LMFDB - Embedded newform 273.2.e.a.209.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(209,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("273.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.e (of order $2$, degree $1$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.5
Character	$\chi$	$=$	273.209
Dual form			273.2.e.a.209.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.95979i q^{2} +(-1.02881 - 1.39340i) q^{3} -1.84076 q^{4} -2.34217 q^{5} +(-2.73076 + 2.01624i) q^{6} +(0.446056 - 2.60788i) q^{7} -0.312071i q^{8} +(-0.883116 + 2.86707i) q^{9} +O(q^{10})$	\(q-1.95979i q^{2} +(-1.02881 - 1.39340i) q^{3} -1.84076 q^{4} -2.34217 q^{5} +(-2.73076 + 2.01624i) q^{6} +(0.446056 - 2.60788i) q^{7} -0.312071i q^{8} +(-0.883116 + 2.86707i) q^{9} +4.59015i q^{10} +2.13986i q^{11} +(1.89379 + 2.56492i) q^{12} -1.00000i q^{13} +(-5.11089 - 0.874174i) q^{14} +(2.40964 + 3.26357i) q^{15} -4.29312 q^{16} +0.386232 q^{17} +(5.61885 + 1.73072i) q^{18} +7.19715i q^{19} +4.31138 q^{20} +(-4.09272 + 2.06147i) q^{21} +4.19367 q^{22} -7.49393i q^{23} +(-0.434839 + 0.321060i) q^{24} +0.485757 q^{25} -1.95979 q^{26} +(4.90353 - 1.71913i) q^{27} +(-0.821083 + 4.80049i) q^{28} -8.05737i q^{29} +(6.39591 - 4.72238i) q^{30} -5.54810i q^{31} +7.78945i q^{32} +(2.98168 - 2.20150i) q^{33} -0.756933i q^{34} +(-1.04474 + 6.10809i) q^{35} +(1.62561 - 5.27760i) q^{36} -9.24562 q^{37} +14.1049 q^{38} +(-1.39340 + 1.02881i) q^{39} +0.730923i q^{40} +3.60438 q^{41} +(4.04004 + 8.02085i) q^{42} +6.60412 q^{43} -3.93898i q^{44} +(2.06841 - 6.71517i) q^{45} -14.6865 q^{46} -7.17955 q^{47} +(4.41679 + 5.98202i) q^{48} +(-6.60207 - 2.32652i) q^{49} -0.951981i q^{50} +(-0.397358 - 0.538175i) q^{51} +1.84076i q^{52} -4.94463i q^{53} +(-3.36913 - 9.60987i) q^{54} -5.01192i q^{55} +(-0.813843 - 0.139201i) q^{56} +(10.0285 - 7.40447i) q^{57} -15.7907 q^{58} -4.12586 q^{59} +(-4.43557 - 6.00747i) q^{60} -5.98258i q^{61} -10.8731 q^{62} +(7.08306 + 3.58193i) q^{63} +6.67943 q^{64} +2.34217i q^{65} +(-4.31447 - 5.84345i) q^{66} +1.15836 q^{67} -0.710962 q^{68} +(-10.4420 + 7.70980i) q^{69} +(11.9706 + 2.04746i) q^{70} +8.44499i q^{71} +(0.894730 + 0.275595i) q^{72} -7.31768i q^{73} +18.1194i q^{74} +(-0.499750 - 0.676854i) q^{75} -13.2482i q^{76} +(5.58050 + 0.954498i) q^{77} +(2.01624 + 2.73076i) q^{78} +13.6087 q^{79} +10.0552 q^{80} +(-7.44021 - 5.06391i) q^{81} -7.06382i q^{82} +6.26727 q^{83} +(7.53372 - 3.79468i) q^{84} -0.904622 q^{85} -12.9427i q^{86} +(-11.2271 + 8.28947i) q^{87} +0.667788 q^{88} +8.04153 q^{89} +(-13.1603 - 4.05364i) q^{90} +(-2.60788 - 0.446056i) q^{91} +13.7945i q^{92} +(-7.73071 + 5.70792i) q^{93} +14.0704i q^{94} -16.8569i q^{95} +(10.8538 - 8.01384i) q^{96} -6.02252i q^{97} +(-4.55948 + 12.9386i) q^{98} +(-6.13514 - 1.88974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9	$ 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9 - 12 * q^15 + 16 * q^16 - 20 * q^18 - 4 * q^21 - 16 * q^22 - 28 * q^28 + 16 * q^30 + 24 * q^36 + 24 * q^37 + 32 * q^43 - 24 * q^46 - 24 * q^49 - 8 * q^51 + 32 * q^57 + 24 * q^58 - 28 * q^60 + 8 * q^63 + 48 * q^64 - 32 * q^67 - 8 * q^70 + 64 * q^72 + 20 * q^78 - 32 * q^79 + 32 * q^81 - 48 * q^84 - 16 * q^85 + 64 * q^88 + 4 * q^91 - 52 * q^93 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.95979i		−	1.38578i	−0.721044	−	0.692889i	$-0.756338\pi$
$2$		−	1.95979i		−	1.38578i	0.721044	−	0.692889i	$-0.243662\pi$
$3$	−1.02881	−	1.39340i	−0.593982	−	0.804479i
$3$	−1.02881	−	1.39340i	−0.593982	−	0.804479i
$4$	−1.84076			−0.920381
$5$	−2.34217			−1.04745			−0.523725	−	0.851887i	$-0.675458\pi$
$5$	−2.34217			−1.04745			−0.523725	+	0.851887i	$0.675458\pi$
$6$	−2.73076	+	2.01624i	−1.11483	+	0.823127i
$7$	0.446056	−	2.60788i	0.168593	−	0.985686i
$7$	0.446056	−	2.60788i	0.168593	−	0.985686i
$8$		−	0.312071i		−	0.110334i
$9$	−0.883116	+	2.86707i	−0.294372	+	0.955691i
$10$			4.59015i			1.45153i
$11$			2.13986i			0.645192i	0.946537	+	0.322596i	$0.104556\pi$
$11$			2.13986i			0.645192i	−0.946537	+	0.322596i	$0.895444\pi$
$12$	1.89379	+	2.56492i	0.546690	+	0.740427i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−5.11089	−	0.874174i	−1.36594	−	0.233633i
$15$	2.40964	+	3.26357i	0.622166	+	0.842651i
$16$	−4.29312			−1.07328
$17$	0.386232			0.0936751			0.0468376	−	0.998903i	$-0.485086\pi$
$17$	0.386232			0.0936751			0.0468376	+	0.998903i	$0.485086\pi$
$18$	5.61885	+	1.73072i	1.32438	+	0.407934i
$19$			7.19715i			1.65114i	0.564301	+	0.825569i	$0.309146\pi$
$19$			7.19715i			1.65114i	−0.564301	+	0.825569i	$0.690854\pi$
$20$	4.31138			0.964054
$21$	−4.09272	+	2.06147i	−0.893104	+	0.449849i
$22$	4.19367			0.894093
$23$		−	7.49393i		−	1.56259i	−0.624161	−	0.781296i	$-0.714559\pi$
$23$		−	7.49393i		−	1.56259i	0.624161	−	0.781296i	$-0.285441\pi$
$24$	−0.434839	+	0.321060i	−0.0887611	+	0.0655362i
$25$	0.485757			0.0971515
$26$	−1.95979			−0.384346
$27$	4.90353	−	1.71913i	0.943684	−	0.330847i
$28$	−0.821083	+	4.80049i	−0.155170	+	0.907207i
$29$		−	8.05737i		−	1.49622i	−0.663577	−	0.748108i	$-0.730962\pi$
$29$		−	8.05737i		−	1.49622i	0.663577	−	0.748108i	$-0.269038\pi$
$30$	6.39591	−	4.72238i	1.16773	−	0.862184i
$31$		−	5.54810i		−	0.996468i	−0.867042	−	0.498234i	$-0.833982\pi$
$31$		−	5.54810i		−	0.996468i	0.867042	−	0.498234i	$-0.166018\pi$
$32$			7.78945i			1.37699i
$33$	2.98168	−	2.20150i	0.519043	−	0.383232i
$34$		−	0.756933i		−	0.129813i
$35$	−1.04474	+	6.10809i	−0.176593	+	1.03246i
$36$	1.62561	−	5.27760i	0.270934	−	0.879600i
$37$	−9.24562			−1.51997			−0.759985	−	0.649940i	$-0.774794\pi$
$37$	−9.24562			−1.51997			−0.759985	+	0.649940i	$0.774794\pi$
$38$	14.1049			2.28811
$39$	−1.39340	+	1.02881i	−0.223122	+	0.164741i
$40$			0.730923i			0.115569i
$41$	3.60438			0.562910			0.281455	−	0.959574i	$-0.409183\pi$
$41$	3.60438			0.562910			0.281455	+	0.959574i	$0.409183\pi$
$42$	4.04004	+	8.02085i	0.623391	+	1.23764i
$43$	6.60412			1.00712			0.503559	−	0.863961i	$-0.332023\pi$
$43$	6.60412			1.00712			0.503559	+	0.863961i	$0.332023\pi$
$44$		−	3.93898i		−	0.593823i
$45$	2.06841	−	6.71517i	0.308340	−	1.00104i
$46$	−14.6865			−2.16541
$47$	−7.17955			−1.04725			−0.523623	−	0.851950i	$-0.675420\pi$
$47$	−7.17955			−1.04725			−0.523623	+	0.851950i	$0.675420\pi$
$48$	4.41679	+	5.98202i	0.637508	+	0.863430i
$49$	−6.60207	−	2.32652i	−0.943153	−	0.332360i
$50$		−	0.951981i		−	0.134630i
$51$	−0.397358	−	0.538175i	−0.0556413	−	0.0753596i
$52$			1.84076i			0.255268i
$53$		−	4.94463i		−	0.679197i	−0.940570	−	0.339599i	$-0.889709\pi$
$53$		−	4.94463i		−	0.679197i	0.940570	−	0.339599i	$-0.110291\pi$
$54$	−3.36913	−	9.60987i	−0.458480	−	1.30774i
$55$		−	5.01192i		−	0.675807i
$56$	−0.813843	−	0.139201i	−0.108754	−	0.0186015i
$57$	10.0285	−	7.40447i	1.32831	−	0.980746i
$58$	−15.7907			−2.07342
$59$	−4.12586			−0.537142			−0.268571	−	0.963260i	$-0.586551\pi$
$59$	−4.12586			−0.537142			−0.268571	+	0.963260i	$0.586551\pi$
$60$	−4.43557	−	6.00747i	−0.572630	−	0.775561i
$61$		−	5.98258i		−	0.765991i	−0.923750	−	0.382996i	$-0.874892\pi$
$61$		−	5.98258i		−	0.765991i	0.923750	−	0.382996i	$-0.125108\pi$
$62$	−10.8731			−1.38088
$63$	7.08306	+	3.58193i	0.892382	+	0.451281i
$64$	6.67943			0.834928
$65$			2.34217i			0.290510i
$66$	−4.31447	−	5.84345i	−0.531075	−	0.719279i
$67$	1.15836			0.141516			0.0707582	−	0.997493i	$-0.477458\pi$
$67$	1.15836			0.141516			0.0707582	+	0.997493i	$0.477458\pi$
$68$	−0.710962			−0.0862168
$69$	−10.4420	+	7.70980i	−1.25707	+	0.928151i
$70$	11.9706	+	2.04746i	1.43076	+	0.244719i
$71$			8.44499i			1.00224i	0.865379	+	0.501118i	$0.167078\pi$
$71$			8.44499i			1.00224i	−0.865379	+	0.501118i	$0.832922\pi$
$72$	0.894730	+	0.275595i	0.105445	+	0.0324791i
$73$		−	7.31768i		−	0.856469i	−0.903668	−	0.428235i	$-0.859136\pi$
$73$		−	7.31768i		−	0.856469i	0.903668	−	0.428235i	$-0.140864\pi$
$74$			18.1194i			2.10634i
$75$	−0.499750	−	0.676854i	−0.0577062	−	0.0781563i
$76$		−	13.2482i		−	1.51968i
$77$	5.58050	+	0.954498i	0.635957	+	0.108775i
$78$	2.01624	+	2.73076i	0.228294	+	0.309198i
$79$	13.6087			1.53110			0.765549	−	0.643378i	$-0.222468\pi$
$79$	13.6087			1.53110			0.765549	+	0.643378i	$0.222468\pi$
$80$	10.0552			1.12421
$81$	−7.44021	−	5.06391i	−0.826690	−	0.562657i
$82$		−	7.06382i		−	0.780069i
$83$	6.26727			0.687922			0.343961	−	0.938984i	$-0.388231\pi$
$83$	6.26727			0.687922			0.343961	+	0.938984i	$0.388231\pi$
$84$	7.53372	−	3.79468i	0.821997	−	0.414033i
$85$	−0.904622			−0.0981200
$86$		−	12.9427i		−	1.39564i
$87$	−11.2271	+	8.28947i	−1.20367	+	0.888725i
$88$	0.667788			0.0711864
$89$	8.04153			0.852401			0.426200	−	0.904629i	$-0.359852\pi$
$89$	8.04153			0.852401			0.426200	+	0.904629i	$0.359852\pi$
$90$	−13.1603	−	4.05364i	−1.38722	−	0.427291i
$91$	−2.60788	−	0.446056i	−0.273380	−	0.0467594i
$92$			13.7945i			1.43818i
$93$	−7.73071	+	5.70792i	−0.801638	+	0.591884i
$94$			14.0704i			1.45125i
$95$		−	16.8569i		−	1.72949i
$96$	10.8538	−	8.01384i	1.10776	−	0.817909i
$97$		−	6.02252i		−	0.611494i	−0.952113	−	0.305747i	$-0.901094\pi$
$97$		−	6.02252i		−	0.611494i	0.952113	−	0.305747i	$-0.0989062\pi$
$98$	−4.55948	+	12.9386i	−0.460577	+	1.30700i
$99$	−6.13514	−	1.88974i	−0.616604	−	0.189926i
$100$	−0.894164			−0.0894164
$101$	8.20905			0.816831			0.408416	−	0.912796i	$-0.366081\pi$
$101$	8.20905			0.816831			0.408416	+	0.912796i	$0.366081\pi$
$102$	−1.05471	+	0.778737i	−0.104432	+	0.0771065i
$103$		−	3.52554i		−	0.347382i	−0.984800	−	0.173691i	$-0.944431\pi$
$103$		−	3.52554i		−	0.347382i	0.984800	−	0.173691i	$-0.0555693\pi$
$104$	−0.312071			−0.0306011
$105$	9.58584	−	4.82831i	0.935482	−	0.471195i
$106$	−9.69042			−0.941217
$107$			7.11958i			0.688276i	0.938919	+	0.344138i	$0.111829\pi$
$107$			7.11958i			0.688276i	−0.938919	+	0.344138i	$0.888171\pi$
$108$	−9.02623	+	3.16451i	−0.868550	+	0.304505i
$109$	5.89715			0.564845			0.282422	−	0.959290i	$-0.408862\pi$
$109$	5.89715			0.564845			0.282422	+	0.959290i	$0.408862\pi$
$110$	−9.82229			−0.936518
$111$	9.51195	+	12.8828i	0.902835	+	1.22278i
$112$	−1.91497	+	11.1959i	−0.180948	+	1.05792i
$113$		−	1.95538i		−	0.183947i	−0.995761	−	0.0919733i	$-0.970683\pi$
$113$		−	1.95538i		−	0.183947i	0.995761	−	0.0919733i	$-0.0293174\pi$
$114$	−14.5112	−	19.6537i	−1.35910	−	1.84074i
$115$			17.5521i			1.63674i
$116$			14.8317i			1.37709i
$117$	2.86707	+	0.883116i	0.265061	+	0.0816441i
$118$			8.08581i			0.744359i
$119$	0.172281	−	1.00725i	0.0157930	−	0.0923342i
$120$	1.01847	−	0.751978i	0.0929728	−	0.0686459i
$121$	6.42100			0.583727
$122$	−11.7246			−1.06149
$123$	−3.70821	−	5.02234i	−0.334358	−	0.452849i
$124$			10.2127i			0.917131i
$125$	10.5731			0.945689
$126$	7.01983	−	13.8813i	0.625376	−	1.23664i
$127$	−1.95534			−0.173508			−0.0867541	−	0.996230i	$-0.527649\pi$
$127$	−1.95534			−0.173508			−0.0867541	+	0.996230i	$0.527649\pi$
$128$			2.48865i			0.219968i
$129$	−6.79436	−	9.20217i	−0.598210	−	0.810206i
$130$	4.59015			0.402583
$131$	−2.02273			−0.176727			−0.0883636	−	0.996088i	$-0.528164\pi$
$131$	−2.02273			−0.176727			−0.0883636	+	0.996088i	$0.528164\pi$
$132$	−5.48856	+	4.05244i	−0.477718	+	0.352720i
$133$	18.7693	+	3.21033i	1.62750	+	0.278371i
$134$		−	2.27014i		−	0.196110i
$135$	−11.4849	+	4.02649i	−0.988462	+	0.346546i
$136$		−	0.120532i		−	0.0103355i
$137$		−	17.9791i		−	1.53606i	−0.640416	−	0.768028i	$-0.721238\pi$
$137$		−	17.9791i		−	1.53606i	0.640416	−	0.768028i	$-0.278762\pi$
$138$	15.1096	+	20.4641i	1.28621	+	1.74202i
$139$			6.67425i			0.566102i	0.959105	+	0.283051i	$0.0913466\pi$
$139$			6.67425i			0.566102i	−0.959105	+	0.283051i	$0.908653\pi$
$140$	1.92312	−	11.2436i	0.162533	−	0.950254i
$141$	7.38637	+	10.0040i	0.622044	+	0.842487i
$142$	16.5504			1.38888
$143$	2.13986			0.178944
$144$	3.79132	−	12.3087i	0.315943	−	1.02572i
$145$			18.8717i			1.56721i
$146$	−14.3411			−1.18688
$147$	3.55048	+	11.5928i	0.292839	+	0.956162i
$148$	17.0190			1.39895
$149$			4.82883i			0.395593i	0.980243	+	0.197797i	$0.0633786\pi$
$149$			4.82883i			0.395593i	−0.980243	+	0.197797i	$0.936621\pi$
$150$	−1.32649	+	0.979404i	−0.108307	+	0.0799680i
$151$	−0.677731			−0.0551530			−0.0275765	−	0.999620i	$-0.508779\pi$
$151$	−0.677731			−0.0551530			−0.0275765	+	0.999620i	$0.508779\pi$
$152$	2.24602			0.182176
$153$	−0.341088	+	1.10736i	−0.0275753	+	0.0895245i
$154$	1.87061	−	10.9366i	0.150738	−	0.881295i
$155$			12.9946i			1.04375i
$156$	2.56492	−	1.89379i	0.205358	−	0.151624i
$157$			19.0946i			1.52392i	0.647627	+	0.761958i	$0.275762\pi$
$157$			19.0946i			1.52392i	−0.647627	+	0.761958i	$0.724238\pi$
$158$		−	26.6701i		−	2.12176i
$159$	−6.88984	+	5.08707i	−0.546400	+	0.403431i
$160$		−	18.2442i		−	1.44233i
$161$	−19.5433	−	3.34271i	−1.54022	−	0.263443i
$162$	−9.92419	+	14.5812i	−0.779718	+	1.14561i
$163$	−12.2898			−0.962609			−0.481304	−	0.876554i	$-0.659837\pi$
$163$	−12.2898			−0.962609			−0.481304	+	0.876554i	$0.659837\pi$
$164$	−6.63482			−0.518092
$165$	−6.98359	+	5.15629i	−0.543672	+	0.401417i
$166$		−	12.2825i		−	0.953307i
$167$	−12.4313			−0.961963			−0.480982	−	0.876731i	$-0.659720\pi$
$167$	−12.4313			−0.961963			−0.480982	+	0.876731i	$0.659720\pi$
$168$	0.643324	+	1.27722i	0.0496335	+	0.0985395i
$169$	−1.00000			−0.0769231
$170$			1.77287i			0.135973i
$171$	−20.6347	−	6.35591i	−1.57798	−	0.486049i
$172$	−12.1566			−0.926934
$173$	10.8406			0.824195			0.412098	−	0.911140i	$-0.364796\pi$
$173$	10.8406			0.824195			0.412098	+	0.911140i	$0.364796\pi$
$174$	16.2456	+	22.0028i	1.23158	+	1.66803i
$175$	0.216675	−	1.26680i	0.0163791	−	0.0957608i
$176$		−	9.18667i		−	0.692472i
$177$	4.24471	+	5.74897i	0.319052	+	0.432119i
$178$		−	15.7597i		−	1.18124i
$179$			10.3092i			0.770543i	0.922803	+	0.385272i	$0.125892\pi$
$179$			10.3092i			0.770543i	−0.922803	+	0.385272i	$0.874108\pi$
$180$	−3.80745	+	12.3610i	−0.283790	+	0.921337i
$181$		−	16.4638i		−	1.22375i	−0.790956	−	0.611873i	$-0.790416\pi$
$181$		−	16.4638i		−	1.22375i	0.790956	−	0.611873i	$-0.209584\pi$
$182$	−0.874174	+	5.11089i	−0.0647981	+	0.378844i
$183$	−8.33612	+	6.15492i	−0.616224	+	0.454985i
$184$	−2.33864			−0.172407
$185$	21.6548			1.59209
$186$	11.1863	+	15.1505i	0.820220	+	1.11089i
$187$			0.826483i			0.0604385i
$188$	13.2159			0.963865
$189$	−2.29604	−	13.5546i	−0.167012	−	0.985955i
$190$	−33.0360			−2.39668
$191$		−	9.77776i		−	0.707494i	−0.935341	−	0.353747i	$-0.884907\pi$
$191$		−	9.77776i		−	0.707494i	0.935341	−	0.353747i	$-0.115093\pi$
$192$	−6.87184	−	9.30710i	−0.495932	−	0.671682i
$193$	11.3439			0.816549			0.408274	−	0.912859i	$-0.366131\pi$
$193$	11.3439			0.816549			0.408274	+	0.912859i	$0.366131\pi$
$194$	−11.8028			−0.847395
$195$	3.26357	−	2.40964i	0.233709	−	0.172558i
$196$	12.1528	+	4.28257i	0.868060	+	0.305898i
$197$			10.8752i			0.774824i	0.921907	+	0.387412i	$0.126631\pi$
$197$			10.8752i			0.774824i	−0.921907	+	0.387412i	$0.873369\pi$
$198$	−3.70350	+	12.0236i	−0.263196	+	0.854477i
$199$		−	10.8998i		−	0.772669i	−0.922359	−	0.386335i	$-0.873741\pi$
$199$		−	10.8998i		−	0.772669i	0.922359	−	0.386335i	$-0.126259\pi$
$200$		−	0.151591i		−	0.0107191i
$201$	−1.19173	−	1.61406i	−0.0840581	−	0.113847i
$202$		−	16.0880i		−	1.13195i
$203$	−21.0127	−	3.59404i	−1.47480	−	0.252252i
$204$	0.731442	+	0.990653i	0.0512112	+	0.0693596i
$205$	−8.44208			−0.589620
$206$	−6.90930			−0.481394
$207$	21.4856	+	6.61801i	1.49336	+	0.459983i
$208$			4.29312i			0.297674i
$209$	−15.4009			−1.06530
$210$	−9.46245	−	18.7862i	−0.652971	−	1.29637i
$211$	24.2877			1.67204			0.836018	−	0.548702i	$-0.184878\pi$
$211$	24.2877			1.67204			0.836018	+	0.548702i	$0.184878\pi$
$212$			9.10189i			0.625121i
$213$	11.7672	−	8.68826i	0.806277	−	0.595309i
$214$	13.9529			0.953798
$215$	−15.4680			−1.05491
$216$	−0.536490	−	1.53025i	−0.0365036	−	0.104120i
$217$	−14.4688	−	2.47476i	−0.982205	−	0.167998i
$218$		−	11.5572i		−	0.782749i
$219$	−10.1964	+	7.52847i	−0.689011	+	0.508727i
$220$			9.22575i			0.622000i
$221$		−	0.386232i		−	0.0259808i
$222$	25.2476	−	18.6414i	1.69451	−	1.25113i
$223$			8.90547i			0.596354i	0.954511	+	0.298177i	$0.0963786\pi$
$223$			8.90547i			0.596354i	−0.954511	+	0.298177i	$0.903621\pi$
$224$	20.3140	+	3.47453i	1.35728	+	0.232152i
$225$	−0.428980	+	1.39270i	−0.0285987	+	0.0928468i
$226$	−3.83213			−0.254909
$227$	−2.14733			−0.142524			−0.0712618	−	0.997458i	$-0.522703\pi$
$227$	−2.14733			−0.142524			−0.0712618	+	0.997458i	$0.522703\pi$
$228$	−18.4601	+	13.6299i	−1.22255	+	0.902660i
$229$		−	16.3973i		−	1.08356i	−0.840519	−	0.541782i	$-0.817750\pi$
$229$		−	16.3973i		−	1.08356i	0.840519	−	0.541782i	$-0.182250\pi$
$230$	34.3983			2.26815
$231$	−4.41126	−	8.75785i	−0.290239	−	0.576224i
$232$	−2.51447			−0.165083
$233$		−	14.1122i		−	0.924518i	−0.886745	−	0.462259i	$-0.847039\pi$
$233$		−	14.1122i		−	0.924518i	0.886745	−	0.462259i	$-0.152961\pi$
$234$	1.73072	−	5.61885i	0.113141	−	0.367316i
$235$	16.8157			1.09694
$236$	7.59474			0.494375
$237$	−14.0007	−	18.9623i	−0.909444	−	1.23174i
$238$	−1.97399	−	0.337634i	−0.127955	−	0.0218856i
$239$			17.2159i			1.11360i	0.830645	+	0.556802i	$0.187972\pi$
$239$			17.2159i			1.11360i	−0.830645	+	0.556802i	$0.812028\pi$
$240$	−10.3449	−	14.0109i	−0.667758	−	0.904400i
$241$		−	4.23660i		−	0.272903i	−0.990647	−	0.136452i	$-0.956430\pi$
$241$		−	4.23660i		−	0.272903i	0.990647	−	0.136452i	$-0.0435698\pi$
$242$		−	12.5838i		−	0.808916i
$243$	0.598489	+	15.5770i	0.0383931	+	0.999263i
$244$			11.0125i			0.705004i
$245$	15.4632	+	5.44910i	0.987905	+	0.348131i
$246$	−9.84271	+	7.26730i	−0.627549	+	0.463346i
$247$	7.19715			0.457943
$248$	−1.73140			−0.109944
$249$	−6.44780	−	8.73280i	−0.408613	−	0.553419i
$250$		−	20.7211i		−	1.31051i
$251$	5.57818			0.352092			0.176046	−	0.984382i	$-0.443669\pi$
$251$	5.57818			0.352092			0.176046	+	0.984382i	$0.443669\pi$
$252$	−13.0382	−	6.59349i	−0.821332	−	0.415351i
$253$	16.0360			1.00817
$254$			3.83205i			0.240444i
$255$	0.930680	+	1.26050i	0.0582815	+	0.0789354i
$256$	18.2361			1.13976
$257$	−2.26918			−0.141547			−0.0707736	−	0.997492i	$-0.522547\pi$
$257$	−2.26918			−0.141547			−0.0707736	+	0.997492i	$0.522547\pi$
$258$	−18.0343	+	13.3155i	−1.12277	+	0.828986i
$259$	−4.12406	+	24.1115i	−0.256257	+	1.49821i
$260$		−	4.31138i		−	0.267380i
$261$	23.1011	+	7.11559i	1.42992	+	0.440444i
$262$			3.96413i			0.244905i
$263$		−	20.7382i		−	1.27877i	−0.768887	−	0.639385i	$-0.779189\pi$
$263$		−	20.7382i		−	1.27877i	0.768887	−	0.639385i	$-0.220811\pi$
$264$	−0.687025	−	0.930495i	−0.0422834	−	0.0572680i
$265$			11.5812i			0.711425i
$266$	6.29156	−	36.7838i	0.385760	−	2.25536i
$267$	−8.27318	−	11.2051i	−0.506310	−	0.685738i
$268$	−2.13227			−0.130249
$269$	−20.8890			−1.27362			−0.636811	−	0.771020i	$-0.719747\pi$
$269$	−20.8890			−1.27362			−0.636811	+	0.771020i	$0.719747\pi$
$270$	7.89107	+	22.5079i	0.480235	+	1.36979i
$271$		−	29.0462i		−	1.76443i	−0.470847	−	0.882215i	$-0.656052\pi$
$271$		−	29.0462i		−	1.76443i	0.470847	−	0.882215i	$-0.343948\pi$
$272$	−1.65814			−0.100540
$273$	2.06147	+	4.09272i	0.124766	+	0.247703i
$274$	−35.2352			−2.12863
$275$			1.03945i			0.0626814i
$276$	19.2213	−	14.1919i	1.15699	−	0.854253i
$277$	−17.0773			−1.02607			−0.513037	−	0.858366i	$-0.671480\pi$
$277$	−17.0773			−1.02607			−0.513037	+	0.858366i	$0.671480\pi$
$278$	13.0801			0.784492
$279$	15.9068	+	4.89962i	0.952316	+	0.293332i
$280$	1.90616	+	0.326032i	0.113915	+	0.0194842i
$281$		−	2.42881i		−	0.144891i	−0.997372	−	0.0724453i	$-0.976920\pi$
$281$		−	2.42881i		−	0.144891i	0.997372	−	0.0724453i	$-0.0230803\pi$
$282$	19.6057	−	14.4757i	1.16750	−	0.862016i
$283$			31.4848i			1.87158i	0.352561	+	0.935789i	$0.385311\pi$
$283$			31.4848i			1.87158i	−0.352561	+	0.935789i	$0.614689\pi$
$284$		−	15.5452i		−	0.922439i
$285$	−23.4884	+	17.3425i	−1.39133	+	1.02728i
$286$		−	4.19367i		−	0.247977i
$287$	1.60776	−	9.39980i	0.0949029	−	0.554852i
$288$	−22.3329	−	6.87899i	−1.31598	−	0.405348i
$289$	−16.8508			−0.991225
$290$	36.9846			2.17181
$291$	−8.39176	+	6.19600i	−0.491934	+	0.363216i
$292$			13.4701i			0.788279i
$293$	−13.2977			−0.776857			−0.388429	−	0.921479i	$-0.626982\pi$
$293$	−13.2977			−0.776857			−0.388429	+	0.921479i	$0.626982\pi$
$294$	22.7195	−	6.95818i	1.32503	−	0.405809i
$295$	9.66347			0.562629
$296$			2.88529i			0.167704i
$297$	3.67870	+	10.4929i	0.213460	+	0.608858i
$298$	9.46348			0.548205
$299$	−7.49393			−0.433385
$300$	0.919922	+	1.24593i	0.0531117	+	0.0719336i
$301$	2.94581	−	17.2227i	0.169794	−	0.992703i
$302$			1.32821i			0.0764298i
$303$	−8.44552	−	11.4385i	−0.485183	−	0.657123i
$304$		−	30.8982i		−	1.77213i
$305$			14.0122i			0.802338i
$306$	2.17018	+	0.668459i	0.124061	+	0.0382133i
$307$			8.51269i			0.485845i	0.970046	+	0.242923i	$0.0781061\pi$
$307$			8.51269i			0.485845i	−0.970046	+	0.242923i	$0.921894\pi$
$308$	−10.2724	−	1.75700i	−0.585323	−	0.100115i
$309$	−4.91248	+	3.62710i	−0.279461	+	0.206338i
$310$	25.4666			1.44641
$311$	31.0133			1.75860			0.879301	−	0.476267i	$-0.158010\pi$
$311$	31.0133			1.75860			0.879301	+	0.476267i	$0.158010\pi$
$312$	0.321060	+	0.434839i	0.0181765	+	0.0246179i
$313$		−	26.6294i		−	1.50518i	−0.658488	−	0.752591i	$-0.728804\pi$
$313$		−	26.6294i		−	1.50518i	0.658488	−	0.752591i	$-0.271196\pi$
$314$	37.4213			2.11181
$315$	−16.5897	−	8.38950i	−0.934725	−	0.472695i
$316$	−25.0504			−1.40919
$317$			34.5760i			1.94198i	0.239119	+	0.970990i	$0.423141\pi$
$317$			34.5760i			1.94198i	−0.239119	+	0.970990i	$0.576859\pi$
$318$	9.96957	+	13.5026i	0.559065	+	0.757189i
$319$	17.2417			0.965347
$320$	−15.6444			−0.874546
$321$	9.92041	−	7.32467i	0.553704	−	0.408823i
$322$	−6.55100	+	38.3006i	−0.365073	+	2.13441i
$323$			2.77977i			0.154671i
$324$	13.6957	+	9.32147i	0.760870	+	0.517859i
$325$		−	0.485757i		−	0.0269450i
$326$			24.0853i			1.33396i
$327$	−6.06702	−	8.21708i	−0.335507	−	0.454405i
$328$		−	1.12482i		−	0.0621080i
$329$	−3.20248	+	18.7234i	−0.176559	+	1.03225i
$330$	10.1052	+	13.6864i	0.556274	+	0.753409i
$331$	5.80048			0.318823			0.159412	−	0.987212i	$-0.449040\pi$
$331$	5.80048			0.318823			0.159412	+	0.987212i	$0.449040\pi$
$332$	−11.5366			−0.633151
$333$	8.16495	−	26.5079i	0.447437	−	1.45262i
$334$			24.3627i			1.33307i
$335$	−2.71308			−0.148231
$336$	17.5705	−	8.85013i	0.958551	−	0.482814i
$337$	−2.07199			−0.112869			−0.0564343	−	0.998406i	$-0.517973\pi$
$337$	−2.07199			−0.112869			−0.0564343	+	0.998406i	$0.517973\pi$
$338$			1.95979i			0.106598i
$339$	−2.72462	+	2.01171i	−0.147981	+	0.109261i
$340$	1.66519			0.0903078
$341$	11.8722			0.642914
$342$	−12.4562	+	40.4397i	−0.673556	+	2.18673i
$343$	−9.01218	+	16.1796i	−0.486612	+	0.873618i
$344$		−	2.06095i		−	0.111119i
$345$	24.4570	−	18.0577i	1.31672	−	0.972192i
$346$		−	21.2452i		−	1.14215i
$347$		−	22.3305i		−	1.19876i	−0.800463	−	0.599382i	$-0.795413\pi$
$347$		−	22.3305i		−	1.19876i	0.800463	−	0.599382i	$-0.204587\pi$
$348$	20.6665	−	15.2590i	1.10784	−	0.817966i
$349$		−	20.3242i		−	1.08793i	−0.839108	−	0.543965i	$-0.816922\pi$
$349$		−	20.3242i		−	1.08793i	0.839108	−	0.543965i	$-0.183078\pi$
$350$	−2.48265	−	0.424637i	−0.132703	−	0.0226978i
$351$	−1.71913	−	4.90353i	−0.0917604	−	0.261731i
$352$	−16.6683			−0.888426
$353$	−8.59768			−0.457608			−0.228804	−	0.973472i	$-0.573482\pi$
$353$	−8.59768			−0.457608			−0.228804	+	0.973472i	$0.573482\pi$
$354$	11.2668	−	8.31873i	0.598821	−	0.442136i
$355$		−	19.7796i		−	1.04979i
$356$	−14.8026			−0.784534
$357$	−1.58074	+	0.796206i	−0.0836617	+	0.0421397i
$358$	20.2038			1.06780
$359$			28.2547i			1.49123i	0.666379	+	0.745613i	$0.267843\pi$
$359$			28.2547i			1.49123i	−0.666379	+	0.745613i	$0.732157\pi$
$360$	−2.09561	−	0.645489i	−0.110448	−	0.0340203i
$361$	−32.7989			−1.72626
$362$	−32.2656			−1.69584
$363$	−6.60596	−	8.94700i	−0.346723	−	0.469596i
$364$	4.80049	+	0.821083i	0.251614	+	0.0430365i
$365$			17.1392i			0.897109i
$366$	12.0623	+	16.3370i	0.630508	+	0.853949i
$367$			13.5404i			0.706806i	0.935471	+	0.353403i	$0.114975\pi$
$367$			13.5404i			0.706806i	−0.935471	+	0.353403i	$0.885025\pi$
$368$			32.1723i			1.67710i
$369$	−3.18309	+	10.3340i	−0.165705	+	0.537968i
$370$		−	42.4388i		−	2.20629i
$371$	−12.8950	−	2.20558i	−0.669475	−	0.114508i
$372$	14.2304	−	10.5069i	0.737812	−	0.544759i
$373$	10.5134			0.544363			0.272182	−	0.962246i	$-0.412255\pi$
$373$	10.5134			0.544363			0.272182	+	0.962246i	$0.412255\pi$
$374$	1.61973			0.0837543
$375$	−10.8777	−	14.7326i	−0.561722	−	0.760786i
$376$			2.24053i			0.115546i
$377$	−8.05737			−0.414976
$378$	−26.5642	+	4.49974i	−1.36631	+	0.231442i
$379$	12.2829			0.630929			0.315464	−	0.948937i	$-0.397840\pi$
$379$	12.2829			0.630929			0.315464	+	0.948937i	$0.397840\pi$
$380$			31.0296i			1.59179i
$381$	2.01166	+	2.72456i	0.103061	+	0.139584i
$382$	−19.1623			−0.980430
$383$	6.09116			0.311244			0.155622	−	0.987817i	$-0.450262\pi$
$383$	6.09116			0.311244			0.155622	+	0.987817i	$0.450262\pi$
$384$	3.46768	−	2.56034i	0.176960	−	0.130657i
$385$	−13.0705	−	2.23560i	−0.666133	−	0.113936i
$386$		−	22.2315i		−	1.13156i
$387$	−5.83220	+	18.9345i	−0.296468	+	0.962494i
$388$			11.0860i			0.562808i
$389$		−	0.382254i		−	0.0193810i	−0.999953	−	0.00969052i	$-0.996915\pi$
$389$		−	0.382254i		−	0.0193810i	0.999953	−	0.00969052i	$-0.00308464\pi$
$390$	−4.72238	−	6.39591i	−0.239127	−	0.323869i
$391$		−	2.89440i		−	0.146376i
$392$	−0.726039	+	2.06031i	−0.0366705	+	0.104062i
$393$	2.08100	+	2.81847i	0.104973	+	0.142173i
$394$	21.3130			1.07373
$395$	−31.8739			−1.60375
$396$	11.2933	+	3.47857i	0.567511	+	0.174805i
$397$			37.3774i			1.87592i	0.346748	+	0.937958i	$0.387286\pi$
$397$			37.3774i			1.87592i	−0.346748	+	0.937958i	$0.612714\pi$
$398$	−21.3614			−1.07075
$399$	−14.8367	−	29.4559i	−0.742764	−	1.47464i
$400$	−2.08541			−0.104271
$401$			2.09102i			0.104420i	0.998636	+	0.0522102i	$0.0166266\pi$
$401$			2.09102i			0.104420i	−0.998636	+	0.0522102i	$0.983373\pi$
$402$	−3.16321	+	2.33553i	−0.157767	+	0.116486i
$403$	−5.54810			−0.276371
$404$	−15.1109			−0.751796
$405$	17.4262	+	11.8605i	0.865917	+	0.589355i
$406$	−7.04355	+	41.1803i	−0.349565	+	2.04374i
$407$		−	19.7843i		−	0.980673i
$408$	−0.167949	+	0.124004i	−0.00831471	+	0.00613911i
$409$			6.28937i			0.310989i	0.987837	+	0.155495i	$0.0496971\pi$
$409$			6.28937i			0.310989i	−0.987837	+	0.155495i	$0.950303\pi$
$410$			16.5447i			0.817083i
$411$	−25.0520	+	18.4970i	−1.23572	+	0.912389i
$412$			6.48968i			0.319724i
$413$	−1.84037	+	10.7598i	−0.0905585	+	0.529453i
$414$	12.9699	−	42.1073i	0.637435	−	2.06946i
$415$	−14.6790			−0.720564
$416$	7.78945			0.381909
$417$	9.29988	−	6.86650i	0.455417	−	0.336254i
$418$			30.1825i			1.47627i
$419$	−20.9435			−1.02316			−0.511579	−	0.859236i	$-0.670939\pi$
$419$	−20.9435			−1.02316			−0.511579	+	0.859236i	$0.670939\pi$
$420$	−17.6453	+	8.88777i	−0.861000	+	0.433679i
$421$	−39.8452			−1.94194			−0.970969	−	0.239206i	$-0.923113\pi$
$421$	−39.8452			−1.94194			−0.970969	+	0.239206i	$0.923113\pi$
$422$		−	47.5988i		−	2.31707i
$423$	6.34038	−	20.5843i	0.308280	−	1.00084i
$424$	−1.54308			−0.0749384
$425$	0.187615			0.00910068
$426$	−17.0271	−	23.0613i	−0.824967	−	1.11732i
$427$	−15.6019	−	2.66857i	−0.755027	−	0.129141i
$428$		−	13.1055i		−	0.633477i
$429$	−2.20150	−	2.98168i	−0.106290	−	0.143957i
$430$			30.3139i			1.46187i
$431$			23.6427i			1.13883i	0.822051	+	0.569414i	$0.192830\pi$
$431$			23.6427i			1.13883i	−0.822051	+	0.569414i	$0.807170\pi$
$432$	−21.0514	+	7.38043i	−1.01284	+	0.355091i
$433$			0.701236i			0.0336992i	0.999858	+	0.0168496i	$0.00536365\pi$
$433$			0.701236i			0.0336992i	−0.999858	+	0.0168496i	$0.994636\pi$
$434$	−4.85001	+	28.3557i	−0.232808	+	1.36112i
$435$	26.2958	−	19.4154i	1.26079	−	0.930895i
$436$	−10.8553			−0.519872
$437$	53.9349			2.58006
$438$	14.7542	+	19.9828i	0.704983	+	0.954817i
$439$		−	3.14857i		−	0.150273i	−0.997173	−	0.0751366i	$-0.976061\pi$
$439$		−	3.14857i		−	0.150273i	0.997173	−	0.0751366i	$-0.0239393\pi$
$440$	−1.56407			−0.0745642
$441$	12.5007	−	16.8740i	0.595271	−	0.803525i
$442$	−0.756933			−0.0360036
$443$		−	22.7025i		−	1.07863i	−0.842104	−	0.539315i	$-0.818683\pi$
$443$		−	22.7025i		−	1.07863i	0.842104	−	0.539315i	$-0.181317\pi$
$444$	−17.5092	−	23.7142i	−0.830952	−	1.12543i
$445$	−18.8346			−0.892847
$446$	17.4528			0.826415
$447$	6.72849	−	4.96793i	0.318246	−	0.234975i
$448$	2.97940	−	17.4191i	0.140763	−	0.822977i
$449$		−	25.3593i		−	1.19678i	−0.801204	−	0.598391i	$-0.795807\pi$
$449$		−	25.3593i		−	1.19678i	0.801204	−	0.598391i	$-0.204193\pi$
$450$	2.72940	+	0.840709i	0.128665	+	0.0396314i
$451$			7.71288i			0.363185i
$452$			3.59939i			0.169301i
$453$	0.697254	+	0.944350i	0.0327599	+	0.0443694i
$454$			4.20832i			0.197506i
$455$	6.10809	+	1.04474i	0.286352	+	0.0489781i
$456$	−2.31072	−	3.12960i	−0.108209	−	0.146557i
$457$	27.9331			1.30666			0.653329	−	0.757074i	$-0.273372\pi$
$457$	27.9331			1.30666			0.653329	+	0.757074i	$0.273372\pi$
$458$	−32.1352			−1.50158
$459$	1.89390	−	0.663984i	0.0883997	−	0.0309921i
$460$		−	32.3092i		−	1.50642i
$461$	−28.3996			−1.32270			−0.661350	−	0.750078i	$-0.730016\pi$
$461$	−28.3996			−1.32270			−0.661350	+	0.750078i	$0.730016\pi$
$462$	−17.1635	+	8.64512i	−0.798519	+	0.402207i
$463$	2.99152			0.139028			0.0695139	−	0.997581i	$-0.477855\pi$
$463$	2.99152			0.139028			0.0695139	+	0.997581i	$0.477855\pi$
$464$			34.5912i			1.60586i
$465$	18.1066	−	13.3689i	0.839675	−	0.619969i
$466$	−27.6568			−1.28118
$467$	28.2897			1.30909			0.654546	−	0.756022i	$-0.272860\pi$
$467$	28.2897			1.30909			0.654546	+	0.756022i	$0.272860\pi$
$468$	−5.27760	−	1.62561i	−0.243957	−	0.0751437i
$469$	0.516694	−	3.02087i	0.0238587	−	0.139491i
$470$		−	32.9552i		−	1.52011i
$471$	26.6064	−	19.6446i	1.22596	−	0.905177i
$472$			1.28756i			0.0592648i
$473$			14.1319i			0.649785i
$474$	−37.1621	+	27.4384i	−1.70691	+	1.26029i
$475$			3.49607i			0.160411i
$476$	−0.317129	+	1.85410i	−0.0145356	+	0.0849827i
$477$	14.1766	+	4.36668i	0.649103	+	0.199937i
$478$	33.7395			1.54321
$479$	0.730482			0.0333766			0.0166883	−	0.999861i	$-0.494688\pi$
$479$	0.730482			0.0333766			0.0166883	+	0.999861i	$0.494688\pi$
$480$	−25.4215	+	18.7698i	−1.16033	+	0.856719i
$481$			9.24562i			0.421564i
$482$	−8.30282			−0.378183
$483$	15.4485	+	30.6705i	0.702931	+	1.39556i
$484$	−11.8195			−0.537251
$485$			14.1058i			0.640509i
$486$	30.5275	−	1.17291i	1.38476	−	0.0532043i
$487$	6.23260			0.282426			0.141213	−	0.989979i	$-0.454900\pi$
$487$	6.23260			0.282426			0.141213	+	0.989979i	$0.454900\pi$
$488$	−1.86699			−0.0845147
$489$	12.6438	+	17.1245i	0.571772	+	0.774398i
$490$	10.6791	−	30.3045i	0.482432	−	1.36902i
$491$			8.36866i			0.377672i	0.982009	+	0.188836i	$0.0604715\pi$
$491$			8.36866i			0.377672i	−0.982009	+	0.188836i	$0.939529\pi$
$492$	6.82594	+	9.24494i	0.307737	+	0.416794i
$493$		−	3.11202i		−	0.140158i
$494$		−	14.1049i		−	0.634608i
$495$	14.3695	+	4.42610i	0.645862	+	0.198938i
$496$			23.8187i			1.06949i
$497$	22.0235	+	3.76694i	0.987889	+	0.168970i
$498$	−17.1144	+	12.6363i	−0.766915	+	0.566247i
$499$	25.2530			1.13048			0.565239	−	0.824927i	$-0.308784\pi$
$499$	25.2530			1.13048			0.565239	+	0.824927i	$0.308784\pi$
$500$	−19.4626			−0.870394
$501$	12.7894	+	17.3218i	0.571388	+	0.773879i
$502$		−	10.9320i		−	0.487921i
$503$	42.0742			1.87600			0.937998	−	0.346639i	$-0.112677\pi$
$503$	42.0742			1.87600			0.937998	+	0.346639i	$0.112677\pi$
$504$	1.11782	−	2.21042i	0.0497915	−	0.0984598i
$505$	−19.2270			−0.855590
$506$		−	31.4271i		−	1.39710i
$507$	1.02881	+	1.39340i	0.0456909	+	0.0618830i
$508$	3.59931			0.159694
$509$	26.3789			1.16922			0.584612	−	0.811313i	$-0.301247\pi$
$509$	26.3789			1.16922			0.584612	+	0.811313i	$0.301247\pi$
$510$	2.47031	−	1.82393i	0.109387	−	0.0807652i
$511$	−19.0836	−	3.26409i	−0.844210	−	0.144395i
$512$		−	30.7615i		−	1.35948i
$513$	12.3728	+	35.2914i	0.546274	+	1.55815i
$514$			4.44710i			0.196153i
$515$			8.25741i			0.363865i
$516$	12.5068	+	16.9390i	0.550581	+	0.745698i
$517$		−	15.3632i		−	0.675675i
$518$	47.2533	+	8.08229i	2.07619	+	0.355115i
$519$	−11.1529	−	15.1053i	−0.489557	−	0.663047i
$520$	0.730923			0.0320531
$521$	−12.0203			−0.526617			−0.263308	−	0.964712i	$-0.584814\pi$
$521$	−12.0203			−0.526617			−0.263308	+	0.964712i	$0.584814\pi$
$522$	13.9450	−	45.2732i	0.610358	−	1.98155i
$523$		−	1.54955i		−	0.0677570i	−0.999426	−	0.0338785i	$-0.989214\pi$
$523$		−	1.54955i		−	0.0677570i	0.999426	−	0.0338785i	$-0.0107859\pi$
$524$	3.72337			0.162656
$525$	−1.98807	+	1.00137i	−0.0867664	+	0.0437035i
$526$	−40.6424			−1.77209
$527$		−	2.14286i		−	0.0933443i
$528$	−12.8007	+	9.45131i	−0.557079	+	0.411315i
$529$	−33.1590			−1.44169
$530$	22.6966			0.985878
$531$	3.64361	−	11.8291i	0.158119	−	0.513341i
$532$	−34.5498	−	5.90946i	−1.49792	−	0.256207i
$533$		−	3.60438i		−	0.156123i
$534$	−21.9595	+	16.2137i	−0.950281	+	0.701634i
$535$		−	16.6753i		−	0.720935i
$536$		−	0.361491i		−	0.0156140i
$537$	14.3648	−	10.6061i	0.619886	−	0.457688i
$538$			40.9379i			1.76496i
$539$	4.97843	−	14.1275i	0.214436	−	0.608515i
$540$	21.1410	−	7.41182i	0.909762	−	0.318954i
$541$	39.7222			1.70779			0.853895	−	0.520445i	$-0.174234\pi$
$541$	39.7222			1.70779			0.853895	+	0.520445i	$0.174234\pi$
$542$	−56.9243			−2.44511
$543$	−22.9406	+	16.9381i	−0.984478	+	0.726882i
$544$			3.00854i			0.128990i
$545$	−13.8121			−0.591646
$546$	8.02085	−	4.04004i	0.343261	−	0.172898i
$547$	36.3913			1.55598			0.777989	−	0.628278i	$-0.216240\pi$
$547$	36.3913			1.55598			0.777989	+	0.628278i	$0.216240\pi$
$548$			33.0952i			1.41376i
$549$	17.1525	+	5.28331i	0.732051	+	0.225486i
$550$	2.03711			0.0868625
$551$	57.9901			2.47046
$552$	2.40600	+	3.25865i	0.102406	+	0.138697i
$553$	6.07024	−	35.4898i	0.258133	−	1.50918i
$554$			33.4678i			1.42191i
$555$	−22.2786	−	30.1738i	−0.945674	−	1.28081i
$556$		−	12.2857i		−	0.521030i
$557$		−	20.8772i		−	0.884594i	−0.896869	−	0.442297i	$-0.854164\pi$
$557$		−	20.8772i		−	0.884594i	0.896869	−	0.442297i	$-0.145836\pi$
$558$	9.60220	−	31.1740i	0.406494	−	1.31970i
$559$		−	6.60412i		−	0.279325i
$560$	4.48519	−	26.2228i	0.189534	−	1.10811i
$561$	1.15162	−	0.850291i	0.0486215	−	0.0358993i
$562$	−4.75995			−0.200786
$563$	−37.6007			−1.58468			−0.792339	−	0.610080i	$-0.791137\pi$
$563$	−37.6007			−1.58468			−0.792339	+	0.610080i	$0.791137\pi$
$564$	−13.5966	−	18.4149i	−0.572518	−	0.775409i
$565$			4.57983i			0.192675i
$566$	61.7035			2.59359
$567$	−16.5248	+	17.1444i	−0.693978	+	0.719997i
$568$	2.63543			0.110580
$569$		−	22.6173i		−	0.948167i	−0.880480	−	0.474084i	$-0.842779\pi$
$569$		−	22.6173i		−	0.948167i	0.880480	−	0.474084i	$-0.157221\pi$
$570$	33.9876	+	46.0323i	1.42359	+	1.92808i
$571$	−2.67628			−0.111999			−0.0559994	−	0.998431i	$-0.517835\pi$
$571$	−2.67628			−0.111999			−0.0559994	+	0.998431i	$0.517835\pi$
$572$	−3.93898			−0.164697
$573$	−13.6243	+	10.0594i	−0.569164	+	0.420238i
$574$	−18.4216	−	3.15086i	−0.768902	−	0.131514i
$575$		−	3.64023i		−	0.151808i
$576$	−5.89871	+	19.1504i	−0.245779	+	0.797934i
$577$			12.3160i			0.512723i	0.966581	+	0.256361i	$0.0825237\pi$
$577$			12.3160i			0.512723i	−0.966581	+	0.256361i	$0.917476\pi$
$578$			33.0240i			1.37362i
$579$	−11.6706	−	15.8065i	−0.485015	−	0.656896i
$580$		−	34.7384i		−	1.44243i
$581$	2.79555	−	16.3443i	0.115979	−	0.678075i
$582$	12.1428	+	16.4461i	0.503337	+	0.681711i
$583$	10.5808			0.438213
$584$	−2.28363			−0.0944974
$585$	−6.71517	−	2.06841i	−0.277638	−	0.0855181i
$586$			26.0606i			1.07655i
$587$	27.6343			1.14059			0.570294	−	0.821441i	$-0.306829\pi$
$587$	27.6343			1.14059			0.570294	+	0.821441i	$0.306829\pi$
$588$	−6.53559	−	21.3397i	−0.269523	−	0.880034i
$589$	39.9305			1.64531
$590$		−	18.9383i		−	0.779679i
$591$	15.1534	−	11.1884i	0.623329	−	0.460231i
$592$	39.6925			1.63135
$593$	3.59753			0.147733			0.0738664	−	0.997268i	$-0.476466\pi$
$593$	3.59753			0.147733			0.0738664	+	0.997268i	$0.476466\pi$
$594$	20.5638	−	7.20947i	0.843742	−	0.295808i
$595$	−0.403512	+	2.35914i	−0.0165424	+	0.0967155i
$596$		−	8.88874i		−	0.364097i
$597$	−15.1878	+	11.2138i	−0.621596	+	0.458951i
$598$			14.6865i			0.600576i
$599$			41.8062i			1.70816i	0.520145	+	0.854078i	$0.325878\pi$
$599$			41.8062i			1.70816i	−0.520145	+	0.854078i	$0.674122\pi$
$600$	−0.211226	+	0.155957i	−0.00862327	+	0.00636694i
$601$			32.8060i			1.33819i	0.743179	+	0.669093i	$0.233317\pi$
$601$			32.8060i			1.33819i	−0.743179	+	0.669093i	$0.766683\pi$
$602$	−33.7529	−	5.77315i	−1.37567	−	0.235296i
$603$	−1.02297	+	3.32111i	−0.0416584	+	0.135246i
$604$	1.24754			0.0507618
$605$	−15.0391			−0.611425
$606$	−22.4170	+	16.5514i	−0.910627	+	0.672356i
$607$		−	0.975154i		−	0.0395803i	−0.999804	−	0.0197901i	$-0.993700\pi$
$607$		−	0.975154i		−	0.0395803i	0.999804	−	0.0197901i	$-0.00629981\pi$
$608$	−56.0618			−2.27361
$609$	16.6100	+	32.9766i	0.673072	+	1.33628i
$610$	27.4610			1.11186
$611$			7.17955i			0.290454i
$612$	0.627862	−	2.03838i	0.0253798	−	0.0823966i
$613$	−27.1265			−1.09563			−0.547814	−	0.836600i	$-0.684540\pi$
$613$	−27.1265			−1.09563			−0.547814	+	0.836600i	$0.684540\pi$
$614$	16.6831			0.673273
$615$	8.68526	+	11.7632i	0.350224	+	0.474337i
$616$	0.297871	−	1.74151i	0.0120016	−	0.0701675i
$617$			0.933503i			0.0375814i	0.999823	+	0.0187907i	$0.00598162\pi$
$617$			0.933503i			0.0375814i	−0.999823	+	0.0187907i	$0.994018\pi$
$618$	7.10833	+	9.62741i	0.285939	+	0.387271i
$619$			1.63685i			0.0657904i	0.999459	+	0.0328952i	$0.0104728\pi$
$619$			1.63685i			0.0657904i	−0.999459	+	0.0328952i	$0.989527\pi$
$620$		−	23.9200i		−	0.960649i
$621$	−12.8830	−	36.7467i	−0.516979	−	1.47459i
$622$		−	60.7794i		−	2.43703i
$623$	3.58697	−	20.9713i	0.143709	−	0.840199i
$624$	5.98202	−	4.41679i	0.239473	−	0.176813i
$625$	−27.1928			−1.08771
$626$	−52.1879			−2.08585
$627$	15.8445	+	21.4596i	0.632770	+	0.857013i
$628$		−	35.1486i		−	1.40258i
$629$	−3.57096			−0.142383
$630$	−16.4416	+	32.5123i	−0.655050	+	1.29532i
$631$	−8.24540			−0.328244			−0.164122	−	0.986440i	$-0.552479\pi$
$631$	−8.24540			−0.328244			−0.164122	+	0.986440i	$0.552479\pi$
$632$		−	4.24688i		−	0.168932i
$633$	−24.9874	−	33.8425i	−0.993159	−	1.34512i
$634$	67.7615			2.69115
$635$	4.57973			0.181741
$636$	12.6826	−	9.36408i	0.502896	−	0.371310i
$637$	−2.32652	+	6.60207i	−0.0921801	+	0.261583i
$638$		−	33.7900i		−	1.33776i
$639$	−24.2124	−	7.45790i	−0.957828	−	0.295030i
$640$		−	5.82885i		−	0.230405i
$641$		−	10.3952i		−	0.410584i	−0.978701	−	0.205292i	$-0.934186\pi$
$641$		−	10.3952i		−	0.410584i	0.978701	−	0.205292i	$-0.0658144\pi$
$642$	−14.3548	−	19.4419i	−0.566539	−	0.767310i
$643$		−	19.1567i		−	0.755465i	−0.925915	−	0.377732i	$-0.876704\pi$
$643$		−	19.1567i		−	0.755465i	0.925915	−	0.377732i	$-0.123296\pi$
$644$	35.9745	+	6.15314i	1.41759	+	0.242468i
$645$	15.9135	+	21.5530i	0.626595	+	0.848650i
$646$	5.44776			0.214339
$647$	2.70289			0.106262			0.0531309	−	0.998588i	$-0.483080\pi$
$647$	2.70289			0.106262			0.0531309	+	0.998588i	$0.483080\pi$
$648$	−1.58030	+	2.32187i	−0.0620800	+	0.0912118i
$649$		−	8.82877i		−	0.346560i
$650$	−0.951981			−0.0373398
$651$	11.4372	+	22.7068i	0.448261	+	0.889950i
$652$	22.6225			0.885967
$653$		−	27.0698i		−	1.05932i	−0.848210	−	0.529661i	$-0.822319\pi$
$653$		−	27.0698i		−	1.05932i	0.848210	−	0.529661i	$-0.177681\pi$
$654$	−16.1037	+	11.8901i	−0.629705	+	0.464939i
$655$	4.73759			0.185113
$656$	−15.4740			−0.604160
$657$	20.9803	+	6.46236i	0.818520	+	0.252121i
$658$	36.6939	+	6.27618i	1.43048	+	0.244671i
$659$			5.08450i			0.198064i	0.995084	+	0.0990320i	$0.0315746\pi$
$659$			5.08450i			0.198064i	−0.995084	+	0.0990320i	$0.968425\pi$
$660$	12.8551	−	9.49151i	0.500386	−	0.369456i
$661$			6.68692i			0.260091i	0.991508	+	0.130045i	$0.0415123\pi$
$661$			6.68692i			0.260091i	−0.991508	+	0.130045i	$0.958488\pi$
$662$		−	11.3677i		−	0.441818i
$663$	−0.538175	+	0.397358i	−0.0209010	+	0.0154321i
$664$		−	1.95583i		−	0.0759010i
$665$	−43.9609	−	7.51914i	−1.70473	−	0.291580i
$666$	−51.9498	−	16.0016i	−2.01301	−	0.620048i
$667$	−60.3814			−2.33798
$668$	22.8831			0.885373
$669$	12.4089	−	9.16200i	0.479754	−	0.354223i
$670$			5.31705i			0.205416i
$671$	12.8019			0.494212
$672$	−16.0577	−	31.8800i	−0.619440	−	1.22980i
$673$	−15.4729			−0.596438			−0.298219	−	0.954497i	$-0.596393\pi$
$673$	−15.4729			−0.596438			−0.298219	+	0.954497i	$0.596393\pi$
$674$			4.06066i			0.156411i
$675$	2.38193	−	0.835081i	0.0916804	−	0.0321423i
$676$	1.84076			0.0707986
$677$	16.0079			0.615234			0.307617	−	0.951510i	$-0.400468\pi$
$677$	16.0079			0.615234			0.307617	+	0.951510i	$0.400468\pi$
$678$	3.94251	+	5.33968i	0.151411	+	0.205069i
$679$	−15.7060	−	2.68638i	−0.602741	−	0.103094i
$680$			0.282306i			0.0108259i
$681$	2.20919	+	2.99209i	0.0846564	+	0.114657i
$682$		−	23.2669i		−	0.890936i
$683$		−	10.0991i		−	0.386433i	−0.981156	−	0.193217i	$-0.938108\pi$
$683$		−	10.0991i		−	0.386433i	0.981156	−	0.193217i	$-0.0618920\pi$
$684$	37.9837	+	11.6997i	1.45234	+	0.447350i
$685$			42.1101i			1.60894i
$686$	31.7086	+	17.6619i	1.21064	+	0.674336i
$687$	−22.8479	+	16.8696i	−0.871703	+	0.643616i
$688$	−28.3523			−1.08092
$689$	−4.94463			−0.188375
$690$	−35.3892	−	47.9305i	−1.34724	−	1.82468i
$691$		−	13.5251i		−	0.514521i	−0.966342	−	0.257260i	$-0.917180\pi$
$691$		−	13.5251i		−	0.514521i	0.966342	−	0.257260i	$-0.0828198\pi$
$692$	−19.9550			−0.758574
$693$	−7.66484	+	15.1568i	−0.291163	+	0.575758i
$694$	−43.7630			−1.66122
$695$		−	15.6322i		−	0.592964i
$696$	2.58690	+	3.50366i	0.0980563	+	0.132806i
$697$	1.39213			0.0527307
$698$	−39.8311			−1.50763
$699$	−19.6639	+	14.5187i	−0.743755	+	0.549147i
$700$	−0.398847	+	2.33187i	−0.0150750	+	0.0881365i
$701$			10.4978i			0.396496i	0.980152	+	0.198248i	$0.0635252\pi$
$701$			10.4978i			0.396496i	−0.980152	+	0.198248i	$0.936475\pi$
$702$	−9.60987	+	3.36913i	−0.362701	+	0.127160i
$703$		−	66.5421i		−	2.50968i
$704$			14.2930i			0.538689i
$705$	−17.3001	−	23.4310i	−0.651560	−	0.882463i
$706$			16.8496i			0.634144i
$707$	3.66170	−	21.4082i	0.137712	−	0.805139i
$708$	−7.81351	−	10.5825i	−0.293650	−	0.397714i
$709$	−23.5865			−0.885810			−0.442905	−	0.896569i	$-0.646052\pi$
$709$	−23.5865			−0.885810			−0.442905	+	0.896569i	$0.646052\pi$
$710$	−38.7638			−1.45478
$711$	−12.0181	+	39.0171i	−0.450712	+	1.46326i
$712$		−	2.50953i		−	0.0940485i
$713$	−41.5771			−1.55707
$714$	1.56039	+	3.09791i	0.0583963	+	0.115937i
$715$	−5.01192			−0.187435
$716$		−	18.9767i		−	0.709194i
$717$	23.9886	−	17.7118i	0.895870	−	0.661460i
$718$	55.3732			2.06651
$719$	−15.2147			−0.567411			−0.283706	−	0.958911i	$-0.591564\pi$
$719$	−15.2147			−0.567411			−0.283706	+	0.958911i	$0.591564\pi$
$720$	−8.87991	+	28.8290i	−0.330935	+	1.07439i
$721$	−9.19418	−	1.57259i	−0.342409	−	0.0585662i
$722$			64.2789i			2.39221i
$723$	−5.90327	+	4.35864i	−0.219545	+	0.162099i
$724$			30.3060i			1.12631i
$725$		−	3.91393i		−	0.145360i
$726$	−17.5342	+	12.9463i	−0.650756	+	0.480481i
$727$		−	12.7108i		−	0.471418i	−0.971824	−	0.235709i	$-0.924259\pi$
$727$		−	12.7108i		−	0.471418i	0.971824	−	0.235709i	$-0.0757412\pi$
$728$	−0.139201	+	0.813843i	−0.00515913	+	0.0301630i
$729$	21.0892	−	16.8596i	0.781081	−	0.624430i
$730$	33.5893			1.24319
$731$	2.55073			0.0943420
$732$	15.3448	−	11.3297i	0.567161	−	0.418759i
$733$		−	15.9532i		−	0.589247i	−0.955613	−	0.294623i	$-0.904806\pi$
$733$		−	15.9532i		−	0.589247i	0.955613	−	0.294623i	$-0.0951942\pi$
$734$	26.5364			0.979476
$735$	−8.31582	−	27.1524i	−0.306734	−	1.00153i
$736$	58.3736			2.15168
$737$			2.47873i			0.0913053i
$738$	20.2525	+	6.23817i	0.745505	+	0.229630i
$739$	20.5383			0.755514			0.377757	−	0.925905i	$-0.376695\pi$
$739$	20.5383			0.755514			0.377757	+	0.925905i	$0.376695\pi$
$740$	−39.8614			−1.46533
$741$	−7.40447	−	10.0285i	−0.272010	−	0.368406i
$742$	−4.32247	+	25.2715i	−0.158683	+	0.927744i
$743$			44.8112i			1.64396i	0.569515	+	0.821981i	$0.307131\pi$
$743$			44.8112i			1.64396i	−0.569515	+	0.821981i	$0.692869\pi$
$744$	1.78128	+	2.41253i	0.0653047	+	0.0884476i
$745$		−	11.3099i		−	0.414364i
$746$		−	20.6040i		−	0.754367i
$747$	−5.53472	+	17.9687i	−0.202505	+	0.657441i
$748$		−	1.52136i		−	0.0556264i
$749$	18.5670	+	3.17573i	0.678424	+	0.116039i
$750$	−28.8727	+	21.3180i	−1.05428	+	0.778422i
$751$	35.8517			1.30825			0.654124	−	0.756387i	$-0.273037\pi$
$751$	35.8517			1.30825			0.654124	+	0.756387i	$0.273037\pi$
$752$	30.8227			1.12399
$753$	−5.73887	−	7.77263i	−0.209136	−	0.283250i
$754$			15.7907i			0.575064i
$755$	1.58736			0.0577700
$756$	4.22646	+	24.9509i	0.153715	+	0.907455i
$757$	15.3396			0.557526			0.278763	−	0.960360i	$-0.410076\pi$
$757$	15.3396			0.557526			0.278763	+	0.960360i	$0.410076\pi$
$758$		−	24.0718i		−	0.874327i
$759$	−16.4979	−	22.3445i	−0.598836	−	0.811053i
$760$	−5.26056			−0.190820
$761$	28.4406			1.03097			0.515485	−	0.856899i	$-0.327612\pi$
$761$	28.4406			1.03097			0.515485	+	0.856899i	$0.327612\pi$
$762$	5.33956	−	3.94243i	0.193432	−	0.142819i
$763$	2.63046	−	15.3791i	0.0952290	−	0.556759i
$764$			17.9985i			0.651164i
$765$	0.798886	−	2.59362i	0.0288838	−	0.0937724i
$766$		−	11.9374i		−	0.431315i
$767$			4.12586i			0.148976i
$768$	−18.7614	−	25.4101i	−0.676994	−	0.916909i
$769$			10.3421i			0.372945i	0.982460	+	0.186473i	$0.0597056\pi$
$769$			10.3421i			0.372945i	−0.982460	+	0.186473i	$0.940294\pi$
$770$	−4.38129	+	25.6153i	−0.157891	+	0.923113i
$771$	2.33454	+	3.16186i	0.0840765	+	0.113872i
$772$	−20.8813			−0.751536
$773$	−6.56498			−0.236126			−0.118063	−	0.993006i	$-0.537668\pi$
$773$	−6.56498			−0.236126			−0.118063	+	0.993006i	$0.537668\pi$
$774$	37.1076	+	11.4299i	1.33380	+	0.410838i
$775$		−	2.69503i		−	0.0968084i
$776$	−1.87945			−0.0674684
$777$	37.8397	−	19.0596i	1.35749	−	0.683758i
$778$	−0.749136			−0.0268578
$779$			25.9413i			0.929443i
$780$	−6.00747	+	4.43557i	−0.215102	+	0.158819i
$781$	−18.0711			−0.646635
$782$	−5.67240			−0.202845
$783$	−13.8517	−	39.5096i	−0.495018	−	1.41196i
$784$	28.3435	+	9.98803i	1.01227	+	0.356715i
$785$		−	44.7228i		−	1.59622i
$786$	5.52361	−	4.07832i	0.197021	−	0.145469i
$787$			32.9790i			1.17557i	0.809016	+	0.587787i	$0.200000\pi$
$787$			32.9790i			1.17557i	−0.809016	+	0.587787i	$0.800000\pi$
$788$		−	20.0186i		−	0.713133i
$789$	−28.8965	+	21.3356i	−1.02874	+	0.759566i
$790$			62.4660i			2.22244i
$791$	−5.09939	−	0.872208i	−0.181314	−	0.0310122i
$792$	−0.589734	+	1.91460i	−0.0209553	+	0.0680322i
$793$	−5.98258			−0.212448
$794$	73.2517			2.59960
$795$	16.1372	−	11.9148i	0.572326	−	0.422573i
$796$			20.0640i			0.711150i
$797$	−55.1447			−1.95333			−0.976663	−	0.214780i	$-0.931097\pi$
$797$	−55.1447			−1.95333			−0.976663	+	0.214780i	$0.931097\pi$
$798$	−57.7273	+	29.0767i	−2.04352	+	1.02931i
$799$	−2.77298			−0.0981008
$800$			3.78378i			0.133777i
$801$	−7.10160	+	23.0557i	−0.250923	+	0.814632i
$802$	4.09795			0.144704
$803$	15.6588			0.552587
$804$	2.19369	+	2.97110i	0.0773655	+	0.104783i
$805$	45.7736	+	7.82920i	1.61331	+	0.275943i
$806$			10.8731i			0.382988i
$807$	21.4907	+	29.1066i	0.756508	+	1.02460i
$808$		−	2.56181i		−	0.0901240i
$809$			9.00815i			0.316710i	0.987382	+	0.158355i	$0.0506190\pi$
$809$			9.00815i			0.316710i	−0.987382	+	0.158355i	$0.949381\pi$
$810$	23.2441	−	34.1517i	0.816716	−	1.19997i
$811$			25.0449i			0.879445i	0.898134	+	0.439722i	$0.144923\pi$
$811$			25.0449i			0.879445i	−0.898134	+	0.439722i	$0.855077\pi$
$812$	38.6793	+	6.61577i	1.35738	+	0.232168i
$813$	−40.4729	+	29.8829i	−1.41945	+	1.04804i
$814$	−38.7731			−1.35900
$815$	28.7847			1.00828
$816$	1.70591	+	2.31045i	0.0597186	+	0.0808819i
$817$			47.5308i			1.66289i
$818$	12.3258			0.430962
$819$	3.58193	−	7.08306i	0.125163	−	0.247502i
$820$	15.5399			0.542675
$821$		−	35.1854i		−	1.22798i	−0.789314	−	0.613990i	$-0.789564\pi$
$821$		−	35.1854i		−	1.22798i	0.789314	−	0.613990i	$-0.210436\pi$
$822$	36.2502	+	49.0966i	1.26437	+	1.71244i
$823$	−10.3312			−0.360123			−0.180062	−	0.983655i	$-0.557630\pi$
$823$	−10.3312			−0.360123			−0.180062	+	0.983655i	$0.557630\pi$
$824$	−1.10022			−0.0383279
$825$	1.44837	−	1.06940i	0.0504258	−	0.0372316i
$826$	21.0868	+	3.60672i	0.733704	+	0.125494i
$827$		−	31.7482i		−	1.10399i	−0.833847	−	0.551996i	$-0.813866\pi$
$827$		−	31.7482i		−	1.10399i	0.833847	−	0.551996i	$-0.186134\pi$
$828$	−39.5500	−	12.1822i	−1.37446	−	0.423360i
$829$			38.1096i			1.32360i	0.749679	+	0.661801i	$0.230208\pi$
$829$			38.1096i			1.32360i	−0.749679	+	0.661801i	$0.769792\pi$
$830$			28.7677i			0.998542i
$831$	17.5692	+	23.7954i	0.609469	+	0.825455i
$832$		−	6.67943i		−	0.231567i
$833$	−2.54993	−	0.898577i	−0.0883499	−	0.0311339i
$834$	−13.4569	−	18.2258i	−0.465974	−	0.631107i
$835$	29.1162			1.00761
$836$	28.3494			0.980484
$837$	−9.53791	−	27.2053i	−0.329678	−	0.940352i
$838$			41.0448i			1.41787i
$839$	−21.0801			−0.727765			−0.363883	−	0.931445i	$-0.618549\pi$
$839$	−21.0801			−0.727765			−0.363883	+	0.931445i	$0.618549\pi$
$840$	−1.50677	−	2.99146i	−0.0519887	−	0.103215i
$841$	−35.9212			−1.23866
$842$			78.0881i			2.69109i
$843$	−3.38430	+	2.49877i	−0.116561	+	0.0860623i
$844$	−44.7080			−1.53891
$845$	2.34217			0.0805731
$846$	−40.3408	−	12.4258i	−1.38695	−	0.427207i
$847$	2.86412	−	16.7452i	0.0984125	−	0.575371i
$848$			21.2279i			0.728969i
$849$	43.8709	−	32.3918i	1.50564	−	1.11168i
$850$		−	0.367686i		−	0.0126115i
$851$			69.2860i			2.37509i
$852$	−21.6607	+	15.9930i	−0.742083	+	0.547912i
$853$		−	11.9297i		−	0.408466i	−0.978922	−	0.204233i	$-0.934530\pi$
$853$		−	11.9297i		−	0.408466i	0.978922	−	0.204233i	$-0.0654701\pi$
$854$	−5.22982	+	30.5763i	−0.178961	+	1.04630i
$855$	48.3301	+	14.8866i	1.65285	+	0.509112i
$856$	2.22181			0.0759401
$857$	−22.0041			−0.751645			−0.375823	−	0.926692i	$-0.622640\pi$
$857$	−22.0041			−0.751645			−0.375823	+	0.926692i	$0.622640\pi$
$858$	−5.84345	+	4.31447i	−0.199492	+	0.147294i
$859$			12.0317i			0.410515i	0.978708	+	0.205258i	$0.0658033\pi$
$859$			12.0317i			0.410515i	−0.978708	+	0.205258i	$0.934197\pi$
$860$	28.4729			0.970917
$861$	−14.7517	+	7.43032i	−0.502738	+	0.253225i
$862$	46.3346			1.57816
$863$		−	44.3047i		−	1.50815i	−0.656789	−	0.754074i	$-0.728086\pi$
$863$		−	44.3047i		−	1.50815i	0.656789	−	0.754074i	$-0.271914\pi$
$864$	13.3911	+	38.1958i	0.455574	+	1.29945i
$865$	−25.3905			−0.863303
$866$	1.37427			0.0466997
$867$	17.3362	+	23.4799i	0.588769	+	0.797419i
$868$	26.6336	+	4.55545i	0.904003	+	0.154622i
$869$			29.1207i			0.987852i
$870$	−38.0499	−	51.5342i	−1.29001	−	1.74717i
$871$		−	1.15836i		−	0.0392496i
$872$		−	1.84033i		−	0.0623214i
$873$	17.2670	+	5.31858i	0.584399	+	0.180007i
$874$		−	105.701i		−	3.57539i
$875$	4.71620	−	27.5734i	0.159437	−	0.932152i
$876$	18.7692	−	13.8581i	0.634153	−	0.468223i
$877$	21.1861			0.715402			0.357701	−	0.933836i	$-0.383561\pi$
$877$	21.1861			0.715402			0.357701	+	0.933836i	$0.383561\pi$
$878$	−6.17053			−0.208245
$879$	13.6807	+	18.5289i	0.461439	+	0.624965i
$880$			21.5167i			0.725329i
$881$	8.00201			0.269594			0.134797	−	0.990873i	$-0.456962\pi$
$881$	8.00201			0.269594			0.134797	+	0.990873i	$0.456962\pi$
$882$	−33.0695	−	24.4987i	−1.11351	−	0.824914i
$883$	−8.15769			−0.274528			−0.137264	−	0.990534i	$-0.543831\pi$
$883$	−8.15769			−0.274528			−0.137264	+	0.990534i	$0.543831\pi$
$884$			0.710962i			0.0239122i
$885$	−9.94184	−	13.4651i	−0.334191	−	0.452623i
$886$	−44.4921			−1.49474
$887$	−4.59026			−0.154126			−0.0770629	−	0.997026i	$-0.524554\pi$
$887$	−4.59026			−0.154126			−0.0770629	+	0.997026i	$0.524554\pi$
$888$	4.02036	−	2.96840i	0.134914	−	0.0996131i
$889$	−0.872190	+	5.09929i	−0.0292523	+	0.171025i
$890$			36.9119i			1.23729i
$891$	10.8361	−	15.9210i	0.363022	−	0.533374i
$892$		−	16.3929i		−	0.548873i
$893$		−	51.6723i		−	1.72915i
$894$	−9.73609	−	13.1864i	−0.325623	−	0.441019i
$895$		−	24.1458i		−	0.807105i
$896$	6.49011	+	1.11008i	0.216819	+	0.0370851i
$897$	7.70980	+	10.4420i	0.257423	+	0.348649i
$898$	−49.6989			−1.65847
$899$	−44.7031			−1.49093
$900$	0.789651	−	2.56363i	0.0263217	−	0.0854545i
$901$		−	1.90978i		−	0.0636239i
$902$	15.1156			0.503294
$903$	−27.0288	+	13.6142i	−0.899462	+	0.453052i
$904$	−0.610217			−0.0202955
$905$			38.5610i			1.28181i
$906$	1.85072	−	1.36647i	0.0614862	−	0.0453979i
$907$	49.4710			1.64266			0.821329	−	0.570454i	$-0.193233\pi$
$907$	49.4710			1.64266			0.821329	+	0.570454i	$0.193233\pi$
$908$	3.95273			0.131176
$909$	−7.24954	+	23.5359i	−0.240452	+	0.780638i
$910$	2.04746	−	11.9706i	0.0678728	−	0.396820i
$911$			16.8538i			0.558392i	0.960234	+	0.279196i	$0.0900678\pi$
$911$			16.8538i			0.558392i	−0.960234	+	0.279196i	$0.909932\pi$
$912$	−43.0535	+	31.7883i	−1.42564	+	1.05261i
$913$			13.4111i			0.443842i
$914$		−	54.7430i		−	1.81074i
$915$	19.5246	−	14.4159i	0.645463	−	0.476574i
$916$			30.1835i			0.997291i
$917$	−0.902253	+	5.27505i	−0.0297950	+	0.174197i
$918$	−1.30127	−	3.71164i	−0.0429482	−	0.122502i
$919$	−51.5781			−1.70140			−0.850702	−	0.525648i	$-0.823823\pi$
$919$	−51.5781			−1.70140			−0.850702	+	0.525648i	$0.823823\pi$
$920$	5.47748			0.180587
$921$	11.8616	−	8.75791i	0.390852	−	0.288583i
$922$			55.6571i			1.83297i
$923$	8.44499			0.277970
$924$	8.12008	+	16.1211i	0.267131	+	0.530346i
$925$	−4.49113			−0.147667
$926$		−	5.86274i		−	0.192662i
$927$	10.1080	+	3.11346i	0.331990	+	0.102259i
$928$	62.7625			2.06028
$929$	−44.3642			−1.45554			−0.727770	−	0.685821i	$-0.759443\pi$
$929$	−44.3642			−1.45554			−0.727770	+	0.685821i	$0.759443\pi$
$930$	−26.2002	−	35.4851i	−0.859139	−	1.16360i
$931$	16.7443	−	47.5160i	0.548772	−	1.55728i
$932$			25.9771i			0.850910i
$933$	−31.9066	−	43.2138i	−1.04458	−	1.41476i
$934$		−	55.4418i		−	1.81411i
$935$		−	1.93576i		−	0.0633063i
$936$	0.275595	−	0.894730i	0.00900809	−	0.0292452i
$937$			13.8586i			0.452739i	0.974041	+	0.226370i	$0.0726857\pi$
$937$			13.8586i			0.452739i	−0.974041	+	0.226370i	$0.927314\pi$
$938$	−5.92025	−	1.01261i	−0.193303	−	0.0330629i
$939$	−37.1053	+	27.3965i	−1.21089	+	0.894050i
$940$	−30.9538			−1.00960
$941$	−49.3440			−1.60857			−0.804284	−	0.594246i	$-0.797451\pi$
$941$	−49.3440			−1.60857			−0.804284	+	0.594246i	$0.797451\pi$
$942$	−38.4993	−	52.1428i	−1.25438	−	1.69890i
$943$		−	27.0110i		−	0.879599i
$944$	17.7128			0.576503
$945$	5.37771	+	31.7473i	0.174937	+	1.03274i
$946$	27.6955			0.900458
$947$		−	6.53681i		−	0.212418i	−0.994344	−	0.106209i	$-0.966129\pi$
$947$		−	6.53681i		−	0.212418i	0.994344	−	0.106209i	$-0.0338712\pi$
$948$	25.7720	+	34.9051i	0.837035	+	1.13367i
$949$	−7.31768			−0.237542
$950$	6.85155			0.222294
$951$	48.1781	−	35.5720i	1.56228	−	1.15350i
$952$	−0.314333	−	0.0537640i	−0.0101876	−	0.00174250i
$953$			3.01642i			0.0977115i	0.998806	+	0.0488557i	$0.0155575\pi$
$953$			3.01642i			0.0977115i	−0.998806	+	0.0488557i	$0.984443\pi$
$954$	8.55776	−	27.7831i	0.277068	−	0.899513i
$955$			22.9012i			0.741064i
$956$		−	31.6904i		−	1.02494i
$957$	−17.7383	−	24.0245i	−0.573398	−	0.776601i
$958$		−	1.43159i		−	0.0462525i
$959$	−46.8873	−	8.01968i	−1.51407	−	0.258969i
$960$	16.0950	+	21.7988i	0.519464	+	0.703553i
$961$	0.218573			0.00705076
$962$	18.1194			0.584194
$963$	−20.4124	−	6.28742i	−0.657779	−	0.202609i
$964$			7.79857i			0.251175i
$965$	−26.5692			−0.855294
$966$	60.1077	−	30.2758i	1.93393	−	0.974107i
$967$	−16.1771			−0.520220			−0.260110	−	0.965579i	$-0.583759\pi$
$967$	−16.1771			−0.520220			−0.260110	+	0.965579i	$0.583759\pi$
$968$		−	2.00381i		−	0.0644047i
$969$	3.87333	−	2.85985i	0.124429	−	0.0918715i
$970$	27.6443			0.887604
$971$	39.1873			1.25758			0.628789	−	0.777576i	$-0.283551\pi$
$971$	39.1873			1.25758			0.628789	+	0.777576i	$0.283551\pi$
$972$	−1.10168	−	28.6735i	−0.0353363	−	0.919703i
$973$	17.4056	+	2.97709i	0.557999	+	0.0954410i
$974$		−	12.2146i		−	0.391380i
$975$	−0.676854	+	0.499750i	−0.0216767	+	0.0160048i
$976$			25.6839i			0.822123i
$977$			29.4214i			0.941273i	0.882327	+	0.470636i	$0.155976\pi$
$977$			29.4214i			0.941273i	−0.882327	+	0.470636i	$0.844024\pi$
$978$	33.5604	−	24.7791i	1.07314	−	0.792349i
$979$			17.2078i			0.549962i
$980$	−28.4640	−	10.0305i	−0.909250	−	0.320413i
$981$	−5.20787	+	16.9076i	−0.166274	+	0.539817i
$982$	16.4008			0.523370
$983$	22.1097			0.705189			0.352594	−	0.935776i	$-0.385300\pi$
$983$	22.1097			0.705189			0.352594	+	0.935776i	$0.385300\pi$
$984$	−1.56733	+	1.15722i	−0.0499645	+	0.0368910i
$985$		−	25.4715i		−	0.811589i
$986$	−6.09889			−0.194228
$987$	29.3839	−	14.8004i	0.935300	−	0.471103i
$988$	−13.2482			−0.421483
$989$		−	49.4908i		−	1.57372i
$990$	8.67421	−	28.1612i	0.275685	−	0.895022i
$991$	−25.1057			−0.797508			−0.398754	−	0.917058i	$-0.630557\pi$
$991$	−25.1057			−0.797508			−0.398754	+	0.917058i	$0.630557\pi$
$992$	43.2167			1.37213
$993$	−5.96757	−	8.08238i	−0.189375	−	0.256487i
$994$	7.38239	−	43.1614i	0.234155	−	1.36900i
$995$			25.5293i			0.809332i
$996$	11.8689	+	16.0750i	0.376080	+	0.509356i
$997$		−	41.2425i		−	1.30616i	−0.757288	−	0.653081i	$-0.773476\pi$
$997$		−	41.2425i		−	1.30616i	0.757288	−	0.653081i	$-0.226524\pi$
$998$		−	49.4904i		−	1.56659i
$999$	−45.3362	+	15.8944i	−1.43437	+	0.502878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.e.a.209.5	✓	32
3.2	odd	2	inner	273.2.e.a.209.28	yes	32
7.6	odd	2	inner	273.2.e.a.209.6	yes	32
21.20	even	2	inner	273.2.e.a.209.27	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.e.a.209.5	✓	32	1.1	even	1	trivial
273.2.e.a.209.6	yes	32	7.6	odd	2	inner
273.2.e.a.209.27	yes	32	21.20	even	2	inner
273.2.e.a.209.28	yes	32	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.95979i q^{2} +(-1.02881 - 1.39340i) q^{3} -1.84076 q^{4} -2.34217 q^{5} +(-2.73076 + 2.01624i) q^{6} +(0.446056 - 2.60788i) q^{7} -0.312071i q^{8} +(-0.883116 + 2.86707i) q^{9} +O(q^{10})\)	\(q-1.95979i q^{2} +(-1.02881 - 1.39340i) q^{3} -1.84076 q^{4} -2.34217 q^{5} +(-2.73076 + 2.01624i) q^{6} +(0.446056 - 2.60788i) q^{7} -0.312071i q^{8} +(-0.883116 + 2.86707i) q^{9} +4.59015i q^{10} +2.13986i q^{11} +(1.89379 + 2.56492i) q^{12} -1.00000i q^{13} +(-5.11089 - 0.874174i) q^{14} +(2.40964 + 3.26357i) q^{15} -4.29312 q^{16} +0.386232 q^{17} +(5.61885 + 1.73072i) q^{18} +7.19715i q^{19} +4.31138 q^{20} +(-4.09272 + 2.06147i) q^{21} +4.19367 q^{22} -7.49393i q^{23} +(-0.434839 + 0.321060i) q^{24} +0.485757 q^{25} -1.95979 q^{26} +(4.90353 - 1.71913i) q^{27} +(-0.821083 + 4.80049i) q^{28} -8.05737i q^{29} +(6.39591 - 4.72238i) q^{30} -5.54810i q^{31} +7.78945i q^{32} +(2.98168 - 2.20150i) q^{33} -0.756933i q^{34} +(-1.04474 + 6.10809i) q^{35} +(1.62561 - 5.27760i) q^{36} -9.24562 q^{37} +14.1049 q^{38} +(-1.39340 + 1.02881i) q^{39} +0.730923i q^{40} +3.60438 q^{41} +(4.04004 + 8.02085i) q^{42} +6.60412 q^{43} -3.93898i q^{44} +(2.06841 - 6.71517i) q^{45} -14.6865 q^{46} -7.17955 q^{47} +(4.41679 + 5.98202i) q^{48} +(-6.60207 - 2.32652i) q^{49} -0.951981i q^{50} +(-0.397358 - 0.538175i) q^{51} +1.84076i q^{52} -4.94463i q^{53} +(-3.36913 - 9.60987i) q^{54} -5.01192i q^{55} +(-0.813843 - 0.139201i) q^{56} +(10.0285 - 7.40447i) q^{57} -15.7907 q^{58} -4.12586 q^{59} +(-4.43557 - 6.00747i) q^{60} -5.98258i q^{61} -10.8731 q^{62} +(7.08306 + 3.58193i) q^{63} +6.67943 q^{64} +2.34217i q^{65} +(-4.31447 - 5.84345i) q^{66} +1.15836 q^{67} -0.710962 q^{68} +(-10.4420 + 7.70980i) q^{69} +(11.9706 + 2.04746i) q^{70} +8.44499i q^{71} +(0.894730 + 0.275595i) q^{72} -7.31768i q^{73} +18.1194i q^{74} +(-0.499750 - 0.676854i) q^{75} -13.2482i q^{76} +(5.58050 + 0.954498i) q^{77} +(2.01624 + 2.73076i) q^{78} +13.6087 q^{79} +10.0552 q^{80} +(-7.44021 - 5.06391i) q^{81} -7.06382i q^{82} +6.26727 q^{83} +(7.53372 - 3.79468i) q^{84} -0.904622 q^{85} -12.9427i q^{86} +(-11.2271 + 8.28947i) q^{87} +0.667788 q^{88} +8.04153 q^{89} +(-13.1603 - 4.05364i) q^{90} +(-2.60788 - 0.446056i) q^{91} +13.7945i q^{92} +(-7.73071 + 5.70792i) q^{93} +14.0704i q^{94} -16.8569i q^{95} +(10.8538 - 8.01384i) q^{96} -6.02252i q^{97} +(-4.55948 + 12.9386i) q^{98} +(-6.13514 - 1.88974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9	\( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9 - 12 * q^15 + 16 * q^16 - 20 * q^18 - 4 * q^21 - 16 * q^22 - 28 * q^28 + 16 * q^30 + 24 * q^36 + 24 * q^37 + 32 * q^43 - 24 * q^46 - 24 * q^49 - 8 * q^51 + 32 * q^57 + 24 * q^58 - 28 * q^60 + 8 * q^63 + 48 * q^64 - 32 * q^67 - 8 * q^70 + 64 * q^72 + 20 * q^78 - 32 * q^79 + 32 * q^81 - 48 * q^84 - 16 * q^85 + 64 * q^88 + 4 * q^91 - 52 * q^93 + 20 * q^99

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