LMFDB - Embedded newform 684.3.g.b.343.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + \cdots + 16384 $ x^14 - 2x^13 + x^12 + 14x^11 - 42x^10 + 28x^9 + 132x^8 - 440x^7 + 528x^6 + 448x^5 - 2688x^4 + 3584x^3 + 1024x^2 - 8192x + 16384
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.6
Root			$0.711746 - 1.86907i$ of defining polynomial
Character	$\chi$	$=$	684.343
Dual form			684.3.g.b.343.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.711746 + 1.86907i) q^{2} +(-2.98683 - 2.66060i) q^{4} -4.97973 q^{5} +12.2628i q^{7} +(7.09872 - 3.68892i) q^{8} +O(q^{10})$	\(q+(-0.711746 + 1.86907i) q^{2} +(-2.98683 - 2.66060i) q^{4} -4.97973 q^{5} +12.2628i q^{7} +(7.09872 - 3.68892i) q^{8} +(3.54430 - 9.30745i) q^{10} +13.4463i q^{11} +14.1766 q^{13} +(-22.9201 - 8.72803i) q^{14} +(1.84237 + 15.8936i) q^{16} +5.89478 q^{17} +4.35890i q^{19} +(14.8736 + 13.2491i) q^{20} +(-25.1320 - 9.57032i) q^{22} -0.906592i q^{23} -0.202335 q^{25} +(-10.0901 + 26.4969i) q^{26} +(32.6266 - 36.6271i) q^{28} +10.3853 q^{29} +43.2608i q^{31} +(-31.0175 - 7.86868i) q^{32} +(-4.19559 + 11.0178i) q^{34} -61.0656i q^{35} -1.61331 q^{37} +(-8.14708 - 3.10243i) q^{38} +(-35.3497 + 18.3698i) q^{40} -69.3758 q^{41} -32.0147i q^{43} +(35.7752 - 40.1617i) q^{44} +(1.69448 + 0.645264i) q^{46} -38.9732i q^{47} -101.377 q^{49} +(0.144011 - 0.378179i) q^{50} +(-42.3430 - 37.7182i) q^{52} +8.31560 q^{53} -66.9586i q^{55} +(45.2367 + 87.0505i) q^{56} +(-7.39169 + 19.4108i) q^{58} -20.9242i q^{59} -118.329 q^{61} +(-80.8574 - 30.7907i) q^{62} +(36.7837 - 52.3733i) q^{64} -70.5953 q^{65} +57.4499i q^{67} +(-17.6067 - 15.6837i) q^{68} +(114.136 + 43.4632i) q^{70} -11.3393i q^{71} -23.5952 q^{73} +(1.14827 - 3.01539i) q^{74} +(11.5973 - 13.0193i) q^{76} -164.889 q^{77} -0.286369i q^{79} +(-9.17448 - 79.1456i) q^{80} +(49.3780 - 129.668i) q^{82} +24.9311i q^{83} -29.3544 q^{85} +(59.8376 + 22.7863i) q^{86} +(49.6022 + 95.4512i) q^{88} +43.7018 q^{89} +173.845i q^{91} +(-2.41208 + 2.70784i) q^{92} +(72.8436 + 27.7390i) q^{94} -21.7061i q^{95} +115.905 q^{97} +(72.1549 - 189.481i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8	$ 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98}+O(q^{100}) $ 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8 - 12 * q^10 + 54 * q^13 - 30 * q^14 + 58 * q^16 - 34 * q^17 - 32 * q^20 + 36 * q^22 - 86 * q^25 + 16 * q^26 + 18 * q^28 - 54 * q^29 - 72 * q^32 - 82 * q^34 + 100 * q^37 - 148 * q^40 - 224 * q^41 + 96 * q^44 + 46 * q^46 - 220 * q^49 + 58 * q^50 - 288 * q^52 - 14 * q^53 - 12 * q^56 - 72 * q^58 + 28 * q^61 - 396 * q^62 - 118 * q^64 + 472 * q^65 - 30 * q^68 + 156 * q^70 + 70 * q^73 + 224 * q^74 - 228 * q^77 + 348 * q^80 - 400 * q^82 + 48 * q^85 + 124 * q^86 + 472 * q^88 - 126 * q^92 - 88 * q^94 + 308 * q^97 - 68 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−0.711746	+	1.86907i	−0.355873	+	0.934534i
$2$	−0.711746	+	1.86907i	−0.355873	+	0.934534i
$3$		0			0
$3$		0			0
$4$	−2.98683	−	2.66060i	−0.746709	−	0.665151i
$5$	−4.97973			−0.995945			−0.497973	−	0.867193i	$-0.665922\pi$
$5$	−4.97973			−0.995945			−0.497973	+	0.867193i	$0.665922\pi$
$6$		0			0
$7$			12.2628i			1.75183i	0.482461	+	0.875917i	$0.339743\pi$
$7$			12.2628i			1.75183i	−0.482461	+	0.875917i	$0.660257\pi$
$8$	7.09872	−	3.68892i	0.887340	−	0.461116i
$9$		0			0
$10$	3.54430	−	9.30745i	0.354430	−	0.930745i
$11$			13.4463i			1.22239i	0.791481	+	0.611193i	$0.209310\pi$
$11$			13.4463i			1.22239i	−0.791481	+	0.611193i	$0.790690\pi$
$12$		0			0
$13$	14.1766			1.09050			0.545252	−	0.838272i	$-0.316434\pi$
$13$	14.1766			1.09050			0.545252	+	0.838272i	$0.316434\pi$
$14$	−22.9201	−	8.72803i	−1.63715	−	0.623431i
$15$		0			0
$16$	1.84237	+	15.8936i	0.115148	+	0.993348i
$17$	5.89478			0.346752			0.173376	−	0.984856i	$-0.444532\pi$
$17$	5.89478			0.346752			0.173376	+	0.984856i	$0.444532\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	14.8736	+	13.2491i	0.743681	+	0.662454i
$21$		0			0
$22$	−25.1320	−	9.57032i	−1.14236	−	0.435014i
$23$		−	0.906592i		−	0.0394171i	−0.999806	−	0.0197085i	$-0.993726\pi$
$23$		−	0.906592i		−	0.0394171i	0.999806	−	0.0197085i	$-0.00627383\pi$
$24$		0			0
$25$	−0.202335			−0.00809341
$26$	−10.0901	+	26.4969i	−0.388081	+	1.01911i
$27$		0			0
$28$	32.6266	−	36.6271i	1.16524	−	1.30811i
$29$	10.3853			0.358114			0.179057	−	0.983839i	$-0.442695\pi$
$29$	10.3853			0.358114			0.179057	+	0.983839i	$0.442695\pi$
$30$		0			0
$31$			43.2608i			1.39551i	0.716337	+	0.697755i	$0.245817\pi$
$31$			43.2608i			1.39551i	−0.716337	+	0.697755i	$0.754183\pi$
$32$	−31.0175	−	7.86868i	−0.969296	−	0.245896i
$33$		0			0
$34$	−4.19559	+	11.0178i	−0.123400	+	0.324052i
$35$		−	61.0656i		−	1.74473i
$36$		0			0
$37$	−1.61331			−0.0436030			−0.0218015	−	0.999762i	$-0.506940\pi$
$37$	−1.61331			−0.0436030			−0.0218015	+	0.999762i	$0.506940\pi$
$38$	−8.14708	−	3.10243i	−0.214397	−	0.0816429i
$39$		0			0
$40$	−35.3497	+	18.3698i	−0.883742	+	0.459246i
$41$	−69.3758			−1.69209			−0.846047	−	0.533109i	$-0.821024\pi$
$41$	−69.3758			−1.69209			−0.846047	+	0.533109i	$0.821024\pi$
$42$		0			0
$43$		−	32.0147i		−	0.744527i	−0.928127	−	0.372264i	$-0.878582\pi$
$43$		−	32.0147i		−	0.744527i	0.928127	−	0.372264i	$-0.121418\pi$
$44$	35.7752	−	40.1617i	0.813072	−	0.912767i
$45$		0			0
$46$	1.69448	+	0.645264i	0.0368366	+	0.0140275i
$47$		−	38.9732i		−	0.829217i	−0.910000	−	0.414609i	$-0.863918\pi$
$47$		−	38.9732i		−	0.829217i	0.910000	−	0.414609i	$-0.136082\pi$
$48$		0			0
$49$	−101.377			−2.06893
$50$	0.144011	−	0.378179i	0.00288023	−	0.00756357i
$51$		0			0
$52$	−42.3430	−	37.7182i	−0.814289	−	0.725350i
$53$	8.31560			0.156898			0.0784491	−	0.996918i	$-0.475003\pi$
$53$	8.31560			0.156898			0.0784491	+	0.996918i	$0.475003\pi$
$54$		0			0
$55$		−	66.9586i		−	1.21743i
$56$	45.2367	+	87.0505i	0.807798	+	1.55447i
$57$		0			0
$58$	−7.39169	+	19.4108i	−0.127443	+	0.334669i
$59$		−	20.9242i		−	0.354648i	−0.984153	−	0.177324i	$-0.943256\pi$
$59$		−	20.9242i		−	0.354648i	0.984153	−	0.177324i	$-0.0567440\pi$
$60$		0			0
$61$	−118.329			−1.93983			−0.969913	−	0.243453i	$-0.921720\pi$
$61$	−118.329			−1.93983			−0.969913	+	0.243453i	$0.921720\pi$
$62$	−80.8574	−	30.7907i	−1.30415	−	0.496624i
$63$		0			0
$64$	36.7837	−	52.3733i	0.574745	−	0.818333i
$65$	−70.5953			−1.08608
$66$		0			0
$67$			57.4499i			0.857462i	0.903432	+	0.428731i	$0.141039\pi$
$67$			57.4499i			0.857462i	−0.903432	+	0.428731i	$0.858961\pi$
$68$	−17.6067	−	15.6837i	−0.258923	−	0.230642i
$69$		0			0
$70$	114.136	+	43.4632i	1.63051	+	0.620903i
$71$		−	11.3393i		−	0.159709i	−0.996807	−	0.0798545i	$-0.974554\pi$
$71$		−	11.3393i		−	0.159709i	0.996807	−	0.0798545i	$-0.0254456\pi$
$72$		0			0
$73$	−23.5952			−0.323222			−0.161611	−	0.986855i	$-0.551669\pi$
$73$	−23.5952			−0.323222			−0.161611	+	0.986855i	$0.551669\pi$
$74$	1.14827	−	3.01539i	0.0155171	−	0.0407485i
$75$		0			0
$76$	11.5973	−	13.0193i	0.152596	−	0.171307i
$77$	−164.889			−2.14142
$78$		0			0
$79$		−	0.286369i		−	0.00362492i	−0.999998	−	0.00181246i	$-0.999423\pi$
$79$		−	0.286369i		−	0.00362492i	0.999998	−	0.00181246i	$-0.000576925\pi$
$80$	−9.17448	−	79.1456i	−0.114681	−	0.989320i
$81$		0			0
$82$	49.3780	−	129.668i	0.602170	−	1.58132i
$83$			24.9311i			0.300375i	0.988658	+	0.150188i	$0.0479878\pi$
$83$			24.9311i			0.300375i	−0.988658	+	0.150188i	$0.952012\pi$
$84$		0			0
$85$	−29.3544			−0.345346
$86$	59.8376	+	22.7863i	0.695786	+	0.264957i
$87$		0			0
$88$	49.6022	+	95.4512i	0.563662	+	1.08467i
$89$	43.7018			0.491031			0.245515	−	0.969393i	$-0.421043\pi$
$89$	43.7018			0.491031			0.245515	+	0.969393i	$0.421043\pi$
$90$		0			0
$91$			173.845i			1.91038i
$92$	−2.41208	+	2.70784i	−0.0262183	+	0.0294331i
$93$		0			0
$94$	72.8436	+	27.7390i	0.774932	+	0.295096i
$95$		−	21.7061i		−	0.228485i
$96$		0			0
$97$	115.905			1.19490			0.597448	−	0.801908i	$-0.296182\pi$
$97$	115.905			1.19490			0.597448	+	0.801908i	$0.296182\pi$
$98$	72.1549	−	189.481i	0.736275	−	1.93348i
$99$		0			0
$100$	0.604342	+	0.538334i	0.00604342	+	0.00538334i
$101$	10.3010			0.101990			0.0509950	−	0.998699i	$-0.483761\pi$
$101$	10.3010			0.101990			0.0509950	+	0.998699i	$0.483761\pi$
$102$		0			0
$103$		−	110.807i		−	1.07579i	−0.843011	−	0.537897i	$-0.819219\pi$
$103$		−	110.807i		−	1.07579i	0.843011	−	0.537897i	$-0.180781\pi$
$104$	100.635	−	52.2962i	0.967648	−	0.502848i
$105$		0			0
$106$	−5.91860	+	15.5424i	−0.0558358	+	0.146627i
$107$			29.6484i			0.277088i	0.990356	+	0.138544i	$0.0442422\pi$
$107$			29.6484i			0.277088i	−0.990356	+	0.138544i	$0.955758\pi$
$108$		0			0
$109$	−1.00851			−0.00925235			−0.00462617	−	0.999989i	$-0.501473\pi$
$109$	−1.00851			−0.00925235			−0.00462617	+	0.999989i	$0.501473\pi$
$110$	125.150	+	47.6576i	1.13773	+	0.433251i
$111$		0			0
$112$	−194.900	+	22.5927i	−1.74018	+	0.201720i
$113$	59.0375			0.522456			0.261228	−	0.965277i	$-0.415873\pi$
$113$	59.0375			0.522456			0.261228	+	0.965277i	$0.415873\pi$
$114$		0			0
$115$			4.51458i			0.0392572i
$116$	−31.0192	−	27.6312i	−0.267407	−	0.238200i
$117$		0			0
$118$	39.1088	+	14.8927i	0.331431	+	0.126210i
$119$			72.2868i			0.607452i
$120$		0			0
$121$	−59.8017			−0.494229
$122$	84.2205	−	221.166i	0.690332	−	1.81283i
$123$		0			0
$124$	115.100	−	129.213i	0.928225	−	1.04204i
$125$	125.501			1.00401
$126$		0			0
$127$		−	209.454i		−	1.64925i	−0.565681	−	0.824624i	$-0.691387\pi$
$127$		−	209.454i		−	1.64925i	0.565681	−	0.824624i	$-0.308613\pi$
$128$	71.7086	+	106.028i	0.560224	+	0.828341i
$129$		0			0
$130$	50.2460	−	131.948i	0.386507	−	1.01498i
$131$			46.0795i			0.351752i	0.984412	+	0.175876i	$0.0562758\pi$
$131$			46.0795i			0.351752i	−0.984412	+	0.175876i	$0.943724\pi$
$132$		0			0
$133$	−53.4525			−0.401899
$134$	−107.378	−	40.8898i	−0.801327	−	0.305147i
$135$		0			0
$136$	41.8454	−	21.7454i	0.307687	−	0.159893i
$137$	−206.272			−1.50564			−0.752819	−	0.658228i	$-0.771306\pi$
$137$	−206.272			−1.50564			−0.752819	+	0.658228i	$0.771306\pi$
$138$		0			0
$139$		−	125.355i		−	0.901835i	−0.892566	−	0.450918i	$-0.851097\pi$
$139$		−	125.355i		−	0.901835i	0.892566	−	0.450918i	$-0.148903\pi$
$140$	−162.471	+	182.393i	−1.16051	+	1.30281i
$141$		0			0
$142$	21.1940	+	8.07073i	0.149253	+	0.0568361i
$143$			190.621i			1.33302i
$144$		0			0
$145$	−51.7159			−0.356661
$146$	16.7938	−	44.1011i	0.115026	−	0.302062i
$147$		0			0
$148$	4.81869	+	4.29238i	0.0325587	+	0.0290026i
$149$	170.871			1.14679			0.573394	−	0.819280i	$-0.305626\pi$
$149$	170.871			1.14679			0.573394	+	0.819280i	$0.305626\pi$
$150$		0			0
$151$			131.745i			0.872482i	0.899830	+	0.436241i	$0.143690\pi$
$151$			131.745i			0.872482i	−0.899830	+	0.436241i	$0.856310\pi$
$152$	16.0796	+	30.9426i	0.105787	+	0.203570i
$153$		0			0
$154$	117.359	−	308.189i	0.762074	−	2.00123i
$155$		−	215.427i		−	1.38985i
$156$		0			0
$157$	−3.40126			−0.0216641			−0.0108320	−	0.999941i	$-0.503448\pi$
$157$	−3.40126			−0.0216641			−0.0108320	+	0.999941i	$0.503448\pi$
$158$	0.535243	+	0.203822i	0.00338761	+	0.00129001i
$159$		0			0
$160$	154.459	+	39.1839i	0.965366	+	0.244899i
$161$	11.1174			0.0690522
$162$		0			0
$163$			170.519i			1.04613i	0.852293	+	0.523064i	$0.175211\pi$
$163$			170.519i			1.04613i	−0.852293	+	0.523064i	$0.824789\pi$
$164$	207.214	+	184.582i	1.26350	+	1.12550i
$165$		0			0
$166$	−46.5980	−	17.7446i	−0.280711	−	0.106895i
$167$			245.186i			1.46818i	0.679053	+	0.734089i	$0.262390\pi$
$167$			245.186i			1.46818i	−0.679053	+	0.734089i	$0.737610\pi$
$168$		0			0
$169$	31.9746			0.189199
$170$	20.8929	−	54.8654i	0.122899	−	0.322738i
$171$		0			0
$172$	−85.1784	+	95.6225i	−0.495223	+	0.555945i
$173$	−62.3081			−0.360162			−0.180081	−	0.983652i	$-0.557636\pi$
$173$	−62.3081			−0.360162			−0.180081	+	0.983652i	$0.557636\pi$
$174$		0			0
$175$		−	2.48121i		−	0.0141783i
$176$	−213.709	+	24.7729i	−1.21426	+	0.140755i
$177$		0			0
$178$	−31.1046	+	81.6816i	−0.174745	+	0.458885i
$179$			129.080i			0.721115i	0.932737	+	0.360557i	$0.117414\pi$
$179$			129.080i			0.721115i	−0.932737	+	0.360557i	$0.882586\pi$
$180$		0			0
$181$	−198.677			−1.09766			−0.548831	−	0.835933i	$-0.684927\pi$
$181$	−198.677			−1.09766			−0.548831	+	0.835933i	$0.684927\pi$
$182$	−324.928	−	123.733i	−1.78532	−	0.679854i
$183$		0			0
$184$	−3.34435	−	6.43565i	−0.0181758	−	0.0349763i
$185$	8.03384			0.0434261
$186$		0			0
$187$			79.2628i			0.423865i
$188$	−103.692	+	116.407i	−0.551555	+	0.619184i
$189$		0			0
$190$	40.5702	+	15.4492i	0.213528	+	0.0813118i
$191$		−	380.217i		−	1.99067i	−0.0965041	−	0.995333i	$-0.530766\pi$
$191$		−	380.217i		−	1.99067i	0.0965041	−	0.995333i	$-0.469234\pi$
$192$		0			0
$193$	−264.689			−1.37145			−0.685724	−	0.727862i	$-0.740514\pi$
$193$	−264.689			−1.37145			−0.685724	+	0.727862i	$0.740514\pi$
$194$	−82.4948	+	216.634i	−0.425231	+	1.11667i
$195$		0			0
$196$	302.797	+	269.725i	1.54488	+	1.37615i
$197$	−125.565			−0.637386			−0.318693	−	0.947858i	$-0.603244\pi$
$197$	−125.565			−0.637386			−0.318693	+	0.947858i	$0.603244\pi$
$198$		0			0
$199$			14.4081i			0.0724026i	0.999345	+	0.0362013i	$0.0115258\pi$
$199$			14.4081i			0.0724026i	−0.999345	+	0.0362013i	$0.988474\pi$
$200$	−1.43632	+	0.746400i	−0.00718161	+	0.00373200i
$201$		0			0
$202$	−7.33168	+	19.2532i	−0.0362955	+	0.0953131i
$203$			127.353i			0.627356i
$204$		0			0
$205$	345.473			1.68523
$206$	207.105	+	78.8663i	1.00537	+	0.382846i
$207$		0			0
$208$	26.1184	+	225.316i	0.125569	+	1.08325i
$209$	−58.6109			−0.280435
$210$		0			0
$211$			81.1242i			0.384475i	0.981348	+	0.192237i	$0.0615744\pi$
$211$			81.1242i			0.384475i	−0.981348	+	0.192237i	$0.938426\pi$
$212$	−24.8373	−	22.1245i	−0.117157	−	0.104361i
$213$		0			0
$214$	−55.4148	−	21.1021i	−0.258948	−	0.0986080i
$215$			159.424i			0.741508i
$216$		0			0
$217$	−530.500			−2.44470
$218$	0.717800	−	1.88497i	0.00329266	−	0.00864664i
$219$		0			0
$220$	−178.150	+	199.994i	−0.809775	+	0.909066i
$221$	83.5677			0.378134
$222$		0			0
$223$		−	181.944i		−	0.815892i	−0.913006	−	0.407946i	$-0.866245\pi$
$223$		−	181.944i		−	0.815892i	0.913006	−	0.407946i	$-0.133755\pi$
$224$	96.4924	−	380.363i	0.430770	−	1.69805i
$225$		0			0
$226$	−42.0197	+	110.345i	−0.185928	+	0.488253i
$227$			423.077i			1.86377i	0.362748	+	0.931887i	$0.381838\pi$
$227$			423.077i			1.86377i	−0.362748	+	0.931887i	$0.618162\pi$
$228$		0			0
$229$	360.509			1.57427			0.787137	−	0.616778i	$-0.211562\pi$
$229$	360.509			1.57427			0.787137	+	0.616778i	$0.211562\pi$
$230$	−8.43806	−	3.21324i	−0.0366872	−	0.0139706i
$231$		0			0
$232$	73.7223	−	38.3106i	0.317769	−	0.165132i
$233$	−2.13039			−0.00914329			−0.00457164	−	0.999990i	$-0.501455\pi$
$233$	−2.13039			−0.00914329			−0.00457164	+	0.999990i	$0.501455\pi$
$234$		0			0
$235$			194.076i			0.825855i
$236$	−55.6711	+	62.4972i	−0.235894	+	0.264819i
$237$		0			0
$238$	−135.109	−	51.4499i	−0.567685	−	0.216176i
$239$		−	228.926i		−	0.957847i	−0.877857	−	0.478924i	$-0.841027\pi$
$239$		−	228.926i		−	0.957847i	0.877857	−	0.478924i	$-0.158973\pi$
$240$		0			0
$241$	245.133			1.01715			0.508575	−	0.861017i	$-0.330172\pi$
$241$	245.133			1.01715			0.508575	+	0.861017i	$0.330172\pi$
$242$	42.5636	−	111.774i	0.175883	−	0.461874i
$243$		0			0
$244$	353.430	+	314.828i	1.44848	+	1.29028i
$245$	504.831			2.06054
$246$		0			0
$247$			61.7942i			0.250179i
$248$	159.586	+	307.096i	0.643491	+	1.23829i
$249$		0			0
$250$	−89.3246	+	234.569i	−0.357299	+	0.938278i
$251$			178.193i			0.709934i	0.934879	+	0.354967i	$0.115508\pi$
$251$			178.193i			0.709934i	−0.934879	+	0.354967i	$0.884492\pi$
$252$		0			0
$253$	12.1903			0.0481829
$254$	391.485	+	149.078i	1.54128	+	0.586923i
$255$		0			0
$256$	−249.211	+	58.5636i	−0.973482	+	0.228764i
$257$	239.267			0.930998			0.465499	−	0.885048i	$-0.345875\pi$
$257$	239.267			0.930998			0.465499	+	0.885048i	$0.345875\pi$
$258$		0			0
$259$		−	19.7838i		−	0.0763852i
$260$	210.857	+	187.826i	0.810987	+	0.722409i
$261$		0			0
$262$	−86.1257	−	32.7969i	−0.328724	−	0.125179i
$263$			39.7564i			0.151165i	0.997140	+	0.0755825i	$0.0240816\pi$
$263$			39.7564i			0.151165i	−0.997140	+	0.0755825i	$0.975918\pi$
$264$		0			0
$265$	−41.4094			−0.156262
$266$	38.0446	−	99.9064i	0.143025	−	0.375588i
$267$		0			0
$268$	152.852	−	171.593i	0.570342	−	0.640274i
$269$	25.6332			0.0952905			0.0476453	−	0.998864i	$-0.484828\pi$
$269$	25.6332			0.0952905			0.0476453	+	0.998864i	$0.484828\pi$
$270$		0			0
$271$			53.7535i			0.198353i	0.995070	+	0.0991763i	$0.0316208\pi$
$271$			53.7535i			0.198353i	−0.995070	+	0.0991763i	$0.968379\pi$
$272$	10.8604	+	93.6892i	0.0399278	+	0.344446i
$273$		0			0
$274$	146.813	−	385.537i	0.535816	−	1.40707i
$275$		−	2.72065i		−	0.00989328i
$276$		0			0
$277$	353.449			1.27599			0.637995	−	0.770040i	$-0.279764\pi$
$277$	353.449			1.27599			0.637995	+	0.770040i	$0.279764\pi$
$278$	234.297	+	89.2210i	0.842796	+	0.320939i
$279$		0			0
$280$	−225.266	−	433.488i	−0.804523	−	1.54817i
$281$	−221.272			−0.787445			−0.393722	−	0.919229i	$-0.628813\pi$
$281$	−221.272			−0.787445			−0.393722	+	0.919229i	$0.628813\pi$
$282$		0			0
$283$		−	81.0003i		−	0.286220i	−0.989707	−	0.143110i	$-0.954290\pi$
$283$		−	81.0003i		−	0.286220i	0.989707	−	0.143110i	$-0.0457103\pi$
$284$	−30.1695	+	33.8687i	−0.106231	+	0.119256i
$285$		0			0
$286$	−356.285	−	135.674i	−1.24575	−	0.474385i
$287$		−	850.745i		−	2.96427i
$288$		0			0
$289$	−254.252			−0.879763
$290$	36.8086	−	96.6606i	0.126926	−	0.333312i
$291$		0			0
$292$	70.4750	+	62.7776i	0.241353	+	0.214992i
$293$	−517.659			−1.76675			−0.883377	−	0.468664i	$-0.844736\pi$
$293$	−517.659			−1.76675			−0.883377	+	0.468664i	$0.844736\pi$
$294$		0			0
$295$			104.197i			0.353210i
$296$	−11.4524	+	5.95138i	−0.0386906	+	0.0201060i
$297$		0			0
$298$	−121.617	+	319.371i	−0.408111	+	1.07171i
$299$		−	12.8524i		−	0.0429845i
$300$		0			0
$301$	392.591			1.30429
$302$	−246.240	−	93.7688i	−0.815364	−	0.310493i
$303$		0			0
$304$	−69.2785	+	8.03069i	−0.227890	+	0.0264167i
$305$	589.248			1.93196
$306$		0			0
$307$			249.101i			0.811405i	0.914005	+	0.405703i	$0.132973\pi$
$307$			249.101i			0.811405i	−0.914005	+	0.405703i	$0.867027\pi$
$308$	492.497	+	438.705i	1.59902	+	1.42437i
$309$		0			0
$310$	402.648	+	153.329i	1.29886	+	0.494610i
$311$			252.481i			0.811835i	0.913910	+	0.405917i	$0.133048\pi$
$311$			252.481i			0.811835i	−0.913910	+	0.405917i	$0.866952\pi$
$312$		0			0
$313$	−595.875			−1.90376			−0.951878	−	0.306478i	$-0.900849\pi$
$313$	−595.875			−1.90376			−0.951878	+	0.306478i	$0.900849\pi$
$314$	2.42083	−	6.35719i	0.00770966	−	0.0202458i
$315$		0			0
$316$	−0.761914	+	0.855337i	−0.00241112	+	0.00270676i
$317$	−491.836			−1.55153			−0.775766	−	0.631020i	$-0.782636\pi$
$317$	−491.836			−1.55153			−0.775766	+	0.631020i	$0.782636\pi$
$318$		0			0
$319$			139.643i			0.437753i
$320$	−183.173	+	260.805i	−0.572414	+	0.815014i
$321$		0			0
$322$	−7.91277	+	20.7792i	−0.0245738	+	0.0645316i
$323$			25.6948i			0.0795504i
$324$		0			0
$325$	−2.86842			−0.00882590
$326$	−318.711	−	121.366i	−0.977643	−	0.372289i
$327$		0			0
$328$	−492.480	+	255.922i	−1.50146	+	0.780251i
$329$	477.923			1.45265
$330$		0			0
$331$			413.971i			1.25067i	0.780358	+	0.625333i	$0.215037\pi$
$331$			413.971i			1.25067i	−0.780358	+	0.625333i	$0.784963\pi$
$332$	66.3319	−	74.4652i	0.199795	−	0.224293i
$333$		0			0
$334$	−458.269	−	174.510i	−1.37206	−	0.522485i
$335$		−	286.085i		−	0.853985i
$336$		0			0
$337$	393.328			1.16715			0.583573	−	0.812061i	$-0.301654\pi$
$337$	393.328			1.16715			0.583573	+	0.812061i	$0.301654\pi$
$338$	−22.7578	+	59.7627i	−0.0673307	+	0.176813i
$339$		0			0
$340$	87.6768	+	78.1005i	0.257873	+	0.229707i
$341$	−581.696			−1.70585
$342$		0			0
$343$		−	642.295i		−	1.87258i
$344$	−118.100	−	227.263i	−0.343313	−	0.660649i
$345$		0			0
$346$	44.3475	−	116.458i	0.128172	−	0.336584i
$347$			476.716i			1.37382i	0.726742	+	0.686911i	$0.241034\pi$
$347$			476.716i			1.37382i	−0.726742	+	0.686911i	$0.758966\pi$
$348$		0			0
$349$	−118.794			−0.340383			−0.170191	−	0.985411i	$-0.554439\pi$
$349$	−118.794			−0.340383			−0.170191	+	0.985411i	$0.554439\pi$
$350$	4.63754	+	1.76599i	0.0132501	+	0.00504568i
$351$		0			0
$352$	105.804	−	417.069i	0.300580	−	1.18485i
$353$	−297.291			−0.842185			−0.421092	−	0.907018i	$-0.638353\pi$
$353$	−297.291			−0.842185			−0.421092	+	0.907018i	$0.638353\pi$
$354$		0			0
$355$			56.4668i			0.159061i
$356$	−130.530	−	116.273i	−0.366657	−	0.326610i
$357$		0			0
$358$	−241.259	−	91.8719i	−0.673907	−	0.256625i
$359$		−	212.978i		−	0.593252i	−0.954994	−	0.296626i	$-0.904139\pi$
$359$		−	212.978i		−	0.593252i	0.954994	−	0.296626i	$-0.0958615\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	141.407	−	371.341i	0.390628	−	1.02580i
$363$		0			0
$364$	462.532	−	519.246i	1.27069	−	1.42650i
$365$	117.498			0.321912
$366$		0			0
$367$			326.797i			0.890456i	0.895417	+	0.445228i	$0.146877\pi$
$367$			326.797i			0.890456i	−0.895417	+	0.445228i	$0.853123\pi$
$368$	14.4090	−	1.67028i	0.0391549	−	0.00453879i
$369$		0			0
$370$	−5.71805	+	15.0158i	−0.0154542	+	0.0405832i
$371$			101.973i			0.274860i
$372$		0			0
$373$	235.813			0.632205			0.316103	−	0.948725i	$-0.397626\pi$
$373$	235.813			0.632205			0.316103	+	0.948725i	$0.397626\pi$
$374$	−148.148	−	56.4150i	−0.396116	−	0.150842i
$375$		0			0
$376$	−143.769	−	276.660i	−0.382365	−	0.735798i
$377$	147.228			0.390524
$378$		0			0
$379$		−	471.811i		−	1.24489i	−0.782666	−	0.622443i	$-0.786140\pi$
$379$		−	471.811i		−	1.24489i	0.782666	−	0.622443i	$-0.213860\pi$
$380$	−57.7514	+	64.8326i	−0.151977	+	0.170612i
$381$		0			0
$382$	710.652	+	270.618i	1.86034	+	0.708424i
$383$			131.099i			0.342294i	0.985246	+	0.171147i	$0.0547473\pi$
$383$			131.099i			0.342294i	−0.985246	+	0.171147i	$0.945253\pi$
$384$		0			0
$385$	821.104			2.13274
$386$	188.392	−	494.722i	0.488061	−	1.28166i
$387$		0			0
$388$	−346.189	−	308.377i	−0.892239	−	0.794786i
$389$	−20.4959			−0.0526887			−0.0263444	−	0.999653i	$-0.508387\pi$
$389$	−20.4959			−0.0526887			−0.0263444	+	0.999653i	$0.508387\pi$
$390$		0			0
$391$		−	5.34417i		−	0.0136679i
$392$	−719.650	+	373.973i	−1.83584	+	0.954014i
$393$		0			0
$394$	89.3704	−	234.690i	0.226828	−	0.595659i
$395$			1.42604i			0.00361022i
$396$		0			0
$397$	9.07740			0.0228650			0.0114325	−	0.999935i	$-0.496361\pi$
$397$	9.07740			0.0228650			0.0114325	+	0.999935i	$0.496361\pi$
$398$	−26.9298	−	10.2549i	−0.0676628	−	0.0257661i
$399$		0			0
$400$	−0.372776	−	3.21583i	−0.000931939	−	0.00803958i
$401$	336.682			0.839606			0.419803	−	0.907615i	$-0.362099\pi$
$401$	336.682			0.839606			0.419803	+	0.907615i	$0.362099\pi$
$402$		0			0
$403$			613.289i			1.52181i
$404$	−30.7673	−	27.4068i	−0.0761568	−	0.0678387i
$405$		0			0
$406$	−238.032	−	90.6432i	−0.586286	−	0.223259i
$407$		−	21.6930i		−	0.0532997i
$408$		0			0
$409$	75.6667			0.185004			0.0925020	−	0.995712i	$-0.470514\pi$
$409$	75.6667			0.185004			0.0925020	+	0.995712i	$0.470514\pi$
$410$	−245.889	+	645.712i	−0.599729	+	1.57491i
$411$		0			0
$412$	−294.813	+	330.961i	−0.715565	+	0.803304i
$413$	256.591			0.621285
$414$		0			0
$415$		−	124.150i		−	0.299157i
$416$	−439.721	−	111.551i	−1.05702	−	0.268151i
$417$		0			0
$418$	41.7160	−	109.548i	0.0997992	−	0.262076i
$419$		−	619.532i		−	1.47860i	−0.673378	−	0.739298i	$-0.735157\pi$
$419$		−	619.532i		−	1.47860i	0.673378	−	0.739298i	$-0.264843\pi$
$420$		0			0
$421$	−18.4384			−0.0437967			−0.0218983	−	0.999760i	$-0.506971\pi$
$421$	−18.4384			−0.0437967			−0.0218983	+	0.999760i	$0.506971\pi$
$422$	−151.627	−	57.7398i	−0.359305	−	0.136824i
$423$		0			0
$424$	59.0301	−	30.6756i	0.139222	−	0.0723482i
$425$	−1.19272			−0.00280641
$426$		0			0
$427$		−	1451.05i		−	3.39825i
$428$	78.8826	−	88.5548i	0.184305	−	0.206904i
$429$		0			0
$430$	−297.975	−	113.470i	−0.692965	−	0.263883i
$431$		−	496.147i		−	1.15115i	−0.817748	−	0.575577i	$-0.804778\pi$
$431$		−	496.147i		−	1.15115i	0.817748	−	0.575577i	$-0.195222\pi$
$432$		0			0
$433$	623.687			1.44039			0.720193	−	0.693774i	$-0.244053\pi$
$433$	623.687			1.44039			0.720193	+	0.693774i	$0.244053\pi$
$434$	377.582	−	991.542i	0.870004	−	2.28466i
$435$		0			0
$436$	3.01224	+	2.68324i	0.00690881	+	0.00615421i
$437$	3.95174			0.00904289
$438$		0			0
$439$			105.337i			0.239947i	0.992777	+	0.119974i	$0.0382810\pi$
$439$			105.337i			0.239947i	−0.992777	+	0.119974i	$0.961719\pi$
$440$	−247.005	−	475.321i	−0.561376	−	1.08027i
$441$		0			0
$442$	−59.4790	+	156.194i	−0.134568	+	0.353380i
$443$		−	113.329i		−	0.255821i	−0.991786	−	0.127911i	$-0.959173\pi$
$443$		−	113.329i		−	0.255821i	0.991786	−	0.127911i	$-0.0408271\pi$
$444$		0			0
$445$	−217.623			−0.489040
$446$	340.066	+	129.498i	0.762479	+	0.290354i
$447$		0			0
$448$	642.246	+	451.072i	1.43358	+	1.00686i
$449$	−413.979			−0.922003			−0.461001	−	0.887399i	$-0.652510\pi$
$449$	−413.979			−0.922003			−0.461001	+	0.887399i	$0.652510\pi$
$450$		0			0
$451$		−	932.845i		−	2.06839i
$452$	−176.335	−	157.076i	−0.390122	−	0.347512i
$453$		0			0
$454$	−790.760	−	301.123i	−1.74176	−	0.663267i
$455$		−	865.700i		−	1.90264i
$456$		0			0
$457$	320.223			0.700707			0.350353	−	0.936618i	$-0.386061\pi$
$457$	320.223			0.700707			0.350353	+	0.936618i	$0.386061\pi$
$458$	−256.591	+	673.816i	−0.560242	+	1.47121i
$459$		0			0
$460$	12.0115	−	13.4843i	0.0261120	−	0.0293137i
$461$	460.179			0.998218			0.499109	−	0.866539i	$-0.333661\pi$
$461$	460.179			0.998218			0.499109	+	0.866539i	$0.333661\pi$
$462$		0			0
$463$		−	323.224i		−	0.698108i	−0.937103	−	0.349054i	$-0.886503\pi$
$463$		−	323.224i		−	0.698108i	0.937103	−	0.349054i	$-0.113497\pi$
$464$	19.1335	+	165.059i	0.0412360	+	0.355732i
$465$		0			0
$466$	1.51629	−	3.98184i	0.00325385	−	0.00854472i
$467$			523.352i			1.12067i	0.828267	+	0.560334i	$0.189327\pi$
$467$			523.352i			1.12067i	−0.828267	+	0.560334i	$0.810673\pi$
$468$		0			0
$469$	−704.500			−1.50213
$470$	−362.741	−	138.133i	−0.771790	−	0.293900i
$471$		0			0
$472$	−77.1879	−	148.535i	−0.163534	−	0.314693i
$473$	430.477			0.910100
$474$		0			0
$475$		−	0.881959i		−	0.00185676i
$476$	192.327	−	215.909i	0.404048	−	0.453590i
$477$		0			0
$478$	427.878	+	162.937i	0.895141	+	0.340872i
$479$			458.055i			0.956274i	0.878285	+	0.478137i	$0.158688\pi$
$479$			458.055i			0.956274i	−0.878285	+	0.478137i	$0.841312\pi$
$480$		0			0
$481$	−22.8712			−0.0475492
$482$	−174.473	+	458.171i	−0.361977	+	0.950562i
$483$		0			0
$484$	178.618	+	159.109i	0.369045	+	0.328737i
$485$	−577.174			−1.19005
$486$		0			0
$487$		−	49.8747i		−	0.102412i	−0.998688	−	0.0512060i	$-0.983693\pi$
$487$		−	49.8747i		−	0.102412i	0.998688	−	0.0512060i	$-0.0163065\pi$
$488$	−839.987	+	436.508i	−1.72128	+	0.894484i
$489$		0			0
$490$	−359.312	+	943.565i	−0.733289	+	1.92564i
$491$			381.364i			0.776709i	0.921510	+	0.388354i	$0.126956\pi$
$491$			381.364i			0.776709i	−0.921510	+	0.388354i	$0.873044\pi$
$492$		0			0
$493$	61.2191			0.124177
$494$	−115.498	−	43.9817i	−0.233801	−	0.0890319i
$495$		0			0
$496$	−687.569	+	79.7022i	−1.38623	+	0.160690i
$497$	139.053			0.279784
$498$		0			0
$499$			191.567i			0.383903i	0.981404	+	0.191951i	$0.0614816\pi$
$499$			191.567i			0.383903i	−0.981404	+	0.191951i	$0.938518\pi$
$500$	−374.850	−	333.908i	−0.749700	−	0.667816i
$501$		0			0
$502$	−333.056	−	126.829i	−0.663458	−	0.252646i
$503$		−	393.811i		−	0.782925i	−0.920194	−	0.391463i	$-0.871969\pi$
$503$		−	393.811i		−	0.782925i	0.920194	−	0.391463i	$-0.128031\pi$
$504$		0			0
$505$	−51.2961			−0.101576
$506$	−8.67638	+	22.7845i	−0.0171470	+	0.0450286i
$507$		0			0
$508$	−557.276	+	625.606i	−1.09700	+	1.23151i
$509$	711.118			1.39709			0.698544	−	0.715567i	$-0.253832\pi$
$509$	711.118			1.39709			0.698544	+	0.715567i	$0.253832\pi$
$510$		0			0
$511$		−	289.345i		−	0.566232i
$512$	67.9159	−	507.476i	0.132648	−	0.991163i
$513$		0			0
$514$	−170.297	+	447.206i	−0.331317	+	0.870050i
$515$			551.787i			1.07143i
$516$		0			0
$517$	524.044			1.01362
$518$	36.9772	+	14.0810i	0.0713846	+	0.0271834i
$519$		0			0
$520$	−501.137	+	260.421i	−0.963724	+	0.500809i
$521$	−401.456			−0.770549			−0.385274	−	0.922802i	$-0.625893\pi$
$521$	−401.456			−0.770549			−0.385274	+	0.922802i	$0.625893\pi$
$522$		0			0
$523$			83.5113i			0.159677i	0.996808	+	0.0798387i	$0.0254405\pi$
$523$			83.5113i			0.159677i	−0.996808	+	0.0798387i	$0.974559\pi$
$524$	122.599	−	137.632i	0.233968	−	0.262656i
$525$		0			0
$526$	−74.3074	−	28.2965i	−0.141269	−	0.0537956i
$527$			255.013i			0.483896i
$528$		0			0
$529$	528.178			0.998446
$530$	29.4730	−	77.3970i	0.0556094	−	0.146032i
$531$		0			0
$532$	159.654	+	142.216i	0.300101	+	0.267323i
$533$	−983.510			−1.84523
$534$		0			0
$535$		−	147.641i		−	0.275964i
$536$	211.928	+	407.821i	0.395389	+	0.760860i
$537$		0			0
$538$	−18.2443	+	47.9101i	−0.0339113	+	0.0890523i
$539$		−	1363.15i		−	2.52903i
$540$		0			0
$541$	315.779			0.583694			0.291847	−	0.956465i	$-0.405730\pi$
$541$	315.779			0.583694			0.291847	+	0.956465i	$0.405730\pi$
$542$	−100.469	−	38.2589i	−0.185367	−	0.0705883i
$543$		0			0
$544$	−182.841	−	46.3842i	−0.336105	−	0.0852650i
$545$	5.02208			0.00921483
$546$		0			0
$547$		−	115.726i		−	0.211564i	−0.994389	−	0.105782i	$-0.966265\pi$
$547$		−	115.726i		−	0.211564i	0.994389	−	0.105782i	$-0.0337346\pi$
$548$	616.101	+	548.809i	1.12427	+	1.00148i
$549$		0			0
$550$	5.08508	+	1.93641i	0.00924561	+	0.00352075i
$551$			45.2684i			0.0821569i
$552$		0			0
$553$	3.51170			0.00635027
$554$	−251.566	+	660.621i	−0.454091	+	1.19246i
$555$		0			0
$556$	−333.520	+	374.415i	−0.599857	+	0.673408i
$557$	597.571			1.07284			0.536419	−	0.843952i	$-0.319777\pi$
$557$	597.571			1.07284			0.536419	+	0.843952i	$0.319777\pi$
$558$		0			0
$559$		−	453.857i		−	0.811910i
$560$	970.551	−	112.505i	1.73313	−	0.200902i
$561$		0			0
$562$	157.490	−	413.573i	0.280230	−	0.735894i
$563$		−	622.336i		−	1.10539i	−0.833383	−	0.552696i	$-0.813599\pi$
$563$		−	622.336i		−	1.10539i	0.833383	−	0.552696i	$-0.186401\pi$
$564$		0			0
$565$	−293.991			−0.520337
$566$	151.395	+	57.6516i	0.267482	+	0.101858i
$567$		0			0
$568$	−41.8300	−	80.4948i	−0.0736443	−	0.141716i
$569$	−497.207			−0.873826			−0.436913	−	0.899504i	$-0.643928\pi$
$569$	−497.207			−0.873826			−0.436913	+	0.899504i	$0.643928\pi$
$570$		0			0
$571$			623.096i			1.09124i	0.838034	+	0.545619i	$0.183705\pi$
$571$			623.096i			1.09124i	−0.838034	+	0.545619i	$0.816295\pi$
$572$	507.168	−	569.355i	0.886658	−	0.995376i
$573$		0			0
$574$	1590.10	+	605.514i	2.77021	+	1.05490i
$575$			0.183436i			0.000319019i
$576$		0			0
$577$	−934.139			−1.61896			−0.809479	−	0.587148i	$-0.800251\pi$
$577$	−934.139			−1.61896			−0.809479	+	0.587148i	$0.800251\pi$
$578$	180.963	−	475.214i	0.313084	−	0.822169i
$579$		0			0
$580$	154.467	+	137.596i	0.266322	+	0.237234i
$581$	−305.727			−0.526208
$582$		0			0
$583$			111.814i			0.191790i
$584$	−167.496	+	87.0410i	−0.286808	+	0.149043i
$585$		0			0
$586$	368.442	−	967.540i	0.628740	−	1.65109i
$587$			778.304i			1.32590i	0.748663	+	0.662951i	$0.230696\pi$
$587$			778.304i			1.32590i	−0.748663	+	0.662951i	$0.769304\pi$
$588$		0			0
$589$	−188.569			−0.320152
$590$	−194.751	−	74.1617i	−0.330087	−	0.125698i
$591$		0			0
$592$	−2.97231	−	25.6412i	−0.00502079	−	0.0433129i
$593$	1012.64			1.70766			0.853832	−	0.520549i	$-0.174273\pi$
$593$	1012.64			1.70766			0.853832	+	0.520549i	$0.174273\pi$
$594$		0			0
$595$		−	359.969i		−	0.604989i
$596$	−510.365	−	454.621i	−0.856317	−	0.762788i
$597$		0			0
$598$	24.0219	+	9.14761i	0.0401705	+	0.0152970i
$599$			37.3119i			0.0622903i	0.999515	+	0.0311452i	$0.00991541\pi$
$599$			37.3119i			0.0622903i	−0.999515	+	0.0311452i	$0.990085\pi$
$600$		0			0
$601$	−181.988			−0.302808			−0.151404	−	0.988472i	$-0.548379\pi$
$601$	−181.988			−0.302808			−0.151404	+	0.988472i	$0.548379\pi$
$602$	−279.425	+	733.779i	−0.464161	+	1.21890i
$603$		0			0
$604$	350.521	−	393.500i	0.580332	−	0.651490i
$605$	297.796			0.492225
$606$		0			0
$607$			218.379i			0.359767i	0.983688	+	0.179884i	$0.0575721\pi$
$607$			218.379i			0.359767i	−0.983688	+	0.179884i	$0.942428\pi$
$608$	34.2988	−	135.202i	0.0564125	−	0.222372i
$609$		0			0
$610$	−419.395	+	1101.34i	−0.687532	+	1.80548i
$611$		−	552.506i		−	0.904265i
$612$		0			0
$613$	641.406			1.04634			0.523170	−	0.852229i	$-0.324749\pi$
$613$	641.406			1.04634			0.523170	+	0.852229i	$0.324749\pi$
$614$	−465.588	−	177.297i	−0.758286	−	0.288757i
$615$		0			0
$616$	−1170.50	+	608.264i	−1.90017	+	0.987442i
$617$	223.015			0.361450			0.180725	−	0.983534i	$-0.442156\pi$
$617$	223.015			0.361450			0.180725	+	0.983534i	$0.442156\pi$
$618$		0			0
$619$			126.536i			0.204420i	0.994763	+	0.102210i	$0.0325914\pi$
$619$			126.536i			0.204420i	−0.994763	+	0.102210i	$0.967409\pi$
$620$	−573.166	+	643.445i	−0.924461	+	1.03781i
$621$		0			0
$622$	−471.903	−	179.702i	−0.758687	−	0.288910i
$623$			535.908i			0.860205i
$624$		0			0
$625$	−619.901			−0.991841
$626$	424.112	−	1113.73i	0.677495	−	1.77912i
$627$		0			0
$628$	10.1590	+	9.04941i	0.0161768	+	0.0144099i
$629$	−9.51011			−0.0151194
$630$		0			0
$631$			250.558i			0.397081i	0.980093	+	0.198541i	$0.0636202\pi$
$631$			250.558i			0.397081i	−0.980093	+	0.198541i	$0.936380\pi$
$632$	−1.05639	−	2.03285i	−0.00167151	−	0.00321654i
$633$		0			0
$634$	350.062	−	919.275i	0.552149	−	1.44996i
$635$			1043.03i			1.64256i
$636$		0			0
$637$	−1437.18			−2.25617
$638$	−261.003	−	99.3906i	−0.409095	−	0.155785i
$639$		0			0
$640$	−357.089	−	527.989i	−0.557952	−	0.824982i
$641$	744.927			1.16213			0.581067	−	0.813856i	$-0.302636\pi$
$641$	744.927			1.16213			0.581067	+	0.813856i	$0.302636\pi$
$642$		0			0
$643$			1161.89i			1.80699i	0.428604	+	0.903493i	$0.359006\pi$
$643$			1161.89i			1.80699i	−0.428604	+	0.903493i	$0.640994\pi$
$644$	−33.2058	−	29.5790i	−0.0515619	−	0.0459301i
$645$		0			0
$646$	−48.0253	−	18.2882i	−0.0743425	−	0.0283098i
$647$			550.347i			0.850614i	0.905049	+	0.425307i	$0.139834\pi$
$647$			550.347i			0.850614i	−0.905049	+	0.425307i	$0.860166\pi$
$648$		0			0
$649$	281.352			0.433517
$650$	2.04158	−	5.36127i	0.00314090	−	0.00824810i
$651$		0			0
$652$	453.683	−	509.312i	0.695833	−	0.781153i
$653$	170.874			0.261675			0.130838	−	0.991404i	$-0.458233\pi$
$653$	170.874			0.261675			0.130838	+	0.991404i	$0.458233\pi$
$654$		0			0
$655$		−	229.463i		−	0.350326i
$656$	−127.816	−	1102.63i	−0.194841	−	1.68084i
$657$		0			0
$658$	−340.160	+	893.270i	−0.516960	+	1.35755i
$659$			933.406i			1.41640i	0.706013	+	0.708199i	$0.250492\pi$
$659$			933.406i			1.41640i	−0.706013	+	0.708199i	$0.749508\pi$
$660$		0			0
$661$	−498.493			−0.754150			−0.377075	−	0.926183i	$-0.623070\pi$
$661$	−498.493			−0.754150			−0.377075	+	0.926183i	$0.623070\pi$
$662$	−773.740	−	294.642i	−1.16879	−	0.445079i
$663$		0			0
$664$	91.9691	+	176.979i	0.138508	+	0.266535i
$665$	266.179			0.400269
$666$		0			0
$667$		−	9.41523i		−	0.0141158i
$668$	652.342	−	732.329i	0.976560	−	1.09630i
$669$		0			0
$670$	534.712	+	203.620i	0.798078	+	0.303910i
$671$		−	1591.09i		−	2.37122i
$672$		0			0
$673$	779.779			1.15866			0.579331	−	0.815093i	$-0.303314\pi$
$673$	779.779			1.15866			0.579331	+	0.815093i	$0.303314\pi$
$674$	−279.950	+	735.157i	−0.415356	+	1.09074i
$675$		0			0
$676$	−95.5028	−	85.0718i	−0.141276	−	0.125846i
$677$	−910.302			−1.34461			−0.672306	−	0.740273i	$-0.734696\pi$
$677$	−910.302			−1.34461			−0.672306	+	0.740273i	$0.734696\pi$
$678$		0			0
$679$			1421.32i			2.09326i
$680$	−208.379	+	108.286i	−0.306439	+	0.159244i
$681$		0			0
$682$	414.020	−	1087.23i	0.607067	−	1.59418i
$683$			93.5131i			0.136915i	0.997654	+	0.0684576i	$0.0218078\pi$
$683$			93.5131i			0.136915i	−0.997654	+	0.0684576i	$0.978192\pi$
$684$		0			0
$685$	1027.18			1.49953
$686$	1200.49	+	457.151i	1.74999	+	0.666401i
$687$		0			0
$688$	508.827	−	58.9827i	0.739575	−	0.0857307i
$689$	117.887			0.171098
$690$		0			0
$691$			663.683i			0.960468i	0.877140	+	0.480234i	$0.159448\pi$
$691$			663.683i			0.960468i	−0.877140	+	0.480234i	$0.840552\pi$
$692$	186.104	+	165.777i	0.268936	+	0.239562i
$693$		0			0
$694$	−891.015	−	339.301i	−1.28388	−	0.488906i
$695$			624.234i			0.898179i
$696$		0			0
$697$	−408.956			−0.586737
$698$	84.5509	−	222.033i	0.121133	−	0.318099i
$699$		0			0
$700$	−6.60151	+	7.41095i	−0.00943073	+	0.0105871i
$701$	−959.216			−1.36835			−0.684177	−	0.729316i	$-0.739838\pi$
$701$	−959.216			−1.36835			−0.684177	+	0.729316i	$0.739838\pi$
$702$		0			0
$703$		−	7.03225i		−	0.0100032i
$704$	704.225	+	494.603i	1.00032	+	0.702560i
$705$		0			0
$706$	211.596	−	555.658i	0.299711	−	0.787051i
$707$			126.319i			0.178670i
$708$		0			0
$709$	825.957			1.16496			0.582480	−	0.812845i	$-0.302082\pi$
$709$	825.957			1.16496			0.582480	+	0.812845i	$0.302082\pi$
$710$	−105.540	−	40.1900i	−0.148648	−	0.0566056i
$711$		0			0
$712$	310.227	−	161.212i	0.435711	−	0.226422i
$713$	39.2199			0.0550069
$714$		0			0
$715$		−	949.243i		−	1.32761i
$716$	343.430	−	385.539i	0.479650	−	0.538463i
$717$		0			0
$718$	398.070	+	151.586i	0.554414	+	0.211122i
$719$			1019.44i			1.41786i	0.705281	+	0.708928i	$0.250821\pi$
$719$			1019.44i			1.41786i	−0.705281	+	0.708928i	$0.749179\pi$
$720$		0			0
$721$	1358.81			1.88461
$722$	13.5232	−	35.5123i	0.0187302	−	0.0491860i
$723$		0			0
$724$	593.415	+	528.601i	0.819634	+	0.730111i
$725$	−2.10131			−0.00289836
$726$		0			0
$727$			227.791i			0.313330i	0.987652	+	0.156665i	$0.0500742\pi$
$727$			227.791i			0.313330i	−0.987652	+	0.156665i	$0.949926\pi$
$728$	641.301	+	1234.08i	0.880907	+	1.69516i
$729$		0			0
$730$	−83.6286	+	219.611i	−0.114560	+	0.300837i
$731$		−	188.720i		−	0.258166i
$732$		0			0
$733$	−998.335			−1.36198			−0.680992	−	0.732291i	$-0.738451\pi$
$733$	−998.335			−1.36198			−0.680992	+	0.732291i	$0.738451\pi$
$734$	−610.807	−	232.597i	−0.832162	−	0.316889i
$735$		0			0
$736$	−7.13369	+	28.1202i	−0.00969251	+	0.0382068i
$737$	−772.486			−1.04815
$738$		0			0
$739$			614.741i			0.831856i	0.909398	+	0.415928i	$0.136543\pi$
$739$			614.741i			0.831856i	−0.909398	+	0.415928i	$0.863457\pi$
$740$	−23.9957	−	21.3749i	−0.0324267	−	0.0288850i
$741$		0			0
$742$	−190.594	−	72.5788i	−0.256866	−	0.0978151i
$743$			156.926i			0.211206i	0.994408	+	0.105603i	$0.0336772\pi$
$743$			156.926i			0.211206i	−0.994408	+	0.105603i	$0.966323\pi$
$744$		0			0
$745$	−850.893			−1.14214
$746$	−167.839	+	440.750i	−0.224985	+	0.590817i
$747$		0			0
$748$	210.887	−	236.745i	0.281934	−	0.316504i
$749$	−363.573			−0.485412
$750$		0			0
$751$		−	766.925i		−	1.02120i	−0.859817	−	0.510602i	$-0.829422\pi$
$751$		−	766.925i		−	1.02120i	0.859817	−	0.510602i	$-0.170578\pi$
$752$	619.424	−	71.8030i	0.823702	−	0.0954827i
$753$		0			0
$754$	−104.789	+	275.179i	−0.138977	+	0.364958i
$755$		−	656.053i		−	0.868944i
$756$		0			0
$757$	163.896			0.216507			0.108253	−	0.994123i	$-0.465474\pi$
$757$	163.896			0.216507			0.108253	+	0.994123i	$0.465474\pi$
$758$	881.848	+	335.810i	1.16339	+	0.443021i
$759$		0			0
$760$	−80.0722	−	154.086i	−0.105358	−	0.202744i
$761$	512.227			0.673098			0.336549	−	0.941666i	$-0.390740\pi$
$761$	512.227			0.673098			0.336549	+	0.941666i	$0.390740\pi$
$762$		0			0
$763$		−	12.3672i		−	0.0162086i
$764$	−1011.61	+	1135.65i	−1.32409	+	1.48645i
$765$		0			0
$766$	−245.032	−	93.3089i	−0.319886	−	0.121813i
$767$		−	296.633i		−	0.386745i
$768$		0			0
$769$	1124.70			1.46255			0.731275	−	0.682083i	$-0.238926\pi$
$769$	1124.70			1.46255			0.731275	+	0.682083i	$0.238926\pi$
$770$	−584.417	+	1534.70i	−0.758983	+	1.99312i
$771$		0			0
$772$	790.583	+	704.234i	1.02407	+	0.912220i
$773$	−669.217			−0.865740			−0.432870	−	0.901456i	$-0.642499\pi$
$773$	−669.217			−0.865740			−0.432870	+	0.901456i	$0.642499\pi$
$774$		0			0
$775$		−	8.75319i		−	0.0112944i
$776$	822.776	−	427.564i	1.06028	−	0.550985i
$777$		0			0
$778$	14.5879	−	38.3083i	0.0187505	−	0.0492394i
$779$		−	302.402i		−	0.388193i
$780$		0			0
$781$	152.472			0.195226
$782$	9.98861	+	3.80369i	0.0127732	+	0.00486405i
$783$		0			0
$784$	−186.774	−	1611.25i	−0.238232	−	2.05516i
$785$	16.9373			0.0215762
$786$		0			0
$787$			1456.58i			1.85080i	0.378995	+	0.925399i	$0.376270\pi$
$787$			1456.58i			1.85080i	−0.378995	+	0.925399i	$0.623730\pi$
$788$	375.042	+	334.079i	0.475942	+	0.423958i
$789$		0			0
$790$	−2.66536	−	1.01498i	−0.00337388	−	0.00128478i
$791$			723.968i			0.915257i
$792$		0			0
$793$	−1677.50			−2.11539
$794$	−6.46080	+	16.9663i	−0.00813703	+	0.0213681i
$795$		0			0
$796$	38.3343	−	43.0347i	0.0481587	−	0.0540637i
$797$	672.133			0.843329			0.421665	−	0.906752i	$-0.361446\pi$
$797$	672.133			0.843329			0.421665	+	0.906752i	$0.361446\pi$
$798$		0			0
$799$		−	229.739i		−	0.287533i
$800$	6.27593	+	1.59211i	0.00784491	+	0.00199014i
$801$		0			0
$802$	−239.632	+	629.282i	−0.298793	+	0.784641i
$803$		−	317.267i		−	0.395103i
$804$		0			0
$805$	−55.3616			−0.0687722
$806$	−1146.28	−	436.506i	−1.42218	−	0.541571i
$807$		0			0
$808$	73.1238	−	37.9996i	0.0904998	−	0.0470291i
$809$	−517.842			−0.640102			−0.320051	−	0.947400i	$-0.603700\pi$
$809$	−517.842			−0.640102			−0.320051	+	0.947400i	$0.603700\pi$
$810$		0			0
$811$		−	264.166i		−	0.325729i	−0.986648	−	0.162865i	$-0.947927\pi$
$811$		−	264.166i		−	0.325729i	0.986648	−	0.162865i	$-0.0520734\pi$
$812$	338.837	−	380.383i	0.417286	−	0.468452i
$813$		0			0
$814$	40.5456	+	15.4399i	0.0498104	+	0.0189679i
$815$		−	849.137i		−	1.04189i
$816$		0			0
$817$	139.549			0.170806
$818$	−53.8555	+	141.426i	−0.0658380	+	0.172893i
$819$		0			0
$820$	−1031.87	−	919.166i	−1.25838	−	1.12093i
$821$	876.553			1.06766			0.533832	−	0.845590i	$-0.320751\pi$
$821$	876.553			1.06766			0.533832	+	0.845590i	$0.320751\pi$
$822$		0			0
$823$			560.045i			0.680492i	0.940337	+	0.340246i	$0.110510\pi$
$823$			560.045i			0.680492i	−0.940337	+	0.340246i	$0.889490\pi$
$824$	−408.758	−	786.586i	−0.496065	−	0.954595i
$825$		0			0
$826$	−182.627	+	479.585i	−0.221098	+	0.580612i
$827$			445.217i			0.538352i	0.963091	+	0.269176i	$0.0867513\pi$
$827$			445.217i			0.538352i	−0.963091	+	0.269176i	$0.913249\pi$
$828$		0			0
$829$	−376.283			−0.453900			−0.226950	−	0.973906i	$-0.572875\pi$
$829$	−376.283			−0.453900			−0.226950	+	0.973906i	$0.572875\pi$
$830$	232.045	+	88.3634i	0.279573	+	0.106462i
$831$		0			0
$832$	521.466	−	742.473i	0.626762	−	0.892395i
$833$	−597.598			−0.717404
$834$		0			0
$835$		−	1220.96i		−	1.46222i
$836$	175.061	+	155.940i	0.209403	+	0.186531i
$837$		0			0
$838$	1157.95	+	440.949i	1.38180	+	0.526193i
$839$		−	756.891i		−	0.902135i	−0.892490	−	0.451068i	$-0.851043\pi$
$839$		−	756.891i		−	0.902135i	0.892490	−	0.451068i	$-0.148957\pi$
$840$		0			0
$841$	−733.146			−0.871755
$842$	13.1235	−	34.4626i	0.0155861	−	0.0409295i
$843$		0			0
$844$	215.839	−	242.305i	0.255734	−	0.287091i
$845$	−159.225			−0.188432
$846$		0			0
$847$		−	733.339i		−	0.865808i
$848$	15.3204	+	132.165i	0.0180665	+	0.155855i
$849$		0			0
$850$	0.848916	−	2.22928i	0.000998725	−	0.00262268i
$851$			1.46261i			0.00171870i
$852$		0			0
$853$	−688.346			−0.806971			−0.403486	−	0.914986i	$-0.632201\pi$
$853$	−688.346			−0.806971			−0.403486	+	0.914986i	$0.632201\pi$
$854$	2712.12	+	1032.78i	3.17578	+	1.20935i
$855$		0			0
$856$	109.371	+	210.466i	0.127769	+	0.245871i
$857$	−1311.51			−1.53035			−0.765176	−	0.643822i	$-0.777348\pi$
$857$	−1311.51			−1.53035			−0.765176	+	0.643822i	$0.777348\pi$
$858$		0			0
$859$		−	947.410i		−	1.10292i	−0.834201	−	0.551461i	$-0.814071\pi$
$859$		−	947.410i		−	1.10292i	0.834201	−	0.551461i	$-0.185929\pi$
$860$	424.165	−	476.174i	0.493215	−	0.553691i
$861$		0			0
$862$	927.333	+	353.131i	1.07579	+	0.409664i
$863$			1271.16i			1.47295i	0.676463	+	0.736477i	$0.263512\pi$
$863$			1271.16i			1.47295i	−0.676463	+	0.736477i	$0.736488\pi$
$864$		0			0
$865$	310.277			0.358702
$866$	−443.907	+	1165.71i	−0.512594	+	1.34609i
$867$		0			0
$868$	1584.52	+	1411.45i	1.82548	+	1.62610i
$869$	3.85059			0.00443106
$870$		0			0
$871$			814.442i			0.935065i
$872$	−7.15910	+	3.72030i	−0.00820998	+	0.00426640i
$873$		0			0
$874$	−2.81264	+	7.38608i	−0.00321812	+	0.00845090i
$875$			1539.00i			1.75885i
$876$		0			0
$877$	−797.891			−0.909796			−0.454898	−	0.890543i	$-0.650324\pi$
$877$	−797.891			−0.909796			−0.454898	+	0.890543i	$0.650324\pi$
$878$	−196.882	−	74.9731i	−0.224239	−	0.0853908i
$879$		0			0
$880$	1064.21	−	123.362i	1.20933	−	0.140185i
$881$	440.769			0.500305			0.250153	−	0.968206i	$-0.419519\pi$
$881$	440.769			0.500305			0.250153	+	0.968206i	$0.419519\pi$
$882$		0			0
$883$			148.904i			0.168634i	0.996439	+	0.0843170i	$0.0268708\pi$
$883$			148.904i			0.168634i	−0.996439	+	0.0843170i	$0.973129\pi$
$884$	−249.603	−	222.341i	−0.282356	−	0.251517i
$885$		0			0
$886$	211.819	+	80.6613i	0.239074	+	0.0910399i
$887$		−	607.820i		−	0.685254i	−0.939472	−	0.342627i	$-0.888683\pi$
$887$		−	607.820i		−	0.685254i	0.939472	−	0.342627i	$-0.111317\pi$
$888$		0			0
$889$	2568.51			2.88921
$890$	154.892	−	406.752i	0.174036	−	0.457025i
$891$		0			0
$892$	−484.081	+	543.436i	−0.542691	+	0.609234i
$893$	169.880			0.190236
$894$		0			0
$895$		−	642.781i		−	0.718191i
$896$	−1300.20	+	879.352i	−1.45112	+	0.981420i
$897$		0			0
$898$	294.648	−	773.756i	0.328116	−	0.861643i
$899$			449.276i			0.499751i
$900$		0			0
$901$	49.0187			0.0544047
$902$	1743.55	+	663.949i	1.93298	+	0.736085i
$903$		0			0
$904$	419.091	−	217.785i	0.463596	−	0.240913i
$905$	989.356			1.09321
$906$		0			0
$907$		−	131.690i		−	0.145193i	−0.997361	−	0.0725966i	$-0.976871\pi$
$907$		−	131.690i		−	0.145193i	0.997361	−	0.0725966i	$-0.0231286\pi$
$908$	1125.64	−	1263.66i	1.23969	−	1.39170i
$909$		0			0
$910$	1618.05	+	616.158i	1.77808	+	0.677097i
$911$		−	645.749i		−	0.708835i	−0.935087	−	0.354417i	$-0.884679\pi$
$911$		−	645.749i		−	0.708835i	0.935087	−	0.354417i	$-0.115321\pi$
$912$		0			0
$913$	−335.230			−0.367175
$914$	−227.917	+	598.519i	−0.249363	+	0.654835i
$915$		0			0
$916$	−1076.78	−	959.171i	−1.17552	−	1.04713i
$917$	−565.066			−0.616211
$918$		0			0
$919$		−	745.172i		−	0.810851i	−0.914128	−	0.405425i	$-0.867123\pi$
$919$		−	745.172i		−	0.810851i	0.914128	−	0.405425i	$-0.132877\pi$
$920$	16.6540	+	32.0478i	0.0181021	+	0.0348345i
$921$		0			0
$922$	−327.530	+	860.105i	−0.355239	+	0.932869i
$923$		−	160.753i		−	0.174163i
$924$		0			0
$925$	0.326429			0.000352897
$926$	604.128	+	230.054i	0.652406	+	0.248438i
$927$		0			0
$928$	−322.126	−	81.7185i	−0.347118	−	0.0880588i
$929$	−156.417			−0.168372			−0.0841859	−	0.996450i	$-0.526829\pi$
$929$	−156.417			−0.168372			−0.0841859	+	0.996450i	$0.526829\pi$
$930$		0			0
$931$		−	441.894i		−	0.474644i
$932$	6.36311	+	5.66812i	0.00682737	+	0.00608167i
$933$		0			0
$934$	−978.180	−	372.494i	−1.04730	−	0.398815i
$935$		−	394.707i		−	0.422146i
$936$		0			0
$937$	−1489.44			−1.58959			−0.794793	−	0.606880i	$-0.792421\pi$
$937$	−1489.44			−1.58959			−0.794793	+	0.606880i	$0.792421\pi$
$938$	501.425	−	1316.76i	0.534568	−	1.40379i
$939$		0			0
$940$	516.359	−	579.673i	0.549318	−	0.616673i
$941$	985.993			1.04781			0.523907	−	0.851775i	$-0.324474\pi$
$941$	985.993			1.04781			0.523907	+	0.851775i	$0.324474\pi$
$942$		0			0
$943$			62.8956i			0.0666974i
$944$	332.561	−	38.5501i	0.352289	−	0.0408370i
$945$		0			0
$946$	−306.391	+	804.592i	−0.323880	+	0.850520i
$947$		−	1612.77i		−	1.70304i	−0.524326	−	0.851518i	$-0.675683\pi$
$947$		−	1612.77i		−	1.70304i	0.524326	−	0.851518i	$-0.324317\pi$
$948$		0			0
$949$	−334.499			−0.352475
$950$	1.64844	+	0.627731i	0.00173520	+	0.000660769i
$951$		0			0
$952$	266.661	+	513.144i	0.280106	+	0.539017i
$953$	1434.39			1.50513			0.752565	−	0.658518i	$-0.228816\pi$
$953$	1434.39			1.50513			0.752565	+	0.658518i	$0.228816\pi$
$954$		0			0
$955$			1893.38i			1.98259i
$956$	−609.080	+	683.763i	−0.637113	+	0.715233i
$957$		0			0
$958$	−856.137	−	326.019i	−0.893671	−	0.340312i
$959$		−	2529.48i		−	2.63763i
$960$		0			0
$961$	−910.496			−0.947447
$962$	16.2785	−	42.7478i	0.0169215	−	0.0444364i
$963$		0			0
$964$	−732.173	−	652.203i	−0.759516	−	0.676559i
$965$	1318.08			1.36589
$966$		0			0
$967$		−	920.021i		−	0.951418i	−0.879603	−	0.475709i	$-0.842192\pi$
$967$		−	920.021i		−	0.951418i	0.879603	−	0.475709i	$-0.157808\pi$
$968$	−424.516	+	220.604i	−0.438549	+	0.227897i
$969$		0			0
$970$	410.802	−	1078.78i	0.423507	−	1.11214i
$971$			345.002i			0.355306i	0.984093	+	0.177653i	$0.0568504\pi$
$971$			345.002i			0.355306i	−0.984093	+	0.177653i	$0.943150\pi$
$972$		0			0
$973$	1537.21			1.57987
$974$	93.2192	+	35.4981i	0.0957076	+	0.0364457i
$975$		0			0
$976$	−218.006	−	1880.68i	−0.223367	−	1.92692i
$977$	−254.828			−0.260827			−0.130413	−	0.991460i	$-0.541630\pi$
$977$	−254.828			−0.260827			−0.130413	+	0.991460i	$0.541630\pi$
$978$		0			0
$979$			587.625i			0.600230i
$980$	−1507.85	−	1343.16i	−1.53862	−	1.37057i
$981$		0			0
$982$	−712.795	−	271.434i	−0.725861	−	0.276410i
$983$		−	712.458i		−	0.724779i	−0.932027	−	0.362390i	$-0.881961\pi$
$983$		−	712.458i		−	0.724779i	0.932027	−	0.362390i	$-0.118039\pi$
$984$		0			0
$985$	625.279			0.634801
$986$	−43.5724	+	114.423i	−0.0441911	+	0.116047i
$987$		0			0
$988$	164.410	−	184.569i	0.166407	−	0.186811i
$989$	−29.0243			−0.0293471
$990$		0			0
$991$			1719.28i			1.73490i	0.497526	+	0.867449i	$0.334242\pi$
$991$			1719.28i			1.73490i	−0.497526	+	0.867449i	$0.665758\pi$
$992$	340.405	−	1341.84i	0.343151	−	1.35266i
$993$		0			0
$994$	−98.9701	+	259.899i	−0.0995675	+	0.261467i
$995$		−	71.7485i		−	0.0721091i
$996$		0			0
$997$	488.006			0.489475			0.244737	−	0.969589i	$-0.421298\pi$
$997$	488.006			0.489475			0.244737	+	0.969589i	$0.421298\pi$
$998$	−358.053	−	136.347i	−0.358770	−	0.136621i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.b.343.6		14
3.2	odd	2		76.3.b.b.39.9	✓	14
4.3	odd	2	inner	684.3.g.b.343.5		14
12.11	even	2		76.3.b.b.39.10	yes	14
24.5	odd	2		1216.3.d.d.191.12		14
24.11	even	2		1216.3.d.d.191.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.b.39.9	✓	14	3.2	odd	2
76.3.b.b.39.10	yes	14	12.11	even	2
684.3.g.b.343.5		14	4.3	odd	2	inner
684.3.g.b.343.6		14	1.1	even	1	trivial
1216.3.d.d.191.3		14	24.11	even	2
1216.3.d.d.191.12		14	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.711746 + 1.86907i) q^{2} +(-2.98683 - 2.66060i) q^{4} -4.97973 q^{5} +12.2628i q^{7} +(7.09872 - 3.68892i) q^{8} +O(q^{10})\)	\(q+(-0.711746 + 1.86907i) q^{2} +(-2.98683 - 2.66060i) q^{4} -4.97973 q^{5} +12.2628i q^{7} +(7.09872 - 3.68892i) q^{8} +(3.54430 - 9.30745i) q^{10} +13.4463i q^{11} +14.1766 q^{13} +(-22.9201 - 8.72803i) q^{14} +(1.84237 + 15.8936i) q^{16} +5.89478 q^{17} +4.35890i q^{19} +(14.8736 + 13.2491i) q^{20} +(-25.1320 - 9.57032i) q^{22} -0.906592i q^{23} -0.202335 q^{25} +(-10.0901 + 26.4969i) q^{26} +(32.6266 - 36.6271i) q^{28} +10.3853 q^{29} +43.2608i q^{31} +(-31.0175 - 7.86868i) q^{32} +(-4.19559 + 11.0178i) q^{34} -61.0656i q^{35} -1.61331 q^{37} +(-8.14708 - 3.10243i) q^{38} +(-35.3497 + 18.3698i) q^{40} -69.3758 q^{41} -32.0147i q^{43} +(35.7752 - 40.1617i) q^{44} +(1.69448 + 0.645264i) q^{46} -38.9732i q^{47} -101.377 q^{49} +(0.144011 - 0.378179i) q^{50} +(-42.3430 - 37.7182i) q^{52} +8.31560 q^{53} -66.9586i q^{55} +(45.2367 + 87.0505i) q^{56} +(-7.39169 + 19.4108i) q^{58} -20.9242i q^{59} -118.329 q^{61} +(-80.8574 - 30.7907i) q^{62} +(36.7837 - 52.3733i) q^{64} -70.5953 q^{65} +57.4499i q^{67} +(-17.6067 - 15.6837i) q^{68} +(114.136 + 43.4632i) q^{70} -11.3393i q^{71} -23.5952 q^{73} +(1.14827 - 3.01539i) q^{74} +(11.5973 - 13.0193i) q^{76} -164.889 q^{77} -0.286369i q^{79} +(-9.17448 - 79.1456i) q^{80} +(49.3780 - 129.668i) q^{82} +24.9311i q^{83} -29.3544 q^{85} +(59.8376 + 22.7863i) q^{86} +(49.6022 + 95.4512i) q^{88} +43.7018 q^{89} +173.845i q^{91} +(-2.41208 + 2.70784i) q^{92} +(72.8436 + 27.7390i) q^{94} -21.7061i q^{95} +115.905 q^{97} +(72.1549 - 189.481i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8	\( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8 - 12 * q^10 + 54 * q^13 - 30 * q^14 + 58 * q^16 - 34 * q^17 - 32 * q^20 + 36 * q^22 - 86 * q^25 + 16 * q^26 + 18 * q^28 - 54 * q^29 - 72 * q^32 - 82 * q^34 + 100 * q^37 - 148 * q^40 - 224 * q^41 + 96 * q^44 + 46 * q^46 - 220 * q^49 + 58 * q^50 - 288 * q^52 - 14 * q^53 - 12 * q^56 - 72 * q^58 + 28 * q^61 - 396 * q^62 - 118 * q^64 + 472 * q^65 - 30 * q^68 + 156 * q^70 + 70 * q^73 + 224 * q^74 - 228 * q^77 + 348 * q^80 - 400 * q^82 + 48 * q^85 + 124 * q^86 + 472 * q^88 - 126 * q^92 - 88 * q^94 + 308 * q^97 - 68 * q^98

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