LMFDB - Embedded newform 684.3.s.a.445.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, degree $2$, 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:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.35
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.84984 + 0.937239i) q^{3} +(-3.40921 - 5.90492i) q^{5} +(3.70019 + 6.40891i) q^{7} +(7.24317 + 5.34196i) q^{9} +O(q^{10})$	\(q+(2.84984 + 0.937239i) q^{3} +(-3.40921 - 5.90492i) q^{5} +(3.70019 + 6.40891i) q^{7} +(7.24317 + 5.34196i) q^{9} +(2.17728 + 3.77116i) q^{11} +5.09601i q^{13} +(-4.18137 - 20.0233i) q^{15} +(7.11551 - 12.3244i) q^{17} +(17.8833 + 6.41783i) q^{19} +(4.53826 + 21.7323i) q^{21} -8.51341 q^{23} +(-10.7454 + 18.6115i) q^{25} +(15.6352 + 22.0123i) q^{27} +(9.80640 + 5.66173i) q^{29} +(8.16773 + 4.71564i) q^{31} +(2.67042 + 12.7878i) q^{33} +(25.2294 - 43.6986i) q^{35} +33.2038i q^{37} +(-4.77618 + 14.5228i) q^{39} +(-0.373372 + 0.215567i) q^{41} +76.3776 q^{43} +(6.85038 - 60.9821i) q^{45} +(23.8498 - 41.3090i) q^{47} +(-2.88279 + 4.99314i) q^{49} +(31.8290 - 28.4537i) q^{51} +(-7.51673 + 4.33978i) q^{53} +(14.8456 - 25.7133i) q^{55} +(44.9494 + 35.0507i) q^{57} +(56.4083 - 32.5673i) q^{59} +(-3.68786 + 6.38756i) q^{61} +(-7.43508 + 66.1871i) q^{63} +(30.0915 - 17.3733i) q^{65} -55.2757i q^{67} +(-24.2619 - 7.97910i) q^{69} +(42.1958 + 24.3618i) q^{71} +(-41.5917 + 72.0390i) q^{73} +(-48.0660 + 42.9689i) q^{75} +(-16.1127 + 27.9080i) q^{77} +105.437i q^{79} +(23.9269 + 77.3854i) q^{81} +(-42.1532 - 73.0115i) q^{83} -97.0330 q^{85} +(22.6403 + 25.3260i) q^{87} +(-55.8744 + 32.2591i) q^{89} +(-32.6599 + 18.8562i) q^{91} +(18.8570 + 21.0939i) q^{93} +(-23.0710 - 127.479i) q^{95} -103.160i q^{97} +(-4.37498 + 38.9461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	2.84984	+	0.937239i	0.949946	+	0.312413i
$3$	2.84984	+	0.937239i	0.949946	+	0.312413i
$4$		0			0
$5$	−3.40921	−	5.90492i	−0.681841	−	1.18098i	−0.974418	−	0.224742i	$-0.927846\pi$
$5$	−3.40921	−	5.90492i	−0.681841	−	1.18098i	0.292577	−	0.956242i	$-0.405487\pi$
$6$		0			0
$7$	3.70019	+	6.40891i	0.528598	+	0.915559i	0.999444	+	0.0333436i	$0.0106156\pi$
$7$	3.70019	+	6.40891i	0.528598	+	0.915559i	−0.470846	+	0.882216i	$0.656051\pi$
$8$		0			0
$9$	7.24317	+	5.34196i	0.804796	+	0.593551i
$10$		0			0
$11$	2.17728	+	3.77116i	0.197935	+	0.342833i	0.947859	−	0.318691i	$-0.103243\pi$
$11$	2.17728	+	3.77116i	0.197935	+	0.342833i	−0.749924	+	0.661524i	$0.769910\pi$
$12$		0			0
$13$			5.09601i			0.392001i	0.980604	+	0.196000i	$0.0627954\pi$
$13$			5.09601i			0.392001i	−0.980604	+	0.196000i	$0.937205\pi$
$14$		0			0
$15$	−4.18137	−	20.0233i	−0.278758	−	1.33489i
$16$		0			0
$17$	7.11551	−	12.3244i	0.418559	−	0.724966i	−0.577235	−	0.816578i	$-0.695868\pi$
$17$	7.11551	−	12.3244i	0.418559	−	0.724966i	0.995795	+	0.0916116i	$0.0292018\pi$
$18$		0			0
$19$	17.8833	+	6.41783i	0.941225	+	0.337781i
$19$	17.8833	+	6.41783i	0.941225	+	0.337781i
$20$		0			0
$21$	4.53826	+	21.7323i	0.216108	+	1.03487i
$22$		0			0
$23$	−8.51341			−0.370148			−0.185074	−	0.982725i	$-0.559253\pi$
$23$	−8.51341			−0.370148			−0.185074	+	0.982725i	$0.559253\pi$
$24$		0			0
$25$	−10.7454	+	18.6115i	−0.429815	+	0.744461i
$26$		0			0
$27$	15.6352	+	22.0123i	0.579080	+	0.815270i
$28$		0			0
$29$	9.80640	+	5.66173i	0.338152	+	0.195232i	0.659454	−	0.751744i	$-0.270787\pi$
$29$	9.80640	+	5.66173i	0.338152	+	0.195232i	−0.321303	+	0.946977i	$0.604121\pi$
$30$		0			0
$31$	8.16773	+	4.71564i	0.263475	+	0.152117i	0.625919	−	0.779888i	$-0.284724\pi$
$31$	8.16773	+	4.71564i	0.263475	+	0.152117i	−0.362444	+	0.932006i	$0.618057\pi$
$32$		0			0
$33$	2.67042	+	12.7878i	0.0809220	+	0.387510i
$34$		0			0
$35$	25.2294	−	43.6986i	0.720840	−	1.24853i
$36$		0			0
$37$			33.2038i			0.897400i	0.893683	+	0.448700i	$0.148113\pi$
$37$			33.2038i			0.897400i	−0.893683	+	0.448700i	$0.851887\pi$
$38$		0			0
$39$	−4.77618	+	14.5228i	−0.122466	+	0.372380i
$40$		0			0
$41$	−0.373372	+	0.215567i	−0.00910665	+	0.00525772i	−0.504546	−	0.863385i	$-0.668340\pi$
$41$	−0.373372	+	0.215567i	−0.00910665	+	0.00525772i	0.495440	+	0.868642i	$0.335007\pi$
$42$		0			0
$43$	76.3776			1.77622			0.888111	−	0.459629i	$-0.152018\pi$
$43$	76.3776			1.77622			0.888111	+	0.459629i	$0.152018\pi$
$44$		0			0
$45$	6.85038	−	60.9821i	0.152231	−	1.35516i
$46$		0			0
$47$	23.8498	−	41.3090i	0.507442	−	0.878916i	−0.492521	−	0.870301i	$-0.663924\pi$
$47$	23.8498	−	41.3090i	0.507442	−	0.878916i	0.999963	−	0.00861497i	$-0.00274226\pi$
$48$		0			0
$49$	−2.88279	+	4.99314i	−0.0588325	+	0.101901i
$50$		0			0
$51$	31.8290	−	28.4537i	0.624098	−	0.557916i
$52$		0			0
$53$	−7.51673	+	4.33978i	−0.141825	+	0.0818827i	−0.569234	−	0.822176i	$-0.692760\pi$
$53$	−7.51673	+	4.33978i	−0.141825	+	0.0818827i	0.427408	+	0.904059i	$0.359427\pi$
$54$		0			0
$55$	14.8456	−	25.7133i	0.269920	−	0.467515i
$56$		0			0
$57$	44.9494	+	35.0507i	0.788586	+	0.614924i
$58$		0			0
$59$	56.4083	−	32.5673i	0.956072	−	0.551989i	0.0611105	−	0.998131i	$-0.480536\pi$
$59$	56.4083	−	32.5673i	0.956072	−	0.551989i	0.894962	+	0.446142i	$0.147202\pi$
$60$		0			0
$61$	−3.68786	+	6.38756i	−0.0604567	+	0.104714i	−0.894670	−	0.446728i	$-0.852589\pi$
$61$	−3.68786	+	6.38756i	−0.0604567	+	0.104714i	0.834213	+	0.551442i	$0.185922\pi$
$62$		0			0
$63$	−7.43508	+	66.1871i	−0.118017	+	1.05059i
$64$		0			0
$65$	30.0915	−	17.3733i	0.462946	−	0.267282i
$66$		0			0
$67$		−	55.2757i		−	0.825010i	−0.910955	−	0.412505i	$-0.864654\pi$
$67$		−	55.2757i		−	0.825010i	0.910955	−	0.412505i	$-0.135346\pi$
$68$		0			0
$69$	−24.2619	−	7.97910i	−0.351621	−	0.115639i
$70$		0			0
$71$	42.1958	+	24.3618i	0.594307	+	0.343123i	0.766799	−	0.641888i	$-0.221848\pi$
$71$	42.1958	+	24.3618i	0.594307	+	0.343123i	−0.172492	+	0.985011i	$0.555182\pi$
$72$		0			0
$73$	−41.5917	+	72.0390i	−0.569750	+	0.986836i	0.426841	+	0.904327i	$0.359627\pi$
$73$	−41.5917	+	72.0390i	−0.569750	+	0.986836i	−0.996590	+	0.0825086i	$0.973707\pi$
$74$		0			0
$75$	−48.0660	+	42.9689i	−0.640880	+	0.572918i
$76$		0			0
$77$	−16.1127	+	27.9080i	−0.209256	+	0.362442i
$78$		0			0
$79$			105.437i			1.33465i	0.744767	+	0.667325i	$0.232561\pi$
$79$			105.437i			1.33465i	−0.744767	+	0.667325i	$0.767439\pi$
$80$		0			0
$81$	23.9269	+	77.3854i	0.295394	+	0.955375i
$82$		0			0
$83$	−42.1532	−	73.0115i	−0.507870	−	0.879657i	−0.999958	−	0.00911142i	$-0.997100\pi$
$83$	−42.1532	−	73.0115i	−0.507870	−	0.879657i	0.492089	−	0.870545i	$-0.336234\pi$
$84$		0			0
$85$	−97.0330			−1.14156
$86$		0			0
$87$	22.6403	+	25.3260i	0.260233	+	0.291103i
$88$		0			0
$89$	−55.8744	+	32.2591i	−0.627803	+	0.362462i	−0.779901	−	0.625903i	$-0.784730\pi$
$89$	−55.8744	+	32.2591i	−0.627803	+	0.362462i	0.152098	+	0.988365i	$0.451397\pi$
$90$		0			0
$91$	−32.6599	+	18.8562i	−0.358900	+	0.207211i
$92$		0			0
$93$	18.8570	+	21.0939i	0.202764	+	0.226816i
$94$		0			0
$95$	−23.0710	−	127.479i	−0.242852	−	1.34188i
$96$		0			0
$97$		−	103.160i		−	1.06351i	−0.846898	−	0.531755i	$-0.821533\pi$
$97$		−	103.160i		−	1.06351i	0.846898	−	0.531755i	$-0.178467\pi$
$98$		0			0
$99$	−4.37498	+	38.9461i	−0.0441917	+	0.393395i
$100$		0			0
$101$	−48.0253	+	83.1823i	−0.475498	+	0.823587i	−0.999606	−	0.0280646i	$-0.991066\pi$
$101$	−48.0253	+	83.1823i	−0.475498	+	0.823587i	0.524108	+	0.851652i	$0.324399\pi$
$102$		0			0
$103$	−99.9028	−	57.6789i	−0.969930	−	0.559990i	−0.0707153	−	0.997497i	$-0.522528\pi$
$103$	−99.9028	−	57.6789i	−0.969930	−	0.559990i	−0.899215	+	0.437507i	$0.855862\pi$
$104$		0			0
$105$	112.856	−	100.888i	1.07482	−	0.960839i
$106$		0			0
$107$			108.224i			1.01144i	0.862699	+	0.505718i	$0.168772\pi$
$107$			108.224i			1.01144i	−0.862699	+	0.505718i	$0.831228\pi$
$108$		0			0
$109$	−90.8195	−	52.4347i	−0.833207	−	0.481052i	0.0217427	−	0.999764i	$-0.493079\pi$
$109$	−90.8195	−	52.4347i	−0.833207	−	0.481052i	−0.854949	+	0.518712i	$0.826412\pi$
$110$		0			0
$111$	−31.1199	+	94.6255i	−0.280359	+	0.852482i
$112$		0			0
$113$	64.6628	+	37.3331i	0.572237	+	0.330381i	0.758042	−	0.652205i	$-0.226156\pi$
$113$	64.6628	+	37.3331i	0.572237	+	0.330381i	−0.185805	+	0.982587i	$0.559489\pi$
$114$		0			0
$115$	29.0240	+	50.2710i	0.252382	+	0.437139i
$116$		0			0
$117$	−27.2227	+	36.9112i	−0.232672	+	0.315481i
$118$		0			0
$119$	105.315			0.884999
$120$		0			0
$121$	51.0189	−	88.3673i	0.421644	−	0.730308i
$122$		0			0
$123$	−1.26609	+	0.264391i	−0.0102934	+	0.00214952i
$124$		0			0
$125$	−23.9276			−0.191421
$126$		0			0
$127$	55.6956	−	32.1558i	0.438548	−	0.253196i	−0.264434	−	0.964404i	$-0.585185\pi$
$127$	55.6956	−	32.1558i	0.438548	−	0.253196i	0.702981	+	0.711208i	$0.251852\pi$
$128$		0			0
$129$	217.664	+	71.5840i	1.68732	+	0.554915i
$130$		0			0
$131$	38.0853	+	65.9657i	0.290728	+	0.503555i	0.973982	−	0.226625i	$-0.0727693\pi$
$131$	38.0853	+	65.9657i	0.290728	+	0.503555i	−0.683254	+	0.730180i	$0.739436\pi$
$132$		0			0
$133$	25.0401	+	138.360i	0.188272	+	1.04030i
$134$		0			0
$135$	76.6773	−	167.369i	0.567980	−	1.23977i
$136$		0			0
$137$	55.0556	−	95.3590i	0.401865	−	0.696051i	−0.592086	−	0.805875i	$-0.701695\pi$
$137$	55.0556	−	95.3590i	0.401865	−	0.696051i	0.993951	+	0.109824i	$0.0350286\pi$
$138$		0			0
$139$	−227.726			−1.63832			−0.819159	−	0.573567i	$-0.805559\pi$
$139$	−227.726			−1.63832			−0.819159	+	0.573567i	$0.805559\pi$
$140$		0			0
$141$	106.684	−	95.3712i	0.756628	−	0.676391i
$142$		0			0
$143$	−19.2179	+	11.0955i	−0.134391	+	0.0775906i
$144$		0			0
$145$		−	77.2080i		−	0.532469i
$146$		0			0
$147$	−12.8953	+	11.5278i	−0.0877229	+	0.0784203i
$148$		0			0
$149$	57.0181	+	98.7582i	0.382672	+	0.662807i	0.991443	−	0.130539i	$-0.0416707\pi$
$149$	57.0181	+	98.7582i	0.382672	+	0.662807i	−0.608772	+	0.793346i	$0.708337\pi$
$150$		0			0
$151$	−174.049	+	100.487i	−1.15264	+	0.665480i	−0.949530	−	0.313675i	$-0.898440\pi$
$151$	−174.049	+	100.487i	−1.15264	+	0.665480i	−0.203114	+	0.979155i	$0.565106\pi$
$152$		0			0
$153$	117.375	−	51.2571i	0.767160	−	0.335014i
$154$		0			0
$155$		−	64.3064i		−	0.414880i
$156$		0			0
$157$	−27.5519	−	47.7213i	−0.175490	−	0.303957i	0.764841	−	0.644219i	$-0.222818\pi$
$157$	−27.5519	−	47.7213i	−0.175490	−	0.303957i	−0.940331	+	0.340262i	$0.889484\pi$
$158$		0			0
$159$	−25.4889	+	5.32272i	−0.160307	+	0.0334762i
$160$		0			0
$161$	−31.5012	−	54.5617i	−0.195660	−	0.338893i
$162$		0			0
$163$	−124.653			−0.764745			−0.382373	−	0.924008i	$-0.624893\pi$
$163$	−124.653			−0.764745			−0.382373	+	0.924008i	$0.624893\pi$
$164$		0			0
$165$	66.4071	−	59.3650i	0.402468	−	0.359788i
$166$		0			0
$167$			81.5243i			0.488169i	0.969754	+	0.244085i	$0.0784875\pi$
$167$			81.5243i			0.488169i	−0.969754	+	0.244085i	$0.921513\pi$
$168$		0			0
$169$	143.031			0.846335
$170$		0			0
$171$	95.2477	+	142.017i	0.557004	+	0.830510i
$172$		0			0
$173$		−	245.971i		−	1.42180i	−0.703294	−	0.710899i	$-0.748288\pi$
$173$		−	245.971i		−	1.42180i	0.703294	−	0.710899i	$-0.251712\pi$
$174$		0			0
$175$	−159.040			−0.908798
$176$		0			0
$177$	191.278	−	39.9436i	1.08067	−	0.225670i
$178$		0			0
$179$		−	311.071i		−	1.73783i	−0.494964	−	0.868914i	$-0.664819\pi$
$179$		−	311.071i		−	1.73783i	0.494964	−	0.868914i	$-0.335181\pi$
$180$		0			0
$181$	−50.1888	+	28.9765i	−0.277286	+	0.160091i	−0.632194	−	0.774810i	$-0.717845\pi$
$181$	−50.1888	+	28.9765i	−0.277286	+	0.160091i	0.354908	+	0.934901i	$0.384512\pi$
$182$		0			0
$183$	−16.4965	+	14.7471i	−0.0901446	+	0.0805853i
$184$		0			0
$185$	196.066	−	113.199i	1.05981	−	0.611884i
$186$		0			0
$187$	61.9699			0.331390
$188$		0			0
$189$	−83.2219	+	181.654i	−0.440327	+	0.961133i
$190$		0			0
$191$	−147.359	−	255.233i	−0.771513	−	1.33630i	−0.936734	−	0.350043i	$-0.886167\pi$
$191$	−147.359	−	255.233i	−0.771513	−	1.33630i	0.165221	−	0.986257i	$-0.447166\pi$
$192$		0			0
$193$	−31.2635	+	18.0500i	−0.161987	+	0.0935232i	−0.578802	−	0.815468i	$-0.696480\pi$
$193$	−31.2635	+	18.0500i	−0.161987	+	0.0935232i	0.416815	+	0.908991i	$0.363146\pi$
$194$		0			0
$195$	102.039	−	21.3083i	0.523277	−	0.109273i
$196$		0			0
$197$	−230.429			−1.16969			−0.584844	−	0.811146i	$-0.698844\pi$
$197$	−230.429			−1.16969			−0.584844	+	0.811146i	$0.698844\pi$
$198$		0			0
$199$	−38.8365	−	67.2667i	−0.195158	−	0.338024i	0.751794	−	0.659398i	$-0.229189\pi$
$199$	−38.8365	−	67.2667i	−0.195158	−	0.338024i	−0.946952	+	0.321374i	$0.895855\pi$
$200$		0			0
$201$	51.8065	−	157.527i	0.257744	−	0.783716i
$202$		0			0
$203$			83.7979i			0.412797i
$204$		0			0
$205$	2.54581	+	1.46982i	0.0124186	+	0.00716987i
$206$		0			0
$207$	−61.6641	−	45.4783i	−0.297894	−	0.219702i
$208$		0			0
$209$	14.7342	+	81.4142i	0.0704987	+	0.389542i
$210$		0			0
$211$	−101.774	+	58.7591i	−0.482340	+	0.278479i	−0.721391	−	0.692528i	$-0.756497\pi$
$211$	−101.774	+	58.7591i	−0.482340	+	0.278479i	0.239051	+	0.971007i	$0.423164\pi$
$212$		0			0
$213$	97.4185	+	108.975i	0.457364	+	0.511618i
$214$		0			0
$215$	−260.387	−	451.003i	−1.21110	−	2.09769i
$216$		0			0
$217$			69.7950i			0.321636i
$218$		0			0
$219$	−186.047	+	166.318i	−0.849532	+	0.759444i
$220$		0			0
$221$	62.8054	+	36.2607i	0.284187	+	0.164076i
$222$		0			0
$223$			241.538i			1.08313i	0.840659	+	0.541565i	$0.182168\pi$
$223$			241.538i			1.08313i	−0.840659	+	0.541565i	$0.817832\pi$
$224$		0			0
$225$	−177.253	+	77.4051i	−0.787789	+	0.344023i
$226$		0			0
$227$	−319.299	+	184.347i	−1.40660	+	0.812103i	−0.995059	−	0.0992858i	$-0.968344\pi$
$227$	−319.299	+	184.347i	−1.40660	+	0.812103i	−0.411545	+	0.911389i	$0.635011\pi$
$228$		0			0
$229$	−110.036	+	190.588i	−0.480506	+	0.832261i	−0.999750	−	0.0223649i	$-0.992880\pi$
$229$	−110.036	+	190.588i	−0.480506	+	0.832261i	0.519244	+	0.854626i	$0.326214\pi$
$230$		0			0
$231$	−72.0751	+	64.4320i	−0.312014	+	0.278926i
$232$		0			0
$233$	−18.3618	+	31.8035i	−0.0788059	+	0.136496i	−0.902735	−	0.430197i	$-0.858444\pi$
$233$	−18.3618	+	31.8035i	−0.0788059	+	0.136496i	0.823929	+	0.566693i	$0.191777\pi$
$234$		0			0
$235$	−325.235			−1.38398
$236$		0			0
$237$	−98.8200	+	300.479i	−0.416962	+	1.26785i
$238$		0			0
$239$	34.5559	−	59.8525i	0.144585	−	0.250429i	−0.784633	−	0.619961i	$-0.787149\pi$
$239$	34.5559	−	59.8525i	0.144585	−	0.250429i	0.929218	+	0.369532i	$0.120482\pi$
$240$		0			0
$241$	−209.398	−	120.896i	−0.868871	−	0.501643i	−0.00189818	−	0.999998i	$-0.500604\pi$
$241$	−209.398	−	120.896i	−0.868871	−	0.501643i	−0.866973	+	0.498355i	$0.833938\pi$
$242$		0			0
$243$	−4.34065	+	242.961i	−0.0178628	+	0.999840i
$244$		0			0
$245$	39.3121			0.160458
$246$		0			0
$247$	−32.7053	+	91.1333i	−0.132410	+	0.368961i
$248$		0			0
$249$	−51.7007	−	247.579i	−0.207633	−	0.994292i
$250$		0			0
$251$	−205.737	−	356.346i	−0.819668	−	1.41971i	−0.905927	−	0.423433i	$-0.860825\pi$
$251$	−205.737	−	356.346i	−0.819668	−	1.41971i	0.0862599	−	0.996273i	$-0.472508\pi$
$252$		0			0
$253$	−18.5361	−	32.1055i	−0.0732652	−	0.126899i
$254$		0			0
$255$	−276.528	−	90.9430i	−1.08442	−	0.356639i
$256$		0			0
$257$		−	27.9371i		−	0.108705i	−0.998522	−	0.0543523i	$-0.982691\pi$
$257$		−	27.9371i		−	0.108705i	0.998522	−	0.0543523i	$-0.0173094\pi$
$258$		0			0
$259$	−212.800	+	122.860i	−0.821623	+	0.474364i
$260$		0			0
$261$	40.7847	+	93.3943i	0.156263	+	0.357832i
$262$		0			0
$263$	34.5943			0.131537			0.0657686	−	0.997835i	$-0.479050\pi$
$263$	34.5943			0.131537			0.0657686	+	0.997835i	$0.479050\pi$
$264$		0			0
$265$	51.2521	+	29.5904i	0.193404	+	0.111662i
$266$		0			0
$267$	−189.468	+	39.5656i	−0.709617	+	0.148186i
$268$		0			0
$269$	−332.317	−	191.863i	−1.23538	−	0.713247i	−0.267233	−	0.963632i	$-0.586109\pi$
$269$	−332.317	−	191.863i	−1.23538	−	0.713247i	−0.968146	+	0.250385i	$0.919443\pi$
$270$		0			0
$271$	125.316	−	217.054i	0.462422	−	0.800939i	−0.536659	−	0.843799i	$-0.680314\pi$
$271$	125.316	−	217.054i	0.462422	−	0.800939i	0.999081	+	0.0428603i	$0.0136471\pi$
$272$		0			0
$273$	−110.748	+	23.1270i	−0.405671	+	0.0847143i
$274$		0			0
$275$	−93.5828			−0.340301
$276$		0			0
$277$	97.8217	+	169.432i	0.353147	+	0.611668i	0.986799	−	0.161950i	$-0.0517782\pi$
$277$	97.8217	+	169.432i	0.353147	+	0.611668i	−0.633652	+	0.773618i	$0.718445\pi$
$278$		0			0
$279$	33.9695	+	77.7878i	0.121754	+	0.278809i
$280$		0			0
$281$	313.077	+	180.755i	1.11415	+	0.643256i	0.939902	−	0.341446i	$-0.110917\pi$
$281$	313.077	+	180.755i	1.11415	+	0.643256i	0.174250	+	0.984701i	$0.444250\pi$
$282$		0			0
$283$	113.253	+	196.160i	0.400187	+	0.693145i	0.993748	−	0.111644i	$-0.0356118\pi$
$283$	113.253	+	196.160i	0.400187	+	0.693145i	−0.593561	+	0.804789i	$0.702278\pi$
$284$		0			0
$285$	53.7297	−	384.918i	0.188525	−	1.35059i
$286$		0			0
$287$	−2.76310	−	1.59527i	−0.00962752	−	0.00555845i
$288$		0			0
$289$	43.2390	+	74.8922i	0.149616	+	0.259142i
$290$		0			0
$291$	96.6859	−	293.991i	0.332254	−	1.01028i
$292$		0			0
$293$	200.162	+	115.563i	0.683146	+	0.394415i	0.801039	−	0.598612i	$-0.204281\pi$
$293$	200.162	+	115.563i	0.683146	+	0.394415i	−0.117893	+	0.993026i	$0.537614\pi$
$294$		0			0
$295$	−384.615	−	222.057i	−1.30378	−	0.752737i
$296$		0			0
$297$	−48.9698	+	106.890i	−0.164882	+	0.359898i
$298$		0			0
$299$		−	43.3844i		−	0.145098i
$300$		0			0
$301$	282.611	+	489.497i	0.938908	+	1.62624i
$302$		0			0
$303$	−214.826	+	192.045i	−0.708997	+	0.633812i
$304$		0			0
$305$	50.2907			0.164887
$306$		0			0
$307$	−150.342	−	86.8000i	−0.489714	−	0.282736i	0.234742	−	0.972058i	$-0.424575\pi$
$307$	−150.342	−	86.8000i	−0.489714	−	0.282736i	−0.724456	+	0.689321i	$0.757909\pi$
$308$		0			0
$309$	−230.648	−	258.008i	−0.746434	−	0.834979i
$310$		0			0
$311$	180.905	−	313.337i	0.581688	−	1.00751i	−0.413592	−	0.910462i	$-0.635726\pi$
$311$	180.905	−	313.337i	0.581688	−	1.00751i	0.995279	−	0.0970504i	$-0.0309408\pi$
$312$		0			0
$313$	297.335	−	514.999i	0.949951	−	1.64536i	0.204431	−	0.978881i	$-0.434466\pi$
$313$	297.335	−	514.999i	0.949951	−	1.64536i	0.745521	−	0.666483i	$-0.232201\pi$
$314$		0			0
$315$	416.177	−	181.742i	1.32120	−	0.576959i
$316$		0			0
$317$	−360.967	−	208.404i	−1.13870	−	0.657427i	−0.192590	−	0.981279i	$-0.561689\pi$
$317$	−360.967	−	208.404i	−1.13870	−	0.657427i	−0.946108	+	0.323852i	$0.895022\pi$
$318$		0			0
$319$			49.3087i			0.154573i
$320$		0			0
$321$	−101.431	+	308.420i	−0.315986	+	0.960810i
$322$		0			0
$323$	206.345	−	174.735i	0.638838	−	0.540975i
$324$		0			0
$325$	−94.8445	−	54.7585i	−0.291829	−	0.168488i
$326$		0			0
$327$	−209.677	−	234.550i	−0.641215	−	0.717278i
$328$		0			0
$329$	352.995			1.07293
$330$		0			0
$331$	282.303	−	162.988i	0.852880	−	0.492410i	−0.00874183	−	0.999962i	$-0.502783\pi$
$331$	282.303	−	162.988i	0.852880	−	0.492410i	0.861621	+	0.507552i	$0.169449\pi$
$332$		0			0
$333$	−177.373	+	240.501i	−0.532653	+	0.722224i
$334$		0			0
$335$	−326.398	+	188.446i	−0.974324	+	0.562526i
$336$		0			0
$337$	−193.357	+	111.635i	−0.573760	+	0.331261i	−0.758650	−	0.651499i	$-0.774141\pi$
$337$	−193.357	+	111.635i	−0.573760	+	0.331261i	0.184890	+	0.982759i	$0.440807\pi$
$338$		0			0
$339$	149.288	+	166.998i	0.440379	+	0.492619i
$340$		0			0
$341$			41.0691i			0.120437i
$342$		0			0
$343$	319.951			0.932802
$344$		0			0
$345$	35.5977	+	170.467i	0.103182	+	0.494106i
$346$		0			0
$347$	153.116	+	265.205i	0.441257	+	0.764280i	0.997783	−	0.0665503i	$-0.0211993\pi$
$347$	153.116	+	265.205i	0.441257	+	0.764280i	−0.556526	+	0.830830i	$0.687866\pi$
$348$		0			0
$349$	−168.436	−	291.740i	−0.482625	−	0.835931i	0.517176	−	0.855879i	$-0.326983\pi$
$349$	−168.436	−	291.740i	−0.482625	−	0.835931i	−0.999801	+	0.0199480i	$0.993650\pi$
$350$		0			0
$351$	−112.175	+	79.6770i	−0.319587	+	0.227000i
$352$		0			0
$353$	108.109	+	187.250i	0.306258	+	0.530454i	0.977541	−	0.210747i	$-0.0675897\pi$
$353$	108.109	+	187.250i	0.306258	+	0.530454i	−0.671283	+	0.741201i	$0.734256\pi$
$354$		0			0
$355$		−	332.217i		−	0.935823i
$356$		0			0
$357$	300.131	+	98.7052i	0.840702	+	0.276485i
$358$		0			0
$359$	275.951	−	477.961i	0.768666	−	1.33137i	−0.169620	−	0.985509i	$-0.554254\pi$
$359$	275.951	−	477.961i	0.768666	−	1.33137i	0.938286	−	0.345859i	$-0.112413\pi$
$360$		0			0
$361$	278.623	+	229.544i	0.771808	+	0.635855i
$362$		0			0
$363$	228.217	−	204.016i	0.628697	−	0.562027i
$364$		0			0
$365$	567.179			1.55392
$366$		0			0
$367$	−171.129	+	296.404i	−0.466292	+	0.807641i	−0.999259	−	0.0384951i	$-0.987744\pi$
$367$	−171.129	+	296.404i	−0.466292	+	0.807641i	0.532967	+	0.846136i	$0.321077\pi$
$368$		0			0
$369$	−3.85595	−	0.433155i	−0.0104497	−	0.00117386i
$370$		0			0
$371$	−55.6266	−	32.1160i	−0.149937	−	0.0865661i
$372$		0			0
$373$	−70.4600	−	40.6801i	−0.188901	−	0.109062i	0.402567	−	0.915390i	$-0.368118\pi$
$373$	−70.4600	−	40.6801i	−0.188901	−	0.109062i	−0.591468	+	0.806329i	$0.701451\pi$
$374$		0			0
$375$	−68.1898	−	22.4259i	−0.181839	−	0.0598023i
$376$		0			0
$377$	−28.8522	+	49.9735i	−0.0765311	+	0.132556i
$378$		0			0
$379$		−	265.656i		−	0.700939i	−0.936574	−	0.350469i	$-0.886022\pi$
$379$		−	265.656i		−	0.700939i	0.936574	−	0.350469i	$-0.113978\pi$
$380$		0			0
$381$	188.861	−	39.4390i	0.495698	−	0.103514i
$382$		0			0
$383$	−232.114	+	134.011i	−0.606041	+	0.349898i	−0.771414	−	0.636333i	$-0.780450\pi$
$383$	−232.114	+	134.011i	−0.606041	+	0.349898i	0.165373	+	0.986231i	$0.447117\pi$
$384$		0			0
$385$	219.726			0.570717
$386$		0			0
$387$	553.215	+	408.006i	1.42950	+	1.05428i
$388$		0			0
$389$	−96.0199	+	166.311i	−0.246838	+	0.427535i	−0.962647	−	0.270761i	$-0.912725\pi$
$389$	−96.0199	+	166.311i	−0.246838	+	0.427535i	0.715809	+	0.698296i	$0.246058\pi$
$390$		0			0
$391$	−60.5773	+	104.923i	−0.154929	+	0.268345i
$392$		0			0
$393$	46.7114	+	223.687i	0.118859	+	0.569177i
$394$		0			0
$395$	622.599	−	359.458i	1.57620	−	0.910019i
$396$		0			0
$397$	231.035	−	400.165i	0.581953	−	1.00797i	−0.413295	−	0.910597i	$-0.635622\pi$
$397$	231.035	−	400.165i	0.581953	−	1.00797i	0.995248	−	0.0973746i	$-0.0310445\pi$
$398$		0			0
$399$	−58.3156	+	417.771i	−0.146154	+	1.04705i
$400$		0			0
$401$	53.4667	−	30.8690i	0.133333	−	0.0769801i	−0.431850	−	0.901946i	$-0.642139\pi$
$401$	53.4667	−	30.8690i	0.133333	−	0.0769801i	0.565183	+	0.824966i	$0.308806\pi$
$402$		0			0
$403$	−24.0309	+	41.6228i	−0.0596301	+	0.103282i
$404$		0			0
$405$	375.383	−	405.109i	0.926871	−	1.00027i
$406$		0			0
$407$	−125.217	+	72.2940i	−0.307658	+	0.177627i
$408$		0			0
$409$		−	316.847i		−	0.774687i	−0.921935	−	0.387344i	$-0.873393\pi$
$409$		−	316.847i		−	0.774687i	0.921935	−	0.387344i	$-0.126607\pi$
$410$		0			0
$411$	246.274	−	220.158i	0.599206	−	0.535664i
$412$		0			0
$413$	417.443	+	241.011i	1.01076	+	0.583561i
$414$		0			0
$415$	−287.418	+	497.822i	−0.692573	+	1.19957i
$416$		0			0
$417$	−648.983	−	213.434i	−1.55631	−	0.511832i
$418$		0			0
$419$	−196.953	+	341.133i	−0.470055	+	0.814160i	−0.999414	−	0.0342385i	$-0.989099\pi$
$419$	−196.953	+	341.133i	−0.470055	+	0.814160i	0.529358	+	0.848398i	$0.322433\pi$
$420$		0			0
$421$		−	14.7005i		−	0.0349181i	−0.999848	−	0.0174591i	$-0.994442\pi$
$421$		−	14.7005i		−	0.0349181i	0.999848	−	0.0174591i	$-0.00555768\pi$
$422$		0			0
$423$	393.419	−	171.804i	0.930069	−	0.406155i
$424$		0			0
$425$	152.918	+	264.861i	0.359806	+	0.623202i
$426$		0			0
$427$	−54.5831			−0.127829
$428$		0			0
$429$	−65.1670	+	13.6085i	−0.151904	+	0.0317215i
$430$		0			0
$431$	−426.955	+	246.503i	−0.990615	+	0.571932i	−0.905458	−	0.424436i	$-0.860472\pi$
$431$	−426.955	+	246.503i	−0.990615	+	0.571932i	−0.0851566	+	0.996368i	$0.527139\pi$
$432$		0			0
$433$	577.503	−	333.422i	1.33373	−	0.770027i	0.347857	−	0.937548i	$-0.386909\pi$
$433$	577.503	−	333.422i	1.33373	−	0.770027i	0.985869	+	0.167521i	$0.0535761\pi$
$434$		0			0
$435$	72.3623	−	220.030i	0.166350	−	0.505817i
$436$		0			0
$437$	−152.248	−	54.6377i	−0.348393	−	0.125029i
$438$		0			0
$439$			407.203i			0.927570i	0.885948	+	0.463785i	$0.153509\pi$
$439$			407.203i			0.927570i	−0.885948	+	0.463785i	$0.846491\pi$
$440$		0			0
$441$	−47.5537	+	20.7664i	−0.107832	+	0.0470894i
$442$		0			0
$443$	−125.129	+	216.730i	−0.282459	+	0.489233i	−0.971990	−	0.235023i	$-0.924483\pi$
$443$	−125.129	+	216.730i	−0.282459	+	0.489233i	0.689531	+	0.724256i	$0.257817\pi$
$444$		0			0
$445$	380.975	+	219.956i	0.856123	+	0.494283i
$446$		0			0
$447$	69.9323	+	334.885i	0.156448	+	0.749183i
$448$		0			0
$449$			761.855i			1.69678i	0.529371	+	0.848390i	$0.322428\pi$
$449$			761.855i			1.69678i	−0.529371	+	0.848390i	$0.677572\pi$
$450$		0			0
$451$	−1.62587	−	0.938699i	−0.00360504	−	0.00208137i
$452$		0			0
$453$	−590.193	+	123.247i	−1.30286	+	0.272069i
$454$		0			0
$455$	222.689	+	128.569i	0.489425	+	0.282570i
$456$		0			0
$457$	228.695	+	396.112i	0.500427	+	0.866766i	1.00000		0.000493522i	$0.000157093\pi$
$457$	228.695	+	396.112i	0.500427	+	0.866766i	−0.499573	+	0.866272i	$0.666510\pi$
$458$		0			0
$459$	382.541	−	36.0658i	0.833423	−	0.0785746i
$460$		0			0
$461$	−317.850			−0.689480			−0.344740	−	0.938698i	$-0.612033\pi$
$461$	−317.850			−0.689480			−0.344740	+	0.938698i	$0.612033\pi$
$462$		0			0
$463$	391.136	−	677.468i	0.844786	−	1.46321i	−0.0410200	−	0.999158i	$-0.513061\pi$
$463$	391.136	−	677.468i	0.844786	−	1.46321i	0.885807	−	0.464055i	$-0.153606\pi$
$464$		0			0
$465$	60.2704	−	183.263i	0.129614	−	0.394113i
$466$		0			0
$467$	687.036			1.47117			0.735585	−	0.677433i	$-0.236907\pi$
$467$	687.036			1.47117			0.735585	+	0.677433i	$0.236907\pi$
$468$		0			0
$469$	354.257	−	204.530i	0.755346	−	0.436099i
$470$		0			0
$471$	−33.7923	−	161.821i	−0.0717458	−	0.343569i
$472$		0			0
$473$	166.296	+	288.032i	0.351576	+	0.608948i
$474$		0			0
$475$	−311.608	+	263.873i	−0.656017	+	0.555522i
$476$		0			0
$477$	−77.6279	−	8.72026i	−0.162742	−	0.0182815i
$478$		0			0
$479$	−169.112	+	292.911i	−0.353053	+	0.611506i	−0.986783	−	0.162049i	$-0.948190\pi$
$479$	−169.112	+	292.911i	−0.353053	+	0.611506i	0.633730	+	0.773555i	$0.281523\pi$
$480$		0			0
$481$	−169.207			−0.351781
$482$		0			0
$483$	−38.6361	−	185.016i	−0.0799919	−	0.383057i
$484$		0			0
$485$	−609.154	+	351.695i	−1.25599	+	0.725145i
$486$		0			0
$487$			629.561i			1.29273i	0.763027	+	0.646367i	$0.223712\pi$
$487$			629.561i			1.29273i	−0.763027	+	0.646367i	$0.776288\pi$
$488$		0			0
$489$	−355.242	−	116.830i	−0.726467	−	0.238916i
$490$		0			0
$491$	−245.878	−	425.874i	−0.500771	−	0.867361i	−1.00000		0.000890341i	$-0.999717\pi$
$491$	−245.878	−	425.874i	−0.500771	−	0.867361i	0.499229	−	0.866470i	$-0.333617\pi$
$492$		0			0
$493$	139.555	−	80.5722i	0.283073	−	0.163432i
$494$		0			0
$495$	244.889	−	106.941i	0.494725	−	0.216043i
$496$		0			0
$497$			360.573i			0.725498i
$498$		0			0
$499$	−155.001	−	268.470i	−0.310624	−	0.538016i	0.667874	−	0.744274i	$-0.267205\pi$
$499$	−155.001	−	268.470i	−0.310624	−	0.538016i	−0.978498	+	0.206259i	$0.933871\pi$
$500$		0			0
$501$	−76.4077	+	232.331i	−0.152510	+	0.463735i
$502$		0			0
$503$	−392.457	−	679.756i	−0.780233	−	1.35140i	−0.931806	−	0.362957i	$-0.881767\pi$
$503$	−392.457	−	679.756i	−0.780233	−	1.35140i	0.151573	−	0.988446i	$-0.451566\pi$
$504$		0			0
$505$	654.913			1.29686
$506$		0			0
$507$	407.614	+	134.054i	0.803973	+	0.264406i
$508$		0			0
$509$		−	819.253i		−	1.60953i	−0.593591	−	0.804767i	$-0.702290\pi$
$509$		−	819.253i		−	1.60953i	0.593591	−	0.804767i	$-0.297710\pi$
$510$		0			0
$511$	−615.589			−1.20468
$512$		0			0
$513$	138.337	+	493.996i	0.269662	+	0.962955i
$514$		0			0
$515$			786.557i			1.52730i
$516$		0			0
$517$	207.711			0.401762
$518$		0			0
$519$	230.533	−	700.978i	0.444188	−	1.35063i
$520$		0			0
$521$			316.315i			0.607130i	0.952811	+	0.303565i	$0.0981770\pi$
$521$			316.315i			0.607130i	−0.952811	+	0.303565i	$0.901823\pi$
$522$		0			0
$523$	−284.438	+	164.220i	−0.543859	+	0.313997i	−0.746641	−	0.665227i	$-0.768335\pi$
$523$	−284.438	+	164.220i	−0.543859	+	0.313997i	0.202783	+	0.979224i	$0.435002\pi$
$524$		0			0
$525$	−453.237	−	149.058i	−0.863309	−	0.283920i
$526$		0			0
$527$	116.235	−	67.1084i	0.220560	−	0.127340i
$528$		0			0
$529$	−456.522			−0.862990
$530$		0			0
$531$	582.548	+	65.4401i	1.09708	+	0.123239i
$532$		0			0
$533$	−1.09853	−	1.90271i	−0.00206103	−	0.00356981i
$534$		0			0
$535$	639.052	−	368.957i	1.19449	−	0.689639i
$536$		0			0
$537$	291.548	−	886.503i	0.542920	−	1.65084i
$538$		0			0
$539$	−25.1066			−0.0465800
$540$		0			0
$541$	193.895	+	335.836i	0.358401	+	0.620768i	0.987694	−	0.156400i	$-0.0499888\pi$
$541$	193.895	+	335.836i	0.358401	+	0.620768i	−0.629293	+	0.777168i	$0.716655\pi$
$542$		0			0
$543$	−170.188	+	35.5395i	−0.313421	+	0.0654503i
$544$		0			0
$545$			715.042i			1.31200i
$546$		0			0
$547$	−571.011	−	329.673i	−1.04390	−	0.602693i	−0.122961	−	0.992411i	$-0.539239\pi$
$547$	−571.011	−	329.673i	−1.04390	−	0.602693i	−0.920934	+	0.389718i	$0.872572\pi$
$548$		0			0
$549$	−60.8338	+	26.5658i	−0.110808	+	0.0483894i
$550$		0			0
$551$	139.035	+	164.186i	0.252331	+	0.297978i
$552$		0			0
$553$	−675.739	+	390.138i	−1.22195	+	0.705494i
$554$		0			0
$555$	664.850	−	138.837i	1.19793	−	0.250157i
$556$		0			0
$557$	240.816	+	417.106i	0.432345	+	0.748844i	0.997075	−	0.0764324i	$-0.0243529\pi$
$557$	240.816	+	417.106i	0.432345	+	0.748844i	−0.564730	+	0.825276i	$0.691020\pi$
$558$		0			0
$559$			389.221i			0.696280i
$560$		0			0
$561$	176.604	+	58.0806i	0.314803	+	0.103530i
$562$		0			0
$563$	706.308	+	407.787i	1.25454	+	0.724311i	0.972009	−	0.234946i	$-0.0754912\pi$
$563$	706.308	+	407.787i	1.25454	+	0.724311i	0.282535	+	0.959257i	$0.408825\pi$
$564$		0			0
$565$		−	509.104i		−	0.901070i
$566$		0			0
$567$	−407.422	+	439.686i	−0.718558	+	0.775461i
$568$		0			0
$569$	362.066	−	209.039i	0.636319	−	0.367379i	−0.146876	−	0.989155i	$-0.546922\pi$
$569$	362.066	−	209.039i	0.636319	−	0.367379i	0.783195	+	0.621776i	$0.213589\pi$
$570$		0			0
$571$	78.0813	−	135.241i	0.136745	−	0.236849i	−0.789518	−	0.613728i	$-0.789669\pi$
$571$	78.0813	−	135.241i	0.136745	−	0.236849i	0.926263	+	0.376879i	$0.123003\pi$
$572$		0			0
$573$	−180.735	−	865.484i	−0.315419	−	1.51044i
$574$		0			0
$575$	91.4798	−	158.448i	0.159095	−	0.275561i
$576$		0			0
$577$	−5.72191			−0.00991665			−0.00495832	−	0.999988i	$-0.501578\pi$
$577$	−5.72191			−0.00991665			−0.00495832	+	0.999988i	$0.501578\pi$
$578$		0			0
$579$	−106.013	+	22.1382i	−0.183097	+	0.0382352i
$580$		0			0
$581$	311.950	−	540.313i	0.536918	−	0.929970i
$582$		0			0
$583$	−32.7321	−	18.8979i	−0.0561442	−	0.0324149i
$584$		0			0
$585$	310.766	+	34.9096i	0.531223	+	0.0596745i
$586$		0			0
$587$	−284.957			−0.485447			−0.242723	−	0.970096i	$-0.578041\pi$
$587$	−284.957			−0.485447			−0.242723	+	0.970096i	$0.578041\pi$
$588$		0			0
$589$	115.802	+	136.750i	0.196607	+	0.232174i
$590$		0			0
$591$	−656.684	−	215.967i	−1.11114	−	0.365426i
$592$		0			0
$593$	−513.723	−	889.794i	−0.866312	−	1.50050i	−0.865739	−	0.500496i	$-0.833151\pi$
$593$	−513.723	−	889.794i	−0.866312	−	1.50050i	−0.000572553	−	1.00000i	$-0.500182\pi$
$594$		0			0
$595$	−359.040	−	621.876i	−0.603429	−	1.04517i
$596$		0			0
$597$	−47.6327	−	228.098i	−0.0797867	−	0.382074i
$598$		0			0
$599$			757.966i			1.26539i	0.774403	+	0.632693i	$0.218050\pi$
$599$			757.966i			1.26539i	−0.774403	+	0.632693i	$0.781950\pi$
$600$		0			0
$601$	951.713	−	549.472i	1.58355	−	0.914262i	0.589213	−	0.807978i	$-0.299438\pi$
$601$	951.713	−	549.472i	1.58355	−	0.914262i	0.994336	−	0.106284i	$-0.0338954\pi$
$602$		0			0
$603$	295.281	−	400.371i	0.489686	−	0.663965i
$604$		0			0
$605$	−695.735			−1.14998
$606$		0			0
$607$	751.726	+	434.009i	1.23843	+	0.715007i	0.968773	−	0.247950i	$-0.0797567\pi$
$607$	751.726	+	434.009i	1.23843	+	0.715007i	0.269656	+	0.962957i	$0.413090\pi$
$608$		0			0
$609$	−78.5386	+	238.810i	−0.128963	+	0.392135i
$610$		0			0
$611$	210.511	+	121.539i	0.344536	+	0.198918i
$612$		0			0
$613$	483.508	−	837.461i	0.788757	−	1.36617i	−0.137972	−	0.990436i	$-0.544058\pi$
$613$	483.508	−	837.461i	0.788757	−	1.36617i	0.926729	−	0.375731i	$-0.122608\pi$
$614$		0			0
$615$	5.87757	+	6.57479i	0.00955702	+	0.0106907i
$616$		0			0
$617$	−534.249			−0.865882			−0.432941	−	0.901422i	$-0.642524\pi$
$617$	−534.249			−0.865882			−0.432941	+	0.901422i	$0.642524\pi$
$618$		0			0
$619$	92.9003	+	160.908i	0.150081	+	0.259948i	0.931257	−	0.364363i	$-0.118713\pi$
$619$	92.9003	+	160.908i	0.150081	+	0.259948i	−0.781176	+	0.624311i	$0.785380\pi$
$620$		0			0
$621$	−133.109	−	187.400i	−0.214346	−	0.301771i
$622$		0			0
$623$	−413.492	−	238.730i	−0.663711	−	0.383194i
$624$		0			0
$625$	350.208	+	606.579i	0.560333	+	0.970526i
$626$		0			0
$627$	−34.3143	+	245.827i	−0.0547278	+	0.392068i
$628$		0			0
$629$	409.218	+	236.262i	0.650585	+	0.375615i
$630$		0			0
$631$	29.5776	+	51.2300i	0.0468742	+	0.0811885i	0.888511	−	0.458856i	$-0.151741\pi$
$631$	29.5776	+	51.2300i	0.0468742	+	0.0811885i	−0.841636	+	0.540045i	$0.818407\pi$
$632$		0			0
$633$	−345.110	+	72.0677i	−0.545198	+	0.113851i
$634$		0			0
$635$	−379.755	−	219.252i	−0.598040	−	0.345278i
$636$		0			0
$637$	−25.4451	−	14.6907i	−0.0399452	−	0.0230624i
$638$		0			0
$639$	175.492	+	401.865i	0.274635	+	0.628896i
$640$		0			0
$641$			670.263i			1.04565i	0.852440	+	0.522826i	$0.175122\pi$
$641$			670.263i			1.04565i	−0.852440	+	0.522826i	$0.824878\pi$
$642$		0			0
$643$	265.269	+	459.460i	0.412550	+	0.714557i	0.995168	−	0.0981891i	$-0.0313050\pi$
$643$	265.269	+	459.460i	0.412550	+	0.714557i	−0.582618	+	0.812746i	$0.697972\pi$
$644$		0			0
$645$	−319.363	−	1529.33i	−0.495136	−	2.37106i
$646$		0			0
$647$	−982.685			−1.51883			−0.759416	−	0.650605i	$-0.774515\pi$
$647$	−982.685			−1.51883			−0.759416	+	0.650605i	$0.774515\pi$
$648$		0			0
$649$	245.634	+	141.817i	0.378480	+	0.218516i
$650$		0			0
$651$	−65.4146	+	198.905i	−0.100483	+	0.305537i
$652$		0			0
$653$	36.3213	−	62.9103i	0.0556222	−	0.0963404i	−0.836874	−	0.547396i	$-0.815619\pi$
$653$	36.3213	−	62.9103i	0.0556222	−	0.0963404i	0.892496	+	0.451056i	$0.148952\pi$
$654$		0			0
$655$	259.681	−	449.781i	0.396460	−	0.686689i
$656$		0			0
$657$	−686.085	+	299.609i	−1.04427	+	0.456026i
$658$		0			0
$659$	318.387	+	183.821i	0.483137	+	0.278939i	0.721723	−	0.692182i	$-0.243351\pi$
$659$	318.387	+	183.821i	0.483137	+	0.278939i	−0.238586	+	0.971121i	$0.576684\pi$
$660$		0			0
$661$		−	259.916i		−	0.393216i	−0.980482	−	0.196608i	$-0.937007\pi$
$661$		−	259.916i		−	0.393216i	0.980482	−	0.196608i	$-0.0629927\pi$
$662$		0			0
$663$	145.000	+	162.201i	0.218703	+	0.244647i
$664$		0			0
$665$	731.635	−	619.556i	1.10020	−	0.931663i
$666$		0			0
$667$	−83.4860	−	48.2006i	−0.125166	−	0.0722648i
$668$		0			0
$669$	−226.379	+	688.345i	−0.338384	+	1.02892i
$670$		0			0
$671$	−32.1180			−0.0478659
$672$		0			0
$673$	630.689	−	364.128i	0.937130	−	0.541052i	0.0480706	−	0.998844i	$-0.484693\pi$
$673$	630.689	−	364.128i	0.937130	−	0.541052i	0.889060	+	0.457792i	$0.151359\pi$
$674$		0			0
$675$	−577.688	+	54.4641i	−0.855834	+	0.0806875i
$676$		0			0
$677$	−937.670	+	541.364i	−1.38504	+	0.799651i	−0.992751	−	0.120192i	$-0.961649\pi$
$677$	−937.670	+	541.364i	−1.38504	+	0.799651i	−0.392286	+	0.919843i	$0.628316\pi$
$678$		0			0
$679$	661.146	−	381.713i	0.973706	−	0.562169i
$680$		0			0
$681$	−1082.73	+	226.101i	−1.58991	+	0.332013i
$682$		0			0
$683$			350.099i			0.512590i	0.966599	+	0.256295i	$0.0825019\pi$
$683$			350.099i			0.512590i	−0.966599	+	0.256295i	$0.917498\pi$
$684$		0			0
$685$	−750.783			−1.09603
$686$		0			0
$687$	−492.211	+	440.015i	−0.716464	+	0.640487i
$688$		0			0
$689$	−22.1156	−	38.3053i	−0.0320981	−	0.0555955i
$690$		0			0
$691$	−145.503	−	252.019i	−0.210569	−	0.364717i	0.741324	−	0.671148i	$-0.234198\pi$
$691$	−145.503	−	252.019i	−0.210569	−	0.364717i	−0.951893	+	0.306431i	$0.900865\pi$
$692$		0			0
$693$	−265.791	+	116.069i	−0.383536	+	0.167488i
$694$		0			0
$695$	776.365	+	1344.70i	1.11707	+	1.93483i
$696$		0			0
$697$			6.13547i			0.00880268i
$698$		0			0
$699$	−82.1356	+	73.4256i	−0.117504	+	0.105044i
$700$		0			0
$701$	22.5413	−	39.0426i	0.0321559	−	0.0556956i	−0.849500	−	0.527589i	$-0.823096\pi$
$701$	22.5413	−	39.0426i	0.0321559	−	0.0556956i	0.881655	+	0.471894i	$0.156429\pi$
$702$		0			0
$703$	−213.096	+	593.792i	−0.303124	+	0.844655i
$704$		0			0
$705$	−926.868	−	304.823i	−1.31471	−	0.432373i
$706$		0			0
$707$	−710.811			−1.00539
$708$		0			0
$709$	−420.596	+	728.494i	−0.593224	+	1.02749i	0.400571	+	0.916266i	$0.368812\pi$
$709$	−420.596	+	728.494i	−0.593224	+	1.02749i	−0.993795	+	0.111229i	$0.964521\pi$
$710$		0			0
$711$	−563.242	+	763.700i	−0.792183	+	1.07412i
$712$		0			0
$713$	−69.5352	−	40.1462i	−0.0975249	−	0.0563060i
$714$		0			0
$715$	131.035	+	75.6534i	0.183266	+	0.105809i
$716$		0			0
$717$	154.575	−	138.183i	0.215585	−	0.192724i
$718$		0			0
$719$	470.810	−	815.466i	0.654812	−	1.13417i	−0.327129	−	0.944980i	$-0.606081\pi$
$719$	470.810	−	815.466i	0.654812	−	1.13417i	0.981941	−	0.189188i	$-0.0605855\pi$
$720$		0			0
$721$		−	853.692i		−	1.18404i
$722$		0			0
$723$	−483.442	−	540.790i	−0.668661	−	0.747980i
$724$		0			0
$725$	−210.747	+	121.675i	−0.290685	+	0.167827i
$726$		0			0
$727$	902.210			1.24100			0.620502	−	0.784205i	$-0.286929\pi$
$727$	902.210			1.24100			0.620502	+	0.784205i	$0.286929\pi$
$728$		0			0
$729$	−240.083	+	688.332i	−0.329332	+	0.944214i
$730$		0			0
$731$	543.465	−	941.310i	0.743455	−	1.28770i
$732$		0			0
$733$	177.764	−	307.897i	0.242516	−	0.420051i	−0.718914	−	0.695099i	$-0.755361\pi$
$733$	177.764	−	307.897i	0.242516	−	0.420051i	0.961430	+	0.275048i	$0.0886939\pi$
$734$		0			0
$735$	112.033	+	36.8448i	0.152426	+	0.0501290i
$736$		0			0
$737$	208.454	−	120.351i	0.282841	−	0.163298i
$738$		0			0
$739$	−620.346	+	1074.47i	−0.839440	+	1.45395i	0.0509230	+	0.998703i	$0.483784\pi$
$739$	−620.346	+	1074.47i	−0.839440	+	1.45395i	−0.890363	+	0.455251i	$0.849550\pi$
$740$		0			0
$741$	−178.619	+	229.063i	−0.241051	+	0.309126i
$742$		0			0
$743$	1083.12	−	625.340i	1.45777	−	0.841642i	0.458866	−	0.888506i	$-0.348256\pi$
$743$	1083.12	−	625.340i	1.45777	−	0.841642i	0.998901	+	0.0468633i	$0.0149225\pi$
$744$		0			0
$745$	388.773	−	673.374i	0.521843	−	0.903858i
$746$		0			0
$747$	84.7017	−	754.015i	0.113389	−	1.00939i
$748$		0			0
$749$	−693.596	+	400.448i	−0.926030	+	0.534644i
$750$		0			0
$751$		−	1328.63i		−	1.76914i	−0.466404	−	0.884572i	$-0.654451\pi$
$751$		−	1328.63i		−	1.76914i	0.466404	−	0.884572i	$-0.345549\pi$
$752$		0			0
$753$	−252.335	−	1208.35i	−0.335106	−	1.60472i
$754$		0			0
$755$	1186.74	+	685.165i	1.57184	+	0.907503i
$756$		0			0
$757$	−708.415	+	1227.01i	−0.935819	+	1.62089i	−0.162652	+	0.986683i	$0.552005\pi$
$757$	−708.415	+	1227.01i	−0.935819	+	1.62089i	−0.773167	+	0.634203i	$0.781328\pi$
$758$		0			0
$759$	−22.7344	−	108.868i	−0.0299531	−	0.143436i
$760$		0			0
$761$	−172.332	+	298.487i	−0.226454	+	0.392231i	−0.956755	−	0.290896i	$-0.906047\pi$
$761$	−172.332	+	298.487i	−0.226454	+	0.392231i	0.730300	+	0.683126i	$0.239380\pi$
$762$		0			0
$763$		−	776.073i		−	1.01713i
$764$		0			0
$765$	−702.826	−	518.346i	−0.918727	−	0.677577i
$766$		0			0
$767$	165.963	+	287.457i	0.216380	+	0.374781i
$768$		0			0
$769$	755.420			0.982341			0.491170	−	0.871063i	$-0.336569\pi$
$769$	755.420			0.982341			0.491170	+	0.871063i	$0.336569\pi$
$770$		0			0
$771$	26.1837	−	79.6162i	0.0339607	−	0.103264i
$772$		0			0
$773$	−328.092	+	189.424i	−0.424440	+	0.245050i	−0.696975	−	0.717095i	$-0.745471\pi$
$773$	−328.092	+	189.424i	−0.424440	+	0.245050i	0.272535	+	0.962146i	$0.412138\pi$
$774$		0			0
$775$	−175.531	+	101.343i	−0.226491	+	0.130765i
$776$		0			0
$777$	−721.596	+	150.687i	−0.928695	+	0.193935i
$778$		0			0
$779$	−8.06059	+	1.45880i	−0.0103474	+	0.00187265i
$780$		0			0
$781$			212.170i			0.271664i
$782$		0			0
$783$	28.6971	+	304.384i	0.0366502	+	0.388740i
$784$		0			0
$785$	−187.860	+	325.384i	−0.239312	+	0.414501i
$786$		0			0
$787$	148.831	+	85.9278i	0.189112	+	0.109184i	0.591567	−	0.806256i	$-0.298510\pi$
$787$	148.831	+	85.9278i	0.189112	+	0.109184i	−0.402455	+	0.915440i	$0.631843\pi$
$788$		0			0
$789$	98.5882	+	32.4231i	0.124953	+	0.0410939i
$790$		0			0
$791$			552.558i			0.698556i
$792$		0			0
$793$	−32.5510	−	18.7934i	−0.0410480	−	0.0236991i
$794$		0			0
$795$	118.327	+	132.363i	0.148839	+	0.166495i
$796$		0			0
$797$	−715.645	−	413.178i	−0.897924	−	0.518417i	−0.0213978	−	0.999771i	$-0.506812\pi$
$797$	−715.645	−	413.178i	−0.897924	−	0.518417i	−0.876526	+	0.481355i	$0.840145\pi$
$798$		0			0
$799$	−339.407	−	587.870i	−0.424789	−	0.735757i
$800$		0			0
$801$	−577.035	−	64.8207i	−0.720393	−	0.0809248i
$802$		0			0
$803$	−362.228			−0.451093
$804$		0			0
$805$	−214.788	+	372.024i	−0.266818	+	0.462142i
$806$		0			0
$807$	−767.229	−	858.240i	−0.950717	−	1.06349i
$808$		0			0
$809$	−432.334			−0.534405			−0.267203	−	0.963640i	$-0.586099\pi$
$809$	−432.334			−0.534405			−0.267203	+	0.963640i	$0.586099\pi$
$810$		0			0
$811$	600.564	−	346.736i	0.740523	−	0.427541i	−0.0817364	−	0.996654i	$-0.526047\pi$
$811$	600.564	−	346.736i	0.740523	−	0.427541i	0.822259	+	0.569113i	$0.192713\pi$
$812$		0			0
$813$	560.564	−	501.119i	0.689500	−	0.616382i
$814$		0			0
$815$	424.969	+	736.068i	0.521435	+	0.903151i
$816$		0			0
$817$	1365.88	+	490.179i	1.67182	+	0.599974i
$818$		0			0
$819$	−337.290	−	37.8892i	−0.411832	−	0.0462628i
$820$		0			0
$821$	−1.66142	+	2.87767i	−0.00202366	+	0.00350507i	−0.867035	−	0.498246i	$-0.833977\pi$
$821$	−1.66142	+	2.87767i	−0.00202366	+	0.00350507i	0.865012	+	0.501752i	$0.167311\pi$
$822$		0			0
$823$	587.328			0.713643			0.356822	−	0.934173i	$-0.383860\pi$
$823$	587.328			0.713643			0.356822	+	0.934173i	$0.383860\pi$
$824$		0			0
$825$	−266.696	−	87.7094i	−0.323268	−	0.106314i
$826$		0			0
$827$	165.584	−	95.5997i	0.200222	−	0.115598i	−0.396537	−	0.918019i	$-0.629788\pi$
$827$	165.584	−	95.5997i	0.200222	−	0.115598i	0.596759	+	0.802421i	$0.296455\pi$
$828$		0			0
$829$		−	94.1061i		−	0.113518i	−0.998388	−	0.0567588i	$-0.981923\pi$
$829$		−	94.1061i		−	0.113518i	0.998388	−	0.0567588i	$-0.0180766\pi$
$830$		0			0
$831$	119.978	+	574.537i	0.144378	+	0.691380i
$832$		0			0
$833$	41.0251	+	71.0575i	0.0492498	+	0.0853031i
$834$		0			0
$835$	481.394	−	277.933i	0.576520	−	0.332854i
$836$		0			0
$837$	23.9017	+	253.520i	0.0285564	+	0.302892i
$838$		0			0
$839$		−	1113.89i		−	1.32764i	−0.747890	−	0.663822i	$-0.768933\pi$
$839$		−	1113.89i		−	1.32764i	0.747890	−	0.663822i	$-0.231067\pi$
$840$		0			0
$841$	−356.390	−	617.285i	−0.423769	−	0.733989i
$842$		0			0
$843$	722.808	+	808.550i	0.857423	+	0.959134i
$844$		0			0
$845$	−487.621	−	844.584i	−0.577066	−	0.999508i
$846$		0			0
$847$	755.118			0.891521
$848$		0			0
$849$	138.904	+	665.169i	0.163609	+	0.783474i
$850$		0			0
$851$		−	282.678i		−	0.332171i
$852$		0			0
$853$	−463.152			−0.542969			−0.271484	−	0.962443i	$-0.587515\pi$
$853$	−463.152			−0.542969			−0.271484	+	0.962443i	$0.587515\pi$
$854$		0			0
$855$	513.881	−	1046.60i	0.601030	−	1.22409i
$856$		0			0
$857$			1199.08i			1.39916i	0.714555	+	0.699579i	$0.246629\pi$
$857$			1199.08i			1.39916i	−0.714555	+	0.699579i	$0.753371\pi$
$858$		0			0
$859$	−215.415			−0.250774			−0.125387	−	0.992108i	$-0.540017\pi$
$859$	−215.415			−0.250774			−0.125387	+	0.992108i	$0.540017\pi$
$860$		0			0
$861$	−6.37923	−	7.13596i	−0.00740909	−	0.00828799i
$862$		0			0
$863$		−	1437.80i		−	1.66605i	−0.553235	−	0.833025i	$-0.686607\pi$
$863$		−	1437.80i		−	1.66605i	0.553235	−	0.833025i	$-0.313393\pi$
$864$		0			0
$865$	−1452.44	+	838.566i	−1.67912	+	0.969440i
$866$		0			0
$867$	53.0324	+	253.956i	0.0611677	+	0.292913i
$868$		0			0
$869$	−397.622	+	229.567i	−0.457562	+	0.264174i
$870$		0			0
$871$	281.685			0.323405
$872$		0			0
$873$	551.079	−	747.208i	0.631247	−	0.855909i
$874$		0			0
$875$	−88.5366	−	153.350i	−0.101185	−	0.175257i
$876$		0			0
$877$	745.262	−	430.277i	0.849786	−	0.490624i	−0.0107929	−	0.999942i	$-0.503436\pi$
$877$	745.262	−	430.277i	0.849786	−	0.490624i	0.860578	+	0.509318i	$0.170102\pi$
$878$		0			0
$879$	462.118	+	516.937i	0.525732	+	0.588096i
$880$		0			0
$881$	−532.775			−0.604739			−0.302369	−	0.953191i	$-0.597778\pi$
$881$	−532.775			−0.604739			−0.302369	+	0.953191i	$0.597778\pi$
$882$		0			0
$883$	−555.585	−	962.302i	−0.629202	−	1.08981i	−0.987712	−	0.156284i	$-0.950049\pi$
$883$	−555.585	−	962.302i	−0.629202	−	1.08981i	0.358510	−	0.933526i	$-0.383285\pi$
$884$		0			0
$885$	−887.970	−	993.304i	−1.00336	−	1.12238i
$886$		0			0
$887$			91.5586i			0.103223i	0.998667	+	0.0516114i	$0.0164357\pi$
$887$			91.5586i			0.103223i	−0.998667	+	0.0516114i	$0.983564\pi$
$888$		0			0
$889$	412.168	+	237.965i	0.463631	+	0.267678i
$890$		0			0
$891$	−239.737	+	258.722i	−0.269065	+	0.290373i
$892$		0			0
$893$	691.627	−	585.677i	0.774498	−	0.655853i
$894$		0			0
$895$	−1836.85	+	1060.51i	−2.05235	+	1.18492i
$896$		0			0
$897$	40.6616	−	123.639i	0.0453306	−	0.137836i
$898$		0			0
$899$	53.3974	+	92.4870i	0.0593964	+	0.102878i
$900$		0			0
$901$			123.519i			0.137091i
$902$		0			0
$903$	346.621	+	1659.86i	0.383855	+	1.83816i
$904$		0			0
$905$	342.208	+	197.574i	0.378130	+	0.218313i
$906$		0			0
$907$			936.792i			1.03285i	0.856334	+	0.516423i	$0.172737\pi$
$907$			936.792i			1.03285i	−0.856334	+	0.516423i	$0.827263\pi$
$908$		0			0
$909$	−792.212	+	345.954i	−0.871521	+	0.380588i
$910$		0			0
$911$	606.515	−	350.171i	0.665768	−	0.384381i	−0.128703	−	0.991683i	$-0.541081\pi$
$911$	606.515	−	350.171i	0.665768	−	0.384381i	0.794471	+	0.607302i	$0.207748\pi$
$912$		0			0
$913$	183.559	−	317.933i	0.201050	−	0.348229i
$914$		0			0
$915$	143.320	+	47.1344i	0.156634	+	0.0515130i
$916$		0			0
$917$	−281.846	+	488.171i	−0.307356	+	0.532357i
$918$		0			0
$919$	905.446			0.985251			0.492625	−	0.870241i	$-0.336037\pi$
$919$	905.446			0.985251			0.492625	+	0.870241i	$0.336037\pi$
$920$		0			0
$921$	−347.098	−	388.273i	−0.376871	−	0.421577i
$922$		0			0
$923$	−124.148	+	215.030i	−0.134505	+	0.232969i
$924$		0			0
$925$	−617.973	−	356.787i	−0.668079	−	0.385716i
$926$		0			0
$927$	−415.494	−	951.455i	−0.448214	−	1.02638i
$928$		0			0
$929$	−1353.19			−1.45661			−0.728303	−	0.685255i	$-0.759691\pi$
$929$	−1353.19			−1.45661			−0.728303	+	0.685255i	$0.759691\pi$
$930$		0			0
$931$	−83.5989	+	70.7924i	−0.0897948	+	0.0760391i
$932$		0			0
$933$	809.221	−	723.408i	0.867332	−	0.775356i
$934$		0			0
$935$	−211.268	−	365.927i	−0.225955	−	0.391366i
$936$		0			0
$937$	124.786	+	216.136i	0.133176	+	0.230668i	0.924899	−	0.380212i	$-0.124149\pi$
$937$	124.786	+	216.136i	0.133176	+	0.230668i	−0.791723	+	0.610880i	$0.790816\pi$
$938$		0			0
$939$	1330.03	−	1188.99i	1.41644	−	1.26623i
$940$		0			0
$941$			940.164i			0.999112i	0.866282	+	0.499556i	$0.166503\pi$
$941$			940.164i			0.999112i	−0.866282	+	0.499556i	$0.833497\pi$
$942$		0			0
$943$	3.17867	−	1.83521i	0.00337081	−	0.00194614i
$944$		0			0
$945$	1356.37	−	127.878i	1.43532	−	0.135321i
$946$		0			0
$947$	−1610.91			−1.70107			−0.850535	−	0.525918i	$-0.823722\pi$
$947$	−1610.91			−1.70107			−0.850535	+	0.525918i	$0.823722\pi$
$948$		0			0
$949$	−367.111	−	211.952i	−0.386840	−	0.223342i
$950$		0			0
$951$	−833.374	−	932.232i	−0.876313	−	0.980265i
$952$		0			0
$953$	−171.006	−	98.7303i	−0.179440	−	0.103599i	0.407590	−	0.913165i	$-0.366369\pi$
$953$	−171.006	−	98.7303i	−0.179440	−	0.103599i	−0.587029	+	0.809566i	$0.699703\pi$
$954$		0			0
$955$	−1004.75	+	1740.29i	−1.05210	+	1.82229i
$956$		0			0
$957$	−46.2141	+	140.522i	−0.0482906	+	0.146836i
$958$		0			0
$959$	814.864			0.849702
$960$		0			0
$961$	−436.025	−	755.218i	−0.453721	−	0.785867i
$962$		0			0
$963$	−578.127	+	783.882i	−0.600339	+	0.814000i
$964$		0			0
$965$	213.167	+	123.072i	0.220899	+	0.127536i
$966$		0			0
$967$	−602.605	−	1043.74i	−0.623169	−	1.07936i	−0.988892	−	0.148637i	$-0.952511\pi$
$967$	−602.605	−	1043.74i	−0.623169	−	1.07936i	0.365722	−	0.930724i	$-0.380822\pi$
$968$		0			0
$969$	751.818	−	304.572i	0.775870	−	0.314316i
$970$		0			0
$971$	−971.217	−	560.732i	−1.00022	−	0.577479i	−0.0919089	−	0.995767i	$-0.529297\pi$
$971$	−971.217	−	560.732i	−1.00022	−	0.577479i	−0.908314	+	0.418288i	$0.862630\pi$
$972$		0			0
$973$	−842.630	−	1459.48i	−0.866012	−	1.49998i
$974$		0			0
$975$	−218.970	−	244.945i	−0.224584	−	0.251225i
$976$		0			0
$977$	724.515	+	418.299i	0.741571	+	0.428146i	0.822640	−	0.568562i	$-0.192500\pi$
$977$	724.515	+	418.299i	0.741571	+	0.428146i	−0.0810693	+	0.996708i	$0.525834\pi$
$978$		0			0
$979$	−243.309	−	140.474i	−0.248528	−	0.143488i
$980$		0			0
$981$	−377.717	−	864.947i	−0.385033	−	0.881700i
$982$		0			0
$983$			473.499i			0.481687i	0.970564	+	0.240844i	$0.0774241\pi$
$983$			473.499i			0.481687i	−0.970564	+	0.240844i	$0.922576\pi$
$984$		0			0
$985$	785.578	+	1360.66i	0.797541	+	1.38138i
$986$		0			0
$987$	1005.98	+	330.840i	1.01923	+	0.335198i
$988$		0			0
$989$	−650.234			−0.657466
$990$		0			0
$991$	579.617	+	334.642i	0.584881	+	0.337681i	0.763071	−	0.646315i	$-0.223691\pi$
$991$	579.617	+	334.642i	0.584881	+	0.337681i	−0.178190	+	0.983996i	$0.557024\pi$
$992$		0			0
$993$	957.277	−	199.904i	0.964025	−	0.201313i
$994$		0			0
$995$	−264.803	+	458.652i	−0.266134	+	0.460957i
$996$		0			0
$997$	223.254	−	386.687i	0.223926	−	0.387851i	−0.732071	−	0.681228i	$-0.761446\pi$
$997$	223.254	−	386.687i	0.223926	−	0.387851i	0.955997	+	0.293378i	$0.0947794\pi$
$998$		0			0
$999$	−730.892	+	519.147i	−0.731623	+	0.519667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.35	✓	80
3.2	odd	2		2052.3.s.a.901.35		80
9.2	odd	6		2052.3.bl.a.1585.6		80
9.7	even	3		684.3.bl.a.673.32	yes	80
19.12	odd	6		684.3.bl.a.373.32	yes	80
57.50	even	6		2052.3.bl.a.145.6		80
171.88	odd	6	inner	684.3.s.a.601.35	yes	80
171.164	even	6		2052.3.s.a.829.35		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.35	✓	80	1.1	even	1	trivial
684.3.s.a.601.35	yes	80	171.88	odd	6	inner
684.3.bl.a.373.32	yes	80	19.12	odd	6
684.3.bl.a.673.32	yes	80	9.7	even	3
2052.3.s.a.829.35		80	171.164	even	6
2052.3.s.a.901.35		80	3.2	odd	2
2052.3.bl.a.145.6		80	57.50	even	6
2052.3.bl.a.1585.6		80	9.2	odd	6

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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.84984 + 0.937239i) q^{3} +(-3.40921 - 5.90492i) q^{5} +(3.70019 + 6.40891i) q^{7} +(7.24317 + 5.34196i) q^{9} +O(q^{10})\)	\(q+(2.84984 + 0.937239i) q^{3} +(-3.40921 - 5.90492i) q^{5} +(3.70019 + 6.40891i) q^{7} +(7.24317 + 5.34196i) q^{9} +(2.17728 + 3.77116i) q^{11} +5.09601i q^{13} +(-4.18137 - 20.0233i) q^{15} +(7.11551 - 12.3244i) q^{17} +(17.8833 + 6.41783i) q^{19} +(4.53826 + 21.7323i) q^{21} -8.51341 q^{23} +(-10.7454 + 18.6115i) q^{25} +(15.6352 + 22.0123i) q^{27} +(9.80640 + 5.66173i) q^{29} +(8.16773 + 4.71564i) q^{31} +(2.67042 + 12.7878i) q^{33} +(25.2294 - 43.6986i) q^{35} +33.2038i q^{37} +(-4.77618 + 14.5228i) q^{39} +(-0.373372 + 0.215567i) q^{41} +76.3776 q^{43} +(6.85038 - 60.9821i) q^{45} +(23.8498 - 41.3090i) q^{47} +(-2.88279 + 4.99314i) q^{49} +(31.8290 - 28.4537i) q^{51} +(-7.51673 + 4.33978i) q^{53} +(14.8456 - 25.7133i) q^{55} +(44.9494 + 35.0507i) q^{57} +(56.4083 - 32.5673i) q^{59} +(-3.68786 + 6.38756i) q^{61} +(-7.43508 + 66.1871i) q^{63} +(30.0915 - 17.3733i) q^{65} -55.2757i q^{67} +(-24.2619 - 7.97910i) q^{69} +(42.1958 + 24.3618i) q^{71} +(-41.5917 + 72.0390i) q^{73} +(-48.0660 + 42.9689i) q^{75} +(-16.1127 + 27.9080i) q^{77} +105.437i q^{79} +(23.9269 + 77.3854i) q^{81} +(-42.1532 - 73.0115i) q^{83} -97.0330 q^{85} +(22.6403 + 25.3260i) q^{87} +(-55.8744 + 32.2591i) q^{89} +(-32.6599 + 18.8562i) q^{91} +(18.8570 + 21.0939i) q^{93} +(-23.0710 - 127.479i) q^{95} -103.160i q^{97} +(-4.37498 + 38.9461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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