LMFDB - Embedded newform 135.4.j.a.19.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,4,Mod(19,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("135.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	135.j (of order $6$, degree $2$, 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:	$7.96525785077$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.16
Character	$\chi$	$=$	135.19
Dual form			135.4.j.a.64.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.37720 + 2.52718i) q^{2} +(8.77324 + 15.1957i) q^{4} +(3.07459 - 10.7493i) q^{5} +(18.1967 + 10.5059i) q^{7} +48.2513i q^{8} +O(q^{10})$	\(q+(4.37720 + 2.52718i) q^{2} +(8.77324 + 15.1957i) q^{4} +(3.07459 - 10.7493i) q^{5} +(18.1967 + 10.5059i) q^{7} +48.2513i q^{8} +(40.6234 - 39.2817i) q^{10} +(-14.2815 + 24.7362i) q^{11} +(-8.72122 + 5.03520i) q^{13} +(53.1003 + 91.9724i) q^{14} +(-51.7535 + 89.6398i) q^{16} -82.7541i q^{17} -1.91981 q^{19} +(190.317 - 47.5855i) q^{20} +(-125.026 + 72.1836i) q^{22} +(-147.712 + 85.2818i) q^{23} +(-106.094 - 66.0991i) q^{25} -50.8993 q^{26} +368.682i q^{28} +(128.214 - 222.074i) q^{29} +(-24.0262 - 41.6147i) q^{31} +(-118.776 + 68.5756i) q^{32} +(209.134 - 362.231i) q^{34} +(168.878 - 163.300i) q^{35} -161.834i q^{37} +(-8.40337 - 4.85169i) q^{38} +(518.666 + 148.353i) q^{40} +(139.674 + 241.922i) q^{41} +(-233.024 - 134.536i) q^{43} -501.179 q^{44} -862.088 q^{46} +(8.30380 + 4.79420i) q^{47} +(49.2462 + 85.2969i) q^{49} +(-297.349 - 557.447i) q^{50} +(-153.027 - 88.3500i) q^{52} -35.7716i q^{53} +(221.987 + 229.569i) q^{55} +(-506.921 + 878.013i) q^{56} +(1122.44 - 648.040i) q^{58} +(281.385 + 487.374i) q^{59} +(39.6621 - 68.6968i) q^{61} -242.874i q^{62} +134.846 q^{64} +(27.3106 + 109.228i) q^{65} +(-404.219 + 233.376i) q^{67} +(1257.51 - 726.021i) q^{68} +(1151.90 - 288.013i) q^{70} -316.854 q^{71} -633.515i q^{73} +(408.984 - 708.381i) q^{74} +(-16.8429 - 29.1728i) q^{76} +(-519.751 + 300.078i) q^{77} +(-395.658 + 685.299i) q^{79} +(804.442 + 831.918i) q^{80} +1411.92i q^{82} +(197.521 + 114.039i) q^{83} +(-889.546 - 254.435i) q^{85} +(-679.994 - 1177.78i) q^{86} +(-1193.55 - 689.099i) q^{88} +53.9091 q^{89} -211.596 q^{91} +(-2591.83 - 1496.39i) q^{92} +(24.2316 + 41.9704i) q^{94} +(-5.90261 + 20.6365i) q^{95} +(-83.7394 - 48.3470i) q^{97} +497.815i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 54 q^{4} - 3 q^{5}+O(q^{10}) $ 32 * q + 54 * q^4 - 3 * q^5	$ 32 q + 54 q^{4} - 3 q^{5} - 20 q^{10} - 90 q^{11} + 102 q^{14} - 146 q^{16} - 8 q^{19} + 6 q^{20} + 71 q^{25} + 936 q^{26} + 516 q^{29} - 38 q^{31} + 212 q^{34} + 534 q^{35} + 44 q^{40} - 576 q^{41} - 3288 q^{44} - 580 q^{46} - 4 q^{49} - 558 q^{50} + 30 q^{55} - 2430 q^{56} + 2202 q^{59} - 20 q^{61} + 644 q^{64} - 339 q^{65} + 636 q^{70} + 5904 q^{71} + 4080 q^{74} + 396 q^{76} - 218 q^{79} - 2532 q^{80} - 704 q^{85} - 6108 q^{86} - 8148 q^{89} - 1884 q^{91} - 1078 q^{94} + 1692 q^{95}+O(q^{100}) $ 32 * q + 54 * q^4 - 3 * q^5 - 20 * q^10 - 90 * q^11 + 102 * q^14 - 146 * q^16 - 8 * q^19 + 6 * q^20 + 71 * q^25 + 936 * q^26 + 516 * q^29 - 38 * q^31 + 212 * q^34 + 534 * q^35 + 44 * q^40 - 576 * q^41 - 3288 * q^44 - 580 * q^46 - 4 * q^49 - 558 * q^50 + 30 * q^55 - 2430 * q^56 + 2202 * q^59 - 20 * q^61 + 644 * q^64 - 339 * q^65 + 636 * q^70 + 5904 * q^71 + 4080 * q^74 + 396 * q^76 - 218 * q^79 - 2532 * q^80 - 704 * q^85 - 6108 * q^86 - 8148 * q^89 - 1884 * q^91 - 1078 * q^94 + 1692 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	4.37720	+	2.52718i	1.54757	+	0.893492i	0.998326	+	0.0578315i	$0.0184186\pi$
$2$	4.37720	+	2.52718i	1.54757	+	0.893492i	0.549247	+	0.835660i	$0.314915\pi$
$3$		0			0
$3$		0			0
$4$	8.77324	+	15.1957i	1.09665	+	1.89946i
$5$	3.07459	−	10.7493i	0.274999	−	0.961444i
$5$	3.07459	−	10.7493i	0.274999	−	0.961444i
$6$		0			0
$7$	18.1967	+	10.5059i	0.982529	+	0.567263i	0.903033	−	0.429572i	$-0.141336\pi$
$7$	18.1967	+	10.5059i	0.982529	+	0.567263i	0.0794959	+	0.996835i	$0.474669\pi$
$8$			48.2513i			2.13243i
$9$		0			0
$10$	40.6234	−	39.2817i	1.28462	−	1.24220i
$11$	−14.2815	+	24.7362i	−0.391457	+	0.678023i	−0.992642	−	0.121087i	$-0.961362\pi$
$11$	−14.2815	+	24.7362i	−0.391457	+	0.678023i	0.601185	+	0.799110i	$0.294695\pi$
$12$		0			0
$13$	−8.72122	+	5.03520i	−0.186064	+	0.107424i	−0.590139	−	0.807302i	$-0.700927\pi$
$13$	−8.72122	+	5.03520i	−0.186064	+	0.107424i	0.404075	+	0.914726i	$0.367594\pi$
$14$	53.1003	+	91.9724i	1.01369	+	1.75576i
$15$		0			0
$16$	−51.7535	+	89.6398i	−0.808649	+	1.40062i
$17$		−	82.7541i		−	1.18064i	−0.807171	−	0.590318i	$-0.799002\pi$
$17$		−	82.7541i		−	1.18064i	0.807171	−	0.590318i	$-0.200998\pi$
$18$		0			0
$19$	−1.91981			−0.0231807			−0.0115904	−	0.999933i	$-0.503689\pi$
$19$	−1.91981			−0.0231807			−0.0115904	+	0.999933i	$0.503689\pi$
$20$	190.317	−	47.5855i	2.12781	−	0.532022i
$21$		0			0
$22$	−125.026	+	72.1836i	−1.21162	+	0.699527i
$23$	−147.712	+	85.2818i	−1.33914	+	0.773151i	−0.986679	−	0.162677i	$-0.947987\pi$
$23$	−147.712	+	85.2818i	−1.33914	+	0.773151i	−0.352458	+	0.935828i	$0.614654\pi$
$24$		0			0
$25$	−106.094	−	66.0991i	−0.848751	−	0.528793i
$26$	−50.8993			−0.383930
$27$		0			0
$28$			368.682i			2.48837i
$29$	128.214	−	222.074i	0.820993	−	1.42200i	−0.0839514	−	0.996470i	$-0.526754\pi$
$29$	128.214	−	222.074i	0.820993	−	1.42200i	0.904944	−	0.425531i	$-0.139913\pi$
$30$		0			0
$31$	−24.0262	−	41.6147i	−0.139201	−	0.241104i	0.787993	−	0.615684i	$-0.211120\pi$
$31$	−24.0262	−	41.6147i	−0.139201	−	0.241104i	−0.927195	+	0.374580i	$0.877787\pi$
$32$	−118.776	+	68.5756i	−0.656153	+	0.378830i
$33$		0			0
$34$	209.134	−	362.231i	1.05489	−	1.82712i
$35$	168.878	−	163.300i	0.815587	−	0.788650i
$36$		0			0
$37$		−	161.834i		−	0.719065i	−0.933132	−	0.359533i	$-0.882936\pi$
$37$		−	161.834i		−	0.719065i	0.933132	−	0.359533i	$-0.117064\pi$
$38$	−8.40337	−	4.85169i	−0.0358739	−	0.0207118i
$39$		0			0
$40$	518.666	+	148.353i	2.05021	+	0.586416i
$41$	139.674	+	241.922i	0.532034	+	0.921510i	0.999301	+	0.0373937i	$0.0119055\pi$
$41$	139.674	+	241.922i	0.532034	+	0.921510i	−0.467266	+	0.884117i	$0.654761\pi$
$42$		0			0
$43$	−233.024	−	134.536i	−0.826414	−	0.477130i	0.0262093	−	0.999656i	$-0.491656\pi$
$43$	−233.024	−	134.536i	−0.826414	−	0.477130i	−0.852623	+	0.522526i	$0.824990\pi$
$44$	−501.179			−1.71717
$45$		0			0
$46$	−862.088			−2.76322
$47$	8.30380	+	4.79420i	0.0257709	+	0.0148789i	0.512830	−	0.858490i	$-0.328597\pi$
$47$	8.30380	+	4.79420i	0.0257709	+	0.0148789i	−0.487059	+	0.873369i	$0.661930\pi$
$48$		0			0
$49$	49.2462	+	85.2969i	0.143575	+	0.248679i
$50$	−297.349	−	557.447i	−0.841031	−	1.57670i
$51$		0			0
$52$	−153.027	−	88.3500i	−0.408096	−	0.235614i
$53$		−	35.7716i		−	0.0927095i	−0.998925	−	0.0463547i	$-0.985240\pi$
$53$		−	35.7716i		−	0.0927095i	0.998925	−	0.0463547i	$-0.0147605\pi$
$54$		0			0
$55$	221.987	+	229.569i	0.544231	+	0.562820i
$56$	−506.921	+	878.013i	−1.20965	+	2.09517i
$57$		0			0
$58$	1122.44	−	648.040i	2.54109	−	1.46710i
$59$	281.385	+	487.374i	0.620903	+	1.07544i	0.989318	+	0.145774i	$0.0465671\pi$
$59$	281.385	+	487.374i	0.620903	+	1.07544i	−0.368415	+	0.929661i	$0.620100\pi$
$60$		0			0
$61$	39.6621	−	68.6968i	0.0832494	−	0.144192i	−0.821395	−	0.570360i	$-0.806804\pi$
$61$	39.6621	−	68.6968i	0.0832494	−	0.144192i	0.904644	+	0.426168i	$0.140137\pi$
$62$		−	242.874i		−	0.497501i
$63$		0			0
$64$	134.846			0.263372
$65$	27.3106	+	109.228i	0.0521148	+	0.208432i
$66$		0			0
$67$	−404.219	+	233.376i	−0.737063	+	0.425544i	−0.821001	−	0.570927i	$-0.806584\pi$
$67$	−404.219	+	233.376i	−0.737063	+	0.425544i	0.0839374	+	0.996471i	$0.473250\pi$
$68$	1257.51	−	726.021i	2.24257	−	1.29475i
$69$		0			0
$70$	1151.90	−	288.013i	1.96683	−	0.491773i
$71$	−316.854			−0.529628			−0.264814	−	0.964299i	$-0.585311\pi$
$71$	−316.854			−0.529628			−0.264814	+	0.964299i	$0.585311\pi$
$72$		0			0
$73$		−	633.515i		−	1.01572i	−0.861440	−	0.507859i	$-0.830437\pi$
$73$		−	633.515i		−	1.01572i	0.861440	−	0.507859i	$-0.169563\pi$
$74$	408.984	−	708.381i	0.642479	−	1.11281i
$75$		0			0
$76$	−16.8429	−	29.1728i	−0.0254213	−	0.0440309i
$77$	−519.751	+	300.078i	−0.769235	+	0.444118i
$78$		0			0
$79$	−395.658	+	685.299i	−0.563481	+	0.975977i	0.433709	+	0.901053i	$0.357205\pi$
$79$	−395.658	+	685.299i	−0.563481	+	0.975977i	−0.997189	+	0.0749238i	$0.976129\pi$
$80$	804.442	+	831.918i	1.12424	+	1.16264i
$81$		0			0
$82$			1411.92i			1.90147i
$83$	197.521	+	114.039i	0.261214	+	0.150812i	0.624888	−	0.780714i	$-0.285145\pi$
$83$	197.521	+	114.039i	0.261214	+	0.150812i	−0.363674	+	0.931526i	$0.618478\pi$
$84$		0			0
$85$	−889.546	−	254.435i	−1.13512	−	0.324674i
$86$	−679.994	−	1177.78i	−0.852624	−	1.47679i
$87$		0			0
$88$	−1193.55	−	689.099i	−1.44583	−	0.834752i
$89$	53.9091			0.0642062			0.0321031	−	0.999485i	$-0.489780\pi$
$89$	53.9091			0.0642062			0.0321031	+	0.999485i	$0.489780\pi$
$90$		0			0
$91$	−211.596			−0.243751
$92$	−2591.83	−	1496.39i	−2.93714	−	1.69576i
$93$		0			0
$94$	24.2316	+	41.9704i	0.0265883	+	0.0460522i
$95$	−5.90261	+	20.6365i	−0.00637469	+	0.0222870i
$96$		0			0
$97$	−83.7394	−	48.3470i	−0.0876541	−	0.0506071i	0.455532	−	0.890219i	$-0.349449\pi$
$97$	−83.7394	−	48.3470i	−0.0876541	−	0.0506071i	−0.543186	+	0.839612i	$0.682782\pi$
$98$			497.815i			0.513132i
$99$		0			0
$100$	73.6360	−	2192.07i	0.0736360	−	2.19207i
$101$	−541.711	+	938.271i	−0.533686	+	0.924371i	0.465540	+	0.885027i	$0.345860\pi$
$101$	−541.711	+	938.271i	−0.533686	+	0.924371i	−0.999226	+	0.0393438i	$0.987473\pi$
$102$		0			0
$103$	372.670	−	215.161i	0.356507	−	0.205830i	−0.311040	−	0.950397i	$-0.600677\pi$
$103$	372.670	−	215.161i	0.356507	−	0.205830i	0.667548	+	0.744567i	$0.267344\pi$
$104$	−242.955	−	420.810i	−0.229074	−	0.396767i
$105$		0			0
$106$	90.4010	−	156.579i	0.0828351	−	0.143475i
$107$			12.9348i			0.0116865i	0.999983	+	0.00584323i	$0.00185997\pi$
$107$			12.9348i			0.0116865i	−0.999983	+	0.00584323i	$0.998140\pi$
$108$		0			0
$109$	20.1087			0.0176703			0.00883517	−	0.999961i	$-0.497188\pi$
$109$	20.1087			0.0176703			0.00883517	+	0.999961i	$0.497188\pi$
$110$	391.519	+	1565.87i	0.339363	+	1.35727i
$111$		0			0
$112$	−1883.49	+	1087.43i	−1.58904	+	0.917434i
$113$	−979.163	+	565.320i	−0.815150	+	0.470627i	−0.848741	−	0.528809i	$-0.822639\pi$
$113$	−979.163	+	565.320i	−0.815150	+	0.470627i	0.0335912	+	0.999436i	$0.489306\pi$
$114$		0			0
$115$	462.563	+	1850.01i	0.375080	+	1.50012i
$116$	4499.42			3.60138
$117$		0			0
$118$			2844.44i			2.21909i
$119$	869.403	−	1505.85i	0.669731	−	1.16001i
$120$		0			0
$121$	257.579	+	446.140i	0.193523	+	0.335192i
$122$	347.218	−	200.466i	0.257669	−	0.148765i
$123$		0			0
$124$	421.576	−	730.191i	0.305312	−	0.528815i
$125$	−1036.71	+	937.204i	−0.741811	+	0.670609i
$126$		0			0
$127$			277.149i			0.193646i	0.995302	+	0.0968228i	$0.0308680\pi$
$127$			277.149i			0.193646i	−0.995302	+	0.0968228i	$0.969132\pi$
$128$	1540.46	+	889.385i	1.06374	+	0.614151i
$129$		0			0
$130$	−156.494	+	547.131i	−0.105581	+	0.369127i
$131$	−251.299	−	435.263i	−0.167604	−	0.290299i	0.769973	−	0.638077i	$-0.220270\pi$
$131$	−251.299	−	435.263i	−0.167604	−	0.290299i	−0.937577	+	0.347778i	$0.886936\pi$
$132$		0			0
$133$	−34.9341	−	20.1692i	−0.0227757	−	0.0131496i
$134$	−2359.13			−1.52088
$135$		0			0
$136$	3992.99			2.51762
$137$	1923.55	+	1110.56i	1.19956	+	0.692566i	0.960457	−	0.278428i	$-0.0898134\pi$
$137$	1923.55	+	1110.56i	1.19956	+	0.692566i	0.239103	+	0.970994i	$0.423147\pi$
$138$		0			0
$139$	1316.39	+	2280.06i	0.803273	+	1.39131i	0.917451	+	0.397850i	$0.130244\pi$
$139$	1316.39	+	2280.06i	0.803273	+	1.39131i	−0.114177	+	0.993460i	$0.536423\pi$
$140$	3963.06	+	1133.54i	2.39243	+	0.684299i
$141$		0			0
$142$	−1386.93	−	800.745i	−0.819638	−	0.473218i
$143$		−	287.640i		−	0.168208i
$144$		0			0
$145$	−1992.92	−	2060.99i	−1.14140	−	1.18039i
$146$	1601.00	−	2773.02i	0.907535	−	1.57190i
$147$		0			0
$148$	2459.19	−	1419.81i	1.36584	−	0.788567i
$149$	1282.86	+	2221.97i	0.705340	+	1.22169i	0.966569	+	0.256408i	$0.0825392\pi$
$149$	1282.86	+	2221.97i	0.705340	+	1.22169i	−0.261228	+	0.965277i	$0.584128\pi$
$150$		0			0
$151$	752.244	−	1302.93i	0.405409	−	0.702189i	−0.588960	−	0.808162i	$-0.700462\pi$
$151$	752.244	−	1302.93i	0.405409	−	0.702189i	0.994369	+	0.105973i	$0.0337957\pi$
$152$		−	92.6331i		−	0.0494312i
$153$		0			0
$154$	−3033.40			−1.58726
$155$	−521.198	+	130.317i	−0.270088	+	0.0675309i
$156$		0			0
$157$	1037.66	−	599.094i	0.527481	−	0.304541i	−0.212509	−	0.977159i	$-0.568164\pi$
$157$	1037.66	−	599.094i	0.527481	−	0.304541i	0.739990	+	0.672618i	$0.234830\pi$
$158$	−3463.74	+	1999.79i	−1.74405	+	1.00693i
$159$		0			0
$160$	371.950	+	1487.60i	0.183782	+	0.735033i
$161$	−3583.83			−1.75432
$162$		0			0
$163$			2204.91i			1.05952i	0.848148	+	0.529760i	$0.177718\pi$
$163$			2204.91i			1.05952i	−0.848148	+	0.529760i	$0.822282\pi$
$164$	−2450.79	+	4244.88i	−1.16692	+	2.02116i
$165$		0			0
$166$	576.392	+	998.341i	0.269498	+	0.466785i
$167$	−980.439	+	566.057i	−0.454303	+	0.262292i	−0.709646	−	0.704558i	$-0.751145\pi$
$167$	−980.439	+	566.057i	−0.454303	+	0.262292i	0.255343	+	0.966851i	$0.417812\pi$
$168$		0			0
$169$	−1047.79	+	1814.83i	−0.476920	+	0.826050i
$170$	−3250.72	−	3361.75i	−1.46658	−	1.51667i
$171$		0			0
$172$		−	4721.28i		−	2.09299i
$173$	−1605.61	−	926.998i	−0.705619	−	0.407389i	0.103818	−	0.994596i	$-0.466894\pi$
$173$	−1605.61	−	926.998i	−0.705619	−	0.407389i	−0.809437	+	0.587207i	$0.800227\pi$
$174$		0			0
$175$	−1236.13	−	2317.39i	−0.533957	−	1.00102i
$176$	−1478.23	−	2560.38i	−0.633102	−	1.09657i
$177$		0			0
$178$	235.971	+	136.238i	0.0993638	+	0.0573677i
$179$	3205.81			1.33862			0.669312	−	0.742981i	$-0.266589\pi$
$179$	3205.81			1.33862			0.669312	+	0.742981i	$0.266589\pi$
$180$		0			0
$181$	2278.79			0.935806			0.467903	−	0.883780i	$-0.345010\pi$
$181$	2278.79			0.935806			0.467903	+	0.883780i	$0.345010\pi$
$182$	−926.199	−	534.741i	−0.377222	−	0.217789i
$183$		0			0
$184$	−4114.95	−	7127.31i	−1.64869	−	2.85561i
$185$	−1739.60	−	497.574i	−0.691341	−	0.197743i
$186$		0			0
$187$	2047.02	+	1181.85i	0.800498	+	0.462168i
$188$			168.243i			0.0652679i
$189$		0			0
$190$	−77.9890	+	75.4132i	−0.0297785	+	0.0287950i
$191$	1694.33	−	2934.66i	0.641870	−	1.11175i	−0.343145	−	0.939282i	$-0.611492\pi$
$191$	1694.33	−	2934.66i	0.641870	−	1.11175i	0.985015	−	0.172469i	$-0.0551744\pi$
$192$		0			0
$193$	−2406.01	+	1389.11i	−0.897349	+	0.518085i	−0.876339	−	0.481695i	$-0.840021\pi$
$193$	−2406.01	+	1389.11i	−0.897349	+	0.518085i	−0.0210098	+	0.999779i	$0.506688\pi$
$194$	−244.363	−	423.249i	−0.0904341	−	0.156636i
$195$		0			0
$196$	−864.097	+	1496.66i	−0.314904	+	0.545430i
$197$		−	2941.71i		−	1.06390i	−0.846776	−	0.531950i	$-0.821459\pi$
$197$		−	2941.71i		−	1.06390i	0.846776	−	0.531950i	$-0.178541\pi$
$198$		0			0
$199$	4929.28			1.75592			0.877959	−	0.478737i	$-0.158905\pi$
$199$	4929.28			1.75592			0.877959	+	0.478737i	$0.158905\pi$
$200$	3189.37	−	5119.16i	1.12761	−	1.80990i
$201$		0			0
$202$	−4742.35	+	2738.00i	−1.65183	+	0.953687i
$203$	4666.15	−	2694.00i	1.61330	−	0.931438i
$204$		0			0
$205$	3029.93	−	757.582i	1.03229	−	0.258107i
$206$	2175.00			0.735628
$207$		0			0
$208$		−	1042.36i		−	0.347474i
$209$	27.4177	−	47.4888i	0.00907425	−	0.0157171i
$210$		0			0
$211$	−2709.25	−	4692.57i	−0.883947	−	1.53104i	−0.846916	−	0.531727i	$-0.821543\pi$
$211$	−2709.25	−	4692.57i	−0.883947	−	1.53104i	−0.0370311	−	0.999314i	$-0.511790\pi$
$212$	543.574	−	313.832i	0.176098	−	0.101670i
$213$		0			0
$214$	−32.6884	+	56.6180i	−0.0104417	+	0.0180856i
$215$	−2162.62	+	2091.19i	−0.685998	+	0.663341i
$216$		0			0
$217$		−	1009.67i		−	0.315855i
$218$	88.0199	+	50.8183i	0.0273461	+	0.0157883i
$219$		0			0
$220$	−1540.92	+	5387.31i	−0.472221	+	1.65097i
$221$	416.683	+	721.716i	0.126829	+	0.219674i
$222$		0			0
$223$	−3537.15	−	2042.18i	−1.06218	−	0.613248i	−0.136143	−	0.990689i	$-0.543471\pi$
$223$	−3537.15	−	2042.18i	−1.06218	−	0.613248i	−0.926033	+	0.377442i	$0.876804\pi$
$224$	−2881.78			−0.859586
$225$		0			0
$226$	−5714.65			−1.68201
$227$	192.110	+	110.915i	0.0561708	+	0.0324302i	0.527822	−	0.849355i	$-0.323009\pi$
$227$	192.110	+	110.915i	0.0561708	+	0.0324302i	−0.471652	+	0.881785i	$0.656342\pi$
$228$		0			0
$229$	−799.037	−	1383.97i	−0.230576	−	0.399369i	0.727402	−	0.686212i	$-0.240728\pi$
$229$	−799.037	−	1383.97i	−0.230576	−	0.399369i	−0.957978	+	0.286843i	$0.907394\pi$
$230$	−2650.56	+	9266.82i	−0.759883	+	2.65668i
$231$		0			0
$232$	10715.3	+	6186.50i	3.03231	+	1.75071i
$233$		−	6620.40i		−	1.86144i	−0.365727	−	0.930722i	$-0.619180\pi$
$233$		−	6620.40i		−	1.86144i	0.365727	−	0.930722i	$-0.380820\pi$
$234$		0			0
$235$	77.0650	−	74.5197i	0.0213922	−	0.0206857i
$236$	−4937.32	+	8551.69i	−1.36183	+	2.35876i
$237$		0			0
$238$	7611.09	−	4394.27i	2.07292	−	1.19680i
$239$	−1778.60	−	3080.62i	−0.481372	−	0.833761i	0.518399	−	0.855139i	$-0.326528\pi$
$239$	−1778.60	−	3080.62i	−0.481372	−	0.833761i	−0.999771	+	0.0213776i	$0.993195\pi$
$240$		0			0
$241$	−1483.67	+	2569.79i	−0.396563	+	0.686867i	−0.993299	−	0.115570i	$-0.963131\pi$
$241$	−1483.67	+	2569.79i	−0.396563	+	0.686867i	0.596736	+	0.802437i	$0.296464\pi$
$242$			2603.79i			0.691645i
$243$		0			0
$244$	1391.86			0.365183
$245$	1068.29	−	267.108i	0.278574	−	0.0696527i
$246$		0			0
$247$	16.7431	−	9.66661i	0.00431310	−	0.00249017i
$248$	2007.96	−	1159.30i	0.514136	−	0.296836i
$249$		0			0
$250$	−6906.38	+	1482.37i	−1.74719	+	0.375014i
$251$	903.562			0.227220			0.113610	−	0.993525i	$-0.463759\pi$
$251$	903.562			0.227220			0.113610	+	0.993525i	$0.463759\pi$
$252$		0			0
$253$		−	4871.79i		−	1.21062i
$254$	−700.404	+	1213.14i	−0.173021	+	0.299681i
$255$		0			0
$256$	3955.88	+	6851.79i	0.965791	+	1.67280i
$257$	−1285.61	+	742.247i	−0.312039	+	0.180156i	−0.647839	−	0.761778i	$-0.724327\pi$
$257$	−1285.61	+	742.247i	−0.312039	+	0.180156i	0.335799	+	0.941934i	$0.390994\pi$
$258$		0			0
$259$	1700.21	−	2944.85i	0.407899	−	0.706502i
$260$	−1420.19	+	1373.29i	−0.338756	+	0.327568i
$261$		0			0
$262$		−	2540.31i		−	0.599011i
$263$	2352.69	+	1358.33i	0.551609	+	0.318472i	0.749771	−	0.661698i	$-0.230164\pi$
$263$	2352.69	+	1358.33i	0.551609	+	0.318472i	−0.198162	+	0.980169i	$0.563497\pi$
$264$		0			0
$265$	−384.518	−	109.983i	−0.0891350	−	0.0254950i
$266$	−101.942	−	176.569i	−0.0234981	−	0.0406998i
$267$		0			0
$268$	−7092.62	−	4094.93i	−1.61661	−	0.933349i
$269$	7492.51			1.69824			0.849120	−	0.528201i	$-0.177133\pi$
$269$	7492.51			1.69824			0.849120	+	0.528201i	$0.177133\pi$
$270$		0			0
$271$	2013.02			0.451226			0.225613	−	0.974217i	$-0.427561\pi$
$271$	2013.02			0.451226			0.225613	+	0.974217i	$0.427561\pi$
$272$	7418.06	+	4282.82i	1.65362	+	0.954720i
$273$		0			0
$274$	5613.16	+	9722.28i	1.23760	+	2.14359i
$275$	3150.22	−	1680.37i	0.690783	−	0.368473i
$276$		0			0
$277$	−3092.55	−	1785.48i	−0.670806	−	0.387290i	0.125576	−	0.992084i	$-0.459922\pi$
$277$	−3092.55	−	1785.48i	−0.670806	−	0.387290i	−0.796382	+	0.604794i	$0.793255\pi$
$278$			13307.0i			2.87087i
$279$		0			0
$280$	7879.43	+	8148.56i	1.68174	+	1.73918i
$281$	−3380.70	+	5855.54i	−0.717707	+	1.24310i	0.244200	+	0.969725i	$0.421475\pi$
$281$	−3380.70	+	5855.54i	−0.717707	+	1.24310i	−0.961906	+	0.273379i	$0.911859\pi$
$282$		0			0
$283$	−3474.74	+	2006.14i	−0.729866	+	0.421388i	−0.818373	−	0.574687i	$-0.805124\pi$
$283$	−3474.74	+	2006.14i	−0.729866	+	0.421388i	0.0885075	+	0.996076i	$0.471790\pi$
$284$	−2779.83	−	4814.81i	−0.580819	−	1.00601i
$285$		0			0
$286$	726.917	−	1259.06i	0.150292	−	0.260313i
$287$			5869.58i			1.20721i
$288$		0			0
$289$	−1935.23			−0.393901
$290$	−3514.93	−	14057.8i	−0.711737	−	2.84657i
$291$		0			0
$292$	9626.71	−	5557.98i	1.92932	−	1.11389i
$293$	2118.34	−	1223.02i	0.422371	−	0.243856i	−0.273720	−	0.961809i	$-0.588254\pi$
$293$	2118.34	−	1223.02i	0.422371	−	0.243856i	0.696091	+	0.717953i	$0.254921\pi$
$294$		0			0
$295$	6104.06	−	1526.22i	1.20472	−	0.301219i
$296$	7808.72			1.53335
$297$		0			0
$298$			12968.0i			2.52086i
$299$	858.821	−	1487.52i	0.166110	−	0.287711i
$300$		0			0
$301$	−2826.84	−	4896.23i	−0.541317	−	0.937588i
$302$	6585.45	−	3802.11i	1.25480	−	0.724459i
$303$		0			0
$304$	99.3568	−	172.091i	0.0187451	−	0.0324674i
$305$	−616.496	−	637.553i	−0.115739	−	0.119692i
$306$		0			0
$307$			5539.06i			1.02974i	0.857268	+	0.514871i	$0.172160\pi$
$307$			5539.06i			1.02974i	−0.857268	+	0.514871i	$0.827840\pi$
$308$	−9119.79	−	5265.32i	−1.68717	−	0.974088i
$309$		0			0
$310$	−2610.72	−	746.738i	−0.478319	−	0.136812i
$311$	−1762.60	−	3052.92i	−0.321376	−	0.556640i	0.659396	−	0.751796i	$-0.270812\pi$
$311$	−1762.60	−	3052.92i	−0.321376	−	0.556640i	−0.980772	+	0.195156i	$0.937479\pi$
$312$		0			0
$313$	5984.75	+	3455.30i	1.08076	+	0.623977i	0.931101	−	0.364761i	$-0.118849\pi$
$313$	5984.75	+	3455.30i	1.08076	+	0.623977i	0.149659	+	0.988738i	$0.452183\pi$
$314$	6056.07			1.08842
$315$		0			0
$316$	−13884.8			−2.47177
$317$	−3645.67	−	2104.83i	−0.645934	−	0.372930i	0.140963	−	0.990015i	$-0.454980\pi$
$317$	−3645.67	−	2104.83i	−0.645934	−	0.372930i	−0.786897	+	0.617085i	$0.788314\pi$
$318$		0			0
$319$	3662.17	+	6343.07i	0.642766	+	1.11330i
$320$	414.597	−	1449.50i	0.0724271	−	0.253217i
$321$		0			0
$322$	−15687.1	−	9056.98i	−2.71494	−	1.56747i
$323$			158.872i			0.0273680i
$324$		0			0
$325$	1258.09	+	42.2617i	0.214727	+	0.00721310i
$326$	−5572.19	+	9651.32i	−0.946672	+	1.63968i
$327$		0			0
$328$	−11673.1	+	6739.44i	−1.96505	+	1.13452i
$329$	100.734	+	174.477i	0.0168805	+	0.0292378i
$330$		0			0
$331$	848.119	−	1468.99i	0.140836	−	0.243936i	−0.786975	−	0.616984i	$-0.788354\pi$
$331$	848.119	−	1468.99i	0.140836	−	0.243936i	0.927812	+	0.373049i	$0.121688\pi$
$332$			4001.96i			0.661554i
$333$		0			0
$334$	−5722.10			−0.937423
$335$	1265.82	+	5062.60i	0.206445	+	0.825669i
$336$		0			0
$337$	6239.90	−	3602.61i	1.00863	−	0.582334i	0.0978413	−	0.995202i	$-0.468806\pi$
$337$	6239.90	−	3602.61i	1.00863	−	0.582334i	0.910791	+	0.412868i	$0.135473\pi$
$338$	−9172.80	+	5295.92i	−1.47614	+	0.852248i
$339$		0			0
$340$	−3937.89	−	15749.5i	−0.628124	−	2.51216i
$341$	1372.52			0.217965
$342$		0			0
$343$		−	5137.53i		−	0.808747i
$344$	6491.55	−	11243.7i	1.01744	−	1.76227i
$345$		0			0
$346$	−4685.37	−	8115.30i	−0.727998	−	1.26093i
$347$	5626.26	−	3248.32i	0.870413	−	0.502533i	0.00292757	−	0.999996i	$-0.499068\pi$
$347$	5626.26	−	3248.32i	0.870413	−	0.502533i	0.867485	+	0.497463i	$0.165735\pi$
$348$		0			0
$349$	−3232.25	+	5598.43i	−0.495755	+	0.858673i	−0.999988	−	0.00489459i	$-0.998442\pi$
$349$	−3232.25	+	5598.43i	−0.495755	+	0.858673i	0.504233	+	0.863568i	$0.331775\pi$
$350$	445.684	−	13267.6i	0.0680652	−	2.02624i
$351$		0			0
$352$		−	3917.44i		−	0.593183i
$353$	−10261.5	−	5924.50i	−1.54721	−	0.893284i	−0.998353	−	0.0573694i	$-0.981729\pi$
$353$	−10261.5	−	5924.50i	−1.54721	−	0.893284i	−0.548860	−	0.835914i	$-0.684938\pi$
$354$		0			0
$355$	−974.194	+	3405.95i	−0.145647	+	0.509208i
$356$	472.957	+	819.186i	0.0704121	+	0.121957i
$357$		0			0
$358$	14032.5	+	8101.66i	2.07162	+	1.19605i
$359$	−11702.9			−1.72048			−0.860242	−	0.509886i	$-0.829688\pi$
$359$	−11702.9			−1.72048			−0.860242	+	0.509886i	$0.829688\pi$
$360$		0			0
$361$	−6855.31			−0.999463
$362$	9974.70	+	5758.90i	1.44823	+	0.836135i
$363$		0			0
$364$	−1856.39	−	3215.35i	−0.267311	−	0.462995i
$365$	−6809.83	−	1947.80i	−0.976556	−	0.279322i
$366$		0			0
$367$	2234.79	+	1290.26i	0.317861	+	0.183517i	0.650439	−	0.759559i	$-0.274585\pi$
$367$	2234.79	+	1290.26i	0.317861	+	0.183517i	−0.332578	+	0.943076i	$0.607918\pi$
$368$		−	17654.5i		−	2.50083i
$369$		0			0
$370$	−6357.13	−	6574.26i	−0.893220	−	0.923729i
$371$	375.811	−	650.924i	0.0525907	−	0.0910897i
$372$		0			0
$373$	−3896.74	+	2249.78i	−0.540926	+	0.312304i	−0.745454	−	0.666557i	$-0.767767\pi$
$373$	−3896.74	+	2249.78i	−0.540926	+	0.312304i	0.204528	+	0.978861i	$0.434434\pi$
$374$	5973.48	+	10346.4i	0.825886	+	1.43048i
$375$		0			0
$376$	−231.326	+	400.669i	−0.0317281	+	0.0549546i
$377$			2582.34i			0.352777i
$378$		0			0
$379$	5888.24			0.798044			0.399022	−	0.916941i	$-0.369350\pi$
$379$	5888.24			0.798044			0.399022	+	0.916941i	$0.369350\pi$
$380$	−365.371	+	91.3549i	−0.0493241	+	0.0123327i
$381$		0			0
$382$	14832.8	−	8563.72i	1.98668	−	1.14701i
$383$	−6945.66	+	4010.08i	−0.926650	+	0.535001i	−0.885750	−	0.464162i	$-0.846356\pi$
$383$	−6945.66	+	4010.08i	−0.926650	+	0.535001i	−0.0408993	+	0.999163i	$0.513022\pi$
$384$		0			0
$385$	1627.60	+	6509.56i	0.215456	+	0.861709i
$386$	−14042.1			−1.85162
$387$		0			0
$388$		−	1696.64i		−	0.221994i
$389$	83.6900	−	144.955i	0.0109081	−	0.0188934i	−0.860520	−	0.509417i	$-0.829861\pi$
$389$	83.6900	−	144.955i	0.0109081	−	0.0188934i	0.871428	+	0.490524i	$0.163194\pi$
$390$		0			0
$391$	7057.41	+	12223.8i	0.912810	+	1.58103i
$392$	−4115.68	+	2376.19i	−0.530289	+	0.306163i
$393$		0			0
$394$	7434.22	−	12876.5i	0.950586	−	1.64646i
$395$	6149.99	+	6360.04i	0.783391	+	0.810148i
$396$		0			0
$397$			5893.09i			0.745002i	0.928032	+	0.372501i	$0.121500\pi$
$397$			5893.09i			0.745002i	−0.928032	+	0.372501i	$0.878500\pi$
$398$	21576.4	+	12457.2i	2.71741	+	1.56890i
$399$		0			0
$400$	11415.8	−	6089.36i	1.42698	−	0.761170i
$401$	−1316.43	−	2280.12i	−0.163938	−	0.283950i	0.772339	−	0.635210i	$-0.219087\pi$
$401$	−1316.43	−	2280.12i	−0.163938	−	0.283950i	−0.936278	+	0.351260i	$0.885753\pi$
$402$		0			0
$403$	419.076	+	241.954i	0.0518007	+	0.0299071i
$404$	−19010.2			−2.34108
$405$		0			0
$406$	27232.9			3.32893
$407$	4003.17	+	2311.23i	0.487543	+	0.281483i
$408$		0			0
$409$	−6845.15	−	11856.2i	−0.827558	−	1.43337i	−0.899949	−	0.435996i	$-0.856396\pi$
$409$	−6845.15	−	11856.2i	−0.827558	−	1.43337i	0.0723910	−	0.997376i	$-0.476937\pi$
$410$	15177.1	+	4341.08i	1.82816	+	0.522904i
$411$		0			0
$412$	6539.04	+	3775.32i	0.781931	+	0.451448i
$413$			11824.8i			1.40886i
$414$		0			0
$415$	1833.13	−	1772.59i	0.216831	−	0.209669i
$416$	690.584	−	1196.13i	0.0813910	−	0.140973i
$417$		0			0
$418$	240.025	−	138.578i	0.0280861	−	0.0162155i
$419$	−129.486	−	224.277i	−0.0150974	−	0.0261495i	0.858378	−	0.513018i	$-0.171473\pi$
$419$	−129.486	−	224.277i	−0.0150974	−	0.0261495i	−0.873475	+	0.486868i	$0.838139\pi$
$420$		0			0
$421$	−6821.55	+	11815.3i	−0.789696	+	1.36779i	0.136457	+	0.990646i	$0.456428\pi$
$421$	−6821.55	+	11815.3i	−0.789696	+	1.36779i	−0.926153	+	0.377147i	$0.876905\pi$
$422$		−	27387.1i		−	3.15920i
$423$		0			0
$424$	1726.02			0.197696
$425$	−5469.97	+	8779.70i	−0.624312	+	1.00207i
$426$		0			0
$427$	1443.44	−	833.369i	0.163590	−	0.0944486i
$428$	−196.553	+	113.480i	−0.0221980	+	0.0128160i
$429$		0			0
$430$	−14751.0	+	3688.24i	−1.65432	+	0.413635i
$431$	13258.5			1.48176			0.740881	−	0.671636i	$-0.234408\pi$
$431$	13258.5			1.48176			0.740881	+	0.671636i	$0.234408\pi$
$432$		0			0
$433$		−	14980.2i		−	1.66259i	−0.555832	−	0.831295i	$-0.687600\pi$
$433$		−	14980.2i		−	1.66259i	0.555832	−	0.831295i	$-0.312400\pi$
$434$	2551.60	−	4419.50i	0.282214	−	0.488809i
$435$		0			0
$436$	176.419	+	305.566i	0.0193783	+	0.0335641i
$437$	283.579	−	163.724i	0.0310422	−	0.0179222i
$438$		0			0
$439$	−3681.30	+	6376.19i	−0.400225	+	0.693210i	−0.993753	−	0.111604i	$-0.964401\pi$
$439$	−3681.30	+	6376.19i	−0.400225	+	0.693210i	0.593528	+	0.804813i	$0.297735\pi$
$440$	−11077.0	+	10711.2i	−1.20017	+	1.16053i
$441$		0			0
$442$			4212.13i			0.453282i
$443$	1375.08	+	793.903i	0.147476	+	0.0851456i	0.571922	−	0.820308i	$-0.306198\pi$
$443$	1375.08	+	793.903i	0.147476	+	0.0851456i	−0.424446	+	0.905453i	$0.639531\pi$
$444$		0			0
$445$	165.748	−	579.484i	0.0176567	−	0.0617307i
$446$	−10321.9	−	17878.0i	−1.09586	−	1.89809i
$447$		0			0
$448$	2453.76	+	1416.68i	0.258770	+	0.149401i
$449$	−7331.63			−0.770604			−0.385302	−	0.922791i	$-0.625903\pi$
$449$	−7331.63			−0.770604			−0.385302	+	0.922791i	$0.625903\pi$
$450$		0			0
$451$	−7978.99			−0.833074
$452$	−17180.9	−	9919.38i	−1.78788	−	1.03223i
$453$		0			0
$454$	560.601	+	970.990i	0.0579523	+	0.100376i
$455$	−650.571	+	2274.51i	−0.0670313	+	0.234353i
$456$		0			0
$457$	−5453.21	−	3148.41i	−0.558185	−	0.322268i	0.194232	−	0.980956i	$-0.437779\pi$
$457$	−5453.21	−	3148.41i	−0.558185	−	0.322268i	−0.752417	+	0.658687i	$0.771112\pi$
$458$		−	8077.23i		−	0.824070i
$459$		0			0
$460$	−24054.0	+	23259.5i	−2.43809	+	2.35757i
$461$	3167.73	−	5486.67i	0.320034	−	0.554316i	−0.660461	−	0.750861i	$-0.729639\pi$
$461$	3167.73	−	5486.67i	0.320034	−	0.554316i	0.980495	+	0.196545i	$0.0629723\pi$
$462$		0			0
$463$	1988.15	−	1147.86i	0.199562	−	0.115217i	−0.396889	−	0.917867i	$-0.629910\pi$
$463$	1988.15	−	1147.86i	0.199562	−	0.115217i	0.596451	+	0.802649i	$0.296577\pi$
$464$	13271.1	+	22986.2i	1.32779	+	2.29980i
$465$		0			0
$466$	16730.9	−	28978.8i	1.66319	−	2.88072i
$467$			6182.82i			0.612648i	0.951927	+	0.306324i	$0.0990991\pi$
$467$			6182.82i			0.612648i	−0.951927	+	0.306324i	$0.900901\pi$
$468$		0			0
$469$	−9807.26			−0.965581
$470$	525.653	−	131.431i	0.0515884	−	0.0128988i
$471$		0			0
$472$	−23516.4	+	13577.2i	−2.29328	+	1.32403i
$473$	6655.84	−	3842.75i	0.647011	−	0.373552i
$474$		0			0
$475$	203.680	+	126.898i	0.0196747	+	0.0122578i
$476$	30509.9			2.93786
$477$		0			0
$478$		−	17979.3i		−	1.72041i
$479$	−1949.18	+	3376.08i	−0.185930	+	0.322040i	−0.943889	−	0.330262i	$-0.892863\pi$
$479$	−1949.18	+	3376.08i	−0.185930	+	0.322040i	0.757960	+	0.652302i	$0.226196\pi$
$480$		0			0
$481$	814.869	+	1411.39i	0.0772449	+	0.133792i
$482$	−12988.6	+	7499.00i	−1.22742	+	0.708652i
$483$		0			0
$484$	−4519.61	+	7828.19i	−0.424456	+	0.735180i
$485$	−777.159	+	751.491i	−0.0727608	+	0.0703576i
$486$		0			0
$487$			14776.3i			1.37490i	0.726232	+	0.687450i	$0.241270\pi$
$487$			14776.3i			1.37490i	−0.726232	+	0.687450i	$0.758730\pi$
$488$	3314.71	+	1913.75i	0.307479	+	0.177523i
$489$		0			0
$490$	5351.15	+	1530.58i	0.493348	+	0.141111i
$491$	1818.62	+	3149.94i	0.167155	+	0.289521i	0.937418	−	0.348205i	$-0.113209\pi$
$491$	1818.62	+	3149.94i	0.167155	+	0.289521i	−0.770263	+	0.637726i	$0.779875\pi$
$492$		0			0
$493$	−18377.5	−	10610.2i	−1.67886	−	0.969293i
$494$	97.7169			0.00889978
$495$		0			0
$496$	4973.77			0.450260
$497$	−5765.68	−	3328.82i	−0.520375	−	0.300439i
$498$		0			0
$499$	−1628.87	−	2821.29i	−0.146129	−	0.253103i	0.783665	−	0.621184i	$-0.213348\pi$
$499$	−1628.87	−	2821.29i	−0.146129	−	0.253103i	−0.929794	+	0.368081i	$0.880015\pi$
$500$	−23336.8	−	7531.25i	−2.08731	−	0.673616i
$501$		0			0
$502$	3955.07	+	2283.46i	0.351640	+	0.203019i
$503$		−	20857.4i		−	1.84888i	−0.381327	−	0.924440i	$-0.624533\pi$
$503$		−	20857.4i		−	1.84888i	0.381327	−	0.924440i	$-0.375467\pi$
$504$		0			0
$505$	8420.19	+	8707.79i	0.741968	+	0.767310i
$506$	12311.9	−	21324.8i	1.08168	−	1.87352i
$507$		0			0
$508$	−4211.47	+	2431.49i	−0.367822	+	0.212362i
$509$	9953.74	+	17240.4i	0.866781	+	1.50131i	0.865267	+	0.501311i	$0.167149\pi$
$509$	9953.74	+	17240.4i	0.866781	+	1.50131i	0.00151390	+	0.999999i	$0.499518\pi$
$510$		0			0
$511$	6655.62	−	11527.9i	0.576179	−	0.997971i
$512$			25758.7i			2.22340i
$513$		0			0
$514$	−7503.15			−0.643871
$515$	−1167.02	−	4667.46i	−0.0998544	−	0.399365i
$516$		0			0
$517$	−237.181	+	136.937i	−0.0201764	+	0.0116489i
$518$	14884.3	−	8593.46i	1.26251	−	0.728909i
$519$		0			0
$520$	−5270.39	+	1317.77i	−0.444465	+	0.111131i
$521$	4264.69			0.358617			0.179308	−	0.983793i	$-0.442614\pi$
$521$	4264.69			0.358617			0.179308	+	0.983793i	$0.442614\pi$
$522$		0			0
$523$			3687.86i			0.308334i	0.988045	+	0.154167i	$0.0492694\pi$
$523$			3687.86i			0.308334i	−0.988045	+	0.154167i	$0.950731\pi$
$524$	4409.42	−	7637.34i	0.367607	−	0.636715i
$525$		0			0
$526$	6865.46	+	11891.3i	0.569103	+	0.985716i
$527$	−3443.78	+	1988.27i	−0.284656	+	0.164346i
$528$		0			0
$529$	8462.46	−	14657.4i	0.695525	−	1.20469i
$530$	−1405.17	−	1453.16i	−0.115163	−	0.119097i
$531$		0			0
$532$		−	707.798i		−	0.0576822i
$533$	−2436.25	−	1406.57i	−0.197985	−	0.114307i
$534$		0			0
$535$	139.039	+	39.7690i	0.0112359	+	0.00321377i
$536$	−11260.7	−	19504.1i	−0.907440	−	1.57173i
$537$		0			0
$538$	32796.2	+	18934.9i	2.62815	+	1.51736i
$539$	−2813.23			−0.224813
$540$		0			0
$541$	21551.0			1.71266			0.856331	−	0.516428i	$-0.172739\pi$
$541$	21551.0			1.71266			0.856331	+	0.516428i	$0.172739\pi$
$542$	8811.39	+	5087.26i	0.698305	+	0.403167i
$543$		0			0
$544$	5674.91	+	9829.23i	0.447261	+	0.774678i
$545$	61.8260	−	216.154i	0.00485933	−	0.0169891i
$546$		0			0
$547$	−17240.0	−	9953.52i	−1.34759	−	0.778029i	−0.359678	−	0.933076i	$-0.617114\pi$
$547$	−17240.0	−	9953.52i	−1.34759	−	0.778029i	−0.987907	+	0.155048i	$0.950447\pi$
$548$			38972.8i			3.03802i
$549$		0			0
$550$	18035.7	+	605.855i	1.39826	+	0.0469704i
$551$	−246.146	+	426.338i	−0.0190312	+	0.0329630i
$552$		0			0
$553$	−14399.3	+	8313.45i	−1.10727	+	0.639283i
$554$	−9024.46	−	15630.8i	−0.692081	−	1.19872i
$555$		0			0
$556$	−23098.1	+	40007.0i	−1.76183	+	3.05157i
$557$			1747.00i			0.132896i	0.997790	+	0.0664479i	$0.0211666\pi$
$557$			1747.00i			0.132896i	−0.997790	+	0.0664479i	$0.978833\pi$
$558$		0			0
$559$	2709.67			0.205021
$560$	5898.16	+	23589.5i	0.445076	+	1.78007i
$561$		0			0
$562$	−29596.0	+	17087.2i	−2.22141	+	1.28253i
$563$	1837.74	−	1061.02i	0.137569	−	0.0794257i	−0.429636	−	0.903002i	$-0.641358\pi$
$563$	1837.74	−	1061.02i	0.137569	−	0.0794257i	0.567205	+	0.823577i	$0.308025\pi$
$564$		0			0
$565$	3066.26	+	12263.4i	0.228316	+	0.913143i
$566$	−20279.5			−1.50603
$567$		0			0
$568$		−	15288.6i		−	1.12939i
$569$	−5376.54	+	9312.43i	−0.396127	+	0.686112i	−0.993244	−	0.116042i	$-0.962979\pi$
$569$	−5376.54	+	9312.43i	−0.396127	+	0.686112i	0.597118	+	0.802154i	$0.296313\pi$
$570$		0			0
$571$	−362.873	−	628.514i	−0.0265950	−	0.0460639i	0.852422	−	0.522855i	$-0.175133\pi$
$571$	−362.873	−	628.514i	−0.0265950	−	0.0460639i	−0.879017	+	0.476791i	$0.841800\pi$
$572$	4370.89	−	2523.54i	0.319504	−	0.184466i
$573$		0			0
$574$	−14833.5	+	25692.3i	−1.07864	+	1.86825i
$575$	21308.4	+	715.791i	1.54543	+	0.0519140i
$576$		0			0
$577$		−	23839.3i		−	1.72001i	−0.510290	−	0.860003i	$-0.670462\pi$
$577$		−	23839.3i		−	1.72001i	0.510290	−	0.860003i	$-0.329538\pi$
$578$	−8470.91	−	4890.68i	−0.609590	−	0.351947i
$579$		0			0
$580$	13833.8	−	48365.5i	0.990378	−	3.46253i
$581$	2396.15	+	4150.26i	0.171100	+	0.296354i
$582$		0			0
$583$	884.853	+	510.870i	0.0628592	+	0.0362917i
$584$	30567.9			2.16594
$585$		0			0
$586$	12363.2			0.871534
$587$	−6735.67	−	3888.84i	−0.473613	−	0.273440i	0.244138	−	0.969740i	$-0.421495\pi$
$587$	−6735.67	−	3888.84i	−0.473613	−	0.273440i	−0.717751	+	0.696300i	$0.754828\pi$
$588$		0			0
$589$	46.1257	+	79.8921i	0.00322679	+	0.00558896i
$590$	30575.7	+	8745.48i	2.13353	+	0.610247i
$591$		0			0
$592$	14506.8	+	8375.51i	1.00714	+	0.581472i
$593$		−	6677.79i		−	0.462435i	−0.972902	−	0.231217i	$-0.925729\pi$
$593$		−	6677.79i		−	0.462435i	0.972902	−	0.231217i	$-0.0742709\pi$
$594$		0			0
$595$	−13513.7	−	13975.3i	−0.931108	−	0.962911i
$596$	−22509.6	+	38987.8i	−1.54703	+	2.67953i
$597$		0			0
$598$	7518.46	−	4340.79i	0.514135	−	0.296836i
$599$	−6473.45	−	11212.3i	−0.441566	−	0.764815i	0.556240	−	0.831022i	$-0.312244\pi$
$599$	−6473.45	−	11212.3i	−0.441566	−	0.764815i	−0.997806	+	0.0662068i	$0.978910\pi$
$600$		0			0
$601$	2183.05	−	3781.15i	0.148167	−	0.256633i	−0.782383	−	0.622797i	$-0.785996\pi$
$601$	2183.05	−	3781.15i	0.148167	−	0.256633i	0.930550	+	0.366165i	$0.119329\pi$
$602$		−	28575.7i		−	1.93465i
$603$		0			0
$604$	26398.5			1.77838
$605$	5587.64	−	1397.09i	0.375487	−	0.0938842i
$606$		0			0
$607$	20938.3	−	12088.7i	1.40010	−	0.808347i	0.405697	−	0.914008i	$-0.367029\pi$
$607$	20938.3	−	12088.7i	1.40010	−	0.808347i	0.994402	+	0.105660i	$0.0336956\pi$
$608$	228.028	−	131.652i	0.0152101	−	0.00878156i
$609$		0			0
$610$	−1087.32	−	4348.69i	−0.0721707	−	0.288645i
$611$	−96.5591			−0.00639339
$612$		0			0
$613$			7772.63i			0.512127i	0.966660	+	0.256063i	$0.0824256\pi$
$613$			7772.63i			0.512127i	−0.966660	+	0.256063i	$0.917574\pi$
$614$	−13998.2	+	24245.5i	−0.920066	+	1.59360i
$615$		0			0
$616$	−14479.2	−	25078.6i	−0.947048	−	1.64034i
$617$	542.357	−	313.130i	0.0353881	−	0.0204313i	−0.482202	−	0.876060i	$-0.660163\pi$
$617$	542.357	−	313.130i	0.0353881	−	0.0204313i	0.517590	+	0.855629i	$0.326829\pi$
$618$		0			0
$619$	11417.5	−	19775.8i	0.741373	−	1.28410i	−0.210497	−	0.977594i	$-0.567508\pi$
$619$	11417.5	−	19775.8i	0.741373	−	1.28410i	0.951870	−	0.306501i	$-0.0991583\pi$
$620$	−6552.85	−	6776.67i	−0.424466	−	0.438964i
$621$		0			0
$622$		−	17817.6i		−	1.14859i
$623$	980.967	+	566.361i	0.0630844	+	0.0364218i
$624$		0			0
$625$	6886.80	+	14025.4i	0.440756	+	0.897627i
$626$	17464.3	+	30249.0i	1.11504	+	1.93130i
$627$		0			0
$628$	18207.3	+	10512.0i	1.15693	+	0.667953i
$629$	−13392.5			−0.848954
$630$		0			0
$631$	−26862.1			−1.69471			−0.847355	−	0.531027i	$-0.821806\pi$
$631$	−26862.1			−1.69471			−0.847355	+	0.531027i	$0.821806\pi$
$632$	−33066.6	−	19091.0i	−2.08120	−	1.20158i
$633$		0			0
$634$	−10638.5	−	18426.5i	−0.666420	−	1.15427i
$635$	2979.15	+	852.118i	0.186179	+	0.0532524i
$636$		0			0
$637$	−858.973	−	495.929i	−0.0534282	−	0.0308468i
$638$			37019.8i			2.29723i
$639$		0			0
$640$	14296.5	−	13824.3i	0.883000	−	0.853836i
$641$	4304.99	−	7456.46i	0.265268	−	0.459458i	−0.702366	−	0.711816i	$-0.747873\pi$
$641$	4304.99	−	7456.46i	0.265268	−	0.459458i	0.967634	+	0.252358i	$0.0812062\pi$
$642$		0			0
$643$	−14872.6	+	8586.71i	−0.912160	+	0.526636i	−0.881125	−	0.472882i	$-0.843214\pi$
$643$	−14872.6	+	8586.71i	−0.912160	+	0.526636i	−0.0310345	+	0.999518i	$0.509880\pi$
$644$	−31441.8	−	54458.8i	−1.92388	−	3.33227i
$645$		0			0
$646$	−401.497	+	695.413i	−0.0244531	+	0.0423540i
$647$			1258.94i			0.0764978i	0.999268	+	0.0382489i	$0.0121780\pi$
$647$			1258.94i			0.0764978i	−0.999268	+	0.0382489i	$0.987822\pi$
$648$		0			0
$649$	−16074.4			−0.972226
$650$	5400.11	+	3364.40i	0.325861	+	0.203020i
$651$		0			0
$652$	−33505.1	+	19344.2i	−2.01252	+	1.16193i
$653$	2200.06	−	1270.21i	0.131845	−	0.0761209i	−0.432627	−	0.901573i	$-0.642413\pi$
$653$	2200.06	−	1270.21i	0.131845	−	0.0761209i	0.564472	+	0.825452i	$0.309080\pi$
$654$		0			0
$655$	−5451.40	+	1363.03i	−0.325197	+	0.0813100i
$656$	−28914.5			−1.72092
$657$		0			0
$658$			1018.29i			0.0603302i
$659$	13099.9	−	22689.7i	0.774356	−	1.34122i	−0.160800	−	0.986987i	$-0.551407\pi$
$659$	13099.9	−	22689.7i	0.774356	−	1.34122i	0.935156	−	0.354237i	$-0.115259\pi$
$660$		0			0
$661$	2721.89	+	4714.44i	0.160165	+	0.277414i	0.934928	−	0.354838i	$-0.115464\pi$
$661$	2721.89	+	4714.44i	0.160165	+	0.277414i	−0.774763	+	0.632252i	$0.782131\pi$
$662$	7424.77	−	4286.69i	0.435909	−	0.251672i
$663$		0			0
$664$	−5502.52	+	9530.64i	−0.321595	+	0.557019i
$665$	−324.212	+	313.504i	−0.0189059	+	0.0182815i
$666$		0			0
$667$			43737.3i			2.53901i
$668$	−17203.3	−	9932.30i	−0.996428	−	0.575288i
$669$		0			0
$670$	−7253.35	+	25358.9i	−0.418241	+	1.46224i
$671$	1132.87	+	1962.18i	0.0651771	+	0.112890i
$672$		0			0
$673$	14567.3	+	8410.41i	0.834364	+	0.481720i	0.855344	−	0.518060i	$-0.173346\pi$
$673$	14567.3	+	8410.41i	0.834364	+	0.481720i	−0.0209808	+	0.999780i	$0.506679\pi$
$674$	36417.7			2.08124
$675$		0			0
$676$	−36770.2			−2.09207
$677$	20091.4	+	11599.7i	1.14058	+	0.658515i	0.946574	−	0.322485i	$-0.104518\pi$
$677$	20091.4	+	11599.7i	1.14058	+	0.658515i	0.194007	+	0.981000i	$0.437852\pi$
$678$		0			0
$679$	−1015.85	−	1759.51i	−0.0574151	−	0.0994459i
$680$	12276.8	−	42921.7i	0.692343	−	2.42055i
$681$		0			0
$682$	6007.79	+	3468.60i	0.337317	+	0.194750i
$683$		−	24902.4i		−	1.39512i	−0.716528	−	0.697558i	$-0.754270\pi$
$683$		−	24902.4i		−	1.39512i	0.716528	−	0.697558i	$-0.245730\pi$
$684$		0			0
$685$	17851.8	−	17262.2i	0.995742	−	0.962855i
$686$	12983.4	−	22488.0i	0.722609	−	1.25160i
$687$		0			0
$688$	24119.6	−	13925.5i	1.33656	−	0.771662i
$689$	180.117	+	311.972i	0.00995923	+	0.0172499i
$690$		0			0
$691$	−4233.73	+	7333.03i	−0.233080	+	0.403707i	−0.958713	−	0.284375i	$-0.908214\pi$
$691$	−4233.73	+	7333.03i	−0.233080	+	0.403707i	0.725633	+	0.688082i	$0.241547\pi$
$692$		−	32531.1i		−	1.78706i
$693$		0			0
$694$	32836.3			1.79604
$695$	28556.4	−	7140.03i	1.55857	−	0.389693i
$696$		0			0
$697$	20020.1	−	11558.6i	1.08797	−	0.628139i
$698$	−28296.4	+	16336.9i	−1.53443	+	0.885906i
$699$		0			0
$700$	24369.5	−	39114.9i	1.31583	−	2.11200i
$701$	−5972.30			−0.321784			−0.160892	−	0.986972i	$-0.551437\pi$
$701$	−5972.30			−0.321784			−0.160892	+	0.986972i	$0.551437\pi$
$702$		0			0
$703$			310.691i			0.0166685i
$704$	−1925.80	+	3335.59i	−0.103099	+	0.178572i
$705$		0			0
$706$	−29944.5	−	51865.4i	−1.59628	−	2.76484i
$707$	−19714.7	+	11382.3i	−1.04872	+	0.605480i
$708$		0			0
$709$	−3774.89	+	6538.30i	−0.199956	+	0.346334i	−0.948514	−	0.316735i	$-0.897413\pi$
$709$	−3774.89	+	6538.30i	−0.199956	+	0.346334i	0.748558	+	0.663070i	$0.230747\pi$
$710$	−12871.7	+	12446.5i	−0.680373	+	0.657902i
$711$		0			0
$712$			2601.18i			0.136915i
$713$	7097.94	+	4098.00i	0.372819	+	0.215247i
$714$		0			0
$715$	−3091.92	−	884.374i	−0.161722	−	0.0462570i
$716$	28125.4	+	48714.6i	1.46801	+	2.54267i
$717$		0			0
$718$	−51225.8	−	29575.2i	−2.66257	−	1.53724i
$719$	−31449.7			−1.63126			−0.815631	−	0.578573i	$-0.803610\pi$
$719$	−31449.7			−1.63126			−0.815631	+	0.578573i	$0.803610\pi$
$720$		0			0
$721$	9041.81			0.467038
$722$	−30007.1	−	17324.6i	−1.54674	−	0.893012i
$723$		0			0
$724$	19992.3	+	34627.8i	1.02626	+	1.77753i
$725$	−28281.6	+	15085.8i	−1.44876	+	0.772789i
$726$		0			0
$727$	−6895.32	−	3981.01i	−0.351765	−	0.203092i	0.313697	−	0.949523i	$-0.398432\pi$
$727$	−6895.32	−	3981.01i	−0.351765	−	0.203092i	−0.665462	+	0.746431i	$0.731766\pi$
$728$		−	10209.8i		−	0.519780i
$729$		0			0
$730$	−24885.5	−	25735.5i	−1.26172	−	1.30481i
$731$	−11133.4	+	19283.7i	−0.563317	+	0.975694i
$732$		0			0
$733$	9529.06	−	5501.61i	0.480169	−	0.277226i	−0.240318	−	0.970694i	$-0.577252\pi$
$733$	9529.06	−	5501.61i	0.480169	−	0.277226i	0.720487	+	0.693469i	$0.243918\pi$
$734$	6521.41	+	11295.4i	0.327942	+	0.568012i
$735$		0			0
$736$	11696.5	−	20258.9i	0.585786	−	1.01461i
$737$		−	13331.8i		−	0.666328i
$738$		0			0
$739$	−24719.1			−1.23046			−0.615228	−	0.788349i	$-0.710936\pi$
$739$	−24719.1			−1.23046			−0.615228	+	0.788349i	$0.710936\pi$
$740$	−7700.97	−	30799.8i	−0.382559	−	1.53003i
$741$		0			0
$742$	3290.00	−	1899.48i	0.162776	−	0.0939786i
$743$	−11541.3	+	6663.39i	−0.569866	+	0.329012i	−0.757096	−	0.653304i	$-0.773382\pi$
$743$	−11541.3	+	6663.39i	−0.569866	+	0.329012i	0.187230	+	0.982316i	$0.440049\pi$
$744$		0			0
$745$	27828.9	−	6958.13i	1.36855	−	0.342183i
$746$	−22742.4			−1.11616
$747$		0			0
$748$			41474.6i			2.02735i
$749$	−135.891	+	235.370i	−0.00662929	+	0.0114823i
$750$		0			0
$751$	11900.5	+	20612.2i	0.578234	+	1.00153i	0.995682	+	0.0928298i	$0.0295913\pi$
$751$	11900.5	+	20612.2i	0.578234	+	1.00153i	−0.417448	+	0.908701i	$0.637075\pi$
$752$	−859.503	+	496.234i	−0.0416793	+	0.0240636i
$753$		0			0
$754$	−6526.02	+	11303.4i	−0.315204	+	0.545949i
$755$	−11692.7	−	12092.0i	−0.563629	−	0.582880i
$756$		0			0
$757$			20867.5i			1.00191i	0.865474	+	0.500953i	$0.167017\pi$
$757$			20867.5i			1.00191i	−0.865474	+	0.500953i	$0.832983\pi$
$758$	25774.0	+	14880.6i	1.23503	+	0.713046i
$759$		0			0
$760$	−995.739	−	284.808i	−0.0475253	−	0.0135935i
$761$	−7743.76	−	13412.6i	−0.368871	−	0.638904i	0.620518	−	0.784192i	$-0.286922\pi$
$761$	−7743.76	−	13412.6i	−0.368871	−	0.638904i	−0.989389	+	0.145288i	$0.953589\pi$
$762$		0			0
$763$	365.912	+	211.260i	0.0173616	+	0.0100237i
$764$	59458.9			2.81564
$765$		0			0
$766$	−40536.7			−1.91208
$767$	−4908.05	−	2833.66i	−0.231055	−	0.133400i
$768$		0			0
$769$	−9233.99	−	15993.7i	−0.433012	−	0.749999i	0.564119	−	0.825693i	$-0.309216\pi$
$769$	−9233.99	−	15993.7i	−0.433012	−	0.749999i	−0.997131	+	0.0756946i	$0.975883\pi$
$770$	−9326.46	+	32606.9i	−0.436496	+	1.52607i
$771$		0			0
$772$	−42217.0	−	24374.0i	−1.96816	−	1.13632i
$773$			15379.9i			0.715621i	0.933794	+	0.357810i	$0.116477\pi$
$773$			15379.9i			0.715621i	−0.933794	+	0.357810i	$0.883523\pi$
$774$		0			0
$775$	−201.658	+	6003.17i	−0.00934681	+	0.278246i
$776$	2332.80	−	4040.53i	0.107916	−	0.186916i
$777$		0			0
$778$	732.655	−	422.999i	0.0337622	−	0.0194926i
$779$	−268.147	−	464.444i	−0.0123329	−	0.0213613i
$780$		0			0
$781$	4525.13	−	7837.76i	0.207327	−	0.359100i
$782$			71341.3i			3.26235i
$783$		0			0
$784$	−10194.7			−0.464407
$785$	−3249.45	−	12996.1i	−0.147742	−	0.590892i
$786$		0			0
$787$	33127.1	−	19125.9i	1.50045	−	0.866284i	0.500448	−	0.865767i	$-0.333169\pi$
$787$	33127.1	−	19125.9i	1.50045	−	0.866284i	1.00000		0.000517066i	$-0.000164587\pi$
$788$	44701.4	−	25808.3i	2.02084	−	1.16673i
$789$		0			0
$790$	10846.7	+	43381.3i	0.488494	+	1.95372i
$791$	−23756.7			−1.06788
$792$		0			0
$793$			798.826i			0.0357720i
$794$	−14892.9	+	25795.2i	−0.665653	+	1.15295i
$795$		0			0
$796$	43245.8	+	74903.9i	1.92564	+	3.33530i
$797$	33759.1	−	19490.8i	1.50039	−	0.866249i	0.500388	−	0.865801i	$-0.333191\pi$
$797$	33759.1	−	19490.8i	1.50039	−	0.866249i	1.00000		0.000448165i	$-0.000142655\pi$
$798$		0			0
$799$	396.740	−	687.174i	0.0175665	−	0.0304261i
$800$	17134.2	+	575.572i	0.757233	+	0.0254369i
$801$		0			0
$802$		−	13307.4i		−	0.585911i
$803$	15670.8	+	9047.53i	0.688680	+	0.397609i
$804$		0			0
$805$	−11018.8	+	38523.6i	−0.482437	+	1.68668i
$806$	1222.92	+	2118.16i	0.0534436	+	0.0925670i
$807$		0			0
$808$	−45272.8	−	26138.2i	−1.97115	−	1.13804i
$809$	−4490.50			−0.195152			−0.0975758	−	0.995228i	$-0.531109\pi$
$809$	−4490.50			−0.195152			−0.0975758	+	0.995228i	$0.531109\pi$
$810$		0			0
$811$	33791.9			1.46312			0.731562	−	0.681775i	$-0.238792\pi$
$811$	33791.9			1.46312			0.731562	+	0.681775i	$0.238792\pi$
$812$	81874.5	+	47270.2i	3.53846	+	2.04293i
$813$		0			0
$814$	11681.8	+	20233.5i	0.503006	+	0.871231i
$815$	23701.2	+	6779.18i	1.01867	+	0.291367i
$816$		0			0
$817$	447.361	+	258.284i	0.0191569	+	0.0110602i
$818$		−	69195.7i		−	2.95766i
$819$		0			0
$820$	38094.3	+	39395.4i	1.62233	+	1.67774i
$821$	3382.78	−	5859.15i	0.143800	−	0.249069i	−0.785125	−	0.619338i	$-0.787401\pi$
$821$	3382.78	−	5859.15i	0.143800	−	0.249069i	0.928925	+	0.370269i	$0.120734\pi$
$822$		0			0
$823$	34076.3	−	19674.0i	1.44329	−	0.833282i	0.445219	−	0.895422i	$-0.353126\pi$
$823$	34076.3	−	19674.0i	1.44329	−	0.833282i	0.998067	+	0.0621398i	$0.0197925\pi$
$824$	10381.8	+	17981.8i	0.438916	+	0.760225i
$825$		0			0
$826$	−29883.3	+	51759.4i	−1.25881	+	2.18031i
$827$			632.071i			0.0265771i	0.999912	+	0.0132885i	$0.00423000\pi$
$827$			632.071i			0.0265771i	−0.999912	+	0.0132885i	$0.995770\pi$
$828$		0			0
$829$	19585.8			0.820560			0.410280	−	0.911959i	$-0.365431\pi$
$829$	19585.8			0.820560			0.410280	+	0.911959i	$0.365431\pi$
$830$	12503.6	−	3126.31i	0.522899	−	0.130742i
$831$		0			0
$832$	−1176.02	+	678.978i	−0.0490040	+	0.0282925i
$833$	7058.66	−	4075.32i	0.293599	−	0.169510i
$834$		0			0
$835$	3070.26	+	12279.4i	0.127246	+	0.508918i
$836$	962.167			0.0398053
$837$		0			0
$838$		−	1308.94i		−	0.0539577i
$839$	−5836.32	+	10108.8i	−0.240157	+	0.415965i	−0.960759	−	0.277385i	$-0.910532\pi$
$839$	−5836.32	+	10108.8i	−0.240157	+	0.415965i	0.720602	+	0.693349i	$0.243866\pi$
$840$		0			0
$841$	−20683.3	−	35824.5i	−0.848057	−	1.46888i
$842$	−59718.5	+	34478.5i	−2.44422	+	1.41117i
$843$		0			0
$844$	47537.9	−	82338.0i	1.93877	−	3.35805i
$845$	16286.6	+	16842.9i	0.663048	+	0.685695i
$846$		0			0
$847$			10824.4i			0.439114i
$848$	3206.55	+	1851.31i	0.129851	+	0.0749694i
$849$		0			0
$850$	−46131.0	+	24606.9i	−1.86151	+	0.992952i
$851$	13801.5	+	23904.9i	0.555946	+	0.962927i
$852$		0			0
$853$	19140.0	+	11050.5i	0.768276	+	0.443565i	0.832259	−	0.554386i	$-0.187047\pi$
$853$	19140.0	+	11050.5i	0.768276	+	0.443565i	−0.0639830	+	0.997951i	$0.520380\pi$
$854$	8424.28			0.337556
$855$		0			0
$856$	−624.118			−0.0249205
$857$	25892.3	+	14948.9i	1.03205	+	0.595853i	0.917571	−	0.397573i	$-0.130147\pi$
$857$	25892.3	+	14948.9i	1.03205	+	0.595853i	0.114477	+	0.993426i	$0.463481\pi$
$858$		0			0
$859$	7041.73	+	12196.6i	0.279698	+	0.484452i	0.971310	−	0.237818i	$-0.0764322\pi$
$859$	7041.73	+	12196.6i	0.279698	+	0.484452i	−0.691611	+	0.722270i	$0.743099\pi$
$860$	−50750.3	−	14516.0i	−2.01229	−	0.575571i
$861$		0			0
$862$	58035.1	+	33506.6i	2.29313	+	1.32394i
$863$			11367.8i			0.448396i	0.974544	+	0.224198i	$0.0719762\pi$
$863$			11367.8i			0.448396i	−0.974544	+	0.224198i	$0.928024\pi$
$864$		0			0
$865$	−14901.1	+	14409.0i	−0.585727	+	0.566381i
$866$	37857.5	−	65571.2i	1.48551	−	2.57298i
$867$		0			0
$868$	15342.6	−	8858.04i	0.599955	−	0.346384i
$869$	−11301.1	−	19574.2i	−0.441157	−	0.764106i
$870$		0			0
$871$	2350.19	−	4070.65i	0.0914272	−	0.158357i
$872$			970.272i			0.0376807i
$873$		0			0
$874$	1655.04			0.0640534
$875$	−28710.9	+	6162.45i	−1.10926	+	0.238090i
$876$		0			0
$877$	−38815.9	+	22410.4i	−1.49455	+	0.862879i	−0.999980	−	0.00625950i	$-0.998008\pi$
$877$	−38815.9	+	22410.4i	−1.49455	+	0.862879i	−0.494569	+	0.869138i	$0.664674\pi$
$878$	−32227.5	+	18606.6i	−1.23875	+	0.715195i
$879$		0			0
$880$	−32067.1	+	8017.84i	−1.22839	+	0.307138i
$881$	−11986.7			−0.458391			−0.229196	−	0.973380i	$-0.573610\pi$
$881$	−11986.7			−0.458391			−0.229196	+	0.973380i	$0.573610\pi$
$882$		0			0
$883$		−	14223.4i		−	0.542078i	−0.962568	−	0.271039i	$-0.912633\pi$
$883$		−	14223.4i		−	0.542078i	0.962568	−	0.271039i	$-0.0873672\pi$
$884$	−7311.32	+	12663.6i	−0.278175	+	0.481813i
$885$		0			0
$886$	4012.67	+	6950.14i	0.152154	+	0.263538i
$887$	−20039.8	+	11570.0i	−0.758592	+	0.437973i	−0.828790	−	0.559560i	$-0.810970\pi$
$887$	−20039.8	+	11570.0i	−0.758592	+	0.437973i	0.0701980	+	0.997533i	$0.477637\pi$
$888$		0			0
$889$	−2911.69	+	5043.19i	−0.109848	+	0.190262i
$890$	2189.97	−	2117.64i	0.0824809	−	0.0797567i
$891$		0			0
$892$		−	71666.0i		−	2.69008i
$893$	−15.9417	−	9.20394i	−0.000597389	−	0.000344903i
$894$		0			0
$895$	9856.55	−	34460.2i	0.368121	−	1.28701i
$896$	18687.5	+	32367.7i	0.696770	+	1.20684i
$897$		0			0
$898$	−32092.0	−	18528.3i	−1.19257	−	0.688528i
$899$	−12322.0			−0.457133
$900$		0			0
$901$	−2960.24			−0.109456
$902$	−34925.6	−	20164.3i	−1.28924	−	0.744344i
$903$		0			0
$904$	−27277.4	−	47245.9i	−1.00358	−	1.73825i
$905$	7006.33	−	24495.3i	0.257346	−	0.899726i
$906$		0			0
$907$	−21240.0	−	12262.9i	−0.777576	−	0.448934i	0.0579945	−	0.998317i	$-0.481529\pi$
$907$	−21240.0	−	12262.9i	−0.777576	−	0.448934i	−0.835571	+	0.549383i	$0.814863\pi$
$908$			3892.32i			0.142259i
$909$		0			0
$910$	−8595.76	+	8311.86i	−0.313128	+	0.302786i
$911$	−4226.93	+	7321.26i	−0.153726	+	0.266261i	−0.932594	−	0.360926i	$-0.882461\pi$
$911$	−4226.93	+	7321.26i	−0.153726	+	0.266261i	0.778868	+	0.627187i	$0.215794\pi$
$912$		0			0
$913$	−5641.78	+	3257.28i	−0.204508	+	0.118073i
$914$	−15913.2	−	27562.5i	−0.575888	−	0.997467i
$915$		0			0
$916$	14020.3	−	24283.8i	0.505724	−	0.875940i
$917$		−	10560.5i		−	0.380302i
$918$		0			0
$919$	−29199.7			−1.04811			−0.524053	−	0.851686i	$-0.675581\pi$
$919$	−29199.7			−1.04811			−0.524053	+	0.851686i	$0.675581\pi$
$920$	−89265.2	+	22319.2i	−3.19890	+	0.799830i
$921$		0			0
$922$	27731.5	−	16010.8i	0.990553	−	0.571896i
$923$	2763.35	−	1595.42i	0.0985447	−	0.0568948i
$924$		0			0
$925$	−10697.1	+	17169.6i	−0.380237	+	0.610307i
$926$	11603.4			0.411783
$927$		0			0
$928$			35169.5i			1.24407i
$929$	25303.4	−	43826.7i	0.893624	−	1.54780i	0.0581262	−	0.998309i	$-0.481487\pi$
$929$	25303.4	−	43826.7i	0.893624	−	1.54780i	0.835498	−	0.549493i	$-0.185179\pi$
$930$		0			0
$931$	−94.5431	−	163.754i	−0.00332817	−	0.00576456i
$932$	100602.	−	58082.3i	3.53574	−	2.04136i
$933$		0			0
$934$	−15625.1	+	27063.4i	−0.547396	+	0.948118i
$935$	18997.8	−	18370.3i	0.664485	−	0.642539i
$936$		0			0
$937$		−	30351.9i		−	1.05822i	−0.848553	−	0.529110i	$-0.822526\pi$
$937$		−	30351.9i		−	1.05822i	0.848553	−	0.529110i	$-0.177474\pi$
$938$	−42928.3	−	24784.7i	−1.49431	−	0.862738i
$939$		0			0
$940$	1808.49	+	517.277i	0.0627515	+	0.0179486i
$941$	−11250.3	−	19486.0i	−0.389743	−	0.675054i	0.602672	−	0.797989i	$-0.294103\pi$
$941$	−11250.3	−	19486.0i	−0.389743	−	0.675054i	−0.992415	+	0.122935i	$0.960769\pi$
$942$		0			0
$943$	−41263.1	−	23823.3i	−1.42493	−	0.822686i
$944$	−58250.8			−2.00837
$945$		0			0
$946$	38845.3			1.33506
$947$	−31722.1	−	18314.7i	−1.08852	−	0.628457i	−0.155338	−	0.987861i	$-0.549647\pi$
$947$	−31722.1	−	18314.7i	−1.08852	−	0.628457i	−0.933182	+	0.359404i	$0.882980\pi$
$948$		0			0
$949$	3189.88	+	5525.03i	0.109112	+	0.188988i
$950$	570.853	+	1070.19i	0.0194957	+	0.0365490i
$951$		0			0
$952$	72659.1	+	41949.8i	2.47363	+	1.42815i
$953$			29632.2i			1.00722i	0.863931	+	0.503611i	$0.167995\pi$
$953$			29632.2i			1.00722i	−0.863931	+	0.503611i	$0.832005\pi$
$954$		0			0
$955$	−26336.1	−	27235.6i	−0.892373	−	0.922853i
$956$	31208.1	−	54054.1i	1.05580	−	1.82870i
$957$		0			0
$958$	−17063.9	+	9851.85i	−0.575480	+	0.332254i
$959$	23334.8	+	40417.0i	0.785734	+	1.36093i
$960$		0			0
$961$	13741.0	−	23800.1i	0.461246	−	0.798901i
$962$			8237.27i			0.276071i
$963$		0			0
$964$	−52066.4			−1.73957
$965$	7534.44	+	30133.8i	0.251339	+	1.00522i
$966$		0			0
$967$	−43054.3	+	24857.4i	−1.43178	+	0.826639i	−0.997257	−	0.0740216i	$-0.976417\pi$
$967$	−43054.3	+	24857.4i	−1.43178	+	0.826639i	−0.434524	+	0.900660i	$0.643083\pi$
$968$	−21526.8	+	12428.5i	−0.714772	+	0.412674i
$969$		0			0
$970$	−5300.93	+	1325.41i	−0.175467	+	0.0438724i
$971$	22201.1			0.733745			0.366872	−	0.930271i	$-0.380429\pi$
$971$	22201.1			0.733745			0.366872	+	0.930271i	$0.380429\pi$
$972$		0			0
$973$			55319.4i			1.82267i
$974$	−37342.2	+	64678.6i	−1.22846	+	2.12776i
$975$		0			0
$976$	4105.31	+	7110.61i	0.134639	+	0.233202i
$977$	6847.97	−	3953.68i	0.224244	−	0.129467i	−0.383670	−	0.923470i	$-0.625340\pi$
$977$	6847.97	−	3953.68i	0.224244	−	0.129467i	0.607914	+	0.794003i	$0.292007\pi$
$978$		0			0
$979$	−769.901	+	1333.51i	−0.0251340	+	0.0435333i
$980$	13431.3	+	13890.0i	0.437802	+	0.452756i
$981$		0			0
$982$			18383.9i			0.597406i
$983$	−7088.28	−	4092.42i	−0.229991	−	0.132785i	0.380577	−	0.924749i	$-0.375725\pi$
$983$	−7088.28	−	4092.42i	−0.229991	−	0.132785i	−0.610568	+	0.791964i	$0.709059\pi$
$984$		0			0
$985$	−31621.3	−	9044.55i	−1.02288	−	0.292572i
$986$	−53627.9	−	92886.3i	−1.73211	−	3.00010i
$987$		0			0
$988$	293.782	+	169.615i	0.00945996	+	0.00546171i
$989$	45894.0			1.47558
$990$		0			0
$991$	−4964.85			−0.159146			−0.0795729	−	0.996829i	$-0.525356\pi$
$991$	−4964.85			−0.159146			−0.0795729	+	0.996829i	$0.525356\pi$
$992$	5707.50	+	3295.23i	0.182675	+	0.105467i
$993$		0			0
$994$	−16825.0	−	29141.8i	−0.536879	−	0.929901i
$995$	15155.5	−	52986.2i	0.482876	−	1.68822i
$996$		0			0
$997$	6147.30	+	3549.14i	0.195273	+	0.112741i	0.594449	−	0.804134i	$-0.297370\pi$
$997$	6147.30	+	3549.14i	0.195273	+	0.112741i	−0.399176	+	0.916874i	$0.630704\pi$
$998$		−	16465.8i		−	0.522261i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.4.j.a.19.16		32
3.2	odd	2		45.4.j.a.34.1	yes	32
5.4	even	2	inner	135.4.j.a.19.1		32
9.2	odd	6		405.4.b.e.244.16		16
9.4	even	3	inner	135.4.j.a.64.1		32
9.5	odd	6		45.4.j.a.4.16	yes	32
9.7	even	3		405.4.b.f.244.1		16
15.2	even	4		225.4.e.g.151.16		32
15.8	even	4		225.4.e.g.151.1		32
15.14	odd	2		45.4.j.a.34.16	yes	32
45.2	even	12		2025.4.a.bk.1.1		16
45.4	even	6	inner	135.4.j.a.64.16		32
45.7	odd	12		2025.4.a.bl.1.16		16
45.14	odd	6		45.4.j.a.4.1	✓	32
45.23	even	12		225.4.e.g.76.1		32
45.29	odd	6		405.4.b.e.244.1		16
45.32	even	12		225.4.e.g.76.16		32
45.34	even	6		405.4.b.f.244.16		16
45.38	even	12		2025.4.a.bk.1.16		16
45.43	odd	12		2025.4.a.bl.1.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.j.a.4.1	✓	32	45.14	odd	6
45.4.j.a.4.16	yes	32	9.5	odd	6
45.4.j.a.34.1	yes	32	3.2	odd	2
45.4.j.a.34.16	yes	32	15.14	odd	2
135.4.j.a.19.1		32	5.4	even	2	inner
135.4.j.a.19.16		32	1.1	even	1	trivial
135.4.j.a.64.1		32	9.4	even	3	inner
135.4.j.a.64.16		32	45.4	even	6	inner
225.4.e.g.76.1		32	45.23	even	12
225.4.e.g.76.16		32	45.32	even	12
225.4.e.g.151.1		32	15.8	even	4
225.4.e.g.151.16		32	15.2	even	4
405.4.b.e.244.1		16	45.29	odd	6
405.4.b.e.244.16		16	9.2	odd	6
405.4.b.f.244.1		16	9.7	even	3
405.4.b.f.244.16		16	45.34	even	6
2025.4.a.bk.1.1		16	45.2	even	12
2025.4.a.bk.1.16		16	45.38	even	12
2025.4.a.bl.1.1		16	45.43	odd	12
2025.4.a.bl.1.16		16	45.7	odd	12

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	135.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.37720 + 2.52718i) q^{2} +(8.77324 + 15.1957i) q^{4} +(3.07459 - 10.7493i) q^{5} +(18.1967 + 10.5059i) q^{7} +48.2513i q^{8} +O(q^{10})\)	\(q+(4.37720 + 2.52718i) q^{2} +(8.77324 + 15.1957i) q^{4} +(3.07459 - 10.7493i) q^{5} +(18.1967 + 10.5059i) q^{7} +48.2513i q^{8} +(40.6234 - 39.2817i) q^{10} +(-14.2815 + 24.7362i) q^{11} +(-8.72122 + 5.03520i) q^{13} +(53.1003 + 91.9724i) q^{14} +(-51.7535 + 89.6398i) q^{16} -82.7541i q^{17} -1.91981 q^{19} +(190.317 - 47.5855i) q^{20} +(-125.026 + 72.1836i) q^{22} +(-147.712 + 85.2818i) q^{23} +(-106.094 - 66.0991i) q^{25} -50.8993 q^{26} +368.682i q^{28} +(128.214 - 222.074i) q^{29} +(-24.0262 - 41.6147i) q^{31} +(-118.776 + 68.5756i) q^{32} +(209.134 - 362.231i) q^{34} +(168.878 - 163.300i) q^{35} -161.834i q^{37} +(-8.40337 - 4.85169i) q^{38} +(518.666 + 148.353i) q^{40} +(139.674 + 241.922i) q^{41} +(-233.024 - 134.536i) q^{43} -501.179 q^{44} -862.088 q^{46} +(8.30380 + 4.79420i) q^{47} +(49.2462 + 85.2969i) q^{49} +(-297.349 - 557.447i) q^{50} +(-153.027 - 88.3500i) q^{52} -35.7716i q^{53} +(221.987 + 229.569i) q^{55} +(-506.921 + 878.013i) q^{56} +(1122.44 - 648.040i) q^{58} +(281.385 + 487.374i) q^{59} +(39.6621 - 68.6968i) q^{61} -242.874i q^{62} +134.846 q^{64} +(27.3106 + 109.228i) q^{65} +(-404.219 + 233.376i) q^{67} +(1257.51 - 726.021i) q^{68} +(1151.90 - 288.013i) q^{70} -316.854 q^{71} -633.515i q^{73} +(408.984 - 708.381i) q^{74} +(-16.8429 - 29.1728i) q^{76} +(-519.751 + 300.078i) q^{77} +(-395.658 + 685.299i) q^{79} +(804.442 + 831.918i) q^{80} +1411.92i q^{82} +(197.521 + 114.039i) q^{83} +(-889.546 - 254.435i) q^{85} +(-679.994 - 1177.78i) q^{86} +(-1193.55 - 689.099i) q^{88} +53.9091 q^{89} -211.596 q^{91} +(-2591.83 - 1496.39i) q^{92} +(24.2316 + 41.9704i) q^{94} +(-5.90261 + 20.6365i) q^{95} +(-83.7394 - 48.3470i) q^{97} +497.815i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 54 q^{4} - 3 q^{5}+O(q^{10}) \) 32 * q + 54 * q^4 - 3 * q^5	\( 32 q + 54 q^{4} - 3 q^{5} - 20 q^{10} - 90 q^{11} + 102 q^{14} - 146 q^{16} - 8 q^{19} + 6 q^{20} + 71 q^{25} + 936 q^{26} + 516 q^{29} - 38 q^{31} + 212 q^{34} + 534 q^{35} + 44 q^{40} - 576 q^{41} - 3288 q^{44} - 580 q^{46} - 4 q^{49} - 558 q^{50} + 30 q^{55} - 2430 q^{56} + 2202 q^{59} - 20 q^{61} + 644 q^{64} - 339 q^{65} + 636 q^{70} + 5904 q^{71} + 4080 q^{74} + 396 q^{76} - 218 q^{79} - 2532 q^{80} - 704 q^{85} - 6108 q^{86} - 8148 q^{89} - 1884 q^{91} - 1078 q^{94} + 1692 q^{95}+O(q^{100}) \) 32 * q + 54 * q^4 - 3 * q^5 - 20 * q^10 - 90 * q^11 + 102 * q^14 - 146 * q^16 - 8 * q^19 + 6 * q^20 + 71 * q^25 + 936 * q^26 + 516 * q^29 - 38 * q^31 + 212 * q^34 + 534 * q^35 + 44 * q^40 - 576 * q^41 - 3288 * q^44 - 580 * q^46 - 4 * q^49 - 558 * q^50 + 30 * q^55 - 2430 * q^56 + 2202 * q^59 - 20 * q^61 + 644 * q^64 - 339 * q^65 + 636 * q^70 + 5904 * q^71 + 4080 * q^74 + 396 * q^76 - 218 * q^79 - 2532 * q^80 - 704 * q^85 - 6108 * q^86 - 8148 * q^89 - 1884 * q^91 - 1078 * q^94 + 1692 * q^95

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