LMFDB - Embedded newform 354.3.b.a.119.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,3,Mod(119,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("354.119");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	354.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:	$9.64580135835$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.4
Character	$\chi$	$=$	354.119
Dual form			354.3.b.a.119.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-2.67506 - 1.35797i) q^{3} -2.00000 q^{4} -1.30422i q^{5} +(-1.92046 + 3.78310i) q^{6} +6.99884 q^{7} +2.82843i q^{8} +(5.31185 + 7.26528i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-2.67506 - 1.35797i) q^{3} -2.00000 q^{4} -1.30422i q^{5} +(-1.92046 + 3.78310i) q^{6} +6.99884 q^{7} +2.82843i q^{8} +(5.31185 + 7.26528i) q^{9} -1.84445 q^{10} +17.0193i q^{11} +(5.35011 + 2.71593i) q^{12} -9.38034 q^{13} -9.89786i q^{14} +(-1.77109 + 3.48887i) q^{15} +4.00000 q^{16} +16.9118i q^{17} +(10.2747 - 7.51209i) q^{18} +13.0956 q^{19} +2.60845i q^{20} +(-18.7223 - 9.50420i) q^{21} +24.0689 q^{22} -4.64185i q^{23} +(3.84091 - 7.56620i) q^{24} +23.2990 q^{25} +13.2658i q^{26} +(-4.34350 - 26.6483i) q^{27} -13.9977 q^{28} -39.4853i q^{29} +(4.93401 + 2.50470i) q^{30} +41.0400 q^{31} -5.65685i q^{32} +(23.1116 - 45.5276i) q^{33} +23.9168 q^{34} -9.12805i q^{35} +(-10.6237 - 14.5306i) q^{36} +65.8959 q^{37} -18.5200i q^{38} +(25.0929 + 12.7382i) q^{39} +3.68890 q^{40} +77.9155i q^{41} +(-13.4410 + 26.4773i) q^{42} -74.0514 q^{43} -34.0386i q^{44} +(9.47554 - 6.92784i) q^{45} -6.56457 q^{46} -51.6818i q^{47} +(-10.7002 - 5.43187i) q^{48} -0.0161733 q^{49} -32.9498i q^{50} +(22.9656 - 45.2399i) q^{51} +18.7607 q^{52} +78.0721i q^{53} +(-37.6864 + 6.14264i) q^{54} +22.1969 q^{55} +19.7957i q^{56} +(-35.0315 - 17.7834i) q^{57} -55.8406 q^{58} +7.68115i q^{59} +(3.54218 - 6.97774i) q^{60} +73.8558 q^{61} -58.0393i q^{62} +(37.1768 + 50.8485i) q^{63} -8.00000 q^{64} +12.2341i q^{65} +(-64.3857 - 32.6848i) q^{66} -87.3096 q^{67} -33.8235i q^{68} +(-6.30348 + 12.4172i) q^{69} -12.9090 q^{70} +31.0106i q^{71} +(-20.5493 + 15.0242i) q^{72} -14.4031 q^{73} -93.1909i q^{74} +(-62.3261 - 31.6393i) q^{75} -26.1912 q^{76} +119.115i q^{77} +(18.0145 - 35.4868i) q^{78} +109.298 q^{79} -5.21689i q^{80} +(-24.5685 + 77.1841i) q^{81} +110.189 q^{82} -21.4489i q^{83} +(37.4446 + 19.0084i) q^{84} +22.0567 q^{85} +104.724i q^{86} +(-53.6197 + 105.625i) q^{87} -48.1378 q^{88} +37.4175i q^{89} +(-9.79744 - 13.4004i) q^{90} -65.6516 q^{91} +9.28371i q^{92} +(-109.784 - 55.7309i) q^{93} -73.0891 q^{94} -17.0796i q^{95} +(-7.68182 + 15.1324i) q^{96} +167.676 q^{97} +0.0228725i q^{98} +(-123.650 + 90.4039i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−2.67506	−	1.35797i	−0.891685	−	0.452656i
$3$	−2.67506	−	1.35797i	−0.891685	−	0.452656i
$4$	−2.00000			−0.500000
$5$		−	1.30422i		−	0.260845i	−0.991459	−	0.130422i	$-0.958367\pi$
$5$		−	1.30422i		−	0.260845i	0.991459	−	0.130422i	$-0.0416333\pi$
$6$	−1.92046	+	3.78310i	−0.320076	+	0.630517i
$7$	6.99884			0.999835			0.499917	−	0.866073i	$-0.333364\pi$
$7$	6.99884			0.999835			0.499917	+	0.866073i	$0.333364\pi$
$8$			2.82843i			0.353553i
$9$	5.31185	+	7.26528i	0.590206	+	0.807253i
$10$	−1.84445			−0.184445
$11$			17.0193i			1.54721i	0.633669	+	0.773604i	$0.281548\pi$
$11$			17.0193i			1.54721i	−0.633669	+	0.773604i	$0.718452\pi$
$12$	5.35011	+	2.71593i	0.445843	+	0.226328i
$13$	−9.38034			−0.721565			−0.360782	−	0.932650i	$-0.617490\pi$
$13$	−9.38034			−0.721565			−0.360782	+	0.932650i	$0.617490\pi$
$14$		−	9.89786i		−	0.706990i
$15$	−1.77109	+	3.48887i	−0.118073	+	0.232591i
$16$	4.00000			0.250000
$17$			16.9118i			0.994810i	0.867519	+	0.497405i	$0.165714\pi$
$17$			16.9118i			0.994810i	−0.867519	+	0.497405i	$0.834286\pi$
$18$	10.2747	−	7.51209i	0.570814	−	0.417339i
$19$	13.0956			0.689242			0.344621	−	0.938742i	$-0.388007\pi$
$19$	13.0956			0.689242			0.344621	+	0.938742i	$0.388007\pi$
$20$			2.60845i			0.130422i
$21$	−18.7223	−	9.50420i	−0.891538	−	0.452581i
$22$	24.0689			1.09404
$23$		−	4.64185i		−	0.201820i	−0.994896	−	0.100910i	$-0.967825\pi$
$23$		−	4.64185i		−	0.201820i	0.994896	−	0.100910i	$-0.0321754\pi$
$24$	3.84091	−	7.56620i	0.160038	−	0.315258i
$25$	23.2990			0.931960
$26$			13.2658i			0.510223i
$27$	−4.34350	−	26.6483i	−0.160870	−	0.986976i
$28$	−13.9977			−0.499917
$29$		−	39.4853i		−	1.36156i	−0.732487	−	0.680780i	$-0.761641\pi$
$29$		−	39.4853i		−	1.36156i	0.732487	−	0.680780i	$-0.238359\pi$
$30$	4.93401	+	2.50470i	0.164467	+	0.0834900i
$31$	41.0400			1.32387			0.661935	−	0.749561i	$-0.269736\pi$
$31$	41.0400			1.32387			0.661935	+	0.749561i	$0.269736\pi$
$32$		−	5.65685i		−	0.176777i
$33$	23.1116	−	45.5276i	0.700352	−	1.37962i
$34$	23.9168			0.703437
$35$		−	9.12805i		−	0.260802i
$36$	−10.6237	−	14.5306i	−0.295103	−	0.403626i
$37$	65.8959			1.78097			0.890486	−	0.455011i	$-0.150365\pi$
$37$	65.8959			1.78097			0.890486	+	0.455011i	$0.150365\pi$
$38$		−	18.5200i		−	0.487368i
$39$	25.0929	+	12.7382i	0.643409	+	0.326620i
$40$	3.68890			0.0922225
$41$			77.9155i			1.90038i	0.311675	+	0.950189i	$0.399110\pi$
$41$			77.9155i			1.90038i	−0.311675	+	0.950189i	$0.600890\pi$
$42$	−13.4410	+	26.4773i	−0.320023	+	0.630413i
$43$	−74.0514			−1.72213			−0.861063	−	0.508499i	$-0.830201\pi$
$43$	−74.0514			−1.72213			−0.861063	+	0.508499i	$0.830201\pi$
$44$		−	34.0386i		−	0.773604i
$45$	9.47554	−	6.92784i	0.210568	−	0.153952i
$46$	−6.56457			−0.142708
$47$		−	51.6818i		−	1.09961i	−0.835292	−	0.549806i	$-0.814702\pi$
$47$		−	51.6818i		−	1.09961i	0.835292	−	0.549806i	$-0.185298\pi$
$48$	−10.7002	−	5.43187i	−0.222921	−	0.113164i
$49$	−0.0161733			−0.000330068
$50$		−	32.9498i		−	0.658995i
$51$	22.9656	−	45.2399i	0.450306	−	0.887057i
$52$	18.7607			0.360782
$53$			78.0721i			1.47306i	0.676405	+	0.736530i	$0.263537\pi$
$53$			78.0721i			1.47306i	−0.676405	+	0.736530i	$0.736463\pi$
$54$	−37.6864	+	6.14264i	−0.697897	+	0.113753i
$55$	22.1969			0.403581
$56$			19.7957i			0.353495i
$57$	−35.0315	−	17.7834i	−0.614587	−	0.311989i
$58$	−55.8406			−0.962769
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	3.54218	−	6.97774i	0.0590364	−	0.116296i
$61$	73.8558			1.21075			0.605376	−	0.795940i	$-0.293023\pi$
$61$	73.8558			1.21075			0.605376	+	0.795940i	$0.293023\pi$
$62$		−	58.0393i		−	0.936117i
$63$	37.1768	+	50.8485i	0.590108	+	0.807120i
$64$	−8.00000			−0.125000
$65$			12.2341i			0.188216i
$66$	−64.3857	−	32.6848i	−0.975541	−	0.495224i
$67$	−87.3096			−1.30313			−0.651564	−	0.758593i	$-0.725887\pi$
$67$	−87.3096			−1.30313			−0.651564	+	0.758593i	$0.725887\pi$
$68$		−	33.8235i		−	0.497405i
$69$	−6.30348	+	12.4172i	−0.0913548	+	0.179960i
$70$	−12.9090			−0.184415
$71$			31.0106i			0.436769i	0.975863	+	0.218385i	$0.0700787\pi$
$71$			31.0106i			0.436769i	−0.975863	+	0.218385i	$0.929921\pi$
$72$	−20.5493	+	15.0242i	−0.285407	+	0.208669i
$73$	−14.4031			−0.197303			−0.0986514	−	0.995122i	$-0.531453\pi$
$73$	−14.4031			−0.197303			−0.0986514	+	0.995122i	$0.531453\pi$
$74$		−	93.1909i		−	1.25934i
$75$	−62.3261	−	31.6393i	−0.831015	−	0.421857i
$76$	−26.1912			−0.344621
$77$			119.115i			1.54695i
$78$	18.0145	−	35.4868i	0.230955	−	0.454959i
$79$	109.298			1.38351			0.691757	−	0.722131i	$-0.256837\pi$
$79$	109.298			1.38351			0.691757	+	0.722131i	$0.256837\pi$
$80$		−	5.21689i		−	0.0652111i
$81$	−24.5685	+	77.1841i	−0.303314	+	0.952891i
$82$	110.189			1.34377
$83$		−	21.4489i		−	0.258420i	−0.991617	−	0.129210i	$-0.958756\pi$
$83$		−	21.4489i		−	0.258420i	0.991617	−	0.129210i	$-0.0412442\pi$
$84$	37.4446	+	19.0084i	0.445769	+	0.226290i
$85$	22.0567			0.259491
$86$			104.724i			1.21773i
$87$	−53.6197	+	105.625i	−0.616318	+	1.21408i
$88$	−48.1378			−0.547021
$89$			37.4175i			0.420422i	0.977656	+	0.210211i	$0.0674150\pi$
$89$			37.4175i			0.420422i	−0.977656	+	0.210211i	$0.932585\pi$
$90$	−9.79744	−	13.4004i	−0.108860	−	0.148894i
$91$	−65.6516			−0.721446
$92$			9.28371i			0.100910i
$93$	−109.784	−	55.7309i	−1.18048	−	0.599257i
$94$	−73.0891			−0.777543
$95$		−	17.0796i		−	0.179785i
$96$	−7.68182	+	15.1324i	−0.0800190	+	0.157629i
$97$	167.676			1.72861			0.864307	−	0.502965i	$-0.167758\pi$
$97$	167.676			1.72861			0.864307	+	0.502965i	$0.167758\pi$
$98$			0.0228725i			0.000233393i
$99$	−123.650	+	90.4039i	−1.24899	+	0.913171i
$100$	−46.5980			−0.465980
$101$		−	54.6617i		−	0.541205i	−0.962691	−	0.270603i	$-0.912777\pi$
$101$		−	54.6617i		−	0.541205i	0.962691	−	0.270603i	$-0.0872229\pi$
$102$	−63.9789	−	32.4783i	−0.627244	−	0.318415i
$103$	34.4982			0.334934			0.167467	−	0.985878i	$-0.446441\pi$
$103$	34.4982			0.334934			0.167467	+	0.985878i	$0.446441\pi$
$104$		−	26.5316i		−	0.255112i
$105$	−12.3956	+	24.4181i	−0.118053	+	0.232553i
$106$	110.411			1.04161
$107$		−	48.7200i		−	0.455327i	−0.973740	−	0.227664i	$-0.926891\pi$
$107$		−	48.7200i		−	0.455327i	0.973740	−	0.227664i	$-0.0731087\pi$
$108$	8.68700	+	53.2967i	0.0804352	+	0.493488i
$109$	158.102			1.45047			0.725237	−	0.688500i	$-0.241730\pi$
$109$	158.102			1.45047			0.725237	+	0.688500i	$0.241730\pi$
$110$		−	31.3912i		−	0.285375i
$111$	−176.275	−	89.4845i	−1.58807	−	0.806167i
$112$	27.9954			0.249959
$113$			144.469i			1.27849i	0.769005	+	0.639243i	$0.220752\pi$
$113$			144.469i			1.27849i	−0.769005	+	0.639243i	$0.779248\pi$
$114$	−25.1495	+	49.5420i	−0.220610	+	0.434579i
$115$	−6.05401			−0.0526436
$116$			78.9705i			0.680780i
$117$	−49.8270	−	68.1508i	−0.425872	−	0.582485i
$118$	10.8628			0.0920575
$119$			118.363i			0.994646i
$120$	−9.86801	−	5.00940i	−0.0822334	−	0.0417450i
$121$	−168.656			−1.39385
$122$		−	104.448i		−	0.856130i
$123$	105.807	−	208.428i	0.860217	−	1.69454i
$124$	−82.0799			−0.661935
$125$		−	62.9927i		−	0.503941i
$126$	71.9107	−	52.5760i	0.570720	−	0.417270i
$127$	−218.026			−1.71674			−0.858370	−	0.513030i	$-0.828523\pi$
$127$	−218.026			−1.71674			−0.858370	+	0.513030i	$0.828523\pi$
$128$			11.3137i			0.0883883i
$129$	198.092	+	100.559i	1.53559	+	0.779530i
$130$	17.3016			0.133089
$131$			94.1164i			0.718446i	0.933252	+	0.359223i	$0.116958\pi$
$131$			94.1164i			0.718446i	−0.933252	+	0.359223i	$0.883042\pi$
$132$	−46.2233	+	91.0551i	−0.350176	+	0.689811i
$133$	91.6541			0.689129
$134$			123.474i			0.921451i
$135$	−34.7554	+	5.66489i	−0.257447	+	0.0419622i
$136$	−47.8337			−0.351718
$137$			110.837i			0.809027i	0.914532	+	0.404514i	$0.132559\pi$
$137$			110.837i			0.809027i	−0.914532	+	0.404514i	$0.867441\pi$
$138$	17.5606	+	8.91447i	0.127251	+	0.0645976i
$139$	138.219			0.994379			0.497189	−	0.867642i	$-0.334365\pi$
$139$	138.219			0.994379			0.497189	+	0.867642i	$0.334365\pi$
$140$			18.2561i			0.130401i
$141$	−70.1822	+	138.252i	−0.497746	+	0.980508i
$142$	43.8556			0.308842
$143$		−	159.647i		−	1.11641i
$144$	21.2474	+	29.0611i	0.147551	+	0.201813i
$145$	−51.4976			−0.355156
$146$			20.3691i			0.139514i
$147$	0.0432645	+	0.0219628i	0.000294316	+	0.000149407i
$148$	−131.792			−0.890486
$149$			102.144i			0.685530i	0.939421	+	0.342765i	$0.111363\pi$
$149$			102.144i			0.685530i	−0.939421	+	0.342765i	$0.888637\pi$
$150$	−44.7447	+	88.1425i	−0.298298	+	0.587617i
$151$	88.9033			0.588764			0.294382	−	0.955688i	$-0.404886\pi$
$151$	88.9033			0.588764			0.294382	+	0.955688i	$0.404886\pi$
$152$			37.0400i			0.243684i
$153$	−122.869	+	89.8328i	−0.803063	+	0.587142i
$154$	168.455			1.09386
$155$		−	53.5253i		−	0.345324i
$156$	−50.1859	−	25.4764i	−0.321704	−	0.163310i
$157$	50.7572			0.323294			0.161647	−	0.986849i	$-0.448319\pi$
$157$	50.7572			0.323294			0.161647	+	0.986849i	$0.448319\pi$
$158$		−	154.570i		−	0.978292i
$159$	106.019	−	208.847i	0.666789	−	1.31351i
$160$	−7.37780			−0.0461112
$161$		−	32.4876i		−	0.201786i
$162$	109.155	+	34.7450i	0.673795	+	0.214476i
$163$	−136.487			−0.837341			−0.418671	−	0.908138i	$-0.637504\pi$
$163$	−136.487			−0.837341			−0.418671	+	0.908138i	$0.637504\pi$
$164$		−	155.831i		−	0.950189i
$165$	−59.3781	−	30.1427i	−0.359867	−	0.182683i
$166$	−30.3333			−0.182731
$167$		−	298.310i		−	1.78629i	−0.449769	−	0.893145i	$-0.648494\pi$
$167$		−	298.310i		−	1.78629i	0.449769	−	0.893145i	$-0.351506\pi$
$168$	26.8819	−	52.9547i	0.160012	−	0.315206i
$169$	−81.0092			−0.479344
$170$		−	31.1929i		−	0.183488i
$171$	69.5619	+	95.1432i	0.406795	+	0.556393i
$172$	148.103			0.861063
$173$			21.6651i			0.125232i	0.998038	+	0.0626160i	$0.0199443\pi$
$173$			21.6651i			0.125232i	−0.998038	+	0.0626160i	$0.980056\pi$
$174$	149.377	+	75.8297i	0.858487	+	0.435803i
$175$	163.066			0.931806
$176$			68.0772i			0.386802i
$177$	10.4307	−	20.5475i	0.0589307	−	0.116088i
$178$	52.9164			0.297283
$179$		−	43.8825i		−	0.245153i	−0.992459	−	0.122577i	$-0.960884\pi$
$179$		−	43.8825i		−	0.245153i	0.992459	−	0.122577i	$-0.0391158\pi$
$180$	−18.9511	+	13.8557i	−0.105284	+	0.0769760i
$181$	−292.928			−1.61839			−0.809194	−	0.587541i	$-0.800096\pi$
$181$	−292.928			−1.61839			−0.809194	+	0.587541i	$0.800096\pi$
$182$			92.8453i			0.510139i
$183$	−197.568	−	100.294i	−1.07961	−	0.548053i
$184$	13.1291			0.0713540
$185$		−	85.9430i		−	0.464557i
$186$	−78.8154	+	155.258i	−0.423739	+	0.834722i
$187$	−287.826			−1.53918
$188$			103.364i			0.549806i
$189$	−30.3995	−	186.508i	−0.160844	−	0.986813i
$190$	−24.1542			−0.127127
$191$			289.248i			1.51439i	0.653190	+	0.757194i	$0.273430\pi$
$191$			289.248i			1.51439i	−0.653190	+	0.757194i	$0.726570\pi$
$192$	21.4005	+	10.8637i	0.111461	+	0.0565820i
$193$	79.2513			0.410629			0.205314	−	0.978696i	$-0.434178\pi$
$193$	79.2513			0.410629			0.205314	+	0.978696i	$0.434178\pi$
$194$		−	237.129i		−	1.22231i
$195$	16.6134	−	32.7268i	0.0851971	−	0.167830i
$196$	0.0323466			0.000165034
$197$		−	174.777i		−	0.887192i	−0.896227	−	0.443596i	$-0.853703\pi$
$197$		−	174.777i		−	0.887192i	0.896227	−	0.443596i	$-0.146297\pi$
$198$	127.850	+	174.867i	0.645709	+	0.883168i
$199$	−109.385			−0.549673			−0.274836	−	0.961491i	$-0.588624\pi$
$199$	−109.385			−0.549673			−0.274836	+	0.961491i	$0.588624\pi$
$200$			65.8995i			0.329498i
$201$	233.558	+	118.564i	1.16198	+	0.589869i
$202$	−77.3033			−0.382690
$203$		−	276.351i		−	1.36134i
$204$	−45.9312	+	90.4799i	−0.225153	+	0.443529i
$205$	101.619			0.495703
$206$		−	48.7878i		−	0.236834i
$207$	33.7243	−	24.6568i	0.162920	−	0.119115i
$208$	−37.5214			−0.180391
$209$			222.878i			1.06640i
$210$	34.5323	+	17.5300i	0.164440	+	0.0834763i
$211$	−176.742			−0.837639			−0.418820	−	0.908069i	$-0.637556\pi$
$211$	−176.742			−0.837639			−0.418820	+	0.908069i	$0.637556\pi$
$212$		−	156.144i		−	0.736530i
$213$	42.1114	−	82.9551i	0.197706	−	0.389461i
$214$	−68.9005			−0.321965
$215$			96.5795i			0.449207i
$216$	75.3729	−	12.2853i	0.348949	−	0.0568763i
$217$	287.232			1.32365
$218$		−	223.589i		−	1.02564i
$219$	38.5291	+	19.5589i	0.175932	+	0.0893102i
$220$	−44.3939			−0.201790
$221$		−	158.638i		−	0.717820i
$222$	−126.550	+	249.291i	−0.570046	+	1.12293i
$223$	19.9047			0.0892587			0.0446293	−	0.999004i	$-0.485789\pi$
$223$	19.9047			0.0892587			0.0446293	+	0.999004i	$0.485789\pi$
$224$		−	39.5914i		−	0.176748i
$225$	123.761	+	169.274i	0.550048	+	0.752327i
$226$	204.310			0.904026
$227$		−	142.743i		−	0.628822i	−0.949287	−	0.314411i	$-0.898193\pi$
$227$		−	142.743i		−	0.628822i	0.949287	−	0.314411i	$-0.101807\pi$
$228$	70.0630	+	35.5668i	0.307294	+	0.155995i
$229$	−42.6927			−0.186431			−0.0932155	−	0.995646i	$-0.529715\pi$
$229$	−42.6927			−0.186431			−0.0932155	+	0.995646i	$0.529715\pi$
$230$			8.56166i			0.0372246i
$231$	161.755	−	318.640i	0.700237	−	1.37940i
$232$	111.681			0.481385
$233$			194.880i			0.836395i	0.908356	+	0.418198i	$0.137338\pi$
$233$			194.880i			0.836395i	−0.908356	+	0.418198i	$0.862662\pi$
$234$	−96.3797	+	70.4660i	−0.411879	+	0.301137i
$235$	−67.4046			−0.286828
$236$		−	15.3623i		−	0.0650945i
$237$	−292.377	−	148.422i	−1.23366	−	0.626255i
$238$	167.390			0.703321
$239$		−	85.1758i		−	0.356384i	−0.983996	−	0.178192i	$-0.942975\pi$
$239$		−	85.1758i		−	0.356384i	0.983996	−	0.178192i	$-0.0570249\pi$
$240$	−7.08437	+	13.9555i	−0.0295182	+	0.0581478i
$241$	132.814			0.551095			0.275547	−	0.961288i	$-0.411141\pi$
$241$	132.814			0.551095			0.275547	+	0.961288i	$0.411141\pi$
$242$			238.516i			0.985603i
$243$	170.536	−	173.109i	0.701792	−	0.712382i
$244$	−147.712			−0.605376
$245$			0.0210936i			8.60963e-5i
$246$	−294.762	−	149.633i	−1.19822	−	0.608265i
$247$	−122.841			−0.497333
$248$			116.079i			0.468059i
$249$	−29.1269	+	57.3770i	−0.116975	+	0.230430i
$250$	−89.0851			−0.356340
$251$		−	47.2918i		−	0.188413i	−0.995553	−	0.0942067i	$-0.969969\pi$
$251$		−	47.2918i		−	0.188413i	0.995553	−	0.0942067i	$-0.0300315\pi$
$252$	−74.3537	−	101.697i	−0.295054	−	0.403560i
$253$	79.0010			0.312257
$254$			308.335i			1.21392i
$255$	−59.0029	−	29.9523i	−0.231384	−	0.117460i
$256$	16.0000			0.0625000
$257$		−	142.229i		−	0.553419i	−0.960954	−	0.276710i	$-0.910756\pi$
$257$		−	142.229i		−	0.553419i	0.960954	−	0.276710i	$-0.0892440\pi$
$258$	142.212	−	280.144i	0.551211	−	1.08583i
$259$	461.195			1.78068
$260$		−	24.4681i		−	0.0941081i
$261$	286.871	−	209.740i	1.09912	−	0.803601i
$262$	133.101			0.508018
$263$		−	100.721i		−	0.382970i	−0.981496	−	0.191485i	$-0.938670\pi$
$263$		−	100.721i		−	0.382970i	0.981496	−	0.191485i	$-0.0613304\pi$
$264$	128.771	+	65.3696i	0.487770	+	0.247612i
$265$	101.823			0.384240
$266$		−	129.618i		−	0.487288i
$267$	50.8118	−	100.094i	0.190306	−	0.374884i
$268$	174.619			0.651564
$269$		−	53.2886i		−	0.198099i	−0.995083	−	0.0990495i	$-0.968420\pi$
$269$		−	53.2886i		−	0.198099i	0.995083	−	0.0990495i	$-0.0315802\pi$
$270$	8.01137	+	49.1515i	0.0296717	+	0.182043i
$271$	18.4888			0.0682243			0.0341122	−	0.999418i	$-0.489140\pi$
$271$	18.4888			0.0682243			0.0341122	+	0.999418i	$0.489140\pi$
$272$			67.6471i			0.248702i
$273$	175.622	+	89.1526i	0.643303	+	0.326566i
$274$	156.747			0.572069
$275$			396.532i			1.44194i
$276$	12.6070	−	24.8344i	0.0456774	−	0.0899798i
$277$	−372.194			−1.34366			−0.671831	−	0.740705i	$-0.734492\pi$
$277$	−372.194			−1.34366			−0.671831	+	0.740705i	$0.734492\pi$
$278$		−	195.471i		−	0.703132i
$279$	217.998	+	298.167i	0.781356	+	1.06870i
$280$	25.8180			0.0922073
$281$		−	497.569i		−	1.77071i	−0.464918	−	0.885354i	$-0.653916\pi$
$281$		−	497.569i		−	1.77071i	0.464918	−	0.885354i	$-0.346084\pi$
$282$	195.517	+	99.2526i	0.693324	+	0.351959i
$283$	127.722			0.451316			0.225658	−	0.974207i	$-0.427547\pi$
$283$	127.722			0.451316			0.225658	+	0.974207i	$0.427547\pi$
$284$		−	62.0212i		−	0.218385i
$285$	−23.1935	+	45.6889i	−0.0813808	+	0.160312i
$286$	−225.775			−0.789422
$287$			545.318i			1.90006i
$288$	41.0986	−	30.0484i	0.142703	−	0.104335i
$289$	2.99215			0.0103535
$290$			72.8286i			0.251133i
$291$	−448.541	−	227.698i	−1.54138	−	0.782467i
$292$	28.8062			0.0986514
$293$			202.698i			0.691803i	0.938271	+	0.345902i	$0.112427\pi$
$293$			202.698i			0.691803i	−0.938271	+	0.345902i	$0.887573\pi$
$294$	0.0310601	−	0.0611853i	0.000105647	−	0.000208113i
$295$	10.0179			0.0339591
$296$			186.382i			0.629668i
$297$	453.536	−	73.9233i	1.52706	−	0.248900i
$298$	144.453			0.484743
$299$			43.5422i			0.145626i
$300$	124.652	+	63.2785i	0.415508	+	0.210928i
$301$	−518.274			−1.72184
$302$		−	125.728i		−	0.416319i
$303$	−74.2288	+	146.223i	−0.244979	+	0.482585i
$304$	52.3824			0.172311
$305$		−	96.3244i		−	0.315818i
$306$	127.043	+	173.763i	0.415172	+	0.567851i
$307$	0.472725			0.00153982			0.000769911	−	1.00000i	$-0.499755\pi$
$307$	0.472725			0.00153982			0.000769911		1.00000i	$0.499755\pi$
$308$		−	238.231i		−	0.773476i
$309$	−92.2846	−	46.8474i	−0.298656	−	0.151610i
$310$	−75.6961			−0.244181
$311$		−	275.080i		−	0.884503i	−0.896891	−	0.442251i	$-0.854180\pi$
$311$		−	275.080i		−	0.884503i	0.896891	−	0.442251i	$-0.145820\pi$
$312$	−36.0291	+	70.9736i	−0.115478	+	0.227479i
$313$	515.241			1.64614			0.823068	−	0.567943i	$-0.192261\pi$
$313$	515.241			1.64614			0.823068	+	0.567943i	$0.192261\pi$
$314$		−	71.7815i		−	0.228604i
$315$	66.3178	−	48.4869i	0.210533	−	0.153927i
$316$	−218.595			−0.691757
$317$		−	169.331i		−	0.534167i	−0.963673	−	0.267084i	$-0.913940\pi$
$317$		−	169.331i		−	0.534167i	0.963673	−	0.267084i	$-0.0860600\pi$
$318$	−295.355	−	149.934i	−0.928789	−	0.471491i
$319$	672.011			2.10662
$320$			10.4338i			0.0326056i
$321$	−66.1602	+	130.329i	−0.206107	+	0.406009i
$322$	−45.9444			−0.142685
$323$			221.470i			0.685665i
$324$	49.1369	−	154.368i	0.151657	−	0.476445i
$325$	−218.553			−0.672470
$326$			193.021i			0.592090i
$327$	−422.931	−	214.697i	−1.29337	−	0.656565i
$328$	−220.378			−0.671885
$329$		−	361.713i		−	1.09943i
$330$	−42.6282	+	83.9733i	−0.129176	+	0.254464i
$331$	−55.0200			−0.166224			−0.0831118	−	0.996540i	$-0.526486\pi$
$331$	−55.0200			−0.166224			−0.0831118	+	0.996540i	$0.526486\pi$
$332$			42.8978i			0.129210i
$333$	350.029	+	478.752i	1.05114	+	1.43769i
$334$	−421.875			−1.26310
$335$			113.871i			0.339914i
$336$	−74.8892	−	38.0168i	−0.222885	−	0.113145i
$337$	−295.151			−0.875818			−0.437909	−	0.899019i	$-0.644281\pi$
$337$	−295.151			−0.875818			−0.437909	+	0.899019i	$0.644281\pi$
$338$			114.564i			0.338948i
$339$	196.184	−	386.463i	0.578714	−	1.14001i
$340$	−44.1134			−0.129745
$341$			698.471i			2.04830i
$342$	134.553	−	98.3754i	0.393429	−	0.287647i
$343$	−343.057			−1.00016
$344$		−	209.449i		−	0.608863i
$345$	16.1948	+	8.22115i	0.0469415	+	0.0238294i
$346$	30.6391			0.0885524
$347$		−	325.432i		−	0.937843i	−0.883240	−	0.468922i	$-0.844643\pi$
$347$		−	325.432i		−	0.937843i	0.883240	−	0.468922i	$-0.155357\pi$
$348$	107.239	−	211.251i	0.308159	−	0.607042i
$349$	−325.456			−0.932538			−0.466269	−	0.884643i	$-0.654402\pi$
$349$	−325.456			−0.932538			−0.466269	+	0.884643i	$0.654402\pi$
$350$		−	230.610i		−	0.658887i
$351$	40.7435	+	249.971i	0.116078	+	0.712167i
$352$	96.2756			0.273510
$353$		−	203.900i		−	0.577619i	−0.957387	−	0.288810i	$-0.906741\pi$
$353$		−	203.900i		−	0.577619i	0.957387	−	0.288810i	$-0.0932594\pi$
$354$	−29.0585	−	14.7513i	−0.0820863	−	0.0416703i
$355$	40.4448			0.113929
$356$		−	74.8350i		−	0.210211i
$357$	160.733	−	316.627i	0.450232	−	0.886911i
$358$	−62.0592			−0.173350
$359$		−	67.3730i		−	0.187669i	−0.995588	−	0.0938343i	$-0.970088\pi$
$359$		−	67.3730i		−	0.187669i	0.995588	−	0.0938343i	$-0.0299124\pi$
$360$	19.5949	+	26.8009i	0.0544302	+	0.0744469i
$361$	−189.505			−0.524945
$362$			414.263i			1.14437i
$363$	451.165	+	229.029i	1.24288	+	0.630935i
$364$	131.303			0.360723
$365$			18.7848i			0.0514653i
$366$	−141.837	+	279.404i	−0.387532	+	0.763399i
$367$	114.615			0.312301			0.156151	−	0.987733i	$-0.450091\pi$
$367$	114.615			0.312301			0.156151	+	0.987733i	$0.450091\pi$
$368$		−	18.5674i		−	0.0504549i
$369$	−566.077	+	413.876i	−1.53409	+	1.12161i
$370$	−121.542			−0.328491
$371$			546.415i			1.47282i
$372$	219.568	+	111.462i	0.590238	+	0.299629i
$373$	−115.679			−0.310130			−0.155065	−	0.987904i	$-0.549559\pi$
$373$	−115.679			−0.310130			−0.155065	+	0.987904i	$0.549559\pi$
$374$			407.048i			1.08836i
$375$	−85.5419	+	168.509i	−0.228112	+	0.449357i
$376$	146.178			0.388772
$377$			370.385i			0.982454i
$378$	−263.762	+	42.9914i	−0.697782	+	0.113734i
$379$	−620.955			−1.63840			−0.819201	−	0.573506i	$-0.805583\pi$
$379$	−620.955			−1.63840			−0.819201	+	0.573506i	$0.805583\pi$
$380$			34.1592i			0.0898926i
$381$	583.232	+	296.072i	1.53079	+	0.777092i
$382$	409.059			1.07083
$383$		−	205.384i		−	0.536249i	−0.963384	−	0.268125i	$-0.913596\pi$
$383$		−	205.384i		−	0.536249i	0.963384	−	0.268125i	$-0.0864039\pi$
$384$	15.3636	−	30.2648i	0.0400095	−	0.0788146i
$385$	155.353			0.403514
$386$		−	112.078i		−	0.290358i
$387$	−393.350	−	538.004i	−1.01641	−	1.39019i
$388$	−335.351			−0.864307
$389$		−	94.6525i		−	0.243323i	−0.992572	−	0.121661i	$-0.961178\pi$
$389$		−	94.6525i		−	0.243323i	0.992572	−	0.121661i	$-0.0388222\pi$
$390$	−46.2827	−	23.4950i	−0.118673	−	0.0602435i
$391$	78.5019			0.200772
$392$		−	0.0457450i		−	0.000116697i
$393$	127.807	−	251.767i	0.325209	−	0.640628i
$394$	−247.172			−0.627339
$395$		−	142.548i		−	0.360882i
$396$	247.300	−	180.808i	0.624494	−	0.456586i
$397$	−382.598			−0.963722			−0.481861	−	0.876248i	$-0.660039\pi$
$397$	−382.598			−0.963722			−0.481861	+	0.876248i	$0.660039\pi$
$398$			154.694i			0.388677i
$399$	−245.180	−	124.463i	−0.614486	−	0.311938i
$400$	93.1960			0.232990
$401$			541.806i			1.35114i	0.737297	+	0.675569i	$0.236102\pi$
$401$			541.806i			1.35114i	−0.737297	+	0.675569i	$0.763898\pi$
$402$	167.674	−	330.301i	0.417100	−	0.821645i
$403$	−384.969			−0.955258
$404$			109.323i			0.270603i
$405$	100.665	+	32.0427i	0.248556	+	0.0791179i
$406$	−390.820			−0.962610
$407$			1121.50i			2.75553i
$408$	127.958	+	64.9566i	0.313622	+	0.159207i
$409$	−237.723			−0.581230			−0.290615	−	0.956840i	$-0.593860\pi$
$409$	−237.723			−0.581230			−0.290615	+	0.956840i	$0.593860\pi$
$410$		−	143.711i		−	0.350515i
$411$	150.513	−	296.495i	0.366211	−	0.721398i
$412$	−68.9964			−0.167467
$413$			53.7591i			0.130167i
$414$	−34.8700	−	47.6934i	−0.0842271	−	0.115202i
$415$	−27.9741			−0.0674076
$416$			53.0632i			0.127556i
$417$	−369.743	−	187.696i	−0.886673	−	0.450111i
$418$	315.197			0.754060
$419$			31.2014i			0.0744664i	0.999307	+	0.0372332i	$0.0118544\pi$
$419$			31.2014i			0.0744664i	−0.999307	+	0.0372332i	$0.988146\pi$
$420$	24.7912	−	48.8361i	0.0590266	−	0.116276i
$421$	−271.047			−0.643818			−0.321909	−	0.946771i	$-0.604325\pi$
$421$	−271.047			−0.643818			−0.321909	+	0.946771i	$0.604325\pi$
$422$			249.951i			0.592300i
$423$	375.482	−	274.526i	0.887665	−	0.648998i
$424$	−220.821			−0.520805
$425$			394.027i			0.927123i
$426$	−117.316	−	59.5545i	−0.275390	−	0.139799i
$427$	516.905			1.21055
$428$			97.4401i			0.227664i
$429$	−216.795	+	427.064i	−0.505350	+	0.995487i
$430$	136.584			0.317637
$431$			147.107i			0.341317i	0.985330	+	0.170658i	$0.0545894\pi$
$431$			147.107i			0.341317i	−0.985330	+	0.170658i	$0.945411\pi$
$432$	−17.3740	−	106.593i	−0.0402176	−	0.246744i
$433$	208.289			0.481036			0.240518	−	0.970645i	$-0.422683\pi$
$433$	208.289			0.481036			0.240518	+	0.970645i	$0.422683\pi$
$434$		−	406.208i		−	0.935963i
$435$	137.759	+	69.9320i	0.316687	+	0.160763i
$436$	−316.203			−0.725237
$437$		−	60.7879i		−	0.139103i
$438$	27.6605	−	54.4884i	0.0631518	−	0.124403i
$439$	241.334			0.549735			0.274868	−	0.961482i	$-0.411366\pi$
$439$	241.334			0.549735			0.274868	+	0.961482i	$0.411366\pi$
$440$			62.7824i			0.142687i
$441$	−0.0859102	−	0.117504i	−0.000194808	−	0.000266448i
$442$	−224.348			−0.507575
$443$		−	139.352i		−	0.314564i	−0.987554	−	0.157282i	$-0.949727\pi$
$443$		−	139.352i		−	0.314564i	0.987554	−	0.157282i	$-0.0502732\pi$
$444$	352.551	+	178.969i	0.794033	+	0.403083i
$445$	48.8008			0.109665
$446$		−	28.1495i		−	0.0631154i
$447$	138.708	−	273.241i	0.310309	−	0.611277i
$448$	−55.9908			−0.124979
$449$		−	261.937i		−	0.583378i	−0.956513	−	0.291689i	$-0.905783\pi$
$449$		−	261.937i		−	0.583378i	0.956513	−	0.291689i	$-0.0942172\pi$
$450$	239.389	−	175.024i	0.531976	−	0.388943i
$451$	−1326.07			−2.94028
$452$		−	288.938i		−	0.639243i
$453$	−237.821	−	120.728i	−0.524992	−	0.266507i
$454$	−201.869			−0.444645
$455$			85.6243i			0.188185i
$456$	50.2991	−	99.0840i	0.110305	−	0.217289i
$457$	−250.330			−0.547769			−0.273884	−	0.961763i	$-0.588309\pi$
$457$	−250.330			−0.547769			−0.273884	+	0.961763i	$0.588309\pi$
$458$			60.3766i			0.131827i
$459$	450.671	−	73.4562i	0.981853	−	0.160035i
$460$	12.1080			0.0263218
$461$		−	73.2482i		−	0.158890i	−0.996839	−	0.0794450i	$-0.974685\pi$
$461$		−	73.2482i		−	0.158890i	0.996839	−	0.0794450i	$-0.0253148\pi$
$462$	−450.625	−	228.756i	−0.975380	−	0.495142i
$463$	193.009			0.416866			0.208433	−	0.978037i	$-0.433164\pi$
$463$	193.009			0.416866			0.208433	+	0.978037i	$0.433164\pi$
$464$		−	157.941i		−	0.340390i
$465$	−72.6855	+	143.183i	−0.156313	+	0.307921i
$466$	275.602			0.591421
$467$		−	452.909i		−	0.969828i	−0.874562	−	0.484914i	$-0.838851\pi$
$467$		−	452.909i		−	0.969828i	0.874562	−	0.484914i	$-0.161149\pi$
$468$	99.6540	+	136.302i	0.212936	+	0.291243i
$469$	−611.067			−1.30291
$470$			95.3245i			0.202818i
$471$	−135.778	−	68.9266i	−0.288277	−	0.146341i
$472$	−21.7256			−0.0460287
$473$		−	1260.30i		−	2.66449i
$474$	−209.901	+	413.484i	−0.442829	+	0.872329i
$475$	305.115			0.642346
$476$		−	236.726i		−	0.497323i
$477$	−567.216	+	414.708i	−1.18913	+	0.869408i
$478$	−120.457			−0.252002
$479$		−	392.565i		−	0.819552i	−0.912186	−	0.409776i	$-0.865607\pi$
$479$		−	392.565i		−	0.819552i	0.912186	−	0.409776i	$-0.134393\pi$
$480$	19.7360	+	10.0188i	0.0411167	+	0.0208725i
$481$	−618.126			−1.28509
$482$		−	187.827i		−	0.389683i
$483$	−44.1171	+	86.9062i	−0.0913397	+	0.179930i
$484$	337.312			0.696926
$485$		−	218.686i		−	0.450899i
$486$	−244.813	−	241.174i	−0.503730	−	0.496242i
$487$	−556.262			−1.14222			−0.571111	−	0.820873i	$-0.693488\pi$
$487$	−556.262			−1.14222			−0.571111	+	0.820873i	$0.693488\pi$
$488$			208.896i			0.428065i
$489$	365.109	+	185.344i	0.746645	+	0.379027i
$490$	0.0298309			6.08793e−5
$491$			111.896i			0.227894i	0.993487	+	0.113947i	$0.0363495\pi$
$491$			111.896i			0.227894i	−0.993487	+	0.113947i	$0.963651\pi$
$492$	−211.613	+	416.857i	−0.430108	+	0.847270i
$493$	667.766			1.35449
$494$			173.724i			0.351668i
$495$	117.907	+	161.267i	0.238196	+	0.325792i
$496$	164.160			0.330967
$497$			217.038i			0.436697i
$498$	81.1434	+	41.1917i	0.162938	+	0.0827142i
$499$	−704.693			−1.41221			−0.706105	−	0.708107i	$-0.749550\pi$
$499$	−704.693			−1.41221			−0.706105	+	0.708107i	$0.749550\pi$
$500$			125.985i			0.251971i
$501$	−405.096	+	797.997i	−0.808574	+	1.59281i
$502$	−66.8807			−0.133228
$503$		−	641.888i		−	1.27612i	−0.769987	−	0.638060i	$-0.779737\pi$
$503$		−	641.888i		−	1.27612i	0.769987	−	0.638060i	$-0.220263\pi$
$504$	−143.821	+	105.152i	−0.285360	+	0.208635i
$505$	−71.2910			−0.141170
$506$		−	111.724i		−	0.220799i
$507$	216.704	+	110.008i	0.427424	+	0.216978i
$508$	436.052			0.858370
$509$			807.355i			1.58616i	0.609119	+	0.793079i	$0.291523\pi$
$509$			807.355i			1.58616i	−0.609119	+	0.793079i	$0.708477\pi$
$510$	−42.3589	+	83.4428i	−0.0830567	+	0.163613i
$511$	−100.805			−0.197270
$512$		−	22.6274i		−	0.0441942i
$513$	−56.8808	−	348.976i	−0.110879	−	0.680265i
$514$	−201.142			−0.391326
$515$		−	44.9933i		−	0.0873657i
$516$	−396.183	−	201.119i	−0.767797	−	0.389765i
$517$	879.587			1.70133
$518$		−	652.229i		−	1.25913i
$519$	29.4205	−	57.9555i	0.0566870	−	0.111668i
$520$	−34.6031			−0.0665445
$521$			939.510i			1.80328i	0.432484	+	0.901641i	$0.357637\pi$
$521$			939.510i			1.80328i	−0.432484	+	0.901641i	$0.642363\pi$
$522$	−296.617	−	405.697i	−0.568232	−	0.777198i
$523$	436.424			0.834463			0.417232	−	0.908800i	$-0.363000\pi$
$523$	436.424			0.834463			0.417232	+	0.908800i	$0.363000\pi$
$524$		−	188.233i		−	0.359223i
$525$	−436.211	−	221.438i	−0.830878	−	0.421787i
$526$	−142.441			−0.270801
$527$			694.058i			1.31700i
$528$	92.4465	−	182.110i	0.175088	−	0.344906i
$529$	507.453			0.959269
$530$		−	144.000i		−	0.271698i
$531$	−55.8056	+	40.8011i	−0.105095	+	0.0768382i
$532$	−183.308			−0.344564
$533$		−	730.874i		−	1.37125i
$534$	−141.554	−	71.8587i	−0.265083	−	0.134567i
$535$	−63.5418			−0.118770
$536$		−	246.949i		−	0.460726i
$537$	−59.5909	+	117.388i	−0.110970	+	0.218600i
$538$	−75.3615			−0.140077
$539$		−	0.275258i		−	0.000510683i
$540$	69.5107	−	11.3298i	0.128724	−	0.0209811i
$541$	895.623			1.65549			0.827747	−	0.561101i	$-0.189622\pi$
$541$	895.623			1.65549			0.827747	+	0.561101i	$0.189622\pi$
$542$		−	26.1471i		−	0.0482419i
$543$	783.600	+	397.787i	1.44309	+	0.732573i
$544$	95.6674			0.175859
$545$		−	206.200i		−	0.378348i
$546$	126.081	−	248.366i	0.230917	−	0.454884i
$547$	917.580			1.67748			0.838738	−	0.544535i	$-0.183294\pi$
$547$	917.580			1.67748			0.838738	+	0.544535i	$0.183294\pi$
$548$		−	221.673i		−	0.404514i
$549$	392.311	+	536.583i	0.714592	+	0.977382i
$550$	560.782			1.01960
$551$		−	517.084i		−	0.938446i
$552$	−35.1212	−	17.8289i	−0.0636254	−	0.0322988i
$553$	764.957			1.38329
$554$			526.362i			0.950112i
$555$	−116.708	+	229.902i	−0.210284	+	0.414238i
$556$	−276.437			−0.497189
$557$		−	960.859i		−	1.72506i	−0.506005	−	0.862530i	$-0.668878\pi$
$557$		−	960.859i		−	1.72506i	0.506005	−	0.862530i	$-0.331122\pi$
$558$	421.671	−	308.296i	0.755683	−	0.552502i
$559$	694.627			1.24262
$560$		−	36.5122i		−	0.0652004i
$561$	769.951	+	390.858i	1.37246	+	0.696717i
$562$	−703.668			−1.25208
$563$			1034.83i			1.83807i	0.394178	+	0.919034i	$0.371029\pi$
$563$			1034.83i			1.83807i	−0.394178	+	0.919034i	$0.628971\pi$
$564$	140.364	−	276.503i	0.248873	−	0.490254i
$565$	188.420			0.333486
$566$		−	180.627i		−	0.319129i
$567$	−171.951	+	540.200i	−0.303264	+	0.952733i
$568$	−87.7113			−0.154421
$569$			715.737i			1.25789i	0.777451	+	0.628943i	$0.216512\pi$
$569$			715.737i			1.25789i	−0.777451	+	0.628943i	$0.783488\pi$
$570$	64.6138	+	32.8006i	0.113358	+	0.0575449i
$571$	−553.505			−0.969361			−0.484681	−	0.874691i	$-0.661064\pi$
$571$	−553.505			−0.969361			−0.484681	+	0.874691i	$0.661064\pi$
$572$			319.293i			0.558205i
$573$	392.789	−	773.755i	0.685496	−	1.35036i
$574$	771.197			1.34355
$575$		−	108.151i		−	0.188088i
$576$	−42.4948	−	58.1222i	−0.0737757	−	0.100907i
$577$	978.850			1.69645			0.848223	−	0.529639i	$-0.177672\pi$
$577$	978.850			1.69645			0.848223	+	0.529639i	$0.177672\pi$
$578$		−	4.23154i		−	0.00732100i
$579$	−212.002	−	107.621i	−0.366152	−	0.185873i
$580$	102.995			0.177578
$581$		−	150.118i		−	0.258378i
$582$	−322.013	+	634.333i	−0.553287	+	1.08992i
$583$	−1328.73			−2.27913
$584$		−	40.7381i		−	0.0697570i
$585$	−88.8838	+	64.9855i	−0.151938	+	0.111086i
$586$	286.659			0.489179
$587$		−	915.371i		−	1.55941i	−0.626150	−	0.779703i	$-0.715370\pi$
$587$		−	915.371i		−	1.55941i	0.626150	−	0.779703i	$-0.284630\pi$
$588$	−0.0865290	−	0.0439256i	−0.000147158	−	7.47035e-5i
$589$	537.443			0.912467
$590$		−	14.1675i		−	0.0240127i
$591$	−237.341	+	467.538i	−0.401592	+	0.791096i
$592$	263.584			0.445243
$593$		−	36.3730i		−	0.0613373i	−0.999530	−	0.0306686i	$-0.990236\pi$
$593$		−	36.3730i		−	0.0613373i	0.999530	−	0.0306686i	$-0.00976366\pi$
$594$	−104.543	−	641.396i	−0.175999	−	1.07979i
$595$	154.371			0.259448
$596$		−	204.288i		−	0.342765i
$597$	292.611	+	148.541i	0.490135	+	0.248812i
$598$	61.5779			0.102973
$599$		−	766.476i		−	1.27959i	−0.768544	−	0.639797i	$-0.779019\pi$
$599$		−	766.476i		−	1.27959i	0.768544	−	0.639797i	$-0.220981\pi$
$600$	89.4894	−	176.285i	0.149149	−	0.293808i
$601$	32.8523			0.0546627			0.0273313	−	0.999626i	$-0.491299\pi$
$601$	32.8523			0.0546627			0.0273313	+	0.999626i	$0.491299\pi$
$602$			732.950i			1.21753i
$603$	−463.776	−	634.328i	−0.769114	−	1.05195i
$604$	−177.807			−0.294382
$605$			219.965i			0.363579i
$606$	206.791	+	104.975i	0.341239	+	0.173227i
$607$	736.900			1.21400			0.607001	−	0.794701i	$-0.292372\pi$
$607$	736.900			1.21400			0.607001	+	0.794701i	$0.292372\pi$
$608$		−	74.0799i		−	0.121842i
$609$	−375.276	+	739.255i	−0.616217	+	1.21388i
$610$	−136.223			−0.223317
$611$			484.793i			0.793442i
$612$	245.737	−	179.666i	0.401532	−	0.293571i
$613$	607.367			0.990811			0.495406	−	0.868662i	$-0.335019\pi$
$613$	607.367			0.990811			0.495406	+	0.868662i	$0.335019\pi$
$614$		−	0.668534i		−	0.00108882i
$615$	−271.837	−	137.995i	−0.442011	−	0.224383i
$616$	−336.909			−0.546930
$617$		−	328.555i		−	0.532504i	−0.963903	−	0.266252i	$-0.914215\pi$
$617$		−	328.555i		−	0.532504i	0.963903	−	0.266252i	$-0.0857853\pi$
$618$	−66.2522	+	130.510i	−0.107204	+	0.211181i
$619$	34.1186			0.0551189			0.0275595	−	0.999620i	$-0.491226\pi$
$619$	34.1186			0.0551189			0.0275595	+	0.999620i	$0.491226\pi$
$620$			107.051i			0.172662i
$621$	−123.698	+	20.1619i	−0.199191	+	0.0324668i
$622$	−389.022			−0.625438
$623$			261.879i			0.420352i
$624$	100.372	+	50.9528i	0.160852	+	0.0816551i
$625$	500.319			0.800510
$626$		−	728.660i		−	1.16399i
$627$	302.661	−	596.211i	0.482713	−	0.950895i
$628$	−101.514			−0.161647
$629$			1114.42i			1.77173i
$630$	−68.5708	−	93.7876i	−0.108843	−	0.148869i
$631$	−1216.81			−1.92838			−0.964189	−	0.265215i	$-0.914557\pi$
$631$	−1216.81			−1.92838			−0.964189	+	0.265215i	$0.914557\pi$
$632$			309.140i			0.489146i
$633$	472.794	+	240.010i	0.746911	+	0.379162i
$634$	−239.470			−0.377713
$635$			284.355i			0.447803i
$636$	−212.039	+	417.695i	−0.333394	+	0.656753i
$637$	0.151711			0.000238165
$638$		−	950.367i		−	1.48960i
$639$	−225.301	+	164.724i	−0.352583	+	0.257784i
$640$	14.7556			0.0230556
$641$		−	1047.99i		−	1.63493i	−0.575979	−	0.817465i	$-0.695379\pi$
$641$		−	1047.99i		−	1.63493i	0.575979	−	0.817465i	$-0.304621\pi$
$642$	184.313	+	93.5647i	0.287092	+	0.145739i
$643$	727.998			1.13219			0.566095	−	0.824340i	$-0.308454\pi$
$643$	727.998			1.13219			0.566095	+	0.824340i	$0.308454\pi$
$644$			64.9752i			0.100893i
$645$	131.152	−	258.356i	0.203336	−	0.400551i
$646$	313.206			0.484838
$647$			653.806i			1.01052i	0.862968	+	0.505259i	$0.168603\pi$
$647$			653.806i			1.01052i	−0.862968	+	0.505259i	$0.831397\pi$
$648$	−218.310	−	69.4901i	−0.336898	−	0.107238i
$649$	−130.728			−0.201429
$650$			309.080i			0.475508i
$651$	−768.363	−	390.052i	−1.18028	−	0.599158i
$652$	272.973			0.418671
$653$		−	524.103i		−	0.802608i	−0.915945	−	0.401304i	$-0.868557\pi$
$653$		−	524.103i		−	0.802608i	0.915945	−	0.401304i	$-0.131443\pi$
$654$	−303.627	+	598.114i	−0.464262	+	0.914548i
$655$	122.749			0.187403
$656$			311.662i			0.475094i
$657$	−76.5071	−	104.642i	−0.116449	−	0.159273i
$658$	−511.539			−0.777415
$659$			468.777i			0.711347i	0.934610	+	0.355673i	$0.115748\pi$
$659$			468.777i			0.711347i	−0.934610	+	0.355673i	$0.884252\pi$
$660$	118.756	+	60.2854i	0.179934	+	0.0913416i
$661$	264.037			0.399450			0.199725	−	0.979852i	$-0.435995\pi$
$661$	264.037			0.399450			0.199725	+	0.979852i	$0.435995\pi$
$662$			77.8100i			0.117538i
$663$	−215.425	+	424.366i	−0.324925	+	0.640069i
$664$	60.6667			0.0913654
$665$		−	119.537i		−	0.179755i
$666$	677.058	−	495.016i	1.01660	−	0.743268i
$667$	−183.285			−0.274790
$668$			596.621i			0.893145i
$669$	−53.2461	−	27.0299i	−0.0795906	−	0.0404034i
$670$	161.038			0.240356
$671$			1256.97i			1.87328i
$672$	−53.7639	+	105.909i	−0.0800058	+	0.157603i
$673$	−456.702			−0.678606			−0.339303	−	0.940677i	$-0.610191\pi$
$673$	−456.702			−0.678606			−0.339303	+	0.940677i	$0.610191\pi$
$674$			417.406i			0.619297i
$675$	−101.199	−	620.880i	−0.149925	−	0.919822i
$676$	162.018			0.239672
$677$			371.692i			0.549028i	0.961583	+	0.274514i	$0.0885170\pi$
$677$			371.692i			0.549028i	−0.961583	+	0.274514i	$0.911483\pi$
$678$	−546.541	−	277.446i	−0.806107	−	0.409213i
$679$	1173.53			1.72833
$680$			62.3858i			0.0917438i
$681$	−193.840	+	381.845i	−0.284640	+	0.560712i
$682$	987.787			1.44837
$683$		−	392.453i		−	0.574602i	−0.957840	−	0.287301i	$-0.907242\pi$
$683$		−	392.453i		−	0.574602i	0.957840	−	0.287301i	$-0.0927580\pi$
$684$	−139.124	−	190.286i	−0.203397	−	0.278196i
$685$	144.556			0.211030
$686$			485.155i			0.707223i
$687$	114.205	+	57.9753i	0.166238	+	0.0843891i
$688$	−296.206			−0.430531
$689$		−	732.343i		−	1.06291i
$690$	11.6265	−	22.9029i	0.0168499	−	0.0331927i
$691$	65.7402			0.0951378			0.0475689	−	0.998868i	$-0.484853\pi$
$691$	65.7402			0.0951378			0.0475689	+	0.998868i	$0.484853\pi$
$692$		−	43.3303i		−	0.0626160i
$693$	−865.406	+	632.723i	−1.24878	+	0.913020i
$694$	−460.230			−0.663155
$695$		−	180.268i		−	0.259378i
$696$	−298.754	−	151.659i	−0.429244	−	0.217901i
$697$	−1317.69			−1.89051
$698$			460.264i			0.659404i
$699$	264.641	−	521.315i	0.378599	−	0.745802i
$700$	−326.132			−0.465903
$701$		−	1313.03i		−	1.87308i	−0.350559	−	0.936541i	$-0.614009\pi$
$701$		−	1313.03i		−	1.87308i	0.350559	−	0.936541i	$-0.385991\pi$
$702$	353.512	−	57.6200i	0.503578	−	0.0820798i
$703$	862.947			1.22752
$704$		−	136.154i		−	0.193401i
$705$	180.311	+	91.5332i	0.255760	+	0.129834i
$706$	−288.358			−0.408438
$707$		−	382.569i		−	0.541116i
$708$	−20.8615	+	41.0950i	−0.0294654	+	0.0580438i
$709$	230.080			0.324513			0.162257	−	0.986749i	$-0.448123\pi$
$709$	230.080			0.324513			0.162257	+	0.986749i	$0.448123\pi$
$710$		−	57.1975i		−	0.0805599i
$711$	580.573	+	794.077i	0.816558	+	1.11685i
$712$	−105.833			−0.148641
$713$		−	190.501i		−	0.267183i
$714$	−447.779	−	227.311i	−0.627141	−	0.318362i
$715$	−208.215			−0.291210
$716$			87.7649i			0.122577i
$717$	−115.666	+	227.850i	−0.161319	+	0.317783i
$718$	−95.2798			−0.132702
$719$			836.800i			1.16384i	0.813247	+	0.581919i	$0.197698\pi$
$719$			836.800i			1.16384i	−0.813247	+	0.581919i	$0.802302\pi$
$720$	37.9022	−	27.7114i	0.0526419	−	0.0384880i
$721$	241.447			0.334879
$722$			268.001i			0.371192i
$723$	−355.284	−	180.357i	−0.491403	−	0.249456i
$724$	585.857			0.809194
$725$		−	919.967i		−	1.26892i
$726$	323.897	−	638.043i	0.446139	−	0.878847i
$727$	−807.119			−1.11021			−0.555103	−	0.831782i	$-0.687321\pi$
$727$	−807.119			−1.11021			−0.555103	+	0.831782i	$0.687321\pi$
$728$		−	185.691i		−	0.255070i
$729$	−691.268	+	231.494i	−0.948241	+	0.317550i
$730$	26.5658			0.0363915
$731$		−	1252.34i		−	1.71319i
$732$	395.137	+	200.587i	0.539805	+	0.274027i
$733$	263.494			0.359474			0.179737	−	0.983715i	$-0.442475\pi$
$733$	263.494			0.359474			0.179737	+	0.983715i	$0.442475\pi$
$734$		−	162.090i		−	0.220830i
$735$	0.0286444	−	0.0564266i	3.89720e−5	−	7.67709e-5i
$736$	−26.2583			−0.0356770
$737$		−	1485.95i		−	2.01621i
$738$	585.308	+	800.554i	0.793101	+	1.08476i
$739$	122.702			0.166038			0.0830192	−	0.996548i	$-0.473544\pi$
$739$	122.702			0.166038			0.0830192	+	0.996548i	$0.473544\pi$
$740$			171.886i			0.232278i
$741$	328.607	+	166.814i	0.443465	+	0.225121i
$742$	772.747			1.04144
$743$		−	409.388i		−	0.550994i	−0.961302	−	0.275497i	$-0.911158\pi$
$743$		−	409.388i		−	0.550994i	0.961302	−	0.275497i	$-0.0888424\pi$
$744$	157.631	−	310.517i	0.211869	−	0.417361i
$745$	133.218			0.178817
$746$			163.594i			0.219295i
$747$	155.832	−	113.933i	0.208611	−	0.152521i
$748$	575.652			0.769589
$749$		−	340.984i		−	0.455252i
$750$	238.308	+	120.975i	0.317743	+	0.161299i
$751$	769.324			1.02440			0.512200	−	0.858866i	$-0.328831\pi$
$751$	769.324			1.02440			0.512200	+	0.858866i	$0.328831\pi$
$752$		−	206.727i		−	0.274903i
$753$	−64.2207	+	126.508i	−0.0852864	+	0.168006i
$754$	523.804			0.694700
$755$		−	115.950i		−	0.153576i
$756$	60.7990	+	373.015i	0.0804219	+	0.493406i
$757$	−1273.85			−1.68276			−0.841380	−	0.540444i	$-0.818256\pi$
$757$	−1273.85			−1.68276			−0.841380	+	0.540444i	$0.818256\pi$
$758$			878.162i			1.15853i
$759$	−211.332	−	107.281i	−0.278435	−	0.141345i
$760$	48.3084			0.0635636
$761$		−	1310.89i		−	1.72259i	−0.508102	−	0.861297i	$-0.669653\pi$
$761$		−	1310.89i		−	1.72259i	0.508102	−	0.861297i	$-0.330347\pi$
$762$	418.709	−	824.815i	0.549487	−	1.08243i
$763$	1106.53			1.45023
$764$		−	578.496i		−	0.757194i
$765$	117.162	+	160.248i	0.153153	+	0.209475i
$766$	−290.456			−0.379186
$767$		−	72.0518i		−	0.0939397i
$768$	−42.8009	−	21.7275i	−0.0557303	−	0.0282910i
$769$	325.583			0.423385			0.211692	−	0.977336i	$-0.432103\pi$
$769$	325.583			0.423385			0.211692	+	0.977336i	$0.432103\pi$
$770$		−	219.702i		−	0.285328i
$771$	−193.142	+	380.470i	−0.250508	+	0.493476i
$772$	−158.503			−0.205314
$773$		−	1314.44i		−	1.70044i	−0.526431	−	0.850218i	$-0.676470\pi$
$773$		−	1314.44i		−	1.70044i	0.526431	−	0.850218i	$-0.323530\pi$
$774$	−760.852	+	556.281i	−0.983013	+	0.718709i
$775$	956.190			1.23379
$776$			474.258i			0.611157i
$777$	−1233.72	−	626.288i	−1.58780	−	0.806034i
$778$	−133.859			−0.172055
$779$			1020.35i			1.30982i
$780$	−33.2269	+	65.4536i	−0.0425986	+	0.0839148i
$781$	−527.779			−0.675773
$782$		−	111.019i		−	0.141967i
$783$	−1052.22	+	171.504i	−1.34383	+	0.219035i
$784$	−0.0646933			−8.25169e−5
$785$		−	66.1987i		−	0.0843295i
$786$	−356.052	−	180.746i	−0.452992	−	0.229957i
$787$	116.820			0.148437			0.0742185	−	0.997242i	$-0.476354\pi$
$787$	116.820			0.148437			0.0742185	+	0.997242i	$0.476354\pi$
$788$			349.554i			0.443596i
$789$	−136.776	+	269.435i	−0.173354	+	0.341489i
$790$	−201.594			−0.255182
$791$			1011.12i			1.27828i
$792$	−255.701	−	349.734i	−0.322855	−	0.441584i
$793$	−692.793			−0.873635
$794$			541.075i			0.681454i
$795$	−272.384	−	138.273i	−0.342621	−	0.173928i
$796$	218.770			0.274836
$797$		−	595.837i		−	0.747599i	−0.927509	−	0.373800i	$-0.878055\pi$
$797$		−	595.837i		−	0.747599i	0.927509	−	0.373800i	$-0.121945\pi$
$798$	−176.018	+	346.737i	−0.220573	+	0.434507i
$799$	874.030			1.09391
$800$		−	131.799i		−	0.164749i
$801$	−271.849	+	198.756i	−0.339386	+	0.248135i
$802$	766.230			0.955398
$803$		−	245.130i		−	0.305268i
$804$	−467.116	−	237.127i	−0.580990	−	0.294934i
$805$	−42.3711			−0.0526349
$806$			544.428i			0.675469i
$807$	−72.3642	+	142.550i	−0.0896706	+	0.176642i
$808$	154.607			0.191345
$809$			426.502i			0.527197i	0.964632	+	0.263599i	$0.0849094\pi$
$809$			426.502i			0.527197i	−0.964632	+	0.263599i	$0.915091\pi$
$810$	45.3153	−	142.362i	0.0559448	−	0.175756i
$811$	129.520			0.159704			0.0798520	−	0.996807i	$-0.474555\pi$
$811$	129.520			0.159704			0.0798520	+	0.996807i	$0.474555\pi$
$812$			552.703i			0.680668i
$813$	−49.4586	−	25.1072i	−0.0608346	−	0.0308821i
$814$	1586.04			1.94846
$815$			178.009i			0.218416i
$816$	91.8625	−	180.960i	0.112577	−	0.221764i
$817$	−969.748			−1.18696
$818$			336.191i			0.410992i
$819$	−348.731	−	476.977i	−0.425801	−	0.582389i
$820$	−203.238			−0.247852
$821$			45.9586i			0.0559788i	0.999608	+	0.0279894i	$0.00891047\pi$
$821$			45.9586i			0.0559788i	−0.999608	+	0.0279894i	$0.991090\pi$
$822$	−419.307	−	212.857i	−0.510105	−	0.258950i
$823$	−636.646			−0.773568			−0.386784	−	0.922170i	$-0.626414\pi$
$823$	−636.646			−0.773568			−0.386784	+	0.922170i	$0.626414\pi$
$824$			97.5756i			0.118417i
$825$	538.478	−	1060.75i	0.652700	−	1.28575i
$826$	76.0269			0.0920423
$827$			94.1604i			0.113858i	0.998378	+	0.0569289i	$0.0181308\pi$
$827$			94.1604i			0.113858i	−0.998378	+	0.0569289i	$0.981869\pi$
$828$	−67.4487	+	49.3137i	−0.0814598	+	0.0595576i
$829$	−639.682			−0.771631			−0.385816	−	0.922576i	$-0.626080\pi$
$829$	−639.682			−0.771631			−0.385816	+	0.922576i	$0.626080\pi$
$830$			39.5614i			0.0476644i
$831$	995.640	+	505.427i	1.19812	+	0.608216i
$832$	75.0427			0.0901956
$833$		−	0.273519i		−	0.000328355i
$834$	−265.443	+	522.895i	−0.318277	+	0.626972i
$835$	−389.063			−0.465944
$836$		−	445.756i		−	0.533201i
$837$	−178.257	−	1093.65i	−0.212971	−	1.30663i
$838$	44.1255			0.0526557
$839$		−	587.675i		−	0.700447i	−0.936666	−	0.350223i	$-0.886106\pi$
$839$		−	587.675i		−	0.700447i	0.936666	−	0.350223i	$-0.113894\pi$
$840$	−69.0647	−	35.0600i	−0.0822199	−	0.0417381i
$841$	−718.086			−0.853848
$842$			383.319i			0.455248i
$843$	−675.682	+	1331.02i	−0.801521	+	1.57891i
$844$	353.484			0.418820
$845$			105.654i			0.125034i
$846$	−388.238	−	531.012i	−0.458911	−	0.627674i
$847$	−1180.40			−1.39362
$848$			312.289i			0.368265i
$849$	−341.665	−	173.443i	−0.402432	−	0.204291i
$850$	557.239			0.655575
$851$		−	305.879i		−	0.359435i
$852$	−84.2228	+	165.910i	−0.0988530	+	0.194730i
$853$	693.140			0.812591			0.406295	−	0.913742i	$-0.366820\pi$
$853$	693.140			0.812591			0.406295	+	0.913742i	$0.366820\pi$
$854$		−	731.015i		−	0.855989i
$855$	124.088	−	90.7242i	0.145132	−	0.106110i
$856$	137.801			0.160983
$857$			861.820i			1.00562i	0.864396	+	0.502812i	$0.167701\pi$
$857$			861.820i			1.00562i	−0.864396	+	0.502812i	$0.832299\pi$
$858$	603.960	+	306.594i	0.703916	+	0.357336i
$859$	−907.901			−1.05693			−0.528464	−	0.848956i	$-0.677232\pi$
$859$	−907.901			−1.05693			−0.528464	+	0.848956i	$0.677232\pi$
$860$		−	193.159i		−	0.224603i
$861$	740.524	−	1458.76i	0.860075	−	1.69426i
$862$	208.041			0.241347
$863$			534.585i			0.619450i	0.950826	+	0.309725i	$0.100237\pi$
$863$			534.585i			0.619450i	−0.950826	+	0.309725i	$0.899763\pi$
$864$	−150.746	+	24.5705i	−0.174474	+	0.0284381i
$865$	28.2562			0.0326661
$866$		−	294.565i		−	0.340144i
$867$	−8.00417	−	4.06324i	−0.00923203	−	0.00468655i
$868$	−574.465			−0.661826
$869$			1860.17i			2.14058i
$870$	98.8988	−	194.821i	0.113677	−	0.223932i
$871$	818.994			0.940292
$872$			447.179i			0.512820i
$873$	890.668	+	1218.21i	1.02024	+	1.39543i
$874$	−85.9671			−0.0983605
$875$		−	440.876i		−	0.503858i
$876$	−77.0582	−	39.1179i	−0.0879660	−	0.0446551i
$877$	−397.932			−0.453743			−0.226871	−	0.973925i	$-0.572850\pi$
$877$	−397.932			−0.453743			−0.226871	+	0.973925i	$0.572850\pi$
$878$		−	341.298i		−	0.388722i
$879$	275.258	−	542.229i	0.313149	−	0.616871i
$880$	88.7878			0.100895
$881$			1057.38i			1.20021i	0.799922	+	0.600104i	$0.204874\pi$
$881$			1057.38i			1.20021i	−0.799922	+	0.600104i	$0.795126\pi$
$882$	−0.166175	+	0.121495i	−0.000188407	+	0.000137750i
$883$	−1018.53			−1.15348			−0.576741	−	0.816927i	$-0.695676\pi$
$883$	−1018.53			−1.15348			−0.576741	+	0.816927i	$0.695676\pi$
$884$			317.276i			0.358910i
$885$	−26.7985	−	13.6040i	−0.0302808	−	0.0153718i
$886$	−197.073			−0.222430
$887$			638.919i			0.720315i	0.932892	+	0.360158i	$0.117277\pi$
$887$			638.919i			0.720315i	−0.932892	+	0.360158i	$0.882723\pi$
$888$	253.100	−	498.582i	0.285023	−	0.561466i
$889$	−1525.93			−1.71646
$890$		−	69.0147i		−	0.0775446i
$891$	−1313.62	−	418.138i	−1.47432	−	0.469290i
$892$	−39.8094			−0.0446293
$893$		−	676.804i		−	0.757900i
$894$	−386.421	−	196.163i	−0.432238	−	0.219422i
$895$	−57.2325			−0.0639469
$896$			79.1829i			0.0883738i
$897$	59.1288	−	116.478i	0.0659184	−	0.129853i
$898$	−370.434			−0.412511
$899$		−	1620.47i		−	1.80253i
$900$	−247.522	−	338.547i	−0.275024	−	0.376164i
$901$	−1320.34			−1.46541
$902$			1875.34i			2.07909i
$903$	1386.41	+	703.799i	1.53534	+	0.779401i
$904$	−408.620			−0.452013
$905$			382.044i			0.422148i
$906$	−170.735	+	336.330i	−0.188449	+	0.371225i
$907$	1388.89			1.53130			0.765652	−	0.643255i	$-0.222417\pi$
$907$	1388.89			1.53130			0.765652	+	0.643255i	$0.222417\pi$
$908$			285.485i			0.314411i
$909$	397.132	−	290.355i	0.436889	−	0.319422i
$910$	121.091			0.133067
$911$		−	570.711i		−	0.626467i	−0.949676	−	0.313234i	$-0.898588\pi$
$911$		−	570.711i		−	0.626467i	0.949676	−	0.313234i	$-0.101412\pi$
$912$	−140.126	−	71.1336i	−0.153647	−	0.0779974i
$913$	365.045			0.399830
$914$			354.020i			0.387331i
$915$	−130.805	+	257.673i	−0.142957	+	0.281610i
$916$	85.3854			0.0932155
$917$			658.706i			0.718327i
$918$	−103.883	−	637.344i	−0.113162	−	0.694275i
$919$	−554.158			−0.603001			−0.301500	−	0.953466i	$-0.597487\pi$
$919$	−554.158			−0.603001			−0.301500	+	0.953466i	$0.597487\pi$
$920$		−	17.1233i		−	0.0186123i
$921$	−1.26457	−	0.641945i	−0.00137304	−	0.000697009i
$922$	−103.589			−0.112352
$923$		−	290.890i		−	0.315157i
$924$	−323.509	+	637.281i	−0.350118	+	0.689698i
$925$	1535.31			1.65979
$926$		−	272.956i		−	0.294769i
$927$	183.249	+	250.639i	0.197680	+	0.270376i
$928$	−223.362			−0.240692
$929$		−	745.835i		−	0.802837i	−0.915895	−	0.401418i	$-0.868517\pi$
$929$		−	745.835i		−	0.802837i	0.915895	−	0.401418i	$-0.131483\pi$
$930$	202.491	+	102.793i	0.217733	+	0.110530i
$931$	−0.211799			−0.000227497
$932$		−	389.760i		−	0.418198i
$933$	−373.550	+	735.855i	−0.400375	+	0.788698i
$934$	−640.511			−0.685772
$935$			375.390i			0.401486i
$936$	192.759	−	140.932i	0.205940	−	0.150568i
$937$	−1565.70			−1.67097			−0.835486	−	0.549511i	$-0.814814\pi$
$937$	−1565.70			−1.67097			−0.835486	+	0.549511i	$0.814814\pi$
$938$			864.179i			0.921299i
$939$	−1378.30	−	699.680i	−1.46784	−	0.745133i
$940$	134.809			0.143414
$941$			9.93492i			0.0105578i	0.999986	+	0.00527892i	$0.00168034\pi$
$941$			9.93492i			0.0105578i	−0.999986	+	0.00527892i	$0.998320\pi$
$942$	−97.4769	+	192.020i	−0.103479	+	0.203842i
$943$	361.672			0.383534
$944$			30.7246i			0.0325472i
$945$	−243.247	+	39.6477i	−0.257405	+	0.0419552i
$946$	−1782.34			−1.88408
$947$		−	430.462i		−	0.454553i	−0.973830	−	0.227277i	$-0.927018\pi$
$947$		−	430.462i		−	0.454553i	0.973830	−	0.227277i	$-0.0729822\pi$
$948$	584.754	+	296.845i	0.616829	+	0.313128i
$949$	135.106			0.142367
$950$		−	431.497i		−	0.454208i
$951$	−229.946	+	452.970i	−0.241794	+	0.476309i
$952$	−334.781			−0.351660
$953$			1572.04i			1.64957i	0.565445	+	0.824786i	$0.308704\pi$
$953$			1572.04i			1.64957i	−0.565445	+	0.824786i	$0.691296\pi$
$954$	586.485	+	802.164i	0.614764	+	0.840843i
$955$	377.244			0.395020
$956$			170.352i			0.178192i
$957$	−1797.67	−	912.569i	−1.87844	−	0.953572i
$958$	−555.171			−0.579511
$959$			775.729i			0.808894i
$960$	14.1687	−	27.9110i	0.0147591	−	0.0290739i
$961$	723.278			0.752631
$962$			874.163i			0.908693i
$963$	353.965	−	258.794i	0.367564	−	0.268737i
$964$	−265.628			−0.275547
$965$		−	103.361i		−	0.107110i
$966$	122.904	+	62.3910i	0.127230	+	0.0645870i
$967$	696.632			0.720405			0.360203	−	0.932874i	$-0.382708\pi$
$967$	696.632			0.720405			0.360203	+	0.932874i	$0.382708\pi$
$968$		−	477.032i		−	0.492801i
$969$	300.749	−	592.444i	0.310370	−	0.611398i
$970$	−309.269			−0.318834
$971$			330.227i			0.340090i	0.985436	+	0.170045i	$0.0543912\pi$
$971$			330.227i			0.340090i	−0.985436	+	0.170045i	$0.945609\pi$
$972$	−341.071	+	346.218i	−0.350896	+	0.356191i
$973$	967.371			0.994214
$974$			786.674i			0.807673i
$975$	584.641	+	296.787i	0.599631	+	0.304397i
$976$	295.423			0.302688
$977$		−	640.395i		−	0.655471i	−0.944770	−	0.327735i	$-0.893715\pi$
$977$		−	640.395i		−	0.655471i	0.944770	−	0.327735i	$-0.106285\pi$
$978$	262.116	−	516.343i	0.268013	−	0.527958i
$979$	−636.820			−0.650480
$980$		−	0.0421872i		−	4.30482e-5i
$981$	839.812	+	1148.65i	0.856078	+	1.17090i
$982$	158.245			0.161146
$983$			695.588i			0.707617i	0.935318	+	0.353809i	$0.115114\pi$
$983$			695.588i			0.707617i	−0.935318	+	0.353809i	$0.884886\pi$
$984$	589.524	+	299.266i	0.599110	+	0.304133i
$985$	−227.948			−0.231419
$986$		−	944.363i		−	0.957772i
$987$	−491.194	+	967.602i	−0.497664	+	0.980347i
$988$	245.683			0.248667
$989$			343.736i			0.347559i
$990$	228.066	−	166.746i	0.230370	−	0.168430i
$991$	651.187			0.657101			0.328550	−	0.944486i	$-0.393440\pi$
$991$	651.187			0.657101			0.328550	+	0.944486i	$0.393440\pi$
$992$		−	232.157i		−	0.234029i
$993$	147.182	+	74.7153i	0.148219	+	0.0752420i
$994$	306.939			0.308792
$995$			142.662i			0.143379i
$996$	58.2538	−	114.754i	0.0584877	−	0.115215i
$997$	−1474.34			−1.47878			−0.739390	−	0.673277i	$-0.764886\pi$
$997$	−1474.34			−1.47878			−0.739390	+	0.673277i	$0.764886\pi$
$998$			996.587i			0.998584i
$999$	−286.219	−	1756.02i	−0.286505	−	1.75778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.b.a.119.4	✓	40
3.2	odd	2	inner	354.3.b.a.119.24	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.b.a.119.4	✓	40	1.1	even	1	trivial
354.3.b.a.119.24	yes	40	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	354.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-2.67506 - 1.35797i) q^{3} -2.00000 q^{4} -1.30422i q^{5} +(-1.92046 + 3.78310i) q^{6} +6.99884 q^{7} +2.82843i q^{8} +(5.31185 + 7.26528i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-2.67506 - 1.35797i) q^{3} -2.00000 q^{4} -1.30422i q^{5} +(-1.92046 + 3.78310i) q^{6} +6.99884 q^{7} +2.82843i q^{8} +(5.31185 + 7.26528i) q^{9} -1.84445 q^{10} +17.0193i q^{11} +(5.35011 + 2.71593i) q^{12} -9.38034 q^{13} -9.89786i q^{14} +(-1.77109 + 3.48887i) q^{15} +4.00000 q^{16} +16.9118i q^{17} +(10.2747 - 7.51209i) q^{18} +13.0956 q^{19} +2.60845i q^{20} +(-18.7223 - 9.50420i) q^{21} +24.0689 q^{22} -4.64185i q^{23} +(3.84091 - 7.56620i) q^{24} +23.2990 q^{25} +13.2658i q^{26} +(-4.34350 - 26.6483i) q^{27} -13.9977 q^{28} -39.4853i q^{29} +(4.93401 + 2.50470i) q^{30} +41.0400 q^{31} -5.65685i q^{32} +(23.1116 - 45.5276i) q^{33} +23.9168 q^{34} -9.12805i q^{35} +(-10.6237 - 14.5306i) q^{36} +65.8959 q^{37} -18.5200i q^{38} +(25.0929 + 12.7382i) q^{39} +3.68890 q^{40} +77.9155i q^{41} +(-13.4410 + 26.4773i) q^{42} -74.0514 q^{43} -34.0386i q^{44} +(9.47554 - 6.92784i) q^{45} -6.56457 q^{46} -51.6818i q^{47} +(-10.7002 - 5.43187i) q^{48} -0.0161733 q^{49} -32.9498i q^{50} +(22.9656 - 45.2399i) q^{51} +18.7607 q^{52} +78.0721i q^{53} +(-37.6864 + 6.14264i) q^{54} +22.1969 q^{55} +19.7957i q^{56} +(-35.0315 - 17.7834i) q^{57} -55.8406 q^{58} +7.68115i q^{59} +(3.54218 - 6.97774i) q^{60} +73.8558 q^{61} -58.0393i q^{62} +(37.1768 + 50.8485i) q^{63} -8.00000 q^{64} +12.2341i q^{65} +(-64.3857 - 32.6848i) q^{66} -87.3096 q^{67} -33.8235i q^{68} +(-6.30348 + 12.4172i) q^{69} -12.9090 q^{70} +31.0106i q^{71} +(-20.5493 + 15.0242i) q^{72} -14.4031 q^{73} -93.1909i q^{74} +(-62.3261 - 31.6393i) q^{75} -26.1912 q^{76} +119.115i q^{77} +(18.0145 - 35.4868i) q^{78} +109.298 q^{79} -5.21689i q^{80} +(-24.5685 + 77.1841i) q^{81} +110.189 q^{82} -21.4489i q^{83} +(37.4446 + 19.0084i) q^{84} +22.0567 q^{85} +104.724i q^{86} +(-53.6197 + 105.625i) q^{87} -48.1378 q^{88} +37.4175i q^{89} +(-9.79744 - 13.4004i) q^{90} -65.6516 q^{91} +9.28371i q^{92} +(-109.784 - 55.7309i) q^{93} -73.0891 q^{94} -17.0796i q^{95} +(-7.68182 + 15.1324i) q^{96} +167.676 q^{97} +0.0228725i q^{98} +(-123.650 + 90.4039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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