LMFDB - Embedded newform 450.6.f.g.107.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,6,Mod(107,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("450.107");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	450.f (of order $4$, degree $2$, 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:	$72.1727189158$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 252 x^{14} + 27174 x^{12} - 1635700 x^{10} + 60061815 x^{8} - 1376564028 x^{6} + \cdots + 498214340649 $ x^16 - 252x^14 + 27174x^12 - 1635700x^10 + 60061815x^8 - 1376564028x^6 + 19220200150x^4 - 149540021784*x^2 + 498214340649
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{8}\cdot 5^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.7
Root			$-3.79037 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	450.107
Dual form			450.6.f.g.143.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.82843 - 2.82843i) q^{2} -16.0000i q^{4} +(140.653 + 140.653i) q^{7} +(-45.2548 - 45.2548i) q^{8} +O(q^{10})$	\(q+(2.82843 - 2.82843i) q^{2} -16.0000i q^{4} +(140.653 + 140.653i) q^{7} +(-45.2548 - 45.2548i) q^{8} -540.947i q^{11} +(-798.801 + 798.801i) q^{13} +795.655 q^{14} -256.000 q^{16} +(598.220 - 598.220i) q^{17} -1784.25i q^{19} +(-1530.03 - 1530.03i) q^{22} +(-718.106 - 718.106i) q^{23} +4518.70i q^{26} +(2250.45 - 2250.45i) q^{28} +5380.98 q^{29} +1803.17 q^{31} +(-724.077 + 724.077i) q^{32} -3384.05i q^{34} +(7344.12 + 7344.12i) q^{37} +(-5046.62 - 5046.62i) q^{38} -12486.0i q^{41} +(9900.97 - 9900.97i) q^{43} -8655.16 q^{44} -4062.22 q^{46} +(-1821.38 + 1821.38i) q^{47} +22759.7i q^{49} +(12780.8 + 12780.8i) q^{52} +(16089.2 + 16089.2i) q^{53} -12730.5i q^{56} +(15219.7 - 15219.7i) q^{58} +45243.7 q^{59} +605.793 q^{61} +(5100.13 - 5100.13i) q^{62} +4096.00i q^{64} +(-23073.5 - 23073.5i) q^{67} +(-9571.53 - 9571.53i) q^{68} +11301.7i q^{71} +(41883.4 - 41883.4i) q^{73} +41544.6 q^{74} -28548.0 q^{76} +(76086.0 - 76086.0i) q^{77} -61935.6i q^{79} +(-35315.9 - 35315.9i) q^{82} +(-82133.1 - 82133.1i) q^{83} -56008.3i q^{86} +(-24480.5 + 24480.5i) q^{88} -10787.0 q^{89} -224708. q^{91} +(-11489.7 + 11489.7i) q^{92} +10303.3i q^{94} +(51439.5 + 51439.5i) q^{97} +(64374.2 + 64374.2i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 528 q^{7}+O(q^{10}) $ 16 * q + 528 * q^7	$ 16 q + 528 q^{7} - 192 q^{13} - 4096 q^{16} + 2688 q^{22} + 8448 q^{28} + 13024 q^{31} + 47328 q^{37} + 55440 q^{43} + 44544 q^{46} + 3072 q^{52} + 101184 q^{58} + 28400 q^{61} - 242256 q^{67} + 430944 q^{73} - 7168 q^{76} - 158208 q^{82} + 43008 q^{88} - 185472 q^{91} - 457152 q^{97}+O(q^{100}) $ 16 * q + 528 * q^7 - 192 * q^13 - 4096 * q^16 + 2688 * q^22 + 8448 * q^28 + 13024 * q^31 + 47328 * q^37 + 55440 * q^43 + 44544 * q^46 + 3072 * q^52 + 101184 * q^58 + 28400 * q^61 - 242256 * q^67 + 430944 * q^73 - 7168 * q^76 - 158208 * q^82 + 43008 * q^88 - 185472 * q^91 - 457152 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.82843	−	2.82843i	0.500000	−	0.500000i
$2$	2.82843	−	2.82843i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	16.0000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	140.653	+	140.653i	1.08494	+	1.08494i	0.996041	+	0.0888972i	$0.0283343\pi$
$7$	140.653	+	140.653i	1.08494	+	1.08494i	0.0888972	+	0.996041i	$0.471666\pi$
$8$	−45.2548	−	45.2548i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$		−	540.947i		−	1.34795i	−0.738755	−	0.673974i	$-0.764586\pi$
$11$		−	540.947i		−	1.34795i	0.738755	−	0.673974i	$-0.235414\pi$
$12$		0			0
$13$	−798.801	+	798.801i	−1.31093	+	1.31093i	−0.390205	+	0.920728i	$0.627596\pi$
$13$	−798.801	+	798.801i	−1.31093	+	1.31093i	−0.920728	+	0.390205i	$0.872404\pi$
$14$	795.655			1.08494
$15$		0			0
$16$	−256.000			−0.250000
$17$	598.220	−	598.220i	0.502041	−	0.502041i	−0.410031	−	0.912072i	$-0.634482\pi$
$17$	598.220	−	598.220i	0.502041	−	0.502041i	0.912072	+	0.410031i	$0.134482\pi$
$18$		0			0
$19$		−	1784.25i		−	1.13389i	−0.823755	−	0.566946i	$-0.808125\pi$
$19$		−	1784.25i		−	1.13389i	0.823755	−	0.566946i	$-0.191875\pi$
$20$		0			0
$21$		0			0
$22$	−1530.03	−	1530.03i	−0.673974	−	0.673974i
$23$	−718.106	−	718.106i	−0.283054	−	0.283054i	0.551272	−	0.834326i	$-0.314143\pi$
$23$	−718.106	−	718.106i	−0.283054	−	0.283054i	−0.834326	+	0.551272i	$0.814143\pi$
$24$		0			0
$25$		0			0
$26$			4518.70i			1.31093i
$27$		0			0
$28$	2250.45	−	2250.45i	0.542469	−	0.542469i
$29$	5380.98			1.18814			0.594068	−	0.804415i	$-0.297521\pi$
$29$	5380.98			1.18814			0.594068	+	0.804415i	$0.297521\pi$
$30$		0			0
$31$	1803.17			0.337002			0.168501	−	0.985702i	$-0.446107\pi$
$31$	1803.17			0.337002			0.168501	+	0.985702i	$0.446107\pi$
$32$	−724.077	+	724.077i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	3384.05i		−	0.502041i
$35$		0			0
$36$		0			0
$37$	7344.12	+	7344.12i	0.881932	+	0.881932i	0.993731	−	0.111799i	$-0.0356612\pi$
$37$	7344.12	+	7344.12i	0.881932	+	0.881932i	−0.111799	+	0.993731i	$0.535661\pi$
$38$	−5046.62	−	5046.62i	−0.566946	−	0.566946i
$39$		0			0
$40$		0			0
$41$		−	12486.0i		−	1.16002i	−0.814610	−	0.580009i	$-0.803049\pi$
$41$		−	12486.0i		−	1.16002i	0.814610	−	0.580009i	$-0.196951\pi$
$42$		0			0
$43$	9900.97	−	9900.97i	0.816594	−	0.816594i	−0.169018	−	0.985613i	$-0.554060\pi$
$43$	9900.97	−	9900.97i	0.816594	−	0.816594i	0.985613	+	0.169018i	$0.0540598\pi$
$44$	−8655.16			−0.673974
$45$		0			0
$46$	−4062.22			−0.283054
$47$	−1821.38	+	1821.38i	−0.120270	+	0.120270i	−0.764680	−	0.644410i	$-0.777103\pi$
$47$	−1821.38	+	1821.38i	−0.120270	+	0.120270i	0.644410	+	0.764680i	$0.277103\pi$
$48$		0			0
$49$			22759.7i			1.35418i
$50$		0			0
$51$		0			0
$52$	12780.8	+	12780.8i	0.655466	+	0.655466i
$53$	16089.2	+	16089.2i	0.786764	+	0.786764i	0.980962	−	0.194199i	$-0.0622106\pi$
$53$	16089.2	+	16089.2i	0.786764	+	0.786764i	−0.194199	+	0.980962i	$0.562211\pi$
$54$		0			0
$55$		0			0
$56$		−	12730.5i		−	0.542469i
$57$		0			0
$58$	15219.7	−	15219.7i	0.594068	−	0.594068i
$59$	45243.7			1.69211			0.846054	−	0.533096i	$-0.178972\pi$
$59$	45243.7			1.69211			0.846054	+	0.533096i	$0.178972\pi$
$60$		0			0
$61$	605.793			0.0208449			0.0104224	−	0.999946i	$-0.496682\pi$
$61$	605.793			0.0208449			0.0104224	+	0.999946i	$0.496682\pi$
$62$	5100.13	−	5100.13i	0.168501	−	0.168501i
$63$		0			0
$64$			4096.00i			0.125000i
$65$		0			0
$66$		0			0
$67$	−23073.5	−	23073.5i	−0.627951	−	0.627951i	0.319601	−	0.947552i	$-0.396451\pi$
$67$	−23073.5	−	23073.5i	−0.627951	−	0.627951i	−0.947552	+	0.319601i	$0.896451\pi$
$68$	−9571.53	−	9571.53i	−0.251020	−	0.251020i
$69$		0			0
$70$		0			0
$71$			11301.7i			0.266072i	0.991111	+	0.133036i	$0.0424727\pi$
$71$			11301.7i			0.266072i	−0.991111	+	0.133036i	$0.957527\pi$
$72$		0			0
$73$	41883.4	−	41883.4i	0.919889	−	0.919889i	−0.0771322	−	0.997021i	$-0.524576\pi$
$73$	41883.4	−	41883.4i	0.919889	−	0.919889i	0.997021	+	0.0771322i	$0.0245764\pi$
$74$	41544.6			0.881932
$75$		0			0
$76$	−28548.0			−0.566946
$77$	76086.0	−	76086.0i	1.46244	−	1.46244i
$78$		0			0
$79$		−	61935.6i		−	1.11654i	−0.829661	−	0.558268i	$-0.811466\pi$
$79$		−	61935.6i		−	1.11654i	0.829661	−	0.558268i	$-0.188534\pi$
$80$		0			0
$81$		0			0
$82$	−35315.9	−	35315.9i	−0.580009	−	0.580009i
$83$	−82133.1	−	82133.1i	−1.30865	−	1.30865i	−0.922391	−	0.386258i	$-0.873767\pi$
$83$	−82133.1	−	82133.1i	−1.30865	−	1.30865i	−0.386258	−	0.922391i	$-0.626233\pi$
$84$		0			0
$85$		0			0
$86$		−	56008.3i		−	0.816594i
$87$		0			0
$88$	−24480.5	+	24480.5i	−0.336987	+	0.336987i
$89$	−10787.0			−0.144353			−0.0721765	−	0.997392i	$-0.522995\pi$
$89$	−10787.0			−0.144353			−0.0721765	+	0.997392i	$0.522995\pi$
$90$		0			0
$91$	−224708.			−2.84456
$92$	−11489.7	+	11489.7i	−0.141527	+	0.141527i
$93$		0			0
$94$			10303.3i			0.120270i
$95$		0			0
$96$		0			0
$97$	51439.5	+	51439.5i	0.555096	+	0.555096i	0.927907	−	0.372812i	$-0.121606\pi$
$97$	51439.5	+	51439.5i	0.555096	+	0.555096i	−0.372812	+	0.927907i	$0.621606\pi$
$98$	64374.2	+	64374.2i	0.677091	+	0.677091i
$99$		0			0
$100$		0			0
$101$		−	183902.i		−	1.79384i	−0.442194	−	0.896919i	$-0.645800\pi$
$101$		−	183902.i		−	1.79384i	0.442194	−	0.896919i	$-0.354200\pi$
$102$		0			0
$103$	84524.9	−	84524.9i	0.785039	−	0.785039i	−0.195637	−	0.980676i	$-0.562677\pi$
$103$	84524.9	−	84524.9i	0.785039	−	0.785039i	0.980676	+	0.195637i	$0.0626774\pi$
$104$	72299.3			0.655466
$105$		0			0
$106$	91014.2			0.786764
$107$	−21138.5	+	21138.5i	−0.178491	+	0.178491i	−0.790698	−	0.612207i	$-0.790282\pi$
$107$	−21138.5	+	21138.5i	−0.178491	+	0.178491i	0.612207	+	0.790698i	$0.290282\pi$
$108$		0			0
$109$		−	52674.2i		−	0.424651i	−0.977199	−	0.212325i	$-0.931896\pi$
$109$		−	52674.2i		−	0.424651i	0.977199	−	0.212325i	$-0.0681037\pi$
$110$		0			0
$111$		0			0
$112$	−36007.3	−	36007.3i	−0.271235	−	0.271235i
$113$	171149.	+	171149.i	1.26089	+	1.26089i	0.950661	+	0.310230i	$0.100406\pi$
$113$	171149.	+	171149.i	1.26089	+	1.26089i	0.310230	+	0.950661i	$0.399594\pi$
$114$		0			0
$115$		0			0
$116$		−	86095.6i		−	0.594068i
$117$		0			0
$118$	127969.	−	127969.i	0.846054	−	0.846054i
$119$	168283.			1.08937
$120$		0			0
$121$	−131573.			−0.816965
$122$	1713.44	−	1713.44i	0.0104224	−	0.0104224i
$123$		0			0
$124$		−	28850.7i		−	0.168501i
$125$		0			0
$126$		0			0
$127$	−80016.7	−	80016.7i	−0.440222	−	0.440222i	0.451865	−	0.892086i	$-0.350759\pi$
$127$	−80016.7	−	80016.7i	−0.440222	−	0.440222i	−0.892086	+	0.451865i	$0.850759\pi$
$128$	11585.2	+	11585.2i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$			185291.i			0.943357i	0.881771	+	0.471678i	$0.156352\pi$
$131$			185291.i			0.943357i	−0.881771	+	0.471678i	$0.843648\pi$
$132$		0			0
$133$	250961.	−	250961.i	1.23020	−	1.23020i
$134$	−130523.			−0.627951
$135$		0			0
$136$	−54144.7			−0.251020
$137$	−30362.4	+	30362.4i	−0.138209	+	0.138209i	−0.772826	−	0.634618i	$-0.781158\pi$
$137$	−30362.4	+	30362.4i	−0.138209	+	0.138209i	0.634618	+	0.772826i	$0.281158\pi$
$138$		0			0
$139$		−	75341.5i		−	0.330748i	−0.986231	−	0.165374i	$-0.947117\pi$
$139$		−	75341.5i		−	0.330748i	0.986231	−	0.165374i	$-0.0528831\pi$
$140$		0			0
$141$		0			0
$142$	31966.2	+	31966.2i	0.133036	+	0.133036i
$143$	432110.	+	432110.i	1.76707	+	1.76707i
$144$		0			0
$145$		0			0
$146$		−	236929.i		−	0.919889i
$147$		0			0
$148$	117506.	−	117506.i	0.440966	−	0.440966i
$149$	−125123.			−0.461713			−0.230857	−	0.972988i	$-0.574153\pi$
$149$	−125123.			−0.461713			−0.230857	+	0.972988i	$0.574153\pi$
$150$		0			0
$151$	−419846.			−1.49847			−0.749234	−	0.662306i	$-0.769578\pi$
$151$	−419846.			−1.49847			−0.749234	+	0.662306i	$0.769578\pi$
$152$	−80745.9	+	80745.9i	−0.283473	+	0.283473i
$153$		0			0
$154$		−	430408.i		−	1.46244i
$155$		0			0
$156$		0			0
$157$	149608.	+	149608.i	0.484400	+	0.484400i	0.906534	−	0.422133i	$-0.138719\pi$
$157$	149608.	+	149608.i	0.484400	+	0.484400i	−0.422133	+	0.906534i	$0.638719\pi$
$158$	−175180.	−	175180.i	−0.558268	−	0.558268i
$159$		0			0
$160$		0			0
$161$		−	202008.i		−	0.614192i
$162$		0			0
$163$	−231571.	+	231571.i	−0.682677	+	0.682677i	−0.960603	−	0.277925i	$-0.910353\pi$
$163$	−231571.	+	231571.i	−0.682677	+	0.682677i	0.277925	+	0.960603i	$0.410353\pi$
$164$	−199777.			−0.580009
$165$		0			0
$166$	−464615.			−1.30865
$167$	175238.	−	175238.i	0.486224	−	0.486224i	−0.420889	−	0.907112i	$-0.638282\pi$
$167$	175238.	−	175238.i	0.486224	−	0.486224i	0.907112	+	0.420889i	$0.138282\pi$
$168$		0			0
$169$		−	904875.i		−	2.43709i
$170$		0			0
$171$		0			0
$172$	−158415.	−	158415.i	−0.408297	−	0.408297i
$173$	173263.	+	173263.i	0.440139	+	0.440139i	0.892059	−	0.451919i	$-0.149261\pi$
$173$	173263.	+	173263.i	0.440139	+	0.440139i	−0.451919	+	0.892059i	$0.649261\pi$
$174$		0			0
$175$		0			0
$176$			138483.i			0.336987i
$177$		0			0
$178$	−30510.3	+	30510.3i	−0.0721765	+	0.0721765i
$179$	819035.			1.91060			0.955301	−	0.295636i	$-0.0955315\pi$
$179$	819035.			1.91060			0.955301	+	0.295636i	$0.0955315\pi$
$180$		0			0
$181$	−268935.			−0.610169			−0.305085	−	0.952325i	$-0.598685\pi$
$181$	−268935.			−0.610169			−0.305085	+	0.952325i	$0.598685\pi$
$182$	−635571.	+	635571.i	−1.42228	+	1.42228i
$183$		0			0
$184$			64995.5i			0.141527i
$185$		0			0
$186$		0			0
$187$	−323606.	−	323606.i	−0.676725	−	0.676725i
$188$	29142.1	+	29142.1i	0.0601348	+	0.0601348i
$189$		0			0
$190$		0			0
$191$		−	513760.i		−	1.01901i	−0.860469	−	0.509503i	$-0.829829\pi$
$191$		−	513760.i		−	1.01901i	0.860469	−	0.509503i	$-0.170171\pi$
$192$		0			0
$193$	−187981.	+	187981.i	−0.363263	+	0.363263i	−0.865013	−	0.501750i	$-0.832690\pi$
$193$	−187981.	+	187981.i	−0.363263	+	0.363263i	0.501750	+	0.865013i	$0.332690\pi$
$194$	290986.			0.555096
$195$		0			0
$196$	364156.			0.677091
$197$	745856.	−	745856.i	1.36927	−	1.36927i	0.507790	−	0.861481i	$-0.330462\pi$
$197$	745856.	−	745856.i	1.36927	−	1.36927i	0.861481	−	0.507790i	$-0.169538\pi$
$198$		0			0
$199$			411062.i			0.735825i	0.929860	+	0.367913i	$0.119927\pi$
$199$			411062.i			0.735825i	−0.929860	+	0.367913i	$0.880073\pi$
$200$		0			0
$201$		0			0
$202$	−520154.	−	520154.i	−0.896919	−	0.896919i
$203$	756852.	+	756852.i	1.28905	+	1.28905i
$204$		0			0
$205$		0			0
$206$		−	478145.i		−	0.785039i
$207$		0			0
$208$	204493.	−	204493.i	0.327733	−	0.327733i
$209$	−965185.			−1.52843
$210$		0			0
$211$	−243588.			−0.376660			−0.188330	−	0.982106i	$-0.560307\pi$
$211$	−243588.			−0.376660			−0.188330	+	0.982106i	$0.560307\pi$
$212$	257427.	−	257427.i	0.393382	−	0.393382i
$213$		0			0
$214$			119578.i			0.178491i
$215$		0			0
$216$		0			0
$217$	253622.	+	253622.i	0.365626	+	0.365626i
$218$	−148985.	−	148985.i	−0.212325	−	0.212325i
$219$		0			0
$220$		0			0
$221$			955719.i			1.31628i
$222$		0			0
$223$	438788.	−	438788.i	0.590871	−	0.590871i	−0.346995	−	0.937867i	$-0.612798\pi$
$223$	438788.	−	438788.i	0.590871	−	0.590871i	0.937867	+	0.346995i	$0.112798\pi$
$224$	−203688.			−0.271235
$225$		0			0
$226$	968164.			1.26089
$227$	−584859.	+	584859.i	−0.753332	+	0.753332i	−0.975100	−	0.221767i	$-0.928817\pi$
$227$	−584859.	+	584859.i	−0.753332	+	0.753332i	0.221767	+	0.975100i	$0.428817\pi$
$228$		0			0
$229$			28534.6i			0.0359570i	0.999838	+	0.0179785i	$0.00572304\pi$
$229$			28534.6i			0.0359570i	−0.999838	+	0.0179785i	$0.994277\pi$
$230$		0			0
$231$		0			0
$232$	−243515.	−	243515.i	−0.297034	−	0.297034i
$233$	−479688.	−	479688.i	−0.578854	−	0.578854i	0.355734	−	0.934587i	$-0.384231\pi$
$233$	−479688.	−	479688.i	−0.578854	−	0.578854i	−0.934587	+	0.355734i	$0.884231\pi$
$234$		0			0
$235$		0			0
$236$		−	723900.i		−	0.846054i
$237$		0			0
$238$	475977.	−	475977.i	0.544683	−	0.544683i
$239$	−794921.			−0.900180			−0.450090	−	0.892983i	$-0.648608\pi$
$239$	−794921.			−0.900180			−0.450090	+	0.892983i	$0.648608\pi$
$240$		0			0
$241$	−1.58233e6			−1.75491			−0.877455	−	0.479660i	$-0.840760\pi$
$241$	−1.58233e6			−1.75491			−0.877455	+	0.479660i	$0.840760\pi$
$242$	−372145.	+	372145.i	−0.408482	+	0.408482i
$243$		0			0
$244$		−	9692.69i		−	0.0104224i
$245$		0			0
$246$		0			0
$247$	1.42526e6	+	1.42526e6i	1.48646	+	1.48646i
$248$	−81602.1	−	81602.1i	−0.0842504	−	0.0842504i
$249$		0			0
$250$		0			0
$251$			1.37423e6i			1.37682i	0.725323	+	0.688408i	$0.241690\pi$
$251$			1.37423e6i			1.37682i	−0.725323	+	0.688408i	$0.758310\pi$
$252$		0			0
$253$	−388458.	+	388458.i	−0.381542	+	0.381542i
$254$	−452643.			−0.440222
$255$		0			0
$256$	65536.0			0.0625000
$257$	353875.	−	353875.i	0.334209	−	0.334209i	−0.519974	−	0.854182i	$-0.674058\pi$
$257$	353875.	−	353875.i	0.334209	−	0.334209i	0.854182	+	0.519974i	$0.174058\pi$
$258$		0			0
$259$			2.06595e6i			1.91368i
$260$		0			0
$261$		0			0
$262$	524082.	+	524082.i	0.471678	+	0.471678i
$263$	−877240.	−	877240.i	−0.782040	−	0.782040i	0.198135	−	0.980175i	$-0.436512\pi$
$263$	−877240.	−	877240.i	−0.782040	−	0.782040i	−0.980175	+	0.198135i	$0.936512\pi$
$264$		0			0
$265$		0			0
$266$		−	1.41965e6i		−	1.23020i
$267$		0			0
$268$	−369176.	+	369176.i	−0.313976	+	0.313976i
$269$	1.98017e6			1.66849			0.834243	−	0.551398i	$-0.185905\pi$
$269$	1.98017e6			1.66849			0.834243	+	0.551398i	$0.185905\pi$
$270$		0			0
$271$	678161.			0.560931			0.280466	−	0.959864i	$-0.409511\pi$
$271$	678161.			0.560931			0.280466	+	0.959864i	$0.409511\pi$
$272$	−153144.	+	153144.i	−0.125510	+	0.125510i
$273$		0			0
$274$			171756.i			0.138209i
$275$		0			0
$276$		0			0
$277$	−747103.	−	747103.i	−0.585034	−	0.585034i	0.351248	−	0.936282i	$-0.385757\pi$
$277$	−747103.	−	747103.i	−0.585034	−	0.585034i	−0.936282	+	0.351248i	$0.885757\pi$
$278$	−213098.	−	213098.i	−0.165374	−	0.165374i
$279$		0			0
$280$		0			0
$281$			2.28008e6i			1.72260i	0.508100	+	0.861298i	$0.330348\pi$
$281$			2.28008e6i			1.72260i	−0.508100	+	0.861298i	$0.669652\pi$
$282$		0			0
$283$	−433565.	+	433565.i	−0.321801	+	0.321801i	−0.849458	−	0.527656i	$-0.823071\pi$
$283$	−433565.	+	433565.i	−0.321801	+	0.321801i	0.527656	+	0.849458i	$0.323071\pi$
$284$	180828.			0.133036
$285$		0			0
$286$	2.44438e6			1.76707
$287$	1.75620e6	−	1.75620e6i	1.25855	−	1.25855i
$288$		0			0
$289$			704122.i			0.495910i
$290$		0			0
$291$		0			0
$292$	−670135.	−	670135.i	−0.459944	−	0.459944i
$293$	−233140.	−	233140.i	−0.158653	−	0.158653i	0.623317	−	0.781970i	$-0.285785\pi$
$293$	−233140.	−	233140.i	−0.158653	−	0.158653i	−0.781970	+	0.623317i	$0.785785\pi$
$294$		0			0
$295$		0			0
$296$		−	664713.i		−	0.440966i
$297$		0			0
$298$	−353902.	+	353902.i	−0.230857	+	0.230857i
$299$	1.14725e6			0.742129
$300$		0			0
$301$	2.78521e6			1.77191
$302$	−1.18750e6	+	1.18750e6i	−0.749234	+	0.749234i
$303$		0			0
$304$			456768.i			0.283473i
$305$		0			0
$306$		0			0
$307$	667932.	+	667932.i	0.404470	+	0.404470i	0.879805	−	0.475335i	$-0.157673\pi$
$307$	667932.	+	667932.i	0.404470	+	0.404470i	−0.475335	+	0.879805i	$0.657673\pi$
$308$	−1.21738e6	−	1.21738e6i	−0.731220	−	0.731220i
$309$		0			0
$310$		0			0
$311$			1.00168e6i			0.587259i	0.955919	+	0.293630i	$0.0948632\pi$
$311$			1.00168e6i			0.587259i	−0.955919	+	0.293630i	$0.905137\pi$
$312$		0			0
$313$	−1.80630e6	+	1.80630e6i	−1.04215	+	1.04215i	−0.0430780	+	0.999072i	$0.513716\pi$
$313$	−1.80630e6	+	1.80630e6i	−1.04215	+	1.04215i	−0.999072	+	0.0430780i	$0.986284\pi$
$314$	846308.			0.484400
$315$		0			0
$316$	−990970.			−0.558268
$317$	1.09346e6	−	1.09346e6i	0.611158	−	0.611158i	−0.332090	−	0.943248i	$-0.607754\pi$
$317$	1.09346e6	−	1.09346e6i	0.611158	−	0.611158i	0.943248	+	0.332090i	$0.107754\pi$
$318$		0			0
$319$		−	2.91082e6i		−	1.60155i
$320$		0			0
$321$		0			0
$322$	−571365.	−	571365.i	−0.307096	−	0.307096i
$323$	−1.06737e6	−	1.06737e6i	−0.569260	−	0.569260i
$324$		0			0
$325$		0			0
$326$			1.30996e6i			0.682677i
$327$		0			0
$328$	−565054.	+	565054.i	−0.290005	+	0.290005i
$329$	−512366.			−0.260970
$330$		0			0
$331$	2.52662e6			1.26757			0.633783	−	0.773511i	$-0.281501\pi$
$331$	2.52662e6			1.26757			0.633783	+	0.773511i	$0.281501\pi$
$332$	−1.31413e6	+	1.31413e6i	−0.654325	+	0.654325i
$333$		0			0
$334$		−	991294.i		−	0.486224i
$335$		0			0
$336$		0			0
$337$	2.55352e6	+	2.55352e6i	1.22480	+	1.22480i	0.965906	+	0.258893i	$0.0833578\pi$
$337$	2.55352e6	+	2.55352e6i	1.22480	+	1.22480i	0.258893	+	0.965906i	$0.416642\pi$
$338$	−2.55937e6	−	2.55937e6i	−1.21855	−	1.21855i
$339$		0			0
$340$		0			0
$341$		−	975419.i		−	0.454261i
$342$		0			0
$343$	−837270.	+	837270.i	−0.384265	+	0.384265i
$344$	−896133.			−0.408297
$345$		0			0
$346$	980123.			0.440139
$347$	847128.	−	847128.i	0.377681	−	0.377681i	−0.492584	−	0.870265i	$-0.663948\pi$
$347$	847128.	−	847128.i	0.377681	−	0.377681i	0.870265	+	0.492584i	$0.163948\pi$
$348$		0			0
$349$			4.05487e6i			1.78202i	0.453981	+	0.891011i	$0.350003\pi$
$349$			4.05487e6i			1.78202i	−0.453981	+	0.891011i	$0.649997\pi$
$350$		0			0
$351$		0			0
$352$	391688.	+	391688.i	0.168494	+	0.168494i
$353$	659897.	+	659897.i	0.281864	+	0.281864i	0.833852	−	0.551988i	$-0.186131\pi$
$353$	659897.	+	659897.i	0.281864	+	0.281864i	−0.551988	+	0.833852i	$0.686131\pi$
$354$		0			0
$355$		0			0
$356$			172592.i			0.0721765i
$357$		0			0
$358$	2.31658e6	−	2.31658e6i	0.955301	−	0.955301i
$359$	−3.58684e6			−1.46884			−0.734422	−	0.678693i	$-0.762547\pi$
$359$	−3.58684e6			−1.46884			−0.734422	+	0.678693i	$0.762547\pi$
$360$		0			0
$361$	−707445.			−0.285709
$362$	−760662.	+	760662.i	−0.305085	+	0.305085i
$363$		0			0
$364$			3.59533e6i			1.42228i
$365$		0			0
$366$		0			0
$367$	1.33916e6	+	1.33916e6i	0.519001	+	0.519001i	0.917269	−	0.398268i	$-0.130389\pi$
$367$	1.33916e6	+	1.33916e6i	0.519001	+	0.519001i	−0.398268	+	0.917269i	$0.630389\pi$
$368$	183835.	+	183835.i	0.0707635	+	0.0707635i
$369$		0			0
$370$		0			0
$371$			4.52599e6i			1.70718i
$372$		0			0
$373$	−2.26970e6	+	2.26970e6i	−0.844689	+	0.844689i	−0.989464	−	0.144776i	$-0.953754\pi$
$373$	−2.26970e6	+	2.26970e6i	−0.844689	+	0.844689i	0.144776	+	0.989464i	$0.453754\pi$
$374$	−1.83059e6			−0.676725
$375$		0			0
$376$	164852.			0.0601348
$377$	−4.29833e6	+	4.29833e6i	−1.55757	+	1.55757i
$378$		0			0
$379$			4.67739e6i			1.67265i	0.548232	+	0.836326i	$0.315301\pi$
$379$			4.67739e6i			1.67265i	−0.548232	+	0.836326i	$0.684699\pi$
$380$		0			0
$381$		0			0
$382$	−1.45313e6	−	1.45313e6i	−0.509503	−	0.509503i
$383$	−1.60463e6	−	1.60463e6i	−0.558957	−	0.558957i	0.370054	−	0.929010i	$-0.379339\pi$
$383$	−1.60463e6	−	1.60463e6i	−0.558957	−	0.558957i	−0.929010	+	0.370054i	$0.879339\pi$
$384$		0			0
$385$		0			0
$386$			1.06338e6i			0.363263i
$387$		0			0
$388$	823033.	−	823033.i	0.277548	−	0.277548i
$389$	1.68645e6			0.565067			0.282533	−	0.959257i	$-0.408825\pi$
$389$	1.68645e6			0.565067			0.282533	+	0.959257i	$0.408825\pi$
$390$		0			0
$391$	−859171.			−0.284209
$392$	1.02999e6	−	1.02999e6i	0.338545	−	0.338545i
$393$		0			0
$394$		−	4.21920e6i		−	1.36927i
$395$		0			0
$396$		0			0
$397$	−1.40797e6	−	1.40797e6i	−0.448349	−	0.448349i	0.446456	−	0.894805i	$-0.352686\pi$
$397$	−1.40797e6	−	1.40797e6i	−0.448349	−	0.448349i	−0.894805	+	0.446456i	$0.852686\pi$
$398$	1.16266e6	+	1.16266e6i	0.367913	+	0.367913i
$399$		0			0
$400$		0			0
$401$			1.35644e6i			0.421251i	0.977567	+	0.210625i	$0.0675500\pi$
$401$			1.35644e6i			0.421251i	−0.977567	+	0.210625i	$0.932450\pi$
$402$		0			0
$403$	−1.44037e6	+	1.44037e6i	−0.441787	+	0.441787i
$404$	−2.94243e6			−0.896919
$405$		0			0
$406$	4.28140e6			1.28905
$407$	3.97278e6	−	3.97278e6i	1.18880	−	1.18880i
$408$		0			0
$409$			2.99089e6i			0.884082i	0.896995	+	0.442041i	$0.145746\pi$
$409$			2.99089e6i			0.884082i	−0.896995	+	0.442041i	$0.854254\pi$
$410$		0			0
$411$		0			0
$412$	−1.35240e6	−	1.35240e6i	−0.392520	−	0.392520i
$413$	6.36368e6	+	6.36368e6i	1.83583	+	1.83583i
$414$		0			0
$415$		0			0
$416$		−	1.15679e6i		−	0.327733i
$417$		0			0
$418$	−2.72995e6	+	2.72995e6i	−0.764213	+	0.764213i
$419$	−1.50892e6			−0.419887			−0.209944	−	0.977714i	$-0.567328\pi$
$419$	−1.50892e6			−0.419887			−0.209944	+	0.977714i	$0.567328\pi$
$420$		0			0
$421$	5.92470e6			1.62915			0.814576	−	0.580057i	$-0.196970\pi$
$421$	5.92470e6			1.62915			0.814576	+	0.580057i	$0.196970\pi$
$422$	−688971.	+	688971.i	−0.188330	+	0.188330i
$423$		0			0
$424$		−	1.45623e6i		−	0.393382i
$425$		0			0
$426$		0			0
$427$	85206.8	+	85206.8i	0.0226154	+	0.0226154i
$428$	338216.	+	338216.i	0.0892453	+	0.0892453i
$429$		0			0
$430$		0			0
$431$		−	2.78110e6i		−	0.721148i	−0.932731	−	0.360574i	$-0.882581\pi$
$431$		−	2.78110e6i		−	0.721148i	0.932731	−	0.360574i	$-0.117419\pi$
$432$		0			0
$433$	−674431.	+	674431.i	−0.172869	+	0.172869i	−0.788239	−	0.615369i	$-0.789007\pi$
$433$	−674431.	+	674431.i	−0.172869	+	0.172869i	0.615369	+	0.788239i	$0.289007\pi$
$434$	1.43470e6			0.365626
$435$		0			0
$436$	−842788.			−0.212325
$437$	−1.28128e6	+	1.28128e6i	−0.320952	+	0.320952i
$438$		0			0
$439$		−	6.04061e6i		−	1.49596i	−0.663722	−	0.747980i	$-0.731024\pi$
$439$		−	6.04061e6i		−	1.49596i	0.663722	−	0.747980i	$-0.268976\pi$
$440$		0			0
$441$		0			0
$442$	2.70318e6	+	2.70318e6i	0.658142	+	0.658142i
$443$	−1.88878e6	−	1.88878e6i	−0.457269	−	0.457269i	0.440489	−	0.897758i	$-0.354805\pi$
$443$	−1.88878e6	−	1.88878e6i	−0.457269	−	0.457269i	−0.897758	+	0.440489i	$0.854805\pi$
$444$		0			0
$445$		0			0
$446$		−	2.48216e6i		−	0.590871i
$447$		0			0
$448$	−576116.	+	576116.i	−0.135617	+	0.135617i
$449$	−2.99443e6			−0.700969			−0.350485	−	0.936569i	$-0.613983\pi$
$449$	−2.99443e6			−0.700969			−0.350485	+	0.936569i	$0.613983\pi$
$450$		0			0
$451$	−6.75429e6			−1.56365
$452$	2.73838e6	−	2.73838e6i	0.630446	−	0.630446i
$453$		0			0
$454$			3.30846e6i			0.753332i
$455$		0			0
$456$		0			0
$457$	−4.15779e6	−	4.15779e6i	−0.931263	−	0.931263i	0.0665219	−	0.997785i	$-0.478810\pi$
$457$	−4.15779e6	−	4.15779e6i	−0.931263	−	0.931263i	−0.997785	+	0.0665219i	$0.978810\pi$
$458$	80708.1	+	80708.1i	0.0179785	+	0.0179785i
$459$		0			0
$460$		0			0
$461$			5.95742e6i			1.30559i	0.757535	+	0.652794i	$0.226403\pi$
$461$			5.95742e6i			1.30559i	−0.757535	+	0.652794i	$0.773597\pi$
$462$		0			0
$463$	−1.41469e6	+	1.41469e6i	−0.306697	+	0.306697i	−0.843627	−	0.536930i	$-0.819584\pi$
$463$	−1.41469e6	+	1.41469e6i	−0.306697	+	0.306697i	0.536930	+	0.843627i	$0.319584\pi$
$464$	−1.37753e6			−0.297034
$465$		0			0
$466$	−2.71352e6			−0.578854
$467$	−1.26542e6	+	1.26542e6i	−0.268500	+	0.268500i	−0.828495	−	0.559996i	$-0.810803\pi$
$467$	−1.26542e6	+	1.26542e6i	−0.268500	+	0.268500i	0.559996	+	0.828495i	$0.310803\pi$
$468$		0			0
$469$		−	6.49072e6i		−	1.36258i
$470$		0			0
$471$		0			0
$472$	−2.04750e6	−	2.04750e6i	−0.423027	−	0.423027i
$473$	−5.35590e6	−	5.35590e6i	−1.10073	−	1.10073i
$474$		0			0
$475$		0			0
$476$		−	2.69253e6i		−	0.544683i
$477$		0			0
$478$	−2.24838e6	+	2.24838e6i	−0.450090	+	0.450090i
$479$	−433242.			−0.0862764			−0.0431382	−	0.999069i	$-0.513736\pi$
$479$	−433242.			−0.0862764			−0.0431382	+	0.999069i	$0.513736\pi$
$480$		0			0
$481$	−1.17330e7			−2.31231
$482$	−4.47551e6	+	4.47551e6i	−0.877455	+	0.877455i
$483$		0			0
$484$			2.10517e6i			0.408482i
$485$		0			0
$486$		0			0
$487$	−1.57807e6	−	1.57807e6i	−0.301511	−	0.301511i	0.540094	−	0.841605i	$-0.318389\pi$
$487$	−1.57807e6	−	1.57807e6i	−0.301511	−	0.301511i	−0.841605	+	0.540094i	$0.818389\pi$
$488$	−27415.1	−	27415.1i	−0.00521122	−	0.00521122i
$489$		0			0
$490$		0			0
$491$		−	7.51329e6i		−	1.40646i	−0.710964	−	0.703228i	$-0.751741\pi$
$491$		−	7.51329e6i		−	1.40646i	0.710964	−	0.703228i	$-0.248259\pi$
$492$		0			0
$493$	3.21901e6	−	3.21901e6i	0.596492	−	0.596492i
$494$	8.06249e6			1.48646
$495$		0			0
$496$	−461611.			−0.0842504
$497$	−1.58963e6	+	1.58963e6i	−0.288672	+	0.288672i
$498$		0			0
$499$		−	7.36148e6i		−	1.32347i	−0.749738	−	0.661735i	$-0.769821\pi$
$499$		−	7.36148e6i		−	1.32347i	0.749738	−	0.661735i	$-0.230179\pi$
$500$		0			0
$501$		0			0
$502$	3.88692e6	+	3.88692e6i	0.688408	+	0.688408i
$503$	617251.	+	617251.i	0.108778	+	0.108778i	0.759401	−	0.650623i	$-0.225492\pi$
$503$	617251.	+	617251.i	0.108778	+	0.108778i	−0.650623	+	0.759401i	$0.725492\pi$
$504$		0			0
$505$		0			0
$506$			2.19745e6i			0.381542i
$507$		0			0
$508$	−1.28027e6	+	1.28027e6i	−0.220111	+	0.220111i
$509$	−6.12846e6			−1.04847			−0.524236	−	0.851573i	$-0.675649\pi$
$509$	−6.12846e6			−1.04847			−0.524236	+	0.851573i	$0.675649\pi$
$510$		0			0
$511$	1.17821e7			1.99604
$512$	185364.	−	185364.i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	2.00182e6i		−	0.334209i
$515$		0			0
$516$		0			0
$517$	985270.	+	985270.i	0.162117	+	0.162117i
$518$	5.84338e6	+	5.84338e6i	0.956842	+	0.956842i
$519$		0			0
$520$		0			0
$521$			5.64518e6i			0.911137i	0.890201	+	0.455568i	$0.150564\pi$
$521$			5.64518e6i			0.911137i	−0.890201	+	0.455568i	$0.849436\pi$
$522$		0			0
$523$	6.09740e6	−	6.09740e6i	0.974744	−	0.974744i	−0.0249444	−	0.999689i	$-0.507941\pi$
$523$	6.09740e6	−	6.09740e6i	0.974744	−	0.974744i	0.999689	+	0.0249444i	$0.00794089\pi$
$524$	2.96465e6			0.471678
$525$		0			0
$526$	−4.96242e6			−0.782040
$527$	1.07869e6	−	1.07869e6i	0.169189	−	0.169189i
$528$		0			0
$529$		−	5.40499e6i		−	0.839761i
$530$		0			0
$531$		0			0
$532$	−4.01537e6	−	4.01537e6i	−0.615101	−	0.615101i
$533$	9.97387e6	+	9.97387e6i	1.52071	+	1.52071i
$534$		0			0
$535$		0			0
$536$			2.08837e6i			0.313976i
$537$		0			0
$538$	5.60077e6	−	5.60077e6i	0.834243	−	0.834243i
$539$	1.23118e7			1.82537
$540$		0			0
$541$	−311432.			−0.0457477			−0.0228739	−	0.999738i	$-0.507282\pi$
$541$	−311432.			−0.0457477			−0.0228739	+	0.999738i	$0.507282\pi$
$542$	1.91813e6	−	1.91813e6i	0.280466	−	0.280466i
$543$		0			0
$544$			866316.i			0.125510i
$545$		0			0
$546$		0			0
$547$	−1.47279e6	−	1.47279e6i	−0.210461	−	0.210461i	0.594002	−	0.804463i	$-0.297547\pi$
$547$	−1.47279e6	−	1.47279e6i	−0.210461	−	0.210461i	−0.804463	+	0.594002i	$0.797547\pi$
$548$	485799.	+	485799.i	0.0691043	+	0.0691043i
$549$		0			0
$550$		0			0
$551$		−	9.60100e6i		−	1.34722i
$552$		0			0
$553$	8.71145e6	−	8.71145e6i	1.21137	−	1.21137i
$554$	−4.22625e6			−0.585034
$555$		0			0
$556$	−1.20546e6			−0.165374
$557$	254284.	−	254284.i	0.0347281	−	0.0347281i	−0.689530	−	0.724258i	$-0.742183\pi$
$557$	254284.	−	254284.i	0.0347281	−	0.0347281i	0.724258	+	0.689530i	$0.242183\pi$
$558$		0			0
$559$			1.58178e7i			2.14100i
$560$		0			0
$561$		0			0
$562$	6.44903e6	+	6.44903e6i	0.861298	+	0.861298i
$563$	4.03909e6	+	4.03909e6i	0.537047	+	0.537047i	0.922660	−	0.385613i	$-0.126010\pi$
$563$	4.03909e6	+	4.03909e6i	0.537047	+	0.537047i	−0.385613	+	0.922660i	$0.626010\pi$
$564$		0			0
$565$		0			0
$566$			2.45261e6i			0.321801i
$567$		0			0
$568$	511459.	−	511459.i	0.0665181	−	0.0665181i
$569$	−2.72030e6			−0.352238			−0.176119	−	0.984369i	$-0.556354\pi$
$569$	−2.72030e6			−0.352238			−0.176119	+	0.984369i	$0.556354\pi$
$570$		0			0
$571$	−2.34348e6			−0.300796			−0.150398	−	0.988626i	$-0.548055\pi$
$571$	−2.34348e6			−0.300796			−0.150398	+	0.988626i	$0.548055\pi$
$572$	6.91375e6	−	6.91375e6i	0.883535	−	0.883535i
$573$		0			0
$574$		−	9.93458e6i		−	1.25855i
$575$		0			0
$576$		0			0
$577$	5.80678e6	+	5.80678e6i	0.726099	+	0.726099i	0.969840	−	0.243741i	$-0.0783748\pi$
$577$	5.80678e6	+	5.80678e6i	0.726099	+	0.726099i	−0.243741	+	0.969840i	$0.578375\pi$
$578$	1.99156e6	+	1.99156e6i	0.247955	+	0.247955i
$579$		0			0
$580$		0			0
$581$		−	2.31046e7i		−	2.83961i
$582$		0			0
$583$	8.70340e6	−	8.70340e6i	1.06052	−	1.06052i
$584$	−3.79086e6			−0.459944
$585$		0			0
$586$	−1.31884e6			−0.158653
$587$	−7.26783e6	+	7.26783e6i	−0.870581	+	0.870581i	−0.992536	−	0.121954i	$-0.961084\pi$
$587$	−7.26783e6	+	7.26783e6i	−0.870581	+	0.870581i	0.121954	+	0.992536i	$0.461084\pi$
$588$		0			0
$589$		−	3.21730e6i		−	0.382123i
$590$		0			0
$591$		0			0
$592$	−1.88009e6	−	1.88009e6i	−0.220483	−	0.220483i
$593$	−8.83276e6	−	8.83276e6i	−1.03148	−	1.03148i	−0.999488	−	0.0319896i	$-0.989816\pi$
$593$	−8.83276e6	−	8.83276e6i	−1.03148	−	1.03148i	−0.0319896	−	0.999488i	$-0.510184\pi$
$594$		0			0
$595$		0			0
$596$			2.00197e6i			0.230857i
$597$		0			0
$598$	3.24491e6	−	3.24491e6i	0.371065	−	0.371065i
$599$	1.64552e7			1.87386			0.936928	−	0.349522i	$-0.113656\pi$
$599$	1.64552e7			1.87386			0.936928	+	0.349522i	$0.113656\pi$
$600$		0			0
$601$	−1.36957e7			−1.54668			−0.773338	−	0.633994i	$-0.781414\pi$
$601$	−1.36957e7			−1.54668			−0.773338	+	0.633994i	$0.781414\pi$
$602$	7.87776e6	−	7.87776e6i	0.885954	−	0.885954i
$603$		0			0
$604$			6.71753e6i			0.749234i
$605$		0			0
$606$		0			0
$607$	2.85652e6	+	2.85652e6i	0.314677	+	0.314677i	0.846718	−	0.532041i	$-0.178575\pi$
$607$	2.85652e6	+	2.85652e6i	0.314677	+	0.314677i	−0.532041	+	0.846718i	$0.678575\pi$
$608$	1.29193e6	+	1.29193e6i	0.141736	+	0.141736i
$609$		0			0
$610$		0			0
$611$		−	2.90984e6i		−	0.315331i
$612$		0			0
$613$	−8.97843e6	+	8.97843e6i	−0.965049	+	0.965049i	−0.999409	−	0.0343607i	$-0.989061\pi$
$613$	−8.97843e6	+	8.97843e6i	−0.965049	+	0.965049i	0.0343607	+	0.999409i	$0.489061\pi$
$614$	3.77839e6			0.404470
$615$		0			0
$616$	−6.88652e6			−0.731220
$617$	3.16198e6	−	3.16198e6i	0.334385	−	0.334385i	−0.519864	−	0.854249i	$-0.674017\pi$
$617$	3.16198e6	−	3.16198e6i	0.334385	−	0.334385i	0.854249	+	0.519864i	$0.174017\pi$
$618$		0			0
$619$			2.02582e6i			0.212508i	0.994339	+	0.106254i	$0.0338856\pi$
$619$			2.02582e6i			0.212508i	−0.994339	+	0.106254i	$0.966114\pi$
$620$		0			0
$621$		0			0
$622$	2.83319e6	+	2.83319e6i	0.293630	+	0.293630i
$623$	−1.51723e6	−	1.51723e6i	−0.156614	−	0.156614i
$624$		0			0
$625$		0			0
$626$			1.02180e7i			1.04215i
$627$		0			0
$628$	2.39372e6	−	2.39372e6i	0.242200	−	0.242200i
$629$	8.78680e6			0.885532
$630$		0			0
$631$	−1.08365e7			−1.08347			−0.541734	−	0.840550i	$-0.682232\pi$
$631$	−1.08365e7			−1.08347			−0.541734	+	0.840550i	$0.682232\pi$
$632$	−2.80289e6	+	2.80289e6i	−0.279134	+	0.279134i
$633$		0			0
$634$		−	6.18553e6i		−	0.611158i
$635$		0			0
$636$		0			0
$637$	−1.81805e7	−	1.81805e7i	−1.77524	−	1.77524i
$638$	−8.23305e6	−	8.23305e6i	−0.800773	−	0.800773i
$639$		0			0
$640$		0			0
$641$		−	1.19747e7i		−	1.15112i	−0.817760	−	0.575559i	$-0.804785\pi$
$641$		−	1.19747e7i		−	1.15112i	0.817760	−	0.575559i	$-0.195215\pi$
$642$		0			0
$643$	6.52742e6	−	6.52742e6i	0.622607	−	0.622607i	−0.323590	−	0.946197i	$-0.604890\pi$
$643$	6.52742e6	−	6.52742e6i	0.622607	−	0.622607i	0.946197	+	0.323590i	$0.104890\pi$
$644$	−3.23213e6			−0.307096
$645$		0			0
$646$	−6.03798e6			−0.569260
$647$	−7.04412e6	+	7.04412e6i	−0.661555	+	0.661555i	−0.955747	−	0.294191i	$-0.904950\pi$
$647$	−7.04412e6	+	7.04412e6i	−0.661555	+	0.661555i	0.294191	+	0.955747i	$0.404950\pi$
$648$		0			0
$649$		−	2.44745e7i		−	2.28088i
$650$		0			0
$651$		0			0
$652$	3.70514e6	+	3.70514e6i	0.341339	+	0.341339i
$653$	1.42497e6	+	1.42497e6i	0.130774	+	0.130774i	0.769464	−	0.638690i	$-0.220523\pi$
$653$	1.42497e6	+	1.42497e6i	0.130774	+	0.130774i	−0.638690	+	0.769464i	$0.720523\pi$
$654$		0			0
$655$		0			0
$656$			3.19643e6i			0.290005i
$657$		0			0
$658$	−1.44919e6	+	1.44919e6i	−0.130485	+	0.130485i
$659$	8.38442e6			0.752072			0.376036	−	0.926605i	$-0.377287\pi$
$659$	8.38442e6			0.752072			0.376036	+	0.926605i	$0.377287\pi$
$660$		0			0
$661$	8.38637e6			0.746569			0.373285	−	0.927717i	$-0.378231\pi$
$661$	8.38637e6			0.746569			0.373285	+	0.927717i	$0.378231\pi$
$662$	7.14637e6	−	7.14637e6i	0.633783	−	0.633783i
$663$		0			0
$664$			7.43384e6i			0.654325i
$665$		0			0
$666$		0			0
$667$	−3.86411e6	−	3.86411e6i	−0.336306	−	0.336306i
$668$	−2.80380e6	−	2.80380e6i	−0.243112	−	0.243112i
$669$		0			0
$670$		0			0
$671$		−	327702.i		−	0.0280978i
$672$		0			0
$673$	7.15707e6	−	7.15707e6i	0.609113	−	0.609113i	−0.333602	−	0.942714i	$-0.608264\pi$
$673$	7.15707e6	−	7.15707e6i	0.609113	−	0.609113i	0.942714	+	0.333602i	$0.108264\pi$
$674$	1.44449e7			1.22480
$675$		0			0
$676$	−1.44780e7			−1.21855
$677$	1.19723e6	−	1.19723e6i	0.100393	−	0.100393i	−0.655126	−	0.755519i	$-0.727385\pi$
$677$	1.19723e6	−	1.19723e6i	0.100393	−	0.100393i	0.755519	+	0.655126i	$0.227385\pi$
$678$		0			0
$679$			1.44703e7i			1.20449i
$680$		0			0
$681$		0			0
$682$	−2.75890e6	−	2.75890e6i	−0.227130	−	0.227130i
$683$	−6.40752e6	−	6.40752e6i	−0.525580	−	0.525580i	0.393672	−	0.919251i	$-0.371205\pi$
$683$	−6.40752e6	−	6.40752e6i	−0.525580	−	0.525580i	−0.919251	+	0.393672i	$0.871205\pi$
$684$		0			0
$685$		0			0
$686$			4.73632e6i			0.384265i
$687$		0			0
$688$	−2.53465e6	+	2.53465e6i	−0.204149	+	0.204149i
$689$	−2.57041e7			−2.06279
$690$		0			0
$691$	1.04957e7			0.836214			0.418107	−	0.908398i	$-0.362694\pi$
$691$	1.04957e7			0.836214			0.418107	+	0.908398i	$0.362694\pi$
$692$	2.77221e6	−	2.77221e6i	0.220070	−	0.220070i
$693$		0			0
$694$		−	4.79208e6i		−	0.377681i
$695$		0			0
$696$		0			0
$697$	−7.46940e6	−	7.46940e6i	−0.582377	−	0.582377i
$698$	1.14689e7	+	1.14689e7i	0.891011	+	0.891011i
$699$		0			0
$700$		0			0
$701$		−	1.30048e7i		−	0.999560i	−0.866152	−	0.499780i	$-0.833414\pi$
$701$		−	1.30048e7i		−	0.999560i	0.866152	−	0.499780i	$-0.166586\pi$
$702$		0			0
$703$	1.31037e7	−	1.31037e7i	1.00002	−	1.00002i
$704$	2.21572e6			0.168494
$705$		0			0
$706$	3.73294e6			0.281864
$707$	2.58665e7	−	2.58665e7i	1.94620	−	1.94620i
$708$		0			0
$709$		−	5.36809e6i		−	0.401056i	−0.979688	−	0.200528i	$-0.935734\pi$
$709$		−	5.36809e6i		−	0.401056i	0.979688	−	0.200528i	$-0.0642657\pi$
$710$		0			0
$711$		0			0
$712$	488164.	+	488164.i	0.0360883	+	0.0360883i
$713$	−1.29487e6	−	1.29487e6i	−0.0953896	−	0.0953896i
$714$		0			0
$715$		0			0
$716$		−	1.31046e7i		−	0.955301i
$717$		0			0
$718$	−1.01451e7	+	1.01451e7i	−0.734422	+	0.734422i
$719$	4.98201e6			0.359403			0.179702	−	0.983721i	$-0.442487\pi$
$719$	4.98201e6			0.359403			0.179702	+	0.983721i	$0.442487\pi$
$720$		0			0
$721$	2.37774e7			1.70344
$722$	−2.00096e6	+	2.00096e6i	−0.142855	+	0.142855i
$723$		0			0
$724$			4.30296e6i			0.305085i
$725$		0			0
$726$		0			0
$727$	−2.33509e6	−	2.33509e6i	−0.163858	−	0.163858i	0.620416	−	0.784273i	$-0.286964\pi$
$727$	−2.33509e6	−	2.33509e6i	−0.163858	−	0.163858i	−0.784273	+	0.620416i	$0.786964\pi$
$728$	1.01691e7	+	1.01691e7i	0.711141	+	0.711141i
$729$		0			0
$730$		0			0
$731$		−	1.18459e7i		−	0.819927i
$732$		0			0
$733$	−1.25922e7	+	1.25922e7i	−0.865650	+	0.865650i	−0.991987	−	0.126337i	$-0.959678\pi$
$733$	−1.25922e7	+	1.25922e7i	−0.865650	+	0.865650i	0.126337	+	0.991987i	$0.459678\pi$
$734$	7.57545e6			0.519001
$735$		0			0
$736$	1.03993e6			0.0707635
$737$	−1.24815e7	+	1.24815e7i	−0.846446	+	0.846446i
$738$		0			0
$739$			3.79608e6i			0.255696i	0.991794	+	0.127848i	$0.0408070\pi$
$739$			3.79608e6i			0.255696i	−0.991794	+	0.127848i	$0.959193\pi$
$740$		0			0
$741$		0			0
$742$	1.28014e7	+	1.28014e7i	0.853590	+	0.853590i
$743$	−1.26035e7	−	1.26035e7i	−0.837563	−	0.837563i	0.150974	−	0.988538i	$-0.451759\pi$
$743$	−1.26035e7	−	1.26035e7i	−0.837563	−	0.837563i	−0.988538	+	0.150974i	$0.951759\pi$
$744$		0			0
$745$		0			0
$746$			1.28394e7i			0.844689i
$747$		0			0
$748$	−5.17769e6	+	5.17769e6i	−0.338362	+	0.338362i
$749$	−5.94641e6			−0.387302
$750$		0			0
$751$	−1.62657e7			−1.05238			−0.526190	−	0.850367i	$-0.676380\pi$
$751$	−1.62657e7			−1.05238			−0.526190	+	0.850367i	$0.676380\pi$
$752$	466273.	−	466273.i	0.0300674	−	0.0300674i
$753$		0			0
$754$			2.43150e7i			1.55757i
$755$		0			0
$756$		0			0
$757$	1.96785e7	+	1.96785e7i	1.24811	+	1.24811i	0.956554	+	0.291555i	$0.0941727\pi$
$757$	1.96785e7	+	1.96785e7i	1.24811	+	1.24811i	0.291555	+	0.956554i	$0.405827\pi$
$758$	1.32297e7	+	1.32297e7i	0.836326	+	0.836326i
$759$		0			0
$760$		0			0
$761$			1.76431e7i			1.10437i	0.833723	+	0.552183i	$0.186205\pi$
$761$			1.76431e7i			1.10437i	−0.833723	+	0.552183i	$0.813795\pi$
$762$		0			0
$763$	7.40881e6	−	7.40881e6i	0.460720	−	0.460720i
$764$	−8.22016e6			−0.509503
$765$		0			0
$766$	−9.07717e6			−0.558957
$767$	−3.61408e7	+	3.61408e7i	−2.21824	+	2.21824i
$768$		0			0
$769$			3.37152e6i			0.205594i	0.994702	+	0.102797i	$0.0327791\pi$
$769$			3.37152e6i			0.205594i	−0.994702	+	0.102797i	$0.967221\pi$
$770$		0			0
$771$		0			0
$772$	3.00770e6	+	3.00770e6i	0.181631	+	0.181631i
$773$	1.91448e7	+	1.91448e7i	1.15240	+	1.15240i	0.986071	+	0.166324i	$0.0531898\pi$
$773$	1.91448e7	+	1.91448e7i	1.15240	+	1.15240i	0.166324	+	0.986071i	$0.446810\pi$
$774$		0			0
$775$		0			0
$776$		−	4.65578e6i		−	0.277548i
$777$		0			0
$778$	4.77000e6	−	4.77000e6i	0.282533	−	0.282533i
$779$	−2.22782e7			−1.31534
$780$		0			0
$781$	6.11365e6			0.358652
$782$	−2.43010e6	+	2.43010e6i	−0.142105	+	0.142105i
$783$		0			0
$784$		−	5.82649e6i		−	0.338545i
$785$		0			0
$786$		0			0
$787$	6.34689e6	+	6.34689e6i	0.365279	+	0.365279i	0.865752	−	0.500473i	$-0.166841\pi$
$787$	6.34689e6	+	6.34689e6i	0.365279	+	0.365279i	−0.500473	+	0.865752i	$0.666841\pi$
$788$	−1.19337e7	−	1.19337e7i	−0.684635	−	0.684635i
$789$		0			0
$790$		0			0
$791$			4.81453e7i			2.73598i
$792$		0			0
$793$	−483908.	+	483908.i	−0.0273263	+	0.0273263i
$794$	−7.96467e6			−0.448349
$795$		0			0
$796$	6.57699e6			0.367913
$797$	−1.07553e7	+	1.07553e7i	−0.599758	+	0.599758i	−0.940248	−	0.340490i	$-0.889407\pi$
$797$	−1.07553e7	+	1.07553e7i	−0.599758	+	0.599758i	0.340490	+	0.940248i	$0.389407\pi$
$798$		0			0
$799$			2.17917e6i			0.120760i
$800$		0			0
$801$		0			0
$802$	3.83660e6	+	3.83660e6i	0.210625	+	0.210625i
$803$	−2.26567e7	−	2.26567e7i	−1.23996	−	1.23996i
$804$		0			0
$805$		0			0
$806$			8.14798e6i			0.441787i
$807$		0			0
$808$	−8.32246e6	+	8.32246e6i	−0.448460	+	0.448460i
$809$	−1.62013e7			−0.870320			−0.435160	−	0.900353i	$-0.643308\pi$
$809$	−1.62013e7			−0.870320			−0.435160	+	0.900353i	$0.643308\pi$
$810$		0			0
$811$	−826427.			−0.0441217			−0.0220609	−	0.999757i	$-0.507023\pi$
$811$	−826427.			−0.0441217			−0.0220609	+	0.999757i	$0.507023\pi$
$812$	1.21096e7	−	1.21096e7i	0.644527	−	0.644527i
$813$		0			0
$814$		−	2.24734e7i		−	1.18880i
$815$		0			0
$816$		0			0
$817$	−1.76658e7	−	1.76658e7i	−0.925929	−	0.925929i
$818$	8.45953e6	+	8.45953e6i	0.442041	+	0.442041i
$819$		0			0
$820$		0			0
$821$		−	8.76364e6i		−	0.453761i	−0.973923	−	0.226880i	$-0.927147\pi$
$821$		−	8.76364e6i		−	0.453761i	0.973923	−	0.226880i	$-0.0728526\pi$
$822$		0			0
$823$	−1.62027e7	+	1.62027e7i	−0.833849	+	0.833849i	−0.988041	−	0.154192i	$-0.950723\pi$
$823$	−1.62027e7	+	1.62027e7i	−0.833849	+	0.833849i	0.154192	+	0.988041i	$0.450723\pi$
$824$	−7.65032e6			−0.392520
$825$		0			0
$826$	3.59984e7			1.83583
$827$	−5.28656e6	+	5.28656e6i	−0.268788	+	0.268788i	−0.828612	−	0.559824i	$-0.810869\pi$
$827$	−5.28656e6	+	5.28656e6i	−0.268788	+	0.268788i	0.559824	+	0.828612i	$0.310869\pi$
$828$		0			0
$829$		−	3.49472e6i		−	0.176614i	−0.996093	−	0.0883072i	$-0.971854\pi$
$829$		−	3.49472e6i		−	0.176614i	0.996093	−	0.0883072i	$-0.0281457\pi$
$830$		0			0
$831$		0			0
$832$	−3.27189e6	−	3.27189e6i	−0.163867	−	0.163867i
$833$	1.36153e7	+	1.36153e7i	0.679854	+	0.679854i
$834$		0			0
$835$		0			0
$836$			1.54430e7i			0.764213i
$837$		0			0
$838$	−4.26788e6	+	4.26788e6i	−0.209944	+	0.209944i
$839$	2.31902e7			1.13737			0.568683	−	0.822557i	$-0.307453\pi$
$839$	2.31902e7			1.13737			0.568683	+	0.822557i	$0.307453\pi$
$840$		0			0
$841$	8.44375e6			0.411666
$842$	1.67576e7	−	1.67576e7i	0.814576	−	0.814576i
$843$		0			0
$844$			3.89741e6i			0.188330i
$845$		0			0
$846$		0			0
$847$	−1.85062e7	−	1.85062e7i	−0.886356	−	0.886356i
$848$	−4.11883e6	−	4.11883e6i	−0.196691	−	0.196691i
$849$		0			0
$850$		0			0
$851$		−	1.05477e7i		−	0.499269i
$852$		0			0
$853$	−2.30682e7	+	2.30682e7i	−1.08553	+	1.08553i	−0.0895430	+	0.995983i	$0.528541\pi$
$853$	−2.30682e7	+	2.30682e7i	−1.08553	+	1.08553i	−0.995983	+	0.0895430i	$0.971459\pi$
$854$	482003.			0.0226154
$855$		0			0
$856$	1.91324e6			0.0892453
$857$	−7.59368e6	+	7.59368e6i	−0.353183	+	0.353183i	−0.861293	−	0.508109i	$-0.830345\pi$
$857$	−7.59368e6	+	7.59368e6i	−0.353183	+	0.353183i	0.508109	+	0.861293i	$0.330345\pi$
$858$		0			0
$859$		−	1.42112e6i		−	0.0657127i	−0.999460	−	0.0328563i	$-0.989540\pi$
$859$		−	1.42112e6i		−	0.0657127i	0.999460	−	0.0328563i	$-0.0104604\pi$
$860$		0			0
$861$		0			0
$862$	−7.86615e6	−	7.86615e6i	−0.360574	−	0.360574i
$863$	−1.78343e7	−	1.78343e7i	−0.815133	−	0.815133i	0.170266	−	0.985398i	$-0.445537\pi$
$863$	−1.78343e7	−	1.78343e7i	−0.815133	−	0.815133i	−0.985398	+	0.170266i	$0.945537\pi$
$864$		0			0
$865$		0			0
$866$			3.81516e6i			0.172869i
$867$		0			0
$868$	4.05795e6	−	4.05795e6i	0.182813	−	0.182813i
$869$	−3.35039e7			−1.50503
$870$		0			0
$871$	3.68623e7			1.64640
$872$	−2.38376e6	+	2.38376e6i	−0.106163	+	0.106163i
$873$		0			0
$874$			7.24801e6i			0.320952i
$875$		0			0
$876$		0			0
$877$	6.43434e6	+	6.43434e6i	0.282491	+	0.282491i	0.834102	−	0.551611i	$-0.185987\pi$
$877$	6.43434e6	+	6.43434e6i	0.282491	+	0.282491i	−0.551611	+	0.834102i	$0.685987\pi$
$878$	−1.70854e7	−	1.70854e7i	−0.747980	−	0.747980i
$879$		0			0
$880$		0			0
$881$			2.64210e7i			1.14686i	0.819256	+	0.573428i	$0.194387\pi$
$881$			2.64210e7i			1.14686i	−0.819256	+	0.573428i	$0.805613\pi$
$882$		0			0
$883$	−1.32206e7	+	1.32206e7i	−0.570622	+	0.570622i	−0.932302	−	0.361680i	$-0.882203\pi$
$883$	−1.32206e7	+	1.32206e7i	−0.570622	+	0.570622i	0.361680	+	0.932302i	$0.382203\pi$
$884$	1.52915e7			0.658142
$885$		0			0
$886$	−1.06846e7			−0.457269
$887$	3.04269e7	−	3.04269e7i	1.29852	−	1.29852i	0.369150	−	0.929370i	$-0.379649\pi$
$887$	3.04269e7	−	3.04269e7i	1.29852	−	1.29852i	0.929370	−	0.369150i	$-0.120351\pi$
$888$		0			0
$889$		−	2.25092e7i		−	0.955226i
$890$		0			0
$891$		0			0
$892$	−7.02061e6	−	7.02061e6i	−0.295436	−	0.295436i
$893$	3.24979e6	+	3.24979e6i	0.136373	+	0.136373i
$894$		0			0
$895$		0			0
$896$			3.25900e6i			0.135617i
$897$		0			0
$898$	−8.46954e6	+	8.46954e6i	−0.350485	+	0.350485i
$899$	9.70280e6			0.400404
$900$		0			0
$901$	1.92498e7			0.789975
$902$	−1.91040e7	+	1.91040e7i	−0.781823	+	0.781823i
$903$		0			0
$904$		−	1.54906e7i		−	0.630446i
$905$		0			0
$906$		0			0
$907$	2.23326e7	+	2.23326e7i	0.901408	+	0.901408i	0.995558	−	0.0941500i	$-0.0300133\pi$
$907$	2.23326e7	+	2.23326e7i	0.901408	+	0.901408i	−0.0941500	+	0.995558i	$0.530013\pi$
$908$	9.35775e6	+	9.35775e6i	0.376666	+	0.376666i
$909$		0			0
$910$		0			0
$911$		−	2.60012e7i		−	1.03800i	−0.854775	−	0.518999i	$-0.826305\pi$
$911$		−	2.60012e7i		−	1.03800i	0.854775	−	0.518999i	$-0.173695\pi$
$912$		0			0
$913$	−4.44297e7	+	4.44297e7i	−1.76399	+	1.76399i
$914$	−2.35200e7			−0.931263
$915$		0			0
$916$	456554.			0.0179785
$917$	−2.60618e7	+	2.60618e7i	−1.02348	+	1.02348i
$918$		0			0
$919$			1.80057e7i			0.703268i	0.936138	+	0.351634i	$0.114374\pi$
$919$			1.80057e7i			0.703268i	−0.936138	+	0.351634i	$0.885626\pi$
$920$		0			0
$921$		0			0
$922$	1.68501e7	+	1.68501e7i	0.652794	+	0.652794i
$923$	−9.02785e6	−	9.02785e6i	−0.348803	−	0.348803i
$924$		0			0
$925$		0			0
$926$			8.00270e6i			0.306697i
$927$		0			0
$928$	−3.89624e6	+	3.89624e6i	−0.148517	+	0.148517i
$929$	4.92761e6			0.187326			0.0936628	−	0.995604i	$-0.470142\pi$
$929$	4.92761e6			0.187326			0.0936628	+	0.995604i	$0.470142\pi$
$930$		0			0
$931$	4.06090e7			1.53549
$932$	−7.67501e6	+	7.67501e6i	−0.289427	+	0.289427i
$933$		0			0
$934$			7.15832e6i			0.268500i
$935$		0			0
$936$		0			0
$937$	2.59273e6	+	2.59273e6i	0.0964737	+	0.0964737i	0.753696	−	0.657223i	$-0.228269\pi$
$937$	2.59273e6	+	2.59273e6i	0.0964737	+	0.0964737i	−0.657223	+	0.753696i	$0.728269\pi$
$938$	−1.83585e7	−	1.83585e7i	−0.681288	−	0.681288i
$939$		0			0
$940$		0			0
$941$		−	9.69862e6i		−	0.357056i	−0.983935	−	0.178528i	$-0.942867\pi$
$941$		−	9.69862e6i		−	0.357056i	0.983935	−	0.178528i	$-0.0571335\pi$
$942$		0			0
$943$	−8.96630e6	+	8.96630e6i	−0.328348	+	0.328348i
$944$	−1.15824e7			−0.423027
$945$		0			0
$946$	−3.02975e7			−1.10073
$947$	2.70302e7	−	2.70302e7i	0.979431	−	0.979431i	−0.0203616	−	0.999793i	$-0.506482\pi$
$947$	2.70302e7	−	2.70302e7i	0.979431	−	0.979431i	0.999793	+	0.0203616i	$0.00648173\pi$
$948$		0			0
$949$			6.69131e7i			2.41182i
$950$		0			0
$951$		0			0
$952$	−7.61564e6	−	7.61564e6i	−0.272342	−	0.272342i
$953$	1.51028e7	+	1.51028e7i	0.538674	+	0.538674i	0.923139	−	0.384466i	$-0.125614\pi$
$953$	1.51028e7	+	1.51028e7i	0.538674	+	0.538674i	−0.384466	+	0.923139i	$0.625614\pi$
$954$		0			0
$955$		0			0
$956$			1.27187e7i			0.450090i
$957$		0			0
$958$	−1.22539e6	+	1.22539e6i	−0.0431382	+	0.0431382i
$959$	−8.54115e6			−0.299895
$960$		0			0
$961$	−2.53777e7			−0.886430
$962$	−3.31859e7	+	3.31859e7i	−1.15615	+	1.15615i
$963$		0			0
$964$			2.53173e7i			0.877455i
$965$		0			0
$966$		0			0
$967$	−2.69949e6	−	2.69949e6i	−0.0928360	−	0.0928360i	0.659164	−	0.752000i	$-0.270910\pi$
$967$	−2.69949e6	−	2.69949e6i	−0.0928360	−	0.0928360i	−0.752000	+	0.659164i	$0.770910\pi$
$968$	5.95431e6	+	5.95431e6i	0.204241	+	0.204241i
$969$		0			0
$970$		0			0
$971$		−	5.74219e6i		−	0.195447i	−0.995214	−	0.0977235i	$-0.968844\pi$
$971$		−	5.74219e6i		−	0.195447i	0.995214	−	0.0977235i	$-0.0311561\pi$
$972$		0			0
$973$	1.05970e7	−	1.05970e7i	0.358841	−	0.358841i
$974$	−8.92690e6			−0.301511
$975$		0			0
$976$	−155083.			−0.00521122
$977$	3.62050e6	−	3.62050e6i	0.121348	−	0.121348i	−0.643825	−	0.765173i	$-0.722654\pi$
$977$	3.62050e6	−	3.62050e6i	0.121348	−	0.121348i	0.765173	+	0.643825i	$0.222654\pi$
$978$		0			0
$979$			5.83520e6i			0.194581i
$980$		0			0
$981$		0			0
$982$	−2.12508e7	−	2.12508e7i	−0.703228	−	0.703228i
$983$	−9.59647e6	−	9.59647e6i	−0.316758	−	0.316758i	0.530762	−	0.847521i	$-0.321906\pi$
$983$	−9.59647e6	−	9.59647e6i	−0.316758	−	0.316758i	−0.847521	+	0.530762i	$0.821906\pi$
$984$		0			0
$985$		0			0
$986$		−	1.82095e7i		−	0.596492i
$987$		0			0
$988$	2.28042e7	−	2.28042e7i	0.743228	−	0.743228i
$989$	−1.42199e7			−0.462280
$990$		0			0
$991$	3.21393e7			1.03956			0.519782	−	0.854299i	$-0.326013\pi$
$991$	3.21393e7			1.03956			0.519782	+	0.854299i	$0.326013\pi$
$992$	−1.30563e6	+	1.30563e6i	−0.0421252	+	0.0421252i
$993$		0			0
$994$			8.99230e6i			0.288672i
$995$		0			0
$996$		0			0
$997$	−3.23317e6	−	3.23317e6i	−0.103013	−	0.103013i	0.653722	−	0.756735i	$-0.273207\pi$
$997$	−3.23317e6	−	3.23317e6i	−0.103013	−	0.103013i	−0.756735	+	0.653722i	$0.773207\pi$
$998$	−2.08214e7	−	2.08214e7i	−0.661735	−	0.661735i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.6.f.g.107.7	yes	16
3.2	odd	2	inner	450.6.f.g.107.3	yes	16
5.2	odd	4		450.6.f.f.143.6	yes	16
5.3	odd	4	inner	450.6.f.g.143.3	yes	16
5.4	even	2		450.6.f.f.107.2	✓	16
15.2	even	4		450.6.f.f.143.2	yes	16
15.8	even	4	inner	450.6.f.g.143.7	yes	16
15.14	odd	2		450.6.f.f.107.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.6.f.f.107.2	✓	16	5.4	even	2
450.6.f.f.107.6	yes	16	15.14	odd	2
450.6.f.f.143.2	yes	16	15.2	even	4
450.6.f.f.143.6	yes	16	5.2	odd	4
450.6.f.g.107.3	yes	16	3.2	odd	2	inner
450.6.f.g.107.7	yes	16	1.1	even	1	trivial
450.6.f.g.143.3	yes	16	5.3	odd	4	inner
450.6.f.g.143.7	yes	16	15.8	even	4	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	450.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.82843 - 2.82843i) q^{2} -16.0000i q^{4} +(140.653 + 140.653i) q^{7} +(-45.2548 - 45.2548i) q^{8} +O(q^{10})\)	\(q+(2.82843 - 2.82843i) q^{2} -16.0000i q^{4} +(140.653 + 140.653i) q^{7} +(-45.2548 - 45.2548i) q^{8} -540.947i q^{11} +(-798.801 + 798.801i) q^{13} +795.655 q^{14} -256.000 q^{16} +(598.220 - 598.220i) q^{17} -1784.25i q^{19} +(-1530.03 - 1530.03i) q^{22} +(-718.106 - 718.106i) q^{23} +4518.70i q^{26} +(2250.45 - 2250.45i) q^{28} +5380.98 q^{29} +1803.17 q^{31} +(-724.077 + 724.077i) q^{32} -3384.05i q^{34} +(7344.12 + 7344.12i) q^{37} +(-5046.62 - 5046.62i) q^{38} -12486.0i q^{41} +(9900.97 - 9900.97i) q^{43} -8655.16 q^{44} -4062.22 q^{46} +(-1821.38 + 1821.38i) q^{47} +22759.7i q^{49} +(12780.8 + 12780.8i) q^{52} +(16089.2 + 16089.2i) q^{53} -12730.5i q^{56} +(15219.7 - 15219.7i) q^{58} +45243.7 q^{59} +605.793 q^{61} +(5100.13 - 5100.13i) q^{62} +4096.00i q^{64} +(-23073.5 - 23073.5i) q^{67} +(-9571.53 - 9571.53i) q^{68} +11301.7i q^{71} +(41883.4 - 41883.4i) q^{73} +41544.6 q^{74} -28548.0 q^{76} +(76086.0 - 76086.0i) q^{77} -61935.6i q^{79} +(-35315.9 - 35315.9i) q^{82} +(-82133.1 - 82133.1i) q^{83} -56008.3i q^{86} +(-24480.5 + 24480.5i) q^{88} -10787.0 q^{89} -224708. q^{91} +(-11489.7 + 11489.7i) q^{92} +10303.3i q^{94} +(51439.5 + 51439.5i) q^{97} +(64374.2 + 64374.2i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 528 q^{7}+O(q^{10}) \) 16 * q + 528 * q^7	\( 16 q + 528 q^{7} - 192 q^{13} - 4096 q^{16} + 2688 q^{22} + 8448 q^{28} + 13024 q^{31} + 47328 q^{37} + 55440 q^{43} + 44544 q^{46} + 3072 q^{52} + 101184 q^{58} + 28400 q^{61} - 242256 q^{67} + 430944 q^{73} - 7168 q^{76} - 158208 q^{82} + 43008 q^{88} - 185472 q^{91} - 457152 q^{97}+O(q^{100}) \) 16 * q + 528 * q^7 - 192 * q^13 - 4096 * q^16 + 2688 * q^22 + 8448 * q^28 + 13024 * q^31 + 47328 * q^37 + 55440 * q^43 + 44544 * q^46 + 3072 * q^52 + 101184 * q^58 + 28400 * q^61 - 242256 * q^67 + 430944 * q^73 - 7168 * q^76 - 158208 * q^82 + 43008 * q^88 - 185472 * q^91 - 457152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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