LMFDB - Embedded newform 1045.2.f.b.626.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(626,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.f (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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.3
Character	$\chi$	$=$	1045.626
Dual form			1045.2.f.b.626.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36088 q^{2} +2.84862i q^{3} +3.57375 q^{4} +1.00000 q^{5} -6.72526i q^{6} -0.816397i q^{7} -3.71543 q^{8} -5.11466 q^{9} +O(q^{10})$	\(q-2.36088 q^{2} +2.84862i q^{3} +3.57375 q^{4} +1.00000 q^{5} -6.72526i q^{6} -0.816397i q^{7} -3.71543 q^{8} -5.11466 q^{9} -2.36088 q^{10} +(-3.22730 + 0.764557i) q^{11} +10.1803i q^{12} +0.847115 q^{13} +1.92741i q^{14} +2.84862i q^{15} +1.62418 q^{16} -4.07317i q^{17} +12.0751 q^{18} +(-2.17793 - 3.77579i) q^{19} +3.57375 q^{20} +2.32561 q^{21} +(7.61926 - 1.80503i) q^{22} +6.65502 q^{23} -10.5839i q^{24} +1.00000 q^{25} -1.99994 q^{26} -6.02387i q^{27} -2.91760i q^{28} -7.23296 q^{29} -6.72526i q^{30} -5.91078i q^{31} +3.59636 q^{32} +(-2.17793 - 9.19336i) q^{33} +9.61626i q^{34} -0.816397i q^{35} -18.2785 q^{36} -9.96068i q^{37} +(5.14184 + 8.91419i) q^{38} +2.41311i q^{39} -3.71543 q^{40} -11.6419 q^{41} -5.49048 q^{42} +5.14349i q^{43} +(-11.5336 + 2.73233i) q^{44} -5.11466 q^{45} -15.7117 q^{46} -10.6739 q^{47} +4.62668i q^{48} +6.33350 q^{49} -2.36088 q^{50} +11.6029 q^{51} +3.02738 q^{52} -1.18952i q^{53} +14.2216i q^{54} +(-3.22730 + 0.764557i) q^{55} +3.03326i q^{56} +(10.7558 - 6.20412i) q^{57} +17.0761 q^{58} +1.07635i q^{59} +10.1803i q^{60} -13.4275i q^{61} +13.9546i q^{62} +4.17559i q^{63} -11.7389 q^{64} +0.847115 q^{65} +(5.14184 + 21.7044i) q^{66} -9.83025i q^{67} -14.5565i q^{68} +18.9576i q^{69} +1.92741i q^{70} -4.42462i q^{71} +19.0032 q^{72} +4.87650i q^{73} +23.5160i q^{74} +2.84862i q^{75} +(-7.78339 - 13.4937i) q^{76} +(0.624182 + 2.63476i) q^{77} -5.69707i q^{78} +5.76276 q^{79} +1.62418 q^{80} +1.81576 q^{81} +27.4852 q^{82} +11.9058i q^{83} +8.31114 q^{84} -4.07317i q^{85} -12.1431i q^{86} -20.6040i q^{87} +(11.9908 - 2.84066i) q^{88} -5.52282i q^{89} +12.0751 q^{90} -0.691582i q^{91} +23.7834 q^{92} +16.8376 q^{93} +25.1998 q^{94} +(-2.17793 - 3.77579i) q^{95} +10.2447i q^{96} +13.9387i q^{97} -14.9526 q^{98} +(16.5065 - 3.91045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) $ 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9	$ 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9} - 4 q^{11} + 48 q^{16} + 40 q^{20} + 24 q^{23} + 40 q^{25} - 24 q^{26} + 24 q^{36} - 28 q^{38} - 60 q^{42} - 48 q^{44} - 28 q^{45} - 36 q^{49} - 4 q^{55} - 36 q^{58} - 40 q^{64} - 28 q^{66} + 8 q^{77} + 48 q^{80} + 80 q^{81} + 8 q^{82} + 4 q^{92} + 56 q^{93} - 16 q^{99}+O(q^{100}) $ 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9 - 4 * q^11 + 48 * q^16 + 40 * q^20 + 24 * q^23 + 40 * q^25 - 24 * q^26 + 24 * q^36 - 28 * q^38 - 60 * q^42 - 48 * q^44 - 28 * q^45 - 36 * q^49 - 4 * q^55 - 36 * q^58 - 40 * q^64 - 28 * q^66 + 8 * q^77 + 48 * q^80 + 80 * q^81 + 8 * q^82 + 4 * q^92 + 56 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−2.36088			−1.66939			−0.834697	−	0.550710i	$-0.814357\pi$
$2$	−2.36088			−1.66939			−0.834697	+	0.550710i	$0.814357\pi$
$3$			2.84862i			1.64465i	0.569015	+	0.822327i	$0.307325\pi$
$3$			2.84862i			1.64465i	−0.569015	+	0.822327i	$0.692675\pi$
$4$	3.57375			1.78687
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		−	6.72526i		−	2.74557i
$7$		−	0.816397i		−	0.308569i	−0.988026	−	0.154285i	$-0.950693\pi$
$7$		−	0.816397i		−	0.308569i	0.988026	−	0.154285i	$-0.0493072\pi$
$8$	−3.71543			−1.31360
$9$	−5.11466			−1.70489
$10$	−2.36088			−0.746575
$11$	−3.22730	+	0.764557i	−0.973067	+	0.230522i
$11$	−3.22730	+	0.764557i	−0.973067	+	0.230522i
$12$			10.1803i			2.93879i
$13$	0.847115			0.234948			0.117474	−	0.993076i	$-0.462520\pi$
$13$	0.847115			0.234948			0.117474	+	0.993076i	$0.462520\pi$
$14$			1.92741i			0.515123i
$15$			2.84862i			0.735512i
$16$	1.62418			0.406045
$17$		−	4.07317i		−	0.987889i	−0.869494	−	0.493944i	$-0.835555\pi$
$17$		−	4.07317i		−	0.987889i	0.869494	−	0.493944i	$-0.164445\pi$
$18$	12.0751			2.84613
$19$	−2.17793	−	3.77579i	−0.499652	−	0.866226i
$19$	−2.17793	−	3.77579i	−0.499652	−	0.866226i
$20$	3.57375			0.799114
$21$	2.32561			0.507489
$22$	7.61926	−	1.80503i	1.62443	−	0.384833i
$23$	6.65502			1.38767			0.693833	−	0.720136i	$-0.255920\pi$
$23$	6.65502			1.38767			0.693833	+	0.720136i	$0.255920\pi$
$24$		−	10.5839i		−	2.16042i
$25$	1.00000			0.200000
$26$	−1.99994			−0.392220
$27$		−	6.02387i		−	1.15929i
$28$		−	2.91760i		−	0.551374i
$29$	−7.23296			−1.34313			−0.671563	−	0.740947i	$-0.734377\pi$
$29$	−7.23296			−1.34313			−0.671563	+	0.740947i	$0.734377\pi$
$30$		−	6.72526i		−	1.22786i
$31$		−	5.91078i		−	1.06161i	−0.847495	−	0.530804i	$-0.821890\pi$
$31$		−	5.91078i		−	1.06161i	0.847495	−	0.530804i	$-0.178110\pi$
$32$	3.59636			0.635753
$33$	−2.17793	−	9.19336i	−0.379130	−	1.60036i
$34$			9.61626i			1.64917i
$35$		−	0.816397i		−	0.137996i
$36$	−18.2785			−3.04642
$37$		−	9.96068i		−	1.63753i	−0.574132	−	0.818763i	$-0.694660\pi$
$37$		−	9.96068i		−	1.63753i	0.574132	−	0.818763i	$-0.305340\pi$
$38$	5.14184	+	8.91419i	0.834116	+	1.44607i
$39$			2.41311i			0.386407i
$40$	−3.71543			−0.587461
$41$	−11.6419			−1.81816			−0.909081	−	0.416618i	$-0.863215\pi$
$41$	−11.6419			−1.81816			−0.909081	+	0.416618i	$0.863215\pi$
$42$	−5.49048			−0.847199
$43$			5.14349i			0.784374i	0.919885	+	0.392187i	$0.128281\pi$
$43$			5.14349i			0.784374i	−0.919885	+	0.392187i	$0.871719\pi$
$44$	−11.5336	+	2.73233i	−1.73875	+	0.411915i
$45$	−5.11466			−0.762448
$46$	−15.7117			−2.31656
$47$	−10.6739			−1.55695			−0.778476	−	0.627674i	$-0.784007\pi$
$47$	−10.6739			−1.55695			−0.778476	+	0.627674i	$0.784007\pi$
$48$			4.62668i			0.667804i
$49$	6.33350			0.904785
$50$	−2.36088			−0.333879
$51$	11.6029			1.62473
$52$	3.02738			0.419822
$53$		−	1.18952i		−	0.163393i	−0.996657	−	0.0816964i	$-0.973966\pi$
$53$		−	1.18952i		−	0.163393i	0.996657	−	0.0816964i	$-0.0260338\pi$
$54$			14.2216i			1.93532i
$55$	−3.22730	+	0.764557i	−0.435169	+	0.103093i
$56$			3.03326i			0.405337i
$57$	10.7558	−	6.20412i	1.42464	−	0.821755i
$58$	17.0761			2.24221
$59$			1.07635i			0.140128i	0.997542	+	0.0700642i	$0.0223204\pi$
$59$			1.07635i			0.140128i	−0.997542	+	0.0700642i	$0.977680\pi$
$60$			10.1803i			1.31427i
$61$		−	13.4275i		−	1.71921i	−0.510955	−	0.859607i	$-0.670708\pi$
$61$		−	13.4275i		−	1.71921i	0.510955	−	0.859607i	$-0.329292\pi$
$62$			13.9546i			1.77224i
$63$			4.17559i			0.526075i
$64$	−11.7389			−1.46737
$65$	0.847115			0.105072
$66$	5.14184	+	21.7044i	0.632917	+	2.67163i
$67$		−	9.83025i		−	1.20096i	−0.799641	−	0.600478i	$-0.794977\pi$
$67$		−	9.83025i		−	1.20096i	0.799641	−	0.600478i	$-0.205023\pi$
$68$		−	14.5565i		−	1.76523i
$69$			18.9576i			2.28223i
$70$			1.92741i			0.230370i
$71$		−	4.42462i		−	0.525106i	−0.964918	−	0.262553i	$-0.915436\pi$
$71$		−	4.42462i		−	0.525106i	0.964918	−	0.262553i	$-0.0845644\pi$
$72$	19.0032			2.23954
$73$			4.87650i			0.570752i	0.958416	+	0.285376i	$0.0921184\pi$
$73$			4.87650i			0.570752i	−0.958416	+	0.285376i	$0.907882\pi$
$74$			23.5160i			2.73368i
$75$			2.84862i			0.328931i
$76$	−7.78339	−	13.4937i	−0.892816	−	1.54784i
$77$	0.624182	+	2.63476i	0.0711321	+	0.300258i
$78$		−	5.69707i		−	0.645066i
$79$	5.76276			0.648361			0.324180	−	0.945995i	$-0.394911\pi$
$79$	5.76276			0.648361			0.324180	+	0.945995i	$0.394911\pi$
$80$	1.62418			0.181589
$81$	1.81576			0.201752
$82$	27.4852			3.03523
$83$			11.9058i			1.30683i	0.756999	+	0.653416i	$0.226665\pi$
$83$			11.9058i			1.30683i	−0.756999	+	0.653416i	$0.773335\pi$
$84$	8.31114			0.906819
$85$		−	4.07317i		−	0.441797i
$86$		−	12.1431i		−	1.30943i
$87$		−	20.6040i		−	2.20898i
$88$	11.9908	−	2.84066i	1.27822	−	0.302815i
$89$		−	5.52282i		−	0.585418i	−0.956202	−	0.292709i	$-0.905443\pi$
$89$		−	5.52282i		−	0.585418i	0.956202	−	0.292709i	$-0.0945567\pi$
$90$	12.0751			1.27283
$91$		−	0.691582i		−	0.0724975i
$92$	23.7834			2.47959
$93$	16.8376			1.74598
$94$	25.1998			2.59917
$95$	−2.17793	−	3.77579i	−0.223451	−	0.387388i
$96$			10.2447i			1.04559i
$97$			13.9387i			1.41526i	0.706582	+	0.707632i	$0.250236\pi$
$97$			13.9387i			1.41526i	−0.706582	+	0.707632i	$0.749764\pi$
$98$	−14.9526			−1.51044
$99$	16.5065	−	3.91045i	1.65897	−	0.393015i
$100$	3.57375			0.357375
$101$		−	8.51567i		−	0.847340i	−0.905817	−	0.423670i	$-0.860742\pi$
$101$		−	8.51567i		−	0.847340i	0.905817	−	0.423670i	$-0.139258\pi$
$102$	−27.3931			−2.71232
$103$		−	6.79840i		−	0.669866i	−0.942242	−	0.334933i	$-0.891286\pi$
$103$		−	6.79840i		−	0.669866i	0.942242	−	0.334933i	$-0.108714\pi$
$104$	−3.14740			−0.308628
$105$	2.32561			0.226956
$106$			2.80831i			0.272767i
$107$	3.00909			0.290900			0.145450	−	0.989366i	$-0.453537\pi$
$107$	3.00909			0.290900			0.145450	+	0.989366i	$0.453537\pi$
$108$		−	21.5278i		−	2.07151i
$109$	−1.63260			−0.156374			−0.0781872	−	0.996939i	$-0.524913\pi$
$109$	−1.63260			−0.156374			−0.0781872	+	0.996939i	$0.524913\pi$
$110$	7.61926	−	1.80503i	0.726468	−	0.172102i
$111$	28.3742			2.69316
$112$		−	1.32598i		−	0.125293i
$113$		−	3.15758i		−	0.297040i	−0.988909	−	0.148520i	$-0.952549\pi$
$113$		−	3.15758i		−	0.297040i	0.988909	−	0.148520i	$-0.0474510\pi$
$114$	−25.3932	+	14.6472i	−2.37829	+	1.37183i
$115$	6.65502			0.620583
$116$	−25.8488			−2.40000
$117$	−4.33271			−0.400559
$118$		−	2.54112i		−	0.233929i
$119$	−3.32532			−0.304832
$120$		−	10.5839i		−	0.966170i
$121$	9.83091	−	4.93490i	0.893719	−	0.448628i
$122$			31.7007i			2.87005i
$123$		−	33.1635i		−	2.99025i
$124$		−	21.1237i		−	1.89696i
$125$	1.00000			0.0894427
$126$		−	9.85807i		−	0.878226i
$127$	2.49536			0.221428			0.110714	−	0.993852i	$-0.464686\pi$
$127$	2.49536			0.221428			0.110714	+	0.993852i	$0.464686\pi$
$128$	20.5215			1.81386
$129$	−14.6519			−1.29002
$130$	−1.99994			−0.175406
$131$			17.7293i			1.54902i	0.632564	+	0.774508i	$0.282003\pi$
$131$			17.7293i			1.54902i	−0.632564	+	0.774508i	$0.717997\pi$
$132$	−7.78339	−	32.8548i	−0.677457	−	2.85964i
$133$	−3.08254	+	1.77806i	−0.267291	+	0.154177i
$134$			23.2080i			2.00487i
$135$		−	6.02387i		−	0.518452i
$136$			15.1336i			1.29769i
$137$	−4.54017			−0.387893			−0.193946	−	0.981012i	$-0.562129\pi$
$137$	−4.54017			−0.387893			−0.193946	+	0.981012i	$0.562129\pi$
$138$		−	44.7567i		−	3.80994i
$139$		−	13.9077i		−	1.17963i	−0.807538	−	0.589816i	$-0.799200\pi$
$139$		−	13.9077i		−	1.17963i	0.807538	−	0.589816i	$-0.200800\pi$
$140$		−	2.91760i		−	0.246582i
$141$		−	30.4060i		−	2.56065i
$142$			10.4460i			0.876608i
$143$	−2.73389	+	0.647668i	−0.228620	+	0.0541607i
$144$	−8.30714			−0.692261
$145$	−7.23296			−0.600664
$146$		−	11.5128i		−	0.952809i
$147$			18.0418i			1.48806i
$148$		−	35.5970i		−	2.92605i
$149$			1.33047i			0.108996i	0.998514	+	0.0544980i	$0.0173559\pi$
$149$			1.33047i			0.108996i	−0.998514	+	0.0544980i	$0.982644\pi$
$150$		−	6.72526i		−	0.549115i
$151$	7.12659			0.579954			0.289977	−	0.957034i	$-0.406352\pi$
$151$	7.12659			0.579954			0.289977	+	0.957034i	$0.406352\pi$
$152$	8.09196	+	14.0287i	0.656345	+	1.13788i
$153$			20.8329i			1.68424i
$154$	−1.47362	−	6.22034i	−0.118747	−	0.501249i
$155$		−	5.91078i		−	0.474766i
$156$			8.62386i			0.690461i
$157$	−3.34810			−0.267208			−0.133604	−	0.991035i	$-0.542655\pi$
$157$	−3.34810			−0.267208			−0.133604	+	0.991035i	$0.542655\pi$
$158$	−13.6052			−1.08237
$159$	3.38849			0.268725
$160$	3.59636			0.284317
$161$		−	5.43313i		−	0.428191i
$162$	−4.28680			−0.336803
$163$	−3.20509			−0.251042			−0.125521	−	0.992091i	$-0.540060\pi$
$163$	−3.20509			−0.251042			−0.125521	+	0.992091i	$0.540060\pi$
$164$	−41.6053			−3.24883
$165$	−2.17793	−	9.19336i	−0.169552	−	0.715702i
$166$		−	28.1082i		−	2.18162i
$167$	9.53668			0.737971			0.368985	−	0.929435i	$-0.379705\pi$
$167$	9.53668			0.737971			0.368985	+	0.929435i	$0.379705\pi$
$168$	−8.64063			−0.666639
$169$	−12.2824			−0.944800
$170$			9.61626i			0.737533i
$171$	11.1394	+	19.3119i	0.851851	+	1.47682i
$172$			18.3815i			1.40158i
$173$	13.5827			1.03268			0.516338	−	0.856385i	$-0.327295\pi$
$173$	13.5827			1.03268			0.516338	+	0.856385i	$0.327295\pi$
$174$			48.6435i			3.68765i
$175$		−	0.816397i		−	0.0617138i
$176$	−5.24172	+	1.24178i	−0.395109	+	0.0936026i
$177$	−3.06611			−0.230463
$178$			13.0387i			0.977293i
$179$			20.6841i			1.54600i	0.634403	+	0.773002i	$0.281246\pi$
$179$			20.6841i			1.54600i	−0.634403	+	0.773002i	$0.718754\pi$
$180$	−18.2785			−1.36240
$181$			12.1550i			0.903474i	0.892151	+	0.451737i	$0.149196\pi$
$181$			12.1550i			0.903474i	−0.892151	+	0.451737i	$0.850804\pi$
$182$			1.63274i			0.121027i
$183$	38.2499			2.82751
$184$	−24.7262			−1.82284
$185$		−	9.96068i		−	0.732324i
$186$	−39.7515			−2.91472
$187$	3.11417	+	13.1453i	0.227730	+	0.961282i
$188$	−38.1459			−2.78208
$189$	−4.91787			−0.357722
$190$	5.14184	+	8.91419i	0.373028	+	0.646703i
$191$	−9.92179			−0.717915			−0.358958	−	0.933354i	$-0.616868\pi$
$191$	−9.92179			−0.717915			−0.358958	+	0.933354i	$0.616868\pi$
$192$		−	33.4398i		−	2.41331i
$193$	−12.4257			−0.894423			−0.447212	−	0.894428i	$-0.647583\pi$
$193$	−12.4257			−0.894423			−0.447212	+	0.894428i	$0.647583\pi$
$194$		−	32.9076i		−	2.36263i
$195$			2.41311i			0.172807i
$196$	22.6343			1.61674
$197$		−	7.39245i		−	0.526690i	−0.964702	−	0.263345i	$-0.915174\pi$
$197$		−	7.39245i		−	0.526690i	0.964702	−	0.263345i	$-0.0848258\pi$
$198$	−38.9699	+	9.23209i	−2.76947	+	0.656096i
$199$	14.2974			1.01352			0.506759	−	0.862088i	$-0.330843\pi$
$199$	14.2974			1.01352			0.506759	+	0.862088i	$0.330843\pi$
$200$	−3.71543			−0.262721
$201$	28.0027			1.97516
$202$			20.1045i			1.41454i
$203$			5.90496i			0.414447i
$204$	41.4659			2.90320
$205$	−11.6419			−0.813107
$206$			16.0502i			1.11827i
$207$	−34.0381			−2.36581
$208$	1.37587			0.0953994
$209$	9.91565	+	10.5205i	0.685880	+	0.727715i
$210$	−5.49048			−0.378879
$211$	21.8467			1.50399			0.751996	−	0.659168i	$-0.229091\pi$
$211$	21.8467			1.50399			0.751996	+	0.659168i	$0.229091\pi$
$212$		−	4.25104i		−	0.291963i
$213$	12.6041			0.863617
$214$	−7.10410			−0.485626
$215$			5.14349i			0.350783i
$216$			22.3813i			1.52285i
$217$	−4.82555			−0.327579
$218$	3.85436			0.261050
$219$	−13.8913			−0.938689
$220$	−11.5336	+	2.73233i	−0.777592	+	0.184214i
$221$		−	3.45044i		−	0.232102i
$222$	−66.9881			−4.49595
$223$			9.36132i			0.626880i	0.949608	+	0.313440i	$0.101482\pi$
$223$			9.36132i			0.626880i	−0.949608	+	0.313440i	$0.898518\pi$
$224$		−	2.93606i		−	0.196174i
$225$	−5.11466			−0.340977
$226$			7.45467i			0.495877i
$227$	−7.17116			−0.475966			−0.237983	−	0.971269i	$-0.576486\pi$
$227$	−7.17116			−0.475966			−0.237983	+	0.971269i	$0.576486\pi$
$228$	38.4386	−	22.1719i	2.54566	−	1.46837i
$229$	2.25855			0.149249			0.0746245	−	0.997212i	$-0.476224\pi$
$229$	2.25855			0.149249			0.0746245	+	0.997212i	$0.476224\pi$
$230$	−15.7117			−1.03600
$231$	−7.50543	+	1.77806i	−0.493821	+	0.116988i
$232$	26.8735			1.76433
$233$			15.4002i			1.00890i	0.863441	+	0.504450i	$0.168305\pi$
$233$			15.4002i			1.00890i	−0.863441	+	0.504450i	$0.831695\pi$
$234$	10.2290			0.668690
$235$	−10.6739			−0.696290
$236$			3.84659i			0.250392i
$237$			16.4159i			1.06633i
$238$	7.85068			0.508884
$239$		−	2.32244i		−	0.150226i	−0.997175	−	0.0751130i	$-0.976068\pi$
$239$		−	2.32244i		−	0.150226i	0.997175	−	0.0751130i	$-0.0239317\pi$
$240$			4.62668i			0.298651i
$241$	−9.29149			−0.598517			−0.299259	−	0.954172i	$-0.596739\pi$
$241$	−9.29149			−0.598517			−0.299259	+	0.954172i	$0.596739\pi$
$242$	−23.2096	+	11.6507i	−1.49197	+	0.748936i
$243$		−	12.8992i		−	0.827483i
$244$		−	47.9865i		−	3.07202i
$245$	6.33350			0.404632
$246$			78.2949i			4.99190i
$247$	−1.84496	−	3.19853i	−0.117392	−	0.203518i
$248$			21.9611i			1.39453i
$249$	−33.9152			−2.14929
$250$	−2.36088			−0.149315
$251$	10.2736			0.648462			0.324231	−	0.945978i	$-0.394894\pi$
$251$	10.2736			0.648462			0.324231	+	0.945978i	$0.394894\pi$
$252$			14.9225i			0.940030i
$253$	−21.4777	+	5.08814i	−1.35029	+	0.319888i
$254$	−5.89125			−0.369650
$255$	11.6029			0.726603
$256$	−24.9709			−1.56068
$257$		−	7.05755i		−	0.440238i	−0.975473	−	0.220119i	$-0.929355\pi$
$257$		−	7.05755i		−	0.440238i	0.975473	−	0.220119i	$-0.0706446\pi$
$258$	34.5913			2.15356
$259$	−8.13187			−0.505290
$260$	3.02738			0.187750
$261$	36.9941			2.28988
$262$		−	41.8567i		−	2.58592i
$263$		−	21.7696i		−	1.34237i	−0.741291	−	0.671184i	$-0.765786\pi$
$263$		−	21.7696i		−	1.34237i	0.741291	−	0.671184i	$-0.234214\pi$
$264$	8.09196	+	34.1573i	0.498026	+	2.10224i
$265$		−	1.18952i		−	0.0730715i
$266$	7.27751	−	4.19778i	0.446213	−	0.257382i
$267$	15.7324			0.962810
$268$		−	35.1308i		−	2.14596i
$269$		−	28.4722i		−	1.73598i	−0.496579	−	0.867991i	$-0.665411\pi$
$269$		−	28.4722i		−	1.73598i	0.496579	−	0.867991i	$-0.334589\pi$
$270$			14.2216i			0.865501i
$271$			2.09559i			0.127298i	0.997972	+	0.0636489i	$0.0202738\pi$
$271$			2.09559i			0.127298i	−0.997972	+	0.0636489i	$0.979726\pi$
$272$		−	6.61557i		−	0.401128i
$273$	1.97006			0.119233
$274$	10.7188			0.647546
$275$	−3.22730	+	0.764557i	−0.194613	+	0.0461045i
$276$			67.7498i			4.07806i
$277$		−	21.7214i		−	1.30511i	−0.757741	−	0.652555i	$-0.773697\pi$
$277$		−	21.7214i		−	1.30511i	0.757741	−	0.652555i	$-0.226303\pi$
$278$			32.8343i			1.96927i
$279$			30.2317i			1.80992i
$280$			3.03326i			0.181272i
$281$	−31.4529			−1.87632			−0.938162	−	0.346197i	$-0.887473\pi$
$281$	−31.4529			−1.87632			−0.938162	+	0.346197i	$0.887473\pi$
$282$			71.7849i			4.27473i
$283$			3.33020i			0.197960i	0.995089	+	0.0989799i	$0.0315579\pi$
$283$			3.33020i			0.197960i	−0.995089	+	0.0989799i	$0.968442\pi$
$284$		−	15.8125i		−	0.938298i
$285$	10.7558	−	6.20412i	0.637119	−	0.367500i
$286$	6.45439	−	1.52906i	0.381656	−	0.0904155i
$287$			9.50443i			0.561029i
$288$	−18.3942			−1.08389
$289$	0.409297			0.0240763
$290$	17.0761			1.00275
$291$	−39.7062			−2.32762
$292$			17.4274i			1.01986i
$293$	−5.33197			−0.311497			−0.155749	−	0.987797i	$-0.549779\pi$
$293$	−5.33197			−0.311497			−0.155749	+	0.987797i	$0.549779\pi$
$294$		−	42.5944i		−	2.48415i
$295$			1.07635i			0.0626673i
$296$			37.0082i			2.15106i
$297$	4.60559	+	19.4408i	0.267243	+	1.12807i
$298$		−	3.14107i		−	0.181957i
$299$	5.63757			0.326029
$300$			10.1803i			0.587758i
$301$	4.19913			0.242034
$302$	−16.8250			−0.968171
$303$	24.2579			1.39358
$304$	−3.53736	−	6.13257i	−0.202882	−	0.351727i
$305$		−	13.4275i		−	0.768856i
$306$		−	49.1839i		−	2.81166i
$307$	−13.6897			−0.781313			−0.390657	−	0.920536i	$-0.627752\pi$
$307$	−13.6897			−0.781313			−0.390657	+	0.920536i	$0.627752\pi$
$308$	2.23067	+	9.41596i	0.127104	+	0.536524i
$309$	19.3661			1.10170
$310$			13.9546i			0.792571i
$311$	−4.15889			−0.235829			−0.117914	−	0.993024i	$-0.537621\pi$
$311$	−4.15889			−0.235829			−0.117914	+	0.993024i	$0.537621\pi$
$312$		−	8.96575i		−	0.507586i
$313$	−18.9740			−1.07247			−0.536236	−	0.844068i	$-0.680154\pi$
$313$	−18.9740			−1.07247			−0.536236	+	0.844068i	$0.680154\pi$
$314$	7.90446			0.446075
$315$			4.17559i			0.235268i
$316$	20.5946			1.15854
$317$			11.2084i			0.629525i	0.949170	+	0.314762i	$0.101925\pi$
$317$			11.2084i			0.629525i	−0.949170	+	0.314762i	$0.898075\pi$
$318$	−7.99981			−0.448607
$319$	23.3429	−	5.53000i	1.30695	−	0.309621i
$320$	−11.7389			−0.656227
$321$			8.57177i			0.478430i
$322$			12.8270i			0.714819i
$323$	−15.3794	+	8.87109i	−0.855735	+	0.493601i
$324$	6.48908			0.360505
$325$	0.847115			0.0469895
$326$	7.56683			0.419088
$327$		−	4.65065i		−	0.257182i
$328$	43.2547			2.38834
$329$			8.71416i			0.480427i
$330$	5.14184	+	21.7044i	0.283049	+	1.19479i
$331$			10.9168i			0.600044i	0.953932	+	0.300022i	$0.0969941\pi$
$331$			10.9168i			0.600044i	−0.953932	+	0.300022i	$0.903006\pi$
$332$			42.5484i			2.33514i
$333$			50.9455i			2.79180i
$334$	−22.5150			−1.23196
$335$		−	9.83025i		−	0.537084i
$336$	3.77721			0.206064
$337$	9.53539			0.519426			0.259713	−	0.965686i	$-0.416372\pi$
$337$	9.53539			0.519426			0.259713	+	0.965686i	$0.416372\pi$
$338$	28.9972			1.57724
$339$	8.99477			0.488529
$340$		−	14.5565i		−	0.789436i
$341$	4.51913	+	19.0759i	0.244725	+	1.03302i
$342$	−26.2988	−	45.5930i	−1.42207	−	2.46539i
$343$		−	10.8854i		−	0.587758i
$344$		−	19.1103i		−	1.03036i
$345$			18.9576i			1.02064i
$346$	−32.0672			−1.72394
$347$			26.9335i			1.44587i	0.690918	+	0.722933i	$0.257207\pi$
$347$			26.9335i			1.44587i	−0.690918	+	0.722933i	$0.742793\pi$
$348$		−	73.6334i		−	3.94717i
$349$			4.07633i			0.218201i	0.994031	+	0.109100i	$0.0347970\pi$
$349$			4.07633i			0.218201i	−0.994031	+	0.109100i	$0.965203\pi$
$350$			1.92741i			0.103025i
$351$		−	5.10291i		−	0.272373i
$352$	−11.6065	+	2.74962i	−0.618630	+	0.146555i
$353$	−26.2293			−1.39604			−0.698022	−	0.716076i	$-0.745936\pi$
$353$	−26.2293			−1.39604			−0.698022	+	0.716076i	$0.745936\pi$
$354$	7.23871			0.384733
$355$		−	4.42462i		−	0.234834i
$356$		−	19.7372i		−	1.04607i
$357$		−	9.47259i		−	0.501343i
$358$		−	48.8327i		−	2.58089i
$359$		−	31.4145i		−	1.65799i	−0.559254	−	0.828996i	$-0.688912\pi$
$359$		−	31.4145i		−	1.65799i	0.559254	−	0.828996i	$-0.311088\pi$
$360$	19.0032			1.00155
$361$	−9.51321	+	16.4469i	−0.500695	+	0.865624i
$362$		−	28.6965i		−	1.50825i
$363$	14.0577	+	28.0046i	0.737837	+	1.46986i
$364$		−	2.47154i		−	0.129544i
$365$			4.87650i			0.255248i
$366$	−90.3034			−4.72023
$367$	−23.5115			−1.22729			−0.613646	−	0.789581i	$-0.710298\pi$
$367$	−23.5115			−1.22729			−0.613646	+	0.789581i	$0.710298\pi$
$368$	10.8090			0.563456
$369$	59.5445			3.09976
$370$			23.5160i			1.22254i
$371$	−0.971119			−0.0504180
$372$	60.1734			3.11984
$373$	6.36695			0.329668			0.164834	−	0.986321i	$-0.447291\pi$
$373$	6.36695			0.329668			0.164834	+	0.986321i	$0.447291\pi$
$374$	−7.35217	−	31.0345i	−0.380172	−	1.60476i
$375$			2.84862i			0.147102i
$376$	39.6582			2.04522
$377$	−6.12715			−0.315564
$378$	11.6105			0.597179
$379$		−	15.7886i		−	0.811006i	−0.914094	−	0.405503i	$-0.867096\pi$
$379$		−	15.7886i		−	0.811006i	0.914094	−	0.405503i	$-0.132904\pi$
$380$	−7.78339	−	13.4937i	−0.399279	−	0.692214i
$381$			7.10836i			0.364172i
$382$	23.4241			1.19848
$383$		−	26.4866i		−	1.35340i	−0.736258	−	0.676701i	$-0.763409\pi$
$383$		−	26.4866i		−	1.35340i	0.736258	−	0.676701i	$-0.236591\pi$
$384$			58.4580i			2.98317i
$385$	0.624182	+	2.63476i	0.0318112	+	0.134280i
$386$	29.3356			1.49314
$387$		−	26.3072i		−	1.33727i
$388$			49.8135i			2.52890i
$389$	−37.6856			−1.91074			−0.955368	−	0.295419i	$-0.904541\pi$
$389$	−37.6856			−1.91074			−0.955368	+	0.295419i	$0.904541\pi$
$390$		−	5.69707i		−	0.288482i
$391$		−	27.1070i		−	1.37086i
$392$	−23.5317			−1.18853
$393$	−50.5041			−2.54760
$394$			17.4527i			0.879253i
$395$	5.76276			0.289956
$396$	58.9902	−	13.9750i	2.96437	−	0.702268i
$397$	−0.450735			−0.0226217			−0.0113109	−	0.999936i	$-0.503600\pi$
$397$	−0.450735			−0.0226217			−0.0113109	+	0.999936i	$0.503600\pi$
$398$	−33.7545			−1.69196
$399$	−5.06502	−	8.78101i	−0.253568	−	0.439600i
$400$	1.62418			0.0812091
$401$		−	31.5366i		−	1.57486i	−0.616401	−	0.787432i	$-0.711410\pi$
$401$		−	31.5366i		−	1.57486i	0.616401	−	0.787432i	$-0.288590\pi$
$402$	−66.1109			−3.29731
$403$		−	5.00712i		−	0.249422i
$404$		−	30.4328i		−	1.51409i
$405$	1.81576			0.0902260
$406$		−	13.9409i		−	0.691875i
$407$	7.61550	+	32.1461i	0.377487	+	1.59342i
$408$	−43.1099			−2.13426
$409$	−27.9234			−1.38073			−0.690363	−	0.723463i	$-0.742549\pi$
$409$	−27.9234			−1.38073			−0.690363	+	0.723463i	$0.742549\pi$
$410$	27.4852			1.35740
$411$		−	12.9332i		−	0.637950i
$412$		−	24.2958i		−	1.19697i
$413$	0.878726			0.0432393
$414$	80.3599			3.94947
$415$			11.9058i			0.584433i
$416$	3.04653			0.149369
$417$	39.6177			1.94009
$418$	−23.4096	−	24.8375i	−1.14500	−	1.21484i
$419$	−16.0830			−0.785706			−0.392853	−	0.919601i	$-0.628512\pi$
$419$	−16.0830			−0.785706			−0.392853	+	0.919601i	$0.628512\pi$
$420$	8.31114			0.405542
$421$		−	18.3336i		−	0.893526i	−0.894652	−	0.446763i	$-0.852577\pi$
$421$		−	18.3336i		−	0.893526i	0.894652	−	0.446763i	$-0.147423\pi$
$422$	−51.5775			−2.51075
$423$	54.5935			2.65443
$424$			4.41957i			0.214633i
$425$		−	4.07317i		−	0.197578i
$426$	−29.7567			−1.44172
$427$	−10.9622			−0.530496
$428$	10.7537			0.519801
$429$	−1.84496	−	7.78784i	−0.0890756	−	0.376000i
$430$		−	12.1431i		−	0.585595i
$431$	5.96248			0.287203			0.143601	−	0.989636i	$-0.454132\pi$
$431$	5.96248			0.287203			0.143601	+	0.989636i	$0.454132\pi$
$432$		−	9.78386i		−	0.470726i
$433$		−	18.3000i		−	0.879443i	−0.898134	−	0.439722i	$-0.855077\pi$
$433$		−	18.3000i		−	0.879443i	0.898134	−	0.439722i	$-0.144923\pi$
$434$	11.3925			0.546859
$435$		−	20.6040i		−	0.987885i
$436$	−5.83449			−0.279421
$437$	−14.4942	−	25.1280i	−0.693351	−	1.20203i
$438$	32.7957			1.56704
$439$	−15.2740			−0.728986			−0.364493	−	0.931206i	$-0.618758\pi$
$439$	−15.2740			−0.728986			−0.364493	+	0.931206i	$0.618758\pi$
$440$	11.9908	−	2.84066i	0.571639	−	0.135423i
$441$	−32.3937			−1.54256
$442$			8.14608i			0.387469i
$443$	27.4543			1.30439			0.652195	−	0.758051i	$-0.273848\pi$
$443$	27.4543			1.30439			0.652195	+	0.758051i	$0.273848\pi$
$444$	101.402			4.81234
$445$		−	5.52282i		−	0.261807i
$446$		−	22.1009i		−	1.04651i
$447$	−3.79000			−0.179261
$448$			9.58363i			0.452784i
$449$			15.6461i			0.738383i	0.929353	+	0.369191i	$0.120365\pi$
$449$			15.6461i			0.738383i	−0.929353	+	0.369191i	$0.879635\pi$
$450$	12.0751			0.569225
$451$	37.5720	−	8.90091i	1.76919	−	0.419127i
$452$		−	11.2844i		−	0.530774i
$453$			20.3010i			0.953823i
$454$	16.9302			0.794575
$455$		−	0.691582i		−	0.0324219i
$456$	−39.9625	+	23.0510i	−1.87141	+	1.07946i
$457$		−	25.8941i		−	1.21127i	−0.795741	−	0.605637i	$-0.792918\pi$
$457$		−	25.8941i		−	1.21127i	0.795741	−	0.605637i	$-0.207082\pi$
$458$	−5.33216			−0.249155
$459$	−24.5362			−1.14525
$460$	23.7834			1.10890
$461$			7.69173i			0.358240i	0.983827	+	0.179120i	$0.0573250\pi$
$461$			7.69173i			0.358240i	−0.983827	+	0.179120i	$0.942675\pi$
$462$	17.7194	−	4.19778i	0.824382	−	0.195298i
$463$	2.69828			0.125400			0.0626999	−	0.998032i	$-0.480029\pi$
$463$	2.69828			0.125400			0.0626999	+	0.998032i	$0.480029\pi$
$464$	−11.7476			−0.545370
$465$	16.8376			0.780825
$466$		−	36.3580i		−	1.68425i
$467$	17.9822			0.832118			0.416059	−	0.909338i	$-0.363411\pi$
$467$	17.9822			0.832118			0.416059	+	0.909338i	$0.363411\pi$
$468$	−15.4840			−0.715748
$469$	−8.02538			−0.370578
$470$	25.1998			1.16238
$471$		−	9.53748i		−	0.439464i
$472$		−	3.99909i		−	0.184073i
$473$	−3.93249	−	16.5996i	−0.180816	−	0.763249i
$474$		−	38.7560i		−	1.78012i
$475$	−2.17793	−	3.77579i	−0.0999305	−	0.173245i
$476$	−11.8839			−0.544696
$477$			6.08398i			0.278566i
$478$			5.48299i			0.250786i
$479$		−	28.6988i		−	1.31128i	−0.755072	−	0.655641i	$-0.772398\pi$
$479$		−	28.6988i		−	1.31128i	0.755072	−	0.655641i	$-0.227602\pi$
$480$			10.2447i			0.467604i
$481$		−	8.43785i		−	0.384733i
$482$	21.9361			0.999161
$483$	15.4770			0.704226
$484$	35.1332	−	17.6361i	1.59696	−	0.801641i
$485$			13.9387i			0.632925i
$486$			30.4534i			1.38139i
$487$			23.5094i			1.06531i	0.846332	+	0.532655i	$0.178806\pi$
$487$			23.5094i			1.06531i	−0.846332	+	0.532655i	$0.821194\pi$
$488$			49.8889i			2.25837i
$489$		−	9.13009i		−	0.412877i
$490$	−14.9526			−0.675490
$491$			39.7226i			1.79265i	0.443393	+	0.896327i	$0.353775\pi$
$491$			39.7226i			1.79265i	−0.443393	+	0.896327i	$0.646225\pi$
$492$		−	118.518i		−	5.34320i
$493$			29.4611i			1.32686i
$494$	4.35573	+	7.55134i	0.195974	+	0.339751i
$495$	16.5065	−	3.91045i	0.741913	−	0.175761i
$496$		−	9.60019i		−	0.431061i
$497$	−3.61224			−0.162031
$498$	80.0696			3.58801
$499$	−6.65874			−0.298086			−0.149043	−	0.988831i	$-0.547619\pi$
$499$	−6.65874			−0.298086			−0.149043	+	0.988831i	$0.547619\pi$
$500$	3.57375			0.159823
$501$			27.1664i			1.21371i
$502$	−24.2547			−1.08254
$503$		−	17.0466i		−	0.760071i	−0.924972	−	0.380036i	$-0.875912\pi$
$503$		−	17.0466i		−	0.760071i	0.924972	−	0.380036i	$-0.124088\pi$
$504$		−	15.5141i		−	0.691054i
$505$		−	8.51567i		−	0.378942i
$506$	50.7063	−	12.0125i	2.25417	−	0.534019i
$507$		−	34.9879i		−	1.55387i
$508$	8.91780			0.395664
$509$		−	0.793357i		−	0.0351649i	−0.999845	−	0.0175825i	$-0.994403\pi$
$509$		−	0.793357i		−	0.0351649i	0.999845	−	0.0175825i	$-0.00559696\pi$
$510$	−27.3931			−1.21299
$511$	3.98116			0.176116
$512$	17.9102			0.791527
$513$	−22.7449	+	13.1196i	−1.00421	+	0.579244i
$514$			16.6620i			0.734931i
$515$		−	6.79840i		−	0.299573i
$516$	−52.3621			−2.30511
$517$	34.4479	−	8.16082i	1.51502	−	0.358912i
$518$	19.1984			0.843527
$519$			38.6921i			1.69840i
$520$	−3.14740			−0.138023
$521$		−	33.0727i		−	1.44894i	−0.689305	−	0.724472i	$-0.742084\pi$
$521$		−	33.0727i		−	1.44894i	0.689305	−	0.724472i	$-0.257916\pi$
$522$	−87.3386			−3.82271
$523$	9.09432			0.397667			0.198833	−	0.980033i	$-0.436285\pi$
$523$	9.09432			0.397667			0.198833	+	0.980033i	$0.436285\pi$
$524$			63.3601i			2.76790i
$525$	2.32561			0.101498
$526$			51.3953i			2.24094i
$527$	−24.0756			−1.04875
$528$	−3.53736	−	14.9317i	−0.153944	−	0.649818i
$529$	21.2892			0.925619
$530$			2.80831i			0.121985i
$531$		−	5.50515i		−	0.238903i
$532$	−11.0162	+	6.35433i	−0.477615	+	0.275495i
$533$	−9.86205			−0.427173
$534$	−37.1424			−1.60731
$535$	3.00909			0.130094
$536$			36.5236i			1.57758i
$537$	−58.9213			−2.54264
$538$			67.2195i			2.89804i
$539$	−20.4401	+	4.84232i	−0.880417	+	0.208573i
$540$		−	21.5278i		−	0.926409i
$541$			6.94138i			0.298433i	0.988805	+	0.149217i	$0.0476752\pi$
$541$			6.94138i			0.298433i	−0.988805	+	0.149217i	$0.952325\pi$
$542$		−	4.94742i		−	0.212510i
$543$	−34.6250			−1.48590
$544$		−	14.6486i		−	0.628053i
$545$	−1.63260			−0.0699328
$546$	−4.65107			−0.199047
$547$	32.0782			1.37157			0.685783	−	0.727806i	$-0.259460\pi$
$547$	32.0782			1.37157			0.685783	+	0.727806i	$0.259460\pi$
$548$	−16.2254			−0.693116
$549$			68.6771i			2.93107i
$550$	7.61926	−	1.80503i	0.324886	−	0.0769665i
$551$	15.7529	+	27.3101i	0.671096	+	1.16345i
$552$		−	70.4358i		−	2.99795i
$553$		−	4.70470i		−	0.200064i
$554$			51.2815i			2.17874i
$555$	28.3742			1.20442
$556$		−	49.7024i		−	2.10785i
$557$			23.0265i			0.975666i	0.872937	+	0.487833i	$0.162212\pi$
$557$			23.0265i			0.975666i	−0.872937	+	0.487833i	$0.837788\pi$
$558$		−	71.3733i		−	3.02147i
$559$			4.35713i			0.184287i
$560$		−	1.32598i		−	0.0560327i
$561$	−37.4461	+	8.87109i	−1.58098	+	0.374538i
$562$	74.2565			3.13232
$563$	42.3024			1.78283			0.891416	−	0.453186i	$-0.149713\pi$
$563$	42.3024			1.78283			0.891416	+	0.453186i	$0.149713\pi$
$564$		−	108.663i		−	4.57555i
$565$		−	3.15758i		−	0.132841i
$566$		−	7.86220i		−	0.330473i
$567$		−	1.48238i		−	0.0622543i
$568$			16.4394i			0.689780i
$569$	−44.8350			−1.87958			−0.939790	−	0.341752i	$-0.888980\pi$
$569$	−44.8350			−1.87958			−0.939790	+	0.341752i	$0.888980\pi$
$570$	−25.3932	+	14.6472i	−1.06360	+	0.613502i
$571$			7.04029i			0.294627i	0.989090	+	0.147314i	$0.0470626\pi$
$571$			7.04029i			0.294627i	−0.989090	+	0.147314i	$0.952937\pi$
$572$	−9.77025	+	2.31460i	−0.408515	+	0.0967783i
$573$		−	28.2634i		−	1.18072i
$574$		−	22.4388i		−	0.936578i
$575$	6.65502			0.277533
$576$	60.0407			2.50170
$577$	39.3534			1.63830			0.819152	−	0.573576i	$-0.194444\pi$
$577$	39.3534			1.63830			0.819152	+	0.573576i	$0.194444\pi$
$578$	−0.966300			−0.0401928
$579$		−	35.3962i		−	1.47102i
$580$	−25.8488			−1.07331
$581$	9.71986			0.403248
$582$	93.7415			3.88571
$583$	0.909454	+	3.83893i	0.0376657	+	0.158992i
$584$		−	18.1183i		−	0.749741i
$585$	−4.33271			−0.179135
$586$	12.5881			0.520011
$587$	36.0334			1.48726			0.743629	−	0.668592i	$-0.233103\pi$
$587$	36.0334			1.48726			0.743629	+	0.668592i	$0.233103\pi$
$588$			64.4767i			2.65897i
$589$	−22.3179	+	12.8733i	−0.919593	+	0.530435i
$590$		−	2.54112i		−	0.104616i
$591$	21.0583			0.866223
$592$		−	16.1780i		−	0.664910i
$593$		−	37.9044i		−	1.55655i	−0.627925	−	0.778274i	$-0.716096\pi$
$593$		−	37.9044i		−	1.55655i	0.627925	−	0.778274i	$-0.283904\pi$
$594$	−10.8732	−	45.8974i	−0.446134	−	1.88319i
$595$	−3.32532			−0.136325
$596$			4.75475i			0.194762i
$597$			40.7280i			1.66689i
$598$	−13.3096			−0.544270
$599$		−	15.2290i		−	0.622239i	−0.950371	−	0.311120i	$-0.899296\pi$
$599$		−	15.2290i		−	0.622239i	0.950371	−	0.311120i	$-0.100704\pi$
$600$		−	10.5839i		−	0.432084i
$601$	−35.3214			−1.44079			−0.720395	−	0.693565i	$-0.756039\pi$
$601$	−35.3214			−1.44079			−0.720395	+	0.693565i	$0.756039\pi$
$602$	−9.91363			−0.404049
$603$			50.2784i			2.04749i
$604$	25.4686			1.03630
$605$	9.83091	−	4.93490i	0.399683	−	0.200632i
$606$	−57.2700			−2.32644
$607$	19.6434			0.797303			0.398651	−	0.917103i	$-0.369478\pi$
$607$	19.6434			0.797303			0.398651	+	0.917103i	$0.369478\pi$
$608$	−7.83264	−	13.5791i	−0.317656	−	0.550706i
$609$	−16.8210			−0.681622
$610$			31.7007i			1.28352i
$611$	−9.04205			−0.365802
$612$			74.4514i			3.00952i
$613$			41.5180i			1.67690i	0.544982	+	0.838448i	$0.316537\pi$
$613$			41.5180i			1.67690i	−0.544982	+	0.838448i	$0.683463\pi$
$614$	32.3198			1.30432
$615$		−	33.1635i		−	1.33728i
$616$	−2.31910	−	9.78925i	−0.0934393	−	0.394420i
$617$	22.7442			0.915648			0.457824	−	0.889043i	$-0.348629\pi$
$617$	22.7442			0.915648			0.457824	+	0.889043i	$0.348629\pi$
$618$	−45.7209			−1.83917
$619$	−34.4908			−1.38630			−0.693152	−	0.720792i	$-0.743778\pi$
$619$	−34.4908			−1.38630			−0.693152	+	0.720792i	$0.743778\pi$
$620$		−	21.1237i		−	0.848347i
$621$		−	40.0889i		−	1.60871i
$622$	9.81863			0.393691
$623$	−4.50881			−0.180642
$624$			3.91933i			0.156899i
$625$	1.00000			0.0400000
$626$	44.7952			1.79038
$627$	−29.9688	+	28.2460i	−1.19684	+	1.12803i
$628$	−11.9653			−0.477466
$629$	−40.5715			−1.61769
$630$		−	9.85807i		−	0.392755i
$631$	8.33119			0.331660			0.165830	−	0.986154i	$-0.446970\pi$
$631$	8.33119			0.331660			0.165830	+	0.986154i	$0.446970\pi$
$632$	−21.4111			−0.851689
$633$			62.2332i			2.47355i
$634$		−	26.4616i		−	1.05092i
$635$	2.49536			0.0990255
$636$	12.1096			0.480177
$637$	5.36520			0.212577
$638$	−55.1098	+	13.0557i	−2.18182	+	0.516879i
$639$			22.6304i			0.895245i
$640$	20.5215			0.811183
$641$		−	30.5278i		−	1.20577i	−0.797827	−	0.602887i	$-0.794017\pi$
$641$		−	30.5278i		−	1.20577i	0.797827	−	0.602887i	$-0.205983\pi$
$642$		−	20.2369i		−	0.798687i
$643$	−26.1509			−1.03129			−0.515645	−	0.856802i	$-0.672448\pi$
$643$	−26.1509			−1.03129			−0.515645	+	0.856802i	$0.672448\pi$
$644$		−	19.4167i		−	0.765123i
$645$	−14.6519			−0.576916
$646$	36.3090	−	20.9436i	1.42856	−	0.824014i
$647$	−3.51466			−0.138175			−0.0690877	−	0.997611i	$-0.522009\pi$
$647$	−3.51466			−0.138175			−0.0690877	+	0.997611i	$0.522009\pi$
$648$	−6.74634			−0.265021
$649$	−0.822928	−	3.47369i	−0.0323027	−	0.136354i
$650$	−1.99994			−0.0784440
$651$		−	13.7462i		−	0.538755i
$652$	−11.4542			−0.448580
$653$	−7.27705			−0.284773			−0.142387	−	0.989811i	$-0.545478\pi$
$653$	−7.27705			−0.284773			−0.142387	+	0.989811i	$0.545478\pi$
$654$			10.9796i			0.429338i
$655$			17.7293i			0.692741i
$656$	−18.9086			−0.738257
$657$		−	24.9417i		−	0.973067i
$658$		−	20.5731i		−	0.802022i
$659$	19.6294			0.764654			0.382327	−	0.924027i	$-0.375123\pi$
$659$	19.6294			0.764654			0.382327	+	0.924027i	$0.375123\pi$
$660$	−7.78339	−	32.8548i	−0.302968	−	1.27887i
$661$			43.1568i			1.67860i	0.543666	+	0.839302i	$0.317036\pi$
$661$			43.1568i			1.67860i	−0.543666	+	0.839302i	$0.682964\pi$
$662$		−	25.7734i		−	1.00171i
$663$	9.82902			0.381727
$664$		−	44.2352i		−	1.71666i
$665$	−3.08254	+	1.77806i	−0.119536	+	0.0689502i
$666$		−	120.276i		−	4.66061i
$667$	−48.1354			−1.86381
$668$	34.0817			1.31866
$669$	−26.6669			−1.03100
$670$			23.2080i			0.896604i
$671$	10.2661	+	43.3345i	0.396318	+	1.67291i
$672$	8.36373			0.322638
$673$	−5.33543			−0.205666			−0.102833	−	0.994699i	$-0.532791\pi$
$673$	−5.33543			−0.205666			−0.102833	+	0.994699i	$0.532791\pi$
$674$	−22.5119			−0.867126
$675$		−	6.02387i		−	0.231859i
$676$	−43.8942			−1.68824
$677$	40.3963			1.55256			0.776279	−	0.630390i	$-0.217105\pi$
$677$	40.3963			1.55256			0.776279	+	0.630390i	$0.217105\pi$
$678$	−21.2356			−0.815547
$679$	11.3795			0.436706
$680$			15.1336i			0.580346i
$681$		−	20.4279i		−	0.782800i
$682$	−10.6691	−	45.0358i	−0.408542	−	1.72451i
$683$			23.3006i			0.891574i	0.895139	+	0.445787i	$0.147076\pi$
$683$			23.3006i			0.891574i	−0.895139	+	0.445787i	$0.852924\pi$
$684$	39.8094	+	69.0158i	1.52215	+	2.63889i
$685$	−4.54017			−0.173471
$686$			25.6992i			0.981199i
$687$			6.43375i			0.245463i
$688$			8.35395i			0.318492i
$689$		−	1.00766i		−	0.0383888i
$690$		−	44.7567i		−	1.70386i
$691$	−18.7123			−0.711851			−0.355925	−	0.934514i	$-0.615834\pi$
$691$	−18.7123			−0.711851			−0.355925	+	0.934514i	$0.615834\pi$
$692$	48.5413			1.84526
$693$	−3.19248	−	13.4759i	−0.121272	−	0.511906i
$694$		−	63.5868i		−	2.41372i
$695$		−	13.9077i		−	0.527547i
$696$			76.5526i			2.90172i
$697$			47.4195i			1.79614i
$698$		−	9.62372i		−	0.364263i
$699$	−43.8694			−1.65929
$700$		−	2.91760i		−	0.110275i
$701$		−	34.9037i		−	1.31829i	−0.752014	−	0.659147i	$-0.770917\pi$
$701$		−	34.9037i		−	1.31829i	0.752014	−	0.659147i	$-0.229083\pi$
$702$			12.0474i			0.454698i
$703$	−37.6095	+	21.6937i	−1.41847	+	0.818194i
$704$	37.8851	−	8.97508i	1.42785	−	0.338261i
$705$		−	30.4060i		−	1.14516i
$706$	61.9242			2.33055
$707$	−6.95216			−0.261463
$708$	−10.9575			−0.411808
$709$	−39.8663			−1.49721			−0.748605	−	0.663017i	$-0.769276\pi$
$709$	−39.8663			−1.49721			−0.748605	+	0.663017i	$0.769276\pi$
$710$			10.4460i			0.392031i
$711$	−29.4745			−1.10538
$712$			20.5197i			0.769007i
$713$		−	39.3364i		−	1.47316i
$714$			22.3636i			0.836938i
$715$	−2.73389	+	0.647668i	−0.102242	+	0.0242214i
$716$			73.9199i			2.76252i
$717$	6.61575			0.247070
$718$			74.1658i			2.76784i
$719$	−9.54561			−0.355991			−0.177996	−	0.984031i	$-0.556961\pi$
$719$	−9.54561			−0.355991			−0.177996	+	0.984031i	$0.556961\pi$
$720$	−8.30714			−0.309589
$721$	−5.55019			−0.206700
$722$	22.4595	−	38.8290i	0.835857	−	1.44507i
$723$		−	26.4680i		−	0.984354i
$724$			43.4389i			1.61440i
$725$	−7.23296			−0.268625
$726$	−33.1885	−	66.1154i	−1.23174	−	2.45377i
$727$	−16.5187			−0.612646			−0.306323	−	0.951928i	$-0.599099\pi$
$727$	−16.5187			−0.612646			−0.306323	+	0.951928i	$0.599099\pi$
$728$			2.56953i			0.0952329i
$729$	42.1922			1.56267
$730$		−	11.5128i		−	0.426109i
$731$	20.9503			0.774874
$732$	136.695			5.05241
$733$			45.9031i			1.69547i	0.530420	+	0.847735i	$0.322034\pi$
$733$			45.9031i			1.69547i	−0.530420	+	0.847735i	$0.677966\pi$
$734$	55.5079			2.04883
$735$			18.0418i			0.665480i
$736$	23.9339			0.882214
$737$	7.51578	+	31.7251i	0.276847	+	1.16861i
$738$	−140.577			−5.17472
$739$			7.26985i			0.267426i	0.991020	+	0.133713i	$0.0426900\pi$
$739$			7.26985i			0.267426i	−0.991020	+	0.133713i	$0.957310\pi$
$740$		−	35.5970i		−	1.30857i
$741$	9.11141	−	5.25560i	0.334716	−	0.193069i
$742$	2.29269			0.0841674
$743$	−8.31661			−0.305107			−0.152553	−	0.988295i	$-0.548750\pi$
$743$	−8.31661			−0.305107			−0.152553	+	0.988295i	$0.548750\pi$
$744$	−62.5589			−2.29352
$745$			1.33047i			0.0487445i
$746$	−15.0316			−0.550345
$747$		−	60.8942i		−	2.22800i
$748$	11.1293	+	46.9781i	0.406926	+	1.71769i
$749$		−	2.45661i		−	0.0897627i
$750$		−	6.72526i		−	0.245572i
$751$			19.6289i			0.716269i	0.933670	+	0.358135i	$0.116587\pi$
$751$			19.6289i			0.716269i	−0.933670	+	0.358135i	$0.883413\pi$
$752$	−17.3364			−0.632193
$753$			29.2655i			1.06650i
$754$	14.4655			0.526801
$755$	7.12659			0.259363
$756$	−17.5752			−0.639205
$757$	−7.35662			−0.267381			−0.133690	−	0.991023i	$-0.542683\pi$
$757$	−7.35662			−0.267381			−0.133690	+	0.991023i	$0.542683\pi$
$758$			37.2750i			1.35389i
$759$	−14.4942	−	61.1819i	−0.526106	−	2.22076i
$760$	8.09196	+	14.0287i	0.293526	+	0.508874i
$761$			46.8595i			1.69866i	0.527866	+	0.849328i	$0.322992\pi$
$761$			46.8595i			1.69866i	−0.527866	+	0.849328i	$0.677008\pi$
$762$		−	16.7820i		−	0.607946i
$763$			1.33285i			0.0482523i
$764$	−35.4580			−1.28282
$765$			20.8329i			0.753214i
$766$			62.5317i			2.25936i
$767$			0.911790i			0.0329228i
$768$		−	71.1326i		−	2.56678i
$769$		−	21.4842i		−	0.774738i	−0.921925	−	0.387369i	$-0.873384\pi$
$769$		−	21.4842i		−	0.774738i	0.921925	−	0.387369i	$-0.126616\pi$
$770$	−1.47362	−	6.22034i	−0.0531055	−	0.224165i
$771$	20.1043			0.724039
$772$	−44.4064			−1.59822
$773$		−	10.4285i		−	0.375086i	−0.982256	−	0.187543i	$-0.939948\pi$
$773$		−	10.4285i		−	0.375086i	0.982256	−	0.187543i	$-0.0600524\pi$
$774$			62.1081i			2.23243i
$775$		−	5.91078i		−	0.212322i
$776$		−	51.7884i		−	1.85909i
$777$		−	23.1646i		−	0.831027i
$778$	88.9711			3.18977
$779$	25.3553	+	43.9575i	0.908449	+	1.57494i
$780$			8.62386i			0.308784i
$781$	3.38287	+	14.2796i	0.121049	+	0.510963i
$782$			63.9963i			2.28850i
$783$			43.5704i			1.55708i
$784$	10.2867			0.367384
$785$	−3.34810			−0.119499
$786$	119.234			4.25294
$787$	16.6195			0.592421			0.296210	−	0.955123i	$-0.404277\pi$
$787$	16.6195			0.592421			0.296210	+	0.955123i	$0.404277\pi$
$788$		−	26.4187i		−	0.941129i
$789$	62.0133			2.20773
$790$	−13.6052			−0.484050
$791$	−2.57784			−0.0916575
$792$	−61.3289	+	14.5290i	−2.17923	+	0.516265i
$793$		−	11.3746i		−	0.403925i
$794$	1.06413			0.0377646
$795$	3.38849			0.120177
$796$	51.0954			1.81103
$797$			2.86249i			0.101395i	0.998714	+	0.0506973i	$0.0161444\pi$
$797$			2.86249i			0.101395i	−0.998714	+	0.0506973i	$0.983856\pi$
$798$	11.9579	+	20.7309i	0.423305	+	0.733866i
$799$			43.4767i			1.53809i
$800$	3.59636			0.127151
$801$			28.2474i			0.998071i
$802$			74.4542i			2.62907i
$803$	−3.72836	−	15.7379i	−0.131571	−	0.555380i
$804$	100.075			3.52936
$805$		−	5.43313i		−	0.191493i
$806$			11.8212i			0.416384i
$807$	81.1067			2.85509
$808$			31.6394i			1.11307i
$809$			18.9854i			0.667492i	0.942663	+	0.333746i	$0.108313\pi$
$809$			18.9854i			0.667492i	−0.942663	+	0.333746i	$0.891687\pi$
$810$	−4.28680			−0.150623
$811$	−51.2154			−1.79842			−0.899208	−	0.437522i	$-0.855856\pi$
$811$	−51.2154			−1.79842			−0.899208	+	0.437522i	$0.855856\pi$
$812$			21.1029i			0.740565i
$813$	−5.96954			−0.209361
$814$	−17.9793	−	75.8930i	−0.630174	−	2.66005i
$815$	−3.20509			−0.112269
$816$	18.8453			0.659716
$817$	19.4207	−	11.2022i	0.679445	−	0.391914i
$818$	65.9239			2.30497
$819$			3.53721i			0.123600i
$820$	−41.6053			−1.45292
$821$			1.02122i			0.0356407i	0.999841	+	0.0178203i	$0.00567269\pi$
$821$			1.02122i			0.0356407i	−0.999841	+	0.0178203i	$0.994327\pi$
$822$			30.5338i			1.06499i
$823$	−18.5728			−0.647406			−0.323703	−	0.946159i	$-0.604928\pi$
$823$	−18.5728			−0.647406			−0.323703	+	0.946159i	$0.604928\pi$
$824$			25.2590i			0.879937i
$825$	−2.17793	−	9.19336i	−0.0758259	−	0.320072i
$826$	−2.07457			−0.0721834
$827$	−24.1998			−0.841509			−0.420754	−	0.907175i	$-0.638235\pi$
$827$	−24.1998			−0.841509			−0.420754	+	0.907175i	$0.638235\pi$
$828$	−121.644			−4.22741
$829$			15.4487i			0.536554i	0.963342	+	0.268277i	$0.0864542\pi$
$829$			15.4487i			0.536554i	−0.963342	+	0.268277i	$0.913546\pi$
$830$		−	28.1082i		−	0.975649i
$831$	61.8760			2.14645
$832$	−9.94424			−0.344754
$833$		−	25.7974i		−	0.893827i
$834$	−93.5325			−3.23877
$835$	9.53668			0.330031
$836$	35.4360	+	37.5974i	1.22558	+	1.30033i
$837$	−35.6058			−1.23072
$838$	37.9700			1.31165
$839$		−	18.4891i		−	0.638314i	−0.947702	−	0.319157i	$-0.896600\pi$
$839$		−	18.4891i		−	0.638314i	0.947702	−	0.319157i	$-0.103400\pi$
$840$	−8.64063			−0.298130
$841$	23.3157			0.803988
$842$			43.2834i			1.49165i
$843$		−	89.5975i		−	3.08590i
$844$	78.0748			2.68744
$845$	−12.2824			−0.422527
$846$	−128.889			−4.43128
$847$	−4.02884	−	8.02592i	−0.138433	−	0.275774i
$848$		−	1.93199i		−	0.0663449i
$849$	−9.48648			−0.325575
$850$			9.61626i			0.329835i
$851$		−	66.2885i		−	2.27234i
$852$	45.0438			1.54317
$853$			5.28373i			0.180911i	0.995900	+	0.0904557i	$0.0288324\pi$
$853$			5.28373i			0.180911i	−0.995900	+	0.0904557i	$0.971168\pi$
$854$	25.8803			0.885607
$855$	11.1394	+	19.3119i	0.380959	+	0.660453i
$856$	−11.1801			−0.382127
$857$	−15.5264			−0.530372			−0.265186	−	0.964197i	$-0.585433\pi$
$857$	−15.5264			−0.530372			−0.265186	+	0.964197i	$0.585433\pi$
$858$	4.35573	+	18.3861i	0.148702	+	0.627692i
$859$	14.3026			0.487997			0.243999	−	0.969776i	$-0.421541\pi$
$859$	14.3026			0.487997			0.243999	+	0.969776i	$0.421541\pi$
$860$			18.3815i			0.626805i
$861$	−27.0745			−0.922698
$862$	−14.0767			−0.479454
$863$		−	27.4745i		−	0.935244i	−0.883929	−	0.467622i	$-0.845111\pi$
$863$		−	27.4745i		−	0.935244i	0.883929	−	0.467622i	$-0.154889\pi$
$864$		−	21.6640i		−	0.737025i
$865$	13.5827			0.461827
$866$			43.2041i			1.46814i
$867$			1.16593i			0.0395971i
$868$	−17.2453			−0.585343
$869$	−18.5981	+	4.40595i	−0.630899	+	0.149462i
$870$			48.6435i			1.64917i
$871$		−	8.32735i		−	0.282162i
$872$	6.06580			0.205414
$873$		−	71.2918i		−	2.41286i
$874$	34.2190	+	59.3240i	1.15748	+	2.00667i
$875$		−	0.816397i		−	0.0275993i
$876$	−49.6441			−1.67732
$877$	12.0107			0.405572			0.202786	−	0.979223i	$-0.435000\pi$
$877$	12.0107			0.405572			0.202786	+	0.979223i	$0.435000\pi$
$878$	36.0600			1.21697
$879$		−	15.1888i		−	0.512305i
$880$	−5.24172	+	1.24178i	−0.176698	+	0.0418603i
$881$	45.6978			1.53960			0.769799	−	0.638286i	$-0.220356\pi$
$881$	45.6978			1.53960			0.769799	+	0.638286i	$0.220356\pi$
$882$	76.4775			2.57513
$883$	0.721229			0.0242713			0.0121356	−	0.999926i	$-0.496137\pi$
$883$	0.721229			0.0242713			0.0121356	+	0.999926i	$0.496137\pi$
$884$		−	12.3310i		−	0.414737i
$885$	−3.06611			−0.103066
$886$	−64.8162			−2.17754
$887$	−48.2972			−1.62166			−0.810831	−	0.585280i	$-0.800984\pi$
$887$	−48.2972			−1.62166			−0.810831	+	0.585280i	$0.800984\pi$
$888$	−105.422			−3.53775
$889$		−	2.03721i		−	0.0683257i
$890$			13.0387i			0.437059i
$891$	−5.86001	+	1.38825i	−0.196318	+	0.0465083i
$892$			33.4550i			1.12016i
$893$	23.2471	+	40.3025i	0.777935	+	1.34867i
$894$	8.94773			0.299257
$895$			20.6841i			0.691394i
$896$		−	16.7537i		−	0.559701i
$897$			16.0593i			0.536205i
$898$		−	36.9384i		−	1.23265i
$899$			42.7524i			1.42587i
$900$	−18.2785			−0.609284
$901$	−4.84511			−0.161414
$902$	−88.7028	+	21.0140i	−2.95348	+	0.699688i
$903$			11.9617i			0.398061i
$904$			11.7318i			0.390193i
$905$			12.1550i			0.404046i
$906$		−	47.9282i		−	1.59231i
$907$			35.6225i			1.18282i	0.806369	+	0.591412i	$0.201429\pi$
$907$			35.6225i			1.18282i	−0.806369	+	0.591412i	$0.798571\pi$
$908$	−25.6279			−0.850492
$909$			43.5547i			1.44462i
$910$			1.63274i			0.0541249i
$911$		−	46.0769i		−	1.52660i	−0.646046	−	0.763299i	$-0.723578\pi$
$911$		−	46.0769i		−	1.52660i	0.646046	−	0.763299i	$-0.276422\pi$
$912$	17.4694	−	10.0766i	0.578469	−	0.333670i
$913$	−9.10266	−	38.4236i	−0.301254	−	1.27164i
$914$			61.1328i			2.02209i
$915$	38.2499			1.26450
$916$	8.07148			0.266689
$917$	14.4742			0.477979
$918$	57.9271			1.91188
$919$		−	20.1297i		−	0.664017i	−0.943276	−	0.332009i	$-0.892274\pi$
$919$		−	20.1297i		−	0.664017i	0.943276	−	0.332009i	$-0.107726\pi$
$920$	−24.7262			−0.815200
$921$		−	38.9969i		−	1.28499i
$922$		−	18.1592i		−	0.598043i
$923$		−	3.74816i		−	0.123372i
$924$	−26.8225	+	6.35433i	−0.882396	+	0.209042i
$925$		−	9.96068i		−	0.327505i
$926$	−6.37032			−0.209342
$927$			34.7715i			1.14205i
$928$	−26.0123			−0.853897
$929$	16.5752			0.543814			0.271907	−	0.962323i	$-0.412346\pi$
$929$	16.5752			0.543814			0.271907	+	0.962323i	$0.412346\pi$
$930$	−39.7515			−1.30350
$931$	−13.7939	−	23.9140i	−0.452078	−	0.783748i
$932$			55.0364i			1.80278i
$933$		−	11.8471i		−	0.387857i
$934$	−42.4539			−1.38913
$935$	3.11417	+	13.1453i	0.101844	+	0.429898i
$936$	16.0979			0.526175
$937$			27.4203i			0.895782i	0.894088	+	0.447891i	$0.147825\pi$
$937$			27.4203i			0.895782i	−0.894088	+	0.447891i	$0.852175\pi$
$938$	18.9470			0.618640
$939$		−	54.0497i		−	1.76384i
$940$	−38.1459			−1.24418
$941$	33.1918			1.08202			0.541011	−	0.841016i	$-0.318042\pi$
$941$	33.1918			1.08202			0.541011	+	0.841016i	$0.318042\pi$
$942$			22.5168i			0.733638i
$943$	−77.4772			−2.52300
$944$			1.74818i			0.0568985i
$945$	−4.91787			−0.159978
$946$	9.28412	+	39.1896i	0.301853	+	1.27416i
$947$	3.61105			0.117343			0.0586717	−	0.998277i	$-0.481313\pi$
$947$	3.61105			0.117343			0.0586717	+	0.998277i	$0.481313\pi$
$948$			58.6664i			1.90540i
$949$			4.13096i			0.134097i
$950$	5.14184	+	8.91419i	0.166823	+	0.289214i
$951$	−31.9284			−1.03535
$952$	12.3550			0.400428
$953$	6.96977			0.225773			0.112887	−	0.993608i	$-0.463990\pi$
$953$	6.96977			0.225773			0.112887	+	0.993608i	$0.463990\pi$
$954$		−	14.3635i		−	0.465037i
$955$	−9.92179			−0.321061
$956$		−	8.29981i		−	0.268435i
$957$	15.7529	+	66.4952i	0.509219	+	2.14948i
$958$			67.7544i			2.18905i
$959$			3.70658i			0.119692i
$960$		−	33.4398i		−	1.07927i
$961$	−3.93738			−0.127012
$962$			19.9207i			0.642270i
$963$	−15.3905			−0.495951
$964$	−33.2054			−1.06948
$965$	−12.4257			−0.399998
$966$	−36.5392			−1.17563
$967$		−	54.3445i		−	1.74760i	−0.486284	−	0.873801i	$-0.661648\pi$
$967$		−	54.3445i		−	1.74760i	0.486284	−	0.873801i	$-0.338352\pi$
$968$	−36.5260	+	18.3353i	−1.17399	+	0.589318i
$969$	−25.2704	−	43.8102i	−0.811803	−	1.40739i
$970$		−	32.9076i		−	1.05660i
$971$		−	10.7150i		−	0.343861i	−0.985109	−	0.171931i	$-0.945000\pi$
$971$		−	10.7150i		−	0.343861i	0.985109	−	0.171931i	$-0.0550005\pi$
$972$		−	46.0984i		−	1.47861i
$973$	−11.3542			−0.363998
$974$		−	55.5027i		−	1.77842i
$975$			2.41311i			0.0772815i
$976$		−	21.8087i		−	0.698079i
$977$		−	37.3829i		−	1.19598i	−0.801502	−	0.597992i	$-0.795965\pi$
$977$		−	37.3829i		−	1.19598i	0.801502	−	0.597992i	$-0.204035\pi$
$978$			21.5550i			0.689254i
$979$	4.22251	+	17.8238i	0.134952	+	0.569651i
$980$	22.6343			0.723027
$981$	8.35018			0.266601
$982$		−	93.7802i		−	2.99265i
$983$		−	39.3275i		−	1.25435i	−0.778878	−	0.627175i	$-0.784211\pi$
$983$		−	39.3275i		−	1.25435i	0.778878	−	0.627175i	$-0.215789\pi$
$984$			123.217i			3.92800i
$985$		−	7.39245i		−	0.235543i
$986$		−	69.5540i		−	2.21505i
$987$	−24.8234			−0.790136
$988$	−6.59343	−	11.4307i	−0.209765	−	0.363660i
$989$			34.2300i			1.08845i
$990$	−38.9699	+	9.23209i	−1.23855	+	0.293415i
$991$			18.2007i			0.578165i	0.957304	+	0.289083i	$0.0933503\pi$
$991$			18.2007i			0.578165i	−0.957304	+	0.289083i	$0.906650\pi$
$992$		−	21.2573i		−	0.674921i
$993$	−31.0980			−0.986865
$994$	8.52807			0.270494
$995$	14.2974			0.453259
$996$	−121.204			−3.84051
$997$			16.4066i			0.519603i	0.965662	+	0.259801i	$0.0836571\pi$
$997$			16.4066i			0.519603i	−0.965662	+	0.259801i	$0.916343\pi$
$998$	15.7205			0.497623
$999$	−60.0019			−1.89837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.f.b.626.3	✓	40
11.10	odd	2	inner	1045.2.f.b.626.37	yes	40
19.18	odd	2	inner	1045.2.f.b.626.38	yes	40
209.208	even	2	inner	1045.2.f.b.626.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.f.b.626.3	✓	40	1.1	even	1	trivial
1045.2.f.b.626.4	yes	40	209.208	even	2	inner
1045.2.f.b.626.37	yes	40	11.10	odd	2	inner
1045.2.f.b.626.38	yes	40	19.18	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.36088 q^{2} +2.84862i q^{3} +3.57375 q^{4} +1.00000 q^{5} -6.72526i q^{6} -0.816397i q^{7} -3.71543 q^{8} -5.11466 q^{9} +O(q^{10})\)	\(q-2.36088 q^{2} +2.84862i q^{3} +3.57375 q^{4} +1.00000 q^{5} -6.72526i q^{6} -0.816397i q^{7} -3.71543 q^{8} -5.11466 q^{9} -2.36088 q^{10} +(-3.22730 + 0.764557i) q^{11} +10.1803i q^{12} +0.847115 q^{13} +1.92741i q^{14} +2.84862i q^{15} +1.62418 q^{16} -4.07317i q^{17} +12.0751 q^{18} +(-2.17793 - 3.77579i) q^{19} +3.57375 q^{20} +2.32561 q^{21} +(7.61926 - 1.80503i) q^{22} +6.65502 q^{23} -10.5839i q^{24} +1.00000 q^{25} -1.99994 q^{26} -6.02387i q^{27} -2.91760i q^{28} -7.23296 q^{29} -6.72526i q^{30} -5.91078i q^{31} +3.59636 q^{32} +(-2.17793 - 9.19336i) q^{33} +9.61626i q^{34} -0.816397i q^{35} -18.2785 q^{36} -9.96068i q^{37} +(5.14184 + 8.91419i) q^{38} +2.41311i q^{39} -3.71543 q^{40} -11.6419 q^{41} -5.49048 q^{42} +5.14349i q^{43} +(-11.5336 + 2.73233i) q^{44} -5.11466 q^{45} -15.7117 q^{46} -10.6739 q^{47} +4.62668i q^{48} +6.33350 q^{49} -2.36088 q^{50} +11.6029 q^{51} +3.02738 q^{52} -1.18952i q^{53} +14.2216i q^{54} +(-3.22730 + 0.764557i) q^{55} +3.03326i q^{56} +(10.7558 - 6.20412i) q^{57} +17.0761 q^{58} +1.07635i q^{59} +10.1803i q^{60} -13.4275i q^{61} +13.9546i q^{62} +4.17559i q^{63} -11.7389 q^{64} +0.847115 q^{65} +(5.14184 + 21.7044i) q^{66} -9.83025i q^{67} -14.5565i q^{68} +18.9576i q^{69} +1.92741i q^{70} -4.42462i q^{71} +19.0032 q^{72} +4.87650i q^{73} +23.5160i q^{74} +2.84862i q^{75} +(-7.78339 - 13.4937i) q^{76} +(0.624182 + 2.63476i) q^{77} -5.69707i q^{78} +5.76276 q^{79} +1.62418 q^{80} +1.81576 q^{81} +27.4852 q^{82} +11.9058i q^{83} +8.31114 q^{84} -4.07317i q^{85} -12.1431i q^{86} -20.6040i q^{87} +(11.9908 - 2.84066i) q^{88} -5.52282i q^{89} +12.0751 q^{90} -0.691582i q^{91} +23.7834 q^{92} +16.8376 q^{93} +25.1998 q^{94} +(-2.17793 - 3.77579i) q^{95} +10.2447i q^{96} +13.9387i q^{97} -14.9526 q^{98} +(16.5065 - 3.91045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) \) 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9} - 4 q^{11} + 48 q^{16} + 40 q^{20} + 24 q^{23} + 40 q^{25} - 24 q^{26} + 24 q^{36} - 28 q^{38} - 60 q^{42} - 48 q^{44} - 28 q^{45} - 36 q^{49} - 4 q^{55} - 36 q^{58} - 40 q^{64} - 28 q^{66} + 8 q^{77} + 48 q^{80} + 80 q^{81} + 8 q^{82} + 4 q^{92} + 56 q^{93} - 16 q^{99}+O(q^{100}) \) 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9 - 4 * q^11 + 48 * q^16 + 40 * q^20 + 24 * q^23 + 40 * q^25 - 24 * q^26 + 24 * q^36 - 28 * q^38 - 60 * q^42 - 48 * q^44 - 28 * q^45 - 36 * q^49 - 4 * q^55 - 36 * q^58 - 40 * q^64 - 28 * q^66 + 8 * q^77 + 48 * q^80 + 80 * q^81 + 8 * q^82 + 4 * q^92 + 56 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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