LMFDB - Embedded newform 690.3.f.a.229.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(229,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("690.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.f (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.43
Character	$\chi$	$=$	690.229
Dual form			690.3.f.a.229.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(-0.120547 - 4.99855i) q^{5} -2.44949 q^{6} -0.825820 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(-0.120547 - 4.99855i) q^{5} -2.44949 q^{6} -0.825820 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(7.06901 - 0.170480i) q^{10} +20.1213i q^{11} -3.46410i q^{12} -8.65029i q^{13} -1.16789i q^{14} +(8.65774 - 0.208794i) q^{15} +4.00000 q^{16} +10.6539 q^{17} -4.24264i q^{18} +23.3331i q^{19} +(0.241095 + 9.99709i) q^{20} -1.43036i q^{21} -28.4559 q^{22} +(-10.9463 - 20.2281i) q^{23} +4.89898 q^{24} +(-24.9709 + 1.20512i) q^{25} +12.2334 q^{26} -5.19615i q^{27} +1.65164 q^{28} -27.2981 q^{29} +(0.295280 + 12.2439i) q^{30} -3.63914 q^{31} +5.65685i q^{32} -34.8512 q^{33} +15.0669i q^{34} +(0.0995505 + 4.12790i) q^{35} +6.00000 q^{36} -21.2571 q^{37} -32.9979 q^{38} +14.9827 q^{39} +(-14.1380 + 0.340960i) q^{40} -56.4682 q^{41} +2.02284 q^{42} -37.6726 q^{43} -40.2427i q^{44} +(0.361642 + 14.9956i) q^{45} +(28.6069 - 15.4804i) q^{46} +37.2452i q^{47} +6.92820i q^{48} -48.3180 q^{49} +(-1.70430 - 35.3142i) q^{50} +18.4532i q^{51} +17.3006i q^{52} -19.9220 q^{53} +7.34847 q^{54} +(100.577 - 2.42558i) q^{55} +2.33577i q^{56} -40.4141 q^{57} -38.6053i q^{58} +20.2095 q^{59} +(-17.3155 + 0.417589i) q^{60} +36.3871i q^{61} -5.14652i q^{62} +2.47746 q^{63} -8.00000 q^{64} +(-43.2389 + 1.04277i) q^{65} -49.2870i q^{66} -43.4353 q^{67} -21.3079 q^{68} +(35.0362 - 18.9596i) q^{69} +(-5.83773 + 0.140786i) q^{70} -76.9413 q^{71} +8.48528i q^{72} -73.5162i q^{73} -30.0621i q^{74} +(-2.08734 - 43.2509i) q^{75} -46.6661i q^{76} -16.6166i q^{77} +21.1888i q^{78} +74.2700i q^{79} +(-0.482190 - 19.9942i) q^{80} +9.00000 q^{81} -79.8581i q^{82} +115.343 q^{83} +2.86072i q^{84} +(-1.28430 - 53.2542i) q^{85} -53.2770i q^{86} -47.2817i q^{87} +56.9117 q^{88} -85.7222i q^{89} +(-21.2070 + 0.511440i) q^{90} +7.14358i q^{91} +(21.8926 + 40.4563i) q^{92} -6.30318i q^{93} -52.6726 q^{94} +(116.631 - 2.81274i) q^{95} -9.79796 q^{96} -117.419 q^{97} -68.3320i q^{98} -60.3640i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) $ 48 * q - 96 * q^4 - 144 * q^9	$ 48 q - 96 q^{4} - 144 q^{9} + 192 q^{16} + 96 q^{25} + 64 q^{26} - 152 q^{29} - 8 q^{31} + 56 q^{35} + 288 q^{36} - 48 q^{39} + 40 q^{41} - 160 q^{46} + 424 q^{49} + 96 q^{50} + 32 q^{55} + 360 q^{59} - 384 q^{64} + 192 q^{69} - 496 q^{70} - 152 q^{71} + 144 q^{75} + 432 q^{81} - 136 q^{85} + 256 q^{94} + 496 q^{95}+O(q^{100}) $ 48 * q - 96 * q^4 - 144 * q^9 + 192 * q^16 + 96 * q^25 + 64 * q^26 - 152 * q^29 - 8 * q^31 + 56 * q^35 + 288 * q^36 - 48 * q^39 + 40 * q^41 - 160 * q^46 + 424 * q^49 + 96 * q^50 + 32 * q^55 + 360 * q^59 - 384 * q^64 + 192 * q^69 - 496 * q^70 - 152 * q^71 + 144 * q^75 + 432 * q^81 - 136 * q^85 + 256 * q^94 + 496 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−2.00000			−0.500000
$5$	−0.120547	−	4.99855i	−0.0241095	−	0.999709i
$5$	−0.120547	−	4.99855i	−0.0241095	−	0.999709i
$6$	−2.44949			−0.408248
$7$	−0.825820			−0.117974			−0.0589871	−	0.998259i	$-0.518787\pi$
$7$	−0.825820			−0.117974			−0.0589871	+	0.998259i	$0.518787\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−3.00000			−0.333333
$10$	7.06901	−	0.170480i	0.706901	−	0.0170480i
$11$			20.1213i			1.82921i	0.404346	+	0.914606i	$0.367499\pi$
$11$			20.1213i			1.82921i	−0.404346	+	0.914606i	$0.632501\pi$
$12$		−	3.46410i		−	0.288675i
$13$		−	8.65029i		−	0.665407i	−0.943032	−	0.332703i	$-0.892039\pi$
$13$		−	8.65029i		−	0.665407i	0.943032	−	0.332703i	$-0.107961\pi$
$14$		−	1.16789i		−	0.0834204i
$15$	8.65774	−	0.208794i	0.577182	−	0.0139196i
$16$	4.00000			0.250000
$17$	10.6539			0.626702			0.313351	−	0.949637i	$-0.398548\pi$
$17$	10.6539			0.626702			0.313351	+	0.949637i	$0.398548\pi$
$18$		−	4.24264i		−	0.235702i
$19$			23.3331i			1.22806i	0.789284	+	0.614028i	$0.210452\pi$
$19$			23.3331i			1.22806i	−0.789284	+	0.614028i	$0.789548\pi$
$20$	0.241095	+	9.99709i	0.0120547	+	0.499855i
$21$		−	1.43036i		−	0.0681125i
$22$	−28.4559			−1.29345
$23$	−10.9463	−	20.2281i	−0.475927	−	0.879485i
$23$	−10.9463	−	20.2281i	−0.475927	−	0.879485i
$24$	4.89898			0.204124
$25$	−24.9709	+	1.20512i	−0.998837	+	0.0482050i
$26$	12.2334			0.470514
$27$		−	5.19615i		−	0.192450i
$28$	1.65164			0.0589871
$29$	−27.2981			−0.941313			−0.470657	−	0.882316i	$-0.655983\pi$
$29$	−27.2981			−0.941313			−0.470657	+	0.882316i	$0.655983\pi$
$30$	0.295280	+	12.2439i	0.00984266	+	0.408130i
$31$	−3.63914			−0.117392			−0.0586958	−	0.998276i	$-0.518694\pi$
$31$	−3.63914			−0.117392			−0.0586958	+	0.998276i	$0.518694\pi$
$32$			5.65685i			0.176777i
$33$	−34.8512			−1.05610
$34$			15.0669i			0.443145i
$35$	0.0995505	+	4.12790i	0.00284430	+	0.117940i
$36$	6.00000			0.166667
$37$	−21.2571			−0.574517			−0.287259	−	0.957853i	$-0.592744\pi$
$37$	−21.2571			−0.574517			−0.287259	+	0.957853i	$0.592744\pi$
$38$	−32.9979			−0.868367
$39$	14.9827			0.384173
$40$	−14.1380	+	0.340960i	−0.353451	+	0.00852399i
$41$	−56.4682			−1.37727			−0.688636	−	0.725107i	$-0.741790\pi$
$41$	−56.4682			−1.37727			−0.688636	+	0.725107i	$0.741790\pi$
$42$	2.02284			0.0481628
$43$	−37.6726			−0.876106			−0.438053	−	0.898949i	$-0.644332\pi$
$43$	−37.6726			−0.876106			−0.438053	+	0.898949i	$0.644332\pi$
$44$		−	40.2427i		−	0.914606i
$45$	0.361642	+	14.9956i	0.00803650	+	0.333236i
$46$	28.6069	−	15.4804i	0.621890	−	0.336531i
$47$			37.2452i			0.792451i	0.918153	+	0.396225i	$0.129680\pi$
$47$			37.2452i			0.792451i	−0.918153	+	0.396225i	$0.870320\pi$
$48$			6.92820i			0.144338i
$49$	−48.3180			−0.986082
$50$	−1.70430	−	35.3142i	−0.0340861	−	0.706285i
$51$			18.4532i			0.361827i
$52$			17.3006i			0.332703i
$53$	−19.9220			−0.375888			−0.187944	−	0.982180i	$-0.560182\pi$
$53$	−19.9220			−0.375888			−0.187944	+	0.982180i	$0.560182\pi$
$54$	7.34847			0.136083
$55$	100.577	−	2.42558i	1.82868	−	0.0441014i
$56$			2.33577i			0.0417102i
$57$	−40.4141			−0.709019
$58$		−	38.6053i		−	0.665609i
$59$	20.2095			0.342534			0.171267	−	0.985225i	$-0.445214\pi$
$59$	20.2095			0.342534			0.171267	+	0.985225i	$0.445214\pi$
$60$	−17.3155	+	0.417589i	−0.288591	+	0.00695981i
$61$			36.3871i			0.596509i	0.954486	+	0.298255i	$0.0964045\pi$
$61$			36.3871i			0.596509i	−0.954486	+	0.298255i	$0.903596\pi$
$62$		−	5.14652i		−	0.0830084i
$63$	2.47746			0.0393247
$64$	−8.00000			−0.125000
$65$	−43.2389	+	1.04277i	−0.665213	+	0.0160426i
$66$		−	49.2870i		−	0.746773i
$67$	−43.4353			−0.648288			−0.324144	−	0.946008i	$-0.605076\pi$
$67$	−43.4353			−0.648288			−0.324144	+	0.946008i	$0.605076\pi$
$68$	−21.3079			−0.313351
$69$	35.0362	−	18.9596i	0.507771	−	0.274777i
$70$	−5.83773	+	0.140786i	−0.0833961	+	0.00201122i
$71$	−76.9413			−1.08368			−0.541840	−	0.840482i	$-0.682272\pi$
$71$	−76.9413			−1.08368			−0.541840	+	0.840482i	$0.682272\pi$
$72$			8.48528i			0.117851i
$73$		−	73.5162i		−	1.00707i	−0.863975	−	0.503535i	$-0.832032\pi$
$73$		−	73.5162i		−	1.00707i	0.863975	−	0.503535i	$-0.167968\pi$
$74$		−	30.0621i		−	0.406245i
$75$	−2.08734	−	43.2509i	−0.0278311	−	0.576679i
$76$		−	46.6661i		−	0.614028i
$77$		−	16.6166i		−	0.215800i
$78$			21.1888i			0.271651i
$79$			74.2700i			0.940126i	0.882633	+	0.470063i	$0.155769\pi$
$79$			74.2700i			0.940126i	−0.882633	+	0.470063i	$0.844231\pi$
$80$	−0.482190	−	19.9942i	−0.00602737	−	0.249927i
$81$	9.00000			0.111111
$82$		−	79.8581i		−	0.973879i
$83$	115.343			1.38967			0.694837	−	0.719167i	$-0.255476\pi$
$83$	115.343			1.38967			0.694837	+	0.719167i	$0.255476\pi$
$84$			2.86072i			0.0340562i
$85$	−1.28430	−	53.2542i	−0.0151095	−	0.626520i
$86$		−	53.2770i		−	0.619501i
$87$		−	47.2817i		−	0.543467i
$88$	56.9117			0.646724
$89$		−	85.7222i		−	0.963171i	−0.876399	−	0.481585i	$-0.840061\pi$
$89$		−	85.7222i		−	0.963171i	0.876399	−	0.481585i	$-0.159939\pi$
$90$	−21.2070	+	0.511440i	−0.235634	+	0.00568266i
$91$			7.14358i			0.0785008i
$92$	21.8926	+	40.4563i	0.237964	+	0.439742i
$93$		−	6.30318i		−	0.0677761i
$94$	−52.6726			−0.560347
$95$	116.631	−	2.81274i	1.22770	−	0.0296078i
$96$	−9.79796			−0.102062
$97$	−117.419			−1.21050			−0.605252	−	0.796034i	$-0.706928\pi$
$97$	−117.419			−1.21050			−0.605252	+	0.796034i	$0.706928\pi$
$98$		−	68.3320i		−	0.697265i
$99$		−	60.3640i		−	0.609737i
$100$	49.9419	−	2.41025i	0.499419	−	0.0241025i
$101$	195.194			1.93261			0.966307	−	0.257392i	$-0.0828631\pi$
$101$	195.194			1.93261			0.966307	+	0.257392i	$0.0828631\pi$
$102$	−26.0967			−0.255850
$103$	−34.8053			−0.337915			−0.168958	−	0.985623i	$-0.554040\pi$
$103$	−34.8053			−0.337915			−0.168958	+	0.985623i	$0.554040\pi$
$104$	−24.4667			−0.235257
$105$	−7.14973	+	0.172426i	−0.0680927	+	0.00164216i
$106$		−	28.1740i		−	0.265793i
$107$	−16.6340			−0.155458			−0.0777290	−	0.996975i	$-0.524767\pi$
$107$	−16.6340			−0.155458			−0.0777290	+	0.996975i	$0.524767\pi$
$108$			10.3923i			0.0962250i
$109$			127.161i			1.16661i	0.812252	+	0.583306i	$0.198241\pi$
$109$			127.161i			1.16661i	−0.812252	+	0.583306i	$0.801759\pi$
$110$	3.43028	+	142.238i	0.0311844	+	1.29307i
$111$		−	36.8184i		−	0.331698i
$112$	−3.30328			−0.0294936
$113$	157.542			1.39417			0.697087	−	0.716987i	$-0.254479\pi$
$113$	157.542			1.39417			0.697087	+	0.716987i	$0.254479\pi$
$114$		−	57.1541i		−	0.501352i
$115$	−99.7918	+	57.1542i	−0.867755	+	0.496993i
$116$	54.5962			0.470657
$117$			25.9509i			0.221802i
$118$			28.5806i			0.242208i
$119$	−8.79823			−0.0739347
$120$	−0.590559	−	24.4878i	−0.00492133	−	0.204065i
$121$	−283.868			−2.34602
$122$	−51.4591			−0.421796
$123$		−	97.8058i		−	0.795169i
$124$	7.27828			0.0586958
$125$	9.03405	+	124.673i	0.0722724	+	0.997385i
$126$			3.50366i			0.0278068i
$127$			243.667i			1.91864i	0.282318	+	0.959321i	$0.408897\pi$
$127$			243.667i			1.91864i	−0.282318	+	0.959321i	$0.591103\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	65.2508i		−	0.505820i
$130$	−1.47470	−	61.1490i	−0.0113438	−	0.470377i
$131$	64.8374			0.494942			0.247471	−	0.968895i	$-0.420400\pi$
$131$	64.8374			0.494942			0.247471	+	0.968895i	$0.420400\pi$
$132$	69.7024			0.528048
$133$		−	19.2689i		−	0.144879i
$134$		−	61.4268i		−	0.458409i
$135$	−25.9732	+	0.626383i	−0.192394	+	0.00463987i
$136$		−	30.1339i		−	0.221573i
$137$	−76.2724			−0.556733			−0.278366	−	0.960475i	$-0.589793\pi$
$137$	−76.2724			−0.556733			−0.278366	+	0.960475i	$0.589793\pi$
$138$	26.8129	+	49.5486i	0.194296	+	0.359048i
$139$	−195.945			−1.40968			−0.704839	−	0.709367i	$-0.748981\pi$
$139$	−195.945			−1.40968			−0.704839	+	0.709367i	$0.748981\pi$
$140$	−0.199101	−	8.25580i	−0.00142215	−	0.0589700i
$141$	−64.5106			−0.457522
$142$		−	108.811i		−	0.766277i
$143$	174.055			1.21717
$144$	−12.0000			−0.0833333
$145$	3.29071	+	136.451i	0.0226946	+	0.941040i
$146$	103.968			0.712107
$147$		−	83.6893i		−	0.569315i
$148$	42.5143			0.287259
$149$		−	43.1457i		−	0.289569i	−0.989463	−	0.144784i	$-0.953751\pi$
$149$		−	43.1457i		−	0.289569i	0.989463	−	0.144784i	$-0.0462488\pi$
$150$	61.1661	−	2.95194i	0.407774	−	0.0196796i
$151$	−76.8010			−0.508616			−0.254308	−	0.967123i	$-0.581848\pi$
$151$	−76.8010			−0.508616			−0.254308	+	0.967123i	$0.581848\pi$
$152$	65.9959			0.434183
$153$	−31.9618			−0.208901
$154$	23.4994			0.152594
$155$	0.438689	+	18.1904i	0.00283025	+	0.117358i
$156$	−29.9655			−0.192086
$157$	88.6539			0.564674			0.282337	−	0.959315i	$-0.408890\pi$
$157$	88.6539			0.564674			0.282337	+	0.959315i	$0.408890\pi$
$158$	−105.034			−0.664770
$159$		−	34.5060i		−	0.217019i
$160$	28.2760	−	0.681919i	0.176725	−	0.00426200i
$161$	9.03969	+	16.7048i	0.0561471	+	0.103757i
$162$			12.7279i			0.0785674i
$163$		−	79.6550i		−	0.488681i	−0.969690	−	0.244340i	$-0.921429\pi$
$163$		−	79.6550i		−	0.488681i	0.969690	−	0.244340i	$-0.0785715\pi$
$164$	112.936			0.688636
$165$	4.20122	+	174.205i	0.0254619	+	1.05579i
$166$			163.120i			0.982648i
$167$		−	132.184i		−	0.791519i	−0.918354	−	0.395760i	$-0.870481\pi$
$167$		−	132.184i		−	0.791519i	0.918354	−	0.395760i	$-0.129519\pi$
$168$	−4.04567			−0.0240814
$169$	94.1725			0.557234
$170$	75.3128	−	1.81628i	0.443016	−	0.0106840i
$171$		−	69.9992i		−	0.409352i
$172$	75.3451			0.438053
$173$			24.2899i			0.140404i	0.997533	+	0.0702021i	$0.0223644\pi$
$173$			24.2899i			0.140404i	−0.997533	+	0.0702021i	$0.977636\pi$
$174$	66.8664			0.384289
$175$	20.6215	−	0.995215i	0.117837	−	0.00568694i
$176$			80.4853i			0.457303i
$177$			35.0039i			0.197762i
$178$	121.230			0.681065
$179$	−28.8102			−0.160951			−0.0804754	−	0.996757i	$-0.525644\pi$
$179$	−28.8102			−0.160951			−0.0804754	+	0.996757i	$0.525644\pi$
$180$	−0.723285	−	29.9913i	−0.00401825	−	0.166618i
$181$			189.492i			1.04692i	0.852051	+	0.523459i	$0.175359\pi$
$181$			189.492i			1.04692i	−0.852051	+	0.523459i	$0.824641\pi$
$182$	−10.1025			−0.0555085
$183$	−63.0243			−0.344395
$184$	−57.2138	+	30.9609i	−0.310945	+	0.168266i
$185$	2.56249	+	106.255i	0.0138513	+	0.574350i
$186$	8.91404			0.0479249
$187$			214.371i			1.14637i
$188$		−	74.4904i		−	0.396225i
$189$			4.29108i			0.0227042i
$190$	3.97782	+	164.942i	0.0209359	+	0.868114i
$191$		−	69.8790i		−	0.365859i	−0.983126	−	0.182929i	$-0.941442\pi$
$191$		−	69.8790i		−	0.365859i	0.983126	−	0.182929i	$-0.0585580\pi$
$192$		−	13.8564i		−	0.0721688i
$193$		−	251.371i		−	1.30244i	−0.758888	−	0.651221i	$-0.774257\pi$
$193$		−	251.371i		−	1.30244i	0.758888	−	0.651221i	$-0.225743\pi$
$194$		−	166.055i		−	0.855955i
$195$	−1.80613	−	74.8919i	−0.00926221	−	0.384061i
$196$	96.6360			0.493041
$197$			289.126i			1.46765i	0.679341	+	0.733823i	$0.262266\pi$
$197$			289.126i			1.46765i	−0.679341	+	0.733823i	$0.737734\pi$
$198$	85.3676			0.431150
$199$			297.933i			1.49715i	0.663050	+	0.748575i	$0.269262\pi$
$199$			297.933i			1.49715i	−0.663050	+	0.748575i	$0.730738\pi$
$200$	3.40861	+	70.6285i	0.0170430	+	0.353142i
$201$		−	75.2322i		−	0.374290i
$202$			276.046i			1.36656i
$203$	22.5433			0.111051
$204$		−	36.9063i		−	0.180913i
$205$	6.80710	+	282.259i	0.0332053	+	1.37687i
$206$		−	49.2221i		−	0.238942i
$207$	32.8390	+	60.6844i	0.158642	+	0.293162i
$208$		−	34.6011i		−	0.166352i
$209$	−469.493			−2.24638
$210$	−0.243848	−	10.1112i	−0.00116118	−	0.0481488i
$211$	−126.230			−0.598246			−0.299123	−	0.954214i	$-0.596694\pi$
$211$	−126.230			−0.598246			−0.299123	+	0.954214i	$0.596694\pi$
$212$	39.8441			0.187944
$213$		−	133.266i		−	0.625663i
$214$		−	23.5240i		−	0.109925i
$215$	4.54133	+	188.308i	0.0211225	+	0.875851i
$216$	−14.6969			−0.0680414
$217$	3.00527			0.0138492
$218$	−179.833			−0.824920
$219$	127.334			0.581433
$220$	−201.155	+	4.85115i	−0.914340	+	0.0220507i
$221$		−	92.1596i		−	0.417012i
$222$	52.0691			0.234546
$223$		−	140.231i		−	0.628840i	−0.949284	−	0.314420i	$-0.898190\pi$
$223$		−	140.231i		−	0.628840i	0.949284	−	0.314420i	$-0.101810\pi$
$224$		−	4.67154i		−	0.0208551i
$225$	74.9128	−	3.61537i	0.332946	−	0.0160683i
$226$			222.798i			0.985830i
$227$	294.520			1.29744			0.648722	−	0.761025i	$-0.275304\pi$
$227$	294.520			1.29744			0.648722	+	0.761025i	$0.275304\pi$
$228$	80.8281			0.354509
$229$		−	21.7864i		−	0.0951369i	−0.998868	−	0.0475685i	$-0.984853\pi$
$229$		−	21.7864i		−	0.0951369i	0.998868	−	0.0475685i	$-0.0151472\pi$
$230$	−80.8282	−	141.127i	−0.351427	−	0.613595i
$231$	28.7808			0.124592
$232$			77.2106i			0.332804i
$233$		−	182.967i		−	0.785266i	−0.919695	−	0.392633i	$-0.871564\pi$
$233$		−	182.967i		−	0.785266i	0.919695	−	0.392633i	$-0.128436\pi$
$234$	−36.7001			−0.156838
$235$	186.172	−	4.48981i	0.792220	−	0.0191056i
$236$	−40.4191			−0.171267
$237$	−128.639			−0.542782
$238$		−	12.4426i		−	0.0522797i
$239$	95.5019			0.399590			0.199795	−	0.979838i	$-0.435972\pi$
$239$	95.5019			0.399590			0.199795	+	0.979838i	$0.435972\pi$
$240$	34.6309	−	0.835177i	0.144296	−	0.00347991i
$241$			105.768i			0.438871i	0.975627	+	0.219435i	$0.0704215\pi$
$241$			105.768i			0.438871i	−0.975627	+	0.219435i	$0.929578\pi$
$242$		−	401.450i		−	1.65889i
$243$			15.5885i			0.0641500i
$244$		−	72.7742i		−	0.298255i
$245$	5.82461	+	241.520i	0.0237739	+	0.985795i
$246$	138.318			0.562269
$247$	201.838			0.817157
$248$			10.2930i			0.0415042i
$249$			199.780i			0.802329i
$250$	−176.314	+	12.7761i	−0.705258	+	0.0511043i
$251$		−	215.087i		−	0.856919i	−0.903561	−	0.428459i	$-0.859057\pi$
$251$		−	215.087i		−	0.856919i	0.903561	−	0.428459i	$-0.140943\pi$
$252$	−4.95492			−0.0196624
$253$	407.017	−	220.255i	1.60876	−	0.870572i
$254$	−344.598			−1.35668
$255$	92.2390	−	2.22448i	0.361721	−	0.00872345i
$256$	16.0000			0.0625000
$257$			419.045i			1.63052i	0.579092	+	0.815262i	$0.303407\pi$
$257$			419.045i			1.63052i	−0.579092	+	0.815262i	$0.696593\pi$
$258$	92.2785			0.357669
$259$	17.5546			0.0677782
$260$	86.4777	−	2.08554i	0.332607	−	0.00802131i
$261$	81.8942			0.313771
$262$			91.6940i			0.349977i
$263$	338.044			1.28534			0.642669	−	0.766144i	$-0.277827\pi$
$263$	338.044			1.28534			0.642669	+	0.766144i	$0.277827\pi$
$264$			98.5740i			0.373386i
$265$	2.40155	+	99.5812i	0.00906246	+	0.375778i
$266$	27.2503			0.102445
$267$	148.475			0.556087
$268$	86.8707			0.324144
$269$	−0.492344			−0.00183027			−0.000915137	−	1.00000i	$-0.500291\pi$
$269$	−0.492344			−0.00183027			−0.000915137		1.00000i	$0.500291\pi$
$270$	−0.885839	−	36.7317i	−0.00328089	−	0.136043i
$271$	162.212			0.598567			0.299284	−	0.954164i	$-0.403252\pi$
$271$	162.212			0.598567			0.299284	+	0.954164i	$0.403252\pi$
$272$	42.6157			0.156676
$273$	−12.3730			−0.0453225
$274$		−	107.865i		−	0.393670i
$275$	−24.2487	−	502.449i	−0.0881771	−	1.82709i
$276$	−70.0724	+	37.9192i	−0.253885	+	0.137388i
$277$		−	466.556i		−	1.68432i	−0.539229	−	0.842159i	$-0.681284\pi$
$277$		−	466.556i		−	1.68432i	0.539229	−	0.842159i	$-0.318716\pi$
$278$		−	277.108i		−	0.996793i
$279$	10.9174			0.0391306
$280$	11.6755	−	0.281571i	0.0416981	−	0.00100561i
$281$			197.700i			0.703559i	0.936083	+	0.351780i	$0.114423\pi$
$281$			197.700i			0.703559i	−0.936083	+	0.351780i	$0.885577\pi$
$282$		−	91.2317i		−	0.323517i
$283$	−280.867			−0.992464			−0.496232	−	0.868190i	$-0.665284\pi$
$283$	−280.867			−0.992464			−0.496232	+	0.868190i	$0.665284\pi$
$284$	153.883			0.541840
$285$	4.87181	+	202.012i	0.0170941	+	0.708812i
$286$			246.151i			0.860669i
$287$	46.6325			0.162483
$288$		−	16.9706i		−	0.0589256i
$289$	−175.494			−0.607245
$290$	−192.970	+	4.65377i	−0.665415	+	0.0160475i
$291$		−	203.375i		−	0.698884i
$292$			147.032i			0.503535i
$293$	−198.909			−0.678869			−0.339434	−	0.940630i	$-0.610236\pi$
$293$	−198.909			−0.678869			−0.339434	+	0.940630i	$0.610236\pi$
$294$	118.354			0.402566
$295$	−2.43621	−	101.018i	−0.00825833	−	0.342435i
$296$			60.1243i			0.203122i
$297$	104.554			0.352032
$298$	61.0173			0.204756
$299$	−174.979	+	94.6888i	−0.585215	+	0.316685i
$300$	4.17467	+	86.5019i	0.0139156	+	0.288340i
$301$	31.1107			0.103358
$302$		−	108.613i		−	0.359646i
$303$			338.086i			1.11580i
$304$			93.3323i			0.307014i
$305$	181.882	−	4.38637i	0.596336	−	0.0143815i
$306$		−	45.2008i		−	0.147715i
$307$			291.925i			0.950895i	0.879744	+	0.475448i	$0.157714\pi$
$307$			291.925i			0.950895i	−0.879744	+	0.475448i	$0.842286\pi$
$308$			33.2332i			0.107900i
$309$		−	60.2845i		−	0.195095i
$310$	−25.7251	+	0.620400i	−0.0829843	+	0.00200129i
$311$	336.264			1.08123			0.540617	−	0.841269i	$-0.318191\pi$
$311$	336.264			1.08123			0.540617	+	0.841269i	$0.318191\pi$
$312$		−	42.3776i		−	0.135826i
$313$	439.891			1.40540			0.702702	−	0.711484i	$-0.251977\pi$
$313$	439.891			1.40540			0.702702	+	0.711484i	$0.251977\pi$
$314$			125.376i			0.399285i
$315$	−0.298651	−	12.3837i	−0.000948100	−	0.0393133i
$316$		−	148.540i		−	0.470063i
$317$		−	323.129i		−	1.01933i	−0.860372	−	0.509667i	$-0.829769\pi$
$317$		−	323.129i		−	1.01933i	0.860372	−	0.509667i	$-0.170231\pi$
$318$	48.7988			0.153455
$319$		−	549.274i		−	1.72186i
$320$	0.964380	+	39.9884i	0.00301369	+	0.124964i
$321$		−	28.8110i		−	0.0897538i
$322$	−23.6242	+	12.7841i	−0.0733670	+	0.0397020i
$323$			248.589i			0.769625i
$324$	−18.0000			−0.0555556
$325$	10.4247	+	216.006i	0.0320759	+	0.664633i
$326$	112.649			0.345550
$327$	−220.249			−0.673544
$328$			159.716i			0.486939i
$329$		−	30.7578i		−	0.0934888i
$330$	−246.363	+	5.94142i	−0.746556	+	0.0180043i
$331$	−83.8990			−0.253471			−0.126736	−	0.991937i	$-0.540450\pi$
$331$	−83.8990			−0.253471			−0.126736	+	0.991937i	$0.540450\pi$
$332$	−230.686			−0.694837
$333$	63.7714			0.191506
$334$	186.936			0.559689
$335$	5.23602	+	217.113i	0.0156299	+	0.648100i
$336$		−	5.72145i		−	0.0170281i
$337$	−374.474			−1.11120			−0.555599	−	0.831451i	$-0.687511\pi$
$337$	−374.474			−1.11120			−0.555599	+	0.831451i	$0.687511\pi$
$338$			133.180i			0.394024i
$339$			272.870i			0.804927i
$340$	2.56861	+	106.508i	0.00755473	+	0.313260i
$341$		−	73.2244i		−	0.214734i
$342$	98.9938			0.289456
$343$	80.3671			0.234307
$344$			106.554i			0.309750i
$345$	−98.9939	−	172.844i	−0.286939	−	0.500998i
$346$	−34.3512			−0.0992808
$347$			73.1525i			0.210814i	0.994429	+	0.105407i	$0.0336145\pi$
$347$			73.1525i			0.210814i	−0.994429	+	0.105407i	$0.966385\pi$
$348$			94.5633i			0.271734i
$349$	342.990			0.982779			0.491389	−	0.870940i	$-0.336489\pi$
$349$	342.990			0.982779			0.491389	+	0.870940i	$0.336489\pi$
$350$	1.40745	+	29.1632i	0.00402128	+	0.0833234i
$351$	−44.9482			−0.128058
$352$	−113.823			−0.323362
$353$		−	253.570i		−	0.718329i	−0.933274	−	0.359164i	$-0.883062\pi$
$353$		−	253.570i		−	0.718329i	0.933274	−	0.359164i	$-0.116938\pi$
$354$	−49.5030			−0.139839
$355$	9.27507	+	384.594i	0.0261270	+	1.08336i
$356$			171.444i			0.481585i
$357$		−	15.2390i		−	0.0426862i
$358$		−	40.7438i		−	0.113809i
$359$		−	57.6776i		−	0.160662i	−0.996768	−	0.0803310i	$-0.974402\pi$
$359$		−	57.6776i		−	0.160662i	0.996768	−	0.0803310i	$-0.0255977\pi$
$360$	42.4141	−	1.02288i	0.117817	−	0.00284133i
$361$	−183.432			−0.508122
$362$	−267.983			−0.740283
$363$		−	491.674i		−	1.35447i
$364$		−	14.2872i		−	0.0392504i
$365$	−367.474	+	8.86219i	−1.00678	+	0.0242800i
$366$		−	89.1298i		−	0.243524i
$367$	−675.757			−1.84130			−0.920649	−	0.390391i	$-0.872340\pi$
$367$	−675.757			−1.84130			−0.920649	+	0.390391i	$0.872340\pi$
$368$	−43.7853	−	80.9126i	−0.118982	−	0.219871i
$369$	169.405			0.459091
$370$	−150.267	+	3.62391i	−0.406127	+	0.00979436i
$371$	16.4520			0.0443450
$372$			12.6064i			0.0338881i
$373$	230.444			0.617813			0.308906	−	0.951092i	$-0.400037\pi$
$373$	230.444			0.617813			0.308906	+	0.951092i	$0.400037\pi$
$374$	−303.167			−0.810607
$375$	−215.940	+	15.6474i	−0.575840	+	0.0417265i
$376$	105.345			0.280174
$377$			236.136i			0.626356i
$378$	−6.06851			−0.0160543
$379$		−	63.5057i		−	0.167561i	−0.996484	−	0.0837806i	$-0.973301\pi$
$379$		−	63.5057i		−	0.167561i	0.996484	−	0.0837806i	$-0.0266995\pi$
$380$	−233.263	+	5.62548i	−0.613850	+	0.0148039i
$381$	−422.044			−1.10773
$382$	98.8238			0.258701
$383$	468.858			1.22417			0.612086	−	0.790791i	$-0.290331\pi$
$383$	468.858			1.22417			0.612086	+	0.790791i	$0.290331\pi$
$384$	19.5959			0.0510310
$385$	−83.0588	+	2.00309i	−0.215737	+	0.00520283i
$386$	355.493			0.920966
$387$	113.018			0.292035
$388$	234.838			0.605252
$389$		−	555.447i		−	1.42789i	−0.700204	−	0.713943i	$-0.746908\pi$
$389$		−	555.447i		−	1.42789i	0.700204	−	0.713943i	$-0.253092\pi$
$390$	105.913	−	2.55425i	0.271572	−	0.00654937i
$391$	−116.621	−	215.509i	−0.298265	−	0.551175i
$392$			136.664i			0.348633i
$393$			112.302i			0.285755i
$394$	−408.886			−1.03778
$395$	371.242	−	8.95306i	0.939853	−	0.0226660i
$396$			120.728i			0.304869i
$397$			770.094i			1.93978i	0.243538	+	0.969891i	$0.421692\pi$
$397$			770.094i			1.93978i	−0.243538	+	0.969891i	$0.578308\pi$
$398$	−421.341			−1.05864
$399$	33.3747			0.0836459
$400$	−99.8837	+	4.82050i	−0.249709	+	0.0120512i
$401$			718.953i			1.79290i	0.443145	+	0.896450i	$0.353863\pi$
$401$			718.953i			1.79290i	−0.443145	+	0.896450i	$0.646137\pi$
$402$	106.394			0.264663
$403$			31.4796i			0.0781132i
$404$	−390.388			−0.966307
$405$	−1.08493	−	44.9869i	−0.00267883	−	0.111079i
$406$			31.8810i			0.0785247i
$407$		−	427.722i		−	1.05091i
$408$	52.1934			0.127925
$409$	573.915			1.40321			0.701607	−	0.712564i	$-0.252466\pi$
$409$	573.915			1.40321			0.701607	+	0.712564i	$0.252466\pi$
$410$	−399.174	+	9.62669i	−0.973596	+	0.0234797i
$411$		−	132.108i		−	0.321430i
$412$	69.6105			0.168958
$413$	−16.6894			−0.0404102
$414$	−85.8208	+	46.4413i	−0.207297	+	0.112177i
$415$	−13.9043	−	576.547i	−0.0335043	−	1.38927i
$416$	48.9334			0.117628
$417$		−	339.387i		−	0.813878i
$418$		−	663.963i		−	1.58843i
$419$		−	583.805i		−	1.39333i	−0.717397	−	0.696664i	$-0.754667\pi$
$419$		−	583.805i		−	1.39333i	0.717397	−	0.696664i	$-0.245333\pi$
$420$	14.2995	−	0.344853i	0.0340463	−	0.000821078i
$421$			55.9733i			0.132953i	0.997788	+	0.0664766i	$0.0211758\pi$
$421$			55.9733i			0.132953i	−0.997788	+	0.0664766i	$0.978824\pi$
$422$		−	178.516i		−	0.423024i
$423$		−	111.736i		−	0.264150i
$424$			56.3480i			0.132896i
$425$	−266.039	+	12.8393i	−0.625973	+	0.0302101i
$426$	188.467			0.442410
$427$		−	30.0492i		−	0.0703727i
$428$	33.2680			0.0777290
$429$			301.473i			0.702734i
$430$	−266.308	+	6.42241i	−0.619320	+	0.0149358i
$431$		−	102.969i		−	0.238906i	−0.992840	−	0.119453i	$-0.961886\pi$
$431$		−	102.969i		−	0.238906i	0.992840	−	0.119453i	$-0.0381141\pi$
$432$		−	20.7846i		−	0.0481125i
$433$	−586.051			−1.35347			−0.676733	−	0.736229i	$-0.736605\pi$
$433$	−586.051			−1.35347			−0.676733	+	0.736229i	$0.736605\pi$
$434$			4.25010i			0.00979286i
$435$	−236.340	+	5.69968i	−0.543309	+	0.0131027i
$436$		−	254.322i		−	0.583306i
$437$	471.985	−	255.411i	1.08006	−	0.584465i
$438$			180.077i			0.411135i
$439$	862.821			1.96542			0.982712	−	0.185143i	$-0.0592748\pi$
$439$	862.821			1.96542			0.982712	+	0.185143i	$0.0592748\pi$
$440$	−6.86056	−	284.476i	−0.0155922	−	0.646536i
$441$	144.954			0.328694
$442$	130.333			0.294872
$443$		−	529.609i		−	1.19551i	−0.801681	−	0.597753i	$-0.796060\pi$
$443$		−	529.609i		−	1.19551i	0.801681	−	0.597753i	$-0.203940\pi$
$444$			73.6369i			0.165849i
$445$	−428.486	+	10.3336i	−0.962891	+	0.0232216i
$446$	198.317			0.444657
$447$	74.7306			0.167183
$448$	6.60656			0.0147468
$449$	331.457			0.738212			0.369106	−	0.929387i	$-0.379664\pi$
$449$	331.457			0.738212			0.369106	+	0.929387i	$0.379664\pi$
$450$	5.11291	+	105.943i	0.0113620	+	0.235428i
$451$		−	1136.22i		−	2.51932i
$452$	−315.083			−0.697087
$453$		−	133.023i		−	0.293649i
$454$			416.514i			0.917432i
$455$	35.7075	−	0.861140i	0.0784780	−	0.00189262i
$456$			114.308i			0.250676i
$457$	122.702			0.268493			0.134247	−	0.990948i	$-0.457139\pi$
$457$	122.702			0.268493			0.134247	+	0.990948i	$0.457139\pi$
$458$	30.8106			0.0672720
$459$		−	55.3595i		−	0.120609i
$460$	199.584	−	114.308i	0.433877	−	0.248496i
$461$	−208.699			−0.452708			−0.226354	−	0.974045i	$-0.572681\pi$
$461$	−208.699			−0.452708			−0.226354	+	0.974045i	$0.572681\pi$
$462$			40.7022i			0.0881000i
$463$			123.422i			0.266571i	0.991078	+	0.133285i	$0.0425527\pi$
$463$			123.422i			0.266571i	−0.991078	+	0.133285i	$0.957447\pi$
$464$	−109.192			−0.235328
$465$	−31.5067	+	0.759832i	−0.0677564	+	0.00163405i
$466$	258.754			0.555267
$467$	−726.554			−1.55579			−0.777895	−	0.628395i	$-0.783712\pi$
$467$	−726.554			−1.55579			−0.777895	+	0.628395i	$0.783712\pi$
$468$		−	51.9017i		−	0.110901i
$469$	35.8697			0.0764813
$470$	6.34955	+	263.287i	0.0135097	+	0.560184i
$471$			153.553i			0.326015i
$472$		−	57.1612i		−	0.121104i
$473$		−	758.022i		−	1.60258i
$474$		−	181.924i		−	0.383805i
$475$	−28.1192	−	582.649i	−0.0591984	−	1.22663i
$476$	17.5965			0.0369673
$477$	59.7661			0.125296
$478$			135.060i			0.282553i
$479$			679.033i			1.41761i	0.705406	+	0.708803i	$0.250765\pi$
$479$			679.033i			1.41761i	−0.705406	+	0.708803i	$0.749235\pi$
$480$	1.18112	+	48.9756i	0.00246066	+	0.102032i
$481$			183.880i			0.382288i
$482$	−149.578			−0.310328
$483$	−28.9336	+	15.6572i	−0.0599039	+	0.0324166i
$484$	567.736			1.17301
$485$	14.1545	+	586.924i	0.0291846	+	1.21015i
$486$	−22.0454			−0.0453609
$487$		−	867.014i		−	1.78032i	−0.455652	−	0.890158i	$-0.650594\pi$
$487$		−	867.014i		−	1.78032i	0.455652	−	0.890158i	$-0.349406\pi$
$488$	102.918			0.210898
$489$	137.966			0.282140
$490$	−341.561	+	8.23725i	−0.697063	+	0.0168107i
$491$	−454.964			−0.926606			−0.463303	−	0.886200i	$-0.653336\pi$
$491$	−454.964			−0.926606			−0.463303	+	0.886200i	$0.653336\pi$
$492$			195.612i			0.397584i
$493$	−290.832			−0.589923
$494$			285.442i			0.577817i
$495$	−301.732	+	7.27673i	−0.609560	+	0.0147005i
$496$	−14.5566			−0.0293479
$497$	63.5396			0.127846
$498$	−282.531			−0.567332
$499$	240.468			0.481900			0.240950	−	0.970538i	$-0.422541\pi$
$499$	240.468			0.481900			0.240950	+	0.970538i	$0.422541\pi$
$500$	−18.0681	−	249.346i	−0.0361362	−	0.498692i
$501$	228.949			0.456984
$502$	304.178			0.605933
$503$	−923.756			−1.83649			−0.918246	−	0.396010i	$-0.870395\pi$
$503$	−923.756			−1.83649			−0.918246	+	0.396010i	$0.870395\pi$
$504$		−	7.00731i		−	0.0139034i
$505$	−23.5301	−	975.686i	−0.0465943	−	1.93205i
$506$	311.487	+	575.610i	0.615587	+	1.13757i
$507$			163.112i			0.321719i
$508$		−	487.335i		−	0.959321i
$509$	−747.855			−1.46926			−0.734631	−	0.678467i	$-0.762645\pi$
$509$	−747.855			−1.46926			−0.734631	+	0.678467i	$0.762645\pi$
$510$	3.14589	+	130.446i	0.00616841	+	0.255776i
$511$			60.7111i			0.118808i
$512$			22.6274i			0.0441942i
$513$	121.242			0.236340
$514$	−592.619			−1.15295
$515$	4.19569	+	173.976i	0.00814696	+	0.337817i
$516$			130.502i			0.252910i
$517$	−749.423			−1.44956
$518$			24.8259i			0.0479264i
$519$	−42.0714			−0.0810624
$520$	2.94940	+	122.298i	0.00567192	+	0.235188i
$521$		−	59.5180i		−	0.114238i	−0.998367	−	0.0571190i	$-0.981809\pi$
$521$		−	59.5180i		−	0.114238i	0.998367	−	0.0571190i	$-0.0181914\pi$
$522$			115.816i			0.221870i
$523$	−561.141			−1.07293			−0.536464	−	0.843923i	$-0.680240\pi$
$523$	−561.141			−1.07293			−0.536464	+	0.843923i	$0.680240\pi$
$524$	−129.675			−0.247471
$525$	1.72376	+	35.7175i	0.00328336	+	0.0680333i
$526$			478.067i			0.908872i
$527$	−38.7712			−0.0735696
$528$	−139.405			−0.264024
$529$	−289.356	+	442.848i	−0.546987	+	0.837141i
$530$	−140.829	+	3.39631i	−0.265715	+	0.00640813i
$531$	−60.6286			−0.114178
$532$			38.5378i			0.0724395i
$533$			488.466i			0.916447i
$534$			209.976i			0.393213i
$535$	2.00519	+	83.1459i	0.00374802	+	0.155413i
$536$			122.854i			0.229205i
$537$		−	49.9007i		−	0.0929250i
$538$		−	0.696279i		−	0.00129420i
$539$		−	972.223i		−	1.80375i
$540$	51.9464	−	1.25277i	0.0961971	−	0.00231994i
$541$	−456.359			−0.843548			−0.421774	−	0.906701i	$-0.638592\pi$
$541$	−456.359			−0.843548			−0.421774	+	0.906701i	$0.638592\pi$
$542$			229.402i			0.423251i
$543$	−328.210			−0.604439
$544$			60.2678i			0.110786i
$545$	635.619	−	15.3289i	1.16627	−	0.0281264i
$546$		−	17.4981i		−	0.0320478i
$547$			456.346i			0.834271i	0.908844	+	0.417135i	$0.136966\pi$
$547$			456.346i			0.834271i	−0.908844	+	0.417135i	$0.863034\pi$
$548$	152.545			0.278366
$549$		−	109.161i		−	0.198836i
$550$	710.570	−	34.2929i	1.29194	−	0.0623506i
$551$		−	636.948i		−	1.15599i
$552$	−53.6258	−	99.0973i	−0.0971482	−	0.179524i
$553$		−	61.3336i		−	0.110911i
$554$	659.810			1.19099
$555$	−184.039	+	4.43837i	−0.331601	+	0.00799706i
$556$	391.891			0.704839
$557$	627.784			1.12708			0.563540	−	0.826088i	$-0.309439\pi$
$557$	627.784			1.12708			0.563540	+	0.826088i	$0.309439\pi$
$558$			15.4396i			0.0276695i
$559$			325.878i			0.582967i
$560$	0.398202	+	16.5116i	0.000711075	+	0.0294850i
$561$	−371.302			−0.661858
$562$	−279.590			−0.497492
$563$	445.396			0.791112			0.395556	−	0.918442i	$-0.370552\pi$
$563$	445.396			0.791112			0.395556	+	0.918442i	$0.370552\pi$
$564$	129.021			0.228761
$565$	−18.9912	−	787.479i	−0.0336128	−	1.39377i
$566$		−	397.207i		−	0.701778i
$567$	−7.43238			−0.0131082
$568$			217.623i			0.383139i
$569$			797.219i			1.40109i	0.713609	+	0.700544i	$0.247059\pi$
$569$			797.219i			1.40109i	−0.713609	+	0.700544i	$0.752941\pi$
$570$	−285.687	+	6.88978i	−0.501206	+	0.0120873i
$571$		−	298.881i		−	0.523434i	−0.965145	−	0.261717i	$-0.915711\pi$
$571$		−	298.881i		−	0.523434i	0.965145	−	0.261717i	$-0.0842887\pi$
$572$	−348.111			−0.608585
$573$	121.034			0.211229
$574$			65.9484i			0.114893i
$575$	297.717	+	491.924i	0.517769	+	0.855520i
$576$	24.0000			0.0416667
$577$			503.840i			0.873207i	0.899654	+	0.436603i	$0.143819\pi$
$577$			503.840i			0.873207i	−0.899654	+	0.436603i	$0.856181\pi$
$578$		−	248.186i		−	0.429387i
$579$	435.388			0.751966
$580$	−6.58143	−	272.901i	−0.0113473	−	0.470520i
$581$	−95.2525			−0.163946
$582$	287.616			0.494186
$583$		−	400.858i		−	0.687578i
$584$	−207.935			−0.356053
$585$	129.717	−	3.12831i	0.221738	−	0.00534754i
$586$		−	281.299i		−	0.480033i
$587$			131.633i			0.224247i	0.993694	+	0.112124i	$0.0357652\pi$
$587$			131.633i			0.224247i	−0.993694	+	0.112124i	$0.964235\pi$
$588$			167.379i			0.284657i
$589$		−	84.9123i		−	0.144164i
$590$	142.861	−	3.44532i	0.242138	−	0.00583952i
$591$	−500.781			−0.847345
$592$	−85.0285			−0.143629
$593$		−	830.118i		−	1.39986i	−0.714211	−	0.699931i	$-0.753214\pi$
$593$		−	830.118i		−	1.39986i	0.714211	−	0.699931i	$-0.246786\pi$
$594$			147.861i			0.248924i
$595$	1.06060	+	43.9784i	0.00178253	+	0.0739132i
$596$			86.2915i			0.144784i
$597$	−516.035			−0.864380
$598$	−133.910	−	247.458i	−0.223930	−	0.413810i
$599$	729.774			1.21832			0.609160	−	0.793047i	$-0.291507\pi$
$599$	729.774			1.21832			0.609160	+	0.793047i	$0.291507\pi$
$600$	−122.332	+	5.90388i	−0.203887	+	0.00983980i
$601$	102.025			0.169759			0.0848796	−	0.996391i	$-0.472949\pi$
$601$	102.025			0.169759			0.0848796	+	0.996391i	$0.472949\pi$
$602$			43.9972i			0.0730851i
$603$	130.306			0.216096
$604$	153.602			0.254308
$605$	34.2196	+	1418.93i	0.0565613	+	2.34534i
$606$	−478.126			−0.788986
$607$		−	390.426i		−	0.643207i	−0.946874	−	0.321603i	$-0.895778\pi$
$607$		−	390.426i		−	0.643207i	0.946874	−	0.321603i	$-0.104222\pi$
$608$	−131.992			−0.217092
$609$			39.0461i			0.0641152i
$610$	6.20326	+	257.221i	0.0101693	+	0.421673i
$611$	322.182			0.527302
$612$	63.9236			0.104450
$613$	761.231			1.24181			0.620907	−	0.783885i	$-0.286765\pi$
$613$	761.231			1.24181			0.620907	+	0.783885i	$0.286765\pi$
$614$	−412.844			−0.672384
$615$	−488.887	+	11.7902i	−0.794938	+	0.0191711i
$616$	−46.9988			−0.0762968
$617$	−463.396			−0.751046			−0.375523	−	0.926813i	$-0.622537\pi$
$617$	−463.396			−0.751046			−0.375523	+	0.926813i	$0.622537\pi$
$618$	85.2551			0.137953
$619$		−	805.250i		−	1.30089i	−0.759554	−	0.650444i	$-0.774583\pi$
$619$		−	805.250i		−	1.30089i	0.759554	−	0.650444i	$-0.225417\pi$
$620$	−0.877379	−	36.3808i	−0.00141513	−	0.0586788i
$621$	−105.109	+	56.8788i	−0.169257	+	0.0915922i
$622$			475.549i			0.764548i
$623$			70.7911i			0.113629i
$624$	59.9309			0.0960432
$625$	622.095	−	60.1862i	0.995353	−	0.0962978i
$626$			622.100i			0.993771i
$627$		−	813.185i		−	1.29695i
$628$	−177.308			−0.282337
$629$	−226.472			−0.360051
$630$	17.5132	−	0.422357i	0.0277987	−	0.000670408i
$631$		−	13.0784i		−	0.0207264i	−0.999946	−	0.0103632i	$-0.996701\pi$
$631$		−	13.0784i		−	0.0207264i	0.999946	−	0.0103632i	$-0.00329877\pi$
$632$	210.067			0.332385
$633$		−	218.637i		−	0.345398i
$634$	456.973			0.720778
$635$	1217.98	−	29.3735i	1.91808	−	0.0462575i
$636$			69.0120i			0.108509i
$637$			417.965i			0.656146i
$638$	776.791			1.21754
$639$	230.824			0.361227
$640$	−56.5521	+	1.36384i	−0.0883627	+	0.00213100i
$641$		−	137.430i		−	0.214400i	−0.994237	−	0.107200i	$-0.965811\pi$
$641$		−	137.430i		−	0.214400i	0.994237	−	0.107200i	$-0.0341885\pi$
$642$	40.7448			0.0634655
$643$	−579.499			−0.901242			−0.450621	−	0.892715i	$-0.648797\pi$
$643$	−579.499			−0.901242			−0.450621	+	0.892715i	$0.648797\pi$
$644$	−18.0794	−	33.4096i	−0.0280736	−	0.0518783i
$645$	−326.159	+	7.86582i	−0.505673	+	0.0121951i
$646$	−351.558			−0.544207
$647$			921.171i			1.42376i	0.702303	+	0.711878i	$0.252155\pi$
$647$			921.171i			1.42376i	−0.702303	+	0.711878i	$0.747845\pi$
$648$		−	25.4558i		−	0.0392837i
$649$			406.643i			0.626568i
$650$	−305.478	+	14.7427i	−0.469967	+	0.0226811i
$651$			5.20529i			0.00799584i
$652$			159.310i			0.244340i
$653$			306.177i			0.468877i	0.972131	+	0.234439i	$0.0753252\pi$
$653$			306.177i			0.468877i	−0.972131	+	0.234439i	$0.924675\pi$
$654$		−	311.479i		−	0.476268i
$655$	−7.81599	−	324.093i	−0.0119328	−	0.494798i
$656$	−225.873			−0.344318
$657$			220.548i			0.335690i
$658$	43.4981			0.0661065
$659$			881.248i			1.33725i	0.743599	+	0.668626i	$0.233117\pi$
$659$			881.248i			1.33725i	−0.743599	+	0.668626i	$0.766883\pi$
$660$	−8.40244	−	348.410i	−0.0127310	−	0.527895i
$661$		−	520.095i		−	0.786830i	−0.919361	−	0.393415i	$-0.871294\pi$
$661$		−	520.095i		−	0.786830i	0.919361	−	0.393415i	$-0.128706\pi$
$662$		−	118.651i		−	0.179231i
$663$	159.625			0.240762
$664$		−	326.239i		−	0.491324i
$665$	−96.3165	+	2.32282i	−0.144837	+	0.00349296i
$666$			90.1864i			0.135415i
$667$	298.814	+	552.190i	0.447996	+	0.827871i
$668$			264.367i			0.395760i
$669$	242.888			0.363061
$670$	−307.045	+	7.40485i	−0.458276	+	0.0110520i
$671$	−732.157			−1.09114
$672$	8.09135			0.0120407
$673$			1001.26i			1.48776i	0.668311	+	0.743882i	$0.267017\pi$
$673$			1001.26i			1.48776i	−0.668311	+	0.743882i	$0.732983\pi$
$674$		−	529.586i		−	0.785735i
$675$	6.26201	+	129.753i	0.00927705	+	0.192226i
$676$	−188.345			−0.278617
$677$	494.031			0.729735			0.364868	−	0.931059i	$-0.381114\pi$
$677$	494.031			0.729735			0.364868	+	0.931059i	$0.381114\pi$
$678$	−385.897			−0.569169
$679$	96.9668			0.142808
$680$	−150.626	+	3.63256i	−0.221508	+	0.00534200i
$681$			510.123i			0.749080i
$682$	103.555			0.151840
$683$			619.675i			0.907285i	0.891184	+	0.453642i	$0.149876\pi$
$683$			619.675i			0.907285i	−0.891184	+	0.453642i	$0.850124\pi$
$684$			139.998i			0.204676i
$685$	9.19445	+	381.251i	0.0134225	+	0.556571i
$686$			113.656i			0.165680i
$687$	37.7351			0.0549273
$688$	−150.690			−0.219027
$689$			172.331i			0.250118i
$690$	244.439	−	139.999i	0.354259	−	0.202896i
$691$	131.685			0.190572			0.0952859	−	0.995450i	$-0.469623\pi$
$691$	131.685			0.190572			0.0952859	+	0.995450i	$0.469623\pi$
$692$		−	48.5799i		−	0.0702021i
$693$			49.8498i			0.0719333i
$694$	−103.453			−0.149068
$695$	23.6207	+	979.442i	0.0339866	+	1.40927i
$696$	−133.733			−0.192145
$697$	−601.608			−0.863140
$698$			485.061i			0.694930i
$699$	316.908			0.453373
$700$	−41.2430	+	1.99043i	−0.0589185	+	0.00284347i
$701$		−	612.758i		−	0.874120i	−0.899432	−	0.437060i	$-0.856020\pi$
$701$		−	612.758i		−	0.874120i	0.899432	−	0.437060i	$-0.143980\pi$
$702$		−	63.5664i		−	0.0905504i
$703$		−	495.994i		−	0.705539i
$704$		−	160.971i		−	0.228652i
$705$	7.77658	+	322.459i	0.0110306	+	0.457389i
$706$	358.602			0.507935
$707$	−161.195			−0.227999
$708$		−	70.0079i		−	0.0988812i
$709$			952.179i			1.34299i	0.741010	+	0.671494i	$0.234347\pi$
$709$			952.179i			1.34299i	−0.741010	+	0.671494i	$0.765653\pi$
$710$	−543.899	+	13.1169i	−0.766055	+	0.0184746i
$711$		−	222.810i		−	0.313375i
$712$	−242.459			−0.340532
$713$	39.8352	+	73.6131i	0.0558699	+	0.103244i
$714$	21.5512			0.0301837
$715$	−20.9819	−	870.024i	−0.0293454	−	1.21682i
$716$	57.6204			0.0804754
$717$			165.414i			0.230703i
$718$	81.5685			0.113605
$719$	−144.350			−0.200764			−0.100382	−	0.994949i	$-0.532007\pi$
$719$	−144.350			−0.200764			−0.100382	+	0.994949i	$0.532007\pi$
$720$	1.44657	+	59.9826i	0.00200912	+	0.0833091i
$721$	28.7429			0.0398653
$722$		−	259.412i		−	0.359296i
$723$	−183.195			−0.253382
$724$		−	378.985i		−	0.523459i
$725$	681.659	−	32.8976i	0.940219	−	0.0453760i
$726$	695.332			0.957758
$727$	702.389			0.966147			0.483073	−	0.875580i	$-0.339520\pi$
$727$	702.389			0.966147			0.483073	+	0.875580i	$0.339520\pi$
$728$	20.2051			0.0277542
$729$	−27.0000			−0.0370370
$730$	−12.5330	−	519.687i	−0.0171685	−	0.711900i
$731$	−401.361			−0.549057
$732$	126.049			0.172197
$733$	384.841			0.525022			0.262511	−	0.964929i	$-0.415449\pi$
$733$	384.841			0.525022			0.262511	+	0.964929i	$0.415449\pi$
$734$		−	955.664i		−	1.30199i
$735$	−418.325	+	10.0885i	−0.569149	+	0.0137259i
$736$	114.428	−	61.9218i	0.155472	−	0.0841328i
$737$		−	873.977i		−	1.18586i
$738$			239.574i			0.324626i
$739$	838.367			1.13446			0.567231	−	0.823559i	$-0.308015\pi$
$739$	838.367			1.13446			0.567231	+	0.823559i	$0.308015\pi$
$740$	−5.12499	−	212.510i	−0.00692566	−	0.287175i
$741$			349.593i			0.471786i
$742$			23.2667i			0.0313567i
$743$	646.228			0.869756			0.434878	−	0.900489i	$-0.356792\pi$
$743$	646.228			0.869756			0.434878	+	0.900489i	$0.356792\pi$
$744$	−17.8281			−0.0239625
$745$	−215.666	+	5.20111i	−0.289485	+	0.00698135i
$746$			325.897i			0.436860i
$747$	−346.029			−0.463225
$748$		−	428.743i		−	0.573186i
$749$	13.7367			0.0183400
$750$	−22.1288	−	305.386i	−0.0295051	−	0.407181i
$751$			117.146i			0.155987i	0.996954	+	0.0779936i	$0.0248514\pi$
$751$			117.146i			0.155987i	−0.996954	+	0.0779936i	$0.975149\pi$
$752$			148.981i			0.198113i
$753$	372.541			0.494742
$754$	−333.947			−0.442901
$755$	9.25816	+	383.893i	0.0122625	+	0.508468i
$756$		−	8.58217i		−	0.0113521i
$757$	1095.80			1.44756			0.723778	−	0.690033i	$-0.242404\pi$
$757$	1095.80			1.44756			0.723778	+	0.690033i	$0.242404\pi$
$758$	89.8106			0.118484
$759$	381.492	+	704.975i	0.502625	+	0.928821i
$760$	−7.95564	−	329.883i	−0.0104679	−	0.434057i
$761$	−749.241			−0.984548			−0.492274	−	0.870440i	$-0.663834\pi$
$761$	−749.241			−0.984548			−0.492274	+	0.870440i	$0.663834\pi$
$762$		−	596.861i		−	0.783282i
$763$		−	105.012i		−	0.137630i
$764$			139.758i			0.182929i
$765$	3.85291	+	159.763i	0.00503649	+	0.208840i
$766$			663.065i			0.865621i
$767$		−	174.818i		−	0.227925i
$768$			27.7128i			0.0360844i
$769$			289.069i			0.375902i	0.982178	+	0.187951i	$0.0601846\pi$
$769$			289.069i			0.375902i	−0.982178	+	0.187951i	$0.939815\pi$
$770$	−2.83279	−	117.463i	−0.00367895	−	0.152549i
$771$	−725.807			−0.941383
$772$			502.743i			0.651221i
$773$	−60.7604			−0.0786033			−0.0393017	−	0.999227i	$-0.512513\pi$
$773$	−60.7604			−0.0786033			−0.0393017	+	0.999227i	$0.512513\pi$
$774$			159.831i			0.206500i
$775$	90.8728	−	4.38562i	0.117255	−	0.00565886i
$776$			332.111i			0.427978i
$777$			30.4054i			0.0391318i
$778$	785.521			1.00967
$779$		−	1317.58i		−	1.69137i
$780$	3.61226	+	149.784i	0.00463110	+	0.192031i
$781$		−	1548.16i		−	1.98228i
$782$	304.776	−	164.928i	0.389739	−	0.210905i
$783$			141.845i			0.181156i
$784$	−193.272			−0.246521
$785$	−10.6870	−	443.141i	−0.0136140	−	0.564510i
$786$	−158.819			−0.202059
$787$	−329.594			−0.418798			−0.209399	−	0.977830i	$-0.567151\pi$
$787$	−329.594			−0.418798			−0.209399	+	0.977830i	$0.567151\pi$
$788$		−	578.252i		−	0.733823i
$789$			585.510i			0.742091i
$790$	12.6615	+	525.015i	0.0160273	+	0.664576i
$791$	−130.101			−0.164477
$792$	−170.735			−0.215575
$793$	314.759			0.396921
$794$	−1089.08			−1.37163
$795$	−172.480	+	4.15961i	−0.216956	+	0.00523221i
$796$		−	595.866i		−	0.748575i
$797$	832.607			1.04468			0.522338	−	0.852738i	$-0.325060\pi$
$797$	832.607			1.04468			0.522338	+	0.852738i	$0.325060\pi$
$798$			47.1990i			0.0591466i
$799$			396.808i			0.496631i
$800$	−6.81721	−	141.257i	−0.00852151	−	0.176571i
$801$			257.167i			0.321057i
$802$	−1016.75			−1.26777
$803$	1479.24			1.84215
$804$			150.464i			0.187145i
$805$	82.4100	−	47.1990i	0.102373	−	0.0586323i
$806$	−44.5189			−0.0552344
$807$		−	0.852764i		−	0.00105671i
$808$		−	552.092i		−	0.683282i
$809$	−1505.04			−1.86037			−0.930187	−	0.367087i	$-0.880355\pi$
$809$	−1505.04			−1.86037			−0.930187	+	0.367087i	$0.880355\pi$
$810$	63.6211	−	1.53432i	0.0785446	−	0.00189422i
$811$	319.774			0.394296			0.197148	−	0.980374i	$-0.436832\pi$
$811$	319.774			0.394296			0.197148	+	0.980374i	$0.436832\pi$
$812$	−45.0866			−0.0555254
$813$			280.959i			0.345583i
$814$	604.890			0.743108
$815$	−398.159	+	9.60221i	−0.488539	+	0.0117818i
$816$			73.8126i			0.0904566i
$817$		−	879.016i		−	1.07591i
$818$			811.638i			0.992222i
$819$		−	21.4307i		−	0.0261669i
$820$	−13.6142	−	564.518i	−0.0166027	−	0.688436i
$821$	−268.967			−0.327610			−0.163805	−	0.986493i	$-0.552377\pi$
$821$	−268.967			−0.327610			−0.163805	+	0.986493i	$0.552377\pi$
$822$	186.829			0.227285
$823$			794.032i			0.964802i	0.875951	+	0.482401i	$0.160235\pi$
$823$			794.032i			0.964802i	−0.875951	+	0.482401i	$0.839765\pi$
$824$			98.4442i			0.119471i
$825$	870.267	−	42.0000i	1.05487	−	0.0509091i
$826$		−	23.6024i		−	0.0285744i
$827$	1358.09			1.64218			0.821092	−	0.570796i	$-0.193365\pi$
$827$	1358.09			1.64218			0.821092	+	0.570796i	$0.193365\pi$
$828$	−65.6779	−	121.369i	−0.0793212	−	0.146581i
$829$	−175.202			−0.211342			−0.105671	−	0.994401i	$-0.533699\pi$
$829$	−175.202			−0.211342			−0.105671	+	0.994401i	$0.533699\pi$
$830$	815.361	−	19.6637i	0.982362	−	0.0236911i
$831$	808.099			0.972442
$832$			69.2023i			0.0831758i
$833$	−514.777			−0.617980
$834$	479.966			0.575499
$835$	−660.726	+	15.9344i	−0.791289	+	0.0190831i
$836$	938.985			1.12319
$837$			18.9095i			0.0225920i
$838$	825.624			0.985232
$839$			242.954i			0.289576i	0.989463	+	0.144788i	$0.0462500\pi$
$839$			242.954i			0.289576i	−0.989463	+	0.144788i	$0.953750\pi$
$840$	0.487696	+	20.2225i	0.000580590	+	0.0240744i
$841$	−95.8147			−0.113929
$842$	−79.1582			−0.0940121
$843$	−342.427			−0.406200
$844$	252.460			0.299123
$845$	−11.3523	−	470.726i	−0.0134346	−	0.557072i
$846$	158.018			0.186782
$847$	234.424			0.276770
$848$	−79.6882			−0.0939719
$849$		−	486.477i		−	0.573000i
$850$	−18.1575	−	376.236i	−0.0213618	−	0.442630i
$851$	232.688	+	429.992i	0.273428	+	0.505279i
$852$			266.532i			0.312831i
$853$		−	284.008i		−	0.332952i	−0.986045	−	0.166476i	$-0.946761\pi$
$853$		−	284.008i		−	0.332952i	0.986045	−	0.166476i	$-0.0532389\pi$
$854$	42.4959			0.0497610
$855$	−349.894	+	8.43823i	−0.409233	+	0.00986927i
$856$			47.0481i			0.0549627i
$857$			1182.47i			1.37978i	0.723913	+	0.689891i	$0.242342\pi$
$857$			1182.47i			1.37978i	−0.723913	+	0.689891i	$0.757658\pi$
$858$	−426.347			−0.496908
$859$	1452.40			1.69080			0.845400	−	0.534134i	$-0.179362\pi$
$859$	1452.40			1.69080			0.845400	+	0.534134i	$0.179362\pi$
$860$	−9.08266	−	376.616i	−0.0105612	−	0.437926i
$861$			80.7699i			0.0938094i
$862$	145.620			0.168932
$863$			1384.47i			1.60426i	0.597152	+	0.802128i	$0.296299\pi$
$863$			1384.47i			1.60426i	−0.597152	+	0.802128i	$0.703701\pi$
$864$	29.3939			0.0340207
$865$	121.414	−	2.92809i	0.140363	−	0.00338507i
$866$		−	828.801i		−	0.957045i
$867$		−	303.964i		−	0.350593i
$868$	−6.01055			−0.00692460
$869$	−1494.41			−1.71969
$870$	−8.06057	−	334.235i	−0.00926502	−	0.384178i
$871$			375.728i			0.431375i
$872$	359.665			0.412460
$873$	352.257			0.403501
$874$	361.206	+	667.487i	0.413279	+	0.763715i
$875$	−7.46050	−	102.958i	−0.00852628	−	0.117666i
$876$	−254.667			−0.290716
$877$		−	435.665i		−	0.496768i	−0.968662	−	0.248384i	$-0.920101\pi$
$877$		−	435.665i		−	0.496768i	0.968662	−	0.248384i	$-0.0798994\pi$
$878$			1220.21i			1.38976i
$879$		−	344.520i		−	0.391945i
$880$	402.310	−	9.70230i	0.457170	−	0.0110253i
$881$			590.298i			0.670032i	0.942212	+	0.335016i	$0.108742\pi$
$881$			590.298i			0.670032i	−0.942212	+	0.335016i	$0.891258\pi$
$882$			204.996i			0.232422i
$883$			114.672i			0.129867i	0.997890	+	0.0649333i	$0.0206835\pi$
$883$			114.672i			0.129867i	−0.997890	+	0.0649333i	$0.979317\pi$
$884$			184.319i			0.208506i
$885$	174.969	−	4.21963i	0.197705	−	0.00476795i
$886$	748.980			0.845350
$887$		−	224.781i		−	0.253417i	−0.991940	−	0.126708i	$-0.959559\pi$
$887$		−	224.781i		−	0.253417i	0.991940	−	0.126708i	$-0.0404413\pi$
$888$	−104.138			−0.117273
$889$		−	201.225i		−	0.226350i
$890$	−14.6139	−	605.971i	−0.0164201	−	0.680867i
$891$			181.092i			0.203246i
$892$			280.463i			0.314420i
$893$	−869.044			−0.973174
$894$			105.685i			0.118216i
$895$	3.47300	+	144.009i	0.00388044	+	0.160904i
$896$			9.34308i			0.0104275i
$897$	−164.006	−	303.073i	−0.182838	−	0.337874i
$898$			468.751i			0.521995i
$899$	99.3416			0.110502
$900$	−149.826	+	7.23074i	−0.166473	+	0.00803416i
$901$	−212.248			−0.235570
$902$	1606.85			1.78143
$903$			53.8854i			0.0596737i
$904$		−	445.595i		−	0.492915i
$905$	947.186	−	22.8428i	1.04661	−	0.0252407i
$906$	188.123			0.207641
$907$	−320.565			−0.353435			−0.176717	−	0.984262i	$-0.556548\pi$
$907$	−320.565			−0.353435			−0.176717	+	0.984262i	$0.556548\pi$
$908$	−589.040			−0.648722
$909$	−585.582			−0.644205
$910$	1.21784	+	50.4980i	0.00133828	+	0.0554923i
$911$		−	69.6863i		−	0.0764943i	−0.999268	−	0.0382472i	$-0.987823\pi$
$911$		−	69.6863i		−	0.0764943i	0.999268	−	0.0382472i	$-0.0121774\pi$
$912$	−161.656			−0.177255
$913$			2320.85i			2.54201i
$914$			173.526i			0.189854i
$915$	7.59741	+	315.030i	0.00830319	+	0.344295i
$916$			43.5727i			0.0475685i
$917$	−53.5440			−0.0583904
$918$	78.2901			0.0852833
$919$		−	671.144i		−	0.730299i	−0.930949	−	0.365149i	$-0.881018\pi$
$919$		−	671.144i		−	0.730299i	0.930949	−	0.365149i	$-0.118982\pi$
$920$	161.656	+	282.254i	0.175713	+	0.306798i
$921$	−505.629			−0.549000
$922$		−	295.144i		−	0.320113i
$923$			665.564i			0.721088i
$924$	−57.5616			−0.0622961
$925$	530.811	−	25.6175i	0.573849	−	0.0276946i
$926$	−174.545			−0.188494
$927$	104.416			0.112638
$928$		−	154.421i		−	0.166402i
$929$	−748.401			−0.805598			−0.402799	−	0.915288i	$-0.631963\pi$
$929$	−748.401			−0.805598			−0.402799	+	0.915288i	$0.631963\pi$
$930$	−1.07456	−	44.5572i	−0.00115545	−	0.0479110i
$931$		−	1127.41i		−	1.21096i
$932$			365.934i			0.392633i
$933$			582.426i			0.624251i
$934$		−	1027.50i		−	1.10011i
$935$	1071.55	−	25.8419i	1.14604	−	0.0276384i
$936$	73.4001			0.0784189
$937$	1162.94			1.24113			0.620567	−	0.784153i	$-0.286903\pi$
$937$	1162.94			1.24113			0.620567	+	0.784153i	$0.286903\pi$
$938$			50.7275i			0.0540805i
$939$			761.914i			0.811410i
$940$	−372.344	+	8.97962i	−0.396110	+	0.00955279i
$941$			95.6129i			0.101608i	0.998709	+	0.0508039i	$0.0161783\pi$
$941$			95.6129i			0.101608i	−0.998709	+	0.0508039i	$0.983822\pi$
$942$	−217.157			−0.230527
$943$	618.119	+	1142.25i	0.655481	+	1.21129i
$944$	80.8381			0.0856336
$945$	21.4492	−	0.517279i	0.0226976	−	0.000547386i
$946$	1072.01			1.13320
$947$		−	398.622i		−	0.420931i	−0.977601	−	0.210466i	$-0.932502\pi$
$947$		−	398.622i		−	0.420931i	0.977601	−	0.210466i	$-0.0674980\pi$
$948$	257.279			0.271391
$949$	−635.936			−0.670112
$950$	823.989	−	39.7666i	0.867357	−	0.0418596i
$951$	559.676			0.588513
$952$			24.8851i			0.0261399i
$953$	−1003.78			−1.05329			−0.526645	−	0.850085i	$-0.676550\pi$
$953$	−1003.78			−1.05329			−0.526645	+	0.850085i	$0.676550\pi$
$954$			84.5221i			0.0885975i
$955$	−349.293	+	8.42374i	−0.365752	+	0.00882067i
$956$	−191.004			−0.199795
$957$	951.370			0.994117
$958$	−960.298			−1.00240
$959$	62.9873			0.0656801
$960$	−69.2619	+	1.67035i	−0.0721478	+	0.00173995i
$961$	−947.757			−0.986219
$962$	−260.046			−0.270318
$963$	49.9020			0.0518194
$964$		−	211.536i		−	0.219435i
$965$	−1256.49	+	30.3022i	−1.30206	+	0.0314012i
$966$	−22.1426	−	40.9182i	−0.0229220	−	0.0423584i
$967$			4.98244i			0.00515247i	0.999997	+	0.00257623i	$0.000820042\pi$
$967$			4.98244i			0.00515247i	−0.999997	+	0.00257623i	$0.999180\pi$
$968$			802.901i			0.829443i
$969$	−430.569			−0.444343
$970$	−830.035	+	20.0175i	−0.855706	+	0.0206366i
$971$		−	497.122i		−	0.511970i	−0.966681	−	0.255985i	$-0.917600\pi$
$971$		−	497.122i		−	0.511970i	0.966681	−	0.255985i	$-0.0823997\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	161.815			0.166306
$974$	1226.14			1.25887
$975$	−374.133	+	18.0561i	−0.383726	+	0.0185190i
$976$			145.548i			0.149127i
$977$	−1098.55			−1.12441			−0.562207	−	0.826997i	$-0.690047\pi$
$977$	−1098.55			−1.12441			−0.562207	+	0.826997i	$0.690047\pi$
$978$			195.114i			0.199503i
$979$	1724.85			1.76184
$980$	−11.6492	−	483.040i	−0.0118870	−	0.492898i
$981$		−	381.482i		−	0.388871i
$982$		−	643.416i		−	0.655210i
$983$	−1024.84			−1.04256			−0.521280	−	0.853385i	$-0.674545\pi$
$983$	−1024.84			−1.04256			−0.521280	+	0.853385i	$0.674545\pi$
$984$	−276.636			−0.281135
$985$	1445.21	−	34.8534i	1.46722	−	0.0353842i
$986$		−	411.299i		−	0.417138i
$987$	53.2741			0.0539758
$988$	−403.675			−0.408578
$989$	412.376	+	762.046i	0.416963	+	0.770522i
$990$	−10.2908	−	426.714i	−0.0103948	−	0.431024i
$991$	−937.596			−0.946110			−0.473055	−	0.881033i	$-0.656849\pi$
$991$	−937.596			−0.946110			−0.473055	+	0.881033i	$0.656849\pi$
$992$		−	20.5861i		−	0.0207521i
$993$		−	145.317i		−	0.146342i
$994$			89.8586i			0.0904010i
$995$	1489.23	−	35.9150i	1.49671	−	0.0360955i
$996$		−	399.560i		−	0.401164i
$997$		−	1084.66i		−	1.08792i	−0.839110	−	0.543962i	$-0.816924\pi$
$997$		−	1084.66i		−	1.08792i	0.839110	−	0.543962i	$-0.183076\pi$
$998$			340.073i			0.340755i
$999$			110.455i			0.110566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.f.a.229.43	yes	48
5.4	even	2	inner	690.3.f.a.229.42	yes	48
23.22	odd	2	inner	690.3.f.a.229.44	yes	48
115.114	odd	2	inner	690.3.f.a.229.41	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.f.a.229.41	✓	48	115.114	odd	2	inner
690.3.f.a.229.42	yes	48	5.4	even	2	inner
690.3.f.a.229.43	yes	48	1.1	even	1	trivial
690.3.f.a.229.44	yes	48	23.22	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(-0.120547 - 4.99855i) q^{5} -2.44949 q^{6} -0.825820 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +1.73205i q^{3} -2.00000 q^{4} +(-0.120547 - 4.99855i) q^{5} -2.44949 q^{6} -0.825820 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(7.06901 - 0.170480i) q^{10} +20.1213i q^{11} -3.46410i q^{12} -8.65029i q^{13} -1.16789i q^{14} +(8.65774 - 0.208794i) q^{15} +4.00000 q^{16} +10.6539 q^{17} -4.24264i q^{18} +23.3331i q^{19} +(0.241095 + 9.99709i) q^{20} -1.43036i q^{21} -28.4559 q^{22} +(-10.9463 - 20.2281i) q^{23} +4.89898 q^{24} +(-24.9709 + 1.20512i) q^{25} +12.2334 q^{26} -5.19615i q^{27} +1.65164 q^{28} -27.2981 q^{29} +(0.295280 + 12.2439i) q^{30} -3.63914 q^{31} +5.65685i q^{32} -34.8512 q^{33} +15.0669i q^{34} +(0.0995505 + 4.12790i) q^{35} +6.00000 q^{36} -21.2571 q^{37} -32.9979 q^{38} +14.9827 q^{39} +(-14.1380 + 0.340960i) q^{40} -56.4682 q^{41} +2.02284 q^{42} -37.6726 q^{43} -40.2427i q^{44} +(0.361642 + 14.9956i) q^{45} +(28.6069 - 15.4804i) q^{46} +37.2452i q^{47} +6.92820i q^{48} -48.3180 q^{49} +(-1.70430 - 35.3142i) q^{50} +18.4532i q^{51} +17.3006i q^{52} -19.9220 q^{53} +7.34847 q^{54} +(100.577 - 2.42558i) q^{55} +2.33577i q^{56} -40.4141 q^{57} -38.6053i q^{58} +20.2095 q^{59} +(-17.3155 + 0.417589i) q^{60} +36.3871i q^{61} -5.14652i q^{62} +2.47746 q^{63} -8.00000 q^{64} +(-43.2389 + 1.04277i) q^{65} -49.2870i q^{66} -43.4353 q^{67} -21.3079 q^{68} +(35.0362 - 18.9596i) q^{69} +(-5.83773 + 0.140786i) q^{70} -76.9413 q^{71} +8.48528i q^{72} -73.5162i q^{73} -30.0621i q^{74} +(-2.08734 - 43.2509i) q^{75} -46.6661i q^{76} -16.6166i q^{77} +21.1888i q^{78} +74.2700i q^{79} +(-0.482190 - 19.9942i) q^{80} +9.00000 q^{81} -79.8581i q^{82} +115.343 q^{83} +2.86072i q^{84} +(-1.28430 - 53.2542i) q^{85} -53.2770i q^{86} -47.2817i q^{87} +56.9117 q^{88} -85.7222i q^{89} +(-21.2070 + 0.511440i) q^{90} +7.14358i q^{91} +(21.8926 + 40.4563i) q^{92} -6.30318i q^{93} -52.6726 q^{94} +(116.631 - 2.81274i) q^{95} -9.79796 q^{96} -117.419 q^{97} -68.3320i q^{98} -60.3640i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) \) 48 * q - 96 * q^4 - 144 * q^9	\( 48 q - 96 q^{4} - 144 q^{9} + 192 q^{16} + 96 q^{25} + 64 q^{26} - 152 q^{29} - 8 q^{31} + 56 q^{35} + 288 q^{36} - 48 q^{39} + 40 q^{41} - 160 q^{46} + 424 q^{49} + 96 q^{50} + 32 q^{55} + 360 q^{59} - 384 q^{64} + 192 q^{69} - 496 q^{70} - 152 q^{71} + 144 q^{75} + 432 q^{81} - 136 q^{85} + 256 q^{94} + 496 q^{95}+O(q^{100}) \) 48 * q - 96 * q^4 - 144 * q^9 + 192 * q^16 + 96 * q^25 + 64 * q^26 - 152 * q^29 - 8 * q^31 + 56 * q^35 + 288 * q^36 - 48 * q^39 + 40 * q^41 - 160 * q^46 + 424 * q^49 + 96 * q^50 + 32 * q^55 + 360 * q^59 - 384 * q^64 + 192 * q^69 - 496 * q^70 - 152 * q^71 + 144 * q^75 + 432 * q^81 - 136 * q^85 + 256 * q^94 + 496 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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