LMFDB - Embedded newform 240.3.bg.c.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,3,Mod(97,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("240.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	240.bg (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53952634465$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.1
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	240.97
Dual form			240.3.bg.c.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 1.22474i) q^{3} +(4.67423 - 1.77526i) q^{5} +(0.550510 + 0.550510i) q^{7} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.22474 + 1.22474i) q^{3} +(4.67423 - 1.77526i) q^{5} +(0.550510 + 0.550510i) q^{7} -3.00000i q^{9} +1.55051 q^{11} +(9.55051 - 9.55051i) q^{13} +(-3.55051 + 7.89898i) q^{15} +(11.1464 + 11.1464i) q^{17} +12.6969i q^{19} -1.34847 q^{21} +(21.3485 - 21.3485i) q^{23} +(18.6969 - 16.5959i) q^{25} +(3.67423 + 3.67423i) q^{27} +44.0454i q^{29} +44.4949 q^{31} +(-1.89898 + 1.89898i) q^{33} +(3.55051 + 1.59592i) q^{35} +(20.6515 + 20.6515i) q^{37} +23.3939i q^{39} -48.2929 q^{41} +(36.2929 - 36.2929i) q^{43} +(-5.32577 - 14.0227i) q^{45} +(-42.5403 - 42.5403i) q^{47} -48.3939i q^{49} -27.3031 q^{51} +(-54.4949 + 54.4949i) q^{53} +(7.24745 - 2.75255i) q^{55} +(-15.5505 - 15.5505i) q^{57} +47.4393i q^{59} -59.8888 q^{61} +(1.65153 - 1.65153i) q^{63} +(27.6867 - 61.5959i) q^{65} +(-81.2827 - 81.2827i) q^{67} +52.2929i q^{69} -87.5959 q^{71} +(75.9898 - 75.9898i) q^{73} +(-2.57321 + 43.2247i) q^{75} +(0.853572 + 0.853572i) q^{77} +97.3031i q^{79} -9.00000 q^{81} +(-41.0556 + 41.0556i) q^{83} +(71.8888 + 32.3133i) q^{85} +(-53.9444 - 53.9444i) q^{87} -52.2020i q^{89} +10.5153 q^{91} +(-54.4949 + 54.4949i) q^{93} +(22.5403 + 59.3485i) q^{95} +(-37.0000 - 37.0000i) q^{97} -4.65153i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5} + 12 q^{7}+O(q^{10}) $ 4 * q + 4 * q^5 + 12 * q^7	$ 4 q + 4 q^{5} + 12 q^{7} + 16 q^{11} + 48 q^{13} - 24 q^{15} - 24 q^{17} + 24 q^{21} + 56 q^{23} + 16 q^{25} + 80 q^{31} + 12 q^{33} + 24 q^{35} + 112 q^{37} - 56 q^{41} + 8 q^{43} - 36 q^{45} + 16 q^{47} - 168 q^{51} - 120 q^{53} - 20 q^{55} - 72 q^{57} - 24 q^{61} + 36 q^{63} - 144 q^{65} + 8 q^{67} - 272 q^{71} + 108 q^{73} + 24 q^{75} + 72 q^{77} - 36 q^{81} - 272 q^{83} + 72 q^{85} - 108 q^{87} + 336 q^{91} - 120 q^{93} - 96 q^{95} - 148 q^{97}+O(q^{100}) $ 4 * q + 4 * q^5 + 12 * q^7 + 16 * q^11 + 48 * q^13 - 24 * q^15 - 24 * q^17 + 24 * q^21 + 56 * q^23 + 16 * q^25 + 80 * q^31 + 12 * q^33 + 24 * q^35 + 112 * q^37 - 56 * q^41 + 8 * q^43 - 36 * q^45 + 16 * q^47 - 168 * q^51 - 120 * q^53 - 20 * q^55 - 72 * q^57 - 24 * q^61 + 36 * q^63 - 144 * q^65 + 8 * q^67 - 272 * q^71 + 108 * q^73 + 24 * q^75 + 72 * q^77 - 36 * q^81 - 272 * q^83 + 72 * q^85 - 108 * q^87 + 336 * q^91 - 120 * q^93 - 96 * q^95 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$		0			0
$5$	4.67423	−	1.77526i	0.934847	−	0.355051i
$5$	4.67423	−	1.77526i	0.934847	−	0.355051i
$6$		0			0
$7$	0.550510	+	0.550510i	0.0786443	+	0.0786443i	0.745335	−	0.666690i	$-0.232290\pi$
$7$	0.550510	+	0.550510i	0.0786443	+	0.0786443i	−0.666690	+	0.745335i	$0.732290\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	1.55051			0.140955			0.0704777	−	0.997513i	$-0.477548\pi$
$11$	1.55051			0.140955			0.0704777	+	0.997513i	$0.477548\pi$
$12$		0			0
$13$	9.55051	−	9.55051i	0.734655	−	0.734655i	−0.236883	−	0.971538i	$-0.576126\pi$
$13$	9.55051	−	9.55051i	0.734655	−	0.734655i	0.971538	+	0.236883i	$0.0761260\pi$
$14$		0			0
$15$	−3.55051	+	7.89898i	−0.236701	+	0.526599i
$16$		0			0
$17$	11.1464	+	11.1464i	0.655672	+	0.655672i	0.954353	−	0.298681i	$-0.0965466\pi$
$17$	11.1464	+	11.1464i	0.655672	+	0.655672i	−0.298681	+	0.954353i	$0.596547\pi$
$18$		0			0
$19$			12.6969i			0.668260i	0.942527	+	0.334130i	$0.108442\pi$
$19$			12.6969i			0.668260i	−0.942527	+	0.334130i	$0.891558\pi$
$20$		0			0
$21$	−1.34847			−0.0642128
$22$		0			0
$23$	21.3485	−	21.3485i	0.928194	−	0.928194i	−0.0693950	−	0.997589i	$-0.522107\pi$
$23$	21.3485	−	21.3485i	0.928194	−	0.928194i	0.997589	+	0.0693950i	$0.0221069\pi$
$24$		0			0
$25$	18.6969	−	16.5959i	0.747878	−	0.663837i
$26$		0			0
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$		0			0
$29$			44.0454i			1.51881i	0.650620	+	0.759404i	$0.274509\pi$
$29$			44.0454i			1.51881i	−0.650620	+	0.759404i	$0.725491\pi$
$30$		0			0
$31$	44.4949			1.43532			0.717660	−	0.696394i	$-0.245213\pi$
$31$	44.4949			1.43532			0.717660	+	0.696394i	$0.245213\pi$
$32$		0			0
$33$	−1.89898	+	1.89898i	−0.0575448	+	0.0575448i
$34$		0			0
$35$	3.55051	+	1.59592i	0.101443	+	0.0455977i
$36$		0			0
$37$	20.6515	+	20.6515i	0.558149	+	0.558149i	0.928780	−	0.370631i	$-0.120858\pi$
$37$	20.6515	+	20.6515i	0.558149	+	0.558149i	−0.370631	+	0.928780i	$0.620858\pi$
$38$		0			0
$39$			23.3939i			0.599843i
$40$		0			0
$41$	−48.2929			−1.17787			−0.588937	−	0.808179i	$-0.700454\pi$
$41$	−48.2929			−1.17787			−0.588937	+	0.808179i	$0.700454\pi$
$42$		0			0
$43$	36.2929	−	36.2929i	0.844020	−	0.844020i	−0.145359	−	0.989379i	$-0.546434\pi$
$43$	36.2929	−	36.2929i	0.844020	−	0.844020i	0.989379	+	0.145359i	$0.0464337\pi$
$44$		0			0
$45$	−5.32577	−	14.0227i	−0.118350	−	0.311616i
$46$		0			0
$47$	−42.5403	−	42.5403i	−0.905113	−	0.905113i	0.0907599	−	0.995873i	$-0.471070\pi$
$47$	−42.5403	−	42.5403i	−0.905113	−	0.905113i	−0.995873	+	0.0907599i	$0.971070\pi$
$48$		0			0
$49$		−	48.3939i		−	0.987630i
$50$		0			0
$51$	−27.3031			−0.535354
$52$		0			0
$53$	−54.4949	+	54.4949i	−1.02821	+	1.02821i	−0.0286151	+	0.999591i	$0.509110\pi$
$53$	−54.4949	+	54.4949i	−1.02821	+	1.02821i	−0.999591	+	0.0286151i	$0.990890\pi$
$54$		0			0
$55$	7.24745	−	2.75255i	0.131772	−	0.0500464i
$56$		0			0
$57$	−15.5505	−	15.5505i	−0.272816	−	0.272816i
$58$		0			0
$59$			47.4393i			0.804056i	0.915627	+	0.402028i	$0.131694\pi$
$59$			47.4393i			0.804056i	−0.915627	+	0.402028i	$0.868306\pi$
$60$		0			0
$61$	−59.8888			−0.981783			−0.490892	−	0.871221i	$-0.663329\pi$
$61$	−59.8888			−0.981783			−0.490892	+	0.871221i	$0.663329\pi$
$62$		0			0
$63$	1.65153	−	1.65153i	0.0262148	−	0.0262148i
$64$		0			0
$65$	27.6867	−	61.5959i	0.425950	−	0.947630i
$66$		0			0
$67$	−81.2827	−	81.2827i	−1.21317	−	1.21317i	−0.969977	−	0.243197i	$-0.921804\pi$
$67$	−81.2827	−	81.2827i	−1.21317	−	1.21317i	−0.243197	−	0.969977i	$-0.578196\pi$
$68$		0			0
$69$			52.2929i			0.757867i
$70$		0			0
$71$	−87.5959			−1.23375			−0.616873	−	0.787063i	$-0.711601\pi$
$71$	−87.5959			−1.23375			−0.616873	+	0.787063i	$0.711601\pi$
$72$		0			0
$73$	75.9898	−	75.9898i	1.04096	−	1.04096i	0.0418314	−	0.999125i	$-0.486681\pi$
$73$	75.9898	−	75.9898i	1.04096	−	1.04096i	0.999125	−	0.0418314i	$-0.0133192\pi$
$74$		0			0
$75$	−2.57321	+	43.2247i	−0.0343095	+	0.576330i
$76$		0			0
$77$	0.853572	+	0.853572i	0.0110853	+	0.0110853i
$78$		0			0
$79$			97.3031i			1.23168i	0.787870	+	0.615842i	$0.211184\pi$
$79$			97.3031i			1.23168i	−0.787870	+	0.615842i	$0.788816\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	−41.0556	+	41.0556i	−0.494646	+	0.494646i	−0.909766	−	0.415120i	$-0.863739\pi$
$83$	−41.0556	+	41.0556i	−0.494646	+	0.494646i	0.415120	+	0.909766i	$0.363739\pi$
$84$		0			0
$85$	71.8888	+	32.3133i	0.845750	+	0.380156i
$86$		0			0
$87$	−53.9444	−	53.9444i	−0.620050	−	0.620050i
$88$		0			0
$89$		−	52.2020i		−	0.586540i	−0.956030	−	0.293270i	$-0.905257\pi$
$89$		−	52.2020i		−	0.586540i	0.956030	−	0.293270i	$-0.0947435\pi$
$90$		0			0
$91$	10.5153			0.115553
$92$		0			0
$93$	−54.4949	+	54.4949i	−0.585967	+	0.585967i
$94$		0			0
$95$	22.5403	+	59.3485i	0.237266	+	0.624721i
$96$		0			0
$97$	−37.0000	−	37.0000i	−0.381443	−	0.381443i	0.490179	−	0.871622i	$-0.336932\pi$
$97$	−37.0000	−	37.0000i	−0.381443	−	0.381443i	−0.871622	+	0.490179i	$0.836932\pi$
$98$		0			0
$99$		−	4.65153i		−	0.0469852i
$100$		0			0
$101$	−18.3383			−0.181567			−0.0907835	−	0.995871i	$-0.528937\pi$
$101$	−18.3383			−0.181567			−0.0907835	+	0.995871i	$0.528937\pi$
$102$		0			0
$103$	10.6413	−	10.6413i	0.103314	−	0.103314i	−0.653560	−	0.756874i	$-0.726725\pi$
$103$	10.6413	−	10.6413i	0.103314	−	0.103314i	0.756874	+	0.653560i	$0.226725\pi$
$104$		0			0
$105$	−6.30306	+	2.39388i	−0.0600292	+	0.0227988i
$106$		0			0
$107$	66.9444	+	66.9444i	0.625648	+	0.625648i	0.946970	−	0.321322i	$-0.104127\pi$
$107$	66.9444	+	66.9444i	0.625648	+	0.625648i	−0.321322	+	0.946970i	$0.604127\pi$
$108$		0			0
$109$			97.2827i			0.892501i	0.894908	+	0.446251i	$0.147241\pi$
$109$			97.2827i			0.892501i	−0.894908	+	0.446251i	$0.852759\pi$
$110$		0			0
$111$	−50.5857			−0.455727
$112$		0			0
$113$	30.1362	−	30.1362i	0.266692	−	0.266692i	−0.561074	−	0.827766i	$-0.689612\pi$
$113$	30.1362	−	30.1362i	0.266692	−	0.266692i	0.827766	+	0.561074i	$0.189612\pi$
$114$		0			0
$115$	61.8888	−	137.687i	0.538163	−	1.19728i
$116$		0			0
$117$	−28.6515	−	28.6515i	−0.244885	−	0.244885i
$118$		0			0
$119$			12.2724i			0.103130i
$120$		0			0
$121$	−118.596			−0.980132
$122$		0			0
$123$	59.1464	−	59.1464i	0.480865	−	0.480865i
$124$		0			0
$125$	57.9319	−	110.765i	0.463455	−	0.886120i
$126$		0			0
$127$	−66.0556	−	66.0556i	−0.520123	−	0.520123i	0.397486	−	0.917608i	$-0.369883\pi$
$127$	−66.0556	−	66.0556i	−0.520123	−	0.520123i	−0.917608	+	0.397486i	$0.869883\pi$
$128$		0			0
$129$			88.8990i			0.689139i
$130$		0			0
$131$	−86.8536			−0.663004			−0.331502	−	0.943454i	$-0.607555\pi$
$131$	−86.8536			−0.663004			−0.331502	+	0.943454i	$0.607555\pi$
$132$		0			0
$133$	−6.98979	+	6.98979i	−0.0525548	+	0.0525548i
$134$		0			0
$135$	23.6969	+	10.6515i	0.175533	+	0.0789002i
$136$		0			0
$137$	−71.5301	−	71.5301i	−0.522118	−	0.522118i	0.396093	−	0.918210i	$-0.370366\pi$
$137$	−71.5301	−	71.5301i	−0.522118	−	0.522118i	−0.918210	+	0.396093i	$0.870366\pi$
$138$		0			0
$139$		−	23.2122i		−	0.166995i	−0.996508	−	0.0834973i	$-0.973391\pi$
$139$		−	23.2122i		−	0.166995i	0.996508	−	0.0834973i	$-0.0266090\pi$
$140$		0			0
$141$	104.202			0.739022
$142$		0			0
$143$	14.8082	−	14.8082i	0.103554	−	0.103554i
$144$		0			0
$145$	78.1918	+	205.879i	0.539254	+	1.41985i
$146$		0			0
$147$	59.2702	+	59.2702i	0.403198	+	0.403198i
$148$		0			0
$149$			137.530i			0.923021i	0.887135	+	0.461510i	$0.152692\pi$
$149$			137.530i			0.923021i	−0.887135	+	0.461510i	$0.847308\pi$
$150$		0			0
$151$	291.394			1.92976			0.964880	−	0.262690i	$-0.0846095\pi$
$151$	291.394			1.92976			0.964880	+	0.262690i	$0.0846095\pi$
$152$		0			0
$153$	33.4393	−	33.4393i	0.218557	−	0.218557i
$154$		0			0
$155$	207.980	−	78.9898i	1.34180	−	0.509612i
$156$		0			0
$157$	−52.6311	−	52.6311i	−0.335230	−	0.335230i	0.519339	−	0.854569i	$-0.326178\pi$
$157$	−52.6311	−	52.6311i	−0.335230	−	0.335230i	−0.854569	+	0.519339i	$0.826178\pi$
$158$		0			0
$159$		−	133.485i		−	0.839526i
$160$		0			0
$161$	23.5051			0.145994
$162$		0			0
$163$	−117.576	+	117.576i	−0.721322	+	0.721322i	−0.968875	−	0.247552i	$-0.920374\pi$
$163$	−117.576	+	117.576i	−0.721322	+	0.721322i	0.247552	+	0.968875i	$0.420374\pi$
$164$		0			0
$165$	−5.50510	+	12.2474i	−0.0333643	+	0.0742270i
$166$		0			0
$167$	146.338	+	146.338i	0.876277	+	0.876277i	0.993147	−	0.116870i	$-0.0372861\pi$
$167$	146.338	+	146.338i	0.876277	+	0.876277i	−0.116870	+	0.993147i	$0.537286\pi$
$168$		0			0
$169$		−	13.4245i		−	0.0794349i
$170$		0			0
$171$	38.0908			0.222753
$172$		0			0
$173$	3.75255	−	3.75255i	0.0216910	−	0.0216910i	−0.696178	−	0.717869i	$-0.745118\pi$
$173$	3.75255	−	3.75255i	0.0216910	−	0.0216910i	0.717869	+	0.696178i	$0.245118\pi$
$174$		0			0
$175$	19.4291	+	1.15663i	0.111023	+	0.00660933i
$176$		0			0
$177$	−58.1010	−	58.1010i	−0.328254	−	0.328254i
$178$		0			0
$179$		−	77.2372i		−	0.431493i	−0.976449	−	0.215746i	$-0.930782\pi$
$179$		−	77.2372i		−	0.431493i	0.976449	−	0.215746i	$-0.0692185\pi$
$180$		0			0
$181$	160.656			0.887603			0.443801	−	0.896125i	$-0.353630\pi$
$181$	160.656			0.887603			0.443801	+	0.896125i	$0.353630\pi$
$182$		0			0
$183$	73.3485	−	73.3485i	0.400811	−	0.400811i
$184$		0			0
$185$	133.192	+	59.8684i	0.719956	+	0.323613i
$186$		0			0
$187$	17.2827	+	17.2827i	0.0924206	+	0.0924206i
$188$		0			0
$189$			4.04541i			0.0214043i
$190$		0			0
$191$	−251.868			−1.31868			−0.659341	−	0.751844i	$-0.729165\pi$
$191$	−251.868			−1.31868			−0.659341	+	0.751844i	$0.729165\pi$
$192$		0			0
$193$	173.384	−	173.384i	0.898361	−	0.898361i	−0.0969302	−	0.995291i	$-0.530902\pi$
$193$	173.384	−	173.384i	0.898361	−	0.898361i	0.995291	+	0.0969302i	$0.0309024\pi$
$194$		0			0
$195$	41.5301	+	109.348i	0.212975	+	0.560761i
$196$		0			0
$197$	−2.09082	−	2.09082i	−0.0106133	−	0.0106133i	0.701780	−	0.712394i	$-0.252389\pi$
$197$	−2.09082	−	2.09082i	−0.0106133	−	0.0106133i	−0.712394	+	0.701780i	$0.752389\pi$
$198$		0			0
$199$			304.565i			1.53048i	0.643746	+	0.765239i	$0.277379\pi$
$199$			304.565i			1.53048i	−0.643746	+	0.765239i	$0.722621\pi$
$200$		0			0
$201$	199.101			0.990552
$202$		0			0
$203$	−24.2474	+	24.2474i	−0.119446	+	0.119446i
$204$		0			0
$205$	−225.732	+	85.7321i	−1.10113	+	0.418206i
$206$		0			0
$207$	−64.0454	−	64.0454i	−0.309398	−	0.309398i
$208$		0			0
$209$			19.6867i			0.0941949i
$210$		0			0
$211$	−273.151			−1.29455			−0.647277	−	0.762255i	$-0.724092\pi$
$211$	−273.151			−1.29455			−0.647277	+	0.762255i	$0.724092\pi$
$212$		0			0
$213$	107.283	−	107.283i	0.503674	−	0.503674i
$214$		0			0
$215$	105.212	−	234.070i	0.489359	−	1.08870i
$216$		0			0
$217$	24.4949	+	24.4949i	0.112880	+	0.112880i
$218$		0			0
$219$			186.136i			0.849937i
$220$		0			0
$221$	212.908			0.963385
$222$		0			0
$223$	−174.662	+	174.662i	−0.783236	+	0.783236i	−0.980376	−	0.197139i	$-0.936835\pi$
$223$	−174.662	+	174.662i	−0.783236	+	0.783236i	0.197139	+	0.980376i	$0.436835\pi$
$224$		0			0
$225$	−49.7878	−	56.0908i	−0.221279	−	0.249293i
$226$		0			0
$227$	77.6163	+	77.6163i	0.341922	+	0.341922i	0.857090	−	0.515167i	$-0.172270\pi$
$227$	77.6163	+	77.6163i	0.341922	+	0.341922i	−0.515167	+	0.857090i	$0.672270\pi$
$228$		0			0
$229$			8.96938i			0.0391676i	0.999808	+	0.0195838i	$0.00623412\pi$
$229$			8.96938i			0.0391676i	−0.999808	+	0.0195838i	$0.993766\pi$
$230$		0			0
$231$	−2.09082			−0.00905115
$232$		0			0
$233$	−50.4699	+	50.4699i	−0.216609	+	0.216609i	−0.807068	−	0.590459i	$-0.798947\pi$
$233$	−50.4699	+	50.4699i	−0.216609	+	0.216609i	0.590459	+	0.807068i	$0.298947\pi$
$234$		0			0
$235$	−274.363	−	123.323i	−1.16750	−	0.524781i
$236$		0			0
$237$	−119.171	−	119.171i	−0.502833	−	0.502833i
$238$		0			0
$239$		−	279.737i		−	1.17045i	−0.810872	−	0.585223i	$-0.801007\pi$
$239$		−	279.737i		−	1.17045i	0.810872	−	0.585223i	$-0.198993\pi$
$240$		0			0
$241$	−397.131			−1.64784			−0.823922	−	0.566703i	$-0.808219\pi$
$241$	−397.131			−1.64784			−0.823922	+	0.566703i	$0.808219\pi$
$242$		0			0
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−85.9115	−	226.204i	−0.350659	−	0.923283i
$246$		0			0
$247$	121.262	+	121.262i	0.490940	+	0.490940i
$248$		0			0
$249$		−	100.565i		−	0.403877i
$250$		0			0
$251$	−53.8638			−0.214597			−0.107298	−	0.994227i	$-0.534220\pi$
$251$	−53.8638			−0.214597			−0.107298	+	0.994227i	$0.534220\pi$
$252$		0			0
$253$	33.1010	−	33.1010i	0.130834	−	0.130834i
$254$		0			0
$255$	−127.621	+	48.4699i	−0.500474	+	0.190078i
$256$		0			0
$257$	309.732	+	309.732i	1.20518	+	1.20518i	0.972569	+	0.232614i	$0.0747280\pi$
$257$	309.732	+	309.732i	1.20518	+	1.20518i	0.232614	+	0.972569i	$0.425272\pi$
$258$		0			0
$259$			22.7378i			0.0877906i
$260$		0			0
$261$	132.136			0.506269
$262$		0			0
$263$	128.854	−	128.854i	0.489938	−	0.489938i	−0.418349	−	0.908286i	$-0.637391\pi$
$263$	128.854	−	128.854i	0.489938	−	0.489938i	0.908286	+	0.418349i	$0.137391\pi$
$264$		0			0
$265$	−157.980	+	351.464i	−0.596149	+	1.32628i
$266$		0			0
$267$	63.9342	+	63.9342i	0.239454	+	0.239454i
$268$		0			0
$269$		−	112.227i		−	0.417201i	−0.978001	−	0.208600i	$-0.933109\pi$
$269$		−	112.227i		−	0.417201i	0.978001	−	0.208600i	$-0.0668908\pi$
$270$		0			0
$271$	−167.616			−0.618510			−0.309255	−	0.950979i	$-0.600080\pi$
$271$	−167.616			−0.618510			−0.309255	+	0.950979i	$0.600080\pi$
$272$		0			0
$273$	−12.8786	+	12.8786i	−0.0471742	+	0.0471742i
$274$		0			0
$275$	28.9898	−	25.7321i	0.105417	−	0.0935714i
$276$		0			0
$277$	−298.136	−	298.136i	−1.07630	−	1.07630i	−0.996838	−	0.0794665i	$-0.974678\pi$
$277$	−298.136	−	298.136i	−1.07630	−	1.07630i	−0.0794665	−	0.996838i	$-0.525322\pi$
$278$		0			0
$279$		−	133.485i		−	0.478440i
$280$		0			0
$281$	−336.434			−1.19727			−0.598636	−	0.801021i	$-0.704291\pi$
$281$	−336.434			−1.19727			−0.598636	+	0.801021i	$0.704291\pi$
$282$		0			0
$283$	−20.1612	+	20.1612i	−0.0712411	+	0.0712411i	−0.741830	−	0.670588i	$-0.766042\pi$
$283$	−20.1612	+	20.1612i	−0.0712411	+	0.0712411i	0.670588	+	0.741830i	$0.266042\pi$
$284$		0			0
$285$	−100.293	−	45.0806i	−0.351905	−	0.158178i
$286$		0			0
$287$	−26.5857	−	26.5857i	−0.0926331	−	0.0926331i
$288$		0			0
$289$		−	40.5143i		−	0.140188i
$290$		0			0
$291$	90.6311			0.311447
$292$		0			0
$293$	−246.586	+	246.586i	−0.841589	+	0.841589i	−0.989066	−	0.147476i	$-0.952885\pi$
$293$	−246.586	+	246.586i	−0.841589	+	0.841589i	0.147476	+	0.989066i	$0.452885\pi$
$294$		0			0
$295$	84.2168	+	221.742i	0.285481	+	0.751669i
$296$		0			0
$297$	5.69694	+	5.69694i	0.0191816	+	0.0191816i
$298$		0			0
$299$		−	407.778i		−	1.36380i
$300$		0			0
$301$	39.9592			0.132755
$302$		0			0
$303$	22.4597	−	22.4597i	0.0741244	−	0.0741244i
$304$		0			0
$305$	−279.934	+	106.318i	−0.917817	+	0.348583i
$306$		0			0
$307$	−365.373	−	365.373i	−1.19014	−	1.19014i	−0.977027	−	0.213114i	$-0.931639\pi$
$307$	−365.373	−	365.373i	−1.19014	−	1.19014i	−0.213114	−	0.977027i	$-0.568361\pi$
$308$		0			0
$309$			26.0658i			0.0843554i
$310$		0			0
$311$	154.384			0.496411			0.248205	−	0.968707i	$-0.420159\pi$
$311$	154.384			0.496411			0.248205	+	0.968707i	$0.420159\pi$
$312$		0			0
$313$	−258.959	+	258.959i	−0.827346	+	0.827346i	−0.987149	−	0.159803i	$-0.948914\pi$
$313$	−258.959	+	258.959i	−0.827346	+	0.827346i	0.159803	+	0.987149i	$0.448914\pi$
$314$		0			0
$315$	4.78775	−	10.6515i	0.0151992	−	0.0338144i
$316$		0			0
$317$	−2.85357	−	2.85357i	−0.00900180	−	0.00900180i	0.702592	−	0.711593i	$-0.252026\pi$
$317$	−2.85357	−	2.85357i	−0.00900180	−	0.00900180i	−0.711593	+	0.702592i	$0.752026\pi$
$318$		0			0
$319$			68.2929i			0.214084i
$320$		0			0
$321$	−163.980			−0.510840
$322$		0			0
$323$	−141.526	+	141.526i	−0.438159	+	0.438159i
$324$		0			0
$325$	20.0658	−	337.065i	0.0617410	−	1.03712i
$326$		0			0
$327$	−119.146	−	119.146i	−0.364362	−	0.364362i
$328$		0			0
$329$		−	46.8377i		−	0.142364i
$330$		0			0
$331$	497.646			1.50346			0.751731	−	0.659470i	$-0.229219\pi$
$331$	497.646			1.50346			0.751731	+	0.659470i	$0.229219\pi$
$332$		0			0
$333$	61.9546	−	61.9546i	0.186050	−	0.186050i
$334$		0			0
$335$	−524.232	−	235.637i	−1.56487	−	0.703393i
$336$		0			0
$337$	274.757	+	274.757i	0.815303	+	0.815303i	0.985423	−	0.170120i	$-0.0544156\pi$
$337$	274.757	+	274.757i	0.815303	+	0.815303i	−0.170120	+	0.985423i	$0.554416\pi$
$338$		0			0
$339$			73.8184i			0.217753i
$340$		0			0
$341$	68.9898			0.202316
$342$		0			0
$343$	53.6163	−	53.6163i	0.156316	−	0.156316i
$344$		0			0
$345$	92.8332	+	244.429i	0.269082	+	0.708490i
$346$		0			0
$347$	465.848	+	465.848i	1.34250	+	1.34250i	0.893563	+	0.448939i	$0.148198\pi$
$347$	465.848	+	465.848i	1.34250	+	1.34250i	0.448939	+	0.893563i	$0.351802\pi$
$348$		0			0
$349$		−	74.7173i		−	0.214090i	−0.994254	−	0.107045i	$-0.965861\pi$
$349$		−	74.7173i		−	0.214090i	0.994254	−	0.107045i	$-0.0341389\pi$
$350$		0			0
$351$	70.1816			0.199948
$352$		0			0
$353$	−34.8332	+	34.8332i	−0.0986775	+	0.0986775i	−0.754722	−	0.656045i	$-0.772228\pi$
$353$	−34.8332	+	34.8332i	−0.0986775	+	0.0986775i	0.656045	+	0.754722i	$0.272228\pi$
$354$		0			0
$355$	−409.444	+	155.505i	−1.15336	+	0.438043i
$356$		0			0
$357$	−15.0306	−	15.0306i	−0.0421026	−	0.0421026i
$358$		0			0
$359$			129.889i			0.361807i	0.983501	+	0.180904i	$0.0579022\pi$
$359$			129.889i			0.361807i	−0.983501	+	0.180904i	$0.942098\pi$
$360$		0			0
$361$	199.788			0.553429
$362$		0			0
$363$	145.250	−	145.250i	0.400137	−	0.400137i
$364$		0			0
$365$	220.293	−	490.095i	0.603542	−	1.34273i
$366$		0			0
$367$	160.056	+	160.056i	0.436119	+	0.436119i	0.890704	−	0.454585i	$-0.150212\pi$
$367$	160.056	+	160.056i	0.436119	+	0.436119i	−0.454585	+	0.890704i	$0.650212\pi$
$368$		0			0
$369$			144.879i			0.392625i
$370$		0			0
$371$	−60.0000			−0.161725
$372$		0			0
$373$	−30.0250	+	30.0250i	−0.0804960	+	0.0804960i	−0.746208	−	0.665712i	$-0.768128\pi$
$373$	−30.0250	+	30.0250i	−0.0804960	+	0.0804960i	0.665712	+	0.746208i	$0.268128\pi$
$374$		0			0
$375$	64.7071	+	206.611i	0.172552	+	0.550962i
$376$		0			0
$377$	420.656	+	420.656i	1.11580	+	1.11580i
$378$		0			0
$379$		−	424.343i		−	1.11964i	−0.828615	−	0.559819i	$-0.810871\pi$
$379$		−	424.343i		−	1.11964i	0.828615	−	0.559819i	$-0.189129\pi$
$380$		0			0
$381$	161.803			0.424679
$382$		0			0
$383$	−325.460	+	325.460i	−0.849764	+	0.849764i	−0.990103	−	0.140339i	$-0.955181\pi$
$383$	−325.460	+	325.460i	−0.849764	+	0.849764i	0.140339	+	0.990103i	$0.455181\pi$
$384$		0			0
$385$	5.50510	+	2.47449i	0.0142990	+	0.00642724i
$386$		0			0
$387$	−108.879	−	108.879i	−0.281340	−	0.281340i
$388$		0			0
$389$		−	698.116i		−	1.79464i	−0.441378	−	0.897321i	$-0.645510\pi$
$389$		−	698.116i		−	1.79464i	0.441378	−	0.897321i	$-0.354490\pi$
$390$		0			0
$391$	475.918			1.21718
$392$		0			0
$393$	106.373	−	106.373i	0.270670	−	0.270670i
$394$		0			0
$395$	172.738	+	454.817i	0.437311	+	1.15144i
$396$		0			0
$397$	257.984	+	257.984i	0.649834	+	0.649834i	0.952953	−	0.303119i	$-0.0980278\pi$
$397$	257.984	+	257.984i	0.649834	+	0.649834i	−0.303119	+	0.952953i	$0.598028\pi$
$398$		0			0
$399$		−	17.1214i		−	0.0429109i
$400$		0			0
$401$	−357.151			−0.890651			−0.445325	−	0.895369i	$-0.646912\pi$
$401$	−357.151			−0.890651			−0.445325	+	0.895369i	$0.646912\pi$
$402$		0			0
$403$	424.949	−	424.949i	1.05446	−	1.05446i
$404$		0			0
$405$	−42.0681	+	15.9773i	−0.103872	+	0.0394501i
$406$		0			0
$407$	32.0204	+	32.0204i	0.0786742	+	0.0786742i
$408$		0			0
$409$		−	66.3837i		−	0.162307i	−0.996702	−	0.0811536i	$-0.974140\pi$
$409$		−	66.3837i		−	0.162307i	0.996702	−	0.0811536i	$-0.0258604\pi$
$410$		0			0
$411$	175.212			0.426307
$412$		0			0
$413$	−26.1158	+	26.1158i	−0.0632344	+	0.0632344i
$414$		0			0
$415$	−119.019	+	264.788i	−0.286794	+	0.638043i
$416$		0			0
$417$	28.4291	+	28.4291i	0.0681753	+	0.0681753i
$418$		0			0
$419$			414.772i			0.989909i	0.868919	+	0.494955i	$0.164815\pi$
$419$			414.772i			0.989909i	−0.868919	+	0.494955i	$0.835185\pi$
$420$		0			0
$421$	762.727			1.81170			0.905851	−	0.423597i	$-0.139233\pi$
$421$	762.727			1.81170			0.905851	+	0.423597i	$0.139233\pi$
$422$		0			0
$423$	−127.621	+	127.621i	−0.301704	+	0.301704i
$424$		0			0
$425$	393.389	+	23.4189i	0.925622	+	0.0551032i
$426$		0			0
$427$	−32.9694	−	32.9694i	−0.0772117	−	0.0772117i
$428$		0			0
$429$			36.2724i			0.0845512i
$430$		0			0
$431$	−21.3439			−0.0495218			−0.0247609	−	0.999693i	$-0.507882\pi$
$431$	−21.3439			−0.0495218			−0.0247609	+	0.999693i	$0.507882\pi$
$432$		0			0
$433$	288.868	−	288.868i	0.667132	−	0.667132i	−0.289919	−	0.957051i	$-0.593628\pi$
$433$	288.868	−	288.868i	0.667132	−	0.667132i	0.957051	+	0.289919i	$0.0936283\pi$
$434$		0			0
$435$	−347.914	−	156.384i	−0.799802	−	0.359503i
$436$		0			0
$437$	271.060	+	271.060i	0.620275	+	0.620275i
$438$		0			0
$439$		−	410.182i		−	0.934355i	−0.884164	−	0.467177i	$-0.845271\pi$
$439$		−	410.182i		−	0.934355i	0.884164	−	0.467177i	$-0.154729\pi$
$440$		0			0
$441$	−145.182			−0.329210
$442$		0			0
$443$	−262.747	+	262.747i	−0.593108	+	0.593108i	−0.938470	−	0.345362i	$-0.887756\pi$
$443$	−262.747	+	262.747i	−0.593108	+	0.593108i	0.345362	+	0.938470i	$0.387756\pi$
$444$		0			0
$445$	−92.6719	−	244.005i	−0.208252	−	0.548325i
$446$		0			0
$447$	−168.439	−	168.439i	−0.376822	−	0.376822i
$448$		0			0
$449$		−	841.242i		−	1.87359i	−0.349879	−	0.936795i	$-0.613777\pi$
$449$		−	841.242i		−	1.87359i	0.349879	−	0.936795i	$-0.386223\pi$
$450$		0			0
$451$	−74.8786			−0.166028
$452$		0			0
$453$	−356.883	+	356.883i	−0.787822	+	0.787822i
$454$		0			0
$455$	49.1510	−	18.6674i	0.108024	−	0.0410272i
$456$		0			0
$457$	−23.8286	−	23.8286i	−0.0521413	−	0.0521413i	0.680555	−	0.732697i	$-0.261739\pi$
$457$	−23.8286	−	23.8286i	−0.0521413	−	0.0521413i	−0.732697	+	0.680555i	$0.761739\pi$
$458$		0			0
$459$			81.9092i			0.178451i
$460$		0			0
$461$	44.3179			0.0961342			0.0480671	−	0.998844i	$-0.484694\pi$
$461$	44.3179			0.0961342			0.0480671	+	0.998844i	$0.484694\pi$
$462$		0			0
$463$	193.116	−	193.116i	0.417097	−	0.417097i	−0.467105	−	0.884202i	$-0.654703\pi$
$463$	193.116	−	193.116i	0.417097	−	0.417097i	0.884202	+	0.467105i	$0.154703\pi$
$464$		0			0
$465$	−157.980	+	351.464i	−0.339741	+	0.755837i
$466$		0			0
$467$	−377.369	−	377.369i	−0.808070	−	0.808070i	0.176271	−	0.984342i	$-0.443596\pi$
$467$	−377.369	−	377.369i	−0.808070	−	0.808070i	−0.984342	+	0.176271i	$0.943596\pi$
$468$		0			0
$469$		−	89.4939i		−	0.190818i
$470$		0			0
$471$	128.919			0.273714
$472$		0			0
$473$	56.2724	−	56.2724i	0.118969	−	0.118969i
$474$		0			0
$475$	210.717	+	237.394i	0.443615	+	0.499777i
$476$		0			0
$477$	163.485	+	163.485i	0.342735	+	0.342735i
$478$		0			0
$479$		−	112.141i		−	0.234114i	−0.993125	−	0.117057i	$-0.962654\pi$
$479$		−	112.141i		−	0.234114i	0.993125	−	0.117057i	$-0.0373461\pi$
$480$		0			0
$481$	394.465			0.820094
$482$		0			0
$483$	−28.7878	+	28.7878i	−0.0596020	+	0.0596020i
$484$		0			0
$485$	−238.631	−	107.262i	−0.492023	−	0.221159i
$486$		0			0
$487$	41.9444	+	41.9444i	0.0861281	+	0.0861281i	0.748858	−	0.662730i	$-0.230602\pi$
$487$	41.9444	+	41.9444i	0.0861281	+	0.0861281i	−0.662730	+	0.748858i	$0.730602\pi$
$488$		0			0
$489$		−	288.000i		−	0.588957i
$490$		0			0
$491$	926.468			1.88690			0.943450	−	0.331515i	$-0.107560\pi$
$491$	926.468			1.88690			0.943450	+	0.331515i	$0.107560\pi$
$492$		0			0
$493$	−490.949	+	490.949i	−0.995840	+	0.995840i
$494$		0			0
$495$	−8.25765	−	21.7423i	−0.0166821	−	0.0439239i
$496$		0			0
$497$	−48.2225	−	48.2225i	−0.0970271	−	0.0970271i
$498$		0			0
$499$		−	67.5255i		−	0.135322i	−0.997708	−	0.0676608i	$-0.978446\pi$
$499$		−	67.5255i		−	0.135322i	0.997708	−	0.0676608i	$-0.0215536\pi$
$500$		0			0
$501$	−358.454			−0.715477
$502$		0			0
$503$	180.470	−	180.470i	0.358787	−	0.358787i	−0.504579	−	0.863366i	$-0.668352\pi$
$503$	180.470	−	180.470i	0.358787	−	0.358787i	0.863366	+	0.504579i	$0.168352\pi$
$504$		0			0
$505$	−85.7173	+	32.5551i	−0.169737	+	0.0644655i
$506$		0			0
$507$	16.4416	+	16.4416i	0.0324291	+	0.0324291i
$508$		0			0
$509$			920.772i			1.80898i	0.426493	+	0.904491i	$0.359749\pi$
$509$			920.772i			1.80898i	−0.426493	+	0.904491i	$0.640251\pi$
$510$		0			0
$511$	83.6663			0.163731
$512$		0			0
$513$	−46.6515	+	46.6515i	−0.0909387	+	0.0909387i
$514$		0			0
$515$	30.8490	−	68.6311i	0.0599009	−	0.133264i
$516$		0			0
$517$	−65.9592	−	65.9592i	−0.127581	−	0.127581i
$518$		0			0
$519$			9.19184i			0.0177107i
$520$		0			0
$521$	−333.687			−0.640474			−0.320237	−	0.947338i	$-0.603762\pi$
$521$	−333.687			−0.640474			−0.320237	+	0.947338i	$0.603762\pi$
$522$		0			0
$523$	380.474	−	380.474i	0.727485	−	0.727485i	−0.242633	−	0.970118i	$-0.578011\pi$
$523$	380.474	−	380.474i	0.727485	−	0.727485i	0.970118	+	0.242633i	$0.0780112\pi$
$524$		0			0
$525$	−25.2122	+	22.3791i	−0.0480233	+	0.0426268i
$526$		0			0
$527$	495.959	+	495.959i	0.941099	+	0.941099i
$528$		0			0
$529$		−	382.514i		−	0.723089i
$530$		0			0
$531$	142.318			0.268019
$532$		0			0
$533$	−461.221	+	461.221i	−0.865331	+	0.865331i
$534$		0			0
$535$	431.757	+	194.070i	0.807023	+	0.362748i
$536$		0			0
$537$	94.5959	+	94.5959i	0.176156	+	0.176156i
$538$		0			0
$539$		−	75.0352i		−	0.139212i
$540$		0			0
$541$	156.515			0.289307			0.144654	−	0.989482i	$-0.453793\pi$
$541$	156.515			0.289307			0.144654	+	0.989482i	$0.453793\pi$
$542$		0			0
$543$	−196.763	+	196.763i	−0.362362	+	0.362362i
$544$		0			0
$545$	172.702	+	454.722i	0.316884	+	0.834352i
$546$		0			0
$547$	12.6061	+	12.6061i	0.0230459	+	0.0230459i	0.718536	−	0.695490i	$-0.244813\pi$
$547$	12.6061	+	12.6061i	0.0230459	+	0.0230459i	−0.695490	+	0.718536i	$0.744813\pi$
$548$		0			0
$549$			179.666i			0.327261i
$550$		0			0
$551$	−559.242			−1.01496
$552$		0			0
$553$	−53.5663	+	53.5663i	−0.0968650	+	0.0968650i
$554$		0			0
$555$	−236.449	+	89.8025i	−0.426035	+	0.161806i
$556$		0			0
$557$	−21.0194	−	21.0194i	−0.0377368	−	0.0377368i	0.687987	−	0.725723i	$-0.258495\pi$
$557$	−21.0194	−	21.0194i	−0.0377368	−	0.0377368i	−0.725723	+	0.687987i	$0.758495\pi$
$558$		0			0
$559$		−	693.231i		−	1.24013i
$560$		0			0
$561$	−42.3337			−0.0754611
$562$		0			0
$563$	−360.536	+	360.536i	−0.640383	+	0.640383i	−0.950650	−	0.310266i	$-0.899582\pi$
$563$	−360.536	+	360.536i	−0.640383	+	0.640383i	0.310266	+	0.950650i	$0.399582\pi$
$564$		0			0
$565$	87.3643	−	194.363i	0.154627	−	0.344006i
$566$		0			0
$567$	−4.95459	−	4.95459i	−0.00873826	−	0.00873826i
$568$		0			0
$569$		−	486.504i		−	0.855016i	−0.904012	−	0.427508i	$-0.859392\pi$
$569$		−	486.504i		−	0.855016i	0.904012	−	0.427508i	$-0.140608\pi$
$570$		0			0
$571$	−447.040			−0.782907			−0.391453	−	0.920198i	$-0.628028\pi$
$571$	−447.040			−0.782907			−0.391453	+	0.920198i	$0.628028\pi$
$572$		0			0
$573$	308.474	−	308.474i	0.538350	−	0.538350i
$574$		0			0
$575$	44.8536	−	753.448i	0.0780062	−	1.31035i
$576$		0			0
$577$	−248.444	−	248.444i	−0.430579	−	0.430579i	0.458247	−	0.888825i	$-0.348478\pi$
$577$	−248.444	−	248.444i	−0.430579	−	0.430579i	−0.888825	+	0.458247i	$0.848478\pi$
$578$		0			0
$579$			424.702i			0.733509i
$580$		0			0
$581$	−45.2031			−0.0778022
$582$		0			0
$583$	−84.4949	+	84.4949i	−0.144931	+	0.144931i
$584$		0			0
$585$	−184.788	−	83.0602i	−0.315877	−	0.141983i
$586$		0			0
$587$	−547.712	−	547.712i	−0.933069	−	0.933069i	0.0648271	−	0.997897i	$-0.479350\pi$
$587$	−547.712	−	547.712i	−0.933069	−	0.933069i	−0.997897	+	0.0648271i	$0.979350\pi$
$588$		0			0
$589$			564.949i			0.959166i
$590$		0			0
$591$	5.12143			0.00866570
$592$		0			0
$593$	−78.9444	+	78.9444i	−0.133127	+	0.133127i	−0.770530	−	0.637403i	$-0.780009\pi$
$593$	−78.9444	+	78.9444i	−0.133127	+	0.133127i	0.637403	+	0.770530i	$0.280009\pi$
$594$		0			0
$595$	21.7867	+	57.3643i	0.0366163	+	0.0964106i
$596$		0			0
$597$	−373.015	−	373.015i	−0.624815	−	0.624815i
$598$		0			0
$599$			381.807i			0.637408i	0.947854	+	0.318704i	$0.103248\pi$
$599$			381.807i			0.637408i	−0.947854	+	0.318704i	$0.896752\pi$
$600$		0			0
$601$	−231.757			−0.385619			−0.192810	−	0.981236i	$-0.561760\pi$
$601$	−231.757			−0.385619			−0.192810	+	0.981236i	$0.561760\pi$
$602$		0			0
$603$	−243.848	+	243.848i	−0.404391	+	0.404391i
$604$		0			0
$605$	−554.345	+	210.538i	−0.916273	+	0.347997i
$606$		0			0
$607$	−96.8434	−	96.8434i	−0.159544	−	0.159544i	0.622821	−	0.782365i	$-0.285987\pi$
$607$	−96.8434	−	96.8434i	−0.159544	−	0.159544i	−0.782365	+	0.622821i	$0.785987\pi$
$608$		0			0
$609$		−	59.3939i		−	0.0975269i
$610$		0			0
$611$	−812.563			−1.32989
$612$		0			0
$613$	105.712	−	105.712i	0.172450	−	0.172450i	−0.615605	−	0.788055i	$-0.711088\pi$
$613$	105.712	−	105.712i	0.172450	−	0.172450i	0.788055	+	0.615605i	$0.211088\pi$
$614$		0			0
$615$	171.464	−	381.464i	0.278804	−	0.620267i
$616$		0			0
$617$	−41.9250	−	41.9250i	−0.0679498	−	0.0679498i	0.672315	−	0.740265i	$-0.265300\pi$
$617$	−41.9250	−	41.9250i	−0.0679498	−	0.0679498i	−0.740265	+	0.672315i	$0.765300\pi$
$618$		0			0
$619$			434.363i			0.701718i	0.936428	+	0.350859i	$0.114110\pi$
$619$			434.363i			0.701718i	−0.936428	+	0.350859i	$0.885890\pi$
$620$		0			0
$621$	156.879			0.252622
$622$		0			0
$623$	28.7378	−	28.7378i	0.0461280	−	0.0461280i
$624$		0			0
$625$	74.1510	−	620.586i	0.118642	−	0.992937i
$626$		0			0
$627$	−24.1112	−	24.1112i	−0.0384549	−	0.0384549i
$628$		0			0
$629$			460.382i			0.731926i
$630$		0			0
$631$	−816.413			−1.29384			−0.646920	−	0.762558i	$-0.723943\pi$
$631$	−816.413			−1.29384			−0.646920	+	0.762558i	$0.723943\pi$
$632$		0			0
$633$	334.540	−	334.540i	0.528500	−	0.528500i
$634$		0			0
$635$	−426.025	−	191.494i	−0.670906	−	0.301565i
$636$		0			0
$637$	−462.186	−	462.186i	−0.725567	−	0.725567i
$638$		0			0
$639$			262.788i			0.411248i
$640$		0			0
$641$	−937.959			−1.46327			−0.731637	−	0.681694i	$-0.761244\pi$
$641$	−937.959			−1.46327			−0.731637	+	0.681694i	$0.761244\pi$
$642$		0			0
$643$	−62.8786	+	62.8786i	−0.0977894	+	0.0977894i	−0.754309	−	0.656520i	$-0.772028\pi$
$643$	−62.8786	+	62.8786i	−0.0977894	+	0.0977894i	0.656520	+	0.754309i	$0.272028\pi$
$644$		0			0
$645$	157.818	+	415.535i	0.244680	+	0.644240i
$646$		0			0
$647$	86.3087	+	86.3087i	0.133398	+	0.133398i	0.770653	−	0.637255i	$-0.219930\pi$
$647$	86.3087	+	86.3087i	0.133398	+	0.133398i	−0.637255	+	0.770653i	$0.719930\pi$
$648$		0			0
$649$			73.5551i			0.113336i
$650$		0			0
$651$	−60.0000			−0.0921659
$652$		0			0
$653$	294.904	−	294.904i	0.451613	−	0.451613i	−0.444276	−	0.895890i	$-0.646539\pi$
$653$	294.904	−	294.904i	0.451613	−	0.451613i	0.895890	+	0.444276i	$0.146539\pi$
$654$		0			0
$655$	−405.974	+	154.187i	−0.619808	+	0.235400i
$656$		0			0
$657$	−227.969	−	227.969i	−0.346985	−	0.346985i
$658$		0			0
$659$		−	1156.80i		−	1.75539i	−0.479220	−	0.877695i	$-0.659081\pi$
$659$		−	1156.80i		−	1.75539i	0.479220	−	0.877695i	$-0.340919\pi$
$660$		0			0
$661$	908.838			1.37494			0.687472	−	0.726211i	$-0.258720\pi$
$661$	908.838			1.37494			0.687472	+	0.726211i	$0.258720\pi$
$662$		0			0
$663$	−260.758	+	260.758i	−0.393300	+	0.393300i
$664$		0			0
$665$	−20.2633	+	45.0806i	−0.0304711	+	0.0677904i
$666$		0			0
$667$	940.302	+	940.302i	1.40975	+	1.40975i
$668$		0			0
$669$		−	427.832i		−	0.639510i
$670$		0			0
$671$	−92.8582			−0.138388
$672$		0			0
$673$	833.756	−	833.756i	1.23886	−	1.23886i	0.278400	−	0.960465i	$-0.410196\pi$
$673$	833.756	−	833.756i	1.23886	−	1.23886i	0.960465	−	0.278400i	$-0.0898040\pi$
$674$		0			0
$675$	129.674	+	7.71964i	0.192110	+	0.0114365i
$676$		0			0
$677$	−200.257	−	200.257i	−0.295800	−	0.295800i	0.543566	−	0.839366i	$-0.317074\pi$
$677$	−200.257	−	200.257i	−0.295800	−	0.295800i	−0.839366	+	0.543566i	$0.817074\pi$
$678$		0			0
$679$		−	40.7378i		−	0.0599967i
$680$		0			0
$681$	−190.120			−0.279178
$682$		0			0
$683$	−156.025	+	156.025i	−0.228441	+	0.228441i	−0.812041	−	0.583600i	$-0.801643\pi$
$683$	−156.025	+	156.025i	−0.228441	+	0.228441i	0.583600	+	0.812041i	$0.301643\pi$
$684$		0			0
$685$	−461.333	−	207.364i	−0.673478	−	0.302722i
$686$		0			0
$687$	−10.9852	−	10.9852i	−0.0159901	−	0.0159901i
$688$		0			0
$689$			1040.91i			1.51075i
$690$		0			0
$691$	−774.940			−1.12148			−0.560738	−	0.827993i	$-0.689482\pi$
$691$	−774.940			−1.12148			−0.560738	+	0.827993i	$0.689482\pi$
$692$		0			0
$693$	2.56072	−	2.56072i	0.00369512	−	0.00369512i
$694$		0			0
$695$	−41.2077	−	108.499i	−0.0592916	−	0.156114i
$696$		0			0
$697$	−538.293	−	538.293i	−0.772300	−	0.772300i
$698$		0			0
$699$		−	123.626i		−	0.176861i
$700$		0			0
$701$	280.309			0.399870			0.199935	−	0.979809i	$-0.435927\pi$
$701$	280.309			0.399870			0.199935	+	0.979809i	$0.435927\pi$
$702$		0			0
$703$	−262.211	+	262.211i	−0.372989	+	0.372989i
$704$		0			0
$705$	487.065	−	184.985i	0.690872	−	0.262390i
$706$		0			0
$707$	−10.0954	−	10.0954i	−0.0142792	−	0.0142792i
$708$		0			0
$709$			926.686i			1.30703i	0.756913	+	0.653516i	$0.226707\pi$
$709$			926.686i			1.30703i	−0.756913	+	0.653516i	$0.773293\pi$
$710$		0			0
$711$	291.909			0.410561
$712$		0			0
$713$	949.898	−	949.898i	1.33226	−	1.33226i
$714$		0			0
$715$	42.9286	−	95.5051i	0.0600399	−	0.133574i
$716$		0			0
$717$	342.606	+	342.606i	0.477833	+	0.477833i
$718$		0			0
$719$			938.565i			1.30538i	0.757627	+	0.652688i	$0.226359\pi$
$719$			938.565i			1.30538i	−0.757627	+	0.652688i	$0.773641\pi$
$720$		0			0
$721$	11.7163			0.0162501
$722$		0			0
$723$	486.384	−	486.384i	0.672730	−	0.672730i
$724$		0			0
$725$	730.974	+	823.514i	1.00824	+	1.13588i
$726$		0			0
$727$	−404.803	−	404.803i	−0.556812	−	0.556812i	0.371586	−	0.928398i	$-0.378814\pi$
$727$	−404.803	−	404.803i	−0.556812	−	0.556812i	−0.928398	+	0.371586i	$0.878814\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	809.071			1.10680
$732$		0			0
$733$	−644.529	+	644.529i	−0.879303	+	0.879303i	−0.993462	−	0.114159i	$-0.963583\pi$
$733$	−644.529	+	644.529i	−0.879303	+	0.879303i	0.114159	+	0.993462i	$0.463583\pi$
$734$		0			0
$735$	382.262	+	171.823i	0.520085	+	0.233773i
$736$		0			0
$737$	−126.030	−	126.030i	−0.171004	−	0.171004i
$738$		0			0
$739$			1182.11i			1.59961i	0.600262	+	0.799803i	$0.295063\pi$
$739$			1182.11i			1.59961i	−0.600262	+	0.799803i	$0.704937\pi$
$740$		0			0
$741$	−297.031			−0.400851
$742$		0			0
$743$	570.681	−	570.681i	0.768077	−	0.768077i	−0.209691	−	0.977768i	$-0.567246\pi$
$743$	570.681	−	570.681i	0.768077	−	0.768077i	0.977768	+	0.209691i	$0.0672458\pi$
$744$		0			0
$745$	244.151	+	642.848i	0.327719	+	0.862883i
$746$		0			0
$747$	123.167	+	123.167i	0.164882	+	0.164882i
$748$		0			0
$749$			73.7071i			0.0984074i
$750$		0			0
$751$	−180.050			−0.239747			−0.119873	−	0.992789i	$-0.538249\pi$
$751$	−180.050			−0.239747			−0.119873	+	0.992789i	$0.538249\pi$
$752$		0			0
$753$	65.9694	−	65.9694i	0.0876087	−	0.0876087i
$754$		0			0
$755$	1362.04	−	517.298i	1.80403	−	0.685164i
$756$		0			0
$757$	−187.176	−	187.176i	−0.247260	−	0.247260i	0.572585	−	0.819845i	$-0.305941\pi$
$757$	−187.176	−	187.176i	−0.247260	−	0.247260i	−0.819845	+	0.572585i	$0.805941\pi$
$758$		0			0
$759$			81.0806i			0.106826i
$760$		0			0
$761$	912.130			1.19859			0.599297	−	0.800527i	$-0.295447\pi$
$761$	912.130			1.19859			0.599297	+	0.800527i	$0.295447\pi$
$762$		0			0
$763$	−53.5551	+	53.5551i	−0.0701902	+	0.0701902i
$764$		0			0
$765$	96.9398	−	215.666i	0.126719	−	0.281917i
$766$		0			0
$767$	453.069	+	453.069i	0.590703	+	0.590703i
$768$		0			0
$769$			201.778i			0.262390i	0.991357	+	0.131195i	$0.0418813\pi$
$769$			201.778i			0.262390i	−0.991357	+	0.131195i	$0.958119\pi$
$770$		0			0
$771$	−758.686			−0.984028
$772$		0			0
$773$	−147.793	+	147.793i	−0.191195	+	0.191195i	−0.796212	−	0.605018i	$-0.793166\pi$
$773$	−147.793	+	147.793i	−0.191195	+	0.191195i	0.605018	+	0.796212i	$0.293166\pi$
$774$		0			0
$775$	831.918	−	738.434i	1.07344	−	0.952818i
$776$		0			0
$777$	−27.8480	−	27.8480i	−0.0358404	−	0.0358404i
$778$		0			0
$779$		−	613.171i		−	0.787126i
$780$		0			0
$781$	−135.818			−0.173903
$782$		0			0
$783$	−161.833	+	161.833i	−0.206683	+	0.206683i
$784$		0			0
$785$	−339.444	−	152.577i	−0.432413	−	0.194365i
$786$		0			0
$787$	447.576	+	447.576i	0.568711	+	0.568711i	0.931767	−	0.363056i	$-0.118267\pi$
$787$	447.576	+	447.576i	0.568711	+	0.568711i	−0.363056	+	0.931767i	$0.618267\pi$
$788$		0			0
$789$			315.626i			0.400032i
$790$		0			0
$791$	33.1806			0.0419477
$792$		0			0
$793$	−571.968	+	571.968i	−0.721272	+	0.721272i
$794$		0			0
$795$	−236.969	−	623.939i	−0.298075	−	0.784829i
$796$		0			0
$797$	−128.338	−	128.338i	−0.161027	−	0.161027i	0.621995	−	0.783021i	$-0.286323\pi$
$797$	−128.338	−	128.338i	−0.161027	−	0.161027i	−0.783021	+	0.621995i	$0.786323\pi$
$798$		0			0
$799$		−	948.345i		−	1.18691i
$800$		0			0
$801$	−156.606			−0.195513
$802$		0			0
$803$	117.823	−	117.823i	0.146728	−	0.146728i
$804$		0			0
$805$	109.868	−	41.7276i	0.136482	−	0.0518355i
$806$		0			0
$807$	137.449	+	137.449i	0.170322	+	0.170322i
$808$		0			0
$809$		−	699.212i		−	0.864292i	−0.901804	−	0.432146i	$-0.857757\pi$
$809$		−	699.212i		−	0.864292i	0.901804	−	0.432146i	$-0.142243\pi$
$810$		0			0
$811$	90.5041			0.111596			0.0557978	−	0.998442i	$-0.482230\pi$
$811$	90.5041			0.111596			0.0557978	+	0.998442i	$0.482230\pi$
$812$		0			0
$813$	205.287	−	205.287i	0.252506	−	0.252506i
$814$		0			0
$815$	−340.849	+	758.302i	−0.418220	+	0.930432i
$816$		0			0
$817$	460.808	+	460.808i	0.564025	+	0.564025i
$818$		0			0
$819$		−	31.5459i		−	0.0385176i
$820$		0			0
$821$	250.783			0.305461			0.152730	−	0.988268i	$-0.451193\pi$
$821$	250.783			0.305461			0.152730	+	0.988268i	$0.451193\pi$
$822$		0			0
$823$	27.0954	−	27.0954i	0.0329227	−	0.0329227i	−0.690454	−	0.723377i	$-0.742589\pi$
$823$	27.0954	−	27.0954i	0.0329227	−	0.0329227i	0.723377	+	0.690454i	$0.242589\pi$
$824$		0			0
$825$	−3.98979	+	67.0204i	−0.00483611	+	0.0812369i
$826$		0			0
$827$	−589.930	−	589.930i	−0.713337	−	0.713337i	0.253895	−	0.967232i	$-0.418288\pi$
$827$	−589.930	−	589.930i	−0.713337	−	0.713337i	−0.967232	+	0.253895i	$0.918288\pi$
$828$		0			0
$829$			1576.77i			1.90202i	0.309160	+	0.951010i	$0.399952\pi$
$829$			1576.77i			1.90202i	−0.309160	+	0.951010i	$0.600048\pi$
$830$		0			0
$831$	730.282			0.878799
$832$		0			0
$833$	539.419	−	539.419i	0.647562	−	0.647562i
$834$		0			0
$835$	943.807	+	424.232i	1.13031	+	0.508062i
$836$		0			0
$837$	163.485	+	163.485i	0.195322	+	0.195322i
$838$		0			0
$839$			963.523i			1.14842i	0.818708	+	0.574209i	$0.194690\pi$
$839$			963.523i			1.14842i	−0.818708	+	0.574209i	$0.805310\pi$
$840$		0			0
$841$	−1099.00			−1.30678
$842$		0			0
$843$	412.045	−	412.045i	0.488785	−	0.488785i
$844$		0			0
$845$	−23.8319	−	62.7492i	−0.0282034	−	0.0742594i
$846$		0			0
$847$	−65.2883	−	65.2883i	−0.0770818	−	0.0770818i
$848$		0			0
$849$		−	49.3847i		−	0.0581681i
$850$		0			0
$851$	881.757			1.03614
$852$		0			0
$853$	254.166	−	254.166i	0.297967	−	0.297967i	−0.542250	−	0.840217i	$-0.682427\pi$
$853$	254.166	−	254.166i	0.297967	−	0.297967i	0.840217	+	0.542250i	$0.182427\pi$
$854$		0			0
$855$	178.045	−	67.6209i	0.208240	−	0.0790888i
$856$		0			0
$857$	−699.206	−	699.206i	−0.815876	−	0.815876i	0.169632	−	0.985508i	$-0.445742\pi$
$857$	−699.206	−	699.206i	−0.815876	−	0.815876i	−0.985508	+	0.169632i	$0.945742\pi$
$858$		0			0
$859$			246.708i			0.287204i	0.989636	+	0.143602i	$0.0458685\pi$
$859$			246.708i			0.287204i	−0.989636	+	0.143602i	$0.954131\pi$
$860$		0			0
$861$	65.1214			0.0756346
$862$		0			0
$863$	1051.01	−	1051.01i	1.21786	−	1.21786i	0.249483	−	0.968379i	$-0.419739\pi$
$863$	1051.01	−	1051.01i	1.21786	−	1.21786i	0.968379	−	0.249483i	$-0.0802605\pi$
$864$		0			0
$865$	10.8786	−	24.2020i	0.0125764	−	0.0279792i
$866$		0			0
$867$	49.6197	+	49.6197i	0.0572314	+	0.0572314i
$868$		0			0
$869$			150.869i			0.173613i
$870$		0			0
$871$	−1552.58			−1.78253
$872$		0			0
$873$	−111.000	+	111.000i	−0.127148	+	0.127148i
$874$		0			0
$875$	92.8694	−	29.0852i	0.106136	−	0.0332402i
$876$		0			0
$877$	30.2974	+	30.2974i	0.0345467	+	0.0345467i	0.724169	−	0.689622i	$-0.242223\pi$
$877$	30.2974	+	30.2974i	0.0345467	+	0.0345467i	−0.689622	+	0.724169i	$0.742223\pi$
$878$		0			0
$879$		−	604.009i		−	0.687155i
$880$		0			0
$881$	751.294			0.852774			0.426387	−	0.904541i	$-0.359786\pi$
$881$	751.294			0.852774			0.426387	+	0.904541i	$0.359786\pi$
$882$		0			0
$883$	666.929	−	666.929i	0.755298	−	0.755298i	−0.220164	−	0.975463i	$-0.570659\pi$
$883$	666.929	−	666.929i	0.755298	−	0.755298i	0.975463	+	0.220164i	$0.0706594\pi$
$884$		0			0
$885$	−374.722	−	168.434i	−0.423415	−	0.190321i
$886$		0			0
$887$	269.662	+	269.662i	0.304015	+	0.304015i	0.842583	−	0.538567i	$-0.181034\pi$
$887$	269.662	+	269.662i	0.304015	+	0.304015i	−0.538567	+	0.842583i	$0.681034\pi$
$888$		0			0
$889$		−	72.7286i		−	0.0818094i
$890$		0			0
$891$	−13.9546			−0.0156617
$892$		0			0
$893$	540.132	−	540.132i	0.604851	−	0.604851i
$894$		0			0
$895$	−137.116	−	361.025i	−0.153202	−	0.403380i
$896$		0			0
$897$	499.423	+	499.423i	0.556771	+	0.556771i
$898$		0			0
$899$			1959.80i			2.17997i
$900$		0			0
$901$	−1214.85			−1.34833
$902$		0			0
$903$	−48.9398	+	48.9398i	−0.0541969	+	0.0541969i
$904$		0			0
$905$	750.944	−	285.206i	0.829773	−	0.315144i
$906$		0			0
$907$	−578.515	−	578.515i	−0.637834	−	0.637834i	0.312187	−	0.950021i	$-0.398938\pi$
$907$	−578.515	−	578.515i	−0.637834	−	0.637834i	−0.950021	+	0.312187i	$0.898938\pi$
$908$		0			0
$909$			55.0148i			0.0605223i
$910$		0			0
$911$	−90.4745			−0.0993134			−0.0496567	−	0.998766i	$-0.515813\pi$
$911$	−90.4745			−0.0993134			−0.0496567	+	0.998766i	$0.515813\pi$
$912$		0			0
$913$	−63.6571	+	63.6571i	−0.0697231	+	0.0697231i
$914$		0			0
$915$	212.636	−	473.060i	0.232389	−	0.517006i
$916$		0			0
$917$	−47.8138	−	47.8138i	−0.0521415	−	0.0521415i
$918$		0			0
$919$			1467.08i			1.59639i	0.602402	+	0.798193i	$0.294210\pi$
$919$			1467.08i			1.59639i	−0.602402	+	0.798193i	$0.705790\pi$
$920$		0			0
$921$	894.979			0.971747
$922$		0			0
$923$	−836.586	+	836.586i	−0.906377	+	0.906377i
$924$		0			0
$925$	728.852	+	43.3893i	0.787948	+	0.0469073i
$926$		0			0
$927$	−31.9240	−	31.9240i	−0.0344379	−	0.0344379i
$928$		0			0
$929$			907.444i			0.976796i	0.872621	+	0.488398i	$0.162419\pi$
$929$			907.444i			0.976796i	−0.872621	+	0.488398i	$0.837581\pi$
$930$		0			0
$931$	614.454			0.659994
$932$		0			0
$933$	−189.081	+	189.081i	−0.202659	+	0.202659i
$934$		0			0
$935$	111.464	+	50.1021i	0.119213	+	0.0535851i
$936$		0			0
$937$	158.898	+	158.898i	0.169582	+	0.169582i	0.786795	−	0.617214i	$-0.211739\pi$
$937$	158.898	+	158.898i	0.169582	+	0.169582i	−0.617214	+	0.786795i	$0.711739\pi$
$938$		0			0
$939$		−	634.318i		−	0.675525i
$940$		0			0
$941$	−666.497			−0.708286			−0.354143	−	0.935191i	$-0.615227\pi$
$941$	−666.497			−0.708286			−0.354143	+	0.935191i	$0.615227\pi$
$942$		0			0
$943$	−1030.98	+	1030.98i	−1.09330	+	1.09330i
$944$		0			0
$945$	7.18163	+	18.9092i	0.00759961	+	0.0200097i
$946$		0			0
$947$	−1038.08	−	1038.08i	−1.09618	−	1.09618i	−0.994854	−	0.101323i	$-0.967692\pi$
$947$	−1038.08	−	1038.08i	−1.09618	−	1.09618i	−0.101323	−	0.994854i	$-0.532308\pi$
$948$		0			0
$949$		−	1451.48i		−	1.52949i
$950$		0			0
$951$	6.98979			0.00734994
$952$		0			0
$953$	−262.045	+	262.045i	−0.274969	+	0.274969i	−0.831097	−	0.556128i	$-0.812286\pi$
$953$	−262.045	+	262.045i	−0.274969	+	0.274969i	0.556128	+	0.831097i	$0.312286\pi$
$954$		0			0
$955$	−1177.29	+	447.131i	−1.23277	+	0.468200i
$956$		0			0
$957$	−83.6413	−	83.6413i	−0.0873995	−	0.0873995i
$958$		0			0
$959$		−	78.7561i		−	0.0821232i
$960$		0			0
$961$	1018.80			1.06014
$962$		0			0
$963$	200.833	−	200.833i	0.208549	−	0.208549i
$964$		0			0
$965$	502.636	−	1118.24i	0.520866	−	1.15879i
$966$		0			0
$967$	−1277.98	−	1277.98i	−1.32160	−	1.32160i	−0.912484	−	0.409111i	$-0.865839\pi$
$967$	−1277.98	−	1277.98i	−1.32160	−	1.32160i	−0.409111	−	0.912484i	$-0.634161\pi$
$968$		0			0
$969$		−	346.665i		−	0.357756i
$970$		0			0
$971$	−1640.26			−1.68924			−0.844622	−	0.535363i	$-0.820175\pi$
$971$	−1640.26			−1.68924			−0.844622	+	0.535363i	$0.820175\pi$
$972$		0			0
$973$	12.7786	−	12.7786i	0.0131332	−	0.0131332i
$974$		0			0
$975$	388.243	+	437.394i	0.398198	+	0.448609i
$976$		0			0
$977$	−761.480	−	761.480i	−0.779406	−	0.779406i	0.200323	−	0.979730i	$-0.435801\pi$
$977$	−761.480	−	761.480i	−0.779406	−	0.779406i	−0.979730	+	0.200323i	$0.935801\pi$
$978$		0			0
$979$		−	80.9398i		−	0.0826760i
$980$		0			0
$981$	291.848			0.297500
$982$		0			0
$983$	−215.035	+	215.035i	−0.218754	+	0.218754i	−0.807973	−	0.589219i	$-0.799435\pi$
$983$	−215.035	+	215.035i	−0.218754	+	0.218754i	0.589219	+	0.807973i	$0.299435\pi$
$984$		0			0
$985$	−13.4847	−	6.06123i	−0.0136900	−	0.00615353i
$986$		0			0
$987$	57.3643	+	57.3643i	0.0581199	+	0.0581199i
$988$		0			0
$989$		−	1549.59i		−	1.56683i
$990$		0			0
$991$	1240.62			1.25189			0.625946	−	0.779867i	$-0.284713\pi$
$991$	1240.62			1.25189			0.625946	+	0.779867i	$0.284713\pi$
$992$		0			0
$993$	−609.489	+	609.489i	−0.613786	+	0.613786i
$994$		0			0
$995$	540.681	+	1423.61i	0.543398	+	1.43076i
$996$		0			0
$997$	899.358	+	899.358i	0.902064	+	0.902064i	0.995615	−	0.0935507i	$-0.0298217\pi$
$997$	899.358	+	899.358i	0.902064	+	0.902064i	−0.0935507	+	0.995615i	$0.529822\pi$
$998$		0			0
$999$			151.757i			0.151909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.3.bg.c.97.1		4
3.2	odd	2		720.3.bh.g.577.1		4
4.3	odd	2		120.3.u.a.97.2	yes	4
5.2	odd	4		1200.3.bg.e.193.2		4
5.3	odd	4	inner	240.3.bg.c.193.1		4
5.4	even	2		1200.3.bg.e.1057.2		4
8.3	odd	2		960.3.bg.c.577.1		4
8.5	even	2		960.3.bg.d.577.2		4
12.11	even	2		360.3.v.b.217.1		4
15.8	even	4		720.3.bh.g.433.1		4
20.3	even	4		120.3.u.a.73.2	✓	4
20.7	even	4		600.3.u.e.193.1		4
20.19	odd	2		600.3.u.e.457.1		4
40.3	even	4		960.3.bg.c.193.1		4
40.13	odd	4		960.3.bg.d.193.2		4
60.23	odd	4		360.3.v.b.73.1		4
60.47	odd	4		1800.3.v.n.793.1		4
60.59	even	2		1800.3.v.n.1657.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.u.a.73.2	✓	4	20.3	even	4
120.3.u.a.97.2	yes	4	4.3	odd	2
240.3.bg.c.97.1		4	1.1	even	1	trivial
240.3.bg.c.193.1		4	5.3	odd	4	inner
360.3.v.b.73.1		4	60.23	odd	4
360.3.v.b.217.1		4	12.11	even	2
600.3.u.e.193.1		4	20.7	even	4
600.3.u.e.457.1		4	20.19	odd	2
720.3.bh.g.433.1		4	15.8	even	4
720.3.bh.g.577.1		4	3.2	odd	2
960.3.bg.c.193.1		4	40.3	even	4
960.3.bg.c.577.1		4	8.3	odd	2
960.3.bg.d.193.2		4	40.13	odd	4
960.3.bg.d.577.2		4	8.5	even	2
1200.3.bg.e.193.2		4	5.2	odd	4
1200.3.bg.e.1057.2		4	5.4	even	2
1800.3.v.n.793.1		4	60.47	odd	4
1800.3.v.n.1657.1		4	60.59	even	2

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 1.22474i) q^{3} +(4.67423 - 1.77526i) q^{5} +(0.550510 + 0.550510i) q^{7} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.22474 + 1.22474i) q^{3} +(4.67423 - 1.77526i) q^{5} +(0.550510 + 0.550510i) q^{7} -3.00000i q^{9} +1.55051 q^{11} +(9.55051 - 9.55051i) q^{13} +(-3.55051 + 7.89898i) q^{15} +(11.1464 + 11.1464i) q^{17} +12.6969i q^{19} -1.34847 q^{21} +(21.3485 - 21.3485i) q^{23} +(18.6969 - 16.5959i) q^{25} +(3.67423 + 3.67423i) q^{27} +44.0454i q^{29} +44.4949 q^{31} +(-1.89898 + 1.89898i) q^{33} +(3.55051 + 1.59592i) q^{35} +(20.6515 + 20.6515i) q^{37} +23.3939i q^{39} -48.2929 q^{41} +(36.2929 - 36.2929i) q^{43} +(-5.32577 - 14.0227i) q^{45} +(-42.5403 - 42.5403i) q^{47} -48.3939i q^{49} -27.3031 q^{51} +(-54.4949 + 54.4949i) q^{53} +(7.24745 - 2.75255i) q^{55} +(-15.5505 - 15.5505i) q^{57} +47.4393i q^{59} -59.8888 q^{61} +(1.65153 - 1.65153i) q^{63} +(27.6867 - 61.5959i) q^{65} +(-81.2827 - 81.2827i) q^{67} +52.2929i q^{69} -87.5959 q^{71} +(75.9898 - 75.9898i) q^{73} +(-2.57321 + 43.2247i) q^{75} +(0.853572 + 0.853572i) q^{77} +97.3031i q^{79} -9.00000 q^{81} +(-41.0556 + 41.0556i) q^{83} +(71.8888 + 32.3133i) q^{85} +(-53.9444 - 53.9444i) q^{87} -52.2020i q^{89} +10.5153 q^{91} +(-54.4949 + 54.4949i) q^{93} +(22.5403 + 59.3485i) q^{95} +(-37.0000 - 37.0000i) q^{97} -4.65153i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} + 12 q^{7}+O(q^{10}) \) 4 * q + 4 * q^5 + 12 * q^7	\( 4 q + 4 q^{5} + 12 q^{7} + 16 q^{11} + 48 q^{13} - 24 q^{15} - 24 q^{17} + 24 q^{21} + 56 q^{23} + 16 q^{25} + 80 q^{31} + 12 q^{33} + 24 q^{35} + 112 q^{37} - 56 q^{41} + 8 q^{43} - 36 q^{45} + 16 q^{47} - 168 q^{51} - 120 q^{53} - 20 q^{55} - 72 q^{57} - 24 q^{61} + 36 q^{63} - 144 q^{65} + 8 q^{67} - 272 q^{71} + 108 q^{73} + 24 q^{75} + 72 q^{77} - 36 q^{81} - 272 q^{83} + 72 q^{85} - 108 q^{87} + 336 q^{91} - 120 q^{93} - 96 q^{95} - 148 q^{97}+O(q^{100}) \) 4 * q + 4 * q^5 + 12 * q^7 + 16 * q^11 + 48 * q^13 - 24 * q^15 - 24 * q^17 + 24 * q^21 + 56 * q^23 + 16 * q^25 + 80 * q^31 + 12 * q^33 + 24 * q^35 + 112 * q^37 - 56 * q^41 + 8 * q^43 - 36 * q^45 + 16 * q^47 - 168 * q^51 - 120 * q^53 - 20 * q^55 - 72 * q^57 - 24 * q^61 + 36 * q^63 - 144 * q^65 + 8 * q^67 - 272 * q^71 + 108 * q^73 + 24 * q^75 + 72 * q^77 - 36 * q^81 - 272 * q^83 + 72 * q^85 - 108 * q^87 + 336 * q^91 - 120 * q^93 - 96 * q^95 - 148 * q^97

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