LMFDB - Embedded newform 414.3.k.b.35.8

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			35.8
Character	$\chi$	$=$	414.35
Dual form			414.3.k.b.71.8

$q$-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 $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{10}{11}\right)$

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	0.826659	+	0.562704i	$0.190239\pi$
$5$	2.17725	+	7.41503i	0.435450	+	1.48301i	−0.391209	+	0.920302i	$0.627943\pi$
$6$		0			0
$7$	6.85488	+	7.91095i	0.979268	+	1.13014i	0.991486	+	0.130210i	$0.0415653\pi$
$7$	6.85488	+	7.91095i	0.979268	+	1.13014i	−0.0122182	+	0.999925i	$0.503889\pi$
$8$	−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	$-0.812439\pi$
$11$	0.214579	−	0.333892i	0.0195072	−	0.0303538i	0.850870	+	0.525376i	$0.176075\pi$
$12$		0			0
$13$	7.09545	−	8.18859i	0.545804	−	0.629891i	−0.414096	−	0.910233i	$-0.635902\pi$
$13$	7.09545	−	8.18859i	0.545804	−	0.629891i	0.959900	+	0.280342i	$0.0904478\pi$
$14$	−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	$-0.735097\pi$
$17$	−9.43996	+	4.31109i	−0.555292	+	0.253593i	0.117945	+	0.993020i	$0.462369\pi$
$18$		0			0
$19$	6.43909	−	14.0996i	0.338899	−	0.742086i	−0.661067	−	0.750327i	$-0.729896\pi$
$19$	6.43909	−	14.0996i	0.338899	−	0.742086i	0.999966	+	0.00824092i	$0.00262319\pi$
$20$	−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	$-0.377346\pi$
$29$	38.3477	−	17.5128i	1.32234	−	0.603890i	0.946472	+	0.322785i	$0.104619\pi$
$30$		0			0
$31$	−1.84235	−	12.8139i	−0.0594308	−	0.413350i	−0.997719	−	0.0674970i	$-0.978499\pi$
$31$	−1.84235	−	12.8139i	−0.0594308	−	0.413350i	0.938289	−	0.345853i	$-0.112410\pi$
$32$	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	−0.0811391	−	0.996703i	$-0.525856\pi$
$37$	−25.4655	−	7.47734i	−0.688256	−	0.202090i	−0.607117	+	0.794613i	$0.707674\pi$
$38$	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	0.930170	+	0.367128i	$0.119659\pi$
$41$	14.1920	+	48.3334i	0.346146	+	1.17886i	−0.584025	+	0.811736i	$0.698523\pi$
$42$		0			0
$43$	2.60054	−	18.0871i	0.0604777	−	0.420631i	−0.936981	−	0.349381i	$-0.886392\pi$
$43$	2.60054	−	18.0871i	0.0604777	−	0.420631i	0.997458	−	0.0712505i	$-0.0226990\pi$
$44$	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	$-0.895331\pi$
$53$	−40.3577	+	34.9701i	−0.761466	+	0.659814i	0.184956	+	0.982747i	$0.440786\pi$
$54$		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	$-0.138191\pi$
$59$	36.5799	+	31.6966i	0.619998	+	0.537231i	−0.287235	+	0.957860i	$0.592736\pi$
$60$		0			0
$61$	−9.80873	−	68.2212i	−0.160799	−	1.11838i	−0.897132	−	0.441762i	$-0.854354\pi$
$61$	−9.80873	−	68.2212i	−0.160799	−	1.11838i	0.736334	−	0.676619i	$-0.236555\pi$
$62$	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	0.208997	−	0.977916i	$-0.432980\pi$
$67$	79.4192	−	51.0396i	1.18536	−	0.761785i	0.976364	+	0.216131i	$0.0693438\pi$
$68$		−	20.7556i		−	0.305229i
$69$		0			0
$70$	−114.403			−1.63433
$71$	−59.1643	−	92.0615i	−0.833300	−	1.29664i	−0.952736	−	0.303799i	$-0.901745\pi$
$71$	−59.1643	−	92.0615i	−0.833300	−	1.29664i	0.119436	−	0.992842i	$-0.461891\pi$
$72$		0			0
$73$	−6.28038	+	13.7521i	−0.0860325	+	0.188385i	−0.947758	−	0.318989i	$-0.896657\pi$
$73$	−6.28038	+	13.7521i	−0.0860325	+	0.188385i	0.861726	+	0.507374i	$0.169384\pi$
$74$	−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	−0.771950	−	0.635683i	$-0.780718\pi$
$79$	−2.59730	+	2.99744i	−0.0328772	+	0.0379423i	0.739073	+	0.673626i	$0.235264\pi$
$80$	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	−0.557633	−	0.830088i	$-0.688290\pi$
$83$	29.9013	−	101.835i	0.360257	−	1.22692i	0.917890	−	0.396835i	$-0.129892\pi$
$84$		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	$-0.270065\pi$
$89$	96.4907	+	13.8733i	1.08417	+	0.155879i	0.423007	+	0.906126i	$0.360974\pi$
$90$		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	0.510836	−	0.859678i	$-0.329336\pi$
$97$	136.320	−	40.0270i	1.40536	−	0.412650i	0.894520	+	0.447028i	$0.147518\pi$
$98$	−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	0.821503	+	0.570204i	$0.193136\pi$
$101$	−17.9643	+	61.1809i	−0.177865	+	0.605751i	−0.999368	+	0.0355476i	$0.988682\pi$
$102$		0			0
$103$	−159.755	−	102.668i	−1.55102	−	0.996779i	−0.985033	−	0.172364i	$-0.944859\pi$
$103$	−159.755	−	102.668i	−1.55102	−	0.996779i	−0.565986	−	0.824415i	$-0.691504\pi$
$104$	−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	$-0.557565\pi$
$107$	−8.05726	+	1.15846i	−0.0753015	+	0.0108267i	0.104561	+	0.994518i	$0.466656\pi$
$108$		0			0
$109$	80.0266	+	175.234i	0.734189	+	1.60765i	0.792884	+	0.609373i	$0.208579\pi$
$109$	80.0266	+	175.234i	0.734189	+	1.60765i	−0.0586952	+	0.998276i	$0.518694\pi$
$110$	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	−0.949647	−	0.313322i	$-0.898558\pi$
$113$	−94.9377	−	147.726i	−0.840157	−	1.30731i	0.109490	−	0.993988i	$-0.465078\pi$
$114$		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	0.996793	+	0.0800193i	$0.0254982\pi$
$127$	188.425	+	121.094i	1.48366	+	0.953493i	0.486871	+	0.873474i	$0.338138\pi$
$128$	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	$-0.674269\pi$
$131$	32.8193	−	28.4381i	0.250529	−	0.217085i	0.771067	+	0.636754i	$0.219723\pi$
$132$		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	$-0.966962\pi$
$149$	−72.5921	+	112.955i	−0.487195	+	0.758090i	0.507423	+	0.861697i	$0.330598\pi$
$150$		0			0
$151$	−38.5745	+	44.5173i	−0.255460	+	0.294817i	−0.868964	−	0.494875i	$-0.835214\pi$
$151$	−38.5745	+	44.5173i	−0.255460	+	0.294817i	0.613504	+	0.789692i	$0.289759\pi$
$152$	−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	0.361056	+	0.932544i	$0.382416\pi$
$157$	−91.0843	+	199.447i	−0.580155	+	1.27036i	−0.941211	+	0.337818i	$0.890311\pi$
$158$	−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	0.433426	−	0.901189i	$-0.357305\pi$
$163$	233.616	−	150.136i	1.43323	−	0.921080i	0.999802	−	0.0198904i	$-0.00633172\pi$
$164$	−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	$-0.409152\pi$
$167$	198.914	−	90.8409i	1.19110	−	0.543958i	0.909552	+	0.415589i	$0.136425\pi$
$168$		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	0.0836422	+	0.996496i	$0.473345\pi$
$173$	−148.356	+	230.846i	−0.857549	+	1.33437i	−0.941191	+	0.337876i	$0.890292\pi$
$174$		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	0.895065	+	0.445937i	$0.147129\pi$
$179$	68.5892	+	233.593i	0.383180	+	1.30499i	−0.511885	+	0.859054i	$0.671052\pi$
$180$		0			0
$181$	26.2047	−	182.258i	0.144778	−	1.00695i	−0.779820	−	0.626004i	$-0.784689\pi$
$181$	26.2047	−	182.258i	0.144778	−	1.00695i	0.924597	−	0.380946i	$-0.124402\pi$
$182$	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	$-0.607175\pi$
$191$	106.359	−	92.1603i	0.556852	−	0.482515i	0.887226	+	0.461335i	$0.152629\pi$
$192$		0			0
$193$	−364.220	−	106.945i	−1.88715	−	0.554117i	−0.994680	−	0.103010i	$-0.967153\pi$
$193$	−364.220	−	106.945i	−1.88715	−	0.554117i	−0.892470	−	0.451107i	$-0.851029\pi$
$194$	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	$-0.428328\pi$
$197$	−139.830	−	121.163i	−0.709796	−	0.615042i	−0.933062	+	0.359716i	$0.882874\pi$
$198$		0			0
$199$	−19.0391	−	132.420i	−0.0956739	−	0.665427i	−0.980065	−	0.198679i	$-0.936335\pi$
$199$	−19.0391	−	132.420i	−0.0956739	−	0.665427i	0.884391	−	0.466748i	$-0.154574\pi$
$200$	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	0.651017	+	0.759063i	$0.274343\pi$
$211$	−73.6327	+	161.233i	−0.348970	+	0.764138i	−0.999987	+	0.00507499i	$0.998385\pi$
$212$	−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	0.490708	−	0.871324i	$-0.336738\pi$
$223$	−98.4729	−	113.644i	−0.441582	−	0.509613i	−0.932290	+	0.361711i	$0.882193\pi$
$224$	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	$-0.475037\pi$
$227$	−28.9087	−	4.15644i	−0.127351	−	0.0183103i	−0.205696	+	0.978616i	$0.565946\pi$
$228$		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	$-0.203544\pi$
$233$	327.182	+	47.0417i	1.40421	+	0.201896i	0.601792	+	0.798653i	$0.294453\pi$
$234$		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	$-0.848858\pi$
$239$	25.3309	−	86.2691i	0.105987	−	0.360959i	0.995360	+	0.0962243i	$0.0306766\pi$
$240$		0			0
$241$	119.043	+	76.5040i	0.493953	+	0.317444i	0.763793	−	0.645461i	$-0.223335\pi$
$241$	119.043	+	76.5040i	0.493953	+	0.317444i	−0.269841	+	0.962905i	$0.586971\pi$
$242$	−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	$-0.208926\pi$
$251$	−23.0848	−	35.9207i	−0.0919714	−	0.143110i	−0.884191	+	0.467126i	$0.845289\pi$
$252$		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	$-0.489782\pi$
$257$	−180.478	−	82.4214i	−0.702247	−	0.320706i	−0.734342	+	0.678779i	$0.762509\pi$
$258$		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	$-0.511209\pi$
$263$	−270.739	−	234.597i	−1.02943	−	0.892002i	−0.994218	+	0.107378i	$0.965754\pi$
$264$		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	$-0.911710\pi$
$269$	−222.628	+	192.908i	−0.827612	+	0.717130i	0.134166	+	0.990959i	$0.457164\pi$
$270$		0			0
$271$	340.168	−	99.8824i	1.25523	−	0.368570i	0.414515	−	0.910043i	$-0.363951\pi$
$271$	340.168	−	99.8824i	1.25523	−	0.368570i	0.840718	+	0.541473i	$0.182133\pi$
$272$	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	−0.996556	−	0.0829263i	$-0.973573\pi$
$281$	−57.0523	−	194.302i	−0.203033	−	0.691467i	0.793523	−	0.608541i	$-0.208245\pi$
$282$		0			0
$283$	5.73619	+	6.61992i	0.0202692	+	0.0233919i	0.765794	−	0.643086i	$-0.222346\pi$
$283$	5.73619	+	6.61992i	0.0202692	+	0.0233919i	−0.745524	+	0.666478i	$0.767801\pi$
$284$	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	$-0.666586\pi$
$293$	−50.5346	+	23.0784i	−0.172473	+	0.0787659i	0.327307	+	0.944918i	$0.393859\pi$
$294$		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	0.822408	+	0.568898i	$0.192630\pi$
$307$	59.4323	+	413.361i	0.193590	+	1.34645i	−0.628817	+	0.777553i	$0.716461\pi$
$308$	−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	−0.330942	−	0.943651i	$-0.607366\pi$
$311$	206.787	−	321.768i	0.664912	−	1.03462i	0.995854	−	0.0909714i	$-0.0289972\pi$
$312$		0			0
$313$	−290.730	−	85.3659i	−0.928848	−	0.272735i	−0.217894	−	0.975972i	$-0.569919\pi$
$313$	−290.730	−	85.3659i	−0.928848	−	0.272735i	−0.710955	+	0.703238i	$0.751737\pi$
$314$	−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	$-0.147979\pi$
$317$	−31.8532	−	108.482i	−0.100483	−	0.342215i	−0.994355	+	0.106109i	$0.966161\pi$
$318$		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	−0.0981597	−	0.995171i	$-0.531296\pi$
$331$	−237.912	−	69.8572i	−0.718767	−	0.211049i	−0.620607	+	0.784122i	$0.713114\pi$
$332$	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	0.611266	+	0.791426i	$0.290661\pi$
$337$	83.4853	+	580.653i	0.247731	+	1.72301i	−0.363535	+	0.931581i	$0.618430\pi$
$338$	−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	$-0.188895\pi$
$347$	−8.34115	−	12.9791i	−0.0240379	−	0.0374037i	−0.853065	+	0.521805i	$0.825259\pi$
$348$		0			0
$349$	53.7344	−	117.662i	0.153967	−	0.337140i	−0.816893	−	0.576790i	$-0.804305\pi$
$349$	53.7344	−	117.662i	0.153967	−	0.337140i	0.970859	+	0.239649i	$0.0770325\pi$
$350$	−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	$-0.532160\pi$
$353$	29.1790	−	4.19531i	0.0826601	−	0.0118847i	0.183521	+	0.983016i	$0.441251\pi$
$354$		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	−0.737829	−	0.674987i	$-0.764149\pi$
$359$	88.9595	−	302.968i	0.247798	−	0.843922i	0.985627	−	0.168935i	$-0.0540328\pi$
$360$		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	−0.688609	−	0.725133i	$-0.741778\pi$
$373$	−326.699	+	95.9274i	−0.875868	+	0.257178i	−0.187259	+	0.982311i	$0.559960\pi$
$374$	−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	0.325988	−	0.945374i	$-0.394303\pi$
$379$	−151.044	−	97.0703i	−0.398534	−	0.256122i	−0.724522	+	0.689252i	$0.757939\pi$
$380$	−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	$-0.545186\pi$
$383$	0.639392	−	0.0919307i	0.00166943	−	0.000240028i	0.143150	+	0.989701i	$0.454277\pi$
$384$		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	$-0.224776\pi$
$389$	−56.5933	−	88.0609i	−0.145484	−	0.226378i	−0.906346	+	0.422536i	$0.861140\pi$
$390$		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	0.772030	−	0.635586i	$-0.219241\pi$
$397$	−84.9125	−	185.933i	−0.213885	−	0.468344i	−0.985916	+	0.167242i	$0.946514\pi$
$398$	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	$-0.0621283\pi$
$401$	372.390	+	322.678i	0.928654	+	0.804684i	−0.0523581	+	0.998628i	$0.516674\pi$
$402$		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	0.367198	−	0.930143i	$-0.380317\pi$
$409$	482.202	−	141.587i	1.17898	−	0.346179i	0.811780	+	0.583964i	$0.198499\pi$
$410$	−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	−0.957685	−	0.287817i	$-0.907071\pi$
$419$	−128.899	−	438.990i	−0.307635	−	1.04771i	0.650051	−	0.759891i	$-0.274748\pi$
$420$		0			0
$421$	−135.667	−	156.568i	−0.322250	−	0.371897i	0.571392	−	0.820678i	$-0.306404\pi$
$421$	−135.667	−	156.568i	−0.322250	−	0.371897i	−0.893642	+	0.448781i	$0.851858\pi$
$422$	−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	$-0.928056\pi$
$431$	−622.110	+	284.108i	−1.44341	+	0.659183i	−0.468843	+	0.883281i	$0.655329\pi$
$432$		0			0
$433$	−323.484	+	708.331i	−0.747076	+	1.63587i	0.0244753	+	0.999700i	$0.492208\pi$
$433$	−323.484	+	708.331i	−0.747076	+	1.63587i	−0.771551	+	0.636167i	$0.780519\pi$
$434$	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	−0.391392	−	0.920224i	$-0.628006\pi$
$439$	124.273	−	79.8656i	0.283083	−	0.181926i	0.674475	+	0.738298i	$0.264370\pi$
$440$	−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	$-0.413124\pi$
$443$	520.016	−	237.483i	1.17385	−	0.536079i	0.904296	+	0.426906i	$0.140396\pi$
$444$		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	$-0.845283\pi$
$449$	−41.2854	+	64.2414i	−0.0919497	+	0.143077i	0.792231	+	0.610221i	$0.208919\pi$
$450$		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	−0.829677	−	0.558244i	$-0.811475\pi$
$457$	56.5161	−	393.078i	0.123668	−	0.860127i	0.953345	−	0.301884i	$-0.0976154\pi$
$458$	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	−0.890265	−	0.455444i	$-0.849481\pi$
$463$	42.7124	−	297.071i	0.0922513	−	0.641622i	0.982516	−	0.186178i	$-0.0596103\pi$
$464$	−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	$-0.581404\pi$
$467$	312.270	−	270.583i	0.668671	−	0.579407i	0.921630	+	0.388070i	$0.126858\pi$
$468$		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	$-0.508220\pi$
$479$	−382.352	−	174.614i	−0.798230	−	0.364539i	−0.772408	+	0.635127i	$0.780948\pi$
$480$		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	−0.530283	−	0.847821i	$-0.677914\pi$
$487$	222.909	−	488.103i	0.457719	−	1.00226i	0.988002	−	0.154444i	$-0.0493585\pi$
$488$	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	$-0.661854\pi$
$491$	−347.574	+	49.9736i	−0.707891	+	0.101779i	−0.221040	+	0.975265i	$0.570945\pi$
$492$		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	0.866182	−	0.499729i	$-0.166567\pi$
$499$	123.886	+	142.972i	0.248268	+	0.286517i	−0.617913	+	0.786246i	$0.712022\pi$
$500$	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	$-0.360018\pi$
$503$	291.381	+	41.8942i	0.579285	+	0.0832887i	0.153557	+	0.988140i	$0.450927\pi$
$504$		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	$-0.746682\pi$
$509$	−800.318	−	115.068i	−1.57233	−	0.226067i	−0.872636	+	0.488372i	$0.837591\pi$
$510$		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	$-0.600463\pi$
$521$	−177.353	+	25.4995i	−0.340409	+	0.0489434i	−0.0300095	+	0.999550i	$0.509554\pi$
$522$		0			0
$523$	−289.038	−	632.906i	−0.552655	−	1.21014i	−0.955531	−	0.294890i	$-0.904717\pi$
$523$	−289.038	−	632.906i	−0.552655	−	1.21014i	0.402877	−	0.915254i	$-0.368010\pi$
$524$	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	0.945213	+	0.326454i	$0.105854\pi$
$541$	884.439	+	568.394i	1.63482	+	1.05064i	0.689609	+	0.724182i	$0.257782\pi$
$542$	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	0.0299023	−	0.999553i	$-0.490480\pi$
$547$	325.715	−	95.6385i	0.595457	−	0.174842i	0.565554	+	0.824711i	$0.308662\pi$
$548$	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	−0.908658	−	0.417542i	$-0.862892\pi$
$557$	−206.082	−	701.853i	−0.369987	−	1.26006i	0.538671	−	0.842516i	$-0.318927\pi$
$558$		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	$-0.653917\pi$
$563$	300.394	−	467.422i	0.533560	−	0.830235i	0.998480	+	0.0551177i	$0.0175534\pi$
$564$		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	$-0.413848\pi$
$569$	666.120	−	304.207i	1.17069	−	0.534634i	0.903323	+	0.428962i	$0.141121\pi$
$570$		0			0
$571$	−107.957	+	236.393i	−0.189067	+	0.413998i	−0.980300	−	0.197517i	$-0.936712\pi$
$571$	−107.957	+	236.393i	−0.189067	+	0.413998i	0.791233	+	0.611515i	$0.209440\pi$
$572$	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	−0.713452	−	0.700704i	$-0.752869\pi$
$577$	−214.902	+	138.109i	−0.372447	+	0.239357i	0.341004	+	0.940062i	$0.389233\pi$
$578$	−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	$-0.916501\pi$
$587$	−192.947	+	300.231i	−0.328699	+	0.511466i	0.637091	+	0.770788i	$0.280137\pi$
$588$		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	$-0.0989279\pi$
$593$	−8.41659	−	28.6643i	−0.0141932	−	0.0483377i	−0.966285	+	0.257474i	$0.917110\pi$
$594$		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	−0.690664	−	0.723176i	$-0.742682\pi$
$601$	105.635	−	734.708i	0.175765	−	1.22248i	0.866429	−	0.499300i	$-0.166409\pi$
$602$	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	0.354900	−	0.934904i	$-0.384515\pi$
$607$	89.8448	+	26.3808i	0.148014	+	0.0434610i	−0.206886	+	0.978365i	$0.566333\pi$
$608$	−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	0.768727	+	0.639577i	$0.220891\pi$
$613$	129.544	+	901.001i	0.211329	+	1.46982i	−0.557398	+	0.830245i	$0.688200\pi$
$614$	−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	$-0.417934\pi$
$617$	−190.549	−	87.0207i	−0.308831	−	0.141038i	−0.563801	+	0.825910i	$0.690662\pi$
$618$		0			0
$619$	−442.527	+	284.395i	−0.714906	+	0.459442i	−0.846862	−	0.531813i	$-0.821511\pi$
$619$	−442.527	+	284.395i	−0.714906	+	0.459442i	0.131955	+	0.991256i	$0.457874\pi$
$620$			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	−0.0629522	−	0.998017i	$-0.520052\pi$
$631$	589.269	−	680.052i	0.933865	−	1.07774i	0.996817	−	0.0797211i	$-0.0254030\pi$
$632$	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	$-0.463592\pi$
$641$	−36.0611	−	5.18480i	−0.0562575	−	0.00808861i	−0.170386	+	0.985377i	$0.554501\pi$
$642$		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	$-0.679863\pi$
$647$	−832.802	−	119.739i	−1.28718	−	0.185068i	−0.751713	+	0.659491i	$0.770772\pi$
$648$		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	0.765731	+	0.643161i	$0.222377\pi$
$653$	−147.684	+	502.964i	−0.226162	+	0.770237i	−0.991893	+	0.127076i	$0.959441\pi$
$654$		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	$-0.484263\pi$
$659$	249.250	−	35.8367i	0.378224	−	0.0543804i	0.328805	+	0.944398i	$0.393354\pi$
$660$		0			0
$661$	314.017	+	687.602i	0.475064	+	1.04024i	0.983791	+	0.179317i	$0.0573887\pi$
$661$	314.017	+	687.602i	0.475064	+	1.04024i	−0.508728	+	0.860927i	$0.669884\pi$
$662$	−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	0.695927	−	0.718113i	$-0.254994\pi$
$673$	−203.597	−	445.815i	−0.302522	−	0.662430i	−0.998449	+	0.0556828i	$0.982266\pi$
$674$	−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	$-0.328243\pi$
$677$	−177.566	−	153.861i	−0.262283	−	0.227269i	−0.776068	+	0.630650i	$0.782788\pi$
$678$		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	$-0.905711\pi$
$683$	−548.881	+	475.608i	−0.803632	+	0.696352i	0.152815	+	0.988255i	$0.451166\pi$
$684$		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	$-0.874623\pi$
$701$	−133.697	+	208.037i	−0.190724	+	0.296772i	0.732702	+	0.680550i	$0.238259\pi$
$702$		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	−0.555628	−	0.831431i	$-0.687522\pi$
$709$	309.539	−	677.795i	0.436585	−	0.955987i	0.992213	−	0.124556i	$-0.0397506\pi$
$710$	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	$-0.827082\pi$
$719$	−737.674	+	336.884i	−1.02597	+	0.468546i	−0.169932	+	0.985456i	$0.554355\pi$
$720$		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	0.400161	−	0.916445i	$-0.368954\pi$
$727$	175.447	+	51.5160i	0.241331	+	0.0708610i	−0.158831	+	0.987306i	$0.550772\pi$
$728$	−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	−0.957246	−	0.289276i	$-0.906585\pi$
$733$	31.3162	−	217.809i	0.0427233	−	0.297147i	0.999969	−	0.00787097i	$-0.00250543\pi$
$734$	−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	0.935678	+	0.352856i	$0.114790\pi$
$739$	−45.4556	+	316.150i	−0.0615095	+	0.427808i	−0.997187	+	0.0749522i	$0.976120\pi$
$740$	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	$-0.795236\pi$
$743$	−237.966	+	206.199i	−0.320277	+	0.277522i	0.479852	+	0.877350i	$0.340690\pi$
$744$		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	−0.999529	−	0.0306937i	$-0.990228\pi$
$751$	−36.9006	−	256.650i	−0.0491353	−	0.341744i	0.950393	−	0.311050i	$-0.100681\pi$
$752$	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	−0.950425	−	0.310954i	$-0.899351\pi$
$757$	−804.231	+	516.848i	−1.06239	+	0.682758i	−0.111967	+	0.993712i	$0.535715\pi$
$758$		−	253.917i		−	0.334983i
$759$		0			0
$760$	−338.812			−0.445805
$761$	−571.286	−	888.939i	−0.750705	−	1.16812i	−0.980812	−	0.194954i	$-0.937544\pi$
$761$	−571.286	−	888.939i	−0.750705	−	1.16812i	0.230108	−	0.973165i	$-0.426092\pi$
$762$		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	−0.0449032	+	0.998991i	$0.514298\pi$
$769$	−790.021	+	911.733i	−1.02734	+	1.18561i	−0.982433	+	0.186617i	$0.940248\pi$
$770$	−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	−0.567044	−	0.823687i	$-0.691913\pi$
$773$	274.649	−	935.369i	0.355303	−	1.21005i	0.922347	−	0.386363i	$-0.126269\pi$
$774$		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	−0.795271	−	0.606254i	$-0.792671\pi$
$787$	−894.448	+	262.634i	−1.13653	+	0.333715i	−0.341258	+	0.939970i	$0.610853\pi$
$788$	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	$-0.311524\pi$
$797$	1057.94	−	152.108i	1.32740	−	0.190851i	0.769280	+	0.638911i	$0.220615\pi$
$798$		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	$-0.357665\pi$
$809$	27.6065	+	12.6075i	0.0341242	+	0.0155840i	−0.398280	+	0.917264i	$0.630393\pi$
$810$		0			0
$811$	116.016	+	254.039i	0.143053	+	0.313242i	0.967573	−	0.252590i	$-0.0812824\pi$
$811$	116.016	+	254.039i	0.143053	+	0.313242i	−0.824521	+	0.565832i	$0.808555\pi$
$812$	−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	$-0.594565\pi$
$821$	502.507	−	435.425i	0.612067	−	0.530359i	0.904801	+	0.425835i	$0.140019\pi$
$822$		0			0
$823$	292.416	−	85.8612i	0.355305	−	0.104327i	−0.0992086	−	0.995067i	$-0.531631\pi$
$823$	292.416	−	85.8612i	0.355305	−	0.104327i	0.454514	+	0.890740i	$0.349813\pi$
$824$	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	0.364066	+	0.931373i	$0.381388\pi$
$839$	−532.244	+	828.188i	−0.634379	+	0.987113i	−0.998445	+	0.0557401i	$0.982248\pi$
$840$		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	−0.713413	−	0.700743i	$-0.752852\pi$
$853$	−317.621	+	204.122i	−0.372357	+	0.239299i	0.341056	+	0.940043i	$0.389215\pi$
$854$	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	$-0.814271\pi$
$857$	−826.742	+	377.560i	−0.964693	+	0.440560i	−0.130144	+	0.991495i	$0.541544\pi$
$858$		0			0
$859$	−69.5473	−	483.712i	−0.0809631	−	0.563110i	−0.989414	−	0.145119i	$-0.953643\pi$
$859$	−69.5473	−	483.712i	−0.0809631	−	0.563110i	0.908451	−	0.417991i	$-0.137266\pi$
$860$	−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	0.305446	+	0.952209i	$0.401194\pi$
$863$	−593.400	+	923.348i	−0.687601	+	1.06993i	−0.993047	+	0.117719i	$0.962442\pi$
$864$		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	−0.999756	−	0.0220917i	$-0.992967\pi$
$877$	−30.0576	+	209.055i	−0.0342732	+	0.238375i	0.965483	+	0.260467i	$0.0838765\pi$
$878$	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	$-0.551403\pi$
$881$	698.875	−	605.579i	0.793275	−	0.687377i	0.954061	+	0.299612i	$0.0968574\pi$
$882$		0			0
$883$	667.168	+	195.898i	0.755569	+	0.221855i	0.636760	−	0.771062i	$-0.280274\pi$
$883$	667.168	+	195.898i	0.755569	+	0.221855i	0.118809	+	0.992917i	$0.462092\pi$
$884$	−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	−0.914099	−	0.405491i	$-0.867101\pi$
$887$	−1282.20	−	1111.04i	−1.44555	−	1.25258i	−0.531453	−	0.847088i	$-0.678354\pi$
$888$		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	0.261075	−	0.965319i	$-0.415923\pi$
$907$	1069.73	−	1234.53i	1.17941	−	1.36112i	0.918338	−	0.395797i	$-0.129532\pi$
$908$	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	$-0.973905\pi$
$911$	−103.801	+	353.514i	−0.113942	+	0.388051i	0.882700	+	0.469938i	$0.155724\pi$
$912$		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	$-0.855366\pi$
$929$	87.9320	−	299.469i	0.0946523	−	0.322356i	0.993185	+	0.116551i	$0.0371839\pi$
$930$		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	−0.762392	−	0.647115i	$-0.775975\pi$
$937$	−704.801	−	1543.30i	−0.752189	−	1.64706i	0.0102036	−	0.999948i	$-0.496752\pi$
$938$	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	$-0.300918\pi$
$941$	−371.886	−	578.666i	−0.395203	−	0.614948i	−0.980652	+	0.195762i	$0.937282\pi$
$942$		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	$-0.715350\pi$
$947$	−1539.25	−	702.953i	−1.62540	−	0.742295i	−0.999299	+	0.0374484i	$0.988077\pi$
$948$		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	0.997871	+	0.0652245i	$0.0207763\pi$
$953$	1147.83	+	994.604i	1.20444	+	1.04366i	0.206572	+	0.978431i	$0.433769\pi$
$954$		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	$-0.153250\pi$
$971$	−106.471	−	362.607i	−0.109651	−	0.373437i	−0.995975	+	0.0896280i	$0.971432\pi$
$972$		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	$-0.796919\pi$
$977$	70.5157	−	109.725i	0.0721757	−	0.112308i	0.875465	+	0.483281i	$0.160555\pi$
$978$		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	$-0.630907\pi$
$983$	30.6544	−	13.9994i	0.0311845	−	0.0142415i	0.430946	+	0.902378i	$0.358180\pi$
$984$		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	−0.658705	−	0.752401i	$-0.728896\pi$
$991$	−245.702	+	157.903i	−0.247934	+	0.159337i	0.410772	+	0.911738i	$0.365259\pi$
$992$	−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	−0.978634	−	0.205612i	$-0.934082\pi$
$997$	−97.2764	−	676.572i	−0.0975691	−	0.678608i	0.881065	−	0.472996i	$-0.156827\pi$
$998$	−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.35.8	yes	80
3.2	odd	2	inner	414.3.k.b.35.1	✓	80
23.2	even	11	inner	414.3.k.b.71.1	yes	80
69.2	odd	22	inner	414.3.k.b.71.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.b.35.1	✓	80	3.2	odd	2	inner
414.3.k.b.35.8	yes	80	1.1	even	1	trivial
414.3.k.b.71.1	yes	80	23.2	even	11	inner
414.3.k.b.71.8	yes	80	69.2	odd	22	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
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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