LMFDB - Embedded newform 684.3.g.b.343.8

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			343.8
Root			$0.645572 - 1.89294i$ of defining polynomial
Character	$\chi$	$=$	684.343
Dual form			684.3.g.b.343.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.645572 + 1.89294i) q^{2} +(-3.16647 - 2.44406i) q^{4} +2.38184 q^{5} -12.3764i q^{7} +(6.67066 - 4.41614i) q^{8} +O(q^{10})$	\(q+(-0.645572 + 1.89294i) q^{2} +(-3.16647 - 2.44406i) q^{4} +2.38184 q^{5} -12.3764i q^{7} +(6.67066 - 4.41614i) q^{8} +(-1.53765 + 4.50868i) q^{10} -9.15034i q^{11} +0.940214 q^{13} +(23.4279 + 7.98989i) q^{14} +(4.05310 + 15.4781i) q^{16} -27.1792 q^{17} +4.35890i q^{19} +(-7.54202 - 5.82136i) q^{20} +(17.3211 + 5.90721i) q^{22} +13.8004i q^{23} -19.3269 q^{25} +(-0.606976 + 1.77977i) q^{26} +(-30.2488 + 39.1897i) q^{28} -49.8488 q^{29} +24.6752i q^{31} +(-31.9158 - 2.31995i) q^{32} +(17.5461 - 51.4487i) q^{34} -29.4787i q^{35} -27.3757 q^{37} +(-8.25115 - 2.81398i) q^{38} +(15.8884 - 10.5185i) q^{40} +38.4024 q^{41} +41.2108i q^{43} +(-22.3640 + 28.9743i) q^{44} +(-26.1234 - 8.90917i) q^{46} +45.1842i q^{47} -104.176 q^{49} +(12.4769 - 36.5846i) q^{50} +(-2.97716 - 2.29794i) q^{52} +19.9964 q^{53} -21.7946i q^{55} +(-54.6561 - 82.5591i) q^{56} +(32.1810 - 94.3610i) q^{58} -34.7054i q^{59} +33.2008 q^{61} +(-46.7088 - 15.9296i) q^{62} +(24.9955 - 58.9171i) q^{64} +2.23944 q^{65} -3.48192i q^{67} +(86.0622 + 66.4277i) q^{68} +(55.8015 + 19.0306i) q^{70} -88.8887i q^{71} -19.8573 q^{73} +(17.6730 - 51.8206i) q^{74} +(10.6534 - 13.8023i) q^{76} -113.249 q^{77} +51.7431i q^{79} +(9.65383 + 36.8664i) q^{80} +(-24.7915 + 72.6936i) q^{82} -6.62943i q^{83} -64.7365 q^{85} +(-78.0097 - 26.6046i) q^{86} +(-40.4091 - 61.0388i) q^{88} -31.5105 q^{89} -11.6365i q^{91} +(33.7291 - 43.6987i) q^{92} +(-85.5312 - 29.1697i) q^{94} +10.3822i q^{95} +159.282 q^{97} +(67.2534 - 197.200i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.645572	+	1.89294i	−0.322786	+	0.946472i
$2$	−0.645572	+	1.89294i	−0.322786	+	0.946472i
$3$		0			0
$3$		0			0
$4$	−3.16647	−	2.44406i	−0.791618	−	0.611016i
$5$	2.38184			0.476367			0.238184	−	0.971220i	$-0.423448\pi$
$5$	2.38184			0.476367			0.238184	+	0.971220i	$0.423448\pi$
$6$		0			0
$7$		−	12.3764i		−	1.76806i	−0.467427	−	0.884032i	$-0.654819\pi$
$7$		−	12.3764i		−	1.76806i	0.467427	−	0.884032i	$-0.345181\pi$
$8$	6.67066	−	4.41614i	0.833833	−	0.552017i
$9$		0			0
$10$	−1.53765	+	4.50868i	−0.153765	+	0.450868i
$11$		−	9.15034i		−	0.831849i	−0.909399	−	0.415925i	$-0.863458\pi$
$11$		−	9.15034i		−	0.831849i	0.909399	−	0.415925i	$-0.136542\pi$
$12$		0			0
$13$	0.940214			0.0723242			0.0361621	−	0.999346i	$-0.488487\pi$
$13$	0.940214			0.0723242			0.0361621	+	0.999346i	$0.488487\pi$
$14$	23.4279	+	7.98989i	1.67342	+	0.570706i
$15$		0			0
$16$	4.05310	+	15.4781i	0.253319	+	0.967383i
$17$	−27.1792			−1.59878			−0.799388	−	0.600814i	$-0.794843\pi$
$17$	−27.1792			−1.59878			−0.799388	+	0.600814i	$0.794843\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	−7.54202	−	5.82136i	−0.377101	−	0.291068i
$21$		0			0
$22$	17.3211	+	5.90721i	0.787322	+	0.268509i
$23$			13.8004i			0.600018i	0.953936	+	0.300009i	$0.0969898\pi$
$23$			13.8004i			0.600018i	−0.953936	+	0.300009i	$0.903010\pi$
$24$		0			0
$25$	−19.3269			−0.773074
$26$	−0.606976	+	1.77977i	−0.0233452	+	0.0684528i
$27$		0			0
$28$	−30.2488	+	39.1897i	−1.08032	+	1.39963i
$29$	−49.8488			−1.71892			−0.859462	−	0.511200i	$-0.829201\pi$
$29$	−49.8488			−1.71892			−0.859462	+	0.511200i	$0.829201\pi$
$30$		0			0
$31$			24.6752i			0.795974i	0.917391	+	0.397987i	$0.130291\pi$
$31$			24.6752i			0.795974i	−0.917391	+	0.397987i	$0.869709\pi$
$32$	−31.9158	−	2.31995i	−0.997369	−	0.0724986i
$33$		0			0
$34$	17.5461	−	51.4487i	0.516063	−	1.51320i
$35$		−	29.4787i		−	0.842248i
$36$		0			0
$37$	−27.3757			−0.739883			−0.369942	−	0.929055i	$-0.620622\pi$
$37$	−27.3757			−0.739883			−0.369942	+	0.929055i	$0.620622\pi$
$38$	−8.25115	−	2.81398i	−0.217136	−	0.0740522i
$39$		0			0
$40$	15.8884	−	10.5185i	0.397211	−	0.262963i
$41$	38.4024			0.936644			0.468322	−	0.883558i	$-0.344859\pi$
$41$	38.4024			0.936644			0.468322	+	0.883558i	$0.344859\pi$
$42$		0			0
$43$			41.2108i			0.958391i	0.877708	+	0.479195i	$0.159071\pi$
$43$			41.2108i			0.958391i	−0.877708	+	0.479195i	$0.840929\pi$
$44$	−22.3640	+	28.9743i	−0.508273	+	0.658507i
$45$		0			0
$46$	−26.1234	−	8.90917i	−0.567901	−	0.193678i
$47$			45.1842i			0.961367i	0.876894	+	0.480683i	$0.159611\pi$
$47$			45.1842i			0.961367i	−0.876894	+	0.480683i	$0.840389\pi$
$48$		0			0
$49$	−104.176			−2.12605
$50$	12.4769	−	36.5846i	0.249538	−	0.731693i
$51$		0			0
$52$	−2.97716	−	2.29794i	−0.0572531	−	0.0441912i
$53$	19.9964			0.377291			0.188646	−	0.982045i	$-0.439590\pi$
$53$	19.9964			0.377291			0.188646	+	0.982045i	$0.439590\pi$
$54$		0			0
$55$		−	21.7946i		−	0.396266i
$56$	−54.6561	−	82.5591i	−0.976001	−	1.47427i
$57$		0			0
$58$	32.1810	−	94.3610i	0.554845	−	1.62691i
$59$		−	34.7054i		−	0.588228i	−0.955770	−	0.294114i	$-0.904976\pi$
$59$		−	34.7054i		−	0.588228i	0.955770	−	0.294114i	$-0.0950245\pi$
$60$		0			0
$61$	33.2008			0.544276			0.272138	−	0.962258i	$-0.412269\pi$
$61$	33.2008			0.544276			0.272138	+	0.962258i	$0.412269\pi$
$62$	−46.7088	−	15.9296i	−0.753367	−	0.256929i
$63$		0			0
$64$	24.9955	−	58.9171i	0.390555	−	0.920580i
$65$	2.23944			0.0344529
$66$		0			0
$67$		−	3.48192i		−	0.0519690i	−0.999662	−	0.0259845i	$-0.991728\pi$
$67$		−	3.48192i		−	0.0519690i	0.999662	−	0.0259845i	$-0.00827205\pi$
$68$	86.0622	+	66.4277i	1.26562	+	0.976878i
$69$		0			0
$70$	55.8015	+	19.0306i	0.797164	+	0.271866i
$71$		−	88.8887i		−	1.25195i	−0.779842	−	0.625977i	$-0.784700\pi$
$71$		−	88.8887i		−	1.25195i	0.779842	−	0.625977i	$-0.215300\pi$
$72$		0			0
$73$	−19.8573			−0.272018			−0.136009	−	0.990708i	$-0.543428\pi$
$73$	−19.8573			−0.272018			−0.136009	+	0.990708i	$0.543428\pi$
$74$	17.6730	−	51.8206i	0.238824	−	0.700279i
$75$		0			0
$76$	10.6534	−	13.8023i	0.140177	−	0.181610i
$77$	−113.249			−1.47076
$78$		0			0
$79$			51.7431i			0.654976i	0.944855	+	0.327488i	$0.106202\pi$
$79$			51.7431i			0.654976i	−0.944855	+	0.327488i	$0.893798\pi$
$80$	9.65383	+	36.8664i	0.120673	+	0.460830i
$81$		0			0
$82$	−24.7915	+	72.6936i	−0.302336	+	0.886507i
$83$		−	6.62943i		−	0.0798727i	−0.999202	−	0.0399363i	$-0.987284\pi$
$83$		−	6.62943i		−	0.0798727i	0.999202	−	0.0399363i	$-0.0127155\pi$
$84$		0			0
$85$	−64.7365			−0.761605
$86$	−78.0097	−	26.6046i	−0.907090	−	0.309355i
$87$		0			0
$88$	−40.4091	−	61.0388i	−0.459195	−	0.693623i
$89$	−31.5105			−0.354051			−0.177025	−	0.984206i	$-0.556647\pi$
$89$	−31.5105			−0.354051			−0.177025	+	0.984206i	$0.556647\pi$
$90$		0			0
$91$		−	11.6365i		−	0.127874i
$92$	33.7291	−	43.6987i	0.366621	−	0.474986i
$93$		0			0
$94$	−85.5312	−	29.1697i	−0.909907	−	0.310316i
$95$			10.3822i			0.109286i
$96$		0			0
$97$	159.282			1.64208			0.821039	−	0.570873i	$-0.193395\pi$
$97$	159.282			1.64208			0.821039	+	0.570873i	$0.193395\pi$
$98$	67.2534	−	197.200i	0.686259	−	2.01225i
$99$		0			0
$100$	61.1980	+	47.2361i	0.611980	+	0.472361i
$101$	−35.1573			−0.348092			−0.174046	−	0.984738i	$-0.555684\pi$
$101$	−35.1573			−0.348092			−0.174046	+	0.984738i	$0.555684\pi$
$102$		0			0
$103$		−	117.214i		−	1.13800i	−0.822339	−	0.568998i	$-0.807331\pi$
$103$		−	117.214i		−	1.13800i	0.822339	−	0.568998i	$-0.192669\pi$
$104$	6.27185	−	4.15211i	0.0603063	−	0.0399242i
$105$		0			0
$106$	−12.9092	+	37.8522i	−0.121784	+	0.357096i
$107$		−	191.832i		−	1.79282i	−0.443228	−	0.896409i	$-0.646167\pi$
$107$		−	191.832i		−	1.79282i	0.443228	−	0.896409i	$-0.353833\pi$
$108$		0			0
$109$	−183.807			−1.68630			−0.843152	−	0.537675i	$-0.819303\pi$
$109$	−183.807			−1.68630			−0.843152	+	0.537675i	$0.819303\pi$
$110$	41.2560	+	14.0700i	0.375055	+	0.127909i
$111$		0			0
$112$	191.564	−	50.1630i	1.71039	−	0.447884i
$113$	−72.9718			−0.645768			−0.322884	−	0.946439i	$-0.604652\pi$
$113$	−72.9718			−0.645768			−0.322884	+	0.946439i	$0.604652\pi$
$114$		0			0
$115$			32.8704i			0.285829i
$116$	157.845	+	121.834i	1.36073	+	1.05029i
$117$		0			0
$118$	65.6954	+	22.4049i	0.556741	+	0.189872i
$119$			336.382i			2.82674i
$120$		0			0
$121$	37.2713			0.308027
$122$	−21.4335	+	62.8473i	−0.175685	+	0.515142i
$123$		0			0
$124$	60.3078	−	78.1334i	0.486353	−	0.630108i
$125$	−105.579			−0.844635
$126$		0			0
$127$		−	11.4215i		−	0.0899331i	−0.998988	−	0.0449665i	$-0.985682\pi$
$127$		−	11.4215i		−	0.0899331i	0.998988	−	0.0449665i	$-0.0143181\pi$
$128$	95.3904	+	85.3503i	0.745237	+	0.666799i
$129$		0			0
$130$	−1.44572	+	4.23913i	−0.0111209	+	0.0326087i
$131$			36.9512i			0.282070i	0.990005	+	0.141035i	$0.0450430\pi$
$131$			36.9512i			0.282070i	−0.990005	+	0.141035i	$0.954957\pi$
$132$		0			0
$133$	53.9477			0.405622
$134$	6.59108	+	2.24783i	0.0491872	+	0.0167749i
$135$		0			0
$136$	−181.303	+	120.027i	−1.33311	+	0.882552i
$137$	162.786			1.18822			0.594109	−	0.804385i	$-0.297505\pi$
$137$	162.786			1.18822			0.594109	+	0.804385i	$0.297505\pi$
$138$		0			0
$139$		−	229.233i		−	1.64916i	−0.565744	−	0.824581i	$-0.691411\pi$
$139$		−	229.233i		−	1.64916i	0.565744	−	0.824581i	$-0.308589\pi$
$140$	−72.0478	+	93.3434i	−0.514627	+	0.666739i
$141$		0			0
$142$	168.261	+	57.3841i	1.18494	+	0.404113i
$143$		−	8.60328i		−	0.0601628i
$144$		0			0
$145$	−118.732			−0.818839
$146$	12.8193	−	37.5887i	0.0878035	−	0.257457i
$147$		0			0
$148$	86.6844	+	66.9079i	0.585705	+	0.452081i
$149$	110.328			0.740459			0.370229	−	0.928940i	$-0.379279\pi$
$149$	110.328			0.740459			0.370229	+	0.928940i	$0.379279\pi$
$150$		0			0
$151$		−	104.737i		−	0.693621i	−0.937935	−	0.346810i	$-0.887265\pi$
$151$		−	104.737i		−	0.693621i	0.937935	−	0.346810i	$-0.112735\pi$
$152$	19.2495	+	29.0767i	0.126641	+	0.191294i
$153$		0			0
$154$	73.1102	−	214.373i	0.474742	−	1.39204i
$155$			58.7723i			0.379176i
$156$		0			0
$157$	−147.695			−0.940732			−0.470366	−	0.882471i	$-0.655878\pi$
$157$	−147.695			−0.940732			−0.470366	+	0.882471i	$0.655878\pi$
$158$	−97.9468	−	33.4039i	−0.619917	−	0.211417i
$159$		0			0
$160$	−76.0182	−	5.52575i	−0.475114	−	0.0345360i
$161$	170.800			1.06087
$162$		0			0
$163$			183.104i			1.12334i	0.827363	+	0.561668i	$0.189840\pi$
$163$			183.104i			1.12334i	−0.827363	+	0.561668i	$0.810160\pi$
$164$	−121.600	−	93.8580i	−0.741465	−	0.572305i
$165$		0			0
$166$	12.5491	+	4.27978i	0.0755973	+	0.0257818i
$167$		−	214.501i		−	1.28444i	−0.766522	−	0.642218i	$-0.778014\pi$
$167$		−	214.501i		−	1.28444i	0.766522	−	0.642218i	$-0.221986\pi$
$168$		0			0
$169$	−168.116			−0.994769
$170$	41.7921	−	122.542i	0.245836	−	0.720838i
$171$		0			0
$172$	100.722	−	130.493i	0.585592	−	0.758680i
$173$	−27.1849			−0.157138			−0.0785692	−	0.996909i	$-0.525035\pi$
$173$	−27.1849			−0.157138			−0.0785692	+	0.996909i	$0.525035\pi$
$174$		0			0
$175$			239.198i			1.36684i
$176$	141.630	−	37.0873i	0.804717	−	0.210723i
$177$		0			0
$178$	20.3423	−	59.6476i	0.114283	−	0.335099i
$179$		−	185.284i		−	1.03511i	−0.855651	−	0.517553i	$-0.826843\pi$
$179$		−	185.284i		−	1.03511i	0.855651	−	0.517553i	$-0.173157\pi$
$180$		0			0
$181$	17.0150			0.0940053			0.0470026	−	0.998895i	$-0.485033\pi$
$181$	17.0150			0.0940053			0.0470026	+	0.998895i	$0.485033\pi$
$182$	22.0273	+	7.51221i	0.121029	+	0.0412759i
$183$		0			0
$184$	60.9445	+	92.0580i	0.331220	+	0.500315i
$185$	−65.2044			−0.352456
$186$		0			0
$187$			248.699i			1.32994i
$188$	110.433	−	143.075i	0.587411	−	0.761036i
$189$		0			0
$190$	−19.6529	−	6.70245i	−0.103436	−	0.0352761i
$191$			2.41797i			0.0126595i	0.999980	+	0.00632976i	$0.00201484\pi$
$191$			2.41797i			0.0126595i	−0.999980	+	0.00632976i	$0.997985\pi$
$192$		0			0
$193$	−150.712			−0.780892			−0.390446	−	0.920626i	$-0.627679\pi$
$193$	−150.712			−0.780892			−0.390446	+	0.920626i	$0.627679\pi$
$194$	−102.828	+	301.511i	−0.530040	+	1.55418i
$195$		0			0
$196$	329.872	+	254.614i	1.68302	+	1.29905i
$197$	−268.203			−1.36144			−0.680718	−	0.732545i	$-0.738332\pi$
$197$	−268.203			−1.36144			−0.680718	+	0.732545i	$0.738332\pi$
$198$		0			0
$199$		−	308.615i		−	1.55083i	−0.631452	−	0.775415i	$-0.717541\pi$
$199$		−	308.615i		−	1.55083i	0.631452	−	0.775415i	$-0.282459\pi$
$200$	−128.923	+	85.3500i	−0.644615	+	0.426750i
$201$		0			0
$202$	22.6966	−	66.5507i	0.112359	−	0.329459i
$203$			616.951i			3.03917i
$204$		0			0
$205$	91.4683			0.446187
$206$	221.879	+	75.6698i	1.07708	+	0.367329i
$207$		0			0
$208$	3.81078	+	14.5528i	0.0183211	+	0.0699652i
$209$	39.8854			0.190839
$210$		0			0
$211$			334.011i			1.58299i	0.611176	+	0.791495i	$0.290697\pi$
$211$			334.011i			1.58299i	−0.611176	+	0.791495i	$0.709303\pi$
$212$	−63.3182	−	48.8726i	−0.298671	−	0.230531i
$213$		0			0
$214$	363.126	+	123.841i	1.69685	+	0.578697i
$215$			98.1574i			0.456546i
$216$		0			0
$217$	305.391			1.40733
$218$	118.661	−	347.937i	0.544316	−	1.59604i
$219$		0			0
$220$	−53.2675	+	69.0121i	−0.242125	+	0.313691i
$221$	−25.5543			−0.115630
$222$		0			0
$223$			290.142i			1.30108i	0.759470	+	0.650542i	$0.225458\pi$
$223$			290.142i			1.30108i	−0.759470	+	0.650542i	$0.774542\pi$
$224$	−28.7128	+	395.004i	−0.128182	+	1.76341i
$225$		0			0
$226$	47.1086	−	138.132i	0.208445	−	0.611202i
$227$		−	76.2561i		−	0.335930i	−0.985793	−	0.167965i	$-0.946280\pi$
$227$		−	76.2561i		−	0.335930i	0.985793	−	0.167965i	$-0.0537195\pi$
$228$		0			0
$229$	−212.780			−0.929169			−0.464585	−	0.885529i	$-0.653796\pi$
$229$	−212.780			−0.929169			−0.464585	+	0.885529i	$0.653796\pi$
$230$	−62.2218	−	21.2202i	−0.270529	−	0.0922617i
$231$		0			0
$232$	−332.525	+	220.139i	−1.43330	+	0.948875i
$233$	108.504			0.465680			0.232840	−	0.972515i	$-0.425198\pi$
$233$	108.504			0.465680			0.232840	+	0.972515i	$0.425198\pi$
$234$		0			0
$235$			107.622i			0.457964i
$236$	−84.8223	+	109.894i	−0.359416	+	0.465652i
$237$		0			0
$238$	−636.752	−	217.159i	−2.67543	−	0.912432i
$239$		−	14.5126i		−	0.0607222i	−0.999539	−	0.0303611i	$-0.990334\pi$
$239$		−	14.5126i		−	0.0607222i	0.999539	−	0.0303611i	$-0.00966573\pi$
$240$		0			0
$241$	−278.238			−1.15451			−0.577257	−	0.816563i	$-0.695877\pi$
$241$	−278.238			−1.15451			−0.577257	+	0.816563i	$0.695877\pi$
$242$	−24.0613	+	70.5524i	−0.0994268	+	0.291539i
$243$		0			0
$244$	−105.130	−	81.1449i	−0.430859	−	0.332561i
$245$	−248.131			−1.01278
$246$		0			0
$247$			4.09830i			0.0165923i
$248$	108.969	+	164.600i	0.439391	+	0.663710i
$249$		0			0
$250$	68.1591	−	199.856i	0.272636	−	0.799423i
$251$			344.252i			1.37152i	0.727828	+	0.685760i	$0.240530\pi$
$251$			344.252i			1.37152i	−0.727828	+	0.685760i	$0.759470\pi$
$252$		0			0
$253$	126.279			0.499125
$254$	21.6203	+	7.37340i	0.0851191	+	0.0290291i
$255$		0			0
$256$	−223.145	+	125.469i	−0.871659	+	0.490113i
$257$	−50.0048			−0.194571			−0.0972856	−	0.995257i	$-0.531016\pi$
$257$	−50.0048			−0.194571			−0.0972856	+	0.995257i	$0.531016\pi$
$258$		0			0
$259$			338.814i			1.30816i
$260$	−7.09112	−	5.47333i	−0.0272735	−	0.0210513i
$261$		0			0
$262$	−69.9465	−	23.8546i	−0.266971	−	0.0910483i
$263$			155.273i			0.590391i	0.955437	+	0.295195i	$0.0953848\pi$
$263$			155.273i			0.590391i	−0.955437	+	0.295195i	$0.904615\pi$
$264$		0			0
$265$	47.6283			0.179729
$266$	−34.8271	+	102.120i	−0.130929	+	0.383909i
$267$		0			0
$268$	−8.51004	+	11.0254i	−0.0317539	+	0.0411396i
$269$	457.281			1.69993			0.849964	−	0.526840i	$-0.176623\pi$
$269$	457.281			1.69993			0.849964	+	0.526840i	$0.176623\pi$
$270$		0			0
$271$		−	349.279i		−	1.28885i	−0.764666	−	0.644427i	$-0.777096\pi$
$271$		−	349.279i		−	1.28885i	0.764666	−	0.644427i	$-0.222904\pi$
$272$	−110.160	−	420.683i	−0.405000	−	1.54663i
$273$		0			0
$274$	−105.090	+	308.144i	−0.383540	+	1.12461i
$275$			176.847i			0.643081i
$276$		0			0
$277$	−108.548			−0.391870			−0.195935	−	0.980617i	$-0.562774\pi$
$277$	−108.548			−0.391870			−0.195935	+	0.980617i	$0.562774\pi$
$278$	433.926	+	147.987i	1.56089	+	0.532326i
$279$		0			0
$280$	−130.182	−	196.642i	−0.464935	−	0.702294i
$281$	−190.452			−0.677767			−0.338883	−	0.940828i	$-0.610049\pi$
$281$	−190.452			−0.677767			−0.338883	+	0.940828i	$0.610049\pi$
$282$		0			0
$283$		−	289.950i		−	1.02456i	−0.858819	−	0.512279i	$-0.828802\pi$
$283$		−	289.950i		−	1.02456i	0.858819	−	0.512279i	$-0.171198\pi$
$284$	−217.250	+	281.464i	−0.764964	+	0.991069i
$285$		0			0
$286$	16.2855	+	5.55404i	0.0569424	+	0.0194197i
$287$		−	475.285i		−	1.65605i
$288$		0			0
$289$	449.709			1.55609
$290$	76.6499	−	224.752i	0.264310	−	0.775009i
$291$		0			0
$292$	62.8776	+	48.5325i	0.215334	+	0.166207i
$293$	177.881			0.607102			0.303551	−	0.952815i	$-0.401828\pi$
$293$	177.881			0.607102			0.303551	+	0.952815i	$0.401828\pi$
$294$		0			0
$295$		−	82.6627i		−	0.280212i
$296$	−182.614	+	120.895i	−0.616939	+	0.408428i
$297$		0			0
$298$	−71.2249	+	208.845i	−0.239010	+	0.700823i
$299$			12.9754i			0.0433958i
$300$		0			0
$301$	510.043			1.69450
$302$	198.261	+	67.6151i	0.656492	+	0.223891i
$303$		0			0
$304$	−67.4676	+	17.6671i	−0.221933	+	0.0581153i
$305$	79.0790			0.259275
$306$		0			0
$307$		−	554.295i		−	1.80552i	−0.430143	−	0.902761i	$-0.641537\pi$
$307$		−	554.295i		−	1.80552i	0.430143	−	0.902761i	$-0.358463\pi$
$308$	358.599	+	276.787i	1.16428	+	0.898659i
$309$		0			0
$310$	−111.253	−	37.9418i	−0.358880	−	0.122393i
$311$		−	67.7563i		−	0.217866i	−0.994049	−	0.108933i	$-0.965257\pi$
$311$		−	67.7563i		−	0.217866i	0.994049	−	0.108933i	$-0.0347434\pi$
$312$		0			0
$313$	447.248			1.42891			0.714454	−	0.699683i	$-0.246675\pi$
$313$	447.248			1.42891			0.714454	+	0.699683i	$0.246675\pi$
$314$	95.3477	−	279.578i	0.303655	−	0.890376i
$315$		0			0
$316$	126.463	−	163.843i	0.400201	−	0.518491i
$317$	−67.2154			−0.212036			−0.106018	−	0.994364i	$-0.533810\pi$
$317$	−67.2154			−0.212036			−0.106018	+	0.994364i	$0.533810\pi$
$318$		0			0
$319$			456.133i			1.42989i
$320$	59.5352	−	140.331i	0.186048	−	0.438534i
$321$		0			0
$322$	−110.264	+	323.315i	−0.342434	+	1.00408i
$323$		−	118.471i		−	0.366785i
$324$		0			0
$325$	−18.1714			−0.0559119
$326$	−346.605	−	118.207i	−1.06321	−	0.362597i
$327$		0			0
$328$	256.170	−	169.590i	0.781005	−	0.517043i
$329$	559.220			1.69976
$330$		0			0
$331$		−	178.449i		−	0.539122i	−0.962983	−	0.269561i	$-0.913121\pi$
$331$		−	178.449i		−	0.539122i	0.962983	−	0.269561i	$-0.0868785\pi$
$332$	−16.2028	+	20.9919i	−0.0488035	+	0.0632287i
$333$		0			0
$334$	406.038	+	138.476i	1.21568	+	0.414598i
$335$		−	8.29337i		−	0.0247563i
$336$		0			0
$337$	−280.146			−0.831292			−0.415646	−	0.909526i	$-0.636445\pi$
$337$	−280.146			−0.831292			−0.415646	+	0.909526i	$0.636445\pi$
$338$	108.531	−	318.234i	0.321098	−	0.941521i
$339$		0			0
$340$	204.986	+	158.220i	0.602901	+	0.465353i
$341$	225.787			0.662131
$342$		0			0
$343$			682.888i			1.99093i
$344$	181.992	+	274.903i	0.529048	+	0.799138i
$345$		0			0
$346$	17.5498	−	51.4596i	0.0507221	−	0.148727i
$347$			89.6003i			0.258214i	0.991631	+	0.129107i	$0.0412111\pi$
$347$			89.6003i			0.258214i	−0.991631	+	0.129107i	$0.958789\pi$
$348$		0			0
$349$	5.38420			0.0154275			0.00771376	−	0.999970i	$-0.497545\pi$
$349$	5.38420			0.0154275			0.00771376	+	0.999970i	$0.497545\pi$
$350$	−452.788	−	154.419i	−1.29368	−	0.441198i
$351$		0			0
$352$	−21.2284	+	292.040i	−0.0603079	+	0.829660i
$353$	−357.844			−1.01372			−0.506861	−	0.862028i	$-0.669194\pi$
$353$	−357.844			−1.01372			−0.506861	+	0.862028i	$0.669194\pi$
$354$		0			0
$355$		−	211.718i		−	0.596390i
$356$	99.7772	+	77.0137i	0.280273	+	0.216331i
$357$		0			0
$358$	350.732	+	119.614i	0.979699	+	0.334118i
$359$		−	415.792i		−	1.15820i	−0.815258	−	0.579098i	$-0.803405\pi$
$359$		−	415.792i		−	1.15820i	0.815258	−	0.579098i	$-0.196595\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	−10.9844	+	32.2084i	−0.0303436	+	0.0889734i
$363$		0			0
$364$	−28.4404	+	36.8467i	−0.0781329	+	0.101227i
$365$	−47.2968			−0.129580
$366$		0			0
$367$		−	262.695i		−	0.715789i	−0.933762	−	0.357894i	$-0.883495\pi$
$367$		−	262.695i		−	0.715789i	0.933762	−	0.357894i	$-0.116505\pi$
$368$	−213.605	+	55.9345i	−0.580448	+	0.151996i
$369$		0			0
$370$	42.0942	−	123.428i	0.113768	−	0.333590i
$371$		−	247.485i		−	0.667075i
$372$		0			0
$373$	158.344			0.424516			0.212258	−	0.977214i	$-0.431918\pi$
$373$	158.344			0.424516			0.212258	+	0.977214i	$0.431918\pi$
$374$	−470.773	−	160.553i	−1.25875	−	0.429287i
$375$		0			0
$376$	199.540	+	301.409i	0.530691	+	0.801619i
$377$	−46.8685			−0.124320
$378$		0			0
$379$		−	539.136i		−	1.42252i	−0.702928	−	0.711261i	$-0.748124\pi$
$379$		−	539.136i		−	1.42252i	0.702928	−	0.711261i	$-0.251876\pi$
$380$	25.3747	−	32.8749i	0.0667756	−	0.0865129i
$381$		0			0
$382$	−4.57708	−	1.56097i	−0.0119819	−	0.00408631i
$383$		−	422.810i		−	1.10394i	−0.833863	−	0.551971i	$-0.813876\pi$
$383$		−	422.810i		−	1.10394i	0.833863	−	0.551971i	$-0.186124\pi$
$384$		0			0
$385$	−269.740			−0.700623
$386$	97.2956	−	285.290i	0.252061	−	0.739092i
$387$		0			0
$388$	−504.361	−	389.294i	−1.29990	−	1.00334i
$389$	487.091			1.25216			0.626081	−	0.779758i	$-0.284658\pi$
$389$	487.091			1.25216			0.626081	+	0.779758i	$0.284658\pi$
$390$		0			0
$391$		−	375.085i		−	0.959296i
$392$	−694.926	+	460.057i	−1.77277	+	1.17362i
$393$		0			0
$394$	173.144	−	507.693i	0.439453	−	1.28856i
$395$			123.244i			0.312009i
$396$		0			0
$397$	−646.684			−1.62893			−0.814464	−	0.580215i	$-0.802969\pi$
$397$	−646.684			−1.62893			−0.814464	+	0.580215i	$0.802969\pi$
$398$	584.191	+	199.233i	1.46782	+	0.500586i
$399$		0			0
$400$	−78.3337	−	299.143i	−0.195834	−	0.747859i
$401$	14.0555			0.0350512			0.0175256	−	0.999846i	$-0.494421\pi$
$401$	14.0555			0.0350512			0.0175256	+	0.999846i	$0.494421\pi$
$402$		0			0
$403$			23.2000i			0.0575682i
$404$	111.325	+	85.9266i	0.275556	+	0.212690i
$405$		0			0
$406$	−1167.85	−	398.286i	−2.87649	−	0.981001i
$407$			250.497i			0.615471i
$408$		0			0
$409$	143.668			0.351266			0.175633	−	0.984456i	$-0.443803\pi$
$409$	143.668			0.351266			0.175633	+	0.984456i	$0.443803\pi$
$410$	−59.0494	+	173.144i	−0.144023	+	0.422303i
$411$		0			0
$412$	−286.477	+	371.153i	−0.695333	+	0.900858i
$413$	−429.530			−1.04002
$414$		0			0
$415$		−	15.7902i		−	0.0380488i
$416$	−30.0077	−	2.18125i	−0.0721338	−	0.00524340i
$417$		0			0
$418$	−25.7489	+	75.5008i	−0.0616003	+	0.180624i
$419$		−	572.449i		−	1.36623i	−0.730312	−	0.683114i	$-0.760625\pi$
$419$		−	572.449i		−	1.36623i	0.730312	−	0.683114i	$-0.239375\pi$
$420$		0			0
$421$	718.562			1.70680			0.853399	−	0.521258i	$-0.174537\pi$
$421$	718.562			1.70680			0.853399	+	0.521258i	$0.174537\pi$
$422$	−632.264	−	215.628i	−1.49825	−	0.510967i
$423$		0			0
$424$	133.390	−	88.3070i	0.314598	−	0.208271i
$425$	525.289			1.23597
$426$		0			0
$427$		−	410.908i		−	0.962314i
$428$	−468.849	+	607.429i	−1.09544	+	1.41923i
$429$		0			0
$430$	−185.807	−	63.3677i	−0.432108	−	0.147367i
$431$		−	252.198i		−	0.585147i	−0.956243	−	0.292573i	$-0.905488\pi$
$431$		−	252.198i		−	0.585147i	0.956243	−	0.292573i	$-0.0945116\pi$
$432$		0			0
$433$	239.008			0.551982			0.275991	−	0.961160i	$-0.410994\pi$
$433$	239.008			0.551982			0.275991	+	0.961160i	$0.410994\pi$
$434$	−197.152	+	578.089i	−0.454268	+	1.33200i
$435$		0			0
$436$	582.021	+	449.237i	1.33491	+	1.03036i
$437$	−60.1547			−0.137654
$438$		0			0
$439$		−	17.2750i		−	0.0393508i	−0.999806	−	0.0196754i	$-0.993737\pi$
$439$		−	17.2750i		−	0.0393508i	0.999806	−	0.0196754i	$-0.00626327\pi$
$440$	−96.2480	−	145.385i	−0.218745	−	0.330420i
$441$		0			0
$442$	16.4971	−	48.3728i	0.0373238	−	0.109441i
$443$			161.249i			0.363993i	0.983299	+	0.181997i	$0.0582560\pi$
$443$			161.249i			0.363993i	−0.983299	+	0.181997i	$0.941744\pi$
$444$		0			0
$445$	−75.0529			−0.168658
$446$	−549.222	−	187.307i	−1.23144	−	0.419972i
$447$		0			0
$448$	−729.184	−	309.355i	−1.62764	−	0.690525i
$449$	−561.952			−1.25156			−0.625782	−	0.779998i	$-0.715220\pi$
$449$	−561.952			−1.25156			−0.625782	+	0.779998i	$0.715220\pi$
$450$		0			0
$451$		−	351.395i		−	0.779147i
$452$	231.063	+	178.348i	0.511202	+	0.394575i
$453$		0			0
$454$	144.349	+	49.2288i	0.317948	+	0.108434i
$455$		−	27.7163i		−	0.0609149i
$456$		0			0
$457$	−107.375			−0.234957			−0.117479	−	0.993075i	$-0.537481\pi$
$457$	−107.375			−0.234957			−0.117479	+	0.993075i	$0.537481\pi$
$458$	137.365	−	402.780i	0.299923	−	0.879433i
$459$		0			0
$460$	80.3373	−	104.083i	0.174646	−	0.226268i
$461$	−666.303			−1.44534			−0.722672	−	0.691191i	$-0.757086\pi$
$461$	−666.303			−1.44534			−0.722672	+	0.691191i	$0.757086\pi$
$462$		0			0
$463$			272.358i			0.588246i	0.955768	+	0.294123i	$0.0950276\pi$
$463$			272.358i			0.588246i	−0.955768	+	0.294123i	$0.904972\pi$
$464$	−202.042	−	771.566i	−0.435436	−	1.66286i
$465$		0			0
$466$	−70.0469	+	205.391i	−0.150315	+	0.440753i
$467$			703.386i			1.50618i	0.657917	+	0.753090i	$0.271438\pi$
$467$			703.386i			1.50618i	−0.657917	+	0.753090i	$0.728562\pi$
$468$		0			0
$469$	−43.0938			−0.0918844
$470$	−203.721	−	69.4775i	−0.433450	−	0.147824i
$471$		0			0
$472$	−153.264	−	231.508i	−0.324712	−	0.490484i
$473$	377.093			0.797237
$474$		0			0
$475$		−	84.2438i		−	0.177355i
$476$	822.139	−	1065.14i	1.72718	−	2.23770i
$477$		0			0
$478$	27.4716	+	9.36894i	0.0574719	+	0.0196003i
$479$		−	451.971i		−	0.943572i	−0.881713	−	0.471786i	$-0.843609\pi$
$479$		−	451.971i		−	0.943572i	0.881713	−	0.471786i	$-0.156391\pi$
$480$		0			0
$481$	−25.7390			−0.0535114
$482$	179.623	−	526.689i	0.372661	−	1.09272i
$483$		0			0
$484$	−118.018	−	91.0934i	−0.243840	−	0.188209i
$485$	379.383			0.782232
$486$		0			0
$487$		−	293.894i		−	0.603478i	−0.953391	−	0.301739i	$-0.902433\pi$
$487$		−	293.894i		−	0.603478i	0.953391	−	0.301739i	$-0.0975671\pi$
$488$	221.472	−	146.619i	0.453835	−	0.300449i
$489$		0			0
$490$	160.187	−	469.699i	0.326912	−	0.958568i
$491$		−	91.3499i		−	0.186049i	−0.995664	−	0.0930243i	$-0.970347\pi$
$491$		−	91.3499i		−	0.186049i	0.995664	−	0.0930243i	$-0.0296534\pi$
$492$		0			0
$493$	1354.85			2.74818
$494$	−7.75785	−	2.64575i	−0.0157041	−	0.00535576i
$495$		0			0
$496$	−381.926	+	100.011i	−0.770012	+	0.201635i
$497$	−1100.13			−2.21353
$498$		0			0
$499$			758.796i			1.52063i	0.649553	+	0.760316i	$0.274956\pi$
$499$			758.796i			1.52063i	−0.649553	+	0.760316i	$0.725044\pi$
$500$	334.314	+	258.043i	0.668628	+	0.516085i
$501$		0			0
$502$	−651.649	−	222.239i	−1.29811	−	0.442708i
$503$		−	55.4556i		−	0.110250i	−0.998479	−	0.0551248i	$-0.982444\pi$
$503$		−	55.4556i		−	0.110250i	0.998479	−	0.0551248i	$-0.0175557\pi$
$504$		0			0
$505$	−83.7389			−0.165820
$506$	−81.5220	+	239.038i	−0.161111	+	0.472408i
$507$		0			0
$508$	−27.9149	+	36.1659i	−0.0549505	+	0.0711927i
$509$	479.828			0.942688			0.471344	−	0.881949i	$-0.343769\pi$
$509$	479.828			0.942688			0.471344	+	0.881949i	$0.343769\pi$
$510$		0			0
$511$			245.763i			0.480945i
$512$	−93.4494	−	503.400i	−0.182518	−	0.983202i
$513$		0			0
$514$	32.2817	−	94.6563i	0.0628049	−	0.184156i
$515$		−	279.184i		−	0.542104i
$516$		0			0
$517$	413.451			0.799712
$518$	−641.355	−	218.729i	−1.23814	−	0.422256i
$519$		0			0
$520$	14.9385	−	9.88966i	0.0287279	−	0.0190186i
$521$	−29.8875			−0.0573656			−0.0286828	−	0.999589i	$-0.509131\pi$
$521$	−29.8875			−0.0573656			−0.0286828	+	0.999589i	$0.509131\pi$
$522$		0			0
$523$			324.051i			0.619600i	0.950802	+	0.309800i	$0.100262\pi$
$523$			324.051i			0.619600i	−0.950802	+	0.309800i	$0.899738\pi$
$524$	90.3110	−	117.005i	0.172349	−	0.223292i
$525$		0			0
$526$	−293.923	−	100.240i	−0.558788	−	0.190570i
$527$		−	670.652i		−	1.27259i
$528$		0			0
$529$	338.548			0.639978
$530$	−30.7475	+	90.1577i	−0.0580141	+	0.170109i
$531$		0			0
$532$	−170.824	−	131.852i	−0.321097	−	0.247841i
$533$	36.1065			0.0677420
$534$		0			0
$535$		−	456.912i		−	0.854040i
$536$	−15.3766	−	23.2267i	−0.0286878	−	0.0433334i
$537$		0			0
$538$	−295.208	+	865.607i	−0.548713	+	1.60893i
$539$			953.250i			1.76855i
$540$		0			0
$541$	−584.274			−1.07999			−0.539994	−	0.841669i	$-0.681574\pi$
$541$	−584.274			−1.07999			−0.539994	+	0.841669i	$0.681574\pi$
$542$	661.166	+	225.485i	1.21986	+	0.416024i
$543$		0			0
$544$	867.446	+	63.0545i	1.59457	+	0.115909i
$545$	−437.799			−0.803301
$546$		0			0
$547$		−	173.706i		−	0.317562i	−0.987314	−	0.158781i	$-0.949244\pi$
$547$		−	173.706i		−	0.317562i	0.987314	−	0.158781i	$-0.0507564\pi$
$548$	−515.457	−	397.859i	−0.940614	−	0.726020i
$549$		0			0
$550$	−334.762	−	114.168i	−0.608658	−	0.207578i
$551$		−	217.286i		−	0.394348i
$552$		0			0
$553$	640.396			1.15804
$554$	70.0755	−	205.475i	0.126490	−	0.370894i
$555$		0			0
$556$	−560.261	+	725.862i	−1.00766	+	1.30551i
$557$	590.355			1.05988			0.529942	−	0.848034i	$-0.322214\pi$
$557$	590.355			1.05988			0.529942	+	0.848034i	$0.322214\pi$
$558$		0			0
$559$			38.7470i			0.0693148i
$560$	456.275	−	119.480i	0.814776	−	0.213357i
$561$		0			0
$562$	122.951	−	360.516i	0.218774	−	0.641487i
$563$			1015.03i			1.80290i	0.432882	+	0.901450i	$0.357497\pi$
$563$			1015.03i			1.80290i	−0.432882	+	0.901450i	$0.642503\pi$
$564$		0			0
$565$	−173.807			−0.307623
$566$	548.859	+	187.183i	0.969715	+	0.330713i
$567$		0			0
$568$	−392.545	−	592.947i	−0.691100	−	1.04392i
$569$	98.2869			0.172736			0.0863681	−	0.996263i	$-0.472474\pi$
$569$	98.2869			0.172736			0.0863681	+	0.996263i	$0.472474\pi$
$570$		0			0
$571$		−	366.213i		−	0.641354i	−0.947189	−	0.320677i	$-0.896090\pi$
$571$		−	366.213i		−	0.641354i	0.947189	−	0.320677i	$-0.103910\pi$
$572$	−21.0270	+	27.2421i	−0.0367604	+	0.0476260i
$573$		0			0
$574$	899.689	+	306.831i	1.56740	+	0.534549i
$575$		−	266.719i		−	0.463859i
$576$		0			0
$577$	−267.138			−0.462977			−0.231489	−	0.972838i	$-0.574360\pi$
$577$	−267.138			−0.462977			−0.231489	+	0.972838i	$0.574360\pi$
$578$	−290.320	+	851.275i	−0.502284	+	1.47279i
$579$		0			0
$580$	375.961	+	290.188i	0.648208	+	0.500324i
$581$	−82.0488			−0.141220
$582$		0			0
$583$		−	182.974i		−	0.313850i
$584$	−132.461	+	87.6925i	−0.226817	+	0.150158i
$585$		0			0
$586$	−114.835	+	336.719i	−0.195964	+	0.574605i
$587$			245.452i			0.418147i	0.977900	+	0.209074i	$0.0670448\pi$
$587$			245.452i			0.418147i	−0.977900	+	0.209074i	$0.932955\pi$
$588$		0			0
$589$	−107.557			−0.182609
$590$	156.476	+	53.3647i	0.265213	+	0.0904487i
$591$		0			0
$592$	−110.956	−	423.724i	−0.187426	−	0.715750i
$593$	−33.3697			−0.0562726			−0.0281363	−	0.999604i	$-0.508957\pi$
$593$	−33.3697			−0.0562726			−0.0281363	+	0.999604i	$0.508957\pi$
$594$		0			0
$595$			801.207i			1.34657i
$596$	−349.352	−	269.649i	−0.586160	−	0.452432i
$597$		0			0
$598$	−24.5616	−	8.37653i	−0.0410729	−	0.0140076i
$599$		−	427.260i		−	0.713288i	−0.934240	−	0.356644i	$-0.883921\pi$
$599$		−	427.260i		−	0.713288i	0.934240	−	0.356644i	$-0.116079\pi$
$600$		0			0
$601$	−316.625			−0.526831			−0.263415	−	0.964683i	$-0.584849\pi$
$601$	−316.625			−0.526831			−0.263415	+	0.964683i	$0.584849\pi$
$602$	−329.270	+	965.483i	−0.546960	+	1.60379i
$603$		0			0
$604$	−255.983	+	331.646i	−0.423813	+	0.549083i
$605$	88.7741			0.146734
$606$		0			0
$607$			467.840i			0.770741i	0.922762	+	0.385370i	$0.125926\pi$
$607$			467.840i			0.770741i	−0.922762	+	0.385370i	$0.874074\pi$
$608$	10.1124	−	139.118i	0.0166323	−	0.228812i
$609$		0			0
$610$	−51.0512	+	149.692i	−0.0836905	+	0.245397i
$611$			42.4829i			0.0695300i
$612$		0			0
$613$	−636.118			−1.03771			−0.518856	−	0.854861i	$-0.673642\pi$
$613$	−636.118			−1.03771			−0.518856	+	0.854861i	$0.673642\pi$
$614$	1049.25	+	357.838i	1.70888	+	0.582797i
$615$		0			0
$616$	−755.444	+	500.122i	−1.22637	+	0.811886i
$617$	−331.487			−0.537256			−0.268628	−	0.963244i	$-0.586570\pi$
$617$	−331.487			−0.537256			−0.268628	+	0.963244i	$0.586570\pi$
$618$		0			0
$619$			479.724i			0.774999i	0.921870	+	0.387500i	$0.126661\pi$
$619$			479.724i			0.774999i	−0.921870	+	0.387500i	$0.873339\pi$
$620$	143.643	−	186.101i	0.231683	−	0.300163i
$621$		0			0
$622$	128.259	+	43.7416i	0.206204	+	0.0703241i
$623$			389.988i			0.625984i
$624$		0			0
$625$	231.698			0.370718
$626$	−288.731	+	846.615i	−0.461231	+	1.35242i
$627$		0			0
$628$	467.672	+	360.976i	0.744700	+	0.574802i
$629$	744.049			1.18291
$630$		0			0
$631$		−	389.892i		−	0.617896i	−0.951079	−	0.308948i	$-0.900023\pi$
$631$		−	389.892i		−	0.617896i	0.951079	−	0.308948i	$-0.0999768\pi$
$632$	228.505	+	345.161i	0.361558	+	0.546141i
$633$		0			0
$634$	43.3924	−	127.235i	0.0684423	−	0.200686i
$635$		−	27.2042i		−	0.0428412i
$636$		0			0
$637$	−97.9481			−0.153765
$638$	−863.435	−	294.467i	−1.35335	−	0.461547i
$639$		0			0
$640$	227.204	+	203.291i	0.355007	+	0.317642i
$641$	170.264			0.265623			0.132811	−	0.991141i	$-0.457600\pi$
$641$	170.264			0.265623			0.132811	+	0.991141i	$0.457600\pi$
$642$		0			0
$643$			420.651i			0.654200i	0.944990	+	0.327100i	$0.106071\pi$
$643$			420.651i			0.654200i	−0.944990	+	0.327100i	$0.893929\pi$
$644$	−540.834	−	417.447i	−0.839805	−	0.648209i
$645$		0			0
$646$	224.260	+	76.4819i	0.347151	+	0.118393i
$647$			178.658i			0.276133i	0.990423	+	0.138067i	$0.0440888\pi$
$647$			178.658i			0.276133i	−0.990423	+	0.138067i	$0.955911\pi$
$648$		0			0
$649$	−317.566			−0.489317
$650$	11.7309	−	34.3974i	0.0180476	−	0.0529191i
$651$		0			0
$652$	447.517	−	579.793i	0.686376	−	0.889253i
$653$	950.370			1.45539			0.727696	−	0.685900i	$-0.240591\pi$
$653$	950.370			1.45539			0.727696	+	0.685900i	$0.240591\pi$
$654$		0			0
$655$			88.0117i			0.134369i
$656$	155.649	+	594.397i	0.237270	+	0.906094i
$657$		0			0
$658$	−361.017	+	1058.57i	−0.548658	+	1.60877i
$659$		−	327.948i		−	0.497645i	−0.968549	−	0.248823i	$-0.919956\pi$
$659$		−	327.948i		−	0.497645i	0.968549	−	0.248823i	$-0.0800436\pi$
$660$		0			0
$661$	256.403			0.387902			0.193951	−	0.981011i	$-0.437870\pi$
$661$	256.403			0.387902			0.193951	+	0.981011i	$0.437870\pi$
$662$	337.794	+	115.202i	0.510264	+	0.174021i
$663$		0			0
$664$	−29.2765	−	44.2227i	−0.0440911	−	0.0666005i
$665$	128.495			0.193225
$666$		0			0
$667$		−	687.935i		−	1.03139i
$668$	−524.254	+	679.211i	−0.784811	+	1.01678i
$669$		0			0
$670$	15.6989	+	5.35397i	0.0234312	+	0.00799100i
$671$		−	303.799i		−	0.452755i
$672$		0			0
$673$	−624.347			−0.927707			−0.463853	−	0.885912i	$-0.653534\pi$
$673$	−624.347			−0.927707			−0.463853	+	0.885912i	$0.653534\pi$
$674$	180.854	−	530.300i	0.268330	−	0.786795i
$675$		0			0
$676$	532.335	+	410.886i	0.787477	+	0.607820i
$677$	135.259			0.199791			0.0998955	−	0.994998i	$-0.468149\pi$
$677$	135.259			0.199791			0.0998955	+	0.994998i	$0.468149\pi$
$678$		0			0
$679$		−	1971.34i		−	2.90330i
$680$	−431.835	+	285.885i	−0.635052	+	0.420419i
$681$		0			0
$682$	−145.762	+	427.401i	−0.213727	+	0.626688i
$683$			84.9635i			0.124398i	0.998064	+	0.0621988i	$0.0198113\pi$
$683$			84.9635i			0.124398i	−0.998064	+	0.0621988i	$0.980189\pi$
$684$		0			0
$685$	387.729			0.566028
$686$	−1292.67	−	440.853i	−1.88436	−	0.642644i
$687$		0			0
$688$	−637.866	+	167.032i	−0.927131	+	0.242778i
$689$	18.8009			0.0272873
$690$		0			0
$691$			673.647i			0.974887i	0.873155	+	0.487443i	$0.162070\pi$
$691$			673.647i			0.974887i	−0.873155	+	0.487443i	$0.837930\pi$
$692$	86.0804	+	66.4418i	0.124394	+	0.0960141i
$693$		0			0
$694$	−169.608	−	57.8435i	−0.244392	−	0.0833479i
$695$		−	545.997i		−	0.785607i
$696$		0			0
$697$	−1043.75			−1.49749
$698$	−3.47589	+	10.1920i	−0.00497979	+	0.0146017i
$699$		0			0
$700$	584.615	−	757.413i	0.835164	−	1.08202i
$701$	−406.227			−0.579496			−0.289748	−	0.957103i	$-0.593571\pi$
$701$	−406.227			−0.579496			−0.289748	+	0.957103i	$0.593571\pi$
$702$		0			0
$703$		−	119.328i		−	0.169741i
$704$	−539.112	−	228.717i	−0.765784	−	0.324883i
$705$		0			0
$706$	231.014	−	677.378i	0.327215	−	0.959459i
$707$			435.122i			0.615448i
$708$		0			0
$709$	668.985			0.943561			0.471780	−	0.881716i	$-0.343611\pi$
$709$	668.985			0.943561			0.471780	+	0.881716i	$0.343611\pi$
$710$	400.771	+	136.680i	0.564466	+	0.192506i
$711$		0			0
$712$	−210.196	+	139.155i	−0.295219	+	0.195442i
$713$	−340.528			−0.477599
$714$		0			0
$715$		−	20.4916i		−	0.0286596i
$716$	−452.846	+	586.697i	−0.632467	+	0.819409i
$717$		0			0
$718$	787.072	+	268.424i	1.09620	+	0.373850i
$719$		−	357.444i		−	0.497140i	−0.968614	−	0.248570i	$-0.920039\pi$
$719$		−	357.444i		−	0.497140i	0.968614	−	0.248570i	$-0.0799606\pi$
$720$		0			0
$721$	−1450.69			−2.01205
$722$	12.2659	−	35.9659i	0.0169887	−	0.0498143i
$723$		0			0
$724$	−53.8774	−	41.5857i	−0.0744163	−	0.0574387i
$725$	963.420			1.32886
$726$		0			0
$727$			931.519i			1.28132i	0.767825	+	0.640659i	$0.221339\pi$
$727$			931.519i			1.28132i	−0.767825	+	0.640659i	$0.778661\pi$
$728$	−51.3884	−	77.6232i	−0.0705885	−	0.106625i
$729$		0			0
$730$	30.5335	−	89.5303i	0.0418267	−	0.122644i
$731$		−	1120.08i		−	1.53225i
$732$		0			0
$733$	−342.315			−0.467006			−0.233503	−	0.972356i	$-0.575019\pi$
$733$	−342.315			−0.467006			−0.233503	+	0.972356i	$0.575019\pi$
$734$	497.266	+	169.588i	0.677474	+	0.231047i
$735$		0			0
$736$	32.0164	−	440.451i	0.0435005	−	0.598440i
$737$	−31.8608			−0.0432303
$738$		0			0
$739$		−	233.486i		−	0.315949i	−0.987443	−	0.157975i	$-0.949504\pi$
$739$		−	233.486i		−	0.315949i	0.987443	−	0.157975i	$-0.0504964\pi$
$740$	206.468	+	159.364i	0.279011	+	0.215356i
$741$		0			0
$742$	468.475	+	159.769i	0.631368	+	0.215323i
$743$			684.601i			0.921401i	0.887556	+	0.460701i	$0.152402\pi$
$743$			684.601i			0.921401i	−0.887556	+	0.460701i	$0.847598\pi$
$744$		0			0
$745$	262.784			0.352730
$746$	−102.223	+	299.737i	−0.137028	+	0.401792i
$747$		0			0
$748$	607.836	−	787.499i	0.812615	−	1.05281i
$749$	−2374.19			−3.16982
$750$		0			0
$751$		−	985.017i		−	1.31161i	−0.754931	−	0.655804i	$-0.772330\pi$
$751$		−	985.017i		−	1.31161i	0.754931	−	0.655804i	$-0.227670\pi$
$752$	−699.367	+	183.136i	−0.930010	+	0.243532i
$753$		0			0
$754$	30.2570	−	88.7195i	0.0401287	−	0.117665i
$755$		−	249.466i		−	0.330418i
$756$		0			0
$757$	1162.89			1.53619			0.768094	−	0.640338i	$-0.221206\pi$
$757$	1162.89			1.53619			0.768094	+	0.640338i	$0.221206\pi$
$758$	1020.55	+	348.051i	1.34638	+	0.459171i
$759$		0			0
$760$	45.8491	+	69.2561i	0.0603278	+	0.0911264i
$761$	460.254			0.604802			0.302401	−	0.953181i	$-0.402212\pi$
$761$	460.254			0.604802			0.302401	+	0.953181i	$0.402212\pi$
$762$		0			0
$763$			2274.88i			2.98149i
$764$	5.90967	−	7.65643i	0.00773516	−	0.0100215i
$765$		0			0
$766$	800.356	+	272.954i	1.04485	+	0.356337i
$767$		−	32.6305i		−	0.0425431i
$768$		0			0
$769$	757.145			0.984584			0.492292	−	0.870430i	$-0.336159\pi$
$769$	757.145			0.984584			0.492292	+	0.870430i	$0.336159\pi$
$770$	174.137	−	510.603i	0.226151	−	0.663120i
$771$		0			0
$772$	477.226	+	368.350i	0.618168	+	0.477138i
$773$	−1071.48			−1.38614			−0.693068	−	0.720872i	$-0.743742\pi$
$773$	−1071.48			−1.38614			−0.693068	+	0.720872i	$0.743742\pi$
$774$		0			0
$775$		−	476.894i		−	0.615347i
$776$	1062.51	−	703.409i	1.36922	−	0.906455i
$777$		0			0
$778$	−314.452	+	922.036i	−0.404180	+	1.18514i
$779$			167.392i			0.214881i
$780$		0			0
$781$	−813.362			−1.04144
$782$	710.014	+	242.144i	0.907946	+	0.309647i
$783$		0			0
$784$	−422.238	−	1612.46i	−0.538568	−	2.05670i
$785$	−351.785			−0.448134
$786$		0			0
$787$			625.691i			0.795033i	0.917595	+	0.397517i	$0.130128\pi$
$787$			625.691i			0.795033i	−0.917595	+	0.397517i	$0.869872\pi$
$788$	849.257	+	655.505i	1.07774	+	0.831859i
$789$		0			0
$790$	−233.293	−	79.5627i	−0.295308	−	0.100712i
$791$			903.132i			1.14176i
$792$		0			0
$793$	31.2159			0.0393643
$794$	417.481	−	1224.14i	0.525795	−	1.54173i
$795$		0			0
$796$	−754.275	+	977.221i	−0.947582	+	1.22766i
$797$	549.357			0.689281			0.344641	−	0.938735i	$-0.388001\pi$
$797$	549.357			0.689281			0.344641	+	0.938735i	$0.388001\pi$
$798$		0			0
$799$		−	1228.07i		−	1.53701i
$800$	616.832	+	44.8374i	0.771040	+	0.0560468i
$801$		0			0
$802$	−9.07386	+	26.6063i	−0.0113140	+	0.0331750i
$803$			181.701i			0.226278i
$804$		0			0
$805$	406.818			0.505364
$806$	−43.9162	−	14.9773i	−0.0544867	−	0.0185822i
$807$		0			0
$808$	−234.522	+	155.259i	−0.290250	+	0.192153i
$809$	7.38519			0.00912879			0.00456440	−	0.999990i	$-0.498547\pi$
$809$	7.38519			0.00912879			0.00456440	+	0.999990i	$0.498547\pi$
$810$		0			0
$811$			1100.76i			1.35729i	0.734466	+	0.678645i	$0.237433\pi$
$811$			1100.76i			1.35729i	−0.734466	+	0.678645i	$0.762567\pi$
$812$	1507.87	−	1953.56i	1.85698	−	2.40586i
$813$		0			0
$814$	−474.176	−	161.714i	−0.582526	−	0.198666i
$815$			436.123i			0.535121i
$816$		0			0
$817$	−179.634			−0.219870
$818$	−92.7479	+	271.955i	−0.113384	+	0.332463i
$819$		0			0
$820$	−289.632	−	223.554i	−0.353210	−	0.272627i
$821$	−80.5795			−0.0981480			−0.0490740	−	0.998795i	$-0.515627\pi$
$821$	−80.5795			−0.0981480			−0.0490740	+	0.998795i	$0.515627\pi$
$822$		0			0
$823$			980.615i			1.19151i	0.803165	+	0.595756i	$0.203148\pi$
$823$			980.615i			1.19151i	−0.803165	+	0.595756i	$0.796852\pi$
$824$	−517.631	−	781.892i	−0.628193	−	0.948898i
$825$		0			0
$826$	277.293	−	813.076i	0.335705	−	0.984353i
$827$			1517.68i			1.83516i	0.397553	+	0.917579i	$0.369859\pi$
$827$			1517.68i			1.83516i	−0.397553	+	0.917579i	$0.630141\pi$
$828$		0			0
$829$	−229.487			−0.276823			−0.138412	−	0.990375i	$-0.544200\pi$
$829$	−229.487			−0.276823			−0.138412	+	0.990375i	$0.544200\pi$
$830$	29.8900	+	10.1937i	0.0360121	+	0.0122816i
$831$		0			0
$832$	23.5011	−	55.3947i	0.0282465	−	0.0665802i
$833$	2831.43			3.39908
$834$		0			0
$835$		−	510.906i		−	0.611863i
$836$	−126.296	−	97.4825i	−0.151072	−	0.116606i
$837$		0			0
$838$	1083.61	+	369.557i	1.29310	+	0.440999i
$839$			949.272i			1.13143i	0.824600	+	0.565716i	$0.191400\pi$
$839$			949.272i			1.13143i	−0.824600	+	0.565716i	$0.808600\pi$
$840$		0			0
$841$	1643.90			1.95470
$842$	−463.884	+	1360.20i	−0.550931	+	1.61544i
$843$		0			0
$844$	816.344	−	1057.64i	0.967232	−	1.25312i
$845$	−400.425			−0.473876
$846$		0			0
$847$		−	461.286i		−	0.544611i
$848$	81.0476	+	309.508i	0.0955750	+	0.364985i
$849$		0			0
$850$	−339.112	+	994.342i	−0.398955	+	1.16981i
$851$		−	377.796i		−	0.443944i
$852$		0			0
$853$	245.110			0.287350			0.143675	−	0.989625i	$-0.454108\pi$
$853$	245.110			0.287350			0.143675	+	0.989625i	$0.454108\pi$
$854$	777.826	+	265.271i	0.910803	+	0.310622i
$855$		0			0
$856$	−847.154	−	1279.64i	−0.989666	−	1.49491i
$857$	−659.731			−0.769814			−0.384907	−	0.922955i	$-0.625766\pi$
$857$	−659.731			−0.769814			−0.384907	+	0.922955i	$0.625766\pi$
$858$		0			0
$859$			1240.81i			1.44449i	0.691639	+	0.722244i	$0.256889\pi$
$859$			1240.81i			1.44449i	−0.691639	+	0.722244i	$0.743111\pi$
$860$	239.903	−	310.813i	0.278957	−	0.361410i
$861$		0			0
$862$	477.397	+	162.812i	0.553825	+	0.188877i
$863$			1063.44i			1.23226i	0.787646	+	0.616129i	$0.211300\pi$
$863$			1063.44i			1.23226i	−0.787646	+	0.616129i	$0.788700\pi$
$864$		0			0
$865$	−64.7501			−0.0748556
$866$	−154.297	+	452.429i	−0.178172	+	0.522435i
$867$		0			0
$868$	−967.013	−	746.396i	−1.11407	−	0.859903i
$869$	473.467			0.544841
$870$		0			0
$871$		−	3.27375i		−	0.00375861i
$872$	−1226.12	+	811.718i	−1.40610	+	0.930869i
$873$		0			0
$874$	38.8342	−	113.869i	0.0444327	−	0.130285i
$875$			1306.70i			1.49337i
$876$		0			0
$877$	−867.685			−0.989379			−0.494689	−	0.869070i	$-0.664718\pi$
$877$	−867.685			−0.989379			−0.494689	+	0.869070i	$0.664718\pi$
$878$	32.7006	+	11.1522i	0.0372444	+	0.0127019i
$879$		0			0
$880$	337.340	−	88.3358i	0.383341	−	0.100382i
$881$	−1540.22			−1.74826			−0.874132	−	0.485688i	$-0.838569\pi$
$881$	−1540.22			−1.74826			−0.874132	+	0.485688i	$0.838569\pi$
$882$		0			0
$883$		−	590.651i		−	0.668914i	−0.942411	−	0.334457i	$-0.891447\pi$
$883$		−	590.651i		−	0.668914i	0.942411	−	0.334457i	$-0.108553\pi$
$884$	80.9169	+	62.4563i	0.0915350	+	0.0706519i
$885$		0			0
$886$	−305.235	−	104.098i	−0.344509	−	0.117492i
$887$		−	336.467i		−	0.379332i	−0.981849	−	0.189666i	$-0.939259\pi$
$887$		−	336.467i		−	0.379332i	0.981849	−	0.189666i	$-0.0607405\pi$
$888$		0			0
$889$	−141.358			−0.159007
$890$	48.4521	−	142.071i	0.0544405	−	0.159630i
$891$		0			0
$892$	709.125	−	918.726i	0.794983	−	1.02996i
$893$	−196.954			−0.220553
$894$		0			0
$895$		−	441.316i		−	0.493091i
$896$	1056.33	−	1180.59i	1.17894	−	1.31763i
$897$		0			0
$898$	362.781	−	1063.74i	0.403987	−	1.18457i
$899$		−	1230.03i		−	1.36822i
$900$		0			0
$901$	−543.488			−0.603205
$902$	665.171	+	226.851i	0.737440	+	0.251498i
$903$		0			0
$904$	−486.770	+	322.253i	−0.538463	+	0.356475i
$905$	40.5269			0.0447811
$906$		0			0
$907$			850.338i			0.937528i	0.883323	+	0.468764i	$0.155301\pi$
$907$			850.338i			0.937528i	−0.883323	+	0.468764i	$0.844699\pi$
$908$	−186.375	+	241.463i	−0.205259	+	0.265928i
$909$		0			0
$910$	52.4653	+	17.8929i	0.0576542	+	0.0196625i
$911$		−	1658.66i		−	1.82070i	−0.413837	−	0.910351i	$-0.635812\pi$
$911$		−	1658.66i		−	1.82070i	0.413837	−	0.910351i	$-0.364188\pi$
$912$		0			0
$913$	−60.6616			−0.0664420
$914$	69.3186	−	203.256i	0.0758409	−	0.222380i
$915$		0			0
$916$	673.761	+	520.047i	0.735547	+	0.567737i
$917$	457.324			0.498718
$918$		0			0
$919$		−	684.608i		−	0.744948i	−0.928043	−	0.372474i	$-0.878510\pi$
$919$		−	684.608i		−	0.744948i	0.928043	−	0.372474i	$-0.121490\pi$
$920$	145.160	+	219.267i	0.157783	+	0.238334i
$921$		0			0
$922$	430.147	−	1261.27i	0.466537	−	1.36798i
$923$		−	83.5744i		−	0.0905465i
$924$		0			0
$925$	529.086			0.571985
$926$	−515.558	−	175.827i	−0.556758	−	0.189878i
$927$		0			0
$928$	1590.96	+	115.647i	1.71440	+	0.124620i
$929$	191.705			0.206356			0.103178	−	0.994663i	$-0.467099\pi$
$929$	191.705			0.206356			0.103178	+	0.994663i	$0.467099\pi$
$930$		0			0
$931$		−	454.094i		−	0.487749i
$932$	−343.574	−	265.190i	−0.368641	−	0.284538i
$933$		0			0
$934$	−1331.47	−	454.087i	−1.42556	−	0.486174i
$935$			592.361i			0.633541i
$936$		0			0
$937$	1030.61			1.09990			0.549951	−	0.835197i	$-0.314646\pi$
$937$	1030.61			1.09990			0.549951	+	0.835197i	$0.314646\pi$
$938$	27.8202	−	81.5742i	0.0296590	−	0.0869660i
$939$		0			0
$940$	263.034	−	340.781i	0.279823	−	0.362533i
$941$	551.115			0.585669			0.292835	−	0.956163i	$-0.405401\pi$
$941$	551.115			0.585669			0.292835	+	0.956163i	$0.405401\pi$
$942$		0			0
$943$			529.970i			0.562004i
$944$	537.175	−	140.665i	0.569041	−	0.149009i
$945$		0			0
$946$	−243.441	+	713.816i	−0.257337	+	0.754562i
$947$			1465.05i			1.54704i	0.633773	+	0.773519i	$0.281506\pi$
$947$			1465.05i			1.54704i	−0.633773	+	0.773519i	$0.718494\pi$
$948$		0			0
$949$	−18.6701			−0.0196734
$950$	159.469	+	54.3855i	0.167862	+	0.0572478i
$951$		0			0
$952$	1485.51	+	2243.89i	1.56041	+	2.35703i
$953$	572.440			0.600671			0.300336	−	0.953834i	$-0.402901\pi$
$953$	572.440			0.600671			0.300336	+	0.953834i	$0.402901\pi$
$954$		0			0
$955$			5.75920i			0.00603058i
$956$	−35.4697	+	45.9538i	−0.0371022	+	0.0480688i
$957$		0			0
$958$	855.556	+	291.780i	0.893065	+	0.304572i
$959$		−	2014.71i		−	2.10084i
$960$		0			0
$961$	352.134			0.366425
$962$	16.6164	−	48.7225i	0.0172727	−	0.0506471i
$963$		0			0
$964$	881.033	+	680.031i	0.913934	+	0.705426i
$965$	−358.972			−0.371992
$966$		0			0
$967$			228.290i			0.236080i	0.993009	+	0.118040i	$0.0376612\pi$
$967$			228.290i			0.236080i	−0.993009	+	0.118040i	$0.962339\pi$
$968$	248.624	−	164.595i	0.256843	−	0.170036i
$969$		0			0
$970$	−244.919	+	718.150i	−0.252494	+	0.740361i
$971$			1338.46i			1.37843i	0.724555	+	0.689217i	$0.242045\pi$
$971$			1338.46i			1.37843i	−0.724555	+	0.689217i	$0.757955\pi$
$972$		0			0
$973$	−2837.10			−2.91582
$974$	556.324	+	189.730i	0.571175	+	0.194794i
$975$		0			0
$976$	134.566	+	513.887i	0.137875	+	0.526523i
$977$	−396.018			−0.405341			−0.202671	−	0.979247i	$-0.564962\pi$
$977$	−396.018			−0.405341			−0.202671	+	0.979247i	$0.564962\pi$
$978$		0			0
$979$			288.332i			0.294517i
$980$	785.701	+	606.449i	0.801736	+	0.618825i
$981$		0			0
$982$	172.920	+	58.9729i	0.176090	+	0.0600539i
$983$		−	169.385i		−	0.172315i	−0.996282	−	0.0861573i	$-0.972541\pi$
$983$		−	169.385i		−	0.172315i	0.996282	−	0.0861573i	$-0.0274588\pi$
$984$		0			0
$985$	−638.816			−0.648544
$986$	−874.654	+	2564.66i	−0.887073	+	2.60107i
$987$		0			0
$988$	10.0165	−	12.9772i	0.0101382	−	0.0131348i
$989$	−568.727			−0.575052
$990$		0			0
$991$			899.988i			0.908161i	0.890961	+	0.454080i	$0.150032\pi$
$991$			899.988i			0.908161i	−0.890961	+	0.454080i	$0.849968\pi$
$992$	57.2454	−	787.529i	0.0577070	−	0.793880i
$993$		0			0
$994$	710.211	−	2082.48i	0.714498	−	2.09505i
$995$		−	735.071i		−	0.738765i
$996$		0			0
$997$	−1265.57			−1.26938			−0.634689	−	0.772768i	$-0.718872\pi$
$997$	−1265.57			−1.26938			−0.634689	+	0.772768i	$0.718872\pi$
$998$	−1436.36	−	489.857i	−1.43924	−	0.490839i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.b.343.8		14
3.2	odd	2		76.3.b.b.39.7	✓	14
4.3	odd	2	inner	684.3.g.b.343.7		14
12.11	even	2		76.3.b.b.39.8	yes	14
24.5	odd	2		1216.3.d.d.191.9		14
24.11	even	2		1216.3.d.d.191.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.b.39.7	✓	14	3.2	odd	2
76.3.b.b.39.8	yes	14	12.11	even	2
684.3.g.b.343.7		14	4.3	odd	2	inner
684.3.g.b.343.8		14	1.1	even	1	trivial
1216.3.d.d.191.6		14	24.11	even	2
1216.3.d.d.191.9		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)

\(f(q)\)	\(=\)	\(q+(-0.645572 + 1.89294i) q^{2} +(-3.16647 - 2.44406i) q^{4} +2.38184 q^{5} -12.3764i q^{7} +(6.67066 - 4.41614i) q^{8} +O(q^{10})\)	\(q+(-0.645572 + 1.89294i) q^{2} +(-3.16647 - 2.44406i) q^{4} +2.38184 q^{5} -12.3764i q^{7} +(6.67066 - 4.41614i) q^{8} +(-1.53765 + 4.50868i) q^{10} -9.15034i q^{11} +0.940214 q^{13} +(23.4279 + 7.98989i) q^{14} +(4.05310 + 15.4781i) q^{16} -27.1792 q^{17} +4.35890i q^{19} +(-7.54202 - 5.82136i) q^{20} +(17.3211 + 5.90721i) q^{22} +13.8004i q^{23} -19.3269 q^{25} +(-0.606976 + 1.77977i) q^{26} +(-30.2488 + 39.1897i) q^{28} -49.8488 q^{29} +24.6752i q^{31} +(-31.9158 - 2.31995i) q^{32} +(17.5461 - 51.4487i) q^{34} -29.4787i q^{35} -27.3757 q^{37} +(-8.25115 - 2.81398i) q^{38} +(15.8884 - 10.5185i) q^{40} +38.4024 q^{41} +41.2108i q^{43} +(-22.3640 + 28.9743i) q^{44} +(-26.1234 - 8.90917i) q^{46} +45.1842i q^{47} -104.176 q^{49} +(12.4769 - 36.5846i) q^{50} +(-2.97716 - 2.29794i) q^{52} +19.9964 q^{53} -21.7946i q^{55} +(-54.6561 - 82.5591i) q^{56} +(32.1810 - 94.3610i) q^{58} -34.7054i q^{59} +33.2008 q^{61} +(-46.7088 - 15.9296i) q^{62} +(24.9955 - 58.9171i) q^{64} +2.23944 q^{65} -3.48192i q^{67} +(86.0622 + 66.4277i) q^{68} +(55.8015 + 19.0306i) q^{70} -88.8887i q^{71} -19.8573 q^{73} +(17.6730 - 51.8206i) q^{74} +(10.6534 - 13.8023i) q^{76} -113.249 q^{77} +51.7431i q^{79} +(9.65383 + 36.8664i) q^{80} +(-24.7915 + 72.6936i) q^{82} -6.62943i q^{83} -64.7365 q^{85} +(-78.0097 - 26.6046i) q^{86} +(-40.4091 - 61.0388i) q^{88} -31.5105 q^{89} -11.6365i q^{91} +(33.7291 - 43.6987i) q^{92} +(-85.5312 - 29.1697i) q^{94} +10.3822i q^{95} +159.282 q^{97} +(67.2534 - 197.200i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8}+O(q^{10}) \) 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

Introduction

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