LMFDB - Embedded newform 136.3.t.b.57.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,3,Mod(41,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 0, 11]))

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

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

chi := DirichletCharacter("136.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	136.t (of order $16$, degree $8$, 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:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			57.1
Character	$\chi$	$=$	136.57
Dual form			136.3.t.b.105.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.88441 + 0.772657i) q^{3} +(2.37425 - 3.55331i) q^{5} +(2.98990 + 4.47471i) q^{7} +(6.17671 - 2.55848i) q^{9} +O(q^{10})$	\(q+(-3.88441 + 0.772657i) q^{3} +(2.37425 - 3.55331i) q^{5} +(2.98990 + 4.47471i) q^{7} +(6.17671 - 2.55848i) q^{9} +(-4.17961 + 21.0123i) q^{11} +(-13.3335 + 13.3335i) q^{13} +(-6.47705 + 15.6370i) q^{15} +(16.7847 + 2.69670i) q^{17} +(3.71010 + 1.53677i) q^{19} +(-15.0714 - 15.0714i) q^{21} +(-8.85270 - 1.76091i) q^{23} +(2.57812 + 6.22413i) q^{25} +(7.62133 - 5.09241i) q^{27} +(13.2033 + 8.82216i) q^{29} +(-5.26646 - 26.4763i) q^{31} -84.8498i q^{33} +22.9988 q^{35} +(-9.96827 + 1.98281i) q^{37} +(41.4904 - 62.0948i) q^{39} +(27.7865 + 41.5855i) q^{41} +(-59.9178 + 24.8188i) q^{43} +(5.57397 - 28.0222i) q^{45} +(-26.7435 + 26.7435i) q^{47} +(7.66801 - 18.5122i) q^{49} +(-67.2824 + 2.49378i) q^{51} +(-51.4656 - 21.3177i) q^{53} +(64.7398 + 64.7398i) q^{55} +(-15.5989 - 3.10282i) q^{57} +(-12.3776 - 29.8821i) q^{59} +(30.4030 - 20.3146i) q^{61} +(29.9162 + 19.9894i) q^{63} +(15.7210 + 79.0348i) q^{65} -61.9779i q^{67} +35.7481 q^{69} +(105.788 - 21.0426i) q^{71} +(13.4011 - 20.0562i) q^{73} +(-14.8236 - 22.1851i) q^{75} +(-106.521 + 44.1223i) q^{77} +(19.4638 - 97.8509i) q^{79} +(-68.2167 + 68.2167i) q^{81} +(-43.3105 + 104.561i) q^{83} +(49.4333 - 53.2388i) q^{85} +(-58.1035 - 24.0672i) q^{87} +(72.1279 + 72.1279i) q^{89} +(-99.5291 - 19.7976i) q^{91} +(40.9142 + 98.7756i) q^{93} +(14.2693 - 9.53445i) q^{95} +(-75.6411 - 50.5417i) q^{97} +(27.9433 + 140.480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{15}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.88441	+	0.772657i	−1.29480	+	0.257552i	−0.793951	−	0.607981i	$-0.791980\pi$
$3$	−3.88441	+	0.772657i	−1.29480	+	0.257552i	−0.500851	+	0.865533i	$0.666980\pi$
$4$		0			0
$5$	2.37425	−	3.55331i	0.474849	−	0.710662i	−0.514295	−	0.857614i	$-0.671946\pi$
$5$	2.37425	−	3.55331i	0.474849	−	0.710662i	0.989144	+	0.146952i	$0.0469462\pi$
$6$		0			0
$7$	2.98990	+	4.47471i	0.427129	+	0.639244i	0.981147	−	0.193261i	$-0.0619063\pi$
$7$	2.98990	+	4.47471i	0.427129	+	0.639244i	−0.554018	+	0.832504i	$0.686906\pi$
$8$		0			0
$9$	6.17671	−	2.55848i	0.686301	−	0.284275i
$10$		0			0
$11$	−4.17961	+	21.0123i	−0.379964	+	1.91021i	0.0329848	+	0.999456i	$0.489499\pi$
$11$	−4.17961	+	21.0123i	−0.379964	+	1.91021i	−0.412949	+	0.910754i	$0.635501\pi$
$12$		0			0
$13$	−13.3335	+	13.3335i	−1.02565	+	1.02565i	−0.0259889	+	0.999662i	$0.508273\pi$
$13$	−13.3335	+	13.3335i	−1.02565	+	1.02565i	−0.999662	+	0.0259889i	$0.991727\pi$
$14$		0			0
$15$	−6.47705	+	15.6370i	−0.431803	+	1.04247i
$16$		0			0
$17$	16.7847	+	2.69670i	0.987338	+	0.158629i
$17$	16.7847	+	2.69670i	0.987338	+	0.158629i
$18$		0			0
$19$	3.71010	+	1.53677i	0.195268	+	0.0808828i	0.478175	−	0.878265i	$-0.341299\pi$
$19$	3.71010	+	1.53677i	0.195268	+	0.0808828i	−0.282906	+	0.959148i	$0.591299\pi$
$20$		0			0
$21$	−15.0714	−	15.0714i	−0.717687	−	0.717687i
$22$		0			0
$23$	−8.85270	−	1.76091i	−0.384900	−	0.0765614i	−0.00115234	−	0.999999i	$-0.500367\pi$
$23$	−8.85270	−	1.76091i	−0.384900	−	0.0765614i	−0.383748	+	0.923438i	$0.625367\pi$
$24$		0			0
$25$	2.57812	+	6.22413i	0.103125	+	0.248965i
$26$		0			0
$27$	7.62133	−	5.09241i	0.282272	−	0.188608i
$28$		0			0
$29$	13.2033	+	8.82216i	0.455286	+	0.304212i	0.761986	−	0.647594i	$-0.224225\pi$
$29$	13.2033	+	8.82216i	0.455286	+	0.304212i	−0.306700	+	0.951806i	$0.599225\pi$
$30$		0			0
$31$	−5.26646	−	26.4763i	−0.169886	−	0.854074i	−0.967881	−	0.251410i	$-0.919106\pi$
$31$	−5.26646	−	26.4763i	−0.169886	−	0.854074i	0.797995	−	0.602664i	$-0.205894\pi$
$32$		0			0
$33$		−	84.8498i		−	2.57121i
$34$		0			0
$35$	22.9988			0.657108
$36$		0			0
$37$	−9.96827	+	1.98281i	−0.269413	+	0.0535895i	−0.327948	−	0.944696i	$-0.606357\pi$
$37$	−9.96827	+	1.98281i	−0.269413	+	0.0535895i	0.0585352	+	0.998285i	$0.481357\pi$
$38$		0			0
$39$	41.4904	−	62.0948i	1.06386	−	1.59217i
$40$		0			0
$41$	27.7865	+	41.5855i	0.677721	+	1.01428i	0.997761	+	0.0668767i	$0.0213034\pi$
$41$	27.7865	+	41.5855i	0.677721	+	1.01428i	−0.320041	+	0.947404i	$0.603697\pi$
$42$		0			0
$43$	−59.9178	+	24.8188i	−1.39344	+	0.577180i	−0.948039	−	0.318153i	$-0.896937\pi$
$43$	−59.9178	+	24.8188i	−1.39344	+	0.577180i	−0.445397	+	0.895333i	$0.646937\pi$
$44$		0			0
$45$	5.57397	−	28.0222i	0.123866	−	0.622716i
$46$		0			0
$47$	−26.7435	+	26.7435i	−0.569010	+	0.569010i	−0.931851	−	0.362841i	$-0.881807\pi$
$47$	−26.7435	+	26.7435i	−0.569010	+	0.569010i	0.362841	+	0.931851i	$0.381807\pi$
$48$		0			0
$49$	7.66801	−	18.5122i	0.156490	−	0.377800i
$50$		0			0
$51$	−67.2824	+	2.49378i	−1.31926	+	0.0488976i
$52$		0			0
$53$	−51.4656	−	21.3177i	−0.971048	−	0.402221i	−0.159946	−	0.987126i	$-0.551132\pi$
$53$	−51.4656	−	21.3177i	−0.971048	−	0.402221i	−0.811102	+	0.584904i	$0.801132\pi$
$54$		0			0
$55$	64.7398	+	64.7398i	1.17709	+	1.17709i
$56$		0			0
$57$	−15.5989	−	3.10282i	−0.273665	−	0.0544354i
$58$		0			0
$59$	−12.3776	−	29.8821i	−0.209789	−	0.506476i	0.783601	−	0.621265i	$-0.213381\pi$
$59$	−12.3776	−	29.8821i	−0.209789	−	0.506476i	−0.993390	+	0.114789i	$0.963381\pi$
$60$		0			0
$61$	30.4030	−	20.3146i	0.498409	−	0.333026i	−0.280825	−	0.959759i	$-0.590608\pi$
$61$	30.4030	−	20.3146i	0.498409	−	0.333026i	0.779234	+	0.626732i	$0.215608\pi$
$62$		0			0
$63$	29.9162	+	19.9894i	0.474861	+	0.317292i
$64$		0			0
$65$	15.7210	+	79.0348i	0.241862	+	1.21592i
$66$		0			0
$67$		−	61.9779i		−	0.925044i	−0.886608	−	0.462522i	$-0.846945\pi$
$67$		−	61.9779i		−	0.925044i	0.886608	−	0.462522i	$-0.153055\pi$
$68$		0			0
$69$	35.7481			0.518088
$70$		0			0
$71$	105.788	−	21.0426i	1.48997	−	0.296374i	0.618097	−	0.786102i	$-0.287904\pi$
$71$	105.788	−	21.0426i	1.48997	−	0.296374i	0.871876	+	0.489727i	$0.162904\pi$
$72$		0			0
$73$	13.4011	−	20.0562i	0.183577	−	0.274743i	−0.728255	−	0.685307i	$-0.759668\pi$
$73$	13.4011	−	20.0562i	0.183577	−	0.274743i	0.911832	+	0.410564i	$0.134668\pi$
$74$		0			0
$75$	−14.8236	−	22.1851i	−0.197648	−	0.295801i
$76$		0			0
$77$	−106.521	+	44.1223i	−1.38338	+	0.573016i
$78$		0			0
$79$	19.4638	−	97.8509i	0.246377	−	1.23862i	−0.637335	−	0.770587i	$-0.719963\pi$
$79$	19.4638	−	97.8509i	0.246377	−	1.23862i	0.883712	−	0.468032i	$-0.155037\pi$
$80$		0			0
$81$	−68.2167	+	68.2167i	−0.842182	+	0.842182i
$82$		0			0
$83$	−43.3105	+	104.561i	−0.521813	+	1.25977i	0.414963	+	0.909838i	$0.363794\pi$
$83$	−43.3105	+	104.561i	−0.521813	+	1.25977i	−0.936776	+	0.349929i	$0.886206\pi$
$84$		0			0
$85$	49.4333	−	53.2388i	0.581568	−	0.626339i
$86$		0			0
$87$	−58.1035	−	24.0672i	−0.667856	−	0.276635i
$88$		0			0
$89$	72.1279	+	72.1279i	0.810425	+	0.810425i	0.984698	−	0.174272i	$-0.0557572\pi$
$89$	72.1279	+	72.1279i	0.810425	+	0.810425i	−0.174272	+	0.984698i	$0.555757\pi$
$90$		0			0
$91$	−99.5291	−	19.7976i	−1.09373	−	0.217556i
$92$		0			0
$93$	40.9142	+	98.7756i	0.439938	+	1.06210i
$94$		0			0
$95$	14.2693	−	9.53445i	0.150203	−	0.100363i
$96$		0			0
$97$	−75.6411	−	50.5417i	−0.779805	−	0.521049i	0.100796	−	0.994907i	$-0.467861\pi$
$97$	−75.6411	−	50.5417i	−0.779805	−	0.521049i	−0.880601	+	0.473858i	$0.842861\pi$
$98$		0			0
$99$	27.9433	+	140.480i	0.282256	+	1.41899i
$100$		0			0
$101$			75.3134i			0.745677i	0.927896	+	0.372839i	$0.121615\pi$
$101$			75.3134i			0.745677i	−0.927896	+	0.372839i	$0.878385\pi$
$102$		0			0
$103$	157.565			1.52976			0.764879	−	0.644174i	$-0.222799\pi$
$103$	157.565			1.52976			0.764879	+	0.644174i	$0.222799\pi$
$104$		0			0
$105$	−89.3367	+	17.7702i	−0.850825	+	0.169240i
$106$		0			0
$107$	65.0809	−	97.4005i	0.608233	−	0.910285i	−0.391719	−	0.920085i	$-0.628119\pi$
$107$	65.0809	−	97.4005i	0.608233	−	0.910285i	0.999952	+	0.00979981i	$0.00311943\pi$
$108$		0			0
$109$	65.0603	+	97.3697i	0.596884	+	0.893300i	0.999759	−	0.0219552i	$-0.00698913\pi$
$109$	65.0603	+	97.3697i	0.596884	+	0.893300i	−0.402875	+	0.915255i	$0.631989\pi$
$110$		0			0
$111$	37.1888	−	15.4041i	0.335034	−	0.138776i
$112$		0			0
$113$	−30.6827	+	154.252i	−0.271528	+	1.36507i	0.568572	+	0.822634i	$0.307496\pi$
$113$	−30.6827	+	154.252i	−0.271528	+	1.36507i	−0.840100	+	0.542432i	$0.817504\pi$
$114$		0			0
$115$	−27.2756	+	27.2756i	−0.237179	+	0.237179i
$116$		0			0
$117$	−48.2436	+	116.470i	−0.412338	+	0.995473i
$118$		0			0
$119$	38.1179	+	83.1697i	0.320318	+	0.698905i
$120$		0			0
$121$	−312.259	−	129.342i	−2.58065	−	1.06894i
$122$		0			0
$123$	−140.066	−	140.066i	−1.13874	−	1.13874i
$124$		0			0
$125$	133.023	+	26.4599i	1.06418	+	0.211679i
$126$		0			0
$127$	−5.31710	−	12.8366i	−0.0418669	−	0.101076i	0.901563	−	0.432648i	$-0.142421\pi$
$127$	−5.31710	−	12.8366i	−0.0418669	−	0.101076i	−0.943430	+	0.331573i	$0.892421\pi$
$128$		0			0
$129$	213.569	−	142.702i	1.65557	−	1.10622i
$130$		0			0
$131$	158.915	+	106.184i	1.21309	+	0.810564i	0.986554	−	0.163438i	$-0.0522582\pi$
$131$	158.915	+	106.184i	1.21309	+	0.810564i	0.226541	+	0.974002i	$0.427258\pi$
$132$		0			0
$133$	4.21623	+	21.1964i	0.0317009	+	0.159371i
$134$		0			0
$135$		−	39.1716i		−	0.290160i
$136$		0			0
$137$	−116.068			−0.847215			−0.423608	−	0.905846i	$-0.639236\pi$
$137$	−116.068			−0.847215			−0.423608	+	0.905846i	$0.639236\pi$
$138$		0			0
$139$	−20.5728	+	4.09219i	−0.148006	+	0.0294402i	−0.268537	−	0.963269i	$-0.586540\pi$
$139$	−20.5728	+	4.09219i	−0.148006	+	0.0294402i	0.120531	+	0.992710i	$0.461540\pi$
$140$		0			0
$141$	83.2190	−	124.546i	0.590206	−	0.883306i
$142$		0			0
$143$	−224.438	−	335.896i	−1.56950	−	2.34892i
$144$		0			0
$145$	62.6957	−	25.9694i	0.432384	−	0.179099i
$146$		0			0
$147$	−15.4821	+	77.8337i	−0.105320	+	0.529481i
$148$		0			0
$149$	176.631	−	176.631i	1.18545	−	1.18545i	0.207133	−	0.978313i	$-0.433587\pi$
$149$	176.631	−	176.631i	1.18545	−	1.18545i	0.978313	−	0.207133i	$-0.0664134\pi$
$150$		0			0
$151$	−29.9488	+	72.3028i	−0.198336	+	0.478826i	−0.991488	−	0.130198i	$-0.958439\pi$
$151$	−29.9488	+	72.3028i	−0.198336	+	0.478826i	0.793152	+	0.609024i	$0.208439\pi$
$152$		0			0
$153$	110.574	−	26.2867i	0.722706	−	0.171808i
$154$		0			0
$155$	−106.582	−	44.1479i	−0.687628	−	0.284825i
$156$		0			0
$157$	−144.649	−	144.649i	−0.921333	−	0.921333i	0.0757909	−	0.997124i	$-0.475852\pi$
$157$	−144.649	−	144.649i	−0.921333	−	0.921333i	−0.997124	+	0.0757909i	$0.975852\pi$
$158$		0			0
$159$	216.385	+	43.0416i	1.36091	+	0.270702i
$160$		0			0
$161$	−18.5892	−	44.8782i	−0.115461	−	0.278747i
$162$		0			0
$163$	−37.6308	+	25.1441i	−0.230864	+	0.154258i	−0.665622	−	0.746289i	$-0.731834\pi$
$163$	−37.6308	+	25.1441i	−0.230864	+	0.154258i	0.434758	+	0.900547i	$0.356834\pi$
$164$		0			0
$165$	−301.498	−	201.454i	−1.82726	−	1.22093i
$166$		0			0
$167$	33.6644	+	169.242i	0.201583	+	1.01343i	0.940542	+	0.339676i	$0.110317\pi$
$167$	33.6644	+	169.242i	0.201583	+	1.01343i	−0.738959	+	0.673750i	$0.764683\pi$
$168$		0			0
$169$		−	186.563i		−	1.10392i
$170$		0			0
$171$	26.8480			0.157006
$172$		0			0
$173$	256.897	−	51.1001i	1.48496	−	0.295376i	0.615008	−	0.788521i	$-0.289153\pi$
$173$	256.897	−	51.1001i	1.48496	−	0.295376i	0.869947	+	0.493145i	$0.164153\pi$
$174$		0			0
$175$	−20.1428	+	30.1459i	−0.115102	+	0.172262i
$176$		0			0
$177$	71.1681	+	106.511i	0.402080	+	0.601755i
$178$		0			0
$179$	93.7135	−	38.8174i	0.523539	−	0.216857i	−0.105232	−	0.994448i	$-0.533558\pi$
$179$	93.7135	−	38.8174i	0.523539	−	0.216857i	0.628771	+	0.777591i	$0.283558\pi$
$180$		0			0
$181$	63.3076	−	318.269i	0.349766	−	1.75839i	−0.259808	−	0.965660i	$-0.583659\pi$
$181$	63.3076	−	318.269i	0.349766	−	1.75839i	0.609573	−	0.792730i	$-0.291341\pi$
$182$		0			0
$183$	−102.401	+	102.401i	−0.559570	+	0.559570i
$184$		0			0
$185$	−16.6216	+	40.1280i	−0.0898463	+	0.216908i
$186$		0			0
$187$	−126.818	+	341.415i	−0.678169	+	1.82575i
$188$		0			0
$189$	45.5741	+	18.8774i	0.241133	+	0.0998805i
$190$		0			0
$191$	−79.8072	−	79.8072i	−0.417839	−	0.417839i	0.466619	−	0.884458i	$-0.345472\pi$
$191$	−79.8072	−	79.8072i	−0.417839	−	0.417839i	−0.884458	+	0.466619i	$0.845472\pi$
$192$		0			0
$193$	290.140	+	57.7125i	1.50332	+	0.299028i	0.876981	−	0.480524i	$-0.159554\pi$
$193$	290.140	+	57.7125i	1.50332	+	0.299028i	0.626336	+	0.779553i	$0.284554\pi$
$194$		0			0
$195$	−122.134	−	294.857i	−0.626326	−	1.51209i
$196$		0			0
$197$	−140.834	+	94.1026i	−0.714896	+	0.477678i	−0.859060	−	0.511876i	$-0.828951\pi$
$197$	−140.834	+	94.1026i	−0.714896	+	0.477678i	0.144164	+	0.989554i	$0.453951\pi$
$198$		0			0
$199$	−115.179	−	76.9603i	−0.578790	−	0.386735i	0.231438	−	0.972850i	$-0.425657\pi$
$199$	−115.179	−	76.9603i	−0.578790	−	0.386735i	−0.810228	+	0.586114i	$0.800657\pi$
$200$		0			0
$201$	47.8877	+	240.748i	0.238247	+	1.19775i
$202$		0			0
$203$			85.4582i			0.420977i
$204$		0			0
$205$	213.738			1.04263
$206$		0			0
$207$	−59.1859	+	11.7728i	−0.285922	+	0.0568734i
$208$		0			0
$209$	−47.7979	+	71.5346i	−0.228698	+	0.342271i
$210$		0			0
$211$	89.8413	+	134.457i	0.425788	+	0.637237i	0.980894	−	0.194543i	$-0.0623223\pi$
$211$	89.8413	+	134.457i	0.425788	+	0.637237i	−0.555106	+	0.831780i	$0.687322\pi$
$212$		0			0
$213$	−394.665	+	163.476i	−1.85289	+	0.767492i
$214$		0			0
$215$	−54.0708	+	271.832i	−0.251492	+	1.26434i
$216$		0			0
$217$	102.727	−	102.727i	0.473399	−	0.473399i
$218$		0			0
$219$	−36.5589	+	88.2610i	−0.166936	+	0.403018i
$220$		0			0
$221$	−259.755	+	187.843i	−1.17536	+	0.849966i
$222$		0			0
$223$	77.9790	+	32.3000i	0.349682	+	0.144843i	0.550609	−	0.834763i	$-0.314396\pi$
$223$	77.9790	+	32.3000i	0.349682	+	0.144843i	−0.200927	+	0.979606i	$0.564396\pi$
$224$		0			0
$225$	31.8486	+	31.8486i	0.141549	+	0.141549i
$226$		0			0
$227$	57.0676	+	11.3515i	0.251399	+	0.0500064i	0.319181	−	0.947694i	$-0.396592\pi$
$227$	57.0676	+	11.3515i	0.251399	+	0.0500064i	−0.0677818	+	0.997700i	$0.521592\pi$
$228$		0			0
$229$	43.7441	+	105.608i	0.191022	+	0.461168i	0.990153	−	0.139989i	$-0.0447066\pi$
$229$	43.7441	+	105.608i	0.191022	+	0.461168i	−0.799131	+	0.601157i	$0.794707\pi$
$230$		0			0
$231$	379.678	−	253.693i	1.64363	−	1.09824i
$232$		0			0
$233$	−188.882	−	126.207i	−0.810654	−	0.541662i	0.0797594	−	0.996814i	$-0.474585\pi$
$233$	−188.882	−	126.207i	−0.810654	−	0.541662i	−0.890414	+	0.455152i	$0.849585\pi$
$234$		0			0
$235$	31.5323	+	158.523i	0.134180	+	0.674568i
$236$		0			0
$237$			395.132i			1.66722i
$238$		0			0
$239$	90.5139			0.378719			0.189360	−	0.981908i	$-0.439359\pi$
$239$	90.5139			0.378719			0.189360	+	0.981908i	$0.439359\pi$
$240$		0			0
$241$	−149.534	+	29.7441i	−0.620471	+	0.123419i	−0.495309	−	0.868717i	$-0.664945\pi$
$241$	−149.534	+	29.7441i	−0.620471	+	0.123419i	−0.125162	+	0.992136i	$0.539945\pi$
$242$		0			0
$243$	166.442	−	249.098i	0.684946	−	1.02509i
$244$		0			0
$245$	−47.5739	−	71.1993i	−0.194179	−	0.290610i
$246$		0			0
$247$	−69.9589	+	28.9779i	−0.283235	+	0.117320i
$248$		0			0
$249$	87.4460	−	439.621i	0.351189	−	1.76554i
$250$		0			0
$251$	264.671	−	264.671i	1.05446	−	1.05446i	0.0560355	−	0.998429i	$-0.482154\pi$
$251$	264.671	−	264.671i	1.05446	−	1.05446i	0.998429	−	0.0560355i	$-0.0178460\pi$
$252$		0			0
$253$	74.0017	−	178.656i	0.292497	−	0.706149i
$254$		0			0
$255$	−150.884	+	244.996i	−0.591701	+	0.960769i
$256$		0			0
$257$	−55.4327	−	22.9610i	−0.215691	−	0.0893422i	0.272222	−	0.962235i	$-0.412242\pi$
$257$	−55.4327	−	22.9610i	−0.215691	−	0.0893422i	−0.487913	+	0.872892i	$0.662242\pi$
$258$		0			0
$259$	−38.6767	−	38.6767i	−0.149331	−	0.149331i
$260$		0			0
$261$	104.124	+	20.7116i	0.398943	+	0.0793548i
$262$		0			0
$263$	13.7525	+	33.2014i	0.0522908	+	0.126241i	0.947866	−	0.318669i	$-0.103236\pi$
$263$	13.7525	+	33.2014i	0.0522908	+	0.126241i	−0.895575	+	0.444910i	$0.853236\pi$
$264$		0			0
$265$	−197.940	+	132.260i	−0.746945	+	0.499092i
$266$		0			0
$267$	−335.904	−	224.444i	−1.25807	−	0.840614i
$268$		0			0
$269$	70.2103	+	352.971i	0.261005	+	1.31216i	0.859542	+	0.511065i	$0.170749\pi$
$269$	70.2103	+	352.971i	0.261005	+	1.31216i	−0.598537	+	0.801095i	$0.704251\pi$
$270$		0			0
$271$			296.760i			1.09506i	0.836788	+	0.547528i	$0.184431\pi$
$271$			296.760i			1.09506i	−0.836788	+	0.547528i	$0.815569\pi$
$272$		0			0
$273$	401.908			1.47219
$274$		0			0
$275$	−141.559	+	28.1578i	−0.514760	+	0.102392i
$276$		0			0
$277$	−100.128	+	149.852i	−0.361472	+	0.540982i	−0.966978	−	0.254859i	$-0.917971\pi$
$277$	−100.128	+	149.852i	−0.361472	+	0.540982i	0.605506	+	0.795841i	$0.292971\pi$
$278$		0			0
$279$	−100.268	−	150.062i	−0.359385	−	0.537858i
$280$		0			0
$281$	85.3015	−	35.3330i	0.303564	−	0.125740i	−0.225702	−	0.974196i	$-0.572467\pi$
$281$	85.3015	−	35.3330i	0.303564	−	0.125740i	0.529266	+	0.848456i	$0.322467\pi$
$282$		0			0
$283$	−7.04471	+	35.4161i	−0.0248930	+	0.125145i	−0.991234	−	0.132120i	$-0.957822\pi$
$283$	−7.04471	+	35.4161i	−0.0248930	+	0.125145i	0.966341	+	0.257266i	$0.0828215\pi$
$284$		0			0
$285$	−48.0610	+	48.0610i	−0.168635	+	0.168635i
$286$		0			0
$287$	−103.004	+	248.673i	−0.358898	+	0.866457i
$288$		0			0
$289$	274.456	+	90.5268i	0.949674	+	0.313241i
$290$		0			0
$291$	332.872	+	137.880i	1.14389	+	0.473815i
$292$		0			0
$293$	95.2618	+	95.2618i	0.325126	+	0.325126i	0.850729	−	0.525604i	$-0.176161\pi$
$293$	95.2618	+	95.2618i	0.325126	+	0.325126i	−0.525604	+	0.850729i	$0.676161\pi$
$294$		0			0
$295$	−135.568	−	26.9661i	−0.459551	−	0.0914104i
$296$		0			0
$297$	75.1491	+	181.426i	0.253027	+	0.610862i
$298$		0			0
$299$	141.516	−	94.5581i	0.473299	−	0.316248i
$300$		0			0
$301$	−290.205	−	193.909i	−0.964136	−	0.644215i
$302$		0			0
$303$	−58.1914	−	292.548i	−0.192051	−	0.965505i
$304$		0			0
$305$		−	156.263i		−	0.512338i
$306$		0			0
$307$	47.8576			0.155888			0.0779441	−	0.996958i	$-0.475164\pi$
$307$	47.8576			0.155888			0.0779441	+	0.996958i	$0.475164\pi$
$308$		0			0
$309$	−612.047	+	121.744i	−1.98073	+	0.393993i
$310$		0			0
$311$	51.9078	−	77.6854i	0.166906	−	0.249792i	−0.738583	−	0.674163i	$-0.764505\pi$
$311$	51.9078	−	77.6854i	0.166906	−	0.249792i	0.905489	+	0.424370i	$0.139505\pi$
$312$		0			0
$313$	138.420	+	207.160i	0.442236	+	0.661853i	0.983895	−	0.178745i	$-0.0572037\pi$
$313$	138.420	+	207.160i	0.442236	+	0.661853i	−0.541659	+	0.840598i	$0.682204\pi$
$314$		0			0
$315$	142.057	−	58.8419i	0.450974	−	0.186800i
$316$		0			0
$317$	113.642	−	571.318i	0.358493	−	1.80226i	−0.207923	−	0.978145i	$-0.566670\pi$
$317$	113.642	−	571.318i	0.358493	−	1.80226i	0.566416	−	0.824120i	$-0.308330\pi$
$318$		0			0
$319$	−240.558	+	240.558i	−0.754102	+	0.754102i
$320$		0			0
$321$	−177.544	+	428.629i	−0.553096	+	1.33529i
$322$		0			0
$323$	58.1288	+	35.7994i	0.179965	+	0.110834i
$324$		0			0
$325$	−117.365	−	48.6140i	−0.361122	−	0.149581i
$326$		0			0
$327$	−327.954	−	327.954i	−1.00292	−	1.00292i
$328$		0			0
$329$	−199.630	−	39.7088i	−0.606777	−	0.120695i
$330$		0			0
$331$	100.147	+	241.775i	0.302558	+	0.730438i	0.999906	+	0.0137063i	$0.00436298\pi$
$331$	100.147	+	241.775i	0.302558	+	0.730438i	−0.697349	+	0.716732i	$0.745637\pi$
$332$		0			0
$333$	−56.4981	+	37.7508i	−0.169664	+	0.113366i
$334$		0			0
$335$	−220.227	−	147.151i	−0.657393	−	0.439256i
$336$		0			0
$337$	−32.8510	−	165.153i	−0.0974807	−	0.490068i	−0.998423	−	0.0561305i	$-0.982124\pi$
$337$	−32.8510	−	165.153i	−0.0974807	−	0.490068i	0.900943	−	0.433938i	$-0.142876\pi$
$338$		0			0
$339$		−	622.886i		−	1.83742i
$340$		0			0
$341$	578.340			1.69601
$342$		0			0
$343$	364.399	−	72.4834i	1.06239	−	0.211322i
$344$		0			0
$345$	84.8747	−	127.024i	0.246014	−	0.368186i
$346$		0			0
$347$	−139.062	−	208.122i	−0.400756	−	0.599774i	0.575128	−	0.818063i	$-0.304952\pi$
$347$	−139.062	−	208.122i	−0.400756	−	0.599774i	−0.975884	+	0.218290i	$0.929952\pi$
$348$		0			0
$349$	514.848	−	213.257i	1.47521	−	0.611052i	0.507169	−	0.861847i	$-0.330692\pi$
$349$	514.848	−	213.257i	1.47521	−	0.611052i	0.968040	+	0.250795i	$0.0806920\pi$
$350$		0			0
$351$	−33.7193	+	169.518i	−0.0960663	+	0.482958i
$352$		0			0
$353$	88.8966	−	88.8966i	0.251832	−	0.251832i	−0.569890	−	0.821721i	$-0.693014\pi$
$353$	88.8966	−	88.8966i	0.251832	−	0.251832i	0.821721	+	0.569890i	$0.193014\pi$
$354$		0			0
$355$	176.396	−	425.858i	0.496891	−	1.19960i
$356$		0			0
$357$	−212.327	−	293.613i	−0.594753	−	0.822446i
$358$		0			0
$359$	−492.338	−	203.933i	−1.37141	−	0.568058i	−0.429242	−	0.903189i	$-0.641219\pi$
$359$	−492.338	−	203.933i	−1.37141	−	0.568058i	−0.942171	+	0.335131i	$0.891219\pi$
$360$		0			0
$361$	−243.862	−	243.862i	−0.675519	−	0.675519i
$362$		0			0
$363$	1312.88	+	261.147i	3.61674	+	0.719414i
$364$		0			0
$365$	−39.4483	−	95.2367i	−0.108078	−	0.260923i
$366$		0			0
$367$	469.869	−	313.956i	1.28030	−	0.855467i	0.285603	−	0.958348i	$-0.407806\pi$
$367$	469.869	−	313.956i	1.28030	−	0.855467i	0.994694	+	0.102881i	$0.0328060\pi$
$368$		0			0
$369$	278.025	+	185.770i	0.753456	+	0.503443i
$370$		0			0
$371$	−58.4864	−	294.031i	−0.157645	−	0.792537i
$372$		0			0
$373$			223.582i			0.599417i	0.954031	+	0.299708i	$0.0968894\pi$
$373$			223.582i			0.599417i	−0.954031	+	0.299708i	$0.903111\pi$
$374$		0			0
$375$	−537.159			−1.43242
$376$		0			0
$377$	−293.675	+	58.4157i	−0.778980	+	0.154949i
$378$		0			0
$379$	−11.6764	+	17.4750i	−0.0308085	+	0.0461082i	−0.846554	−	0.532303i	$-0.821327\pi$
$379$	−11.6764	+	17.4750i	−0.0308085	+	0.0461082i	0.815746	+	0.578411i	$0.196327\pi$
$380$		0			0
$381$	30.5721	+	45.7543i	0.0802416	+	0.120090i
$382$		0			0
$383$	291.453	−	120.724i	0.760973	−	0.315205i	0.0317632	−	0.999495i	$-0.489888\pi$
$383$	291.453	−	120.724i	0.760973	−	0.315205i	0.729210	+	0.684290i	$0.239888\pi$
$384$		0			0
$385$	−96.1259	+	483.258i	−0.249678	+	1.25521i
$386$		0			0
$387$	−306.597	+	306.597i	−0.792239	+	0.792239i
$388$		0			0
$389$	33.3540	−	80.5238i	0.0857430	−	0.207002i	−0.875192	−	0.483775i	$-0.839265\pi$
$389$	33.3540	−	80.5238i	0.0857430	−	0.207002i	0.960935	+	0.276773i	$0.0892652\pi$
$390$		0			0
$391$	−143.842	−	53.4295i	−0.367882	−	0.136648i
$392$		0			0
$393$	−699.336	−	289.674i	−1.77948	−	0.737085i
$394$		0			0
$395$	−301.483	−	301.483i	−0.763248	−	0.763248i
$396$		0			0
$397$	−523.720	−	104.174i	−1.31920	−	0.262404i	−0.515215	−	0.857061i	$-0.672288\pi$
$397$	−523.720	−	104.174i	−1.31920	−	0.262404i	−0.803980	+	0.594657i	$0.797288\pi$
$398$		0			0
$399$	−32.7551	−	79.0778i	−0.0820929	−	0.198190i
$400$		0			0
$401$	−208.595	+	139.379i	−0.520188	+	0.347578i	−0.787783	−	0.615953i	$-0.788771\pi$
$401$	−208.595	+	139.379i	−0.520188	+	0.347578i	0.267595	+	0.963531i	$0.413771\pi$
$402$		0			0
$403$	423.241	+	282.801i	1.05023	+	0.701739i
$404$		0			0
$405$	80.4319	+	404.358i	0.198597	+	0.998416i
$406$		0			0
$407$		−	217.744i		−	0.534997i
$408$		0			0
$409$	−284.881			−0.696530			−0.348265	−	0.937396i	$-0.613229\pi$
$409$	−284.881			−0.696530			−0.348265	+	0.937396i	$0.613229\pi$
$410$		0			0
$411$	450.857	−	89.6811i	1.09698	−	0.218202i
$412$		0			0
$413$	96.7058	−	144.730i	0.234154	−	0.350437i
$414$		0			0
$415$	268.707	+	402.148i	0.647486	+	0.969032i
$416$		0			0
$417$	76.7514	−	31.7915i	0.184056	−	0.0762386i
$418$		0			0
$419$	−70.2112	+	352.976i	−0.167569	+	0.842424i	0.801947	+	0.597395i	$0.203797\pi$
$419$	−70.2112	+	352.976i	−0.167569	+	0.842424i	−0.969516	+	0.245029i	$0.921203\pi$
$420$		0			0
$421$	127.566	−	127.566i	0.303007	−	0.303007i	−0.539182	−	0.842189i	$-0.681267\pi$
$421$	127.566	−	127.566i	0.303007	−	0.303007i	0.842189	+	0.539182i	$0.181267\pi$
$422$		0			0
$423$	−96.7641	+	233.609i	−0.228757	+	0.552268i
$424$		0			0
$425$	26.4885	+	111.423i	0.0623259	+	0.262172i
$426$		0			0
$427$	181.804	+	75.3056i	0.425770	+	0.176360i
$428$		0			0
$429$	1131.34	+	1131.34i	2.63716	+	2.63716i
$430$		0			0
$431$	−549.906	−	109.383i	−1.27588	−	0.253789i	−0.489760	−	0.871857i	$-0.662916\pi$
$431$	−549.906	−	109.383i	−1.27588	−	0.253789i	−0.786125	+	0.618068i	$0.787916\pi$
$432$		0			0
$433$	33.8216	+	81.6526i	0.0781100	+	0.188574i	0.958111	−	0.286398i	$-0.0924580\pi$
$433$	33.8216	+	81.6526i	0.0781100	+	0.188574i	−0.880001	+	0.474972i	$0.842458\pi$
$434$		0			0
$435$	−223.470	+	149.318i	−0.513725	+	0.343260i
$436$		0			0
$437$	−30.1383	−	20.1377i	−0.0689663	−	0.0460818i
$438$		0			0
$439$	56.3579	+	283.330i	0.128378	+	0.645399i	0.990366	+	0.138471i	$0.0442189\pi$
$439$	56.3579	+	283.330i	0.128378	+	0.645399i	−0.861989	+	0.506928i	$0.830781\pi$
$440$		0			0
$441$		−	133.963i		−	0.303771i
$442$		0			0
$443$	−44.0116			−0.0993491			−0.0496745	−	0.998765i	$-0.515818\pi$
$443$	−44.0116			−0.0993491			−0.0496745	+	0.998765i	$0.515818\pi$
$444$		0			0
$445$	427.542	−	85.0434i	0.960768	−	0.191109i
$446$		0			0
$447$	−549.633	+	822.584i	−1.22960	+	1.84023i
$448$		0			0
$449$	−102.441	−	153.314i	−0.228154	−	0.341456i	0.699676	−	0.714460i	$-0.253328\pi$
$449$	−102.441	−	153.314i	−0.228154	−	0.341456i	−0.927830	+	0.373004i	$0.878328\pi$
$450$		0			0
$451$	−989.944	+	410.048i	−2.19500	+	0.909198i
$452$		0			0
$453$	60.4681	−	303.994i	0.133484	−	0.671067i
$454$		0			0
$455$	−306.653	+	306.653i	−0.673964	+	0.673964i
$456$		0			0
$457$	−253.683	+	612.445i	−0.555105	+	1.34014i	0.358496	+	0.933531i	$0.383290\pi$
$457$	−253.683	+	612.445i	−0.555105	+	1.34014i	−0.913601	+	0.406611i	$0.866710\pi$
$458$		0			0
$459$	141.655	−	64.9224i	0.308616	−	0.141443i
$460$		0			0
$461$	376.784	+	156.069i	0.817319	+	0.338545i	0.751870	−	0.659311i	$-0.229152\pi$
$461$	376.784	+	156.069i	0.817319	+	0.338545i	0.0654489	+	0.997856i	$0.479152\pi$
$462$		0			0
$463$	−259.451	−	259.451i	−0.560370	−	0.560370i	0.369043	−	0.929412i	$-0.379686\pi$
$463$	−259.451	−	259.451i	−0.560370	−	0.560370i	−0.929412	+	0.369043i	$0.879686\pi$
$464$		0			0
$465$	448.121	+	89.1367i	0.963700	+	0.191692i
$466$		0			0
$467$	121.771	+	293.981i	0.260751	+	0.629509i	0.998985	−	0.0450357i	$-0.0143402\pi$
$467$	121.771	+	293.981i	0.260751	+	0.629509i	−0.738234	+	0.674544i	$0.764340\pi$
$468$		0			0
$469$	277.333	−	185.308i	0.591328	−	0.395113i
$470$		0			0
$471$	673.641	+	450.113i	1.43024	+	0.955653i
$472$		0			0
$473$	−271.067	−	1362.74i	−0.573079	−	2.88106i
$474$		0			0
$475$			27.0541i			0.0569560i
$476$		0			0
$477$	−372.429			−0.780773
$478$		0			0
$479$	245.923	−	48.9170i	0.513408	−	0.102123i	0.0684146	−	0.997657i	$-0.478206\pi$
$479$	245.923	−	48.9170i	0.513408	−	0.102123i	0.444994	+	0.895534i	$0.353206\pi$
$480$		0			0
$481$	106.474	−	159.349i	0.221359	−	0.331287i
$482$		0			0
$483$	106.883	+	159.962i	0.221291	+	0.331185i
$484$		0			0
$485$	−359.181	+	148.778i	−0.740579	+	0.306758i
$486$		0			0
$487$	−46.2764	+	232.647i	−0.0950234	+	0.477715i	0.903744	+	0.428074i	$0.140808\pi$
$487$	−46.2764	+	232.647i	−0.0950234	+	0.477715i	−0.998767	+	0.0496408i	$0.984192\pi$
$488$		0			0
$489$	126.746	−	126.746i	0.259194	−	0.259194i
$490$		0			0
$491$	228.472	−	551.580i	0.465320	−	1.12338i	−0.500864	−	0.865526i	$-0.666984\pi$
$491$	228.472	−	551.580i	0.465320	−	1.12338i	0.966184	−	0.257855i	$-0.0830158\pi$
$492$		0			0
$493$	197.823	+	183.683i	0.401264	+	0.372582i
$494$		0			0
$495$	565.515	+	234.244i	1.14245	+	0.473220i
$496$		0			0
$497$	410.455	+	410.455i	0.825866	+	0.825866i
$498$		0			0
$499$	−890.058	−	177.043i	−1.78368	−	0.354797i	−0.810662	−	0.585515i	$-0.800893\pi$
$499$	−890.058	−	177.043i	−1.78368	−	0.354797i	−0.973021	+	0.230718i	$0.925893\pi$
$500$		0			0
$501$	−261.532	−	631.395i	−0.522020	−	1.26027i
$502$		0			0
$503$	245.454	−	164.007i	0.487980	−	0.326058i	−0.287122	−	0.957894i	$-0.592698\pi$
$503$	245.454	−	164.007i	0.487980	−	0.326058i	0.775102	+	0.631836i	$0.217698\pi$
$504$		0			0
$505$	267.612	+	178.812i	0.529924	+	0.354084i
$506$		0			0
$507$	144.149	+	724.685i	0.284317	+	1.42936i
$508$		0			0
$509$		−	650.195i		−	1.27740i	−0.769457	−	0.638698i	$-0.779473\pi$
$509$		−	650.195i		−	1.27740i	0.769457	−	0.638698i	$-0.220527\pi$
$510$		0			0
$511$	129.814			0.254039
$512$		0			0
$513$	36.1018	−	7.18109i	0.0703738	−	0.0139982i
$514$		0			0
$515$	374.098	−	559.877i	0.726404	−	1.08714i
$516$		0			0
$517$	−450.165	−	673.719i	−0.870725	−	1.30313i
$518$		0			0
$519$	−958.411	+	396.987i	−1.84665	+	0.764907i
$520$		0			0
$521$	−49.5833	+	249.272i	−0.0951695	+	0.478449i	0.903578	+	0.428423i	$0.140931\pi$
$521$	−49.5833	+	249.272i	−0.0951695	+	0.478449i	−0.998748	+	0.0500266i	$0.984069\pi$
$522$		0			0
$523$	−530.317	+	530.317i	−1.01399	+	1.01399i	−0.0140891	+	0.999901i	$0.504485\pi$
$523$	−530.317	+	530.317i	−1.01399	+	1.01399i	−0.999901	+	0.0140891i	$0.995515\pi$
$524$		0			0
$525$	54.9506	−	132.662i	0.104668	−	0.252690i
$526$		0			0
$527$	−16.9977	−	458.600i	−0.0322537	−	0.870209i
$528$		0			0
$529$	−413.463	−	171.262i	−0.781593	−	0.323746i
$530$		0			0
$531$	−152.905	−	152.905i	−0.287957	−	0.287957i
$532$		0			0
$533$	−924.970	−	183.988i	−1.73540	−	0.345193i
$534$		0			0
$535$	−191.576	−	462.505i	−0.358086	−	0.864496i
$536$		0			0
$537$	−334.029	+	223.191i	−0.622028	+	0.415626i
$538$		0			0
$539$	356.935	+	238.496i	0.662217	+	0.442479i
$540$		0			0
$541$	150.615	+	757.193i	0.278401	+	1.39962i	0.826374	+	0.563122i	$0.190400\pi$
$541$	150.615	+	757.193i	0.278401	+	1.39962i	−0.547973	+	0.836496i	$0.684600\pi$
$542$		0			0
$543$			1285.20i			2.36685i
$544$		0			0
$545$	500.454			0.918264
$546$		0			0
$547$	757.244	−	150.625i	1.38436	−	0.275366i	0.553964	−	0.832541i	$-0.313115\pi$
$547$	757.244	−	150.625i	1.38436	−	0.275366i	0.830395	+	0.557175i	$0.188115\pi$
$548$		0			0
$549$	135.816	−	203.263i	0.247388	−	0.370242i
$550$		0			0
$551$	35.4278	+	53.0215i	0.0642973	+	0.0962278i
$552$		0			0
$553$	496.049	−	205.470i	0.897014	−	0.371555i
$554$		0			0
$555$	33.5598	−	168.716i	0.0604680	−	0.303993i
$556$		0			0
$557$	410.913	−	410.913i	0.737725	−	0.737725i	−0.234412	−	0.972137i	$-0.575316\pi$
$557$	410.913	−	410.913i	0.737725	−	0.737725i	0.972137	+	0.234412i	$0.0753164\pi$
$558$		0			0
$559$	467.992	−	1129.83i	0.837194	−	2.02117i
$560$		0			0
$561$	228.814	−	1424.18i	0.407869	−	2.53865i
$562$		0			0
$563$	96.6264	+	40.0240i	0.171628	+	0.0710905i	0.466843	−	0.884340i	$-0.345391\pi$
$563$	96.6264	+	40.0240i	0.171628	+	0.0710905i	−0.295215	+	0.955431i	$0.595391\pi$
$564$		0			0
$565$	475.258	+	475.258i	0.841165	+	0.841165i
$566$		0			0
$567$	−509.211	−	101.288i	−0.898080	−	0.178639i
$568$		0			0
$569$	110.987	+	267.946i	0.195056	+	0.470906i	0.990901	−	0.134594i	$-0.0429730\pi$
$569$	110.987	+	267.946i	0.195056	+	0.470906i	−0.795845	+	0.605500i	$0.792973\pi$
$570$		0			0
$571$	−243.853	+	162.937i	−0.427062	+	0.285354i	−0.750468	−	0.660906i	$-0.770172\pi$
$571$	−243.853	+	162.937i	−0.427062	+	0.285354i	0.323406	+	0.946260i	$0.395172\pi$
$572$		0			0
$573$	371.667	+	248.340i	0.648634	+	0.433403i
$574$		0			0
$575$	−11.8632	−	59.6402i	−0.0206316	−	0.103722i
$576$		0			0
$577$			154.738i			0.268176i	0.990969	+	0.134088i	$0.0428105\pi$
$577$			154.738i			0.268176i	−0.990969	+	0.134088i	$0.957190\pi$
$578$		0			0
$579$	−1171.62			−2.02352
$580$		0			0
$581$	−597.373	+	118.825i	−1.02818	+	0.204518i
$582$		0			0
$583$	663.041	−	992.310i	1.13729	−	1.70208i
$584$		0			0
$585$	299.313	+	447.954i	0.511646	+	0.765733i
$586$		0			0
$587$	48.6051	−	20.1329i	0.0828026	−	0.0342980i	−0.340898	−	0.940100i	$-0.610731\pi$
$587$	48.6051	−	20.1329i	0.0828026	−	0.0342980i	0.423700	+	0.905802i	$0.360731\pi$
$588$		0			0
$589$	21.1490	−	106.323i	0.0359066	−	0.180514i
$590$		0			0
$591$	474.350	−	474.350i	0.802622	−	0.802622i
$592$		0			0
$593$	−202.855	+	489.736i	−0.342083	+	0.825861i	0.655422	+	0.755263i	$0.272491\pi$
$593$	−202.855	+	489.736i	−0.342083	+	0.825861i	−0.997505	+	0.0705983i	$0.977509\pi$
$594$		0			0
$595$	386.029	+	62.0208i	0.648788	+	0.104237i
$596$		0			0
$597$	506.867	+	209.951i	0.849024	+	0.351677i
$598$		0			0
$599$	365.345	+	365.345i	0.609924	+	0.609924i	0.942926	−	0.333002i	$-0.108061\pi$
$599$	365.345	+	365.345i	0.609924	+	0.609924i	−0.333002	+	0.942926i	$0.608061\pi$
$600$		0			0
$601$	−82.7052	−	16.4511i	−0.137613	−	0.0273729i	0.125803	−	0.992055i	$-0.459849\pi$
$601$	−82.7052	−	16.4511i	−0.137613	−	0.0273729i	−0.263416	+	0.964682i	$0.584849\pi$
$602$		0			0
$603$	−158.569	−	382.820i	−0.262967	−	0.634859i
$604$		0			0
$605$	−1200.97	+	802.462i	−1.98507	+	1.32638i
$606$		0			0
$607$	−275.083	−	183.805i	−0.453185	−	0.302809i	0.307949	−	0.951403i	$-0.400357\pi$
$607$	−275.083	−	183.805i	−0.453185	−	0.302809i	−0.761134	+	0.648594i	$0.775357\pi$
$608$		0			0
$609$	−66.0299	−	331.955i	−0.108423	−	0.545082i
$610$		0			0
$611$		−	713.166i		−	1.16721i
$612$		0			0
$613$	−900.466			−1.46895			−0.734475	−	0.678636i	$-0.762571\pi$
$613$	−900.466			−1.46895			−0.734475	+	0.678636i	$0.762571\pi$
$614$		0			0
$615$	−830.246	+	165.146i	−1.34999	+	0.268531i
$616$		0			0
$617$	−304.949	+	456.388i	−0.494244	+	0.739688i	−0.991808	−	0.127739i	$-0.959228\pi$
$617$	−304.949	+	456.388i	−0.494244	+	0.739688i	0.497564	+	0.867427i	$0.334228\pi$
$618$		0			0
$619$	−142.532	−	213.314i	−0.230261	−	0.344611i	0.698290	−	0.715815i	$-0.253945\pi$
$619$	−142.532	−	213.314i	−0.230261	−	0.344611i	−0.928551	+	0.371205i	$0.878945\pi$
$620$		0			0
$621$	−76.4367	+	31.6611i	−0.123086	+	0.0509841i
$622$		0			0
$623$	−107.096	+	538.406i	−0.171903	+	0.864216i
$624$		0			0
$625$	290.755	−	290.755i	0.465208	−	0.465208i
$626$		0			0
$627$	130.395	−	314.801i	0.207966	−	0.502075i
$628$		0			0
$629$	−172.662	+	6.39959i	−0.274502	+	0.0101742i
$630$		0			0
$631$	257.269	+	106.564i	0.407717	+	0.168882i	0.577110	−	0.816667i	$-0.304181\pi$
$631$	257.269	+	106.564i	0.407717	+	0.168882i	−0.169393	+	0.985549i	$0.554181\pi$
$632$		0			0
$633$	−452.869	−	452.869i	−0.715434	−	0.715434i
$634$		0			0
$635$	−58.2365	−	11.5840i	−0.0917111	−	0.0182425i
$636$		0			0
$637$	144.591	+	349.073i	0.226987	+	0.547995i
$638$		0			0
$639$	599.586	−	400.630i	0.938319	−	0.626965i
$640$		0			0
$641$	147.436	+	98.5133i	0.230009	+	0.153687i	0.665235	−	0.746634i	$-0.268332\pi$
$641$	147.436	+	98.5133i	0.230009	+	0.153687i	−0.435226	+	0.900321i	$0.643332\pi$
$642$		0			0
$643$	−168.591	−	847.563i	−0.262194	−	1.31814i	−0.857436	−	0.514591i	$-0.827944\pi$
$643$	−168.591	−	847.563i	−0.262194	−	1.31814i	0.595242	−	0.803547i	$-0.297056\pi$
$644$		0			0
$645$		−	1097.69i		−	1.70184i
$646$		0			0
$647$	790.391			1.22162			0.610812	−	0.791776i	$-0.290843\pi$
$647$	790.391			1.22162			0.610812	+	0.791776i	$0.290843\pi$
$648$		0			0
$649$	679.625	−	135.186i	1.04719	−	0.208299i
$650$		0			0
$651$	−319.662	+	478.409i	−0.491033	+	0.734883i
$652$		0			0
$653$	324.288	+	485.331i	0.496612	+	0.743232i	0.992109	−	0.125377i	$-0.0400141\pi$
$653$	324.288	+	485.331i	0.496612	+	0.743232i	−0.495497	+	0.868610i	$0.665014\pi$
$654$		0			0
$655$	754.608	−	312.569i	1.15207	−	0.477205i
$656$		0			0
$657$	31.4616	−	158.168i	0.0478867	−	0.240743i
$658$		0			0
$659$	−403.947	+	403.947i	−0.612969	+	0.612969i	−0.943719	−	0.330750i	$-0.892698\pi$
$659$	−403.947	+	403.947i	−0.612969	+	0.612969i	0.330750	+	0.943719i	$0.392698\pi$
$660$		0			0
$661$	121.197	−	292.595i	0.183354	−	0.442655i	−0.805300	−	0.592867i	$-0.797996\pi$
$661$	121.197	−	292.595i	0.183354	−	0.442655i	0.988654	+	0.150213i	$0.0479958\pi$
$662$		0			0
$663$	863.857	−	930.359i	1.30295	−	1.40326i
$664$		0			0
$665$	85.3277	+	35.3439i	0.128312	+	0.0531487i
$666$		0			0
$667$	−101.350	−	101.350i	−0.151949	−	0.151949i
$668$		0			0
$669$	−327.859	−	65.2152i	−0.490073	−	0.0974816i
$670$		0			0
$671$	299.784	+	723.744i	0.446773	+	1.07860i
$672$		0			0
$673$	−1099.83	+	734.881i	−1.63422	+	1.09195i	−0.714293	+	0.699846i	$0.753252\pi$
$673$	−1099.83	+	734.881i	−1.63422	+	1.09195i	−0.919922	+	0.392101i	$0.871748\pi$
$674$		0			0
$675$	51.3446	+	34.3073i	0.0760660	+	0.0508257i
$676$		0			0
$677$	−99.8384	−	501.921i	−0.147472	−	0.741391i	−0.981769	−	0.190076i	$-0.939126\pi$
$677$	−99.8384	−	501.921i	−0.147472	−	0.741391i	0.834298	−	0.551314i	$-0.185874\pi$
$678$		0			0
$679$		−	489.587i		−	0.721041i
$680$		0			0
$681$	−230.445			−0.338392
$682$		0			0
$683$	109.775	−	21.8355i	0.160724	−	0.0319700i	−0.114072	−	0.993472i	$-0.536390\pi$
$683$	109.775	−	21.8355i	0.160724	−	0.0319700i	0.274796	+	0.961502i	$0.411390\pi$
$684$		0			0
$685$	−275.575	+	412.427i	−0.402299	+	0.602084i
$686$		0			0
$687$	−251.518	−	376.424i	−0.366111	−	0.547924i
$688$		0			0
$689$	970.453	−	401.975i	1.40850	−	0.583418i
$690$		0			0
$691$	3.66989	−	18.4498i	0.00531099	−	0.0267001i	−0.978039	−	0.208422i	$-0.933167\pi$
$691$	3.66989	−	18.4498i	0.00531099	−	0.0267001i	0.983350	+	0.181722i	$0.0581672\pi$
$692$		0			0
$693$	−545.061	+	545.061i	−0.786524	+	0.786524i
$694$		0			0
$695$	−34.3041	+	82.8175i	−0.0493585	+	0.119162i
$696$		0			0
$697$	354.247	+	772.934i	0.508245	+	1.10894i
$698$		0			0
$699$	831.211	+	344.299i	1.18914	+	0.492559i
$700$		0			0
$701$	175.249	+	175.249i	0.249998	+	0.249998i	0.820970	−	0.570972i	$-0.193433\pi$
$701$	175.249	+	175.249i	0.249998	+	0.249998i	−0.570972	+	0.820970i	$0.693433\pi$
$702$		0			0
$703$	−40.0304	−	7.96253i	−0.0569422	−	0.0113265i
$704$		0			0
$705$	−244.968	−	591.406i	−0.347473	−	0.838874i
$706$		0			0
$707$	−337.005	+	225.180i	−0.476670	+	0.318500i
$708$		0			0
$709$	946.982	+	632.753i	1.33566	+	0.892459i	0.998794	−	0.0490944i	$-0.0156335\pi$
$709$	946.982	+	632.753i	1.33566	+	0.892459i	0.336865	+	0.941553i	$0.390634\pi$
$710$		0			0
$711$	−130.127	−	654.194i	−0.183020	−	0.920105i
$712$		0			0
$713$			243.661i			0.341740i
$714$		0			0
$715$	−1726.41			−2.41456
$716$		0			0
$717$	−351.593	+	69.9362i	−0.490367	+	0.0975400i
$718$		0			0
$719$	−535.039	+	800.742i	−0.744143	+	1.11369i	0.245396	+	0.969423i	$0.421082\pi$
$719$	−535.039	+	800.742i	−0.744143	+	1.11369i	−0.989539	+	0.144265i	$0.953918\pi$
$720$		0			0
$721$	471.104	+	705.057i	0.653404	+	0.977888i
$722$		0			0
$723$	557.868	−	231.076i	0.771601	−	0.319608i
$724$		0			0
$725$	−20.8706	+	104.924i	−0.0287870	+	0.144722i
$726$		0			0
$727$	455.675	−	455.675i	0.626788	−	0.626788i	−0.320470	−	0.947259i	$-0.603841\pi$
$727$	455.675	−	455.675i	0.626788	−	0.626788i	0.947259	+	0.320470i	$0.103841\pi$
$728$		0			0
$729$	−121.793	+	294.035i	−0.167069	+	0.403340i
$730$		0			0
$731$	−1072.63	+	254.996i	−1.46735	+	0.348832i
$732$		0			0
$733$	−1151.43	−	476.938i	−1.57085	−	0.650665i	−0.583915	−	0.811815i	$-0.698480\pi$
$733$	−1151.43	−	476.938i	−1.57085	−	0.650665i	−0.986930	+	0.161149i	$0.948480\pi$
$734$		0			0
$735$	239.809	+	239.809i	0.326271	+	0.326271i
$736$		0			0
$737$	1302.30	+	259.043i	1.76703	+	0.351484i
$738$		0			0
$739$	324.856	+	784.273i	0.439589	+	1.06126i	0.976091	+	0.217363i	$0.0697456\pi$
$739$	324.856	+	784.273i	0.439589	+	1.06126i	−0.536502	+	0.843899i	$0.680254\pi$
$740$		0			0
$741$	249.359	−	166.616i	0.336517	−	0.224853i
$742$		0			0
$743$	83.7999	+	55.9933i	0.112786	+	0.0753611i	0.610684	−	0.791874i	$-0.290895\pi$
$743$	83.7999	+	55.9933i	0.112786	+	0.0753611i	−0.497898	+	0.867236i	$0.665895\pi$
$744$		0			0
$745$	−208.260	−	1046.99i	−0.279543	−	1.40536i
$746$		0			0
$747$			756.650i			1.01292i
$748$		0			0
$749$	630.424			0.841688
$750$		0			0
$751$	27.3313	−	5.43653i	0.0363932	−	0.00723905i	−0.176860	−	0.984236i	$-0.556594\pi$
$751$	27.3313	−	5.43653i	0.0363932	−	0.00723905i	0.213253	+	0.976997i	$0.431594\pi$
$752$		0			0
$753$	−823.589	+	1232.59i	−1.09374	+	1.63690i
$754$		0			0
$755$	185.808	+	278.082i	0.246104	+	0.368320i
$756$		0			0
$757$	−366.940	+	151.991i	−0.484729	+	0.200781i	−0.611645	−	0.791132i	$-0.709492\pi$
$757$	−366.940	+	151.991i	−0.484729	+	0.200781i	0.126917	+	0.991913i	$0.459492\pi$
$758$		0			0
$759$	−149.413	+	751.150i	−0.196855	+	0.989657i
$760$		0			0
$761$	−215.620	+	215.620i	−0.283337	+	0.283337i	−0.834438	−	0.551101i	$-0.814208\pi$
$761$	−215.620	+	215.620i	−0.283337	+	0.283337i	0.551101	+	0.834438i	$0.314208\pi$
$762$		0			0
$763$	−241.177	+	582.252i	−0.316090	+	0.763109i
$764$		0			0
$765$	169.125	−	455.315i	0.221079	−	0.595183i
$766$		0			0
$767$	563.467	+	233.396i	0.734638	+	0.304297i
$768$		0			0
$769$	−370.377	−	370.377i	−0.481634	−	0.481634i	0.424019	−	0.905653i	$-0.360619\pi$
$769$	−370.377	−	370.377i	−0.481634	−	0.481634i	−0.905653	+	0.424019i	$0.860619\pi$
$770$		0			0
$771$	233.064	+	46.3593i	0.302288	+	0.0601288i
$772$		0			0
$773$	247.049	+	596.430i	0.319598	+	0.771578i	0.999275	+	0.0380665i	$0.0121199\pi$
$773$	247.049	+	596.430i	0.319598	+	0.771578i	−0.679677	+	0.733511i	$0.737880\pi$
$774$		0			0
$775$	151.214	−	101.038i	0.195115	−	0.130372i
$776$		0			0
$777$	180.120	+	120.352i	0.231814	+	0.154893i
$778$		0			0
$779$	39.1833	+	196.988i	0.0502995	+	0.252873i
$780$		0			0
$781$			2310.80i			2.95877i
$782$		0			0
$783$	145.553			0.185891
$784$		0			0
$785$	−857.416	+	170.551i	−1.09225	+	0.217262i
$786$		0			0
$787$	−358.757	+	536.918i	−0.455854	+	0.682234i	−0.986202	−	0.165546i	$-0.947061\pi$
$787$	−358.757	+	536.918i	−0.455854	+	0.682234i	0.530348	+	0.847780i	$0.322061\pi$
$788$		0			0
$789$	−79.0735	−	118.342i	−0.100220	−	0.149990i
$790$		0			0
$791$	−781.973	+	323.904i	−0.988587	+	0.409486i
$792$		0			0
$793$	−134.513	+	676.241i	−0.169625	+	0.852763i
$794$		0			0
$795$	666.690	−	666.690i	0.838604	−	0.838604i
$796$		0			0
$797$	581.239	−	1403.24i	0.729284	−	1.76065i	0.0843132	−	0.996439i	$-0.473130\pi$
$797$	581.239	−	1403.24i	0.729284	−	1.76065i	0.644971	−	0.764207i	$-0.276870\pi$
$798$		0			0
$799$	−521.001	+	376.763i	−0.652067	+	0.471544i
$800$		0			0
$801$	630.051	+	260.976i	0.786580	+	0.325812i
$802$		0			0
$803$	365.416	+	365.416i	0.455063	+	0.455063i
$804$		0			0
$805$	−203.601	−	40.4988i	−0.252921	−	0.0503091i
$806$		0			0
$807$	−545.451	−	1316.84i	−0.675900	−	1.63177i
$808$		0			0
$809$	327.870	−	219.076i	0.405279	−	0.270799i	−0.336179	−	0.941798i	$-0.609135\pi$
$809$	327.870	−	219.076i	0.405279	−	0.270799i	0.741458	+	0.671000i	$0.234135\pi$
$810$		0			0
$811$	−248.713	−	166.185i	−0.306674	−	0.204913i	0.392704	−	0.919665i	$-0.371540\pi$
$811$	−248.713	−	166.185i	−0.306674	−	0.204913i	−0.699378	+	0.714752i	$0.746540\pi$
$812$		0			0
$813$	−229.294	−	1152.74i	−0.282034	−	1.41788i
$814$		0			0
$815$			193.412i			0.237316i
$816$		0			0
$817$	−260.442			−0.318778
$818$		0			0
$819$	−665.414	+	132.359i	−0.812472	+	0.161611i
$820$		0			0
$821$	−392.139	+	586.877i	−0.477635	+	0.714832i	−0.989548	−	0.144206i	$-0.953937\pi$
$821$	−392.139	+	586.877i	−0.477635	+	0.714832i	0.511912	+	0.859038i	$0.328937\pi$
$822$		0			0
$823$	292.200	+	437.308i	0.355042	+	0.531358i	0.965402	−	0.260766i	$-0.0839751\pi$
$823$	292.200	+	437.308i	0.355042	+	0.531358i	−0.610360	+	0.792124i	$0.708975\pi$
$824$		0			0
$825$	528.116	−	218.753i	0.640141	−	0.265155i
$826$		0			0
$827$	100.384	−	504.665i	0.121384	−	0.610236i	−0.871426	−	0.490528i	$-0.836804\pi$
$827$	100.384	−	504.665i	0.121384	−	0.610236i	0.992809	−	0.119708i	$-0.0381960\pi$
$828$		0			0
$829$	190.285	−	190.285i	0.229536	−	0.229536i	−0.582963	−	0.812499i	$-0.698107\pi$
$829$	190.285	−	190.285i	0.229536	−	0.229536i	0.812499	+	0.582963i	$0.198107\pi$
$830$		0			0
$831$	273.153	−	659.450i	0.328704	−	0.793562i
$832$		0			0
$833$	178.627	−	290.045i	0.214439	−	0.348193i
$834$		0			0
$835$	681.297	+	282.203i	0.815925	+	0.337967i
$836$		0			0
$837$	−174.966	−	174.966i	−0.209039	−	0.209039i
$838$		0			0
$839$	33.5177	+	6.66709i	0.0399496	+	0.00794647i	0.215025	−	0.976609i	$-0.431017\pi$
$839$	33.5177	+	6.66709i	0.0399496	+	0.00794647i	−0.175075	+	0.984555i	$0.556017\pi$
$840$		0			0
$841$	−225.340	−	544.020i	−0.267943	−	0.646872i
$842$		0			0
$843$	−304.045	+	203.157i	−0.360671	+	0.240992i
$844$		0			0
$845$	−662.914	−	442.945i	−0.784514	−	0.524196i
$846$		0			0
$847$	−354.857	−	1783.99i	−0.418957	−	2.10624i
$848$		0			0
$849$		−	143.014i		−	0.168450i
$850$		0			0
$851$	91.7377			0.107800
$852$		0			0
$853$	480.247	−	95.5271i	0.563010	−	0.111990i	0.0946230	−	0.995513i	$-0.469835\pi$
$853$	480.247	−	95.5271i	0.563010	−	0.111990i	0.468387	+	0.883524i	$0.344835\pi$
$854$		0			0
$855$	63.7437	−	95.3993i	0.0745541	−	0.111578i
$856$		0			0
$857$	−267.768	−	400.744i	−0.312449	−	0.467612i	0.641696	−	0.766959i	$-0.278231\pi$
$857$	−267.768	−	400.744i	−0.312449	−	0.467612i	−0.954144	+	0.299347i	$0.903231\pi$
$858$		0			0
$859$	1526.20	−	632.171i	1.77671	−	0.735938i	0.783260	−	0.621694i	$-0.213555\pi$
$859$	1526.20	−	632.171i	1.77671	−	0.735938i	0.993453	−	0.114244i	$-0.0364446\pi$
$860$		0			0
$861$	207.970	−	1045.54i	0.241545	−	1.21433i
$862$		0			0
$863$	−569.302	+	569.302i	−0.659678	+	0.659678i	−0.955304	−	0.295626i	$-0.904472\pi$
$863$	−569.302	+	569.302i	−0.659678	+	0.659678i	0.295626	+	0.955304i	$0.404472\pi$
$864$		0			0
$865$	428.363	−	1034.16i	0.495217	−	1.19556i
$866$		0			0
$867$	−1136.04	−	139.583i	−1.31032	−	0.160995i
$868$		0			0
$869$	1974.72	+	817.957i	2.27241	+	0.941262i
$870$		0			0
$871$	826.381	+	826.381i	0.948772	+	0.948772i
$872$		0			0
$873$	−596.523	−	118.656i	−0.683302	−	0.135917i
$874$		0			0
$875$	279.325	+	674.350i	0.319229	+	0.770686i
$876$		0			0
$877$	971.662	−	649.244i	1.10794	−	0.740301i	0.139666	−	0.990199i	$-0.455397\pi$
$877$	971.662	−	649.244i	1.10794	−	0.740301i	0.968272	+	0.249898i	$0.0803971\pi$
$878$		0			0
$879$	−443.640	−	296.431i	−0.504710	−	0.337237i
$880$		0			0
$881$	83.8159	+	421.371i	0.0951372	+	0.478287i	0.998752	+	0.0499414i	$0.0159035\pi$
$881$	83.8159	+	421.371i	0.0951372	+	0.478287i	−0.903615	+	0.428346i	$0.859097\pi$
$882$		0			0
$883$		−	1224.35i		−	1.38658i	−0.720657	−	0.693291i	$-0.756160\pi$
$883$		−	1224.35i		−	1.38658i	0.720657	−	0.693291i	$-0.243840\pi$
$884$		0			0
$885$	547.435			0.618571
$886$		0			0
$887$	987.477	−	196.421i	1.11328	−	0.221445i	0.396013	−	0.918245i	$-0.370394\pi$
$887$	987.477	−	196.421i	1.11328	−	0.221445i	0.717265	+	0.696800i	$0.245394\pi$
$888$		0			0
$889$	41.5424	−	62.1727i	0.0467294	−	0.0699355i
$890$		0			0
$891$	−1148.27	−	1718.51i	−1.28875	−	1.92874i
$892$		0			0
$893$	−140.319	+	58.1222i	−0.157133	+	0.0650865i
$894$		0			0
$895$	84.5686	−	425.155i	0.0944900	−	0.475034i
$896$		0			0
$897$	−476.646	+	476.646i	−0.531378	+	0.531378i
$898$		0			0
$899$	164.043	−	396.036i	0.182473	−	0.440529i
$900$		0			0
$901$	−806.349	−	496.600i	−0.894949	−	0.551165i
$902$		0			0
$903$	1277.10	+	528.992i	1.41429	+	0.585816i
$904$		0			0
$905$	−980.599	−	980.599i	−1.08353	−	1.08353i
$906$		0			0
$907$	−690.956	−	137.440i	−0.761803	−	0.151532i	−0.201125	−	0.979566i	$-0.564460\pi$
$907$	−690.956	−	137.440i	−0.761803	−	0.151532i	−0.560679	+	0.828034i	$0.689460\pi$
$908$		0			0
$909$	192.688	+	465.189i	0.211978	+	0.511759i
$910$		0			0
$911$	21.3997	−	14.2988i	0.0234903	−	0.0156957i	−0.543770	−	0.839235i	$-0.683003\pi$
$911$	21.3997	−	14.2988i	0.0234903	−	0.0156957i	0.567260	+	0.823539i	$0.308003\pi$
$912$		0			0
$913$	−2016.04	−	1347.08i	−2.20815	−	1.47544i
$914$		0			0
$915$	120.738	+	606.989i	0.131954	+	0.663376i
$916$		0			0
$917$			1028.58i			1.12168i
$918$		0			0
$919$	−567.119			−0.617105			−0.308552	−	0.951207i	$-0.599844\pi$
$919$	−567.119			−0.617105			−0.308552	+	0.951207i	$0.599844\pi$
$920$		0			0
$921$	−185.899	+	36.9775i	−0.201844	+	0.0401493i
$922$		0			0
$923$	−1129.95	+	1691.09i	−1.22422	+	1.83217i
$924$		0			0
$925$	−38.0407	−	56.9319i	−0.0411250	−	0.0615480i
$926$		0			0
$927$	973.234	−	403.127i	1.04987	−	0.434872i
$928$		0			0
$929$	−32.1967	+	161.864i	−0.0346574	+	0.174234i	−0.994237	−	0.107202i	$-0.965811\pi$
$929$	−32.1967	+	161.864i	−0.0346574	+	0.174234i	0.959580	+	0.281436i	$0.0908108\pi$
$930$		0			0
$931$	56.8981	−	56.8981i	0.0611151	−	0.0611151i
$932$		0			0
$933$	−141.607	+	341.869i	−0.151776	+	0.366419i
$934$		0			0
$935$	912.058	+	1261.23i	0.975463	+	1.34890i
$936$		0			0
$937$	1150.85	+	476.696i	1.22822	+	0.508747i	0.900016	−	0.435858i	$-0.143555\pi$
$937$	1150.85	+	476.696i	1.22822	+	0.508747i	0.328209	+	0.944605i	$0.393555\pi$
$938$		0			0
$939$	−697.743	−	697.743i	−0.743071	−	0.743071i
$940$		0			0
$941$	−1103.65	−	219.530i	−1.17285	−	0.233295i	−0.430049	−	0.902805i	$-0.641504\pi$
$941$	−1103.65	−	219.530i	−1.17285	−	0.233295i	−0.742803	+	0.669511i	$0.766504\pi$
$942$		0			0
$943$	−172.758	−	417.074i	−0.183200	−	0.442284i
$944$		0			0
$945$	175.281	−	117.119i	0.185483	−	0.123936i
$946$		0			0
$947$	992.051	+	662.867i	1.04757	+	0.699965i	0.955261	−	0.295765i	$-0.0955745\pi$
$947$	992.051	+	662.867i	1.04757	+	0.699965i	0.0923114	+	0.995730i	$0.470574\pi$
$948$		0			0
$949$	88.7352	+	446.102i	0.0935040	+	0.470076i
$950$		0			0
$951$			2307.04i			2.42591i
$952$		0			0
$953$	−386.315			−0.405367			−0.202684	−	0.979244i	$-0.564966\pi$
$953$	−386.315			−0.405367			−0.202684	+	0.979244i	$0.564966\pi$
$954$		0			0
$955$	−473.062	+	94.0978i	−0.495352	+	0.0985317i
$956$		0			0
$957$	748.558	−	1120.30i	0.782192	−	1.17063i
$958$		0			0
$959$	−347.034	−	519.372i	−0.361870	−	0.541577i
$960$		0			0
$961$	214.589	−	88.8857i	0.223298	−	0.0924930i
$962$		0			0
$963$	152.789	−	768.123i	0.158660	−	0.797636i
$964$		0			0
$965$	893.935	−	893.935i	0.926357	−	0.926357i
$966$		0			0
$967$	36.2641	−	87.5493i	0.0375016	−	0.0905370i	−0.904019	−	0.427492i	$-0.859397\pi$
$967$	36.2641	−	87.5493i	0.0375016	−	0.0905370i	0.941521	+	0.336955i	$0.109397\pi$
$968$		0			0
$969$	−253.457	−	94.1457i	−0.261565	−	0.0971575i
$970$		0			0
$971$	−1595.61	−	660.923i	−1.64326	−	0.680662i	−0.646642	−	0.762794i	$-0.723827\pi$
$971$	−1595.61	−	660.923i	−1.64326	−	0.680662i	−0.996622	+	0.0821315i	$0.973827\pi$
$972$		0			0
$973$	−79.8221	−	79.8221i	−0.0820371	−	0.0820371i
$974$		0			0
$975$	493.454	+	98.1540i	0.506106	+	0.100671i
$976$		0			0
$977$	255.580	+	617.025i	0.261597	+	0.631551i	0.999038	−	0.0438610i	$-0.0139659\pi$
$977$	255.580	+	617.025i	0.261597	+	0.631551i	−0.737441	+	0.675412i	$0.763966\pi$
$978$		0			0
$979$	−1817.04	+	1214.11i	−1.85602	+	1.24015i
$980$		0			0
$981$	650.977	+	434.969i	0.663585	+	0.443393i
$982$		0			0
$983$	56.5973	+	284.534i	0.0575761	+	0.289455i	0.998836	−	0.0482272i	$-0.0153572\pi$
$983$	56.5973	+	284.534i	0.0575761	+	0.289455i	−0.941260	+	0.337682i	$0.890357\pi$
$984$		0			0
$985$			723.851i			0.734874i
$986$		0			0
$987$	806.124			0.816742
$988$		0			0
$989$	574.138	−	114.203i	0.580524	−	0.115473i
$990$		0			0
$991$	619.705	−	927.454i	0.625333	−	0.935876i	−0.374629	−	0.927175i	$-0.622230\pi$
$991$	619.705	−	927.454i	0.625333	−	0.935876i	0.999962	−	0.00870184i	$-0.00276992\pi$
$992$		0			0
$993$	−575.819	−	861.774i	−0.579878	−	0.867849i
$994$		0			0
$995$	−546.928	+	226.545i	−0.549676	+	0.227683i
$996$		0			0
$997$	274.097	−	1377.98i	0.274922	−	1.38213i	−0.558507	−	0.829500i	$-0.688626\pi$
$997$	274.097	−	1377.98i	0.274922	−	1.38213i	0.833429	−	0.552626i	$-0.186374\pi$
$998$		0			0
$999$	−65.8742	+	65.8742i	−0.0659401	+	0.0659401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.b.57.1	✓	40
4.3	odd	2		272.3.bh.g.193.5		40
17.3	odd	16	inner	136.3.t.b.105.1	yes	40
68.3	even	16		272.3.bh.g.241.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.b.57.1	✓	40	1.1	even	1	trivial
136.3.t.b.105.1	yes	40	17.3	odd	16	inner
272.3.bh.g.193.5		40	4.3	odd	2
272.3.bh.g.241.5		40	68.3	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.88441 + 0.772657i) q^{3} +(2.37425 - 3.55331i) q^{5} +(2.98990 + 4.47471i) q^{7} +(6.17671 - 2.55848i) q^{9} +O(q^{10})\)	\(q+(-3.88441 + 0.772657i) q^{3} +(2.37425 - 3.55331i) q^{5} +(2.98990 + 4.47471i) q^{7} +(6.17671 - 2.55848i) q^{9} +(-4.17961 + 21.0123i) q^{11} +(-13.3335 + 13.3335i) q^{13} +(-6.47705 + 15.6370i) q^{15} +(16.7847 + 2.69670i) q^{17} +(3.71010 + 1.53677i) q^{19} +(-15.0714 - 15.0714i) q^{21} +(-8.85270 - 1.76091i) q^{23} +(2.57812 + 6.22413i) q^{25} +(7.62133 - 5.09241i) q^{27} +(13.2033 + 8.82216i) q^{29} +(-5.26646 - 26.4763i) q^{31} -84.8498i q^{33} +22.9988 q^{35} +(-9.96827 + 1.98281i) q^{37} +(41.4904 - 62.0948i) q^{39} +(27.7865 + 41.5855i) q^{41} +(-59.9178 + 24.8188i) q^{43} +(5.57397 - 28.0222i) q^{45} +(-26.7435 + 26.7435i) q^{47} +(7.66801 - 18.5122i) q^{49} +(-67.2824 + 2.49378i) q^{51} +(-51.4656 - 21.3177i) q^{53} +(64.7398 + 64.7398i) q^{55} +(-15.5989 - 3.10282i) q^{57} +(-12.3776 - 29.8821i) q^{59} +(30.4030 - 20.3146i) q^{61} +(29.9162 + 19.9894i) q^{63} +(15.7210 + 79.0348i) q^{65} -61.9779i q^{67} +35.7481 q^{69} +(105.788 - 21.0426i) q^{71} +(13.4011 - 20.0562i) q^{73} +(-14.8236 - 22.1851i) q^{75} +(-106.521 + 44.1223i) q^{77} +(19.4638 - 97.8509i) q^{79} +(-68.2167 + 68.2167i) q^{81} +(-43.3105 + 104.561i) q^{83} +(49.4333 - 53.2388i) q^{85} +(-58.1035 - 24.0672i) q^{87} +(72.1279 + 72.1279i) q^{89} +(-99.5291 - 19.7976i) q^{91} +(40.9142 + 98.7756i) q^{93} +(14.2693 - 9.53445i) q^{95} +(-75.6411 - 50.5417i) q^{97} +(27.9433 + 140.480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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