.807862	+	0.589372i	$0.799375\pi$
$224$	370.996	+	99.2203i	0.110662	+	0.0295957i
$225$	90.4361	−	668.914i	0.0267959	−	0.198197i
$226$	1178.37	−	765.402i	0.346832	−	0.225282i
$227$		−	6173.94i		−	1.80519i	−0.430486	−	0.902597i	$-0.641658\pi$
$227$		−	6173.94i		−	1.80519i	0.430486	−	0.902597i	$-0.358342\pi$
$228$	778.108	+	2519.73i	0.226015	+	0.731900i
$229$		−	226.643i		−	0.0654017i	−0.999465	−	0.0327008i	$-0.989589\pi$
$229$		−	226.643i		−	0.0654017i	0.999465	−	0.0327008i	$-0.0104109\pi$
$230$	1134.41	+	1746.48i	0.325222	+	0.500694i
$231$	−409.691	+	358.029i	−0.116691	+	0.101976i
$232$	−72.2272	+	11.4606i	−0.0204394	+	0.00324322i
$233$		−	4126.81i		−	1.16033i	−0.814500	−	0.580163i	$-0.802989\pi$
$233$		−	4126.81i		−	1.16033i	0.814500	−	0.580163i	$-0.197011\pi$
$234$	677.818	+	1433.56i	0.189360	+	0.400490i
$235$	2347.06			0.651512
$236$	−4662.27	−	2074.72i	−1.28597	−	0.572258i
$237$	−2783.98	−	3185.69i	−0.763033	−	0.873135i
$238$	−74.2784	−	114.355i	−0.0202301	−	0.0311451i
$239$	244.736			0.0662370			0.0331185	−	0.999451i	$-0.489456\pi$
$239$	244.736			0.0662370			0.0331185	+	0.999451i	$0.489456\pi$
$240$	−1650.98	−	197.690i	−0.444042	−	0.0531702i
$241$	−1557.57			−0.416315			−0.208158	−	0.978095i	$-0.566747\pi$
$241$	−1557.57			−0.416315			−0.208158	+	0.978095i	$0.566747\pi$
$242$	1702.52	+	2621.12i	0.452241	+	0.696247i
$243$	−3411.81	+	1645.74i	−0.900691	+	0.434461i
$244$	−2461.20	−	1095.24i	−0.645746	−	0.287359i
$245$	1692.50			0.441345
$246$	−296.802	+	1045.78i	−0.0769244	+	0.271043i
$247$		−	1317.29i		−	0.339340i
$248$	−472.316	−	2976.63i	−0.120936	−	0.762162i
$249$	1269.31	+	1452.46i	0.323048	+	0.369663i
$250$	−192.587	−	296.497i	−0.0487211	−	0.0750084i
$251$		−	5433.22i		−	1.36630i	−0.730278	−	0.683151i	$-0.760609\pi$
$251$		−	5433.22i		−	1.36630i	0.730278	−	0.683151i	$-0.239391\pi$
$252$	240.719	−	389.928i	0.0601741	−	0.0974729i
$253$			7268.19i			1.80611i
$254$	5665.52	−	3679.99i	1.39955	−	0.909068i
$255$	388.509	+	444.570i	0.0954094	+	0.109177i
$256$	−425.072	+	4073.88i	−0.103777	+	0.994601i
$257$			2032.67i			0.493364i	0.969096	+	0.246682i	$0.0793404\pi$
$257$			2032.67i			0.493364i	−0.969096	+	0.246682i	$0.920660\pi$
$258$	−5351.21	−	1518.72i	−1.29129	−	0.366478i
$259$	545.683			0.130915
$260$	758.833	+	337.682i	0.181003	+	0.0805468i
$261$	−11.6914	+	86.4761i	−0.00277272	+	0.0205086i
$262$	1462.36	−	949.864i	0.344828	−	0.223980i
$263$	−4114.19			−0.964608			−0.482304	−	0.876004i	$-0.660200\pi$
$263$	−4114.19			−0.964608			−0.482304	+	0.876004i	$0.660200\pi$
$264$	−4456.24	−	3717.22i	−1.03887	−	0.866588i
$265$	−3013.05			−0.698453
$266$	−319.239	+	207.359i	−0.0735856	+	0.0477970i
$267$	765.600	+	876.073i	0.175483	+	0.200805i
$268$	−2225.92	+	5002.04i	−0.507350	+	1.14011i
$269$	5616.09			1.27293			0.636467	−	0.771304i	$-0.280395\pi$
$269$	5616.09			1.27293			0.636467	+	0.771304i	$0.280395\pi$
$270$	−792.550	+	1818.92i	−0.178641	+	0.409985i
$271$		−	4147.27i		−	0.929626i	−0.885409	−	0.464813i	$-0.846122\pi$
$271$		−	4147.27i		−	0.929626i	0.885409	−	0.464813i	$-0.153878\pi$
$272$	1080.45	−	973.584i	0.240853	−	0.217030i
$273$	−172.359	+	150.624i	−0.0382111	+	0.0333927i
$274$	4792.11	−	3112.68i	1.05658	−	0.686291i
$275$		−	1233.91i		−	0.270572i
$276$	−1806.19	−	5848.94i	−0.393913	−	1.27560i
$277$		−	2991.20i		−	0.648823i	−0.945916	−	0.324412i	$-0.894834\pi$
$277$		−	2991.20i		−	0.648823i	0.945916	−	0.324412i	$-0.105166\pi$
$278$	1855.59	+	2856.77i	0.400328	+	0.616324i
$279$	−3563.85	−	481.827i	−0.764739	−	0.103391i
$280$	−37.6148	−	237.056i	−0.00802826	−	0.0505957i
$281$		−	1078.93i		−	0.229052i	−0.993420	−	0.114526i	$-0.963465\pi$
$281$		−	1078.93i		−	0.229052i	0.993420	−	0.114526i	$-0.0365349\pi$
$282$	−6636.80	−	1883.58i	−1.40147	−	0.397750i
$283$	−4578.66			−0.961742			−0.480871	−	0.876791i	$-0.659680\pi$
$283$	−4578.66			−0.961742			−0.480871	+	0.876791i	$0.659680\pi$
$284$	−2923.28	+	6569.13i	−0.610791	+	1.37256i
$285$	1241.08	−	1084.58i	0.257948	−	0.225421i
$286$	1578.99	+	2430.92i	0.326459	+	0.502600i
$287$	−156.921			−0.0322744
$288$	4509.83	+	1883.96i	0.922723	+	0.385464i
$289$	4396.58			0.894888
$290$	24.8973	+	38.3306i	0.00504145	+	0.00776155i
$291$	−6387.94	+	5582.42i	−1.28683	+	1.12456i
$292$	1089.78	−	2448.93i	0.218406	−	0.490798i
$293$	−3633.82			−0.724539			−0.362269	−	0.932073i	$-0.617998\pi$
$293$	−3633.82			−0.724539			−0.362269	+	0.932073i	$0.617998\pi$
$294$	−4785.89	−	1358.28i	−0.949383	−	0.269443i
$295$			3189.41i			0.629474i
$296$	912.092	+	5748.18i	0.179102	+	1.12874i
$297$	−5777.52	+	3816.90i	−1.12877	+	0.745720i
$298$	−2913.75	−	4485.86i	−0.566406	−	0.872009i
$299$			3057.76i			0.591421i
$300$	306.633	+	992.963i	0.0590116	+	0.191096i
$301$		−	802.957i		−	0.153760i
$302$	−7742.27	+	5028.93i	−1.47522	+	0.958220i
$303$	3553.52	−	3105.42i	0.673743	−	0.588784i
$304$	−2717.90	−	3016.24i	−0.512771	−	0.569057i
$305$			1683.68i			0.316090i
$306$	−741.812	−	1568.90i	−0.138584	−	0.293099i
$307$	6970.15			1.29579			0.647895	−	0.761730i	$-0.275650\pi$
$307$	6970.15			1.29579			0.647895	+	0.761730i	$0.275650\pi$
$308$	340.570	−	765.321i	0.0630057	−	0.141585i
$309$	−3019.76	−	3455.50i	−0.555949	−	0.636170i
$310$	−1579.68	+	1026.07i	−0.289419	+	0.187989i
$311$	−2894.18			−0.527698			−0.263849	−	0.964564i	$-0.584992\pi$
$311$	−2894.18			−0.527698			−0.263849	+	0.964564i	$0.584992\pi$
$312$	−1874.76	−	1563.85i	−0.340184	−	0.283768i
$313$	7221.16			1.30404			0.652019	−	0.758202i	$-0.273922\pi$
$313$	7221.16			1.30404			0.652019	+	0.758202i	$0.273922\pi$
$314$	4308.16	−	2798.33i	0.774278	−	0.502926i
$315$	−283.822	−	38.3722i	−0.0507668	−	0.00686358i
$316$	5951.02	+	2648.22i	1.05940	+	0.471436i
$317$	4590.18			0.813281			0.406640	−	0.913588i	$-0.366700\pi$
$317$	4590.18			0.813281			0.406640	+	0.913588i	$0.366700\pi$
$318$	8520.02	+	2418.05i	1.50245	+	0.426408i
$319$			159.517i			0.0279976i
$320$	2434.26	−	792.463i	0.425247	−	0.138438i
$321$	3281.54	+	3755.05i	0.570585	+	0.652918i
$322$	741.036	−	481.334i	0.128249	−	0.0833033i
$323$			1441.65i			0.248346i
$324$	3700.84	−	4507.33i	0.634574	−	0.772862i
$325$		−	519.110i		−	0.0886001i
$326$	−3224.23	−	4963.85i	−0.547771	−	0.843319i
$327$	6359.71	+	7277.39i	1.07551	+	1.23070i
$328$	−262.289	−	1653.00i	−0.0441539	−	0.278266i
$329$		−	995.862i		−	0.166880i
$330$	−990.244	+	3489.13i	−0.165185	+	0.582031i
$331$	3675.01			0.610263			0.305131	−	0.952310i	$-0.401300\pi$
$331$	3675.01			0.610263			0.305131	+	0.952310i	$0.401300\pi$
$332$	−2713.26	−	1207.41i	−0.448523	−	0.199594i
$333$	6882.17	+	930.458i	1.13255	+	0.153119i
$334$	3662.37	+	5638.39i	0.599988	+	0.923709i
$335$	3421.85			0.558076
$336$	−83.8803	+	700.512i	−0.0136192	+	0.113738i
$337$	−6118.28			−0.988973			−0.494487	−	0.869185i	$-0.664644\pi$
$337$	−6118.28			−0.988973			−0.494487	+	0.869185i	$0.664644\pi$
$338$	−2720.62	−	4188.52i	−0.437817	−	0.674040i
$339$	1698.65	+	1943.76i	0.272147	+	0.311417i
$340$	−830.476	−	369.564i	−0.132467	−	0.0589483i
$341$	−6574.02			−1.04400
$342$	−4379.82	+	2070.88i	−0.692496	+	0.327427i
$343$		−	1445.81i		−	0.227598i
$344$	8458.29	−	1342.12i	1.32570	−	0.210355i
$345$	−2880.87	+	2517.59i	−0.449568	+	0.392877i
$346$	−2093.98	−	3223.79i	−0.325356	−	0.500901i
$347$			1384.77i			0.214231i	0.994247	+	0.107116i	$0.0341615\pi$
$347$			1384.77i			0.214231i	−0.994247	+	0.107116i	$0.965838\pi$
$348$	−39.6410	−	128.369i	−0.00610627	−	0.0197738i
$349$			6121.18i			0.938852i	0.882972	+	0.469426i	$0.155539\pi$
$349$			6121.18i			0.938852i	−0.882972	+	0.469426i	$0.844461\pi$
$350$	−125.804	+	81.7150i	−0.0192129	+	0.0124796i
$351$	−2430.63	+	1605.79i	−0.369623	+	0.244190i
$352$	8631.09	+	2308.33i	1.30693	+	0.349529i
$353$			3303.52i			0.498098i	0.968491	+	0.249049i	$0.0801181\pi$
$353$			3303.52i			0.498098i	−0.968491	+	0.249049i	$0.919882\pi$
$354$	2559.59	−	9018.74i	0.384296	−	1.35407i
$355$	4493.88			0.671860
$356$	−1636.54	−	728.266i	−0.243642	−	0.108421i
$357$	188.632	−	164.845i	0.0279649	−	0.0244385i
$358$	3353.64	−	2178.33i	0.495099	−	0.321588i
$359$	−4286.17			−0.630126			−0.315063	−	0.949071i	$-0.602026\pi$
$359$	−4286.17			−0.630126			−0.315063	+	0.949071i	$0.602026\pi$
$360$	−70.1890	−	3053.89i	−0.0102758	−	0.447096i
$361$	−2834.41			−0.413240
$362$	−8955.68	+	5817.09i	−1.30028	+	0.844584i
$363$	−4323.60	+	3778.40i	−0.625153	+	0.546321i
$364$	143.279	−	321.974i	0.0206315	−	0.0463627i
$365$	−1675.29			−0.240243
$366$	1351.20	−	4760.97i	0.192974	−	0.679944i
$367$		−	4206.09i		−	0.598245i	−0.954215	−	0.299122i	$-0.903306\pi$
$367$		−	4206.09i		−	0.598245i	0.954215	−	0.299122i	$-0.0966939\pi$
$368$	6308.95	+	7001.48i	0.893687	+	0.991787i
$369$	−1979.10	−	267.570i	−0.279208	−	0.0377484i
$370$	3050.53	−	1981.44i	0.428620	−	0.278407i
$371$			1278.44i			0.178904i
$372$	5290.32	−	1633.69i	0.737340	−	0.227695i
$373$			12816.9i			1.77917i	0.456767	+	0.889586i	$0.349007\pi$
$373$			12816.9i			1.77917i	−0.456767	+	0.889586i	$0.650993\pi$
$374$	−1728.06	−	2660.43i	−0.238920	−	0.367828i
$375$	489.080	−	427.406i	0.0673492	−	0.0588565i
$376$	10490.3	−	1664.55i	1.43882	−	0.228305i
$377$			67.1096i			0.00916796i
$378$	771.771	+	336.280i	0.105015	+	0.0457577i
$379$	−3874.74			−0.525150			−0.262575	−	0.964912i	$-0.584572\pi$
$379$	−3874.74			−0.525150			−0.262575	+	0.964912i	$0.584572\pi$
$380$	−1031.69	+	2318.39i	−0.139275	+	0.312977i
$381$	8166.97	+	9345.43i	1.09818	+	1.25664i
$382$	−429.905	−	661.858i	−0.0575807	−	0.0886482i
$383$	155.778			0.0207830			0.0103915	−	0.999946i	$-0.496692\pi$
$383$	155.778			0.0207830			0.0103915	+	0.999946i	$0.496692\pi$
$384$	−7519.35	+	287.295i	−0.999271	+	0.0381796i
$385$	−523.549			−0.0693052
$386$	478.966	+	737.390i	0.0631573	+	0.0972336i
$387$	1369.14	−	10126.9i	0.179838	−	1.33018i
$388$	5310.19	−	11933.0i	0.694805	−	1.56135i
$389$	−3847.71			−0.501509			−0.250754	−	0.968051i	$-0.580679\pi$
$389$	−3847.71			−0.501509			−0.250754	+	0.968051i	$0.580679\pi$
$390$	−416.601	+	1467.89i	−0.0540907	+	0.190589i
$391$		−	3346.45i		−	0.432832i
$392$	7564.72	−	1200.33i	0.974684	−	0.154658i
$393$	2108.02	+	2412.20i	0.270575	+	0.309617i
$394$	8363.23	+	12875.6i	1.06937	+	1.64635i
$395$		−	4071.03i		−	0.518572i
$396$	5600.25	−	9071.54i	0.710664	−	1.15117i
$397$		−	5159.76i		−	0.652294i	−0.945319	−	0.326147i	$-0.894250\pi$
$397$		−	5159.76i		−	0.652294i	0.945319	−	0.326147i	$-0.105750\pi$
$398$	−5448.43	+	3538.98i	−0.686193	+	0.445711i
$399$	−460.190	−	526.593i	−0.0577401	−	0.0660718i
$400$	−1071.06	−	1188.63i	−0.133882	−	0.148578i
$401$		−	2057.57i		−	0.256235i	−0.991759	−	0.128118i	$-0.959107\pi$
$401$		−	2057.57i		−	0.256235i	0.991759	−	0.128118i	$-0.0408935\pi$
$402$	−9676.00	−	2746.13i	−1.20049	−	0.340708i
$403$	−2765.72			−0.341862
$404$	−2953.98	+	6638.13i	−0.363777	+	0.817473i
$405$	−3514.14	−	967.904i	−0.431158	−	0.118754i
$406$	16.2637	−	10.5640i	0.00198807	−	0.00129133i
$407$	12695.1			1.54613
$408$	2051.76	+	1711.50i	0.248964	+	0.207676i
$409$	−15650.6			−1.89210			−0.946052	−	0.324014i	$-0.894968\pi$
$409$	−15650.6			−1.89210			−0.946052	+	0.324014i	$0.894968\pi$
$410$	−877.235	+	569.801i	−0.105667	+	0.0686353i
$411$	6907.93	+	7904.72i	0.829059	+	0.948689i
$412$	6455.03	+	2872.50i	0.771885	+	0.343491i
$413$	1353.27			0.161236
$414$	10166.7	−	4807.04i	1.20692	−	0.570660i
$415$			1856.12i			0.219550i
$416$	3631.14	+	971.124i	0.427960	+	0.114455i
$417$	−4712.33	+	4118.10i	−0.553390	+	0.483608i
$418$	−7426.98	+	4824.13i	−0.869056	+	0.564488i
$419$			14028.9i			1.63569i	0.575438	+	0.817846i	$0.304832\pi$
$419$			14028.9i			1.63569i	−0.575438	+	0.817846i	$0.695168\pi$
$420$	421.316	−	130.105i	0.0489479	−	0.0151154i
$421$		−	1330.48i		−	0.154023i	−0.997030	−	0.0770117i	$-0.975462\pi$
$421$		−	1330.48i		−	0.154023i	0.997030	−	0.0770117i	$-0.0245379\pi$
$422$	3151.59	+	4852.03i	0.363548	+	0.559699i
$423$	1698.07	−	12559.8i	0.195184	−	1.44369i
$424$	−13467.0	+	2136.87i	−1.54249	+	0.244754i
$425$			568.120i			0.0648421i
$426$	−12707.4	−	3606.47i	−1.44525	−	0.410173i
$427$	714.390			0.0809643
$428$	−7014.61	−	3121.52i	−0.792205	−	0.352533i
$429$	−4009.87	+	3504.23i	−0.451279	+	0.394372i
$430$	−2915.64	−	4488.76i	−0.326987	−	0.503413i
$431$	1425.04			0.159262			0.0796309	−	0.996824i	$-0.474626\pi$
$431$	1425.04			0.159262			0.0796309	+	0.996824i	$0.474626\pi$
$432$	−2252.36	+	8691.86i	−0.250849	+	0.968026i
$433$	6105.13			0.677584			0.338792	−	0.940861i	$-0.389982\pi$
$433$	6105.13			0.677584			0.338792	+	0.940861i	$0.389982\pi$
$434$	435.363	+	670.261i	0.0481522	+	0.0741326i
$435$	−63.2273	+	55.2543i	−0.00696901	+	0.00609021i
$436$	−13594.5	−	6049.58i	−1.49325	−	0.664501i
$437$	−9342.11			−1.02264
$438$	4737.24	+	1344.47i	0.516790	+	0.146669i
$439$		−	488.265i		−	0.0530834i	−0.999648	−	0.0265417i	$-0.991551\pi$
$439$		−	488.265i		−	0.0530834i	0.999648	−	0.0265417i	$-0.00844948\pi$
$440$	−875.095	−	5515.02i	−0.0948148	−	0.597542i
$441$	1224.50	−	9057.08i	0.132221	−	0.977981i
$442$	−727.004	−	1119.26i	−0.0782354	−	0.120447i
$443$			4153.50i			0.445460i	0.974880	+	0.222730i	$0.0714969\pi$
$443$			4153.50i			0.445460i	−0.974880	+	0.222730i	$0.928503\pi$
$444$	−10216.2	+	3154.82i	−1.09198	+	0.337210i
$445$			1119.54i			0.119262i
$446$	9310.79	−	6047.75i	0.988518	−	0.642084i
$447$	7399.54	−	6466.46i	0.782967	−	0.684235i
$448$	−336.243	−	1032.86i	−0.0354598	−	0.108924i
$449$		−	18142.3i		−	1.90688i	−0.301582	−	0.953440i	$-0.597515\pi$
$449$		−	18142.3i		−	1.90688i	0.301582	−	0.953440i	$-0.402485\pi$
$450$	−1725.98	+	816.081i	−0.180808	+	0.0854899i
$451$	−3650.72			−0.381165
$452$	−3631.02	−	1615.81i	−0.377852	−	0.168145i
$453$	−11160.7	−	12771.1i	−1.15756	−	1.32459i
$454$	−14644.4	+	9512.17i	−1.51387	+	0.983322i
$455$	−220.259			−0.0226943
$456$	4777.90	−	5727.79i	0.490670	−	0.588220i
$457$	−1622.04			−0.166030			−0.0830150	−	0.996548i	$-0.526455\pi$
$457$	−1622.04			−0.166030			−0.0830150	+	0.996548i	$0.526455\pi$
$458$	−537.591	+	349.188i	−0.0548471	+	0.0356255i
$459$	2660.11	−	1757.39i	0.270509	−	0.178711i
$460$	2394.82	−	5381.59i	0.242737	−	0.545474i
$461$	−7442.29			−0.751892			−0.375946	−	0.926642i	$-0.622682\pi$
$461$	−7442.29			−0.751892			−0.375946	+	0.926642i	$0.622682\pi$
$462$	1480.44	+	420.163i	0.149083	+	0.0423111i
$463$		−	6376.48i		−	0.640044i	−0.947410	−	0.320022i	$-0.896310\pi$
$463$		−	6376.48i		−	0.640044i	0.947410	−	0.320022i	$-0.103690\pi$
$464$	138.464	+	153.664i	0.0138536	+	0.0153743i
$465$	−2277.14	−	2605.73i	−0.227097	−	0.259866i
$466$	−9788.67	+	6358.15i	−0.973072	+	0.632051i
$467$		−	9624.46i		−	0.953676i	−0.878991	−	0.476838i	$-0.841783\pi$
$467$		−	9624.46i		−	0.953676i	0.878991	−	0.476838i	$-0.158217\pi$
$468$	2356.05	−	3816.44i	0.232711	−	0.376956i
$469$		−	1451.90i		−	0.142948i
$470$	−3616.10	−	5567.16i	−0.354890	−	0.546370i
$471$	6210.30	+	7106.42i	0.607549	+	0.695216i
$472$	2261.96	+	14255.3i	0.220583	+	1.39015i
$473$		−	18680.5i		−	1.81592i
$474$	−3267.12	+	11511.7i	−0.316590	+	1.11551i
$475$	1585.99			0.153201
$476$	−156.807	+	352.373i	−0.0150992	+	0.0339306i
$477$	−2179.90	+	16123.8i	−0.209247	+	1.54771i
$478$	−377.064	−	580.507i	−0.0360805	−	0.0555477i
$479$	2607.21			0.248699			0.124349	−	0.992239i	$-0.460316\pi$
$479$	2607.21			0.248699			0.124349	+	0.992239i	$0.460316\pi$
$480$	2074.73	+	4220.65i	0.197288	+	0.401345i
$481$	5340.90			0.506287
$482$	2399.74	+	3694.51i	0.226774	+	0.349130i
$483$	1068.22	+	1222.36i	0.100633	+	0.115154i
$484$	3594.14	−	8076.69i	0.337542	−	0.758517i
$485$	−8163.22			−0.764273
$486$	9160.20	+	5557.15i	0.854970	+	0.518678i
$487$		−	2039.84i		−	0.189803i	−0.995487	−	0.0949013i	$-0.969746\pi$
$487$		−	2039.84i		−	0.189803i	0.995487	−	0.0949013i	$-0.0302535\pi$
$488$	1194.08	+	7525.33i	0.110765	+	0.698065i
$489$	8188.01	−	7155.50i	0.757207	−	0.661723i
$490$	−2607.62	−	4014.55i	−0.240409	−	0.370121i
$491$		−	661.803i		−	0.0608284i	−0.999537	−	0.0304142i	$-0.990317\pi$
$491$		−	661.803i		−	0.0608284i	0.999537	−	0.0304142i	$-0.00968263\pi$
$492$	2937.85	−	907.226i	0.269204	−	0.0831319i
$493$		−	73.4456i		−	0.00670958i
$494$	−3124.57	+	2029.54i	−0.284577	+	0.184845i
$495$	−6603.02	−	892.717i	−0.599563	−	0.0810598i
$496$	−6332.79	+	5706.40i	−0.573287	+	0.516582i
$497$		−	1906.76i		−	0.172093i
$498$	1489.59	−	5248.56i	0.134036	−	0.472276i
$499$	−1563.40			−0.140255			−0.0701277	−	0.997538i	$-0.522341\pi$
$499$	−1563.40			−0.140255			−0.0701277	+	0.997538i	$0.522341\pi$
$500$	−406.564	+	913.622i	−0.0363642	+	0.0817169i
$501$	−9300.68	+	8127.86i	−0.829389	+	0.724802i
$502$	−12887.4	+	8370.93i	−1.14581	+	0.744249i
$503$	−3880.18			−0.343953			−0.171977	−	0.985101i	$-0.555015\pi$
$503$	−3880.18			−0.343953			−0.171977	+	0.985101i	$0.555015\pi$
$504$	−1295.77	+	29.7813i	−0.114521	+	0.00263207i
$505$	4541.08			0.400149
$506$	17239.9	−	11198.1i	1.51464	−	0.983824i
$507$	6909.09	−	6037.85i	0.605214	−	0.528896i
$508$	−17457.7	−	7768.71i	−1.52472	−	0.678506i
$509$	20738.2			1.80590			0.902951	−	0.429744i	$-0.141396\pi$
$509$	20738.2			1.80590			0.902951	+	0.429744i	$0.141396\pi$
$510$	455.933	−	1606.48i	0.0395864	−	0.139483i
$511$			710.829i			0.0615366i
$512$	10318.0	−	5268.36i	0.890620	−	0.454747i
$513$	−4906.02	−	7426.10i	−0.422234	−	0.639123i
$514$	4821.44	−	3131.73i	0.413745	−	0.268745i
$515$		−	4415.82i		−	0.377834i
$516$	4642.23	+	15032.8i	0.396051	+	1.28252i
$517$		−	23168.4i		−	1.97088i
$518$	−840.731	−	1294.34i	−0.0713120	−	0.109788i
$519$	5317.73	−	4647.16i	0.449754	−	0.393040i
$520$	−368.157	−	2320.20i	−0.0310476	−	0.195668i
$521$			16321.6i			1.37248i	0.727374	+	0.686241i	$0.240741\pi$
$521$			16321.6i			1.37248i	−0.727374	+	0.686241i	$0.759259\pi$
$522$	223.132	−	105.502i	0.0187092	−	0.00884613i
$523$	10585.2			0.885010			0.442505	−	0.896766i	$-0.354090\pi$
$523$	10585.2			0.885010			0.442505	+	0.896766i	$0.354090\pi$
$524$	−4506.11	−	2005.23i	−0.375668	−	0.167173i
$525$	−181.349	−	207.517i	−0.0150757	−	0.0172511i
$526$	6338.72	+	9758.75i	0.525440	+	0.808939i
$527$	3026.84			0.250192
$528$	−1951.45	+	16297.2i	−0.160844	+	1.34326i
$529$	9518.45			0.782317
$530$	4642.19	+	7146.86i	0.380460	+	0.585736i
$531$	17067.6	+	2307.50i	1.39486	+	0.188582i
$532$	983.699	+	437.749i	0.0801669	+	0.0356745i
$533$	−1535.87			−0.124814
$534$	898.465	−	3165.75i	0.0728097	−	0.256545i
$535$			4798.62i			0.387781i
$536$	15294.2	−	2426.80i	1.23248	−	0.195563i
$537$	4834.35	+	5531.93i	0.388487	+	0.444544i
$538$	−8652.69	−	13321.2i	−0.693391	−	1.06751i
$539$		−	16707.0i		−	1.33511i
$540$	5535.50	−	922.493i	0.441130	−	0.0735144i
$541$			15140.9i			1.20325i	0.798778	+	0.601626i	$0.205480\pi$
$541$			15140.9i			1.20325i	−0.798778	+	0.601626i	$0.794520\pi$
$542$	−9837.21	+	6389.68i	−0.779602	+	0.506384i
$543$	−12909.8	−	14772.6i	−1.02028	−	1.16750i
$544$	−3973.96	−	1062.81i	−0.313203	−	0.0837640i
$545$			9299.85i			0.730939i
$546$	622.830	+	176.764i	0.0488181	+	0.0138550i
$547$	−699.173			−0.0546517			−0.0273258	−	0.999627i	$-0.508699\pi$
$547$	−699.173			−0.0546517			−0.0273258	+	0.999627i	$0.508699\pi$
$548$	−14766.4	−	6571.07i	−1.15107	−	0.512230i
$549$	9009.91	+	1218.12i	0.700426	+	0.0946964i
$550$	−2926.79	+	1901.07i	−0.226907	+	0.147385i
$551$	−205.034			−0.0158525
$552$	−11090.7	+	13295.7i	−0.855169	+	1.02518i
$553$	−1727.35			−0.132829
$554$	−7095.05	+	4608.53i	−0.544115	+	0.353426i
$555$	4397.40	+	5031.93i	0.336323	+	0.384853i
$556$	3917.29	−	8802.84i	0.298795	−	0.671445i
$557$	13008.4			0.989559			0.494779	−	0.869019i	$-0.335249\pi$
$557$	13008.4			0.989559			0.494779	+	0.869019i	$0.335249\pi$
$558$	4347.93	+	9195.71i	0.329861	+	0.697644i
$559$		−	7858.98i		−	0.594633i
$560$	−504.337	+	454.452i	−0.0380574	+	0.0342930i
$561$	4388.46	−	3835.07i	0.330269	−	0.288622i
$562$	−2559.19	+	1662.30i	−0.192087	+	0.124769i
$563$			4124.28i			0.308735i	0.988014	+	0.154367i	$0.0493339\pi$
$563$			4124.28i			0.308735i	−0.988014	+	0.154367i	$0.950666\pi$
$564$	5757.49	+	18644.3i	0.429848	+	1.39197i
$565$			2483.95i			0.184957i
$566$	7054.32	+	10860.5i	0.523879	+	0.806536i
$567$	−410.684	+	1491.06i	−0.0304181	+	0.110438i
$568$	20085.7	−	3187.09i	1.48376	−	0.235436i
$569$			7809.64i			0.575390i	0.957722	+	0.287695i	$0.0928890\pi$
$569$			7809.64i			0.575390i	−0.957722	+	0.287695i	$0.907111\pi$
$570$	−4484.72	−	1272.80i	−0.329552	−	0.0935295i
$571$	−19888.2			−1.45761			−0.728806	−	0.684720i	$-0.759925\pi$
$571$	−19888.2			−1.45761			−0.728806	+	0.684720i	$0.759925\pi$
$572$	3333.35	−	7490.62i	0.243661	−	0.547550i
$573$	1091.75	−	954.083i	0.0795963	−	0.0695592i
$574$	241.768	+	372.213i	0.0175805	+	0.0270660i
$575$	−3681.50			−0.267007
$576$	−2479.56	−	13599.8i	−0.179366	−	0.983782i
$577$	−15380.8			−1.10972			−0.554862	−	0.831942i	$-0.687229\pi$
$577$	−15380.8			−1.10972			−0.554862	+	0.831942i	$0.687229\pi$
$578$	−6773.80	−	10428.6i	−0.487462	−	0.750470i
$579$	−1216.35	+	1062.96i	−0.0873050	+	0.0762958i
$580$	52.5599	−	118.111i	0.00376281	−	0.00845571i
$581$	787.554			0.0562362
$582$	23083.2	+	6551.21i	1.64404	+	0.466592i
$583$			29742.5i			2.11288i
$584$	−7487.82	+	1188.13i	−0.530562	+	0.0841868i
$585$	−2777.92	−	375.570i	−0.196330	−	0.0265435i
$586$	5598.61	+	8619.32i	0.394670	+	0.607612i
$587$			19039.0i			1.33871i	0.742942	+	0.669356i	$0.233430\pi$
$587$			19039.0i			1.33871i	−0.742942	+	0.669356i	$0.766570\pi$
$588$	4151.80	+	13444.7i	0.291186	+	0.942942i
$589$		−	8449.87i		−	0.591122i
$590$	7565.20	−	4913.92i	0.527889	−	0.342886i
$591$	−21238.6	+	18560.4i	−1.47824	+	1.29183i
$592$	12229.3	−	11019.7i	0.849021	−	0.765042i
$593$			10069.9i			0.697337i	0.937246	+	0.348668i	$0.113366\pi$
$593$			10069.9i			0.697337i	−0.937246	+	0.348668i	$0.886634\pi$
$594$	17955.0	+	7823.45i	1.24024	+	0.540404i
$595$	241.055			0.0166089
$596$	−6151.13	+	13822.7i	−0.422752	+	0.949998i
$597$	−7854.03	−	8987.33i	−0.538432	−	0.616126i
$598$	7252.93	−	4711.08i	0.495977	−	0.322158i
$599$	2164.05			0.147614			0.0738068	−	0.997273i	$-0.476485\pi$
$599$	2164.05			0.147614			0.0738068	+	0.997273i	$0.476485\pi$
$600$	1882.85	−	2257.18i	0.128112	−	0.153582i
$601$	9974.80			0.677006			0.338503	−	0.940965i	$-0.390079\pi$
$601$	9974.80			0.677006			0.338503	+	0.940965i	$0.390079\pi$
$602$	−1904.59	+	1237.11i	−0.128946	+	0.0837557i
$603$	2475.67	−	18311.4i	0.167192	−	1.23665i
$604$	23857.0	+	10616.4i	1.60716	+	0.715191i
$605$	−5525.18			−0.371290
$606$	−12840.8	−	3644.34i	−0.860765	−	0.244293i
$607$			1696.56i			0.113445i	0.998390	+	0.0567225i	$0.0180650\pi$
$607$			1696.56i			0.113445i	−0.998390	+	0.0567225i	$0.981935\pi$
$608$	−2966.99	+	11093.9i	−0.197907	+	0.739995i
$609$	23.4445	+	26.8275i	0.00155997	+	0.00178507i
$610$	3993.65	−	2594.04i	0.265079	−	0.172180i
$611$		−	9747.06i		−	0.645374i
$612$	−2578.49	+	4176.76i	−0.170309	+	0.275875i
$613$		−	24762.2i		−	1.63154i	−0.578374	−	0.815772i	$-0.696312\pi$
$613$		−	24762.2i		−	1.63154i	0.578374	−	0.815772i	$-0.303688\pi$
$614$	−10738.9	−	16533.0i	−0.705840	−	1.08667i
$615$	−1264.55	−	1447.02i	−0.0829134	−	0.0948775i
$616$	−2340.04	+	371.305i	−0.153056	+	0.0242862i
$617$			6264.97i			0.408781i	0.978889	+	0.204391i	$0.0655213\pi$
$617$			6264.97i			0.408781i	−0.978889	+	0.204391i	$0.934479\pi$
$618$	−3543.82	+	12486.7i	−0.230669	+	0.812763i
$619$	−19064.8			−1.23793			−0.618965	−	0.785419i	$-0.712448\pi$
$619$	−19064.8			−1.23793			−0.618965	+	0.785419i	$0.712448\pi$
$620$	4867.61	+	2166.10i	0.315303	+	0.140311i
$621$	11388.1	+	17237.9i	0.735895	+	1.11390i
$622$	4459.06	+	6864.92i	0.287447	+	0.442538i
$623$	475.025			0.0305481
$624$	−820.983	+	6856.30i	−0.0526693	+	0.439859i
$625$	625.000			0.0400000
$626$	−11125.6	−	17128.4i	−0.710334	−	1.09359i
$627$	−10706.2	−	12251.0i	−0.681918	−	0.780316i
$628$	−13275.1	−	5907.46i	−0.843527	−	0.375372i
$629$	−5845.15			−0.370527
$630$	346.265	+	732.337i	0.0218977	+	0.0463127i
$631$			25692.3i			1.62091i	0.585803	+	0.810454i	$0.300779\pi$
$631$			25692.3i			1.62091i	−0.585803	+	0.810454i	$0.699221\pi$
$632$	−2887.21	−	18195.8i	−0.181720	−	1.14523i
$633$	−8003.55	+	6994.30i	−0.502548	+	0.439176i
$634$	−7072.06	−	10887.8i	−0.443009	−	0.682033i
$635$			11942.6i			0.746345i
$636$	−7391.20	−	23934.7i	−0.460818	−	1.49226i
$637$		−	7028.73i		−	0.437188i
$638$	378.370	−	245.767i	0.0234793	−	0.0152508i
$639$	3251.27	−	24048.2i	0.201281	−	1.48878i
$640$	−5630.15	−	4553.05i	−0.347736	−	0.281211i
$641$			21723.0i			1.33855i	0.743017	+	0.669273i	$0.233394\pi$
$641$			21723.0i			1.33855i	−0.743017	+	0.669273i	$0.766606\pi$
$642$	3851.03	−	13569.1i	0.236742	−	0.834160i
$643$	−6066.07			−0.372041			−0.186021	−	0.982546i	$-0.559559\pi$
$643$	−6066.07			−0.372041			−0.186021	+	0.982546i	$0.559559\pi$
$644$	−2283.42	−	1016.13i	−0.139720	−	0.0621756i
$645$	7404.34	−	6470.65i	0.452009	−	0.395010i
$646$	3419.56	−	2221.15i	0.208268	−	0.135279i
$647$	−20896.7			−1.26976			−0.634880	−	0.772610i	$-0.718951\pi$
$647$	−20896.7			−1.26976			−0.634880	+	0.772610i	$0.718951\pi$
$648$	−16393.1	−	1833.85i	−0.993801	−	0.111174i
$649$	31483.5			1.90421
$650$	−1231.32	+	799.791i	−0.0743018	+	0.0482621i
$651$	−1105.61	+	966.196i	−0.0665629	+	0.0581693i
$652$	−6806.56	+	15295.6i	−0.408843	+	0.918743i
$653$	15326.8			0.918506			0.459253	−	0.888305i	$-0.348117\pi$
$653$	15326.8			0.918506			0.459253	+	0.888305i	$0.348117\pi$
$654$	7463.40	−	26297.3i	0.446241	−	1.57233i
$655$			3082.58i			0.183888i
$656$	−3516.75	+	3168.90i	−0.209308	+	0.188605i
$657$	−1212.05	+	8965.00i	−0.0719737	+	0.532356i
$658$	−2362.16	+	1534.32i	−0.139949	+	0.0909028i
$659$			24317.8i			1.43746i	0.695290	+	0.718729i	$0.255276\pi$
$659$			24317.8i			1.43746i	−0.695290	+	0.718729i	$0.744724\pi$
$660$	9801.78	−	3026.85i	0.578082	−	0.178515i
$661$		−	15557.6i		−	0.915463i	−0.889090	−	0.457731i	$-0.848662\pi$
$661$		−	15557.6i		−	0.915463i	0.889090	−	0.457731i	$-0.151338\pi$
$662$	−5662.08	−	8717.03i	−0.332421	−	0.511778i
$663$	1846.25	−	1613.43i	0.108148	−	0.0945106i
$664$	1316.37	+	8296.04i	0.0769354	+	0.484862i
$665$		−	672.939i		−	0.0392413i
$666$	−8396.31	−	17757.9i	−0.488514	−	1.03319i
$667$	475.937			0.0276287
$668$	7731.51	−	17374.1i	0.447816	−	1.00632i
$669$	13421.7	+	15358.4i	0.775655	+	0.887579i
$670$	−5272.03	−	8116.54i	−0.303994	−	0.468014i
$671$	16620.0			0.956199
$672$	1790.83	−	880.314i	0.102802	−	0.0505340i
$673$	−1782.31			−0.102085			−0.0510425	−	0.998696i	$-0.516254\pi$
$673$	−1782.31			−0.102085			−0.0510425	+	0.998696i	$0.516254\pi$
$674$	9426.41	+	14512.4i	0.538712	+	0.829372i
$675$	−1933.34	−	2926.44i	−0.110244	−	0.166872i
$676$	−5743.42	+	12906.5i	−0.326776	+	0.734324i
$677$	18582.5			1.05492			0.527461	−	0.849579i	$-0.323144\pi$
$677$	18582.5			1.05492			0.527461	+	0.849579i	$0.323144\pi$
$678$	1993.44	−	7023.89i	0.112917	−	0.397862i
$679$			3463.67i			0.195764i
$680$	402.915	+	2539.25i	0.0227222	+	0.143200i
$681$	−21110.3	−	24156.4i	−1.18788	−	1.35929i
$682$	10128.6	+	15593.4i	0.568684	+	0.875516i
$683$		−	8579.39i		−	0.480646i	−0.970693	−	0.240323i	$-0.922747\pi$
$683$		−	8579.39i		−	0.480646i	0.970693	−	0.240323i	$-0.0772534\pi$
$684$	11660.0	+	7198.24i	0.651802	+	0.402385i
$685$			10101.5i			0.563445i
$686$	−3429.42	+	2227.55i	−0.190868	+	0.123977i
$687$	−774.949	−	886.771i	−0.0430366	−	0.0492466i
$688$	−16215.1	−	17995.0i	−0.898540	−	0.997172i
$689$			12512.8i			0.691873i
$690$	10410.2	+	2954.50i	0.574362	+	0.163009i
$691$	9070.98			0.499387			0.249694	−	0.968325i	$-0.419670\pi$
$691$	9070.98			0.499387			0.249694	+	0.968325i	$0.419670\pi$
$692$	−4420.54	+	9933.75i	−0.242838	+	0.545700i
$693$	−378.781	+	2801.67i	−0.0207629	+	0.153574i
$694$	3284.63	−	2133.51i	0.179659	−	0.116696i
$695$	−6021.94			−0.328669
$696$	−243.412	+	291.804i	−0.0132565	+	0.0158920i
$697$	1680.88			0.0913456
$698$	14519.3	−	9430.88i	0.787339	−	0.511410i
$699$	−14110.6	−	16146.7i	−0.763535	−	0.873711i
$700$	387.652	+	172.506i	0.0209312	+	0.00931445i
$701$	5502.03			0.296446			0.148223	−	0.988954i	$-0.452645\pi$
$701$	5502.03			0.296446			0.148223	+	0.988954i	$0.452645\pi$
$702$	7553.75	+	3291.36i	0.406123	+	0.176958i
$703$			16317.6i			0.875433i
$704$	−7822.59	−	24029.1i	−0.418785	−	1.28641i
$705$	9183.19	−	8025.18i	0.490580	−	0.428718i
$706$	7835.87	−	5089.72i	0.417715	−	0.271323i
$707$		−	1926.79i		−	0.102495i
$708$	−25335.8	+	7823.84i	−1.34488	+	0.415308i
$709$		−	25605.1i		−	1.35631i	−0.734920	−	0.678153i	$-0.762780\pi$
$709$		−	25605.1i		−	1.35631i	0.734920	−	0.678153i	$-0.237220\pi$
$710$	−6923.70	−	10659.4i	−0.365974	−	0.563435i
$711$	−21785.4	−	2945.35i	−1.14911	−	0.155357i
$712$	793.989	+	5003.87i	0.0417921	+	0.263382i
$713$			19614.3i			1.03024i
$714$	−681.633	−	193.453i	−0.0357275	−	0.0101398i
$715$	−5124.26			−0.268023
$716$	−10333.9	−	4598.60i	−0.539379	−	0.240025i
$717$	957.563	−	836.814i	0.0498756	−	0.0435863i
$718$	6603.68	+	10166.7i	0.343241	+	0.528436i
$719$	−13697.2			−0.710459			−0.355230	−	0.934779i	$-0.615597\pi$
$719$	−13697.2			−0.710459			−0.355230	+	0.934779i	$0.615597\pi$
$720$	−7135.62	+	4871.61i	−0.369345	+	0.252159i
$721$	−1873.64			−0.0967796
$722$	4366.97	+	6723.15i	0.225099	+	0.346551i
$723$	−6094.21	+	5325.72i	−0.313480	+	0.273950i
$724$	27595.9	+	12280.3i	1.41657	+	0.630376i
$725$	−80.7989			−0.00413903
$726$	15623.6	+	4434.11i	0.798687	+	0.226674i
$727$			15762.1i			0.804107i	0.915616	+	0.402053i	$0.131703\pi$
$727$			15762.1i			0.804107i	−0.915616	+	0.402053i	$0.868297\pi$
$728$	−984.464	+	156.210i	−0.0501191	+	0.00795263i
$729$	−7722.00	+	18105.0i	−0.392318	+	0.919830i
$730$	2581.11	+	3973.74i	0.130865	+	0.201472i
$731$			8600.97i			0.435182i
$732$	−13374.7	+	4130.18i	−0.675331	+	0.208546i
$733$			23392.7i			1.17875i	0.807858	+	0.589377i	$0.200627\pi$
$733$			23392.7i			1.17875i	−0.807858	+	0.589377i	$0.799373\pi$
$734$	−9976.72	+	6480.30i	−0.501700	+	0.325875i
$735$	6622.12	−	5787.07i	0.332327	−	0.290421i
$736$	6887.15	−	25751.8i	0.344924	−	1.28971i
$737$		−	33777.9i		−	1.68823i
$738$	2414.51	+	5106.61i	0.120433	+	0.254711i
$739$	−15282.8			−0.760742			−0.380371	−	0.924834i	$-0.624204\pi$
$739$	−15282.8			−0.760742			−0.380371	+	0.924834i	$0.624204\pi$
$740$	−9399.87	−	4182.96i	−0.466954	−	0.207796i
$741$	−4504.13	−	5154.06i	−0.223297	−	0.255518i
$742$	3032.43	−	1969.69i	0.150032	−	0.0974522i
$743$	5140.07			0.253796			0.126898	−	0.991916i	$-0.459498\pi$
$743$	5140.07			0.253796			0.126898	+	0.991916i	$0.459498\pi$
$744$	−12025.8	−	10031.5i	−0.592592	−	0.494318i
$745$	9455.96			0.465019
$746$	30401.2	−	19746.9i	1.49205	−	0.969148i
$747$	9932.66	+	1342.88i	0.486502	+	0.0657743i
$748$	−3648.05	+	8197.83i	−0.178324	+	0.400725i
$749$	2036.07			0.0993274
$750$	−1767.32	−	501.580i	−0.0860445	−	0.0244202i
$751$		−	18396.1i		−	0.893854i	−0.894570	−	0.446927i	$-0.852518\pi$
$751$		−	18396.1i		−	0.893854i	0.894570	−	0.446927i	$-0.147482\pi$
$752$	−20110.7	−	22318.2i	−0.975214	−	1.08226i
$753$	−18577.5	−	21258.2i	−0.899074	−	1.02881i
$754$	159.182	−	103.396i	0.00768843	−	0.00499396i
$755$		−	16320.3i		−	0.786698i
$756$	−391.416	−	2348.73i	−0.0188302	−	0.112992i
$757$			1913.93i			0.0918929i	0.998944	+	0.0459465i	$0.0146304\pi$
$757$			1913.93i			0.0918929i	−0.998944	+	0.0459465i	$0.985370\pi$
$758$	5969.79	+	9190.77i	0.286059	+	0.440401i
$759$	24851.8	+	28437.8i	1.18849	+	1.35998i
$760$	7088.69	−	1124.80i	0.338334	−	0.0536851i
$761$			21307.3i			1.01497i	0.861662	+	0.507483i	$0.169424\pi$
$761$			21307.3i			1.01497i	−0.861662	+	0.507483i	$0.830576\pi$
$762$	9584.30	−	33770.3i	0.455646	−	1.60547i
$763$	3945.95			0.187225
$764$	−907.558	+	2039.44i	−0.0429768	+	0.0965766i
$765$	3040.19	+	411.029i	0.143684	+	0.0194258i
$766$	−240.006	−	369.501i	−0.0113209	−	0.0174290i
$767$	13245.3			0.623544
$768$	12266.5	+	17393.1i	0.576339	+	0.817211i
$769$	−8997.88			−0.421940			−0.210970	−	0.977493i	$-0.567662\pi$
$769$	−8997.88			−0.421940			−0.210970	+	0.977493i	$0.567662\pi$
$770$	806.629	+	1241.84i	0.0377518	+	0.0581207i
$771$	6950.22	+	7953.11i	0.324651	+	0.371497i
$772$	1011.13	−	2272.19i	0.0471391	−	0.105930i
$773$	−1960.11			−0.0912036			−0.0456018	−	0.998960i	$-0.514521\pi$
$773$	−1960.11			−0.0912036			−0.0456018	+	0.998960i	$0.514521\pi$
$774$	−26130.2	+	12354.9i	−1.21348	+	0.573758i
$775$		−	3329.88i		−	0.154339i
$776$	−36486.0	+	5789.41i	−1.68785	+	0.267819i
$777$	2135.06	−	1865.83i	0.0985776	−	0.0861469i
$778$	5928.16	+	9126.67i	0.273181	+	0.420575i
$779$		−	4692.42i		−	0.215820i
$780$	4123.66	−	1273.41i	0.189296	−	0.0584557i
$781$		−	44360.2i		−	2.03244i
$782$	−7937.70	+	5155.86i	−0.362981	+	0.235772i
$783$	249.939	+	378.325i	0.0114075	+	0.0172672i
$784$	−14502.1	−	16094.0i	−0.660627	−	0.733144i
$785$			9081.38i			0.412902i
$786$	2473.86	−	8716.65i	0.112264	−	0.395563i
$787$	−35288.0			−1.59833			−0.799163	−	0.601115i	$-0.794723\pi$
$787$	−35288.0			−1.59833			−0.799163	+	0.601115i	$0.794723\pi$
$788$	17655.3	−	39674.7i	0.798154	−	1.79359i
$789$	−16097.3	+	14067.5i	−0.726337	+	0.634746i
$790$	−9656.38	+	6272.22i	−0.434884	+	0.282476i
$791$	1053.94			0.0473754
$792$	−30145.7	+	692.852i	−1.35250	+	0.0310852i
$793$	6992.13			0.313112
$794$	−12238.8	+	7949.61i	−0.547026	+	0.355316i
$795$	−11789.0	+	10302.4i	−0.525926	+	0.459606i
$796$	16788.7	+	7471.03i	0.747564	+	0.332668i
$797$	16523.4			0.734363			0.367181	−	0.930149i	$-0.380323\pi$
$797$	16523.4			0.734363			0.367181	+	0.930149i	$0.380323\pi$
$798$	−540.053	+	1902.88i	−0.0239570	+	0.0844124i
$799$			10667.3i			0.472318i
$800$	−1169.22	+	4371.83i	−0.0516726	+	0.193210i
$801$	5991.03	+	809.977i	0.264273	+	0.0357292i
$802$	−4880.51	+	3170.09i	−0.214884	+	0.139576i
$803$			16537.2i			0.726756i
$804$	8394.02	+	27182.2i	0.368202	+	1.19234i
$805$			1562.07i			0.0683920i
$806$	4261.14	+	6560.22i	0.186219	+	0.286692i
$807$	21973.7	−	19202.8i	0.958503	−	0.837636i
$808$	20296.6	−	3220.57i	0.883705	−	0.140222i
$809$		−	37006.7i		−	1.60826i	−0.594451	−	0.804132i	$-0.702631\pi$
$809$		−	37006.7i		−	1.60826i	0.594451	−	0.804132i	$-0.297369\pi$
$810$	3118.38	+	9826.69i	0.135270	+	0.426265i
$811$	8419.68			0.364556			0.182278	−	0.983247i	$-0.441653\pi$
$811$	8419.68			0.364556			0.182278	+	0.983247i	$0.441653\pi$
$812$	−50.1149	−	22.3013i	−0.00216587	−	0.000963819i
$813$	−14180.6	−	16226.8i	−0.611727	−	0.699996i
$814$	−19559.3	−	30112.5i	−0.842204	−	1.29661i
$815$	10463.5			0.449720
$816$	898.494	−	7503.62i	0.0385461	−	0.321911i
$817$	24010.9			1.02819
$818$	24112.8	+	37122.7i	1.03066	+	1.58676i
$819$	−159.355	+	1178.68i	−0.00679893	+	0.0502886i
$820$	2703.11	+	1202.89i	0.115118	+	0.0512277i
$821$	−32309.8			−1.37347			−0.686736	−	0.726907i	$-0.740957\pi$
$821$	−32309.8			−1.37347			−0.686736	+	0.726907i	$0.740957\pi$
$822$	8106.76	−	28564.2i	0.343985	−	1.21203i
$823$			11085.4i			0.469516i	0.972054	+	0.234758i	$0.0754297\pi$
$823$			11085.4i			0.469516i	−0.972054	+	0.234758i	$0.924570\pi$
$824$	−3131.73	−	19736.8i	−0.132402	−	0.834423i
$825$	−4219.03	−	4827.82i	−0.178046	−	0.203737i
$826$	−2084.98	−	3209.93i	−0.0878279	−	0.135215i
$827$			22686.3i			0.953905i	0.878929	+	0.476952i	$0.158259\pi$
$827$			22686.3i			0.953905i	−0.878929	+	0.476952i	$0.841741\pi$
$828$	−27066.0	−	16709.0i	−1.13600	−	0.701301i
$829$			20839.4i			0.873077i	0.899686	+	0.436539i	$0.143796\pi$
$829$			20839.4i			0.873077i	−0.899686	+	0.436539i	$0.856204\pi$
$830$	4402.66	−	2859.71i	0.184119	−	0.119593i
$831$	−10227.7	−	11703.5i	−0.426948	−	0.488555i
$832$	−3291.00	−	10109.2i	−0.137133	−	0.421241i
$833$			7692.33i			0.319956i
$834$	17028.3	+	4832.78i	0.707004	+	0.200654i
$835$	−11885.4			−0.492590
$836$	22885.4	+	10184.1i	0.946781	+	0.421320i
$837$	−15591.5	+	10300.5i	−0.643874	+	0.425373i
$838$	33276.1	−	21614.2i	1.37172	−	0.890991i
$839$	−36416.6			−1.49850			−0.749249	−	0.662288i	$-0.769586\pi$
$839$	−36416.6			−1.49850			−0.749249	+	0.662288i	$0.769586\pi$
$840$	−957.726	−	798.899i	−0.0393389	−	0.0328150i
$841$	−24378.6			−0.999572
$842$	−3155.87	+	2049.87i	−0.129167	+	0.0838994i
$843$	−3689.13	−	4221.46i	−0.150724	−	0.172473i
$844$	6653.23	−	14951.0i	0.271343	−	0.609757i
$845$	8829.20			0.359448
$846$	−32407.8	+	15323.1i	−1.31703	+	0.622719i
$847$			2344.35i			0.0951035i
$848$	25817.2	+	28651.1i	1.04548	+	1.16024i
$849$	−17914.6	+	15655.6i	−0.724180	+	0.632860i
$850$	1347.57	−	875.301i	0.0543778	−	0.0353207i
$851$		−	37877.3i		−	1.52576i
$852$	11023.8	+	35698.1i	0.443273	+	1.43544i
$853$		−	3036.26i		−	0.121875i	−0.998142	−	0.0609376i	$-0.980591\pi$
$853$		−	3036.26i		−	0.121875i	0.998142	−	0.0609376i	$-0.0194091\pi$
$854$	−1100.66	−	1694.51i	−0.0441027	−	0.0678982i
$855$	1147.45	−	8487.14i	0.0458969	−	0.339478i
$856$	3403.22	+	21447.8i	0.135887	+	0.856390i
$857$		−	2455.97i		−	0.0978930i	−0.998801	−	0.0489465i	$-0.984414\pi$
$857$		−	2455.97i		−	0.0978930i	0.998801	−	0.0489465i	$-0.0155864\pi$
$858$	14489.9	+	4112.37i	0.576548	+	0.163629i
$859$	48081.9			1.90982			0.954910	−	0.296897i	$-0.0959518\pi$
$859$	48081.9			1.90982			0.954910	+	0.296897i	$0.0959518\pi$
$860$	−6155.11	+	13831.6i	−0.244055	+	0.548436i
$861$	−613.975	+	536.553i	−0.0243022	+	0.0212377i
$862$	−2195.56	−	3380.16i	−0.0867528	−	0.133560i
$863$	37715.6			1.48767			0.743833	−	0.668366i	$-0.233006\pi$
$863$	37715.6			1.48767			0.743833	+	0.668366i	$0.233006\pi$
$864$	24087.1	−	8048.97i	0.948447	−	0.316934i
$865$	6795.58			0.267118
$866$	−9406.16	−	14481.2i	−0.369093	−	0.568235i
$867$	17202.2	−	15033.0i	0.673839	−	0.588868i
$868$	919.080	−	2065.34i	0.0359396	−	0.0807628i
$869$	−40186.2			−1.56873
$870$	228.476	+	64.8434i	0.00890352	+	0.00252689i
$871$		−	14210.5i		−	0.552819i
$872$	6595.53	+	41566.3i	0.256138	+	1.61424i
$873$	−5905.99	+	43683.9i	−0.228966	+	1.69356i
$874$	14393.3	+	22159.2i	0.557051	+	0.857605i
$875$		−	265.189i		−	0.0102457i
$876$	−4109.60	−	13308.0i	−0.158505	−	0.513283i
$877$			26421.8i			1.01733i	0.860964	+	0.508666i	$0.169861\pi$
$877$			26421.8i			1.01733i	−0.860964	+	0.508666i	$0.830139\pi$
$878$	−1158.15	+	752.268i	−0.0445168	+	0.0289155i
$879$	−14217.8	+	12424.9i	−0.545569	+	0.476772i
$880$	−11733.2	+	10572.7i	−0.449463	+	0.405005i
$881$		−	19571.6i		−	0.748448i	−0.927338	−	0.374224i	$-0.877909\pi$
$881$		−	19571.6i		−	0.748448i	0.927338	−	0.374224i	$-0.122091\pi$
$882$	−23369.7	+	11049.7i	−0.892177	+	0.421840i
$883$	41428.8			1.57892			0.789462	−	0.613799i	$-0.210360\pi$
$883$	41428.8			1.57892			0.789462	+	0.613799i	$0.210360\pi$
$884$	−1534.75	+	3448.87i	−0.0583930	+	0.131219i
$885$	10905.4	+	12479.0i	0.414216	+	0.473986i
$886$	9852.00	−	6399.29i	0.373572	−	0.242650i
$887$	−33612.2			−1.27237			−0.636183	−	0.771539i	$-0.719487\pi$
$887$	−33612.2			−1.27237			−0.636183	+	0.771539i	$0.719487\pi$
$888$	23223.2	+	19371.9i	0.877611	+	0.732069i
$889$	5067.28			0.191171
$890$	2655.53	−	1724.88i	0.100015	−	0.0649640i
$891$	−9554.41	+	34688.9i	−0.359242	+	1.30429i
$892$	−28690.2	−	12767.2i	−1.07693	−	0.479235i
$893$	29779.3			1.11593
$894$	−26738.7	−	7588.67i	−1.00031	−	0.283896i
$895$			7069.31i			0.264023i
$896$	−1931.87	+	2388.88i	−0.0720303	+	0.0890703i
$897$	10455.3	+	11963.9i	0.389176	+	0.445333i
$898$	−43033.1	+	27951.8i	−1.59915	+	1.03871i
$899$			430.482i			0.0159704i
$900$	4594.94	+	2836.65i	0.170183	+	0.105061i
$901$		−	13694.2i		−	0.506348i
$902$	5624.64	+	8659.40i	0.207628	+	0.319652i
$903$	−2745.51	−	3141.68i	−0.101179	−	0.115779i
$904$	1761.63	+	11102.2i	0.0648132	+	0.408465i
$905$		−	18878.1i		−	0.693403i
$906$	−13097.5	+	46149.1i	−0.480282	+	1.69228i
$907$	−6210.83			−0.227373			−0.113686	−	0.993517i	$-0.536266\pi$
$907$	−6210.83			−0.227373			−0.113686	+	0.993517i	$0.536266\pi$
$908$	45125.2	+	20080.8i	1.64927	+	0.733927i
$909$	3285.42	−	24300.7i	0.119879	−	0.886693i
$910$	339.353	+	522.450i	0.0123620	+	0.0190319i
$911$	9675.39			0.351877			0.175939	−	0.984401i	$-0.443704\pi$
$911$	9675.39			0.351877			0.175939	+	0.984401i	$0.443704\pi$
$912$	−20947.5	−	2508.28i	−0.760569	−	0.0910717i
$913$	18322.2			0.664157
$914$	2499.07	+	3847.43i	0.0904396	+	0.139236i
$915$	5756.93	+	6587.64i	0.207998	+	0.238011i
$916$	1656.53	+	737.159i	0.0597524	+	0.0265900i
$917$	1307.95			0.0471016
$918$	−8266.92	−	3602.11i	−0.297221	−	0.129507i
$919$		−	18450.4i		−	0.662267i	−0.943584	−	0.331133i	$-0.892569\pi$
$919$		−	18450.4i		−	0.662267i	0.943584	−	0.331133i	$-0.107431\pi$
$920$	−16454.7	+	2610.94i	−0.589668	+	0.0935655i
$921$	27271.7	−	23832.7i	0.975713	−	0.852675i
$922$	11466.3	+	17652.9i	0.409569	+	0.630551i
$923$		−	18662.5i		−	0.665531i
$924$	−1284.30	−	4158.92i	−0.0457255	−	0.148072i
$925$			6430.36i			0.228572i
$926$	−15124.8	+	9824.22i	−0.536753	+	0.348644i
$927$	−23630.4	−	3194.80i	−0.837245	−	0.113194i
$928$	151.154	−	565.183i	0.00534686	−	0.0199925i
$929$			15358.7i			0.542414i	0.962521	+	0.271207i	$0.0874228\pi$
$929$			15358.7i			0.542414i	−0.962521	+	0.271207i	$0.912577\pi$
$930$	−2672.33	+	9415.95i	−0.0942248	+	0.332001i
$931$	21474.3			0.755951
$932$	30162.7	+	13422.5i	1.06010	+	0.471747i
$933$	−11323.9	+	9895.94i	−0.397350	+	0.347244i
$934$	−22829.0	+	14828.4i	−0.799771	+	0.519485i
$935$	5608.06			0.196153
$936$	−12682.5	+	291.486i	−0.442884	+	0.0101790i
$937$	27357.9			0.953835			0.476918	−	0.878948i	$-0.341754\pi$
$937$	27357.9			0.953835			0.476918	+	0.878948i	$0.341754\pi$
$938$	−3443.86	+	2236.93i	−0.119879	+	0.0778661i
$939$	28253.8	−	24691.0i	0.981924	−	0.858103i
$940$	−7633.84	+	17154.6i	−0.264881	+	0.595235i
$941$	8978.79			0.311052			0.155526	−	0.987832i	$-0.450293\pi$
$941$	8978.79			0.311052			0.155526	+	0.987832i	$0.450293\pi$
$942$	7288.06	−	25679.5i	0.252078	−	0.888199i
$943$			10892.3i			0.376143i
$944$	30328.2	−	27328.4i	1.04566	−	0.942227i
$945$	−1241.70	+	820.321i	−0.0427432	+	0.0282381i
$946$	−44309.7	+	28781.0i	−1.52287	+	0.989166i
$947$			32589.8i			1.11830i	0.829067	+	0.559149i	$0.188872\pi$
$947$			32589.8i			1.11830i	−0.829067	+	0.559149i	$0.811128\pi$
$948$	32339.1	−	9986.51i	1.10794	−	0.342138i
$949$			6957.28i			0.237980i
$950$	−2443.53	−	3761.93i	−0.0834511	−	0.128477i
$951$	17959.7	−	15695.0i	0.612390	−	0.535167i
$952$	1077.41	−	170.958i	0.0366797	−	0.00582014i
$953$		−	34147.8i		−	1.16071i	−0.814364	−	0.580354i	$-0.802914\pi$
$953$		−	34147.8i		−	1.16071i	0.814364	−	0.580354i	$-0.197086\pi$
$954$	41603.7	−	19671.1i	1.41192	−	0.667585i
$955$	1395.16			0.0472738
$956$	−796.007	+	1788.77i	−0.0269296	+	0.0605156i
$957$	545.429	+	624.132i	0.0184234	+	0.0210819i
$958$	−4016.92	−	6184.24i	−0.135471	−	0.208563i
$959$	4286.10			0.144323
$960$	6814.73	−	11424.0i	0.229109	−	0.384069i
$961$	12050.0			0.404484
$962$	−8228.71	−	12668.5i	−0.275784	−	0.424582i
$963$	25678.9	+	3471.75i	0.859286	+	0.116174i
$964$	5066.02	−	11384.2i	0.169259	−	0.380355i
$965$	−1554.38			−0.0518521
$966$	1253.60	−	4417.07i	0.0417536	−	0.147119i
$967$		−	55894.9i		−	1.85880i	−0.369074	−	0.929400i	$-0.620325\pi$
$967$		−	55894.9i		−	1.85880i	0.369074	−	0.929400i	$-0.379675\pi$
$968$	−24695.2	+	3918.50i	−0.819972	+	0.130109i
$969$	4929.38	+	5640.67i	0.163420	+	0.187001i
$970$	12577.0	+	19362.9i	0.416314	+	0.640934i
$971$		−	54019.5i		−	1.78534i	−0.450708	−	0.892671i	$-0.648828\pi$
$971$		−	54019.5i		−	1.78534i	0.450708	−	0.892671i	$-0.351172\pi$
$972$	−931.678	−	30289.6i	−0.0307444	−	0.999527i
$973$			2555.12i			0.0841864i
$974$	−4838.44	+	3142.77i	−0.159172	+	0.103389i
$975$	−1774.97	−	2031.09i	−0.0583020	−	0.0667148i
$976$	16010.2	−	14426.6i	0.525075	−	0.473139i
$977$		−	56582.4i		−	1.85285i	−0.376483	−	0.926424i	$-0.622867\pi$
$977$		−	56582.4i		−	1.85285i	0.376483	−	0.926424i	$-0.377133\pi$
$978$	−29587.9	−	8397.29i	−0.967398	−	0.274556i
$979$	11051.3			0.360777
$980$	−5504.87	+	12370.4i	−0.179435	+	0.403223i
$981$	49766.4	+	6728.34i	1.61969	+	0.218980i
$982$	−1569.78	+	1019.64i	−0.0510118	+	0.0331343i
$983$	11171.3			0.362471			0.181236	−	0.983440i	$-0.441990\pi$
$983$	11171.3			0.362471			0.181236	+	0.983440i	$0.441990\pi$
$984$	−6678.25	−	5570.74i	−0.216356	−	0.180476i
$985$	−27141.1			−0.877956
$986$	−174.211	+	113.157i	−0.00562678	+	0.00365483i
$987$	−3405.10	−	3896.44i	−0.109813	−	0.125659i
$988$	9628.02	+	4284.49i	0.310028	+	0.137963i
$989$	−55735.4			−1.79199
$990$	8055.74	+	17037.6i	0.258614	+	0.546959i
$991$		−	16402.0i		−	0.525759i	−0.964829	−	0.262879i	$-0.915328\pi$
$991$		−	16402.0i		−	0.525759i	0.964829	−	0.262879i	$-0.0846722\pi$
$992$	23292.3	+	6229.38i	0.745496	+	0.199378i
$993$	14379.0	−	12565.8i	0.459520	−	0.401574i
$994$	−4522.79	+	2937.74i	−0.144320	+	0.0937419i
$995$		−	11485.0i		−	0.365929i
$996$	−14744.4	+	4553.18i	−0.469072	+	0.144852i
$997$			13250.5i			0.420912i	0.977603	+	0.210456i	$0.0674948\pi$
$997$			13250.5i			0.420912i	−0.977603	+	0.210456i	$0.932505\pi$
$998$	2408.72	+	3708.34i	0.0763996	+	0.117621i
$999$	30108.9	−	19891.3i	0.953557	−	0.629964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.b.a.11.7	✓	24
3.2	odd	2		120.4.b.b.11.18	yes	24
4.3	odd	2		480.4.b.b.431.6		24
8.3	odd	2		120.4.b.b.11.17	yes	24
8.5	even	2		480.4.b.a.431.6		24
12.11	even	2		480.4.b.a.431.5		24
24.5	odd	2		480.4.b.b.431.5		24
24.11	even	2	inner	120.4.b.a.11.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.b.a.11.7	✓	24	1.1	even	1	trivial
120.4.b.a.11.8	yes	24	24.11	even	2	inner
120.4.b.b.11.17	yes	24	8.3	odd	2
120.4.b.b.11.18	yes	24	3.2	odd	2
480.4.b.a.431.5		24	12.11	even	2
480.4.b.a.431.6		24	8.5	even	2
480.4.b.b.431.5		24	24.5	odd	2
480.4.b.b.431.6		24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54070 - 2.37197i) q^{2} +(3.91264 - 3.41925i) q^{3} +(-3.25251 + 7.30898i) q^{4} +5.00000 q^{5} +(-14.1386 - 4.01264i) q^{6} -2.12151i q^{7} +(22.3478 - 3.54604i) q^{8} +(3.61744 - 26.7566i) q^{9} +O(q^{10})\)	\(q+(-1.54070 - 2.37197i) q^{2} +(3.91264 - 3.41925i) q^{3} +(-3.25251 + 7.30898i) q^{4} +5.00000 q^{5} +(-14.1386 - 4.01264i) q^{6} -2.12151i q^{7} +(22.3478 - 3.54604i) q^{8} +(3.61744 - 26.7566i) q^{9} +(-7.70348 - 11.8599i) q^{10} -49.3562i q^{11} +(12.2653 + 39.7185i) q^{12} -20.7644i q^{13} +(-5.03217 + 3.26860i) q^{14} +(19.5632 - 17.0963i) q^{15} +(-42.8423 - 47.5451i) q^{16} +22.7248i q^{17} +(-69.0392 + 32.6433i) q^{18} +63.4396 q^{19} +(-16.2626 + 36.5449i) q^{20} +(-7.25398 - 8.30070i) q^{21} +(-117.072 + 76.0429i) q^{22} -147.260 q^{23} +(75.3141 - 90.2872i) q^{24} +25.0000 q^{25} +(-49.2526 + 31.9916i) q^{26} +(-77.3337 - 117.058i) q^{27} +(15.5061 + 6.90024i) q^{28} -3.23196 q^{29} +(-70.6928 - 20.0632i) q^{30} -133.195i q^{31} +(-46.7687 + 174.873i) q^{32} +(-168.761 - 193.113i) q^{33} +(53.9027 - 35.0120i) q^{34} -10.6076i q^{35} +(183.797 + 113.466i) q^{36} +257.214i q^{37} +(-97.7412 - 150.477i) q^{38} +(-70.9987 - 81.2436i) q^{39} +(111.739 - 17.7302i) q^{40} -73.9667i q^{41} +(-8.51286 + 29.9951i) q^{42} +378.483 q^{43} +(360.744 + 160.532i) q^{44} +(18.0872 - 133.783i) q^{45} +(226.883 + 349.296i) q^{46} +469.412 q^{47} +(-330.195 - 39.5380i) q^{48} +338.499 q^{49} +(-38.5174 - 59.2993i) q^{50} +(77.7019 + 88.9139i) q^{51} +(151.767 + 67.5365i) q^{52} -602.609 q^{53} +(-158.510 + 363.784i) q^{54} -246.781i q^{55} +(-7.52295 - 47.4112i) q^{56} +(248.216 - 216.916i) q^{57} +(4.97946 + 7.66611i) q^{58} +637.883i q^{59} +(61.3267 + 198.593i) q^{60} +336.736i q^{61} +(-315.936 + 205.214i) q^{62} +(-56.7643 - 7.67444i) q^{63} +(486.851 - 158.493i) q^{64} -103.822i q^{65} +(-198.049 + 697.826i) q^{66} +684.370 q^{67} +(-166.095 - 73.9128i) q^{68} +(-576.174 + 503.518i) q^{69} +(-25.1608 + 16.3430i) q^{70} +898.776 q^{71} +(-14.0378 - 610.779i) q^{72} -335.058 q^{73} +(610.105 - 396.289i) q^{74} +(97.8159 - 85.4813i) q^{75} +(-206.338 + 463.679i) q^{76} -104.710 q^{77} +(-83.3201 + 293.579i) q^{78} -814.207i q^{79} +(-214.212 - 237.725i) q^{80} +(-702.828 - 193.581i) q^{81} +(-175.447 + 113.960i) q^{82} +371.223i q^{83} +(84.2633 - 26.0210i) q^{84} +113.624i q^{85} +(-583.128 - 897.753i) q^{86} +(-12.6455 + 11.0509i) q^{87} +(-175.019 - 1103.00i) q^{88} +223.909i q^{89} +(-345.196 + 163.216i) q^{90} -44.0519 q^{91} +(478.964 - 1076.32i) q^{92} +(-455.428 - 521.145i) q^{93} +(-723.221 - 1113.43i) q^{94} +317.198 q^{95} +(414.947 + 844.130i) q^{96} -1632.64 q^{97} +(-521.524 - 802.911i) q^{98} +(-1320.60 - 178.543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8}+O(q^{10}) \) 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8	\( 24 q - 3 q^{2} - 3 q^{4} + 120 q^{5} + 19 q^{6} + 21 q^{8} - 15 q^{10} + 65 q^{12} - 54 q^{14} + 153 q^{16} - 175 q^{18} + 12 q^{19} - 15 q^{20} - 4 q^{21} - 102 q^{22} + 228 q^{23} - 407 q^{24} + 600 q^{25} + 336 q^{26} + 132 q^{27} - 186 q^{28} + 95 q^{30} + 177 q^{32} + 116 q^{33} + 408 q^{34} + 673 q^{36} + 312 q^{38} - 656 q^{39} + 105 q^{40} - 990 q^{42} - 450 q^{44} - 1104 q^{46} - 924 q^{47} - 535 q^{48} - 816 q^{49} - 75 q^{50} - 700 q^{51} - 1548 q^{52} + 528 q^{53} + 1331 q^{54} - 390 q^{56} - 172 q^{57} + 1410 q^{58} + 325 q^{60} - 978 q^{62} + 476 q^{63} + 1137 q^{64} - 2794 q^{66} + 1632 q^{67} - 1608 q^{68} + 980 q^{69} - 270 q^{70} + 216 q^{71} - 3699 q^{72} - 216 q^{73} + 768 q^{74} - 1812 q^{76} + 4140 q^{78} + 765 q^{80} + 152 q^{81} + 2244 q^{82} + 5086 q^{84} - 2808 q^{86} + 252 q^{87} + 2622 q^{88} - 875 q^{90} - 1800 q^{91} - 1836 q^{92} - 1968 q^{94} + 60 q^{95} - 5455 q^{96} + 792 q^{97} + 4851 q^{98} - 1328 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^4 + 120 * q^5 + 19 * q^6 + 21 * q^8 - 15 * q^10 + 65 * q^12 - 54 * q^14 + 153 * q^16 - 175 * q^18 + 12 * q^19 - 15 * q^20 - 4 * q^21 - 102 * q^22 + 228 * q^23 - 407 * q^24 + 600 * q^25 + 336 * q^26 + 132 * q^27 - 186 * q^28 + 95 * q^30 + 177 * q^32 + 116 * q^33 + 408 * q^34 + 673 * q^36 + 312 * q^38 - 656 * q^39 + 105 * q^40 - 990 * q^42 - 450 * q^44 - 1104 * q^46 - 924 * q^47 - 535 * q^48 - 816 * q^49 - 75 * q^50 - 700 * q^51 - 1548 * q^52 + 528 * q^53 + 1331 * q^54 - 390 * q^56 - 172 * q^57 + 1410 * q^58 + 325 * q^60 - 978 * q^62 + 476 * q^63 + 1137 * q^64 - 2794 * q^66 + 1632 * q^67 - 1608 * q^68 + 980 * q^69 - 270 * q^70 + 216 * q^71 - 3699 * q^72 - 216 * q^73 + 768 * q^74 - 1812 * q^76 + 4140 * q^78 + 765 * q^80 + 152 * q^81 + 2244 * q^82 + 5086 * q^84 - 2808 * q^86 + 252 * q^87 + 2622 * q^88 - 875 * q^90 - 1800 * q^91 - 1836 * q^92 - 1968 * q^94 + 60 * q^95 - 5455 * q^96 + 792 * q^97 + 4851 * q^98 - 1328 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more