LMFDB - Embedded newform 405.3.g.h.82.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(82,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(4))

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("405.82");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.g (of order $4$, 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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} + 8 x^{17} + 245 x^{16} - 440 x^{15} + 422 x^{14} + 1724 x^{13} + \cdots + 11449 $ x^20 - 2x^19 + 2x^18 + 8x^17 + 245x^16 - 440x^15 + 422x^14 + 1724x^13 + 15070x^12 - 18240x^11 + 13542x^10 + 50064x^9 + 293818x^8 - 191648x^7 + 30530x^6 - 134164x^5 + 859529x^4 - 948950x^3 + 540800x^2 - 111280*x + 11449
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			82.6
Root			$0.531225 - 0.531225i$ of defining polynomial
Character	$\chi$	$=$	405.82
Dual form			405.3.g.h.163.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.531225 + 0.531225i) q^{2} -3.43560i q^{4} +(-3.56385 + 3.50699i) q^{5} +(1.31570 + 1.31570i) q^{7} +(3.94998 - 3.94998i) q^{8} +(-3.75621 - 0.0302083i) q^{10} -11.6459 q^{11} +(14.4997 - 14.4997i) q^{13} +1.39786i q^{14} -9.54575 q^{16} +(-10.0254 - 10.0254i) q^{17} -10.8032i q^{19} +(12.0486 + 12.2440i) q^{20} +(-6.18658 - 6.18658i) q^{22} +(0.985111 - 0.985111i) q^{23} +(0.402086 - 24.9968i) q^{25} +15.4052 q^{26} +(4.52021 - 4.52021i) q^{28} -24.0140i q^{29} -43.2465 q^{31} +(-20.8708 - 20.8708i) q^{32} -10.6514i q^{34} +(-9.30307 - 0.0748176i) q^{35} +(-32.5443 - 32.5443i) q^{37} +(5.73890 - 5.73890i) q^{38} +(-0.224617 + 27.9296i) q^{40} +41.0818 q^{41} +(5.86628 - 5.86628i) q^{43} +40.0106i q^{44} +1.04663 q^{46} +(-12.6335 - 12.6335i) q^{47} -45.5379i q^{49} +(13.4925 - 13.0653i) q^{50} +(-49.8152 - 49.8152i) q^{52} +(-51.3281 + 51.3281i) q^{53} +(41.5042 - 40.8419i) q^{55} +10.3939 q^{56} +(12.7568 - 12.7568i) q^{58} +28.1110i q^{59} +82.2004 q^{61} +(-22.9736 - 22.9736i) q^{62} +16.0088i q^{64} +(-0.824532 + 102.525i) q^{65} +(23.6529 + 23.6529i) q^{67} +(-34.4432 + 34.4432i) q^{68} +(-4.90228 - 4.98177i) q^{70} +99.6917 q^{71} +(-22.3583 + 22.3583i) q^{73} -34.5767i q^{74} -37.1153 q^{76} +(-15.3224 - 15.3224i) q^{77} +61.1906i q^{79} +(34.0196 - 33.4768i) q^{80} +(21.8237 + 21.8237i) q^{82} +(36.5439 - 36.5439i) q^{83} +(70.8878 + 0.570097i) q^{85} +6.23263 q^{86} +(-46.0009 + 46.0009i) q^{88} -113.914i q^{89} +38.1544 q^{91} +(-3.38445 - 3.38445i) q^{92} -13.4225i q^{94} +(37.8865 + 38.5008i) q^{95} +(21.6459 + 21.6459i) q^{97} +(24.1909 - 24.1909i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{5} + 2 q^{7} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 2 q^{13} - 28 q^{16} + 14 q^{17} + 114 q^{20} - 14 q^{22} - 82 q^{23} + 8 q^{25} - 56 q^{26} - 44 q^{28} + 4 q^{31} + 14 q^{32} + 176 q^{35}+ \cdots - 938 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 + 2 * q^5 + 2 * q^7 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 2 * q^13 - 28 * q^16 + 14 * q^17 + 114 * q^20 - 14 * q^22 - 82 * q^23 + 8 * q^25 - 56 * q^26 - 44 * q^28 + 4 * q^31 + 14 * q^32 + 176 * q^35 - 46 * q^37 - 330 * q^38 - 30 * q^40 + 28 * q^41 + 2 * q^43 - 68 * q^46 - 64 * q^47 + 458 * q^50 + 74 * q^52 - 304 * q^53 + 112 * q^55 + 192 * q^56 - 30 * q^58 - 92 * q^61 - 50 * q^62 + 326 * q^65 + 80 * q^67 - 626 * q^68 + 102 * q^70 + 124 * q^71 - 4 * q^73 + 96 * q^76 - 338 * q^77 + 722 * q^80 + 52 * q^82 - 370 * q^83 + 98 * q^85 + 328 * q^86 + 210 * q^88 + 76 * q^91 - 388 * q^92 + 360 * q^95 - 292 * q^97 - 938 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	0.531225	+	0.531225i	0.265612	+	0.265612i	0.827329	−	0.561717i	$-0.189859\pi$
$2$	0.531225	+	0.531225i	0.265612	+	0.265612i	−0.561717	+	0.827329i	$0.689859\pi$
$3$		0			0
$3$		0			0
$4$		−	3.43560i		−	0.858900i
$5$	−3.56385	+	3.50699i	−0.712770	+	0.701397i
$5$	−3.56385	+	3.50699i	−0.712770	+	0.701397i
$6$		0			0
$7$	1.31570	+	1.31570i	0.187957	+	0.187957i	0.794812	−	0.606856i	$-0.207569\pi$
$7$	1.31570	+	1.31570i	0.187957	+	0.187957i	−0.606856	+	0.794812i	$0.707569\pi$
$8$	3.94998	−	3.94998i	0.493747	−	0.493747i
$9$		0			0
$10$	−3.75621	−	0.0302083i	−0.375621	−	0.00302083i
$11$	−11.6459			−1.05872			−0.529358	−	0.848399i	$-0.677567\pi$
$11$	−11.6459			−1.05872			−0.529358	+	0.848399i	$0.677567\pi$
$12$		0			0
$13$	14.4997	−	14.4997i	1.11536	−	1.11536i	0.122949	−	0.992413i	$-0.460765\pi$
$13$	14.4997	−	14.4997i	1.11536	−	1.11536i	0.992413	−	0.122949i	$-0.0392353\pi$
$14$			1.39786i			0.0998472i
$15$		0			0
$16$	−9.54575			−0.596609
$17$	−10.0254	−	10.0254i	−0.589728	−	0.589728i	0.347830	−	0.937558i	$-0.386919\pi$
$17$	−10.0254	−	10.0254i	−0.589728	−	0.589728i	−0.937558	+	0.347830i	$0.886919\pi$
$18$		0			0
$19$		−	10.8032i		−	0.568587i	−0.958737	−	0.284294i	$-0.908241\pi$
$19$		−	10.8032i		−	0.568587i	0.958737	−	0.284294i	$-0.0917590\pi$
$20$	12.0486	+	12.2440i	0.602430	+	0.612199i
$21$		0			0
$22$	−6.18658	−	6.18658i	−0.281208	−	0.281208i
$23$	0.985111	−	0.985111i	0.0428309	−	0.0428309i	−0.685367	−	0.728198i	$-0.740358\pi$
$23$	0.985111	−	0.985111i	0.0428309	−	0.0428309i	0.728198	+	0.685367i	$0.240358\pi$
$24$		0			0
$25$	0.402086	−	24.9968i	0.0160835	−	0.999871i
$26$	15.4052			0.592508
$27$		0			0
$28$	4.52021	−	4.52021i	0.161436	−	0.161436i
$29$		−	24.0140i		−	0.828070i	−0.910261	−	0.414035i	$-0.864119\pi$
$29$		−	24.0140i		−	0.828070i	0.910261	−	0.414035i	$-0.135881\pi$
$30$		0			0
$31$	−43.2465			−1.39505			−0.697524	−	0.716561i	$-0.745715\pi$
$31$	−43.2465			−1.39505			−0.697524	+	0.716561i	$0.745715\pi$
$32$	−20.8708	−	20.8708i	−0.652214	−	0.652214i
$33$		0			0
$34$		−	10.6514i		−	0.313278i
$35$	−9.30307	−	0.0748176i	−0.265802	−	0.00213765i
$36$		0			0
$37$	−32.5443	−	32.5443i	−0.879576	−	0.879576i	0.113915	−	0.993491i	$-0.463661\pi$
$37$	−32.5443	−	32.5443i	−0.879576	−	0.879576i	−0.993491	+	0.113915i	$0.963661\pi$
$38$	5.73890	−	5.73890i	0.151024	−	0.151024i
$39$		0			0
$40$	−0.224617	+	27.9296i	−0.00561543	+	0.698241i
$41$	41.0818			1.00199			0.500997	−	0.865449i	$-0.332967\pi$
$41$	41.0818			1.00199			0.500997	+	0.865449i	$0.332967\pi$
$42$		0			0
$43$	5.86628	−	5.86628i	0.136425	−	0.136425i	−0.635596	−	0.772022i	$-0.719246\pi$
$43$	5.86628	−	5.86628i	0.136425	−	0.136425i	0.772022	+	0.635596i	$0.219246\pi$
$44$			40.0106i			0.909331i
$45$		0			0
$46$	1.04663			0.0227528
$47$	−12.6335	−	12.6335i	−0.268798	−	0.268798i	0.559818	−	0.828616i	$-0.310871\pi$
$47$	−12.6335	−	12.6335i	−0.268798	−	0.268798i	−0.828616	+	0.559818i	$0.810871\pi$
$48$		0			0
$49$		−	45.5379i		−	0.929345i
$50$	13.4925	−	13.0653i	0.269850	−	0.261306i
$51$		0			0
$52$	−49.8152	−	49.8152i	−0.957985	−	0.957985i
$53$	−51.3281	+	51.3281i	−0.968455	+	0.968455i	−0.999517	−	0.0310621i	$-0.990111\pi$
$53$	−51.3281	+	51.3281i	−0.968455	+	0.968455i	0.0310621	+	0.999517i	$0.490111\pi$
$54$		0			0
$55$	41.5042	−	40.8419i	0.754621	−	0.742580i
$56$	10.3939			0.185606
$57$		0			0
$58$	12.7568	−	12.7568i	0.219946	−	0.219946i
$59$			28.1110i			0.476458i	0.971209	+	0.238229i	$0.0765669\pi$
$59$			28.1110i			0.476458i	−0.971209	+	0.238229i	$0.923433\pi$
$60$		0			0
$61$	82.2004			1.34755			0.673774	−	0.738938i	$-0.264672\pi$
$61$	82.2004			1.34755			0.673774	+	0.738938i	$0.264672\pi$
$62$	−22.9736	−	22.9736i	−0.370542	−	0.370542i
$63$		0			0
$64$			16.0088i			0.250137i
$65$	−0.824532	+	102.525i	−0.0126851	+	1.57731i
$66$		0			0
$67$	23.6529	+	23.6529i	0.353029	+	0.353029i	0.861235	−	0.508206i	$-0.169691\pi$
$67$	23.6529	+	23.6529i	0.353029	+	0.353029i	−0.508206	+	0.861235i	$0.669691\pi$
$68$	−34.4432	+	34.4432i	−0.506517	+	0.506517i
$69$		0			0
$70$	−4.90228	−	4.98177i	−0.0700326	−	0.0711681i
$71$	99.6917			1.40411			0.702054	−	0.712123i	$-0.252266\pi$
$71$	99.6917			1.40411			0.702054	+	0.712123i	$0.252266\pi$
$72$		0			0
$73$	−22.3583	+	22.3583i	−0.306278	+	0.306278i	−0.843464	−	0.537186i	$-0.819487\pi$
$73$	−22.3583	+	22.3583i	−0.306278	+	0.306278i	0.537186	+	0.843464i	$0.319487\pi$
$74$		−	34.5767i		−	0.467252i
$75$		0			0
$76$	−37.1153			−0.488359
$77$	−15.3224	−	15.3224i	−0.198993	−	0.198993i
$78$		0			0
$79$			61.1906i			0.774565i	0.921961	+	0.387282i	$0.126586\pi$
$79$			61.1906i			0.774565i	−0.921961	+	0.387282i	$0.873414\pi$
$80$	34.0196	−	33.4768i	0.425246	−	0.418460i
$81$		0			0
$82$	21.8237	+	21.8237i	0.266142	+	0.266142i
$83$	36.5439	−	36.5439i	0.440288	−	0.440288i	−0.451821	−	0.892109i	$-0.649225\pi$
$83$	36.5439	−	36.5439i	0.440288	−	0.440288i	0.892109	+	0.451821i	$0.149225\pi$
$84$		0			0
$85$	70.8878	+	0.570097i	0.833974	+	0.00670702i
$86$	6.23263			0.0724724
$87$		0			0
$88$	−46.0009	+	46.0009i	−0.522738	+	0.522738i
$89$		−	113.914i		−	1.27993i	−0.768402	−	0.639967i	$-0.778948\pi$
$89$		−	113.914i		−	1.27993i	0.768402	−	0.639967i	$-0.221052\pi$
$90$		0			0
$91$	38.1544			0.419279
$92$	−3.38445	−	3.38445i	−0.0367875	−	0.0367875i
$93$		0			0
$94$		−	13.4225i		−	0.142792i
$95$	37.8865	+	38.5008i	0.398805	+	0.405272i
$96$		0			0
$97$	21.6459	+	21.6459i	0.223154	+	0.223154i	0.809825	−	0.586671i	$-0.199562\pi$
$97$	21.6459	+	21.6459i	0.223154	+	0.223154i	−0.586671	+	0.809825i	$0.699562\pi$
$98$	24.1909	−	24.1909i	0.246845	−	0.246845i
$99$		0			0
$100$	−85.8789	−	1.38141i	−0.858789	−	0.0138141i
$101$	−59.7840			−0.591921			−0.295961	−	0.955200i	$-0.595640\pi$
$101$	−59.7840			−0.591921			−0.295961	+	0.955200i	$0.595640\pi$
$102$		0			0
$103$	35.7928	−	35.7928i	0.347503	−	0.347503i	−0.511676	−	0.859179i	$-0.670975\pi$
$103$	35.7928	−	35.7928i	0.347503	−	0.347503i	0.859179	+	0.511676i	$0.170975\pi$
$104$		−	114.547i		−	1.10141i
$105$		0			0
$106$	−54.5336			−0.514468
$107$	−14.8359	−	14.8359i	−0.138653	−	0.138653i	0.634374	−	0.773027i	$-0.281258\pi$
$107$	−14.8359	−	14.8359i	−0.138653	−	0.138653i	−0.773027	+	0.634374i	$0.781258\pi$
$108$		0			0
$109$			115.290i			1.05770i	0.848714	+	0.528852i	$0.177377\pi$
$109$			115.290i			1.05770i	−0.848714	+	0.528852i	$0.822623\pi$
$110$	43.7443	+	0.351802i	0.397675	+	0.00319820i
$111$		0			0
$112$	−12.5593	−	12.5593i	−0.112137	−	0.112137i
$113$	−74.0927	+	74.0927i	−0.655687	+	0.655687i	−0.954357	−	0.298669i	$-0.903457\pi$
$113$	−74.0927	+	74.0927i	−0.655687	+	0.655687i	0.298669	+	0.954357i	$0.403457\pi$
$114$		0			0
$115$	−0.0560187	+	6.96556i	−0.000487119	+	0.0605701i
$116$	−82.5026			−0.711229
$117$		0			0
$118$	−14.9333	+	14.9333i	−0.126553	+	0.126553i
$119$		−	26.3807i		−	0.221686i
$120$		0			0
$121$	14.6264			0.120879
$122$	43.6669	+	43.6669i	0.357925	+	0.357925i
$123$		0			0
$124$			148.578i			1.19821i
$125$	86.2304	+	90.4949i	0.689843	+	0.723959i
$126$		0			0
$127$	56.0831	+	56.0831i	0.441599	+	0.441599i	0.892549	−	0.450950i	$-0.148915\pi$
$127$	56.0831	+	56.0831i	0.441599	+	0.441599i	−0.450950	+	0.892549i	$0.648915\pi$
$128$	−91.9876	+	91.9876i	−0.718653	+	0.718653i
$129$		0			0
$130$	−54.9019	+	54.0259i	−0.422322	+	0.415584i
$131$	4.63463			0.0353788			0.0176894	−	0.999844i	$-0.494369\pi$
$131$	4.63463			0.0353788			0.0176894	+	0.999844i	$0.494369\pi$
$132$		0			0
$133$	14.2137	−	14.2137i	0.106870	−	0.106870i
$134$			25.1300i			0.187538i
$135$		0			0
$136$	−79.1999			−0.582352
$137$	−1.68190	−	1.68190i	−0.0122766	−	0.0122766i	0.700942	−	0.713218i	$-0.252763\pi$
$137$	−1.68190	−	1.68190i	−0.0122766	−	0.0122766i	−0.713218	+	0.700942i	$0.752763\pi$
$138$		0			0
$139$			256.257i			1.84357i	0.387699	+	0.921786i	$0.373270\pi$
$139$			256.257i			1.84357i	−0.387699	+	0.921786i	$0.626730\pi$
$140$	−0.257043	+	31.9616i	−0.00183602	+	0.228297i
$141$		0			0
$142$	52.9587	+	52.9587i	0.372949	+	0.372949i
$143$	−168.862	+	168.862i	−1.18085	+	1.18085i
$144$		0			0
$145$	84.2169	+	85.5825i	0.580806	+	0.590224i
$146$	−23.7546			−0.162703
$147$		0			0
$148$	−111.809	+	111.809i	−0.755468	+	0.755468i
$149$		−	94.2182i		−	0.632337i	−0.948703	−	0.316168i	$-0.897604\pi$
$149$		−	94.2182i		−	0.632337i	0.948703	−	0.316168i	$-0.102396\pi$
$150$		0			0
$151$	−28.0950			−0.186060			−0.0930299	−	0.995663i	$-0.529655\pi$
$151$	−28.0950			−0.186060			−0.0930299	+	0.995663i	$0.529655\pi$
$152$	−42.6722	−	42.6722i	−0.280738	−	0.280738i
$153$		0			0
$154$		−	16.2793i		−	0.105710i
$155$	154.124	−	151.665i	0.994350	−	0.978484i
$156$		0			0
$157$	27.2828	+	27.2828i	0.173776	+	0.173776i	0.788636	−	0.614860i	$-0.210788\pi$
$157$	27.2828	+	27.2828i	0.173776	+	0.173776i	−0.614860	+	0.788636i	$0.710788\pi$
$158$	−32.5060	+	32.5060i	−0.205734	+	0.205734i
$159$		0			0
$160$	147.574	+	1.18683i	0.922340	+	0.00741768i
$161$	2.59221			0.0161007
$162$		0			0
$163$	140.797	−	140.797i	0.863787	−	0.863787i	−0.127989	−	0.991776i	$-0.540852\pi$
$163$	140.797	−	140.797i	0.863787	−	0.863787i	0.991776	+	0.127989i	$0.0408522\pi$
$164$		−	141.141i		−	0.860613i
$165$		0			0
$166$	38.8260			0.233892
$167$	−200.050	−	200.050i	−1.19790	−	1.19790i	−0.974794	−	0.223108i	$-0.928380\pi$
$167$	−200.050	−	200.050i	−1.19790	−	1.19790i	−0.223108	−	0.974794i	$-0.571620\pi$
$168$		0			0
$169$		−	251.483i		−	1.48807i
$170$	37.3545	+	37.9602i	0.219732	+	0.223295i
$171$		0			0
$172$	−20.1542	−	20.1542i	−0.117176	−	0.117176i
$173$	−219.189	+	219.189i	−1.26699	+	1.26699i	−0.319355	+	0.947635i	$0.603466\pi$
$173$	−219.189	+	219.189i	−1.26699	+	1.26699i	−0.947635	+	0.319355i	$0.896534\pi$
$174$		0			0
$175$	33.4172	−	32.3591i	0.190955	−	0.184909i
$176$	111.169			0.631640
$177$		0			0
$178$	60.5140	−	60.5140i	0.339966	−	0.339966i
$179$		−	151.884i		−	0.848512i	−0.905542	−	0.424256i	$-0.860536\pi$
$179$		−	151.884i		−	0.848512i	0.905542	−	0.424256i	$-0.139464\pi$
$180$		0			0
$181$	48.0978			0.265734			0.132867	−	0.991134i	$-0.457582\pi$
$181$	48.0978			0.265734			0.132867	+	0.991134i	$0.457582\pi$
$182$	20.2686	+	20.2686i	0.111366	+	0.111366i
$183$		0			0
$184$		−	7.78233i		−	0.0422953i
$185$	230.116	+	1.85065i	1.24387	+	0.0100035i
$186$		0			0
$187$	116.754	+	116.754i	0.624354	+	0.624354i
$188$	−43.4036	+	43.4036i	−0.230870	+	0.230870i
$189$		0			0
$190$	−0.326345	+	40.5789i	−0.00171761	+	0.213573i
$191$	363.397			1.90260			0.951300	−	0.308267i	$-0.0997489\pi$
$191$	363.397			1.90260			0.951300	+	0.308267i	$0.0997489\pi$
$192$		0			0
$193$	−8.46304	+	8.46304i	−0.0438499	+	0.0438499i	−0.728692	−	0.684842i	$-0.759871\pi$
$193$	−8.46304	+	8.46304i	−0.0438499	+	0.0438499i	0.684842	+	0.728692i	$0.259871\pi$
$194$			22.9977i			0.118545i
$195$		0			0
$196$	−156.450			−0.798214
$197$	45.3414	+	45.3414i	0.230159	+	0.230159i	0.812759	−	0.582600i	$-0.197964\pi$
$197$	45.3414	+	45.3414i	0.230159	+	0.230159i	−0.582600	+	0.812759i	$0.697964\pi$
$198$		0			0
$199$		−	17.0082i		−	0.0854685i	−0.999086	−	0.0427343i	$-0.986393\pi$
$199$		−	17.0082i		−	0.0854685i	0.999086	−	0.0427343i	$-0.0136069\pi$
$200$	−97.1484	−	100.325i	−0.485742	−	0.501624i
$201$		0			0
$202$	−31.7588	−	31.7588i	−0.157222	−	0.157222i
$203$	31.5952	−	31.5952i	0.155641	−	0.155641i
$204$		0			0
$205$	−146.409	+	144.073i	−0.714192	+	0.702796i
$206$	38.0281			0.184602
$207$		0			0
$208$	−138.411	+	138.411i	−0.665436	+	0.665436i
$209$			125.812i			0.601972i
$210$		0			0
$211$	297.773			1.41125			0.705624	−	0.708586i	$-0.250667\pi$
$211$	297.773			1.41125			0.705624	+	0.708586i	$0.250667\pi$
$212$	176.343	+	176.343i	0.831806	+	0.831806i
$213$		0			0
$214$		−	15.7624i		−	0.0736559i
$215$	−0.333589	+	41.4795i	−0.00155157	+	0.192928i
$216$		0			0
$217$	−56.8993	−	56.8993i	−0.262209	−	0.262209i
$218$	−61.2448	+	61.2448i	−0.280940	+	0.280940i
$219$		0			0
$220$	−140.317	−	142.592i	−0.637802	−	0.648144i
$221$	−290.730			−1.31552
$222$		0			0
$223$	−22.6038	+	22.6038i	−0.101362	+	0.101362i	−0.755969	−	0.654607i	$-0.772834\pi$
$223$	−22.6038	+	22.6038i	−0.101362	+	0.101362i	0.654607	+	0.755969i	$0.272834\pi$
$224$		−	54.9194i		−	0.245176i
$225$		0			0
$226$	−78.7197			−0.348317
$227$	−276.597	−	276.597i	−1.21849	−	1.21849i	−0.968162	−	0.250326i	$-0.919462\pi$
$227$	−276.597	−	276.597i	−1.21849	−	1.21849i	−0.250326	−	0.968162i	$-0.580538\pi$
$228$		0			0
$229$		−	250.833i		−	1.09534i	−0.836694	−	0.547671i	$-0.815515\pi$
$229$		−	250.833i		−	1.09534i	0.836694	−	0.547671i	$-0.184485\pi$
$230$	−3.73004	+	3.67052i	−0.0162176	+	0.0159588i
$231$		0			0
$232$	−94.8548	−	94.8548i	−0.408857	−	0.408857i
$233$	239.086	−	239.086i	1.02612	−	1.02612i	0.0264709	−	0.999650i	$-0.491573\pi$
$233$	239.086	−	239.086i	1.02612	−	1.02612i	0.999650	−	0.0264709i	$-0.00842693\pi$
$234$		0			0
$235$	89.3294	+	0.718409i	0.380125	+	0.00305706i
$236$	96.5783			0.409230
$237$		0			0
$238$	14.0141	−	14.0141i	0.0588826	−	0.0588826i
$239$			39.0847i			0.163534i	0.996651	+	0.0817672i	$0.0260564\pi$
$239$			39.0847i			0.163534i	−0.996651	+	0.0817672i	$0.973944\pi$
$240$		0			0
$241$	83.7050			0.347324			0.173662	−	0.984805i	$-0.444440\pi$
$241$	83.7050			0.347324			0.173662	+	0.984805i	$0.444440\pi$
$242$	7.76989	+	7.76989i	0.0321070	+	0.0321070i
$243$		0			0
$244$		−	282.408i		−	1.15741i
$245$	159.701	+	162.290i	0.651840	+	0.662409i
$246$		0			0
$247$	−156.643	−	156.643i	−0.634181	−	0.634181i
$248$	−170.823	+	170.823i	−0.688801	+	0.688801i
$249$		0			0
$250$	−2.26543	+	93.8808i	−0.00906172	+	0.375523i
$251$	−116.674			−0.464837			−0.232418	−	0.972616i	$-0.574664\pi$
$251$	−116.674			−0.464837			−0.232418	+	0.972616i	$0.574664\pi$
$252$		0			0
$253$	−11.4725	+	11.4725i	−0.0453458	+	0.0453458i
$254$			59.5854i			0.234588i
$255$		0			0
$256$	−33.6971			−0.131629
$257$	−3.38346	−	3.38346i	−0.0131652	−	0.0131652i	0.700494	−	0.713659i	$-0.252963\pi$
$257$	−3.38346	−	3.38346i	−0.0131652	−	0.0131652i	−0.713659	+	0.700494i	$0.752963\pi$
$258$		0			0
$259$		−	85.6368i		−	0.330644i
$260$	352.235	+	2.83276i	1.35475	+	0.0108952i
$261$		0			0
$262$	2.46203	+	2.46203i	0.00939706	+	0.00939706i
$263$	−69.1605	+	69.1605i	−0.262968	+	0.262968i	−0.826259	−	0.563291i	$-0.809535\pi$
$263$	−69.1605	+	69.1605i	−0.262968	+	0.262968i	0.563291	+	0.826259i	$0.309535\pi$
$264$		0			0
$265$	2.91880	−	362.933i	0.0110143	−	1.36956i
$266$	15.1013			0.0567718
$267$		0			0
$268$	81.2620	−	81.2620i	0.303216	−	0.303216i
$269$		−	212.871i		−	0.791340i	−0.918393	−	0.395670i	$-0.870512\pi$
$269$		−	212.871i		−	0.791340i	0.918393	−	0.395670i	$-0.129488\pi$
$270$		0			0
$271$	−180.243			−0.665102			−0.332551	−	0.943085i	$-0.607909\pi$
$271$	−180.243			−0.665102			−0.332551	+	0.943085i	$0.607909\pi$
$272$	95.6997	+	95.6997i	0.351837	+	0.351837i
$273$		0			0
$274$		−	1.78693i		−	0.00652165i
$275$	−4.68265	+	291.109i	−0.0170278	+	1.05858i
$276$		0			0
$277$	−231.418	−	231.418i	−0.835444	−	0.835444i	0.152812	−	0.988255i	$-0.451167\pi$
$277$	−231.418	−	231.418i	−0.835444	−	0.835444i	−0.988255	+	0.152812i	$0.951167\pi$
$278$	−136.130	+	136.130i	−0.489676	+	0.489676i
$279$		0			0
$280$	−37.0424	+	36.4514i	−0.132294	+	0.130184i
$281$	31.2711			0.111285			0.0556426	−	0.998451i	$-0.482279\pi$
$281$	31.2711			0.111285			0.0556426	+	0.998451i	$0.482279\pi$
$282$		0			0
$283$	−143.355	+	143.355i	−0.506554	+	0.506554i	−0.913467	−	0.406913i	$-0.866605\pi$
$283$	−143.355	+	143.355i	−0.506554	+	0.506554i	0.406913	+	0.913467i	$0.366605\pi$
$284$		−	342.501i		−	1.20599i
$285$		0			0
$286$	−179.407			−0.627298
$287$	54.0511	+	54.0511i	0.188331	+	0.188331i
$288$		0			0
$289$		−	87.9840i		−	0.304443i
$290$	−0.725424	+	90.2016i	−0.00250146	+	0.311040i
$291$		0			0
$292$	76.8142	+	76.8142i	0.263062	+	0.263062i
$293$	27.5761	−	27.5761i	0.0941163	−	0.0941163i	−0.658481	−	0.752597i	$-0.728801\pi$
$293$	27.5761	−	27.5761i	0.0941163	−	0.0941163i	0.752597	+	0.658481i	$0.228801\pi$
$294$		0			0
$295$	−98.5850	−	100.184i	−0.334187	−	0.339605i
$296$	−257.098			−0.868576
$297$		0			0
$298$	50.0510	−	50.0510i	0.167957	−	0.167957i
$299$		−	28.5676i		−	0.0955439i
$300$		0			0
$301$	15.4365			0.0512840
$302$	−14.9248	−	14.9248i	−0.0494198	−	0.0494198i
$303$		0			0
$304$			103.124i			0.339224i
$305$	−292.950	+	288.276i	−0.960492	+	0.945166i
$306$		0			0
$307$	−28.4359	−	28.4359i	−0.0926251	−	0.0926251i	0.659276	−	0.751901i	$-0.270863\pi$
$307$	−28.4359	−	28.4359i	−0.0926251	−	0.0926251i	−0.751901	+	0.659276i	$0.770863\pi$
$308$	−52.6417	+	52.6417i	−0.170915	+	0.170915i
$309$		0			0
$310$	162.443	+	1.30640i	0.524009	+	0.00421421i
$311$	431.905			1.38876			0.694381	−	0.719607i	$-0.255678\pi$
$311$	431.905			1.38876			0.694381	+	0.719607i	$0.255678\pi$
$312$		0			0
$313$	146.693	−	146.693i	0.468667	−	0.468667i	−0.432816	−	0.901482i	$-0.642480\pi$
$313$	146.693	−	146.693i	0.468667	−	0.468667i	0.901482	+	0.432816i	$0.142480\pi$
$314$			28.9866i			0.0923141i
$315$		0			0
$316$	210.226			0.665274
$317$	−251.092	−	251.092i	−0.792088	−	0.792088i	0.189745	−	0.981833i	$-0.439234\pi$
$317$	−251.092	−	251.092i	−0.792088	−	0.792088i	−0.981833	+	0.189745i	$0.939234\pi$
$318$		0			0
$319$			279.664i			0.876691i
$320$	−56.1426	−	57.0530i	−0.175446	−	0.178290i
$321$		0			0
$322$	1.37705	+	1.37705i	0.00427654	+	0.00427654i
$323$	−108.306	+	108.306i	−0.335311	+	0.335311i
$324$		0			0
$325$	−356.616	−	368.276i	−1.09728	−	1.13316i
$326$	149.590			0.458865
$327$		0			0
$328$	162.272	−	162.272i	0.494732	−	0.494732i
$329$		−	33.2437i		−	0.101045i
$330$		0			0
$331$	374.902			1.13264			0.566318	−	0.824187i	$-0.308368\pi$
$331$	374.902			1.13264			0.566318	+	0.824187i	$0.308368\pi$
$332$	−125.550	−	125.550i	−0.378163	−	0.378163i
$333$		0			0
$334$		−	212.543i		−	0.636355i
$335$	−167.246	−	1.34503i	−0.499242	−	0.00401503i
$336$		0			0
$337$	−105.111	−	105.111i	−0.311901	−	0.311901i	0.533745	−	0.845646i	$-0.320784\pi$
$337$	−105.111	−	105.111i	−0.311901	−	0.311901i	−0.845646	+	0.533745i	$0.820784\pi$
$338$	133.594	−	133.594i	0.395249	−	0.395249i
$339$		0			0
$340$	1.95862	−	243.542i	0.00576066	−	0.716300i
$341$	503.643			1.47696
$342$		0			0
$343$	124.383	−	124.383i	0.362633	−	0.362633i
$344$		−	46.3433i		−	0.134719i
$345$		0			0
$346$	−232.878			−0.673057
$347$	−170.757	−	170.757i	−0.492095	−	0.492095i	0.416871	−	0.908966i	$-0.363127\pi$
$347$	−170.757	−	170.757i	−0.492095	−	0.492095i	−0.908966	+	0.416871i	$0.863127\pi$
$348$		0			0
$349$		−	382.426i		−	1.09578i	−0.836551	−	0.547889i	$-0.815432\pi$
$349$		−	382.426i		−	1.09578i	0.836551	−	0.547889i	$-0.184568\pi$
$350$	34.9420	+	0.562061i	0.0998343	+	0.00160589i
$351$		0			0
$352$	243.059	+	243.059i	0.690509	+	0.690509i
$353$	368.231	−	368.231i	1.04315	−	1.04315i	0.0441221	−	0.999026i	$-0.485951\pi$
$353$	368.231	−	368.231i	1.04315	−	1.04315i	0.999026	−	0.0441221i	$-0.0140491\pi$
$354$		0			0
$355$	−355.287	+	349.618i	−1.00081	+	0.984838i
$356$	−391.363			−1.09934
$357$		0			0
$358$	80.6843	−	80.6843i	0.225375	−	0.225375i
$359$			326.956i			0.910741i	0.890302	+	0.455370i	$0.150493\pi$
$359$			326.956i			0.910741i	−0.890302	+	0.455370i	$0.849507\pi$
$360$		0			0
$361$	244.292			0.676709
$362$	25.5507	+	25.5507i	0.0705822	+	0.0705822i
$363$		0			0
$364$		−	131.083i		−	0.360119i
$365$	1.27141	−	158.092i	0.00348333	−	0.433129i
$366$		0			0
$367$	369.714	+	369.714i	1.00740	+	1.00740i	0.999972	+	0.00742355i	$0.00236301\pi$
$367$	369.714	+	369.714i	1.00740	+	1.00740i	0.00742355	+	0.999972i	$0.497637\pi$
$368$	−9.40362	+	9.40362i	−0.0255533	+	0.0255533i
$369$		0			0
$370$	121.260	+	123.226i	0.327730	+	0.333044i
$371$	−135.064			−0.364055
$372$		0			0
$373$	17.1762	−	17.1762i	0.0460488	−	0.0460488i	−0.683707	−	0.729756i	$-0.739634\pi$
$373$	17.1762	−	17.1762i	0.0460488	−	0.0460488i	0.729756	+	0.683707i	$0.239634\pi$
$374$			124.045i			0.331672i
$375$		0			0
$376$	−99.8040			−0.265436
$377$	−348.197	−	348.197i	−0.923598	−	0.923598i
$378$		0			0
$379$			364.939i			0.962900i	0.876474	+	0.481450i	$0.159890\pi$
$379$			364.939i			0.962900i	−0.876474	+	0.481450i	$0.840110\pi$
$380$	132.274	−	130.163i	0.348088	−	0.342534i
$381$		0			0
$382$	193.045	+	193.045i	0.505354	+	0.505354i
$383$	−2.37711	+	2.37711i	−0.00620656	+	0.00620656i	−0.710203	−	0.703997i	$-0.751397\pi$
$383$	−2.37711	+	2.37711i	−0.00620656	+	0.00620656i	0.703997	+	0.710203i	$0.251397\pi$
$384$		0			0
$385$	108.342	+	0.871316i	0.281409	+	0.00226316i
$386$	−8.99155			−0.0232942
$387$		0			0
$388$	74.3668	−	74.3668i	0.191667	−	0.191667i
$389$		−	152.199i		−	0.391257i	−0.980678	−	0.195628i	$-0.937325\pi$
$389$		−	152.199i		−	0.391257i	0.980678	−	0.195628i	$-0.0626747\pi$
$390$		0			0
$391$	−19.7522			−0.0505171
$392$	−179.874	−	179.874i	−0.458861	−	0.458861i
$393$		0			0
$394$			48.1730i			0.122266i
$395$	−214.595	−	218.074i	−0.543278	−	0.552087i
$396$		0			0
$397$	−275.868	−	275.868i	−0.694882	−	0.694882i	0.268420	−	0.963302i	$-0.413498\pi$
$397$	−275.868	−	275.868i	−0.694882	−	0.694882i	−0.963302	+	0.268420i	$0.913498\pi$
$398$	9.03520	−	9.03520i	0.0227015	−	0.0227015i
$399$		0			0
$400$	−3.83822	+	238.613i	−0.00959554	+	0.596532i
$401$	674.978			1.68324			0.841618	−	0.540073i	$-0.181603\pi$
$401$	674.978			1.68324			0.841618	+	0.540073i	$0.181603\pi$
$402$		0			0
$403$	−627.062	+	627.062i	−1.55598	+	1.55598i
$404$			205.394i			0.508401i
$405$		0			0
$406$	33.5683			0.0826805
$407$	379.007	+	379.007i	0.931221	+	0.931221i
$408$		0			0
$409$		−	433.258i		−	1.05931i	−0.848213	−	0.529655i	$-0.822321\pi$
$409$		−	433.258i		−	1.05931i	0.848213	−	0.529655i	$-0.177679\pi$
$410$	−154.312	−	1.24101i	−0.376370	−	0.00302686i
$411$		0			0
$412$	−122.970	−	122.970i	−0.298470	−	0.298470i
$413$	−36.9856	+	36.9856i	−0.0895534	+	0.0895534i
$414$		0			0
$415$	−2.07808	+	258.396i	−0.00500743	+	0.622641i
$416$	−605.242			−1.45491
$417$		0			0
$418$	−66.8346	+	66.8346i	−0.159891	+	0.159891i
$419$			499.834i			1.19292i	0.802642	+	0.596461i	$0.203427\pi$
$419$			499.834i			1.19292i	−0.802642	+	0.596461i	$0.796573\pi$
$420$		0			0
$421$	−30.0850			−0.0714608			−0.0357304	−	0.999361i	$-0.511376\pi$
$421$	−30.0850			−0.0714608			−0.0357304	+	0.999361i	$0.511376\pi$
$422$	158.185	+	158.185i	0.374845	+	0.374845i
$423$		0			0
$424$			405.490i			0.956344i
$425$	−254.633	+	246.571i	−0.599136	+	0.580166i
$426$		0			0
$427$	108.151	+	108.151i	0.253280	+	0.253280i
$428$	−50.9701	+	50.9701i	−0.119089	+	0.119089i
$429$		0			0
$430$	−22.2122	+	21.8577i	−0.0516562	+	0.0508320i
$431$	515.749			1.19663			0.598316	−	0.801260i	$-0.295837\pi$
$431$	515.749			1.19663			0.598316	+	0.801260i	$0.295837\pi$
$432$		0			0
$433$	−305.797	+	305.797i	−0.706229	+	0.706229i	−0.965740	−	0.259511i	$-0.916439\pi$
$433$	−305.797	+	305.797i	−0.706229	+	0.706229i	0.259511	+	0.965740i	$0.416439\pi$
$434$		−	60.4526i		−	0.139292i
$435$		0			0
$436$	396.090			0.908463
$437$	−10.6423	−	10.6423i	−0.0243531	−	0.0243531i
$438$		0			0
$439$			505.286i			1.15099i	0.817804	+	0.575497i	$0.195191\pi$
$439$			505.286i			1.15099i	−0.817804	+	0.575497i	$0.804809\pi$
$440$	2.61586	−	325.265i	0.00594514	−	0.739239i
$441$		0			0
$442$	−154.443	−	154.443i	−0.349418	−	0.349418i
$443$	−142.907	+	142.907i	−0.322589	+	0.322589i	−0.849760	−	0.527170i	$-0.823253\pi$
$443$	−142.907	+	142.907i	−0.322589	+	0.322589i	0.527170	+	0.849760i	$0.323253\pi$
$444$		0			0
$445$	399.495	+	405.973i	0.897742	+	0.912299i
$446$	−24.0154			−0.0538462
$447$		0			0
$448$	−21.0627	+	21.0627i	−0.0470149	+	0.0470149i
$449$		−	145.089i		−	0.323138i	−0.986861	−	0.161569i	$-0.948345\pi$
$449$		−	145.089i		−	0.323138i	0.986861	−	0.161569i	$-0.0516554\pi$
$450$		0			0
$451$	−478.433			−1.06083
$452$	254.553	+	254.553i	0.563170	+	0.563170i
$453$		0			0
$454$		−	293.870i		−	0.647291i
$455$	−135.977	+	133.807i	−0.298850	+	0.294081i
$456$		0			0
$457$	209.752	+	209.752i	0.458976	+	0.458976i	0.898319	−	0.439343i	$-0.144789\pi$
$457$	209.752	+	209.752i	0.458976	+	0.458976i	−0.439343	+	0.898319i	$0.644789\pi$
$458$	133.249	−	133.249i	0.290936	−	0.290936i
$459$		0			0
$460$	23.9309	+	0.192458i	0.0520236	+	0.000418387i
$461$	−286.088			−0.620581			−0.310291	−	0.950642i	$-0.600426\pi$
$461$	−286.088			−0.620581			−0.310291	+	0.950642i	$0.600426\pi$
$462$		0			0
$463$	176.942	−	176.942i	0.382164	−	0.382164i	−0.489717	−	0.871881i	$-0.662900\pi$
$463$	176.942	−	176.942i	0.382164	−	0.382164i	0.871881	+	0.489717i	$0.162900\pi$
$464$			229.232i			0.494034i
$465$		0			0
$466$	254.017			0.545101
$467$	−71.3291	−	71.3291i	−0.152739	−	0.152739i	0.626601	−	0.779340i	$-0.284446\pi$
$467$	−71.3291	−	71.3291i	−0.152739	−	0.152739i	−0.779340	+	0.626601i	$0.784446\pi$
$468$		0			0
$469$			62.2401i			0.132708i
$470$	47.0724	+	47.8356i	0.100154	+	0.101778i
$471$		0			0
$472$	111.038	+	111.038i	0.235250	+	0.235250i
$473$	−68.3180	+	68.3180i	−0.144435	+	0.144435i
$474$		0			0
$475$	−270.044	−	4.34380i	−0.568514	−	0.00914484i
$476$	−90.6334			−0.190406
$477$		0			0
$478$	−20.7628	+	20.7628i	−0.0434367	+	0.0434367i
$479$			196.071i			0.409335i	0.978832	+	0.204667i	$0.0656113\pi$
$479$			196.071i			0.409335i	−0.978832	+	0.204667i	$0.934389\pi$
$480$		0			0
$481$	−943.766			−1.96209
$482$	44.4662	+	44.4662i	0.0922535	+	0.0922535i
$483$		0			0
$484$		−	50.2504i		−	0.103823i
$485$	−153.055	−	1.23091i	−0.315577	−	0.00253795i
$486$		0			0
$487$	660.124	+	660.124i	1.35549	+	1.35549i	0.879391	+	0.476100i	$0.157950\pi$
$487$	660.124	+	660.124i	1.35549	+	1.35549i	0.476100	+	0.879391i	$0.342050\pi$
$488$	324.690	−	324.690i	0.665347	−	0.665347i
$489$		0			0
$490$	−1.37562	+	171.050i	−0.00280739	+	0.349081i
$491$	−787.998			−1.60488			−0.802442	−	0.596730i	$-0.796466\pi$
$491$	−787.998			−1.60488			−0.802442	+	0.596730i	$0.796466\pi$
$492$		0			0
$493$	−240.750	+	240.750i	−0.488336	+	0.488336i
$494$		−	166.425i		−	0.336892i
$495$		0			0
$496$	412.820			0.832299
$497$	131.164	+	131.164i	0.263911	+	0.263911i
$498$		0			0
$499$			167.150i			0.334970i	0.985875	+	0.167485i	$0.0535646\pi$
$499$			167.150i			0.334970i	−0.985875	+	0.167485i	$0.946435\pi$
$500$	310.904	−	296.253i	0.621809	−	0.592506i
$501$		0			0
$502$	−61.9801	−	61.9801i	−0.123466	−	0.123466i
$503$	249.990	−	249.990i	0.496998	−	0.496998i	−0.413504	−	0.910502i	$-0.635695\pi$
$503$	249.990	−	249.990i	0.496998	−	0.496998i	0.910502	+	0.413504i	$0.135695\pi$
$504$		0			0
$505$	213.061	−	209.662i	0.421904	−	0.415172i
$506$	−12.1889			−0.0240888
$507$		0			0
$508$	192.679	−	192.679i	0.379289	−	0.379289i
$509$			110.464i			0.217021i	0.994095	+	0.108511i	$0.0346082\pi$
$509$			110.464i			0.217021i	−0.994095	+	0.108511i	$0.965392\pi$
$510$		0			0
$511$	−58.8335			−0.115134
$512$	350.050	+	350.050i	0.683691	+	0.683691i
$513$		0			0
$514$		−	3.59475i		−	0.00699368i
$515$	−2.03537	+	253.085i	−0.00395218	+	0.491428i
$516$		0			0
$517$	147.128	+	147.128i	0.284580	+	0.284580i
$518$	45.4924	−	45.4924i	0.0878232	−	0.0878232i
$519$		0			0
$520$	401.715	+	408.229i	0.772529	+	0.785055i
$521$	−415.088			−0.796715			−0.398357	−	0.917230i	$-0.630420\pi$
$521$	−415.088			−0.796715			−0.398357	+	0.917230i	$0.630420\pi$
$522$		0			0
$523$	−384.585	+	384.585i	−0.735344	+	0.735344i	−0.971673	−	0.236329i	$-0.924056\pi$
$523$	−384.585	+	384.585i	−0.735344	+	0.735344i	0.236329	+	0.971673i	$0.424056\pi$
$524$		−	15.9227i		−	0.0303869i
$525$		0			0
$526$	−73.4796			−0.139695
$527$	433.562	+	433.562i	0.822699	+	0.822699i
$528$		0			0
$529$			527.059i			0.996331i
$530$	194.350	−	191.248i	0.366697	−	0.360846i
$531$		0			0
$532$	−48.8325	−	48.8325i	−0.0917904	−	0.0917904i
$533$	595.674	−	595.674i	1.11759	−	1.11759i
$534$		0			0
$535$	104.902	+	0.843648i	0.196079	+	0.00157691i
$536$	186.857			0.348614
$537$		0			0
$538$	113.082	−	113.082i	0.210190	−	0.210190i
$539$			530.329i			0.983912i
$540$		0			0
$541$	251.489			0.464859			0.232430	−	0.972613i	$-0.425332\pi$
$541$	251.489			0.464859			0.232430	+	0.972613i	$0.425332\pi$
$542$	−95.7493	−	95.7493i	−0.176659	−	0.176659i
$543$		0			0
$544$			418.476i			0.769257i
$545$	−404.320	−	410.876i	−0.741871	−	0.753901i
$546$		0			0
$547$	−394.926	−	394.926i	−0.721986	−	0.721986i	0.247024	−	0.969009i	$-0.420548\pi$
$547$	−394.926	−	394.926i	−0.721986	−	0.721986i	−0.969009	+	0.247024i	$0.920548\pi$
$548$	−5.77833	+	5.77833i	−0.0105444	+	0.0105444i
$549$		0			0
$550$	−157.132	+	152.157i	−0.285694	+	0.276649i
$551$	−259.427			−0.470830
$552$		0			0
$553$	−80.5082	+	80.5082i	−0.145585	+	0.145585i
$554$		−	245.870i		−	0.443808i
$555$		0			0
$556$	880.395			1.58344
$557$	302.419	+	302.419i	0.542943	+	0.542943i	0.924391	−	0.381447i	$-0.124574\pi$
$557$	302.419	+	302.419i	0.542943	+	0.542943i	−0.381447	+	0.924391i	$0.624574\pi$
$558$		0			0
$559$		−	170.119i		−	0.304327i
$560$	88.8048	+	0.714190i	0.158580	+	0.00127534i
$561$		0			0
$562$	16.6120	+	16.6120i	0.0295587	+	0.0295587i
$563$	639.903	−	639.903i	1.13659	−	1.13659i	0.147538	−	0.989056i	$-0.452865\pi$
$563$	639.903	−	639.903i	1.13659	−	1.13659i	0.989056	−	0.147538i	$-0.0471349\pi$
$564$		0			0
$565$	4.21331	−	523.897i	0.00745719	−	0.927252i
$566$	−152.307			−0.269094
$567$		0			0
$568$	393.780	−	393.780i	0.693274	−	0.693274i
$569$		−	224.106i		−	0.393859i	−0.980418	−	0.196929i	$-0.936903\pi$
$569$		−	224.106i		−	0.393859i	0.980418	−	0.196929i	$-0.0630970\pi$
$570$		0			0
$571$	56.6121			0.0991456			0.0495728	−	0.998771i	$-0.484214\pi$
$571$	56.6121			0.0991456			0.0495728	+	0.998771i	$0.484214\pi$
$572$	580.142	+	580.142i	1.01423	+	1.01423i
$573$		0			0
$574$			57.4266i			0.100046i
$575$	−24.2285	−	25.0207i	−0.0421365	−	0.0435142i
$576$		0			0
$577$	−450.543	−	450.543i	−0.780838	−	0.780838i	0.199135	−	0.979972i	$-0.436187\pi$
$577$	−450.543	−	450.543i	−0.780838	−	0.780838i	−0.979972	+	0.199135i	$0.936187\pi$
$578$	46.7393	−	46.7393i	0.0808638	−	0.0808638i
$579$		0			0
$580$	294.027	−	289.336i	0.506943	−	0.498854i
$581$	96.1613			0.165510
$582$		0			0
$583$	597.761	−	597.761i	1.02532	−	1.02532i
$584$			176.630i			0.302448i
$585$		0			0
$586$	29.2982			0.0499969
$587$	−245.508	−	245.508i	−0.418242	−	0.418242i	0.466355	−	0.884598i	$-0.345567\pi$
$587$	−245.508	−	245.508i	−0.418242	−	0.418242i	−0.884598	+	0.466355i	$0.845567\pi$
$588$		0			0
$589$			467.199i			0.793207i
$590$	0.849187	−	105.591i	0.00143930	−	0.178967i
$591$		0			0
$592$	310.660	+	310.660i	0.524763	+	0.524763i
$593$	−235.628	+	235.628i	−0.397350	+	0.397350i	−0.877297	−	0.479948i	$-0.840656\pi$
$593$	−235.628	+	235.628i	−0.397350	+	0.397350i	0.479948	+	0.877297i	$0.340656\pi$
$594$		0			0
$595$	92.5167	+	94.0168i	0.155490	+	0.158011i
$596$	−323.696			−0.543114
$597$		0			0
$598$	15.1758	−	15.1758i	0.0253777	−	0.0253777i
$599$		−	593.319i		−	0.990515i	−0.868746	−	0.495258i	$-0.835074\pi$
$599$		−	593.319i		−	0.990515i	0.868746	−	0.495258i	$-0.164926\pi$
$600$		0			0
$601$	−538.499			−0.896004			−0.448002	−	0.894032i	$-0.647864\pi$
$601$	−538.499			−0.896004			−0.448002	+	0.894032i	$0.647864\pi$
$602$	8.20024	+	8.20024i	0.0136217	+	0.0136217i
$603$		0			0
$604$			96.5233i			0.159807i
$605$	−52.1262	+	51.2945i	−0.0861591	+	0.0847843i
$606$		0			0
$607$	289.365	+	289.365i	0.476714	+	0.476714i	0.904079	−	0.427365i	$-0.140558\pi$
$607$	289.365	+	289.365i	0.476714	+	0.476714i	−0.427365	+	0.904079i	$0.640558\pi$
$608$	−225.471	+	225.471i	−0.370840	+	0.370840i
$609$		0			0
$610$	−308.762	−	2.48314i	−0.506166	−	0.00407072i
$611$	−366.364			−0.599614
$612$		0			0
$613$	−10.5026	+	10.5026i	−0.0171331	+	0.0171331i	−0.715621	−	0.698488i	$-0.753856\pi$
$613$	−10.5026	+	10.5026i	−0.0171331	+	0.0171331i	0.698488	+	0.715621i	$0.253856\pi$
$614$		−	30.2117i		−	0.0492048i
$615$		0			0
$616$	−121.046			−0.196504
$617$	−308.853	−	308.853i	−0.500571	−	0.500571i	0.411044	−	0.911615i	$-0.365164\pi$
$617$	−308.853	−	308.853i	−0.500571	−	0.500571i	−0.911615	+	0.411044i	$0.865164\pi$
$618$		0			0
$619$			10.2905i			0.0166244i	0.999965	+	0.00831222i	$0.00264589\pi$
$619$			10.2905i			0.0166244i	−0.999965	+	0.00831222i	$0.997354\pi$
$620$	−521.060	−	529.509i	−0.840420	−	0.854047i
$621$		0			0
$622$	229.439	+	229.439i	0.368873	+	0.368873i
$623$	149.876	−	149.876i	0.240572	−	0.240572i
$624$		0			0
$625$	−624.677	−	20.1017i	−0.999483	−	0.0321627i
$626$	155.854			0.248967
$627$		0			0
$628$	93.7329	−	93.7329i	0.149256	−	0.149256i
$629$			652.537i			1.03742i
$630$		0			0
$631$	154.559			0.244943			0.122472	−	0.992472i	$-0.460918\pi$
$631$	154.559			0.244943			0.122472	+	0.992472i	$0.460918\pi$
$632$	241.701	+	241.701i	0.382439	+	0.382439i
$633$		0			0
$634$		−	266.773i		−	0.420777i
$635$	−396.554	−	3.18919i	−0.624495	−	0.00502234i
$636$		0			0
$637$	−660.286	−	660.286i	−1.03656	−	1.03656i
$638$	−148.565	+	148.565i	−0.232860	+	0.232860i
$639$		0			0
$640$	5.23092	−	650.430i	0.00817331	−	1.01630i
$641$	605.632			0.944824			0.472412	−	0.881378i	$-0.343383\pi$
$641$	605.632			0.944824			0.472412	+	0.881378i	$0.343383\pi$
$642$		0			0
$643$	−329.925	+	329.925i	−0.513103	+	0.513103i	−0.915476	−	0.402373i	$-0.868186\pi$
$643$	−329.925	+	329.925i	−0.513103	+	0.513103i	0.402373	+	0.915476i	$0.368186\pi$
$644$		−	8.90581i		−	0.0138289i
$645$		0			0
$646$	−115.069			−0.178126
$647$	−117.084	−	117.084i	−0.180965	−	0.180965i	0.610811	−	0.791776i	$-0.290843\pi$
$647$	−117.084	−	117.084i	−0.180965	−	0.180965i	−0.791776	+	0.610811i	$0.790843\pi$
$648$		0			0
$649$		−	327.378i		−	0.504434i
$650$	6.19422	−	385.080i	0.00952958	−	0.592432i
$651$		0			0
$652$	−483.723	−	483.723i	−0.741906	−	0.741906i
$653$	−236.188	+	236.188i	−0.361696	+	0.361696i	−0.864437	−	0.502741i	$-0.832325\pi$
$653$	−236.188	+	236.188i	−0.361696	+	0.361696i	0.502741	+	0.864437i	$0.332325\pi$
$654$		0			0
$655$	−16.5171	+	16.2536i	−0.0252170	+	0.0248146i
$656$	−392.156			−0.597799
$657$		0			0
$658$	17.6599	−	17.6599i	0.0268387	−	0.0268387i
$659$			1226.61i			1.86131i	0.365892	+	0.930657i	$0.380764\pi$
$659$			1226.61i			1.86131i	−0.365892	+	0.930657i	$0.619236\pi$
$660$		0			0
$661$	−159.755			−0.241687			−0.120844	−	0.992672i	$-0.538560\pi$
$661$	−159.755			−0.241687			−0.120844	+	0.992672i	$0.538560\pi$
$662$	199.157	+	199.157i	0.300842	+	0.300842i
$663$		0			0
$664$		−	288.695i		−	0.434782i
$665$	−0.808266	+	100.503i	−0.00121544	+	0.151132i
$666$		0			0
$667$	−23.6565	−	23.6565i	−0.0354670	−	0.0354670i
$668$	−687.290	+	687.290i	−1.02888	+	1.02888i
$669$		0			0
$670$	−88.1307	−	89.5598i	−0.131538	−	0.133671i
$671$	−957.295			−1.42667
$672$		0			0
$673$	33.6536	−	33.6536i	0.0500054	−	0.0500054i	−0.681662	−	0.731667i	$-0.738742\pi$
$673$	33.6536	−	33.6536i	0.0500054	−	0.0500054i	0.731667	+	0.681662i	$0.238742\pi$
$674$		−	111.675i		−	0.165690i
$675$		0			0
$676$	−863.996			−1.27810
$677$	103.682	+	103.682i	0.153150	+	0.153150i	0.779523	−	0.626373i	$-0.215461\pi$
$677$	103.682	+	103.682i	0.153150	+	0.153150i	−0.626373	+	0.779523i	$0.715461\pi$
$678$		0			0
$679$			56.9590i			0.0838865i
$680$	282.257	−	277.753i	0.415084	−	0.408460i
$681$		0			0
$682$	267.548	+	267.548i	0.392299	+	0.392299i
$683$	882.608	−	882.608i	1.29225	−	1.29225i	0.358860	−	0.933391i	$-0.383165\pi$
$683$	882.608	−	882.608i	1.29225	−	1.29225i	0.933391	−	0.358860i	$-0.116835\pi$
$684$		0			0
$685$	11.8924	+	0.0956418i	0.0173612	+	0.000139623i
$686$	132.151			0.192640
$687$		0			0
$688$	−55.9981	+	55.9981i	−0.0813925	+	0.0813925i
$689$			1488.49i			2.16036i
$690$		0			0
$691$	−507.664			−0.734681			−0.367340	−	0.930087i	$-0.619732\pi$
$691$	−507.664			−0.734681			−0.367340	+	0.930087i	$0.619732\pi$
$692$	753.047	+	753.047i	1.08822	+	1.08822i
$693$		0			0
$694$		−	181.421i		−	0.261413i
$695$	−898.688	−	913.260i	−1.29308	−	1.31404i
$696$		0			0
$697$	−411.860	−	411.860i	−0.590904	−	0.590904i
$698$	203.154	−	203.154i	0.291052	−	0.291052i
$699$		0			0
$700$	−111.173	−	114.808i	−0.158819	−	0.164011i
$701$	194.042			0.276807			0.138403	−	0.990376i	$-0.455803\pi$
$701$	194.042			0.276807			0.138403	+	0.990376i	$0.455803\pi$
$702$		0			0
$703$	−351.581	+	351.581i	−0.500115	+	0.500115i
$704$		−	186.436i		−	0.264824i
$705$		0			0
$706$	391.227			0.554146
$707$	−78.6576	−	78.6576i	−0.111255	−	0.111255i
$708$		0			0
$709$		−	478.623i		−	0.675067i	−0.941313	−	0.337534i	$-0.890407\pi$
$709$		−	478.623i		−	0.675067i	0.941313	−	0.337534i	$-0.109593\pi$
$710$	−374.463	−	3.01152i	−0.527412	−	0.00424158i
$711$		0			0
$712$	−449.958	−	449.958i	−0.631963	−	0.631963i
$713$	−42.6026	+	42.6026i	−0.0597512	+	0.0597512i
$714$		0			0
$715$	9.60240	−	1193.99i	0.0134299	−	1.66992i
$716$	−521.811			−0.728787
$717$		0			0
$718$	−173.687	+	173.687i	−0.241904	+	0.241904i
$719$		−	443.536i		−	0.616879i	−0.951244	−	0.308439i	$-0.900193\pi$
$719$		−	443.536i		−	0.616879i	0.951244	−	0.308439i	$-0.0998067\pi$
$720$		0			0
$721$	94.1849			0.130631
$722$	129.774	+	129.774i	0.179742	+	0.179742i
$723$		0			0
$724$		−	165.245i		−	0.228239i
$725$	−600.273	−	9.65571i	−0.827963	−	0.0133182i
$726$		0			0
$727$	204.982	+	204.982i	0.281955	+	0.281955i	0.833888	−	0.551933i	$-0.186110\pi$
$727$	204.982	+	204.982i	0.281955	+	0.281955i	−0.551933	+	0.833888i	$0.686110\pi$
$728$	150.709	−	150.709i	0.207018	−	0.207018i
$729$		0			0
$730$	84.6578	−	83.3070i	0.115970	−	0.114119i
$731$	−117.623			−0.160907
$732$		0			0
$733$	722.853	−	722.853i	0.986157	−	0.986157i	−0.0137487	−	0.999905i	$-0.504376\pi$
$733$	722.853	−	722.853i	0.986157	−	0.986157i	0.999905	+	0.0137487i	$0.00437648\pi$
$734$			392.803i			0.535154i
$735$		0			0
$736$	−41.1202			−0.0558698
$737$	−275.459	−	275.459i	−0.373757	−	0.373757i
$738$		0			0
$739$			153.917i			0.208277i	0.994563	+	0.104138i	$0.0332085\pi$
$739$			153.917i			0.208277i	−0.994563	+	0.104138i	$0.966791\pi$
$740$	6.35808	−	790.585i	0.00859200	−	1.06836i
$741$		0			0
$742$	−71.7496	−	71.7496i	−0.0966975	−	0.0966975i
$743$	923.129	−	923.129i	1.24244	−	1.24244i	0.283447	−	0.958988i	$-0.408522\pi$
$743$	923.129	−	923.129i	1.24244	−	1.24244i	0.958988	−	0.283447i	$-0.0914781\pi$
$744$		0			0
$745$	330.422	+	335.780i	0.443519	+	0.450711i
$746$	18.2489			0.0244623
$747$		0			0
$748$	401.121	−	401.121i	0.536258	−	0.536258i
$749$		−	39.0390i		−	0.0521215i
$750$		0			0
$751$	1457.82			1.94117			0.970583	−	0.240765i	$-0.0773984\pi$
$751$	1457.82			1.94117			0.970583	+	0.240765i	$0.0773984\pi$
$752$	120.596	+	120.596i	0.160367	+	0.160367i
$753$		0			0
$754$		−	369.941i		−	0.490638i
$755$	100.127	−	98.5289i	0.132618	−	0.130502i
$756$		0			0
$757$	−575.216	−	575.216i	−0.759863	−	0.759863i	0.216434	−	0.976297i	$-0.430557\pi$
$757$	−575.216	−	575.216i	−0.759863	−	0.759863i	−0.976297	+	0.216434i	$0.930557\pi$
$758$	−193.865	+	193.865i	−0.255758	+	0.255758i
$759$		0			0
$760$	301.728	+	2.42657i	0.397011	+	0.00319286i
$761$	1013.44			1.33173			0.665863	−	0.746074i	$-0.268063\pi$
$761$	1013.44			1.33173			0.665863	+	0.746074i	$0.268063\pi$
$762$		0			0
$763$	−151.686	+	151.686i	−0.198803	+	0.198803i
$764$		−	1248.49i		−	1.63414i
$765$		0			0
$766$	−2.52556			−0.00329708
$767$	407.602	+	407.602i	0.531424	+	0.531424i
$768$		0			0
$769$		−	561.278i		−	0.729880i	−0.931031	−	0.364940i	$-0.881089\pi$
$769$		−	561.278i		−	0.729880i	0.931031	−	0.364940i	$-0.118911\pi$
$770$	57.0913	+	58.0171i	0.0741446	+	0.0753468i
$771$		0			0
$772$	29.0756	+	29.0756i	0.0376627	+	0.0376627i
$773$	445.834	−	445.834i	0.576758	−	0.576758i	−0.357251	−	0.934008i	$-0.616286\pi$
$773$	445.834	−	445.834i	0.576758	−	0.576758i	0.934008	+	0.357251i	$0.116286\pi$
$774$		0			0
$775$	−17.3888	+	1081.02i	−0.0224372	+	1.39487i
$776$	171.002			0.220363
$777$		0			0
$778$	80.8518	−	80.8518i	0.103923	−	0.103923i
$779$		−	443.813i		−	0.569721i
$780$		0			0
$781$	−1161.00			−1.48655
$782$	−10.4929	−	10.4929i	−0.0134180	−	0.0134180i
$783$		0			0
$784$			434.693i			0.554456i
$785$	−192.913	−	1.55145i	−0.245748	−	0.00197637i
$786$		0			0
$787$	−990.635	−	990.635i	−1.25875	−	1.25875i	−0.951691	−	0.307058i	$-0.900655\pi$
$787$	−990.635	−	990.635i	−1.25875	−	1.25875i	−0.307058	−	0.951691i	$-0.599345\pi$
$788$	155.775	−	155.775i	0.197684	−	0.197684i
$789$		0			0
$790$	1.84847	−	229.844i	0.00233983	−	0.290942i
$791$	−194.967			−0.246482
$792$		0			0
$793$	1191.88	−	1191.88i	1.50300	−	1.50300i
$794$		−	293.096i		−	0.369138i
$795$		0			0
$796$	−58.4335			−0.0734089
$797$	−335.574	−	335.574i	−0.421047	−	0.421047i	0.464517	−	0.885564i	$-0.346228\pi$
$797$	−335.574	−	335.574i	−0.421047	−	0.421047i	−0.885564	+	0.464517i	$0.846228\pi$
$798$		0			0
$799$			253.311i			0.317035i
$800$	−530.095	+	513.312i	−0.662619	+	0.641640i
$801$		0			0
$802$	358.565	+	358.565i	0.447088	+	0.447088i
$803$	260.382	−	260.382i	0.324262	−	0.324262i
$804$		0			0
$805$	−9.23826	+	9.09085i	−0.0114761	+	0.0112930i
$806$	−666.222			−0.826578
$807$		0			0
$808$	−236.145	+	236.145i	−0.292259	+	0.292259i
$809$			806.321i			0.996689i	0.866979	+	0.498344i	$0.166059\pi$
$809$			806.321i			0.996689i	−0.866979	+	0.498344i	$0.833941\pi$
$810$		0			0
$811$	−928.637			−1.14505			−0.572526	−	0.819887i	$-0.694036\pi$
$811$	−928.637			−1.14505			−0.572526	+	0.819887i	$0.694036\pi$
$812$	−108.548	−	108.548i	−0.133680	−	0.133680i
$813$		0			0
$814$			402.676i			0.494688i
$815$	−8.00649	+	995.555i	−0.00982392	+	1.22154i
$816$		0			0
$817$	−63.3743	−	63.3743i	−0.0775696	−	0.0775696i
$818$	230.158	−	230.158i	0.281366	−	0.281366i
$819$		0			0
$820$	494.978	+	503.004i	0.603632	+	0.613419i
$821$	519.179			0.632374			0.316187	−	0.948697i	$-0.397597\pi$
$821$	519.179			0.632374			0.316187	+	0.948697i	$0.397597\pi$
$822$		0			0
$823$	−911.752	+	911.752i	−1.10784	+	1.10784i	−0.114406	+	0.993434i	$0.536496\pi$
$823$	−911.752	+	911.752i	−1.10784	+	1.10784i	−0.993434	+	0.114406i	$0.963504\pi$
$824$		−	282.761i		−	0.343157i
$825$		0			0
$826$	−39.2953			−0.0475730
$827$	−380.149	−	380.149i	−0.459672	−	0.459672i	0.438876	−	0.898548i	$-0.355377\pi$
$827$	−380.149	−	380.149i	−0.459672	−	0.459672i	−0.898548	+	0.438876i	$0.855377\pi$
$828$		0			0
$829$		−	511.167i		−	0.616606i	−0.951288	−	0.308303i	$-0.900239\pi$
$829$		−	511.167i		−	0.616606i	0.951288	−	0.308303i	$-0.0997611\pi$
$830$	−138.370	+	136.162i	−0.166711	+	0.164051i
$831$		0			0
$832$	232.123	+	232.123i	0.278994	+	0.278994i
$833$	−456.534	+	456.534i	−0.548060	+	0.548060i
$834$		0			0
$835$	1414.52	+	11.3759i	1.69403	+	0.0136238i
$836$	432.240			0.517034
$837$		0			0
$838$	−265.524	+	265.524i	−0.316855	+	0.316855i
$839$			1026.58i			1.22358i	0.791022	+	0.611788i	$0.209549\pi$
$839$			1026.58i			1.22358i	−0.791022	+	0.611788i	$0.790451\pi$
$840$		0			0
$841$	264.326			0.314300
$842$	−15.9819	−	15.9819i	−0.0189809	−	0.0189809i
$843$		0			0
$844$		−	1023.03i		−	1.21212i
$845$	881.948	+	896.249i	1.04373	+	1.06065i
$846$		0			0
$847$	19.2439	+	19.2439i	0.0227200	+	0.0227200i
$848$	489.966	−	489.966i	0.577790	−	0.577790i
$849$		0			0
$850$	−266.252	−	4.28280i	−0.313237	−	0.00503859i
$851$	−64.1195			−0.0753460
$852$		0			0
$853$	984.844	−	984.844i	1.15457	−	1.15457i	0.168939	−	0.985627i	$-0.445966\pi$
$853$	984.844	−	984.844i	1.15457	−	1.15457i	0.985627	−	0.168939i	$-0.0540341\pi$
$854$			114.905i			0.134549i
$855$		0			0
$856$	−117.203			−0.136919
$857$	−233.567	−	233.567i	−0.272540	−	0.272540i	0.557582	−	0.830122i	$-0.311729\pi$
$857$	−233.567	−	233.567i	−0.272540	−	0.272540i	−0.830122	+	0.557582i	$0.811729\pi$
$858$		0			0
$859$			305.759i			0.355947i	0.984035	+	0.177974i	$0.0569542\pi$
$859$			305.759i			0.355947i	−0.984035	+	0.177974i	$0.943046\pi$
$860$	142.507	+	1.14608i	0.165706	+	0.00133265i
$861$		0			0
$862$	273.979	+	273.979i	0.317841	+	0.317841i
$863$	386.017	−	386.017i	0.447297	−	0.447297i	−0.447158	−	0.894455i	$-0.647564\pi$
$863$	386.017	−	386.017i	0.447297	−	0.447297i	0.894455	+	0.447158i	$0.147564\pi$
$864$		0			0
$865$	12.4643	−	1549.85i	0.0144096	−	1.79174i
$866$	−324.894			−0.375167
$867$		0			0
$868$	−195.483	+	195.483i	−0.225211	+	0.225211i
$869$		−	712.618i		−	0.820044i
$870$		0			0
$871$	685.921			0.787510
$872$	455.392	+	455.392i	0.522238	+	0.522238i
$873$		0			0
$874$		−	11.3069i		−	0.0129370i
$875$	−5.61084	+	232.517i	−0.00641238	+	0.265733i
$876$		0			0
$877$	295.450	+	295.450i	0.336887	+	0.336887i	0.855194	−	0.518307i	$-0.173438\pi$
$877$	295.450	+	295.450i	0.336887	+	0.336887i	−0.518307	+	0.855194i	$0.673438\pi$
$878$	−268.421	+	268.421i	−0.305718	+	0.305718i
$879$		0			0
$880$	−396.189	+	389.867i	−0.450214	+	0.443031i
$881$	−1495.93			−1.69799			−0.848993	−	0.528403i	$-0.822791\pi$
$881$	−1495.93			−1.69799			−0.848993	+	0.528403i	$0.822791\pi$
$882$		0			0
$883$	−158.383	+	158.383i	−0.179369	+	0.179369i	−0.791081	−	0.611712i	$-0.790481\pi$
$883$	−158.383	+	158.383i	−0.179369	+	0.179369i	0.611712	+	0.791081i	$0.290481\pi$
$884$			998.832i			1.12990i
$885$		0			0
$886$	−151.831			−0.171367
$887$	970.442	+	970.442i	1.09407	+	1.09407i	0.995089	+	0.0989824i	$0.0315588\pi$
$887$	970.442	+	970.442i	1.09407	+	1.09407i	0.0989824	+	0.995089i	$0.468441\pi$
$888$		0			0
$889$			147.577i			0.166003i
$890$	−3.44115	+	427.885i	−0.00386647	+	0.480769i
$891$		0			0
$892$	77.6576	+	77.6576i	0.0870601	+	0.0870601i
$893$	−136.482	+	136.482i	−0.152835	+	0.152835i
$894$		0			0
$895$	532.654	+	541.291i	0.595144	+	0.604794i
$896$	−242.056			−0.270151
$897$		0			0
$898$	77.0748	−	77.0748i	0.0858294	−	0.0858294i
$899$			1038.52i			1.15520i
$900$		0			0
$901$	1029.17			1.14225
$902$	−254.155	−	254.155i	−0.281769	−	0.281769i
$903$		0			0
$904$			585.329i			0.647487i
$905$	−171.413	+	168.678i	−0.189407	+	0.186385i
$906$		0			0
$907$	−392.191	−	392.191i	−0.432405	−	0.432405i	0.457041	−	0.889446i	$-0.348909\pi$
$907$	−392.191	−	392.191i	−0.432405	−	0.432405i	−0.889446	+	0.457041i	$0.848909\pi$
$908$	−950.276	+	950.276i	−1.04656	+	1.04656i
$909$		0			0
$910$	−143.316	−	1.15258i	−0.157490	−	0.00126657i
$911$	968.817			1.06347			0.531733	−	0.846912i	$-0.321541\pi$
$911$	968.817			1.06347			0.531733	+	0.846912i	$0.321541\pi$
$912$		0			0
$913$	−425.586	+	425.586i	−0.466140	+	0.466140i
$914$			222.851i			0.243820i
$915$		0			0
$916$	−861.763			−0.940790
$917$	6.09776	+	6.09776i	0.00664968	+	0.00664968i
$918$		0			0
$919$		−	600.903i		−	0.653866i	−0.945048	−	0.326933i	$-0.893985\pi$
$919$		−	600.903i		−	0.653866i	0.945048	−	0.326933i	$-0.106015\pi$
$920$	27.2925	+	27.7351i	0.0296658	+	0.0301468i
$921$		0			0
$922$	−151.977	−	151.977i	−0.164834	−	0.164834i
$923$	1445.50	−	1445.50i	1.56609	−	1.56609i
$924$		0			0
$925$	−826.588	+	800.417i	−0.893609	+	0.865315i
$926$	187.992			0.203015
$927$		0			0
$928$	−501.193	+	501.193i	−0.540079	+	0.540079i
$929$		−	503.445i		−	0.541921i	−0.962590	−	0.270961i	$-0.912659\pi$
$929$		−	503.445i		−	0.541921i	0.962590	−	0.270961i	$-0.0873413\pi$
$930$		0			0
$931$	−491.953			−0.528413
$932$	−821.404	−	821.404i	−0.881335	−	0.881335i
$933$		0			0
$934$		−	75.7835i		−	0.0811387i
$935$	−825.550	−	6.63928i	−0.882941	−	0.00710083i
$936$		0			0
$937$	1181.10	+	1181.10i	1.26051	+	1.26051i	0.950847	+	0.309660i	$0.100215\pi$
$937$	1181.10	+	1181.10i	1.26051	+	1.26051i	0.309660	+	0.950847i	$0.399785\pi$
$938$	−33.0635	+	33.0635i	−0.0352489	+	0.0352489i
$939$		0			0
$940$	2.46817	−	306.900i	0.00262571	−	0.326490i
$941$	1153.23			1.22554			0.612770	−	0.790262i	$-0.290055\pi$
$941$	1153.23			1.22554			0.612770	+	0.790262i	$0.290055\pi$
$942$		0			0
$943$	40.4701	−	40.4701i	0.0429163	−	0.0429163i
$944$		−	268.341i		−	0.284259i
$945$		0			0
$946$	−72.5844			−0.0767277
$947$	−968.830	−	968.830i	−1.02305	−	1.02305i	−0.999728	−	0.0233233i	$-0.992575\pi$
$947$	−968.830	−	968.830i	−1.02305	−	1.02305i	−0.0233233	−	0.999728i	$-0.507425\pi$
$948$		0			0
$949$			648.378i			0.683222i
$950$	−141.147	−	145.762i	−0.148575	−	0.153433i
$951$		0			0
$952$	−104.203	−	104.203i	−0.109457	−	0.109457i
$953$	77.4456	−	77.4456i	0.0812650	−	0.0812650i	−0.665306	−	0.746571i	$-0.731699\pi$
$953$	77.4456	−	77.4456i	0.0812650	−	0.0812650i	0.746571	+	0.665306i	$0.231699\pi$
$954$		0			0
$955$	−1295.09	+	1274.43i	−1.35612	+	1.33448i
$956$	134.279			0.140460
$957$		0			0
$958$	−104.158	+	104.158i	−0.108724	+	0.108724i
$959$		−	4.42573i		−	0.00461494i
$960$		0			0
$961$	909.261			0.946161
$962$	−501.352	−	501.352i	−0.521156	−	0.521156i
$963$		0			0
$964$		−	287.577i		−	0.298316i
$965$	0.481254	−	59.8408i	0.000498709	−	0.0620112i
$966$		0			0
$967$	1141.27	+	1141.27i	1.18021	+	1.18021i	0.979688	+	0.200527i	$0.0642653\pi$
$967$	1141.27	+	1141.27i	1.18021	+	1.18021i	0.200527	+	0.979688i	$0.435735\pi$
$968$	57.7738	−	57.7738i	0.0596837	−	0.0596837i
$969$		0			0
$970$	−80.6527	−	81.9605i	−0.0831471	−	0.0844954i
$971$	158.612			0.163349			0.0816745	−	0.996659i	$-0.473973\pi$
$971$	158.612			0.163349			0.0816745	+	0.996659i	$0.473973\pi$
$972$		0			0
$973$	−337.156	+	337.156i	−0.346511	+	0.346511i
$974$			701.349i			0.720070i
$975$		0			0
$976$	−784.665			−0.803960
$977$	7.82882	+	7.82882i	0.00801312	+	0.00801312i	0.711102	−	0.703089i	$-0.248196\pi$
$977$	7.82882	+	7.82882i	0.00801312	+	0.00801312i	−0.703089	+	0.711102i	$0.748196\pi$
$978$		0			0
$979$			1326.63i			1.35509i
$980$	557.565	−	548.668i	0.568944	−	0.559865i
$981$		0			0
$982$	−418.604	−	418.604i	−0.426277	−	0.426277i
$983$	806.453	−	806.453i	0.820399	−	0.820399i	−0.165766	−	0.986165i	$-0.553010\pi$
$983$	806.453	−	806.453i	0.820399	−	0.820399i	0.986165	+	0.165766i	$0.0530095\pi$
$984$		0			0
$985$	−320.602	−	2.57836i	−0.325484	−	0.00261762i
$986$	−255.784			−0.259416
$987$		0			0
$988$	−538.161	+	538.161i	−0.544698	+	0.544698i
$989$		−	11.5579i		−	0.0116864i
$990$		0			0
$991$	−95.8581			−0.0967287			−0.0483643	−	0.998830i	$-0.515401\pi$
$991$	−95.8581			−0.0967287			−0.0483643	+	0.998830i	$0.515401\pi$
$992$	902.591	+	902.591i	0.909870	+	0.909870i
$993$		0			0
$994$			139.355i			0.140196i
$995$	59.6477	+	60.6148i	0.0599474	+	0.0609194i
$996$		0			0
$997$	622.312	+	622.312i	0.624184	+	0.624184i	0.946599	−	0.322414i	$-0.104494\pi$
$997$	622.312	+	622.312i	0.624184	+	0.624184i	−0.322414	+	0.946599i	$0.604494\pi$
$998$	−88.7943	+	88.7943i	−0.0889723	+	0.0889723i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.g.h.82.6		20
3.2	odd	2		405.3.g.g.82.5		20
5.3	odd	4	inner	405.3.g.h.163.6		20
9.2	odd	6		135.3.l.a.37.5		40
9.4	even	3		45.3.k.a.7.5	✓	40
9.5	odd	6		135.3.l.a.127.6		40
9.7	even	3		45.3.k.a.22.6	yes	40
15.8	even	4		405.3.g.g.163.5		20
45.4	even	6		225.3.o.b.7.6		40
45.7	odd	12		225.3.o.b.193.6		40
45.13	odd	12		45.3.k.a.43.6	yes	40
45.22	odd	12		225.3.o.b.43.5		40
45.23	even	12		135.3.l.a.73.5		40
45.34	even	6		225.3.o.b.157.5		40
45.38	even	12		135.3.l.a.118.6		40
45.43	odd	12		45.3.k.a.13.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.5	✓	40	9.4	even	3
45.3.k.a.13.5	yes	40	45.43	odd	12
45.3.k.a.22.6	yes	40	9.7	even	3
45.3.k.a.43.6	yes	40	45.13	odd	12
135.3.l.a.37.5		40	9.2	odd	6
135.3.l.a.73.5		40	45.23	even	12
135.3.l.a.118.6		40	45.38	even	12
135.3.l.a.127.6		40	9.5	odd	6
225.3.o.b.7.6		40	45.4	even	6
225.3.o.b.43.5		40	45.22	odd	12
225.3.o.b.157.5		40	45.34	even	6
225.3.o.b.193.6		40	45.7	odd	12
405.3.g.g.82.5		20	3.2	odd	2
405.3.g.g.163.5		20	15.8	even	4
405.3.g.h.82.6		20	1.1	even	1	trivial
405.3.g.h.163.6		20	5.3	odd	4	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.531225 + 0.531225i) q^{2} -3.43560i q^{4} +(-3.56385 + 3.50699i) q^{5} +(1.31570 + 1.31570i) q^{7} +(3.94998 - 3.94998i) q^{8} +(-3.75621 - 0.0302083i) q^{10} -11.6459 q^{11} +(14.4997 - 14.4997i) q^{13} +1.39786i q^{14} -9.54575 q^{16} +(-10.0254 - 10.0254i) q^{17} -10.8032i q^{19} +(12.0486 + 12.2440i) q^{20} +(-6.18658 - 6.18658i) q^{22} +(0.985111 - 0.985111i) q^{23} +(0.402086 - 24.9968i) q^{25} +15.4052 q^{26} +(4.52021 - 4.52021i) q^{28} -24.0140i q^{29} -43.2465 q^{31} +(-20.8708 - 20.8708i) q^{32} -10.6514i q^{34} +(-9.30307 - 0.0748176i) q^{35} +(-32.5443 - 32.5443i) q^{37} +(5.73890 - 5.73890i) q^{38} +(-0.224617 + 27.9296i) q^{40} +41.0818 q^{41} +(5.86628 - 5.86628i) q^{43} +40.0106i q^{44} +1.04663 q^{46} +(-12.6335 - 12.6335i) q^{47} -45.5379i q^{49} +(13.4925 - 13.0653i) q^{50} +(-49.8152 - 49.8152i) q^{52} +(-51.3281 + 51.3281i) q^{53} +(41.5042 - 40.8419i) q^{55} +10.3939 q^{56} +(12.7568 - 12.7568i) q^{58} +28.1110i q^{59} +82.2004 q^{61} +(-22.9736 - 22.9736i) q^{62} +16.0088i q^{64} +(-0.824532 + 102.525i) q^{65} +(23.6529 + 23.6529i) q^{67} +(-34.4432 + 34.4432i) q^{68} +(-4.90228 - 4.98177i) q^{70} +99.6917 q^{71} +(-22.3583 + 22.3583i) q^{73} -34.5767i q^{74} -37.1153 q^{76} +(-15.3224 - 15.3224i) q^{77} +61.1906i q^{79} +(34.0196 - 33.4768i) q^{80} +(21.8237 + 21.8237i) q^{82} +(36.5439 - 36.5439i) q^{83} +(70.8878 + 0.570097i) q^{85} +6.23263 q^{86} +(-46.0009 + 46.0009i) q^{88} -113.914i q^{89} +38.1544 q^{91} +(-3.38445 - 3.38445i) q^{92} -13.4225i q^{94} +(37.8865 + 38.5008i) q^{95} +(21.6459 + 21.6459i) q^{97} +(24.1909 - 24.1909i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{5} + 2 q^{7} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 2 q^{13} - 28 q^{16} + 14 q^{17} + 114 q^{20} - 14 q^{22} - 82 q^{23} + 8 q^{25} - 56 q^{26} - 44 q^{28} + 4 q^{31} + 14 q^{32} + 176 q^{35}+ \cdots - 938 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^5 + 2 * q^7 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 2 * q^13 - 28 * q^16 + 14 * q^17 + 114 * q^20 - 14 * q^22 - 82 * q^23 + 8 * q^25 - 56 * q^26 - 44 * q^28 + 4 * q^31 + 14 * q^32 + 176 * q^35 - 46 * q^37 - 330 * q^38 - 30 * q^40 + 28 * q^41 + 2 * q^43 - 68 * q^46 - 64 * q^47 + 458 * q^50 + 74 * q^52 - 304 * q^53 + 112 * q^55 + 192 * q^56 - 30 * q^58 - 92 * q^61 - 50 * q^62 + 326 * q^65 + 80 * q^67 - 626 * q^68 + 102 * q^70 + 124 * q^71 - 4 * q^73 + 96 * q^76 - 338 * q^77 + 722 * q^80 + 52 * q^82 - 370 * q^83 + 98 * q^85 + 328 * q^86 + 210 * q^88 + 76 * q^91 - 388 * q^92 + 360 * q^95 - 292 * q^97 - 938 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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