LMFDB - Embedded newform 414.3.k.b.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,3,Mod(35,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 20]))

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

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

chi := DirichletCharacter("414.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	414.k (of order $22$, degree $10$, 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:	$11.2806829445$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			71.1
Character	$\chi$	$=$	414.71
Dual form			414.3.k.b.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-2.17725 + 7.41503i) q^{5} +(6.85488 - 7.91095i) q^{7} +(2.79964 + 0.402527i) q^{8} +O(q^{10})$	\(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-2.17725 + 7.41503i) q^{5} +(6.85488 - 7.91095i) q^{7} +(2.79964 + 0.402527i) q^{8} +(-7.15707 - 8.25969i) q^{10} +(-0.214579 - 0.333892i) q^{11} +(7.09545 + 8.18859i) q^{13} +(4.17064 + 14.2039i) q^{14} +(-2.61944 + 3.02300i) q^{16} +(9.43996 + 4.31109i) q^{17} +(6.43909 + 14.0996i) q^{19} +(15.2988 - 2.19964i) q^{20} +0.561299 q^{22} +(21.1528 + 9.03111i) q^{23} +(-29.2109 - 18.7727i) q^{25} +(-15.1671 + 2.18070i) q^{26} +(-20.0873 - 5.89818i) q^{28} +(-38.3477 - 17.5128i) q^{29} +(-1.84235 + 12.8139i) q^{31} +(-1.59372 - 5.42771i) q^{32} +(-12.3466 + 7.93466i) q^{34} +(43.7352 + 68.0532i) q^{35} +(-25.4655 + 7.47734i) q^{37} +(-21.6977 - 3.11966i) q^{38} +(-9.08026 + 19.8830i) q^{40} +(-14.1920 + 48.3334i) q^{41} +(2.60054 + 18.0871i) q^{43} +(-0.429159 + 0.667784i) q^{44} +(-26.9174 + 18.2607i) q^{46} +47.1029i q^{47} +(-8.62036 - 59.9559i) q^{49} +(44.6682 - 20.3993i) q^{50} +(9.00209 - 19.7118i) q^{52} +(40.3577 + 34.9701i) q^{53} +(2.94301 - 0.864146i) q^{55} +(22.3755 - 19.3885i) q^{56} +(50.1552 - 32.2328i) q^{58} +(-36.5799 + 31.6966i) q^{59} +(-9.80873 + 68.2212i) q^{61} +(-13.8362 - 11.9891i) q^{62} +(7.67594 + 2.25386i) q^{64} +(-76.1672 + 34.7844i) q^{65} +(79.4192 + 51.0396i) q^{67} -20.7556i q^{68} -114.403 q^{70} +(59.1643 - 92.0615i) q^{71} +(-6.28038 - 13.7521i) q^{73} +(10.5745 - 36.0136i) q^{74} +(20.3012 - 23.4288i) q^{76} +(-4.11232 - 0.591262i) q^{77} +(-2.59730 - 2.99744i) q^{79} +(-16.7124 - 26.0051i) q^{80} +(-46.6520 - 53.8392i) q^{82} +(-29.9013 - 101.835i) q^{83} +(-52.5200 + 60.6113i) q^{85} +(-23.5068 - 10.7352i) q^{86} +(-0.466344 - 1.02115i) q^{88} +(-96.4907 + 13.8733i) q^{89} +113.418 q^{91} +(-1.14437 - 45.9858i) q^{92} +(-56.0389 - 36.0140i) q^{94} +(-118.569 + 17.0476i) q^{95} +(136.320 + 40.0270i) q^{97} +(77.9213 + 35.5854i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} + 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^4 + 16 * q^7	$ 80 q + 16 q^{4} + 16 q^{7} - 8 q^{10} - 24 q^{13} - 32 q^{16} + 208 q^{19} + 64 q^{22} + 256 q^{25} - 32 q^{28} + 268 q^{34} - 256 q^{37} + 16 q^{40} - 524 q^{43} - 48 q^{46} + 144 q^{49} + 48 q^{52} + 396 q^{55} + 456 q^{58} + 376 q^{61} + 64 q^{64} + 44 q^{67} - 520 q^{70} - 188 q^{73} - 64 q^{76} + 164 q^{79} - 924 q^{82} - 1524 q^{85} + 48 q^{88} + 128 q^{91} - 176 q^{94} - 1144 q^{97}+O(q^{100}) $ 80 * q + 16 * q^4 + 16 * q^7 - 8 * q^10 - 24 * q^13 - 32 * q^16 + 208 * q^19 + 64 * q^22 + 256 * q^25 - 32 * q^28 + 268 * q^34 - 256 * q^37 + 16 * q^40 - 524 * q^43 - 48 * q^46 + 144 * q^49 + 48 * q^52 + 396 * q^55 + 456 * q^58 + 376 * q^61 + 64 * q^64 + 44 * q^67 - 520 * q^70 - 188 * q^73 - 64 * q^76 + 164 * q^79 - 924 * q^82 - 1524 * q^85 + 48 * q^88 + 128 * q^91 - 176 * q^94 - 1144 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.764582	+	1.18971i	−0.382291	+	0.594856i
$2$	−0.764582	+	1.18971i	−0.382291	+	0.594856i
$3$		0			0
$3$		0			0
$4$	−0.830830	−	1.81926i	−0.207708	−	0.454816i
$5$	−2.17725	+	7.41503i	−0.435450	+	1.48301i	0.391209	+	0.920302i	$0.372057\pi$
$5$	−2.17725	+	7.41503i	−0.435450	+	1.48301i	−0.826659	+	0.562704i	$0.809761\pi$
$6$		0			0
$7$	6.85488	−	7.91095i	0.979268	−	1.13014i	−0.0122182	−	0.999925i	$-0.503889\pi$
$7$	6.85488	−	7.91095i	0.979268	−	1.13014i	0.991486	−	0.130210i	$-0.0415653\pi$
$8$	2.79964	+	0.402527i	0.349955	+	0.0503159i
$9$		0			0
$10$	−7.15707	−	8.25969i	−0.715707	−	0.825969i
$11$	−0.214579	−	0.333892i	−0.0195072	−	0.0303538i	0.831363	−	0.555730i	$-0.187561\pi$
$11$	−0.214579	−	0.333892i	−0.0195072	−	0.0303538i	−0.850870	+	0.525376i	$0.823925\pi$
$12$		0			0
$13$	7.09545	+	8.18859i	0.545804	+	0.629891i	0.959900	−	0.280342i	$-0.0904478\pi$
$13$	7.09545	+	8.18859i	0.545804	+	0.629891i	−0.414096	+	0.910233i	$0.635902\pi$
$14$	4.17064	+	14.2039i	0.297903	+	1.01456i
$15$		0			0
$16$	−2.61944	+	3.02300i	−0.163715	+	0.188937i
$17$	9.43996	+	4.31109i	0.555292	+	0.253593i	0.673237	−	0.739427i	$-0.264903\pi$
$17$	9.43996	+	4.31109i	0.555292	+	0.253593i	−0.117945	+	0.993020i	$0.537631\pi$
$18$		0			0
$19$	6.43909	+	14.0996i	0.338899	+	0.742086i	0.999966	−	0.00824092i	$-0.00262319\pi$
$19$	6.43909	+	14.0996i	0.338899	+	0.742086i	−0.661067	+	0.750327i	$0.729896\pi$
$20$	15.2988	−	2.19964i	0.764941	−	0.109982i
$21$		0			0
$22$	0.561299			0.0255136
$23$	21.1528	+	9.03111i	0.919685	+	0.392657i
$23$	21.1528	+	9.03111i	0.919685	+	0.392657i
$24$		0			0
$25$	−29.2109	−	18.7727i	−1.16844	−	0.750908i
$26$	−15.1671	+	2.18070i	−0.583351	+	0.0838731i
$27$		0			0
$28$	−20.0873	−	5.89818i	−0.717405	−	0.210649i
$29$	−38.3477	−	17.5128i	−1.32234	−	0.603890i	−0.375863	−	0.926675i	$-0.622654\pi$
$29$	−38.3477	−	17.5128i	−1.32234	−	0.603890i	−0.946472	+	0.322785i	$0.895381\pi$
$30$		0			0
$31$	−1.84235	+	12.8139i	−0.0594308	+	0.413350i	0.938289	+	0.345853i	$0.112410\pi$
$31$	−1.84235	+	12.8139i	−0.0594308	+	0.413350i	−0.997719	+	0.0674970i	$0.978499\pi$
$32$	−1.59372	−	5.42771i	−0.0498038	−	0.169616i
$33$		0			0
$34$	−12.3466	+	7.93466i	−0.363135	+	0.233372i
$35$	43.7352	+	68.0532i	1.24958	+	1.94438i
$36$		0			0
$37$	−25.4655	+	7.47734i	−0.688256	+	0.202090i	−0.607117	−	0.794613i	$-0.707674\pi$
$37$	−25.4655	+	7.47734i	−0.688256	+	0.202090i	−0.0811391	+	0.996703i	$0.525856\pi$
$38$	−21.6977	−	3.11966i	−0.570993	−	0.0820964i
$39$		0			0
$40$	−9.08026	+	19.8830i	−0.227006	+	0.497075i
$41$	−14.1920	+	48.3334i	−0.346146	+	1.17886i	0.584025	+	0.811736i	$0.301477\pi$
$41$	−14.1920	+	48.3334i	−0.346146	+	1.17886i	−0.930170	+	0.367128i	$0.880341\pi$
$42$		0			0
$43$	2.60054	+	18.0871i	0.0604777	+	0.420631i	0.997458	+	0.0712505i	$0.0226990\pi$
$43$	2.60054	+	18.0871i	0.0604777	+	0.420631i	−0.936981	+	0.349381i	$0.886392\pi$
$44$	−0.429159	+	0.667784i	−0.00975360	+	0.0151769i
$45$		0			0
$46$	−26.9174	+	18.2607i	−0.585161	+	0.396971i
$47$			47.1029i			1.00219i	0.865392	+	0.501095i	$0.167069\pi$
$47$			47.1029i			1.00219i	−0.865392	+	0.501095i	$0.832931\pi$
$48$		0			0
$49$	−8.62036	−	59.9559i	−0.175926	−	1.22359i
$50$	44.6682	−	20.3993i	0.893365	−	0.407986i
$51$		0			0
$52$	9.00209	−	19.7118i	0.173117	−	0.379074i
$53$	40.3577	+	34.9701i	0.761466	+	0.659814i	0.946422	−	0.322933i	$-0.104669\pi$
$53$	40.3577	+	34.9701i	0.761466	+	0.659814i	−0.184956	+	0.982747i	$0.559214\pi$
$54$		0			0
$55$	2.94301	−	0.864146i	0.0535093	−	0.0157117i
$56$	22.3755	−	19.3885i	0.399563	−	0.346224i
$57$		0			0
$58$	50.1552	−	32.2328i	0.864745	−	0.555738i
$59$	−36.5799	+	31.6966i	−0.619998	+	0.537231i	−0.907233	−	0.420629i	$-0.861809\pi$
$59$	−36.5799	+	31.6966i	−0.619998	+	0.537231i	0.287235	+	0.957860i	$0.407264\pi$
$60$		0			0
$61$	−9.80873	+	68.2212i	−0.160799	+	1.11838i	0.736334	+	0.676619i	$0.236555\pi$
$61$	−9.80873	+	68.2212i	−0.160799	+	1.11838i	−0.897132	+	0.441762i	$0.854354\pi$
$62$	−13.8362	−	11.9891i	−0.223164	−	0.193373i
$63$		0			0
$64$	7.67594	+	2.25386i	0.119937	+	0.0352166i
$65$	−76.1672	+	34.7844i	−1.17180	+	0.535144i
$66$		0			0
$67$	79.4192	+	51.0396i	1.18536	+	0.761785i	0.976364	−	0.216131i	$-0.0693438\pi$
$67$	79.4192	+	51.0396i	1.18536	+	0.761785i	0.208997	+	0.977916i	$0.432980\pi$
$68$		−	20.7556i		−	0.305229i
$69$		0			0
$70$	−114.403			−1.63433
$71$	59.1643	−	92.0615i	0.833300	−	1.29664i	−0.119436	−	0.992842i	$-0.538109\pi$
$71$	59.1643	−	92.0615i	0.833300	−	1.29664i	0.952736	−	0.303799i	$-0.0982550\pi$
$72$		0			0
$73$	−6.28038	−	13.7521i	−0.0860325	−	0.188385i	0.861726	−	0.507374i	$-0.169384\pi$
$73$	−6.28038	−	13.7521i	−0.0860325	−	0.188385i	−0.947758	+	0.318989i	$0.896657\pi$
$74$	10.5745	−	36.0136i	0.142899	−	0.486670i
$75$		0			0
$76$	20.3012	−	23.4288i	0.267121	−	0.308274i
$77$	−4.11232	−	0.591262i	−0.0534067	−	0.00767873i
$78$		0			0
$79$	−2.59730	−	2.99744i	−0.0328772	−	0.0379423i	0.739073	−	0.673626i	$-0.235264\pi$
$79$	−2.59730	−	2.99744i	−0.0328772	−	0.0379423i	−0.771950	+	0.635683i	$0.780718\pi$
$80$	−16.7124	−	26.0051i	−0.208906	−	0.325063i
$81$		0			0
$82$	−46.6520	−	53.8392i	−0.568926	−	0.656576i
$83$	−29.9013	−	101.835i	−0.360257	−	1.22692i	−0.917890	−	0.396835i	$-0.870108\pi$
$83$	−29.9013	−	101.835i	−0.360257	−	1.22692i	0.557633	−	0.830088i	$-0.311710\pi$
$84$		0			0
$85$	−52.5200	+	60.6113i	−0.617882	+	0.713074i
$86$	−23.5068	−	10.7352i	−0.273335	−	0.124828i
$87$		0			0
$88$	−0.466344	−	1.02115i	−0.00529936	−	0.0116040i
$89$	−96.4907	+	13.8733i	−1.08417	+	0.155879i	−0.661158	−	0.750247i	$-0.729935\pi$
$89$	−96.4907	+	13.8733i	−1.08417	+	0.155879i	−0.423007	+	0.906126i	$0.639026\pi$
$90$		0			0
$91$	113.418			1.24635
$92$	−1.14437	−	45.9858i	−0.0124388	−	0.499845i
$93$		0			0
$94$	−56.0389	−	36.0140i	−0.596159	−	0.383128i
$95$	−118.569	+	17.0476i	−1.24809	+	0.179449i
$96$		0			0
$97$	136.320	+	40.0270i	1.40536	+	0.412650i	0.894520	−	0.447028i	$-0.147518\pi$
$97$	136.320	+	40.0270i	1.40536	+	0.412650i	0.510836	+	0.859678i	$0.329336\pi$
$98$	77.9213	+	35.5854i	0.795115	+	0.363117i
$99$		0			0
$100$	−9.88322	+	68.7393i	−0.0988322	+	0.687393i
$101$	17.9643	+	61.1809i	0.177865	+	0.605751i	0.999368	+	0.0355476i	$0.0113175\pi$
$101$	17.9643	+	61.1809i	0.177865	+	0.605751i	−0.821503	+	0.570204i	$0.806864\pi$
$102$		0			0
$103$	−159.755	+	102.668i	−1.55102	+	0.996779i	−0.565986	+	0.824415i	$0.691504\pi$
$103$	−159.755	+	102.668i	−1.55102	+	0.996779i	−0.985033	+	0.172364i	$0.944859\pi$
$104$	16.5686	+	25.7812i	0.159313	+	0.247896i
$105$		0			0
$106$	−72.4611	+	21.2765i	−0.683596	+	0.200722i
$107$	8.05726	+	1.15846i	0.0753015	+	0.0108267i	0.179863	−	0.983692i	$-0.442435\pi$
$107$	8.05726	+	1.15846i	0.0753015	+	0.0108267i	−0.104561	+	0.994518i	$0.533344\pi$
$108$		0			0
$109$	80.0266	−	175.234i	0.734189	−	1.60765i	−0.0586952	−	0.998276i	$-0.518694\pi$
$109$	80.0266	−	175.234i	0.734189	−	1.60765i	0.792884	−	0.609373i	$-0.208579\pi$
$110$	−1.22209	+	4.16205i	−0.0111099	+	0.0378368i
$111$		0			0
$112$	5.95883	+	41.4446i	0.0532038	+	0.370041i
$113$	94.9377	−	147.726i	0.840157	−	1.30731i	−0.109490	−	0.993988i	$-0.534922\pi$
$113$	94.9377	−	147.726i	0.840157	−	1.30731i	0.949647	−	0.313322i	$-0.101442\pi$
$114$		0			0
$115$	−113.021	+	137.185i	−0.982789	+	1.19292i
$116$			84.3148i			0.726852i
$117$		0			0
$118$	−9.74158	−	67.7542i	−0.0825558	−	0.574188i
$119$	98.8146	−	45.1271i	0.830375	−	0.379219i
$120$		0			0
$121$	50.1998	−	109.922i	0.414874	−	0.908448i
$122$	−73.6640	−	63.8302i	−0.603803	−	0.523199i
$123$		0			0
$124$	24.8425	−	7.29440i	0.200342	−	0.0588258i
$125$	56.7875	−	49.2066i	0.454300	−	0.393653i
$126$		0			0
$127$	188.425	−	121.094i	1.48366	−	0.953493i	0.486871	−	0.873474i	$-0.338138\pi$
$127$	188.425	−	121.094i	1.48366	−	0.953493i	0.996793	−	0.0800193i	$-0.0254982\pi$
$128$	−8.55033	+	7.40890i	−0.0667995	+	0.0578821i
$129$		0			0
$130$	16.8526	−	117.213i	0.129636	−	0.901635i
$131$	−32.8193	−	28.4381i	−0.250529	−	0.217085i	0.520538	−	0.853838i	$-0.325731\pi$
$131$	−32.8193	−	28.4381i	−0.250529	−	0.217085i	−0.771067	+	0.636754i	$0.780277\pi$
$132$		0			0
$133$	155.681	+	45.7120i	1.17053	+	0.343699i
$134$	−121.445	+	55.4620i	−0.906305	+	0.413896i
$135$		0			0
$136$	24.6931	+	15.8693i	0.181567	+	0.116686i
$137$		−	144.020i		−	1.05124i	−0.850720	−	0.525620i	$-0.823834\pi$
$137$		−	144.020i		−	1.05124i	0.850720	−	0.525620i	$-0.176166\pi$
$138$		0			0
$139$	152.496			1.09710			0.548548	−	0.836119i	$-0.315181\pi$
$139$	152.496			1.09710			0.548548	+	0.836119i	$0.315181\pi$
$140$	87.4703	−	136.106i	0.624788	−	0.972189i
$141$		0			0
$142$	64.2907	+	140.777i	0.452751	+	0.991387i
$143$	1.21157	−	4.12622i	0.00847249	−	0.0288547i
$144$		0			0
$145$	213.351	−	246.220i	1.47138	−	1.69807i
$146$	21.1629	+	3.04277i	0.144951	+	0.0208409i
$147$		0			0
$148$	34.7607	+	40.1160i	0.234870	+	0.271054i
$149$	72.5921	+	112.955i	0.487195	+	0.758090i	0.994618	−	0.103607i	$-0.0330383\pi$
$149$	72.5921	+	112.955i	0.487195	+	0.758090i	−0.507423	+	0.861697i	$0.669402\pi$
$150$		0			0
$151$	−38.5745	−	44.5173i	−0.255460	−	0.294817i	0.613504	−	0.789692i	$-0.289759\pi$
$151$	−38.5745	−	44.5173i	−0.255460	−	0.294817i	−0.868964	+	0.494875i	$0.835214\pi$
$152$	12.3516	+	42.0658i	0.0812607	+	0.276749i
$153$		0			0
$154$	3.84763	−	4.44041i	0.0249846	−	0.0288338i
$155$	−91.0038	−	41.5601i	−0.587121	−	0.268129i
$156$		0			0
$157$	−91.0843	−	199.447i	−0.580155	−	1.27036i	−0.941211	−	0.337818i	$-0.890311\pi$
$157$	−91.0843	−	199.447i	−0.580155	−	1.27036i	0.361056	−	0.932544i	$-0.382416\pi$
$158$	5.55193	−	0.798248i	0.0351388	−	0.00505220i
$159$		0			0
$160$	43.7166			0.273229
$161$	216.444	−	105.431i	1.34437	−	0.654852i
$162$		0			0
$163$	233.616	+	150.136i	1.43323	+	0.921080i	0.999802	+	0.0198904i	$0.00633172\pi$
$163$	233.616	+	150.136i	1.43323	+	0.921080i	0.433426	+	0.901189i	$0.357305\pi$
$164$	99.7224	−	14.3379i	0.608063	−	0.0874263i
$165$		0			0
$166$	144.016	+	42.2869i	0.867565	+	0.254740i
$167$	−198.914	−	90.8409i	−1.19110	−	0.543958i	−0.281549	−	0.959547i	$-0.590848\pi$
$167$	−198.914	−	90.8409i	−1.19110	−	0.543958i	−0.909552	+	0.415589i	$0.863575\pi$
$168$		0			0
$169$	7.34367	−	51.0764i	0.0434537	−	0.302227i
$170$	−31.9542	−	108.826i	−0.187966	−	0.640153i
$171$		0			0
$172$	30.7447	−	19.7584i	0.178748	−	0.114874i
$173$	148.356	+	230.846i	0.857549	+	1.33437i	0.941191	+	0.337876i	$0.109708\pi$
$173$	148.356	+	230.846i	0.857549	+	1.33437i	−0.0836422	+	0.996496i	$0.526655\pi$
$174$		0			0
$175$	−348.747	+	102.401i	−1.99284	+	0.585151i
$176$	1.57143	+	0.225938i	0.00892860	+	0.00128374i
$177$		0			0
$178$	57.2698	−	125.403i	0.321741	−	0.704514i
$179$	−68.5892	+	233.593i	−0.383180	+	1.30499i	0.511885	+	0.859054i	$0.328948\pi$
$179$	−68.5892	+	233.593i	−0.383180	+	1.30499i	−0.895065	+	0.445937i	$0.852871\pi$
$180$		0			0
$181$	26.2047	+	182.258i	0.144778	+	1.00695i	0.924597	+	0.380946i	$0.124402\pi$
$181$	26.2047	+	182.258i	0.144778	+	1.00695i	−0.779820	+	0.626004i	$0.784689\pi$
$182$	−86.7173	+	134.935i	−0.476469	+	0.741400i
$183$		0			0
$184$	55.5848	+	33.7984i	0.302091	+	0.183687i
$185$		−	205.107i		−	1.10869i
$186$		0			0
$187$	−0.586184	−	4.07700i	−0.00313467	−	0.0218021i
$188$	85.6926	−	39.1345i	0.455812	−	0.208162i
$189$		0			0
$190$	70.3737	−	154.097i	0.370388	−	0.811037i
$191$	−106.359	−	92.1603i	−0.556852	−	0.482515i	0.330374	−	0.943850i	$-0.392825\pi$
$191$	−106.359	−	92.1603i	−0.556852	−	0.482515i	−0.887226	+	0.461335i	$0.847371\pi$
$192$		0			0
$193$	−364.220	+	106.945i	−1.88715	+	0.554117i	−0.892470	+	0.451107i	$0.851029\pi$
$193$	−364.220	+	106.945i	−1.88715	+	0.554117i	−0.994680	+	0.103010i	$0.967153\pi$
$194$	−151.848	+	131.577i	−0.782722	+	0.678232i
$195$		0			0
$196$	−101.914	+	65.4959i	−0.519967	+	0.334163i
$197$	139.830	−	121.163i	0.709796	−	0.615042i	−0.223266	−	0.974758i	$-0.571672\pi$
$197$	139.830	−	121.163i	0.709796	−	0.615042i	0.933062	+	0.359716i	$0.117126\pi$
$198$		0			0
$199$	−19.0391	+	132.420i	−0.0956739	+	0.665427i	0.884391	+	0.466748i	$0.154574\pi$
$199$	−19.0391	+	132.420i	−0.0956739	+	0.665427i	−0.980065	+	0.198679i	$0.936335\pi$
$200$	−74.2234	−	64.3150i	−0.371117	−	0.321575i
$201$		0			0
$202$	−86.5228	−	25.4054i	−0.428331	−	0.125769i
$203$	−401.412	+	183.319i	−1.97740	+	0.903048i
$204$		0			0
$205$	−327.494	−	210.468i	−1.59753	−	1.02667i
$206$		−	268.561i		−	1.30369i
$207$		0			0
$208$	−43.3402			−0.208366
$209$	3.32606	−	5.17545i	0.0159142	−	0.0247629i
$210$		0			0
$211$	−73.6327	−	161.233i	−0.348970	−	0.764138i	−0.999987	−	0.00507499i	$-0.998385\pi$
$211$	−73.6327	−	161.233i	−0.348970	−	0.764138i	0.651017	−	0.759063i	$-0.274343\pi$
$212$	30.0895	−	102.476i	0.141932	−	0.483375i
$213$		0			0
$214$	−7.53867	+	8.70009i	−0.0352274	+	0.0406546i
$215$	−139.779	−	20.0971i	−0.650134	−	0.0934751i
$216$		0			0
$217$	88.7406	+	102.412i	0.408943	+	0.471945i
$218$	147.291	+	229.189i	0.675646	+	1.05133i
$219$		0			0
$220$	−4.01725	−	4.63616i	−0.0182602	−	0.0210734i
$221$	31.6791	+	107.889i	0.143344	+	0.488186i
$222$		0			0
$223$	−98.4729	+	113.644i	−0.441582	+	0.509613i	−0.932290	−	0.361711i	$-0.882193\pi$
$223$	−98.4729	+	113.644i	−0.441582	+	0.509613i	0.490708	+	0.871324i	$0.336738\pi$
$224$	−53.8631	−	24.5985i	−0.240460	−	0.109815i
$225$		0			0
$226$	103.164	+	225.897i	0.456477	+	0.999545i
$227$	28.9087	−	4.15644i	0.127351	−	0.0183103i	−0.0783445	−	0.996926i	$-0.524963\pi$
$227$	28.9087	−	4.15644i	0.127351	−	0.0183103i	0.205696	+	0.978616i	$0.434054\pi$
$228$		0			0
$229$	112.703			0.492155			0.246077	−	0.969250i	$-0.420858\pi$
$229$	112.703			0.492155			0.246077	+	0.969250i	$0.420858\pi$
$230$	−76.7975	−	239.352i	−0.333902	−	1.04066i
$231$		0			0
$232$	−100.310	−	64.4656i	−0.432372	−	0.277869i
$233$	−327.182	+	47.0417i	−1.40421	+	0.201896i	−0.802422	−	0.596757i	$-0.796456\pi$
$233$	−327.182	+	47.0417i	−1.40421	+	0.201896i	−0.601792	+	0.798653i	$0.705547\pi$
$234$		0			0
$235$	−349.269	−	102.555i	−1.48625	−	0.436403i
$236$	88.0562	+	40.2139i	0.373119	+	0.170398i
$237$		0			0
$238$	−21.8635	+	152.064i	−0.0918636	+	0.638925i
$239$	−25.3309	−	86.2691i	−0.105987	−	0.360959i	0.889373	−	0.457183i	$-0.151142\pi$
$239$	−25.3309	−	86.2691i	−0.105987	−	0.360959i	−0.995360	+	0.0962243i	$0.969323\pi$
$240$		0			0
$241$	119.043	−	76.5040i	0.493953	−	0.317444i	−0.269841	−	0.962905i	$-0.586971\pi$
$241$	119.043	−	76.5040i	0.493953	−	0.317444i	0.763793	+	0.645461i	$0.223335\pi$
$242$	92.3939	+	143.768i	0.381793	+	0.594082i
$243$		0			0
$244$	132.262	−	38.8356i	0.542056	−	0.159162i
$245$	463.344	+	66.6188i	1.89120	+	0.271913i
$246$		0			0
$247$	−69.7679	+	152.770i	−0.282461	+	0.618504i
$248$	−10.3158	+	35.1325i	−0.0415962	+	0.141663i
$249$		0			0
$250$	15.1231	+	105.183i	0.0604923	+	0.420733i
$251$	23.0848	−	35.9207i	0.0919714	−	0.143110i	−0.792219	−	0.610237i	$-0.791074\pi$
$251$	23.0848	−	35.9207i	0.0919714	−	0.143110i	0.884191	+	0.467126i	$0.154711\pi$
$252$		0			0
$253$	−1.52353	−	9.00062i	−0.00602185	−	0.0355756i
$254$			316.758i			1.24708i
$255$		0			0
$256$	−2.27704	−	15.8371i	−0.00889468	−	0.0618638i
$257$	180.478	−	82.4214i	0.702247	−	0.320706i	−0.0320950	−	0.999485i	$-0.510218\pi$
$257$	180.478	−	82.4214i	0.702247	−	0.320706i	0.734342	+	0.678779i	$0.237491\pi$
$258$		0			0
$259$	−115.410	+	252.712i	−0.445598	+	0.975723i
$260$	126.564	+	109.668i	0.486785	+	0.421801i
$261$		0			0
$262$	58.9261	−	17.3023i	0.224909	−	0.0660392i
$263$	270.739	−	234.597i	1.02943	−	0.892002i	0.0352069	−	0.999380i	$-0.488791\pi$
$263$	270.739	−	234.597i	1.02943	−	0.892002i	0.994218	+	0.107378i	$0.0342455\pi$
$264$		0			0
$265$	−347.173	+	223.115i	−1.31009	+	0.841942i
$266$	−173.415	+	150.265i	−0.651935	+	0.564905i
$267$		0			0
$268$	26.8707	−	186.890i	0.100264	−	0.697350i
$269$	222.628	+	192.908i	0.827612	+	0.717130i	0.961778	−	0.273829i	$-0.0882902\pi$
$269$	222.628	+	192.908i	0.827612	+	0.717130i	−0.134166	+	0.990959i	$0.542836\pi$
$270$		0			0
$271$	340.168	+	99.8824i	1.25523	+	0.368570i	0.840718	−	0.541473i	$-0.182133\pi$
$271$	340.168	+	99.8824i	1.25523	+	0.368570i	0.414515	+	0.910043i	$0.363951\pi$
$272$	−37.7599	+	17.2443i	−0.138823	+	0.0633983i
$273$		0			0
$274$	171.342	+	110.115i	0.625336	+	0.401879i
$275$			13.7815i			0.0501146i
$276$		0			0
$277$	−185.653			−0.670227			−0.335114	−	0.942178i	$-0.608775\pi$
$277$	−185.653			−0.670227			−0.335114	+	0.942178i	$0.608775\pi$
$278$	−116.596	+	181.427i	−0.419410	+	0.652614i
$279$		0			0
$280$	95.0493	+	208.129i	0.339462	+	0.743318i
$281$	57.0523	−	194.302i	0.203033	−	0.691467i	−0.793523	−	0.608541i	$-0.791755\pi$
$281$	57.0523	−	194.302i	0.203033	−	0.691467i	0.996556	−	0.0829263i	$-0.0264266\pi$
$282$		0			0
$283$	5.73619	−	6.61992i	0.0202692	−	0.0233919i	−0.745524	−	0.666478i	$-0.767801\pi$
$283$	5.73619	−	6.61992i	0.0202692	−	0.0233919i	0.765794	+	0.643086i	$0.222346\pi$
$284$	−216.640	−	31.1481i	−0.762816	−	0.109676i
$285$		0			0
$286$	3.98267	+	4.59624i	0.0139254	+	0.0160708i
$287$	285.079	+	443.592i	0.993307	+	1.54562i
$288$		0			0
$289$	−118.727	−	137.019i	−0.410821	−	0.474113i
$290$	129.807	+	442.081i	0.447609	+	1.52442i
$291$		0			0
$292$	−19.8008	+	22.8513i	−0.0678109	+	0.0782580i
$293$	50.5346	+	23.0784i	0.172473	+	0.0787659i	0.499781	−	0.866152i	$-0.333414\pi$
$293$	50.5346	+	23.0784i	0.172473	+	0.0787659i	−0.327307	+	0.944918i	$0.606141\pi$
$294$		0			0
$295$	−155.388	−	340.252i	−0.526739	−	1.15340i
$296$	−74.3039	+	10.6833i	−0.251027	+	0.0360922i
$297$		0			0
$298$	−189.887			−0.637205
$299$	76.1363	+	237.291i	0.254637	+	0.793615i
$300$		0			0
$301$	160.913	+	103.412i	0.534594	+	0.343563i
$302$	82.4562	−	11.8554i	0.273034	−	0.0392563i
$303$		0			0
$304$	−59.4900	−	17.4678i	−0.195691	−	0.0574600i
$305$	−484.506	−	221.267i	−1.58854	−	0.725464i
$306$		0			0
$307$	59.4323	−	413.361i	0.193590	−	1.34645i	−0.628817	−	0.777553i	$-0.716461\pi$
$307$	59.4323	−	413.361i	0.193590	−	1.34645i	0.822408	−	0.568898i	$-0.192630\pi$
$308$	2.34097	+	7.97263i	0.00760057	+	0.0258852i
$309$		0			0
$310$	119.024	−	76.4923i	0.383949	−	0.246749i
$311$	−206.787	−	321.768i	−0.664912	−	1.03462i	−0.995854	−	0.0909714i	$-0.971003\pi$
$311$	−206.787	−	321.768i	−0.664912	−	1.03462i	0.330942	−	0.943651i	$-0.392634\pi$
$312$		0			0
$313$	−290.730	+	85.3659i	−0.928848	+	0.272735i	−0.710955	−	0.703238i	$-0.751737\pi$
$313$	−290.730	+	85.3659i	−0.928848	+	0.272735i	−0.217894	+	0.975972i	$0.569919\pi$
$314$	306.926	+	44.1293i	0.977470	+	0.140539i
$315$		0			0
$316$	−3.29522	+	7.21553i	−0.0104279	+	0.0228340i
$317$	31.8532	−	108.482i	0.100483	−	0.342215i	−0.893871	−	0.448324i	$-0.852021\pi$
$317$	31.8532	−	108.482i	0.100483	−	0.342215i	0.994355	+	0.106109i	$0.0338393\pi$
$318$		0			0
$319$	2.38124	+	16.5619i	0.00746470	+	0.0519181i
$320$	−33.4249	+	52.0101i	−0.104453	+	0.162532i
$321$		0			0
$322$	−40.0564	+	338.117i	−0.124399	+	1.05005i
$323$			160.860i			0.498017i
$324$		0			0
$325$	−53.5426	−	372.397i	−0.164746	−	1.14584i
$326$	−357.237	+	163.145i	−1.09582	+	0.500444i
$327$		0			0
$328$	−59.1879	+	129.603i	−0.180451	+	0.395133i
$329$	372.629	+	322.885i	1.13261	+	0.981412i
$330$		0			0
$331$	−237.912	+	69.8572i	−0.718767	+	0.211049i	−0.620607	−	0.784122i	$-0.713114\pi$
$331$	−237.912	+	69.8572i	−0.718767	+	0.211049i	−0.0981597	+	0.995171i	$0.531296\pi$
$332$	−160.421	+	139.006i	−0.483196	+	0.418692i
$333$		0			0
$334$	260.160	−	167.195i	0.778924	−	0.500584i
$335$	−551.376	+	477.770i	−1.64590	+	1.42618i
$336$		0			0
$337$	83.4853	−	580.653i	0.247731	−	1.72301i	−0.363535	−	0.931581i	$-0.618430\pi$
$337$	83.4853	−	580.653i	0.247731	−	1.72301i	0.611266	−	0.791426i	$-0.290661\pi$
$338$	55.1513	+	47.7889i	0.163170	+	0.141387i
$339$		0			0
$340$	153.903	+	45.1900i	0.452656	+	0.132912i
$341$	4.67377	−	2.13444i	0.0137061	−	0.00625936i
$342$		0			0
$343$	−101.907	−	65.4916i	−0.297105	−	0.190938i
$344$			51.6842i			0.150245i
$345$		0			0
$346$	−388.071			−1.12159
$347$	8.34115	−	12.9791i	0.0240379	−	0.0374037i	−0.829027	−	0.559209i	$-0.811105\pi$
$347$	8.34115	−	12.9791i	0.0240379	−	0.0374037i	0.853065	+	0.521805i	$0.174741\pi$
$348$		0			0
$349$	53.7344	+	117.662i	0.153967	+	0.337140i	0.970859	−	0.239649i	$-0.0770325\pi$
$349$	53.7344	+	117.662i	0.153967	+	0.337140i	−0.816893	+	0.576790i	$0.804305\pi$
$350$	144.817	−	493.203i	0.413764	−	1.40915i
$351$		0			0
$352$	−1.47029	+	1.69680i	−0.00417696	+	0.00482047i
$353$	−29.1790	−	4.19531i	−0.0826601	−	0.0118847i	0.100861	−	0.994901i	$-0.467840\pi$
$353$	−29.1790	−	4.19531i	−0.0826601	−	0.0118847i	−0.183521	+	0.983016i	$0.558749\pi$
$354$		0			0
$355$	553.823	+	639.146i	1.56007	+	1.80041i
$356$	105.407	+	164.016i	0.296086	+	0.460718i
$357$		0			0
$358$	−225.467	−	260.203i	−0.629796	−	0.726823i
$359$	−88.9595	−	302.968i	−0.247798	−	0.843922i	−0.985627	−	0.168935i	$-0.945967\pi$
$359$	−88.9595	−	302.968i	−0.247798	−	0.843922i	0.737829	−	0.674987i	$-0.235851\pi$
$360$		0			0
$361$	79.0667	−	91.2479i	0.219021	−	0.252764i
$362$	−236.870	−	108.175i	−0.654337	−	0.298826i
$363$		0			0
$364$	−94.2310	−	206.337i	−0.258877	−	0.566860i
$365$	115.646	−	16.6274i	0.316839	−	0.0455546i
$366$		0			0
$367$	−471.775			−1.28549			−0.642745	−	0.766080i	$-0.722205\pi$
$367$	−471.775			−1.28549			−0.642745	+	0.766080i	$0.722205\pi$
$368$	−82.7095	+	40.2883i	−0.224754	+	0.109479i
$369$		0			0
$370$	244.019	+	156.821i	0.659510	+	0.423841i
$371$	553.294	−	79.5517i	1.49136	−	0.214425i
$372$		0			0
$373$	−326.699	−	95.9274i	−0.875868	−	0.257178i	−0.187259	−	0.982311i	$-0.559960\pi$
$373$	−326.699	−	95.9274i	−0.875868	−	0.257178i	−0.688609	+	0.725133i	$0.741778\pi$
$374$	5.29864	+	2.41981i	0.0141675	+	0.00647007i
$375$		0			0
$376$	−18.9602	+	131.871i	−0.0504261	+	0.350721i
$377$	−128.689	−	438.275i	−0.341351	−	1.16253i
$378$		0			0
$379$	−151.044	+	97.0703i	−0.398534	+	0.256122i	−0.724522	−	0.689252i	$-0.757939\pi$
$379$	−151.044	+	97.0703i	−0.398534	+	0.256122i	0.325988	+	0.945374i	$0.394303\pi$
$380$	129.525	+	201.544i	0.340854	+	0.530379i
$381$		0			0
$382$	190.964	−	56.0721i	0.499906	−	0.146786i
$383$	−0.639392	−	0.0919307i	−0.00166943	−	0.000240028i	0.141480	−	0.989941i	$-0.454814\pi$
$383$	−0.639392	−	0.0919307i	−0.00166943	−	0.000240028i	−0.143150	+	0.989701i	$0.545723\pi$
$384$		0			0
$385$	13.3378	−	29.2056i	0.0346435	−	0.0758588i
$386$	151.243	−	515.085i	0.391820	−	1.33442i
$387$		0			0
$388$	−40.4386	−	281.257i	−0.104223	−	0.724889i
$389$	56.5933	−	88.0609i	0.145484	−	0.226378i	−0.760862	−	0.648914i	$-0.775224\pi$
$389$	56.5933	−	88.0609i	0.145484	−	0.226378i	0.906346	+	0.422536i	$0.138860\pi$
$390$		0			0
$391$	160.747	+	176.445i	0.411119	+	0.451265i
$392$		−	171.325i		−	0.437053i
$393$		0			0
$394$	37.2381	+	258.997i	0.0945129	+	0.657352i
$395$	27.8811	−	12.7329i	0.0705850	−	0.0322351i
$396$		0			0
$397$	−84.9125	+	185.933i	−0.213885	+	0.468344i	−0.985916	−	0.167242i	$-0.946514\pi$
$397$	−84.9125	+	185.933i	−0.213885	+	0.468344i	0.772030	+	0.635586i	$0.219241\pi$
$398$	−142.985	−	123.897i	−0.359258	−	0.311299i
$399$		0			0
$400$	133.266	−	39.1305i	0.333165	−	0.0978262i
$401$	−372.390	+	322.678i	−0.928654	+	0.804684i	−0.981012	−	0.193945i	$-0.937872\pi$
$401$	−372.390	+	322.678i	−0.928654	+	0.804684i	0.0523581	+	0.998628i	$0.483326\pi$
$402$		0			0
$403$	−118.000	+	75.8338i	−0.292803	+	0.188173i
$404$	96.3789	−	83.5128i	0.238562	−	0.206715i
$405$		0			0
$406$	88.8157	−	617.727i	0.218758	−	1.52149i
$407$	7.96098	+	6.89823i	0.0195602	+	0.0169490i
$408$		0			0
$409$	482.202	+	141.587i	1.17898	+	0.346179i	0.811780	−	0.583964i	$-0.198499\pi$
$409$	482.202	+	141.587i	1.17898	+	0.346179i	0.367198	+	0.930143i	$0.380317\pi$
$410$	500.792	−	228.704i	1.22144	−	0.557815i
$411$		0			0
$412$	319.510	+	205.337i	0.775509	+	0.498390i
$413$			506.658i			1.22677i
$414$		0			0
$415$	820.209			1.97641
$416$	33.1371	−	51.5624i	0.0796566	−	0.123948i
$417$		0			0
$418$	3.61425	+	7.91411i	0.00864654	+	0.0189333i
$419$	128.899	−	438.990i	0.307635	−	1.04771i	−0.650051	−	0.759891i	$-0.725252\pi$
$419$	128.899	−	438.990i	0.307635	−	1.04771i	0.957685	−	0.287817i	$-0.0929295\pi$
$420$		0			0
$421$	−135.667	+	156.568i	−0.322250	+	0.371897i	−0.893642	−	0.448781i	$-0.851858\pi$
$421$	−135.667	+	156.568i	−0.322250	+	0.371897i	0.571392	+	0.820678i	$0.306404\pi$
$422$	248.119	+	35.6742i	0.587960	+	0.0845359i
$423$		0			0
$424$	98.9105	+	114.149i	0.233279	+	0.269219i
$425$	−194.819	−	303.144i	−0.458398	−	0.713281i
$426$		0			0
$427$	472.457	+	545.244i	1.10646	+	1.27692i
$428$	−4.58667	−	15.6208i	−0.0107165	−	0.0364971i
$429$		0			0
$430$	130.782	−	150.931i	0.304144	−	0.351001i
$431$	622.110	+	284.108i	1.44341	+	0.659183i	0.974567	−	0.224098i	$-0.0719436\pi$
$431$	622.110	+	284.108i	1.44341	+	0.659183i	0.468843	+	0.883281i	$0.344671\pi$
$432$		0			0
$433$	−323.484	−	708.331i	−0.747076	−	1.63587i	−0.771551	−	0.636167i	$-0.780519\pi$
$433$	−323.484	−	708.331i	−0.747076	−	1.63587i	0.0244753	−	0.999700i	$-0.492208\pi$
$434$	−189.690	+	27.2734i	−0.437075	+	0.0628419i
$435$		0			0
$436$	−385.285			−0.883681
$437$	8.86909	+	356.398i	0.0202954	+	0.815557i
$438$		0			0
$439$	124.273	+	79.8656i	0.283083	+	0.181926i	0.674475	−	0.738298i	$-0.264370\pi$
$439$	124.273	+	79.8656i	0.283083	+	0.181926i	−0.391392	+	0.920224i	$0.628006\pi$
$440$	8.58721	−	1.23465i	0.0195164	−	0.00280603i
$441$		0			0
$442$	−152.578	−	44.8010i	−0.345200	−	0.101360i
$443$	−520.016	−	237.483i	−1.17385	−	0.536079i	−0.269554	−	0.962985i	$-0.586876\pi$
$443$	−520.016	−	237.483i	−1.17385	−	0.536079i	−0.904296	+	0.426906i	$0.859604\pi$
$444$		0			0
$445$	107.214	−	745.687i	0.240929	−	1.67570i
$446$	−59.9128	−	204.044i	−0.134334	−	0.457498i
$447$		0			0
$448$	70.4478	−	45.2741i	0.157250	−	0.101058i
$449$	41.2854	+	64.2414i	0.0919497	+	0.143077i	0.884181	−	0.467144i	$-0.154717\pi$
$449$	41.2854	+	64.2414i	0.0919497	+	0.143077i	−0.792231	+	0.610221i	$0.791081\pi$
$450$		0			0
$451$	19.1834	−	5.63277i	0.0425354	−	0.0124895i
$452$	−347.630	−	49.9816i	−0.769092	−	0.110579i
$453$		0			0
$454$	−17.1581	+	37.5710i	−0.0377932	+	0.0827555i
$455$	−246.939	+	840.998i	−0.542723	+	1.84835i
$456$		0			0
$457$	56.5161	+	393.078i	0.123668	+	0.860127i	0.953345	+	0.301884i	$0.0976154\pi$
$457$	56.5161	+	393.078i	0.123668	+	0.860127i	−0.829677	+	0.558244i	$0.811475\pi$
$458$	−86.1710	+	134.085i	−0.188146	+	0.292761i
$459$		0			0
$460$	343.477	+	91.6369i	0.746690	+	0.199211i
$461$		−	682.564i		−	1.48062i	−0.672268	−	0.740308i	$-0.734680\pi$
$461$		−	682.564i		−	1.48062i	0.672268	−	0.740308i	$-0.265320\pi$
$462$		0			0
$463$	42.7124	+	297.071i	0.0922513	+	0.641622i	0.982516	+	0.186178i	$0.0596103\pi$
$463$	42.7124	+	297.071i	0.0922513	+	0.641622i	−0.890265	+	0.455444i	$0.849481\pi$
$464$	153.391	−	70.0513i	0.330584	−	0.150973i
$465$		0			0
$466$	194.191	−	425.220i	0.416719	−	0.912488i
$467$	−312.270	−	270.583i	−0.668671	−	0.579407i	0.252958	−	0.967477i	$-0.418596\pi$
$467$	−312.270	−	270.583i	−0.668671	−	0.579407i	−0.921630	+	0.388070i	$0.873142\pi$
$468$		0			0
$469$	948.181	−	278.411i	2.02171	−	0.593627i
$470$	389.056	−	337.119i	0.827778	−	0.717274i
$471$		0			0
$472$	−115.169	+	74.0147i	−0.244002	+	0.156811i
$473$	5.48113	−	4.74943i	0.0115880	−	0.0100411i
$474$		0			0
$475$	76.5968	−	532.742i	0.161256	−	1.12156i
$476$	−164.196	−	142.277i	−0.344950	−	0.298901i
$477$		0			0
$478$	122.003	+	35.8233i	0.255236	+	0.0749442i
$479$	382.352	−	174.614i	0.798230	−	0.364539i	0.0258223	−	0.999667i	$-0.491780\pi$
$479$	382.352	−	174.614i	0.798230	−	0.364539i	0.772408	+	0.635127i	$0.219052\pi$
$480$		0			0
$481$	−241.918	−	155.471i	−0.502948	−	0.323225i
$482$			200.120i			0.415187i
$483$		0			0
$484$	−241.685			−0.499349
$485$	−593.603	+	923.665i	−1.22392	+	1.90446i
$486$		0			0
$487$	222.909	+	488.103i	0.457719	+	1.00226i	0.988002	+	0.154444i	$0.0493585\pi$
$487$	222.909	+	488.103i	0.457719	+	1.00226i	−0.530283	+	0.847821i	$0.677914\pi$
$488$	−54.9218	+	187.046i	−0.112545	+	0.383292i
$489$		0			0
$490$	−433.521	+	500.310i	−0.884737	+	1.02104i
$491$	347.574	+	49.9736i	0.707891	+	0.101779i	0.486850	−	0.873485i	$-0.338146\pi$
$491$	347.574	+	49.9736i	0.707891	+	0.101779i	0.221040	+	0.975265i	$0.429055\pi$
$492$		0			0
$493$	−286.502	−	330.641i	−0.581140	−	0.670671i
$494$	−128.410	−	199.809i	−0.259938	−	0.404472i
$495$		0			0
$496$	−33.9103	−	39.1346i	−0.0683676	−	0.0789004i
$497$	−322.730	−	1099.12i	−0.649355	−	2.21150i
$498$		0			0
$499$	123.886	−	142.972i	0.248268	−	0.286517i	−0.617913	−	0.786246i	$-0.712022\pi$
$499$	123.886	−	142.972i	0.248268	−	0.286517i	0.866182	+	0.499729i	$0.166567\pi$
$500$	−136.701	−	62.4291i	−0.273401	−	0.124858i
$501$		0			0
$502$	25.0851	+	54.9286i	0.0499702	+	0.109420i
$503$	−291.381	+	41.8942i	−0.579285	+	0.0832887i	−0.425728	−	0.904851i	$-0.639982\pi$
$503$	−291.381	+	41.8942i	−0.579285	+	0.0832887i	−0.153557	+	0.988140i	$0.549073\pi$
$504$		0			0
$505$	−492.771			−0.975784
$506$	11.8730	+	5.06915i	0.0234645	+	0.0100181i
$507$		0			0
$508$	−376.851	−	242.187i	−0.741832	−	0.476747i
$509$	800.318	−	115.068i	1.57233	−	0.226067i	0.699698	−	0.714439i	$-0.253318\pi$
$509$	800.318	−	115.068i	1.57233	−	0.226067i	0.872636	+	0.488372i	$0.162409\pi$
$510$		0			0
$511$	−151.843	−	44.5853i	−0.297150	−	0.0872510i
$512$	20.5826	+	9.39977i	0.0402004	+	0.0183589i
$513$		0			0
$514$	−39.9322	+	277.734i	−0.0776890	+	0.540339i
$515$	−413.462	−	1408.12i	−0.802839	−	2.73422i
$516$		0			0
$517$	15.7273	−	10.1073i	0.0304203	−	0.0195499i
$518$	−212.415	−	330.524i	−0.410067	−	0.638076i
$519$		0			0
$520$	−227.242	+	66.7243i	−0.437004	+	0.128316i
$521$	177.353	+	25.4995i	0.340409	+	0.0489434i	0.310400	−	0.950606i	$-0.399537\pi$
$521$	177.353	+	25.4995i	0.340409	+	0.0489434i	0.0300095	+	0.999550i	$0.490446\pi$
$522$		0			0
$523$	−289.038	+	632.906i	−0.552655	+	1.21014i	0.402877	+	0.915254i	$0.368010\pi$
$523$	−289.038	+	632.906i	−0.552655	+	1.21014i	−0.955531	+	0.294890i	$0.904717\pi$
$524$	−24.4691	+	83.3342i	−0.0466968	+	0.159035i
$525$		0			0
$526$	72.1004	+	501.469i	0.137073	+	0.953364i
$527$	−72.6334	+	113.020i	−0.137824	+	0.214459i
$528$		0			0
$529$	365.878	+	382.066i	0.691641	+	0.722241i
$530$		−	583.626i		−	1.10118i
$531$		0			0
$532$	−46.1821	−	321.203i	−0.0868084	−	0.603765i
$533$	−496.481	+	226.735i	−0.931484	+	0.425395i
$534$		0			0
$535$	−26.1327	+	57.2226i	−0.0488461	+	0.106958i
$536$	201.800	+	174.861i	0.376493	+	0.326233i
$537$		0			0
$538$	−399.722	+	117.369i	−0.742977	+	0.218158i
$539$	−18.1690	+	15.7436i	−0.0337088	+	0.0292088i
$540$		0			0
$541$	884.439	−	568.394i	1.63482	−	1.05064i	0.689609	−	0.724182i	$-0.257782\pi$
$541$	884.439	−	568.394i	1.63482	−	1.05064i	0.945213	−	0.326454i	$-0.105854\pi$
$542$	−378.918	+	328.334i	−0.699110	+	0.605782i
$543$		0			0
$544$	8.35468	−	58.1081i	0.0153579	−	0.106816i
$545$	1125.13	+	974.927i	2.06445	+	1.78886i
$546$		0			0
$547$	325.715	+	95.6385i	0.595457	+	0.174842i	0.565554	−	0.824711i	$-0.308662\pi$
$547$	325.715	+	95.6385i	0.595457	+	0.174842i	0.0299023	+	0.999553i	$0.490480\pi$
$548$	−262.010	+	119.656i	−0.478120	+	0.218350i
$549$		0			0
$550$	−16.3960	−	10.5371i	−0.0298110	−	0.0191584i
$551$		−	653.456i		−	1.18595i
$552$		0			0
$553$	−41.5167			−0.0750755
$554$	141.947	−	220.874i	0.256222	−	0.398689i
$555$		0			0
$556$	−126.699	−	277.431i	−0.227875	−	0.498977i
$557$	206.082	−	701.853i	0.369987	−	1.26006i	−0.538671	−	0.842516i	$-0.681073\pi$
$557$	206.082	−	701.853i	0.369987	−	1.26006i	0.908658	−	0.417542i	$-0.137108\pi$
$558$		0			0
$559$	−129.656	+	149.631i	−0.231943	+	0.267677i
$560$	−320.287	−	46.0502i	−0.571940	−	0.0822326i
$561$		0			0
$562$	187.543	+	216.436i	0.333706	+	0.385117i
$563$	−300.394	−	467.422i	−0.533560	−	0.830235i	0.464920	−	0.885353i	$-0.346083\pi$
$563$	−300.394	−	467.422i	−0.533560	−	0.830235i	−0.998480	+	0.0551177i	$0.982447\pi$
$564$		0			0
$565$	888.690	+	1025.60i	1.57290	+	1.81523i
$566$	3.49001	+	11.8859i	0.00616610	+	0.0209998i
$567$		0			0
$568$	202.696	−	233.924i	0.356859	−	0.411837i
$569$	−666.120	−	304.207i	−1.17069	−	0.534634i	−0.267363	−	0.963596i	$-0.586152\pi$
$569$	−666.120	−	304.207i	−1.17069	−	0.534634i	−0.903323	+	0.428962i	$0.858879\pi$
$570$		0			0
$571$	−107.957	−	236.393i	−0.189067	−	0.413998i	0.791233	−	0.611515i	$-0.209440\pi$
$571$	−107.957	−	236.393i	−0.189067	−	0.413998i	−0.980300	+	0.197517i	$0.936712\pi$
$572$	−8.51328	+	1.22402i	−0.0148834	+	0.00213990i
$573$		0			0
$574$	−745.713			−1.29915
$575$	−448.353	−	660.901i	−0.779744	−	1.14939i
$576$		0			0
$577$	−214.902	−	138.109i	−0.372447	−	0.239357i	0.341004	−	0.940062i	$-0.389233\pi$
$577$	−214.902	−	138.109i	−0.372447	−	0.239357i	−0.713452	+	0.700704i	$0.752869\pi$
$578$	253.789	−	36.4894i	0.439082	−	0.0631305i
$579$		0			0
$580$	−625.197	−	183.574i	−1.07793	−	0.316508i
$581$	−1010.58	−	461.516i	−1.73938	−	0.794347i
$582$		0			0
$583$	3.01632	−	20.9790i	0.00517379	−	0.0359845i
$584$	−12.0472	−	41.0289i	−0.0206287	−	0.0702550i
$585$		0			0
$586$	−66.0945	+	42.4764i	−0.112789	+	0.0724853i
$587$	192.947	+	300.231i	0.328699	+	0.511466i	0.965791	−	0.259322i	$-0.0834990\pi$
$587$	192.947	+	300.231i	0.328699	+	0.511466i	−0.637091	+	0.770788i	$0.719863\pi$
$588$		0			0
$589$	−192.534	+	56.5330i	−0.326882	+	0.0959814i
$590$	523.609	+	75.2836i	0.887473	+	0.127599i
$591$		0			0
$592$	44.1014	−	96.5685i	0.0744955	−	0.163122i
$593$	8.41659	−	28.6643i	0.0141932	−	0.0483377i	−0.952092	−	0.305812i	$-0.901072\pi$
$593$	8.41659	−	28.6643i	0.0141932	−	0.0483377i	0.966285	+	0.257474i	$0.0828903\pi$
$594$		0			0
$595$	119.475	+	830.966i	0.200798	+	1.39658i
$596$	145.184	−	225.911i	0.243598	−	0.379045i
$597$		0			0
$598$	−340.520	−	90.8480i	−0.569432	−	0.151920i
$599$		−	408.464i		−	0.681910i	−0.940080	−	0.340955i	$-0.889250\pi$
$599$		−	408.464i		−	0.681910i	0.940080	−	0.340955i	$-0.110750\pi$
$600$		0			0
$601$	105.635	+	734.708i	0.175765	+	1.22248i	0.866429	+	0.499300i	$0.166409\pi$
$601$	105.635	+	734.708i	0.175765	+	1.22248i	−0.690664	+	0.723176i	$0.742682\pi$
$602$	−246.062	+	112.373i	−0.408741	+	0.186666i
$603$		0			0
$604$	−48.9400	+	107.164i	−0.0810264	+	0.177423i
$605$	705.779	+	611.561i	1.16658	+	1.01084i
$606$		0			0
$607$	89.8448	−	26.3808i	0.148014	−	0.0434610i	−0.206886	−	0.978365i	$-0.566333\pi$
$607$	89.8448	−	26.3808i	0.148014	−	0.0434610i	0.354900	+	0.934904i	$0.384515\pi$
$608$	66.2667	−	57.4204i	0.108991	−	0.0944415i
$609$		0			0
$610$	633.688	−	407.247i	1.03883	−	0.667617i
$611$	−385.706	+	334.216i	−0.631271	+	0.546999i
$612$		0			0
$613$	129.544	−	901.001i	0.211329	−	1.46982i	−0.557398	−	0.830245i	$-0.688200\pi$
$613$	129.544	−	901.001i	0.211329	−	1.46982i	0.768727	−	0.639577i	$-0.220891\pi$
$614$	446.339	+	386.755i	0.726937	+	0.629894i
$615$		0			0
$616$	−11.2750	−	3.31064i	−0.0183036	−	0.00537441i
$617$	190.549	−	87.0207i	0.308831	−	0.141038i	−0.254970	−	0.966949i	$-0.582066\pi$
$617$	190.549	−	87.0207i	0.308831	−	0.141038i	0.563801	+	0.825910i	$0.309338\pi$
$618$		0			0
$619$	−442.527	−	284.395i	−0.714906	−	0.459442i	0.131955	−	0.991256i	$-0.457874\pi$
$619$	−442.527	−	284.395i	−0.714906	−	0.459442i	−0.846862	+	0.531813i	$0.821511\pi$
$620$			200.089i			0.322725i
$621$		0			0
$622$	540.917			0.869641
$623$	−551.681	+	858.433i	−0.885524	+	1.37790i
$624$		0			0
$625$	−119.384	−	261.415i	−0.191014	−	0.418263i
$626$	120.726	−	411.154i	0.192852	−	0.656795i
$627$		0			0
$628$	−287.171	+	331.413i	−0.457278	+	0.527727i
$629$	−272.629	−	39.1981i	−0.433432	−	0.0623181i
$630$		0			0
$631$	589.269	+	680.052i	0.933865	+	1.07774i	0.996817	+	0.0797211i	$0.0254030\pi$
$631$	589.269	+	680.052i	0.933865	+	1.07774i	−0.0629522	+	0.998017i	$0.520052\pi$
$632$	−6.06494	−	9.43723i	−0.00959642	−	0.0149323i
$633$		0			0
$634$	104.708	+	120.840i	0.165155	+	0.190599i
$635$	487.664	+	1660.83i	0.767975	+	2.61548i
$636$		0			0
$637$	429.789	−	496.003i	0.674708	−	0.778655i
$638$	−21.5245	−	9.82992i	−0.0337375	−	0.0154074i
$639$		0			0
$640$	−36.3210	−	79.5320i	−0.0567516	−	0.124269i
$641$	36.0611	−	5.18480i	0.0562575	−	0.00808861i	−0.114129	−	0.993466i	$-0.536408\pi$
$641$	36.0611	−	5.18480i	0.0562575	−	0.00808861i	0.170386	+	0.985377i	$0.445499\pi$
$642$		0			0
$643$	−1071.17			−1.66589			−0.832945	−	0.553356i	$-0.813347\pi$
$643$	−1071.17			−1.66589			−0.832945	+	0.553356i	$0.813347\pi$
$644$	−371.636	−	306.174i	−0.577074	−	0.475425i
$645$		0			0
$646$	−191.377	−	122.990i	−0.296249	−	0.190387i
$647$	832.802	−	119.739i	1.28718	−	0.185068i	0.535463	−	0.844559i	$-0.320137\pi$
$647$	832.802	−	119.739i	1.28718	−	0.185068i	0.751713	+	0.659491i	$0.229228\pi$
$648$		0			0
$649$	18.4325	+	5.41228i	0.0284014	+	0.00833941i
$650$	483.983	+	221.028i	0.744589	+	0.340042i
$651$		0			0
$652$	79.0417	−	549.747i	0.121230	−	0.843170i
$653$	147.684	+	502.964i	0.226162	+	0.770237i	0.991893	+	0.127076i	$0.0405591\pi$
$653$	147.684	+	502.964i	0.226162	+	0.770237i	−0.765731	+	0.643161i	$0.777623\pi$
$654$		0			0
$655$	282.325	−	181.439i	0.431030	−	0.277006i
$656$	−108.937	−	169.509i	−0.166062	−	0.258398i
$657$		0			0
$658$	−669.045	+	196.449i	−1.01679	+	0.298555i
$659$	−249.250	−	35.8367i	−0.378224	−	0.0543804i	−0.0494187	−	0.998778i	$-0.515737\pi$
$659$	−249.250	−	35.8367i	−0.378224	−	0.0543804i	−0.328805	+	0.944398i	$0.606646\pi$
$660$		0			0
$661$	314.017	−	687.602i	0.475064	−	1.04024i	−0.508728	−	0.860927i	$-0.669884\pi$
$661$	314.017	−	687.602i	0.475064	−	1.04024i	0.983791	−	0.179317i	$-0.0573887\pi$
$662$	98.7930	−	336.458i	0.149234	−	0.508245i
$663$		0			0
$664$	−42.7217	−	297.136i	−0.0643399	−	0.447494i
$665$	−677.911	+	1054.85i	−1.01942	+	1.58624i
$666$		0			0
$667$	−653.000	−	716.767i	−0.979010	−	1.07461i
$668$			437.350i			0.654716i
$669$		0			0
$670$	−146.837	−	1021.27i	−0.219159	−	1.52429i
$671$	24.8833	−	11.3638i	0.0370838	−	0.0169356i
$672$		0			0
$673$	−203.597	+	445.815i	−0.302522	+	0.662430i	−0.998449	−	0.0556828i	$-0.982266\pi$
$673$	−203.597	+	445.815i	−0.302522	+	0.662430i	0.695927	+	0.718113i	$0.254994\pi$
$674$	626.979	+	543.280i	0.930235	+	0.806054i
$675$		0			0
$676$	−99.0227	+	29.0757i	−0.146483	+	0.0430114i
$677$	177.566	−	153.861i	0.262283	−	0.227269i	−0.513785	−	0.857919i	$-0.671757\pi$
$677$	177.566	−	153.861i	0.262283	−	0.227269i	0.776068	+	0.630650i	$0.217212\pi$
$678$		0			0
$679$	1251.11	−	804.037i	1.84257	−	1.18415i
$680$	−171.435	+	148.549i	−0.252110	+	0.218454i
$681$		0			0
$682$	−1.03411	+	7.19240i	−0.00151629	+	0.0105460i
$683$	548.881	+	475.608i	0.803632	+	0.696352i	0.956448	−	0.291903i	$-0.0942885\pi$
$683$	548.881	+	475.608i	0.803632	+	0.696352i	−0.152815	+	0.988255i	$0.548834\pi$
$684$		0			0
$685$	1067.91	+	313.567i	1.55899	+	0.457762i
$686$	155.832	−	71.1662i	0.227161	−	0.103741i
$687$		0			0
$688$	−61.4894	−	39.5168i	−0.0893741	−	0.0574372i
$689$			578.601i			0.839770i
$690$		0			0
$691$	−508.308			−0.735612			−0.367806	−	0.929903i	$-0.619891\pi$
$691$	−508.308			−0.735612			−0.367806	+	0.929903i	$0.619891\pi$
$692$	296.712	−	461.693i	0.428774	−	0.667186i
$693$		0			0
$694$	9.06388	+	19.8471i	0.0130604	+	0.0285982i
$695$	−332.023	+	1130.77i	−0.477730	+	1.62700i
$696$		0			0
$697$	−342.341	+	395.083i	−0.491164	+	0.566834i
$698$	−181.068	−	26.0337i	−0.259410	−	0.0372975i
$699$		0			0
$700$	476.045	+	549.385i	0.680064	+	0.784836i
$701$	133.697	+	208.037i	0.190724	+	0.296772i	0.923425	−	0.383778i	$-0.125377\pi$
$701$	133.697	+	208.037i	0.190724	+	0.296772i	−0.732702	+	0.680550i	$0.761741\pi$
$702$		0			0
$703$	−269.402	−	310.907i	−0.383218	−	0.442257i
$704$	−0.894553	−	3.04657i	−0.00127067	−	0.00432751i
$705$		0			0
$706$	27.3010	−	31.5070i	0.0386699	−	0.0446274i
$707$	607.142	+	277.272i	0.858758	+	0.392182i
$708$		0			0
$709$	309.539	+	677.795i	0.436585	+	0.955987i	0.992213	+	0.124556i	$0.0397506\pi$
$709$	309.539	+	677.795i	0.436585	+	0.955987i	−0.555628	+	0.831431i	$0.687522\pi$
$710$	−1183.84	+	170.211i	−1.66738	+	0.239734i
$711$		0			0
$712$	−275.723			−0.387252
$713$	−154.694	+	254.410i	−0.216962	+	0.356816i
$714$		0			0
$715$	27.9581	+	17.9676i	0.0391023	+	0.0251295i
$716$	481.954	−	69.2945i	0.673120	−	0.0967800i
$717$		0			0
$718$	428.462	+	125.808i	0.596743	+	0.175220i
$719$	737.674	+	336.884i	1.02597	+	0.468546i	0.856040	−	0.516910i	$-0.172918\pi$
$719$	737.674	+	336.884i	1.02597	+	0.468546i	0.169932	+	0.985456i	$0.445645\pi$
$720$		0			0
$721$	−282.897	+	1967.59i	−0.392368	+	2.72898i
$722$	48.1057	+	163.833i	0.0666285	+	0.226916i
$723$		0			0
$724$	309.804	−	199.099i	0.427906	−	0.274998i
$725$	791.409	+	1231.46i	1.09160	+	1.69856i
$726$		0			0
$727$	175.447	−	51.5160i	0.241331	−	0.0708610i	−0.158831	−	0.987306i	$-0.550772\pi$
$727$	175.447	−	51.5160i	0.241331	−	0.0708610i	0.400161	+	0.916445i	$0.368954\pi$
$728$	317.529	+	45.6538i	0.436167	+	0.0627113i
$729$		0			0
$730$	−68.6391	+	150.299i	−0.0940262	+	0.205889i
$731$	−53.4263	+	181.953i	−0.0730866	+	0.248910i
$732$		0			0
$733$	31.3162	+	217.809i	0.0427233	+	0.297147i	0.999969	+	0.00787097i	$0.00250543\pi$
$733$	31.3162	+	217.809i	0.0427233	+	0.297147i	−0.957246	+	0.289276i	$0.906585\pi$
$734$	360.711	−	561.277i	0.491431	−	0.764682i
$735$		0			0
$736$	15.3067	−	129.204i	0.0207971	−	0.175549i
$737$		−	37.4695i		−	0.0508405i
$738$		0			0
$739$	−45.4556	−	316.150i	−0.0615095	−	0.427808i	−0.997187	−	0.0749522i	$-0.976120\pi$
$739$	−45.4556	−	316.150i	−0.0615095	−	0.427808i	0.935678	−	0.352856i	$-0.114790\pi$
$740$	−373.144	+	170.409i	−0.504249	+	0.230283i
$741$		0			0
$742$	−328.395	+	719.084i	−0.442581	+	0.969116i
$743$	237.966	+	206.199i	0.320277	+	0.277522i	0.800129	−	0.599828i	$-0.204764\pi$
$743$	237.966	+	206.199i	0.320277	+	0.277522i	−0.479852	+	0.877350i	$0.659310\pi$
$744$		0			0
$745$	−995.619	+	292.340i	−1.33640	+	0.392403i
$746$	363.914	−	315.333i	0.487820	−	0.422698i
$747$		0			0
$748$	−6.93012	+	4.45371i	−0.00926486	+	0.00595416i
$749$	64.3961	−	55.7995i	0.0859761	−	0.0744987i
$750$		0			0
$751$	−36.9006	+	256.650i	−0.0491353	+	0.341744i	0.950393	+	0.311050i	$0.100681\pi$
$751$	−36.9006	+	256.650i	−0.0491353	+	0.341744i	−0.999529	+	0.0306937i	$0.990228\pi$
$752$	−142.392	−	123.383i	−0.189351	−	0.164074i
$753$		0			0
$754$	619.815	+	181.994i	0.822035	+	0.241371i
$755$	414.084	−	189.106i	0.548455	−	0.250471i
$756$		0			0
$757$	−804.231	−	516.848i	−1.06239	−	0.682758i	−0.111967	−	0.993712i	$-0.535715\pi$
$757$	−804.231	−	516.848i	−1.06239	−	0.682758i	−0.950425	+	0.310954i	$0.899351\pi$
$758$		−	253.917i		−	0.334983i
$759$		0			0
$760$	−338.812			−0.445805
$761$	571.286	−	888.939i	0.750705	−	1.16812i	−0.230108	−	0.973165i	$-0.573908\pi$
$761$	571.286	−	888.939i	0.750705	−	1.16812i	0.980812	−	0.194954i	$-0.0624558\pi$
$762$		0			0
$763$	−837.693	−	1834.29i	−1.09789	−	2.40405i
$764$	−79.2980	+	270.064i	−0.103793	+	0.353487i
$765$		0			0
$766$	0.598239	−	0.690404i	0.000780990	−	0.000901311i
$767$	−519.101	−	74.6355i	−0.676794	−	0.0973083i
$768$		0			0
$769$	−790.021	−	911.733i	−1.02734	−	1.18561i	−0.982433	−	0.186617i	$-0.940248\pi$
$769$	−790.021	−	911.733i	−1.02734	−	1.18561i	−0.0449032	−	0.998991i	$-0.514298\pi$
$770$	24.5485	+	38.1982i	0.0318811	+	0.0496080i
$771$		0			0
$772$	497.165	+	573.759i	0.643997	+	0.743212i
$773$	−274.649	−	935.369i	−0.355303	−	1.21005i	−0.922347	−	0.386363i	$-0.873731\pi$
$773$	−274.649	−	935.369i	−0.355303	−	1.21005i	0.567044	−	0.823687i	$-0.308087\pi$
$774$		0			0
$775$	294.368	−	339.718i	0.379829	−	0.438346i
$776$	365.533	+	166.933i	0.471048	+	0.215120i
$777$		0			0
$778$	61.4969	+	134.659i	0.0790449	+	0.173084i
$779$	−772.868	+	111.122i	−0.992128	+	0.142646i
$780$		0			0
$781$	−43.4340			−0.0556133
$782$	−332.823	+	56.3367i	−0.425605	+	0.0720418i
$783$		0			0
$784$	203.827	+	130.992i	0.259984	+	0.167081i
$785$	1677.22	−	241.147i	2.13658	−	0.307194i
$786$		0			0
$787$	−894.448	−	262.634i	−1.13653	−	0.333715i	−0.341258	−	0.939970i	$-0.610853\pi$
$787$	−894.448	−	262.634i	−1.13653	−	0.333715i	−0.795271	+	0.606254i	$0.792671\pi$
$788$	−336.603	−	153.721i	−0.427161	−	0.195078i
$789$		0			0
$790$	−6.16891	+	42.9057i	−0.00780875	+	0.0543111i
$791$	−517.867	−	1763.69i	−0.654699	−	2.22970i
$792$		0			0
$793$	−628.233	+	403.741i	−0.792223	+	0.509131i
$794$	−156.284	−	243.182i	−0.196831	−	0.306275i
$795$		0			0
$796$	256.725	−	75.3813i	0.322519	−	0.0947001i
$797$	−1057.94	−	152.108i	−1.32740	−	0.190851i	−0.558117	−	0.829762i	$-0.688476\pi$
$797$	−1057.94	−	152.108i	−1.32740	−	0.190851i	−0.769280	+	0.638911i	$0.779385\pi$
$798$		0			0
$799$	−203.065	+	444.650i	−0.254149	+	0.556508i
$800$	−55.3389	+	188.467i	−0.0691736	+	0.235584i
$801$		0			0
$802$	−99.1712	−	689.751i	−0.123655	−	0.860039i
$803$	−3.24408	+	5.04788i	−0.00403995	+	0.00628628i
$804$		0			0
$805$	310.523	+	1834.49i	0.385743	+	2.27887i
$806$		−	198.367i		−	0.246113i
$807$		0			0
$808$	25.6666	+	178.515i	0.0317656	+	0.220935i
$809$	−27.6065	+	12.6075i	−0.0341242	+	0.0155840i	−0.432404	−	0.901680i	$-0.642335\pi$
$809$	−27.6065	+	12.6075i	−0.0341242	+	0.0155840i	0.398280	+	0.917264i	$0.369607\pi$
$810$		0			0
$811$	116.016	−	254.039i	0.143053	−	0.313242i	−0.824521	−	0.565832i	$-0.808555\pi$
$811$	116.016	−	254.039i	0.143053	−	0.313242i	0.967573	+	0.252590i	$0.0812824\pi$
$812$	667.010	+	577.968i	0.821441	+	0.711783i
$813$		0			0
$814$	−14.2937	+	4.19702i	−0.0175599	+	0.00515604i
$815$	−1621.90	+	1405.39i	−1.99007	+	1.72440i
$816$		0			0
$817$	−238.277	+	153.131i	−0.291649	+	0.187431i
$818$	−537.131	+	465.426i	−0.656639	+	0.568981i
$819$		0			0
$820$	−110.804	+	770.662i	−0.135127	+	0.939831i
$821$	−502.507	−	435.425i	−0.612067	−	0.530359i	0.292734	−	0.956194i	$-0.405435\pi$
$821$	−502.507	−	435.425i	−0.612067	−	0.530359i	−0.904801	+	0.425835i	$0.859981\pi$
$822$		0			0
$823$	292.416	+	85.8612i	0.355305	+	0.104327i	0.454514	−	0.890740i	$-0.349813\pi$
$823$	292.416	+	85.8612i	0.355305	+	0.104327i	−0.0992086	+	0.995067i	$0.531631\pi$
$824$	−488.583	+	223.128i	−0.592940	+	0.270787i
$825$		0			0
$826$	−602.777	−	387.381i	−0.729754	−	0.468985i
$827$		−	18.4010i		−	0.0222503i	−0.999938	−	0.0111251i	$-0.996459\pi$
$827$		−	18.4010i		−	0.0222503i	0.999938	−	0.0111251i	$-0.00354132\pi$
$828$		0			0
$829$	−407.029			−0.490988			−0.245494	−	0.969398i	$-0.578950\pi$
$829$	−407.029			−0.490988			−0.245494	+	0.969398i	$0.578950\pi$
$830$	−627.117	+	975.813i	−0.755562	+	1.17568i
$831$		0			0
$832$	36.0084	+	78.8473i	0.0432793	+	0.0947684i
$833$	177.099	−	603.145i	0.212604	−	0.724064i
$834$		0			0
$835$	1106.67	−	1277.17i	1.32536	−	1.52954i
$836$	−12.1789	−	1.75106i	−0.0145681	−	0.00209457i
$837$		0			0
$838$	423.717	+	488.996i	0.505629	+	0.583527i
$839$	532.244	+	828.188i	0.634379	+	0.987113i	0.998445	+	0.0557401i	$0.0177518\pi$
$839$	532.244	+	828.188i	0.634379	+	0.987113i	−0.364066	+	0.931373i	$0.618612\pi$
$840$		0			0
$841$	613.112	+	707.569i	0.729027	+	0.841342i
$842$	−82.5426	−	281.114i	−0.0980316	−	0.333865i
$843$		0			0
$844$	−232.149	+	267.915i	−0.275059	+	0.317434i
$845$	362.744	+	165.659i	0.429282	+	0.196047i
$846$		0			0
$847$	−525.476	−	1150.63i	−0.620396	−	1.35848i
$848$	−211.429	+	30.3989i	−0.249327	+	0.0358478i
$849$		0			0
$850$	509.610			0.599541
$851$	−606.193	−	71.8152i	−0.712331	−	0.0843892i
$852$		0			0
$853$	−317.621	−	204.122i	−0.372357	−	0.239299i	0.341056	−	0.940043i	$-0.389215\pi$
$853$	−317.621	−	204.122i	−0.372357	−	0.239299i	−0.713413	+	0.700743i	$0.752852\pi$
$854$	−1009.92	+	145.204i	−1.18257	+	0.170028i
$855$		0			0
$856$	22.0911	+	6.48653i	0.0258074	+	0.00757773i
$857$	826.742	+	377.560i	0.964693	+	0.440560i	0.834548	−	0.550935i	$-0.185729\pi$
$857$	826.742	+	377.560i	0.964693	+	0.440560i	0.130144	+	0.991495i	$0.458456\pi$
$858$		0			0
$859$	−69.5473	+	483.712i	−0.0809631	+	0.563110i	0.908451	+	0.417991i	$0.137266\pi$
$859$	−69.5473	+	483.712i	−0.0809631	+	0.563110i	−0.989414	+	0.145119i	$0.953643\pi$
$860$	79.5704	+	270.992i	0.0925237	+	0.315107i
$861$		0			0
$862$	−813.660	+	522.908i	−0.943921	+	0.606621i
$863$	593.400	+	923.348i	0.687601	+	1.06993i	0.993047	+	0.117719i	$0.0375581\pi$
$863$	593.400	+	923.348i	0.687601	+	1.06993i	−0.305446	+	0.952209i	$0.598806\pi$
$864$		0			0
$865$	−2034.74	+	597.453i	−2.35230	+	0.690698i
$866$	1090.04	+	156.724i	1.25871	+	0.180975i
$867$		0			0
$868$	112.586	−	246.530i	0.129708	−	0.284020i
$869$	−0.443495	+	1.51040i	−0.000510351	+	0.00173809i
$870$		0			0
$871$	145.573	+	1012.48i	0.167133	+	1.16243i
$872$	294.582	−	458.378i	0.337823	−	0.525663i
$873$		0			0
$874$	−430.793	−	261.944i	−0.492898	−	0.299707i
$875$		−	786.548i		−	0.898912i
$876$		0			0
$877$	−30.0576	−	209.055i	−0.0342732	−	0.238375i	0.965483	−	0.260467i	$-0.0838765\pi$
$877$	−30.0576	−	209.055i	−0.0342732	−	0.238375i	−0.999756	+	0.0220917i	$0.992967\pi$
$878$	−190.034	+	86.7857i	−0.216440	+	0.0988448i
$879$		0			0
$880$	−5.09674	+	11.1603i	−0.00579175	+	0.0126822i
$881$	−698.875	−	605.579i	−0.793275	−	0.687377i	0.160786	−	0.986989i	$-0.448597\pi$
$881$	−698.875	−	605.579i	−0.793275	−	0.687377i	−0.954061	+	0.299612i	$0.903143\pi$
$882$		0			0
$883$	667.168	−	195.898i	0.755569	−	0.221855i	0.118809	−	0.992917i	$-0.462092\pi$
$883$	667.168	−	195.898i	0.755569	−	0.221855i	0.636760	+	0.771062i	$0.280274\pi$
$884$	169.959	−	147.270i	0.192261	−	0.166595i
$885$		0			0
$886$	680.131	−	437.094i	0.767642	−	0.493334i
$887$	1282.20	−	1111.04i	1.44555	−	1.25258i	0.531453	−	0.847088i	$-0.321646\pi$
$887$	1282.20	−	1111.04i	1.44555	−	1.25258i	0.914099	−	0.405491i	$-0.132899\pi$
$888$		0			0
$889$	333.667	−	2320.71i	0.375329	−	2.61047i
$890$	805.179	+	697.692i	0.904696	+	0.783923i
$891$		0			0
$892$	288.562	+	84.7295i	0.323500	+	0.0949882i
$893$	−664.134	+	303.300i	−0.743711	+	0.339642i
$894$		0			0
$895$	−1582.77	−	1017.18i	−1.76845	−	1.13652i
$896$			118.428i			0.132175i
$897$		0			0
$898$	−107.995			−0.120261
$899$	295.057	−	459.117i	0.328206	−	0.510698i
$900$		0			0
$901$	230.216	+	504.102i	0.255511	+	0.559492i
$902$	−7.96594	+	27.1295i	−0.00883142	+	0.0300770i
$903$		0			0
$904$	325.255	−	375.364i	0.359795	−	0.415226i
$905$	−1408.50	−	202.512i	−1.55636	−	0.223770i
$906$		0			0
$907$	1069.73	+	1234.53i	1.17941	+	1.36112i	0.918338	+	0.395797i	$0.129532\pi$
$907$	1069.73	+	1234.53i	1.17941	+	1.36112i	0.261075	+	0.965319i	$0.415923\pi$
$908$	−31.5799	−	49.1393i	−0.0347796	−	0.0541181i
$909$		0			0
$910$	−811.740	−	936.798i	−0.892022	−	1.02945i
$911$	103.801	+	353.514i	0.113942	+	0.388051i	0.996642	−	0.0818867i	$-0.0260946\pi$
$911$	103.801	+	353.514i	0.113942	+	0.388051i	−0.882700	+	0.469938i	$0.844276\pi$
$912$		0			0
$913$	−27.5855	+	31.8354i	−0.0302142	+	0.0348690i
$914$	−510.861	−	233.302i	−0.558929	−	0.255254i
$915$		0			0
$916$	−93.6374	−	205.037i	−0.102224	−	0.223840i
$917$	−449.944	+	64.6922i	−0.490670	+	0.0705477i
$918$		0			0
$919$	−636.126			−0.692193			−0.346097	−	0.938199i	$-0.612493\pi$
$919$	−636.126			−0.692193			−0.346097	+	0.938199i	$0.612493\pi$
$920$	−371.638	+	338.575i	−0.403954	+	0.368017i
$921$		0			0
$922$	812.055	+	521.876i	0.880754	+	0.566026i
$923$	1173.65	−	168.746i	1.27156	−	0.182823i
$924$		0			0
$925$	884.239	+	259.636i	0.955934	+	0.280688i
$926$	−386.086	−	176.320i	−0.416940	−	0.190410i
$927$		0			0
$928$	−33.9390	+	236.051i	−0.0365722	+	0.254365i
$929$	−87.9320	−	299.469i	−0.0946523	−	0.322356i	0.898532	−	0.438907i	$-0.144634\pi$
$929$	−87.9320	−	299.469i	−0.0946523	−	0.322356i	−0.993185	+	0.116551i	$0.962816\pi$
$930$		0			0
$931$	789.850	−	507.606i	0.848389	−	0.545226i
$932$	357.414	+	556.147i	0.383491	+	0.596724i
$933$		0			0
$934$	560.672	−	164.628i	0.600291	−	0.176261i
$935$	31.5073	+	4.53007i	0.0336977	+	0.00484499i
$936$		0			0
$937$	−704.801	+	1543.30i	−0.752189	+	1.64706i	0.0102036	+	0.999948i	$0.496752\pi$
$937$	−704.801	+	1543.30i	−0.752189	+	1.64706i	−0.762392	+	0.647115i	$0.775975\pi$
$938$	−393.733	+	1340.93i	−0.419758	+	1.42956i
$939$		0			0
$940$	103.609	+	720.619i	0.110223	+	0.766616i
$941$	371.886	−	578.666i	0.395203	−	0.614948i	−0.585448	−	0.810710i	$-0.699082\pi$
$941$	371.886	−	578.666i	0.395203	−	0.614948i	0.980652	+	0.195762i	$0.0627179\pi$
$942$		0			0
$943$	−736.704	+	894.216i	−0.781234	+	0.948267i
$944$		−	193.608i		−	0.205094i
$945$		0			0
$946$	1.45968	+	10.1523i	0.00154300	+	0.0107318i
$947$	1539.25	−	702.953i	1.62540	−	0.742295i	0.626100	−	0.779743i	$-0.284650\pi$
$947$	1539.25	−	702.953i	1.62540	−	0.742295i	0.999299	+	0.0374484i	$0.0119230\pi$
$948$		0			0
$949$	68.0482	−	149.005i	0.0717052	−	0.157012i
$950$	575.246	+	498.453i	0.605522	+	0.524688i
$951$		0			0
$952$	294.810	−	86.5640i	0.309674	−	0.0909286i
$953$	−1147.83	+	994.604i	−1.20444	+	1.04366i	−0.206572	+	0.978431i	$0.566231\pi$
$953$	−1147.83	+	994.604i	−1.20444	+	1.04366i	−0.997871	+	0.0652245i	$0.979224\pi$
$954$		0			0
$955$	914.941	−	587.997i	0.958053	−	0.615703i
$956$	−135.901	+	117.759i	−0.142156	+	0.123178i
$957$		0			0
$958$	−84.5986	+	588.396i	−0.0883075	+	0.614192i
$959$	−1139.33	−	987.238i	−1.18804	−	1.02945i
$960$		0			0
$961$	761.272	+	223.530i	0.792167	+	0.232601i
$962$	369.932	−	168.942i	0.384545	−	0.175616i
$963$		0			0
$964$	−238.085	−	153.008i	−0.246976	−	0.158722i
$965$		−	2933.55i		−	3.03994i
$966$		0			0
$967$	1157.48			1.19698			0.598492	−	0.801129i	$-0.295767\pi$
$967$	1157.48			1.19698			0.598492	+	0.801129i	$0.295767\pi$
$968$	184.788	−	287.536i	0.190897	−	0.297041i
$969$		0			0
$970$	−645.037	−	1412.43i	−0.664986	−	1.45612i
$971$	106.471	−	362.607i	0.109651	−	0.373437i	−0.886324	−	0.463065i	$-0.846750\pi$
$971$	106.471	−	362.607i	0.109651	−	0.373437i	0.995975	+	0.0896280i	$0.0285678\pi$
$972$		0			0
$973$	1045.34	−	1206.39i	1.07435	−	1.23987i
$974$	−751.134	−	107.997i	−0.771185	−	0.110880i
$975$		0			0
$976$	−180.539	−	208.353i	−0.184979	−	0.213477i
$977$	−70.5157	−	109.725i	−0.0721757	−	0.112308i	0.803289	−	0.595589i	$-0.203081\pi$
$977$	−70.5157	−	109.725i	−0.0721757	−	0.112308i	−0.875465	+	0.483281i	$0.839445\pi$
$978$		0			0
$979$	25.3371	+	29.2405i	0.0258806	+	0.0298678i
$980$	−263.763	−	898.293i	−0.269146	−	0.916626i
$981$		0			0
$982$	−325.203	+	375.304i	−0.331164	+	0.382184i
$983$	−30.6544	−	13.9994i	−0.0311845	−	0.0142415i	0.399762	−	0.916619i	$-0.369093\pi$
$983$	−30.6544	−	13.9994i	−0.0311845	−	0.0142415i	−0.430946	+	0.902378i	$0.641820\pi$
$984$		0			0
$985$	593.985	+	1300.65i	0.603030	+	1.32045i
$986$	612.421	−	88.0529i	0.621117	−	0.0893032i
$987$		0			0
$988$	335.895			0.339975
$989$	−108.338	+	406.079i	−0.109543	+	0.410595i
$990$		0			0
$991$	−245.702	−	157.903i	−0.247934	−	0.159337i	0.410772	−	0.911738i	$-0.365259\pi$
$991$	−245.702	−	157.903i	−0.247934	−	0.159337i	−0.658705	+	0.752401i	$0.728896\pi$
$992$	72.4861	−	10.4219i	0.0730707	−	0.0105060i
$993$		0			0
$994$	1554.38	+	456.409i	1.56377	+	0.459164i
$995$	−940.445	−	429.487i	−0.945171	−	0.431645i
$996$		0			0
$997$	−97.2764	+	676.572i	−0.0975691	+	0.678608i	0.881065	+	0.472996i	$0.156827\pi$
$997$	−97.2764	+	676.572i	−0.0975691	+	0.678608i	−0.978634	+	0.205612i	$0.934082\pi$
$998$	75.3745	+	256.702i	0.0755256	+	0.257217i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.3.k.b.71.1	yes	80
3.2	odd	2	inner	414.3.k.b.71.8	yes	80
23.12	even	11	inner	414.3.k.b.35.8	yes	80
69.35	odd	22	inner	414.3.k.b.35.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.b.35.1	✓	80	69.35	odd	22	inner
414.3.k.b.35.8	yes	80	23.12	even	11	inner
414.3.k.b.71.1	yes	80	1.1	even	1	trivial
414.3.k.b.71.8	yes	80	3.2	odd	2	inner

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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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	414.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-2.17725 + 7.41503i) q^{5} +(6.85488 - 7.91095i) q^{7} +(2.79964 + 0.402527i) q^{8} +O(q^{10})\)	\(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-2.17725 + 7.41503i) q^{5} +(6.85488 - 7.91095i) q^{7} +(2.79964 + 0.402527i) q^{8} +(-7.15707 - 8.25969i) q^{10} +(-0.214579 - 0.333892i) q^{11} +(7.09545 + 8.18859i) q^{13} +(4.17064 + 14.2039i) q^{14} +(-2.61944 + 3.02300i) q^{16} +(9.43996 + 4.31109i) q^{17} +(6.43909 + 14.0996i) q^{19} +(15.2988 - 2.19964i) q^{20} +0.561299 q^{22} +(21.1528 + 9.03111i) q^{23} +(-29.2109 - 18.7727i) q^{25} +(-15.1671 + 2.18070i) q^{26} +(-20.0873 - 5.89818i) q^{28} +(-38.3477 - 17.5128i) q^{29} +(-1.84235 + 12.8139i) q^{31} +(-1.59372 - 5.42771i) q^{32} +(-12.3466 + 7.93466i) q^{34} +(43.7352 + 68.0532i) q^{35} +(-25.4655 + 7.47734i) q^{37} +(-21.6977 - 3.11966i) q^{38} +(-9.08026 + 19.8830i) q^{40} +(-14.1920 + 48.3334i) q^{41} +(2.60054 + 18.0871i) q^{43} +(-0.429159 + 0.667784i) q^{44} +(-26.9174 + 18.2607i) q^{46} +47.1029i q^{47} +(-8.62036 - 59.9559i) q^{49} +(44.6682 - 20.3993i) q^{50} +(9.00209 - 19.7118i) q^{52} +(40.3577 + 34.9701i) q^{53} +(2.94301 - 0.864146i) q^{55} +(22.3755 - 19.3885i) q^{56} +(50.1552 - 32.2328i) q^{58} +(-36.5799 + 31.6966i) q^{59} +(-9.80873 + 68.2212i) q^{61} +(-13.8362 - 11.9891i) q^{62} +(7.67594 + 2.25386i) q^{64} +(-76.1672 + 34.7844i) q^{65} +(79.4192 + 51.0396i) q^{67} -20.7556i q^{68} -114.403 q^{70} +(59.1643 - 92.0615i) q^{71} +(-6.28038 - 13.7521i) q^{73} +(10.5745 - 36.0136i) q^{74} +(20.3012 - 23.4288i) q^{76} +(-4.11232 - 0.591262i) q^{77} +(-2.59730 - 2.99744i) q^{79} +(-16.7124 - 26.0051i) q^{80} +(-46.6520 - 53.8392i) q^{82} +(-29.9013 - 101.835i) q^{83} +(-52.5200 + 60.6113i) q^{85} +(-23.5068 - 10.7352i) q^{86} +(-0.466344 - 1.02115i) q^{88} +(-96.4907 + 13.8733i) q^{89} +113.418 q^{91} +(-1.14437 - 45.9858i) q^{92} +(-56.0389 - 36.0140i) q^{94} +(-118.569 + 17.0476i) q^{95} +(136.320 + 40.0270i) q^{97} +(77.9213 + 35.5854i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} + 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^4 + 16 * q^7	\( 80 q + 16 q^{4} + 16 q^{7} - 8 q^{10} - 24 q^{13} - 32 q^{16} + 208 q^{19} + 64 q^{22} + 256 q^{25} - 32 q^{28} + 268 q^{34} - 256 q^{37} + 16 q^{40} - 524 q^{43} - 48 q^{46} + 144 q^{49} + 48 q^{52} + 396 q^{55} + 456 q^{58} + 376 q^{61} + 64 q^{64} + 44 q^{67} - 520 q^{70} - 188 q^{73} - 64 q^{76} + 164 q^{79} - 924 q^{82} - 1524 q^{85} + 48 q^{88} + 128 q^{91} - 176 q^{94} - 1144 q^{97}+O(q^{100}) \) 80 * q + 16 * q^4 + 16 * q^7 - 8 * q^10 - 24 * q^13 - 32 * q^16 + 208 * q^19 + 64 * q^22 + 256 * q^25 - 32 * q^28 + 268 * q^34 - 256 * q^37 + 16 * q^40 - 524 * q^43 - 48 * q^46 + 144 * q^49 + 48 * q^52 + 396 * q^55 + 456 * q^58 + 376 * q^61 + 64 * q^64 + 44 * q^67 - 520 * q^70 - 188 * q^73 - 64 * q^76 + 164 * q^79 - 924 * q^82 - 1524 * q^85 + 48 * q^88 + 128 * q^91 - 176 * q^94 - 1144 * q^97

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