LMFDB - Embedded newform 450.6.f.e.143.1

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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3457x^{8} + 2937456x^{4} + 12960000 $ x^12 + 3457x^8 + 2937456x^4 + 12960000
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.1
Root			$-1.02615 - 1.02615i$ of defining polynomial
Character	$\chi$	$=$	450.143
Dual form			450.6.f.e.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.82843 - 2.82843i) q^{2} +16.0000i q^{4} +(-148.726 + 148.726i) q^{7} +(45.2548 - 45.2548i) q^{8} +O(q^{10})$	\(q+(-2.82843 - 2.82843i) q^{2} +16.0000i q^{4} +(-148.726 + 148.726i) q^{7} +(45.2548 - 45.2548i) q^{8} -299.527i q^{11} +(193.262 + 193.262i) q^{13} +841.322 q^{14} -256.000 q^{16} +(-1522.21 - 1522.21i) q^{17} +1748.19i q^{19} +(-847.191 + 847.191i) q^{22} +(-2539.27 + 2539.27i) q^{23} -1093.25i q^{26} +(-2379.62 - 2379.62i) q^{28} +2617.43 q^{29} -8652.76 q^{31} +(724.077 + 724.077i) q^{32} +8610.89i q^{34} +(5378.10 - 5378.10i) q^{37} +(4944.63 - 4944.63i) q^{38} +1586.56i q^{41} +(-2005.55 - 2005.55i) q^{43} +4792.44 q^{44} +14364.3 q^{46} +(11013.5 + 11013.5i) q^{47} -27431.9i q^{49} +(-3092.19 + 3092.19i) q^{52} +(9879.22 - 9879.22i) q^{53} +13461.2i q^{56} +(-7403.22 - 7403.22i) q^{58} +13932.3 q^{59} -28140.7 q^{61} +(24473.7 + 24473.7i) q^{62} -4096.00i q^{64} +(-24197.7 + 24197.7i) q^{67} +(24355.3 - 24355.3i) q^{68} +6518.47i q^{71} +(61503.1 + 61503.1i) q^{73} -30423.1 q^{74} -27971.0 q^{76} +(44547.6 + 44547.6i) q^{77} -42431.1i q^{79} +(4487.47 - 4487.47i) q^{82} +(33805.9 - 33805.9i) q^{83} +11345.1i q^{86} +(-13555.1 - 13555.1i) q^{88} +63913.9 q^{89} -57486.2 q^{91} +(-40628.3 - 40628.3i) q^{92} -62301.7i q^{94} +(58905.9 - 58905.9i) q^{97} +(-77589.2 + 77589.2i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 144 q^{7}+O(q^{10}) $ 12 * q - 144 * q^7	$ 12 q - 144 q^{7} + 276 q^{13} - 3072 q^{16} - 384 q^{22} - 2304 q^{28} - 58512 q^{31} - 25764 q^{37} - 16080 q^{43} - 60672 q^{46} - 4416 q^{52} - 23952 q^{58} - 145200 q^{61} - 33552 q^{67} + 158988 q^{73} - 86016 q^{76} + 75024 q^{82} - 6144 q^{88} - 465024 q^{91} + 631116 q^{97}+O(q^{100}) $ 12 * q - 144 * q^7 + 276 * q^13 - 3072 * q^16 - 384 * q^22 - 2304 * q^28 - 58512 * q^31 - 25764 * q^37 - 16080 * q^43 - 60672 * q^46 - 4416 * q^52 - 23952 * q^58 - 145200 * q^61 - 33552 * q^67 + 158988 * q^73 - 86016 * q^76 + 75024 * q^82 - 6144 * q^88 - 465024 * q^91 + 631116 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$7$	−148.726	+	148.726i	−1.14721	+	1.14721i	−0.160109	+	0.987099i	$0.551184\pi$
$7$	−148.726	+	148.726i	−1.14721	+	1.14721i	−0.987099	+	0.160109i	$0.948816\pi$
$8$	45.2548	−	45.2548i	0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$		−	299.527i		−	0.746371i	−0.927757	−	0.373186i	$-0.878265\pi$
$11$		−	299.527i		−	0.746371i	0.927757	−	0.373186i	$-0.121735\pi$
$12$		0			0
$13$	193.262	+	193.262i	0.317167	+	0.317167i	0.847678	−	0.530511i	$-0.178000\pi$
$13$	193.262	+	193.262i	0.317167	+	0.317167i	−0.530511	+	0.847678i	$0.678000\pi$
$14$	841.322			1.14721
$15$		0			0
$16$	−256.000			−0.250000
$17$	−1522.21	−	1522.21i	−1.27747	−	1.27747i	−0.942079	−	0.335392i	$-0.891131\pi$
$17$	−1522.21	−	1522.21i	−1.27747	−	1.27747i	−0.335392	−	0.942079i	$-0.608869\pi$
$18$		0			0
$19$			1748.19i			1.11098i	0.831525	+	0.555488i	$0.187468\pi$
$19$			1748.19i			1.11098i	−0.831525	+	0.555488i	$0.812532\pi$
$20$		0			0
$21$		0			0
$22$	−847.191	+	847.191i	−0.373186	+	0.373186i
$23$	−2539.27	+	2539.27i	−1.00090	+	1.00090i	−0.000896947		1.00000i	$0.500286\pi$
$23$	−2539.27	+	2539.27i	−1.00090	+	1.00090i	−1.00000		0.000896947i	$0.999714\pi$
$24$		0			0
$25$		0			0
$26$		−	1093.25i		−	0.317167i
$27$		0			0
$28$	−2379.62	−	2379.62i	−0.573604	−	0.573604i
$29$	2617.43			0.577937			0.288969	−	0.957339i	$-0.406688\pi$
$29$	2617.43			0.577937			0.288969	+	0.957339i	$0.406688\pi$
$30$		0			0
$31$	−8652.76			−1.61715			−0.808575	−	0.588393i	$-0.799761\pi$
$31$	−8652.76			−1.61715			−0.808575	+	0.588393i	$0.799761\pi$
$32$	724.077	+	724.077i	0.125000	+	0.125000i
$33$		0			0
$34$			8610.89i			1.27747i
$35$		0			0
$36$		0			0
$37$	5378.10	−	5378.10i	0.645840	−	0.645840i	−0.306145	−	0.951985i	$-0.599039\pi$
$37$	5378.10	−	5378.10i	0.645840	−	0.645840i	0.951985	+	0.306145i	$0.0990393\pi$
$38$	4944.63	−	4944.63i	0.555488	−	0.555488i
$39$		0			0
$40$		0			0
$41$			1586.56i			0.147400i	0.997280	+	0.0737000i	$0.0234807\pi$
$41$			1586.56i			0.147400i	−0.997280	+	0.0737000i	$0.976519\pi$
$42$		0			0
$43$	−2005.55	−	2005.55i	−0.165410	−	0.165410i	0.619548	−	0.784959i	$-0.287316\pi$
$43$	−2005.55	−	2005.55i	−0.165410	−	0.165410i	−0.784959	+	0.619548i	$0.787316\pi$
$44$	4792.44			0.373186
$45$		0			0
$46$	14364.3			1.00090
$47$	11013.5	+	11013.5i	0.727245	+	0.727245i	0.970070	−	0.242825i	$-0.0780742\pi$
$47$	11013.5	+	11013.5i	0.727245	+	0.727245i	−0.242825	+	0.970070i	$0.578074\pi$
$48$		0			0
$49$		−	27431.9i		−	1.63217i
$50$		0			0
$51$		0			0
$52$	−3092.19	+	3092.19i	−0.158584	+	0.158584i
$53$	9879.22	−	9879.22i	0.483096	−	0.483096i	−0.423023	−	0.906119i	$-0.639031\pi$
$53$	9879.22	−	9879.22i	0.483096	−	0.483096i	0.906119	+	0.423023i	$0.139031\pi$
$54$		0			0
$55$		0			0
$56$			13461.2i			0.573604i
$57$		0			0
$58$	−7403.22	−	7403.22i	−0.288969	−	0.288969i
$59$	13932.3			0.521066			0.260533	−	0.965465i	$-0.416102\pi$
$59$	13932.3			0.521066			0.260533	+	0.965465i	$0.416102\pi$
$60$		0			0
$61$	−28140.7			−0.968301			−0.484151	−	0.874985i	$-0.660871\pi$
$61$	−28140.7			−0.968301			−0.484151	+	0.874985i	$0.660871\pi$
$62$	24473.7	+	24473.7i	0.808575	+	0.808575i
$63$		0			0
$64$		−	4096.00i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	−24197.7	+	24197.7i	−0.658547	+	0.658547i	−0.955036	−	0.296489i	$-0.904184\pi$
$67$	−24197.7	+	24197.7i	−0.658547	+	0.658547i	0.296489	+	0.955036i	$0.404184\pi$
$68$	24355.3	−	24355.3i	0.638735	−	0.638735i
$69$		0			0
$70$		0			0
$71$			6518.47i			0.153462i	0.997052	+	0.0767308i	$0.0244482\pi$
$71$			6518.47i			0.153462i	−0.997052	+	0.0767308i	$0.975552\pi$
$72$		0			0
$73$	61503.1	+	61503.1i	1.35080	+	1.35080i	0.884772	+	0.466025i	$0.154314\pi$
$73$	61503.1	+	61503.1i	1.35080	+	1.35080i	0.466025	+	0.884772i	$0.345686\pi$
$74$	−30423.1			−0.645840
$75$		0			0
$76$	−27971.0			−0.555488
$77$	44547.6	+	44547.6i	0.856243	+	0.856243i
$78$		0			0
$79$		−	42431.1i		−	0.764921i	−0.923972	−	0.382460i	$-0.875077\pi$
$79$		−	42431.1i		−	0.764921i	0.923972	−	0.382460i	$-0.124923\pi$
$80$		0			0
$81$		0			0
$82$	4487.47	−	4487.47i	0.0737000	−	0.0737000i
$83$	33805.9	−	33805.9i	0.538638	−	0.538638i	−0.384491	−	0.923129i	$-0.625623\pi$
$83$	33805.9	−	33805.9i	0.538638	−	0.538638i	0.923129	+	0.384491i	$0.125623\pi$
$84$		0			0
$85$		0			0
$86$			11345.1i			0.165410i
$87$		0			0
$88$	−13555.1	−	13555.1i	−0.186593	−	0.186593i
$89$	63913.9			0.855304			0.427652	−	0.903944i	$-0.359341\pi$
$89$	63913.9			0.855304			0.427652	+	0.903944i	$0.359341\pi$
$90$		0			0
$91$	−57486.2			−0.727713
$92$	−40628.3	−	40628.3i	−0.500448	−	0.500448i
$93$		0			0
$94$		−	62301.7i		−	0.727245i
$95$		0			0
$96$		0			0
$97$	58905.9	−	58905.9i	0.635667	−	0.635667i	−0.313817	−	0.949484i	$-0.601608\pi$
$97$	58905.9	−	58905.9i	0.635667	−	0.635667i	0.949484	+	0.313817i	$0.101608\pi$
$98$	−77589.2	+	77589.2i	−0.816086	+	0.816086i
$99$		0			0
$100$		0			0
$101$		−	140291.i		−	1.36844i	−0.729276	−	0.684220i	$-0.760143\pi$
$101$		−	140291.i		−	1.36844i	0.729276	−	0.684220i	$-0.239857\pi$
$102$		0			0
$103$	−77193.5	−	77193.5i	−0.716948	−	0.716948i	0.251031	−	0.967979i	$-0.419231\pi$
$103$	−77193.5	−	77193.5i	−0.716948	−	0.716948i	−0.967979	+	0.251031i	$0.919231\pi$
$104$	17492.1			0.158584
$105$		0			0
$106$	−55885.3			−0.483096
$107$	65849.8	+	65849.8i	0.556026	+	0.556026i	0.928174	−	0.372148i	$-0.121378\pi$
$107$	65849.8	+	65849.8i	0.556026	+	0.556026i	−0.372148	+	0.928174i	$0.621378\pi$
$108$		0			0
$109$			27880.3i			0.224766i	0.993665	+	0.112383i	$0.0358483\pi$
$109$			27880.3i			0.224766i	−0.993665	+	0.112383i	$0.964152\pi$
$110$		0			0
$111$		0			0
$112$	38073.9	−	38073.9i	0.286802	−	0.286802i
$113$	52351.3	−	52351.3i	0.385684	−	0.385684i	−0.487461	−	0.873145i	$-0.662077\pi$
$113$	52351.3	−	52351.3i	0.385684	−	0.385684i	0.873145	+	0.487461i	$0.162077\pi$
$114$		0			0
$115$		0			0
$116$			41878.9i			0.288969i
$117$		0			0
$118$	−39406.5	−	39406.5i	−0.260533	−	0.260533i
$119$	452784.			2.93105
$120$		0			0
$121$	71334.3			0.442930
$122$	79593.9	+	79593.9i	0.484151	+	0.484151i
$123$		0			0
$124$		−	138444.i		−	0.808575i
$125$		0			0
$126$		0			0
$127$	185568.	−	185568.i	1.02092	−	1.02092i	0.0211467	−	0.999776i	$-0.493268\pi$
$127$	185568.	−	185568.i	1.02092	−	1.02092i	0.999776	−	0.0211467i	$-0.00673172\pi$
$128$	−11585.2	+	11585.2i	−0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$			190849.i			0.971655i	0.874055	+	0.485827i	$0.161482\pi$
$131$			190849.i			0.971655i	−0.874055	+	0.485827i	$0.838518\pi$
$132$		0			0
$133$	−260001.	−	260001.i	−1.27452	−	1.27452i
$134$	136883.			0.658547
$135$		0			0
$136$	−137774.			−0.638735
$137$	−127742.	−	127742.i	−0.581475	−	0.581475i	0.353834	−	0.935308i	$-0.384878\pi$
$137$	−127742.	−	127742.i	−0.581475	−	0.581475i	−0.935308	+	0.353834i	$0.884878\pi$
$138$		0			0
$139$		−	217966.i		−	0.956866i	−0.878124	−	0.478433i	$-0.841205\pi$
$139$		−	217966.i		−	0.956866i	0.878124	−	0.478433i	$-0.158795\pi$
$140$		0			0
$141$		0			0
$142$	18437.0	−	18437.0i	0.0767308	−	0.0767308i
$143$	57887.3	−	57887.3i	0.236724	−	0.236724i
$144$		0			0
$145$		0			0
$146$		−	347914.i		−	1.35080i
$147$		0			0
$148$	86049.6	+	86049.6i	0.322920	+	0.322920i
$149$	−461717.			−1.70377			−0.851883	−	0.523732i	$-0.824539\pi$
$149$	−461717.			−1.70377			−0.851883	+	0.523732i	$0.824539\pi$
$150$		0			0
$151$	−2616.56			−0.00933874			−0.00466937	−	0.999989i	$-0.501486\pi$
$151$	−2616.56			−0.00933874			−0.00466937	+	0.999989i	$0.501486\pi$
$152$	79114.0	+	79114.0i	0.277744	+	0.277744i
$153$		0			0
$154$		−	251999.i		−	0.856243i
$155$		0			0
$156$		0			0
$157$	331986.	−	331986.i	1.07491	−	1.07491i	0.0779479	−	0.996957i	$-0.475163\pi$
$157$	331986.	−	331986.i	1.07491	−	1.07491i	0.996957	−	0.0779479i	$-0.0248368\pi$
$158$	−120013.	+	120013.i	−0.382460	+	0.382460i
$159$		0			0
$160$		0			0
$161$		−	755311.i		−	2.29647i
$162$		0			0
$163$	−15020.2	−	15020.2i	−0.0442800	−	0.0442800i	0.684620	−	0.728900i	$-0.259968\pi$
$163$	−15020.2	−	15020.2i	−0.0442800	−	0.0442800i	−0.728900	+	0.684620i	$0.759968\pi$
$164$	−25385.0			−0.0737000
$165$		0			0
$166$	−191235.			−0.538638
$167$	−153251.	−	153251.i	−0.425217	−	0.425217i	0.461778	−	0.886995i	$-0.347212\pi$
$167$	−153251.	−	153251.i	−0.425217	−	0.425217i	−0.886995	+	0.461778i	$0.847212\pi$
$168$		0			0
$169$		−	296593.i		−	0.798810i
$170$		0			0
$171$		0			0
$172$	32088.8	−	32088.8i	0.0827052	−	0.0827052i
$173$	497806.	−	497806.i	1.26458	−	1.26458i	0.315725	−	0.948851i	$-0.397752\pi$
$173$	497806.	−	497806.i	1.26458	−	1.26458i	0.948851	−	0.315725i	$-0.102248\pi$
$174$		0			0
$175$		0			0
$176$			76679.0i			0.186593i
$177$		0			0
$178$	−180776.	−	180776.i	−0.427652	−	0.427652i
$179$	69083.5			0.161154			0.0805771	−	0.996748i	$-0.474324\pi$
$179$	69083.5			0.161154			0.0805771	+	0.996748i	$0.474324\pi$
$180$		0			0
$181$	−798930.			−1.81264			−0.906321	−	0.422589i	$-0.861121\pi$
$181$	−798930.			−1.81264			−0.906321	+	0.422589i	$0.861121\pi$
$182$	162596.	+	162596.i	0.363857	+	0.363857i
$183$		0			0
$184$			229828.i			0.500448i
$185$		0			0
$186$		0			0
$187$	−455942.	+	455942.i	−0.953467	+	0.953467i
$188$	−176216.	+	176216.i	−0.363622	+	0.363622i
$189$		0			0
$190$		0			0
$191$			172241.i			0.341628i	0.985303	+	0.170814i	$0.0546397\pi$
$191$			172241.i			0.341628i	−0.985303	+	0.170814i	$0.945360\pi$
$192$		0			0
$193$	414251.	+	414251.i	0.800516	+	0.800516i	0.983176	−	0.182660i	$-0.0584708\pi$
$193$	414251.	+	414251.i	0.800516	+	0.800516i	−0.182660	+	0.983176i	$0.558471\pi$
$194$	−333222.			−0.635667
$195$		0			0
$196$	438911.			0.816086
$197$	216065.	+	216065.i	0.396660	+	0.396660i	0.877053	−	0.480393i	$-0.159506\pi$
$197$	216065.	+	216065.i	0.396660	+	0.396660i	−0.480393	+	0.877053i	$0.659506\pi$
$198$		0			0
$199$		−	684282.i		−	1.22491i	−0.790507	−	0.612453i	$-0.790183\pi$
$199$		−	684282.i		−	1.22491i	0.790507	−	0.612453i	$-0.209817\pi$
$200$		0			0
$201$		0			0
$202$	−396802.	+	396802.i	−0.684220	+	0.684220i
$203$	−389281.	+	389281.i	−0.663014	+	0.663014i
$204$		0			0
$205$		0			0
$206$			436673.i			0.716948i
$207$		0			0
$208$	−49475.1	−	49475.1i	−0.0792918	−	0.0792918i
$209$	523631.			0.829200
$210$		0			0
$211$	764382.			1.18196			0.590982	−	0.806685i	$-0.298740\pi$
$211$	764382.			1.18196			0.590982	+	0.806685i	$0.298740\pi$
$212$	158068.	+	158068.i	0.241548	+	0.241548i
$213$		0			0
$214$		−	372503.i		−	0.556026i
$215$		0			0
$216$		0			0
$217$	1.28689e6	−	1.28689e6i	1.85521	−	1.85521i
$218$	78857.3	−	78857.3i	0.112383	−	0.112383i
$219$		0			0
$220$		0			0
$221$		−	588369.i		−	0.810343i
$222$		0			0
$223$	74975.5	+	74975.5i	0.100962	+	0.100962i	0.755783	−	0.654822i	$-0.227256\pi$
$223$	74975.5	+	74975.5i	0.100962	+	0.100962i	−0.654822	+	0.755783i	$0.727256\pi$
$224$	−215378.			−0.286802
$225$		0			0
$226$	−296144.			−0.385684
$227$	−691711.	−	691711.i	−0.890963	−	0.890963i	0.103650	−	0.994614i	$-0.466948\pi$
$227$	−691711.	−	691711.i	−0.890963	−	0.890963i	−0.994614	+	0.103650i	$0.966948\pi$
$228$		0			0
$229$			465990.i			0.587202i	0.955928	+	0.293601i	$0.0948537\pi$
$229$			465990.i			0.587202i	−0.955928	+	0.293601i	$0.905146\pi$
$230$		0			0
$231$		0			0
$232$	118451.	−	118451.i	0.144484	−	0.144484i
$233$	118173.	−	118173.i	0.142603	−	0.142603i	−0.632201	−	0.774804i	$-0.717848\pi$
$233$	118173.	−	118173.i	0.142603	−	0.142603i	0.774804	+	0.632201i	$0.217848\pi$
$234$		0			0
$235$		0			0
$236$			222917.i			0.260533i
$237$		0			0
$238$	−1.28067e6	−	1.28067e6i	−1.46552	−	1.46552i
$239$	1.50955e6			1.70943			0.854715	−	0.519097i	$-0.173732\pi$
$239$	1.50955e6			1.70943			0.854715	+	0.519097i	$0.173732\pi$
$240$		0			0
$241$	1.19777e6			1.32840			0.664200	−	0.747555i	$-0.268772\pi$
$241$	1.19777e6			1.32840			0.664200	+	0.747555i	$0.268772\pi$
$242$	−201764.	−	201764.i	−0.221465	−	0.221465i
$243$		0			0
$244$		−	450251.i		−	0.484151i
$245$		0			0
$246$		0			0
$247$	−337859.	+	337859.i	−0.352365	+	0.352365i
$248$	−391579.	+	391579.i	−0.404287	+	0.404287i
$249$		0			0
$250$		0			0
$251$			314772.i			0.315364i	0.987490	+	0.157682i	$0.0504021\pi$
$251$			314772.i			0.315364i	−0.987490	+	0.157682i	$0.949598\pi$
$252$		0			0
$253$	760581.	+	760581.i	0.747040	+	0.747040i
$254$	−1.04973e6			−1.02092
$255$		0			0
$256$	65536.0			0.0625000
$257$	605352.	+	605352.i	0.571709	+	0.571709i	0.932606	−	0.360897i	$-0.117529\pi$
$257$	605352.	+	605352.i	0.571709	+	0.571709i	−0.360897	+	0.932606i	$0.617529\pi$
$258$		0			0
$259$			1.59973e6i			1.48183i
$260$		0			0
$261$		0			0
$262$	539803.	−	539803.i	0.485827	−	0.485827i
$263$	463557.	−	463557.i	0.413251	−	0.413251i	−0.469618	−	0.882870i	$-0.655608\pi$
$263$	463557.	−	463557.i	0.413251	−	0.413251i	0.882870	+	0.469618i	$0.155608\pi$
$264$		0			0
$265$		0			0
$266$			1.47079e6i			1.27452i
$267$		0			0
$268$	−387163.	−	387163.i	−0.329273	−	0.329273i
$269$	1.07602e6			0.906646			0.453323	−	0.891346i	$-0.350238\pi$
$269$	1.07602e6			0.906646			0.453323	+	0.891346i	$0.350238\pi$
$270$		0			0
$271$	−1.74821e6			−1.44600			−0.723002	−	0.690846i	$-0.757238\pi$
$271$	−1.74821e6			−1.44600			−0.723002	+	0.690846i	$0.757238\pi$
$272$	389685.	+	389685.i	0.319368	+	0.319368i
$273$		0			0
$274$			722616.i			0.581475i
$275$		0			0
$276$		0			0
$277$	−720546.	+	720546.i	−0.564238	+	0.564238i	−0.930508	−	0.366271i	$-0.880634\pi$
$277$	−720546.	+	720546.i	−0.564238	+	0.564238i	0.366271	+	0.930508i	$0.380634\pi$
$278$	−616500.	+	616500.i	−0.478433	+	0.478433i
$279$		0			0
$280$		0			0
$281$			273453.i			0.206593i	0.994651	+	0.103297i	$0.0329391\pi$
$281$			273453.i			0.206593i	−0.994651	+	0.103297i	$0.967061\pi$
$282$		0			0
$283$	1.10987e6	+	1.10987e6i	0.823769	+	0.823769i	0.986646	−	0.162877i	$-0.0520774\pi$
$283$	1.10987e6	+	1.10987e6i	0.823769	+	0.823769i	−0.162877	+	0.986646i	$0.552077\pi$
$284$	−104296.			−0.0767308
$285$		0			0
$286$	−327460.			−0.236724
$287$	−235963.	−	235963.i	−0.169098	−	0.169098i
$288$		0			0
$289$			3.21436e6i			2.26386i
$290$		0			0
$291$		0			0
$292$	−984050.	+	984050.i	−0.675398	+	0.675398i
$293$	182132.	−	182132.i	0.123941	−	0.123941i	−0.642415	−	0.766357i	$-0.722068\pi$
$293$	182132.	−	182132.i	0.123941	−	0.123941i	0.766357	+	0.642415i	$0.222068\pi$
$294$		0			0
$295$		0			0
$296$		−	486770.i		−	0.322920i
$297$		0			0
$298$	1.30593e6	+	1.30593e6i	0.851883	+	0.851883i
$299$	−981489.			−0.634903
$300$		0			0
$301$	596556.			0.379520
$302$	7400.75	+	7400.75i	0.00466937	+	0.00466937i
$303$		0			0
$304$		−	447537.i		−	0.277744i
$305$		0			0
$306$		0			0
$307$	−2.01256e6	+	2.01256e6i	−1.21872	+	1.21872i	−0.250638	+	0.968081i	$0.580640\pi$
$307$	−2.01256e6	+	2.01256e6i	−1.21872	+	1.21872i	−0.968081	+	0.250638i	$0.919360\pi$
$308$	−712761.	+	712761.i	−0.428122	+	0.428122i
$309$		0			0
$310$		0			0
$311$		−	1.05508e6i		−	0.618563i	−0.950970	−	0.309282i	$-0.899911\pi$
$311$		−	1.05508e6i		−	0.618563i	0.950970	−	0.309282i	$-0.100089\pi$
$312$		0			0
$313$	−228345.	−	228345.i	−0.131744	−	0.131744i	0.638160	−	0.769904i	$-0.279696\pi$
$313$	−228345.	−	228345.i	−0.131744	−	0.131744i	−0.769904	+	0.638160i	$0.779696\pi$
$314$	−1.87799e6			−1.07491
$315$		0			0
$316$	678897.			0.382460
$317$	−1.58626e6	−	1.58626e6i	−0.886599	−	0.886599i	0.107596	−	0.994195i	$-0.465685\pi$
$317$	−1.58626e6	−	1.58626e6i	−0.886599	−	0.886599i	−0.994195	+	0.107596i	$0.965685\pi$
$318$		0			0
$319$		−	783993.i		−	0.431356i
$320$		0			0
$321$		0			0
$322$	−2.13634e6	+	2.13634e6i	−1.14824	+	1.14824i
$323$	2.66110e6	−	2.66110e6i	1.41924	−	1.41924i
$324$		0			0
$325$		0			0
$326$			84967.3i			0.0442800i
$327$		0			0
$328$	71799.6	+	71799.6i	0.0368500	+	0.0368500i
$329$	−3.27599e6			−1.66860
$330$		0			0
$331$	2.34167e6			1.17478			0.587390	−	0.809304i	$-0.300155\pi$
$331$	2.34167e6			1.17478			0.587390	+	0.809304i	$0.300155\pi$
$332$	540894.	+	540894.i	0.269319	+	0.269319i
$333$		0			0
$334$			866916.i			0.425217i
$335$		0			0
$336$		0			0
$337$	−554612.	+	554612.i	−0.266020	+	0.266020i	−0.827494	−	0.561474i	$-0.810234\pi$
$337$	−554612.	+	554612.i	−0.266020	+	0.266020i	0.561474	+	0.827494i	$0.310234\pi$
$338$	−838891.	+	838891.i	−0.399405	+	0.399405i
$339$		0			0
$340$		0			0
$341$			2.59174e6i			1.20699i
$342$		0			0
$343$	1.58020e6	+	1.58020e6i	0.725234	+	0.725234i
$344$	−181522.			−0.0827052
$345$		0			0
$346$	−2.81602e6			−1.26458
$347$	−468716.	−	468716.i	−0.208971	−	0.208971i	0.594859	−	0.803830i	$-0.297208\pi$
$347$	−468716.	−	468716.i	−0.208971	−	0.208971i	−0.803830	+	0.594859i	$0.797208\pi$
$348$		0			0
$349$		−	445258.i		−	0.195681i	−0.995202	−	0.0978404i	$-0.968807\pi$
$349$		−	445258.i		−	0.195681i	0.995202	−	0.0978404i	$-0.0311935\pi$
$350$		0			0
$351$		0			0
$352$	216881.	−	216881.i	0.0932964	−	0.0932964i
$353$	−597724.	+	597724.i	−0.255308	+	0.255308i	−0.823142	−	0.567835i	$-0.807781\pi$
$353$	−597724.	+	597724.i	−0.255308	+	0.255308i	0.567835	+	0.823142i	$0.307781\pi$
$354$		0			0
$355$		0			0
$356$			1.02262e6i			0.427652i
$357$		0			0
$358$	−195398.	−	195398.i	−0.0805771	−	0.0805771i
$359$	−2.56995e6			−1.05242			−0.526208	−	0.850356i	$-0.676387\pi$
$359$	−2.56995e6			−1.05242			−0.526208	+	0.850356i	$0.676387\pi$
$360$		0			0
$361$	−580068.			−0.234267
$362$	2.25971e6	+	2.25971e6i	0.906321	+	0.906321i
$363$		0			0
$364$		−	919780.i		−	0.363857i
$365$		0			0
$366$		0			0
$367$	834880.	−	834880.i	0.323563	−	0.323563i	−0.526569	−	0.850132i	$-0.676522\pi$
$367$	834880.	−	834880.i	0.323563	−	0.323563i	0.850132	+	0.526569i	$0.176522\pi$
$368$	650053.	−	650053.i	0.250224	−	0.250224i
$369$		0			0
$370$		0			0
$371$			2.93860e6i			1.10842i
$372$		0			0
$373$	−680958.	−	680958.i	−0.253424	−	0.253424i	0.568949	−	0.822373i	$-0.307350\pi$
$373$	−680958.	−	680958.i	−0.253424	−	0.253424i	−0.822373	+	0.568949i	$0.807350\pi$
$374$	2.57920e6			0.953467
$375$		0			0
$376$	996828.			0.363622
$377$	505850.	+	505850.i	0.183303	+	0.183303i
$378$		0			0
$379$			4.63614e6i			1.65790i	0.559322	+	0.828951i	$0.311062\pi$
$379$			4.63614e6i			1.65790i	−0.559322	+	0.828951i	$0.688938\pi$
$380$		0			0
$381$		0			0
$382$	487171.	−	487171.i	0.170814	−	0.170814i
$383$	492138.	−	492138.i	0.171431	−	0.171431i	−0.616177	−	0.787608i	$-0.711319\pi$
$383$	492138.	−	492138.i	0.171431	−	0.171431i	0.787608	+	0.616177i	$0.211319\pi$
$384$		0			0
$385$		0			0
$386$		−	2.34336e6i		−	0.800516i
$387$		0			0
$388$	942495.	+	942495.i	0.317833	+	0.317833i
$389$	−1.09867e6			−0.368123			−0.184061	−	0.982915i	$-0.558925\pi$
$389$	−1.09867e6			−0.368123			−0.184061	+	0.982915i	$0.558925\pi$
$390$		0			0
$391$	7.73058e6			2.55723
$392$	−1.24143e6	−	1.24143e6i	−0.408043	−	0.408043i
$393$		0			0
$394$		−	1.22225e6i		−	0.396660i
$395$		0			0
$396$		0			0
$397$	1.07385e6	−	1.07385e6i	0.341955	−	0.341955i	−0.515147	−	0.857102i	$-0.672263\pi$
$397$	1.07385e6	−	1.07385e6i	0.341955	−	0.341955i	0.857102	+	0.515147i	$0.172263\pi$
$398$	−1.93544e6	+	1.93544e6i	−0.612453	+	0.612453i
$399$		0			0
$400$		0			0
$401$			1.01424e6i			0.314978i	0.987521	+	0.157489i	$0.0503398\pi$
$401$			1.01424e6i			0.314978i	−0.987521	+	0.157489i	$0.949660\pi$
$402$		0			0
$403$	−1.67225e6	−	1.67225e6i	−0.512907	−	0.512907i
$404$	2.24465e6			0.684220
$405$		0			0
$406$	2.20210e6			0.663014
$407$	−1.61089e6	−	1.61089e6i	−0.482036	−	0.482036i
$408$		0			0
$409$			4.68373e6i			1.38447i	0.721673	+	0.692235i	$0.243374\pi$
$409$			4.68373e6i			1.38447i	−0.721673	+	0.692235i	$0.756626\pi$
$410$		0			0
$411$		0			0
$412$	1.23510e6	−	1.23510e6i	0.358474	−	0.358474i
$413$	−2.07210e6	+	2.07210e6i	−0.597771	+	0.597771i
$414$		0			0
$415$		0			0
$416$			279873.i			0.0792918i
$417$		0			0
$418$	−1.48105e6	−	1.48105e6i	−0.414600	−	0.414600i
$419$	3.35986e6			0.934946			0.467473	−	0.884007i	$-0.345164\pi$
$419$	3.35986e6			0.934946			0.467473	+	0.884007i	$0.345164\pi$
$420$		0			0
$421$	−3.24290e6			−0.891719			−0.445859	−	0.895103i	$-0.647102\pi$
$421$	−3.24290e6			−0.891719			−0.445859	+	0.895103i	$0.647102\pi$
$422$	−2.16200e6	−	2.16200e6i	−0.590982	−	0.590982i
$423$		0			0
$424$		−	894165.i		−	0.241548i
$425$		0			0
$426$		0			0
$427$	4.18526e6	−	4.18526e6i	1.11084	−	1.11084i
$428$	−1.05360e6	+	1.05360e6i	−0.278013	+	0.278013i
$429$		0			0
$430$		0			0
$431$		−	6.54531e6i		−	1.69722i	−0.529022	−	0.848608i	$-0.677441\pi$
$431$		−	6.54531e6i		−	1.69722i	0.529022	−	0.848608i	$-0.322559\pi$
$432$		0			0
$433$	229102.	+	229102.i	0.0587232	+	0.0587232i	0.735859	−	0.677135i	$-0.236779\pi$
$433$	229102.	+	229102.i	0.0587232	+	0.0587232i	−0.677135	+	0.735859i	$0.736779\pi$
$434$	−7.27975e6			−1.85521
$435$		0			0
$436$	−446084.			−0.112383
$437$	−4.43912e6	−	4.43912e6i	−1.11197	−	1.11197i
$438$		0			0
$439$		−	1.97352e6i		−	0.488744i	−0.969682	−	0.244372i	$-0.921418\pi$
$439$		−	1.97352e6i		−	0.488744i	0.969682	−	0.244372i	$-0.0785817\pi$
$440$		0			0
$441$		0			0
$442$	−1.66416e6	+	1.66416e6i	−0.405172	+	0.405172i
$443$	−2.63389e6	+	2.63389e6i	−0.637660	+	0.637660i	−0.949978	−	0.312318i	$-0.898895\pi$
$443$	−2.63389e6	+	2.63389e6i	−0.637660	+	0.637660i	0.312318	+	0.949978i	$0.398895\pi$
$444$		0			0
$445$		0			0
$446$		−	424126.i		−	0.100962i
$447$		0			0
$448$	609182.	+	609182.i	0.143401	+	0.143401i
$449$	7.82998e6			1.83293			0.916463	−	0.400120i	$-0.131032\pi$
$449$	7.82998e6			1.83293			0.916463	+	0.400120i	$0.131032\pi$
$450$		0			0
$451$	475219.			0.110015
$452$	837621.	+	837621.i	0.192842	+	0.192842i
$453$		0			0
$454$			3.91291e6i			0.890963i
$455$		0			0
$456$		0			0
$457$	−5.32966e6	+	5.32966e6i	−1.19374	+	1.19374i	−0.217730	+	0.976009i	$0.569865\pi$
$457$	−5.32966e6	+	5.32966e6i	−1.19374	+	1.19374i	−0.976009	+	0.217730i	$0.930135\pi$
$458$	1.31802e6	−	1.31802e6i	0.293601	−	0.293601i
$459$		0			0
$460$		0			0
$461$		−	1.29678e6i		−	0.284192i	−0.989853	−	0.142096i	$-0.954616\pi$
$461$		−	1.29678e6i		−	0.284192i	0.989853	−	0.142096i	$-0.0453842\pi$
$462$		0			0
$463$	5.30186e6	+	5.30186e6i	1.14941	+	1.14941i	0.986668	+	0.162745i	$0.0520347\pi$
$463$	5.30186e6	+	5.30186e6i	1.14941	+	1.14941i	0.162745	+	0.986668i	$0.447965\pi$
$464$	−670063.			−0.144484
$465$		0			0
$466$	−668488.			−0.142603
$467$	885971.	+	885971.i	0.187987	+	0.187987i	0.794825	−	0.606838i	$-0.207562\pi$
$467$	885971.	+	885971.i	0.187987	+	0.187987i	−0.606838	+	0.794825i	$0.707562\pi$
$468$		0			0
$469$		−	7.19765e6i		−	1.51098i
$470$		0			0
$471$		0			0
$472$	630504.	−	630504.i	0.130266	−	0.130266i
$473$	−600718.	+	600718.i	−0.123458	+	0.123458i
$474$		0			0
$475$		0			0
$476$			7.24454e6i			1.46552i
$477$		0			0
$478$	−4.26964e6	−	4.26964e6i	−0.854715	−	0.854715i
$479$	−1.43334e6			−0.285438			−0.142719	−	0.989763i	$-0.545584\pi$
$479$	−1.43334e6			−0.285438			−0.142719	+	0.989763i	$0.545584\pi$
$480$		0			0
$481$	2.07877e6			0.409678
$482$	−3.38779e6	−	3.38779e6i	−0.664200	−	0.664200i
$483$		0			0
$484$			1.14135e6i			0.221465i
$485$		0			0
$486$		0			0
$487$	−994929.	+	994929.i	−0.190094	+	0.190094i	−0.795737	−	0.605642i	$-0.792916\pi$
$487$	−994929.	+	994929.i	−0.190094	+	0.190094i	0.605642	+	0.795737i	$0.292916\pi$
$488$	−1.27350e6	+	1.27350e6i	−0.242075	+	0.242075i
$489$		0			0
$490$		0			0
$491$		−	709316.i		−	0.132781i	−0.997794	−	0.0663905i	$-0.978852\pi$
$491$		−	709316.i		−	0.132781i	0.997794	−	0.0663905i	$-0.0211483\pi$
$492$		0			0
$493$	−3.98427e6	−	3.98427e6i	−0.738298	−	0.738298i
$494$	1.91122e6			0.352365
$495$		0			0
$496$	2.21511e6			0.404287
$497$	−969467.	−	969467.i	−0.176052	−	0.176052i
$498$		0			0
$499$		−	2.02748e6i		−	0.364507i	−0.983252	−	0.182253i	$-0.941661\pi$
$499$		−	2.02748e6i		−	0.364507i	0.983252	−	0.182253i	$-0.0583391\pi$
$500$		0			0
$501$		0			0
$502$	890311.	−	890311.i	0.157682	−	0.157682i
$503$	696310.	−	696310.i	0.122711	−	0.122711i	−0.643084	−	0.765795i	$-0.722346\pi$
$503$	696310.	−	696310.i	0.122711	−	0.122711i	0.765795	+	0.643084i	$0.222346\pi$
$504$		0			0
$505$		0			0
$506$		−	4.30249e6i		−	0.747040i
$507$		0			0
$508$	2.96908e6	+	2.96908e6i	0.510462	+	0.510462i
$509$	−4.63077e6			−0.792244			−0.396122	−	0.918198i	$-0.629644\pi$
$509$	−4.63077e6			−0.792244			−0.396122	+	0.918198i	$0.629644\pi$
$510$		0			0
$511$	−1.82942e7			−3.09929
$512$	−185364.	−	185364.i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	3.42439e6i		−	0.571709i
$515$		0			0
$516$		0			0
$517$	3.29884e6	−	3.29884e6i	0.542794	−	0.542794i
$518$	4.52472e6	−	4.52472e6i	0.740913	−	0.740913i
$519$		0			0
$520$		0			0
$521$		−	1.05159e7i		−	1.69728i	−0.528971	−	0.848640i	$-0.677422\pi$
$521$		−	1.05159e7i		−	1.69728i	0.528971	−	0.848640i	$-0.322578\pi$
$522$		0			0
$523$	−4.51262e6	−	4.51262e6i	−0.721397	−	0.721397i	0.247493	−	0.968890i	$-0.420393\pi$
$523$	−4.51262e6	−	4.51262e6i	−0.721397	−	0.721397i	−0.968890	+	0.247493i	$0.920393\pi$
$524$	−3.05359e6			−0.485827
$525$		0			0
$526$	−2.62228e6			−0.413251
$527$	1.31713e7	+	1.31713e7i	2.06586	+	2.06586i
$528$		0			0
$529$		−	6.45944e6i		−	1.00359i
$530$		0			0
$531$		0			0
$532$	4.16002e6	−	4.16002e6i	0.637260	−	0.637260i
$533$	−306622.	+	306622.i	−0.0467504	+	0.0467504i
$534$		0			0
$535$		0			0
$536$			2.19012e6i			0.329273i
$537$		0			0
$538$	−3.04343e6	−	3.04343e6i	−0.453323	−	0.453323i
$539$	−8.21661e6			−1.21821
$540$		0			0
$541$	1.01225e7			1.48695			0.743475	−	0.668764i	$-0.233176\pi$
$541$	1.01225e7			1.48695			0.743475	+	0.668764i	$0.233176\pi$
$542$	4.94467e6	+	4.94467e6i	0.723002	+	0.723002i
$543$		0			0
$544$		−	2.20439e6i		−	0.319368i
$545$		0			0
$546$		0			0
$547$	4.06823e6	−	4.06823e6i	0.581349	−	0.581349i	−0.353925	−	0.935274i	$-0.615153\pi$
$547$	4.06823e6	−	4.06823e6i	0.581349	−	0.581349i	0.935274	+	0.353925i	$0.115153\pi$
$548$	2.04387e6	−	2.04387e6i	0.290737	−	0.290737i
$549$		0			0
$550$		0			0
$551$			4.57577e6i			0.642074i
$552$		0			0
$553$	6.31061e6	+	6.31061e6i	0.877523	+	0.877523i
$554$	4.07602e6			0.564238
$555$		0			0
$556$	3.48745e6			0.478433
$557$	−910288.	−	910288.i	−0.124320	−	0.124320i	0.642209	−	0.766529i	$-0.278018\pi$
$557$	−910288.	−	910288.i	−0.124320	−	0.124320i	−0.766529	+	0.642209i	$0.778018\pi$
$558$		0			0
$559$		−	775194.i		−	0.104925i
$560$		0			0
$561$		0			0
$562$	773441.	−	773441.i	0.103297	−	0.103297i
$563$	8.14509e6	−	8.14509e6i	1.08299	−	1.08299i	0.0867627	−	0.996229i	$-0.472348\pi$
$563$	8.14509e6	−	8.14509e6i	1.08299	−	1.08299i	0.996229	−	0.0867627i	$-0.0276522\pi$
$564$		0			0
$565$		0			0
$566$		−	6.27837e6i		−	0.823769i
$567$		0			0
$568$	294992.	+	294992.i	0.0383654	+	0.0383654i
$569$	1.33483e7			1.72840			0.864200	−	0.503149i	$-0.167825\pi$
$569$	1.33483e7			1.72840			0.864200	+	0.503149i	$0.167825\pi$
$570$		0			0
$571$	−1.21487e7			−1.55934			−0.779669	−	0.626192i	$-0.784612\pi$
$571$	−1.21487e7			−1.55934			−0.779669	+	0.626192i	$0.784612\pi$
$572$	926196.	+	926196.i	0.118362	+	0.118362i
$573$		0			0
$574$			1.33481e6i			0.169098i
$575$		0			0
$576$		0			0
$577$	−248053.	+	248053.i	−0.0310174	+	0.0310174i	−0.722445	−	0.691428i	$-0.756982\pi$
$577$	−248053.	+	248053.i	−0.0310174	+	0.0310174i	0.691428	+	0.722445i	$0.256982\pi$
$578$	9.09159e6	−	9.09159e6i	1.13193	−	1.13193i
$579$		0			0
$580$		0			0
$581$			1.00556e7i			1.23586i
$582$		0			0
$583$	−2.95910e6	−	2.95910e6i	−0.360569	−	0.360569i
$584$	5.56663e6			0.675398
$585$		0			0
$586$	−1.03029e6			−0.123941
$587$	5.30886e6	+	5.30886e6i	0.635925	+	0.635925i	0.949548	−	0.313622i	$-0.101543\pi$
$587$	5.30886e6	+	5.30886e6i	0.635925	+	0.635925i	−0.313622	+	0.949548i	$0.601543\pi$
$588$		0			0
$589$		−	1.51267e7i		−	1.79661i
$590$		0			0
$591$		0			0
$592$	−1.37679e6	+	1.37679e6i	−0.161460	+	0.161460i
$593$	493935.	−	493935.i	0.0576811	−	0.0576811i	−0.677678	−	0.735359i	$-0.737014\pi$
$593$	493935.	−	493935.i	0.0576811	−	0.0576811i	0.735359	+	0.677678i	$0.237014\pi$
$594$		0			0
$595$		0			0
$596$		−	7.38747e6i		−	0.851883i
$597$		0			0
$598$	2.77607e6	+	2.77607e6i	0.317451	+	0.317451i
$599$	9.20782e6			1.04855			0.524276	−	0.851549i	$-0.324336\pi$
$599$	9.20782e6			1.04855			0.524276	+	0.851549i	$0.324336\pi$
$600$		0			0
$601$	2.89317e6			0.326729			0.163364	−	0.986566i	$-0.447765\pi$
$601$	2.89317e6			0.326729			0.163364	+	0.986566i	$0.447765\pi$
$602$	−1.68732e6	−	1.68732e6i	−0.189760	−	0.189760i
$603$		0			0
$604$		−	41865.0i		−	0.00466937i
$605$		0			0
$606$		0			0
$607$	−1.30019e6	+	1.30019e6i	−0.143230	+	0.143230i	−0.775086	−	0.631856i	$-0.782293\pi$
$607$	−1.30019e6	+	1.30019e6i	−0.143230	+	0.143230i	0.631856	+	0.775086i	$0.282293\pi$
$608$	−1.26582e6	+	1.26582e6i	−0.138872	+	0.138872i
$609$		0			0
$610$		0			0
$611$			4.25698e6i			0.461316i
$612$		0			0
$613$	−8.21096e6	−	8.21096e6i	−0.882558	−	0.882558i	0.111236	−	0.993794i	$-0.464519\pi$
$613$	−8.21096e6	−	8.21096e6i	−0.882558	−	0.882558i	−0.993794	+	0.111236i	$0.964519\pi$
$614$	1.13848e7			1.21872
$615$		0			0
$616$	4.03198e6			0.428122
$617$	4.68212e6	+	4.68212e6i	0.495142	+	0.495142i	0.909922	−	0.414780i	$-0.136141\pi$
$617$	4.68212e6	+	4.68212e6i	0.495142	+	0.495142i	−0.414780	+	0.909922i	$0.636141\pi$
$618$		0			0
$619$		−	2.83268e6i		−	0.297147i	−0.988901	−	0.148573i	$-0.952532\pi$
$619$		−	2.83268e6i		−	0.297147i	0.988901	−	0.148573i	$-0.0474681\pi$
$620$		0			0
$621$		0			0
$622$	−2.98422e6	+	2.98422e6i	−0.309282	+	0.309282i
$623$	−9.50567e6	+	9.50567e6i	−0.981211	+	0.981211i
$624$		0			0
$625$		0			0
$626$			1.29171e6i			0.131744i
$627$		0			0
$628$	5.31177e6	+	5.31177e6i	0.537453	+	0.537453i
$629$	−1.63732e7			−1.65008
$630$		0			0
$631$	−8.82438e6			−0.882289			−0.441144	−	0.897436i	$-0.645427\pi$
$631$	−8.82438e6			−0.882289			−0.441144	+	0.897436i	$0.645427\pi$
$632$	−1.92021e6	−	1.92021e6i	−0.191230	−	0.191230i
$633$		0			0
$634$			8.97326e6i			0.886599i
$635$		0			0
$636$		0			0
$637$	5.30155e6	−	5.30155e6i	0.517671	−	0.517671i
$638$	−2.21747e6	+	2.21747e6i	−0.215678	+	0.215678i
$639$		0			0
$640$		0			0
$641$		−	2.02407e6i		−	0.194572i	−0.995256	−	0.0972859i	$-0.968984\pi$
$641$		−	2.02407e6i		−	0.194572i	0.995256	−	0.0972859i	$-0.0310161\pi$
$642$		0			0
$643$	−1.17738e7	−	1.17738e7i	−1.12303	−	1.12303i	−0.991284	−	0.131744i	$-0.957942\pi$
$643$	−1.17738e7	−	1.17738e7i	−1.12303	−	1.12303i	−0.131744	−	0.991284i	$-0.542058\pi$
$644$	1.20850e7			1.14824
$645$		0			0
$646$	−1.50535e7			−1.41924
$647$	−3.10170e6	−	3.10170e6i	−0.291299	−	0.291299i	0.546294	−	0.837593i	$-0.316038\pi$
$647$	−3.10170e6	−	3.10170e6i	−0.291299	−	0.291299i	−0.837593	+	0.546294i	$0.816038\pi$
$648$		0			0
$649$		−	4.17310e6i		−	0.388909i
$650$		0			0
$651$		0			0
$652$	240324.	−	240324.i	0.0221400	−	0.0221400i
$653$	−1.37285e7	+	1.37285e7i	−1.25991	+	1.25991i	−0.308773	+	0.951136i	$0.599918\pi$
$653$	−1.37285e7	+	1.37285e7i	−1.25991	+	1.25991i	−0.951136	+	0.308773i	$0.900082\pi$
$654$		0			0
$655$		0			0
$656$		−	406160.i		−	0.0368500i
$657$		0			0
$658$	9.26590e6	+	9.26590e6i	0.834301	+	0.834301i
$659$	8.37025e6			0.750801			0.375401	−	0.926863i	$-0.377505\pi$
$659$	8.37025e6			0.750801			0.375401	+	0.926863i	$0.377505\pi$
$660$		0			0
$661$	−9.92386e6			−0.883440			−0.441720	−	0.897153i	$-0.645631\pi$
$661$	−9.92386e6			−0.883440			−0.441720	+	0.897153i	$0.645631\pi$
$662$	−6.62326e6	−	6.62326e6i	−0.587390	−	0.587390i
$663$		0			0
$664$		−	3.05976e6i		−	0.269319i
$665$		0			0
$666$		0			0
$667$	−6.64637e6	+	6.64637e6i	−0.578455	+	0.578455i
$668$	2.45201e6	−	2.45201e6i	0.212609	−	0.212609i
$669$		0			0
$670$		0			0
$671$			8.42891e6i			0.722712i
$672$		0			0
$673$	−3.57695e6	−	3.57695e6i	−0.304422	−	0.304422i	0.538319	−	0.842741i	$-0.319059\pi$
$673$	−3.57695e6	−	3.57695e6i	−0.304422	−	0.304422i	−0.842741	+	0.538319i	$0.819059\pi$
$674$	3.13736e6			0.266020
$675$		0			0
$676$	4.74548e6			0.399405
$677$	−1.16921e7	−	1.16921e7i	−0.980441	−	0.980441i	0.0193711	−	0.999812i	$-0.493834\pi$
$677$	−1.16921e7	−	1.16921e7i	−0.980441	−	0.980441i	−0.999812	+	0.0193711i	$0.993834\pi$
$678$		0			0
$679$			1.75217e7i			1.45848i
$680$		0			0
$681$		0			0
$682$	7.33054e6	−	7.33054e6i	0.603497	−	0.603497i
$683$	2.80028e6	−	2.80028e6i	0.229694	−	0.229694i	−0.582871	−	0.812565i	$-0.698071\pi$
$683$	2.80028e6	−	2.80028e6i	0.229694	−	0.229694i	0.812565	+	0.582871i	$0.198071\pi$
$684$		0			0
$685$		0			0
$686$		−	8.93899e6i		−	0.725234i
$687$		0			0
$688$	513421.	+	513421.i	0.0413526	+	0.0413526i
$689$	3.81856e6			0.306444
$690$		0			0
$691$	1.64582e6			0.131125			0.0655626	−	0.997848i	$-0.479116\pi$
$691$	1.64582e6			0.131125			0.0655626	+	0.997848i	$0.479116\pi$
$692$	7.96489e6	+	7.96489e6i	0.632288	+	0.632288i
$693$		0			0
$694$			2.65146e6i			0.208971i
$695$		0			0
$696$		0			0
$697$	2.41507e6	−	2.41507e6i	0.188299	−	0.188299i
$698$	−1.25938e6	+	1.25938e6i	−0.0978404	+	0.0978404i
$699$		0			0
$700$		0			0
$701$		−	6.83500e6i		−	0.525344i	−0.964885	−	0.262672i	$-0.915396\pi$
$701$		−	6.83500e6i		−	0.525344i	0.964885	−	0.262672i	$-0.0846037\pi$
$702$		0			0
$703$	9.40194e6	+	9.40194e6i	0.717512	+	0.717512i
$704$	−1.22686e6			−0.0932964
$705$		0			0
$706$	3.38124e6			0.255308
$707$	2.08649e7	+	2.08649e7i	1.56989	+	1.56989i
$708$		0			0
$709$		−	1.15425e7i		−	0.862352i	−0.902268	−	0.431176i	$-0.858099\pi$
$709$		−	1.15425e7i		−	0.862352i	0.902268	−	0.431176i	$-0.141901\pi$
$710$		0			0
$711$		0			0
$712$	2.89241e6	−	2.89241e6i	0.213826	−	0.213826i
$713$	2.19717e7	−	2.19717e7i	1.61860	−	1.61860i
$714$		0			0
$715$		0			0
$716$			1.10534e6i			0.0805771i
$717$		0			0
$718$	7.26890e6	+	7.26890e6i	0.526208	+	0.526208i
$719$	1.27402e6			0.0919084			0.0459542	−	0.998944i	$-0.485367\pi$
$719$	1.27402e6			0.0919084			0.0459542	+	0.998944i	$0.485367\pi$
$720$		0			0
$721$	2.29614e7			1.64498
$722$	1.64068e6	+	1.64068e6i	0.117133	+	0.117133i
$723$		0			0
$724$		−	1.27829e7i		−	0.906321i
$725$		0			0
$726$		0			0
$727$	−5.16629e6	+	5.16629e6i	−0.362529	+	0.362529i	−0.864743	−	0.502214i	$-0.832519\pi$
$727$	−5.16629e6	+	5.16629e6i	−0.362529	+	0.362529i	0.502214	+	0.864743i	$0.332519\pi$
$728$	−2.60153e6	+	2.60153e6i	−0.181928	+	0.181928i
$729$		0			0
$730$		0			0
$731$			6.10572e6i			0.422614i
$732$		0			0
$733$	−5.10747e6	−	5.10747e6i	−0.351112	−	0.351112i	0.509411	−	0.860523i	$-0.329863\pi$
$733$	−5.10747e6	−	5.10747e6i	−0.351112	−	0.351112i	−0.860523	+	0.509411i	$0.829863\pi$
$734$	−4.72280e6			−0.323563
$735$		0			0
$736$	−3.67725e6			−0.250224
$737$	7.24787e6	+	7.24787e6i	0.491520	+	0.491520i
$738$		0			0
$739$			1.03581e7i			0.697698i	0.937179	+	0.348849i	$0.113427\pi$
$739$			1.03581e7i			0.697698i	−0.937179	+	0.348849i	$0.886573\pi$
$740$		0			0
$741$		0			0
$742$	8.31161e6	−	8.31161e6i	0.554211	−	0.554211i
$743$	−1.53246e7	+	1.53246e7i	−1.01840	+	1.01840i	−0.0185675	+	0.999828i	$0.505911\pi$
$743$	−1.53246e7	+	1.53246e7i	−1.01840	+	1.01840i	−0.999828	+	0.0185675i	$0.994089\pi$
$744$		0			0
$745$		0			0
$746$			3.85208e6i			0.253424i
$747$		0			0
$748$	−7.29508e6	−	7.29508e6i	−0.476734	−	0.476734i
$749$	−1.95872e7			−1.27575
$750$		0			0
$751$	−5.50584e6			−0.356224			−0.178112	−	0.984010i	$-0.556999\pi$
$751$	−5.50584e6			−0.356224			−0.178112	+	0.984010i	$0.556999\pi$
$752$	−2.81945e6	−	2.81945e6i	−0.181811	−	0.181811i
$753$		0			0
$754$		−	2.86152e6i		−	0.183303i
$755$		0			0
$756$		0			0
$757$	−72342.5	+	72342.5i	−0.00458832	+	0.00458832i	−0.709397	−	0.704809i	$-0.751033\pi$
$757$	−72342.5	+	72342.5i	−0.00458832	+	0.00458832i	0.704809	+	0.709397i	$0.251033\pi$
$758$	1.31130e7	−	1.31130e7i	0.828951	−	0.828951i
$759$		0			0
$760$		0			0
$761$		−	2.39854e6i		−	0.150136i	−0.997178	−	0.0750680i	$-0.976083\pi$
$761$		−	2.39854e6i		−	0.150136i	0.997178	−	0.0750680i	$-0.0239174\pi$
$762$		0			0
$763$	−4.14652e6	−	4.14652e6i	−0.257853	−	0.257853i
$764$	−2.75585e6			−0.170814
$765$		0			0
$766$	−2.78396e6			−0.171431
$767$	2.69258e6	+	2.69258e6i	0.165265	+	0.165265i
$768$		0			0
$769$			3.62066e6i			0.220786i	0.993888	+	0.110393i	$0.0352110\pi$
$769$			3.62066e6i			0.220786i	−0.993888	+	0.110393i	$0.964789\pi$
$770$		0			0
$771$		0			0
$772$	−6.62801e6	+	6.62801e6i	−0.400258	+	0.400258i
$773$	−1.86029e6	+	1.86029e6i	−0.111978	+	0.111978i	−0.760876	−	0.648898i	$-0.775230\pi$
$773$	−1.86029e6	+	1.86029e6i	−0.111978	+	0.111978i	0.648898	+	0.760876i	$0.275230\pi$
$774$		0			0
$775$		0			0
$776$		−	5.33156e6i		−	0.317833i
$777$		0			0
$778$	3.10750e6	+	3.10750e6i	0.184061	+	0.184061i
$779$	−2.77361e6			−0.163758
$780$		0			0
$781$	1.95246e6			0.114539
$782$	−2.18654e7	−	2.18654e7i	−1.27862	−	1.27862i
$783$		0			0
$784$			7.02257e6i			0.408043i
$785$		0			0
$786$		0			0
$787$	−1.24400e7	+	1.24400e7i	−0.715951	+	0.715951i	−0.967774	−	0.251822i	$-0.918970\pi$
$787$	−1.24400e7	+	1.24400e7i	−0.715951	+	0.715951i	0.251822	+	0.967774i	$0.418970\pi$
$788$	−3.45704e6	+	3.45704e6i	−0.198330	+	0.198330i
$789$		0			0
$790$		0			0
$791$			1.55720e7i			0.884920i
$792$		0			0
$793$	−5.43853e6	−	5.43853e6i	−0.307113	−	0.307113i
$794$	−6.07463e6			−0.341955
$795$		0			0
$796$	1.09485e7			0.612453
$797$	−9.06451e6	−	9.06451e6i	−0.505473	−	0.505473i	0.407660	−	0.913134i	$-0.366345\pi$
$797$	−9.06451e6	−	9.06451e6i	−0.505473	−	0.505473i	−0.913134	+	0.407660i	$0.866345\pi$
$798$		0			0
$799$		−	3.35296e7i		−	1.85807i
$800$		0			0
$801$		0			0
$802$	2.86870e6	−	2.86870e6i	0.157489	−	0.157489i
$803$	1.84219e7	−	1.84219e7i	1.00820	−	1.00820i
$804$		0			0
$805$		0			0
$806$			9.45967e6i			0.512907i
$807$		0			0
$808$	−6.34884e6	−	6.34884e6i	−0.342110	−	0.342110i
$809$	−2.71042e7			−1.45601			−0.728006	−	0.685571i	$-0.759553\pi$
$809$	−2.71042e7			−1.45601			−0.728006	+	0.685571i	$0.759553\pi$
$810$		0			0
$811$	1.95248e7			1.04240			0.521199	−	0.853435i	$-0.325485\pi$
$811$	1.95248e7			1.04240			0.521199	+	0.853435i	$0.325485\pi$
$812$	−6.22849e6	−	6.22849e6i	−0.331507	−	0.331507i
$813$		0			0
$814$			9.11257e6i			0.482036i
$815$		0			0
$816$		0			0
$817$	3.50608e6	−	3.50608e6i	0.183767	−	0.183767i
$818$	1.32476e7	−	1.32476e7i	0.692235	−	0.692235i
$819$		0			0
$820$		0			0
$821$		−	3.24232e7i		−	1.67880i	−0.543517	−	0.839398i	$-0.682908\pi$
$821$		−	3.24232e7i		−	1.67880i	0.543517	−	0.839398i	$-0.317092\pi$
$822$		0			0
$823$	2.33214e7	+	2.33214e7i	1.20021	+	1.20021i	0.974104	+	0.226101i	$0.0725981\pi$
$823$	2.33214e7	+	2.33214e7i	1.20021	+	1.20021i	0.226101	+	0.974104i	$0.427402\pi$
$824$	−6.98676e6			−0.358474
$825$		0			0
$826$	1.17215e7			0.597771
$827$	−2.67706e6	−	2.67706e6i	−0.136111	−	0.136111i	0.635769	−	0.771880i	$-0.280683\pi$
$827$	−2.67706e6	−	2.67706e6i	−0.136111	−	0.136111i	−0.771880	+	0.635769i	$0.780683\pi$
$828$		0			0
$829$			2.75723e6i			0.139343i	0.997570	+	0.0696716i	$0.0221952\pi$
$829$			2.75723e6i			0.139343i	−0.997570	+	0.0696716i	$0.977805\pi$
$830$		0			0
$831$		0			0
$832$	791601.	−	791601.i	0.0396459	−	0.0396459i
$833$	−4.17570e7	+	4.17570e7i	−2.08505	+	2.08505i
$834$		0			0
$835$		0			0
$836$			8.37809e6i			0.414600i
$837$		0			0
$838$	−9.50313e6	−	9.50313e6i	−0.467473	−	0.467473i
$839$	1.04487e7			0.512458			0.256229	−	0.966616i	$-0.417520\pi$
$839$	1.04487e7			0.512458			0.256229	+	0.966616i	$0.417520\pi$
$840$		0			0
$841$	−1.36602e7			−0.665989
$842$	9.17230e6	+	9.17230e6i	0.445859	+	0.445859i
$843$		0			0
$844$			1.22301e7i			0.590982i
$845$		0			0
$846$		0			0
$847$	−1.06093e7	+	1.06093e7i	−0.508133	+	0.508133i
$848$	−2.52908e6	+	2.52908e6i	−0.120774	+	0.120774i
$849$		0			0
$850$		0			0
$851$			2.73129e7i			1.29284i
$852$		0			0
$853$	3.15656e6	+	3.15656e6i	0.148539	+	0.148539i	0.777465	−	0.628926i	$-0.216505\pi$
$853$	3.15656e6	+	3.15656e6i	0.148539	+	0.148539i	−0.628926	+	0.777465i	$0.716505\pi$
$854$	−2.36754e7			−1.11084
$855$		0			0
$856$	5.96004e6			0.278013
$857$	−1.85837e7	−	1.85837e7i	−0.864331	−	0.864331i	0.127507	−	0.991838i	$-0.459303\pi$
$857$	−1.85837e7	−	1.85837e7i	−0.864331	−	0.864331i	−0.991838	+	0.127507i	$0.959303\pi$
$858$		0			0
$859$			2.32905e7i			1.07695i	0.842641	+	0.538475i	$0.180999\pi$
$859$			2.32905e7i			1.07695i	−0.842641	+	0.538475i	$0.819001\pi$
$860$		0			0
$861$		0			0
$862$	−1.85129e7	+	1.85129e7i	−0.848608	+	0.848608i
$863$	−5.36715e6	+	5.36715e6i	−0.245311	+	0.245311i	−0.819043	−	0.573732i	$-0.805495\pi$
$863$	−5.36715e6	+	5.36715e6i	−0.245311	+	0.245311i	0.573732	+	0.819043i	$0.305495\pi$
$864$		0			0
$865$		0			0
$866$		−	1.29600e6i		−	0.0587232i
$867$		0			0
$868$	2.05903e7	+	2.05903e7i	0.927604	+	0.927604i
$869$	−1.27093e7			−0.570915
$870$		0			0
$871$	−9.35298e6			−0.417739
$872$	1.26172e6	+	1.26172e6i	0.0561915	+	0.0561915i
$873$		0			0
$874$			2.51115e7i			1.11197i
$875$		0			0
$876$		0			0
$877$	1.49483e7	−	1.49483e7i	0.656285	−	0.656285i	−0.298214	−	0.954499i	$-0.596391\pi$
$877$	1.49483e7	−	1.49483e7i	0.656285	−	0.656285i	0.954499	+	0.298214i	$0.0963909\pi$
$878$	−5.58197e6	+	5.58197e6i	−0.244372	+	0.244372i
$879$		0			0
$880$		0			0
$881$		−	3.98161e7i		−	1.72830i	−0.503234	−	0.864150i	$-0.667857\pi$
$881$		−	3.98161e7i		−	1.72830i	0.503234	−	0.864150i	$-0.332143\pi$
$882$		0			0
$883$	8.44942e6	+	8.44942e6i	0.364691	+	0.364691i	0.865537	−	0.500846i	$-0.166978\pi$
$883$	8.44942e6	+	8.44942e6i	0.364691	+	0.364691i	−0.500846	+	0.865537i	$0.666978\pi$
$884$	9.41390e6			0.405172
$885$		0			0
$886$	1.48996e7			0.637660
$887$	−1.01948e7	−	1.01948e7i	−0.435081	−	0.435081i	0.455272	−	0.890353i	$-0.349542\pi$
$887$	−1.01948e7	−	1.01948e7i	−0.435081	−	0.435081i	−0.890353	+	0.455272i	$0.849542\pi$
$888$		0			0
$889$			5.51975e7i			2.34242i
$890$		0			0
$891$		0			0
$892$	−1.19961e6	+	1.19961e6i	−0.0504809	+	0.0504809i
$893$	−1.92537e7	+	1.92537e7i	−0.807951	+	0.807951i
$894$		0			0
$895$		0			0
$896$		−	3.44606e6i		−	0.143401i
$897$		0			0
$898$	−2.21465e7	−	2.21465e7i	−0.916463	−	0.916463i
$899$	−2.26480e7			−0.934611
$900$		0			0
$901$	−3.00764e7			−1.23428
$902$	−1.34412e6	−	1.34412e6i	−0.0550075	−	0.0550075i
$903$		0			0
$904$		−	4.73830e6i		−	0.192842i
$905$		0			0
$906$		0			0
$907$	−2.30348e7	+	2.30348e7i	−0.929749	+	0.929749i	−0.997689	−	0.0679406i	$-0.978357\pi$
$907$	−2.30348e7	+	2.30348e7i	−0.929749	+	0.929749i	0.0679406	+	0.997689i	$0.478357\pi$
$908$	1.10674e7	−	1.10674e7i	0.445482	−	0.445482i
$909$		0			0
$910$		0			0
$911$		−	7.74315e6i		−	0.309116i	−0.987984	−	0.154558i	$-0.950605\pi$
$911$		−	7.74315e6i		−	0.309116i	0.987984	−	0.154558i	$-0.0493954\pi$
$912$		0			0
$913$	−1.01258e7	−	1.01258e7i	−0.402024	−	0.402024i
$914$	3.01491e7			1.19374
$915$		0			0
$916$	−7.45584e6			−0.293601
$917$	−2.83843e7	−	2.83843e7i	−1.11469	−	1.11469i
$918$		0			0
$919$		−	2.22571e6i		−	0.0869319i	−0.999055	−	0.0434660i	$-0.986160\pi$
$919$		−	2.22571e6i		−	0.0869319i	0.999055	−	0.0434660i	$-0.0138400\pi$
$920$		0			0
$921$		0			0
$922$	−3.66783e6	+	3.66783e6i	−0.142096	+	0.142096i
$923$	−1.25977e6	+	1.25977e6i	−0.0486730	+	0.0486730i
$924$		0			0
$925$		0			0
$926$		−	2.99919e7i		−	1.14941i
$927$		0			0
$928$	1.89522e6	+	1.89522e6i	0.0722421	+	0.0722421i
$929$	−6.15139e6			−0.233848			−0.116924	−	0.993141i	$-0.537303\pi$
$929$	−6.15139e6			−0.233848			−0.116924	+	0.993141i	$0.537303\pi$
$930$		0			0
$931$	4.79562e7			1.81330
$932$	1.89077e6	+	1.89077e6i	0.0713015	+	0.0713015i
$933$		0			0
$934$		−	5.01181e6i		−	0.187987i
$935$		0			0
$936$		0			0
$937$	1.13103e7	−	1.13103e7i	0.420846	−	0.420846i	−0.464649	−	0.885495i	$-0.653819\pi$
$937$	1.13103e7	−	1.13103e7i	0.420846	−	0.420846i	0.885495	+	0.464649i	$0.153819\pi$
$938$	−2.03580e7	+	2.03580e7i	−0.755490	+	0.755490i
$939$		0			0
$940$		0			0
$941$			4.63930e7i			1.70796i	0.520304	+	0.853981i	$0.325819\pi$
$941$			4.63930e7i			1.70796i	−0.520304	+	0.853981i	$0.674181\pi$
$942$		0			0
$943$	−4.02871e6	−	4.02871e6i	−0.147532	−	0.147532i
$944$	−3.56667e6			−0.130266
$945$		0			0
$946$	3.39817e6			0.123458
$947$	−9.83274e6	−	9.83274e6i	−0.356287	−	0.356287i	0.506155	−	0.862442i	$-0.331066\pi$
$947$	−9.83274e6	−	9.83274e6i	−0.356287	−	0.356287i	−0.862442	+	0.506155i	$0.831066\pi$
$948$		0			0
$949$			2.37724e7i			0.856856i
$950$		0			0
$951$		0			0
$952$	2.04906e7	−	2.04906e7i	0.732762	−	0.732762i
$953$	−7.65696e6	+	7.65696e6i	−0.273102	+	0.273102i	−0.830348	−	0.557246i	$-0.811858\pi$
$953$	−7.65696e6	+	7.65696e6i	−0.273102	+	0.273102i	0.557246	+	0.830348i	$0.311858\pi$
$954$		0			0
$955$		0			0
$956$			2.41527e7i			0.854715i
$957$		0			0
$958$	4.05411e6	+	4.05411e6i	0.142719	+	0.142719i
$959$	3.79970e7			1.33415
$960$		0			0
$961$	4.62410e7			1.61517
$962$	−5.87964e6	−	5.87964e6i	−0.204839	−	0.204839i
$963$		0			0
$964$			1.91642e7i			0.664200i
$965$		0			0
$966$		0			0
$967$	−7.72851e6	+	7.72851e6i	−0.265784	+	0.265784i	−0.827399	−	0.561615i	$-0.810180\pi$
$967$	−7.72851e6	+	7.72851e6i	−0.265784	+	0.265784i	0.561615	+	0.827399i	$0.310180\pi$
$968$	3.22822e6	−	3.22822e6i	0.110733	−	0.110733i
$969$		0			0
$970$		0			0
$971$			3.78060e7i			1.28680i	0.765529	+	0.643402i	$0.222477\pi$
$971$			3.78060e7i			1.28680i	−0.765529	+	0.643402i	$0.777523\pi$
$972$		0			0
$973$	3.24172e7	+	3.24172e7i	1.09772	+	1.09772i
$974$	5.62817e6			0.190094
$975$		0			0
$976$	7.20402e6			0.242075
$977$	4.81434e6	+	4.81434e6i	0.161362	+	0.161362i	0.783170	−	0.621808i	$-0.213602\pi$
$977$	4.81434e6	+	4.81434e6i	0.161362	+	0.161362i	−0.621808	+	0.783170i	$0.713602\pi$
$978$		0			0
$979$		−	1.91440e7i		−	0.638374i
$980$		0			0
$981$		0			0
$982$	−2.00625e6	+	2.00625e6i	−0.0663905	+	0.0663905i
$983$	1.43163e6	−	1.43163e6i	0.0472549	−	0.0472549i	−0.683084	−	0.730339i	$-0.739362\pi$
$983$	1.43163e6	−	1.43163e6i	0.0472549	−	0.0472549i	0.730339	+	0.683084i	$0.239362\pi$
$984$		0			0
$985$		0			0
$986$			2.25384e7i			0.738298i
$987$		0			0
$988$	−5.40574e6	−	5.40574e6i	−0.176182	−	0.176182i
$989$	1.01853e7			0.331117
$990$		0			0
$991$	−2.93087e7			−0.948009			−0.474004	−	0.880522i	$-0.657192\pi$
$991$	−2.93087e7			−0.948009			−0.474004	+	0.880522i	$0.657192\pi$
$992$	−6.26526e6	−	6.26526e6i	−0.202144	−	0.202144i
$993$		0			0
$994$			5.48413e6i			0.176052i
$995$		0			0
$996$		0			0
$997$	4.28898e6	−	4.28898e6i	0.136652	−	0.136652i	−0.635472	−	0.772124i	$-0.719194\pi$
$997$	4.28898e6	−	4.28898e6i	0.136652	−	0.136652i	0.772124	+	0.635472i	$0.219194\pi$
$998$	−5.73458e6	+	5.73458e6i	−0.182253	+	0.182253i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.6.f.e.143.1		12
3.2	odd	2	inner	450.6.f.e.143.4		12
5.2	odd	4	inner	450.6.f.e.107.4		12
5.3	odd	4		90.6.f.c.17.1	✓	12
5.4	even	2		90.6.f.c.53.6	yes	12
15.2	even	4	inner	450.6.f.e.107.1		12
15.8	even	4		90.6.f.c.17.6	yes	12
15.14	odd	2		90.6.f.c.53.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.6.f.c.17.1	✓	12	5.3	odd	4
90.6.f.c.17.6	yes	12	15.8	even	4
90.6.f.c.53.1	yes	12	15.14	odd	2
90.6.f.c.53.6	yes	12	5.4	even	2
450.6.f.e.107.1		12	15.2	even	4	inner
450.6.f.e.107.4		12	5.2	odd	4	inner
450.6.f.e.143.1		12	1.1	even	1	trivial
450.6.f.e.143.4		12	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-2.82843 - 2.82843i) q^{2} +16.0000i q^{4} +(-148.726 + 148.726i) q^{7} +(45.2548 - 45.2548i) q^{8} +O(q^{10})\)	\(q+(-2.82843 - 2.82843i) q^{2} +16.0000i q^{4} +(-148.726 + 148.726i) q^{7} +(45.2548 - 45.2548i) q^{8} -299.527i q^{11} +(193.262 + 193.262i) q^{13} +841.322 q^{14} -256.000 q^{16} +(-1522.21 - 1522.21i) q^{17} +1748.19i q^{19} +(-847.191 + 847.191i) q^{22} +(-2539.27 + 2539.27i) q^{23} -1093.25i q^{26} +(-2379.62 - 2379.62i) q^{28} +2617.43 q^{29} -8652.76 q^{31} +(724.077 + 724.077i) q^{32} +8610.89i q^{34} +(5378.10 - 5378.10i) q^{37} +(4944.63 - 4944.63i) q^{38} +1586.56i q^{41} +(-2005.55 - 2005.55i) q^{43} +4792.44 q^{44} +14364.3 q^{46} +(11013.5 + 11013.5i) q^{47} -27431.9i q^{49} +(-3092.19 + 3092.19i) q^{52} +(9879.22 - 9879.22i) q^{53} +13461.2i q^{56} +(-7403.22 - 7403.22i) q^{58} +13932.3 q^{59} -28140.7 q^{61} +(24473.7 + 24473.7i) q^{62} -4096.00i q^{64} +(-24197.7 + 24197.7i) q^{67} +(24355.3 - 24355.3i) q^{68} +6518.47i q^{71} +(61503.1 + 61503.1i) q^{73} -30423.1 q^{74} -27971.0 q^{76} +(44547.6 + 44547.6i) q^{77} -42431.1i q^{79} +(4487.47 - 4487.47i) q^{82} +(33805.9 - 33805.9i) q^{83} +11345.1i q^{86} +(-13555.1 - 13555.1i) q^{88} +63913.9 q^{89} -57486.2 q^{91} +(-40628.3 - 40628.3i) q^{92} -62301.7i q^{94} +(58905.9 - 58905.9i) q^{97} +(-77589.2 + 77589.2i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 144 q^{7}+O(q^{10}) \) 12 * q - 144 * q^7	\( 12 q - 144 q^{7} + 276 q^{13} - 3072 q^{16} - 384 q^{22} - 2304 q^{28} - 58512 q^{31} - 25764 q^{37} - 16080 q^{43} - 60672 q^{46} - 4416 q^{52} - 23952 q^{58} - 145200 q^{61} - 33552 q^{67} + 158988 q^{73} - 86016 q^{76} + 75024 q^{82} - 6144 q^{88} - 465024 q^{91} + 631116 q^{97}+O(q^{100}) \) 12 * q - 144 * q^7 + 276 * q^13 - 3072 * q^16 - 384 * q^22 - 2304 * q^28 - 58512 * q^31 - 25764 * q^37 - 16080 * q^43 - 60672 * q^46 - 4416 * q^52 - 23952 * q^58 - 145200 * q^61 - 33552 * q^67 + 158988 * q^73 - 86016 * q^76 + 75024 * q^82 - 6144 * q^88 - 465024 * q^91 + 631116 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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