LMFDB - Embedded newform 124.5.o.a.13.1

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			13.1
Character	$\chi$	$=$	124.13
Dual form			124.5.o.a.105.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.03588 - 15.8028i) q^{3} +(11.6814 + 20.2328i) q^{5} +(-44.3877 - 49.2975i) q^{7} +(-146.027 + 162.179i) q^{9} +O(q^{10})$	\(q+(-7.03588 - 15.8028i) q^{3} +(11.6814 + 20.2328i) q^{5} +(-44.3877 - 49.2975i) q^{7} +(-146.027 + 162.179i) q^{9} +(-8.73862 - 41.1120i) q^{11} +(-53.0777 - 5.57869i) q^{13} +(237.547 - 326.956i) q^{15} +(-21.8592 + 102.839i) q^{17} +(42.9106 + 408.267i) q^{19} +(-466.735 + 1048.30i) q^{21} +(169.387 - 55.0371i) q^{23} +(39.5881 - 68.5686i) q^{25} +(2257.73 + 733.580i) q^{27} +(829.026 + 1141.06i) q^{29} +(-431.803 + 858.526i) q^{31} +(-588.202 + 427.354i) q^{33} +(478.917 - 1473.96i) q^{35} +(-2206.77 - 1274.08i) q^{37} +(285.289 + 878.029i) q^{39} +(1127.43 + 501.965i) q^{41} +(-2293.90 + 241.098i) q^{43} +(-4987.15 - 1060.05i) q^{45} +(-3045.14 - 2212.42i) q^{47} +(-209.006 + 1988.56i) q^{49} +(1778.95 - 378.128i) q^{51} +(435.520 + 392.144i) q^{53} +(729.733 - 657.054i) q^{55} +(6149.87 - 3550.63i) q^{57} +(-875.291 + 389.705i) q^{59} +2935.90i q^{61} +14476.8 q^{63} +(-507.151 - 1139.08i) q^{65} +(-3701.69 - 6411.51i) q^{67} +(-2061.53 - 2289.56i) q^{69} +(-969.007 + 1076.19i) q^{71} +(646.656 + 3042.28i) q^{73} +(-1362.12 - 143.164i) q^{75} +(-1638.83 + 2255.66i) q^{77} +(-1984.25 + 9335.16i) q^{79} +(-2444.71 - 23259.8i) q^{81} +(-3537.70 + 7945.80i) q^{83} +(-2336.08 + 759.038i) q^{85} +(12199.0 - 21129.3i) q^{87} +(-11198.0 - 3638.46i) q^{89} +(2080.98 + 2864.22i) q^{91} +(16605.3 + 783.231i) q^{93} +(-7759.14 + 5637.35i) q^{95} +(45.6737 - 140.569i) q^{97} +(7943.58 + 4586.23i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{11}{30}\right)$

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
$3$	−7.03588	−	15.8028i	−0.781764	−	1.75587i	−0.643457	−	0.765482i	$-0.722500\pi$
$3$	−7.03588	−	15.8028i	−0.781764	−	1.75587i	−0.138308	−	0.990389i	$-0.544166\pi$
$4$		0			0
$5$	11.6814	+	20.2328i	0.467257	+	0.809314i	0.999300	−	0.0374038i	$-0.0119088\pi$
$5$	11.6814	+	20.2328i	0.467257	+	0.809314i	−0.532043	+	0.846717i	$0.678575\pi$
$6$		0			0
$7$	−44.3877	−	49.2975i	−0.905872	−	1.00607i	−0.999945	−	0.0105071i	$-0.996655\pi$
$7$	−44.3877	−	49.2975i	−0.905872	−	1.00607i	0.0940732	−	0.995565i	$-0.470011\pi$
$8$		0			0
$9$	−146.027	+	162.179i	−1.80280	+	2.00221i
$10$		0			0
$11$	−8.73862	−	41.1120i	−0.0722200	−	0.339768i	0.927172	−	0.374636i	$-0.122232\pi$
$11$	−8.73862	−	41.1120i	−0.0722200	−	0.339768i	−0.999392	+	0.0348677i	$0.988899\pi$
$12$		0			0
$13$	−53.0777	−	5.57869i	−0.314069	−	0.0330100i	−0.0538173	−	0.998551i	$-0.517139\pi$
$13$	−53.0777	−	5.57869i	−0.314069	−	0.0330100i	−0.260252	+	0.965541i	$0.583806\pi$
$14$		0			0
$15$	237.547	−	326.956i	1.05577	−	1.45314i
$16$		0			0
$17$	−21.8592	+	102.839i	−0.0756373	+	0.355845i	−0.999648	−	0.0265205i	$-0.991557\pi$
$17$	−21.8592	+	102.839i	−0.0756373	+	0.355845i	0.924011	+	0.382366i	$0.124891\pi$
$18$		0			0
$19$	42.9106	+	408.267i	0.118866	+	1.13093i	0.877553	+	0.479479i	$0.159174\pi$
$19$	42.9106	+	408.267i	0.118866	+	1.13093i	−0.758688	+	0.651455i	$0.774159\pi$
$20$		0			0
$21$	−466.735	+	1048.30i	−1.05836	+	2.37711i
$22$		0			0
$23$	169.387	−	55.0371i	0.320202	−	0.104040i	−0.144506	−	0.989504i	$-0.546159\pi$
$23$	169.387	−	55.0371i	0.320202	−	0.104040i	0.464708	+	0.885464i	$0.346159\pi$
$24$		0			0
$25$	39.5881	−	68.5686i	0.0633410	−	0.109710i
$26$		0			0
$27$	2257.73	+	733.580i	3.09702	+	1.00628i
$28$		0			0
$29$	829.026	+	1141.06i	0.985762	+	1.35678i	0.933667	+	0.358143i	$0.116590\pi$
$29$	829.026	+	1141.06i	0.985762	+	1.35678i	0.0520951	+	0.998642i	$0.483410\pi$
$30$		0			0
$31$	−431.803	+	858.526i	−0.449327	+	0.893367i
$31$	−431.803	+	858.526i	−0.449327	+	0.893367i
$32$		0			0
$33$	−588.202	+	427.354i	−0.540131	+	0.392428i
$34$		0			0
$35$	478.917	−	1473.96i	0.390953	−	1.20323i
$36$		0			0
$37$	−2206.77	−	1274.08i	−1.61196	−	0.930666i	−0.988915	−	0.148481i	$-0.952562\pi$
$37$	−2206.77	−	1274.08i	−1.61196	−	0.930666i	−0.623046	−	0.782186i	$-0.714105\pi$
$38$		0			0
$39$	285.289	+	878.029i	0.187567	+	0.577271i
$40$		0			0
$41$	1127.43	+	501.965i	0.670691	+	0.298611i	0.713687	−	0.700464i	$-0.247024\pi$
$41$	1127.43	+	501.965i	0.670691	+	0.298611i	−0.0429964	+	0.999075i	$0.513690\pi$
$42$		0			0
$43$	−2293.90	+	241.098i	−1.24061	+	0.130394i	−0.702011	−	0.712166i	$-0.747714\pi$
$43$	−2293.90	+	241.098i	−1.24061	+	0.130394i	−0.538603	+	0.842559i	$0.681048\pi$
$44$		0			0
$45$	−4987.15	−	1060.05i	−2.46279	−	0.523482i
$46$		0			0
$47$	−3045.14	−	2212.42i	−1.37851	−	1.00155i	−0.997017	−	0.0771792i	$-0.975409\pi$
$47$	−3045.14	−	2212.42i	−1.37851	−	1.00155i	−0.381497	−	0.924370i	$-0.624591\pi$
$48$		0			0
$49$	−209.006	+	1988.56i	−0.0870497	+	0.828223i
$50$		0			0
$51$	1778.95	−	378.128i	0.683949	−	0.145378i
$52$		0			0
$53$	435.520	+	392.144i	0.155044	+	0.139603i	0.743002	−	0.669289i	$-0.233401\pi$
$53$	435.520	+	392.144i	0.155044	+	0.139603i	−0.587958	+	0.808892i	$0.700068\pi$
$54$		0			0
$55$	729.733	−	657.054i	0.241234	−	0.217208i
$56$		0			0
$57$	6149.87	−	3550.63i	1.89285	−	1.09284i
$58$		0			0
$59$	−875.291	+	389.705i	−0.251448	+	0.111952i	−0.528591	−	0.848877i	$-0.677279\pi$
$59$	−875.291	+	389.705i	−0.251448	+	0.111952i	0.277142	+	0.960829i	$0.410613\pi$
$60$		0			0
$61$			2935.90i			0.789008i	0.918894	+	0.394504i	$0.129083\pi$
$61$			2935.90i			0.789008i	−0.918894	+	0.394504i	$0.870917\pi$
$62$		0			0
$63$	14476.8			3.64747
$64$		0			0
$65$	−507.151	−	1139.08i	−0.120036	−	0.269605i
$66$		0			0
$67$	−3701.69	−	6411.51i	−0.824613	−	1.42827i	−0.902214	−	0.431288i	$-0.858059\pi$
$67$	−3701.69	−	6411.51i	−0.824613	−	1.42827i	0.0776011	−	0.996984i	$-0.475274\pi$
$68$		0			0
$69$	−2061.53	−	2289.56i	−0.433003	−	0.480899i
$70$		0			0
$71$	−969.007	+	1076.19i	−0.192225	+	0.213488i	−0.831551	−	0.555448i	$-0.812547\pi$
$71$	−969.007	+	1076.19i	−0.192225	+	0.213488i	0.639326	+	0.768936i	$0.279213\pi$
$72$		0			0
$73$	646.656	+	3042.28i	0.121347	+	0.570891i	0.996245	+	0.0865836i	$0.0275950\pi$
$73$	646.656	+	3042.28i	0.121347	+	0.570891i	−0.874898	+	0.484307i	$0.839072\pi$
$74$		0			0
$75$	−1362.12	−	143.164i	−0.242154	−	0.0254514i
$76$		0			0
$77$	−1638.83	+	2255.66i	−0.276410	+	0.380445i
$78$		0			0
$79$	−1984.25	+	9335.16i	−0.317938	+	1.49578i	0.471454	+	0.881890i	$0.343729\pi$
$79$	−1984.25	+	9335.16i	−0.317938	+	1.49578i	−0.789392	+	0.613889i	$0.789604\pi$
$80$		0			0
$81$	−2444.71	−	23259.8i	−0.372612	−	3.54517i
$82$		0			0
$83$	−3537.70	+	7945.80i	−0.513529	+	1.15340i	0.451741	+	0.892149i	$0.350803\pi$
$83$	−3537.70	+	7945.80i	−0.513529	+	1.15340i	−0.965270	+	0.261255i	$0.915864\pi$
$84$		0			0
$85$	−2336.08	+	759.038i	−0.323333	+	0.105057i
$86$		0			0
$87$	12199.0	−	21129.3i	1.61171	−	2.79156i
$88$		0			0
$89$	−11198.0	−	3638.46i	−1.41371	−	0.459343i	−0.500114	−	0.865959i	$-0.666709\pi$
$89$	−11198.0	−	3638.46i	−1.41371	−	0.459343i	−0.913599	+	0.406616i	$0.866709\pi$
$90$		0			0
$91$	2080.98	+	2864.22i	0.251296	+	0.345879i
$92$		0			0
$93$	16605.3	+	783.231i	1.91991	+	0.0905574i
$94$		0			0
$95$	−7759.14	+	5637.35i	−0.859739	+	0.624637i
$96$		0			0
$97$	45.6737	−	140.569i	0.00485426	−	0.0149399i	−0.948600	−	0.316477i	$-0.897500\pi$
$97$	45.6737	−	140.569i	0.00485426	−	0.0149399i	0.953454	+	0.301538i	$0.0974999\pi$
$98$		0			0
$99$	7943.58	+	4586.23i	0.810486	+	0.467935i
$100$		0			0
$101$	−3683.44	−	11336.5i	−0.361086	−	1.11131i	−0.952396	−	0.304865i	$-0.901389\pi$
$101$	−3683.44	−	11336.5i	−0.361086	−	1.11131i	0.591309	−	0.806445i	$-0.298611\pi$
$102$		0			0
$103$	−1595.51	−	710.368i	−0.150392	−	0.0669590i	0.330160	−	0.943925i	$-0.392897\pi$
$103$	−1595.51	−	710.368i	−0.150392	−	0.0669590i	−0.480553	+	0.876966i	$0.659564\pi$
$104$		0			0
$105$	−26662.3	+	2802.32i	−2.41835	+	0.254179i
$106$		0			0
$107$	−5168.39	−	1098.57i	−0.451427	−	0.0959538i	−0.0234130	−	0.999726i	$-0.507453\pi$
$107$	−5168.39	−	1098.57i	−0.451427	−	0.0959538i	−0.428014	+	0.903772i	$0.640787\pi$
$108$		0			0
$109$	−2675.24	−	1943.68i	−0.225170	−	0.163596i	0.469481	−	0.882943i	$-0.344441\pi$
$109$	−2675.24	−	1943.68i	−0.225170	−	0.163596i	−0.694651	+	0.719347i	$0.744441\pi$
$110$		0			0
$111$	−4607.52	+	43837.6i	−0.373956	+	3.55796i
$112$		0			0
$113$	−16097.2	+	3421.56i	−1.26065	+	0.267958i	−0.789310	−	0.613995i	$-0.789561\pi$
$113$	−16097.2	+	3421.56i	−1.26065	+	0.267958i	−0.471336	+	0.881954i	$0.656228\pi$
$114$		0			0
$115$	3092.24	+	2784.27i	0.233818	+	0.210530i
$116$		0			0
$117$	8655.51	−	7793.45i	0.632296	−	0.569322i
$118$		0			0
$119$	6040.00	−	3487.20i	0.426524	−	0.246254i
$120$		0			0
$121$	11761.4	−	5236.51i	0.803319	−	0.357660i
$122$		0			0
$123$		−	21348.4i		−	1.41109i
$124$		0			0
$125$	16451.6			1.05290
$126$		0			0
$127$	2051.75	+	4608.31i	0.127209	+	0.285716i	0.965911	−	0.258875i	$-0.0833517\pi$
$127$	2051.75	+	4608.31i	0.127209	+	0.285716i	−0.838702	+	0.544591i	$0.816685\pi$
$128$		0			0
$129$	19949.6	+	34553.8i	1.19882	+	2.07642i
$130$		0			0
$131$	−15853.7	−	17607.4i	−0.923824	−	1.02601i	−0.999583	−	0.0288844i	$-0.990805\pi$
$131$	−15853.7	−	17607.4i	−0.923824	−	1.02601i	0.0757587	−	0.997126i	$-0.475862\pi$
$132$		0			0
$133$	18221.9	−	20237.4i	1.03012	−	1.14407i
$134$		0			0
$135$	11531.1	+	54249.5i	0.632708	+	2.97665i
$136$		0			0
$137$	−10626.1	−	1116.85i	−0.566154	−	0.0595052i	−0.182872	−	0.983137i	$-0.558540\pi$
$137$	−10626.1	−	1116.85i	−0.566154	−	0.0595052i	−0.383282	+	0.923631i	$0.625206\pi$
$138$		0			0
$139$	17451.3	−	24019.6i	0.903228	−	1.24319i	−0.0661986	−	0.997806i	$-0.521087\pi$
$139$	17451.3	−	24019.6i	0.903228	−	1.24319i	0.969427	−	0.245381i	$-0.0789129\pi$
$140$		0			0
$141$	−13537.3	+	63688.2i	−0.680919	+	3.20347i
$142$		0			0
$143$	234.475	+	2230.88i	0.0114663	+	0.109095i
$144$		0			0
$145$	−13402.6	+	30102.7i	−0.637460	+	1.43176i
$146$		0			0
$147$	32895.5	−	10688.4i	1.52231	−	0.494627i
$148$		0			0
$149$	−1651.84	+	2861.08i	−0.0744040	+	0.128872i	−0.900827	−	0.434178i	$-0.857039\pi$
$149$	−1651.84	+	2861.08i	−0.0744040	+	0.128872i	0.826423	+	0.563050i	$0.190372\pi$
$150$		0			0
$151$	13081.8	+	4250.54i	0.573739	+	0.186419i	0.581494	−	0.813551i	$-0.302468\pi$
$151$	13081.8	+	4250.54i	0.573739	+	0.186419i	−0.00775460	+	0.999970i	$0.502468\pi$
$152$		0			0
$153$	−13486.4	−	18562.4i	−0.576119	−	0.792960i
$154$		0			0
$155$	−22414.5	+	1292.21i	−0.932966	+	0.0537862i
$156$		0			0
$157$	242.871	−	176.456i	0.00985317	−	0.00715875i	−0.582848	−	0.812581i	$-0.698062\pi$
$157$	242.871	−	176.456i	0.00985317	−	0.00715875i	0.592701	+	0.805423i	$0.298062\pi$
$158$		0			0
$159$	3132.72	−	9641.53i	0.123916	−	0.381375i
$160$		0			0
$161$	−10231.9	−	5907.39i	−0.394734	−	0.227900i
$162$		0			0
$163$	12203.6	+	37558.9i	0.459318	+	1.41363i	0.865990	+	0.500061i	$0.166689\pi$
$163$	12203.6	+	37558.9i	0.459318	+	1.41363i	−0.406672	+	0.913574i	$0.633311\pi$
$164$		0			0
$165$	−15517.6	−	6908.90i	−0.569977	−	0.253770i
$166$		0			0
$167$	34665.7	−	3643.51i	1.24299	−	0.130643i	0.539890	−	0.841736i	$-0.318466\pi$
$167$	34665.7	−	3643.51i	1.24299	−	0.130643i	0.703099	+	0.711092i	$0.251799\pi$
$168$		0			0
$169$	−25150.8	−	5345.96i	−0.880598	−	0.187177i
$170$		0			0
$171$	−72478.5	−	52658.7i	−2.47866	−	1.80085i
$172$		0			0
$173$	1480.72	−	14088.1i	0.0494744	−	0.470718i	−0.941534	−	0.336918i	$-0.890615\pi$
$173$	1480.72	−	14088.1i	0.0494744	−	0.470718i	0.991008	−	0.133800i	$-0.0427179\pi$
$174$		0			0
$175$	−5137.49	+	1092.01i	−0.167755	+	0.0356574i
$176$		0			0
$177$	12316.9	+	11090.2i	0.393146	+	0.353991i
$178$		0			0
$179$	493.354	−	444.218i	0.0153976	−	0.0138640i	−0.661396	−	0.750037i	$-0.730036\pi$
$179$	493.354	−	444.218i	0.0153976	−	0.0138640i	0.676793	+	0.736173i	$0.263369\pi$
$180$		0			0
$181$	−22204.1	+	12819.5i	−0.677759	+	0.391305i	−0.799010	−	0.601317i	$-0.794643\pi$
$181$	−22204.1	+	12819.5i	−0.677759	+	0.391305i	0.121251	+	0.992622i	$0.461309\pi$
$182$		0			0
$183$	46395.5	−	20656.6i	1.38540	−	0.616818i
$184$		0			0
$185$		−	59532.4i		−	1.73944i
$186$		0			0
$187$	4418.95			0.126368
$188$		0			0
$189$	−64051.7	−	143862.i	−1.79311	−	4.02739i
$190$		0			0
$191$	29028.3	+	50278.4i	0.795709	+	1.37821i	0.922388	+	0.386265i	$0.126235\pi$
$191$	29028.3	+	50278.4i	0.795709	+	1.37821i	−0.126678	+	0.991944i	$0.540432\pi$
$192$		0			0
$193$	20159.4	+	22389.3i	0.541207	+	0.601071i	0.950267	−	0.311436i	$-0.100810\pi$
$193$	20159.4	+	22389.3i	0.541207	+	0.601071i	−0.409060	+	0.912508i	$0.634143\pi$
$194$		0			0
$195$	−14432.4	+	16028.8i	−0.379551	+	0.421534i
$196$		0			0
$197$	6223.69	+	29280.2i	0.160367	+	0.754469i	0.982662	+	0.185407i	$0.0593602\pi$
$197$	6223.69	+	29280.2i	0.160367	+	0.754469i	−0.822295	+	0.569062i	$0.807306\pi$
$198$		0			0
$199$	−12107.9	−	1272.59i	−0.305747	−	0.0321353i	−0.0495874	−	0.998770i	$-0.515791\pi$
$199$	−12107.9	−	1272.59i	−0.305747	−	0.0321353i	−0.256160	+	0.966634i	$0.582457\pi$
$200$		0			0
$201$	−75275.5	+	103608.i	−1.86321	+	2.56449i
$202$		0			0
$203$	19452.7	−	91517.8i	0.472050	−	2.22082i
$204$		0			0
$205$	3013.84	+	28674.8i	0.0717155	+	0.682328i
$206$		0			0
$207$	−15809.1	+	35507.9i	−0.368950	+	0.828675i
$208$		0			0
$209$	16409.7	−	5331.83i	0.375671	−	0.122063i
$210$		0			0
$211$	33113.7	−	57354.6i	0.743777	−	1.28826i	−0.206987	−	0.978344i	$-0.566366\pi$
$211$	33113.7	−	57354.6i	0.743777	−	1.28826i	0.950764	−	0.309915i	$-0.100301\pi$
$212$		0			0
$213$	23824.7	+	7741.12i	0.525132	+	0.170626i
$214$		0			0
$215$	−31674.1	−	43595.7i	−0.685216	−	0.943119i
$216$		0			0
$217$	61490.0	−	16821.2i	1.30582	−	0.357221i
$218$		0			0
$219$	43526.8	−	31624.1i	0.907547	−	0.659371i
$220$		0			0
$221$	1733.94	−	5336.53i	0.0355018	−	0.109263i
$222$		0			0
$223$	2980.18	+	1720.61i	0.0599283	+	0.0345996i	0.529665	−	0.848207i	$-0.322318\pi$
$223$	2980.18	+	1720.61i	0.0599283	+	0.0345996i	−0.469736	+	0.882807i	$0.655651\pi$
$224$		0			0
$225$	5339.48	+	16433.2i	0.105471	+	0.324607i
$226$		0			0
$227$	−45396.0	−	20211.6i	−0.880980	−	0.392238i	−0.0841587	−	0.996452i	$-0.526820\pi$
$227$	−45396.0	−	20211.6i	−0.880980	−	0.392238i	−0.796822	+	0.604215i	$0.793487\pi$
$228$		0			0
$229$	73961.0	−	7773.61i	1.41037	−	0.148235i	0.631476	−	0.775396i	$-0.282450\pi$
$229$	73961.0	−	7773.61i	1.41037	−	0.148235i	0.778890	+	0.627160i	$0.215783\pi$
$230$		0			0
$231$	47176.5	+	10027.7i	0.884100	+	0.187921i
$232$		0			0
$233$	40520.2	+	29439.6i	0.746379	+	0.542276i	0.894702	−	0.446663i	$-0.147388\pi$
$233$	40520.2	+	29439.6i	0.746379	+	0.542276i	−0.148323	+	0.988939i	$0.547388\pi$
$234$		0			0
$235$	9192.00	−	87456.1i	0.166446	−	1.58363i
$236$		0			0
$237$	161483.	−	34324.3i	2.87495	−	0.611089i
$238$		0			0
$239$	−20865.2	−	18787.1i	−0.365281	−	0.328900i	0.465967	−	0.884802i	$-0.345706\pi$
$239$	−20865.2	−	18787.1i	−0.365281	−	0.328900i	−0.831248	+	0.555902i	$0.812373\pi$
$240$		0			0
$241$	−33153.8	+	29851.8i	−0.570819	+	0.513968i	−0.903224	−	0.429169i	$-0.858807\pi$
$241$	−33153.8	+	29851.8i	−0.570819	+	0.513968i	0.332405	+	0.943137i	$0.392140\pi$
$242$		0			0
$243$	−183845.	+	106143.i	−3.11344	+	1.79754i
$244$		0			0
$245$	−42675.8	+	19000.5i	−0.710967	+	0.316543i
$246$		0			0
$247$		−	21909.2i		−	0.359115i
$248$		0			0
$249$	150457.			2.42669
$250$		0			0
$251$	−47309.4	−	106259.i	−0.750931	−	1.68662i	−0.726741	−	0.686912i	$-0.758966\pi$
$251$	−47309.4	−	106259.i	−0.750931	−	1.68662i	−0.0241900	−	0.999707i	$-0.507701\pi$
$252$		0			0
$253$	−3742.89	−	6482.88i	−0.0584745	−	0.101281i
$254$		0			0
$255$	28431.3	+	31576.2i	0.437237	+	0.485601i
$256$		0			0
$257$	15486.0	−	17198.9i	0.234462	−	0.260397i	−0.614420	−	0.788979i	$-0.710610\pi$
$257$	15486.0	−	17198.9i	0.234462	−	0.260397i	0.848882	+	0.528583i	$0.177276\pi$
$258$		0			0
$259$	35144.6	+	165342.i	0.523912	+	2.46481i
$260$		0			0
$261$	−306115.	−	32174.0i	−4.49370	−	0.472307i
$262$		0			0
$263$	−55844.1	+	76862.9i	−0.807358	+	1.11123i	0.184368	+	0.982857i	$0.440976\pi$
$263$	−55844.1	+	76862.9i	−0.807358	+	1.11123i	−0.991726	+	0.128376i	$0.959024\pi$
$264$		0			0
$265$	−2846.69	+	13392.6i	−0.0405367	+	0.190710i
$266$		0			0
$267$	21290.0	+	202560.i	0.298643	+	2.84140i
$268$		0			0
$269$	43952.7	−	98719.3i	0.607408	−	1.36426i	−0.303966	−	0.952683i	$-0.598311\pi$
$269$	43952.7	−	98719.3i	0.607408	−	1.36426i	0.911374	−	0.411579i	$-0.135023\pi$
$270$		0			0
$271$	−56200.3	+	18260.6i	−0.765244	+	0.248643i	−0.665528	−	0.746373i	$-0.731794\pi$
$271$	−56200.3	+	18260.6i	−0.765244	+	0.248643i	−0.0997162	+	0.995016i	$0.531794\pi$
$272$		0			0
$273$	30621.4	−	53037.8i	0.410865	−	0.711639i
$274$		0			0
$275$	−3164.94	−	1028.35i	−0.0418504	−	0.0135980i
$276$		0			0
$277$	−58483.5	−	80495.6i	−0.762208	−	1.04909i	−0.997027	−	0.0770502i	$-0.975450\pi$
$277$	−58483.5	−	80495.6i	−0.762208	−	1.04909i	0.234819	−	0.972039i	$-0.424550\pi$
$278$		0			0
$279$	−76180.2	−	195397.i	−0.978664	−	2.51021i
$280$		0			0
$281$	−68006.1	+	49409.3i	−0.861262	+	0.625744i	−0.928228	−	0.372012i	$-0.878668\pi$
$281$	−68006.1	+	49409.3i	−0.861262	+	0.625744i	0.0669658	+	0.997755i	$0.478668\pi$
$282$		0			0
$283$	1734.15	−	5337.15i	0.0216527	−	0.0666403i	−0.939646	−	0.342147i	$-0.888846\pi$
$283$	1734.15	−	5337.15i	0.0216527	−	0.0666403i	0.961299	+	0.275507i	$0.0888458\pi$
$284$		0			0
$285$	143679.	+	82952.9i	1.76890	+	1.02127i
$286$		0			0
$287$	−25298.5	−	77860.7i	−0.307136	−	0.945267i
$288$		0			0
$289$	66202.1	+	29475.1i	0.792641	+	0.352906i
$290$		0			0
$291$	−2542.75	+	267.254i	−0.0300274	+	0.00315600i
$292$		0			0
$293$	−22742.1	−	4833.98i	−0.264908	−	0.0563080i	0.0735426	−	0.997292i	$-0.476570\pi$
$293$	−22742.1	−	4833.98i	−0.264908	−	0.0563080i	−0.338451	+	0.940984i	$0.609903\pi$
$294$		0			0
$295$	−18109.5	−	13157.3i	−0.208095	−	0.151190i
$296$		0			0
$297$	10429.5	−	99230.2i	0.118236	−	1.12494i
$298$		0			0
$299$	−9297.70	+	1976.29i	−0.104000	+	0.0221059i
$300$		0			0
$301$	113706.	+	102382.i	1.25502	+	1.13003i
$302$		0			0
$303$	−153232.	+	137971.i	−1.66903	+	1.50280i
$304$		0			0
$305$	−59401.5	+	34295.5i	−0.638555	+	0.368670i
$306$		0			0
$307$	85173.5	−	37921.7i	0.903708	−	0.402357i	0.0983541	−	0.995151i	$-0.468642\pi$
$307$	85173.5	−	37921.7i	0.903708	−	0.402357i	0.805353	+	0.592795i	$0.201976\pi$
$308$		0			0
$309$			30211.7i			0.316416i
$310$		0			0
$311$	−68982.4			−0.713210			−0.356605	−	0.934255i	$-0.616066\pi$
$311$	−68982.4			−0.713210			−0.356605	+	0.934255i	$0.616066\pi$
$312$		0			0
$313$	43853.6	+	98496.8i	0.447627	+	1.00539i	0.986614	+	0.163073i	$0.0521407\pi$
$313$	43853.6	+	98496.8i	0.447627	+	1.00539i	−0.538987	+	0.842314i	$0.681193\pi$
$314$		0			0
$315$	169110.	+	292907.i	1.70431	+	2.95195i
$316$		0			0
$317$	−47754.2	−	53036.5i	−0.475219	−	0.527784i	0.457103	−	0.889414i	$-0.348887\pi$
$317$	−47754.2	−	53036.5i	−0.475219	−	0.527784i	−0.932322	+	0.361630i	$0.882220\pi$
$318$		0			0
$319$	39666.5	−	44054.2i	0.389801	−	0.432918i
$320$		0			0
$321$	19003.5	+	89404.7i	0.184427	+	0.867661i
$322$		0			0
$323$	−42923.9	−	4511.48i	−0.411428	−	0.0432428i
$324$		0			0
$325$	−2483.77	+	3418.61i	−0.0235150	+	0.0323656i
$326$		0			0
$327$	−11893.0	+	55952.0i	−0.111223	+	0.523263i
$328$		0			0
$329$	26099.7	+	248322.i	0.241126	+	2.29416i
$330$		0			0
$331$	−49609.6	+	111425.i	−0.452804	+	1.01701i	0.532536	+	0.846408i	$0.321239\pi$
$331$	−49609.6	+	111425.i	−0.452804	+	1.01701i	−0.985339	+	0.170606i	$0.945427\pi$
$332$		0			0
$333$	528878.	−	171843.i	4.76943	−	1.54968i
$334$		0			0
$335$	86482.1	−	149791.i	0.770613	−	1.33474i
$336$		0			0
$337$	−144896.	−	47079.5i	−1.27584	−	0.414545i	−0.408726	−	0.912657i	$-0.634027\pi$
$337$	−144896.	−	47079.5i	−1.27584	−	0.414545i	−0.867113	+	0.498112i	$0.834027\pi$
$338$		0			0
$339$	167328.	+	230308.i	1.45603	+	2.00405i
$340$		0			0
$341$	39069.1	+	10249.9i	0.335988	+	0.0881481i
$342$		0			0
$343$	−21546.5	+	15654.4i	−0.183142	+	0.133061i
$344$		0			0
$345$	22242.7	−	68455.9i	0.186874	−	0.575139i
$346$		0			0
$347$	−60185.9	−	34748.4i	−0.499846	−	0.288586i	0.228804	−	0.973473i	$-0.426518\pi$
$347$	−60185.9	−	34748.4i	−0.499846	−	0.288586i	−0.728650	+	0.684886i	$0.759852\pi$
$348$		0			0
$349$	−17047.8	−	52467.6i	−0.139964	−	0.430765i	0.856365	−	0.516371i	$-0.172717\pi$
$349$	−17047.8	−	52467.6i	−0.139964	−	0.430765i	−0.996329	+	0.0856058i	$0.972717\pi$
$350$		0			0
$351$	−115743.	−	51531.9i	−0.939461	−	0.418275i
$352$		0			0
$353$	90835.7	−	9547.22i	0.728966	−	0.0766174i	0.267227	−	0.963633i	$-0.413893\pi$
$353$	90835.7	−	9547.22i	0.728966	−	0.0766174i	0.461739	+	0.887016i	$0.347226\pi$
$354$		0			0
$355$	−33093.8	−	7034.31i	−0.262597	−	0.0558168i
$356$		0			0
$357$	−97604.4	−	70913.7i	−0.765831	−	0.556409i
$358$		0			0
$359$	17561.5	−	167087.i	0.136262	−	1.29644i	−0.686112	−	0.727496i	$-0.740684\pi$
$359$	17561.5	−	167087.i	0.136262	−	1.29644i	0.822374	−	0.568947i	$-0.192649\pi$
$360$		0			0
$361$	−37367.5	+	7942.70i	−0.286734	+	0.0609472i
$362$		0			0
$363$	−165503.	−	149020.i	−1.25601	−	1.13092i
$364$		0			0
$365$	−54000.0	+	48621.9i	−0.405330	+	0.364960i
$366$		0			0
$367$	65497.2	−	37814.8i	0.486285	−	0.280757i	−0.236747	−	0.971571i	$-0.576081\pi$
$367$	65497.2	−	37814.8i	0.486285	−	0.280757i	0.723032	+	0.690815i	$0.242748\pi$
$368$		0			0
$369$	−246043.	+	109546.i	−1.80700	+	0.804530i
$370$		0			0
$371$		−	38876.4i		−	0.282448i
$372$		0			0
$373$	57203.8			0.411156			0.205578	−	0.978641i	$-0.434093\pi$
$373$	57203.8			0.411156			0.205578	+	0.978641i	$0.434093\pi$
$374$		0			0
$375$	−115751.	−	259982.i	−0.823121	−	1.84876i
$376$		0			0
$377$	−37637.2	−	65189.5i	−0.264810	−	0.458664i
$378$		0			0
$379$	−55389.3	−	61516.1i	−0.385610	−	0.428263i	0.518822	−	0.854883i	$-0.326371\pi$
$379$	−55389.3	−	61516.1i	−0.385610	−	0.428263i	−0.904431	+	0.426620i	$0.859704\pi$
$380$		0			0
$381$	58388.5	−	64847.0i	0.402233	−	0.446725i
$382$		0			0
$383$	20820.0	+	97950.4i	0.141933	+	0.667742i	0.990370	+	0.138446i	$0.0442106\pi$
$383$	20820.0	+	97950.4i	0.141933	+	0.667742i	−0.848437	+	0.529296i	$0.822456\pi$
$384$		0			0
$385$	−64782.3	−	6808.90i	−0.437054	−	0.0459362i
$386$		0			0
$387$	295869.	−	407229.i	1.97550	−	2.71905i
$388$		0			0
$389$	−40537.2	+	190713.i	−0.267889	+	1.26032i	0.614168	+	0.789175i	$0.289492\pi$
$389$	−40537.2	+	190713.i	−0.267889	+	1.26032i	−0.882057	+	0.471143i	$0.843842\pi$
$390$		0			0
$391$	1957.32	+	18622.7i	0.0128029	+	0.121812i
$392$		0			0
$393$	−166701.	+	374418.i	−1.07933	+	2.42422i
$394$		0			0
$395$	−212056.	+	68901.1i	−1.35911	+	0.441603i
$396$		0			0
$397$	5850.87	−	10134.0i	0.0371227	−	0.0642984i	−0.846867	−	0.531805i	$-0.821514\pi$
$397$	5850.87	−	10134.0i	0.0371227	−	0.0642984i	0.883990	+	0.467506i	$0.154847\pi$
$398$		0			0
$399$	−448016.	−	145569.i	−2.81415	−	0.914373i
$400$		0			0
$401$	−180371.	−	248260.i	−1.12170	−	1.54389i	−0.802941	−	0.596059i	$-0.796733\pi$
$401$	−180371.	−	248260.i	−1.12170	−	1.54389i	−0.318763	−	0.947834i	$-0.603267\pi$
$402$		0			0
$403$	27708.6	−	43159.7i	0.170610	−	0.265747i
$404$		0			0
$405$	442055.	−	321172.i	2.69505	−	1.95807i
$406$		0			0
$407$	−33095.9	+	101859.i	−0.199795	+	0.614906i
$408$		0			0
$409$	75677.2	+	43692.2i	0.452396	+	0.261191i	0.708841	−	0.705368i	$-0.249218\pi$
$409$	75677.2	+	43692.2i	0.452396	+	0.261191i	−0.256446	+	0.966559i	$0.582552\pi$
$410$		0			0
$411$	57114.9	+	175781.i	0.338116	+	1.04061i
$412$		0			0
$413$	58063.6	+	25851.6i	0.340411	+	0.151561i
$414$		0			0
$415$	−202092.	+	21240.7i	−1.17342	+	0.123331i
$416$		0			0
$417$	−502363.	−	106781.i	−2.88899	−	0.614073i
$418$		0			0
$419$	−24824.3	−	18035.9i	−0.141400	−	0.102733i	0.514837	−	0.857288i	$-0.327853\pi$
$419$	−24824.3	−	18035.9i	−0.141400	−	0.102733i	−0.656236	+	0.754555i	$0.727853\pi$
$420$		0			0
$421$	−25525.8	+	242861.i	−0.144017	+	1.37023i	0.648886	+	0.760886i	$0.275235\pi$
$421$	−25525.8	+	242861.i	−0.144017	+	1.37023i	−0.792903	+	0.609347i	$0.791432\pi$
$422$		0			0
$423$	803480.	−	170785.i	4.49050	−	0.954485i
$424$		0			0
$425$	6186.19	+	5570.07i	0.0342488	+	0.0308377i
$426$		0			0
$427$	144733.	−	130318.i	0.793799	−	0.714740i
$428$		0			0
$429$	33604.5	−	19401.6i	0.182592	−	0.105420i
$430$		0			0
$431$	323680.	−	144112.i	1.74246	−	0.775792i	0.748870	−	0.662717i	$-0.230597\pi$
$431$	323680.	−	144112.i	1.74246	−	0.775792i	0.993586	−	0.113075i	$-0.0360699\pi$
$432$		0			0
$433$			26045.6i			0.138918i	0.997585	+	0.0694591i	$0.0221273\pi$
$433$			26045.6i			0.138918i	−0.997585	+	0.0694591i	$0.977873\pi$
$434$		0			0
$435$	570008.			3.01233
$436$		0			0
$437$	29738.3	+	66793.4i	0.155723	+	0.349760i
$438$		0			0
$439$	32580.4	+	56430.9i	0.169055	+	0.292812i	0.938088	−	0.346398i	$-0.112595\pi$
$439$	32580.4	+	56430.9i	0.169055	+	0.292812i	−0.769033	+	0.639209i	$0.779262\pi$
$440$		0			0
$441$	−291983.	−	324280.i	−1.50134	−	1.66741i
$442$		0			0
$443$	−115981.	+	128810.i	−0.590990	+	0.656361i	−0.962250	−	0.272168i	$-0.912259\pi$
$443$	−115981.	+	128810.i	−0.590990	+	0.656361i	0.371260	+	0.928529i	$0.378926\pi$
$444$		0			0
$445$	−57192.7	−	269070.i	−0.288815	−	1.35877i
$446$		0			0
$447$	56835.3	+	5973.64i	0.284448	+	0.0298967i
$448$		0			0
$449$	−8352.27	+	11495.9i	−0.0414297	+	0.0570231i	−0.829229	−	0.558909i	$-0.811220\pi$
$449$	−8352.27	+	11495.9i	−0.0414297	+	0.0570231i	0.787800	+	0.615932i	$0.211220\pi$
$450$		0			0
$451$	10784.6	−	50737.4i	0.0530212	−	0.249445i
$452$		0			0
$453$	−24871.5	−	236636.i	−0.121201	−	1.15315i
$454$		0			0
$455$	−33642.5	+	75562.4i	−0.162505	+	0.364992i
$456$		0			0
$457$	−136653.	+	44401.1i	−0.654313	+	0.212599i	−0.617315	−	0.786716i	$-0.711780\pi$
$457$	−136653.	+	44401.1i	−0.654313	+	0.212599i	−0.0369980	+	0.999315i	$0.511780\pi$
$458$		0			0
$459$	−124793.	+	216148.i	−0.592331	+	1.02595i
$460$		0			0
$461$	−56686.5	−	18418.6i	−0.266734	−	0.0866671i	0.172597	−	0.984993i	$-0.444784\pi$
$461$	−56686.5	−	18418.6i	−0.266734	−	0.0866671i	−0.439330	+	0.898326i	$0.644784\pi$
$462$		0			0
$463$	−59123.9	−	81377.0i	−0.275804	−	0.379612i	0.648534	−	0.761185i	$-0.275382\pi$
$463$	−59123.9	−	81377.0i	−0.275804	−	0.379612i	−0.924338	+	0.381574i	$0.875382\pi$
$464$		0			0
$465$	178126.	+	345121.i	0.823801	+	1.59612i
$466$		0			0
$467$	−136122.	+	98898.4i	−0.624158	+	0.453477i	−0.854371	−	0.519663i	$-0.826057\pi$
$467$	−136122.	+	98898.4i	−0.624158	+	0.453477i	0.230214	+	0.973140i	$0.426057\pi$
$468$		0			0
$469$	−151762.	+	467077.i	−0.689951	+	2.12345i
$470$		0			0
$471$	−4497.32	−	2596.53i	−0.0202727	−	0.0117045i
$472$		0			0
$473$	29957.5	+	92199.8i	0.133901	+	0.412105i
$474$		0			0
$475$	29693.1	+	13220.2i	0.131604	+	0.0585937i
$476$		0			0
$477$	−127195.	+	13368.7i	−0.559028	+	0.0587562i
$478$		0			0
$479$	−107839.	−	22921.9i	−0.470009	−	0.0999035i	−0.0331825	−	0.999449i	$-0.510564\pi$
$479$	−107839.	−	22921.9i	−0.470009	−	0.0999035i	−0.436826	+	0.899546i	$0.643898\pi$
$480$		0			0
$481$	110023.	+	79936.2i	0.475546	+	0.345504i
$482$		0			0
$483$	−21363.1	+	203257.i	−0.0915737	+	0.871266i
$484$		0			0
$485$	3377.65	−	717.941i	0.0143592	−	0.00305215i
$486$		0			0
$487$	−11025.2	−	9927.17i	−0.0464868	−	0.0418569i	0.645560	−	0.763710i	$-0.276624\pi$
$487$	−11025.2	−	9927.17i	−0.0464868	−	0.0418569i	−0.692047	+	0.721853i	$0.743291\pi$
$488$		0			0
$489$	507674.	−	457112.i	2.12308	−	1.91163i
$490$		0			0
$491$	166865.	−	96339.6i	0.692154	−	0.399615i	−0.112265	−	0.993678i	$-0.535810\pi$
$491$	166865.	−	96339.6i	0.692154	−	0.399615i	0.804418	+	0.594063i	$0.202477\pi$
$492$		0			0
$493$	−135467.	+	60313.9i	−0.557366	+	0.248155i
$494$		0			0
$495$			214295.i			0.874584i
$496$		0			0
$497$	96065.6			0.388915
$498$		0			0
$499$	−39693.0	−	89151.9i	−0.159409	−	0.358038i	0.816129	−	0.577870i	$-0.196116\pi$
$499$	−39693.0	−	89151.9i	−0.159409	−	0.358038i	−0.975538	+	0.219832i	$0.929449\pi$
$500$		0			0
$501$	−301482.	−	522182.i	−1.20112	−	2.08040i
$502$		0			0
$503$	135286.	+	150250.i	0.534707	+	0.593852i	0.948602	−	0.316473i	$-0.102499\pi$
$503$	135286.	+	150250.i	0.534707	+	0.593852i	−0.413895	+	0.910325i	$0.635832\pi$
$504$		0			0
$505$	186341.	−	206953.i	0.730678	−	0.811500i
$506$		0			0
$507$	92476.4	+	435067.i	0.359762	+	1.69255i
$508$		0			0
$509$	192194.	+	20200.4i	0.741831	+	0.0779696i	0.467902	−	0.883780i	$-0.345010\pi$
$509$	192194.	+	20200.4i	0.741831	+	0.0779696i	0.273929	+	0.961750i	$0.411677\pi$
$510$		0			0
$511$	121273.	−	166918.i	0.464433	−	0.639237i
$512$		0			0
$513$	−202616.	+	953234.i	−0.769909	+	3.62214i
$514$		0			0
$515$	−4265.12	−	40579.9i	−0.0160811	−	0.153002i
$516$		0			0
$517$	−64346.8	+	144525.i	−0.240739	+	0.540708i
$518$		0			0
$519$	−233050.	+	75722.7i	−0.865197	+	0.281120i
$520$		0			0
$521$	83462.5	−	144561.i	0.307479	−	0.532570i	−0.670331	−	0.742062i	$-0.733848\pi$
$521$	83462.5	−	144561.i	0.307479	−	0.532570i	0.977810	+	0.209492i	$0.0671812\pi$
$522$		0			0
$523$	−124095.	−	40320.9i	−0.453682	−	0.147410i	0.0732576	−	0.997313i	$-0.476660\pi$
$523$	−124095.	−	40320.9i	−0.453682	−	0.147410i	−0.526939	+	0.849903i	$0.676660\pi$
$524$		0			0
$525$	53403.6	+	73503.7i	0.193755	+	0.266680i
$526$		0			0
$527$	−78851.4	−	63173.0i	−0.283915	−	0.227463i
$528$		0			0
$529$	−200733.	+	145841.i	−0.717312	+	0.521158i
$530$		0			0
$531$	64613.9	−	198861.i	0.229159	−	0.705279i
$532$		0			0
$533$	−57041.1	−	32932.7i	−0.200786	−	0.115924i
$534$		0			0
$535$	−38146.9	−	117404.i	−0.133276	−	0.410181i
$536$		0			0
$537$	−10491.1	−	4670.93i	−0.0363807	−	0.0161978i
$538$		0			0
$539$	83580.2	−	8784.63i	0.287691	−	0.0302375i
$540$		0			0
$541$	−259156.	−	55085.4i	−0.885456	−	0.188210i	−0.257333	−	0.966323i	$-0.582844\pi$
$541$	−259156.	−	55085.4i	−0.885456	−	0.188210i	−0.628124	+	0.778113i	$0.716177\pi$
$542$		0			0
$543$	358810.	+	260691.i	1.21693	+	0.884151i
$544$		0			0
$545$	8075.45	−	76832.8i	0.0271878	−	0.258674i
$546$		0			0
$547$	−195369.	+	41527.0i	−0.652953	+	0.138789i	−0.522465	−	0.852661i	$-0.674988\pi$
$547$	−195369.	+	41527.0i	−0.652953	+	0.138789i	−0.130488	+	0.991450i	$0.541654\pi$
$548$		0			0
$549$	−476141.	−	428719.i	−1.57976	−	1.42242i
$550$		0			0
$551$	−430282.	+	387427.i	−1.41726	+	1.27611i
$552$		0			0
$553$	548277.	−	316548.i	1.79287	−	1.03512i
$554$		0			0
$555$	−940782.	+	418863.i	−3.05424	+	1.35983i
$556$		0			0
$557$			440868.i			1.42101i	0.703691	+	0.710506i	$0.251534\pi$
$557$			440868.i			1.42101i	−0.703691	+	0.710506i	$0.748466\pi$
$558$		0			0
$559$	123100.			0.393943
$560$		0			0
$561$	−31091.2	−	69831.9i	−0.0987897	−	0.221885i
$562$		0			0
$563$	−69343.8	−	120107.i	−0.218771	−	0.378923i	0.735661	−	0.677350i	$-0.236872\pi$
$563$	−69343.8	−	120107.i	−0.218771	−	0.378923i	−0.954433	+	0.298426i	$0.903538\pi$
$564$		0			0
$565$	−257266.	−	285723.i	−0.805908	−	0.895052i
$566$		0			0
$567$	−1.03814e6	+	1.15297e6i	−3.22916	+	3.58634i
$568$		0			0
$569$	79394.6	+	373522.i	0.245226	+	1.15370i	0.912561	+	0.408940i	$0.134101\pi$
$569$	79394.6	+	373522.i	0.245226	+	1.15370i	−0.667336	+	0.744757i	$0.732565\pi$
$570$		0			0
$571$	283234.	+	29769.1i	0.868706	+	0.0913047i	0.528385	−	0.849005i	$-0.322798\pi$
$571$	283234.	+	29769.1i	0.868706	+	0.0913047i	0.340321	+	0.940309i	$0.389464\pi$
$572$		0			0
$573$	590303.	−	812482.i	1.79790	−	2.47460i
$574$		0			0
$575$	2931.89	−	13793.4i	0.00886771	−	0.0417193i
$576$		0			0
$577$	29364.9	+	279388.i	0.0882017	+	0.839183i	0.945775	+	0.324822i	$0.105304\pi$
$577$	29364.9	+	279388.i	0.0882017	+	0.839183i	−0.857574	+	0.514361i	$0.828029\pi$
$578$		0			0
$579$	211976.	−	476105.i	0.632308	−	1.42019i
$580$		0			0
$581$	548739.	−	178296.i	1.62560	−	0.528189i
$582$		0			0
$583$	12316.0	−	21331.9i	0.0362353	−	0.0627613i
$584$		0			0
$585$	258792.	+	84086.8i	0.756205	+	0.245706i
$586$		0			0
$587$	−8341.17	−	11480.6i	−0.0242076	−	0.0333188i	0.796742	−	0.604320i	$-0.206555\pi$
$587$	−8341.17	−	11480.6i	−0.0242076	−	0.0333188i	−0.820949	+	0.571001i	$0.806555\pi$
$588$		0			0
$589$	−369037.	−	139451.i	−1.06375	−	0.401968i
$590$		0			0
$591$	418921.	−	304364.i	1.19938	−	0.871401i
$592$		0			0
$593$	202933.	−	624562.i	0.577088	−	1.77610i	−0.0518669	−	0.998654i	$-0.516517\pi$
$593$	202933.	−	624562.i	0.577088	−	1.77610i	0.628955	−	0.777441i	$-0.283483\pi$
$594$		0			0
$595$	141112.	+	81471.0i	0.398593	+	0.230128i
$596$		0			0
$597$	65079.1	+	200293.i	0.182597	+	0.561975i
$598$		0			0
$599$	242177.	+	107824.i	0.674963	+	0.300513i	0.715447	−	0.698667i	$-0.246223\pi$
$599$	242177.	+	107824.i	0.674963	+	0.300513i	−0.0404838	+	0.999180i	$0.512890\pi$
$600$		0			0
$601$	314180.	−	33021.7i	0.869821	−	0.0914219i	0.340907	−	0.940097i	$-0.389266\pi$
$601$	314180.	−	33021.7i	0.869821	−	0.0914219i	0.528914	+	0.848675i	$0.322599\pi$
$602$		0			0
$603$	1.58036e6	+	335916.i	4.34632	+	0.923838i
$604$		0			0
$605$	243339.	+	176796.i	0.664816	+	0.483017i
$606$		0			0
$607$	−14529.0	+	138235.i	−0.0394330	+	0.375180i	0.956953	+	0.290242i	$0.0937358\pi$
$607$	−14529.0	+	138235.i	−0.0394330	+	0.375180i	−0.996386	+	0.0849377i	$0.972931\pi$
$608$		0			0
$609$	−1.58311e6	+	336500.i	−4.26851	+	0.907300i
$610$		0			0
$611$	149286.	+	134418.i	0.399888	+	0.360060i
$612$		0			0
$613$	−107946.	+	97195.3i	−0.287268	+	0.258657i	−0.800147	−	0.599804i	$-0.795245\pi$
$613$	−107946.	+	97195.3i	−0.287268	+	0.258657i	0.512880	+	0.858461i	$0.328579\pi$
$614$		0			0
$615$	431939.	−	249380.i	1.14201	−	0.659343i
$616$		0			0
$617$	95183.4	−	42378.4i	0.250029	−	0.111320i	−0.277896	−	0.960611i	$-0.589637\pi$
$617$	95183.4	−	42378.4i	0.250029	−	0.111320i	0.527925	+	0.849291i	$0.322970\pi$
$618$		0			0
$619$		−	516913.i		−	1.34908i	−0.738240	−	0.674538i	$-0.764343\pi$
$619$		−	516913.i		−	1.34908i	0.738240	−	0.674538i	$-0.235657\pi$
$620$		0			0
$621$	422804.			1.09637
$622$		0			0
$623$	317688.	+	713538.i	0.818510	+	1.83840i
$624$		0			0
$625$	167435.	+	290007.i	0.428635	+	0.742417i
$626$		0			0
$627$	−199715.	−	221806.i	−0.508013	−	0.564206i
$628$		0			0
$629$	179264.	−	199093.i	0.453098	−	0.503216i
$630$		0			0
$631$	−1889.52	−	8889.47i	−0.00474561	−	0.0223263i	0.975711	−	0.219061i	$-0.0702995\pi$
$631$	−1889.52	−	8889.47i	−0.00474561	−	0.0223263i	−0.980457	+	0.196735i	$0.936966\pi$
$632$		0			0
$633$	−1.13935e6	−	119750.i	−2.84348	−	0.298861i
$634$		0			0
$635$	−69271.7	+	95344.4i	−0.171794	+	0.236455i
$636$		0			0
$637$	22187.1	−	104382.i	0.0546793	−	0.257246i
$638$		0			0
$639$	−33034.8	−	314305.i	−0.0809041	−	0.769751i
$640$		0			0
$641$	220277.	−	494751.i	0.536110	−	1.20412i	−0.419031	−	0.907972i	$-0.637630\pi$
$641$	220277.	−	494751.i	0.536110	−	1.20412i	0.955141	−	0.296151i	$-0.0957031\pi$
$642$		0			0
$643$	−410152.	+	133266.i	−0.992025	+	0.322328i	−0.759674	−	0.650304i	$-0.774642\pi$
$643$	−410152.	+	133266.i	−0.992025	+	0.322328i	−0.232350	+	0.972632i	$0.574642\pi$
$644$		0			0
$645$	−466080.	+	807275.i	−1.12032	+	1.94045i
$646$		0			0
$647$	605828.	+	196846.i	1.44724	+	0.470237i	0.924147	−	0.382037i	$-0.124777\pi$
$647$	605828.	+	196846.i	1.44724	+	0.470237i	0.523095	+	0.852275i	$0.324777\pi$
$648$		0			0
$649$	23670.4	+	32579.5i	0.0561973	+	0.0773490i
$650$		0			0
$651$	−698459.	−	853365.i	−1.64808	−	2.01360i
$652$		0			0
$653$	382907.	−	278198.i	0.897981	−	0.652421i	−0.0399657	−	0.999201i	$-0.512725\pi$
$653$	382907.	−	278198.i	0.897981	−	0.652421i	0.937947	+	0.346780i	$0.112725\pi$
$654$		0			0
$655$	171053.	−	526446.i	0.398701	−	1.22707i
$656$		0			0
$657$	−587823.	−	339380.i	−1.36181	−	0.786240i
$658$		0			0
$659$	−48301.3	−	148656.i	−0.111221	−	0.342304i	0.879919	−	0.475124i	$-0.157597\pi$
$659$	−48301.3	−	148656.i	−0.111221	−	0.342304i	−0.991140	+	0.132820i	$0.957597\pi$
$660$		0			0
$661$	−519232.	−	231177.i	−1.18839	−	0.529105i	−0.285250	−	0.958453i	$-0.592077\pi$
$661$	−519232.	−	231177.i	−1.18839	−	0.529105i	−0.903139	+	0.429348i	$0.858743\pi$
$662$		0			0
$663$	−96532.1	+	10145.9i	−0.219606	+	0.0230815i
$664$		0			0
$665$	622318.	+	132278.i	1.40724	+	0.299119i
$666$		0			0
$667$	203227.	+	147653.i	0.456803	+	0.331887i
$668$		0			0
$669$	6222.30	−	59201.2i	0.0139027	−	0.132275i
$670$		0			0
$671$	120701.	−	25655.7i	0.268080	−	0.0569821i
$672$		0			0
$673$	−276933.	−	249352.i	−0.611427	−	0.550531i	0.304176	−	0.952616i	$-0.401619\pi$
$673$	−276933.	−	249352.i	−0.611427	−	0.550531i	−0.915602	+	0.402085i	$0.868286\pi$
$674$		0			0
$675$	139680.	−	125768.i	0.306567	−	0.276035i
$676$		0			0
$677$	82918.8	−	47873.2i	0.180915	−	0.104452i	−0.406807	−	0.913514i	$-0.633358\pi$
$677$	82918.8	−	47873.2i	0.180915	−	0.104452i	0.587723	+	0.809062i	$0.300025\pi$
$678$		0			0
$679$	−8957.07	+	3987.94i	−0.0194279	+	0.00864987i
$680$		0			0
$681$			859593.i			1.85353i
$682$		0			0
$683$	−759236.			−1.62755			−0.813777	−	0.581178i	$-0.802592\pi$
$683$	−759236.			−1.62755			−0.813777	+	0.581178i	$0.802592\pi$
$684$		0			0
$685$	−101532.	−	228044.i	−0.216381	−	0.486001i
$686$		0			0
$687$	−643226.	−	1.11410e6i	−1.36286	−	2.36054i
$688$		0			0
$689$	−20928.7	−	23243.7i	−0.0440864	−	0.0489629i
$690$		0			0
$691$	−26199.3	+	29097.3i	−0.0548699	+	0.0609392i	−0.769955	−	0.638098i	$-0.779721\pi$
$691$	−26199.3	+	29097.3i	−0.0548699	+	0.0609392i	0.715085	+	0.699038i	$0.246388\pi$
$692$		0			0
$693$	−126508.	−	595171.i	−0.263421	−	1.23930i
$694$		0			0
$695$	689841.	+	72505.2i	1.42817	+	0.150107i
$696$		0			0
$697$	−76266.4	+	104972.i	−0.156989	+	0.216076i
$698$		0			0
$699$	180135.	−	847468.i	0.368675	−	1.73448i
$700$		0			0
$701$	−28914.2	−	275100.i	−0.0588403	−	0.559828i	−0.983738	−	0.179611i	$-0.942516\pi$
$701$	−28914.2	−	275100.i	−0.0588403	−	0.559828i	0.924897	−	0.380217i	$-0.124151\pi$
$702$		0			0
$703$	425472.	−	955625.i	0.860914	−	1.93365i
$704$		0			0
$705$	−1.44673e6	+	470071.i	−2.91078	+	0.945768i
$706$		0			0
$707$	−395361.	+	684785.i	−0.790960	+	1.36998i
$708$		0			0
$709$	696053.	+	226161.i	1.38468	+	0.449910i	0.904205	−	0.427098i	$-0.140464\pi$
$709$	696053.	+	226161.i	1.38468	+	0.449910i	0.480475	+	0.877008i	$0.340464\pi$
$710$		0			0
$711$	−1.22421e6	−	1.68499e6i	−2.42169	−	3.33317i
$712$		0			0
$713$	−25891.0	+	169188.i	−0.0509295	+	0.332806i
$714$		0			0
$715$	−42398.0	+	30804.0i	−0.0829341	+	0.0602552i
$716$		0			0
$717$	−150085.	+	461913.i	−0.291943	+	0.898508i
$718$		0			0
$719$	−52810.2	−	30490.0i	−0.102155	−	0.0589793i	0.448052	−	0.894007i	$-0.352118\pi$
$719$	−52810.2	−	30490.0i	−0.102155	−	0.0589793i	−0.550207	+	0.835028i	$0.685451\pi$
$720$		0			0
$721$	35801.8	+	110186.i	0.0688706	+	0.211962i
$722$		0			0
$723$	705009.	+	313890.i	1.34871	+	0.600484i
$724$		0			0
$725$	111060.	−	11672.9i	0.211292	−	0.0222077i
$726$		0			0
$727$	633351.	+	134623.i	1.19833	+	0.254712i	0.763504	−	0.645803i	$-0.223477\pi$
$727$	633351.	+	134623.i	1.19833	+	0.254712i	0.434824	+	0.900516i	$0.356811\pi$
$728$		0			0
$729$	1.43826e6	+	1.04495e6i	2.70633	+	1.96627i
$730$		0			0
$731$	25348.3	−	241173.i	0.0474367	−	0.451330i
$732$		0			0
$733$	402484.	−	85550.7i	0.749102	−	0.159227i	0.182486	−	0.983208i	$-0.441586\pi$
$733$	402484.	−	85550.7i	0.749102	−	0.159227i	0.566616	+	0.823982i	$0.308252\pi$
$734$		0			0
$735$	600523.	+	540714.i	1.11162	+	1.00090i
$736$		0			0
$737$	−231242.	+	208212.i	−0.425728	+	0.383327i
$738$		0			0
$739$	−353410.	+	204041.i	−0.647128	+	0.373620i	−0.787355	−	0.616500i	$-0.788550\pi$
$739$	−353410.	+	204041.i	−0.647128	+	0.373620i	0.140227	+	0.990119i	$0.455217\pi$
$740$		0			0
$741$	−346228.	+	154151.i	−0.630560	+	0.280743i
$742$		0			0
$743$			529080.i			0.958393i	0.877708	+	0.479196i	$0.159072\pi$
$743$			529080.i			0.958393i	−0.877708	+	0.479196i	$0.840928\pi$
$744$		0			0
$745$	−77183.6			−0.139063
$746$		0			0
$747$	−772045.	−	1.73404e6i	−1.38357	−	3.10755i
$748$		0			0
$749$	175256.	+	303552.i	0.312398	+	0.541090i
$750$		0			0
$751$	113719.	+	126298.i	0.201630	+	0.223932i	0.835476	−	0.549526i	$-0.185192\pi$
$751$	113719.	+	126298.i	0.201630	+	0.223932i	−0.633847	+	0.773459i	$0.718525\pi$
$752$		0			0
$753$	−1.34633e6	+	1.49525e6i	−2.37444	+	2.63708i
$754$		0			0
$755$	66814.0	+	314335.i	0.117212	+	0.551441i
$756$		0			0
$757$	−502891.	−	52855.9i	−0.877570	−	0.0922363i	−0.344980	−	0.938610i	$-0.612114\pi$
$757$	−502891.	−	52855.9i	−0.877570	−	0.0922363i	−0.532590	+	0.846374i	$0.678781\pi$
$758$		0			0
$759$	−76113.4	+	104761.i	−0.132123	+	0.181851i
$760$		0			0
$761$	4190.64	−	19715.4i	0.00723622	−	0.0340437i	−0.974381	−	0.224902i	$-0.927794\pi$
$761$	4190.64	−	19715.4i	0.00723622	−	0.0340437i	0.981618	+	0.190858i	$0.0611271\pi$
$762$		0			0
$763$	22929.4	+	218158.i	0.0393861	+	0.374734i
$764$		0			0
$765$	218030.	−	489703.i	0.372557	−	0.836777i
$766$		0			0
$767$	48632.4	−	15801.6i	0.0826676	−	0.0268603i
$768$		0			0
$769$	−184894.	+	320246.i	−0.312659	+	0.541540i	−0.978937	−	0.204163i	$-0.934553\pi$
$769$	−184894.	+	320246.i	−0.312659	+	0.541540i	0.666278	+	0.745703i	$0.267886\pi$
$770$		0			0
$771$	−380750.	−	123713.i	−0.640517	−	0.208117i
$772$		0			0
$773$	−346920.	−	477495.i	−0.580591	−	0.799116i	0.413169	−	0.910655i	$-0.364422\pi$
$773$	−346920.	−	477495.i	−0.580591	−	0.799116i	−0.993760	+	0.111539i	$0.964422\pi$
$774$		0			0
$775$	41773.7	+	63595.6i	0.0695503	+	0.105882i
$776$		0			0
$777$	2.36560e6	−	1.71871e6i	3.91832	−	2.84683i
$778$		0			0
$779$	−156557.	+	481833.i	−0.257987	+	0.794002i
$780$		0			0
$781$	52712.2	+	30433.4i	0.0864189	+	0.0498940i
$782$		0			0
$783$	1.03466e6	+	3.18435e6i	1.68762	+	5.19395i
$784$		0			0
$785$	6407.29	+	2852.71i	0.0103976	+	0.00462933i
$786$		0			0
$787$	−42724.3	+	4490.51i	−0.0689804	+	0.00725013i	−0.138956	−	0.990299i	$-0.544375\pi$
$787$	−42724.3	+	4490.51i	−0.0689804	+	0.00725013i	0.0699754	+	0.997549i	$0.477708\pi$
$788$		0			0
$789$	1.60756e6	+	341698.i	2.58235	+	0.548895i
$790$		0			0
$791$	883192.	+	641676.i	1.41157	+	1.02556i
$792$		0			0
$793$	16378.5	−	155831.i	0.0260451	−	0.247803i
$794$		0			0
$795$	231670.	−	49243.0i	0.366552	−	0.0779131i
$796$		0			0
$797$	439664.	+	395875.i	0.692156	+	0.623220i	0.938222	−	0.346033i	$-0.112472\pi$
$797$	439664.	+	395875.i	0.692156	+	0.623220i	−0.246067	+	0.969253i	$0.579138\pi$
$798$		0			0
$799$	294088.	−	264798.i	0.460664	−	0.414783i
$800$		0			0
$801$	2.22529e6	−	1.28477e6i	3.46834	−	2.00245i
$802$		0			0
$803$	119423.	−	53170.6i	0.185207	−	0.0824595i
$804$		0			0
$805$		−	276027.i		−	0.425951i
$806$		0			0
$807$	−1.86929e6			−2.87032
$808$		0			0
$809$	−192309.	−	431934.i	−0.293835	−	0.659964i	0.704949	−	0.709258i	$-0.250970\pi$
$809$	−192309.	−	431934.i	−0.293835	−	0.659964i	−0.998784	+	0.0492934i	$0.984303\pi$
$810$		0			0
$811$	−611703.	−	1.05950e6i	−0.930034	−	1.61087i	−0.783259	−	0.621696i	$-0.786444\pi$
$811$	−611703.	−	1.05950e6i	−0.930034	−	1.61087i	−0.146775	−	0.989170i	$-0.546889\pi$
$812$		0			0
$813$	683988.	+	759645.i	1.03483	+	1.14929i
$814$		0			0
$815$	−617367.	+	685655.i	−0.929454	+	1.03226i
$816$		0			0
$817$	−196865.	−	926177.i	−0.294934	−	1.38755i
$818$		0			0
$819$	−768396.	−	80761.7i	−1.14556	−	0.120403i
$820$		0			0
$821$	381523.	−	525122.i	0.566024	−	0.779065i	−0.426053	−	0.904698i	$-0.640096\pi$
$821$	381523.	−	525122.i	0.566024	−	0.779065i	0.992077	+	0.125633i	$0.0400962\pi$
$822$		0			0
$823$	−250433.	+	1.17820e6i	−0.369736	+	1.73947i	0.262716	+	0.964873i	$0.415382\pi$
$823$	−250433.	+	1.17820e6i	−0.369736	+	1.73947i	−0.632453	+	0.774599i	$0.717952\pi$
$824$		0			0
$825$	6017.26	+	57250.4i	0.00884078	+	0.0841144i
$826$		0			0
$827$	−160101.	+	359592.i	−0.234090	+	0.525774i	−0.991948	−	0.126645i	$-0.959579\pi$
$827$	−160101.	+	359592.i	−0.234090	+	0.525774i	0.757858	+	0.652419i	$0.226246\pi$
$828$		0			0
$829$	−649412.	+	211007.i	−0.944955	+	0.307034i	−0.740664	−	0.671876i	$-0.765489\pi$
$829$	−649412.	+	211007.i	−0.944955	+	0.307034i	−0.204291	+	0.978910i	$0.565489\pi$
$830$		0			0
$831$	−860576.	+	1.49056e6i	−1.24620	+	2.15848i
$832$		0			0
$833$	−199934.	−	64962.4i	−0.288135	−	0.0936208i
$834$		0			0
$835$	478664.	+	658824.i	0.686527	+	0.944924i
$836$		0			0
$837$	−1.60469e6	+	1.62156e6i	−2.29056	+	2.31463i
$838$		0			0
$839$	−218619.	+	158836.i	−0.310574	+	0.225645i	−0.732143	−	0.681151i	$-0.761480\pi$
$839$	−218619.	+	158836.i	−0.310574	+	0.225645i	0.421569	+	0.906796i	$0.361480\pi$
$840$		0			0
$841$	−396163.	+	1.21927e6i	−0.560122	+	1.72388i
$842$		0			0
$843$	1.25929e6	+	727052.i	1.77203	+	1.02308i
$844$		0			0
$845$	−185633.	−	571320.i	−0.259981	−	0.800140i
$846$		0			0
$847$	−780208.	−	347371.i	−1.08754	−	0.484202i
$848$		0			0
$849$	−96543.4	+	10147.1i	−0.133939	+	0.0140776i
$850$		0			0
$851$	−443920.	−	94358.2i	−0.612980	−	0.130293i
$852$		0			0
$853$	−267968.	−	194690.i	−0.368286	−	0.267576i	0.388214	−	0.921569i	$-0.373092\pi$
$853$	−267968.	−	194690.i	−0.368286	−	0.267576i	−0.756500	+	0.653994i	$0.773092\pi$
$854$		0			0
$855$	218782.	−	2.08157e6i	0.299282	−	2.84747i
$856$		0			0
$857$	−503037.	+	106924.i	−0.684918	+	0.145584i	−0.537212	−	0.843448i	$-0.680522\pi$
$857$	−503037.	+	106924.i	−0.684918	+	0.145584i	−0.147706	+	0.989031i	$0.547189\pi$
$858$		0			0
$859$	−210581.	−	189608.i	−0.285386	−	0.256963i	0.513987	−	0.857798i	$-0.328168\pi$
$859$	−210581.	−	189608.i	−0.285386	−	0.256963i	−0.799373	+	0.600835i	$0.794835\pi$
$860$		0			0
$861$	−1.05242e6	+	947606.i	−1.41966	+	1.27827i
$862$		0			0
$863$	−680690.	+	392996.i	−0.913961	+	0.527676i	−0.881703	−	0.471804i	$-0.843603\pi$
$863$	−680690.	+	392996.i	−0.913961	+	0.527676i	−0.0322575	+	0.999480i	$0.510270\pi$
$864$		0			0
$865$	302339.	−	134610.i	0.404076	−	0.179906i
$866$		0			0
$867$		−	1.25357e6i		−	1.66766i
$868$		0			0
$869$	401127.			0.531180
$870$		0			0
$871$	160709.	+	360959.i	0.211838	+	0.475797i
$872$		0			0
$873$	16127.8	+	27934.2i	0.0211615	+	0.0366528i
$874$		0			0
$875$	−730248.	−	811022.i	−0.953793	−	1.05929i
$876$		0			0
$877$	638480.	−	709104.i	0.830134	−	0.921958i	−0.167825	−	0.985817i	$-0.553674\pi$
$877$	638480.	−	709104.i	0.830134	−	0.921958i	0.997959	+	0.0638592i	$0.0203409\pi$
$878$		0			0
$879$	83620.0	+	393401.i	0.108226	+	0.509164i
$880$		0			0
$881$	288730.	+	30346.8i	0.371998	+	0.0390986i	0.288683	−	0.957425i	$-0.406783\pi$
$881$	288730.	+	30346.8i	0.371998	+	0.0390986i	0.0833150	+	0.996523i	$0.473449\pi$
$882$		0			0
$883$	146729.	−	201955.i	0.188189	−	0.259020i	−0.704489	−	0.709715i	$-0.748824\pi$
$883$	146729.	−	201955.i	0.188189	−	0.259020i	0.892678	+	0.450695i	$0.148824\pi$
$884$		0			0
$885$	−80506.8	+	378755.i	−0.102789	+	0.483583i
$886$		0			0
$887$	−115175.	−	1.09582e6i	−0.146390	−	1.39281i	−0.783192	−	0.621780i	$-0.786410\pi$
$887$	−115175.	−	1.09582e6i	−0.146390	−	1.39281i	0.636802	−	0.771028i	$-0.280257\pi$
$888$		0			0
$889$	136106.	−	305698.i	0.172216	−	0.386803i
$890$		0			0
$891$	−934895.	+	303766.i	−1.17763	+	0.382634i
$892$		0			0
$893$	772590.	−	1.33817e6i	0.968827	−	1.67806i
$894$		0			0
$895$	14750.9	+	4792.85i	0.0184150	+	0.00598339i
$896$		0			0
$897$	96648.4	+	133025.i	0.120118	+	0.165329i
$898$		0			0
$899$	−1.33760e6	+	219029.i	−1.65504	+	0.271008i
$900$		0			0
$901$	−49847.9	+	36216.6i	−0.0614041	+	0.0446127i
$902$		0			0
$903$	817897.	−	2.51723e6i	1.00305	−	3.08708i
$904$		0			0
$905$	−518751.	−	299501.i	−0.633376	−	0.365680i
$906$		0			0
$907$	196004.	+	603239.i	0.238260	+	0.733288i	0.996672	+	0.0815133i	$0.0259753\pi$
$907$	196004.	+	603239.i	0.238260	+	0.733288i	−0.758412	+	0.651775i	$0.774025\pi$
$908$		0			0
$909$	2.37642e6	+	1.05805e6i	2.87604	+	1.28050i
$910$		0			0
$911$	−308504.	+	32425.1i	−0.371727	+	0.0390701i	−0.288550	−	0.957465i	$-0.593173\pi$
$911$	−308504.	+	32425.1i	−0.371727	+	0.0390701i	−0.0831767	+	0.996535i	$0.526507\pi$
$912$		0			0
$913$	357582.	+	76006.5i	0.428978	+	0.0911820i
$914$		0			0
$915$	959908.	+	697414.i	1.14654	+	0.833007i
$916$		0			0
$917$	−164289.	+	1.56310e6i	−0.195375	+	1.85887i
$918$		0			0
$919$	−641541.	+	136364.i	−0.759615	+	0.161461i	−0.571406	−	0.820668i	$-0.693602\pi$
$919$	−641541.	+	136364.i	−0.759615	+	0.161461i	−0.188210	+	0.982129i	$0.560268\pi$
$920$		0			0
$921$	−1.19854e6	−	1.07917e6i	−1.41297	−	1.27225i
$922$		0			0
$923$	57436.4	−	51715.9i	0.0674192	−	0.0607045i
$924$		0			0
$925$	−174724.	+	100877.i	−0.204206	+	0.117899i
$926$		0			0
$927$	348194.	−	155026.i	0.405193	−	0.180404i
$928$		0			0
$929$			1.29324e6i			1.49846i	0.662308	+	0.749232i	$0.269577\pi$
$929$			1.29324e6i			1.49846i	−0.662308	+	0.749232i	$0.730423\pi$
$930$		0			0
$931$	−820833.			−0.947012
$932$		0			0
$933$	485352.	+	1.09012e6i	0.557562	+	1.25231i
$934$		0			0
$935$	51619.6	+	89407.8i	0.0590462	+	0.102271i
$936$		0			0
$937$	340908.	+	378617.i	0.388292	+	0.431242i	0.905322	−	0.424725i	$-0.139629\pi$
$937$	340908.	+	378617.i	0.388292	+	0.431242i	−0.517030	+	0.855967i	$0.672963\pi$
$938$		0			0
$939$	1.24798e6	−	1.38602e6i	1.41539	−	1.57195i
$940$		0			0
$941$	−170497.	−	802127.i	−0.192548	−	0.905866i	−0.963237	−	0.268654i	$-0.913421\pi$
$941$	−170497.	−	802127.i	−0.192548	−	0.905866i	0.770689	−	0.637212i	$-0.219912\pi$
$942$		0			0
$943$	218599.	+	22975.7i	0.245824	+	0.0258372i
$944$		0			0
$945$	2.16253e6	−	2.97647e6i	2.42158	−	3.33302i
$946$		0			0
$947$	−242773.	+	1.14216e6i	−0.270708	+	1.27358i	0.607123	+	0.794608i	$0.292324\pi$
$947$	−242773.	+	1.14216e6i	−0.270708	+	1.27358i	−0.877830	+	0.478972i	$0.841010\pi$
$948$		0			0
$949$	−17351.1	−	165084.i	−0.0192661	−	0.183305i
$950$		0			0
$951$	−502134.	+	1.12781e6i	−0.555211	+	1.24703i
$952$		0			0
$953$	1.12070e6	−	364138.i	1.23397	−	0.400941i	0.381818	−	0.924238i	$-0.375298\pi$
$953$	1.12070e6	−	364138.i	1.23397	−	0.400941i	0.852150	+	0.523297i	$0.175298\pi$
$954$		0			0
$955$	−678184.	+	1.17465e6i	−0.743602	+	1.28796i
$956$		0			0
$957$	−975270.	−	316884.i	−1.06488	−	0.346001i
$958$		0			0
$959$	416612.	+	573418.i	0.452997	+	0.623496i
$960$		0			0
$961$	−550613.	−	741428.i	−0.596211	−	0.802828i
$962$		0			0
$963$	932889.	−	677783.i	1.00595	−	0.730867i
$964$		0			0
$965$	−217508.	+	669422.i	−0.233572	+	0.718861i
$966$		0			0
$967$	1.06493e6	+	614836.i	1.13885	+	0.657516i	0.946146	−	0.323740i	$-0.104940\pi$
$967$	1.06493e6	+	614836.i	1.13885	+	0.657516i	0.192706	+	0.981257i	$0.438274\pi$
$968$		0			0
$969$	230713.	+	710062.i	0.245711	+	0.756221i
$970$		0			0
$971$	262025.	+	116661.i	0.277910	+	0.123734i	0.540959	−	0.841049i	$-0.318061\pi$
$971$	262025.	+	116661.i	0.277910	+	0.123734i	−0.263049	+	0.964783i	$0.584728\pi$
$972$		0			0
$973$	−1.95873e6	+	205871.i	−2.06894	+	0.217455i
$974$		0			0
$975$	71499.3	+	15197.6i	0.0752129	+	0.0159870i
$976$		0			0
$977$	452350.	+	328652.i	0.473899	+	0.344308i	0.798959	−	0.601386i	$-0.205384\pi$
$977$	452350.	+	328652.i	0.473899	+	0.344308i	−0.325060	+	0.945693i	$0.605384\pi$
$978$		0			0
$979$	−51729.0	+	492168.i	−0.0539720	+	0.513509i
$980$		0			0
$981$	705881.	−	150040.i	0.733489	−	0.155908i
$982$		0			0
$983$	−178236.	−	160484.i	−0.184454	−	0.166083i	0.571731	−	0.820441i	$-0.306272\pi$
$983$	−178236.	−	160484.i	−0.184454	−	0.166083i	−0.756185	+	0.654358i	$0.772939\pi$
$984$		0			0
$985$	−519719.	+	467957.i	−0.535669	+	0.482318i
$986$		0			0
$987$	3.74056e6	−	2.15962e6i	3.83975	−	2.21688i
$988$		0			0
$989$	−375287.	+	167088.i	−0.383681	+	0.170826i
$990$		0			0
$991$			962692.i			0.980257i	0.871650	+	0.490129i	$0.163050\pi$
$991$			962692.i			0.980257i	−0.871650	+	0.490129i	$0.836950\pi$
$992$		0			0
$993$	2.10988e6			2.13973
$994$		0			0
$995$	−115689.	−	259843.i	−0.116855	−	0.262461i
$996$		0			0
$997$	−479310.	−	830189.i	−0.482199	−	0.835193i	0.517592	−	0.855627i	$-0.326828\pi$
$997$	−479310.	−	830189.i	−0.482199	−	0.835193i	−0.999791	+	0.0204345i	$0.993495\pi$
$998$		0			0
$999$	−4.04766e6	−	4.49538e6i	−4.05576	−	4.50438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.o.a.13.1	✓	88
31.12	odd	30	inner	124.5.o.a.105.1	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.o.a.13.1	✓	88	1.1	even	1	trivial
124.5.o.a.105.1	yes	88	31.12	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)

\(f(q)\)	\(=\)	\(q+(-7.03588 - 15.8028i) q^{3} +(11.6814 + 20.2328i) q^{5} +(-44.3877 - 49.2975i) q^{7} +(-146.027 + 162.179i) q^{9} +O(q^{10})\)	\(q+(-7.03588 - 15.8028i) q^{3} +(11.6814 + 20.2328i) q^{5} +(-44.3877 - 49.2975i) q^{7} +(-146.027 + 162.179i) q^{9} +(-8.73862 - 41.1120i) q^{11} +(-53.0777 - 5.57869i) q^{13} +(237.547 - 326.956i) q^{15} +(-21.8592 + 102.839i) q^{17} +(42.9106 + 408.267i) q^{19} +(-466.735 + 1048.30i) q^{21} +(169.387 - 55.0371i) q^{23} +(39.5881 - 68.5686i) q^{25} +(2257.73 + 733.580i) q^{27} +(829.026 + 1141.06i) q^{29} +(-431.803 + 858.526i) q^{31} +(-588.202 + 427.354i) q^{33} +(478.917 - 1473.96i) q^{35} +(-2206.77 - 1274.08i) q^{37} +(285.289 + 878.029i) q^{39} +(1127.43 + 501.965i) q^{41} +(-2293.90 + 241.098i) q^{43} +(-4987.15 - 1060.05i) q^{45} +(-3045.14 - 2212.42i) q^{47} +(-209.006 + 1988.56i) q^{49} +(1778.95 - 378.128i) q^{51} +(435.520 + 392.144i) q^{53} +(729.733 - 657.054i) q^{55} +(6149.87 - 3550.63i) q^{57} +(-875.291 + 389.705i) q^{59} +2935.90i q^{61} +14476.8 q^{63} +(-507.151 - 1139.08i) q^{65} +(-3701.69 - 6411.51i) q^{67} +(-2061.53 - 2289.56i) q^{69} +(-969.007 + 1076.19i) q^{71} +(646.656 + 3042.28i) q^{73} +(-1362.12 - 143.164i) q^{75} +(-1638.83 + 2255.66i) q^{77} +(-1984.25 + 9335.16i) q^{79} +(-2444.71 - 23259.8i) q^{81} +(-3537.70 + 7945.80i) q^{83} +(-2336.08 + 759.038i) q^{85} +(12199.0 - 21129.3i) q^{87} +(-11198.0 - 3638.46i) q^{89} +(2080.98 + 2864.22i) q^{91} +(16605.3 + 783.231i) q^{93} +(-7759.14 + 5637.35i) q^{95} +(45.6737 - 140.569i) q^{97} +(7943.58 + 4586.23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \) 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

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