LMFDB - Embedded newform 400.3.bg.f.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(17,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("400.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, not 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:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	400.17
Dual form			400.3.bg.f.353.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.754209 - 4.76189i) q^{3} +(-3.14938 + 3.88348i) q^{5} +(-8.90117 - 8.90117i) q^{7} +(-13.5472 - 4.40177i) q^{9} +O(q^{10})$	\(q+(0.754209 - 4.76189i) q^{3} +(-3.14938 + 3.88348i) q^{5} +(-8.90117 - 8.90117i) q^{7} +(-13.5472 - 4.40177i) q^{9} +(4.01460 + 12.3557i) q^{11} +(-2.72791 - 5.35383i) q^{13} +(16.1174 + 17.9259i) q^{15} +(4.15299 + 26.2209i) q^{17} +(-6.04756 + 8.32375i) q^{19} +(-49.0997 + 35.6730i) q^{21} +(19.2576 + 9.81225i) q^{23} +(-5.16283 - 24.4611i) q^{25} +(-11.4790 + 22.5288i) q^{27} +(-9.62791 - 13.2517i) q^{29} +(-37.5641 - 27.2919i) q^{31} +(61.8642 - 9.79833i) q^{33} +(62.6007 - 6.53436i) q^{35} +(-5.88824 + 3.00021i) q^{37} +(-27.5518 + 8.95211i) q^{39} +(-17.8034 + 54.7933i) q^{41} +(-17.6211 + 17.6211i) q^{43} +(59.7596 - 38.7476i) q^{45} +(-39.7743 - 6.29963i) q^{47} +109.462i q^{49} +127.993 q^{51} +(1.38006 - 8.71339i) q^{53} +(-60.6265 - 23.3221i) q^{55} +(35.0756 + 35.0756i) q^{57} +(-37.2402 - 12.1001i) q^{59} +(-2.68303 - 8.25750i) q^{61} +(81.4055 + 159.767i) q^{63} +(29.3827 + 6.26745i) q^{65} +(-12.0079 - 75.8151i) q^{67} +(61.2491 - 84.3022i) q^{69} +(-93.0381 + 67.5961i) q^{71} +(37.0673 + 18.8867i) q^{73} +(-120.375 + 6.13602i) q^{75} +(74.2453 - 145.715i) q^{77} +(-21.0739 - 29.0057i) q^{79} +(-5.09389 - 3.70093i) q^{81} +(98.1176 - 15.5403i) q^{83} +(-114.908 - 66.4516i) q^{85} +(-70.3644 + 35.8525i) q^{87} +(-130.370 + 42.3597i) q^{89} +(-23.3737 + 71.9370i) q^{91} +(-158.292 + 158.292i) q^{93} +(-13.2791 - 49.7002i) q^{95} +(-49.9251 - 7.90736i) q^{97} -185.057i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.754209	−	4.76189i	0.251403	−	1.58730i	−0.462219	−	0.886766i	$-0.652947\pi$
$3$	0.754209	−	4.76189i	0.251403	−	1.58730i	0.713622	−	0.700531i	$-0.247053\pi$
$4$		0			0
$5$	−3.14938	+	3.88348i	−0.629876	+	0.776696i
$5$	−3.14938	+	3.88348i	−0.629876	+	0.776696i
$6$		0			0
$7$	−8.90117	−	8.90117i	−1.27160	−	1.27160i	−0.945251	−	0.326345i	$-0.894183\pi$
$7$	−8.90117	−	8.90117i	−1.27160	−	1.27160i	−0.326345	−	0.945251i	$-0.605817\pi$
$8$		0			0
$9$	−13.5472	−	4.40177i	−1.50525	−	0.489085i
$10$		0			0
$11$	4.01460	+	12.3557i	0.364964	+	1.12324i	0.950004	+	0.312239i	$0.101079\pi$
$11$	4.01460	+	12.3557i	0.364964	+	1.12324i	−0.585040	+	0.811005i	$0.698921\pi$
$12$		0			0
$13$	−2.72791	−	5.35383i	−0.209839	−	0.411833i	0.761966	−	0.647617i	$-0.224234\pi$
$13$	−2.72791	−	5.35383i	−0.209839	−	0.411833i	−0.971806	+	0.235784i	$0.924234\pi$
$14$		0			0
$15$	16.1174	+	17.9259i	1.07449	+	1.19506i
$16$		0			0
$17$	4.15299	+	26.2209i	0.244293	+	1.54241i	0.739215	+	0.673470i	$0.235197\pi$
$17$	4.15299	+	26.2209i	0.244293	+	1.54241i	−0.494921	+	0.868938i	$0.664803\pi$
$18$		0			0
$19$	−6.04756	+	8.32375i	−0.318292	+	0.438092i	−0.937945	−	0.346784i	$-0.887274\pi$
$19$	−6.04756	+	8.32375i	−0.318292	+	0.438092i	0.619652	+	0.784876i	$0.287274\pi$
$20$		0			0
$21$	−49.0997	+	35.6730i	−2.33808	+	1.69872i
$22$		0			0
$23$	19.2576	+	9.81225i	0.837288	+	0.426620i	0.819401	−	0.573220i	$-0.194306\pi$
$23$	19.2576	+	9.81225i	0.837288	+	0.426620i	0.0178868	+	0.999840i	$0.494306\pi$
$24$		0			0
$25$	−5.16283	−	24.4611i	−0.206513	−	0.978444i
$26$		0			0
$27$	−11.4790	+	22.5288i	−0.425147	+	0.834398i
$28$		0			0
$29$	−9.62791	−	13.2517i	−0.331997	−	0.456954i	0.610086	−	0.792335i	$-0.291135\pi$
$29$	−9.62791	−	13.2517i	−0.331997	−	0.456954i	−0.942083	+	0.335381i	$0.891135\pi$
$30$		0			0
$31$	−37.5641	−	27.2919i	−1.21174	−	0.880384i	−0.216356	−	0.976314i	$-0.569417\pi$
$31$	−37.5641	−	27.2919i	−1.21174	−	0.880384i	−0.995388	+	0.0959306i	$0.969417\pi$
$32$		0			0
$33$	61.8642	−	9.79833i	1.87467	−	0.296919i
$34$		0			0
$35$	62.6007	−	6.53436i	1.78859	−	0.186696i
$36$		0			0
$37$	−5.88824	+	3.00021i	−0.159142	+	0.0810867i	−0.531747	−	0.846903i	$-0.678464\pi$
$37$	−5.88824	+	3.00021i	−0.159142	+	0.0810867i	0.372606	+	0.927990i	$0.378464\pi$
$38$		0			0
$39$	−27.5518	+	8.95211i	−0.706455	+	0.229541i
$40$		0			0
$41$	−17.8034	+	54.7933i	−0.434230	+	1.33642i	0.459644	+	0.888103i	$0.347977\pi$
$41$	−17.8034	+	54.7933i	−0.434230	+	1.33642i	−0.893874	+	0.448319i	$0.852023\pi$
$42$		0			0
$43$	−17.6211	+	17.6211i	−0.409792	+	0.409792i	−0.881666	−	0.471874i	$-0.843578\pi$
$43$	−17.6211	+	17.6211i	−0.409792	+	0.409792i	0.471874	+	0.881666i	$0.343578\pi$
$44$		0			0
$45$	59.7596	−	38.7476i	1.32799	−	0.861058i
$46$		0			0
$47$	−39.7743	−	6.29963i	−0.846262	−	0.134035i	−0.281779	−	0.959479i	$-0.590924\pi$
$47$	−39.7743	−	6.29963i	−0.846262	−	0.134035i	−0.564483	+	0.825445i	$0.690924\pi$
$48$		0			0
$49$			109.462i			2.23391i
$50$		0			0
$51$	127.993			2.50967
$52$		0			0
$53$	1.38006	−	8.71339i	0.0260390	−	0.164404i	−0.971242	−	0.238094i	$-0.923478\pi$
$53$	1.38006	−	8.71339i	0.0260390	−	0.164404i	0.997281	+	0.0736900i	$0.0234775\pi$
$54$		0			0
$55$	−60.6265	−	23.3221i	−1.10230	−	0.424038i
$56$		0			0
$57$	35.0756	+	35.0756i	0.615362	+	0.615362i
$58$		0			0
$59$	−37.2402	−	12.1001i	−0.631189	−	0.205086i	−0.0240873	−	0.999710i	$-0.507668\pi$
$59$	−37.2402	−	12.1001i	−0.631189	−	0.205086i	−0.607102	+	0.794624i	$0.707668\pi$
$60$		0			0
$61$	−2.68303	−	8.25750i	−0.0439840	−	0.135369i	0.926653	−	0.375918i	$-0.122673\pi$
$61$	−2.68303	−	8.25750i	−0.0439840	−	0.135369i	−0.970637	+	0.240549i	$0.922673\pi$
$62$		0			0
$63$	81.4055	+	159.767i	1.29215	+	2.53599i
$64$		0			0
$65$	29.3827	+	6.26745i	0.452042	+	0.0964223i
$66$		0			0
$67$	−12.0079	−	75.8151i	−0.179223	−	1.13157i	−0.899189	−	0.437560i	$-0.855843\pi$
$67$	−12.0079	−	75.8151i	−0.179223	−	1.13157i	0.719967	−	0.694009i	$-0.244157\pi$
$68$		0			0
$69$	61.2491	−	84.3022i	0.887668	−	1.22177i
$70$		0			0
$71$	−93.0381	+	67.5961i	−1.31040	+	0.952058i	−0.310396	+	0.950607i	$0.600462\pi$
$71$	−93.0381	+	67.5961i	−1.31040	+	0.952058i	−0.999999	+	0.00145081i	$0.999538\pi$
$72$		0			0
$73$	37.0673	+	18.8867i	0.507772	+	0.258723i	0.689056	−	0.724708i	$-0.258025\pi$
$73$	37.0673	+	18.8867i	0.507772	+	0.258723i	−0.181284	+	0.983431i	$0.558025\pi$
$74$		0			0
$75$	−120.375	+	6.13602i	−1.60500	+	0.0818136i
$76$		0			0
$77$	74.2453	−	145.715i	0.964225	−	1.89240i
$78$		0			0
$79$	−21.0739	−	29.0057i	−0.266758	−	0.367161i	0.654534	−	0.756033i	$-0.272865\pi$
$79$	−21.0739	−	29.0057i	−0.266758	−	0.367161i	−0.921292	+	0.388872i	$0.872865\pi$
$80$		0			0
$81$	−5.09389	−	3.70093i	−0.0628876	−	0.0456905i
$82$		0			0
$83$	98.1176	−	15.5403i	1.18214	−	0.187233i	0.465739	−	0.884922i	$-0.345788\pi$
$83$	98.1176	−	15.5403i	1.18214	−	0.187233i	0.716400	+	0.697689i	$0.245788\pi$
$84$		0			0
$85$	−114.908	−	66.4516i	−1.35186	−	0.781783i
$86$		0			0
$87$	−70.3644	+	35.8525i	−0.808787	+	0.412097i
$88$		0			0
$89$	−130.370	+	42.3597i	−1.46483	+	0.475951i	−0.929541	−	0.368719i	$-0.879796\pi$
$89$	−130.370	+	42.3597i	−1.46483	+	0.475951i	−0.535287	+	0.844671i	$0.679796\pi$
$90$		0			0
$91$	−23.3737	+	71.9370i	−0.256854	+	0.790516i
$92$		0			0
$93$	−158.292	+	158.292i	−1.70207	+	1.70207i
$94$		0			0
$95$	−13.2791	−	49.7002i	−0.139780	−	0.523160i
$96$		0			0
$97$	−49.9251	−	7.90736i	−0.514692	−	0.0815192i	−0.106315	−	0.994333i	$-0.533905\pi$
$97$	−49.9251	−	7.90736i	−0.514692	−	0.0815192i	−0.408377	+	0.912813i	$0.633905\pi$
$98$		0			0
$99$		−	185.057i		−	1.86926i
$100$		0			0
$101$	−53.0179			−0.524930			−0.262465	−	0.964942i	$-0.584535\pi$
$101$	−53.0179			−0.524930			−0.262465	+	0.964942i	$0.584535\pi$
$102$		0			0
$103$	12.5816	−	79.4370i	0.122151	−	0.771233i	−0.848225	−	0.529635i	$-0.822329\pi$
$103$	12.5816	−	79.4370i	0.122151	−	0.771233i	0.970377	−	0.241597i	$-0.0776712\pi$
$104$		0			0
$105$	16.0981	−	303.026i	0.153315	−	2.88596i
$106$		0			0
$107$	−70.6144	−	70.6144i	−0.659947	−	0.659947i	0.295420	−	0.955367i	$-0.404540\pi$
$107$	−70.6144	−	70.6144i	−0.659947	−	0.659947i	−0.955367	+	0.295420i	$0.904540\pi$
$108$		0			0
$109$	94.4927	+	30.7026i	0.866906	+	0.281675i	0.708510	−	0.705701i	$-0.249368\pi$
$109$	94.4927	+	30.7026i	0.866906	+	0.281675i	0.158396	+	0.987376i	$0.449368\pi$
$110$		0			0
$111$	9.84569	+	30.3019i	0.0886999	+	0.272990i
$112$		0			0
$113$	−19.0256	−	37.3398i	−0.168368	−	0.330441i	0.791370	−	0.611337i	$-0.209368\pi$
$113$	−19.0256	−	37.3398i	−0.168368	−	0.330441i	−0.959738	+	0.280897i	$0.909368\pi$
$114$		0			0
$115$	−98.7552	+	43.8841i	−0.858741	+	0.381601i
$116$		0			0
$117$	13.3894	+	84.5373i	0.114439	+	0.722541i
$118$		0			0
$119$	196.431	−	270.363i	1.65068	−	2.27196i
$120$		0			0
$121$	−38.6546	+	28.0842i	−0.319460	+	0.232101i
$122$		0			0
$123$	247.492	+	126.104i	2.01213	+	1.02523i
$124$		0			0
$125$	111.254	+	56.9875i	0.890031	+	0.455900i
$126$		0			0
$127$	−91.6843	+	179.941i	−0.721924	+	1.41686i	0.179430	+	0.983771i	$0.442575\pi$
$127$	−91.6843	+	179.941i	−0.721924	+	1.41686i	−0.901353	+	0.433084i	$0.857425\pi$
$128$		0			0
$129$	70.6196	+	97.1995i	0.547439	+	0.753485i
$130$		0			0
$131$	−124.653	−	90.5655i	−0.951548	−	0.691340i	−0.000375264	−	1.00000i	$-0.500119\pi$
$131$	−124.653	−	90.5655i	−0.951548	−	0.691340i	−0.951172	+	0.308660i	$0.900119\pi$
$132$		0			0
$133$	127.921	−	20.2608i	0.961815	−	0.152337i
$134$		0			0
$135$	−51.3383	−	115.530i	−0.380284	−	0.855777i
$136$		0			0
$137$	−27.7390	+	14.1337i	−0.202474	+	0.103166i	−0.552288	−	0.833654i	$-0.686245\pi$
$137$	−27.7390	+	14.1337i	−0.202474	+	0.103166i	0.349813	+	0.936819i	$0.386245\pi$
$138$		0			0
$139$	89.3083	−	29.0180i	0.642505	−	0.208763i	0.0303987	−	0.999538i	$-0.490322\pi$
$139$	89.3083	−	29.0180i	0.642505	−	0.208763i	0.612107	+	0.790775i	$0.290322\pi$
$140$		0			0
$141$	−59.9963	+	184.650i	−0.425506	+	1.30957i
$142$		0			0
$143$	55.1987	−	55.1987i	0.386005	−	0.386005i
$144$		0			0
$145$	81.7845	+	4.34477i	0.564031	+	0.0299639i
$146$		0			0
$147$	521.244	+	82.5570i	3.54588	+	0.561612i
$148$		0			0
$149$		−	158.547i		−	1.06407i	−0.846721	−	0.532037i	$-0.821427\pi$
$149$		−	158.547i		−	1.06407i	0.846721	−	0.532037i	$-0.178573\pi$
$150$		0			0
$151$	104.120			0.689535			0.344767	−	0.938688i	$-0.387958\pi$
$151$	104.120			0.689535			0.344767	+	0.938688i	$0.387958\pi$
$152$		0			0
$153$	59.1569	−	373.502i	0.386646	−	2.44119i
$154$		0			0
$155$	224.291	−	59.9268i	1.44704	−	0.386624i
$156$		0			0
$157$	32.7151	+	32.7151i	0.208376	+	0.208376i	0.803577	−	0.595201i	$-0.202927\pi$
$157$	32.7151	+	32.7151i	0.208376	+	0.208376i	−0.595201	+	0.803577i	$0.702927\pi$
$158$		0			0
$159$	−40.4513	−	13.1434i	−0.254411	−	0.0826631i
$160$		0			0
$161$	−84.0749	−	258.756i	−0.522204	−	1.60718i
$162$		0			0
$163$	−131.398	−	257.882i	−0.806120	−	1.58210i	−0.813100	−	0.582124i	$-0.802222\pi$
$163$	−131.398	−	257.882i	−0.806120	−	1.58210i	0.00697984	−	0.999976i	$-0.497778\pi$
$164$		0			0
$165$	−156.782	+	271.107i	−0.950195	+	1.64307i
$166$		0			0
$167$	18.4127	+	116.253i	0.110256	+	0.696128i	0.979455	+	0.201665i	$0.0646352\pi$
$167$	18.4127	+	116.253i	0.110256	+	0.696128i	−0.869199	+	0.494463i	$0.835365\pi$
$168$		0			0
$169$	78.1137	−	107.514i	0.462211	−	0.636179i
$170$		0			0
$171$	118.567	−	86.1439i	0.693374	−	0.503766i
$172$		0			0
$173$	−183.202	−	93.3461i	−1.05897	−	0.539573i	−0.164352	−	0.986402i	$-0.552553\pi$
$173$	−183.202	−	93.3461i	−1.05897	−	0.539573i	−0.894619	+	0.446829i	$0.852553\pi$
$174$		0			0
$175$	−171.777	+	263.688i	−0.981584	+	1.50679i
$176$		0			0
$177$	−85.7060	+	168.207i	−0.484215	+	0.950325i
$178$		0			0
$179$	31.7410	+	43.6877i	0.177324	+	0.244066i	0.888422	−	0.459027i	$-0.151802\pi$
$179$	31.7410	+	43.6877i	0.177324	+	0.244066i	−0.711098	+	0.703093i	$0.751802\pi$
$180$		0			0
$181$	−0.824611	−	0.599115i	−0.00455586	−	0.00331003i	0.585505	−	0.810669i	$-0.300896\pi$
$181$	−0.824611	−	0.599115i	−0.00455586	−	0.00331003i	−0.590061	+	0.807359i	$0.700896\pi$
$182$		0			0
$183$	−41.3449	+	6.54838i	−0.225928	+	0.0357835i
$184$		0			0
$185$	6.89305	−	32.3157i	0.0372597	−	0.174679i
$186$		0			0
$187$	−307.305	+	156.580i	−1.64334	+	0.837324i
$188$		0			0
$189$	302.709	−	98.3560i	1.60163	−	0.520402i
$190$		0			0
$191$	−14.9388	+	45.9768i	−0.0782134	+	0.240716i	−0.982517	−	0.186174i	$-0.940391\pi$
$191$	−14.9388	+	45.9768i	−0.0782134	+	0.240716i	0.904303	+	0.426891i	$0.140391\pi$
$192$		0			0
$193$	149.390	−	149.390i	0.774042	−	0.774042i	−0.204768	−	0.978811i	$-0.565644\pi$
$193$	149.390	−	149.390i	0.774042	−	0.774042i	0.978811	+	0.204768i	$0.0656440\pi$
$194$		0			0
$195$	52.0056	−	135.190i	0.266695	−	0.693284i
$196$		0			0
$197$	187.891	+	29.7591i	0.953763	+	0.151061i	0.613874	−	0.789404i	$-0.289610\pi$
$197$	187.891	+	29.7591i	0.953763	+	0.151061i	0.339889	+	0.940465i	$0.389610\pi$
$198$		0			0
$199$			375.183i			1.88534i	0.333723	+	0.942671i	$0.391695\pi$
$199$			375.183i			1.88534i	−0.333723	+	0.942671i	$0.608305\pi$
$200$		0			0
$201$	−370.079			−1.84119
$202$		0			0
$203$	−32.2558	+	203.655i	−0.158896	+	1.00323i
$204$		0			0
$205$	−156.719	−	241.704i	−0.764483	−	1.17904i
$206$		0			0
$207$	−217.696	−	217.696i	−1.05167	−	1.05167i
$208$		0			0
$209$	−127.124	−	41.3051i	−0.608249	−	0.197632i
$210$		0			0
$211$	−45.7555	−	140.821i	−0.216851	−	0.667397i	−0.999017	−	0.0443279i	$-0.985885\pi$
$211$	−45.7555	−	140.821i	−0.216851	−	0.667397i	0.782166	−	0.623070i	$-0.214115\pi$
$212$		0			0
$213$	251.715	+	494.019i	1.18176	+	2.31934i
$214$		0			0
$215$	−12.9356	−	123.926i	−0.0601658	−	0.576402i
$216$		0			0
$217$	91.4344	+	577.294i	0.421357	+	2.66034i
$218$		0			0
$219$	117.893	−	162.266i	0.538325	−	0.740940i
$220$		0			0
$221$	129.053	−	93.7628i	0.583952	−	0.424266i
$222$		0			0
$223$	−138.286	−	70.4604i	−0.620118	−	0.315966i	0.115557	−	0.993301i	$-0.463135\pi$
$223$	−138.286	−	70.4604i	−0.620118	−	0.315966i	−0.735675	+	0.677335i	$0.763135\pi$
$224$		0			0
$225$	−37.7300	+	354.106i	−0.167689	+	1.57380i
$226$		0			0
$227$	−101.004	+	198.232i	−0.444953	+	0.873269i	0.554211	+	0.832376i	$0.313020\pi$
$227$	−101.004	+	198.232i	−0.444953	+	0.873269i	−0.999164	+	0.0408924i	$0.986980\pi$
$228$		0			0
$229$	114.503	+	157.600i	0.500013	+	0.688209i	0.982196	−	0.187862i	$-0.0601556\pi$
$229$	114.503	+	157.600i	0.500013	+	0.688209i	−0.482182	+	0.876071i	$0.660156\pi$
$230$		0			0
$231$	−637.880	−	463.447i	−2.76139	−	2.00627i
$232$		0			0
$233$	−74.3632	+	11.7780i	−0.319155	+	0.0505492i	−0.313957	−	0.949437i	$-0.601655\pi$
$233$	−74.3632	+	11.7780i	−0.319155	+	0.0505492i	−0.00519849	+	0.999986i	$0.501655\pi$
$234$		0			0
$235$	149.729	−	134.623i	0.637144	−	0.572863i
$236$		0			0
$237$	−154.016	+	78.4751i	−0.649857	+	0.331119i
$238$		0			0
$239$	−176.947	+	57.4935i	−0.740363	+	0.240558i	−0.654829	−	0.755777i	$-0.727259\pi$
$239$	−176.947	+	57.4935i	−0.740363	+	0.240558i	−0.0855335	+	0.996335i	$0.527259\pi$
$240$		0			0
$241$	94.7266	−	291.538i	0.393056	−	1.20970i	−0.537409	−	0.843322i	$-0.680597\pi$
$241$	94.7266	−	291.538i	0.393056	−	1.20970i	0.930465	−	0.366381i	$-0.119403\pi$
$242$		0			0
$243$	−182.376	+	182.376i	−0.750517	+	0.750517i
$244$		0			0
$245$	−425.092	−	344.736i	−1.73507	−	1.40709i
$246$		0			0
$247$	61.0611	+	9.67114i	0.247211	+	0.0391544i
$248$		0			0
$249$		−	478.946i		−	1.92348i
$250$		0			0
$251$	107.240			0.427250			0.213625	−	0.976916i	$-0.431473\pi$
$251$	107.240			0.427250			0.213625	+	0.976916i	$0.431473\pi$
$252$		0			0
$253$	−43.9253	+	277.333i	−0.173618	+	1.09618i
$254$		0			0
$255$	−403.100	+	497.060i	−1.58078	+	1.94925i
$256$		0			0
$257$	160.335	+	160.335i	0.623871	+	0.623871i	0.946519	−	0.322648i	$-0.104573\pi$
$257$	160.335	+	160.335i	0.623871	+	0.623871i	−0.322648	+	0.946519i	$0.604573\pi$
$258$		0			0
$259$	79.1176	+	25.7069i	0.305473	+	0.0992543i
$260$		0			0
$261$	72.1008	+	221.903i	0.276248	+	0.850205i
$262$		0			0
$263$	−102.150	−	200.481i	−0.388403	−	0.762284i	0.611170	−	0.791499i	$-0.290699\pi$
$263$	−102.150	−	200.481i	−0.388403	−	0.762284i	−0.999573	+	0.0292152i	$0.990699\pi$
$264$		0			0
$265$	29.4919	+	32.8012i	0.111290	+	0.123778i
$266$		0			0
$267$	103.386	+	652.754i	0.387214	+	2.44477i
$268$		0			0
$269$	170.786	−	235.067i	0.634893	−	0.873856i	−0.363437	−	0.931619i	$-0.618397\pi$
$269$	170.786	−	235.067i	0.634893	−	0.873856i	0.998330	+	0.0577632i	$0.0183968\pi$
$270$		0			0
$271$	−174.231	+	126.587i	−0.642921	+	0.467109i	−0.860852	−	0.508855i	$-0.830069\pi$
$271$	−174.231	+	126.587i	−0.642921	+	0.467109i	0.217932	+	0.975964i	$0.430069\pi$
$272$		0			0
$273$	324.927	+	165.559i	1.19021	+	0.606442i
$274$		0			0
$275$	281.507	−	161.992i	1.02366	−	0.589061i
$276$		0			0
$277$	107.660	−	211.294i	0.388662	−	0.762793i	−0.610920	−	0.791692i	$-0.709200\pi$
$277$	107.660	−	211.294i	0.388662	−	0.762793i	0.999582	+	0.0288994i	$0.00920024\pi$
$278$		0			0
$279$	388.757	+	535.078i	1.39339	+	1.91784i
$280$		0			0
$281$	110.713	+	80.4380i	0.393998	+	0.286256i	0.767092	−	0.641537i	$-0.221703\pi$
$281$	110.713	+	80.4380i	0.393998	+	0.286256i	−0.373094	+	0.927794i	$0.621703\pi$
$282$		0			0
$283$	−63.5085	+	10.0588i	−0.224412	+	0.0355433i	−0.267628	−	0.963522i	$-0.586240\pi$
$283$	−63.5085	+	10.0588i	−0.224412	+	0.0355433i	0.0432159	+	0.999066i	$0.486240\pi$
$284$		0			0
$285$	−246.682	+	25.7490i	−0.865551	+	0.0903475i
$286$		0			0
$287$	646.196	−	329.253i	2.25155	−	1.14722i
$288$		0			0
$289$	−395.434	+	128.484i	−1.36829	+	0.444583i
$290$		0			0
$291$	−75.3079	+	231.774i	−0.258790	+	0.796474i
$292$		0			0
$293$	145.169	−	145.169i	0.495458	−	0.495458i	−0.414563	−	0.910021i	$-0.636065\pi$
$293$	145.169	−	145.169i	0.495458	−	0.495458i	0.910021	+	0.414563i	$0.136065\pi$
$294$		0			0
$295$	164.274	−	106.514i	0.556860	−	0.361063i
$296$		0			0
$297$	−324.441	−	51.3865i	−1.09240	−	0.173018i
$298$		0			0
$299$		−	129.869i		−	0.434345i
$300$		0			0
$301$	313.696			1.04218
$302$		0			0
$303$	−39.9866	+	252.465i	−0.131969	+	0.833219i
$304$		0			0
$305$	40.5177	+	15.5865i	0.132845	+	0.0511034i
$306$		0			0
$307$	71.4596	+	71.4596i	0.232767	+	0.232767i	0.813847	−	0.581079i	$-0.197369\pi$
$307$	71.4596	+	71.4596i	0.232767	+	0.232767i	−0.581079	+	0.813847i	$0.697369\pi$
$308$		0			0
$309$	−368.781	−	119.824i	−1.19347	−	0.387780i
$310$		0			0
$311$	148.386	+	456.685i	0.477125	+	1.46844i	0.843071	+	0.537803i	$0.180746\pi$
$311$	148.386	+	456.685i	0.477125	+	1.46844i	−0.365946	+	0.930636i	$0.619254\pi$
$312$		0			0
$313$	−26.3751	−	51.7640i	−0.0842654	−	0.165380i	0.845029	−	0.534721i	$-0.179583\pi$
$313$	−26.3751	−	51.7640i	−0.0842654	−	0.165380i	−0.929294	+	0.369341i	$0.879583\pi$
$314$		0			0
$315$	−876.829	−	187.031i	−2.78358	−	0.593749i
$316$		0			0
$317$	66.1322	+	417.542i	0.208619	+	1.31717i	0.840377	+	0.542002i	$0.182334\pi$
$317$	66.1322	+	417.542i	0.208619	+	1.31717i	−0.631758	+	0.775166i	$0.717666\pi$
$318$		0			0
$319$	125.081	−	172.159i	0.392104	−	0.539685i
$320$		0			0
$321$	−389.516	+	283.000i	−1.21344	+	0.881619i
$322$		0			0
$323$	−243.372	−	124.004i	−0.753473	−	0.383914i
$324$		0			0
$325$	−116.877	+	94.3686i	−0.359621	+	0.290365i
$326$		0			0
$327$	217.469	−	426.808i	0.665044	−	1.30522i
$328$		0			0
$329$	297.964	+	410.112i	0.905665	+	1.24654i
$330$		0			0
$331$	182.712	+	132.748i	0.552001	+	0.401052i	0.828523	−	0.559956i	$-0.189182\pi$
$331$	182.712	+	132.748i	0.552001	+	0.401052i	−0.276522	+	0.961008i	$0.589182\pi$
$332$		0			0
$333$	92.9756	−	14.7259i	0.279206	−	0.0442219i
$334$		0			0
$335$	332.244	+	192.138i	0.991773	+	0.573546i
$336$		0			0
$337$	321.869	−	164.001i	0.955101	−	0.486648i	0.0942743	−	0.995546i	$-0.469947\pi$
$337$	321.869	−	164.001i	0.955101	−	0.486648i	0.860827	+	0.508898i	$0.169947\pi$
$338$		0			0
$339$	−192.157	+	62.4356i	−0.566835	+	0.184176i
$340$		0			0
$341$	186.405	−	573.696i	0.546642	−	1.68239i
$342$		0			0
$343$	538.180	−	538.180i	1.56904	−	1.56904i
$344$		0			0
$345$	134.489	+	503.359i	0.389823	+	1.45901i
$346$		0			0
$347$	−138.832	−	21.9889i	−0.400093	−	0.0633685i	−0.0468544	−	0.998902i	$-0.514920\pi$
$347$	−138.832	−	21.9889i	−0.400093	−	0.0633685i	−0.353239	+	0.935533i	$0.614920\pi$
$348$		0			0
$349$			280.487i			0.803689i	0.915708	+	0.401844i	$0.131631\pi$
$349$			280.487i			0.803689i	−0.915708	+	0.401844i	$0.868369\pi$
$350$		0			0
$351$	151.929			0.432846
$352$		0			0
$353$	−43.3734	+	273.849i	−0.122871	+	0.775776i	0.846899	+	0.531754i	$0.178467\pi$
$353$	−43.3734	+	273.849i	−0.122871	+	0.775776i	−0.969770	+	0.244022i	$0.921533\pi$
$354$		0			0
$355$	30.5040	−	574.197i	0.0859268	−	1.61746i
$356$		0			0
$357$	−1139.29	−	1139.29i	−3.19129	−	3.19129i
$358$		0			0
$359$	−167.509	−	54.4270i	−0.466599	−	0.151607i	0.0662756	−	0.997801i	$-0.478888\pi$
$359$	−167.509	−	54.4270i	−0.466599	−	0.151607i	−0.532875	+	0.846194i	$0.678888\pi$
$360$		0			0
$361$	78.8433	+	242.655i	0.218402	+	0.672174i
$362$		0			0
$363$	104.580	+	205.251i	0.288100	+	0.565428i
$364$		0			0
$365$	−190.085	+	84.4687i	−0.520782	+	0.231421i
$366$		0			0
$367$	55.8459	+	352.597i	0.152169	+	0.960755i	0.939082	+	0.343692i	$0.111678\pi$
$367$	55.8459	+	352.597i	0.152169	+	0.960755i	−0.786914	+	0.617063i	$0.788322\pi$
$368$		0			0
$369$	482.375	−	663.932i	1.30725	−	1.79927i
$370$		0			0
$371$	−89.8435	+	65.2752i	−0.242166	+	0.175944i
$372$		0			0
$373$	−483.472	−	246.341i	−1.29617	−	0.660432i	−0.336534	−	0.941671i	$-0.609255\pi$
$373$	−483.472	−	246.341i	−1.29617	−	0.660432i	−0.959638	+	0.281239i	$0.909255\pi$
$374$		0			0
$375$	355.277	−	486.798i	0.947405	−	1.29813i
$376$		0			0
$377$	−44.6831	+	87.6956i	−0.118523	+	0.232614i
$378$		0			0
$379$	95.3159	+	131.191i	0.251493	+	0.346151i	0.916034	−	0.401102i	$-0.131373\pi$
$379$	95.3159	+	131.191i	0.251493	+	0.346151i	−0.664540	+	0.747252i	$0.731373\pi$
$380$		0			0
$381$	787.708	+	572.303i	2.06748	+	1.50211i
$382$		0			0
$383$	19.2963	−	3.05623i	0.0503819	−	0.00797971i	−0.131193	−	0.991357i	$-0.541881\pi$
$383$	19.2963	−	3.05623i	0.0503819	−	0.00797971i	0.181575	+	0.983377i	$0.441881\pi$
$384$		0			0
$385$	332.053	+	747.241i	0.862476	+	1.94089i
$386$		0			0
$387$	316.281	−	161.153i	0.817263	−	0.416416i
$388$		0			0
$389$	513.958	−	166.995i	1.32123	−	0.429294i	0.438313	−	0.898823i	$-0.355576\pi$
$389$	513.958	−	166.995i	1.32123	−	0.429294i	0.882917	+	0.469529i	$0.155576\pi$
$390$		0			0
$391$	−177.310	+	545.703i	−0.453477	+	1.39566i
$392$		0			0
$393$	−525.277	+	525.277i	−1.33658	+	1.33658i
$394$		0			0
$395$	179.013	+	9.50998i	0.453197	+	0.0240759i
$396$		0			0
$397$	−311.015	−	49.2599i	−0.783413	−	0.124080i	−0.248100	−	0.968734i	$-0.579806\pi$
$397$	−311.015	−	49.2599i	−0.783413	−	0.124080i	−0.535313	+	0.844654i	$0.679806\pi$
$398$		0			0
$399$		−	624.429i		−	1.56498i
$400$		0			0
$401$	−336.885			−0.840112			−0.420056	−	0.907498i	$-0.637990\pi$
$401$	−336.885			−0.840112			−0.420056	+	0.907498i	$0.637990\pi$
$402$		0			0
$403$	−43.6447	+	275.562i	−0.108299	+	0.683776i
$404$		0			0
$405$	30.4151	−	8.12640i	0.0750990	−	0.0200652i
$406$		0			0
$407$	−60.7085	−	60.7085i	−0.149161	−	0.149161i
$408$		0			0
$409$	−393.010	−	127.697i	−0.960906	−	0.312217i	−0.213766	−	0.976885i	$-0.568573\pi$
$409$	−393.010	−	127.697i	−0.960906	−	0.312217i	−0.747139	+	0.664668i	$0.768573\pi$
$410$		0			0
$411$	46.3821	+	142.750i	0.112852	+	0.347323i
$412$		0			0
$413$	223.776	+	439.186i	0.541831	+	1.06340i
$414$		0			0
$415$	−248.659	+	429.980i	−0.599178	+	1.03610i
$416$		0			0
$417$	−70.8234	−	447.162i	−0.169840	−	1.07233i
$418$		0			0
$419$	−85.8577	+	118.173i	−0.204911	+	0.282036i	−0.899087	−	0.437769i	$-0.855769\pi$
$419$	−85.8577	+	118.173i	−0.204911	+	0.282036i	0.694177	+	0.719805i	$0.255769\pi$
$420$		0			0
$421$	−619.383	+	450.008i	−1.47122	+	1.06890i	−0.490961	+	0.871182i	$0.663354\pi$
$421$	−619.383	+	450.008i	−1.47122	+	1.06890i	−0.980258	+	0.197722i	$0.936646\pi$
$422$		0			0
$423$	511.103	+	260.420i	1.20828	+	0.615650i
$424$		0			0
$425$	619.952	−	236.961i	1.45871	−	0.557555i
$426$		0			0
$427$	−49.6194	+	97.3835i	−0.116205	+	0.228064i
$428$		0			0
$429$	−221.219	−	304.481i	−0.515661	−	0.709747i
$430$		0			0
$431$	−172.887	−	125.610i	−0.401130	−	0.291438i	0.368871	−	0.929480i	$-0.379744\pi$
$431$	−172.887	−	125.610i	−0.401130	−	0.291438i	−0.770001	+	0.638043i	$0.779744\pi$
$432$		0			0
$433$	651.399	−	103.171i	1.50438	−	0.238271i	0.650810	−	0.759241i	$-0.274430\pi$
$433$	651.399	−	103.171i	1.50438	−	0.238271i	0.853575	+	0.520970i	$0.174430\pi$
$434$		0			0
$435$	82.3719	−	386.172i	0.189361	−	0.887752i
$436$		0			0
$437$	−198.136	+	100.955i	−0.453401	+	0.231019i
$438$		0			0
$439$	301.650	−	98.0119i	0.687129	−	0.223262i	0.0554152	−	0.998463i	$-0.482352\pi$
$439$	301.650	−	98.0119i	0.687129	−	0.223262i	0.631714	+	0.775202i	$0.282352\pi$
$440$		0			0
$441$	481.825	−	1482.90i	1.09257	−	3.36259i
$442$		0			0
$443$	592.554	−	592.554i	1.33759	−	1.33759i	0.439207	−	0.898386i	$-0.355260\pi$
$443$	592.554	−	592.554i	1.33759	−	1.33759i	0.898386	−	0.439207i	$-0.144740\pi$
$444$		0			0
$445$	246.080	−	639.694i	0.552990	−	1.43752i
$446$		0			0
$447$	−754.984	−	119.578i	−1.68900	−	0.267512i
$448$		0			0
$449$			443.423i			0.987578i	0.869582	+	0.493789i	$0.164389\pi$
$449$			443.423i			0.987578i	−0.869582	+	0.493789i	$0.835611\pi$
$450$		0			0
$451$	−748.482			−1.65961
$452$		0			0
$453$	78.5280	−	495.806i	0.173351	−	1.09450i
$454$		0			0
$455$	−205.753	−	317.328i	−0.452204	−	0.697425i
$456$		0			0
$457$	−411.815	−	411.815i	−0.901126	−	0.901126i	0.0944073	−	0.995534i	$-0.469904\pi$
$457$	−411.815	−	411.815i	−0.901126	−	0.901126i	−0.995534	+	0.0944073i	$0.969904\pi$
$458$		0			0
$459$	−638.397	−	207.428i	−1.39084	−	0.451912i
$460$		0			0
$461$	−34.7547	−	106.964i	−0.0753897	−	0.232026i	0.906259	−	0.422722i	$-0.138925\pi$
$461$	−34.7547	−	106.964i	−0.0753897	−	0.232026i	−0.981649	+	0.190696i	$0.938925\pi$
$462$		0			0
$463$	−191.075	−	375.007i	−0.412690	−	0.809950i	−1.00000		0.000587593i	$-0.999813\pi$
$463$	−191.075	−	375.007i	−0.412690	−	0.809950i	0.587310	−	0.809362i	$-0.300187\pi$
$464$		0			0
$465$	−116.202	−	1113.25i	−0.249898	−	2.39408i
$466$		0			0
$467$	−60.2579	−	380.453i	−0.129032	−	0.814675i	−0.964296	−	0.264826i	$-0.914685\pi$
$467$	−60.2579	−	380.453i	−0.129032	−	0.814675i	0.835264	−	0.549849i	$-0.185315\pi$
$468$		0			0
$469$	−567.958	+	781.728i	−1.21100	+	1.66680i
$470$		0			0
$471$	180.460	−	131.112i	0.383141	−	0.278368i
$472$		0			0
$473$	−288.462	−	146.979i	−0.609856	−	0.310737i
$474$		0			0
$475$	234.830	+	104.956i	0.494380	+	0.220960i
$476$		0			0
$477$	−57.0504	+	111.968i	−0.119602	+	0.234733i
$478$		0			0
$479$	229.301	+	315.605i	0.478707	+	0.658883i	0.978256	−	0.207402i	$-0.0665009\pi$
$479$	229.301	+	315.605i	0.478707	+	0.658883i	−0.499549	+	0.866286i	$0.666501\pi$
$480$		0			0
$481$	32.1252	+	23.3403i	0.0667884	+	0.0485246i
$482$		0			0
$483$	−1295.58	+	205.199i	−2.68235	+	0.424843i
$484$		0			0
$485$	187.941	−	168.980i	0.387508	−	0.348412i
$486$		0			0
$487$	−262.563	+	133.783i	−0.539144	+	0.274707i	−0.702286	−	0.711895i	$-0.747837\pi$
$487$	−262.563	+	133.783i	−0.539144	+	0.274707i	0.163142	+	0.986603i	$0.447837\pi$
$488$		0			0
$489$	−1327.11	+	431.203i	−2.71392	+	0.881807i
$490$		0			0
$491$	42.2330	−	129.980i	0.0860142	−	0.264724i	−0.898794	−	0.438372i	$-0.855555\pi$
$491$	42.2330	−	129.980i	0.0860142	−	0.264724i	0.984808	+	0.173647i	$0.0555553\pi$
$492$		0			0
$493$	307.487	−	307.487i	0.623705	−	0.623705i
$494$		0			0
$495$	718.664	+	582.814i	1.45185	+	1.17740i
$496$		0			0
$497$	1429.83	+	226.463i	2.87693	+	0.455660i
$498$		0			0
$499$			310.719i			0.622684i	0.950298	+	0.311342i	$0.100779\pi$
$499$			310.719i			0.622684i	−0.950298	+	0.311342i	$0.899221\pi$
$500$		0			0
$501$	567.472			1.13268
$502$		0			0
$503$	83.5532	−	527.534i	0.166110	−	1.04878i	−0.753931	−	0.656953i	$-0.771845\pi$
$503$	83.5532	−	527.534i	0.166110	−	1.04878i	0.920041	−	0.391822i	$-0.128155\pi$
$504$		0			0
$505$	166.973	−	205.894i	0.330640	−	0.407711i
$506$		0			0
$507$	−453.057	−	453.057i	−0.893604	−	0.893604i
$508$		0			0
$509$	−246.572	−	80.1162i	−0.484425	−	0.157399i	0.0566150	−	0.998396i	$-0.481969\pi$
$509$	−246.572	−	80.1162i	−0.484425	−	0.157399i	−0.541040	+	0.840997i	$0.681969\pi$
$510$		0			0
$511$	−161.828	−	498.057i	−0.316690	−	0.974671i
$512$		0			0
$513$	−118.104	−	231.792i	−0.230222	−	0.451836i
$514$		0			0
$515$	268.868	+	299.037i	0.522073	+	0.580655i
$516$		0			0
$517$	−81.8419	−	516.729i	−0.158301	−	0.999476i
$518$		0			0
$519$	−582.676	+	801.985i	−1.12269	+	1.54525i
$520$		0			0
$521$	238.023	−	172.934i	0.456858	−	0.331927i	−0.335440	−	0.942062i	$-0.608885\pi$
$521$	238.023	−	172.934i	0.456858	−	0.331927i	0.792297	+	0.610135i	$0.208885\pi$
$522$		0			0
$523$	−222.750	−	113.497i	−0.425909	−	0.217011i	0.227879	−	0.973690i	$-0.426821\pi$
$523$	−222.750	−	113.497i	−0.425909	−	0.217011i	−0.653788	+	0.756678i	$0.726821\pi$
$524$		0			0
$525$	1126.10	+	1016.86i	2.14494	+	1.93688i
$526$		0			0
$527$	559.616	−	1098.31i	1.06189	−	2.08408i
$528$		0			0
$529$	−36.3626	−	50.0488i	−0.0687383	−	0.0946101i
$530$		0			0
$531$	451.240	+	327.845i	0.849792	+	0.617410i
$532$		0			0
$533$	341.920	−	54.1549i	0.641502	−	0.101604i
$534$		0			0
$535$	496.621	−	51.8381i	0.928263	−	0.0968936i
$536$		0			0
$537$	231.975	−	118.197i	0.431984	−	0.220107i
$538$		0			0
$539$	−1352.47	+	439.445i	−2.50923	+	0.815297i
$540$		0			0
$541$	−100.597	+	309.607i	−0.185947	+	0.572286i	−0.999963	−	0.00855608i	$-0.997276\pi$
$541$	−100.597	+	309.607i	−0.185947	+	0.572286i	0.814017	+	0.580842i	$0.197276\pi$
$542$		0			0
$543$	−3.47485	+	3.47485i	−0.00639935	+	0.00639935i
$544$		0			0
$545$	−416.826	+	270.267i	−0.764819	+	0.495902i
$546$		0			0
$547$	940.393	+	148.944i	1.71918	+	0.272292i	0.936637	−	0.350301i	$-0.113921\pi$
$547$	940.393	+	148.944i	1.71918	+	0.272292i	0.782546	+	0.622593i	$0.213921\pi$
$548$		0			0
$549$			123.676i			0.225276i
$550$		0			0
$551$	168.529			0.305860
$552$		0			0
$553$	−70.6025	+	445.767i	−0.127672	+	0.806088i
$554$		0			0
$555$	−148.685	−	57.1967i	−0.267900	−	0.103057i
$556$		0			0
$557$	256.410	+	256.410i	0.460342	+	0.460342i	0.898767	−	0.438426i	$-0.144464\pi$
$557$	256.410	+	256.410i	0.460342	+	0.460342i	−0.438426	+	0.898767i	$0.644464\pi$
$558$		0			0
$559$	142.409	+	46.2715i	0.254757	+	0.0827755i
$560$		0			0
$561$	513.842	+	1581.44i	0.915940	+	2.81897i
$562$		0			0
$563$	155.515	+	305.215i	0.276225	+	0.542123i	0.986887	−	0.161411i	$-0.0516044\pi$
$563$	155.515	+	305.215i	0.276225	+	0.542123i	−0.710662	+	0.703534i	$0.751604\pi$
$564$		0			0
$565$	204.927	+	43.7117i	0.362703	+	0.0773659i
$566$		0			0
$567$	12.3990	+	78.2842i	0.0218677	+	0.138067i
$568$		0			0
$569$	94.8678	−	130.574i	0.166727	−	0.229480i	−0.717475	−	0.696584i	$-0.754702\pi$
$569$	94.8678	−	130.574i	0.166727	−	0.229480i	0.884203	+	0.467103i	$0.154702\pi$
$570$		0			0
$571$	834.421	−	606.242i	1.46133	−	1.06172i	0.478319	−	0.878186i	$-0.341246\pi$
$571$	834.421	−	606.242i	1.46133	−	1.06172i	0.983013	−	0.183534i	$-0.0587538\pi$
$572$		0			0
$573$	207.669	+	105.813i	0.362425	+	0.184665i
$574$		0			0
$575$	140.595	−	521.722i	0.244512	−	0.907342i
$576$		0			0
$577$	−409.616	+	803.917i	−0.709907	+	1.39327i	0.200557	+	0.979682i	$0.435725\pi$
$577$	−409.616	+	803.917i	−0.709907	+	1.39327i	−0.910464	+	0.413589i	$0.864275\pi$
$578$		0			0
$579$	−598.708	−	824.051i	−1.03404	−	1.42323i
$580$		0			0
$581$	−1011.69	−	735.035i	−1.74129	−	1.26512i
$582$		0			0
$583$	113.200	−	17.9292i	0.194168	−	0.0307533i
$584$		0			0
$585$	−370.467	−	214.243i	−0.633277	−	0.366227i
$586$		0			0
$587$	−383.378	+	195.341i	−0.653114	+	0.332778i	−0.748957	−	0.662618i	$-0.769445\pi$
$587$	−383.378	+	195.341i	−0.653114	+	0.332778i	0.0958435	+	0.995396i	$0.469445\pi$
$588$		0			0
$589$	454.342	−	147.625i	0.771378	−	0.250636i
$590$		0			0
$591$	283.419	−	872.273i	0.479558	−	1.47593i
$592$		0			0
$593$	365.736	−	365.736i	0.616755	−	0.616755i	−0.327942	−	0.944698i	$-0.606355\pi$
$593$	365.736	−	365.736i	0.616755	−	0.616755i	0.944698	+	0.327942i	$0.106355\pi$
$594$		0			0
$595$	431.317	+	1614.31i	0.724902	+	2.71313i
$596$		0			0
$597$	1786.58	+	282.967i	2.99260	+	0.473981i
$598$		0			0
$599$			833.096i			1.39081i	0.718617	+	0.695406i	$0.244775\pi$
$599$			833.096i			1.39081i	−0.718617	+	0.695406i	$0.755225\pi$
$600$		0			0
$601$	−1120.65			−1.86465			−0.932325	−	0.361621i	$-0.882223\pi$
$601$	−1120.65			−1.86465			−0.932325	+	0.361621i	$0.882223\pi$
$602$		0			0
$603$	−171.046	+	1079.94i	−0.283658	+	1.79095i
$604$		0			0
$605$	12.6735	−	238.562i	0.0209480	−	0.394318i
$606$		0			0
$607$	−597.745	−	597.745i	−0.984752	−	0.984752i	0.0151334	−	0.999885i	$-0.495183\pi$
$607$	−597.745	−	597.745i	−0.984752	−	0.984752i	−0.999885	+	0.0151334i	$0.995183\pi$
$608$		0			0
$609$	945.455	+	307.197i	1.55247	+	0.504429i
$610$		0			0
$611$	74.7737	+	230.130i	0.122379	+	0.376645i
$612$		0			0
$613$	−452.120	−	887.336i	−0.737554	−	1.44753i	−0.888446	−	0.458981i	$-0.848215\pi$
$613$	−452.120	−	887.336i	−0.737554	−	1.44753i	0.150893	−	0.988550i	$-0.451785\pi$
$614$		0			0
$615$	−1269.17	+	563.983i	−2.06369	+	0.917045i
$616$		0			0
$617$	−159.024	−	1004.04i	−0.257737	−	1.62729i	−0.688790	−	0.724961i	$-0.741858\pi$
$617$	−159.024	−	1004.04i	−0.257737	−	1.62729i	0.431053	−	0.902327i	$-0.358142\pi$
$618$		0			0
$619$	239.281	−	329.341i	0.386560	−	0.532054i	−0.570748	−	0.821126i	$-0.693347\pi$
$619$	239.281	−	329.341i	0.386560	−	0.532054i	0.957307	+	0.289072i	$0.0933465\pi$
$620$		0			0
$621$	−442.115	+	321.216i	−0.711941	+	0.517256i
$622$		0			0
$623$	1537.49	+	783.392i	2.46789	+	1.25745i
$624$		0			0
$625$	−571.690	+	252.577i	−0.914705	+	0.404123i
$626$		0			0
$627$	−292.568	+	574.198i	−0.466616	+	0.915786i
$628$		0			0
$629$	−103.122	−	141.935i	−0.163946	−	0.225652i
$630$		0			0
$631$	−287.861	−	209.143i	−0.456198	−	0.331447i	0.335840	−	0.941919i	$-0.390980\pi$
$631$	−287.861	−	209.143i	−0.456198	−	0.331447i	−0.792038	+	0.610472i	$0.790980\pi$
$632$		0			0
$633$	−705.082	+	111.674i	−1.11387	+	0.176420i
$634$		0			0
$635$	−410.047	−	922.755i	−0.645743	−	1.45316i
$636$		0			0
$637$	586.039	−	298.602i	0.919999	−	0.468763i
$638$		0			0
$639$	1557.95	−	506.209i	2.43811	−	0.792190i
$640$		0			0
$641$	314.654	−	968.405i	0.490880	−	1.51077i	−0.332401	−	0.943138i	$-0.607859\pi$
$641$	314.654	−	968.405i	0.490880	−	1.51077i	0.823281	−	0.567634i	$-0.192141\pi$
$642$		0			0
$643$	−492.145	+	492.145i	−0.765388	+	0.765388i	−0.977291	−	0.211903i	$-0.932034\pi$
$643$	−492.145	+	492.145i	−0.765388	+	0.765388i	0.211903	+	0.977291i	$0.432034\pi$
$644$		0			0
$645$	−599.880	−	31.8684i	−0.930047	−	0.0494084i
$646$		0			0
$647$	−829.589	−	131.394i	−1.28221	−	0.203082i	−0.522103	−	0.852882i	$-0.674852\pi$
$647$	−829.589	−	131.394i	−1.28221	−	0.203082i	−0.760105	+	0.649801i	$0.774852\pi$
$648$		0			0
$649$		−	508.704i		−	0.783828i
$650$		0			0
$651$	2817.97			4.32868
$652$		0			0
$653$	96.8475	−	611.471i	0.148312	−	0.936403i	−0.795508	−	0.605943i	$-0.792796\pi$
$653$	96.8475	−	611.471i	0.148312	−	0.936403i	0.943820	−	0.330460i	$-0.107204\pi$
$654$		0			0
$655$	744.288	−	198.861i	1.13632	−	0.303605i
$656$		0			0
$657$	−419.025	−	419.025i	−0.637786	−	0.637786i
$658$		0			0
$659$	−888.922	−	288.828i	−1.34890	−	0.438283i	−0.456575	−	0.889685i	$-0.650924\pi$
$659$	−888.922	−	288.828i	−1.34890	−	0.438283i	−0.892320	+	0.451402i	$0.850924\pi$
$660$		0			0
$661$	155.326	+	478.045i	0.234987	+	0.723215i	0.997123	+	0.0757987i	$0.0241506\pi$
$661$	155.326	+	478.045i	0.234987	+	0.723215i	−0.762136	+	0.647417i	$0.775849\pi$
$662$		0			0
$663$	−349.155	−	685.255i	−0.526629	−	1.03357i
$664$		0			0
$665$	−324.191	+	560.589i	−0.487505	+	0.842991i
$666$		0			0
$667$	−55.3818	−	349.667i	−0.0830312	−	0.524239i
$668$		0			0
$669$	−439.821	+	605.362i	−0.657431	+	0.904876i
$670$		0			0
$671$	91.2558	−	66.3012i	0.136000	−	0.0988095i
$672$		0			0
$673$	−44.8965	−	22.8759i	−0.0667110	−	0.0339910i	0.420317	−	0.907377i	$-0.361919\pi$
$673$	−44.8965	−	22.8759i	−0.0667110	−	0.0339910i	−0.487028	+	0.873386i	$0.661919\pi$
$674$		0			0
$675$	610.342	+	164.476i	0.904210	+	0.243668i
$676$		0			0
$677$	−506.588	+	994.235i	−0.748284	+	1.46859i	0.130540	+	0.991443i	$0.458329\pi$
$677$	−506.588	+	994.235i	−0.748284	+	1.46859i	−0.878824	+	0.477146i	$0.841671\pi$
$678$		0			0
$679$	374.007	+	514.777i	0.550821	+	0.758140i
$680$		0			0
$681$	867.780	+	630.479i	1.27427	+	0.925814i
$682$		0			0
$683$	−780.752	+	123.659i	−1.14312	+	0.181053i	−0.699141	−	0.714984i	$-0.746434\pi$
$683$	−780.752	+	123.659i	−1.14312	+	0.181053i	−0.443981	+	0.896036i	$0.646434\pi$
$684$		0			0
$685$	32.4725	−	152.236i	0.0474052	−	0.222242i
$686$		0			0
$687$	836.833	−	426.388i	1.21810	−	0.620652i
$688$		0			0
$689$	−50.4147	+	16.3807i	−0.0731708	+	0.0237746i
$690$		0			0
$691$	−50.1120	+	154.229i	−0.0725209	+	0.223196i	−0.980747	−	0.195284i	$-0.937437\pi$
$691$	−50.1120	+	154.229i	−0.0725209	+	0.223196i	0.908226	+	0.418480i	$0.137437\pi$
$692$		0			0
$693$	−1647.22	+	1647.22i	−2.37694	+	2.37694i
$694$		0			0
$695$	−168.575	+	438.215i	−0.242553	+	0.630526i
$696$		0			0
$697$	−1510.67	−	239.266i	−2.16739	−	0.343280i
$698$		0			0
$699$			362.992i			0.519302i
$700$		0			0
$701$	658.554			0.939450			0.469725	−	0.882813i	$-0.344353\pi$
$701$	658.554			0.939450			0.469725	+	0.882813i	$0.344353\pi$
$702$		0			0
$703$	10.6365	−	67.1562i	0.0151301	−	0.0955280i
$704$		0			0
$705$	−528.132	−	814.526i	−0.749123	−	1.15536i
$706$		0			0
$707$	471.921	+	471.921i	0.667498	+	0.667498i
$708$		0			0
$709$	331.478	+	107.704i	0.467528	+	0.151909i	0.533301	−	0.845925i	$-0.320951\pi$
$709$	331.478	+	107.704i	0.467528	+	0.151909i	−0.0657727	+	0.997835i	$0.520951\pi$
$710$		0			0
$711$	157.817	+	485.710i	0.221964	+	0.683136i
$712$		0			0
$713$	−455.600	−	894.165i	−0.638990	−	1.25409i
$714$		0			0
$715$	40.5214	+	388.205i	0.0566733	+	0.542944i
$716$		0			0
$717$	140.323	+	885.963i	0.195708	+	1.23565i
$718$		0			0
$719$	320.791	−	441.531i	0.446163	−	0.614090i	−0.525405	−	0.850852i	$-0.676086\pi$
$719$	320.791	−	441.531i	0.446163	−	0.614090i	0.971568	+	0.236762i	$0.0760862\pi$
$720$		0			0
$721$	−819.073	+	595.091i	−1.13602	+	0.825369i
$722$		0			0
$723$	−1316.83	−	670.958i	−1.82134	−	0.928020i
$724$		0			0
$725$	−274.443	+	303.925i	−0.378542	+	0.419207i
$726$		0			0
$727$	−41.7559	+	81.9507i	−0.0574360	+	0.112724i	−0.917940	−	0.396719i	$-0.870149\pi$
$727$	−41.7559	+	81.9507i	−0.0574360	+	0.112724i	0.860504	+	0.509444i	$0.170149\pi$
$728$		0			0
$729$	697.594	+	960.156i	0.956920	+	1.31709i
$730$		0			0
$731$	−535.221	−	388.861i	−0.732176	−	0.531957i
$732$		0			0
$733$	−584.391	+	92.5585i	−0.797260	+	0.126274i	−0.541757	−	0.840535i	$-0.682241\pi$
$733$	−584.391	+	92.5585i	−0.797260	+	0.126274i	−0.255502	+	0.966808i	$0.582241\pi$
$734$		0			0
$735$	−1962.20	+	1764.24i	−2.66967	+	2.40032i
$736$		0			0
$737$	888.540	−	452.734i	1.20562	−	0.614292i
$738$		0			0
$739$	173.311	−	56.3121i	0.234521	−	0.0762005i	−0.189399	−	0.981900i	$-0.560654\pi$
$739$	173.311	−	56.3121i	0.234521	−	0.0762005i	0.423920	+	0.905700i	$0.360654\pi$
$740$		0			0
$741$	92.1057	−	283.472i	0.124299	−	0.382554i
$742$		0			0
$743$	−640.441	+	640.441i	−0.861966	+	0.861966i	−0.991566	−	0.129600i	$-0.958631\pi$
$743$	−640.441	+	640.441i	−0.861966	+	0.861966i	0.129600	+	0.991566i	$0.458631\pi$
$744$		0			0
$745$	615.714	+	499.325i	0.826462	+	0.670235i
$746$		0			0
$747$	−1397.63	−	221.362i	−1.87099	−	0.296335i
$748$		0			0
$749$			1257.10i			1.67837i
$750$		0			0
$751$	−777.995			−1.03595			−0.517973	−	0.855397i	$-0.673313\pi$
$751$	−777.995			−1.03595			−0.517973	+	0.855397i	$0.673313\pi$
$752$		0			0
$753$	80.8811	−	510.663i	0.107412	−	0.678172i
$754$		0			0
$755$	−327.912	+	404.347i	−0.434321	+	0.535559i
$756$		0			0
$757$	251.685	+	251.685i	0.332477	+	0.332477i	0.853527	−	0.521049i	$-0.174459\pi$
$757$	251.685	+	251.685i	0.332477	+	0.332477i	−0.521049	+	0.853527i	$0.674459\pi$
$758$		0			0
$759$	1287.50	+	418.334i	1.69631	+	0.551165i
$760$		0			0
$761$	185.575	+	571.141i	0.243857	+	0.750514i	0.995822	+	0.0913114i	$0.0291059\pi$
$761$	185.575	+	571.141i	0.243857	+	0.750514i	−0.751966	+	0.659202i	$0.770894\pi$
$762$		0			0
$763$	−567.807	−	1114.38i	−0.744177	−	1.46053i
$764$		0			0
$765$	1264.18	+	1406.03i	1.65252	+	1.83795i
$766$		0			0
$767$	36.8062	+	232.385i	0.0479873	+	0.302980i
$768$		0			0
$769$	−270.713	+	372.604i	−0.352032	+	0.484531i	−0.947907	−	0.318546i	$-0.896805\pi$
$769$	−270.713	+	372.604i	−0.352032	+	0.484531i	0.595875	+	0.803077i	$0.296805\pi$
$770$		0			0
$771$	884.422	−	642.570i	1.14711	−	0.833425i
$772$		0			0
$773$	−1201.64	−	612.268i	−1.55452	−	0.792067i	−0.555302	−	0.831648i	$-0.687398\pi$
$773$	−1201.64	−	612.268i	−1.55452	−	0.792067i	−0.999216	+	0.0395815i	$0.987398\pi$
$774$		0			0
$775$	−473.653	+	1059.76i	−0.611165	+	1.36743i
$776$		0			0
$777$	182.084	−	357.361i	0.234343	−	0.459924i
$778$		0			0
$779$	−348.419	−	479.557i	−0.447264	−	0.615606i
$780$		0			0
$781$	−1208.71	−	878.177i	−1.54764	−	1.12443i
$782$		0			0
$783$	409.062	−	64.7891i	0.522429	−	0.0827447i
$784$		0			0
$785$	−230.081	+	24.0162i	−0.293096	+	0.0305938i
$786$		0			0
$787$	561.745	−	286.223i	0.713780	−	0.363689i	−0.0590908	−	0.998253i	$-0.518820\pi$
$787$	561.745	−	286.223i	0.713780	−	0.363689i	0.772871	+	0.634564i	$0.218820\pi$
$788$		0			0
$789$	−1031.71	+	335.223i	−1.30762	+	0.424870i
$790$		0			0
$791$	−163.018	+	501.718i	−0.206091	+	0.634283i
$792$		0			0
$793$	−36.8902	+	36.8902i	−0.0465198	+	0.0465198i
$794$		0			0
$795$	178.439	−	115.698i	0.224451	−	0.145532i
$796$		0			0
$797$	−635.074	−	100.586i	−0.796831	−	0.126206i	−0.255273	−	0.966869i	$-0.582165\pi$
$797$	−635.074	−	100.586i	−0.796831	−	0.126206i	−0.541558	+	0.840663i	$0.682165\pi$
$798$		0			0
$799$		−	1069.08i		−	1.33802i
$800$		0			0
$801$	1952.61			2.43771
$802$		0			0
$803$	−84.5480	+	533.815i	−0.105290	+	0.664776i
$804$		0			0
$805$	1269.66	+	488.417i	1.57721	+	0.606730i
$806$		0			0
$807$	−990.555	−	990.555i	−1.22745	−	1.22745i
$808$		0			0
$809$	373.580	+	121.383i	0.461780	+	0.150041i	0.530662	−	0.847583i	$-0.321943\pi$
$809$	373.580	+	121.383i	0.461780	+	0.150041i	−0.0688823	+	0.997625i	$0.521943\pi$
$810$		0			0
$811$	254.390	+	782.931i	0.313674	+	0.965390i	0.976297	+	0.216436i	$0.0694434\pi$
$811$	254.390	+	782.931i	0.313674	+	0.965390i	−0.662623	+	0.748954i	$0.730557\pi$
$812$		0			0
$813$	471.384	+	925.144i	0.579808	+	1.13794i
$814$		0			0
$815$	1415.30	+	301.889i	1.73657	+	0.370416i
$816$		0			0
$817$	−40.1089	−	253.238i	−0.0490929	−	0.309961i
$818$		0			0
$819$	633.300	−	871.662i	0.773260	−	1.06430i
$820$		0			0
$821$	202.096	−	146.831i	0.246158	−	0.178844i	−0.457864	−	0.889022i	$-0.651385\pi$
$821$	202.096	−	146.831i	0.246158	−	0.178844i	0.704022	+	0.710178i	$0.251385\pi$
$822$		0			0
$823$	374.056	+	190.591i	0.454503	+	0.231581i	0.666228	−	0.745748i	$-0.267908\pi$
$823$	374.056	+	190.591i	0.454503	+	0.231581i	−0.211724	+	0.977329i	$0.567908\pi$
$824$		0			0
$825$	−559.072	−	1462.68i	−0.677663	−	1.77294i
$826$		0			0
$827$	−371.871	+	729.837i	−0.449662	+	0.882512i	0.549240	+	0.835665i	$0.314917\pi$
$827$	−371.871	+	729.837i	−0.449662	+	0.882512i	−0.998902	+	0.0468470i	$0.985083\pi$
$828$		0			0
$829$	−307.254	−	422.898i	−0.370632	−	0.510131i	0.582441	−	0.812873i	$-0.302098\pi$
$829$	−307.254	−	422.898i	−0.370632	−	0.510131i	−0.953072	+	0.302742i	$0.902098\pi$
$830$		0			0
$831$	−924.959	−	672.022i	−1.11307	−	0.808691i
$832$		0			0
$833$	−2870.19	+	454.593i	−3.44560	+	0.545730i
$834$		0			0
$835$	−509.456	−	294.620i	−0.610127	−	0.352839i
$836$		0			0
$837$	1046.05	−	532.989i	1.24976	−	0.636785i
$838$		0			0
$839$	−1225.96	+	398.337i	−1.46121	+	0.474776i	−0.928440	−	0.371483i	$-0.878849\pi$
$839$	−1225.96	+	398.337i	−1.46121	+	0.474776i	−0.532771	+	0.846259i	$0.678849\pi$
$840$		0			0
$841$	176.973	−	544.667i	0.210432	−	0.647642i
$842$		0			0
$843$	466.538	−	466.538i	0.553425	−	0.553425i
$844$		0			0
$845$	171.520	+	641.956i	0.202982	+	0.759712i
$846$		0			0
$847$	594.054	+	94.0890i	0.701363	+	0.111085i
$848$		0			0
$849$			310.007i			0.365143i
$850$		0			0
$851$	−142.832			−0.167841
$852$		0			0
$853$	224.856	−	1419.68i	0.263606	−	1.66434i	−0.400194	−	0.916430i	$-0.631057\pi$
$853$	224.856	−	1419.68i	0.263606	−	1.66434i	0.663800	−	0.747910i	$-0.268943\pi$
$854$		0			0
$855$	−38.8740	+	731.752i	−0.0454667	+	0.855850i
$856$		0			0
$857$	206.266	+	206.266i	0.240683	+	0.240683i	0.817133	−	0.576449i	$-0.195562\pi$
$857$	206.266	+	206.266i	0.240683	+	0.240683i	−0.576449	+	0.817133i	$0.695562\pi$
$858$		0			0
$859$	1065.18	+	346.097i	1.24002	+	0.402907i	0.854334	−	0.519724i	$-0.173965\pi$
$859$	1065.18	+	346.097i	1.24002	+	0.402907i	0.385685	+	0.922631i	$0.373965\pi$
$860$		0			0
$861$	−1080.50	−	3325.44i	−1.25494	−	3.86230i
$862$		0			0
$863$	82.4134	+	161.745i	0.0954964	+	0.187422i	0.933813	−	0.357761i	$-0.116460\pi$
$863$	82.4134	+	161.745i	0.0954964	+	0.187422i	−0.838317	+	0.545184i	$0.816460\pi$
$864$		0			0
$865$	939.480	−	417.479i	1.08610	−	0.482635i
$866$		0			0
$867$	313.588	+	1979.92i	0.361694	+	2.28364i
$868$		0			0
$869$	273.782	−	376.828i	0.315054	−	0.433634i
$870$		0			0
$871$	−373.145	+	271.105i	−0.428409	+	0.311258i
$872$		0			0
$873$	641.541	+	326.882i	0.734870	+	0.374435i
$874$		0			0
$875$	−483.034	−	1497.55i	−0.552039	−	1.71148i
$876$		0			0
$877$	593.579	−	1164.96i	0.676829	−	1.32835i	−0.255524	−	0.966803i	$-0.582248\pi$
$877$	593.579	−	1164.96i	0.676829	−	1.32835i	0.932353	−	0.361549i	$-0.117752\pi$
$878$		0			0
$879$	−581.792	−	800.768i	−0.661879	−	0.910999i
$880$		0			0
$881$	1129.16	+	820.385i	1.28168	+	0.931198i	0.999603	−	0.0281924i	$-0.00897512\pi$
$881$	1129.16	+	820.385i	1.28168	+	0.931198i	0.282082	+	0.959390i	$0.408975\pi$
$882$		0			0
$883$	1275.60	−	202.035i	1.44462	−	0.228806i	0.615616	−	0.788046i	$-0.288907\pi$
$883$	1275.60	−	202.035i	1.44462	−	0.228806i	0.829006	+	0.559240i	$0.188907\pi$
$884$		0			0
$885$	−383.310	−	862.587i	−0.433118	−	0.974674i
$886$		0			0
$887$	505.539	−	257.585i	0.569942	−	0.290400i	−0.145174	−	0.989406i	$-0.546374\pi$
$887$	505.539	−	257.585i	0.569942	−	0.290400i	0.715116	+	0.699006i	$0.246374\pi$
$888$		0			0
$889$	2417.78	−	785.584i	2.71966	−	0.883672i
$890$		0			0
$891$	25.2775	−	77.7963i	0.0283698	−	0.0873134i
$892$		0			0
$893$	292.974	−	292.974i	0.328078	−	0.328078i
$894$		0			0
$895$	−269.625	−	14.3237i	−0.301257	−	0.0160042i
$896$		0			0
$897$	−618.422	−	97.9484i	−0.689433	−	0.109196i
$898$		0			0
$899$			760.551i			0.845996i
$900$		0			0
$901$	234.204			0.259938
$902$		0			0
$903$	236.593	−	1493.79i	0.262007	−	1.65425i
$904$		0			0
$905$	4.92366	−	1.31552i	0.00544051	−	0.00145361i
$906$		0			0
$907$	718.369	+	718.369i	0.792028	+	0.792028i	0.981824	−	0.189796i	$-0.0607826\pi$
$907$	718.369	+	718.369i	0.792028	+	0.792028i	−0.189796	+	0.981824i	$0.560783\pi$
$908$		0			0
$909$	718.246	+	233.372i	0.790150	+	0.256735i
$910$		0			0
$911$	−9.47382	−	29.1574i	−0.0103994	−	0.0320059i	0.945722	−	0.324976i	$-0.105356\pi$
$911$	−9.47382	−	29.1574i	−0.0103994	−	0.0320059i	−0.956122	+	0.292970i	$0.905356\pi$
$912$		0			0
$913$	585.914	+	1149.92i	0.641746	+	1.25950i
$914$		0			0
$915$	104.780	−	181.185i	0.114514	−	0.198017i
$916$		0			0
$917$	303.416	+	1915.69i	0.330879	+	2.08909i
$918$		0			0
$919$	−856.658	+	1179.09i	−0.932163	+	1.28301i	0.0268466	+	0.999640i	$0.491453\pi$
$919$	−856.658	+	1179.09i	−0.932163	+	1.28301i	−0.959010	+	0.283373i	$0.908547\pi$
$920$		0			0
$921$	394.178	−	286.387i	0.427989	−	0.310952i
$922$		0			0
$923$	615.698	+	313.714i	0.667062	+	0.339885i
$924$		0			0
$925$	103.788	+	128.543i	0.112204	+	0.138966i
$926$		0			0
$927$	−520.109	+	1020.77i	−0.561066	+	1.10115i
$928$		0			0
$929$	367.567	+	505.912i	0.395658	+	0.544577i	0.959648	−	0.281205i	$-0.0907341\pi$
$929$	367.567	+	505.912i	0.395658	+	0.544577i	−0.563989	+	0.825782i	$0.690734\pi$
$930$		0			0
$931$	−911.132	−	661.976i	−0.978659	−	0.711037i
$932$		0			0
$933$	2286.59	−	362.161i	2.45080	−	0.388168i
$934$		0			0
$935$	359.745	−	1686.54i	0.384754	−	1.80379i
$936$		0			0
$937$	595.250	−	303.295i	0.635272	−	0.323687i	−0.106527	−	0.994310i	$-0.533973\pi$
$937$	595.250	−	303.295i	0.635272	−	0.323687i	0.741799	+	0.670623i	$0.233973\pi$
$938$		0			0
$939$	−266.387	+	86.5542i	−0.283692	+	0.0921770i
$940$		0			0
$941$	−46.7004	+	143.729i	−0.0496285	+	0.152741i	−0.972799	−	0.231649i	$-0.925588\pi$
$941$	−46.7004	+	143.729i	−0.0496285	+	0.152741i	0.923171	+	0.384389i	$0.125588\pi$
$942$		0			0
$943$	−880.497	+	880.497i	−0.933719	+	0.933719i
$944$		0			0
$945$	−571.381	+	1485.32i	−0.604636	+	1.57177i
$946$		0			0
$947$	−147.354	−	23.3385i	−0.155600	−	0.0246447i	0.0781482	−	0.996942i	$-0.475099\pi$
$947$	−147.354	−	23.3385i	−0.155600	−	0.0246447i	−0.233749	+	0.972297i	$0.575099\pi$
$948$		0			0
$949$		−	249.974i		−	0.263407i
$950$		0			0
$951$	2038.17			2.14318
$952$		0			0
$953$	−45.3014	+	286.022i	−0.0475356	+	0.300128i	−0.999990	−	0.00455429i	$-0.998550\pi$
$953$	−45.3014	+	286.022i	−0.0475356	+	0.300128i	0.952454	+	0.304682i	$0.0985503\pi$
$954$		0			0
$955$	−131.502	−	202.813i	−0.137698	−	0.212369i
$956$		0			0
$957$	−725.467	−	725.467i	−0.758064	−	0.758064i
$958$		0			0
$959$	372.716	+	121.103i	0.388650	+	0.126280i
$960$		0			0
$961$	369.247	+	1136.42i	0.384232	+	1.18254i
$962$		0			0
$963$	645.802	+	1267.46i	0.670615	+	1.31616i
$964$		0			0
$965$	109.667	+	1050.64i	0.113645	+	1.08875i
$966$		0			0
$967$	−155.287	−	980.444i	−0.160586	−	1.01390i	−0.927954	−	0.372695i	$-0.878434\pi$
$967$	−155.287	−	980.444i	−0.160586	−	1.01390i	0.767368	−	0.641208i	$-0.221566\pi$
$968$		0			0
$969$	−774.047	+	1065.38i	−0.798810	+	1.09947i
$970$		0			0
$971$	−509.387	+	370.091i	−0.524600	+	0.381144i	−0.818334	−	0.574743i	$-0.805102\pi$
$971$	−509.387	+	370.091i	−0.524600	+	0.381144i	0.293734	+	0.955887i	$0.405102\pi$
$972$		0			0
$973$	−1053.24	−	536.654i	−1.08247	−	0.551545i
$974$		0			0
$975$	361.223	+	627.728i	0.370486	+	0.643824i
$976$		0			0
$977$	−472.937	+	928.191i	−0.484070	+	0.950042i	0.511787	+	0.859112i	$0.328984\pi$
$977$	−472.937	+	928.191i	−0.484070	+	0.950042i	−0.995857	+	0.0909292i	$0.971016\pi$
$978$		0			0
$979$	−1046.76	−	1440.75i	−1.06922	−	1.47165i
$980$		0			0
$981$	−1144.97	−	831.870i	−1.16715	−	0.847982i
$982$		0			0
$983$	625.795	−	99.1162i	0.636618	−	0.100830i	0.170221	−	0.985406i	$-0.445552\pi$
$983$	625.795	−	99.1162i	0.636618	−	0.100830i	0.466397	+	0.884576i	$0.345552\pi$
$984$		0			0
$985$	−707.310	+	635.949i	−0.718081	+	0.645634i
$986$		0			0
$987$	2177.64	−	1109.56i	2.20632	−	1.12417i
$988$		0			0
$989$	−512.242	+	166.438i	−0.517940	+	0.168289i
$990$		0			0
$991$	452.455	−	1392.51i	0.456564	−	1.40516i	−0.412725	−	0.910856i	$-0.635423\pi$
$991$	452.455	−	1392.51i	0.456564	−	1.40516i	0.869289	−	0.494304i	$-0.164577\pi$
$992$		0			0
$993$	769.935	−	769.935i	0.775363	−	0.775363i
$994$		0			0
$995$	−1457.02	−	1181.59i	−1.46434	−	1.18753i
$996$		0			0
$997$	34.3594	+	5.44200i	0.0344628	+	0.00545838i	0.173642	−	0.984809i	$-0.444446\pi$
$997$	34.3594	+	5.44200i	0.0344628	+	0.00545838i	−0.139179	+	0.990267i	$0.544446\pi$
$998$		0			0
$999$		−	167.094i		−	0.167261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.f.17.7		64
4.3	odd	2		200.3.u.b.17.2	✓	64
25.3	odd	20	inner	400.3.bg.f.353.7		64
100.3	even	20		200.3.u.b.153.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.b.17.2	✓	64	4.3	odd	2
200.3.u.b.153.2	yes	64	100.3	even	20
400.3.bg.f.17.7		64	1.1	even	1	trivial
400.3.bg.f.353.7		64	25.3	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.754209 - 4.76189i) q^{3} +(-3.14938 + 3.88348i) q^{5} +(-8.90117 - 8.90117i) q^{7} +(-13.5472 - 4.40177i) q^{9} +O(q^{10})\)	\(q+(0.754209 - 4.76189i) q^{3} +(-3.14938 + 3.88348i) q^{5} +(-8.90117 - 8.90117i) q^{7} +(-13.5472 - 4.40177i) q^{9} +(4.01460 + 12.3557i) q^{11} +(-2.72791 - 5.35383i) q^{13} +(16.1174 + 17.9259i) q^{15} +(4.15299 + 26.2209i) q^{17} +(-6.04756 + 8.32375i) q^{19} +(-49.0997 + 35.6730i) q^{21} +(19.2576 + 9.81225i) q^{23} +(-5.16283 - 24.4611i) q^{25} +(-11.4790 + 22.5288i) q^{27} +(-9.62791 - 13.2517i) q^{29} +(-37.5641 - 27.2919i) q^{31} +(61.8642 - 9.79833i) q^{33} +(62.6007 - 6.53436i) q^{35} +(-5.88824 + 3.00021i) q^{37} +(-27.5518 + 8.95211i) q^{39} +(-17.8034 + 54.7933i) q^{41} +(-17.6211 + 17.6211i) q^{43} +(59.7596 - 38.7476i) q^{45} +(-39.7743 - 6.29963i) q^{47} +109.462i q^{49} +127.993 q^{51} +(1.38006 - 8.71339i) q^{53} +(-60.6265 - 23.3221i) q^{55} +(35.0756 + 35.0756i) q^{57} +(-37.2402 - 12.1001i) q^{59} +(-2.68303 - 8.25750i) q^{61} +(81.4055 + 159.767i) q^{63} +(29.3827 + 6.26745i) q^{65} +(-12.0079 - 75.8151i) q^{67} +(61.2491 - 84.3022i) q^{69} +(-93.0381 + 67.5961i) q^{71} +(37.0673 + 18.8867i) q^{73} +(-120.375 + 6.13602i) q^{75} +(74.2453 - 145.715i) q^{77} +(-21.0739 - 29.0057i) q^{79} +(-5.09389 - 3.70093i) q^{81} +(98.1176 - 15.5403i) q^{83} +(-114.908 - 66.4516i) q^{85} +(-70.3644 + 35.8525i) q^{87} +(-130.370 + 42.3597i) q^{89} +(-23.3737 + 71.9370i) q^{91} +(-158.292 + 158.292i) q^{93} +(-13.2791 - 49.7002i) q^{95} +(-49.9251 - 7.90736i) q^{97} -185.057i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more