LMFDB - Embedded newform 387.3.j.f.136.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,3,Mod(37,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("387.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	387.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.5449862307$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			136.6
Character	$\chi$	$=$	387.136
Dual form			387.3.j.f.37.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61273i q^{2} +1.39911 q^{4} +(-0.333970 + 0.192817i) q^{5} +(-8.76989 - 5.06330i) q^{7} -8.70729i q^{8} +O(q^{10})$	\(q-1.61273i q^{2} +1.39911 q^{4} +(-0.333970 + 0.192817i) q^{5} +(-8.76989 - 5.06330i) q^{7} -8.70729i q^{8} +(0.310962 + 0.538602i) q^{10} -7.33614 q^{11} +(-10.6070 + 18.3718i) q^{13} +(-8.16573 + 14.1435i) q^{14} -8.44606 q^{16} +(12.4464 - 21.5579i) q^{17} +(-6.15827 + 3.55548i) q^{19} +(-0.467260 + 0.269773i) q^{20} +11.8312i q^{22} +(-3.21546 - 5.56934i) q^{23} +(-12.4256 + 21.5218i) q^{25} +(29.6287 + 17.1061i) q^{26} +(-12.2700 - 7.08411i) q^{28} +(-46.5628 - 26.8830i) q^{29} +(-1.72811 - 2.99317i) q^{31} -21.2080i q^{32} +(-34.7670 - 20.0727i) q^{34} +3.90517 q^{35} +(8.83540 - 5.10112i) q^{37} +(5.73402 + 9.93161i) q^{38} +(1.67892 + 2.90797i) q^{40} -53.2041 q^{41} +(-21.0737 - 37.4820i) q^{43} -10.2641 q^{44} +(-8.98182 + 5.18566i) q^{46} +59.5806 q^{47} +(26.7740 + 46.3740i) q^{49} +(34.7089 + 20.0392i) q^{50} +(-14.8403 + 25.7041i) q^{52} +(42.5691 + 73.7318i) q^{53} +(2.45005 - 1.41454i) q^{55} +(-44.0876 + 76.3620i) q^{56} +(-43.3550 + 75.0931i) q^{58} +74.1198 q^{59} +(5.41102 + 3.12405i) q^{61} +(-4.82716 + 2.78696i) q^{62} -67.9869 q^{64} -8.18083i q^{65} +(14.6674 + 25.4046i) q^{67} +(17.4139 - 30.1618i) q^{68} -6.29798i q^{70} +(-85.2812 - 49.2371i) q^{71} +(-75.1597 - 43.3935i) q^{73} +(-8.22672 - 14.2491i) q^{74} +(-8.61609 + 4.97450i) q^{76} +(64.3372 + 37.1451i) q^{77} +(72.0690 - 124.827i) q^{79} +(2.82073 - 1.62855i) q^{80} +85.8038i q^{82} +(-6.84004 - 11.8473i) q^{83} +9.59957i q^{85} +(-60.4482 + 33.9862i) q^{86} +63.8780i q^{88} +(-108.450 + 62.6134i) q^{89} +(186.044 - 107.412i) q^{91} +(-4.49877 - 7.79210i) q^{92} -96.0873i q^{94} +(1.37112 - 2.37484i) q^{95} +92.7052 q^{97} +(74.7886 - 43.1792i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 84 q^{4} - 30 q^{7}+O(q^{10}) $ 28 * q - 84 * q^4 - 30 * q^7	$ 28 q - 84 q^{4} - 30 q^{7} + 4 q^{10} - 34 q^{13} + 164 q^{16} - 78 q^{19} + 112 q^{25} + 342 q^{28} - 74 q^{31} + 192 q^{34} - 222 q^{37} + 104 q^{40} + 104 q^{43} + 150 q^{46} + 112 q^{49} - 64 q^{52} - 450 q^{55} + 346 q^{58} - 198 q^{61} - 1264 q^{64} - 26 q^{67} + 342 q^{73} + 282 q^{76} - 48 q^{79} + 684 q^{91} - 480 q^{97}+O(q^{100}) $ 28 * q - 84 * q^4 - 30 * q^7 + 4 * q^10 - 34 * q^13 + 164 * q^16 - 78 * q^19 + 112 * q^25 + 342 * q^28 - 74 * q^31 + 192 * q^34 - 222 * q^37 + 104 * q^40 + 104 * q^43 + 150 * q^46 + 112 * q^49 - 64 * q^52 - 450 * q^55 + 346 * q^58 - 198 * q^61 - 1264 * q^64 - 26 * q^67 + 342 * q^73 + 282 * q^76 - 48 * q^79 + 684 * q^91 - 480 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.61273i		−	0.806364i	−0.915120	−	0.403182i	$-0.867904\pi$
$2$		−	1.61273i		−	0.806364i	0.915120	−	0.403182i	$-0.132096\pi$
$3$		0			0
$3$		0			0
$4$	1.39911			0.349777
$5$	−0.333970	+	0.192817i	−0.0667939	+	0.0385635i	−0.533025	−	0.846099i	$-0.678945\pi$
$5$	−0.333970	+	0.192817i	−0.0667939	+	0.0385635i	0.466231	+	0.884663i	$0.345612\pi$
$6$		0			0
$7$	−8.76989	−	5.06330i	−1.25284	−	0.723329i	−0.281169	−	0.959658i	$-0.590722\pi$
$7$	−8.76989	−	5.06330i	−1.25284	−	0.723329i	−0.971673	+	0.236330i	$0.924055\pi$
$8$		−	8.70729i		−	1.08841i
$9$		0			0
$10$	0.310962	+	0.538602i	0.0310962	+	0.0538602i
$11$	−7.33614			−0.666922			−0.333461	−	0.942764i	$-0.608217\pi$
$11$	−7.33614			−0.666922			−0.333461	+	0.942764i	$0.608217\pi$
$12$		0			0
$13$	−10.6070	+	18.3718i	−0.815920	+	1.41322i	0.0927453	+	0.995690i	$0.470436\pi$
$13$	−10.6070	+	18.3718i	−0.815920	+	1.41322i	−0.908665	+	0.417525i	$0.862898\pi$
$14$	−8.16573	+	14.1435i	−0.583266	+	1.01025i
$15$		0			0
$16$	−8.44606			−0.527879
$17$	12.4464	−	21.5579i	0.732144	−	1.26811i	−0.223821	−	0.974630i	$-0.571853\pi$
$17$	12.4464	−	21.5579i	0.732144	−	1.26811i	0.955965	−	0.293480i	$-0.0948135\pi$
$18$		0			0
$19$	−6.15827	+	3.55548i	−0.324119	+	0.187130i	−0.653227	−	0.757162i	$-0.726585\pi$
$19$	−6.15827	+	3.55548i	−0.324119	+	0.187130i	0.329108	+	0.944292i	$0.393252\pi$
$20$	−0.467260	+	0.269773i	−0.0233630	+	0.0134886i
$21$		0			0
$22$			11.8312i			0.537782i
$23$	−3.21546	−	5.56934i	−0.139802	−	0.242145i	0.787619	−	0.616162i	$-0.211313\pi$
$23$	−3.21546	−	5.56934i	−0.139802	−	0.242145i	−0.927422	+	0.374017i	$0.877980\pi$
$24$		0			0
$25$	−12.4256	+	21.5218i	−0.497026	+	0.860874i
$26$	29.6287	+	17.1061i	1.13957	+	0.657929i
$27$		0			0
$28$	−12.2700	−	7.08411i	−0.438215	−	0.253004i
$29$	−46.5628	−	26.8830i	−1.60561	−	0.927001i	−0.990336	−	0.138690i	$-0.955711\pi$
$29$	−46.5628	−	26.8830i	−1.60561	−	0.927001i	−0.615277	−	0.788311i	$-0.710956\pi$
$30$		0			0
$31$	−1.72811	−	2.99317i	−0.0557454	−	0.0965538i	0.836806	−	0.547499i	$-0.184420\pi$
$31$	−1.72811	−	2.99317i	−0.0557454	−	0.0965538i	−0.892551	+	0.450946i	$0.851087\pi$
$32$		−	21.2080i		−	0.662749i
$33$		0			0
$34$	−34.7670	−	20.0727i	−1.02256	−	0.590375i
$35$	3.90517			0.111576
$36$		0			0
$37$	8.83540	−	5.10112i	0.238794	−	0.137868i	−0.375828	−	0.926689i	$-0.622642\pi$
$37$	8.83540	−	5.10112i	0.238794	−	0.137868i	0.614623	+	0.788821i	$0.289308\pi$
$38$	5.73402	+	9.93161i	0.150895	+	0.261358i
$39$		0			0
$40$	1.67892	+	2.90797i	0.0419730	+	0.0726993i
$41$	−53.2041			−1.29766			−0.648831	−	0.760933i	$-0.724742\pi$
$41$	−53.2041			−1.29766			−0.648831	+	0.760933i	$0.724742\pi$
$42$		0			0
$43$	−21.0737	−	37.4820i	−0.490086	−	0.871674i
$43$	−21.0737	−	37.4820i	−0.490086	−	0.871674i
$44$	−10.2641			−0.233274
$45$		0			0
$46$	−8.98182	+	5.18566i	−0.195257	+	0.112732i
$47$	59.5806			1.26767			0.633836	−	0.773467i	$-0.281479\pi$
$47$	59.5806			1.26767			0.633836	+	0.773467i	$0.281479\pi$
$48$		0			0
$49$	26.7740	+	46.3740i	0.546409	+	0.946407i
$50$	34.7089	+	20.0392i	0.694178	+	0.400784i
$51$		0			0
$52$	−14.8403	+	25.7041i	−0.285390	+	0.494310i
$53$	42.5691	+	73.7318i	0.803190	+	1.39117i	0.917506	+	0.397721i	$0.130199\pi$
$53$	42.5691	+	73.7318i	0.803190	+	1.39117i	−0.114316	+	0.993444i	$0.536468\pi$
$54$		0			0
$55$	2.45005	−	1.41454i	0.0445463	−	0.0257188i
$56$	−44.0876	+	76.3620i	−0.787279	+	1.36361i
$57$		0			0
$58$	−43.3550	+	75.0931i	−0.747500	+	1.29471i
$59$	74.1198			1.25627			0.628134	−	0.778105i	$-0.283819\pi$
$59$	74.1198			1.25627			0.628134	+	0.778105i	$0.283819\pi$
$60$		0			0
$61$	5.41102	+	3.12405i	0.0887052	+	0.0512140i	0.543696	−	0.839282i	$-0.317024\pi$
$61$	5.41102	+	3.12405i	0.0887052	+	0.0512140i	−0.454991	+	0.890496i	$0.650358\pi$
$62$	−4.82716	+	2.78696i	−0.0778575	+	0.0449510i
$63$		0			0
$64$	−67.9869			−1.06230
$65$		−	8.18083i		−	0.125859i
$66$		0			0
$67$	14.6674	+	25.4046i	0.218916	+	0.379173i	0.954477	−	0.298285i	$-0.0964147\pi$
$67$	14.6674	+	25.4046i	0.218916	+	0.379173i	−0.735561	+	0.677458i	$0.763081\pi$
$68$	17.4139	−	30.1618i	0.256087	−	0.443556i
$69$		0			0
$70$		−	6.29798i		−	0.0899711i
$71$	−85.2812	−	49.2371i	−1.20114	−	0.693481i	−0.240335	−	0.970690i	$-0.577257\pi$
$71$	−85.2812	−	49.2371i	−1.20114	−	0.693481i	−0.960810	+	0.277209i	$0.910590\pi$
$72$		0			0
$73$	−75.1597	−	43.3935i	−1.02959	−	0.594431i	−0.112720	−	0.993627i	$-0.535956\pi$
$73$	−75.1597	−	43.3935i	−1.02959	−	0.594431i	−0.916866	+	0.399195i	$0.869290\pi$
$74$	−8.22672	−	14.2491i	−0.111172	−	0.192555i
$75$		0			0
$76$	−8.61609	+	4.97450i	−0.113370	+	0.0654539i
$77$	64.3372	+	37.1451i	0.835548	+	0.482404i
$78$		0			0
$79$	72.0690	−	124.827i	0.912266	−	1.58009i	0.101410	−	0.994845i	$-0.467664\pi$
$79$	72.0690	−	124.827i	0.912266	−	1.58009i	0.810856	−	0.585246i	$-0.199002\pi$
$80$	2.82073	−	1.62855i	0.0352591	−	0.0203569i
$81$		0			0
$82$			85.8038i			1.04639i
$83$	−6.84004	−	11.8473i	−0.0824102	−	0.142739i	0.821875	−	0.569669i	$-0.192928\pi$
$83$	−6.84004	−	11.8473i	−0.0824102	−	0.142739i	−0.904285	+	0.426930i	$0.859595\pi$
$84$		0			0
$85$			9.59957i			0.112936i
$86$	−60.4482	+	33.9862i	−0.702886	+	0.395188i
$87$		0			0
$88$			63.8780i			0.725886i
$89$	−108.450	+	62.6134i	−1.21853	+	0.703522i	−0.964604	−	0.263701i	$-0.915057\pi$
$89$	−108.450	+	62.6134i	−1.21853	+	0.703522i	−0.253931	+	0.967222i	$0.581723\pi$
$90$		0			0
$91$	186.044	−	107.412i	2.04444	−	1.18036i
$92$	−4.49877	−	7.79210i	−0.0488997	−	0.0846968i
$93$		0			0
$94$		−	96.0873i		−	1.02221i
$95$	1.37112	−	2.37484i	0.0144328	−	0.0249983i
$96$		0			0
$97$	92.7052			0.955724			0.477862	−	0.878435i	$-0.341412\pi$
$97$	92.7052			0.955724			0.477862	+	0.878435i	$0.341412\pi$
$98$	74.7886	−	43.1792i	0.763149	−	0.440604i
$99$		0			0
$100$	−17.3848	+	30.1114i	−0.173848	+	0.301114i
$101$	88.2982	−	152.937i	0.874240	−	1.51423i	0.0166694	−	0.999861i	$-0.494694\pi$
$101$	88.2982	−	152.937i	0.874240	−	1.51423i	0.857570	−	0.514367i	$-0.171973\pi$
$102$		0			0
$103$	29.4957	−	51.0880i	0.286366	−	0.496000i	−0.686574	−	0.727060i	$-0.740886\pi$
$103$	29.4957	−	51.0880i	0.286366	−	0.496000i	0.972939	+	0.231060i	$0.0742194\pi$
$104$	159.969	+	92.3579i	1.53816	+	0.888057i
$105$		0			0
$106$	118.909	−	68.6523i	1.12179	−	0.647663i
$107$	−70.0090			−0.654290			−0.327145	−	0.944974i	$-0.606086\pi$
$107$	−70.0090			−0.654290			−0.327145	+	0.944974i	$0.606086\pi$
$108$		0			0
$109$	12.0709	+	20.9075i	0.110743	+	0.191812i	0.916070	−	0.401019i	$-0.131344\pi$
$109$	12.0709	+	20.9075i	0.110743	+	0.191812i	−0.805327	+	0.592830i	$0.798010\pi$
$110$	−2.28126	−	3.95126i	−0.0207388	−	0.0359206i
$111$		0			0
$112$	74.0711	+	42.7649i	0.661349	+	0.381830i
$113$		−	65.8091i		−	0.582382i	−0.956665	−	0.291191i	$-0.905949\pi$
$113$		−	65.8091i		−	0.582382i	0.956665	−	0.291191i	$-0.0940514\pi$
$114$		0			0
$115$	2.14773	+	1.23999i	0.0186759	+	0.0107825i
$116$	−65.1464	−	37.6123i	−0.561607	−	0.324244i
$117$		0			0
$118$		−	119.535i		−	1.01301i
$119$	−218.308	+	126.040i	−1.83452	+	1.05916i
$120$		0			0
$121$	−67.1810			−0.555215
$122$	5.03825	−	8.72650i	0.0412971	−	0.0715287i
$123$		0			0
$124$	−2.41781	−	4.18777i	−0.0194985	−	0.0337723i
$125$		−	19.2244i		−	0.153795i
$126$		0			0
$127$	215.711			1.69851			0.849257	−	0.527980i	$-0.177050\pi$
$127$	215.711			1.69851			0.849257	+	0.527980i	$0.177050\pi$
$128$			24.8125i			0.193848i
$129$		0			0
$130$	−13.1935			−0.101488
$131$		−	174.387i		−	1.33120i	−0.746309	−	0.665600i	$-0.768176\pi$
$131$		−	174.387i		−	1.33120i	0.746309	−	0.665600i	$-0.231824\pi$
$132$		0			0
$133$	72.0098			0.541427
$134$	40.9707	−	23.6544i	0.305752	−	0.176526i
$135$		0			0
$136$	−187.711	−	108.375i	−1.38023	−	0.796874i
$137$			9.42030i			0.0687613i	0.999409	+	0.0343807i	$0.0109459\pi$
$137$			9.42030i			0.0687613i	−0.999409	+	0.0343807i	$0.989054\pi$
$138$		0			0
$139$	13.8244	+	23.9446i	0.0994561	+	0.172263i	0.911460	−	0.411389i	$-0.134956\pi$
$139$	13.8244	+	23.9446i	0.0994561	+	0.172263i	−0.812004	+	0.583652i	$0.801623\pi$
$140$	5.46376			0.0390268
$141$		0			0
$142$	−79.4061	+	137.535i	−0.559198	+	0.968559i
$143$	77.8142	−	134.778i	0.544155	−	0.942504i
$144$		0			0
$145$	20.7341			0.142994
$146$	−69.9819	+	121.212i	−0.479328	+	0.830221i
$147$		0			0
$148$	12.3617	−	7.13702i	0.0835248	−	0.0482231i
$149$	149.349	−	86.2265i	1.00234	−	0.578701i	0.0934005	−	0.995629i	$-0.470226\pi$
$149$	149.349	−	86.2265i	1.00234	−	0.578701i	0.908940	+	0.416927i	$0.136893\pi$
$150$		0			0
$151$			123.932i			0.820743i	0.911919	+	0.410371i	$0.134601\pi$
$151$			123.932i			0.820743i	−0.911919	+	0.410371i	$0.865399\pi$
$152$	30.9586	+	53.6218i	0.203675	+	0.352775i
$153$		0			0
$154$	59.9049	−	103.758i	0.388993	−	0.673756i
$155$	1.15427	+	0.666418i	0.00744690	+	0.00429947i
$156$		0			0
$157$	146.441	+	84.5479i	0.932747	+	0.538521i	0.887679	−	0.460462i	$-0.152316\pi$
$157$	146.441	+	84.5479i	0.932747	+	0.538521i	0.0450674	+	0.998984i	$0.485650\pi$
$158$	−201.312	−	116.228i	−1.27413	−	0.735618i
$159$		0			0
$160$	4.08927	+	7.08282i	0.0255579	+	0.0442676i
$161$			65.1233i			0.404493i
$162$		0			0
$163$	106.675	+	61.5888i	0.654448	+	0.377846i	0.790158	−	0.612903i	$-0.209998\pi$
$163$	106.675	+	61.5888i	0.654448	+	0.377846i	−0.135710	+	0.990749i	$0.543332\pi$
$164$	−74.4384			−0.453892
$165$		0			0
$166$	−19.1065	+	11.0311i	−0.115099	+	0.0664526i
$167$	80.7138	+	139.800i	0.483316	+	0.837128i	0.999816	−	0.0191590i	$-0.00609886\pi$
$167$	80.7138	+	139.800i	0.483316	+	0.837128i	−0.516500	+	0.856287i	$0.672766\pi$
$168$		0			0
$169$	−140.515	−	243.380i	−0.831451	−	1.44012i
$170$	15.4815			0.0910676
$171$		0			0
$172$	−29.4844	−	52.4414i	−0.171421	−	0.304892i
$173$	−98.5221			−0.569492			−0.284746	−	0.958603i	$-0.591909\pi$
$173$	−98.5221			−0.569492			−0.284746	+	0.958603i	$0.591909\pi$
$174$		0			0
$175$	217.943	−	125.830i	1.24539	−	0.719026i
$176$	61.9615			0.352054
$177$		0			0
$178$	100.978	+	174.900i	0.567294	+	0.982583i
$179$	−84.4071	−	48.7324i	−0.471548	−	0.272248i	0.245340	−	0.969437i	$-0.421101\pi$
$179$	−84.4071	−	48.7324i	−0.471548	−	0.272248i	−0.716887	+	0.697189i	$0.754434\pi$
$180$		0			0
$181$	54.0675	−	93.6477i	0.298715	−	0.517390i	−0.677127	−	0.735866i	$-0.736775\pi$
$181$	54.0675	−	93.6477i	0.298715	−	0.517390i	0.975842	+	0.218476i	$0.0701085\pi$
$182$	−173.227	−	300.038i	−0.951797	−	1.64856i
$183$		0			0
$184$	−48.4938	+	27.9979i	−0.263553	+	0.152163i
$185$	−1.96717	+	3.40724i	−0.0106333	+	0.0184175i
$186$		0			0
$187$	−91.3089	+	158.152i	−0.488283	+	0.845731i
$188$	83.3597			0.443403
$189$		0			0
$190$	−3.82998	−	2.21124i	−0.0201578	−	0.0116381i
$191$	21.8539	−	12.6173i	0.114418	−	0.0660593i	−0.441699	−	0.897163i	$-0.645624\pi$
$191$	21.8539	−	12.6173i	0.114418	−	0.0660593i	0.556117	+	0.831104i	$0.312291\pi$
$192$		0			0
$193$	−274.129			−1.42036			−0.710179	−	0.704021i	$-0.751386\pi$
$193$	−274.129			−1.42036			−0.710179	+	0.704021i	$0.751386\pi$
$194$		−	149.508i		−	0.770661i
$195$		0			0
$196$	37.4598	+	64.8822i	0.191121	+	0.331032i
$197$	−43.2189	+	74.8573i	−0.219385	+	0.379987i	−0.954620	−	0.297826i	$-0.903739\pi$
$197$	−43.2189	+	74.8573i	−0.219385	+	0.379987i	0.735235	+	0.677812i	$0.237072\pi$
$198$		0			0
$199$		−	375.894i		−	1.88891i	−0.328637	−	0.944456i	$-0.606589\pi$
$199$		−	375.894i		−	1.88891i	0.328637	−	0.944456i	$-0.393411\pi$
$200$	187.397	+	108.194i	0.936985	+	0.540969i
$201$		0			0
$202$	−246.646	−	142.401i	−1.22102	−	0.704955i
$203$	272.234	+	471.523i	1.34105	+	2.32277i
$204$		0			0
$205$	17.7686	−	10.2587i	0.0866759	−	0.0500424i
$206$	−82.3911	−	47.5685i	−0.399957	−	0.230915i
$207$		0			0
$208$	89.5870	−	155.169i	0.430707	−	0.746006i
$209$	45.1779	−	26.0835i	0.216162	−	0.124801i
$210$		0			0
$211$			251.436i			1.19164i	0.803117	+	0.595821i	$0.203173\pi$
$211$			251.436i			1.19164i	−0.803117	+	0.595821i	$0.796827\pi$
$212$	59.5587	+	103.159i	0.280937	+	0.486598i
$213$		0			0
$214$			112.905i			0.527596i
$215$	14.2652	+	8.45446i	0.0663496	+	0.0393231i
$216$		0			0
$217$			34.9997i			0.161289i
$218$	33.7181	−	19.4671i	0.154670	−	0.0892988i
$219$		0			0
$220$	3.42788	−	1.97909i	0.0155813	−	0.00899586i
$221$	264.038	+	457.327i	1.19474	+	2.06935i
$222$		0			0
$223$		−	81.3499i		−	0.364798i	−0.983225	−	0.182399i	$-0.941614\pi$
$223$		−	81.3499i		−	0.364798i	0.983225	−	0.182399i	$-0.0583862\pi$
$224$	−107.382	+	185.992i	−0.479385	+	0.830320i
$225$		0			0
$226$	−106.132			−0.469612
$227$	−126.922	+	73.2784i	−0.559128	+	0.322812i	−0.752795	−	0.658255i	$-0.771295\pi$
$227$	−126.922	+	73.2784i	−0.559128	+	0.322812i	0.193668	+	0.981067i	$0.437962\pi$
$228$		0			0
$229$	−155.206	+	268.824i	−0.677754	+	1.17390i	0.297902	+	0.954596i	$0.403713\pi$
$229$	−155.206	+	268.824i	−0.677754	+	1.17390i	−0.975656	+	0.219308i	$0.929620\pi$
$230$	1.99977	−	3.46370i	0.00869466	−	0.0150596i
$231$		0			0
$232$	−234.078	+	405.436i	−1.00896	+	1.74757i
$233$	−58.9036	−	34.0080i	−0.252805	−	0.145957i	0.368243	−	0.929730i	$-0.379959\pi$
$233$	−58.9036	−	34.0080i	−0.252805	−	0.145957i	−0.621048	+	0.783773i	$0.713293\pi$
$234$		0			0
$235$	−19.8981	+	11.4882i	−0.0846728	+	0.0488859i
$236$	103.702			0.439414
$237$		0			0
$238$	203.269	+	352.071i	0.854070	+	1.47929i
$239$	−77.5666	−	134.349i	−0.324547	−	0.562131i	0.656874	−	0.754000i	$-0.271878\pi$
$239$	−77.5666	−	134.349i	−0.324547	−	0.562131i	−0.981421	+	0.191869i	$0.938545\pi$
$240$		0			0
$241$	−69.9038	−	40.3590i	−0.290057	−	0.167465i	0.347910	−	0.937528i	$-0.386891\pi$
$241$	−69.9038	−	40.3590i	−0.290057	−	0.167465i	−0.637968	+	0.770063i	$0.720225\pi$
$242$			108.345i			0.447705i
$243$		0			0
$244$	7.57060	+	4.37089i	0.0310270	+	0.0179135i
$245$	−17.8834	−	10.3250i	−0.0729936	−	0.0421429i
$246$		0			0
$247$		−	150.851i		−	0.610734i
$248$	−26.0624	+	15.0471i	−0.105090	+	0.0606739i
$249$		0			0
$250$	−31.0037			−0.124015
$251$	72.0487	−	124.792i	0.287047	−	0.497180i	−0.686057	−	0.727548i	$-0.740660\pi$
$251$	72.0487	−	124.792i	0.287047	−	0.497180i	0.973103	+	0.230369i	$0.0739932\pi$
$252$		0			0
$253$	23.5891	+	40.8574i	0.0932374	+	0.161492i
$254$		−	347.884i		−	1.36962i
$255$		0			0
$256$	−231.932			−0.905984
$257$		−	269.399i		−	1.04825i	−0.851643	−	0.524123i	$-0.824393\pi$
$257$		−	269.399i		−	1.04825i	0.851643	−	0.524123i	$-0.175607\pi$
$258$		0			0
$259$	−103.314			−0.398896
$260$		−	11.4459i		−	0.0440226i
$261$		0			0
$262$	−281.239			−1.07343
$263$	−187.134	+	108.042i	−0.711537	+	0.410806i	−0.811630	−	0.584172i	$-0.801419\pi$
$263$	−187.134	+	108.042i	−0.711537	+	0.410806i	0.100093	+	0.994978i	$0.468086\pi$
$264$		0			0
$265$	−28.4336	−	16.4161i	−0.107296	−	0.0619476i
$266$		−	116.132i		−	0.436587i
$267$		0			0
$268$	20.5212	+	35.5438i	0.0765717	+	0.132626i
$269$	−261.786			−0.973184			−0.486592	−	0.873629i	$-0.661760\pi$
$269$	−261.786			−0.973184			−0.486592	+	0.873629i	$0.661760\pi$
$270$		0			0
$271$	−83.2448	+	144.184i	−0.307176	+	0.532045i	−0.977744	−	0.209804i	$-0.932717\pi$
$271$	−83.2448	+	144.184i	−0.307176	+	0.532045i	0.670567	+	0.741849i	$0.266051\pi$
$272$	−105.123	+	182.079i	−0.386483	+	0.669409i
$273$		0			0
$274$	15.1924			0.0554467
$275$	91.1563	−	157.887i	0.331477	−	0.574136i
$276$		0			0
$277$	257.421	−	148.622i	0.929317	−	0.536542i	0.0427217	−	0.999087i	$-0.486397\pi$
$277$	257.421	−	148.622i	0.929317	−	0.536542i	0.886596	+	0.462545i	$0.153064\pi$
$278$	38.6161	−	22.2950i	0.138907	−	0.0801978i
$279$		0			0
$280$		−	34.0035i		−	0.121441i
$281$	136.626	+	236.643i	0.486213	+	0.842146i	0.999874	−	0.0158469i	$-0.00504443\pi$
$281$	136.626	+	236.643i	0.486213	+	0.842146i	−0.513661	+	0.857993i	$0.671711\pi$
$282$		0			0
$283$	−93.1155	+	161.281i	−0.329030	+	0.569897i	−0.982320	−	0.187211i	$-0.940055\pi$
$283$	−93.1155	+	161.281i	−0.329030	+	0.569897i	0.653289	+	0.757108i	$0.273388\pi$
$284$	−119.318	−	68.8881i	−0.420133	−	0.242564i
$285$		0			0
$286$	−217.360	−	125.493i	−0.760002	−	0.438787i
$287$	466.595	+	269.389i	1.62577	+	0.938636i
$288$		0			0
$289$	−165.328	−	286.357i	−0.572070	−	0.990854i
$290$		−	33.4384i		−	0.115305i
$291$		0			0
$292$	−105.157	−	60.7122i	−0.360125	−	0.207919i
$293$	−354.967			−1.21149			−0.605746	−	0.795658i	$-0.707125\pi$
$293$	−354.967			−1.21149			−0.605746	+	0.795658i	$0.707125\pi$
$294$		0			0
$295$	−24.7538	+	14.2916i	−0.0839110	+	0.0484461i
$296$	−44.4169	−	76.9324i	−0.150057	−	0.259907i
$297$		0			0
$298$	−139.060	−	240.859i	−0.466644	−	0.808251i
$299$	136.425			0.456271
$300$		0			0
$301$	−4.96823	+	435.415i	−0.0165057	+	1.44656i
$302$	199.869			0.661817
$303$		0			0
$304$	52.0131	−	30.0298i	0.171096	−	0.0987822i
$305$	−2.40949			−0.00789996
$306$		0			0
$307$	−0.432779	−	0.749596i	−0.00140970	−	0.00244168i	0.865320	−	0.501220i	$-0.167115\pi$
$307$	−0.432779	−	0.749596i	−0.00140970	−	0.00244168i	−0.866729	+	0.498779i	$0.833782\pi$
$308$	90.0147	+	51.9700i	0.292256	+	0.168734i
$309$		0			0
$310$	1.07475	−	1.86152i	0.00346694	−	0.00600491i
$311$	−43.8480	−	75.9470i	−0.140990	−	0.244203i	0.786879	−	0.617107i	$-0.211695\pi$
$311$	−43.8480	−	75.9470i	−0.140990	−	0.244203i	−0.927870	+	0.372904i	$0.878362\pi$
$312$		0			0
$313$	−71.8241	+	41.4677i	−0.229470	+	0.132485i	−0.610328	−	0.792149i	$-0.708962\pi$
$313$	−71.8241	+	41.4677i	−0.229470	+	0.132485i	0.380858	+	0.924634i	$0.375629\pi$
$314$	136.353	−	236.170i	0.434244	−	0.752133i
$315$		0			0
$316$	100.832	−	174.647i	0.319090	−	0.552680i
$317$	282.584			0.891432			0.445716	−	0.895174i	$-0.352949\pi$
$317$	282.584			0.891432			0.445716	+	0.895174i	$0.352949\pi$
$318$		0			0
$319$	341.591	+	197.218i	1.07082	+	0.618238i
$320$	22.7056	−	13.1091i	0.0709549	−	0.0409658i
$321$		0			0
$322$	105.026			0.326168
$323$			177.012i			0.548026i
$324$		0			0
$325$	−263.597	−	456.563i	−0.811067	−	1.40481i
$326$	99.3260	−	172.038i	0.304681	−	0.527723i
$327$		0			0
$328$			463.264i			1.41239i
$329$	−522.516	−	301.675i	−1.58819	−	0.916944i
$330$		0			0
$331$	−87.2813	−	50.3919i	−0.263690	−	0.152241i	0.362327	−	0.932051i	$-0.381982\pi$
$331$	−87.2813	−	50.3919i	−0.263690	−	0.152241i	−0.626017	+	0.779810i	$0.715316\pi$
$332$	−9.56996	−	16.5757i	−0.0288252	−	0.0499267i
$333$		0			0
$334$	225.460	−	130.169i	0.675030	−	0.389729i
$335$	−9.79690	−	5.65624i	−0.0292445	−	0.0168843i
$336$		0			0
$337$	−162.270	+	281.060i	−0.481513	+	0.834006i	−0.999775	−	0.0212164i	$-0.993246\pi$
$337$	−162.270	+	281.060i	−0.481513	+	0.834006i	0.518261	+	0.855222i	$0.326579\pi$
$338$	−392.505	+	226.613i	−1.16126	+	0.670452i
$339$		0			0
$340$			13.4308i			0.0395025i
$341$	12.6776	+	21.9583i	0.0371778	+	0.0643939i
$342$		0			0
$343$		−	46.0562i		−	0.134275i
$344$	−326.367	+	183.495i	−0.948740	+	0.533416i
$345$		0			0
$346$			158.889i			0.459218i
$347$	−158.881	+	91.7301i	−0.457871	+	0.264352i	−0.711149	−	0.703042i	$-0.751825\pi$
$347$	−158.881	+	91.7301i	−0.457871	+	0.264352i	0.253278	+	0.967394i	$0.418491\pi$
$348$		0			0
$349$	−2.07679	+	1.19903i	−0.00595067	+	0.00343562i	−0.502972	−	0.864302i	$-0.667760\pi$
$349$	−2.07679	+	1.19903i	−0.00595067	+	0.00343562i	0.497022	+	0.867738i	$0.334427\pi$
$350$	−202.929	−	351.483i	−0.579797	−	1.00424i
$351$		0			0
$352$			155.585i			0.442002i
$353$	92.2563	−	159.793i	0.261349	−	0.452670i	−0.705252	−	0.708957i	$-0.749166\pi$
$353$	92.2563	−	159.793i	0.261349	−	0.452670i	0.966601	+	0.256287i	$0.0824993\pi$
$354$		0			0
$355$	37.9751			0.106972
$356$	−151.733	+	87.6030i	−0.426216	+	0.246076i
$357$		0			0
$358$	−78.5922	+	136.126i	−0.219531	+	0.380239i
$359$	−217.377	+	376.509i	−0.605508	+	1.04877i	0.386463	+	0.922305i	$0.373697\pi$
$359$	−217.377	+	376.509i	−0.605508	+	1.04877i	−0.991971	+	0.126466i	$0.959637\pi$
$360$		0			0
$361$	−155.217	+	268.844i	−0.429964	+	0.744720i
$362$	−151.028	−	87.1962i	−0.417205	−	0.240873i
$363$		0			0
$364$	260.296	−	150.282i	0.715098	−	0.412862i
$365$	33.4681			0.0916934
$366$		0			0
$367$	−57.2243	−	99.1154i	−0.155924	−	0.270069i	0.777471	−	0.628919i	$-0.216502\pi$
$367$	−57.2243	−	99.1154i	−0.155924	−	0.270069i	−0.933395	+	0.358850i	$0.883169\pi$
$368$	27.1579	+	47.0389i	0.0737988	+	0.127823i
$369$		0			0
$370$	5.49495	+	3.17251i	0.0148512	+	0.00857435i
$371$		−	862.160i		−	2.32388i
$372$		0			0
$373$	303.292	+	175.106i	0.813115	+	0.469452i	0.848036	−	0.529938i	$-0.177785\pi$
$373$	303.292	+	175.106i	0.813115	+	0.469452i	−0.0349216	+	0.999390i	$0.511118\pi$
$374$	255.056	+	147.256i	0.681967	+	0.393734i
$375$		0			0
$376$		−	518.786i		−	1.37975i
$377$	987.779	−	570.295i	2.62010	−	1.51272i
$378$		0			0
$379$	−467.025			−1.23226			−0.616128	−	0.787646i	$-0.711299\pi$
$379$	−467.025			−1.23226			−0.616128	+	0.787646i	$0.711299\pi$
$380$	1.91834	−	3.32266i	0.00504826	−	0.00874385i
$381$		0			0
$382$	−20.3483	−	35.2443i	−0.0532679	−	0.0922626i
$383$		−	614.784i		−	1.60518i	−0.596530	−	0.802591i	$-0.703454\pi$
$383$		−	614.784i		−	1.60518i	0.596530	−	0.802591i	$-0.296546\pi$
$384$		0			0
$385$	−28.6489			−0.0744127
$386$			442.096i			1.14533i
$387$		0			0
$388$	129.705			0.334290
$389$			408.740i			1.05075i	0.850872	+	0.525373i	$0.176074\pi$
$389$			408.740i			1.05075i	−0.850872	+	0.525373i	$0.823926\pi$
$390$		0			0
$391$	−160.084			−0.409422
$392$	403.792	−	233.129i	1.03008	−	0.594718i
$393$		0			0
$394$	120.725	+	69.7003i	0.306407	+	0.176904i
$395$			55.5847i			0.140721i
$396$		0			0
$397$	−176.548	−	305.791i	−0.444706	−	0.770254i	0.553325	−	0.832965i	$-0.313359\pi$
$397$	−176.548	−	305.791i	−0.444706	−	0.770254i	−0.998032	+	0.0627113i	$0.980025\pi$
$398$	−606.214			−1.52315
$399$		0			0
$400$	104.948	−	181.775i	0.262369	−	0.454437i
$401$	−163.248	+	282.754i	−0.407103	+	0.705123i	−0.994564	−	0.104129i	$-0.966794\pi$
$401$	−163.248	+	282.754i	−0.407103	+	0.705123i	0.587461	+	0.809253i	$0.300128\pi$
$402$		0			0
$403$	73.3198			0.181935
$404$	123.539	−	213.975i	0.305789	−	0.529642i
$405$		0			0
$406$	760.438	−	439.039i	1.87300	−	1.08138i
$407$	−64.8177	+	37.4225i	−0.159257	+	0.0919472i
$408$		0			0
$409$			649.478i			1.58797i	0.607940	+	0.793983i	$0.291996\pi$
$409$			649.478i			1.58797i	−0.607940	+	0.793983i	$0.708004\pi$
$410$	−16.5445	−	28.6559i	−0.0403524	−	0.0698923i
$411$		0			0
$412$	41.2677	−	71.4777i	0.100164	−	0.173490i
$413$	−650.023	−	375.291i	−1.57390	−	0.908694i
$414$		0			0
$415$	4.56873	+	2.63776i	0.0110090	+	0.00635605i
$416$	389.629	+	224.952i	0.936607	+	0.540750i
$417$		0			0
$418$	−42.0656	−	72.8597i	−0.100635	−	0.174306i
$419$			193.021i			0.460670i	0.973111	+	0.230335i	$0.0739822\pi$
$419$			193.021i			0.460670i	−0.973111	+	0.230335i	$0.926018\pi$
$420$		0			0
$421$	201.399	+	116.278i	0.478383	+	0.276194i	0.719742	−	0.694241i	$-0.244260\pi$
$421$	201.399	+	116.278i	0.478383	+	0.276194i	−0.241360	+	0.970436i	$0.577593\pi$
$422$	405.498			0.960897
$423$		0			0
$424$	642.004	−	370.661i	1.51416	−	0.874201i
$425$	309.310	+	535.741i	0.727789	+	1.26057i
$426$		0			0
$427$	−31.6360	−	54.7952i	−0.0740891	−	0.128326i
$428$	−97.9502			−0.228856
$429$		0			0
$430$	13.6347	−	23.0058i	0.0317087	−	0.0535019i
$431$	−331.585			−0.769339			−0.384670	−	0.923054i	$-0.625685\pi$
$431$	−331.585			−0.769339			−0.384670	+	0.923054i	$0.625685\pi$
$432$		0			0
$433$	−302.455	+	174.622i	−0.698510	+	0.403285i	−0.806792	−	0.590835i	$-0.798798\pi$
$433$	−302.455	+	174.622i	−0.698510	+	0.403285i	0.108282	+	0.994120i	$0.465465\pi$
$434$	56.4450			0.130058
$435$		0			0
$436$	16.8886	+	29.2518i	0.0387352	+	0.0670913i
$437$	39.6033	+	22.8650i	0.0906254	+	0.0523226i
$438$		0			0
$439$	250.069	−	433.132i	0.569633	−	0.986633i	−0.426969	−	0.904266i	$-0.640419\pi$
$439$	250.069	−	433.132i	0.569633	−	0.986633i	0.996602	−	0.0823671i	$-0.0262480\pi$
$440$	−12.3168	−	21.3333i	−0.0279927	−	0.0484848i
$441$		0			0
$442$	737.544	−	425.821i	1.66865	−	0.963397i
$443$	−138.034	+	239.082i	−0.311590	+	0.539689i	−0.978707	−	0.205264i	$-0.934195\pi$
$443$	−138.034	+	239.082i	−0.311590	+	0.539689i	0.667117	+	0.744953i	$0.267528\pi$
$444$		0			0
$445$	24.1459	−	41.8220i	0.0542605	−	0.0939819i
$446$	−131.195			−0.294160
$447$		0			0
$448$	596.238	+	344.238i	1.33089	+	0.768389i
$449$	−433.225	+	250.123i	−0.964867	+	0.557066i	−0.897668	−	0.440673i	$-0.854740\pi$
$449$	−433.225	+	250.123i	−0.964867	+	0.557066i	−0.0671997	+	0.997740i	$0.521406\pi$
$450$		0			0
$451$	390.313			0.865439
$452$		−	92.0741i		−	0.203704i
$453$		0			0
$454$	118.178	+	204.691i	0.260304	+	0.450860i
$455$	−41.4220	+	71.7450i	−0.0910374	+	0.157681i
$456$		0			0
$457$		−	258.910i		−	0.566543i	−0.959040	−	0.283271i	$-0.908580\pi$
$457$		−	258.910i		−	0.566543i	0.959040	−	0.283271i	$-0.0914197\pi$
$458$	433.540	+	250.304i	0.946594	+	0.546516i
$459$		0			0
$460$	3.00491	+	1.73488i	0.00653241	+	0.00377149i
$461$	−227.217	−	393.551i	−0.492878	−	0.853689i	0.507089	−	0.861894i	$-0.330722\pi$
$461$	−227.217	−	393.551i	−0.492878	−	0.853689i	−0.999966	+	0.00820488i	$0.997388\pi$
$462$		0			0
$463$	734.960	−	424.330i	1.58739	−	0.916479i	0.593652	−	0.804722i	$-0.297686\pi$
$463$	734.960	−	424.330i	1.58739	−	0.916479i	0.993736	−	0.111757i	$-0.0356477\pi$
$464$	393.272	+	227.056i	0.847569	+	0.489344i
$465$		0			0
$466$	−54.8456	+	94.9954i	−0.117694	+	0.203853i
$467$	662.404	−	382.439i	1.41843	−	0.818928i	0.422264	−	0.906473i	$-0.361235\pi$
$467$	662.404	−	382.439i	1.41843	−	0.818928i	0.996161	+	0.0875446i	$0.0279020\pi$
$468$		0			0
$469$		−	297.061i		−	0.633392i
$470$	18.5273	+	32.0902i	0.0394198	+	0.0682771i
$471$		0			0
$472$		−	645.383i		−	1.36734i
$473$	154.600	+	274.973i	0.326850	+	0.581339i
$474$		0			0
$475$		−	176.716i		−	0.372034i
$476$	−305.437	+	176.344i	−0.641674	+	0.370470i
$477$		0			0
$478$	−216.669	+	125.094i	−0.453282	+	0.261703i
$479$	279.227	+	483.636i	0.582938	+	1.00968i	0.995129	+	0.0985807i	$0.0314302\pi$
$479$	279.227	+	483.636i	0.582938	+	1.00968i	−0.412191	+	0.911097i	$0.635236\pi$
$480$		0			0
$481$			216.429i			0.449957i
$482$	−65.0880	+	112.736i	−0.135037	+	0.233892i
$483$		0			0
$484$	−93.9935			−0.194201
$485$	−30.9607	+	17.8752i	−0.0638366	+	0.0368561i
$486$		0			0
$487$	285.388	−	494.307i	0.586013	−	1.01500i	−0.408736	−	0.912653i	$-0.634030\pi$
$487$	285.388	−	494.307i	0.586013	−	1.01500i	0.994748	−	0.102351i	$-0.0326365\pi$
$488$	27.2020	−	47.1153i	0.0557419	−	0.0965478i
$489$		0			0
$490$	−16.6514	+	28.8411i	−0.0339825	+	0.0588594i
$491$	−1.46902	−	0.848142i	−0.00299190	−	0.00172738i	0.498503	−	0.866888i	$-0.333883\pi$
$491$	−1.46902	−	0.848142i	−0.00299190	−	0.00172738i	−0.501495	+	0.865160i	$0.667217\pi$
$492$		0			0
$493$	−1159.08	+	669.196i	−2.35108	+	1.35740i
$494$	−243.282			−0.492474
$495$		0			0
$496$	14.5957	+	25.2805i	0.0294268	+	0.0509687i
$497$	498.605	+	863.609i	1.00323	+	1.73764i
$498$		0			0
$499$	−248.989	−	143.754i	−0.498975	−	0.288083i	0.229315	−	0.973352i	$-0.426351\pi$
$499$	−248.989	−	143.754i	−0.498975	−	0.288083i	−0.728290	+	0.685269i	$0.759685\pi$
$500$		−	26.8970i		−	0.0537940i
$501$		0			0
$502$	−201.256	−	116.195i	−0.400908	−	0.231464i
$503$	−393.036	−	226.919i	−0.781383	−	0.451132i	0.0555370	−	0.998457i	$-0.482313\pi$
$503$	−393.036	−	226.919i	−0.781383	−	0.451132i	−0.836920	+	0.547325i	$0.815646\pi$
$504$		0			0
$505$			68.1018i			0.134855i
$506$	65.8919	−	38.0427i	0.130221	−	0.0751833i
$507$		0			0
$508$	301.804			0.594101
$509$	49.8513	−	86.3449i	0.0979396	−	0.169636i	−0.812892	−	0.582414i	$-0.802108\pi$
$509$	49.8513	−	86.3449i	0.0979396	−	0.169636i	0.910832	+	0.412778i	$0.135441\pi$
$510$		0			0
$511$	439.429	+	761.113i	0.859939	+	1.48946i
$512$			473.293i			0.924401i
$513$		0			0
$514$	−434.468			−0.845268
$515$			22.7491i			0.0441731i
$516$		0			0
$517$	−437.092			−0.845439
$518$			166.617i			0.321655i
$519$		0			0
$520$	−71.2329			−0.136986
$521$	−41.7631	+	24.1119i	−0.0801595	+	0.0462801i	−0.539544	−	0.841957i	$-0.681403\pi$
$521$	−41.7631	+	24.1119i	−0.0801595	+	0.0462801i	0.459384	+	0.888238i	$0.348070\pi$
$522$		0			0
$523$	289.165	+	166.949i	0.552897	+	0.319215i	0.750289	−	0.661109i	$-0.229914\pi$
$523$	289.165	+	166.949i	0.552897	+	0.319215i	−0.197393	+	0.980324i	$0.563247\pi$
$524$		−	243.987i		−	0.465623i
$525$		0			0
$526$	174.242	+	301.797i	0.331259	+	0.573758i
$527$	−86.0351			−0.163254
$528$		0			0
$529$	243.822	−	422.312i	0.460911	−	0.798320i
$530$	−26.4747	+	45.8556i	−0.0499523	+	0.0865200i
$531$		0			0
$532$	100.750			0.189379
$533$	564.334	−	977.455i	1.05879	−	1.83388i
$534$		0			0
$535$	23.3809	−	13.4990i	0.0437026	−	0.0252317i
$536$	221.205	−	127.713i	0.412696	−	0.238270i
$537$		0			0
$538$			422.190i			0.784740i
$539$	−196.418	−	340.206i	−0.364412	−	0.631180i
$540$		0			0
$541$	179.694	−	311.238i	0.332151	−	0.575302i	−0.650783	−	0.759264i	$-0.725559\pi$
$541$	179.694	−	311.238i	0.332151	−	0.575302i	0.982933	+	0.183962i	$0.0588924\pi$
$542$	232.530	+	134.251i	0.429022	+	0.247696i
$543$		0			0
$544$	−457.199	−	263.964i	−0.840439	−	0.485228i
$545$	−8.06265	−	4.65497i	−0.0147939	−	0.00854124i
$546$		0			0
$547$	251.007	+	434.757i	0.458879	+	0.794803i	0.998902	−	0.0468480i	$-0.0149176\pi$
$547$	251.007	+	434.757i	0.458879	+	0.794803i	−0.540023	+	0.841651i	$0.681584\pi$
$548$			13.1800i			0.0240511i
$549$		0			0
$550$	−254.629	−	147.010i	−0.462962	−	0.267291i
$551$	382.328			0.693880
$552$		0			0
$553$	−1264.08	+	729.814i	−2.28585	+	1.31974i
$554$	−239.687	−	415.150i	−0.432648	−	0.749368i
$555$		0			0
$556$	19.3418	+	33.5010i	0.0347875	+	0.0602537i
$557$	−696.827			−1.25104			−0.625518	−	0.780210i	$-0.715112\pi$
$557$	−696.827			−1.25104			−0.625518	+	0.780210i	$0.715112\pi$
$558$		0			0
$559$	912.139	+	10.4078i	1.63173	+	0.0186186i
$560$	−32.9833			−0.0588988
$561$		0			0
$562$	381.641	−	220.341i	0.679076	−	0.392065i
$563$	−710.021			−1.26114			−0.630569	−	0.776133i	$-0.717179\pi$
$563$	−710.021			−1.26114			−0.630569	+	0.776133i	$0.717179\pi$
$564$		0			0
$565$	12.6891	+	21.9782i	0.0224587	+	0.0388996i
$566$	260.102	+	150.170i	0.459544	+	0.265318i
$567$		0			0
$568$	−428.722	+	742.569i	−0.754793	+	1.30734i
$569$	−208.568	−	361.250i	−0.366551	−	0.634885i	0.622473	−	0.782642i	$-0.286128\pi$
$569$	−208.568	−	361.250i	−0.366551	−	0.634885i	−0.989024	+	0.147756i	$0.952795\pi$
$570$		0			0
$571$	304.333	−	175.707i	0.532983	−	0.307718i	−0.209248	−	0.977863i	$-0.567101\pi$
$571$	304.333	−	175.707i	0.532983	−	0.307718i	0.742230	+	0.670145i	$0.233768\pi$
$572$	108.870	−	188.569i	0.190333	−	0.329666i
$573$		0			0
$574$	434.450	−	752.490i	0.756882	−	1.31096i
$575$	159.816			0.277942
$576$		0			0
$577$	−21.6967	−	12.5266i	−0.0376027	−	0.0217099i	0.481081	−	0.876676i	$-0.340244\pi$
$577$	−21.6967	−	12.5266i	−0.0376027	−	0.0217099i	−0.518683	+	0.854966i	$0.673578\pi$
$578$	−461.815	+	266.629i	−0.798989	+	0.461296i
$579$		0			0
$580$	29.0092			0.0500159
$581$			138.533i			0.238439i
$582$		0			0
$583$	−312.293	−	540.907i	−0.535665	−	0.927799i
$584$	−377.840	+	654.438i	−0.646986	+	1.12061i
$585$		0			0
$586$			572.465i			0.976903i
$587$	458.434	+	264.677i	0.780978	+	0.450898i	0.836777	−	0.547544i	$-0.184437\pi$
$587$	458.434	+	264.677i	0.780978	+	0.450898i	−0.0557986	+	0.998442i	$0.517770\pi$
$588$		0			0
$589$	21.2843	+	12.2885i	0.0361363	+	0.0208633i
$590$	23.0484	+	39.9211i	0.0390652	+	0.0676628i
$591$		0			0
$592$	−74.6243	+	43.0844i	−0.126055	+	0.0727776i
$593$	−239.671	−	138.374i	−0.404167	−	0.233346i	0.284114	−	0.958791i	$-0.408301\pi$
$593$	−239.671	−	138.374i	−0.404167	−	0.233346i	−0.688280	+	0.725445i	$0.741634\pi$
$594$		0			0
$595$	48.6055	−	84.1872i	0.0816899	−	0.141491i
$596$	208.955	−	120.640i	0.350596	−	0.202417i
$597$		0			0
$598$		−	220.016i		−	0.367920i
$599$	−415.499	−	719.666i	−0.693655	−	1.20145i	−0.970632	−	0.240569i	$-0.922666\pi$
$599$	−415.499	−	719.666i	−0.693655	−	1.20145i	0.276977	−	0.960876i	$-0.410667\pi$
$600$		0			0
$601$			626.307i			1.04211i	0.853524	+	0.521054i	$0.174461\pi$
$601$			626.307i			1.04211i	−0.853524	+	0.521054i	$0.825539\pi$
$602$	702.207	+	8.01240i	1.16646	+	0.0133096i
$603$		0			0
$604$			173.395i			0.287077i
$605$	22.4364	−	12.9537i	0.0370850	−	0.0214110i
$606$		0			0
$607$	188.672	−	108.930i	0.310828	−	0.179456i	−0.336469	−	0.941695i	$-0.609233\pi$
$607$	188.672	−	108.930i	0.310828	−	0.179456i	0.647297	+	0.762238i	$0.275899\pi$
$608$	75.4045	+	130.604i	0.124021	+	0.214810i
$609$		0			0
$610$			3.88585i			0.00637024i
$611$	−631.969	+	1094.60i	−1.03432	+	1.79149i
$612$		0			0
$613$	−1098.16			−1.79145			−0.895727	−	0.444605i	$-0.853344\pi$
$613$	−1098.16			−1.79145			−0.895727	+	0.444605i	$0.853344\pi$
$614$	−1.20889	+	0.697955i	−0.00196888	+	0.00113674i
$615$		0			0
$616$	323.433	−	560.203i	0.525054	−	0.909420i
$617$	75.9594	−	131.565i	0.123111	−	0.213234i	−0.797882	−	0.602814i	$-0.794046\pi$
$617$	75.9594	−	131.565i	0.123111	−	0.213234i	0.920993	+	0.389579i	$0.127380\pi$
$618$		0			0
$619$	119.648	−	207.237i	0.193293	−	0.334793i	−0.753047	−	0.657967i	$-0.771417\pi$
$619$	119.648	−	207.237i	0.193293	−	0.334793i	0.946340	+	0.323174i	$0.104750\pi$
$620$	1.61495	+	0.932391i	0.00260476	+	0.00150386i
$621$		0			0
$622$	−122.482	+	70.7149i	−0.196916	+	0.113690i
$623$	1268.12			2.03551
$624$		0			0
$625$	−306.934	−	531.626i	−0.491095	−	0.850601i
$626$	66.8761	+	115.833i	0.106831	+	0.185036i
$627$		0			0
$628$	204.887	+	118.292i	0.326253	+	0.188363i
$629$		−	253.963i		−	0.403757i
$630$		0			0
$631$	−450.730	−	260.229i	−0.714311	−	0.412408i	0.0983443	−	0.995152i	$-0.468645\pi$
$631$	−450.730	−	260.229i	−0.714311	−	0.412408i	−0.812655	+	0.582745i	$0.801979\pi$
$632$	−1086.91	−	627.526i	−1.71979	−	0.992921i
$633$		0			0
$634$		−	455.731i		−	0.718819i
$635$	−72.0410	+	41.5929i	−0.113450	+	0.0655006i
$636$		0			0
$637$	−1135.96			−1.78330
$638$	318.059	−	550.894i	0.498524	−	0.863470i
$639$		0			0
$640$	−4.78429	−	8.28663i	−0.00747545	−	0.0129479i
$641$			70.9966i			0.110759i	0.998465	+	0.0553795i	$0.0176369\pi$
$641$			70.9966i			0.110759i	−0.998465	+	0.0553795i	$0.982363\pi$
$642$		0			0
$643$	919.604			1.43018			0.715089	−	0.699034i	$-0.246386\pi$
$643$	919.604			1.43018			0.715089	+	0.699034i	$0.246386\pi$
$644$			91.1146i			0.141482i
$645$		0			0
$646$	285.473			0.441908
$647$		−	1180.69i		−	1.82487i	−0.409220	−	0.912436i	$-0.634199\pi$
$647$		−	1180.69i		−	1.82487i	0.409220	−	0.912436i	$-0.365801\pi$
$648$		0			0
$649$	−543.753			−0.837833
$650$	−736.311	+	425.110i	−1.13279	+	0.654015i
$651$		0			0
$652$	149.250	+	86.1695i	0.228911	+	0.132162i
$653$			751.382i			1.15066i	0.817921	+	0.575331i	$0.195127\pi$
$653$			751.382i			1.15066i	−0.817921	+	0.575331i	$0.804873\pi$
$654$		0			0
$655$	33.6249	+	58.2400i	0.0513357	+	0.0889160i
$656$	449.365			0.685008
$657$		0			0
$658$	−486.519	+	842.675i	−0.739390	+	1.28066i
$659$	565.416	−	979.329i	0.857991	−	1.48608i	−0.0158511	−	0.999874i	$-0.505046\pi$
$659$	565.416	−	979.329i	0.857991	−	1.48608i	0.873842	−	0.486210i	$-0.161621\pi$
$660$		0			0
$661$	−856.779			−1.29619			−0.648093	−	0.761561i	$-0.724433\pi$
$661$	−856.779			−1.29619			−0.648093	+	0.761561i	$0.724433\pi$
$662$	−81.2684	+	140.761i	−0.122762	+	0.212630i
$663$		0			0
$664$	−103.158	+	59.5583i	−0.155358	+	0.0896962i
$665$	−24.0491	+	13.8847i	−0.0361640	+	0.0208793i
$666$		0			0
$667$			345.765i			0.518388i
$668$	112.927	+	195.596i	0.169053	+	0.292808i
$669$		0			0
$670$	−9.12198	+	15.7997i	−0.0136149	+	0.0235817i
$671$	−39.6960	−	22.9185i	−0.0591594	−	0.0341557i
$672$		0			0
$673$	841.035	+	485.572i	1.24968	+	0.721503i	0.971046	−	0.238894i	$-0.0767849\pi$
$673$	841.035	+	485.572i	1.24968	+	0.721503i	0.278635	+	0.960397i	$0.410118\pi$
$674$	453.273	+	261.697i	0.672512	+	0.388275i
$675$		0			0
$676$	−196.596	−	340.514i	−0.290823	−	0.503719i
$677$		−	1029.20i		−	1.52024i	−0.649785	−	0.760118i	$-0.725141\pi$
$677$		−	1029.20i		−	1.52024i	0.649785	−	0.760118i	$-0.274859\pi$
$678$		0			0
$679$	−813.015	−	469.394i	−1.19737	−	0.691303i
$680$	83.5863			0.122921
$681$		0			0
$682$	35.4128	−	20.4456i	0.0519249	−	0.0299788i
$683$	138.566	+	240.004i	0.202879	+	0.351397i	0.949455	−	0.313903i	$-0.101637\pi$
$683$	138.566	+	240.004i	0.202879	+	0.351397i	−0.746576	+	0.665300i	$0.768303\pi$
$684$		0			0
$685$	−1.81640	−	3.14610i	−0.00265168	−	0.00459284i
$686$	−74.2762			−0.108274
$687$		0			0
$688$	177.990	+	316.575i	0.258706	+	0.460138i
$689$	−1806.11			−2.62136
$690$		0			0
$691$	−261.885	+	151.199i	−0.378994	+	0.218812i	−0.677380	−	0.735633i	$-0.736885\pi$
$691$	−261.885	+	151.199i	−0.378994	+	0.218812i	0.298387	+	0.954445i	$0.403552\pi$
$692$	−137.843			−0.199195
$693$		0			0
$694$	147.936	+	256.232i	0.213164	+	0.369210i
$695$	−9.23386	−	5.33117i	−0.0132861	−	0.00767075i
$696$		0			0
$697$	−662.202	+	1146.97i	−0.950075	+	1.64558i
$698$	1.93371	+	3.34929i	0.00277036	+	0.00479841i
$699$		0			0
$700$	304.926	−	176.049i	0.435609	−	0.251499i
$701$	535.372	−	927.291i	0.763726	−	1.32281i	−0.177192	−	0.984176i	$-0.556701\pi$
$701$	535.372	−	927.291i	0.763726	−	1.32281i	0.940918	−	0.338635i	$-0.109965\pi$
$702$		0			0
$703$	−36.2738	+	62.8281i	−0.0515986	+	0.0893714i
$704$	498.762			0.708469
$705$		0			0
$706$	−257.702	−	148.784i	−0.365017	−	0.210743i
$707$	−1548.73	+	894.161i	−2.19057	+	1.26473i
$708$		0			0
$709$	−154.620			−0.218082			−0.109041	−	0.994037i	$-0.534778\pi$
$709$	−154.620			−0.218082			−0.109041	+	0.994037i	$0.534778\pi$
$710$		−	61.2435i		−	0.0862585i
$711$		0			0
$712$	545.193	+	944.303i	0.765721	+	1.32627i
$713$	−11.1133	+	19.2488i	−0.0155867	+	0.0269969i
$714$		0			0
$715$			60.0157i			0.0839381i
$716$	−118.095	−	68.1820i	−0.164937	−	0.0952262i
$717$		0			0
$718$	607.206	+	350.571i	0.845691	+	0.488260i
$719$	506.496	+	877.277i	0.704445	+	1.22013i	0.966892	+	0.255188i	$0.0821373\pi$
$719$	506.496	+	877.277i	0.704445	+	1.22013i	−0.262447	+	0.964946i	$0.584529\pi$
$720$		0			0
$721$	−517.348	+	298.691i	−0.717542	+	0.414273i
$722$	433.572	+	250.323i	0.600516	+	0.346708i
$723$		0			0
$724$	75.6463	−	131.023i	0.104484	−	0.180971i
$725$	1157.14	−	668.078i	1.59606	−	0.921487i
$726$		0			0
$727$			217.553i			0.299248i	0.988743	+	0.149624i	$0.0478063\pi$
$727$			217.553i			0.299248i	−0.988743	+	0.149624i	$0.952194\pi$
$728$	−935.272	−	1619.94i	−1.28471	−	2.22519i
$729$		0			0
$730$		−	53.9749i		−	0.0739383i
$731$	−1070.32	−	12.2127i	−1.46419	−	0.0167069i
$732$		0			0
$733$			514.085i			0.701343i	0.936498	+	0.350672i	$0.114047\pi$
$733$			514.085i			0.701343i	−0.936498	+	0.350672i	$0.885953\pi$
$734$	−159.846	+	92.2872i	−0.217774	+	0.125732i
$735$		0			0
$736$	−118.114	+	68.1933i	−0.160481	+	0.0926540i
$737$	−107.602	−	186.372i	−0.146000	−	0.252879i
$738$		0			0
$739$		−	50.9641i		−	0.0689635i	−0.999405	−	0.0344818i	$-0.989022\pi$
$739$		−	50.9641i		−	0.0689635i	0.999405	−	0.0344818i	$-0.0109781\pi$
$740$	−2.75228	+	4.76709i	−0.00371930	+	0.00644202i
$741$		0			0
$742$	−1390.43			−1.87389
$743$	1055.01	−	609.110i	1.41993	−	0.819798i	0.423639	−	0.905831i	$-0.360752\pi$
$743$	1055.01	−	609.110i	1.41993	−	0.819798i	0.996292	+	0.0860329i	$0.0274190\pi$
$744$		0			0
$745$	−33.2520	+	57.5941i	−0.0446335	+	0.0773075i
$746$	282.398	−	489.127i	0.378549	−	0.655666i
$747$		0			0
$748$	−127.751	+	221.271i	−0.170790	+	0.295817i
$749$	613.971	+	354.477i	0.819722	+	0.473266i
$750$		0			0
$751$	−1189.33	+	686.661i	−1.58367	+	0.914330i	−0.589347	+	0.807880i	$0.700615\pi$
$751$	−1189.33	+	686.661i	−1.58367	+	0.914330i	−0.994318	+	0.106450i	$0.966052\pi$
$752$	−503.221			−0.669177
$753$		0			0
$754$	−919.730	−	1593.02i	−1.21980	−	2.11276i
$755$	−23.8963	−	41.3896i	−0.0316507	−	0.0548206i
$756$		0			0
$757$	−67.0735	−	38.7249i	−0.0886043	−	0.0511557i	0.455043	−	0.890469i	$-0.349624\pi$
$757$	−67.0735	−	38.7249i	−0.0886043	−	0.0511557i	−0.543647	+	0.839314i	$0.682957\pi$
$758$			753.184i			0.993646i
$759$		0			0
$760$	−20.6785	−	11.9387i	−0.0272085	−	0.0157088i
$761$	−507.129	−	292.791i	−0.666398	−	0.384745i	0.128312	−	0.991734i	$-0.459044\pi$
$761$	−507.129	−	292.791i	−0.666398	−	0.384745i	−0.794710	+	0.606989i	$0.792377\pi$
$762$		0			0
$763$		−	244.475i		−	0.320413i
$764$	30.5759	−	17.6530i	0.0400208	−	0.0231060i
$765$		0			0
$766$	−991.480			−1.29436
$767$	−786.186	+	1361.71i	−1.02501	+	1.77538i
$768$		0			0
$769$	193.902	+	335.847i	0.252148	+	0.436733i	0.964117	−	0.265478i	$-0.0855298\pi$
$769$	193.902	+	335.847i	0.252148	+	0.436733i	−0.711969	+	0.702211i	$0.752196\pi$
$770$			46.2029i			0.0600037i
$771$		0			0
$772$	−383.536			−0.496809
$773$			1301.86i			1.68416i	0.539349	+	0.842082i	$0.318670\pi$
$773$			1301.86i			1.68416i	−0.539349	+	0.842082i	$0.681330\pi$
$774$		0			0
$775$	85.8913			0.110827
$776$		−	807.212i		−	1.04022i
$777$		0			0
$778$	659.187			0.847284
$779$	327.645	−	189.166i	0.420597	−	0.242832i
$780$		0			0
$781$	625.635	+	361.211i	0.801070	+	0.462498i
$782$			258.172i			0.330143i
$783$		0			0
$784$	−226.135	−	391.677i	−0.288438	−	0.499588i
$785$	−65.2092			−0.0830691
$786$		0			0
$787$	419.298	−	726.245i	0.532780	−	0.922802i	−0.466487	−	0.884528i	$-0.654481\pi$
$787$	419.298	−	726.245i	0.532780	−	0.922802i	0.999267	−	0.0382744i	$-0.0121861\pi$
$788$	−60.4679	+	104.734i	−0.0767360	+	0.132911i
$789$		0			0
$790$	89.6429			0.113472
$791$	−333.211	+	577.139i	−0.421253	+	0.729632i
$792$		0			0
$793$	−114.789	+	66.2734i	−0.144753	+	0.0835730i
$794$	−493.157	+	284.725i	−0.621105	+	0.358595i
$795$		0			0
$796$		−	525.916i		−	0.660699i
$797$	165.648	+	286.911i	0.207840	+	0.359989i	0.951034	−	0.309087i	$-0.100023\pi$
$797$	165.648	+	286.911i	0.207840	+	0.359989i	−0.743194	+	0.669076i	$0.766690\pi$
$798$		0			0
$799$	741.567	−	1284.43i	0.928119	−	1.60755i
$800$	456.435	+	263.523i	0.570543	+	0.329403i
$801$		0			0
$802$	456.006	+	263.275i	0.568586	+	0.328273i
$803$	551.383	+	318.341i	0.686653	+	0.396439i
$804$		0			0
$805$	−12.5569	−	21.7492i	−0.0155986	−	0.0270176i
$806$		−	118.245i		−	0.146706i
$807$		0			0
$808$	−1331.67	−	768.838i	−1.64810	−	0.951533i
$809$	1304.13			1.61203			0.806016	−	0.591894i	$-0.201619\pi$
$809$	1304.13			1.61203			0.806016	+	0.591894i	$0.201619\pi$
$810$		0			0
$811$	−237.510	+	137.127i	−0.292861	+	0.169083i	−0.639231	−	0.769015i	$-0.720747\pi$
$811$	−237.510	+	137.127i	−0.292861	+	0.169083i	0.346370	+	0.938098i	$0.387414\pi$
$812$	380.885	+	659.711i	0.469070	+	0.812452i
$813$		0			0
$814$	60.3524	+	104.533i	0.0741429	+	0.128419i
$815$	−47.5016			−0.0582842
$816$		0			0
$817$	263.044	+	155.897i	0.321963	+	0.190816i
$818$	1047.43			1.28048
$819$		0			0
$820$	24.8602	−	14.3530i	0.0303173	−	0.0175037i
$821$	−265.783			−0.323730			−0.161865	−	0.986813i	$-0.551751\pi$
$821$	−265.783			−0.323730			−0.161865	+	0.986813i	$0.551751\pi$
$822$		0			0
$823$	559.039	+	968.284i	0.679270	+	1.17653i	0.975201	+	0.221321i	$0.0710368\pi$
$823$	559.039	+	968.284i	0.679270	+	1.17653i	−0.295931	+	0.955209i	$0.595630\pi$
$824$	−444.838	−	256.828i	−0.539853	−	0.311684i
$825$		0			0
$826$	−605.242	+	1048.31i	−0.732738	+	1.26914i
$827$	259.554	+	449.561i	0.313850	+	0.543604i	0.979192	−	0.202934i	$-0.0650477\pi$
$827$	259.554	+	449.561i	0.313850	+	0.543604i	−0.665342	+	0.746538i	$0.731714\pi$
$828$		0			0
$829$	995.225	−	574.594i	1.20051	−	0.693117i	0.239844	−	0.970811i	$-0.422904\pi$
$829$	995.225	−	574.594i	1.20051	−	0.693117i	0.960669	+	0.277695i	$0.0895704\pi$
$830$	4.25399	−	7.36812i	0.00512529	−	0.00887726i
$831$		0			0
$832$	721.135	−	1249.04i	0.866749	−	1.50125i
$833$	1332.97			1.60020
$834$		0			0
$835$	−53.9119	−	31.1261i	−0.0645652	−	0.0372767i
$836$	63.2088	−	36.4936i	0.0756087	−	0.0436527i
$837$		0			0
$838$	311.290			0.371468
$839$		−	38.9139i		−	0.0463812i	−0.999731	−	0.0231906i	$-0.992618\pi$
$839$		−	38.9139i		−	0.0463812i	0.999731	−	0.0231906i	$-0.00738247\pi$
$840$		0			0
$841$	1024.89	+	1775.17i	1.21866	+	2.11078i
$842$	187.524	−	324.802i	0.222713	−	0.385751i
$843$		0			0
$844$			351.787i			0.416809i
$845$	93.8556	+	54.1876i	0.111072	+	0.0641273i
$846$		0			0
$847$	589.170	+	340.158i	0.695597	+	0.401603i
$848$	−359.541	−	622.743i	−0.423987	−	0.734367i
$849$		0			0
$850$	864.005	−	498.833i	1.01648	−	0.586863i
$851$	−56.8197	−	32.8049i	−0.0667681	−	0.0385486i
$852$		0			0
$853$	581.658	−	1007.46i	0.681897	−	1.18108i	−0.292504	−	0.956264i	$-0.594488\pi$
$853$	581.658	−	1007.46i	0.681897	−	1.18108i	0.974401	−	0.224816i	$-0.0721782\pi$
$854$	−88.3698	+	51.0203i	−0.103477	+	0.0597427i
$855$		0			0
$856$			609.589i			0.712136i
$857$	185.043	+	320.503i	0.215919	+	0.373983i	0.953556	−	0.301214i	$-0.0973920\pi$
$857$	185.043	+	320.503i	0.215919	+	0.373983i	−0.737637	+	0.675197i	$0.764059\pi$
$858$		0			0
$859$		−	1193.31i		−	1.38918i	−0.719406	−	0.694590i	$-0.755586\pi$
$859$		−	1193.31i		−	1.38918i	0.719406	−	0.694590i	$-0.244414\pi$
$860$	19.9585	+	11.8287i	0.0232076	+	0.0137543i
$861$		0			0
$862$			534.757i			0.620368i
$863$	−1041.99	+	601.595i	−1.20741	+	0.697097i	−0.962192	−	0.272371i	$-0.912192\pi$
$863$	−1041.99	+	601.595i	−1.20741	+	0.697097i	−0.245216	+	0.969469i	$0.578859\pi$
$864$		0			0
$865$	32.9034	−	18.9968i	0.0380386	−	0.0219616i
$866$	281.619	+	487.778i	0.325195	+	0.563254i
$867$		0			0
$868$			48.9683i			0.0564151i
$869$	−528.709	+	915.750i	−0.608410	+	1.05380i
$870$		0			0
$871$	−622.304			−0.714471
$872$	182.048	−	105.105i	0.208770	−	0.120533i
$873$		0			0
$874$	36.8750	−	63.8693i	0.0421911	−	0.0730770i
$875$	−97.3389	+	168.596i	−0.111244	+	0.192681i
$876$		0			0
$877$	194.360	−	336.641i	0.221619	−	0.383855i	−0.733681	−	0.679494i	$-0.762199\pi$
$877$	194.360	−	336.641i	0.221619	−	0.383855i	0.955300	+	0.295639i	$0.0955325\pi$
$878$	−698.524	−	403.293i	−0.795586	−	0.459332i
$879$		0			0
$880$	−20.6933	+	11.9473i	−0.0235151	+	0.0135764i
$881$	−22.8162			−0.0258980			−0.0129490	−	0.999916i	$-0.504122\pi$
$881$	−22.8162			−0.0258980			−0.0129490	+	0.999916i	$0.504122\pi$
$882$		0			0
$883$	−446.565	−	773.474i	−0.505737	−	0.875962i	−0.999978	−	0.00663678i	$-0.997887\pi$
$883$	−446.565	−	773.474i	−0.505737	−	0.875962i	0.494241	−	0.869325i	$-0.335446\pi$
$884$	369.418	+	639.850i	0.417893	+	0.723813i
$885$		0			0
$886$	385.575	+	222.612i	0.435186	+	0.251255i
$887$		−	943.629i		−	1.06384i	−0.846793	−	0.531922i	$-0.821470\pi$
$887$		−	943.629i		−	1.06384i	0.846793	−	0.531922i	$-0.178530\pi$
$888$		0			0
$889$	−1891.77	−	1092.21i	−2.12797	−	1.22858i
$890$	−67.4474	−	38.9408i	−0.0757836	−	0.0437537i
$891$		0			0
$892$		−	113.817i		−	0.127598i
$893$	−366.913	+	211.838i	−0.410877	+	0.237220i
$894$		0			0
$895$	37.5859			0.0419954
$896$	125.633	−	217.603i	0.140216	−	0.242861i
$897$		0			0
$898$	403.380	+	698.675i	0.449198	+	0.778034i
$899$			185.827i			0.206704i
$900$		0			0
$901$	2119.33			2.35220
$902$		−	629.469i		−	0.697859i
$903$		0			0
$904$	−573.019			−0.633871
$905$			41.7006i			0.0460780i
$906$		0			0
$907$	−39.4768			−0.0435246			−0.0217623	−	0.999763i	$-0.506928\pi$
$907$	−39.4768			−0.0435246			−0.0217623	+	0.999763i	$0.506928\pi$
$908$	−177.578	+	102.524i	−0.195570	+	0.112912i
$909$		0			0
$910$	115.705	+	66.8024i	0.127149	+	0.0734092i
$911$		−	916.901i		−	1.00648i	−0.864148	−	0.503239i	$-0.832142\pi$
$911$		−	916.901i		−	1.00648i	0.864148	−	0.503239i	$-0.167858\pi$
$912$		0			0
$913$	50.1795	+	86.9135i	0.0549612	+	0.0951955i
$914$	−417.551			−0.456840
$915$		0			0
$916$	−217.150	+	376.114i	−0.237063	+	0.410605i
$917$	−882.974	+	1529.36i	−0.962895	+	1.66778i
$918$		0			0
$919$	561.375			0.610854			0.305427	−	0.952215i	$-0.401201\pi$
$919$	561.375			0.610854			0.305427	+	0.952215i	$0.401201\pi$
$920$	10.7970	−	18.7009i	0.0117358	−	0.0203271i
$921$		0			0
$922$	−634.690	+	366.438i	−0.688384	+	0.397439i
$923$	1809.15	−	1044.51i	1.96008	−	1.13165i
$924$		0			0
$925$			253.539i			0.274096i
$926$	−684.328	−	1185.29i	−0.739015	−	1.28001i
$927$		0			0
$928$	−570.135	+	987.502i	−0.614369	+	1.06412i
$929$	−572.731	−	330.666i	−0.616502	−	0.355938i	0.159004	−	0.987278i	$-0.449172\pi$
$929$	−572.731	−	330.666i	−0.616502	−	0.355938i	−0.775506	+	0.631340i	$0.782505\pi$
$930$		0			0
$931$	−329.763	−	190.389i	−0.354203	−	0.204499i
$932$	−82.4125	−	47.5809i	−0.0884254	−	0.0510524i
$933$		0			0
$934$	−616.771	−	1068.28i	−0.660354	−	1.14377i
$935$		−	70.4238i		−	0.0753196i
$936$		0			0
$937$	−514.269	−	296.913i	−0.548846	−	0.316877i	0.199810	−	0.979835i	$-0.435967\pi$
$937$	−514.269	−	296.913i	−0.548846	−	0.316877i	−0.748657	+	0.662958i	$0.769301\pi$
$938$	−479.078			−0.510744
$939$		0			0
$940$	−27.8396	+	16.0732i	−0.0296166	+	0.0170992i
$941$	613.331	+	1062.32i	0.651787	+	1.12893i	0.982689	+	0.185263i	$0.0593137\pi$
$941$	613.331	+	1062.32i	0.651787	+	1.12893i	−0.330902	+	0.943665i	$0.607353\pi$
$942$		0			0
$943$	171.076	+	296.312i	0.181416	+	0.314222i
$944$	−626.020			−0.663157
$945$		0			0
$946$	443.457	−	249.327i	0.468770	−	0.263560i
$947$	961.651			1.01547			0.507735	−	0.861513i	$-0.330483\pi$
$947$	961.651			1.01547			0.507735	+	0.861513i	$0.330483\pi$
$948$		0			0
$949$	1594.43	−	920.546i	1.68012	−	0.970017i
$950$	−284.995			−0.299995
$951$		0			0
$952$	1097.47	+	1900.87i	1.15280	+	1.99671i
$953$	283.390	+	163.615i	0.297366	+	0.171685i	0.641259	−	0.767324i	$-0.278412\pi$
$953$	283.390	+	163.615i	0.297366	+	0.171685i	−0.343893	+	0.939009i	$0.611746\pi$
$954$		0			0
$955$	−4.86568	+	8.42761i	−0.00509496	+	0.00882472i
$956$	−108.524	−	187.969i	−0.113519	−	0.196621i
$957$		0			0
$958$	779.973	−	450.318i	0.814168	−	0.470060i
$959$	47.6978	−	82.6151i	0.0497371	−	0.0861471i
$960$		0			0
$961$	474.527	−	821.905i	0.493785	−	0.855261i
$962$	349.042			0.362829
$963$		0			0
$964$	−97.8030	−	56.4666i	−0.101455	−	0.0585753i
$965$	91.5508	−	52.8569i	0.0948713	−	0.0547740i
$966$		0			0
$967$	100.856			0.104298			0.0521489	−	0.998639i	$-0.483393\pi$
$967$	100.856			0.104298			0.0521489	+	0.998639i	$0.483393\pi$
$968$			584.965i			0.604302i
$969$		0			0
$970$	28.8278	+	49.9312i	0.0297194	+	0.0514755i
$971$	642.159	−	1112.25i	0.661337	−	1.14547i	−0.318927	−	0.947779i	$-0.603323\pi$
$971$	642.159	−	1112.25i	0.661337	−	1.14547i	0.980264	−	0.197691i	$-0.0633441\pi$
$972$		0			0
$973$		−	279.988i		−	0.287758i
$974$	−797.183	−	460.254i	−0.818463	−	0.472540i
$975$		0			0
$976$	−45.7018	−	26.3859i	−0.0468256	−	0.0270348i
$977$	112.538	+	194.922i	0.115188	+	0.199511i	0.917855	−	0.396916i	$-0.129920\pi$
$977$	112.538	+	194.922i	0.115188	+	0.199511i	−0.802667	+	0.596427i	$0.796586\pi$
$978$		0			0
$979$	795.602	−	459.341i	0.812668	−	0.469194i
$980$	−25.0208	−	14.4458i	−0.0255315	−	0.0147406i
$981$		0			0
$982$	−1.36782	+	2.36914i	−0.00139289	+	0.00241256i
$983$	674.694	−	389.534i	0.686362	−	0.396271i	−0.115886	−	0.993263i	$-0.536971\pi$
$983$	674.694	−	389.534i	0.686362	−	0.396271i	0.802248	+	0.596991i	$0.203637\pi$
$984$		0			0
$985$		−	33.3334i		−	0.0338411i
$986$	1079.23	+	1869.28i	1.09456	+	1.89583i
$987$		0			0
$988$		−	211.057i		−	0.213621i
$989$	−140.988	+	237.888i	−0.142556	+	0.240534i
$990$		0			0
$991$			954.633i			0.963303i	0.876363	+	0.481651i	$0.159963\pi$
$991$			954.633i			0.963303i	−0.876363	+	0.481651i	$0.840037\pi$
$992$	−63.4790	+	36.6496i	−0.0639909	+	0.0369452i
$993$		0			0
$994$	1392.77	−	804.114i	1.40117	−	0.808968i
$995$	72.4789	+	125.537i	0.0728431	+	0.126168i
$996$		0			0
$997$		−	1062.46i		−	1.06566i	−0.846222	−	0.532830i	$-0.821128\pi$
$997$		−	1062.46i		−	1.06566i	0.846222	−	0.532830i	$-0.178872\pi$
$998$	−231.835	+	401.551i	−0.232300	+	0.402355i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.3.j.f.136.6	yes	28
3.2	odd	2	inner	387.3.j.f.136.9	yes	28
43.37	odd	6	inner	387.3.j.f.37.9	yes	28
129.80	even	6	inner	387.3.j.f.37.6	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.3.j.f.37.6	✓	28	129.80	even	6	inner
387.3.j.f.37.9	yes	28	43.37	odd	6	inner
387.3.j.f.136.6	yes	28	1.1	even	1	trivial
387.3.j.f.136.9	yes	28	3.2	odd	2	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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	387.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.61273i q^{2} +1.39911 q^{4} +(-0.333970 + 0.192817i) q^{5} +(-8.76989 - 5.06330i) q^{7} -8.70729i q^{8} +O(q^{10})\)	\(q-1.61273i q^{2} +1.39911 q^{4} +(-0.333970 + 0.192817i) q^{5} +(-8.76989 - 5.06330i) q^{7} -8.70729i q^{8} +(0.310962 + 0.538602i) q^{10} -7.33614 q^{11} +(-10.6070 + 18.3718i) q^{13} +(-8.16573 + 14.1435i) q^{14} -8.44606 q^{16} +(12.4464 - 21.5579i) q^{17} +(-6.15827 + 3.55548i) q^{19} +(-0.467260 + 0.269773i) q^{20} +11.8312i q^{22} +(-3.21546 - 5.56934i) q^{23} +(-12.4256 + 21.5218i) q^{25} +(29.6287 + 17.1061i) q^{26} +(-12.2700 - 7.08411i) q^{28} +(-46.5628 - 26.8830i) q^{29} +(-1.72811 - 2.99317i) q^{31} -21.2080i q^{32} +(-34.7670 - 20.0727i) q^{34} +3.90517 q^{35} +(8.83540 - 5.10112i) q^{37} +(5.73402 + 9.93161i) q^{38} +(1.67892 + 2.90797i) q^{40} -53.2041 q^{41} +(-21.0737 - 37.4820i) q^{43} -10.2641 q^{44} +(-8.98182 + 5.18566i) q^{46} +59.5806 q^{47} +(26.7740 + 46.3740i) q^{49} +(34.7089 + 20.0392i) q^{50} +(-14.8403 + 25.7041i) q^{52} +(42.5691 + 73.7318i) q^{53} +(2.45005 - 1.41454i) q^{55} +(-44.0876 + 76.3620i) q^{56} +(-43.3550 + 75.0931i) q^{58} +74.1198 q^{59} +(5.41102 + 3.12405i) q^{61} +(-4.82716 + 2.78696i) q^{62} -67.9869 q^{64} -8.18083i q^{65} +(14.6674 + 25.4046i) q^{67} +(17.4139 - 30.1618i) q^{68} -6.29798i q^{70} +(-85.2812 - 49.2371i) q^{71} +(-75.1597 - 43.3935i) q^{73} +(-8.22672 - 14.2491i) q^{74} +(-8.61609 + 4.97450i) q^{76} +(64.3372 + 37.1451i) q^{77} +(72.0690 - 124.827i) q^{79} +(2.82073 - 1.62855i) q^{80} +85.8038i q^{82} +(-6.84004 - 11.8473i) q^{83} +9.59957i q^{85} +(-60.4482 + 33.9862i) q^{86} +63.8780i q^{88} +(-108.450 + 62.6134i) q^{89} +(186.044 - 107.412i) q^{91} +(-4.49877 - 7.79210i) q^{92} -96.0873i q^{94} +(1.37112 - 2.37484i) q^{95} +92.7052 q^{97} +(74.7886 - 43.1792i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 84 q^{4} - 30 q^{7}+O(q^{10}) \) 28 * q - 84 * q^4 - 30 * q^7	\( 28 q - 84 q^{4} - 30 q^{7} + 4 q^{10} - 34 q^{13} + 164 q^{16} - 78 q^{19} + 112 q^{25} + 342 q^{28} - 74 q^{31} + 192 q^{34} - 222 q^{37} + 104 q^{40} + 104 q^{43} + 150 q^{46} + 112 q^{49} - 64 q^{52} - 450 q^{55} + 346 q^{58} - 198 q^{61} - 1264 q^{64} - 26 q^{67} + 342 q^{73} + 282 q^{76} - 48 q^{79} + 684 q^{91} - 480 q^{97}+O(q^{100}) \) 28 * q - 84 * q^4 - 30 * q^7 + 4 * q^10 - 34 * q^13 + 164 * q^16 - 78 * q^19 + 112 * q^25 + 342 * q^28 - 74 * q^31 + 192 * q^34 - 222 * q^37 + 104 * q^40 + 104 * q^43 + 150 * q^46 + 112 * q^49 - 64 * q^52 - 450 * q^55 + 346 * q^58 - 198 * q^61 - 1264 * q^64 - 26 * q^67 + 342 * q^73 + 282 * q^76 - 48 * q^79 + 684 * q^91 - 480 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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