LMFDB - Embedded newform 136.3.t.a.57.4

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			57.4
Character	$\chi$	$=$	136.57
Dual form			136.3.t.a.105.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.38842 - 0.872911i) q^{3} +(-0.381945 + 0.571621i) q^{5} +(4.41953 + 6.61429i) q^{7} +(10.1813 - 4.21725i) q^{9} +O(q^{10})$	\(q+(4.38842 - 0.872911i) q^{3} +(-0.381945 + 0.571621i) q^{5} +(4.41953 + 6.61429i) q^{7} +(10.1813 - 4.21725i) q^{9} +(1.23862 - 6.22698i) q^{11} +(-2.83799 + 2.83799i) q^{13} +(-1.17716 + 2.84192i) q^{15} +(4.11219 - 16.4951i) q^{17} +(-27.5156 - 11.3973i) q^{19} +(25.1684 + 25.1684i) q^{21} +(-8.11670 - 1.61451i) q^{23} +(9.38622 + 22.6603i) q^{25} +(7.51579 - 5.02189i) q^{27} +(32.0036 + 21.3841i) q^{29} +(-5.66179 - 28.4637i) q^{31} -28.4078i q^{33} -5.46888 q^{35} +(-21.7778 + 4.33188i) q^{37} +(-9.97699 + 14.9316i) q^{39} +(-14.7557 - 22.0835i) q^{41} +(-59.4946 + 24.6435i) q^{43} +(-1.47804 + 7.43062i) q^{45} +(-49.0098 + 49.0098i) q^{47} +(-5.46511 + 13.1939i) q^{49} +(3.64723 - 75.9772i) q^{51} +(-10.3418 - 4.28372i) q^{53} +(3.08638 + 3.08638i) q^{55} +(-130.699 - 25.9976i) q^{57} +(2.40358 + 5.80276i) q^{59} +(-21.7904 + 14.5599i) q^{61} +(72.8908 + 48.7041i) q^{63} +(-0.538300 - 2.70621i) q^{65} -47.9100i q^{67} -37.0288 q^{69} +(131.598 - 26.1765i) q^{71} +(58.4497 - 87.4761i) q^{73} +(60.9711 + 91.2497i) q^{75} +(46.6611 - 19.3277i) q^{77} +(-22.7627 + 114.436i) q^{79} +(-41.5333 + 41.5333i) q^{81} +(51.5525 - 124.459i) q^{83} +(7.85834 + 8.65085i) q^{85} +(159.112 + 65.9062i) q^{87} +(97.2051 + 97.2051i) q^{89} +(-31.3139 - 6.22872i) q^{91} +(-49.6926 - 119.969i) q^{93} +(17.0244 - 11.3753i) q^{95} +(140.425 + 93.8293i) q^{97} +(-13.6499 - 68.6225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

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

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
$3$	4.38842	−	0.872911i	1.46281	−	0.290970i	0.601425	−	0.798929i	$-0.294600\pi$
$3$	4.38842	−	0.872911i	1.46281	−	0.290970i	0.861381	+	0.507959i	$0.169600\pi$
$4$		0			0
$5$	−0.381945	+	0.571621i	−0.0763890	+	0.114324i	−0.867697	−	0.497094i	$-0.834401\pi$
$5$	−0.381945	+	0.571621i	−0.0763890	+	0.114324i	0.791308	+	0.611418i	$0.209401\pi$
$6$		0			0
$7$	4.41953	+	6.61429i	0.631361	+	0.944898i	0.999883	+	0.0152794i	$0.00486377\pi$
$7$	4.41953	+	6.61429i	0.631361	+	0.944898i	−0.368522	+	0.929619i	$0.620136\pi$
$8$		0			0
$9$	10.1813	−	4.21725i	1.13126	−	0.468583i
$10$		0			0
$11$	1.23862	−	6.22698i	0.112602	−	0.566089i	−0.882755	−	0.469834i	$-0.844314\pi$
$11$	1.23862	−	6.22698i	0.112602	−	0.566089i	0.995357	−	0.0962545i	$-0.0306863\pi$
$12$		0			0
$13$	−2.83799	+	2.83799i	−0.218307	+	0.218307i	−0.807785	−	0.589478i	$-0.799334\pi$
$13$	−2.83799	+	2.83799i	−0.218307	+	0.218307i	0.589478	+	0.807785i	$0.299334\pi$
$14$		0			0
$15$	−1.17716	+	2.84192i	−0.0784774	+	0.189461i
$16$		0			0
$17$	4.11219	−	16.4951i	0.241894	−	0.970303i
$17$	4.11219	−	16.4951i	0.241894	−	0.970303i
$18$		0			0
$19$	−27.5156	−	11.3973i	−1.44819	−	0.599859i	−0.486421	−	0.873725i	$-0.661698\pi$
$19$	−27.5156	−	11.3973i	−1.44819	−	0.599859i	−0.961768	+	0.273865i	$0.911698\pi$
$20$		0			0
$21$	25.1684	+	25.1684i	1.19850	+	1.19850i
$22$		0			0
$23$	−8.11670	−	1.61451i	−0.352900	−	0.0701961i	0.0154572	−	0.999881i	$-0.495080\pi$
$23$	−8.11670	−	1.61451i	−0.352900	−	0.0701961i	−0.368357	+	0.929684i	$0.620080\pi$
$24$		0			0
$25$	9.38622	+	22.6603i	0.375449	+	0.906413i
$26$		0			0
$27$	7.51579	−	5.02189i	0.278363	−	0.185996i
$28$		0			0
$29$	32.0036	+	21.3841i	1.10357	+	0.737383i	0.967388	−	0.253300i	$-0.0815160\pi$
$29$	32.0036	+	21.3841i	1.10357	+	0.737383i	0.136184	+	0.990683i	$0.456516\pi$
$30$		0			0
$31$	−5.66179	−	28.4637i	−0.182638	−	0.918185i	−0.958022	−	0.286694i	$-0.907444\pi$
$31$	−5.66179	−	28.4637i	−0.182638	−	0.918185i	0.775384	−	0.631490i	$-0.217556\pi$
$32$		0			0
$33$		−	28.4078i		−	0.860842i
$34$		0			0
$35$	−5.46888			−0.156254
$36$		0			0
$37$	−21.7778	+	4.33188i	−0.588589	+	0.117078i	−0.480395	−	0.877052i	$-0.659507\pi$
$37$	−21.7778	+	4.33188i	−0.588589	+	0.117078i	−0.108194	+	0.994130i	$0.534507\pi$
$38$		0			0
$39$	−9.97699	+	14.9316i	−0.255820	+	0.382862i
$40$		0			0
$41$	−14.7557	−	22.0835i	−0.359896	−	0.538622i	0.606699	−	0.794932i	$-0.292493\pi$
$41$	−14.7557	−	22.0835i	−0.359896	−	0.538622i	−0.966595	+	0.256310i	$0.917493\pi$
$42$		0			0
$43$	−59.4946	+	24.6435i	−1.38360	+	0.573104i	−0.945440	−	0.325795i	$-0.894368\pi$
$43$	−59.4946	+	24.6435i	−1.38360	+	0.573104i	−0.438155	+	0.898899i	$0.644368\pi$
$44$		0			0
$45$	−1.47804	+	7.43062i	−0.0328454	+	0.165125i
$46$		0			0
$47$	−49.0098	+	49.0098i	−1.04276	+	1.04276i	−0.0437175	+	0.999044i	$0.513920\pi$
$47$	−49.0098	+	49.0098i	−1.04276	+	1.04276i	−0.999044	+	0.0437175i	$0.986080\pi$
$48$		0			0
$49$	−5.46511	+	13.1939i	−0.111533	+	0.269264i
$50$		0			0
$51$	3.64723	−	75.9772i	0.0715143	−	1.48975i
$52$		0			0
$53$	−10.3418	−	4.28372i	−0.195129	−	0.0808249i	0.282979	−	0.959126i	$-0.408677\pi$
$53$	−10.3418	−	4.28372i	−0.195129	−	0.0808249i	−0.478108	+	0.878301i	$0.658677\pi$
$54$		0			0
$55$	3.08638	+	3.08638i	0.0561161	+	0.0561161i
$56$		0			0
$57$	−130.699	−	25.9976i	−2.29296	−	0.456098i
$58$		0			0
$59$	2.40358	+	5.80276i	0.0407387	+	0.0983519i	0.942939	−	0.332965i	$-0.108049\pi$
$59$	2.40358	+	5.80276i	0.0407387	+	0.0983519i	−0.902200	+	0.431317i	$0.858049\pi$
$60$		0			0
$61$	−21.7904	+	14.5599i	−0.357220	+	0.238686i	−0.721210	−	0.692716i	$-0.756414\pi$
$61$	−21.7904	+	14.5599i	−0.357220	+	0.238686i	0.363991	+	0.931403i	$0.381414\pi$
$62$		0			0
$63$	72.8908	+	48.7041i	1.15700	+	0.773080i
$64$		0			0
$65$	−0.538300	−	2.70621i	−0.00828153	−	0.0416341i
$66$		0			0
$67$		−	47.9100i		−	0.715075i	−0.933899	−	0.357537i	$-0.883616\pi$
$67$		−	47.9100i		−	0.715075i	0.933899	−	0.357537i	$-0.116384\pi$
$68$		0			0
$69$	−37.0288			−0.536649
$70$		0			0
$71$	131.598	−	26.1765i	1.85350	−	0.368683i	0.862886	−	0.505398i	$-0.168654\pi$
$71$	131.598	−	26.1765i	1.85350	−	0.368683i	0.990610	+	0.136715i	$0.0436543\pi$
$72$		0			0
$73$	58.4497	−	87.4761i	0.800680	−	1.19830i	−0.176166	−	0.984360i	$-0.556370\pi$
$73$	58.4497	−	87.4761i	0.800680	−	1.19830i	0.976846	−	0.213942i	$-0.0686304\pi$
$74$		0			0
$75$	60.9711	+	91.2497i	0.812948	+	1.21666i
$76$		0			0
$77$	46.6611	−	19.3277i	0.605989	−	0.251009i
$78$		0			0
$79$	−22.7627	+	114.436i	−0.288135	+	1.44855i	0.517266	+	0.855825i	$0.326950\pi$
$79$	−22.7627	+	114.436i	−0.288135	+	1.44855i	−0.805401	+	0.592730i	$0.798050\pi$
$80$		0			0
$81$	−41.5333	+	41.5333i	−0.512757	+	0.512757i
$82$		0			0
$83$	51.5525	−	124.459i	0.621115	−	1.49950i	−0.229281	−	0.973360i	$-0.573637\pi$
$83$	51.5525	−	124.459i	0.621115	−	1.49950i	0.850396	−	0.526144i	$-0.176363\pi$
$84$		0			0
$85$	7.85834	+	8.65085i	0.0924511	+	0.101775i
$86$		0			0
$87$	159.112	+	65.9062i	1.82887	+	0.757542i
$88$		0			0
$89$	97.2051	+	97.2051i	1.09219	+	1.09219i	0.995294	+	0.0968981i	$0.0308921\pi$
$89$	97.2051	+	97.2051i	1.09219	+	1.09219i	0.0968981	+	0.995294i	$0.469108\pi$
$90$		0			0
$91$	−31.3139	−	6.22872i	−0.344109	−	0.0684475i
$92$		0			0
$93$	−49.6926	−	119.969i	−0.534329	−	1.28998i
$94$		0			0
$95$	17.0244	−	11.3753i	0.179204	−	0.119740i
$96$		0			0
$97$	140.425	+	93.8293i	1.44768	+	0.967312i	0.997220	+	0.0745180i	$0.0237418\pi$
$97$	140.425	+	93.8293i	1.44768	+	0.967312i	0.450465	+	0.892794i	$0.351258\pi$
$98$		0			0
$99$	−13.6499	−	68.6225i	−0.137877	−	0.693157i
$100$		0			0
$101$		−	86.2160i		−	0.853623i	−0.904341	−	0.426812i	$-0.859637\pi$
$101$		−	86.2160i		−	0.853623i	0.904341	−	0.426812i	$-0.140363\pi$
$102$		0			0
$103$	−161.863			−1.57149			−0.785745	−	0.618551i	$-0.787720\pi$
$103$	−161.863			−1.57149			−0.785745	+	0.618551i	$0.787720\pi$
$104$		0			0
$105$	−23.9997	+	4.77385i	−0.228569	+	0.0454652i
$106$		0			0
$107$	22.7693	−	34.0766i	0.212797	−	0.318473i	−0.709681	−	0.704523i	$-0.751161\pi$
$107$	22.7693	−	34.0766i	0.212797	−	0.318473i	0.922478	+	0.386050i	$0.126161\pi$
$108$		0			0
$109$	−15.0200	−	22.4791i	−0.137799	−	0.206230i	0.756152	−	0.654396i	$-0.227077\pi$
$109$	−15.0200	−	22.4791i	−0.137799	−	0.206230i	−0.893950	+	0.448166i	$0.852077\pi$
$110$		0			0
$111$	−91.7888	+	38.0202i	−0.826926	+	0.342524i
$112$		0			0
$113$	0.675279	−	3.39485i	0.00597592	−	0.0300430i	−0.977682	−	0.210089i	$-0.932625\pi$
$113$	0.675279	−	3.39485i	0.00597592	−	0.0300430i	0.983658	+	0.180046i	$0.0576246\pi$
$114$		0			0
$115$	4.02302	−	4.02302i	0.0349828	−	0.0349828i
$116$		0			0
$117$	−16.9261	+	40.8631i	−0.144667	+	0.349257i
$118$		0			0
$119$	127.278	−	45.7015i	1.06956	−	0.384046i
$120$		0			0
$121$	74.5484	+	30.8790i	0.616102	+	0.255198i
$122$		0			0
$123$	−84.0312	−	84.0312i	−0.683181	−	0.683181i
$124$		0			0
$125$	−33.3950	−	6.64267i	−0.267160	−	0.0531414i
$126$		0			0
$127$	45.8534	+	110.700i	0.361050	+	0.871652i	0.995147	+	0.0983987i	$0.0313720\pi$
$127$	45.8534	+	110.700i	0.361050	+	0.871652i	−0.634097	+	0.773254i	$0.718628\pi$
$128$		0			0
$129$	−239.576	+	160.079i	−1.85718	+	1.24093i
$130$		0			0
$131$	26.9700	+	18.0208i	0.205878	+	0.137563i	0.654235	−	0.756291i	$-0.272991\pi$
$131$	26.9700	+	18.0208i	0.205878	+	0.137563i	−0.448357	+	0.893855i	$0.647991\pi$
$132$		0			0
$133$	−46.2206	−	232.367i	−0.347523	−	1.74712i
$134$		0			0
$135$			6.21427i			0.0460316i
$136$		0			0
$137$	99.0842			0.723242			0.361621	−	0.932325i	$-0.382223\pi$
$137$	99.0842			0.723242			0.361621	+	0.932325i	$0.382223\pi$
$138$		0			0
$139$	−108.549	+	21.5918i	−0.780930	+	0.155337i	−0.569428	−	0.822041i	$-0.692835\pi$
$139$	−108.549	+	21.5918i	−0.780930	+	0.155337i	−0.211502	+	0.977378i	$0.567835\pi$
$140$		0			0
$141$	−172.294	+	257.857i	−1.22195	+	1.82877i
$142$		0			0
$143$	14.1569	+	21.1873i	0.0989994	+	0.148163i
$144$		0			0
$145$	−24.4472	+	10.1264i	−0.168602	+	0.0698370i
$146$		0			0
$147$	−12.4660	+	62.6711i	−0.0848030	+	0.426334i
$148$		0			0
$149$	192.718	−	192.718i	1.29341	−	1.29341i	0.360746	−	0.932664i	$-0.382522\pi$
$149$	192.718	−	192.718i	1.29341	−	1.29341i	0.932664	−	0.360746i	$-0.117478\pi$
$150$		0			0
$151$	49.2001	−	118.780i	0.325829	−	0.786620i	−0.673064	−	0.739584i	$-0.735022\pi$
$151$	49.2001	−	118.780i	0.325829	−	0.786620i	0.998893	−	0.0470363i	$-0.0149776\pi$
$152$		0			0
$153$	−27.6965	−	185.285i	−0.181023	−	1.21101i
$154$		0			0
$155$	18.4330	+	7.63518i	0.118922	+	0.0492592i
$156$		0			0
$157$	112.384	+	112.384i	0.715825	+	0.715825i	0.967747	−	0.251923i	$-0.0810628\pi$
$157$	112.384	+	112.384i	0.715825	+	0.715825i	−0.251923	+	0.967747i	$0.581063\pi$
$158$		0			0
$159$	−49.1235	−	9.77128i	−0.308953	−	0.0614546i
$160$		0			0
$161$	−25.1931	−	60.8215i	−0.156479	−	0.377774i
$162$		0			0
$163$	29.4056	−	19.6482i	0.180403	−	0.120541i	−0.462090	−	0.886833i	$-0.652900\pi$
$163$	29.4056	−	19.6482i	0.180403	−	0.120541i	0.642493	+	0.766292i	$0.277900\pi$
$164$		0			0
$165$	16.2385	+	10.8502i	0.0984151	+	0.0657588i
$166$		0			0
$167$	2.84302	+	14.2929i	0.0170241	+	0.0855859i	0.988363	−	0.152112i	$-0.0486073\pi$
$167$	2.84302	+	14.2929i	0.0170241	+	0.0855859i	−0.971339	+	0.237698i	$0.923607\pi$
$168$		0			0
$169$			152.892i			0.904684i
$170$		0			0
$171$	−328.211			−1.91936
$172$		0			0
$173$	−73.4970	+	14.6195i	−0.424838	+	0.0845056i	−0.402879	−	0.915253i	$-0.631990\pi$
$173$	−73.4970	+	14.6195i	−0.424838	+	0.0845056i	−0.0219593	+	0.999759i	$0.506990\pi$
$174$		0			0
$175$	−108.399	+	162.231i	−0.619425	+	0.927035i
$176$		0			0
$177$	15.6132	+	23.3668i	0.0882103	+	0.132016i
$178$		0			0
$179$	214.131	−	88.6958i	1.19626	−	0.495507i	0.306472	−	0.951880i	$-0.400852\pi$
$179$	214.131	−	88.6958i	1.19626	−	0.495507i	0.889789	+	0.456373i	$0.150852\pi$
$180$		0			0
$181$	8.24588	−	41.4548i	0.0455573	−	0.229032i	−0.951298	−	0.308272i	$-0.900249\pi$
$181$	8.24588	−	41.4548i	0.0455573	−	0.229032i	0.996856	+	0.0792399i	$0.0252493\pi$
$182$		0			0
$183$	−82.9159	+	82.9159i	−0.453092	+	0.453092i
$184$		0			0
$185$	5.84173	−	14.1032i	0.0315769	−	0.0762335i
$186$		0			0
$187$	−97.6214	−	46.0378i	−0.522040	−	0.246191i
$188$		0			0
$189$	66.4325	+	27.5172i	0.351495	+	0.145594i
$190$		0			0
$191$	−60.8586	−	60.8586i	−0.318631	−	0.318631i	0.529610	−	0.848241i	$-0.322338\pi$
$191$	−60.8586	−	60.8586i	−0.318631	−	0.318631i	−0.848241	+	0.529610i	$0.822338\pi$
$192$		0			0
$193$	−82.9177	−	16.4933i	−0.429625	−	0.0854578i	−0.0244590	−	0.999701i	$-0.507786\pi$
$193$	−82.9177	−	16.4933i	−0.429625	−	0.0854578i	−0.405166	+	0.914243i	$0.632786\pi$
$194$		0			0
$195$	−4.72457	−	11.4061i	−0.0242286	−	0.0584929i
$196$		0			0
$197$	−275.827	+	184.301i	−1.40014	+	0.935541i	−0.400319	+	0.916376i	$0.631101\pi$
$197$	−275.827	+	184.301i	−1.40014	+	0.935541i	−0.999816	+	0.0191648i	$0.993899\pi$
$198$		0			0
$199$	−280.473	−	187.406i	−1.40941	−	0.941740i	−0.999562	−	0.0295869i	$-0.990581\pi$
$199$	−280.473	−	187.406i	−1.40941	−	0.941740i	−0.409851	−	0.912153i	$-0.634419\pi$
$200$		0			0
$201$	−41.8212	−	210.249i	−0.208066	−	1.04602i
$202$		0			0
$203$			306.189i			1.50832i
$204$		0			0
$205$	18.2593			0.0890696
$206$		0			0
$207$	−89.4476	+	17.7922i	−0.432114	+	0.0859528i
$208$		0			0
$209$	−105.052	+	157.222i	−0.502643	+	0.752258i
$210$		0			0
$211$	−93.5790	−	140.051i	−0.443502	−	0.663748i	0.540614	−	0.841270i	$-0.318192\pi$
$211$	−93.5790	−	140.051i	−0.443502	−	0.663748i	−0.984117	+	0.177522i	$0.943192\pi$
$212$		0			0
$213$	554.659	−	229.747i	2.60403	−	1.07863i
$214$		0			0
$215$	8.63694	−	43.4208i	0.0401718	−	0.201957i
$216$		0			0
$217$	163.245	−	163.245i	0.752281	−	0.752281i
$218$		0			0
$219$	180.143	−	434.903i	0.822570	−	1.98586i
$220$		0			0
$221$	35.1428	+	58.4835i	0.159017	+	0.264631i
$222$		0			0
$223$	313.463	+	129.841i	1.40566	+	0.582245i	0.951216	−	0.308527i	$-0.0998361\pi$
$223$	313.463	+	129.841i	1.40566	+	0.582245i	0.454449	+	0.890773i	$0.349836\pi$
$224$		0			0
$225$	191.128	+	191.128i	0.849460	+	0.849460i
$226$		0			0
$227$	−6.26447	−	1.24608i	−0.0275968	−	0.00548934i	0.181273	−	0.983433i	$-0.441978\pi$
$227$	−6.26447	−	1.24608i	−0.0275968	−	0.00548934i	−0.208869	+	0.977944i	$0.566978\pi$
$228$		0			0
$229$	104.462	+	252.193i	0.456165	+	1.10128i	0.969938	+	0.243353i	$0.0782473\pi$
$229$	104.462	+	252.193i	0.456165	+	1.10128i	−0.513773	+	0.857926i	$0.671753\pi$
$230$		0			0
$231$	187.897	−	125.549i	0.813408	−	0.543502i
$232$		0			0
$233$	32.0131	+	21.3905i	0.137395	+	0.0918045i	0.622368	−	0.782725i	$-0.286171\pi$
$233$	32.0131	+	21.3905i	0.137395	+	0.0918045i	−0.484973	+	0.874529i	$0.661171\pi$
$234$		0			0
$235$	−9.29598	−	46.7341i	−0.0395574	−	0.198868i
$236$		0			0
$237$			522.062i			2.20279i
$238$		0			0
$239$	−52.4922			−0.219633			−0.109816	−	0.993952i	$-0.535026\pi$
$239$	−52.4922			−0.219633			−0.109816	+	0.993952i	$0.535026\pi$
$240$		0			0
$241$	222.473	−	44.2526i	0.923123	−	0.183621i	0.289425	−	0.957201i	$-0.406536\pi$
$241$	222.473	−	44.2526i	0.923123	−	0.183621i	0.633698	+	0.773580i	$0.281536\pi$
$242$		0			0
$243$	−191.208	+	286.163i	−0.786863	+	1.17762i
$244$		0			0
$245$	−5.45456	−	8.16332i	−0.0222635	−	0.0333197i
$246$		0			0
$247$	110.435	−	45.7435i	0.447104	−	0.185196i
$248$		0			0
$249$	117.593	−	591.178i	0.472260	−	2.37421i
$250$		0			0
$251$	22.9285	−	22.9285i	0.0913488	−	0.0913488i	−0.659956	−	0.751304i	$-0.729425\pi$
$251$	22.9285	−	22.9285i	0.0913488	−	0.0913488i	0.751304	+	0.659956i	$0.229425\pi$
$252$		0			0
$253$	−20.1070	+	48.5427i	−0.0794745	+	0.191868i
$254$		0			0
$255$	42.0371	+	31.1039i	0.164851	+	0.121976i
$256$		0			0
$257$	101.864	+	42.1933i	0.396356	+	0.164176i	0.571954	−	0.820286i	$-0.306186\pi$
$257$	101.864	+	42.1933i	0.396356	+	0.164176i	−0.175597	+	0.984462i	$0.556186\pi$
$258$		0			0
$259$	−124.900	−	124.900i	−0.482239	−	0.482239i
$260$		0			0
$261$	416.021	+	82.7518i	1.59395	+	0.317057i
$262$		0			0
$263$	−14.5062	−	35.0211i	−0.0551567	−	0.133160i	0.893899	−	0.448268i	$-0.147959\pi$
$263$	−14.5062	−	35.0211i	−0.0551567	−	0.133160i	−0.949056	+	0.315108i	$0.897959\pi$
$264$		0			0
$265$	6.39867	−	4.27545i	0.0241459	−	0.0161338i
$266$		0			0
$267$	511.428	+	341.725i	1.91546	+	1.27987i
$268$		0			0
$269$	−49.9056	−	250.893i	−0.185523	−	0.932686i	−0.955585	−	0.294717i	$-0.904775\pi$
$269$	−49.9056	−	250.893i	−0.185523	−	0.932686i	0.770062	−	0.637969i	$-0.220225\pi$
$270$		0			0
$271$			48.0980i			0.177483i	0.996055	+	0.0887416i	$0.0282845\pi$
$271$			48.0980i			0.177483i	−0.996055	+	0.0887416i	$0.971715\pi$
$272$		0			0
$273$	−142.856			−0.523281
$274$		0			0
$275$	152.731	−	30.3801i	0.555387	−	0.110473i
$276$		0			0
$277$	−78.3738	+	117.295i	−0.282938	+	0.423446i	−0.945530	−	0.325534i	$-0.894456\pi$
$277$	−78.3738	+	117.295i	−0.282938	+	0.423446i	0.662593	+	0.748980i	$0.269456\pi$
$278$		0			0
$279$	−177.683	−	265.922i	−0.636857	−	0.953124i
$280$		0			0
$281$	−303.082	+	125.541i	−1.07858	+	0.446764i	−0.850012	−	0.526763i	$-0.823405\pi$
$281$	−303.082	+	125.541i	−1.07858	+	0.446764i	−0.228572	+	0.973527i	$0.573405\pi$
$282$		0			0
$283$	−104.095	+	523.321i	−0.367827	+	1.84919i	0.143293	+	0.989680i	$0.454231\pi$
$283$	−104.095	+	523.321i	−0.367827	+	1.84919i	−0.511120	+	0.859510i	$0.670769\pi$
$284$		0			0
$285$	64.7805	−	64.7805i	0.227300	−	0.227300i
$286$		0			0
$287$	80.8533	−	195.197i	0.281719	−	0.680129i
$288$		0			0
$289$	−255.180	−	135.662i	−0.882975	−	0.469420i
$290$		0			0
$291$	698.150	+	289.183i	2.39914	+	0.993757i
$292$		0			0
$293$	−396.439	−	396.439i	−1.35303	−	1.35303i	−0.882246	−	0.470789i	$-0.843969\pi$
$293$	−396.439	−	396.439i	−1.35303	−	1.35303i	−0.470789	−	0.882246i	$-0.656031\pi$
$294$		0			0
$295$	−4.23502	−	0.842397i	−0.0143560	−	0.00285558i
$296$		0			0
$297$	−21.9620	−	53.0209i	−0.0739460	−	0.178521i
$298$		0			0
$299$	27.6171	−	18.4532i	0.0923649	−	0.0617163i
$300$		0			0
$301$	−425.937	−	284.602i	−1.41507	−	0.945522i
$302$		0			0
$303$	−75.2589	−	378.352i	−0.248379	−	1.24869i
$304$		0			0
$305$		−	18.0169i		−	0.0590719i
$306$		0			0
$307$	−66.1820			−0.215577			−0.107788	−	0.994174i	$-0.534377\pi$
$307$	−66.1820			−0.215577			−0.107788	+	0.994174i	$0.534377\pi$
$308$		0			0
$309$	−710.325	+	141.292i	−2.29879	+	0.457257i
$310$		0			0
$311$	−199.777	+	298.988i	−0.642370	+	0.961375i	0.357255	+	0.934007i	$0.383713\pi$
$311$	−199.777	+	298.988i	−0.642370	+	0.961375i	−0.999625	+	0.0273680i	$0.991287\pi$
$312$		0			0
$313$	−27.9711	−	41.8617i	−0.0893644	−	0.133743i	0.784094	−	0.620642i	$-0.213128\pi$
$313$	−27.9711	−	41.8617i	−0.0893644	−	0.133743i	−0.873458	+	0.486899i	$0.838128\pi$
$314$		0			0
$315$	−55.6805	+	23.0636i	−0.176764	+	0.0732179i
$316$		0			0
$317$	−79.4410	+	399.377i	−0.250603	+	1.25986i	0.626447	+	0.779464i	$0.284509\pi$
$317$	−79.4410	+	399.377i	−0.250603	+	1.25986i	−0.877049	+	0.480400i	$0.840491\pi$
$318$		0			0
$319$	172.799	−	172.799i	0.541689	−	0.541689i
$320$		0			0
$321$	70.1752	−	169.418i	0.218614	−	0.527782i
$322$		0			0
$323$	−301.150	+	407.006i	−0.932353	+	1.26008i
$324$		0			0
$325$	−90.9479	−	37.6719i	−0.279840	−	0.115913i
$326$		0			0
$327$	−85.5365	−	85.5365i	−0.261579	−	0.261579i
$328$		0			0
$329$	−540.765	−	107.565i	−1.64366	−	0.326945i
$330$		0			0
$331$	−44.3420	−	107.051i	−0.133964	−	0.323417i	0.842635	−	0.538484i	$-0.181003\pi$
$331$	−44.3420	−	107.051i	−0.133964	−	0.323417i	−0.976599	+	0.215067i	$0.931003\pi$
$332$		0			0
$333$	−203.459	+	135.947i	−0.610987	+	0.408248i
$334$		0			0
$335$	27.3864	+	18.2990i	0.0817504	+	0.0546238i
$336$		0			0
$337$	67.3600	+	338.642i	0.199881	+	1.00487i	0.942258	+	0.334888i	$0.108699\pi$
$337$	67.3600	+	338.642i	0.199881	+	1.00487i	−0.742376	+	0.669983i	$0.766301\pi$
$338$		0			0
$339$		−	15.4875i		−	0.0456859i
$340$		0			0
$341$	−184.256			−0.540339
$342$		0			0
$343$	270.880	−	53.8815i	0.789739	−	0.157089i
$344$		0			0
$345$	14.1430	−	21.1664i	0.0409941	−	0.0613520i
$346$		0			0
$347$	0.877077	+	1.31264i	0.00252760	+	0.00378282i	0.832731	−	0.553677i	$-0.186776\pi$
$347$	0.877077	+	1.31264i	0.00252760	+	0.00378282i	−0.830204	+	0.557460i	$0.811776\pi$
$348$		0			0
$349$	369.420	−	153.019i	1.05851	−	0.438449i	0.215587	−	0.976485i	$-0.430833\pi$
$349$	369.420	−	153.019i	1.05851	−	0.438449i	0.842922	+	0.538035i	$0.180833\pi$
$350$		0			0
$351$	−7.07768	+	35.5819i	−0.0201643	+	0.101373i
$352$		0			0
$353$	12.8671	−	12.8671i	0.0364507	−	0.0364507i	−0.688647	−	0.725097i	$-0.741795\pi$
$353$	12.8671	−	12.8671i	0.0364507	−	0.0364507i	0.725097	+	0.688647i	$0.241795\pi$
$354$		0			0
$355$	−35.3002	+	85.2223i	−0.0994373	+	0.240063i
$356$		0			0
$357$	518.654	−	311.659i	1.45281	−	0.872995i
$358$		0			0
$359$	−58.3613	−	24.1740i	−0.162566	−	0.0673371i	0.299916	−	0.953965i	$-0.403041\pi$
$359$	−58.3613	−	24.1740i	−0.162566	−	0.0673371i	−0.462483	+	0.886628i	$0.653041\pi$
$360$		0			0
$361$	371.943	+	371.943i	1.03031	+	1.03031i
$362$		0			0
$363$	354.104	+	70.4357i	0.975494	+	0.194038i
$364$		0			0
$365$	27.6786	+	66.8221i	0.0758318	+	0.183074i
$366$		0			0
$367$	−204.765	+	136.820i	−0.557943	+	0.372805i	−0.802338	−	0.596870i	$-0.796411\pi$
$367$	−204.765	+	136.820i	−0.557943	+	0.372805i	0.244395	+	0.969676i	$0.421411\pi$
$368$		0			0
$369$	−243.365	−	162.611i	−0.659524	−	0.440680i
$370$		0			0
$371$	−17.3722	−	87.3357i	−0.0468252	−	0.235406i
$372$		0			0
$373$		−	529.576i		−	1.41977i	−0.704315	−	0.709887i	$-0.748746\pi$
$373$		−	529.576i		−	1.41977i	0.704315	−	0.709887i	$-0.251254\pi$
$374$		0			0
$375$	−152.350			−0.406265
$376$		0			0
$377$	−151.514	+	30.1380i	−0.401894	+	0.0799417i
$378$		0			0
$379$	167.642	−	250.894i	0.442327	−	0.661989i	−0.541584	−	0.840646i	$-0.682175\pi$
$379$	167.642	−	250.894i	0.442327	−	0.661989i	0.983911	+	0.178657i	$0.0571753\pi$
$380$		0			0
$381$	297.855	+	445.771i	0.781772	+	1.17000i
$382$		0			0
$383$	87.9947	−	36.4486i	0.229751	−	0.0951661i	−0.264838	−	0.964293i	$-0.585318\pi$
$383$	87.9947	−	36.4486i	0.229751	−	0.0951661i	0.494589	+	0.869127i	$0.335318\pi$
$384$		0			0
$385$	−6.77388	+	34.0546i	−0.0175945	+	0.0884535i
$386$		0			0
$387$	−501.807	+	501.807i	−1.29666	+	1.29666i
$388$		0			0
$389$	39.6284	−	95.6714i	0.101872	−	0.245942i	−0.864723	−	0.502249i	$-0.832506\pi$
$389$	39.6284	−	95.6714i	0.101872	−	0.245942i	0.966595	+	0.256307i	$0.0825060\pi$
$390$		0			0
$391$	−60.0090	+	127.247i	−0.153476	+	0.325440i
$392$		0			0
$393$	134.086	+	55.5403i	0.341186	+	0.141324i
$394$		0			0
$395$	−56.7198	−	56.7198i	−0.143594	−	0.143594i
$396$		0			0
$397$	60.8371	+	12.1013i	0.153242	+	0.0304818i	0.271115	−	0.962547i	$-0.412608\pi$
$397$	60.8371	+	12.1013i	0.153242	+	0.0304818i	−0.117873	+	0.993029i	$0.537608\pi$
$398$		0			0
$399$	−405.671	−	979.376i	−1.01672	−	2.45458i
$400$		0			0
$401$	−284.108	+	189.835i	−0.708498	+	0.473403i	−0.856873	−	0.515528i	$-0.827596\pi$
$401$	−284.108	+	189.835i	−0.708498	+	0.473403i	0.148374	+	0.988931i	$0.452596\pi$
$402$		0			0
$403$	96.8480	+	64.7118i	0.240318	+	0.160575i
$404$		0			0
$405$	−7.87788	−	39.6048i	−0.0194516	−	0.0977895i
$406$		0			0
$407$			140.975i			0.346377i
$408$		0			0
$409$	200.502			0.490224			0.245112	−	0.969495i	$-0.421175\pi$
$409$	200.502			0.490224			0.245112	+	0.969495i	$0.421175\pi$
$410$		0			0
$411$	434.823	−	86.4916i	1.05796	−	0.210442i
$412$		0			0
$413$	−27.7584	+	41.5435i	−0.0672117	+	0.100589i
$414$		0			0
$415$	51.4530	+	77.0049i	0.123983	+	0.185554i
$416$		0			0
$417$	−457.512	+	189.508i	−1.09715	+	0.454455i
$418$		0			0
$419$	40.5924	−	204.072i	0.0968792	−	0.487045i	−0.901632	−	0.432503i	$-0.857630\pi$
$419$	40.5924	−	204.072i	0.0968792	−	0.487045i	0.998512	−	0.0545413i	$-0.0173697\pi$
$420$		0			0
$421$	226.375	−	226.375i	0.537708	−	0.537708i	−0.385147	−	0.922855i	$-0.625849\pi$
$421$	226.375	−	226.375i	0.537708	−	0.537708i	0.922855	+	0.385147i	$0.125849\pi$
$422$		0			0
$423$	−292.299	+	705.672i	−0.691014	+	1.66825i
$424$		0			0
$425$	412.383	−	61.6434i	0.970314	−	0.145043i
$426$		0			0
$427$	−192.606	−	79.7802i	−0.451069	−	0.186839i
$428$		0			0
$429$	80.6211	+	80.6211i	0.187928	+	0.187928i
$430$		0			0
$431$	−631.929	−	125.698i	−1.46619	−	0.291644i	−0.603495	−	0.797366i	$-0.706226\pi$
$431$	−631.929	−	125.698i	−1.46619	−	0.291644i	−0.862696	+	0.505723i	$0.831226\pi$
$432$		0			0
$433$	232.202	+	560.585i	0.536263	+	1.29465i	0.927314	+	0.374285i	$0.122112\pi$
$433$	232.202	+	560.585i	0.536263	+	1.29465i	−0.391051	+	0.920369i	$0.627888\pi$
$434$		0			0
$435$	−98.4452	+	65.7790i	−0.226311	+	0.151216i
$436$		0			0
$437$	204.935	+	136.933i	0.468958	+	0.313348i
$438$		0			0
$439$	−56.5809	−	284.452i	−0.128886	−	0.647953i	−0.990174	−	0.139837i	$-0.955342\pi$
$439$	−56.5809	−	284.452i	−0.128886	−	0.647953i	0.861289	−	0.508116i	$-0.169658\pi$
$440$		0			0
$441$			157.380i			0.356870i
$442$		0			0
$443$	209.676			0.473310			0.236655	−	0.971594i	$-0.423949\pi$
$443$	209.676			0.473310			0.236655	+	0.971594i	$0.423949\pi$
$444$		0			0
$445$	−92.6915	+	18.4375i	−0.208295	+	0.0414325i
$446$		0			0
$447$	677.502	−	1013.95i	1.51566	−	2.26835i
$448$		0			0
$449$	357.400	+	534.887i	0.795991	+	1.19128i	0.978126	+	0.208011i	$0.0666991\pi$
$449$	357.400	+	534.887i	0.795991	+	1.19128i	−0.182135	+	0.983273i	$0.558301\pi$
$450$		0			0
$451$	−155.790	+	64.5304i	−0.345433	+	0.143083i
$452$		0			0
$453$	112.227	−	564.202i	0.247741	−	1.24548i
$454$		0			0
$455$	15.5207	−	15.5207i	0.0341113	−	0.0341113i
$456$		0			0
$457$	278.344	−	671.981i	0.609067	−	1.47042i	−0.254950	−	0.966954i	$-0.582059\pi$
$457$	278.344	−	671.981i	0.609067	−	1.47042i	0.864017	−	0.503463i	$-0.167941\pi$
$458$		0			0
$459$	−51.9305	−	144.625i	−0.113138	−	0.315087i
$460$		0			0
$461$	−576.512	−	238.799i	−1.25057	−	0.518003i	−0.343567	−	0.939128i	$-0.611635\pi$
$461$	−576.512	−	238.799i	−1.25057	−	0.518003i	−0.907002	+	0.421126i	$0.861635\pi$
$462$		0			0
$463$	−25.1003	−	25.1003i	−0.0542123	−	0.0542123i	0.679481	−	0.733693i	$-0.262205\pi$
$463$	−25.1003	−	25.1003i	−0.0542123	−	0.0542123i	−0.733693	+	0.679481i	$0.762205\pi$
$464$		0			0
$465$	87.5564	+	17.4160i	0.188293	+	0.0374539i
$466$		0			0
$467$	264.779	+	639.234i	0.566980	+	1.36881i	0.904089	+	0.427344i	$0.140551\pi$
$467$	264.779	+	639.234i	0.566980	+	1.36881i	−0.337110	+	0.941465i	$0.609449\pi$
$468$		0			0
$469$	316.891	−	211.740i	0.675673	−	0.451470i
$470$		0			0
$471$	591.292	+	395.089i	1.25540	+	0.838829i
$472$		0			0
$473$	79.7630	+	400.995i	0.168632	+	0.847770i
$474$		0			0
$475$		−	730.490i		−	1.53787i
$476$		0			0
$477$	−123.359			−0.258614
$478$		0			0
$479$	−74.7781	+	14.8743i	−0.156113	+	0.0310528i	−0.272528	−	0.962148i	$-0.587860\pi$
$479$	−74.7781	+	14.8743i	−0.156113	+	0.0310528i	0.116415	+	0.993201i	$0.462860\pi$
$480$		0			0
$481$	49.5115	−	74.0991i	0.102934	−	0.154052i
$482$		0			0
$483$	−163.650	−	244.919i	−0.338819	−	0.507079i
$484$		0			0
$485$	−107.270	+	44.4325i	−0.221174	+	0.0916134i
$486$		0			0
$487$	−147.687	+	742.473i	−0.303259	+	1.52459i	0.465501	+	0.885047i	$0.345874\pi$
$487$	−147.687	+	742.473i	−0.303259	+	1.52459i	−0.768760	+	0.639538i	$0.779126\pi$
$488$		0			0
$489$	111.893	−	111.893i	0.228820	−	0.228820i
$490$		0			0
$491$	−213.682	+	515.875i	−0.435198	+	1.05066i	0.542389	+	0.840128i	$0.317520\pi$
$491$	−213.682	+	515.875i	−0.435198	+	1.05066i	−0.977587	+	0.210533i	$0.932480\pi$
$492$		0			0
$493$	484.339	−	439.968i	0.982432	−	0.892431i
$494$		0			0
$495$	44.4396	+	18.4075i	0.0897769	+	0.0371868i
$496$		0			0
$497$	754.741	+	754.741i	1.51859	+	1.51859i
$498$		0			0
$499$	36.2186	+	7.20432i	0.0725823	+	0.0144375i	0.231248	−	0.972895i	$-0.425719\pi$
$499$	36.2186	+	7.20432i	0.0725823	+	0.0144375i	−0.158666	+	0.987332i	$0.550719\pi$
$500$		0			0
$501$	24.9528	+	60.2413i	0.0498059	+	0.120242i
$502$		0			0
$503$	277.952	−	185.721i	0.552588	−	0.369227i	−0.247706	−	0.968835i	$-0.579677\pi$
$503$	277.952	−	185.721i	0.552588	−	0.369227i	0.800294	+	0.599608i	$0.204677\pi$
$504$		0			0
$505$	49.2828	+	32.9297i	0.0975898	+	0.0652074i
$506$		0			0
$507$	133.461	+	670.952i	0.263236	+	1.32338i
$508$		0			0
$509$		−	545.832i		−	1.07236i	−0.844103	−	0.536180i	$-0.819867\pi$
$509$		−	545.832i		−	1.07236i	0.844103	−	0.536180i	$-0.180133\pi$
$510$		0			0
$511$	836.912			1.63779
$512$		0			0
$513$	−264.038	+	52.5203i	−0.514693	+	0.102379i
$514$		0			0
$515$	61.8229	−	92.5245i	0.120044	−	0.179659i
$516$		0			0
$517$	244.478	+	365.887i	0.472878	+	0.707712i
$518$		0			0
$519$	−309.774	+	128.313i	−0.596867	+	0.247231i
$520$		0			0
$521$	170.527	−	857.295i	0.327306	−	1.64548i	−0.370237	−	0.928937i	$-0.620723\pi$
$521$	170.527	−	857.295i	0.327306	−	1.64548i	0.697543	−	0.716543i	$-0.254277\pi$
$522$		0			0
$523$	216.459	−	216.459i	0.413879	−	0.413879i	−0.469208	−	0.883088i	$-0.655461\pi$
$523$	216.459	−	216.459i	0.413879	−	0.413879i	0.883088	+	0.469208i	$0.155461\pi$
$524$		0			0
$525$	−334.088	+	806.561i	−0.636359	+	1.53631i
$526$		0			0
$527$	−492.796	−	23.6563i	−0.935096	−	0.0448886i
$528$		0			0
$529$	−425.458	−	176.231i	−0.804269	−	0.333139i
$530$		0			0
$531$	48.9434	+	48.9434i	0.0921721	+	0.0921721i
$532$		0			0
$533$	104.550	+	20.7962i	0.196153	+	0.0390172i
$534$		0			0
$535$	10.7823	+	26.0308i	0.0201538	+	0.0486556i
$536$		0			0
$537$	862.271	−	576.151i	1.60572	−	1.07291i
$538$		0			0
$539$	75.3891	+	50.3734i	0.139868	+	0.0934571i
$540$		0			0
$541$	38.0770	+	191.426i	0.0703827	+	0.353838i	0.999888	−	0.0149712i	$-0.00476566\pi$
$541$	38.0770	+	191.426i	0.0703827	+	0.353838i	−0.929505	+	0.368809i	$0.879766\pi$
$542$		0			0
$543$		−	189.119i		−	0.348286i
$544$		0			0
$545$	18.5863			0.0341034
$546$		0			0
$547$	221.084	−	43.9763i	0.404175	−	0.0803954i	0.0111835	−	0.999937i	$-0.496440\pi$
$547$	221.084	−	43.9763i	0.404175	−	0.0803954i	0.392992	+	0.919542i	$0.371440\pi$
$548$		0			0
$549$	−160.453	+	240.134i	−0.292264	+	0.437403i
$550$		0			0
$551$	−636.876	−	953.152i	−1.15585	−	1.72986i
$552$		0			0
$553$	−857.512	+	355.193i	−1.55065	+	0.642302i
$554$		0			0
$555$	13.3251	−	66.9900i	0.0240093	−	0.120703i
$556$		0			0
$557$	−633.786	+	633.786i	−1.13786	+	1.13786i	−0.149022	+	0.988834i	$0.547612\pi$
$557$	−633.786	+	633.786i	−1.13786	+	1.13786i	−0.988834	+	0.149022i	$0.952388\pi$
$558$		0			0
$559$	98.9073	−	238.783i	0.176936	−	0.427162i
$560$		0			0
$561$	−468.591	−	116.818i	−0.835277	−	0.208232i
$562$		0			0
$563$	−751.603	−	311.324i	−1.33500	−	0.552973i	−0.402920	−	0.915235i	$-0.632005\pi$
$563$	−751.603	−	311.324i	−1.33500	−	0.552973i	−0.932076	+	0.362262i	$0.882005\pi$
$564$		0			0
$565$	1.68265	+	1.68265i	0.00297814	+	0.00297814i
$566$		0			0
$567$	−458.271	−	91.1558i	−0.808238	−	0.160769i
$568$		0			0
$569$	6.42506	+	15.5115i	0.0112919	+	0.0272609i	0.929425	−	0.369011i	$-0.120304\pi$
$569$	6.42506	+	15.5115i	0.0112919	+	0.0272609i	−0.918133	+	0.396272i	$0.870304\pi$
$570$		0			0
$571$	−501.899	+	335.358i	−0.878982	+	0.587317i	−0.911108	−	0.412167i	$-0.864772\pi$
$571$	−501.899	+	335.358i	−0.878982	+	0.587317i	0.0321265	+	0.999484i	$0.489772\pi$
$572$		0			0
$573$	−320.197	−	213.949i	−0.558808	−	0.373384i
$574$		0			0
$575$	−39.5997	−	199.081i	−0.0688691	−	0.346228i
$576$		0			0
$577$		−	202.680i		−	0.351265i	−0.984456	−	0.175632i	$-0.943803\pi$
$577$		−	202.680i		−	0.351265i	0.984456	−	0.175632i	$-0.0561970\pi$
$578$		0			0
$579$	−378.275			−0.653324
$580$		0			0
$581$	1051.04	−	209.066i	1.80903	−	0.359838i
$582$		0			0
$583$	−39.4842	+	59.0923i	−0.0677259	+	0.101359i
$584$		0			0
$585$	−16.8934	−	25.2827i	−0.0288776	−	0.0432184i
$586$		0			0
$587$	179.671	−	74.4223i	0.306084	−	0.126784i	−0.224354	−	0.974508i	$-0.572027\pi$
$587$	179.671	−	74.4223i	0.306084	−	0.126784i	0.530438	+	0.847723i	$0.322027\pi$
$588$		0			0
$589$	−168.623	+	847.725i	−0.286287	+	1.43926i
$590$		0			0
$591$	−1049.56	+	1049.56i	−1.77591	+	1.77591i
$592$		0			0
$593$	165.962	−	400.669i	0.279869	−	0.675664i	−0.719963	−	0.694013i	$-0.755841\pi$
$593$	165.962	−	400.669i	0.279869	−	0.675664i	0.999832	+	0.0183491i	$0.00584103\pi$
$594$		0			0
$595$	−22.4891	+	90.2100i	−0.0377968	+	0.151613i
$596$		0			0
$597$	−1394.42	−	577.589i	−2.33572	−	0.967485i
$598$		0			0
$599$	−119.645	−	119.645i	−0.199741	−	0.199741i	0.600148	−	0.799889i	$-0.295108\pi$
$599$	−119.645	−	119.645i	−0.199741	−	0.199741i	−0.799889	+	0.600148i	$0.795108\pi$
$600$		0			0
$601$	−509.546	−	101.355i	−0.847830	−	0.168644i	−0.247989	−	0.968763i	$-0.579770\pi$
$601$	−509.546	−	101.355i	−0.847830	−	0.168644i	−0.599841	+	0.800119i	$0.704770\pi$
$602$		0			0
$603$	−202.048	−	487.788i	−0.335072	−	0.808935i
$604$		0			0
$605$	−46.1244	+	30.8194i	−0.0762387	+	0.0509411i
$606$		0			0
$607$	585.748	+	391.384i	0.964989	+	0.644785i	0.934956	−	0.354764i	$-0.115439\pi$
$607$	585.748	+	391.384i	0.964989	+	0.644785i	0.0300328	+	0.999549i	$0.490439\pi$
$608$		0			0
$609$	267.275	+	1343.68i	0.438876	+	2.20638i
$610$		0			0
$611$		−	278.179i		−	0.455285i
$612$		0			0
$613$	295.484			0.482030			0.241015	−	0.970521i	$-0.422520\pi$
$613$	295.484			0.482030			0.241015	+	0.970521i	$0.422520\pi$
$614$		0			0
$615$	80.1293	−	15.9387i	0.130292	−	0.0259166i
$616$		0			0
$617$	477.856	−	715.162i	0.774483	−	1.15909i	−0.208969	−	0.977922i	$-0.567011\pi$
$617$	477.856	−	715.162i	0.774483	−	1.15909i	0.983451	−	0.181173i	$-0.0579893\pi$
$618$		0			0
$619$	−520.711	−	779.298i	−0.841213	−	1.25896i	−0.963832	−	0.266510i	$-0.914129\pi$
$619$	−520.711	−	779.298i	−0.841213	−	1.25896i	0.122620	−	0.992454i	$-0.460871\pi$
$620$		0			0
$621$	−69.1113	+	28.6268i	−0.111290	+	0.0460980i
$622$		0			0
$623$	−213.342	+	1072.54i	−0.342443	+	1.72158i
$624$		0			0
$625$	−417.035	+	417.035i	−0.667255	+	0.667255i
$626$		0			0
$627$	−323.773	+	781.657i	−0.516384	+	1.24666i
$628$		0			0
$629$	−18.0996	+	377.042i	−0.0287752	+	0.599430i
$630$		0			0
$631$	95.7919	+	39.6783i	0.151810	+	0.0628817i	0.457295	−	0.889315i	$-0.348819\pi$
$631$	95.7919	+	39.6783i	0.151810	+	0.0628817i	−0.305485	+	0.952197i	$0.598819\pi$
$632$		0			0
$633$	−532.916	−	532.916i	−0.841889	−	0.841889i
$634$		0			0
$635$	−80.7918	−	16.0705i	−0.127231	−	0.0253079i
$636$		0			0
$637$	−21.9344	−	52.9542i	−0.0344339	−	0.0831307i
$638$		0			0
$639$	1229.45	−	821.495i	1.92403	−	1.28559i
$640$		0			0
$641$	−823.807	−	550.451i	−1.28519	−	0.858737i	−0.290032	−	0.957017i	$-0.593666\pi$
$641$	−823.807	−	550.451i	−1.28519	−	0.858737i	−0.995159	+	0.0982797i	$0.968666\pi$
$642$		0			0
$643$	−32.6682	−	164.234i	−0.0508059	−	0.255418i	0.947032	−	0.321139i	$-0.104066\pi$
$643$	−32.6682	−	164.234i	−0.0508059	−	0.255418i	−0.997838	+	0.0657202i	$0.979066\pi$
$644$		0			0
$645$		−	198.088i		−	0.307113i
$646$		0			0
$647$	431.677			0.667198			0.333599	−	0.942715i	$-0.391737\pi$
$647$	431.677			0.667198			0.333599	+	0.942715i	$0.391737\pi$
$648$		0			0
$649$	39.1108	−	7.77962i	0.0602632	−	0.0119871i
$650$		0			0
$651$	573.889	−	858.885i	0.881550	−	1.31933i
$652$		0			0
$653$	580.079	+	868.149i	0.888329	+	1.32948i	0.943628	+	0.331008i	$0.107389\pi$
$653$	580.079	+	868.149i	0.888329	+	1.32948i	−0.0552994	+	0.998470i	$0.517611\pi$
$654$		0			0
$655$	−20.6021	+	8.53368i	−0.0314536	+	0.0130285i
$656$		0			0
$657$	226.187	−	1137.12i	0.344273	−	1.73078i
$658$		0			0
$659$	−265.111	+	265.111i	−0.402293	+	0.402293i	−0.879040	−	0.476747i	$-0.841816\pi$
$659$	−265.111	+	265.111i	−0.402293	+	0.402293i	0.476747	+	0.879040i	$0.341816\pi$
$660$		0			0
$661$	−187.245	+	452.050i	−0.283276	+	0.683888i	−0.999908	−	0.0135629i	$-0.995683\pi$
$661$	−187.245	+	452.050i	−0.283276	+	0.683888i	0.716632	+	0.697451i	$0.245683\pi$
$662$		0			0
$663$	205.272	+	225.974i	0.309611	+	0.340835i
$664$		0			0
$665$	150.479	+	62.3306i	0.226285	+	0.0937303i
$666$		0			0
$667$	−225.239	−	225.239i	−0.337689	−	0.337689i
$668$		0			0
$669$	1488.95	+	296.170i	2.22563	+	0.442706i
$670$		0			0
$671$	63.6739	+	153.722i	0.0948941	+	0.229095i
$672$		0			0
$673$	−109.871	+	73.4132i	−0.163255	+	0.109084i	−0.634514	−	0.772911i	$-0.718800\pi$
$673$	−109.871	+	73.4132i	−0.163255	+	0.109084i	0.471259	+	0.881995i	$0.343800\pi$
$674$		0			0
$675$	184.343	+	123.174i	0.273100	+	0.182480i
$676$		0			0
$677$	−206.368	−	1037.48i	−0.304827	−	1.53247i	−0.764642	−	0.644456i	$-0.777084\pi$
$677$	−206.368	−	1037.48i	−0.304827	−	1.53247i	0.459814	−	0.888015i	$-0.347916\pi$
$678$		0			0
$679$			1343.49i			1.97864i
$680$		0			0
$681$	−28.5788			−0.0419660
$682$		0			0
$683$	392.921	−	78.1569i	0.575288	−	0.114432i	0.101132	−	0.994873i	$-0.467754\pi$
$683$	392.921	−	78.1569i	0.575288	−	0.114432i	0.474155	+	0.880441i	$0.342754\pi$
$684$		0			0
$685$	−37.8447	+	56.6386i	−0.0552477	+	0.0826841i
$686$		0			0
$687$	678.564	+	1015.54i	0.987720	+	1.47823i
$688$		0			0
$689$	41.5072	−	17.1928i	0.0602427	−	0.0249533i
$690$		0			0
$691$	218.548	−	1098.72i	0.316278	−	1.59004i	−0.416217	−	0.909265i	$-0.636644\pi$
$691$	218.548	−	1098.72i	0.316278	−	1.59004i	0.732495	−	0.680772i	$-0.238356\pi$
$692$		0			0
$693$	393.563	−	393.563i	0.567912	−	0.567912i
$694$		0			0
$695$	29.1175	−	70.2959i	0.0418957	−	0.101145i
$696$		0			0
$697$	−424.949	+	152.586i	−0.609683	+	0.218919i
$698$		0			0
$699$	159.159	+	65.9257i	0.227695	+	0.0943143i
$700$		0			0
$701$	−12.6127	−	12.6127i	−0.0179925	−	0.0179925i	0.698053	−	0.716046i	$-0.254050\pi$
$701$	−12.6127	−	12.6127i	−0.0179925	−	0.0179925i	−0.716046	+	0.698053i	$0.754050\pi$
$702$		0			0
$703$	648.601	+	129.015i	0.922619	+	0.183520i
$704$		0			0
$705$	−81.5893	−	196.974i	−0.115730	−	0.279396i
$706$		0			0
$707$	570.257	−	381.034i	0.806587	−	0.538944i
$708$		0			0
$709$	308.127	+	205.884i	0.434593	+	0.290386i	0.753559	−	0.657380i	$-0.228335\pi$
$709$	308.127	+	205.884i	0.434593	+	0.290386i	−0.318966	+	0.947766i	$0.603335\pi$
$710$		0			0
$711$	250.849	+	1261.11i	0.352812	+	1.77371i
$712$		0			0
$713$			240.172i			0.336848i
$714$		0			0
$715$	−17.5183			−0.0245011
$716$		0			0
$717$	−230.358	+	45.8210i	−0.321280	+	0.0639066i
$718$		0			0
$719$	192.247	−	287.718i	0.267381	−	0.400164i	−0.673347	−	0.739327i	$-0.735144\pi$
$719$	192.247	−	287.718i	0.267381	−	0.400164i	0.940728	+	0.339163i	$0.110144\pi$
$720$		0			0
$721$	−715.360	−	1070.61i	−0.992177	−	1.48490i
$722$		0			0
$723$	937.675	−	388.398i	1.29692	−	0.537203i
$724$		0			0
$725$	−184.179	+	925.928i	−0.254039	+	1.27714i
$726$		0			0
$727$	617.900	−	617.900i	0.849931	−	0.849931i	−0.140193	−	0.990124i	$-0.544772\pi$
$727$	617.900	−	617.900i	0.849931	−	0.849931i	0.990124	+	0.140193i	$0.0447724\pi$
$728$		0			0
$729$	−387.006	+	934.316i	−0.530873	+	1.28164i
$730$		0			0
$731$	161.844	+	1082.71i	0.221401	+	1.48114i
$732$		0			0
$733$	−1078.51	−	446.735i	−1.47137	−	0.609461i	−0.504198	−	0.863588i	$-0.668212\pi$
$733$	−1078.51	−	446.735i	−1.47137	−	0.609461i	−0.967171	+	0.254127i	$0.918212\pi$
$734$		0			0
$735$	−31.0627	−	31.0627i	−0.0422622	−	0.0422622i
$736$		0			0
$737$	−298.334	−	59.3424i	−0.404796	−	0.0805189i
$738$		0			0
$739$	216.710	+	523.184i	0.293248	+	0.707962i	1.00000		0.000501221i	$0.000159543\pi$
$739$	216.710	+	523.184i	0.293248	+	0.707962i	−0.706752	+	0.707461i	$0.749840\pi$
$740$		0			0
$741$	444.703	−	297.141i	0.600140	−	0.401000i
$742$		0			0
$743$	−565.840	−	378.082i	−0.761561	−	0.508859i	0.113106	−	0.993583i	$-0.463920\pi$
$743$	−565.840	−	378.082i	−0.761561	−	0.508859i	−0.874667	+	0.484724i	$0.838920\pi$
$744$		0			0
$745$	36.5540	+	183.769i	0.0490658	+	0.246670i
$746$		0			0
$747$		−	1484.57i		−	1.98737i
$748$		0			0
$749$	326.022			0.435276
$750$		0			0
$751$	−802.885	+	159.704i	−1.06909	+	0.212655i	−0.698113	−	0.715988i	$-0.745977\pi$
$751$	−802.885	+	159.704i	−1.06909	+	0.212655i	−0.370975	+	0.928643i	$0.620977\pi$
$752$		0			0
$753$	80.6055	−	120.635i	0.107046	−	0.160205i
$754$		0			0
$755$	49.1052	+	73.4911i	0.0650400	+	0.0973392i
$756$		0			0
$757$	−1275.35	+	528.267i	−1.68474	+	0.697842i	−0.999535	−	0.0305071i	$-0.990288\pi$
$757$	−1275.35	+	528.267i	−1.68474	+	0.697842i	−0.685206	+	0.728349i	$0.740288\pi$
$758$		0			0
$759$	−45.8647	+	230.577i	−0.0604278	+	0.303791i
$760$		0			0
$761$	882.557	−	882.557i	1.15973	−	1.15973i	0.175200	−	0.984533i	$-0.443943\pi$
$761$	882.557	−	882.557i	1.15973	−	1.15973i	0.984533	−	0.175200i	$-0.0560572\pi$
$762$		0			0
$763$	82.3016	−	198.694i	0.107866	−	0.260411i
$764$		0			0
$765$	116.491	+	54.9367i	0.152276	+	0.0718126i
$766$		0			0
$767$	−23.2896	−	9.64686i	−0.0303645	−	0.0125774i
$768$		0			0
$769$	−373.825	−	373.825i	−0.486118	−	0.486118i	0.420961	−	0.907079i	$-0.361693\pi$
$769$	−373.825	−	373.825i	−0.486118	−	0.486118i	−0.907079	+	0.420961i	$0.861693\pi$
$770$		0			0
$771$	483.851	+	96.2440i	0.627563	+	0.124830i
$772$		0			0
$773$	147.885	+	357.026i	0.191313	+	0.461871i	0.990208	−	0.139600i	$-0.0445817\pi$
$773$	147.885	+	357.026i	0.191313	+	0.461871i	−0.798895	+	0.601471i	$0.794582\pi$
$774$		0			0
$775$	591.855	−	395.465i	0.763684	−	0.510277i
$776$		0			0
$777$	−657.139	−	439.086i	−0.845739	−	0.565105i
$778$		0			0
$779$	154.319	+	775.816i	0.198099	+	0.995913i
$780$		0			0
$781$		−	851.882i		−	1.09076i
$782$		0			0
$783$	347.921			0.444344
$784$		0			0
$785$	−107.166	+	21.3166i	−0.136517	+	0.0271550i
$786$		0			0
$787$	−455.538	+	681.761i	−0.578828	+	0.866278i	−0.999155	−	0.0410948i	$-0.986915\pi$
$787$	−455.538	+	681.761i	−0.578828	+	0.866278i	0.420327	+	0.907373i	$0.361915\pi$
$788$		0			0
$789$	−94.2296	−	141.025i	−0.119429	−	0.178738i
$790$		0			0
$791$	25.4390	−	10.5372i	0.0321605	−	0.0133213i
$792$		0			0
$793$	20.5202	−	103.162i	0.0258766	−	0.130091i
$794$		0			0
$795$	24.3479	−	24.3479i	0.0306263	−	0.0306263i
$796$		0			0
$797$	50.6784	−	122.349i	0.0635865	−	0.153511i	−0.888892	−	0.458116i	$-0.848524\pi$
$797$	50.6784	−	122.349i	0.0635865	−	0.153511i	0.952479	+	0.304605i	$0.0985244\pi$
$798$		0			0
$799$	606.886	+	1009.96i	0.759557	+	1.26403i
$800$		0			0
$801$	1399.62	+	579.740i	1.74734	+	0.723770i
$802$		0			0
$803$	−472.314	−	472.314i	−0.588187	−	0.588187i
$804$		0			0
$805$	44.3892	+	8.82957i	0.0551419	+	0.0109684i
$806$		0			0
$807$	−438.014	−	1057.46i	−0.542768	−	1.31036i
$808$		0			0
$809$	−653.455	+	436.625i	−0.807732	+	0.539709i	−0.889496	−	0.456942i	$-0.848945\pi$
$809$	−653.455	+	436.625i	−0.807732	+	0.539709i	0.0817643	+	0.996652i	$0.473945\pi$
$810$		0			0
$811$	−838.425	−	560.217i	−1.03382	−	0.690774i	−0.0817457	−	0.996653i	$-0.526050\pi$
$811$	−838.425	−	560.217i	−1.03382	−	0.690774i	−0.952070	+	0.305879i	$0.901050\pi$
$812$		0			0
$813$	41.9852	+	211.074i	0.0516423	+	0.259624i
$814$		0			0
$815$			24.3134i			0.0298324i
$816$		0			0
$817$	1917.90			2.34749
$818$		0			0
$819$	−345.085	+	68.6418i	−0.421350	+	0.0838117i
$820$		0			0
$821$	607.634	−	909.388i	0.740114	−	1.10766i	−0.250116	−	0.968216i	$-0.580469\pi$
$821$	607.634	−	909.388i	0.740114	−	1.10766i	0.990230	−	0.139443i	$-0.0445313\pi$
$822$		0			0
$823$	16.4222	+	24.5776i	0.0199541	+	0.0298634i	0.841313	−	0.540549i	$-0.181783\pi$
$823$	16.4222	+	24.5776i	0.0199541	+	0.0298634i	−0.821358	+	0.570412i	$0.806783\pi$
$824$		0			0
$825$	643.730	−	266.642i	0.780279	−	0.323202i
$826$		0			0
$827$	141.969	−	713.726i	0.171667	−	0.863030i	−0.794924	−	0.606709i	$-0.792489\pi$
$827$	141.969	−	713.726i	0.171667	−	0.863030i	0.966592	−	0.256321i	$-0.0825106\pi$
$828$		0			0
$829$	8.56992	−	8.56992i	0.0103377	−	0.0103377i	−0.701919	−	0.712257i	$-0.747673\pi$
$829$	8.56992	−	8.56992i	0.0103377	−	0.0103377i	0.712257	+	0.701919i	$0.247673\pi$
$830$		0			0
$831$	−241.549	+	583.151i	−0.290673	+	0.701746i
$832$		0			0
$833$	195.162	+	144.404i	0.234288	+	0.173354i
$834$		0			0
$835$	−9.25597	−	3.83395i	−0.0110850	−	0.00459156i
$836$		0			0
$837$	−185.495	−	185.495i	−0.221618	−	0.221618i
$838$		0			0
$839$	882.646	+	175.569i	1.05202	+	0.209260i	0.690670	−	0.723170i	$-0.257316\pi$
$839$	882.646	+	175.569i	1.05202	+	0.209260i	0.361351	+	0.932430i	$0.382316\pi$
$840$		0			0
$841$	245.113	+	591.755i	0.291454	+	0.703632i
$842$		0			0
$843$	−1220.47	+	815.489i	−1.44776	+	0.967365i
$844$		0			0
$845$	−87.3960	−	58.3962i	−0.103427	−	0.0691079i
$846$		0			0
$847$	125.226	+	629.555i	0.147847	+	0.743276i
$848$		0			0
$849$			2387.42i			2.81203i
$850$		0			0
$851$	183.758			0.215932
$852$		0			0
$853$	−992.350	+	197.391i	−1.16336	+	0.231408i	−0.738758	−	0.673971i	$-0.764587\pi$
$853$	−992.350	+	197.391i	−1.16336	+	0.231408i	−0.424606	+	0.905378i	$0.639587\pi$
$854$		0			0
$855$	125.358	−	187.612i	0.146618	−	0.219429i
$856$		0			0
$857$	145.503	+	217.761i	0.169782	+	0.254097i	0.906597	−	0.421998i	$-0.138671\pi$
$857$	145.503	+	217.761i	0.169782	+	0.254097i	−0.736815	+	0.676095i	$0.763671\pi$
$858$		0			0
$859$	−1073.72	+	444.749i	−1.24996	+	0.517752i	−0.906815	−	0.421529i	$-0.861493\pi$
$859$	−1073.72	+	444.749i	−1.24996	+	0.517752i	−0.343149	+	0.939281i	$0.611493\pi$
$860$		0			0
$861$	184.429	−	927.185i	0.214203	−	1.07687i
$862$		0			0
$863$	499.888	−	499.888i	0.579244	−	0.579244i	−0.355451	−	0.934695i	$-0.615673\pi$
$863$	499.888	−	499.888i	0.579244	−	0.579244i	0.934695	+	0.355451i	$0.115673\pi$
$864$		0			0
$865$	19.7150	−	47.5963i	0.0227919	−	0.0550246i
$866$		0			0
$867$	−1238.26	−	372.594i	−1.42821	−	0.429751i
$868$		0			0
$869$	684.395	+	283.486i	0.787566	+	0.326220i
$870$		0			0
$871$	135.968	+	135.968i	0.156106	+	0.156106i
$872$		0			0
$873$	1825.42	+	363.099i	2.09097	+	0.415920i
$874$		0			0
$875$	−103.653	−	250.241i	−0.118461	−	0.285990i
$876$		0			0
$877$	−936.450	+	625.716i	−1.06779	+	0.713473i	−0.959802	−	0.280679i	$-0.909440\pi$
$877$	−936.450	+	625.716i	−1.06779	+	0.713473i	−0.107987	+	0.994152i	$0.534440\pi$
$878$		0			0
$879$	−2085.80	−	1393.69i	−2.37292	−	1.58554i
$880$		0			0
$881$	95.9481	+	482.364i	0.108908	+	0.547518i	0.996259	+	0.0864226i	$0.0275435\pi$
$881$	95.9481	+	482.364i	0.108908	+	0.547518i	−0.887350	+	0.461096i	$0.847456\pi$
$882$		0			0
$883$		−	945.046i		−	1.07027i	−0.844768	−	0.535133i	$-0.820261\pi$
$883$		−	945.046i		−	1.07027i	0.844768	−	0.535133i	$-0.179739\pi$
$884$		0			0
$885$	−19.3204			−0.0218309
$886$		0			0
$887$	−111.668	+	22.2121i	−0.125894	+	0.0250418i	−0.257635	−	0.966242i	$-0.582943\pi$
$887$	−111.668	+	22.2121i	−0.125894	+	0.0250418i	0.131741	+	0.991284i	$0.457943\pi$
$888$		0			0
$889$	−529.550	+	792.528i	−0.595670	+	0.891483i
$890$		0			0
$891$	207.183	+	310.071i	0.232529	+	0.348004i
$892$		0			0
$893$	1907.11	−	789.952i	2.13563	−	0.884605i
$894$		0			0
$895$	−31.0857	+	156.278i	−0.0347326	+	0.174613i
$896$		0			0
$897$	105.088	−	105.088i	0.117154	−	0.117154i
$898$		0			0
$899$	427.474	−	1032.01i	0.475500	−	1.14796i
$900$		0			0
$901$	−113.188	+	152.974i	−0.125625	+	0.169783i
$902$		0			0
$903$	−2117.62	−	877.148i	−2.34510	−	0.971371i
$904$		0			0
$905$	20.5470	+	20.5470i	0.0227038	+	0.0227038i
$906$		0			0
$907$	462.962	+	92.0888i	0.510432	+	0.101531i	0.443585	−	0.896232i	$-0.353706\pi$
$907$	462.962	+	92.0888i	0.510432	+	0.101531i	0.0668463	+	0.997763i	$0.478706\pi$
$908$		0			0
$909$	−363.594	−	877.794i	−0.399993	−	0.965670i
$910$		0			0
$911$	−132.194	+	88.3295i	−0.145109	+	0.0969588i	−0.626006	−	0.779819i	$-0.715311\pi$
$911$	−132.194	+	88.3295i	−0.145109	+	0.0969588i	0.480896	+	0.876777i	$0.340311\pi$
$912$		0			0
$913$	−711.148	−	475.174i	−0.778913	−	0.520453i
$914$		0			0
$915$	−15.7272	−	79.0658i	−0.0171882	−	0.0864107i
$916$		0			0
$917$			258.031i			0.281386i
$918$		0			0
$919$	954.629			1.03877			0.519385	−	0.854541i	$-0.326161\pi$
$919$	954.629			1.03877			0.519385	+	0.854541i	$0.326161\pi$
$920$		0			0
$921$	−290.435	+	57.7710i	−0.315347	+	0.0627264i
$922$		0			0
$923$	−299.186	+	447.764i	−0.324146	+	0.485118i
$924$		0			0
$925$	−302.573	−	452.832i	−0.327106	−	0.489549i
$926$		0			0
$927$	−1647.99	+	682.618i	−1.77776	+	0.736373i
$928$		0			0
$929$	56.4717	−	283.902i	0.0607876	−	0.305600i	−0.938416	−	0.345508i	$-0.887707\pi$
$929$	56.4717	−	283.902i	0.0607876	−	0.305600i	0.999203	+	0.0399083i	$0.0127066\pi$
$930$		0			0
$931$	300.751	−	300.751i	0.323041	−	0.323041i
$932$		0			0
$933$	−615.716	+	1486.47i	−0.659932	+	1.59322i
$934$		0			0
$935$	63.6022	−	38.2186i	0.0680237	−	0.0408755i
$936$		0			0
$937$	−287.335	−	119.018i	−0.306654	−	0.127020i	0.224049	−	0.974578i	$-0.428072\pi$
$937$	−287.335	−	119.018i	−0.306654	−	0.127020i	−0.530704	+	0.847557i	$0.678072\pi$
$938$		0			0
$939$	−159.290	−	159.290i	−0.169638	−	0.169638i
$940$		0			0
$941$	−1205.54	−	239.796i	−1.28112	−	0.254831i	−0.492827	−	0.870128i	$-0.664036\pi$
$941$	−1205.54	−	239.796i	−1.28112	−	0.254831i	−0.788296	+	0.615296i	$0.789036\pi$
$942$		0			0
$943$	84.1137	+	203.068i	0.0891979	+	0.215343i
$944$		0			0
$945$	−41.1030	+	27.4641i	−0.0434952	+	0.0290626i
$946$		0			0
$947$	−902.709	−	603.171i	−0.953231	−	0.636928i	−0.0213804	−	0.999771i	$-0.506806\pi$
$947$	−902.709	−	603.171i	−0.953231	−	0.636928i	−0.931850	+	0.362843i	$0.881806\pi$
$948$		0			0
$949$	82.3769	+	414.136i	0.0868039	+	0.436393i
$950$		0			0
$951$			1821.98i			1.91586i
$952$		0			0
$953$	−859.235			−0.901611			−0.450805	−	0.892622i	$-0.648863\pi$
$953$	−859.235			−0.901611			−0.450805	+	0.892622i	$0.648863\pi$
$954$		0			0
$955$	58.0327	−	11.5434i	0.0607672	−	0.0120873i
$956$		0			0
$957$	607.475	−	909.151i	0.634771	−	0.950001i
$958$		0			0
$959$	437.905	+	655.371i	0.456627	+	0.683390i
$960$		0			0
$961$	109.720	−	45.4476i	0.114173	−	0.0472920i
$962$		0			0
$963$	88.1120	−	442.969i	0.0914974	−	0.459988i
$964$		0			0
$965$	41.0979	−	41.0979i	0.0425885	−	0.0425885i
$966$		0			0
$967$	257.370	−	621.346i	0.266153	−	0.642550i	−0.733143	−	0.680075i	$-0.761947\pi$
$967$	257.370	−	621.346i	0.266153	−	0.642550i	0.999296	+	0.0375247i	$0.0119473\pi$
$968$		0			0
$969$	−966.293	+	2048.99i	−0.997206	+	2.11454i
$970$		0			0
$971$	359.250	+	148.806i	0.369979	+	0.153250i	0.559923	−	0.828545i	$-0.310831\pi$
$971$	359.250	+	148.806i	0.369979	+	0.153250i	−0.189944	+	0.981795i	$0.560831\pi$
$972$		0			0
$973$	−622.551	−	622.551i	−0.639826	−	0.639826i
$974$		0			0
$975$	−432.002	−	85.9305i	−0.443079	−	0.0881339i
$976$		0			0
$977$	−341.512	−	824.483i	−0.349552	−	0.843893i	−0.996673	−	0.0815056i	$-0.974027\pi$
$977$	−341.512	−	824.483i	−0.349552	−	0.843893i	0.647121	−	0.762387i	$-0.275973\pi$
$978$		0			0
$979$	725.694	−	484.893i	0.741261	−	0.495295i
$980$		0			0
$981$	−247.724	−	165.524i	−0.252522	−	0.168730i
$982$		0			0
$983$	−168.378	−	846.493i	−0.171290	−	0.861132i	−0.966867	−	0.255280i	$-0.917832\pi$
$983$	−168.378	−	846.493i	−0.171290	−	0.861132i	0.795577	−	0.605852i	$-0.207168\pi$
$984$		0			0
$985$		−	228.061i		−	0.231534i
$986$		0			0
$987$	−2467.00			−2.49949
$988$		0			0
$989$	522.687	−	103.969i	0.528500	−	0.105125i
$990$		0			0
$991$	−811.511	+	1214.51i	−0.818881	+	1.22554i	0.152567	+	0.988293i	$0.451246\pi$
$991$	−811.511	+	1214.51i	−0.818881	+	1.22554i	−0.971449	+	0.237249i	$0.923754\pi$
$992$		0			0
$993$	−288.037	−	431.078i	−0.290068	−	0.434117i
$994$		0			0
$995$	214.251	−	88.7455i	0.215327	−	0.0891915i
$996$		0			0
$997$	−25.7221	+	129.314i	−0.0257995	+	0.129703i	−0.991539	−	0.129812i	$-0.958563\pi$
$997$	−25.7221	+	129.314i	−0.0257995	+	0.129703i	0.965739	+	0.259515i	$0.0835626\pi$
$998$		0			0
$999$	−141.923	+	141.923i	−0.142065	+	0.142065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.a.57.4	✓	32
4.3	odd	2		272.3.bh.f.193.1		32
17.3	odd	16	inner	136.3.t.a.105.4	yes	32
68.3	even	16		272.3.bh.f.241.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.a.57.4	✓	32	1.1	even	1	trivial
136.3.t.a.105.4	yes	32	17.3	odd	16	inner
272.3.bh.f.193.1		32	4.3	odd	2
272.3.bh.f.241.1		32	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)

\(f(q)\)	\(=\)	\(q+(4.38842 - 0.872911i) q^{3} +(-0.381945 + 0.571621i) q^{5} +(4.41953 + 6.61429i) q^{7} +(10.1813 - 4.21725i) q^{9} +O(q^{10})\)	\(q+(4.38842 - 0.872911i) q^{3} +(-0.381945 + 0.571621i) q^{5} +(4.41953 + 6.61429i) q^{7} +(10.1813 - 4.21725i) q^{9} +(1.23862 - 6.22698i) q^{11} +(-2.83799 + 2.83799i) q^{13} +(-1.17716 + 2.84192i) q^{15} +(4.11219 - 16.4951i) q^{17} +(-27.5156 - 11.3973i) q^{19} +(25.1684 + 25.1684i) q^{21} +(-8.11670 - 1.61451i) q^{23} +(9.38622 + 22.6603i) q^{25} +(7.51579 - 5.02189i) q^{27} +(32.0036 + 21.3841i) q^{29} +(-5.66179 - 28.4637i) q^{31} -28.4078i q^{33} -5.46888 q^{35} +(-21.7778 + 4.33188i) q^{37} +(-9.97699 + 14.9316i) q^{39} +(-14.7557 - 22.0835i) q^{41} +(-59.4946 + 24.6435i) q^{43} +(-1.47804 + 7.43062i) q^{45} +(-49.0098 + 49.0098i) q^{47} +(-5.46511 + 13.1939i) q^{49} +(3.64723 - 75.9772i) q^{51} +(-10.3418 - 4.28372i) q^{53} +(3.08638 + 3.08638i) q^{55} +(-130.699 - 25.9976i) q^{57} +(2.40358 + 5.80276i) q^{59} +(-21.7904 + 14.5599i) q^{61} +(72.8908 + 48.7041i) q^{63} +(-0.538300 - 2.70621i) q^{65} -47.9100i q^{67} -37.0288 q^{69} +(131.598 - 26.1765i) q^{71} +(58.4497 - 87.4761i) q^{73} +(60.9711 + 91.2497i) q^{75} +(46.6611 - 19.3277i) q^{77} +(-22.7627 + 114.436i) q^{79} +(-41.5333 + 41.5333i) q^{81} +(51.5525 - 124.459i) q^{83} +(7.85834 + 8.65085i) q^{85} +(159.112 + 65.9062i) q^{87} +(97.2051 + 97.2051i) q^{89} +(-31.3139 - 6.22872i) q^{91} +(-49.6926 - 119.969i) q^{93} +(17.0244 - 11.3753i) q^{95} +(140.425 + 93.8293i) q^{97} +(-13.6499 - 68.6225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 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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