LMFDB - Embedded newform 136.3.t.a.41.1

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:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	136.41
Dual form			136.3.t.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15859 + 3.23056i) q^{3} +(-1.60027 - 8.04508i) q^{5} +(0.739073 - 3.71557i) q^{7} +(-2.33284 - 5.63197i) q^{9} +O(q^{10})$	\(q+(-2.15859 + 3.23056i) q^{3} +(-1.60027 - 8.04508i) q^{5} +(0.739073 - 3.71557i) q^{7} +(-2.33284 - 5.63197i) q^{9} +(-0.0729240 + 0.0487263i) q^{11} +(15.0409 - 15.0409i) q^{13} +(29.4444 + 12.1963i) q^{15} +(-14.6619 - 8.60395i) q^{17} +(10.6813 - 25.7869i) q^{19} +(10.4080 + 10.4080i) q^{21} +(12.9453 + 19.3739i) q^{23} +(-39.0654 + 16.1814i) q^{25} +(-11.0663 - 2.20122i) q^{27} +(-22.6794 + 4.51121i) q^{29} +(-31.5440 - 21.0770i) q^{31} -0.340765i q^{33} -31.0748 q^{35} +(18.9394 - 28.3448i) q^{37} +(16.1233 + 81.0575i) q^{39} +(-3.65376 + 18.3687i) q^{41} +(13.4093 + 32.3729i) q^{43} +(-41.5765 + 27.7805i) q^{45} +(-8.80943 + 8.80943i) q^{47} +(32.0108 + 13.2593i) q^{49} +(59.4446 - 28.7938i) q^{51} +(20.8866 - 50.4248i) q^{53} +(0.508704 + 0.508704i) q^{55} +(60.2495 + 90.1697i) q^{57} +(-46.3811 + 19.2117i) q^{59} +(103.351 + 20.5577i) q^{61} +(-22.6501 + 4.50539i) q^{63} +(-145.075 - 96.9357i) q^{65} -20.6073i q^{67} -90.5321 q^{69} +(-0.143006 + 0.214023i) q^{71} +(-2.17331 - 10.9260i) q^{73} +(32.0512 - 161.132i) q^{75} +(0.127150 + 0.306967i) q^{77} +(-117.425 + 78.4609i) q^{79} +(69.7934 - 69.7934i) q^{81} +(86.9756 + 36.0265i) q^{83} +(-45.7565 + 131.725i) q^{85} +(34.3818 - 83.0050i) q^{87} +(89.1111 + 89.1111i) q^{89} +(-44.7692 - 67.0018i) q^{91} +(136.181 - 56.4080i) q^{93} +(-224.550 - 44.6658i) q^{95} +(84.5267 - 16.8134i) q^{97} +(0.444545 + 0.297035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	$ 32 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} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) $ 32 * 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 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{16}\right)$

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
$3$	−2.15859	+	3.23056i	−0.719530	+	1.07685i	0.273827	+	0.961779i	$0.411710\pi$
$3$	−2.15859	+	3.23056i	−0.719530	+	1.07685i	−0.993357	+	0.115073i	$0.963290\pi$
$4$		0			0
$5$	−1.60027	−	8.04508i	−0.320053	−	1.60902i	−0.721014	−	0.692920i	$-0.756324\pi$
$5$	−1.60027	−	8.04508i	−0.320053	−	1.60902i	0.400961	−	0.916095i	$-0.368676\pi$
$6$		0			0
$7$	0.739073	−	3.71557i	0.105582	−	0.530796i	−0.891404	−	0.453210i	$-0.850279\pi$
$7$	0.739073	−	3.71557i	0.105582	−	0.530796i	0.996986	−	0.0775860i	$-0.0247212\pi$
$8$		0			0
$9$	−2.33284	−	5.63197i	−0.259204	−	0.625775i
$10$		0			0
$11$	−0.0729240	+	0.0487263i	−0.00662945	+	0.00442966i	−0.558881	−	0.829248i	$-0.688769\pi$
$11$	−0.0729240	+	0.0487263i	−0.00662945	+	0.00442966i	0.552251	+	0.833678i	$0.313769\pi$
$12$		0			0
$13$	15.0409	−	15.0409i	1.15699	−	1.15699i	0.171872	−	0.985119i	$-0.445018\pi$
$13$	15.0409	−	15.0409i	1.15699	−	1.15699i	0.985119	−	0.171872i	$-0.0549815\pi$
$14$		0			0
$15$	29.4444	+	12.1963i	1.96296	+	0.813085i
$16$		0			0
$17$	−14.6619	−	8.60395i	−0.862466	−	0.506115i
$17$	−14.6619	−	8.60395i	−0.862466	−	0.506115i
$18$		0			0
$19$	10.6813	−	25.7869i	0.562172	−	1.35720i	−0.345853	−	0.938289i	$-0.612410\pi$
$19$	10.6813	−	25.7869i	0.562172	−	1.35720i	0.908025	−	0.418916i	$-0.137590\pi$
$20$		0			0
$21$	10.4080	+	10.4080i	0.495620	+	0.495620i
$22$		0			0
$23$	12.9453	+	19.3739i	0.562837	+	0.842346i	0.998325	−	0.0578489i	$-0.0184242\pi$
$23$	12.9453	+	19.3739i	0.562837	+	0.842346i	−0.435488	+	0.900195i	$0.643424\pi$
$24$		0			0
$25$	−39.0654	+	16.1814i	−1.56262	+	0.647257i
$26$		0			0
$27$	−11.0663	−	2.20122i	−0.409862	−	0.0815266i
$28$		0			0
$29$	−22.6794	+	4.51121i	−0.782048	+	0.155559i	−0.569939	−	0.821687i	$-0.693033\pi$
$29$	−22.6794	+	4.51121i	−0.782048	+	0.155559i	−0.212109	+	0.977246i	$0.568033\pi$
$30$		0			0
$31$	−31.5440	−	21.0770i	−1.01755	−	0.679904i	−0.0693532	−	0.997592i	$-0.522094\pi$
$31$	−31.5440	−	21.0770i	−1.01755	−	0.679904i	−0.948195	+	0.317688i	$0.897094\pi$
$32$		0			0
$33$		−	0.340765i		−	0.0103262i
$34$		0			0
$35$	−31.0748			−0.887851
$36$		0			0
$37$	18.9394	−	28.3448i	0.511875	−	0.766074i	−0.482049	−	0.876144i	$-0.660107\pi$
$37$	18.9394	−	28.3448i	0.511875	−	0.766074i	0.993924	+	0.110070i	$0.0351074\pi$
$38$		0			0
$39$	16.1233	+	81.0575i	0.413419	+	2.07840i
$40$		0			0
$41$	−3.65376	+	18.3687i	−0.0891162	+	0.448017i	0.910303	+	0.413942i	$0.135849\pi$
$41$	−3.65376	+	18.3687i	−0.0891162	+	0.448017i	−0.999419	+	0.0340750i	$0.989151\pi$
$42$		0			0
$43$	13.4093	+	32.3729i	0.311844	+	0.752857i	0.999637	+	0.0269505i	$0.00857964\pi$
$43$	13.4093	+	32.3729i	0.311844	+	0.752857i	−0.687793	+	0.725907i	$0.741420\pi$
$44$		0			0
$45$	−41.5765	+	27.7805i	−0.923922	+	0.617345i
$46$		0			0
$47$	−8.80943	+	8.80943i	−0.187435	+	0.187435i	−0.794586	−	0.607151i	$-0.792312\pi$
$47$	−8.80943	+	8.80943i	−0.187435	+	0.187435i	0.607151	+	0.794586i	$0.292312\pi$
$48$		0			0
$49$	32.0108	+	13.2593i	0.653283	+	0.270599i
$50$		0			0
$51$	59.4446	−	28.7938i	1.16558	−	0.564584i
$52$		0			0
$53$	20.8866	−	50.4248i	0.394088	−	0.951411i	−0.594952	−	0.803761i	$-0.702829\pi$
$53$	20.8866	−	50.4248i	0.394088	−	0.951411i	0.989040	−	0.147650i	$-0.0471710\pi$
$54$		0			0
$55$	0.508704	+	0.508704i	0.00924917	+	0.00924917i
$56$		0			0
$57$	60.2495	+	90.1697i	1.05701	+	1.58193i
$58$		0			0
$59$	−46.3811	+	19.2117i	−0.786121	+	0.325622i	−0.739383	−	0.673285i	$-0.764883\pi$
$59$	−46.3811	+	19.2117i	−0.786121	+	0.325622i	−0.0467379	+	0.998907i	$0.514883\pi$
$60$		0			0
$61$	103.351	+	20.5577i	1.69427	+	0.337012i	0.945452	−	0.325761i	$-0.105621\pi$
$61$	103.351	+	20.5577i	1.69427	+	0.337012i	0.748820	+	0.662773i	$0.230621\pi$
$62$		0			0
$63$	−22.6501	+	4.50539i	−0.359526	+	0.0715142i
$64$		0			0
$65$	−145.075	−	96.9357i	−2.23192	−	1.49132i
$66$		0			0
$67$		−	20.6073i		−	0.307571i	−0.988104	−	0.153786i	$-0.950853\pi$
$67$		−	20.6073i		−	0.307571i	0.988104	−	0.153786i	$-0.0491465\pi$
$68$		0			0
$69$	−90.5321			−1.31206
$70$		0			0
$71$	−0.143006	+	0.214023i	−0.00201416	+	0.00301441i	−0.832475	−	0.554062i	$-0.813077\pi$
$71$	−0.143006	+	0.214023i	−0.00201416	+	0.00301441i	0.830461	+	0.557077i	$0.188077\pi$
$72$		0			0
$73$	−2.17331	−	10.9260i	−0.0297714	−	0.149671i	0.963040	−	0.269357i	$-0.0868112\pi$
$73$	−2.17331	−	10.9260i	−0.0297714	−	0.149671i	−0.992812	+	0.119686i	$0.961811\pi$
$74$		0			0
$75$	32.0512	−	161.132i	0.427349	−	2.14843i
$76$		0			0
$77$	0.127150	+	0.306967i	0.00165130	+	0.00398658i
$78$		0			0
$79$	−117.425	+	78.4609i	−1.48639	+	0.993175i	−0.494080	+	0.869417i	$0.664495\pi$
$79$	−117.425	+	78.4609i	−1.48639	+	0.993175i	−0.992312	+	0.123759i	$0.960505\pi$
$80$		0			0
$81$	69.7934	−	69.7934i	0.861647	−	0.861647i
$82$		0			0
$83$	86.9756	+	36.0265i	1.04790	+	0.434054i	0.839141	−	0.543913i	$-0.183058\pi$
$83$	86.9756	+	36.0265i	1.04790	+	0.434054i	0.208758	+	0.977967i	$0.433058\pi$
$84$		0			0
$85$	−45.7565	+	131.725i	−0.538312	+	1.54971i
$86$		0			0
$87$	34.3818	−	83.0050i	0.395193	−	0.954080i
$88$		0			0
$89$	89.1111	+	89.1111i	1.00125	+	1.00125i	0.999999	+	0.00124905i	$0.000397586\pi$
$89$	89.1111	+	89.1111i	1.00125	+	1.00125i	0.00124905	+	0.999999i	$0.499602\pi$
$90$		0			0
$91$	−44.7692	−	67.0018i	−0.491969	−	0.736284i
$92$		0			0
$93$	136.181	−	56.4080i	1.46431	−	0.606538i
$94$		0			0
$95$	−224.550	−	44.6658i	−2.36369	−	0.470167i
$96$		0			0
$97$	84.5267	−	16.8134i	0.871410	−	0.173334i	0.260922	−	0.965360i	$-0.415973\pi$
$97$	84.5267	−	16.8134i	0.871410	−	0.173334i	0.610488	+	0.792026i	$0.290973\pi$
$98$		0			0
$99$	0.444545	+	0.297035i	0.00449035	+	0.00300036i
$100$		0			0
$101$		−	29.1183i		−	0.288300i	−0.989556	−	0.144150i	$-0.953955\pi$
$101$		−	29.1183i		−	0.288300i	0.989556	−	0.144150i	$-0.0460447\pi$
$102$		0			0
$103$	128.815			1.25063			0.625315	−	0.780373i	$-0.284971\pi$
$103$	128.815			1.25063			0.625315	+	0.780373i	$0.284971\pi$
$104$		0			0
$105$	67.0777	−	100.389i	0.638835	−	0.956084i
$106$		0			0
$107$	−31.6082	−	158.905i	−0.295404	−	1.48510i	−0.788453	−	0.615095i	$-0.789118\pi$
$107$	−31.6082	−	158.905i	−0.295404	−	1.48510i	0.493049	−	0.870002i	$-0.335882\pi$
$108$		0			0
$109$	−20.3278	+	102.195i	−0.186494	+	0.937568i	0.768253	+	0.640147i	$0.221127\pi$
$109$	−20.3278	+	102.195i	−0.186494	+	0.937568i	−0.954746	+	0.297421i	$0.903873\pi$
$110$		0			0
$111$	50.6870	+	122.369i	0.456640	+	1.10243i
$112$		0			0
$113$	66.4011	−	44.3678i	0.587620	−	0.392635i	−0.225918	−	0.974146i	$-0.572538\pi$
$113$	66.4011	−	44.3678i	0.587620	−	0.392635i	0.813539	+	0.581511i	$0.197538\pi$
$114$		0			0
$115$	135.149	−	135.149i	1.17521	−	1.17521i
$116$		0			0
$117$	−119.798	−	49.6219i	−1.02391	−	0.424119i
$118$		0			0
$119$	−42.8048	+	48.1185i	−0.359705	+	0.404357i
$120$		0			0
$121$	−46.3018	+	111.782i	−0.382659	+	0.923821i
$122$		0			0
$123$	−51.4542	−	51.4542i	−0.418327	−	0.418327i
$124$		0			0
$125$	78.7667	+	117.883i	0.630134	+	0.943062i
$126$		0			0
$127$	181.635	−	75.2358i	1.43020	−	0.592408i	0.472799	−	0.881170i	$-0.343244\pi$
$127$	181.635	−	75.2358i	1.43020	−	0.592408i	0.957401	+	0.288762i	$0.0932438\pi$
$128$		0			0
$129$	−133.527	−	26.5603i	−1.03510	−	0.205894i
$130$		0			0
$131$	−149.587	+	29.7546i	−1.14188	+	0.227135i	−0.729569	−	0.683907i	$-0.760279\pi$
$131$	−149.587	+	29.7546i	−1.14188	+	0.227135i	−0.412314	+	0.911042i	$0.635279\pi$
$132$		0			0
$133$	−87.9188	−	58.7454i	−0.661043	−	0.441695i
$134$		0			0
$135$			92.5515i			0.685567i
$136$		0			0
$137$	−45.5719			−0.332641			−0.166321	−	0.986072i	$-0.553189\pi$
$137$	−45.5719			−0.332641			−0.166321	+	0.986072i	$0.553189\pi$
$138$		0			0
$139$	16.3879	−	24.5262i	0.117898	−	0.176447i	−0.767827	−	0.640658i	$-0.778662\pi$
$139$	16.3879	−	24.5262i	0.117898	−	0.176447i	0.885725	+	0.464210i	$0.153662\pi$
$140$		0			0
$141$	−9.44343	−	47.4753i	−0.0669746	−	0.336704i
$142$		0			0
$143$	−0.363955	+	1.82973i	−0.00254514	+	0.0127953i
$144$		0			0
$145$	72.5861	+	175.238i	0.500594	+	1.20854i
$146$		0			0
$147$	−111.933	+	74.7914i	−0.761451	+	0.508785i
$148$		0			0
$149$	−124.513	+	124.513i	−0.835654	+	0.835654i	−0.988284	−	0.152629i	$-0.951226\pi$
$149$	−124.513	+	124.513i	−0.835654	+	0.835654i	0.152629	+	0.988284i	$0.451226\pi$
$150$		0			0
$151$	239.126	+	99.0494i	1.58362	+	0.655956i	0.988982	−	0.148039i	$-0.0472960\pi$
$151$	239.126	+	99.0494i	1.58362	+	0.655956i	0.594637	+	0.803995i	$0.297296\pi$
$152$		0			0
$153$	−14.2533	+	102.647i	−0.0931588	+	0.670897i
$154$		0			0
$155$	−119.088	+	287.503i	−0.768307	+	1.85486i
$156$		0			0
$157$	−130.367	−	130.367i	−0.830365	−	0.830365i	0.157201	−	0.987567i	$-0.449753\pi$
$157$	−130.367	−	130.367i	−0.830365	−	0.830365i	−0.987567	+	0.157201i	$0.949753\pi$
$158$		0			0
$159$	117.815	+	176.322i	0.740972	+	1.10894i
$160$		0			0
$161$	81.5528	−	33.7803i	0.506539	−	0.209815i
$162$		0			0
$163$	−151.539	−	30.1429i	−0.929685	−	0.184926i	−0.293055	−	0.956096i	$-0.594672\pi$
$163$	−151.539	−	30.1429i	−0.929685	−	0.184926i	−0.636630	+	0.771170i	$0.719672\pi$
$164$		0			0
$165$	−2.74148	+	0.545315i	−0.0166150	+	0.00330494i
$166$		0			0
$167$	−1.05603	−	0.705613i	−0.00632350	−	0.00422523i	0.552404	−	0.833576i	$-0.313710\pi$
$167$	−1.05603	−	0.705613i	−0.00632350	−	0.00422523i	−0.558728	+	0.829351i	$0.688710\pi$
$168$		0			0
$169$		−	283.457i		−	1.67726i
$170$		0			0
$171$	−170.149			−0.995022
$172$		0			0
$173$	48.5611	−	72.6768i	0.280700	−	0.420097i	−0.664151	−	0.747599i	$-0.731207\pi$
$173$	48.5611	−	72.6768i	0.280700	−	0.420097i	0.944851	+	0.327501i	$0.106207\pi$
$174$		0			0
$175$	31.2511	+	157.110i	0.178578	+	0.897770i
$176$		0			0
$177$	38.0533	−	191.307i	0.214991	−	1.08083i
$178$		0			0
$179$	74.5625	+	180.010i	0.416550	+	1.00564i	0.983339	+	0.181779i	$0.0581855\pi$
$179$	74.5625	+	180.010i	0.416550	+	1.00564i	−0.566789	+	0.823863i	$0.691815\pi$
$180$		0			0
$181$	−65.0194	+	43.4446i	−0.359223	+	0.240025i	−0.722065	−	0.691826i	$-0.756807\pi$
$181$	−65.0194	+	43.4446i	−0.359223	+	0.240025i	0.362841	+	0.931851i	$0.381807\pi$
$182$		0			0
$183$	−289.504	+	289.504i	−1.58199	+	1.58199i
$184$		0			0
$185$	−258.344	−	107.009i	−1.39645	−	0.578430i
$186$		0			0
$187$	1.48844	−	0.0869862i	0.00795960	−	0.000465167i
$188$		0			0
$189$	−16.3576	+	39.4906i	−0.0865479	+	0.208945i
$190$		0			0
$191$	−190.391	−	190.391i	−0.996811	−	0.996811i	0.00318393	−	0.999995i	$-0.498987\pi$
$191$	−190.391	−	190.391i	−0.996811	−	0.996811i	−0.999995	+	0.00318393i	$0.998987\pi$
$192$		0			0
$193$	−6.85390	−	10.2576i	−0.0355124	−	0.0531481i	0.813289	−	0.581860i	$-0.197675\pi$
$193$	−6.85390	−	10.2576i	−0.0355124	−	0.0531481i	−0.848801	+	0.528712i	$0.822675\pi$
$194$		0			0
$195$	626.313	−	259.427i	3.21186	−	1.33040i
$196$		0			0
$197$	264.356	+	52.5838i	1.34191	+	0.266923i	0.813252	−	0.581912i	$-0.197695\pi$
$197$	264.356	+	52.5838i	1.34191	+	0.266923i	0.528659	+	0.848834i	$0.322695\pi$
$198$		0			0
$199$	28.9406	−	5.75664i	0.145430	−	0.0289278i	−0.121838	−	0.992550i	$-0.538879\pi$
$199$	28.9406	−	5.75664i	0.145430	−	0.0289278i	0.267268	+	0.963622i	$0.413879\pi$
$200$		0			0
$201$	66.5730	+	44.4826i	0.331209	+	0.221307i
$202$		0			0
$203$			87.6011i			0.431532i
$204$		0			0
$205$	153.625			0.749389
$206$		0			0
$207$	78.9143	−	118.104i	0.381229	−	0.570549i
$208$		0			0
$209$	0.477577	+	2.40094i	0.00228506	+	0.0114878i
$210$		0			0
$211$	52.3600	−	263.232i	0.248152	−	1.24754i	−0.632792	−	0.774322i	$-0.718091\pi$
$211$	52.3600	−	263.232i	0.248152	−	1.24754i	0.880944	−	0.473221i	$-0.156909\pi$
$212$		0			0
$213$	−0.382723	−	0.923975i	−0.00179682	−	0.00433791i
$214$		0			0
$215$	238.984	−	159.684i	1.11155	−	0.742716i
$216$		0			0
$217$	−101.627	+	101.627i	−0.468325	+	0.468325i
$218$		0			0
$219$	39.9883	+	16.5637i	0.182595	+	0.0756333i
$220$		0			0
$221$	−349.939	+	91.1173i	−1.58344	+	0.412295i
$222$		0			0
$223$	−2.61383	+	6.31033i	−0.0117212	+	0.0282975i	−0.929632	−	0.368490i	$-0.879875\pi$
$223$	−2.61383	+	6.31033i	−0.0117212	+	0.0282975i	0.917911	+	0.396787i	$0.129875\pi$
$224$		0			0
$225$	182.267	+	182.267i	0.810075	+	0.810075i
$226$		0			0
$227$	116.461	+	174.296i	0.513042	+	0.767822i	0.994054	−	0.108893i	$-0.0347305\pi$
$227$	116.461	+	174.296i	0.513042	+	0.767822i	−0.481012	+	0.876714i	$0.659730\pi$
$228$		0			0
$229$	142.199	−	58.9010i	0.620958	−	0.257209i	−0.0499475	−	0.998752i	$-0.515905\pi$
$229$	142.199	−	58.9010i	0.620958	−	0.257209i	0.670906	+	0.741542i	$0.265905\pi$
$230$		0			0
$231$	−1.26614	−	0.251850i	−0.00548111	−	0.00109026i
$232$		0			0
$233$	−115.303	+	22.9352i	−0.494863	+	0.0984344i	−0.436212	−	0.899844i	$-0.643680\pi$
$233$	−115.303	+	22.9352i	−0.494863	+	0.0984344i	−0.0586517	+	0.998279i	$0.518680\pi$
$234$		0			0
$235$	84.9700	+	56.7751i	0.361574	+	0.241596i
$236$		0			0
$237$		−	548.713i		−	2.31524i
$238$		0			0
$239$	−19.5398			−0.0817565			−0.0408783	−	0.999164i	$-0.513016\pi$
$239$	−19.5398			−0.0817565			−0.0408783	+	0.999164i	$0.513016\pi$
$240$		0			0
$241$	−161.730	+	242.046i	−0.671078	+	1.00434i	0.327158	+	0.944970i	$0.393909\pi$
$241$	−161.730	+	242.046i	−0.671078	+	1.00434i	−0.998236	+	0.0593700i	$0.981091\pi$
$242$		0			0
$243$	55.0053	+	276.530i	0.226359	+	1.13799i
$244$		0			0
$245$	55.4465	−	278.748i	0.226312	−	1.13775i
$246$		0			0
$247$	−227.202	−	548.513i	−0.919845	−	2.22070i
$248$		0			0
$249$	−304.130	+	203.213i	−1.22141	+	0.816118i
$250$		0			0
$251$	231.510	−	231.510i	0.922351	−	0.922351i	−0.0748445	−	0.997195i	$-0.523846\pi$
$251$	231.510	−	231.510i	0.922351	−	0.922351i	0.997195	+	0.0748445i	$0.0238461\pi$
$252$		0			0
$253$	−1.88804	−	0.782052i	−0.00746261	−	0.00309111i
$254$		0			0
$255$	−326.775	−	432.159i	−1.28147	−	1.69474i
$256$		0			0
$257$	78.9538	−	190.611i	0.307213	−	0.741679i	−0.692580	−	0.721341i	$-0.743526\pi$
$257$	78.9538	−	190.611i	0.307213	−	0.741679i	0.999793	−	0.0203374i	$-0.00647404\pi$
$258$		0			0
$259$	−91.3194	−	91.3194i	−0.352585	−	0.352585i
$260$		0			0
$261$	78.3144	+	117.206i	0.300055	+	0.449064i
$262$		0			0
$263$	−19.8413	+	8.21853i	−0.0754422	+	0.0312492i	−0.420085	−	0.907485i	$-0.638000\pi$
$263$	−19.8413	+	8.21853i	−0.0754422	+	0.0312492i	0.344643	+	0.938734i	$0.388000\pi$
$264$		0			0
$265$	−439.096	−	87.3416i	−1.65696	−	0.329591i
$266$		0			0
$267$	−480.233	+	95.5242i	−1.79862	+	0.357769i
$268$		0			0
$269$	33.1072	+	22.1215i	0.123075	+	0.0822361i	0.615584	−	0.788071i	$-0.288920\pi$
$269$	33.1072	+	22.1215i	0.123075	+	0.0822361i	−0.492509	+	0.870307i	$0.663920\pi$
$270$		0			0
$271$		−	138.849i		−	0.512358i	−0.966629	−	0.256179i	$-0.917536\pi$
$271$		−	138.849i		−	0.512358i	0.966629	−	0.256179i	$-0.0824637\pi$
$272$		0			0
$273$	313.091			1.14686
$274$		0			0
$275$	2.06035	−	3.08353i	0.00749217	−	0.0112128i
$276$		0			0
$277$	81.2644	+	408.544i	0.293373	+	1.47489i	0.793306	+	0.608823i	$0.208358\pi$
$277$	81.2644	+	408.544i	0.293373	+	1.47489i	−0.499932	+	0.866064i	$0.666642\pi$
$278$		0			0
$279$	−45.1182	+	226.824i	−0.161714	+	0.812990i
$280$		0			0
$281$	54.2179	+	130.894i	0.192946	+	0.465814i	0.990513	−	0.137417i	$-0.0438799\pi$
$281$	54.2179	+	130.894i	0.192946	+	0.465814i	−0.797567	+	0.603230i	$0.793880\pi$
$282$		0			0
$283$	81.6352	−	54.5469i	0.288464	−	0.192745i	−0.402916	−	0.915237i	$-0.632003\pi$
$283$	81.6352	−	54.5469i	0.288464	−	0.192745i	0.691380	+	0.722492i	$0.257003\pi$
$284$		0			0
$285$	629.007	−	629.007i	2.20704	−	2.20704i
$286$		0			0
$287$	65.5499	+	27.1517i	0.228397	+	0.0946051i
$288$		0			0
$289$	140.944	+	252.301i	0.487696	+	0.873014i
$290$		0			0
$291$	−128.142	+	309.362i	−0.440350	+	1.06310i
$292$		0			0
$293$	167.690	+	167.690i	0.572319	+	0.572319i	0.932776	−	0.360457i	$-0.117379\pi$
$293$	167.690	+	167.690i	0.572319	+	0.572319i	−0.360457	+	0.932776i	$0.617379\pi$
$294$		0			0
$295$	228.782	+	342.396i	0.775531	+	1.16066i
$296$		0			0
$297$	0.914253	−	0.378696i	0.00307829	−	0.00127507i
$298$		0			0
$299$	486.110	+	96.6932i	1.62578	+	0.323389i
$300$		0			0
$301$	130.194	−	25.8972i	0.432539	−	0.0860373i
$302$		0			0
$303$	94.0682	+	62.8544i	0.310456	+	0.207440i
$304$		0			0
$305$		−	864.361i		−	2.83397i
$306$		0			0
$307$	−255.779			−0.833156			−0.416578	−	0.909100i	$-0.636771\pi$
$307$	−255.779			−0.833156			−0.416578	+	0.909100i	$0.636771\pi$
$308$		0			0
$309$	−278.058	+	416.144i	−0.899865	+	1.34674i
$310$		0			0
$311$	−62.5356	−	314.388i	−0.201079	−	1.01089i	−0.941053	−	0.338258i	$-0.890162\pi$
$311$	−62.5356	−	314.388i	−0.201079	−	1.01089i	0.739974	−	0.672635i	$-0.234838\pi$
$312$		0			0
$313$	13.3249	−	66.9888i	0.0425715	−	0.214022i	−0.953644	−	0.300936i	$-0.902701\pi$
$313$	13.3249	−	66.9888i	0.0425715	−	0.214022i	0.996216	+	0.0869148i	$0.0277008\pi$
$314$		0			0
$315$	72.4925	+	175.012i	0.230135	+	0.555595i
$316$		0			0
$317$	301.460	−	201.429i	0.950977	−	0.635423i	0.0197279	−	0.999805i	$-0.493720\pi$
$317$	301.460	−	201.429i	0.950977	−	0.635423i	0.931249	+	0.364383i	$0.118720\pi$
$318$		0			0
$319$	1.43406	−	1.43406i	0.00449548	−	0.00449548i
$320$		0			0
$321$	581.582	+	240.899i	1.81178	+	0.750465i
$322$		0			0
$323$	−378.477	+	286.184i	−1.17176	+	0.886019i
$324$		0			0
$325$	−344.196	+	830.962i	−1.05906	+	2.55681i
$326$		0			0
$327$	−286.267	−	286.267i	−0.875434	−	0.875434i
$328$		0			0
$329$	26.2213	+	39.2429i	0.0796999	+	0.119279i
$330$		0			0
$331$	−461.121	+	191.002i	−1.39311	+	0.577047i	−0.947955	−	0.318405i	$-0.896853\pi$
$331$	−461.121	+	191.002i	−1.39311	+	0.577047i	−0.445159	+	0.895452i	$0.646853\pi$
$332$		0			0
$333$	−203.819	−	40.5422i	−0.612070	−	0.121748i
$334$		0			0
$335$	−165.787	+	32.9771i	−0.494887	+	0.0984391i
$336$		0			0
$337$	−204.911	−	136.917i	−0.608045	−	0.406282i	0.213077	−	0.977035i	$-0.431651\pi$
$337$	−204.911	−	136.917i	−0.608045	−	0.406282i	−0.821122	+	0.570753i	$0.806651\pi$
$338$		0			0
$339$			310.284i			0.915293i
$340$		0			0
$341$	3.32732			0.00975753
$342$		0			0
$343$	176.055	−	263.485i	0.513279	−	0.768177i
$344$		0			0
$345$	144.875	+	728.338i	0.419929	+	2.11112i
$346$		0			0
$347$	47.8276	−	240.446i	0.137832	−	0.692927i	−0.848637	−	0.528976i	$-0.822576\pi$
$347$	47.8276	−	240.446i	0.137832	−	0.692927i	0.986468	−	0.163951i	$-0.0524240\pi$
$348$		0			0
$349$	−87.5473	−	211.358i	−0.250852	−	0.605610i	0.747422	−	0.664350i	$-0.231292\pi$
$349$	−87.5473	−	211.358i	−0.250852	−	0.605610i	−0.998273	+	0.0587404i	$0.981292\pi$
$350$		0			0
$351$	−199.555	+	133.338i	−0.568532	+	0.379881i
$352$		0			0
$353$	−388.219	+	388.219i	−1.09977	+	1.09977i	−0.105334	+	0.994437i	$0.533591\pi$
$353$	−388.219	+	388.219i	−1.09977	+	1.09977i	−0.994437	+	0.105334i	$0.966409\pi$
$354$		0			0
$355$	1.95068	+	0.807997i	0.00549487	+	0.00227605i
$356$		0			0
$357$	−63.0515	−	242.152i	−0.176615	−	0.678296i
$358$		0			0
$359$	152.572	−	368.342i	0.424993	−	1.02602i	−0.555861	−	0.831275i	$-0.687611\pi$
$359$	152.572	−	368.342i	0.424993	−	1.02602i	0.980853	−	0.194748i	$-0.0623888\pi$
$360$		0			0
$361$	−295.608	−	295.608i	−0.818859	−	0.818859i
$362$		0			0
$363$	−261.173	−	390.873i	−0.719484	−	1.07678i
$364$		0			0
$365$	−84.4225	+	34.9689i	−0.231294	+	0.0958053i
$366$		0			0
$367$	404.960	+	80.5516i	1.10343	+	0.219487i	0.713014	−	0.701150i	$-0.247330\pi$
$367$	404.960	+	80.5516i	1.10343	+	0.219487i	0.390421	+	0.920637i	$0.372330\pi$
$368$		0			0
$369$	111.976	−	22.2734i	0.303457	−	0.0603614i
$370$		0			0
$371$	−171.920	−	114.873i	−0.463397	−	0.309632i
$372$		0			0
$373$			340.489i			0.912838i	0.889765	+	0.456419i	$0.150868\pi$
$373$			340.489i			0.912838i	−0.889765	+	0.456419i	$0.849132\pi$
$374$		0			0
$375$	−550.852			−1.46894
$376$		0			0
$377$	−273.266	+	408.971i	−0.724843	+	1.08480i
$378$		0			0
$379$	39.8953	+	200.567i	0.105265	+	0.529201i	0.997051	+	0.0767442i	$0.0244525\pi$
$379$	39.8953	+	200.567i	0.105265	+	0.529201i	−0.891786	+	0.452457i	$0.850548\pi$
$380$		0			0
$381$	−149.022	+	749.186i	−0.391135	+	1.96637i
$382$		0			0
$383$	195.150	+	471.134i	0.509530	+	1.23012i	0.944154	+	0.329503i	$0.106881\pi$
$383$	195.150	+	471.134i	0.509530	+	1.23012i	−0.434624	+	0.900612i	$0.643119\pi$
$384$		0			0
$385$	2.26610	−	1.51416i	0.00588597	−	0.00393288i
$386$		0			0
$387$	151.041	−	151.041i	0.390288	−	0.390288i
$388$		0			0
$389$	−186.645	−	77.3107i	−0.479806	−	0.198742i	0.129653	−	0.991559i	$-0.458614\pi$
$389$	−186.645	−	77.3107i	−0.479806	−	0.198742i	−0.609460	+	0.792817i	$0.708614\pi$
$390$		0			0
$391$	−23.1099	−	395.440i	−0.0591046	−	1.01135i
$392$		0			0
$393$	226.772	−	547.476i	0.577028	−	1.39307i
$394$		0			0
$395$	819.135	+	819.135i	2.07376	+	2.07376i
$396$		0			0
$397$	−111.788	−	167.302i	−0.281581	−	0.421416i	0.663537	−	0.748143i	$-0.269054\pi$
$397$	−111.788	−	167.302i	−0.281581	−	0.421416i	−0.945119	+	0.326727i	$0.894054\pi$
$398$		0			0
$399$	379.561	−	157.219i	0.951281	−	0.394033i
$400$		0			0
$401$	577.972	+	114.966i	1.44133	+	0.286698i	0.852994	−	0.521921i	$-0.174785\pi$
$401$	577.972	+	114.966i	1.44133	+	0.286698i	0.588333	+	0.808619i	$0.299785\pi$
$402$		0			0
$403$	−791.467	+	157.433i	−1.96394	+	0.390652i
$404$		0			0
$405$	−673.181	−	449.805i	−1.66218	−	1.11063i
$406$		0			0
$407$			2.98986i			0.00734609i
$408$		0			0
$409$	207.307			0.506862			0.253431	−	0.967353i	$-0.418441\pi$
$409$	207.307			0.506862			0.253431	+	0.967353i	$0.418441\pi$
$410$		0			0
$411$	98.3709	−	147.222i	0.239345	−	0.358205i
$412$		0			0
$413$	37.1034	+	186.531i	0.0898387	+	0.451650i
$414$		0			0
$415$	150.652	−	757.378i	0.363016	−	1.82501i
$416$		0			0
$417$	43.8585	+	105.884i	0.105176	+	0.253918i
$418$		0			0
$419$	435.437	−	290.950i	1.03923	−	0.694390i	0.0858935	−	0.996304i	$-0.472626\pi$
$419$	435.437	−	290.950i	1.03923	−	0.694390i	0.953335	+	0.301914i	$0.0976255\pi$
$420$		0			0
$421$	−14.3957	+	14.3957i	−0.0341941	+	0.0341941i	−0.723997	−	0.689803i	$-0.757697\pi$
$421$	−14.3957	+	14.3957i	−0.0341941	+	0.0341941i	0.689803	+	0.723997i	$0.257697\pi$
$422$		0			0
$423$	70.1655	+	29.0635i	0.165876	+	0.0687080i
$424$		0			0
$425$	711.999	+	98.8662i	1.67529	+	0.232626i
$426$		0			0
$427$	152.767	−	368.813i	0.357769	−	0.863731i
$428$		0			0
$429$	−5.12541	−	5.12541i	−0.0119473	−	0.0119473i
$430$		0			0
$431$	465.128	+	696.113i	1.07918	+	1.61511i	0.737568	+	0.675273i	$0.235974\pi$
$431$	465.128	+	696.113i	1.07918	+	1.61511i	0.341615	+	0.939840i	$0.389026\pi$
$432$		0			0
$433$	148.913	−	61.6818i	0.343910	−	0.142452i	−0.204042	−	0.978962i	$-0.565408\pi$
$433$	148.913	−	61.6818i	0.343910	−	0.142452i	0.547952	+	0.836510i	$0.315408\pi$
$434$		0			0
$435$	−722.801	−	143.774i	−1.66161	−	0.330515i
$436$		0			0
$437$	637.866	−	126.879i	1.45965	−	0.290342i
$438$		0			0
$439$	186.969	+	124.928i	0.425897	+	0.284575i	0.749989	−	0.661450i	$-0.230059\pi$
$439$	186.969	+	124.928i	0.425897	+	0.284575i	−0.324092	+	0.946025i	$0.605059\pi$
$440$		0			0
$441$		−	211.216i		−	0.478948i
$442$		0			0
$443$	−15.9292			−0.0359577			−0.0179788	−	0.999838i	$-0.505723\pi$
$443$	−15.9292			−0.0359577			−0.0179788	+	0.999838i	$0.505723\pi$
$444$		0			0
$445$	574.304	−	859.507i	1.29057	−	1.93148i
$446$		0			0
$447$	−133.473	−	671.016i	−0.298598	−	1.50115i
$448$		0			0
$449$	81.0014	−	407.222i	0.180404	−	0.906952i	−0.779453	−	0.626461i	$-0.784503\pi$
$449$	81.0014	−	407.222i	0.180404	−	0.906952i	0.959857	−	0.280491i	$-0.0904973\pi$
$450$		0			0
$451$	−0.628592	−	1.51755i	−0.00139377	−	0.00336487i
$452$		0			0
$453$	−836.160	+	558.704i	−1.84583	+	1.23334i
$454$		0			0
$455$	−467.392	+	467.392i	−1.02724	+	1.02724i
$456$		0			0
$457$	−77.7913	−	32.2222i	−0.170222	−	0.0705081i	0.295945	−	0.955205i	$-0.404365\pi$
$457$	−77.7913	−	32.2222i	−0.170222	−	0.0705081i	−0.466167	+	0.884697i	$0.654365\pi$
$458$		0			0
$459$	143.314	+	127.488i	0.312230	+	0.277751i
$460$		0			0
$461$	37.4240	−	90.3495i	0.0811800	−	0.195986i	−0.878078	−	0.478518i	$-0.841174\pi$
$461$	37.4240	−	90.3495i	0.0811800	−	0.195986i	0.959258	+	0.282532i	$0.0911743\pi$
$462$		0			0
$463$	−209.346	−	209.346i	−0.452151	−	0.452151i	0.443917	−	0.896068i	$-0.353589\pi$
$463$	−209.346	−	209.346i	−0.452151	−	0.452151i	−0.896068	+	0.443917i	$0.853589\pi$
$464$		0			0
$465$	−671.733	−	1005.32i	−1.44459	−	2.16198i
$466$		0			0
$467$	140.877	−	58.3533i	0.301665	−	0.124954i	−0.226717	−	0.973961i	$-0.572799\pi$
$467$	140.877	−	58.3533i	0.301665	−	0.124954i	0.528381	+	0.849007i	$0.322799\pi$
$468$		0			0
$469$	−76.5678	−	15.2303i	−0.163258	−	0.0324740i
$470$		0			0
$471$	702.569	−	139.750i	1.49165	−	0.296708i
$472$		0			0
$473$	−2.55527	−	1.70737i	−0.00540225	−	0.00360967i
$474$		0			0
$475$			1180.21i			2.48466i
$476$		0			0
$477$	−332.716			−0.697518
$478$		0			0
$479$	236.440	−	353.857i	0.493611	−	0.738741i	−0.498115	−	0.867111i	$-0.665974\pi$
$479$	236.440	−	353.857i	0.493611	−	0.738741i	0.991726	+	0.128370i	$0.0409744\pi$
$480$		0			0
$481$	−141.465	−	711.195i	−0.294107	−	1.47858i
$482$		0			0
$483$	−66.9099	+	336.379i	−0.138530	+	0.696436i
$484$		0			0
$485$	−270.530	−	653.118i	−0.557795	−	1.34664i
$486$		0			0
$487$	134.367	−	89.7812i	0.275908	−	0.184356i	−0.409916	−	0.912123i	$-0.634442\pi$
$487$	134.367	−	89.7812i	0.275908	−	0.184356i	0.685824	+	0.727768i	$0.259442\pi$
$488$		0			0
$489$	424.488	−	424.488i	0.868073	−	0.868073i
$490$		0			0
$491$	−350.275	−	145.089i	−0.713390	−	0.295496i	−0.00368362	−	0.999993i	$-0.501173\pi$
$491$	−350.275	−	145.089i	−0.713390	−	0.295496i	−0.709707	+	0.704497i	$0.751173\pi$
$492$		0			0
$493$	371.338	+	128.989i	0.753221	+	0.261642i
$494$		0			0
$495$	1.67828	−	4.05173i	0.00339047	−	0.00818532i
$496$		0			0
$497$	0.689526	+	0.689526i	0.00138738	+	0.00138738i
$498$		0			0
$499$	279.737	+	418.656i	0.560595	+	0.838990i	0.998187	−	0.0601837i	$-0.0191687\pi$
$499$	279.737	+	418.656i	0.560595	+	0.838990i	−0.437592	+	0.899174i	$0.644169\pi$
$500$		0			0
$501$	4.55905	−	1.88842i	0.00909990	−	0.00376930i
$502$		0			0
$503$	−375.750	−	74.7414i	−0.747019	−	0.148591i	−0.193120	−	0.981175i	$-0.561861\pi$
$503$	−375.750	−	74.7414i	−0.747019	−	0.148591i	−0.553899	+	0.832584i	$0.686861\pi$
$504$		0			0
$505$	−234.259	+	46.5970i	−0.463879	+	0.0922712i
$506$		0			0
$507$	915.722	+	611.866i	1.80616	+	1.20684i
$508$		0			0
$509$			785.732i			1.54368i	0.635818	+	0.771839i	$0.280663\pi$
$509$			785.732i			1.54368i	−0.635818	+	0.771839i	$0.719337\pi$
$510$		0			0
$511$	−42.2025			−0.0825881
$512$		0			0
$513$	−174.964	+	261.853i	−0.341061	+	0.510434i
$514$		0			0
$515$	−206.138	−	1036.33i	−0.400268	−	2.01228i
$516$		0			0
$517$	0.213168	−	1.07167i	0.000412318	−	0.00207286i
$518$		0			0
$519$	129.963	+	313.759i	0.250411	+	0.604545i
$520$		0			0
$521$	−623.378	+	416.528i	−1.19650	+	0.799478i	−0.984085	−	0.177701i	$-0.943134\pi$
$521$	−623.378	+	416.528i	−1.19650	+	0.799478i	−0.212419	+	0.977179i	$0.568134\pi$
$522$		0			0
$523$	31.8557	−	31.8557i	0.0609095	−	0.0609095i	−0.675996	−	0.736905i	$-0.736286\pi$
$523$	31.8557	−	31.8557i	0.0609095	−	0.0609095i	0.736905	+	0.675996i	$0.236286\pi$
$524$		0			0
$525$	−575.010	−	238.177i	−1.09526	−	0.453671i
$526$		0			0
$527$	281.150	+	580.433i	0.533492	+	1.10139i
$528$		0			0
$529$	−5.33064	+	12.8693i	−0.0100768	+	0.0243276i
$530$		0			0
$531$	216.399	+	216.399i	0.407532	+	0.407532i
$532$		0			0
$533$	221.326	+	331.238i	0.415246	+	0.621459i
$534$		0			0
$535$	−1227.82	+	508.581i	−2.29500	+	0.950620i
$536$		0			0
$537$	−742.482	−	147.689i	−1.38265	−	0.275026i
$538$		0			0
$539$	−2.98044	+	0.592846i	−0.00552957	+	0.00109990i
$540$		0			0
$541$	277.470	+	185.399i	0.512883	+	0.342698i	0.784928	−	0.619587i	$-0.212700\pi$
$541$	277.470	+	185.399i	0.512883	+	0.342698i	−0.272045	+	0.962285i	$0.587700\pi$
$542$		0			0
$543$		−	303.828i		−	0.559536i
$544$		0			0
$545$	854.696			1.56825
$546$		0			0
$547$	−30.8067	+	46.1055i	−0.0563195	+	0.0842880i	−0.858561	−	0.512712i	$-0.828641\pi$
$547$	−30.8067	+	46.1055i	−0.0563195	+	0.0842880i	0.802241	+	0.597000i	$0.203641\pi$
$548$		0			0
$549$	−125.320	−	630.026i	−0.228269	−	1.14759i
$550$		0			0
$551$	−125.915	+	633.017i	−0.228521	+	1.14885i
$552$		0			0
$553$	204.741	+	494.289i	0.370237	+	0.893832i
$554$		0			0
$555$	903.358	−	603.605i	1.62767	−	1.08758i
$556$		0			0
$557$	211.539	−	211.539i	0.379783	−	0.379783i	−0.491240	−	0.871024i	$-0.663456\pi$
$557$	211.539	−	211.539i	0.379783	−	0.379783i	0.871024	+	0.491240i	$0.163456\pi$
$558$		0			0
$559$	688.604	+	285.229i	1.23185	+	0.510249i
$560$		0			0
$561$	−2.93193	+	4.99627i	−0.00522625	+	0.00890601i
$562$		0			0
$563$	307.358	−	742.028i	0.545929	−	1.31799i	−0.374553	−	0.927206i	$-0.622204\pi$
$563$	307.358	−	742.028i	0.545929	−	1.31799i	0.920482	−	0.390784i	$-0.127796\pi$
$564$		0			0
$565$	−463.202	−	463.202i	−0.819826	−	0.819826i
$566$		0			0
$567$	−207.740	−	310.905i	−0.366384	−	0.548333i
$568$		0			0
$569$	−774.395	+	320.765i	−1.36098	+	0.563734i	−0.939326	−	0.343025i	$-0.888549\pi$
$569$	−774.395	+	320.765i	−1.36098	+	0.563734i	−0.421649	+	0.906759i	$0.638549\pi$
$570$		0			0
$571$	−377.773	−	75.1437i	−0.661599	−	0.131600i	−0.147141	−	0.989116i	$-0.547007\pi$
$571$	−377.773	−	75.1437i	−0.661599	−	0.131600i	−0.514458	+	0.857515i	$0.672007\pi$
$572$		0			0
$573$	1026.04	−	204.093i	1.79065	−	0.356183i
$574$		0			0
$575$	−819.211	−	547.379i	−1.42471	−	0.951964i
$576$		0			0
$577$			595.187i			1.03152i	0.856733	+	0.515760i	$0.172490\pi$
$577$			595.187i			1.03152i	−0.856733	+	0.515760i	$0.827510\pi$
$578$		0			0
$579$	47.9324			0.0827849
$580$		0			0
$581$	198.140	−	296.538i	0.341033	−	0.510393i
$582$		0			0
$583$	0.933875	+	4.69491i	0.00160184	+	0.00805301i
$584$		0			0
$585$	−207.504	+	1043.19i	−0.354707	+	1.78323i
$586$		0			0
$587$	−35.6932	−	86.1711i	−0.0608062	−	0.146799i	0.890556	−	0.454873i	$-0.150315\pi$
$587$	−35.6932	−	86.1711i	−0.0608062	−	0.146799i	−0.951362	+	0.308074i	$0.900315\pi$
$588$		0			0
$589$	−880.441	+	588.292i	−1.49481	+	0.998798i
$590$		0			0
$591$	−740.512	+	740.512i	−1.25298	+	1.25298i
$592$		0			0
$593$	119.781	+	49.6147i	0.201991	+	0.0836674i	0.481385	−	0.876509i	$-0.340134\pi$
$593$	119.781	+	49.6147i	0.201991	+	0.0836674i	−0.279395	+	0.960176i	$0.590134\pi$
$594$		0			0
$595$	455.616	+	267.366i	0.765741	+	0.449354i
$596$		0			0
$597$	−43.8737	+	105.920i	−0.0734903	+	0.177421i
$598$		0			0
$599$	113.420	+	113.420i	0.189349	+	0.189349i	0.795415	−	0.606066i	$-0.207253\pi$
$599$	113.420	+	113.420i	0.189349	+	0.189349i	−0.606066	+	0.795415i	$0.707253\pi$
$600$		0			0
$601$	−95.7900	−	143.360i	−0.159384	−	0.238535i	0.743179	−	0.669093i	$-0.233317\pi$
$601$	−95.7900	−	143.360i	−0.159384	−	0.238535i	−0.902563	+	0.430557i	$0.858317\pi$
$602$		0			0
$603$	−116.060	+	48.0735i	−0.192470	+	0.0797238i
$604$		0			0
$605$	973.393	+	193.620i	1.60891	+	0.320033i
$606$		0			0
$607$	−66.0397	+	13.1361i	−0.108797	+	0.0216410i	−0.249188	−	0.968455i	$-0.580164\pi$
$607$	−66.0397	+	13.1361i	−0.108797	+	0.0216410i	0.140392	+	0.990096i	$0.455164\pi$
$608$		0			0
$609$	−283.000	−	189.095i	−0.464697	−	0.310500i
$610$		0			0
$611$			265.003i			0.433721i
$612$		0			0
$613$	778.465			1.26993			0.634964	−	0.772542i	$-0.281015\pi$
$613$	778.465			1.26993			0.634964	+	0.772542i	$0.281015\pi$
$614$		0			0
$615$	−331.613	+	496.293i	−0.539208	+	0.806981i
$616$		0			0
$617$	24.3474	+	122.403i	0.0394609	+	0.198383i	0.995487	−	0.0948984i	$-0.0302526\pi$
$617$	24.3474	+	122.403i	0.0394609	+	0.198383i	−0.956026	+	0.293282i	$0.905253\pi$
$618$		0			0
$619$	−123.777	+	622.270i	−0.199963	+	1.00528i	0.742213	+	0.670164i	$0.233776\pi$
$619$	−123.777	+	622.270i	−0.199963	+	1.00528i	−0.942176	+	0.335119i	$0.891224\pi$
$620$		0			0
$621$	−100.609	−	242.893i	−0.162012	−	0.391131i
$622$		0			0
$623$	396.958	−	265.239i	0.637172	−	0.425745i
$624$		0			0
$625$	74.8434	−	74.8434i	0.119749	−	0.119749i
$626$		0			0
$627$	−8.78727	−	3.63981i	−0.0140148	−	0.00580511i
$628$		0			0
$629$	−521.564	+	252.635i	−0.829196	+	0.401646i
$630$		0			0
$631$	96.7206	−	233.504i	0.153281	−	0.370054i	−0.828521	−	0.559957i	$-0.810817\pi$
$631$	96.7206	−	233.504i	0.153281	−	0.370054i	0.981803	+	0.189903i	$0.0608175\pi$
$632$		0			0
$633$	737.361	+	737.361i	1.16487	+	1.16487i
$634$		0			0
$635$	−895.943	−	1340.87i	−1.41093	−	2.11161i
$636$		0			0
$637$	680.904	−	282.040i	1.06892	−	0.442762i
$638$		0			0
$639$	1.53898	+	0.306122i	0.00240842	+	0.000479065i
$640$		0			0
$641$	744.788	−	148.147i	1.16192	−	0.231119i	0.423776	−	0.905767i	$-0.360705\pi$
$641$	744.788	−	148.147i	1.16192	−	0.231119i	0.738140	+	0.674648i	$0.235705\pi$
$642$		0			0
$643$	−352.476	−	235.517i	−0.548174	−	0.366278i	0.250431	−	0.968135i	$-0.419428\pi$
$643$	−352.476	−	235.517i	−0.548174	−	0.366278i	−0.798604	+	0.601857i	$0.794428\pi$
$644$		0			0
$645$			1116.74i			1.73138i
$646$		0			0
$647$	−112.330			−0.173616			−0.0868080	−	0.996225i	$-0.527667\pi$
$647$	−112.330			−0.173616			−0.0868080	+	0.996225i	$0.527667\pi$
$648$		0			0
$649$	2.44618	−	3.66097i	0.00376916	−	0.00564094i
$650$		0			0
$651$	−108.940	−	547.680i	−0.167343	−	0.841291i
$652$		0			0
$653$	−124.155	+	624.171i	−0.190131	+	0.955852i	0.761396	+	0.648287i	$0.224514\pi$
$653$	−124.155	+	624.171i	−0.190131	+	0.955852i	−0.951527	+	0.307565i	$0.900486\pi$
$654$		0			0
$655$	478.757	+	1155.82i	0.730926	+	1.76461i
$656$		0			0
$657$	−56.4648	+	37.7286i	−0.0859434	+	0.0574255i
$658$		0			0
$659$	−609.424	+	609.424i	−0.924771	+	0.924771i	−0.997362	−	0.0725911i	$-0.976873\pi$
$659$	−609.424	+	609.424i	−0.924771	+	0.924771i	0.0725911	+	0.997362i	$0.476873\pi$
$660$		0			0
$661$	−625.049	−	258.904i	−0.945612	−	0.391685i	−0.144032	−	0.989573i	$-0.546007\pi$
$661$	−625.049	−	258.904i	−0.945612	−	0.391685i	−0.801580	+	0.597888i	$0.796007\pi$
$662$		0			0
$663$	461.016	−	1327.18i	0.695348	−	2.00179i
$664$		0			0
$665$	−331.918	+	801.322i	−0.499125	+	1.20500i
$666$		0			0
$667$	−380.991	−	380.991i	−0.571201	−	0.571201i
$668$		0			0
$669$	−14.7437	−	22.0655i	−0.0220384	−	0.0329829i
$670$		0			0
$671$	−8.53844	+	3.53674i	−0.0127249	+	0.00527085i
$672$		0			0
$673$	−162.715	−	32.3659i	−0.241775	−	0.0480920i	0.0727153	−	0.997353i	$-0.476834\pi$
$673$	−162.715	−	32.3659i	−0.241775	−	0.0480920i	−0.314490	+	0.949261i	$0.601834\pi$
$674$		0			0
$675$	467.927	−	93.0765i	0.693226	−	0.137891i
$676$		0			0
$677$	−175.811	−	117.473i	−0.259691	−	0.173520i	0.418909	−	0.908028i	$-0.362413\pi$
$677$	−175.811	−	117.473i	−0.259691	−	0.173520i	−0.678600	+	0.734508i	$0.737413\pi$
$678$		0			0
$679$		−	326.492i		−	0.480842i
$680$		0			0
$681$	−814.462			−1.19598
$682$		0			0
$683$	−136.286	+	203.966i	−0.199540	+	0.298633i	−0.917723	−	0.397222i	$-0.869974\pi$
$683$	−136.286	+	203.966i	−0.199540	+	0.298633i	0.718183	+	0.695855i	$0.244974\pi$
$684$		0			0
$685$	72.9271	+	366.629i	0.106463	+	0.535225i
$686$		0			0
$687$	−116.667	+	586.526i	−0.169822	+	0.853750i
$688$		0			0
$689$	−444.280	−	1072.59i	−0.644819	−	1.55673i
$690$		0			0
$691$	31.2175	−	20.8589i	0.0451773	−	0.0301865i	−0.532777	−	0.846256i	$-0.678851\pi$
$691$	31.2175	−	20.8589i	0.0451773	−	0.0301865i	0.577954	+	0.816069i	$0.303851\pi$
$692$		0			0
$693$	1.43221	−	1.43221i	0.00206668	−	0.00206668i
$694$		0			0
$695$	−223.540	−	92.5933i	−0.321640	−	0.133228i
$696$		0			0
$697$	211.615	−	237.884i	0.303608	−	0.341297i
$698$		0			0
$699$	174.799	−	422.001i	0.250070	−	0.603721i
$700$		0			0
$701$	−287.297	−	287.297i	−0.409839	−	0.409839i	0.471843	−	0.881682i	$-0.343589\pi$
$701$	−287.297	−	287.297i	−0.409839	−	0.409839i	−0.881682	+	0.471843i	$0.843589\pi$
$702$		0			0
$703$	−528.626	−	791.145i	−0.751958	−	1.12538i
$704$		0			0
$705$	−366.831	+	151.946i	−0.520327	+	0.215527i
$706$		0			0
$707$	−108.191	−	21.5205i	−0.153028	−	0.0304392i
$708$		0			0
$709$	303.065	−	60.2833i	0.427454	−	0.0850259i	0.0233251	−	0.999728i	$-0.492575\pi$
$709$	303.065	−	60.2833i	0.427454	−	0.0850259i	0.404129	+	0.914702i	$0.367575\pi$
$710$		0			0
$711$	715.823	+	478.298i	1.00678	+	0.672711i
$712$		0			0
$713$		−	883.980i		−	1.23980i
$714$		0			0
$715$	15.3027			0.0214024
$716$		0			0
$717$	42.1784	−	63.1245i	0.0588263	−	0.0880397i
$718$		0			0
$719$	26.5894	+	133.674i	0.0369811	+	0.185916i	0.994861	−	0.101254i	$-0.0322854\pi$
$719$	26.5894	+	133.674i	0.0369811	+	0.185916i	−0.957880	+	0.287170i	$0.907285\pi$
$720$		0			0
$721$	95.2036	−	478.621i	0.132044	−	0.663829i
$722$		0			0
$723$	−432.835	−	1044.96i	−0.598665	−	1.44530i
$724$		0			0
$725$	812.983	−	543.218i	1.12136	−	0.749266i
$726$		0			0
$727$	−253.119	+	253.119i	−0.348169	+	0.348169i	−0.859427	−	0.511258i	$-0.829180\pi$
$727$	−253.119	+	253.119i	−0.348169	+	0.348169i	0.511258	+	0.859427i	$0.329180\pi$
$728$		0			0
$729$	−191.376	−	79.2705i	−0.262518	−	0.108739i
$730$		0			0
$731$	81.9287	−	590.021i	0.112078	−	0.807143i
$732$		0			0
$733$	407.121	−	982.876i	0.555417	−	1.34090i	−0.357943	−	0.933743i	$-0.616522\pi$
$733$	407.121	−	982.876i	0.555417	−	1.34090i	0.913360	−	0.407152i	$-0.133478\pi$
$734$		0			0
$735$	780.826	+	780.826i	1.06235	+	1.06235i
$736$		0			0
$737$	1.00412	+	1.50276i	0.00136244	+	0.00203903i
$738$		0			0
$739$	−1310.69	+	542.908i	−1.77361	+	0.734652i	−0.779479	+	0.626428i	$0.784516\pi$
$739$	−1310.69	+	542.908i	−1.77361	+	0.734652i	−0.994127	+	0.108224i	$0.965484\pi$
$740$		0			0
$741$	2262.44	+	450.027i	3.05322	+	0.607324i
$742$		0			0
$743$	−212.178	+	42.2048i	−0.285569	+	0.0568033i	−0.335797	−	0.941935i	$-0.609005\pi$
$743$	−212.178	+	42.2048i	−0.285569	+	0.0568033i	0.0502272	+	0.998738i	$0.484005\pi$
$744$		0			0
$745$	1200.97	+	802.460i	1.61203	+	1.07713i
$746$		0			0
$747$		−	573.888i		−	0.768258i
$748$		0			0
$749$	−613.785			−0.819473
$750$		0			0
$751$	297.756	−	445.624i	0.396480	−	0.593374i	−0.578496	−	0.815685i	$-0.696360\pi$
$751$	297.756	−	445.624i	0.396480	−	0.593374i	0.974976	+	0.222311i	$0.0713601\pi$
$752$		0			0
$753$	248.171	+	1247.64i	0.329577	+	1.65689i
$754$		0			0
$755$	414.194	−	2082.30i	0.548602	−	2.75801i
$756$		0			0
$757$	−407.417	−	983.591i	−0.538199	−	1.29933i	−0.925979	−	0.377575i	$-0.876758\pi$
$757$	−407.417	−	983.591i	−0.538199	−	1.29933i	0.387780	−	0.921752i	$-0.373242\pi$
$758$		0			0
$759$	6.60196	−	4.41129i	0.00869824	−	0.00581198i
$760$		0			0
$761$	201.488	−	201.488i	0.264767	−	0.264767i	−0.562221	−	0.826987i	$-0.690053\pi$
$761$	201.488	−	201.488i	0.264767	−	0.264767i	0.826987	+	0.562221i	$0.190053\pi$
$762$		0			0
$763$	364.689	+	151.059i	0.477967	+	0.197980i
$764$		0			0
$765$	848.614	−	49.5938i	1.10930	−	0.0648285i
$766$		0			0
$767$	−408.652	+	986.574i	−0.532793	+	1.28628i
$768$		0			0
$769$	−534.338	−	534.338i	−0.694848	−	0.694848i	0.268447	−	0.963295i	$-0.413490\pi$
$769$	−534.338	−	534.338i	−0.694848	−	0.694848i	−0.963295	+	0.268447i	$0.913490\pi$
$770$		0			0
$771$	445.352	+	666.517i	0.577629	+	0.864483i
$772$		0			0
$773$	−1405.69	+	582.255i	−1.81848	+	0.753241i	−0.841392	+	0.540425i	$0.818263\pi$
$773$	−1405.69	+	582.255i	−1.81848	+	0.753241i	−0.977092	+	0.212816i	$0.931737\pi$
$774$		0			0
$775$	1573.34	+	312.956i	2.03011	+	0.403814i
$776$		0			0
$777$	492.134	−	97.8915i	0.633377	−	0.125986i
$778$		0			0
$779$	434.645	+	290.421i	0.557953	+	0.372812i
$780$		0			0
$781$		−	0.0225755i		−	2.89059e-5i
$782$		0			0
$783$	260.906			0.333214
$784$		0			0
$785$	−840.193	+	1257.44i	−1.07031	+	1.60183i
$786$		0			0
$787$	27.0318	+	135.898i	0.0343479	+	0.172678i	0.994152	−	0.107994i	$-0.0344426\pi$
$787$	27.0318	+	135.898i	0.0343479	+	0.172678i	−0.959804	+	0.280672i	$0.909443\pi$
$788$		0			0
$789$	16.2788	−	81.8389i	0.0206321	−	0.103725i
$790$		0			0
$791$	−115.776	−	279.509i	−0.146367	−	0.353362i
$792$		0			0
$793$	1863.69	−	1245.28i	2.35018	−	1.57034i
$794$		0			0
$795$	1229.99	−	1229.99i	1.54716	−	1.54716i
$796$		0			0
$797$	−136.696	−	56.6212i	−0.171513	−	0.0710429i	0.295275	−	0.955412i	$-0.404589\pi$
$797$	−136.696	−	56.6212i	−0.171513	−	0.0710429i	−0.466788	+	0.884369i	$0.654589\pi$
$798$		0			0
$799$	204.959	−	53.3673i	0.256520	−	0.0667926i
$800$		0			0
$801$	293.989	−	709.753i	0.367028	−	0.886084i
$802$		0			0
$803$	0.690869	+	0.690869i	0.000860359	+	0.000860359i
$804$		0			0
$805$	−402.271	−	602.041i	−0.499716	−	0.747877i
$806$		0			0
$807$	−142.930	+	59.2034i	−0.177112	+	0.0733623i
$808$		0			0
$809$	−942.361	−	187.447i	−1.16485	−	0.231702i	−0.425456	−	0.904979i	$-0.639886\pi$
$809$	−942.361	−	187.447i	−1.16485	−	0.231702i	−0.739391	+	0.673277i	$0.764886\pi$
$810$		0			0
$811$	−1368.83	+	272.277i	−1.68783	+	0.335730i	−0.943321	−	0.331883i	$-0.892316\pi$
$811$	−1368.83	+	272.277i	−1.68783	+	0.335730i	−0.744508	+	0.667613i	$0.767316\pi$
$812$		0			0
$813$	448.560	+	299.718i	0.551734	+	0.368657i
$814$		0			0
$815$			1267.38i			1.55506i
$816$		0			0
$817$	978.023			1.19709
$818$		0			0
$819$	−272.913	+	408.443i	−0.333227	+	0.498710i
$820$		0			0
$821$	−26.8636	−	135.052i	−0.0327205	−	0.164497i	0.960970	−	0.276652i	$-0.0892248\pi$
$821$	−26.8636	−	135.052i	−0.0327205	−	0.164497i	−0.993691	+	0.112155i	$0.964225\pi$
$822$		0			0
$823$	−82.8060	+	416.294i	−0.100615	+	0.505825i	0.897308	+	0.441405i	$0.145520\pi$
$823$	−82.8060	+	416.294i	−0.100615	+	0.505825i	−0.997923	+	0.0644201i	$0.979480\pi$
$824$		0			0
$825$	5.51407	+	13.3121i	0.00668372	+	0.0161359i
$826$		0			0
$827$	−894.308	+	597.557i	−1.08139	+	0.722560i	−0.962754	−	0.270378i	$-0.912851\pi$
$827$	−894.308	+	597.557i	−1.08139	+	0.722560i	−0.118633	+	0.992938i	$0.537851\pi$
$828$		0			0
$829$	450.914	−	450.914i	0.543925	−	0.543925i	−0.380752	−	0.924677i	$-0.624335\pi$
$829$	450.914	−	450.914i	0.543925	−	0.543925i	0.924677	+	0.380752i	$0.124335\pi$
$830$		0			0
$831$	−1495.24	−	619.349i	−1.79933	−	0.745306i
$832$		0			0
$833$	−355.258	−	469.827i	−0.426480	−	0.564018i
$834$		0			0
$835$	−3.98679	+	9.62497i	−0.00477460	+	0.0115269i
$836$		0			0
$837$	302.679	+	302.679i	0.361624	+	0.361624i
$838$		0			0
$839$	−230.150	−	344.444i	−0.274315	−	0.410541i	0.668576	−	0.743644i	$-0.266904\pi$
$839$	−230.150	−	344.444i	−0.274315	−	0.410541i	−0.942890	+	0.333103i	$0.891904\pi$
$840$		0			0
$841$	−282.978	+	117.214i	−0.336479	+	0.139374i
$842$		0			0
$843$	−539.894	−	107.392i	−0.640443	−	0.127392i
$844$		0			0
$845$	−2280.43	+	453.606i	−2.69873	+	0.536812i
$846$		0			0
$847$	381.115	+	254.653i	0.449959	+	0.300653i
$848$		0			0
$849$			381.472i			0.449319i
$850$		0			0
$851$	794.325			0.933402
$852$		0			0
$853$	−479.018	+	716.901i	−0.561569	+	0.840447i	−0.998248	−	0.0591704i	$-0.981154\pi$
$853$	−479.018	+	716.901i	−0.561569	+	0.840447i	0.436679	+	0.899617i	$0.356154\pi$
$854$		0			0
$855$	272.283	+	1368.86i	0.318460	+	1.60101i
$856$		0			0
$857$	−147.834	+	743.214i	−0.172502	+	0.867227i	0.793476	+	0.608602i	$0.208269\pi$
$857$	−147.834	+	743.214i	−0.172502	+	0.867227i	−0.965978	+	0.258625i	$0.916731\pi$
$858$		0			0
$859$	−588.493	−	1420.75i	−0.685090	−	1.65395i	−0.754446	−	0.656363i	$-0.772094\pi$
$859$	−588.493	−	1420.75i	−0.685090	−	1.65395i	0.0693551	−	0.997592i	$-0.477906\pi$
$860$		0			0
$861$	−229.210	+	153.153i	−0.266214	+	0.177879i
$862$		0			0
$863$	−171.290	+	171.290i	−0.198483	+	0.198483i	−0.799349	−	0.600867i	$-0.794822\pi$
$863$	−171.290	+	171.290i	−0.198483	+	0.198483i	0.600867	+	0.799349i	$0.294822\pi$
$864$		0			0
$865$	−662.402	−	274.376i	−0.765782	−	0.317197i
$866$		0			0
$867$	−1119.31	−	89.2863i	−1.29102	−	0.102983i
$868$		0			0
$869$	4.73999	−	11.4434i	0.00545454	−	0.0131684i
$870$		0			0
$871$	−309.952	−	309.952i	−0.355857	−	0.355857i
$872$		0			0
$873$	−291.880	−	436.829i	−0.334341	−	0.500377i
$874$		0			0
$875$	496.216	−	205.540i	0.567104	−	0.234902i
$876$		0			0
$877$	317.592	+	63.1730i	0.362135	+	0.0720331i	0.372804	−	0.927910i	$-0.378396\pi$
$877$	317.592	+	63.1730i	0.362135	+	0.0720331i	−0.0106695	+	0.999943i	$0.503396\pi$
$878$		0			0
$879$	−903.703	+	179.758i	−1.02810	+	0.204503i
$880$		0			0
$881$	181.644	+	121.371i	0.206179	+	0.137765i	0.654373	−	0.756172i	$-0.272933\pi$
$881$	181.644	+	121.371i	0.206179	+	0.137765i	−0.448194	+	0.893936i	$0.647933\pi$
$882$		0			0
$883$		−	1120.65i		−	1.26914i	−0.772865	−	0.634571i	$-0.781177\pi$
$883$		−	1120.65i		−	1.26914i	0.772865	−	0.634571i	$-0.218823\pi$
$884$		0			0
$885$	−1599.97			−1.80788
$886$		0			0
$887$	−219.375	+	328.318i	−0.247322	+	0.370144i	−0.934272	−	0.356561i	$-0.883949\pi$
$887$	−219.375	+	328.318i	−0.247322	+	0.370144i	0.686950	+	0.726705i	$0.258949\pi$
$888$		0			0
$889$	−145.302	−	730.484i	−0.163445	−	0.821692i
$890$		0			0
$891$	−1.68884	+	8.49038i	−0.00189545	+	0.00952905i
$892$		0			0
$893$	133.072	+	321.264i	0.149017	+	0.359758i
$894$		0			0
$895$	1328.87	−	887.925i	1.48477	−	0.992095i
$896$		0			0
$897$	−1361.68	+	1361.68i	−1.51804	+	1.51804i
$898$		0			0
$899$	810.482	+	335.713i	0.901537	+	0.373429i
$900$		0			0
$901$	−740.091	+	559.617i	−0.821411	+	0.621107i
$902$		0			0
$903$	−197.373	+	476.501i	−0.218575	+	0.527687i
$904$		0			0
$905$	453.563	+	453.563i	0.501175	+	0.501175i
$906$		0			0
$907$	875.138	+	1309.74i	0.964871	+	1.44403i	0.894789	+	0.446490i	$0.147326\pi$
$907$	875.138	+	1309.74i	0.964871	+	1.44403i	0.0700822	+	0.997541i	$0.477674\pi$
$908$		0			0
$909$	−163.993	+	67.9282i	−0.180411	+	0.0747285i
$910$		0			0
$911$	716.336	+	142.488i	0.786318	+	0.156408i	0.571889	−	0.820331i	$-0.306211\pi$
$911$	716.336	+	142.488i	0.786318	+	0.156408i	0.214429	+	0.976740i	$0.431211\pi$
$912$		0			0
$913$	−8.09805	+	1.61080i	−0.00886971	+	0.00176430i
$914$		0			0
$915$	2792.37	+	1865.80i	3.05177	+	2.03913i
$916$		0			0
$917$			577.791i			0.630088i
$918$		0			0
$919$	923.450			1.00484			0.502421	−	0.864623i	$-0.332443\pi$
$919$	923.450			1.00484			0.502421	+	0.864623i	$0.332443\pi$
$920$		0			0
$921$	552.121	−	826.308i	0.599480	−	0.897186i
$922$		0			0
$923$	1.06816	+	5.37003i	0.00115727	+	0.00581801i
$924$		0			0
$925$	−281.216	+	1413.77i	−0.304017	+	1.52840i
$926$		0			0
$927$	−300.504	−	725.482i	−0.324169	−	0.782612i
$928$		0			0
$929$	951.498	−	635.771i	1.02422	−	0.684360i	0.0744207	−	0.997227i	$-0.476289\pi$
$929$	951.498	−	635.771i	1.02422	−	0.684360i	0.949797	+	0.312866i	$0.101289\pi$
$930$		0			0
$931$	683.833	−	683.833i	0.734515	−	0.734515i
$932$		0			0
$933$	1150.64	+	476.609i	1.23327	+	0.510835i
$934$		0			0
$935$	−3.08172	−	11.8355i	−0.00329595	−	0.0126582i
$936$		0			0
$937$	−650.198	+	1569.72i	−0.693915	+	1.67526i	0.0428257	+	0.999083i	$0.486364\pi$
$937$	−650.198	+	1569.72i	−0.693915	+	1.67526i	−0.736740	+	0.676176i	$0.763636\pi$
$938$		0			0
$939$	187.648	+	187.648i	0.199838	+	0.199838i
$940$		0			0
$941$	−864.792	−	1294.25i	−0.919013	−	1.37540i	−0.926850	−	0.375431i	$-0.877495\pi$
$941$	−864.792	−	1294.25i	−0.919013	−	1.37540i	0.00783674	−	0.999969i	$-0.497505\pi$
$942$		0			0
$943$	−403.174	+	167.000i	−0.427544	+	0.177094i
$944$		0			0
$945$	343.882	+	68.4023i	0.363896	+	0.0723834i
$946$		0			0
$947$	1703.17	−	338.781i	1.79849	−	0.357742i	0.821364	−	0.570405i	$-0.193214\pi$
$947$	1703.17	−	338.781i	1.79849	−	0.357742i	0.977126	+	0.212663i	$0.0682137\pi$
$948$		0			0
$949$	−197.025	−	131.648i	−0.207613	−	0.138723i
$950$		0			0
$951$			1408.69i			1.48127i
$952$		0			0
$953$	164.915			0.173049			0.0865243	−	0.996250i	$-0.472424\pi$
$953$	164.915			0.173049			0.0865243	+	0.996250i	$0.472424\pi$
$954$		0			0
$955$	−1227.03	+	1836.39i	−1.28485	+	1.92292i
$956$		0			0
$957$	1.53726	+	7.72835i	0.00160634	+	0.00807560i
$958$		0			0
$959$	−33.6809	+	169.326i	−0.0351209	+	0.176565i
$960$		0			0
$961$	183.024	+	441.859i	0.190452	+	0.459791i
$962$		0			0
$963$	−821.214	+	548.717i	−0.852766	+	0.569800i
$964$		0			0
$965$	−71.5550	+	71.5550i	−0.0741503	+	0.0741503i
$966$		0			0
$967$	709.632	+	293.939i	0.733849	+	0.303970i	0.718132	−	0.695906i	$-0.244997\pi$
$967$	709.632	+	293.939i	0.733849	+	0.303970i	0.0157162	+	0.999876i	$0.494997\pi$
$968$		0			0
$969$	−107.557	−	1840.45i	−0.110998	−	1.89932i
$970$		0			0
$971$	−287.115	+	693.158i	−0.295690	+	0.713860i	0.704302	+	0.709901i	$0.251260\pi$
$971$	−287.115	+	693.158i	−0.295690	+	0.713860i	−0.999992	+	0.00395900i	$0.998740\pi$
$972$		0			0
$973$	−79.0169	−	79.0169i	−0.0812096	−	0.0812096i
$974$		0			0
$975$	−1941.49	−	2905.65i	−1.99127	−	2.98015i
$976$		0			0
$977$	−505.520	+	209.393i	−0.517421	+	0.214323i	−0.626084	−	0.779756i	$-0.715343\pi$
$977$	−505.520	+	209.393i	−0.517421	+	0.214323i	0.108663	+	0.994079i	$0.465343\pi$
$978$		0			0
$979$	−10.8404	−	2.15629i	−0.0110729	−	0.00220254i
$980$		0			0
$981$	622.981	−	123.919i	0.635046	−	0.126319i
$982$		0			0
$983$	−1121.39	−	749.286i	−1.14078	−	0.762245i	−0.166157	−	0.986099i	$-0.553136\pi$
$983$	−1121.39	−	749.286i	−1.14078	−	0.762245i	−0.974623	+	0.223855i	$0.928136\pi$
$984$		0			0
$985$		−	2210.92i		−	2.24458i
$986$		0			0
$987$	−183.377			−0.185793
$988$		0			0
$989$	−453.604	+	678.866i	−0.458649	+	0.686416i
$990$		0			0
$991$	384.547	+	1933.25i	0.388039	+	1.95080i	0.296636	+	0.954991i	$0.404135\pi$
$991$	384.547	+	1933.25i	0.388039	+	1.95080i	0.0914028	+	0.995814i	$0.470865\pi$
$992$		0			0
$993$	378.326	−	1901.97i	0.380993	−	1.91538i
$994$		0			0
$995$	−92.6253	−	223.617i	−0.0930907	−	0.224741i
$996$		0			0
$997$	1258.12	−	840.652i	1.26191	−	0.843182i	0.269127	−	0.963105i	$-0.413265\pi$
$997$	1258.12	−	840.652i	1.26191	−	0.843182i	0.992783	+	0.119923i	$0.0382648\pi$
$998$		0			0
$999$	−271.981	+	271.981i	−0.272253	+	0.272253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.a.41.1	✓	32
4.3	odd	2		272.3.bh.f.177.4		32
17.5	odd	16	inner	136.3.t.a.73.1	yes	32
68.39	even	16		272.3.bh.f.209.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.a.41.1	✓	32	1.1	even	1	trivial
136.3.t.a.73.1	yes	32	17.5	odd	16	inner
272.3.bh.f.177.4		32	4.3	odd	2
272.3.bh.f.209.4		32	68.39	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)

\(f(q)\)	\(=\)	\(q+(-2.15859 + 3.23056i) q^{3} +(-1.60027 - 8.04508i) q^{5} +(0.739073 - 3.71557i) q^{7} +(-2.33284 - 5.63197i) q^{9} +O(q^{10})\)	\(q+(-2.15859 + 3.23056i) q^{3} +(-1.60027 - 8.04508i) q^{5} +(0.739073 - 3.71557i) q^{7} +(-2.33284 - 5.63197i) q^{9} +(-0.0729240 + 0.0487263i) q^{11} +(15.0409 - 15.0409i) q^{13} +(29.4444 + 12.1963i) q^{15} +(-14.6619 - 8.60395i) q^{17} +(10.6813 - 25.7869i) q^{19} +(10.4080 + 10.4080i) q^{21} +(12.9453 + 19.3739i) q^{23} +(-39.0654 + 16.1814i) q^{25} +(-11.0663 - 2.20122i) q^{27} +(-22.6794 + 4.51121i) q^{29} +(-31.5440 - 21.0770i) q^{31} -0.340765i q^{33} -31.0748 q^{35} +(18.9394 - 28.3448i) q^{37} +(16.1233 + 81.0575i) q^{39} +(-3.65376 + 18.3687i) q^{41} +(13.4093 + 32.3729i) q^{43} +(-41.5765 + 27.7805i) q^{45} +(-8.80943 + 8.80943i) q^{47} +(32.0108 + 13.2593i) q^{49} +(59.4446 - 28.7938i) q^{51} +(20.8866 - 50.4248i) q^{53} +(0.508704 + 0.508704i) q^{55} +(60.2495 + 90.1697i) q^{57} +(-46.3811 + 19.2117i) q^{59} +(103.351 + 20.5577i) q^{61} +(-22.6501 + 4.50539i) q^{63} +(-145.075 - 96.9357i) q^{65} -20.6073i q^{67} -90.5321 q^{69} +(-0.143006 + 0.214023i) q^{71} +(-2.17331 - 10.9260i) q^{73} +(32.0512 - 161.132i) q^{75} +(0.127150 + 0.306967i) q^{77} +(-117.425 + 78.4609i) q^{79} +(69.7934 - 69.7934i) q^{81} +(86.9756 + 36.0265i) q^{83} +(-45.7565 + 131.725i) q^{85} +(34.3818 - 83.0050i) q^{87} +(89.1111 + 89.1111i) q^{89} +(-44.7692 - 67.0018i) q^{91} +(136.181 - 56.4080i) q^{93} +(-224.550 - 44.6658i) q^{95} +(84.5267 - 16.8134i) q^{97} +(0.444545 + 0.297035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9} - 24 q^{11} + 48 q^{13} + 96 q^{15} + 40 q^{19} - 80 q^{21} - 48 q^{23} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) \) 32 * 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 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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