LMFDB - Embedded newform 378.3.s.e.53.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,3,Mod(53,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("378.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.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:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.11
Character	$\chi$	$=$	378.53
Dual form			378.3.s.e.107.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.00128 - 4.04219i) q^{5} +(6.42484 - 2.77874i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.00128 - 4.04219i) q^{5} +(6.42484 - 2.77874i) q^{7} -2.82843i q^{8} +(5.71652 - 9.90131i) q^{10} +(-0.831900 - 0.480298i) q^{11} -16.2817 q^{13} +(5.90393 - 7.94629i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(10.0000 + 5.77351i) q^{17} +(6.31367 + 10.9356i) q^{19} -16.1688i q^{20} -1.35849 q^{22} +(-19.6604 + 11.3510i) q^{23} +(20.1786 - 34.9504i) q^{25} +(-19.9409 + 11.5129i) q^{26} +(1.61193 - 13.9069i) q^{28} +41.8238i q^{29} +(12.7406 - 22.0674i) q^{31} +(-4.89898 - 2.82843i) q^{32} +16.3299 q^{34} +(33.7500 - 45.4252i) q^{35} +(-32.3583 - 56.0461i) q^{37} +(15.4653 + 8.92887i) q^{38} +(-11.4330 - 19.8026i) q^{40} -20.4209i q^{41} +30.7575 q^{43} +(-1.66380 + 0.960596i) q^{44} +(-16.0527 + 27.8041i) q^{46} +(-53.3167 + 30.7824i) q^{47} +(33.5573 - 35.7059i) q^{49} -57.0738i q^{50} +(-16.2817 + 28.2007i) q^{52} +(46.9217 + 27.0903i) q^{53} -7.76583 q^{55} +(-7.85945 - 18.1722i) q^{56} +(29.5739 + 51.2235i) q^{58} +(71.7676 + 41.4350i) q^{59} +(-14.0538 - 24.3419i) q^{61} -36.0360i q^{62} -8.00000 q^{64} +(-113.993 + 65.8138i) q^{65} +(28.6849 - 49.6838i) q^{67} +(20.0000 - 11.5470i) q^{68} +(9.21466 - 79.4991i) q^{70} +26.6313i q^{71} +(-40.0885 + 69.4353i) q^{73} +(-79.2612 - 45.7615i) q^{74} +25.2547 q^{76} +(-6.67945 - 0.774208i) q^{77} +(53.2847 + 92.2918i) q^{79} +(-28.0051 - 16.1688i) q^{80} +(-14.4397 - 25.0104i) q^{82} +121.700i q^{83} +93.3505 q^{85} +(37.6701 - 21.7489i) q^{86} +(-1.35849 + 2.35297i) q^{88} +(-75.7166 + 43.7150i) q^{89} +(-104.607 + 45.2425i) q^{91} +45.4038i q^{92} +(-43.5329 + 75.4012i) q^{94} +(88.4076 + 51.0421i) q^{95} -173.692 q^{97} +(15.8512 - 67.4592i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} + 8 q^{7}+O(q^{10}) $ 24 * q + 24 * q^4 + 8 * q^7	$ 24 q + 24 q^{4} + 8 q^{7} + 8 q^{10} - 16 q^{13} - 48 q^{16} - 36 q^{19} + 64 q^{22} + 128 q^{25} + 32 q^{28} + 176 q^{31} + 16 q^{34} - 72 q^{37} - 16 q^{40} + 216 q^{43} + 64 q^{46} - 24 q^{49} - 16 q^{52} + 448 q^{55} + 104 q^{58} - 268 q^{61} - 192 q^{64} - 248 q^{67} - 80 q^{70} - 116 q^{73} - 144 q^{76} + 152 q^{79} + 240 q^{82} - 536 q^{85} + 64 q^{88} + 428 q^{91} + 144 q^{94} + 16 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 + 8 * q^7 + 8 * q^10 - 16 * q^13 - 48 * q^16 - 36 * q^19 + 64 * q^22 + 128 * q^25 + 32 * q^28 + 176 * q^31 + 16 * q^34 - 72 * q^37 - 16 * q^40 + 216 * q^43 + 64 * q^46 - 24 * q^49 - 16 * q^52 + 448 * q^55 + 104 * q^58 - 268 * q^61 - 192 * q^64 - 248 * q^67 - 80 * q^70 - 116 * q^73 - 144 * q^76 + 152 * q^79 + 240 * q^82 - 536 * q^85 + 64 * q^88 + 428 * q^91 + 144 * q^94 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	7.00128	−	4.04219i	1.40026	−	0.808439i	0.405838	−	0.913945i	$-0.366980\pi$
$5$	7.00128	−	4.04219i	1.40026	−	0.808439i	0.994419	+	0.105506i	$0.0336463\pi$
$6$		0			0
$7$	6.42484	−	2.77874i	0.917835	−	0.396962i
$7$	6.42484	−	2.77874i	0.917835	−	0.396962i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	5.71652	−	9.90131i	0.571652	−	0.990131i
$11$	−0.831900	−	0.480298i	−0.0756273	−	0.0436634i	0.461710	−	0.887031i	$-0.347236\pi$
$11$	−0.831900	−	0.480298i	−0.0756273	−	0.0436634i	−0.537337	+	0.843368i	$0.680570\pi$
$12$		0			0
$13$	−16.2817			−1.25244			−0.626219	−	0.779647i	$-0.715399\pi$
$13$	−16.2817			−1.25244			−0.626219	+	0.779647i	$0.715399\pi$
$14$	5.90393	−	7.94629i	0.421709	−	0.567592i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	10.0000	+	5.77351i	0.588236	+	0.339618i	0.764400	−	0.644743i	$-0.223036\pi$
$17$	10.0000	+	5.77351i	0.588236	+	0.339618i	−0.176164	+	0.984361i	$0.556369\pi$
$18$		0			0
$19$	6.31367	+	10.9356i	0.332298	+	0.575558i	0.982962	−	0.183808i	$-0.0588426\pi$
$19$	6.31367	+	10.9356i	0.332298	+	0.575558i	−0.650664	+	0.759366i	$0.725509\pi$
$20$		−	16.1688i		−	0.808439i
$21$		0			0
$22$	−1.35849			−0.0617494
$23$	−19.6604	+	11.3510i	−0.854802	+	0.493520i	−0.862268	−	0.506452i	$-0.830957\pi$
$23$	−19.6604	+	11.3510i	−0.854802	+	0.493520i	0.00746632	+	0.999972i	$0.497623\pi$
$24$		0			0
$25$	20.1786	−	34.9504i	0.807146	−	1.39802i
$26$	−19.9409	+	11.5129i	−0.766959	+	0.442804i
$27$		0			0
$28$	1.61193	−	13.9069i	0.0575690	−	0.496675i
$29$			41.8238i			1.44220i	0.692830	+	0.721101i	$0.256363\pi$
$29$			41.8238i			1.44220i	−0.692830	+	0.721101i	$0.743637\pi$
$30$		0			0
$31$	12.7406	−	22.0674i	0.410989	−	0.711853i	−0.584010	−	0.811747i	$-0.698517\pi$
$31$	12.7406	−	22.0674i	0.410989	−	0.711853i	0.994998	+	0.0998937i	$0.0318503\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	16.3299			0.480292
$35$	33.7500	−	45.4252i	0.964285	−	1.29786i
$36$		0			0
$37$	−32.3583	−	56.0461i	−0.874547	−	1.51476i	−0.857244	−	0.514910i	$-0.827825\pi$
$37$	−32.3583	−	56.0461i	−0.874547	−	1.51476i	−0.0173032	−	0.999850i	$-0.505508\pi$
$38$	15.4653	+	8.92887i	0.406981	+	0.234970i
$39$		0			0
$40$	−11.4330	−	19.8026i	−0.285826	−	0.495066i
$41$		−	20.4209i		−	0.498070i	−0.968494	−	0.249035i	$-0.919887\pi$
$41$		−	20.4209i		−	0.498070i	0.968494	−	0.249035i	$-0.0801135\pi$
$42$		0			0
$43$	30.7575			0.715291			0.357646	−	0.933857i	$-0.383580\pi$
$43$	30.7575			0.715291			0.357646	+	0.933857i	$0.383580\pi$
$44$	−1.66380	+	0.960596i	−0.0378136	+	0.0218317i
$45$		0			0
$46$	−16.0527	+	27.8041i	−0.348971	+	0.604436i
$47$	−53.3167	+	30.7824i	−1.13440	+	0.654945i	−0.945037	−	0.326962i	$-0.893975\pi$
$47$	−53.3167	+	30.7824i	−1.13440	+	0.654945i	−0.189361	+	0.981908i	$0.560642\pi$
$48$		0			0
$49$	33.5573	−	35.7059i	0.684842	−	0.728692i
$50$		−	57.0738i		−	1.14148i
$51$		0			0
$52$	−16.2817	+	28.2007i	−0.313110	+	0.542322i
$53$	46.9217	+	27.0903i	0.885316	+	0.511137i	0.872407	−	0.488780i	$-0.162558\pi$
$53$	46.9217	+	27.0903i	0.885316	+	0.511137i	0.0129082	+	0.999917i	$0.495891\pi$
$54$		0			0
$55$	−7.76583			−0.141197
$56$	−7.85945	−	18.1722i	−0.140347	−	0.324504i
$57$		0			0
$58$	29.5739	+	51.2235i	0.509895	+	0.883164i
$59$	71.7676	+	41.4350i	1.21640	+	0.702289i	0.964146	−	0.265372i	$-0.0854948\pi$
$59$	71.7676	+	41.4350i	1.21640	+	0.702289i	0.252254	+	0.967661i	$0.418828\pi$
$60$		0			0
$61$	−14.0538	−	24.3419i	−0.230390	−	0.399047i	0.727533	−	0.686073i	$-0.240667\pi$
$61$	−14.0538	−	24.3419i	−0.230390	−	0.399047i	−0.957923	+	0.287026i	$0.907333\pi$
$62$		−	36.0360i		−	0.581226i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−113.993	+	65.8138i	−1.75374	+	1.01252i
$66$		0			0
$67$	28.6849	−	49.6838i	0.428134	−	0.741549i	−0.568574	−	0.822632i	$-0.692505\pi$
$67$	28.6849	−	49.6838i	0.428134	−	0.741549i	0.996707	+	0.0810832i	$0.0258380\pi$
$68$	20.0000	−	11.5470i	0.294118	−	0.169809i
$69$		0			0
$70$	9.21466	−	79.4991i	0.131638	−	1.13570i
$71$			26.6313i			0.375089i	0.982256	+	0.187544i	$0.0600528\pi$
$71$			26.6313i			0.375089i	−0.982256	+	0.187544i	$0.939947\pi$
$72$		0			0
$73$	−40.0885	+	69.4353i	−0.549158	+	0.951169i	0.449175	+	0.893444i	$0.351718\pi$
$73$	−40.0885	+	69.4353i	−0.549158	+	0.951169i	−0.998333	+	0.0577251i	$0.981615\pi$
$74$	−79.2612	−	45.7615i	−1.07110	−	0.618398i
$75$		0			0
$76$	25.2547			0.332298
$77$	−6.67945	−	0.774208i	−0.0867461	−	0.0100546i
$78$		0			0
$79$	53.2847	+	92.2918i	0.674490	+	1.16825i	0.976618	+	0.214984i	$0.0689698\pi$
$79$	53.2847	+	92.2918i	0.674490	+	1.16825i	−0.302128	+	0.953267i	$0.597697\pi$
$80$	−28.0051	−	16.1688i	−0.350064	−	0.202110i
$81$		0			0
$82$	−14.4397	−	25.0104i	−0.176094	−	0.305005i
$83$			121.700i			1.46627i	0.680083	+	0.733135i	$0.261944\pi$
$83$			121.700i			1.46627i	−0.680083	+	0.733135i	$0.738056\pi$
$84$		0			0
$85$	93.3505			1.09824
$86$	37.6701	−	21.7489i	0.438025	−	0.252894i
$87$		0			0
$88$	−1.35849	+	2.35297i	−0.0154374	+	0.0267383i
$89$	−75.7166	+	43.7150i	−0.850748	+	0.491180i	−0.860903	−	0.508769i	$-0.830101\pi$
$89$	−75.7166	+	43.7150i	−0.850748	+	0.491180i	0.0101552	+	0.999948i	$0.496767\pi$
$90$		0			0
$91$	−104.607	+	45.2425i	−1.14953	+	0.497171i
$92$			45.4038i			0.493520i
$93$		0			0
$94$	−43.5329	+	75.4012i	−0.463116	+	0.802141i
$95$	88.4076	+	51.0421i	0.930606	+	0.537286i
$96$		0			0
$97$	−173.692			−1.79064			−0.895319	−	0.445425i	$-0.853053\pi$
$97$	−173.692			−1.79064			−0.895319	+	0.445425i	$0.853053\pi$
$98$	15.8512	−	67.4592i	0.161747	−	0.688359i
$99$		0			0
$100$	−40.3573	−	69.9009i	−0.403573	−	0.699009i
$101$	−84.5536	−	48.8170i	−0.837164	−	0.483337i	0.0191352	−	0.999817i	$-0.493909\pi$
$101$	−84.5536	−	48.8170i	−0.837164	−	0.483337i	−0.856299	+	0.516480i	$0.827242\pi$
$102$		0			0
$103$	57.6815	+	99.9073i	0.560015	+	0.969974i	0.997494	+	0.0707458i	$0.0225379\pi$
$103$	57.6815	+	99.9073i	0.560015	+	0.969974i	−0.437480	+	0.899228i	$0.644129\pi$
$104$			46.0516i			0.442804i
$105$		0			0
$106$	76.6229			0.722857
$107$	28.4534	−	16.4276i	0.265920	−	0.153529i	−0.361112	−	0.932522i	$-0.617603\pi$
$107$	28.4534	−	16.4276i	0.265920	−	0.153529i	0.627032	+	0.778994i	$0.284270\pi$
$108$		0			0
$109$	−64.2515	+	111.287i	−0.589463	+	1.02098i	0.404840	+	0.914388i	$0.367327\pi$
$109$	−64.2515	+	111.287i	−0.589463	+	1.02098i	−0.994303	+	0.106592i	$0.966006\pi$
$110$	−9.51116	+	5.49127i	−0.0864651	+	0.0499206i
$111$		0			0
$112$	−22.4755	−	16.6988i	−0.200674	−	0.149097i
$113$		−	154.479i		−	1.36707i	−0.729919	−	0.683534i	$-0.760442\pi$
$113$		−	154.479i		−	1.36707i	0.729919	−	0.683534i	$-0.239558\pi$
$114$		0			0
$115$	−91.7656	+	158.943i	−0.797961	+	1.38211i
$116$	72.4410	+	41.8238i	0.624491	+	0.360550i
$117$		0			0
$118$	117.196			0.993186
$119$	80.2915	+	9.30651i	0.674719	+	0.0782059i
$120$		0			0
$121$	−60.0386	−	103.990i	−0.496187	−	0.859421i
$122$	−34.4246	−	19.8750i	−0.282169	−	0.162910i
$123$		0			0
$124$	−25.4813	−	44.1349i	−0.205494	−	0.355927i
$125$		−	124.154i		−	0.993235i
$126$		0			0
$127$	172.349			1.35708			0.678540	−	0.734563i	$-0.262613\pi$
$127$	172.349			1.35708			0.678540	+	0.734563i	$0.262613\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−93.0747	+	161.210i	−0.715960	+	1.24008i
$131$	132.202	−	76.3270i	1.00918	−	0.582649i	0.0982269	−	0.995164i	$-0.468683\pi$
$131$	132.202	−	76.3270i	1.00918	−	0.582649i	0.910951	+	0.412515i	$0.135350\pi$
$132$		0			0
$133$	70.9515	+	52.7155i	0.533470	+	0.396357i
$134$		−	81.1333i		−	0.605472i
$135$		0			0
$136$	16.3299	−	28.2843i	0.120073	−	0.207973i
$137$	130.533	+	75.3633i	0.952796	+	0.550097i	0.893948	−	0.448170i	$-0.147924\pi$
$137$	130.533	+	75.3633i	0.952796	+	0.550097i	0.0588474	+	0.998267i	$0.481257\pi$
$138$		0			0
$139$	−269.648			−1.93991			−0.969956	−	0.243281i	$-0.921776\pi$
$139$	−269.648			−1.93991			−0.969956	+	0.243281i	$0.921776\pi$
$140$	−44.9287	−	103.882i	−0.320920	−	0.742013i
$141$		0			0
$142$	18.8312	+	32.6165i	0.132614	+	0.229694i
$143$	13.5448	+	7.82007i	0.0947185	+	0.0546858i
$144$		0			0
$145$	169.060	+	292.821i	1.16593	+	2.01945i
$146$			113.387i			0.776626i
$147$		0			0
$148$	−129.433			−0.874547
$149$	177.578	−	102.525i	1.19180	−	0.688087i	0.233086	−	0.972456i	$-0.425118\pi$
$149$	177.578	−	102.525i	1.19180	−	0.688087i	0.958715	+	0.284370i	$0.0917843\pi$
$150$		0			0
$151$	13.7749	−	23.8588i	0.0912243	−	0.158005i	−0.816802	−	0.576918i	$-0.804255\pi$
$151$	13.7749	−	23.8588i	0.0912243	−	0.158005i	0.908027	+	0.418913i	$0.137589\pi$
$152$	30.9305	−	17.8577i	0.203490	−	0.117485i
$153$		0			0
$154$	−8.72807	+	3.77488i	−0.0566758	+	0.0245122i
$155$		−	206.001i		−	1.32904i
$156$		0			0
$157$	−72.4055	+	125.410i	−0.461181	+	0.798789i	−0.999020	−	0.0442582i	$-0.985908\pi$
$157$	−72.4055	+	125.410i	−0.461181	+	0.798789i	0.537839	+	0.843048i	$0.319241\pi$
$158$	130.520	+	75.3560i	0.826078	+	0.476936i
$159$		0			0
$160$	−45.7322			−0.285826
$161$	−94.7740	+	127.559i	−0.588658	+	0.792294i
$162$		0			0
$163$	−143.552	−	248.639i	−0.880686	−	1.52539i	−0.850580	−	0.525846i	$-0.823749\pi$
$163$	−143.552	−	248.639i	−0.880686	−	1.52539i	−0.0301065	−	0.999547i	$-0.509585\pi$
$164$	−35.3700	−	20.4209i	−0.215671	−	0.124518i
$165$		0			0
$166$	86.0552	+	149.052i	0.518405	+	0.897904i
$167$			146.334i			0.876249i	0.898914	+	0.438125i	$0.144357\pi$
$167$			146.334i			0.876249i	−0.898914	+	0.438125i	$0.855643\pi$
$168$		0			0
$169$	96.0938			0.568602
$170$	114.331	−	66.0088i	0.672533	−	0.388287i
$171$		0			0
$172$	30.7575	−	53.2736i	0.178823	−	0.309730i
$173$	−242.873	+	140.223i	−1.40389	+	0.810535i	−0.994789	−	0.101954i	$-0.967490\pi$
$173$	−242.873	+	140.223i	−1.40389	+	0.810535i	−0.409099	+	0.912490i	$0.634157\pi$
$174$		0			0
$175$	32.5266	−	280.622i	0.185866	−	1.60356i
$176$			3.84238i			0.0218317i
$177$		0			0
$178$	−61.8223	+	107.079i	−0.347316	+	0.601570i
$179$	51.2768	+	29.6047i	0.286463	+	0.165389i	0.636346	−	0.771404i	$-0.280445\pi$
$179$	51.2768	+	29.6047i	0.286463	+	0.165389i	−0.349883	+	0.936793i	$0.613779\pi$
$180$		0			0
$181$	237.004			1.30942			0.654708	−	0.755882i	$-0.272792\pi$
$181$	237.004			1.30942			0.654708	+	0.755882i	$0.272792\pi$
$182$	−96.1261	+	129.379i	−0.528165	+	0.710875i
$183$		0			0
$184$	32.1054	+	55.6081i	0.174486	+	0.302218i
$185$	−453.099	−	261.597i	−2.44918	−	1.41404i
$186$		0			0
$187$	−5.54601	−	9.60596i	−0.0296578	−	0.0513688i
$188$			123.130i			0.654945i
$189$		0			0
$190$	144.369			0.759837
$191$	−82.6301	+	47.7065i	−0.432618	+	0.249772i	−0.700461	−	0.713690i	$-0.747022\pi$
$191$	−82.6301	+	47.7065i	−0.432618	+	0.249772i	0.267843	+	0.963463i	$0.413689\pi$
$192$		0			0
$193$	41.1624	−	71.2953i	0.213276	−	0.369406i	−0.739462	−	0.673199i	$-0.764920\pi$
$193$	41.1624	−	71.2953i	0.213276	−	0.369406i	0.952738	+	0.303793i	$0.0982532\pi$
$194$	−212.728	+	122.819i	−1.09654	+	0.633086i
$195$		0			0
$196$	−28.2872	−	93.8288i	−0.144322	−	0.478718i
$197$		−	9.72356i		−	0.0493582i	−0.999695	−	0.0246791i	$-0.992144\pi$
$197$		−	9.72356i		−	0.0493582i	0.999695	−	0.0246791i	$-0.00785640\pi$
$198$		0			0
$199$	78.3044	−	135.627i	0.393490	−	0.681544i	−0.599417	−	0.800437i	$-0.704601\pi$
$199$	78.3044	−	135.627i	0.393490	−	0.681544i	0.992907	+	0.118892i	$0.0379344\pi$
$200$	−98.8548	−	57.0738i	−0.494274	−	0.285369i
$201$		0			0
$202$	−138.075			−0.683542
$203$	116.217	+	268.712i	0.572499	+	1.32370i
$204$		0			0
$205$	−82.5451	−	142.972i	−0.402659	−	0.697426i
$206$	141.290	+	81.5740i	0.685875	+	0.395990i
$207$		0			0
$208$	32.5634	+	56.4015i	0.156555	+	0.271161i
$209$		−	12.1298i		−	0.0580371i
$210$		0			0
$211$	209.927			0.994915			0.497457	−	0.867488i	$-0.334267\pi$
$211$	209.927			0.994915			0.497457	+	0.867488i	$0.334267\pi$
$212$	93.8434	−	54.1805i	0.442658	−	0.255569i
$213$		0			0
$214$	23.2321	−	40.2392i	0.108561	−	0.188034i
$215$	215.342	−	124.328i	1.00159	−	0.578269i
$216$		0			0
$217$	20.5371	−	177.183i	0.0946409	−	0.816511i
$218$			181.731i			0.833627i
$219$		0			0
$220$	−7.76583	+	13.4508i	−0.0352992	+	0.0611400i
$221$	−162.817	−	94.0025i	−0.736729	−	0.425351i
$222$		0			0
$223$	6.37856			0.0286034			0.0143017	−	0.999898i	$-0.495447\pi$
$223$	6.37856			0.0286034			0.0143017	+	0.999898i	$0.495447\pi$
$224$	−39.3346	−	4.55924i	−0.175601	−	0.0203537i
$225$		0			0
$226$	−109.233	−	189.197i	−0.483332	−	0.837155i
$227$	−78.4025	−	45.2657i	−0.345386	−	0.199409i	0.317265	−	0.948337i	$-0.397235\pi$
$227$	−78.4025	−	45.2657i	−0.345386	−	0.199409i	−0.662651	+	0.748928i	$0.730569\pi$
$228$		0			0
$229$	−62.6964	−	108.593i	−0.273783	−	0.474207i	0.696044	−	0.717999i	$-0.254942\pi$
$229$	−62.6964	−	108.593i	−0.273783	−	0.474207i	−0.969827	+	0.243792i	$0.921608\pi$
$230$			259.552i			1.12849i
$231$		0			0
$232$	118.296			0.509895
$233$	−206.920	+	119.465i	−0.888069	+	0.512727i	−0.873311	−	0.487164i	$-0.838031\pi$
$233$	−206.920	+	119.465i	−0.888069	+	0.512727i	−0.0147589	+	0.999891i	$0.504698\pi$
$234$		0			0
$235$	−248.857	+	431.033i	−1.05897	+	1.83418i
$236$	143.535	−	82.8701i	0.608200	−	0.351144i
$237$		0			0
$238$	104.917	−	45.3766i	0.440829	−	0.190658i
$239$			16.8169i			0.0703636i	0.999381	+	0.0351818i	$0.0112010\pi$
$239$			16.8169i			0.0703636i	−0.999381	+	0.0351818i	$0.988799\pi$
$240$		0			0
$241$	−171.105	+	296.362i	−0.709978	+	1.22972i	0.254886	+	0.966971i	$0.417962\pi$
$241$	−171.105	+	296.362i	−0.709978	+	1.22972i	−0.964865	+	0.262748i	$0.915371\pi$
$242$	−147.064	−	84.9074i	−0.607702	−	0.350857i
$243$		0			0
$244$	−56.2151			−0.230390
$245$	90.6138	−	385.632i	0.369852	−	1.57401i
$246$		0			0
$247$	−102.797	−	178.050i	−0.416183	−	0.720851i
$248$	−62.4162	−	36.0360i	−0.251678	−	0.145306i
$249$		0			0
$250$	−87.7904	−	152.057i	−0.351161	−	0.608230i
$251$		−	310.185i		−	1.23580i	−0.786258	−	0.617899i	$-0.787984\pi$
$251$		−	310.185i		−	1.23580i	0.786258	−	0.617899i	$-0.212016\pi$
$252$		0			0
$253$	21.8074			0.0861951
$254$	211.084	−	121.869i	0.831039	−	0.479800i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	55.8903	−	32.2683i	0.217472	−	0.125557i	−0.387307	−	0.921951i	$-0.626595\pi$
$257$	55.8903	−	32.2683i	0.217472	−	0.125557i	0.604779	+	0.796393i	$0.293261\pi$
$258$		0			0
$259$	−363.634	−	270.173i	−1.40399	−	1.04314i
$260$			263.255i			1.01252i
$261$		0			0
$262$	107.943	−	186.962i	0.411995	−	0.713596i
$263$	342.454	+	197.716i	1.30211	+	0.751772i	0.980765	−	0.195192i	$-0.0625330\pi$
$263$	342.454	+	197.716i	1.30211	+	0.751772i	0.321341	+	0.946963i	$0.395866\pi$
$264$		0			0
$265$	438.016			1.65289
$266$	124.173	+	14.3928i	0.466815	+	0.0541081i
$267$		0			0
$268$	−57.3699	−	99.3676i	−0.214067	−	0.370775i
$269$	75.9089	+	43.8261i	0.282189	+	0.162922i	0.634414	−	0.772993i	$-0.281241\pi$
$269$	75.9089	+	43.8261i	0.282189	+	0.162922i	−0.352225	+	0.935915i	$0.614575\pi$
$270$		0			0
$271$	−19.5621	−	33.8826i	−0.0721849	−	0.125028i	0.827674	−	0.561210i	$-0.189664\pi$
$271$	−19.5621	−	33.8826i	−0.0721849	−	0.125028i	−0.899859	+	0.436182i	$0.856331\pi$
$272$		−	46.1881i		−	0.169809i
$273$		0			0
$274$	213.159			0.777954
$275$	−33.5732	+	19.3835i	−0.122085	+	0.0704855i
$276$		0			0
$277$	111.415	−	192.976i	0.402219	−	0.696663i	−0.591775	−	0.806103i	$-0.701573\pi$
$277$	111.415	−	192.976i	0.402219	−	0.696663i	0.993993	+	0.109440i	$0.0349059\pi$
$278$	−330.250	+	190.670i	−1.18795	+	0.685862i
$279$		0			0
$280$	−128.482	−	95.4593i	−0.458864	−	0.340926i
$281$		−	217.979i		−	0.775728i	−0.921717	−	0.387864i	$-0.873213\pi$
$281$		−	217.979i		−	0.775728i	0.921717	−	0.387864i	$-0.126787\pi$
$282$		0			0
$283$	152.677	−	264.444i	0.539493	−	0.934430i	−0.459438	−	0.888210i	$-0.651949\pi$
$283$	152.677	−	264.444i	0.539493	−	0.934430i	0.998931	−	0.0462200i	$-0.0147175\pi$
$284$	46.1267	+	26.6313i	0.162418	+	0.0937721i
$285$		0			0
$286$	22.1185			0.0773374
$287$	−56.7442	−	131.201i	−0.197715	−	0.457146i
$288$		0			0
$289$	−77.8332	−	134.811i	−0.269319	−	0.466474i
$290$	414.111	+	239.087i	1.42797	+	0.824438i
$291$		0			0
$292$	80.1770	+	138.871i	0.274579	+	0.475584i
$293$		−	219.569i		−	0.749382i	−0.927150	−	0.374691i	$-0.877749\pi$
$293$		−	219.569i		−	0.749382i	0.927150	−	0.374691i	$-0.122251\pi$
$294$		0			0
$295$	669.954			2.27103
$296$	−158.522	+	91.5230i	−0.535549	+	0.309199i
$297$		0			0
$298$	144.992	−	251.134i	0.486551	−	0.842730i
$299$	320.105	−	184.813i	1.07059	−	0.618104i
$300$		0			0
$301$	197.612	−	85.4671i	0.656519	−	0.283944i
$302$		−	38.9612i		−	0.129011i
$303$		0			0
$304$	25.2547	−	43.7424i	0.0830746	−	0.143889i
$305$	−196.789	−	113.616i	−0.645210	−	0.372512i
$306$		0			0
$307$	−178.604			−0.581771			−0.290885	−	0.956758i	$-0.593950\pi$
$307$	−178.604			−0.581771			−0.290885	+	0.956758i	$0.593950\pi$
$308$	−8.02042	+	10.7949i	−0.0260403	+	0.0350485i
$309$		0			0
$310$	−145.664	−	252.298i	−0.469885	−	0.813865i
$311$	−95.2225	−	54.9768i	−0.306182	−	0.176774i	0.339035	−	0.940774i	$-0.389900\pi$
$311$	−95.2225	−	54.9768i	−0.306182	−	0.176774i	−0.645217	+	0.764000i	$0.723233\pi$
$312$		0			0
$313$	−130.054	−	225.261i	−0.415509	−	0.719682i	0.579973	−	0.814636i	$-0.303063\pi$
$313$	−130.054	−	225.261i	−0.415509	−	0.719682i	−0.995482	+	0.0949534i	$0.969730\pi$
$314$			204.794i			0.652209i
$315$		0			0
$316$	213.139			0.674490
$317$	−196.176	+	113.262i	−0.618852	+	0.357294i	−0.776422	−	0.630214i	$-0.782967\pi$
$317$	−196.176	+	113.262i	−0.618852	+	0.357294i	0.157570	+	0.987508i	$0.449634\pi$
$318$		0			0
$319$	20.0879	−	34.7933i	0.0629715	−	0.109070i
$320$	−56.0103	+	32.3375i	−0.175032	+	0.101055i
$321$		0			0
$322$	−25.8759	+	223.243i	−0.0803598	+	0.693301i
$323$			145.808i			0.451418i
$324$		0			0
$325$	−328.543	+	569.053i	−1.01090	+	1.75093i
$326$	−351.629	−	203.013i	−1.07862	−	0.622739i
$327$		0			0
$328$	−57.7590			−0.176094
$329$	−257.015	+	345.925i	−0.781202	+	1.05145i
$330$		0			0
$331$	179.234	+	310.442i	0.541492	+	0.937891i	0.998819	+	0.0485926i	$0.0154736\pi$
$331$	179.234	+	310.442i	0.541492	+	0.937891i	−0.457327	+	0.889299i	$0.651193\pi$
$332$	210.791	+	121.700i	0.634914	+	0.366568i
$333$		0			0
$334$	103.474	+	179.221i	0.309801	+	0.536591i
$335$		−	463.800i		−	1.38448i
$336$		0			0
$337$	−147.901			−0.438875			−0.219437	−	0.975627i	$-0.570422\pi$
$337$	−147.901			−0.438875			−0.219437	+	0.975627i	$0.570422\pi$
$338$	117.690	−	67.9486i	0.348196	−	0.201031i
$339$		0			0
$340$	93.3505	−	161.688i	0.274560	−	0.475552i
$341$	−21.1979	+	12.2386i	−0.0621639	+	0.0358903i
$342$		0			0
$343$	116.383	−	322.652i	0.339309	−	0.940675i
$344$		−	86.9954i		−	0.252894i
$345$		0			0
$346$	−198.305	+	343.474i	−0.573135	+	0.992699i
$347$	79.2271	+	45.7418i	0.228320	+	0.131821i	0.609797	−	0.792558i	$-0.291251\pi$
$347$	79.2271	+	45.7418i	0.228320	+	0.131821i	−0.381477	+	0.924378i	$0.624584\pi$
$348$		0			0
$349$	−112.384			−0.322016			−0.161008	−	0.986953i	$-0.551475\pi$
$349$	−112.384			−0.322016			−0.161008	+	0.986953i	$0.551475\pi$
$350$	−158.593	−	366.691i	−0.453123	−	1.04769i
$351$		0			0
$352$	2.71697	+	4.70594i	0.00771868	+	0.0133691i
$353$	338.555	+	195.465i	0.959078	+	0.553724i	0.895889	−	0.444277i	$-0.146540\pi$
$353$	338.555	+	195.465i	0.959078	+	0.553724i	0.0631892	+	0.998002i	$0.479873\pi$
$354$		0			0
$355$	107.649	+	186.453i	0.303236	+	0.525220i
$356$			174.860i			0.491180i
$357$		0			0
$358$	83.7347			0.233896
$359$	−363.231	+	209.712i	−1.01179	+	0.584155i	−0.911714	−	0.410825i	$-0.865241\pi$
$359$	−363.231	+	209.712i	−1.01179	+	0.584155i	−0.100072	+	0.994980i	$0.531907\pi$
$360$		0			0
$361$	100.775	−	174.548i	0.279156	−	0.483512i
$362$	290.270	−	167.587i	0.801850	−	0.462948i
$363$		0			0
$364$	−26.2450	+	226.428i	−0.0721017	+	0.622055i
$365$			648.182i			1.77584i
$366$		0			0
$367$	−80.2011	+	138.912i	−0.218532	+	0.378508i	−0.954359	−	0.298661i	$-0.903460\pi$
$367$	−80.2011	+	138.912i	−0.218532	+	0.378508i	0.735828	+	0.677169i	$0.236793\pi$
$368$	78.6418	+	45.4038i	0.213700	+	0.123380i
$369$		0			0
$370$	−739.907			−1.99975
$371$	376.741	+	43.6677i	1.01548	+	0.117703i
$372$		0			0
$373$	−163.370	−	282.965i	−0.437989	−	0.758620i	0.559545	−	0.828800i	$-0.310976\pi$
$373$	−163.370	−	282.965i	−0.437989	−	0.758620i	−0.997534	+	0.0701802i	$0.977643\pi$
$374$	−13.5849	−	7.84324i	−0.0363232	−	0.0209712i
$375$		0			0
$376$	87.0659	+	150.802i	0.231558	+	0.401070i
$377$		−	680.963i		−	1.80627i
$378$		0			0
$379$	−5.46561			−0.0144211			−0.00721057	−	0.999974i	$-0.502295\pi$
$379$	−5.46561			−0.0144211			−0.00721057	+	0.999974i	$0.502295\pi$
$380$	176.815	−	102.084i	0.465303	−	0.268643i
$381$		0			0
$382$	−67.4672	+	116.857i	−0.176616	+	0.305907i
$383$	101.063	−	58.3488i	0.263872	−	0.152347i	−0.362227	−	0.932090i	$-0.617984\pi$
$383$	101.063	−	58.3488i	0.263872	−	0.152347i	0.626100	+	0.779743i	$0.284650\pi$
$384$		0			0
$385$	−49.8942	+	21.5792i	−0.129595	+	0.0560498i
$386$		−	116.425i		−	0.301618i
$387$		0			0
$388$	−173.692	+	300.843i	−0.447660	+	0.775369i
$389$	−540.110	−	311.832i	−1.38846	−	0.801626i	−0.395315	−	0.918546i	$-0.629365\pi$
$389$	−540.110	−	311.832i	−1.38846	−	0.801626i	−0.993141	+	0.116920i	$0.962698\pi$
$390$		0			0
$391$	−262.139			−0.670433
$392$	−100.992	−	94.9143i	−0.257631	−	0.242128i
$393$		0			0
$394$	−6.87560	−	11.9089i	−0.0174508	−	0.0302256i
$395$	746.123	+	430.774i	1.88892	+	1.09057i
$396$		0			0
$397$	−191.913	−	332.403i	−0.483408	−	0.837287i	0.516411	−	0.856341i	$-0.327268\pi$
$397$	−191.913	−	332.403i	−0.483408	−	0.837287i	−0.999818	+	0.0190541i	$0.993935\pi$
$398$		−	221.478i		−	0.556478i
$399$		0			0
$400$	−161.429			−0.403573
$401$	−72.3141	+	41.7506i	−0.180334	+	0.104116i	−0.587450	−	0.809261i	$-0.699868\pi$
$401$	−72.3141	+	41.7506i	−0.180334	+	0.104116i	0.407115	+	0.913377i	$0.366535\pi$
$402$		0			0
$403$	−207.439	+	359.296i	−0.514738	+	0.891552i
$404$	−169.107	+	97.6341i	−0.418582	+	0.241668i
$405$		0			0
$406$	332.344	+	246.925i	0.818582	+	0.608190i
$407$			62.1664i			0.152743i
$408$		0			0
$409$	−56.1286	+	97.2176i	−0.137234	+	0.237696i	−0.926449	−	0.376421i	$-0.877154\pi$
$409$	−56.1286	+	97.2176i	−0.137234	+	0.237696i	0.789215	+	0.614117i	$0.210488\pi$
$410$	−202.193	−	116.736i	−0.493155	−	0.284723i
$411$		0			0
$412$	230.726			0.560015
$413$	576.233	+	66.7905i	1.39524	+	0.161720i
$414$		0			0
$415$	491.937	+	852.059i	1.18539	+	2.05316i
$416$	79.7637	+	46.0516i	0.191740	+	0.110701i
$417$		0			0
$418$	−8.57704	−	14.8559i	−0.0205192	−	0.0355403i
$419$		−	31.4295i		−	0.0750107i	−0.999296	−	0.0375054i	$-0.988059\pi$
$419$		−	31.4295i		−	0.0750107i	0.999296	−	0.0375054i	$-0.0119411\pi$
$420$		0			0
$421$	356.374			0.846495			0.423247	−	0.906014i	$-0.360890\pi$
$421$	356.374			0.846495			0.423247	+	0.906014i	$0.360890\pi$
$422$	257.107	−	148.441i	0.609259	−	0.351756i
$423$		0			0
$424$	76.6229	−	132.715i	0.180714	−	0.313006i
$425$	403.573	−	233.003i	0.949584	−	0.548243i
$426$		0			0
$427$	−157.933	−	117.341i	−0.369866	−	0.274803i
$428$		−	65.7103i		−	0.153529i
$429$		0			0
$430$	175.826	−	304.540i	0.408898	−	0.708232i
$431$	−124.388	−	71.8154i	−0.288603	−	0.166625i	0.348709	−	0.937231i	$-0.386620\pi$
$431$	−124.388	−	71.8154i	−0.288603	−	0.166625i	−0.637312	+	0.770606i	$0.719954\pi$
$432$		0			0
$433$	−110.430			−0.255035			−0.127517	−	0.991836i	$-0.540701\pi$
$433$	−110.430			−0.255035			−0.127517	+	0.991836i	$0.540701\pi$
$434$	−100.134	−	231.526i	−0.230725	−	0.533469i
$435$		0			0
$436$	128.503	+	222.574i	0.294731	+	0.510490i
$437$	−248.259	−	143.332i	−0.568098	−	0.327992i
$438$		0			0
$439$	270.934	+	469.271i	0.617161	+	1.06895i	0.990001	+	0.141059i	$0.0450507\pi$
$439$	270.934	+	469.271i	0.617161	+	1.06895i	−0.372840	+	0.927896i	$0.621616\pi$
$440$			21.9651i			0.0499206i
$441$		0			0
$442$	−265.879			−0.601537
$443$	−155.643	+	89.8608i	−0.351340	+	0.202846i	−0.665275	−	0.746598i	$-0.731686\pi$
$443$	−155.643	+	89.8608i	−0.351340	+	0.202846i	0.313935	+	0.949444i	$0.398352\pi$
$444$		0			0
$445$	−353.409	+	612.122i	−0.794177	+	1.37556i
$446$	7.81210	−	4.51032i	0.0175159	−	0.0101128i
$447$		0			0
$448$	−51.3988	+	22.2299i	−0.114729	+	0.0496203i
$449$			227.641i			0.506995i	0.967336	+	0.253497i	$0.0815809\pi$
$449$			227.641i			0.506995i	−0.967336	+	0.253497i	$0.918419\pi$
$450$		0			0
$451$	−9.80811	+	16.9881i	−0.0217475	+	0.0376677i
$452$	−267.565	−	154.479i	−0.591958	−	0.341767i
$453$		0			0
$454$	−128.031			−0.282006
$455$	−549.507	+	739.599i	−1.20771	+	1.62549i
$456$		0			0
$457$	−435.606	−	754.492i	−0.953186	−	1.65097i	−0.738465	−	0.674292i	$-0.764449\pi$
$457$	−435.606	−	754.492i	−0.953186	−	1.65097i	−0.214722	−	0.976675i	$-0.568884\pi$
$458$	−153.574	−	88.6661i	−0.335315	−	0.193594i
$459$		0			0
$460$	183.531	+	317.885i	0.398981	+	0.691055i
$461$		−	256.310i		−	0.555986i	−0.960583	−	0.277993i	$-0.910331\pi$
$461$		−	256.310i		−	0.555986i	0.960583	−	0.277993i	$-0.0896693\pi$
$462$		0			0
$463$	−587.171			−1.26819			−0.634094	−	0.773256i	$-0.718627\pi$
$463$	−587.171			−1.26819			−0.634094	+	0.773256i	$0.718627\pi$
$464$	144.882	−	83.6477i	0.312246	−	0.180275i
$465$		0			0
$466$	−168.950	+	292.629i	−0.362553	+	0.627960i
$467$	−289.648	+	167.228i	−0.620231	+	0.358090i	−0.776959	−	0.629551i	$-0.783239\pi$
$467$	−289.648	+	167.228i	−0.620231	+	0.358090i	0.156728	+	0.987642i	$0.449905\pi$
$468$		0			0
$469$	46.2382	−	398.918i	0.0985890	−	0.850572i
$470$			703.874i			1.49760i
$471$		0			0
$472$	117.196	−	202.989i	0.248297	−	0.430062i
$473$	−25.5872	−	14.7728i	−0.0540956	−	0.0312321i
$474$		0			0
$475$	509.605			1.07285
$476$	96.4109	−	129.763i	0.202544	−	0.272610i
$477$		0			0
$478$	11.8914	+	20.5964i	0.0248773	+	0.0430888i
$479$	379.611	+	219.168i	0.792506	+	0.457554i	0.840844	−	0.541277i	$-0.182059\pi$
$479$	379.611	+	219.168i	0.792506	+	0.457554i	−0.0483378	+	0.998831i	$0.515392\pi$
$480$		0			0
$481$	526.847	+	912.526i	1.09532	+	1.89714i
$482$			483.957i			1.00406i
$483$		0			0
$484$	−240.155			−0.496187
$485$	−1216.07	+	702.097i	−2.50735	+	1.44762i
$486$		0			0
$487$	−152.680	+	264.449i	−0.313511	+	0.543017i	−0.979120	−	0.203284i	$-0.934839\pi$
$487$	−152.680	+	264.449i	−0.313511	+	0.543017i	0.665609	+	0.746301i	$0.268172\pi$
$488$	−68.8492	+	39.7501i	−0.141084	+	0.0814551i
$489$		0			0
$490$	−161.704	−	536.374i	−0.330009	−	1.09464i
$491$		−	853.430i		−	1.73815i	−0.494683	−	0.869074i	$-0.664716\pi$
$491$		−	853.430i		−	1.73815i	0.494683	−	0.869074i	$-0.335284\pi$
$492$		0			0
$493$	−241.470	+	418.239i	−0.489798	+	0.848354i
$494$	−251.801	−	145.377i	−0.509718	−	0.294286i
$495$		0			0
$496$	−101.925			−0.205494
$497$	74.0013	+	171.102i	0.148896	+	0.344269i
$498$		0			0
$499$	144.829	+	250.852i	0.290239	+	0.502709i	0.973866	−	0.227123i	$-0.0729319\pi$
$499$	144.829	+	250.852i	0.290239	+	0.502709i	−0.683627	+	0.729831i	$0.739599\pi$
$500$	−215.042	−	124.154i	−0.430083	−	0.248309i
$501$		0			0
$502$	−219.334	−	379.898i	−0.436920	−	0.756768i
$503$			709.082i			1.40971i	0.709353	+	0.704853i	$0.248987\pi$
$503$			709.082i			1.40971i	−0.709353	+	0.704853i	$0.751013\pi$
$504$		0			0
$505$	−789.311			−1.56299
$506$	26.7085	−	15.4201i	0.0527835	−	0.0304746i
$507$		0			0
$508$	172.349	−	298.518i	0.339270	−	0.587633i
$509$	53.7074	−	31.0080i	0.105515	−	0.0609194i	−0.446314	−	0.894877i	$-0.647263\pi$
$509$	53.7074	−	31.0080i	0.105515	−	0.0609194i	0.551829	+	0.833957i	$0.313930\pi$
$510$		0			0
$511$	−64.6200	+	557.507i	−0.126458	+	1.09101i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	45.6342	−	79.0408i	0.0887825	−	0.153776i
$515$	807.689	+	466.320i	1.56833	+	0.905475i
$516$		0			0
$517$	59.1389			0.114389
$518$	−636.400	−	73.7645i	−1.22857	−	0.142402i
$519$		0			0
$520$	186.149	+	322.420i	0.357980	+	0.620039i
$521$	−559.012	−	322.746i	−1.07296	−	0.619474i	−0.143971	−	0.989582i	$-0.545987\pi$
$521$	−559.012	−	322.746i	−1.07296	−	0.619474i	−0.928989	+	0.370108i	$0.879321\pi$
$522$		0			0
$523$	−118.522	−	205.286i	−0.226619	−	0.392516i	0.730185	−	0.683250i	$-0.239434\pi$
$523$	−118.522	−	205.286i	−0.226619	−	0.392516i	−0.956804	+	0.290734i	$0.906101\pi$
$524$		−	305.308i		−	0.582649i
$525$		0			0
$526$	559.225			1.06317
$527$	254.813	−	147.116i	0.483516	−	0.279158i
$528$		0			0
$529$	−6.81137	+	11.7976i	−0.0128759	+	0.0223018i
$530$	536.458	−	309.724i	1.01219	−	0.584386i
$531$		0			0
$532$	162.257	−	70.1761i	0.304995	−	0.131910i
$533$			332.487i			0.623802i
$534$		0			0
$535$	132.807	−	230.028i	0.248237	−	0.429960i
$536$	−140.527	−	81.1333i	−0.262177	−	0.151368i
$537$		0			0
$538$	123.959			0.230407
$539$	−45.0657	+	13.5863i	−0.0836099	+	0.0252064i
$540$		0			0
$541$	487.361	+	844.133i	0.900851	+	1.56032i	0.826391	+	0.563097i	$0.190390\pi$
$541$	487.361	+	844.133i	0.900851	+	1.56032i	0.0744604	+	0.997224i	$0.476277\pi$
$542$	−47.9172	−	27.6650i	−0.0884081	−	0.0510425i
$543$		0			0
$544$	−32.6599	−	56.5686i	−0.0600366	−	0.103986i
$545$			1038.87i			1.90618i
$546$		0			0
$547$	2.05896			0.00376410			0.00188205	−	0.999998i	$-0.499401\pi$
$547$	2.05896			0.00376410			0.00188205	+	0.999998i	$0.499401\pi$
$548$	261.066	−	150.727i	0.476398	−	0.275048i
$549$		0			0
$550$	−27.4124	+	47.4797i	−0.0498408	+	0.0863268i
$551$	−457.368	+	264.062i	−0.830070	+	0.479241i
$552$		0			0
$553$	598.801	+	444.897i	1.08282	+	0.804515i
$554$		−	315.128i		−	0.568823i
$555$		0			0
$556$	−269.648	+	467.044i	−0.484978	+	0.840006i
$557$	70.1366	+	40.4934i	0.125919	+	0.0726991i	0.561636	−	0.827384i	$-0.310172\pi$
$557$	70.1366	+	40.4934i	0.125919	+	0.0726991i	−0.435718	+	0.900083i	$0.643505\pi$
$558$		0			0
$559$	−500.785			−0.895859
$560$	−224.857	−	26.0630i	−0.401531	−	0.0465410i
$561$		0			0
$562$	−154.135	−	266.969i	−0.274261	−	0.475034i
$563$	−479.575	−	276.883i	−0.851821	−	0.491799i	0.00944413	−	0.999955i	$-0.496994\pi$
$563$	−479.575	−	276.883i	−0.851821	−	0.491799i	−0.861265	+	0.508157i	$0.830327\pi$
$564$		0			0
$565$	−624.433	−	1081.55i	−1.10519	−	1.91425i
$566$		−	431.835i		−	0.762959i
$567$		0			0
$568$	75.3246			0.132614
$569$	728.631	−	420.675i	1.28055	−	0.739324i	0.303598	−	0.952800i	$-0.401812\pi$
$569$	728.631	−	420.675i	1.28055	−	0.739324i	0.976948	+	0.213476i	$0.0684787\pi$
$570$		0			0
$571$	163.329	−	282.894i	0.286040	−	0.495436i	−0.686821	−	0.726827i	$-0.740994\pi$
$571$	163.329	−	282.894i	0.286040	−	0.495436i	0.972861	+	0.231391i	$0.0743276\pi$
$572$	27.0895	−	15.6401i	0.0473593	−	0.0273429i
$573$		0			0
$574$	−162.270	−	120.564i	−0.282701	−	0.210041i
$575$			916.188i			1.59337i
$576$		0			0
$577$	121.664	−	210.728i	0.210856	−	0.365213i	−0.741127	−	0.671365i	$-0.765708\pi$
$577$	121.664	−	210.728i	0.210856	−	0.365213i	0.951983	+	0.306152i	$0.0990416\pi$
$578$	−190.652	−	110.073i	−0.329847	−	0.190437i
$579$		0			0
$580$	676.240			1.16593
$581$	338.173	+	781.907i	0.582054	+	1.34579i
$582$		0			0
$583$	−26.0228	−	45.0728i	−0.0446360	−	0.0773118i
$584$	196.393	+	113.387i	0.336289	+	0.194157i
$585$		0			0
$586$	−155.259	−	268.916i	−0.264946	−	0.458901i
$587$		−	720.736i		−	1.22783i	−0.789372	−	0.613915i	$-0.789594\pi$
$587$		−	720.736i		−	1.22783i	0.789372	−	0.613915i	$-0.210406\pi$
$588$		0			0
$589$	321.761			0.546283
$590$	820.522	−	473.729i	1.39072	−	0.802930i
$591$		0			0
$592$	−129.433	+	224.185i	−0.218637	+	0.378690i
$593$	395.373	−	228.269i	0.666733	−	0.384939i	−0.128104	−	0.991761i	$-0.540889\pi$
$593$	395.373	−	228.269i	0.666733	−	0.384939i	0.794838	+	0.606822i	$0.207556\pi$
$594$		0			0
$595$	599.763	−	259.396i	1.00800	−	0.435960i
$596$		−	410.100i		−	0.688087i
$597$		0			0
$598$	261.365	−	452.697i	0.437065	−	0.757019i
$599$	344.933	+	199.147i	0.575848	+	0.332466i	0.759482	−	0.650529i	$-0.225453\pi$
$599$	344.933	+	199.147i	0.575848	+	0.332466i	−0.183634	+	0.982995i	$0.558786\pi$
$600$		0			0
$601$	39.3763			0.0655179			0.0327590	−	0.999463i	$-0.489571\pi$
$601$	39.3763			0.0655179			0.0327590	+	0.999463i	$0.489571\pi$
$602$	181.590	−	244.408i	0.301645	−	0.405994i
$603$		0			0
$604$	−27.5497	−	47.7176i	−0.0456122	−	0.0790026i
$605$	−840.695	−	485.375i	−1.38958	−	0.802273i
$606$		0			0
$607$	−401.100	−	694.726i	−0.660791	−	1.14452i	−0.980408	−	0.196977i	$-0.936888\pi$
$607$	−401.100	−	694.726i	−0.660791	−	1.14452i	0.319617	−	0.947547i	$-0.396446\pi$
$608$		−	71.4310i		−	0.117485i
$609$		0			0
$610$	−321.355			−0.526812
$611$	868.087	−	501.190i	1.42076	−	0.820279i
$612$		0			0
$613$	597.009	−	1034.05i	0.973914	−	1.68687i	0.290439	−	0.956893i	$-0.406199\pi$
$613$	597.009	−	1034.05i	0.973914	−	1.68687i	0.683474	−	0.729975i	$-0.260468\pi$
$614$	−218.744	+	126.292i	−0.356260	+	0.205687i
$615$		0			0
$616$	−2.18979	+	18.8923i	−0.00355486	+	0.0306694i
$617$		−	569.891i		−	0.923649i	−0.886971	−	0.461825i	$-0.847195\pi$
$617$		−	569.891i		−	0.923649i	0.886971	−	0.461825i	$-0.152805\pi$
$618$		0			0
$619$	554.839	−	961.010i	0.896348	−	1.55252i	0.0642195	−	0.997936i	$-0.479544\pi$
$619$	554.839	−	961.010i	0.896348	−	1.55252i	0.832128	−	0.554584i	$-0.187122\pi$
$620$	−356.803	−	206.001i	−0.575489	−	0.332259i
$621$		0			0
$622$	−155.498			−0.249996
$623$	−364.995	+	491.258i	−0.585867	+	0.788537i
$624$		0			0
$625$	2.61045	+	4.52144i	0.00417672	+	0.00723430i
$626$	−318.567	−	183.925i	−0.508892	−	0.293809i
$627$		0			0
$628$	144.811	+	250.820i	0.230591	+	0.399395i
$629$		−	747.282i		−	1.18805i
$630$		0			0
$631$	−254.309			−0.403026			−0.201513	−	0.979486i	$-0.564586\pi$
$631$	−254.309			−0.403026			−0.201513	+	0.979486i	$0.564586\pi$
$632$	261.041	−	150.712i	0.413039	−	0.238468i
$633$		0			0
$634$	−160.177	+	277.435i	−0.252645	+	0.437594i
$635$	1206.67	−	696.669i	1.90026	−	1.09712i
$636$		0			0
$637$	−546.369	+	581.353i	−0.857723	+	0.912642i
$638$		−	56.8171i		−	0.0890551i
$639$		0			0
$640$	−45.7322	+	79.2105i	−0.0714566	+	0.123766i
$641$	460.954	+	266.132i	0.719117	+	0.415182i	0.814428	−	0.580265i	$-0.197051\pi$
$641$	460.954	+	266.132i	0.719117	+	0.415182i	−0.0953106	+	0.995448i	$0.530384\pi$
$642$		0			0
$643$	−287.069			−0.446452			−0.223226	−	0.974767i	$-0.571659\pi$
$643$	−287.069			−0.446452			−0.223226	+	0.974767i	$0.571659\pi$
$644$	126.165	+	291.713i	0.195909	+	0.452970i
$645$		0			0
$646$	103.102	+	178.578i	0.159600	+	0.276436i
$647$	221.996	+	128.169i	0.343116	+	0.198098i	0.661649	−	0.749814i	$-0.269857\pi$
$647$	221.996	+	128.169i	0.343116	+	0.198098i	−0.318533	+	0.947912i	$0.603190\pi$
$648$		0			0
$649$	−39.8023	−	68.9396i	−0.0613287	−	0.106224i
$650$			929.259i			1.42963i
$651$		0			0
$652$	−574.207			−0.880686
$653$	717.114	−	414.026i	1.09818	−	0.634036i	0.162440	−	0.986718i	$-0.448064\pi$
$653$	717.114	−	414.026i	1.09818	−	0.634036i	0.935743	+	0.352682i	$0.114730\pi$
$654$		0			0
$655$	617.057	−	1068.77i	0.942072	−	1.63172i
$656$	−70.7400	+	40.8418i	−0.107835	+	0.0622588i
$657$		0			0
$658$	−70.1722	+	605.408i	−0.106645	+	0.920073i
$659$		−	76.1666i		−	0.115579i	−0.998329	−	0.0577895i	$-0.981595\pi$
$659$		−	76.1666i		−	0.115579i	0.998329	−	0.0577895i	$-0.0184052\pi$
$660$		0			0
$661$	−52.5224	+	90.9715i	−0.0794590	+	0.137627i	−0.903017	−	0.429606i	$-0.858653\pi$
$661$	−52.5224	+	90.9715i	−0.0794590	+	0.137627i	0.823558	+	0.567233i	$0.191986\pi$
$662$	439.031	+	253.475i	0.663189	+	0.382892i
$663$		0			0
$664$	344.221			0.518405
$665$	709.837	+	82.2765i	1.06742	+	0.123724i
$666$		0			0
$667$	−474.741	−	822.275i	−0.711755	−	1.23280i
$668$	253.457	+	146.334i	0.379427	+	0.219062i
$669$		0			0
$670$	−327.956	−	568.037i	−0.489487	−	0.847817i
$671$			27.0000i			0.0402384i
$672$		0			0
$673$	−133.032			−0.197670			−0.0988351	−	0.995104i	$-0.531512\pi$
$673$	−133.032			−0.197670			−0.0988351	+	0.995104i	$0.531512\pi$
$674$	−181.141	+	104.582i	−0.268755	+	0.155166i
$675$		0			0
$676$	96.0938	−	166.439i	0.142151	−	0.246212i
$677$	−582.662	+	336.400i	−0.860652	+	0.496898i	−0.864231	−	0.503096i	$-0.832194\pi$
$677$	−582.662	+	336.400i	−0.860652	+	0.496898i	0.00357830	+	0.999994i	$0.498861\pi$
$678$		0			0
$679$	−1115.94	+	482.644i	−1.64351	+	0.710816i
$680$		−	264.035i		−	0.388287i
$681$		0			0
$682$	−17.3080	+	29.9783i	−0.0253783	+	0.0439565i
$683$	−751.655	−	433.968i	−1.10052	−	0.635386i	−0.164163	−	0.986433i	$-0.552492\pi$
$683$	−751.655	−	433.968i	−1.10052	−	0.635386i	−0.936358	+	0.351047i	$0.885826\pi$
$684$		0			0
$685$	1218.53			1.77888
$686$	−85.6097	−	477.461i	−0.124795	−	0.696007i
$687$		0			0
$688$	−61.5151	−	106.547i	−0.0894114	−	0.154865i
$689$	−763.966	−	441.076i	−1.10880	−	0.640168i
$690$		0			0
$691$	437.812	+	758.312i	0.633592	+	1.09741i	0.986812	+	0.161873i	$0.0517534\pi$
$691$	437.812	+	758.312i	0.633592	+	1.09741i	−0.353220	+	0.935540i	$0.614913\pi$
$692$			560.891i			0.810535i
$693$		0			0
$694$	129.377			0.186423
$695$	−1887.88	+	1089.97i	−2.71637	+	1.56830i
$696$		0			0
$697$	117.900	−	204.209i	0.169154	−	0.292983i
$698$	−137.641	+	79.4673i	−0.197194	+	0.113850i
$699$		0			0
$700$	−453.525	−	336.960i	−0.647894	−	0.481372i
$701$		−	364.294i		−	0.519678i	−0.965652	−	0.259839i	$-0.916330\pi$
$701$		−	364.294i		−	0.519678i	0.965652	−	0.259839i	$-0.0836695\pi$
$702$		0			0
$703$	408.599	−	707.713i	0.581221	−	1.00670i
$704$	6.65520	+	3.84238i	0.00945341	+	0.00545793i
$705$		0			0
$706$	552.858			0.783084
$707$	−678.893	−	78.6898i	−0.960245	−	0.111301i
$708$		0			0
$709$	−250.924	−	434.613i	−0.353912	−	0.612994i	0.633019	−	0.774136i	$-0.281815\pi$
$709$	−250.924	−	434.613i	−0.353912	−	0.612994i	−0.986931	+	0.161142i	$0.948482\pi$
$710$	263.685	+	152.238i	0.371387	+	0.214420i
$711$		0			0
$712$	123.645	+	214.159i	0.173658	+	0.300785i
$713$			578.474i			0.811324i
$714$		0			0
$715$	126.441			0.176840
$716$	102.554	−	59.2094i	0.143231	−	0.0826946i
$717$		0			0
$718$	−296.577	+	513.687i	−0.413060	+	0.715441i
$719$	45.4717	−	26.2531i	0.0632429	−	0.0365133i	−0.468045	−	0.883705i	$-0.655042\pi$
$719$	45.4717	−	26.2531i	0.0632429	−	0.0365133i	0.531288	+	0.847191i	$0.321708\pi$
$720$		0			0
$721$	648.211	+	481.607i	0.899044	+	0.667971i
$722$		−	285.035i		−	0.394786i
$723$		0			0
$724$	237.004	−	410.503i	0.327354	−	0.566994i
$725$	1461.76	+	843.948i	2.01622	+	1.16407i
$726$		0			0
$727$	−694.731			−0.955613			−0.477807	−	0.878465i	$-0.658568\pi$
$727$	−694.731			−0.955613			−0.477807	+	0.878465i	$0.658568\pi$
$728$	127.965	+	295.874i	0.175776	+	0.406421i
$729$		0			0
$730$	458.334	+	793.857i	0.627855	+	1.08748i
$731$	307.576	+	177.579i	0.420760	+	0.242926i
$732$		0			0
$733$	143.786	+	249.044i	0.196160	+	0.339760i	0.947280	−	0.320406i	$-0.103819\pi$
$733$	143.786	+	249.044i	0.196160	+	0.339760i	−0.751120	+	0.660166i	$0.770486\pi$
$734$			226.843i			0.309050i
$735$		0			0
$736$	128.421			0.174486
$737$	−47.7260	+	27.5546i	−0.0647572	+	0.0373876i
$738$		0			0
$739$	464.697	−	804.879i	0.628819	−	1.08915i	−0.358970	−	0.933349i	$-0.616872\pi$
$739$	464.697	−	804.879i	0.628819	−	1.08915i	0.987789	−	0.155797i	$-0.0497946\pi$
$740$	−906.197	+	523.193i	−1.22459	+	0.707018i
$741$		0			0
$742$	492.290	−	212.915i	0.663464	−	0.286947i
$743$		−	959.335i		−	1.29116i	−0.763691	−	0.645582i	$-0.776615\pi$
$743$		−	959.335i		−	1.29116i	0.763691	−	0.645582i	$-0.223385\pi$
$744$		0			0
$745$	828.851	−	1435.61i	1.11255	−	1.92700i
$746$	−400.173	−	231.040i	−0.536425	−	0.309705i
$747$		0			0
$748$	−22.1840			−0.0296578
$749$	137.161	−	184.609i	0.183125	−	0.246474i
$750$		0			0
$751$	−73.5811	−	127.446i	−0.0979775	−	0.169702i	0.812870	−	0.582445i	$-0.197904\pi$
$751$	−73.5811	−	127.446i	−0.0979775	−	0.169702i	−0.910847	+	0.412743i	$0.864571\pi$
$752$	213.267	+	123.130i	0.283600	+	0.163736i
$753$		0			0
$754$	−481.514	−	834.006i	−0.638612	−	1.10611i
$755$		−	222.723i		−	0.294997i
$756$		0			0
$757$	471.524			0.622885			0.311442	−	0.950265i	$-0.399188\pi$
$757$	471.524			0.622885			0.311442	+	0.950265i	$0.399188\pi$
$758$	−6.69398	+	3.86477i	−0.00883110	+	0.00509864i
$759$		0			0
$760$	144.369	−	250.054i	0.189959	−	0.329019i
$761$	−214.794	+	124.011i	−0.282252	+	0.162958i	−0.634443	−	0.772970i	$-0.718770\pi$
$761$	−214.794	+	124.011i	−0.282252	+	0.162958i	0.352190	+	0.935928i	$0.385437\pi$
$762$		0			0
$763$	−103.569	+	893.538i	−0.135739	+	1.17109i
$764$			190.826i			0.249772i
$765$		0			0
$766$	82.5177	−	142.925i	0.107725	−	0.186586i
$767$	−1168.50	−	674.633i	−1.52347	−	0.879574i
$768$		0			0
$769$	−783.203			−1.01847			−0.509235	−	0.860628i	$-0.670071\pi$
$769$	−783.203			−1.01847			−0.509235	+	0.860628i	$0.670071\pi$
$770$	−45.8489	+	61.7095i	−0.0595440	+	0.0801422i
$771$		0			0
$772$	−82.3247	−	142.591i	−0.106638	−	0.184703i
$773$	891.874	+	514.923i	1.15378	+	0.666136i	0.949806	−	0.312839i	$-0.101280\pi$
$773$	891.874	+	514.923i	1.15378	+	0.666136i	0.203976	+	0.978976i	$0.434614\pi$
$774$		0			0
$775$	−514.178	−	890.582i	−0.663456	−	1.14914i
$776$			491.275i			0.633086i
$777$		0			0
$778$	−881.995			−1.13367
$779$	223.314	−	128.931i	0.286668	−	0.165508i
$780$		0			0
$781$	12.7909	−	22.1546i	0.0163777	−	0.0283669i
$782$	−321.054	+	185.361i	−0.410555	+	0.237034i
$783$		0			0
$784$	−190.803	−	44.8340i	−0.243372	−	0.0571862i
$785$			1170.71i			1.49135i
$786$		0			0
$787$	153.236	−	265.413i	0.194709	−	0.337247i	−0.752096	−	0.659054i	$-0.770957\pi$
$787$	153.236	−	265.413i	0.194709	−	0.337247i	0.946805	+	0.321807i	$0.104290\pi$
$788$	−16.8417	−	9.72356i	−0.0213727	−	0.0123395i
$789$		0			0
$790$	1218.41			1.54230
$791$	−429.255	−	992.502i	−0.542674	−	1.25474i
$792$		0			0
$793$	228.819	+	396.327i	0.288549	+	0.499782i
$794$	−470.089	−	271.406i	−0.592051	−	0.341821i
$795$		0			0
$796$	−156.609	−	271.255i	−0.196745	−	0.340772i
$797$			158.510i			0.198883i	0.995043	+	0.0994417i	$0.0317057\pi$
$797$			158.510i			0.198883i	−0.995043	+	0.0994417i	$0.968294\pi$
$798$		0			0
$799$	−710.890			−0.889725
$800$	−197.710	+	114.148i	−0.247137	+	0.142685i
$801$		0			0
$802$	−59.0442	+	102.268i	−0.0736213	+	0.127516i
$803$	66.6993	−	38.5088i	0.0830626	−	0.0479562i
$804$		0			0
$805$	−147.920	+	1276.17i	−0.183751	+	1.58531i
$806$			586.727i			0.727949i
$807$		0			0
$808$	−138.075	+	239.154i	−0.170885	+	0.295982i
$809$	560.327	+	323.505i	0.692617	+	0.399883i	0.804592	−	0.593828i	$-0.202384\pi$
$809$	560.327	+	323.505i	0.692617	+	0.399883i	−0.111975	+	0.993711i	$0.535718\pi$
$810$		0			0
$811$	1035.64			1.27700			0.638499	−	0.769623i	$-0.279556\pi$
$811$	1035.64			1.27700			0.638499	+	0.769623i	$0.279556\pi$
$812$	581.640	+	67.4172i	0.716305	+	0.0830261i
$813$		0			0
$814$	43.9583	+	76.1380i	0.0540028	+	0.0935356i
$815$	−2010.09	−	1160.53i	−2.46637	−	1.42396i
$816$		0			0
$817$	194.193	+	336.352i	0.237690	+	0.411691i
$818$			158.756i			0.194078i
$819$		0			0
$820$	−330.181			−0.402659
$821$	−597.867	+	345.179i	−0.728218	+	0.420437i	−0.817770	−	0.575545i	$-0.804790\pi$
$821$	−597.867	+	345.179i	−0.728218	+	0.420437i	0.0895517	+	0.995982i	$0.471457\pi$
$822$		0			0
$823$	−548.763	+	950.486i	−0.666784	+	1.15490i	0.312015	+	0.950077i	$0.398996\pi$
$823$	−548.763	+	950.486i	−0.666784	+	1.15490i	−0.978798	+	0.204826i	$0.934337\pi$
$824$	282.581	−	163.148i	0.342938	−	0.197995i
$825$		0			0
$826$	752.966	−	325.657i	0.911581	−	0.394258i
$827$		−	1503.76i		−	1.81833i	−0.416440	−	0.909163i	$-0.636722\pi$
$827$		−	1503.76i		−	1.81833i	0.416440	−	0.909163i	$-0.363278\pi$
$828$		0			0
$829$	265.079	−	459.130i	0.319757	−	0.553835i	−0.660680	−	0.750668i	$-0.729732\pi$
$829$	265.079	−	459.130i	0.319757	−	0.553835i	0.980437	+	0.196832i	$0.0630654\pi$
$830$	1204.99	+	695.704i	1.45180	+	0.838197i
$831$		0			0
$832$	130.254			0.156555
$833$	541.721	−	163.316i	0.650325	−	0.196058i
$834$		0			0
$835$	591.509	+	1024.52i	0.708394	+	1.22697i
$836$	−21.0094	−	12.1298i	−0.0251308	−	0.0145093i
$837$		0			0
$838$	−22.2240	−	38.4931i	−0.0265203	−	0.0459345i
$839$		−	128.014i		−	0.152580i	−0.997086	−	0.0762899i	$-0.975693\pi$
$839$		−	128.014i		−	0.152580i	0.997086	−	0.0762899i	$-0.0243074\pi$
$840$		0			0
$841$	−908.233			−1.07994
$842$	436.468	−	251.995i	0.518370	−	0.299281i
$843$		0			0
$844$	209.927	−	363.604i	0.248729	−	0.430811i
$845$	672.780	−	388.430i	0.796189	−	0.459680i
$846$		0			0
$847$	−674.699	−	501.288i	−0.796575	−	0.591839i
$848$		−	216.722i		−	0.255569i
$849$		0			0
$850$	329.516	−	570.739i	0.387666	−	0.671457i
$851$	1272.36	+	734.595i	1.49513	+	0.863213i
$852$		0			0
$853$	−398.565			−0.467251			−0.233626	−	0.972327i	$-0.575059\pi$
$853$	−398.565			−0.467251			−0.233626	+	0.972327i	$0.575059\pi$
$854$	−276.400	−	32.0372i	−0.323654	−	0.0375143i
$855$		0			0
$856$	−46.4642	−	80.4784i	−0.0542806	−	0.0940168i
$857$	554.663	+	320.235i	0.647215	+	0.373670i	0.787388	−	0.616457i	$-0.211433\pi$
$857$	554.663	+	320.235i	0.647215	+	0.373670i	−0.140174	+	0.990127i	$0.544766\pi$
$858$		0			0
$859$	115.884	+	200.717i	0.134906	+	0.233664i	0.925561	−	0.378597i	$-0.123594\pi$
$859$	115.884	+	200.717i	0.134906	+	0.233664i	−0.790656	+	0.612261i	$0.790260\pi$
$860$		−	497.312i		−	0.578269i
$861$		0			0
$862$	−203.124			−0.235643
$863$	−1444.72	+	834.111i	−1.67407	+	0.966525i	−0.708749	+	0.705461i	$0.750740\pi$
$863$	−1444.72	+	834.111i	−1.67407	+	0.966525i	−0.965322	+	0.261064i	$0.915927\pi$
$864$		0			0
$865$	−1133.61	+	1963.48i	−1.31054	+	2.26992i
$866$	−135.249	+	78.0858i	−0.156176	+	0.0901684i
$867$		0			0
$868$	−286.353	−	212.754i	−0.329899	−	0.245108i
$869$		−	102.370i		−	0.117802i
$870$		0			0
$871$	−467.040	+	808.937i	−0.536211	+	0.928745i
$872$	314.767	+	181.731i	0.360971	+	0.208407i
$873$		0			0
$874$	−405.405			−0.463850
$875$	−344.992	−	797.672i	−0.394277	−	0.911625i
$876$		0			0
$877$	542.202	+	939.122i	0.618246	+	1.07083i	0.989806	+	0.142425i	$0.0454900\pi$
$877$	542.202	+	939.122i	0.618246	+	1.07083i	−0.371559	+	0.928409i	$0.621177\pi$
$878$	663.649	+	383.158i	0.755865	+	0.436399i
$879$		0			0
$880$	15.5317	+	26.9016i	0.0176496	+	0.0305700i
$881$		−	1011.00i		−	1.14756i	−0.819009	−	0.573780i	$-0.805476\pi$
$881$		−	1011.00i		−	1.14756i	0.819009	−	0.573780i	$-0.194524\pi$
$882$		0			0
$883$	−722.404			−0.818124			−0.409062	−	0.912507i	$-0.634144\pi$
$883$	−722.404			−0.818124			−0.409062	+	0.912507i	$0.634144\pi$
$884$	−325.634	+	188.005i	−0.368365	+	0.212675i
$885$		0			0
$886$	−127.082	+	220.113i	−0.143434	+	0.248435i
$887$	−1414.43	+	816.623i	−1.59463	+	0.920658i	−0.602128	+	0.798400i	$0.705680\pi$
$887$	−1414.43	+	816.623i	−1.59463	+	0.920658i	−0.992498	+	0.122258i	$0.960986\pi$
$888$		0			0
$889$	1107.32	−	478.913i	1.24558	−	0.538710i
$890$			999.591i			1.12314i
$891$		0			0
$892$	6.37856	−	11.0480i	0.00715085	−	0.0123856i
$893$	−673.248	−	388.700i	−0.753917	−	0.435274i
$894$		0			0
$895$	478.671			0.534828
$896$	−47.2315	+	63.5703i	−0.0527137	+	0.0709490i
$897$		0			0
$898$	160.966	+	278.802i	0.179250	+	0.310470i
$899$	922.945	+	532.863i	1.02664	+	0.592728i
$900$		0			0
$901$	312.812	+	541.806i	0.347183	+	0.601338i
$902$			27.7415i			0.0307556i
$903$		0			0
$904$	−436.932			−0.483332
$905$	1659.33	−	958.017i	1.83352	−	1.05858i
$906$		0			0
$907$	129.116	−	223.635i	0.142355	−	0.246565i	−0.786028	−	0.618191i	$-0.787866\pi$
$907$	129.116	−	223.635i	0.142355	−	0.246565i	0.928383	+	0.371625i	$0.121199\pi$
$908$	−156.805	+	90.5315i	−0.172693	+	0.0997043i
$909$		0			0
$910$	−150.030	+	1294.38i	−0.164868	+	1.42240i
$911$			162.453i			0.178324i	0.996017	+	0.0891621i	$0.0284189\pi$
$911$			162.453i			0.178324i	−0.996017	+	0.0891621i	$0.971581\pi$
$912$		0			0
$913$	58.4525	−	101.243i	0.0640224	−	0.110890i
$914$	−1067.01	−	616.040i	−1.16741	−	0.674005i
$915$		0			0
$916$	−250.786			−0.273783
$917$	637.286	−	857.744i	0.694969	−	0.935381i
$918$		0			0
$919$	−236.149	−	409.021i	−0.256963	−	0.445072i	0.708464	−	0.705747i	$-0.249388\pi$
$919$	−236.149	−	409.021i	−0.256963	−	0.445072i	−0.965427	+	0.260675i	$0.916055\pi$
$920$	449.558	+	259.552i	0.488650	+	0.282122i
$921$		0			0
$922$	−181.238	−	313.914i	−0.196571	−	0.340471i
$923$		−	433.603i		−	0.469775i
$924$		0			0
$925$	−2611.78			−2.82355
$926$	−719.135	+	415.193i	−0.776604	+	0.448372i
$927$		0			0
$928$	118.296	−	204.894i	0.127474	−	0.220791i
$929$	−618.358	+	357.009i	−0.665617	+	0.384294i	−0.794414	−	0.607377i	$-0.792222\pi$
$929$	−618.358	+	357.009i	−0.665617	+	0.384294i	0.128797	+	0.991671i	$0.458888\pi$
$930$		0			0
$931$	602.334	+	141.533i	0.646976	+	0.152023i
$932$			477.862i			0.512727i
$933$		0			0
$934$	−236.496	+	409.624i	−0.253208	+	0.438569i
$935$	−77.6583	−	44.8361i	−0.0830570	−	0.0479530i
$936$		0			0
$937$	193.135			0.206121			0.103060	−	0.994675i	$-0.467137\pi$
$937$	193.135			0.206121			0.103060	+	0.994675i	$0.467137\pi$
$938$	−225.448	−	521.269i	−0.240350	−	0.555724i
$939$		0			0
$940$	497.714	+	862.066i	0.529483	+	0.917092i
$941$	400.942	+	231.484i	0.426081	+	0.245998i	0.697676	−	0.716414i	$-0.254218\pi$
$941$	400.942	+	231.484i	0.426081	+	0.245998i	−0.271595	+	0.962412i	$0.587551\pi$
$942$		0			0
$943$	231.797	+	401.484i	0.245808	+	0.425751i
$944$		−	331.480i		−	0.351144i
$945$		0			0
$946$	−41.7837			−0.0441688
$947$	−1100.98	+	635.650i	−1.16260	+	0.671225i	−0.951925	−	0.306332i	$-0.900898\pi$
$947$	−1100.98	+	635.650i	−1.16260	+	0.671225i	−0.210671	+	0.977557i	$0.567565\pi$
$948$		0			0
$949$	652.709	−	1130.53i	0.687786	−	1.19128i
$950$	624.136	−	360.345i	0.656986	−	0.379311i
$951$		0			0
$952$	26.3228	−	227.099i	0.0276500	−	0.238549i
$953$			850.634i			0.892586i	0.894887	+	0.446293i	$0.147256\pi$
$953$			850.634i			0.892586i	−0.894887	+	0.446293i	$0.852744\pi$
$954$		0			0
$955$	−385.678	+	668.014i	−0.403851	+	0.699491i
$956$	29.1277	+	16.8169i	0.0304684	+	0.0175909i
$957$		0			0
$958$	619.901			0.647079
$959$	1048.07	+	121.481i	1.09288	+	0.126674i
$960$		0			0
$961$	155.852	+	269.943i	0.162177	+	0.280898i
$962$	1290.51	+	745.075i	1.34148	+	0.774506i
$963$		0			0
$964$	342.210	+	592.724i	0.354989	+	0.614859i
$965$		−	665.545i		−	0.689684i
$966$		0			0
$967$	−456.656			−0.472240			−0.236120	−	0.971724i	$-0.575876\pi$
$967$	−456.656			−0.472240			−0.236120	+	0.971724i	$0.575876\pi$
$968$	−294.128	+	169.815i	−0.303851	+	0.175429i
$969$		0			0
$970$	−992.914	+	1719.78i	−1.02362	+	1.77297i
$971$	−669.258	+	386.396i	−0.689246	+	0.397936i	−0.803329	−	0.595535i	$-0.796940\pi$
$971$	−669.258	+	386.396i	−0.689246	+	0.397936i	0.114084	+	0.993471i	$0.463607\pi$
$972$		0			0
$973$	−1732.44	+	749.280i	−1.78052	+	0.770072i
$974$			431.844i			0.443371i
$975$		0			0
$976$	−56.2151	+	97.3674i	−0.0575975	+	0.0997617i
$977$	−1263.91	−	729.718i	−1.29366	−	0.746897i	−0.314362	−	0.949303i	$-0.601791\pi$
$977$	−1263.91	−	729.718i	−1.29366	−	0.746897i	−0.979302	+	0.202406i	$0.935124\pi$
$978$		0			0
$979$	83.9848			0.0857864
$980$	−577.320	−	542.580i	−0.589102	−	0.553653i
$981$		0			0
$982$	−603.466	−	1045.23i	−0.614528	−	1.06439i
$983$	522.380	+	301.596i	0.531414	+	0.306812i	0.741592	−	0.670851i	$-0.234071\pi$
$983$	522.380	+	301.596i	0.531414	+	0.306812i	−0.210178	+	0.977663i	$0.567404\pi$
$984$		0			0
$985$	−39.3045	−	68.0774i	−0.0399031	−	0.0691141i
$986$			682.981i			0.692678i
$987$		0			0
$988$	−411.189			−0.416183
$989$	−604.707	+	349.128i	−0.611432	+	0.353011i
$990$		0			0
$991$	−804.385	+	1393.24i	−0.811690	+	1.40589i	0.0999898	+	0.994988i	$0.468119\pi$
$991$	−804.385	+	1393.24i	−0.811690	+	1.40589i	−0.911680	+	0.410901i	$0.865214\pi$
$992$	−124.832	+	72.0720i	−0.125839	+	0.0726532i
$993$		0			0
$994$	211.620	+	157.229i	0.212897	+	0.158178i
$995$		−	1266.09i		−	1.27245i
$996$		0			0
$997$	679.411	−	1176.77i	0.681455	−	1.18031i	−0.293082	−	0.956087i	$-0.594681\pi$
$997$	679.411	−	1176.77i	0.681455	−	1.18031i	0.974537	−	0.224227i	$-0.0719858\pi$
$998$	354.758	+	204.819i	0.355469	+	0.205230i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.s.e.53.11	yes	24
3.2	odd	2	inner	378.3.s.e.53.2	✓	24
7.2	even	3	inner	378.3.s.e.107.2	yes	24
21.2	odd	6	inner	378.3.s.e.107.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.3.s.e.53.2	✓	24	3.2	odd	2	inner
378.3.s.e.53.11	yes	24	1.1	even	1	trivial
378.3.s.e.107.2	yes	24	7.2	even	3	inner
378.3.s.e.107.11	yes	24	21.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.00128 - 4.04219i) q^{5} +(6.42484 - 2.77874i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.00128 - 4.04219i) q^{5} +(6.42484 - 2.77874i) q^{7} -2.82843i q^{8} +(5.71652 - 9.90131i) q^{10} +(-0.831900 - 0.480298i) q^{11} -16.2817 q^{13} +(5.90393 - 7.94629i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(10.0000 + 5.77351i) q^{17} +(6.31367 + 10.9356i) q^{19} -16.1688i q^{20} -1.35849 q^{22} +(-19.6604 + 11.3510i) q^{23} +(20.1786 - 34.9504i) q^{25} +(-19.9409 + 11.5129i) q^{26} +(1.61193 - 13.9069i) q^{28} +41.8238i q^{29} +(12.7406 - 22.0674i) q^{31} +(-4.89898 - 2.82843i) q^{32} +16.3299 q^{34} +(33.7500 - 45.4252i) q^{35} +(-32.3583 - 56.0461i) q^{37} +(15.4653 + 8.92887i) q^{38} +(-11.4330 - 19.8026i) q^{40} -20.4209i q^{41} +30.7575 q^{43} +(-1.66380 + 0.960596i) q^{44} +(-16.0527 + 27.8041i) q^{46} +(-53.3167 + 30.7824i) q^{47} +(33.5573 - 35.7059i) q^{49} -57.0738i q^{50} +(-16.2817 + 28.2007i) q^{52} +(46.9217 + 27.0903i) q^{53} -7.76583 q^{55} +(-7.85945 - 18.1722i) q^{56} +(29.5739 + 51.2235i) q^{58} +(71.7676 + 41.4350i) q^{59} +(-14.0538 - 24.3419i) q^{61} -36.0360i q^{62} -8.00000 q^{64} +(-113.993 + 65.8138i) q^{65} +(28.6849 - 49.6838i) q^{67} +(20.0000 - 11.5470i) q^{68} +(9.21466 - 79.4991i) q^{70} +26.6313i q^{71} +(-40.0885 + 69.4353i) q^{73} +(-79.2612 - 45.7615i) q^{74} +25.2547 q^{76} +(-6.67945 - 0.774208i) q^{77} +(53.2847 + 92.2918i) q^{79} +(-28.0051 - 16.1688i) q^{80} +(-14.4397 - 25.0104i) q^{82} +121.700i q^{83} +93.3505 q^{85} +(37.6701 - 21.7489i) q^{86} +(-1.35849 + 2.35297i) q^{88} +(-75.7166 + 43.7150i) q^{89} +(-104.607 + 45.2425i) q^{91} +45.4038i q^{92} +(-43.5329 + 75.4012i) q^{94} +(88.4076 + 51.0421i) q^{95} -173.692 q^{97} +(15.8512 - 67.4592i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 8 q^{7}+O(q^{10}) \) 24 * q + 24 * q^4 + 8 * q^7	\( 24 q + 24 q^{4} + 8 q^{7} + 8 q^{10} - 16 q^{13} - 48 q^{16} - 36 q^{19} + 64 q^{22} + 128 q^{25} + 32 q^{28} + 176 q^{31} + 16 q^{34} - 72 q^{37} - 16 q^{40} + 216 q^{43} + 64 q^{46} - 24 q^{49} - 16 q^{52} + 448 q^{55} + 104 q^{58} - 268 q^{61} - 192 q^{64} - 248 q^{67} - 80 q^{70} - 116 q^{73} - 144 q^{76} + 152 q^{79} + 240 q^{82} - 536 q^{85} + 64 q^{88} + 428 q^{91} + 144 q^{94} + 16 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 + 8 * q^7 + 8 * q^10 - 16 * q^13 - 48 * q^16 - 36 * q^19 + 64 * q^22 + 128 * q^25 + 32 * q^28 + 176 * q^31 + 16 * q^34 - 72 * q^37 - 16 * q^40 + 216 * q^43 + 64 * q^46 - 24 * q^49 - 16 * q^52 + 448 * q^55 + 104 * q^58 - 268 * q^61 - 192 * q^64 - 248 * q^67 - 80 * q^70 - 116 * q^73 - 144 * q^76 + 152 * q^79 + 240 * q^82 - 536 * q^85 + 64 * q^88 + 428 * q^91 + 144 * q^94 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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