LMFDB - Embedded newform 124.5.o.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,5,Mod(13,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(30))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("124.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	124.o (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.8178754224$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	124.17
Dual form			124.5.o.a.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.98717 - 3.59007i) q^{3} +(-24.6255 + 42.6526i) q^{5} +(3.33835 - 31.7622i) q^{7} +(-5.45784 - 51.9279i) q^{9} +O(q^{10})$	\(q+(-3.98717 - 3.59007i) q^{3} +(-24.6255 + 42.6526i) q^{5} +(3.33835 - 31.7622i) q^{7} +(-5.45784 - 51.9279i) q^{9} +(41.5486 + 93.3197i) q^{11} +(18.0401 - 84.8722i) q^{13} +(251.312 - 81.6561i) q^{15} +(158.105 - 355.109i) q^{17} +(346.182 - 73.5833i) q^{19} +(-127.339 + 114.657i) q^{21} +(-108.584 - 149.453i) q^{23} +(-900.331 - 1559.42i) q^{25} +(-420.107 + 578.227i) q^{27} +(-348.543 - 113.249i) q^{29} +(209.412 - 937.906i) q^{31} +(169.362 - 521.244i) q^{33} +(1272.53 + 924.550i) q^{35} +(1593.32 - 919.906i) q^{37} +(-376.626 + 273.635i) q^{39} +(606.704 + 673.814i) q^{41} +(-563.985 - 2653.34i) q^{43} +(2349.26 + 1045.96i) q^{45} +(503.510 + 1549.65i) q^{47} +(1350.84 + 287.129i) q^{49} +(-1905.25 + 848.274i) q^{51} +(103.057 - 10.8317i) q^{53} +(-5003.48 - 525.887i) q^{55} +(-1644.46 - 949.427i) q^{57} +(-1883.02 + 2091.31i) q^{59} +3437.31i q^{61} -1667.57 q^{63} +(3175.77 + 2859.48i) q^{65} +(-1881.95 + 3259.64i) q^{67} +(-103.603 + 985.720i) q^{69} +(-250.978 - 2387.89i) q^{71} +(-3871.11 - 8694.65i) q^{73} +(-2008.64 + 9449.91i) q^{75} +(3102.75 - 1008.14i) q^{77} +(214.289 - 481.300i) q^{79} +(-385.993 + 82.0453i) q^{81} +(5346.54 - 4814.04i) q^{83} +(11252.9 + 15488.3i) q^{85} +(983.132 + 1702.83i) q^{87} +(4192.13 - 5769.98i) q^{89} +(-2635.51 - 856.328i) q^{91} +(-4202.10 + 2987.79i) q^{93} +(-5386.39 + 16577.6i) q^{95} +(-12338.0 - 8964.11i) q^{97} +(4619.13 - 2666.85i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) $ 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9	$ 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) $ 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9 - 42 * q^11 + 6 * q^13 + 665 * q^15 - 585 * q^17 - 153 * q^19 - 402 * q^21 - 1365 * q^23 - 5933 * q^25 - 9225 * q^27 - 1140 * q^29 + 117 * q^31 + 5151 * q^33 + 2898 * q^35 + 6594 * q^37 + 3173 * q^39 - 9393 * q^41 - 5322 * q^43 + 2010 * q^45 - 5112 * q^47 - 5210 * q^49 - 1829 * q^51 + 7395 * q^53 + 10585 * q^55 + 40485 * q^57 + 5625 * q^59 - 14954 * q^63 - 17094 * q^65 + 8909 * q^67 - 35370 * q^69 - 11811 * q^71 - 22105 * q^73 + 79377 * q^75 + 71490 * q^77 + 219 * q^79 - 5422 * q^81 + 10545 * q^83 - 53630 * q^85 + 13732 * q^87 - 40305 * q^89 + 42760 * q^91 - 1028 * q^93 + 62319 * q^95 + 35201 * q^97 + 16197 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{7}{30}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.98717	−	3.59007i	−0.443019	−	0.398896i	0.417205	−	0.908812i	$-0.363010\pi$
$3$	−3.98717	−	3.59007i	−0.443019	−	0.398896i	−0.860224	+	0.509916i	$0.829676\pi$
$4$		0			0
$5$	−24.6255	+	42.6526i	−0.985020	+	1.70610i	−0.343173	+	0.939272i	$0.611502\pi$
$5$	−24.6255	+	42.6526i	−0.985020	+	1.70610i	−0.641847	+	0.766832i	$0.721832\pi$
$6$		0			0
$7$	3.33835	−	31.7622i	0.0681295	−	0.648209i	−0.906164	−	0.422927i	$-0.861003\pi$
$7$	3.33835	−	31.7622i	0.0681295	−	0.648209i	0.974293	−	0.225282i	$-0.0723305\pi$
$8$		0			0
$9$	−5.45784	−	51.9279i	−0.0673807	−	0.641085i
$10$		0			0
$11$	41.5486	+	93.3197i	0.343377	+	0.771237i	0.999857	+	0.0168940i	$0.00537778\pi$
$11$	41.5486	+	93.3197i	0.343377	+	0.771237i	−0.656480	+	0.754343i	$0.727956\pi$
$12$		0			0
$13$	18.0401	−	84.8722i	0.106746	−	0.502202i	−0.891995	−	0.452045i	$-0.850695\pi$
$13$	18.0401	−	84.8722i	0.106746	−	0.502202i	0.998741	−	0.0501569i	$-0.0159721\pi$
$14$		0			0
$15$	251.312	−	81.6561i	1.11694	−	0.362916i
$16$		0			0
$17$	158.105	−	355.109i	0.547075	−	1.22875i	−0.402561	−	0.915393i	$-0.631880\pi$
$17$	158.105	−	355.109i	0.547075	−	1.22875i	0.949636	−	0.313357i	$-0.101454\pi$
$18$		0			0
$19$	346.182	−	73.5833i	0.958953	−	0.203832i	0.298257	−	0.954486i	$-0.403595\pi$
$19$	346.182	−	73.5833i	0.958953	−	0.203832i	0.660696	+	0.750654i	$0.270261\pi$
$20$		0			0
$21$	−127.339	+	114.657i	−0.288751	+	0.259992i
$22$		0			0
$23$	−108.584	−	149.453i	−0.205263	−	0.282520i	0.693957	−	0.720016i	$-0.255866\pi$
$23$	−108.584	−	149.453i	−0.205263	−	0.282520i	−0.899221	+	0.437496i	$0.855866\pi$
$24$		0			0
$25$	−900.331	−	1559.42i	−1.44053	−	2.49507i
$26$		0			0
$27$	−420.107	+	578.227i	−0.576278	+	0.793179i
$28$		0			0
$29$	−348.543	−	113.249i	−0.414439	−	0.134659i	0.0943732	−	0.995537i	$-0.469915\pi$
$29$	−348.543	−	113.249i	−0.414439	−	0.134659i	−0.508812	+	0.860877i	$0.669915\pi$
$30$		0			0
$31$	209.412	−	937.906i	0.217910	−	0.975969i
$31$	209.412	−	937.906i	0.217910	−	0.975969i
$32$		0			0
$33$	169.362	−	521.244i	0.155521	−	0.478644i
$34$		0			0
$35$	1272.53	+	924.550i	1.03880	+	0.754735i
$36$		0			0
$37$	1593.32	−	919.906i	1.16386	−	0.671955i	0.211634	−	0.977349i	$-0.432122\pi$
$37$	1593.32	−	919.906i	1.16386	−	0.671955i	0.952226	+	0.305394i	$0.0987882\pi$
$38$		0			0
$39$	−376.626	+	273.635i	−0.247617	+	0.179904i
$40$		0			0
$41$	606.704	+	673.814i	0.360919	+	0.400841i	0.896068	−	0.443917i	$-0.146411\pi$
$41$	606.704	+	673.814i	0.360919	+	0.400841i	−0.535149	+	0.844757i	$0.679745\pi$
$42$		0			0
$43$	−563.985	−	2653.34i	−0.305022	−	1.43501i	−0.817308	−	0.576200i	$-0.804535\pi$
$43$	−563.985	−	2653.34i	−0.305022	−	1.43501i	0.512287	−	0.858815i	$-0.328799\pi$
$44$		0			0
$45$	2349.26	+	1045.96i	1.16013	+	0.516523i
$46$		0			0
$47$	503.510	+	1549.65i	0.227936	+	0.701514i	0.997980	+	0.0635241i	$0.0202340\pi$
$47$	503.510	+	1549.65i	0.227936	+	0.701514i	−0.770045	+	0.637990i	$0.779766\pi$
$48$		0			0
$49$	1350.84	+	287.129i	0.562614	+	0.119587i
$50$		0			0
$51$	−1905.25	+	848.274i	−0.732508	+	0.326134i
$52$		0			0
$53$	103.057	−	10.8317i	0.0366881	−	0.00385608i	−0.0861666	−	0.996281i	$-0.527462\pi$
$53$	103.057	−	10.8317i	0.0366881	−	0.00385608i	0.122855	+	0.992425i	$0.460795\pi$
$54$		0			0
$55$	−5003.48	−	525.887i	−1.65404	−	0.173847i
$56$		0			0
$57$	−1644.46	−	949.427i	−0.506142	−	0.292221i
$58$		0			0
$59$	−1883.02	+	2091.31i	−0.540943	+	0.600778i	−0.950200	−	0.311641i	$-0.899121\pi$
$59$	−1883.02	+	2091.31i	−0.540943	+	0.600778i	0.409257	+	0.912419i	$0.365788\pi$
$60$		0			0
$61$			3437.31i			0.923760i	0.886942	+	0.461880i	$0.152825\pi$
$61$			3437.31i			0.923760i	−0.886942	+	0.461880i	$0.847175\pi$
$62$		0			0
$63$	−1667.57			−0.420147
$64$		0			0
$65$	3175.77	+	2859.48i	0.751662	+	0.676800i
$66$		0			0
$67$	−1881.95	+	3259.64i	−0.419237	+	0.726139i	−0.995863	−	0.0908689i	$-0.971036\pi$
$67$	−1881.95	+	3259.64i	−0.419237	+	0.726139i	0.576626	+	0.817008i	$0.304369\pi$
$68$		0			0
$69$	−103.603	+	985.720i	−0.0217608	+	0.207041i
$70$		0			0
$71$	−250.978	−	2387.89i	−0.0497873	−	0.473694i	−0.990801	−	0.135326i	$-0.956792\pi$
$71$	−250.978	−	2387.89i	−0.0497873	−	0.473694i	0.941014	−	0.338368i	$-0.109875\pi$
$72$		0			0
$73$	−3871.11	−	8694.65i	−0.726423	−	1.63157i	−0.774378	−	0.632724i	$-0.781937\pi$
$73$	−3871.11	−	8694.65i	−0.726423	−	1.63157i	0.0479547	−	0.998850i	$-0.484730\pi$
$74$		0			0
$75$	−2008.64	+	9449.91i	−0.357092	+	1.67998i
$76$		0			0
$77$	3102.75	−	1008.14i	0.523317	−	0.170036i
$78$		0			0
$79$	214.289	−	481.300i	0.0343356	−	0.0771191i	−0.895564	−	0.444934i	$-0.853227\pi$
$79$	214.289	−	481.300i	0.0343356	−	0.0771191i	0.929899	+	0.367815i	$0.119894\pi$
$80$		0			0
$81$	−385.993	+	82.0453i	−0.0588314	+	0.0125050i
$82$		0			0
$83$	5346.54	−	4814.04i	0.776098	−	0.698802i	−0.182613	−	0.983185i	$-0.558456\pi$
$83$	5346.54	−	4814.04i	0.776098	−	0.698802i	0.958711	+	0.284383i	$0.0917888\pi$
$84$		0			0
$85$	11252.9	+	15488.3i	1.55750	+	2.14371i
$86$		0			0
$87$	983.132	+	1702.83i	0.129889	+	0.224975i
$88$		0			0
$89$	4192.13	−	5769.98i	0.529243	−	0.728440i	−0.457772	−	0.889070i	$-0.651352\pi$
$89$	4192.13	−	5769.98i	0.529243	−	0.728440i	0.987015	+	0.160629i	$0.0513523\pi$
$90$		0			0
$91$	−2635.51	−	856.328i	−0.318259	−	0.103409i
$92$		0			0
$93$	−4202.10	+	2987.79i	−0.485849	+	0.345449i
$94$		0			0
$95$	−5386.39	+	16577.6i	−0.596830	+	1.83685i
$96$		0			0
$97$	−12338.0	−	8964.11i	−1.31130	−	0.952717i	−0.999997	−	0.00240638i	$-0.999234\pi$
$97$	−12338.0	−	8964.11i	−1.31130	−	0.952717i	−0.311305	−	0.950310i	$-0.600766\pi$
$98$		0			0
$99$	4619.13	−	2666.85i	0.471291	−	0.272100i
$100$		0			0
$101$	−5763.61	+	4187.51i	−0.565004	+	0.410500i	−0.833287	−	0.552841i	$-0.813544\pi$
$101$	−5763.61	+	4187.51i	−0.565004	+	0.410500i	0.268283	+	0.963340i	$0.413544\pi$
$102$		0			0
$103$	8045.57	+	8935.51i	0.758372	+	0.842257i	0.991489	−	0.130191i	$-0.0415592\pi$
$103$	8045.57	+	8935.51i	0.758372	+	0.842257i	−0.233117	+	0.972449i	$0.574892\pi$
$104$		0			0
$105$	−1754.62	−	8254.82i	−0.159149	−	0.748737i
$106$		0			0
$107$	−9150.38	−	4074.01i	−0.799229	−	0.355840i	−0.0338563	−	0.999427i	$-0.510779\pi$
$107$	−9150.38	−	4074.01i	−0.799229	−	0.355840i	−0.765373	+	0.643587i	$0.777446\pi$
$108$		0			0
$109$	−2852.35	−	8778.63i	−0.240077	−	0.738880i	−0.996407	−	0.0846902i	$-0.973010\pi$
$109$	−2852.35	−	8778.63i	−0.240077	−	0.738880i	0.756331	−	0.654189i	$-0.226990\pi$
$110$		0			0
$111$	−9655.38	−	2052.31i	−0.783652	−	0.166570i
$112$		0			0
$113$	1619.32	−	720.968i	0.126817	−	0.0564624i	−0.342347	−	0.939573i	$-0.611222\pi$
$113$	1619.32	−	720.968i	0.126817	−	0.0564624i	0.469164	+	0.883111i	$0.344555\pi$
$114$		0			0
$115$	9048.52	−	951.037i	0.684198	−	0.0719121i
$116$		0			0
$117$	−4505.69	−	473.567i	−0.329147	−	0.0345947i
$118$		0			0
$119$	−10751.2	−	6207.23i	−0.759215	−	0.438333i
$120$		0			0
$121$	2814.46	−	3125.78i	0.192232	−	0.213495i
$122$		0			0
$123$		−	4864.72i		−	0.321549i
$124$		0			0
$125$	57902.5			3.70576
$126$		0			0
$127$	17450.5	+	15712.5i	1.08193	+	0.974175i	0.999748	−	0.0224420i	$-0.00714411\pi$
$127$	17450.5	+	15712.5i	1.08193	+	0.974175i	0.0821831	+	0.996617i	$0.473811\pi$
$128$		0			0
$129$	−7276.97	+	12604.1i	−0.437291	+	0.757411i
$130$		0			0
$131$	3360.29	−	31971.0i	0.195810	−	1.86300i	−0.250489	−	0.968120i	$-0.580591\pi$
$131$	3360.29	−	31971.0i	0.195810	−	1.86300i	0.446298	−	0.894884i	$-0.352742\pi$
$132$		0			0
$133$	−1181.49	−	11241.2i	−0.0667926	−	0.635489i
$134$		0			0
$135$	−14317.6	−	32157.8i	−0.785601	−	1.76449i
$136$		0			0
$137$	2314.14	−	10887.2i	0.123296	−	0.580062i	−0.872512	−	0.488593i	$-0.837510\pi$
$137$	2314.14	−	10887.2i	0.123296	−	0.580062i	0.995808	−	0.0914690i	$-0.0291563\pi$
$138$		0			0
$139$	−8376.44	+	2721.67i	−0.433541	+	0.140866i	−0.517654	−	0.855590i	$-0.673194\pi$
$139$	−8376.44	+	2721.67i	−0.433541	+	0.140866i	0.0841128	+	0.996456i	$0.473194\pi$
$140$		0			0
$141$	3555.75	−	7986.33i	0.178851	−	0.401707i
$142$		0			0
$143$	8669.79	−	1842.82i	0.423971	−	0.0901179i
$144$		0			0
$145$	13413.4	−	12077.5i	0.637974	−	0.574434i
$146$		0			0
$147$	−4355.21	−	5994.43i	−0.201546	−	0.277404i
$148$		0			0
$149$	−16088.3	−	27865.7i	−0.724664	−	1.25516i	−0.959112	−	0.283027i	$-0.908661\pi$
$149$	−16088.3	−	27865.7i	−0.724664	−	1.25516i	0.234448	−	0.972129i	$-0.424672\pi$
$150$		0			0
$151$	−24643.3	+	33918.6i	−1.08080	+	1.48759i	−0.222164	+	0.975009i	$0.571312\pi$
$151$	−24643.3	+	33918.6i	−1.08080	+	1.48759i	−0.858636	+	0.512585i	$0.828688\pi$
$152$		0			0
$153$	−19302.9	−	6271.91i	−0.824595	−	0.267927i
$154$		0			0
$155$	34847.3	+	32028.4i	1.45046	+	1.33313i
$156$		0			0
$157$	4688.91	−	14431.0i	0.190227	−	0.585460i	−0.809772	−	0.586745i	$-0.800409\pi$
$157$	4688.91	−	14431.0i	0.190227	−	0.585460i	0.999999	+	0.00128530i	$0.000409123\pi$
$158$		0			0
$159$	−449.792	−	326.793i	−0.0177917	−	0.0129264i
$160$		0			0
$161$	−5109.46	+	2949.95i	−0.197117	+	0.113805i
$162$		0			0
$163$	−37137.2	+	26981.7i	−1.39776	+	1.01553i	−0.402801	+	0.915287i	$0.631963\pi$
$163$	−37137.2	+	26981.7i	−1.39776	+	1.01553i	−0.994963	+	0.100247i	$0.968037\pi$
$164$		0			0
$165$	18061.8	+	20059.6i	0.663426	+	0.736809i
$166$		0			0
$167$	−6750.83	−	31760.2i	−0.242061	−	1.13881i	−0.916362	−	0.400350i	$-0.868888\pi$
$167$	−6750.83	−	31760.2i	−0.242061	−	1.13881i	0.674301	−	0.738456i	$-0.264445\pi$
$168$		0			0
$169$	19213.9	+	8554.59i	0.672733	+	0.299520i
$170$		0			0
$171$	−5710.43	−	17574.9i	−0.195288	−	0.601036i
$172$		0			0
$173$	9320.85	+	1981.21i	0.311432	+	0.0661969i	0.360976	−	0.932575i	$-0.382444\pi$
$173$	9320.85	+	1981.21i	0.311432	+	0.0661969i	−0.0495443	+	0.998772i	$0.515777\pi$
$174$		0			0
$175$	−52536.2	+	23390.6i	−1.71547	+	0.763776i
$176$		0			0
$177$	15015.9	−	1578.23i	0.479296	−	0.0503761i
$178$		0			0
$179$	8977.57	+	943.581i	0.280190	+	0.0294492i	0.243581	−	0.969880i	$-0.421678\pi$
$179$	8977.57	+	943.581i	0.280190	+	0.0294492i	0.0366089	+	0.999330i	$0.488344\pi$
$180$		0			0
$181$	−3232.89	−	1866.51i	−0.0986811	−	0.0569735i	0.449847	−	0.893105i	$-0.351478\pi$
$181$	−3232.89	−	1866.51i	−0.0986811	−	0.0569735i	−0.548528	+	0.836132i	$0.684812\pi$
$182$		0			0
$183$	12340.2	−	13705.1i	0.368484	−	0.409243i
$184$		0			0
$185$			90612.6i			2.64756i
$186$		0			0
$187$	39707.7			1.13551
$188$		0			0
$189$	16963.3	+	15273.9i	0.474884	+	0.427588i
$190$		0			0
$191$	−30616.2	+	53028.8i	−0.839236	+	1.45360i	0.0512979	+	0.998683i	$0.483664\pi$
$191$	−30616.2	+	53028.8i	−0.839236	+	1.45360i	−0.890534	+	0.454916i	$0.849669\pi$
$192$		0			0
$193$	5425.12	−	51616.6i	0.145645	−	1.38572i	−0.640634	−	0.767846i	$-0.721329\pi$
$193$	5425.12	−	51616.6i	0.145645	−	1.38572i	0.786279	−	0.617871i	$-0.212005\pi$
$194$		0			0
$195$	−2396.64	−	22802.5i	−0.0630279	−	0.599670i
$196$		0			0
$197$	−9733.80	−	21862.5i	−0.250813	−	0.563335i	0.743632	−	0.668589i	$-0.233101\pi$
$197$	−9733.80	−	21862.5i	−0.250813	−	0.563335i	−0.994445	+	0.105253i	$0.966435\pi$
$198$		0			0
$199$	−532.427	+	2504.87i	−0.0134448	+	0.0632527i	−0.984359	−	0.176177i	$-0.943627\pi$
$199$	−532.427	+	2504.87i	−0.0134448	+	0.0632527i	0.970914	+	0.239429i	$0.0769603\pi$
$200$		0			0
$201$	19206.0	−	6240.40i	0.475384	−	0.154462i
$202$		0			0
$203$	−4760.59	+	10692.5i	−0.115523	+	0.259469i
$204$		0			0
$205$	−43680.3	+	9284.54i	−1.03939	+	0.220929i
$206$		0			0
$207$	−7168.16	+	6454.24i	−0.167289	+	0.150627i
$208$		0			0
$209$	21250.1	+	29248.3i	0.486485	+	0.669589i
$210$		0			0
$211$	−9851.34	−	17063.0i	−0.221274	−	0.383258i	0.733921	−	0.679235i	$-0.237688\pi$
$211$	−9851.34	−	17063.0i	−0.221274	−	0.383258i	−0.955195	+	0.295977i	$0.904355\pi$
$212$		0			0
$213$	−7572.00	+	10422.0i	−0.166898	+	0.229716i
$214$		0			0
$215$	127060.	+	41284.4i	2.74874	+	0.893119i
$216$		0			0
$217$	−29090.9	−	9782.44i	−0.617786	−	0.207744i
$218$		0			0
$219$	−15779.6	+	48564.6i	−0.329009	+	1.01259i
$220$		0			0
$221$	−27286.6	−	19824.9i	−0.558683	−	0.405907i
$222$		0			0
$223$	4272.66	−	2466.82i	0.0859188	−	0.0496052i	−0.456425	−	0.889762i	$-0.650870\pi$
$223$	4272.66	−	2466.82i	0.0859188	−	0.0496052i	0.542344	+	0.840157i	$0.317537\pi$
$224$		0			0
$225$	−76063.4	+	55263.3i	−1.50249	+	1.09162i
$226$		0			0
$227$	−20065.0	−	22284.5i	−0.389393	−	0.432465i	0.516294	−	0.856411i	$-0.327311\pi$
$227$	−20065.0	−	22284.5i	−0.389393	−	0.432465i	−0.905687	+	0.423946i	$0.860644\pi$
$228$		0			0
$229$	−9033.87	−	42501.0i	−0.172267	−	0.810454i	−0.976394	−	0.215996i	$-0.930700\pi$
$229$	−9033.87	−	42501.0i	−0.172267	−	0.810454i	0.804127	−	0.594458i	$-0.202633\pi$
$230$		0			0
$231$	−15990.5	−	7119.42i	−0.299666	−	0.133420i
$232$		0			0
$233$	13377.2	+	41170.9i	0.246408	+	0.758365i	0.995402	+	0.0957884i	$0.0305372\pi$
$233$	13377.2	+	41170.9i	0.246408	+	0.758365i	−0.748994	+	0.662577i	$0.769463\pi$
$234$		0			0
$235$	−78495.6	−	16684.8i	−1.42138	−	0.302123i
$236$		0			0
$237$	−2582.30	+	1149.72i	−0.0459738	+	0.0204689i
$238$		0			0
$239$	45355.1	−	4767.01i	0.794018	−	0.0834547i	0.301171	−	0.953570i	$-0.402623\pi$
$239$	45355.1	−	4767.01i	0.794018	−	0.0834547i	0.492848	+	0.870116i	$0.335956\pi$
$240$		0			0
$241$	−61262.6	−	6438.96i	−1.05478	−	0.110862i	−0.438769	−	0.898600i	$-0.644585\pi$
$241$	−61262.6	−	6438.96i	−1.05478	−	0.110862i	−0.616010	+	0.787738i	$0.711252\pi$
$242$		0			0
$243$	51970.4	+	30005.1i	0.880123	+	0.508139i
$244$		0			0
$245$	−45511.9	+	50546.0i	−0.758215	+	0.842083i
$246$		0			0
$247$		−	30708.7i		−	0.503347i
$248$		0			0
$249$	−38600.3			−0.622575
$250$		0			0
$251$	57268.2	+	51564.5i	0.909005	+	0.818472i	0.983900	−	0.178720i	$-0.0571955\pi$
$251$	57268.2	+	51564.5i	0.909005	+	0.818472i	−0.0748950	+	0.997191i	$0.523862\pi$
$252$		0			0
$253$	9435.42	−	16342.6i	0.147408	−	0.255318i
$254$		0			0
$255$	10736.7	−	102153.i	0.165117	−	1.57098i
$256$		0			0
$257$	4656.11	+	44300.0i	0.0704948	+	0.670714i	0.971522	+	0.236950i	$0.0761479\pi$
$257$	4656.11	+	44300.0i	0.0704948	+	0.670714i	−0.901027	+	0.433763i	$0.857185\pi$
$258$		0			0
$259$	−23899.2	−	53678.5i	−0.356274	−	0.800204i
$260$		0			0
$261$	−3978.46	+	18717.2i	−0.0584029	+	0.274764i
$262$		0			0
$263$	32152.7	−	10447.1i	0.464843	−	0.151037i	−0.0672259	−	0.997738i	$-0.521415\pi$
$263$	32152.7	−	10447.1i	0.464843	−	0.151037i	0.532069	+	0.846701i	$0.321415\pi$
$264$		0			0
$265$	−2075.83	+	4662.39i	−0.0295597	+	0.0663921i
$266$		0			0
$267$	−37429.3	+	7955.85i	−0.525037	+	0.111600i
$268$		0			0
$269$	64772.3	−	58321.2i	0.895127	−	0.805976i	−0.0866051	−	0.996243i	$-0.527602\pi$
$269$	64772.3	−	58321.2i	0.895127	−	0.805976i	0.981732	+	0.190266i	$0.0609352\pi$
$270$		0			0
$271$	64905.3	+	89334.5i	0.883775	+	1.21641i	0.975361	+	0.220615i	$0.0708065\pi$
$271$	64905.3	+	89334.5i	0.883775	+	1.21641i	−0.0915857	+	0.995797i	$0.529194\pi$
$272$		0			0
$273$	7433.94	+	12876.0i	0.0997456	+	0.172765i
$274$		0			0
$275$	108117.	−	148810.i	1.42965	−	1.96774i
$276$		0			0
$277$	41324.8	+	13427.2i	0.538581	+	0.174996i	0.565661	−	0.824638i	$-0.308621\pi$
$277$	41324.8	+	13427.2i	0.538581	+	0.174996i	−0.0270802	+	0.999633i	$0.508621\pi$
$278$		0			0
$279$	−49846.4	−	5755.37i	−0.640362	−	0.0739375i
$280$		0			0
$281$	−3218.61	+	9905.85i	−0.0407620	+	0.125452i	−0.969367	−	0.245618i	$-0.921009\pi$
$281$	−3218.61	+	9905.85i	−0.0407620	+	0.125452i	0.928605	+	0.371070i	$0.121009\pi$
$282$		0			0
$283$	53818.4	+	39101.3i	0.671982	+	0.488223i	0.870688	−	0.491836i	$-0.163674\pi$
$283$	53818.4	+	39101.3i	0.671982	+	0.488223i	−0.198706	+	0.980059i	$0.563674\pi$
$284$		0			0
$285$	80991.1	−	46760.2i	0.997120	−	0.575688i
$286$		0			0
$287$	23427.2	−	17020.9i	0.284418	−	0.206642i
$288$		0			0
$289$	−45218.7	−	50220.4i	−0.541405	−	0.601291i
$290$		0			0
$291$	17012.1	+	80035.8i	0.200897	+	0.945145i
$292$		0			0
$293$	119363.	+	53144.0i	1.39039	+	0.619040i	0.959072	−	0.283161i	$-0.0913832\pi$
$293$	119363.	+	53144.0i	1.39039	+	0.619040i	0.431315	+	0.902202i	$0.358050\pi$
$294$		0			0
$295$	−42829.4	−	131815.i	−0.492151	−	1.51468i
$296$		0			0
$297$	−71414.8	−	15179.7i	−0.809609	−	0.172088i
$298$		0			0
$299$	−14643.3	+	6519.62i	−0.163794	+	0.0729256i
$300$		0			0
$301$	−86158.9	+	9055.66i	−0.950971	+	0.0999510i
$302$		0			0
$303$	38013.9	+	3995.42i	0.414054	+	0.0435189i
$304$		0			0
$305$	−146610.	−	84645.5i	−1.57603	−	0.909922i
$306$		0			0
$307$	106579.	−	118368.i	1.13082	−	1.25590i	0.167991	−	0.985788i	$-0.446272\pi$
$307$	106579.	−	118368.i	1.13082	−	1.25590i	0.962828	−	0.270114i	$-0.0870614\pi$
$308$		0			0
$309$		−	64511.5i		−	0.675648i
$310$		0			0
$311$	−98854.5			−1.02206			−0.511029	−	0.859563i	$-0.670736\pi$
$311$	−98854.5			−1.02206			−0.511029	+	0.859563i	$0.670736\pi$
$312$		0			0
$313$	58959.1	+	53087.0i	0.601814	+	0.541876i	0.912731	−	0.408562i	$-0.133969\pi$
$313$	58959.1	+	53087.0i	0.601814	+	0.541876i	−0.310917	+	0.950437i	$0.600636\pi$
$314$		0			0
$315$	41064.6	−	71126.0i	0.413854	−	0.716816i
$316$		0			0
$317$	−11229.6	+	106842.i	−0.111749	+	1.06322i	0.784639	+	0.619953i	$0.212849\pi$
$317$	−11229.6	+	106842.i	−0.111749	+	1.06322i	−0.896388	+	0.443270i	$0.853818\pi$
$318$		0			0
$319$	−3913.16	−	37231.3i	−0.0384545	−	0.365870i
$320$		0			0
$321$	21858.2	+	49094.2i	0.212131	+	0.476453i
$322$		0			0
$323$	28602.9	−	134566.i	0.274161	−	1.28982i
$324$		0			0
$325$	−148593.	+	48280.9i	−1.40680	+	0.457097i
$326$		0			0
$327$	−20143.0	+	45242.0i	−0.188378	+	0.423103i
$328$		0			0
$329$	50901.1	−	10819.4i	0.470257	−	0.0999562i
$330$		0			0
$331$	−136426.	+	122839.i	−1.24521	+	1.12119i	−0.257269	+	0.966340i	$0.582823\pi$
$331$	−136426.	+	122839.i	−1.24521	+	1.12119i	−0.987938	+	0.154850i	$0.950511\pi$
$332$		0			0
$333$	−56464.9	−	77717.2i	−0.509202	−	0.700856i
$334$		0			0
$335$	−92688.1	−	160540.i	−0.825913	−	1.43052i
$336$		0			0
$337$	−12895.2	+	17748.7i	−0.113545	+	0.156282i	−0.862007	−	0.506896i	$-0.830793\pi$
$337$	−12895.2	+	17748.7i	−0.113545	+	0.156282i	0.748462	+	0.663178i	$0.230793\pi$
$338$		0			0
$339$	−9044.84	−	2938.85i	−0.0787048	−	0.0255727i
$340$		0			0
$341$	96225.9	−	19426.4i	0.827529	−	0.167065i
$342$		0			0
$343$	37325.2	−	114875.i	0.317259	−	0.976423i
$344$		0			0
$345$	−39492.3	−	28692.8i	−0.331798	−	0.241065i
$346$		0			0
$347$	−63826.8	+	36850.4i	−0.530083	+	0.306044i	−0.741050	−	0.671449i	$-0.765672\pi$
$347$	−63826.8	+	36850.4i	−0.530083	+	0.306044i	0.210967	+	0.977493i	$0.432339\pi$
$348$		0			0
$349$	−22989.1	+	16702.5i	−0.188743	+	0.137130i	−0.678144	−	0.734929i	$-0.737215\pi$
$349$	−22989.1	+	16702.5i	−0.188743	+	0.137130i	0.489401	+	0.872059i	$0.337215\pi$
$350$		0			0
$351$	41496.6	+	46086.7i	0.336821	+	0.374077i
$352$		0			0
$353$	−10182.2	−	47903.5i	−0.0817133	−	0.384431i	0.918219	−	0.396073i	$-0.129627\pi$
$353$	−10182.2	−	47903.5i	−0.0817133	−	0.384431i	−0.999932	+	0.0116424i	$0.996294\pi$
$354$		0			0
$355$	108030.	+	48098.2i	0.857214	+	0.381656i
$356$		0			0
$357$	20582.7	+	63346.9i	0.161497	+	0.497038i
$358$		0			0
$359$	146807.	+	31204.8i	1.13909	+	0.242121i	0.738577	−	0.674169i	$-0.235498\pi$
$359$	146807.	+	31204.8i	1.13909	+	0.242121i	0.400514	+	0.916291i	$0.368832\pi$
$360$		0			0
$361$	−4626.65	+	2059.92i	−0.0355019	+	0.0158065i
$362$		0			0
$363$	−22443.5	+	2358.91i	−0.170325	+	0.0179018i
$364$		0			0
$365$	466178.	+	48997.3i	3.49918	+	0.367778i
$366$		0			0
$367$	123871.	+	71517.2i	0.919684	+	0.530980i	0.883534	−	0.468366i	$-0.155157\pi$
$367$	123871.	+	71517.2i	0.919684	+	0.530980i	0.0361500	+	0.999346i	$0.488491\pi$
$368$		0			0
$369$	31678.4	−	35182.4i	0.232654	−	0.258388i
$370$		0			0
$371$		−	3309.48i		−	0.0240443i
$372$		0			0
$373$	75383.5			0.541825			0.270912	−	0.962604i	$-0.412675\pi$
$373$	75383.5			0.541825			0.270912	+	0.962604i	$0.412675\pi$
$374$		0			0
$375$	−230867.	−	207874.i	−1.64172	−	1.47821i
$376$		0			0
$377$	−15899.4	+	27538.6i	−0.111866	+	0.193758i
$378$		0			0
$379$	−26682.5	+	253867.i	−0.185758	+	1.76737i	0.363383	+	0.931640i	$0.381622\pi$
$379$	−26682.5	+	253867.i	−0.185758	+	1.76737i	−0.549141	+	0.835730i	$0.685045\pi$
$380$		0			0
$381$	−13169.2	−	125297.i	−0.0907214	−	0.863156i
$382$		0			0
$383$	55432.6	+	124504.i	0.377892	+	0.848759i	0.997937	+	0.0641932i	$0.0204474\pi$
$383$	55432.6	+	124504.i	0.377892	+	0.848759i	−0.620046	+	0.784566i	$0.712886\pi$
$384$		0			0
$385$	−33406.7	+	157166.i	−0.225378	+	1.06032i
$386$		0			0
$387$	−134704.	+	43768.1i	−0.899414	+	0.292237i
$388$		0			0
$389$	−103242.	+	231885.i	−0.682272	+	1.53241i	0.156355	+	0.987701i	$0.450026\pi$
$389$	−103242.	+	231885.i	−0.682272	+	1.53241i	−0.838626	+	0.544707i	$0.816641\pi$
$390$		0			0
$391$	−70239.8	+	14929.9i	−0.459441	+	0.0976573i
$392$		0			0
$393$	−128176.	+	115410.i	−0.829892	+	0.747239i
$394$		0			0
$395$	15251.7	+	20992.2i	0.0977519	+	0.134544i
$396$		0			0
$397$	−37971.1	−	65768.0i	−0.240920	−	0.417286i	0.720057	−	0.693915i	$-0.244116\pi$
$397$	−37971.1	−	65768.0i	−0.240920	−	0.417286i	−0.960977	+	0.276630i	$0.910782\pi$
$398$		0			0
$399$	−35645.7	+	49062.1i	−0.223904	+	0.308177i
$400$		0			0
$401$	−259730.	−	84391.5i	−1.61523	−	0.524819i	−0.644418	−	0.764673i	$-0.722900\pi$
$401$	−259730.	−	84391.5i	−1.61523	−	0.524819i	−0.970809	+	0.239854i	$0.922900\pi$
$402$		0			0
$403$	−75824.3	−	34693.2i	−0.466873	−	0.213616i
$404$		0			0
$405$	6005.82	−	18484.0i	0.0366153	−	0.112690i
$406$		0			0
$407$	152046.	+	110468.i	0.917879	+	0.666878i
$408$		0			0
$409$	42437.0	−	24501.0i	0.253687	−	0.146466i	−0.367764	−	0.929919i	$-0.619877\pi$
$409$	42437.0	−	24501.0i	0.253687	−	0.146466i	0.621451	+	0.783453i	$0.286543\pi$
$410$		0			0
$411$	−48312.6	+	35101.1i	−0.286007	+	0.207796i
$412$		0			0
$413$	60138.5	+	66790.6i	0.352576	+	0.391575i
$414$		0			0
$415$	73670.4	+	346592.i	0.427757	+	2.01244i
$416$		0			0
$417$	43169.3	+	19220.2i	0.248258	+	0.110531i
$418$		0			0
$419$	−35066.5	−	107924.i	−0.199740	−	0.614736i	−0.999888	−	0.0149343i	$-0.995246\pi$
$419$	−35066.5	−	107924.i	−0.199740	−	0.614736i	0.800149	−	0.599802i	$-0.204754\pi$
$420$		0			0
$421$	23177.5	+	4926.54i	0.130769	+	0.0277957i	0.272831	−	0.962062i	$-0.412040\pi$
$421$	23177.5	+	4926.54i	0.130769	+	0.0277957i	−0.142062	+	0.989858i	$0.545373\pi$
$422$		0			0
$423$	77721.7	−	34603.9i	0.434372	−	0.193395i
$424$		0			0
$425$	−696109.	+	73164.1i	−3.85389	+	0.405060i
$426$		0			0
$427$	109177.	+	11474.9i	0.598789	+	0.0629353i
$428$		0			0
$429$	−41183.8	−	23777.5i	−0.223775	−	0.129197i
$430$		0			0
$431$	33025.1	−	36678.1i	0.177783	−	0.197448i	−0.647667	−	0.761924i	$-0.724255\pi$
$431$	33025.1	−	36678.1i	0.177783	−	0.197448i	0.825449	+	0.564476i	$0.190922\pi$
$432$		0			0
$433$		−	220601.i		−	1.17661i	−0.808640	−	0.588304i	$-0.799796\pi$
$433$		−	220601.i		−	1.17661i	0.808640	−	0.588304i	$-0.200204\pi$
$434$		0			0
$435$	−96840.5			−0.511774
$436$		0			0
$437$	−48587.2	−	43748.1i	−0.254424	−	0.229085i
$438$		0			0
$439$	129327.	−	224001.i	0.671057	−	1.16230i	−0.306548	−	0.951855i	$-0.599174\pi$
$439$	129327.	−	224001.i	0.671057	−	1.16230i	0.977605	−	0.210450i	$-0.0674928\pi$
$440$		0			0
$441$	7537.36	−	71713.2i	0.0387563	−	0.368741i
$442$		0			0
$443$	27506.3	+	261705.i	0.140160	+	1.33354i	0.807979	+	0.589211i	$0.200561\pi$
$443$	27506.3	+	261705.i	0.140160	+	1.33354i	−0.667819	+	0.744324i	$0.732772\pi$
$444$		0			0
$445$	142871.	+	320894.i	0.721481	+	1.62047i
$446$		0			0
$447$	−35893.0	+	168863.i	−0.179637	+	0.845124i
$448$		0			0
$449$	−134778.	+	43792.1i	−0.668540	+	0.217222i	−0.623571	−	0.781767i	$-0.714319\pi$
$449$	−134778.	+	43792.1i	−0.668540	+	0.217222i	−0.0449688	+	0.998988i	$0.514319\pi$
$450$		0			0
$451$	−37672.3	+	84613.5i	−0.185212	+	0.415993i
$452$		0			0
$453$	220027.	−	46768.3i	1.07221	−	0.227905i
$454$		0			0
$455$	101425.	−	91323.7i	0.489918	−	0.441124i
$456$		0			0
$457$	−45559.5	−	62707.3i	−0.218146	−	0.300252i	0.685893	−	0.727702i	$-0.259412\pi$
$457$	−45559.5	−	62707.3i	−0.218146	−	0.300252i	−0.904039	+	0.427451i	$0.859412\pi$
$458$		0			0
$459$	138913.	+	240604.i	0.659351	+	1.14203i
$460$		0			0
$461$	177484.	−	244286.i	0.835135	−	1.14947i	−0.151810	−	0.988410i	$-0.548510\pi$
$461$	177484.	−	244286.i	0.835135	−	1.14947i	0.986945	−	0.161056i	$-0.0514898\pi$
$462$		0			0
$463$	338797.	+	110082.i	1.58044	+	0.513515i	0.962169	−	0.272452i	$-0.0878347\pi$
$463$	338797.	+	110082.i	1.58044	+	0.513515i	0.618268	+	0.785968i	$0.287835\pi$
$464$		0			0
$465$	−23958.1	−	252807.i	−0.110802	−	1.16918i
$466$		0			0
$467$	10832.9	−	33340.3i	0.0496720	−	0.152875i	−0.923144	−	0.384455i	$-0.874390\pi$
$467$	10832.9	−	33340.3i	0.0496720	−	0.152875i	0.972816	+	0.231580i	$0.0743895\pi$
$468$		0			0
$469$	97250.8	+	70656.9i	0.442128	+	0.321224i
$470$		0			0
$471$	−70503.7	+	40705.3i	−0.317812	+	0.183489i
$472$		0			0
$473$	224176.	−	162874.i	1.00200	−	0.727995i
$474$		0			0
$475$	−426425.	−	473593.i	−1.88997	−	2.09903i
$476$		0			0
$477$	−1124.94	−	5292.41i	−0.00494415	−	0.0232604i
$478$		0			0
$479$	−271354.	−	120815.i	−1.18267	−	0.526561i	−0.281308	−	0.959617i	$-0.590768\pi$
$479$	−271354.	−	120815.i	−1.18267	−	0.526561i	−0.901367	+	0.433057i	$0.857435\pi$
$480$		0			0
$481$	−49330.7	−	151824.i	−0.213219	−	0.656222i
$482$		0			0
$483$	30962.8	+	6581.35i	0.132723	+	0.0282112i
$484$		0			0
$485$	686173.	−	305504.i	2.91709	−	1.29877i
$486$		0			0
$487$	−243962.	+	25641.5i	−1.02864	+	0.108115i	−0.603787	−	0.797146i	$-0.706342\pi$
$487$	−243962.	+	25641.5i	−1.02864	+	0.108115i	−0.424857	+	0.905261i	$0.639676\pi$
$488$		0			0
$489$	244939.	+	25744.1i	1.02433	+	0.107661i
$490$		0			0
$491$	−4644.64	−	2681.58i	−0.0192659	−	0.0111232i	0.490336	−	0.871533i	$-0.336874\pi$
$491$	−4644.64	−	2681.58i	−0.0192659	−	0.0111232i	−0.509602	+	0.860410i	$0.670207\pi$
$492$		0			0
$493$	−95321.9	+	105866.i	−0.392192	+	0.435573i
$494$		0			0
$495$			262690.i			1.07210i
$496$		0			0
$497$	−76682.7			−0.310445
$498$		0			0
$499$	90511.8	+	81497.2i	0.363500	+	0.327297i	0.830560	−	0.556929i	$-0.188020\pi$
$499$	90511.8	+	81497.2i	0.363500	+	0.327297i	−0.467060	+	0.884225i	$0.654687\pi$
$500$		0			0
$501$	−87104.4	+	150869.i	−0.347028	+	0.601070i
$502$		0			0
$503$	27097.7	−	257818.i	0.107102	−	1.01901i	−0.800545	−	0.599272i	$-0.795457\pi$
$503$	27097.7	−	257818.i	0.107102	−	1.01901i	0.907647	−	0.419734i	$-0.137877\pi$
$504$		0			0
$505$	−36676.4	−	348952.i	−0.143815	−	1.36831i
$506$		0			0
$507$	−45897.7	−	103088.i	−0.178556	−	0.401044i
$508$		0			0
$509$	−91572.8	+	430816.i	−0.353452	+	1.66286i	0.338535	+	0.940954i	$0.390069\pi$
$509$	−91572.8	+	430816.i	−0.353452	+	1.66286i	−0.691988	+	0.721909i	$0.743265\pi$
$510$		0			0
$511$	−289085.	+	93929.3i	−1.10709	+	0.359716i
$512$		0			0
$513$	−102886.	+	231085.i	−0.390949	+	0.878085i
$514$		0			0
$515$	−579249.	+	123123.i	−2.18399	+	0.464222i
$516$		0			0
$517$	−123692.	+	111373.i	−0.462766	+	0.416676i
$518$		0			0
$519$	−30051.1	−	41361.9i	−0.111565	−	0.153555i
$520$		0			0
$521$	−49778.4	−	86218.7i	−0.183386	−	0.317633i	0.759646	−	0.650337i	$-0.225372\pi$
$521$	−49778.4	−	86218.7i	−0.183386	−	0.317633i	−0.943031	+	0.332704i	$0.892039\pi$
$522$		0			0
$523$	316111.	−	435089.i	1.15567	−	1.59065i	0.429626	−	0.903007i	$-0.358645\pi$
$523$	316111.	−	435089.i	1.15567	−	1.59065i	0.726049	−	0.687643i	$-0.241355\pi$
$524$		0			0
$525$	293445.	+	95346.0i	1.06465	+	0.345927i
$526$		0			0
$527$	−299950.	−	222651.i	−1.08001	−	0.801685i
$528$		0			0
$529$	75929.9	−	233688.i	0.271332	−	0.835074i
$530$		0			0
$531$	118874.	+	86367.4i	0.421599	+	0.306310i
$532$		0			0
$533$	68133.1	−	39336.6i	0.239830	−	0.138466i
$534$		0			0
$535$	399100.	−	289963.i	1.39436	−	1.01306i
$536$		0			0
$537$	−32407.6	−	35992.3i	−0.112382	−	0.124813i
$538$		0			0
$539$	29330.6	+	137990.i	0.100959	+	0.474973i
$540$		0			0
$541$	26481.1	+	11790.1i	0.0904777	+	0.0402833i	0.451476	−	0.892283i	$-0.350897\pi$
$541$	26481.1	+	11790.1i	0.0904777	+	0.0402833i	−0.360999	+	0.932566i	$0.617564\pi$
$542$		0			0
$543$	6189.19	+	19048.4i	0.0209911	+	0.0646039i
$544$		0			0
$545$	444672.	+	94518.0i	1.49709	+	0.318216i
$546$		0			0
$547$	−116778.	+	51992.9i	−0.390289	+	0.173768i	−0.592493	−	0.805576i	$-0.701856\pi$
$547$	−116778.	+	51992.9i	−0.390289	+	0.173768i	0.202204	+	0.979343i	$0.435190\pi$
$548$		0			0
$549$	178492.	−	18760.3i	0.592208	−	0.0622436i
$550$		0			0
$551$	−128993.	−	13557.7i	−0.424876	−	0.0446562i
$552$		0			0
$553$	−14571.8	−	8413.03i	−0.0476500	−	0.0275107i
$554$		0			0
$555$	325305.	−	361288.i	1.05610	−	1.17292i
$556$		0			0
$557$			11581.8i			0.0373307i	0.999826	+	0.0186653i	$0.00594171\pi$
$557$			11581.8i			0.0373307i	−0.999826	+	0.0186653i	$0.994058\pi$
$558$		0			0
$559$	−235369.			−0.753228
$560$		0			0
$561$	−158321.	−	142553.i	−0.503053	−	0.452951i
$562$		0			0
$563$	−86012.2	+	148978.i	−0.271358	+	0.470007i	−0.969210	−	0.246236i	$-0.920806\pi$
$563$	−86012.2	+	148978.i	−0.271358	+	0.470007i	0.697852	+	0.716242i	$0.254140\pi$
$564$		0			0
$565$	−9125.41	+	86822.5i	−0.0285862	+	0.271979i
$566$		0			0
$567$	1317.37	+	12533.9i	0.00409770	+	0.0389870i
$568$		0			0
$569$	−27026.4	−	60702.3i	−0.0834764	−	0.187491i	0.866985	−	0.498335i	$-0.166055\pi$
$569$	−27026.4	−	60702.3i	−0.0834764	−	0.187491i	−0.950461	+	0.310844i	$0.899388\pi$
$570$		0			0
$571$	53258.2	−	250560.i	0.163348	−	0.768493i	−0.817841	−	0.575444i	$-0.804829\pi$
$571$	53258.2	−	250560.i	0.163348	−	0.768493i	0.981189	−	0.193048i	$-0.0618375\pi$
$572$		0			0
$573$	312449.	−	101521.i	0.951633	−	0.309204i
$574$		0			0
$575$	−135299.	+	303886.i	−0.409221	+	0.919125i
$576$		0			0
$577$	374687.	−	79642.1i	1.12542	−	0.239216i	0.392650	−	0.919688i	$-0.371558\pi$
$577$	374687.	−	79642.1i	1.12542	−	0.239216i	0.732775	+	0.680471i	$0.238225\pi$
$578$		0			0
$579$	−206938.	+	186328.i	−0.617281	+	0.555802i
$580$		0			0
$581$	−135056.	−	185889.i	−0.400094	−	0.550682i
$582$		0			0
$583$	5292.69	+	9167.20i	0.0155718	+	0.0269712i
$584$		0			0
$585$	131154.	−	180518.i	0.383238	−	0.527483i
$586$		0			0
$587$	−102770.	−	33392.0i	−0.298257	−	0.0969095i	0.156066	−	0.987747i	$-0.450119\pi$
$587$	−102770.	−	33392.0i	−0.298257	−	0.0969095i	−0.454323	+	0.890837i	$0.650119\pi$
$588$		0			0
$589$	3480.44	−	340095.i	0.0100324	−	0.980325i
$590$		0			0
$591$	−39677.4	+	122114.i	−0.113597	+	0.349617i
$592$		0			0
$593$	37537.9	+	27272.9i	0.106748	+	0.0775572i	0.639879	−	0.768476i	$-0.278985\pi$
$593$	37537.9	+	27272.9i	0.106748	+	0.0775572i	−0.533131	+	0.846033i	$0.678985\pi$
$594$		0			0
$595$	529509.	−	305712.i	1.49568	−	0.863533i
$596$		0			0
$597$	11115.5	−	8075.91i	0.0311876	−	0.0226591i
$598$		0			0
$599$	6343.37	+	7045.02i	0.0176793	+	0.0196349i	0.751920	−	0.659255i	$-0.229128\pi$
$599$	6343.37	+	7045.02i	0.0176793	+	0.0196349i	−0.734240	+	0.678890i	$0.762461\pi$
$600$		0			0
$601$	44957.0	+	211506.i	0.124465	+	0.585564i	0.995534	+	0.0944025i	$0.0300941\pi$
$601$	44957.0	+	211506.i	0.124465	+	0.585564i	−0.871069	+	0.491161i	$0.836573\pi$
$602$		0			0
$603$	179537.	+	79935.2i	0.493765	+	0.219838i
$604$		0			0
$605$	64015.1	+	197018.i	0.174893	+	0.538264i
$606$		0			0
$607$	−486187.	−	103342.i	−1.31955	−	0.280479i	−0.506282	−	0.862368i	$-0.668980\pi$
$607$	−486187.	−	103342.i	−1.31955	−	0.280479i	−0.813268	+	0.581889i	$0.802314\pi$
$608$		0			0
$609$	57367.9	−	25541.8i	0.154680	−	0.0688680i
$610$		0			0
$611$	140605.	−	14778.2i	0.376633	−	0.0395858i
$612$		0			0
$613$	112551.	+	11829.6i	0.299523	+	0.0314811i	0.253098	−	0.967441i	$-0.418551\pi$
$613$	112551.	+	11829.6i	0.299523	+	0.0314811i	0.0464248	+	0.998922i	$0.485217\pi$
$614$		0			0
$615$	207493.	+	119796.i	0.548597	+	0.316732i
$616$		0			0
$617$	46118.9	−	51220.2i	0.121146	−	0.134546i	−0.679521	−	0.733656i	$-0.737812\pi$
$617$	46118.9	−	51220.2i	0.121146	−	0.134546i	0.800667	+	0.599110i	$0.204479\pi$
$618$		0			0
$619$			86578.9i			0.225959i	0.993597	+	0.112980i	$0.0360395\pi$
$619$			86578.9i			0.225959i	−0.993597	+	0.112980i	$0.963960\pi$
$620$		0			0
$621$	132035.			0.342378
$622$		0			0
$623$	−169273.	−	152414.i	−0.436125	−	0.392688i
$624$		0			0
$625$	−863171.	+	1.49506e6i	−2.20972	+	3.82734i
$626$		0			0
$627$	20275.4	−	192907.i	0.0515744	−	0.490698i
$628$		0			0
$629$	−74754.8	−	711245.i	−0.188946	−	1.79770i
$630$		0			0
$631$	−109185.	−	245233.i	−0.274223	−	0.615914i	0.722963	−	0.690887i	$-0.242780\pi$
$631$	−109185.	−	245233.i	−0.274223	−	0.615914i	−0.997186	+	0.0749725i	$0.976113\pi$
$632$		0			0
$633$	−21978.4	+	103400.i	−0.0548515	+	0.258056i
$634$		0			0
$635$	−1.09990e6	+	357381.i	−2.72777	+	0.886306i
$636$		0			0
$637$	48738.6	−	109469.i	0.120114	−	0.269781i
$638$		0			0
$639$	−122628.	+	26065.5i	−0.300324	+	0.0638357i
$640$		0			0
$641$	−491641.	+	442675.i	−1.19655	+	1.07738i	−0.201352	+	0.979519i	$0.564534\pi$
$641$	−491641.	+	442675.i	−1.19655	+	1.07738i	−0.995200	+	0.0978616i	$0.968800\pi$
$642$		0			0
$643$	123504.	+	169989.i	0.298718	+	0.411149i	0.931821	−	0.362918i	$-0.118219\pi$
$643$	123504.	+	169989.i	0.298718	+	0.411149i	−0.633104	+	0.774067i	$0.718219\pi$
$644$		0			0
$645$	−358398.	−	620763.i	−0.861482	−	1.49213i
$646$		0			0
$647$	−270631.	+	372492.i	−0.646501	+	0.889832i	−0.998941	−	0.0460018i	$-0.985352\pi$
$647$	−270631.	+	372492.i	−0.646501	+	0.889832i	0.352440	+	0.935834i	$0.385352\pi$
$648$		0			0
$649$	−273397.	−	88832.2i	−0.649090	−	0.210902i
$650$		0			0
$651$	80870.8	+	143443.i	0.190823	+	0.338467i
$652$		0			0
$653$	208151.	−	640621.i	0.488148	−	1.50236i	−0.339222	−	0.940706i	$-0.610164\pi$
$653$	208151.	−	640621.i	0.488148	−	1.50236i	0.827370	−	0.561657i	$-0.189836\pi$
$654$		0			0
$655$	1.28090e6	+	930627.i	2.98560	+	2.16917i
$656$		0			0
$657$	−430367.	+	248472.i	−0.997030	+	0.575635i
$658$		0			0
$659$	−549985.	+	399587.i	−1.26643	+	0.920112i	−0.999054	−	0.0434815i	$-0.986155\pi$
$659$	−549985.	+	399587.i	−1.26643	+	0.920112i	−0.267371	+	0.963594i	$0.586155\pi$
$660$		0			0
$661$	−294392.	−	326956.i	−0.673788	−	0.748317i	0.305188	−	0.952292i	$-0.401281\pi$
$661$	−294392.	−	326956.i	−0.673788	−	0.748317i	−0.978976	+	0.203975i	$0.934614\pi$
$662$		0			0
$663$	37623.8	+	177006.i	0.0855924	+	0.402681i
$664$		0			0
$665$	508560.	+	226425.i	1.15000	+	0.512014i
$666$		0			0
$667$	20920.9	+	64388.0i	0.0470250	+	0.144728i
$668$		0			0
$669$	−25891.9	−	5503.48i	−0.0578510	−	0.0122966i
$670$		0			0
$671$	−320769.	+	142815.i	−0.712438	+	0.317198i
$672$		0			0
$673$	52562.7	−	5524.56i	0.116051	−	0.0121974i	−0.0463251	−	0.998926i	$-0.514751\pi$
$673$	52562.7	−	5524.56i	0.116051	−	0.0121974i	0.162376	+	0.986729i	$0.448084\pi$
$674$		0			0
$675$	1.27993e6	+	134526.i	2.80918	+	0.295257i
$676$		0			0
$677$	−402887.	−	232607.i	−0.879035	−	0.507511i	−0.00869462	−	0.999962i	$-0.502768\pi$
$677$	−402887.	−	232607.i	−0.879035	−	0.507511i	−0.870340	+	0.492451i	$0.836101\pi$
$678$		0			0
$679$	−325909.	+	361958.i	−0.706898	+	0.785089i
$680$		0			0
$681$			160887.i			0.346918i
$682$		0			0
$683$	712616.			1.52762			0.763808	−	0.645443i	$-0.223327\pi$
$683$	712616.			1.52762			0.763808	+	0.645443i	$0.223327\pi$
$684$		0			0
$685$	407380.	+	366806.i	0.868197	+	0.781728i
$686$		0			0
$687$	−116562.	+	201891.i	−0.246969	+	0.427763i
$688$		0			0
$689$	939.850	−	8942.08i	0.00197979	−	0.0188365i
$690$		0			0
$691$	37114.1	+	353117.i	0.0777289	+	0.739541i	0.962089	+	0.272736i	$0.0879285\pi$
$691$	37114.1	+	353117.i	0.0777289	+	0.739541i	−0.884360	+	0.466805i	$0.845405\pi$
$692$		0			0
$693$	−69285.0	−	155617.i	−0.144269	−	0.324033i
$694$		0			0
$695$	90187.7	−	424300.i	0.186714	−	0.878422i
$696$		0			0
$697$	335200.	−	108913.i	0.689983	−	0.224189i
$698$		0			0
$699$	94468.9	−	212181.i	0.193346	−	0.434261i
$700$		0			0
$701$	−674701.	+	143412.i	−1.37301	+	0.291843i	−0.834609	−	0.550843i	$-0.814306\pi$
$701$	−674701.	+	143412.i	−1.37301	+	0.291843i	−0.538405	+	0.842686i	$0.680973\pi$
$702$		0			0
$703$	483891.	−	435697.i	0.979121	−	0.881605i
$704$		0			0
$705$	253076.	+	348329.i	0.509182	+	0.700829i
$706$		0			0
$707$	113764.	+	197044.i	0.227596	+	0.394208i
$708$		0			0
$709$	−265359.	+	365236.i	−0.527888	+	0.726576i	−0.986807	−	0.161903i	$-0.948237\pi$
$709$	−265359.	+	365236.i	−0.527888	+	0.726576i	0.458919	+	0.888478i	$0.348237\pi$
$710$		0			0
$711$	−26162.4	−	8500.69i	−0.0517534	−	0.0168157i
$712$		0			0
$713$	−162912.	+	70544.5i	−0.320460	+	0.138766i
$714$		0			0
$715$	−134897.	+	415170.i	−0.263870	+	0.812107i
$716$		0			0
$717$	−197953.	−	143821.i	−0.385055	−	0.279759i
$718$		0			0
$719$	460462.	−	265848.i	0.890709	−	0.514251i	0.0165350	−	0.999863i	$-0.494737\pi$
$719$	460462.	−	265848.i	0.890709	−	0.514251i	0.874175	+	0.485612i	$0.161403\pi$
$720$		0			0
$721$	310671.	−	225715.i	0.597626	−	0.434201i
$722$		0			0
$723$	221148.	+	245610.i	0.423065	+	0.469861i
$724$		0			0
$725$	137202.	+	645486.i	0.261027	+	1.22804i
$726$		0			0
$727$	31890.7	+	14198.7i	0.0603387	+	0.0268645i	0.436684	−	0.899615i	$-0.356153\pi$
$727$	31890.7	+	14198.7i	0.0603387	+	0.0268645i	−0.376345	+	0.926479i	$0.622819\pi$
$728$		0			0
$729$	−89617.1	−	275813.i	−0.168630	−	0.518991i
$730$		0			0
$731$	−1.03139e6	−	219230.i	−1.93014	−	0.410265i
$732$		0			0
$733$	−139498.	+	62108.5i	−0.259633	+	0.115596i	−0.532426	−	0.846477i	$-0.678719\pi$
$733$	−139498.	+	62108.5i	−0.259633	+	0.115596i	0.272793	+	0.962073i	$0.412053\pi$
$734$		0			0
$735$	362927.	−	38145.2i	0.671807	−	0.0706098i
$736$		0			0
$737$	−382381.	−	40189.9i	−0.703982	−	0.0739915i
$738$		0			0
$739$	−329829.	−	190427.i	−0.603948	−	0.348689i	0.166645	−	0.986017i	$-0.446707\pi$
$739$	−329829.	−	190427.i	−0.603948	−	0.348689i	−0.770593	+	0.637327i	$0.780040\pi$
$740$		0			0
$741$	−110246.	+	122441.i	−0.200783	+	0.222992i
$742$		0			0
$743$			250299.i			0.453400i	0.973965	+	0.226700i	$0.0727937\pi$
$743$			250299.i			0.453400i	−0.973965	+	0.226700i	$0.927206\pi$
$744$		0			0
$745$	1.58473e6			2.85524
$746$		0			0
$747$	−279164.	−	251360.i	−0.500285	−	0.450459i
$748$		0			0
$749$	−159947.	+	277036.i	−0.285110	+	0.493824i
$750$		0			0
$751$	103852.	−	988090.i	0.184135	−	1.75193i	−0.378846	−	0.925460i	$-0.623679\pi$
$751$	103852.	−	988090.i	0.184135	−	1.75193i	0.562981	−	0.826470i	$-0.309654\pi$
$752$		0			0
$753$	−43218.2	−	411193.i	−0.0762213	−	0.725197i
$754$		0			0
$755$	−839864.	−	1.88637e6i	−1.47338	−	3.30927i
$756$		0			0
$757$	−149998.	+	705683.i	−0.261754	+	1.23145i	0.629158	+	0.777277i	$0.283400\pi$
$757$	−149998.	+	705683.i	−0.261754	+	1.23145i	−0.890912	+	0.454176i	$0.849934\pi$
$758$		0			0
$759$	−96291.7	+	31287.1i	−0.167150	+	0.0543102i
$760$		0			0
$761$	−261057.	+	586345.i	−0.450782	+	1.01247i	0.535063	+	0.844812i	$0.320288\pi$
$761$	−261057.	+	586345.i	−0.450782	+	1.01247i	−0.985845	+	0.167661i	$0.946379\pi$
$762$		0			0
$763$	−288351.	+	61290.9i	−0.495305	+	0.105280i
$764$		0			0
$765$	742858.	−	668872.i	1.26935	−	1.14293i
$766$		0			0
$767$	143524.	+	197544.i	0.243969	+	0.335794i
$768$		0			0
$769$	−452955.	−	784540.i	−0.765953	−	1.32667i	−0.939741	−	0.341886i	$-0.888934\pi$
$769$	−452955.	−	784540.i	−0.765953	−	1.32667i	0.173789	−	0.984783i	$-0.444399\pi$
$770$		0			0
$771$	140475.	−	193347.i	0.236315	−	0.325259i
$772$		0			0
$773$	−122013.	−	39644.3i	−0.204195	−	0.0663471i	0.205133	−	0.978734i	$-0.434237\pi$
$773$	−122013.	−	39644.3i	−0.204195	−	0.0663471i	−0.409329	+	0.912387i	$0.634237\pi$
$774$		0			0
$775$	−1.65113e6	+	517865.i	−2.74902	+	0.862210i
$776$		0			0
$777$	−97419.1	+	299825.i	−0.161362	+	0.496622i
$778$		0			0
$779$	259612.	+	188619.i	0.427808	+	0.310821i
$780$		0			0
$781$	212410.	−	122635.i	0.348235	−	0.201054i
$782$		0			0
$783$	211909.	−	153961.i	0.345641	−	0.251123i
$784$		0			0
$785$	500053.	+	555365.i	0.811478	+	0.901237i
$786$		0			0
$787$	208038.	+	978740.i	0.335886	+	1.58022i	0.744570	+	0.667544i	$0.232655\pi$
$787$	208038.	+	978740.i	0.335886	+	1.58022i	−0.408684	+	0.912676i	$0.634012\pi$
$788$		0			0
$789$	−165704.	−	73776.2i	−0.266182	−	0.118512i
$790$		0			0
$791$	−17493.7	−	53840.1i	−0.0279595	−	0.0860504i
$792$		0			0
$793$	291732.	+	62009.6i	0.463914	+	0.0986080i
$794$		0			0
$795$	25015.0	−	11137.4i	0.0395791	−	0.0176217i
$796$		0			0
$797$	92447.5	−	9716.63i	0.145539	−	0.0152967i	−0.0314789	−	0.999504i	$-0.510022\pi$
$797$	92447.5	−	9716.63i	0.145539	−	0.0152967i	0.177018	+	0.984208i	$0.443355\pi$
$798$		0			0
$799$	629900.	+	66205.1i	0.986683	+	0.103705i
$800$		0			0
$801$	−322503.	−	186197.i	−0.502653	−	0.290207i
$802$		0			0
$803$	650543.	−	722501.i	1.00889	−	1.12049i
$804$		0			0
$805$		−	290576.i		−	0.448403i
$806$		0			0
$807$	−467635.			−0.718059
$808$		0			0
$809$	51986.8	+	46809.1i	0.0794320	+	0.0715209i	0.707890	−	0.706322i	$-0.249647\pi$
$809$	51986.8	+	46809.1i	0.0794320	+	0.0715209i	−0.628458	+	0.777843i	$0.716314\pi$
$810$		0			0
$811$	121503.	−	210450.i	0.184734	−	0.319968i	−0.758753	−	0.651378i	$-0.774191\pi$
$811$	121503.	−	210450.i	0.184734	−	0.319968i	0.943487	+	0.331410i	$0.107524\pi$
$812$		0			0
$813$	61928.1	−	589207.i	0.0936929	−	0.891428i
$814$		0			0
$815$	−236320.	−	2.24844e6i	−0.355783	−	3.38505i
$816$		0			0
$817$	−390483.	−	877040.i	−0.585003	−	1.31394i
$818$		0			0
$819$	−30083.1	+	141530.i	−0.0448492	+	0.210999i
$820$		0			0
$821$	183567.	−	59644.4i	0.272338	−	0.0884879i	−0.169664	−	0.985502i	$-0.554268\pi$
$821$	183567.	−	59644.4i	0.272338	−	0.0884879i	0.442002	+	0.897014i	$0.354268\pi$
$822$		0			0
$823$	−195158.	+	438333.i	−0.288129	+	0.647149i	−0.998386	−	0.0567940i	$-0.981912\pi$
$823$	−195158.	+	438333.i	−0.288129	+	0.647149i	0.710257	+	0.703943i	$0.248579\pi$
$824$		0			0
$825$	−965319.	+	205185.i	−1.41828	+	0.301465i
$826$		0			0
$827$	440708.	−	396815.i	0.644377	−	0.580199i	−0.280786	−	0.959770i	$-0.590595\pi$
$827$	440708.	−	396815.i	0.644377	−	0.580199i	0.925163	+	0.379571i	$0.123928\pi$
$828$		0			0
$829$	691610.	+	951919.i	1.00636	+	1.38513i	0.921343	+	0.388751i	$0.127094\pi$
$829$	691610.	+	951919.i	1.00636	+	1.38513i	0.0850141	+	0.996380i	$0.472906\pi$
$830$		0			0
$831$	−116564.	−	201895.i	−0.168797	−	0.292364i
$832$		0			0
$833$	315536.	−	434298.i	0.454735	−	0.625889i
$834$		0			0
$835$	1.52090e6	+	494170.i	2.18136	+	0.708766i
$836$		0			0
$837$	454348.	+	515108.i	0.648541	+	0.735271i
$838$		0			0
$839$	186416.	−	573731.i	0.264826	−	0.815050i	−0.726908	−	0.686735i	$-0.759043\pi$
$839$	186416.	−	573731.i	0.264826	−	0.815050i	0.991733	−	0.128315i	$-0.0409568\pi$
$840$		0			0
$841$	−463545.	−	336785.i	−0.655390	−	0.476169i
$842$		0			0
$843$	48395.8	−	27941.3i	0.0681009	−	0.0393180i
$844$		0			0
$845$	−838028.	+	608863.i	−1.17367	+	0.852720i
$846$		0			0
$847$	−89886.1	−	99828.6i	−0.125293	−	0.139152i
$848$		0			0
$849$	−74206.7	−	349115.i	−0.102950	−	0.484343i
$850$		0			0
$851$	−310493.	−	138240.i	−0.428739	−	0.190887i
$852$		0			0
$853$	−139320.	−	428783.i	−0.191476	−	0.589304i	−1.00000		0.000839465i	$-0.999733\pi$
$853$	−139320.	−	428783.i	−0.191476	−	0.589304i	0.808523	−	0.588464i	$-0.200267\pi$
$854$		0			0
$855$	890237.	+	189226.i	1.21779	+	0.258850i
$856$		0			0
$857$	854231.	−	380328.i	1.16309	−	0.517841i	0.267866	−	0.963456i	$-0.413682\pi$
$857$	854231.	−	380328.i	1.16309	−	0.517841i	0.895225	+	0.445615i	$0.147015\pi$
$858$		0			0
$859$	502041.	−	52766.7i	0.680383	−	0.0715111i	0.241968	−	0.970284i	$-0.422207\pi$
$859$	502041.	−	52766.7i	0.680383	−	0.0715111i	0.438414	+	0.898773i	$0.355540\pi$
$860$		0			0
$861$	−154514.	−	16240.1i	−0.208431	−	0.0219070i
$862$		0			0
$863$	862575.	+	498008.i	1.15818	+	0.668674i	0.950867	−	0.309601i	$-0.100195\pi$
$863$	862575.	+	498008.i	1.15818	+	0.668674i	0.207311	+	0.978275i	$0.433529\pi$
$864$		0			0
$865$	−314034.	+	348770.i	−0.419706	+	0.466130i
$866$		0			0
$867$			362575.i			0.482348i
$868$		0			0
$869$	53818.2			0.0712671
$870$		0			0
$871$	242702.	+	218530.i	0.319917	+	0.288054i
$872$		0			0
$873$	−398148.	+	689613.i	−0.522416	+	0.904850i
$874$		0			0
$875$	193299.	−	1.83911e6i	0.252472	−	2.40211i
$876$		0			0
$877$	−55932.4	−	532162.i	−0.0727218	−	0.691902i	−0.968773	−	0.247950i	$-0.920243\pi$
$877$	−55932.4	−	532162.i	−0.0727218	−	0.691902i	0.896051	−	0.443951i	$-0.146424\pi$
$878$		0			0
$879$	−285132.	−	640416.i	−0.369035	−	0.828867i
$880$		0			0
$881$	−284858.	+	1.34015e6i	−0.367009	+	1.72664i	0.276334	+	0.961062i	$0.410881\pi$
$881$	−284858.	+	1.34015e6i	−0.367009	+	1.72664i	−0.643342	+	0.765579i	$0.722453\pi$
$882$		0			0
$883$	679311.	−	220722.i	0.871259	−	0.283089i	0.160936	−	0.986965i	$-0.448549\pi$
$883$	679311.	−	220722.i	0.871259	−	0.283089i	0.710323	+	0.703876i	$0.248549\pi$
$884$		0			0
$885$	−302458.	+	679331.i	−0.386170	+	0.867351i
$886$		0			0
$887$	−537090.	+	114162.i	−0.682653	+	0.145102i	−0.536169	−	0.844111i	$-0.680129\pi$
$887$	−537090.	+	114162.i	−0.682653	+	0.145102i	−0.146484	+	0.989213i	$0.546796\pi$
$888$		0			0
$889$	557319.	−	501812.i	0.705181	−	0.634947i
$890$		0			0
$891$	−23693.9	−	32611.9i	−0.0298457	−	0.0410790i
$892$		0			0
$893$	288334.	+	499409.i	0.361571	+	0.626259i
$894$		0			0
$895$	−261323.	+	359681.i	−0.326236	+	0.449026i
$896$		0			0
$897$	81791.2	+	26575.6i	0.101653	+	0.0330292i
$898$		0			0
$899$	−179206.	+	303185.i	−0.221734	+	0.375136i
$900$		0			0
$901$	12447.3	−	38309.0i	0.0153330	−	0.0471901i
$902$		0			0
$903$	376041.	+	273210.i	0.461168	+	0.335058i
$904$		0			0
$905$	159223.	−	91927.5i	0.194406	−	0.112240i
$906$		0			0
$907$	−482322.	+	350427.i	−0.586303	+	0.425974i	−0.840991	−	0.541049i	$-0.818027\pi$
$907$	−482322.	+	350427.i	−0.586303	+	0.425974i	0.254688	+	0.967023i	$0.418027\pi$
$908$		0			0
$909$	248905.	+	276437.i	0.301235	+	0.334556i
$910$		0			0
$911$	98740.7	+	464538.i	0.118976	+	0.559738i	0.996743	+	0.0806495i	$0.0256994\pi$
$911$	98740.7	+	464538.i	0.118976	+	0.559738i	−0.877767	+	0.479089i	$0.840967\pi$
$912$		0			0
$913$	671386.	+	298920.i	0.805436	+	0.358603i
$914$		0			0
$915$	280678.	+	863837.i	0.335247	+	1.03179i
$916$		0			0
$917$	−1.00425e6	−	213461.i	−1.19428	−	0.253851i
$918$		0			0
$919$	−280353.	+	124821.i	−0.331951	+	0.147794i	−0.565943	−	0.824444i	$-0.691488\pi$
$919$	−280353.	+	124821.i	−0.331951	+	0.147794i	0.233992	+	0.972239i	$0.424821\pi$
$920$		0			0
$921$	−849895.	+	89327.5i	−1.00195	+	0.105309i
$922$		0			0
$923$	−207193.	−	21776.9i	−0.243205	−	0.0255619i
$924$		0			0
$925$	−2.86904e6	−	1.65644e6i	−3.35315	−	1.93594i
$926$		0			0
$927$	420090.	−	466558.i	0.488859	−	0.542933i
$928$		0			0
$929$		−	191680.i		−	0.222098i	−0.993815	−	0.111049i	$-0.964579\pi$
$929$		−	191680.i		−	0.222098i	0.993815	−	0.111049i	$-0.0354211\pi$
$930$		0			0
$931$	488763.			0.563896
$932$		0			0
$933$	394150.	+	354894.i	0.452791	+	0.407695i
$934$		0			0
$935$	−977821.	+	1.69364e6i	−1.11850	+	1.93730i
$936$		0			0
$937$	93705.0	−	891543.i	0.106729	−	1.01546i	−0.801787	−	0.597611i	$-0.796117\pi$
$937$	93705.0	−	891543.i	0.106729	−	1.01546i	0.908516	−	0.417851i	$-0.137216\pi$
$938$		0			0
$939$	−44494.2	−	423334.i	−0.0504629	−	0.480122i
$940$		0			0
$941$	256962.	+	577145.i	0.290194	+	0.651787i	0.998536	−	0.0540821i	$-0.0172233\pi$
$941$	256962.	+	577145.i	0.290194	+	0.651787i	−0.708342	+	0.705869i	$0.750557\pi$
$942$		0			0
$943$	34825.2	−	163840.i	0.0391624	−	0.184245i
$944$		0			0
$945$	−1.06920e6	+	347404.i	−1.19728	+	0.389020i
$946$		0			0
$947$	−372196.	+	835965.i	−0.415022	+	0.932155i	0.578197	+	0.815897i	$0.303757\pi$
$947$	−372196.	+	835965.i	−0.415022	+	0.932155i	−0.993219	+	0.116258i	$0.962910\pi$
$948$		0			0
$949$	−807769.	+	171697.i	−0.896923	+	0.190647i
$950$		0			0
$951$	428345.	−	385684.i	0.473623	−	0.426452i
$952$		0			0
$953$	−226168.	−	311294.i	−0.249026	−	0.342756i	0.666144	−	0.745824i	$-0.267944\pi$
$953$	−226168.	−	311294.i	−0.249026	−	0.342756i	−0.915170	+	0.403068i	$0.867944\pi$
$954$		0			0
$955$	−1.50788e6	−	2.61172e6i	−1.65333	−	2.86365i
$956$		0			0
$957$	−118060.	+	162496.i	−0.128908	+	0.177427i
$958$		0			0
$959$	−338076.	−	109847.i	−0.367601	−	0.119441i
$960$		0			0
$961$	−835814.	−	392817.i	−0.905030	−	0.425347i
$962$		0			0
$963$	−161613.	+	497395.i	−0.174271	+	0.536351i
$964$		0			0
$965$	2.06799e6	+	1.50248e6i	2.22072	+	1.61344i
$966$		0			0
$967$	918886.	−	530519.i	0.982672	−	0.567346i	0.0795965	−	0.996827i	$-0.474637\pi$
$967$	918886.	−	530519.i	0.982672	−	0.567346i	0.903076	+	0.429481i	$0.141303\pi$
$968$		0			0
$969$	−597146.	+	433852.i	−0.635964	+	0.462055i
$970$		0			0
$971$	711256.	+	789930.i	0.754375	+	0.837819i	0.991011	−	0.133780i	$-0.0427115\pi$
$971$	711256.	+	789930.i	0.754375	+	0.837819i	−0.236636	+	0.971598i	$0.576045\pi$
$972$		0			0
$973$	58482.9	+	275140.i	0.0617737	+	0.290622i
$974$		0			0
$975$	765799.	+	340956.i	0.805574	+	0.358665i
$976$		0			0
$977$	148714.	+	457695.i	0.155798	+	0.479498i	0.998241	−	0.0592883i	$-0.0188831\pi$
$977$	148714.	+	457695.i	0.155798	+	0.479498i	−0.842443	+	0.538786i	$0.818883\pi$
$978$		0			0
$979$	712630.	+	151474.i	0.743530	+	0.158042i
$980$		0			0
$981$	−440288.	+	196029.i	−0.457508	+	0.203696i
$982$		0			0
$983$	1.11492e6	−	117182.i	1.15381	−	0.121271i	0.491762	−	0.870730i	$-0.336353\pi$
$983$	1.11492e6	−	117182.i	1.15381	−	0.121271i	0.662051	+	0.749459i	$0.269686\pi$
$984$		0			0
$985$	1.17219e6	+	123202.i	1.20816	+	0.126983i
$986$		0			0
$987$	−241794.	−	139600.i	−0.248205	−	0.143301i
$988$		0			0
$989$	−335311.	+	372401.i	−0.342811	+	0.380731i
$990$		0			0
$991$		−	86920.0i		−	0.0885059i	−0.999020	−	0.0442530i	$-0.985909\pi$
$991$		−	86920.0i		−	0.0885059i	0.999020	−	0.0442530i	$-0.0140908\pi$
$992$		0			0
$993$	984953.			0.998889
$994$		0			0
$995$	−93728.1	−	84393.1i	−0.0946724	−	0.0852434i
$996$		0			0
$997$	−428343.	+	741912.i	−0.430925	+	0.746383i	−0.996953	−	0.0780022i	$-0.975146\pi$
$997$	−428343.	+	741912.i	−0.430925	+	0.746383i	0.566028	+	0.824386i	$0.308479\pi$
$998$		0			0
$999$	−137451.	+	1.30776e6i	−0.137727	+	1.31038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.o.a.17.4	✓	88
31.11	odd	30	inner	124.5.o.a.73.4	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.o.a.17.4	✓	88	1.1	even	1	trivial
124.5.o.a.73.4	yes	88	31.11	odd	30	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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.o (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.98717 - 3.59007i) q^{3} +(-24.6255 + 42.6526i) q^{5} +(3.33835 - 31.7622i) q^{7} +(-5.45784 - 51.9279i) q^{9} +O(q^{10})\)	\(q+(-3.98717 - 3.59007i) q^{3} +(-24.6255 + 42.6526i) q^{5} +(3.33835 - 31.7622i) q^{7} +(-5.45784 - 51.9279i) q^{9} +(41.5486 + 93.3197i) q^{11} +(18.0401 - 84.8722i) q^{13} +(251.312 - 81.6561i) q^{15} +(158.105 - 355.109i) q^{17} +(346.182 - 73.5833i) q^{19} +(-127.339 + 114.657i) q^{21} +(-108.584 - 149.453i) q^{23} +(-900.331 - 1559.42i) q^{25} +(-420.107 + 578.227i) q^{27} +(-348.543 - 113.249i) q^{29} +(209.412 - 937.906i) q^{31} +(169.362 - 521.244i) q^{33} +(1272.53 + 924.550i) q^{35} +(1593.32 - 919.906i) q^{37} +(-376.626 + 273.635i) q^{39} +(606.704 + 673.814i) q^{41} +(-563.985 - 2653.34i) q^{43} +(2349.26 + 1045.96i) q^{45} +(503.510 + 1549.65i) q^{47} +(1350.84 + 287.129i) q^{49} +(-1905.25 + 848.274i) q^{51} +(103.057 - 10.8317i) q^{53} +(-5003.48 - 525.887i) q^{55} +(-1644.46 - 949.427i) q^{57} +(-1883.02 + 2091.31i) q^{59} +3437.31i q^{61} -1667.57 q^{63} +(3175.77 + 2859.48i) q^{65} +(-1881.95 + 3259.64i) q^{67} +(-103.603 + 985.720i) q^{69} +(-250.978 - 2387.89i) q^{71} +(-3871.11 - 8694.65i) q^{73} +(-2008.64 + 9449.91i) q^{75} +(3102.75 - 1008.14i) q^{77} +(214.289 - 481.300i) q^{79} +(-385.993 + 82.0453i) q^{81} +(5346.54 - 4814.04i) q^{83} +(11252.9 + 15488.3i) q^{85} +(983.132 + 1702.83i) q^{87} +(4192.13 - 5769.98i) q^{89} +(-2635.51 - 856.328i) q^{91} +(-4202.10 + 2987.79i) q^{93} +(-5386.39 + 16577.6i) q^{95} +(-12338.0 - 8964.11i) q^{97} +(4619.13 - 2666.85i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \) 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) \) 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9 - 42 * q^11 + 6 * q^13 + 665 * q^15 - 585 * q^17 - 153 * q^19 - 402 * q^21 - 1365 * q^23 - 5933 * q^25 - 9225 * q^27 - 1140 * q^29 + 117 * q^31 + 5151 * q^33 + 2898 * q^35 + 6594 * q^37 + 3173 * q^39 - 9393 * q^41 - 5322 * q^43 + 2010 * q^45 - 5112 * q^47 - 5210 * q^49 - 1829 * q^51 + 7395 * q^53 + 10585 * q^55 + 40485 * q^57 + 5625 * q^59 - 14954 * q^63 - 17094 * q^65 + 8909 * q^67 - 35370 * q^69 - 11811 * q^71 - 22105 * q^73 + 79377 * q^75 + 71490 * q^77 + 219 * q^79 - 5422 * q^81 + 10545 * q^83 - 53630 * q^85 + 13732 * q^87 - 40305 * q^89 + 42760 * q^91 - 1028 * q^93 + 62319 * q^95 + 35201 * q^97 + 16197 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more