LMFDB - Embedded newform 450.4.f.a.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,4,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, 4, names="a")

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

chi := DirichletCharacter("450.107");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
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:	$26.5508595026$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	450.107
Dual form			450.4.f.a.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 + 1.41421i) q^{2} -4.00000i q^{4} +(-9.00000 - 9.00000i) q^{7} +(5.65685 + 5.65685i) q^{8} +O(q^{10})$	\(q+(-1.41421 + 1.41421i) q^{2} -4.00000i q^{4} +(-9.00000 - 9.00000i) q^{7} +(5.65685 + 5.65685i) q^{8} +38.1838i q^{11} +(9.00000 - 9.00000i) q^{13} +25.4558 q^{14} -16.0000 q^{16} +(55.1543 - 55.1543i) q^{17} +38.0000i q^{19} +(-54.0000 - 54.0000i) q^{22} +(-29.6985 - 29.6985i) q^{23} +25.4558i q^{26} +(-36.0000 + 36.0000i) q^{28} +76.3675 q^{29} -236.000 q^{31} +(22.6274 - 22.6274i) q^{32} +156.000i q^{34} +(-279.000 - 279.000i) q^{37} +(-53.7401 - 53.7401i) q^{38} +343.654i q^{41} +(-360.000 + 360.000i) q^{43} +152.735 q^{44} +84.0000 q^{46} +(254.558 - 254.558i) q^{47} -181.000i q^{49} +(-36.0000 - 36.0000i) q^{52} +(-352.139 - 352.139i) q^{53} -101.823i q^{56} +(-108.000 + 108.000i) q^{58} -343.654 q^{59} +110.000 q^{61} +(333.754 - 333.754i) q^{62} +64.0000i q^{64} +(-702.000 - 702.000i) q^{67} +(-220.617 - 220.617i) q^{68} +76.3675i q^{71} +(-378.000 + 378.000i) q^{73} +789.131 q^{74} +152.000 q^{76} +(343.654 - 343.654i) q^{77} -272.000i q^{79} +(-486.000 - 486.000i) q^{82} +(59.3970 + 59.3970i) q^{83} -1018.23i q^{86} +(-216.000 + 216.000i) q^{88} -1489.17 q^{89} -162.000 q^{91} +(-118.794 + 118.794i) q^{92} +720.000i q^{94} +(-684.000 - 684.000i) q^{97} +(255.973 + 255.973i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 36 q^{7}+O(q^{10}) $ 4 * q - 36 * q^7	$ 4 q - 36 q^{7} + 36 q^{13} - 64 q^{16} - 216 q^{22} - 144 q^{28} - 944 q^{31} - 1116 q^{37} - 1440 q^{43} + 336 q^{46} - 144 q^{52} - 432 q^{58} + 440 q^{61} - 2808 q^{67} - 1512 q^{73} + 608 q^{76} - 1944 q^{82} - 864 q^{88} - 648 q^{91} - 2736 q^{97}+O(q^{100}) $ 4 * q - 36 * q^7 + 36 * q^13 - 64 * q^16 - 216 * q^22 - 144 * q^28 - 944 * q^31 - 1116 * q^37 - 1440 * q^43 + 336 * q^46 - 144 * q^52 - 432 * q^58 + 440 * q^61 - 2808 * q^67 - 1512 * q^73 + 608 * q^76 - 1944 * q^82 - 864 * q^88 - 648 * q^91 - 2736 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.41421	+	1.41421i	−0.500000	+	0.500000i
$2$	−1.41421	+	1.41421i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	4.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−9.00000	−	9.00000i	−0.485954	−	0.485954i	0.421073	−	0.907027i	$-0.361654\pi$
$7$	−9.00000	−	9.00000i	−0.485954	−	0.485954i	−0.907027	+	0.421073i	$0.861654\pi$
$8$	5.65685	+	5.65685i	0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$			38.1838i			1.04662i	0.852142	+	0.523311i	$0.175303\pi$
$11$			38.1838i			1.04662i	−0.852142	+	0.523311i	$0.824697\pi$
$12$		0			0
$13$	9.00000	−	9.00000i	0.192012	−	0.192012i	−0.604553	−	0.796565i	$-0.706648\pi$
$13$	9.00000	−	9.00000i	0.192012	−	0.192012i	0.796565	+	0.604553i	$0.206648\pi$
$14$	25.4558			0.485954
$15$		0			0
$16$	−16.0000			−0.250000
$17$	55.1543	−	55.1543i	0.786876	−	0.786876i	−0.194105	−	0.980981i	$-0.562180\pi$
$17$	55.1543	−	55.1543i	0.786876	−	0.786876i	0.980981	+	0.194105i	$0.0621802\pi$
$18$		0			0
$19$			38.0000i			0.458831i	0.973329	+	0.229416i	$0.0736815\pi$
$19$			38.0000i			0.458831i	−0.973329	+	0.229416i	$0.926318\pi$
$20$		0			0
$21$		0			0
$22$	−54.0000	−	54.0000i	−0.523311	−	0.523311i
$23$	−29.6985	−	29.6985i	−0.269242	−	0.269242i	0.559553	−	0.828795i	$-0.310973\pi$
$23$	−29.6985	−	29.6985i	−0.269242	−	0.269242i	−0.828795	+	0.559553i	$0.810973\pi$
$24$		0			0
$25$		0			0
$26$			25.4558i			0.192012i
$27$		0			0
$28$	−36.0000	+	36.0000i	−0.242977	+	0.242977i
$29$	76.3675			0.489003			0.244502	−	0.969649i	$-0.421376\pi$
$29$	76.3675			0.489003			0.244502	+	0.969649i	$0.421376\pi$
$30$		0			0
$31$	−236.000			−1.36732			−0.683659	−	0.729802i	$-0.739612\pi$
$31$	−236.000			−1.36732			−0.683659	+	0.729802i	$0.739612\pi$
$32$	22.6274	−	22.6274i	0.125000	−	0.125000i
$33$		0			0
$34$			156.000i			0.786876i
$35$		0			0
$36$		0			0
$37$	−279.000	−	279.000i	−1.23966	−	1.23966i	−0.960141	−	0.279516i	$-0.909826\pi$
$37$	−279.000	−	279.000i	−1.23966	−	1.23966i	−0.279516	−	0.960141i	$-0.590174\pi$
$38$	−53.7401	−	53.7401i	−0.229416	−	0.229416i
$39$		0			0
$40$		0			0
$41$			343.654i			1.30902i	0.756054	+	0.654509i	$0.227125\pi$
$41$			343.654i			1.30902i	−0.756054	+	0.654509i	$0.772875\pi$
$42$		0			0
$43$	−360.000	+	360.000i	−1.27673	+	1.27673i	−0.334247	+	0.942486i	$0.608482\pi$
$43$	−360.000	+	360.000i	−1.27673	+	1.27673i	−0.942486	+	0.334247i	$0.891518\pi$
$44$	152.735			0.523311
$45$		0			0
$46$	84.0000			0.269242
$47$	254.558	−	254.558i	0.790025	−	0.790025i	−0.191473	−	0.981498i	$-0.561326\pi$
$47$	254.558	−	254.558i	0.790025	−	0.790025i	0.981498	+	0.191473i	$0.0613265\pi$
$48$		0			0
$49$		−	181.000i		−	0.527697i
$50$		0			0
$51$		0			0
$52$	−36.0000	−	36.0000i	−0.0960058	−	0.0960058i
$53$	−352.139	−	352.139i	−0.912642	−	0.912642i	0.0838373	−	0.996479i	$-0.473282\pi$
$53$	−352.139	−	352.139i	−0.912642	−	0.912642i	−0.996479	+	0.0838373i	$0.973282\pi$
$54$		0			0
$55$		0			0
$56$		−	101.823i		−	0.242977i
$57$		0			0
$58$	−108.000	+	108.000i	−0.244502	+	0.244502i
$59$	−343.654			−0.758304			−0.379152	−	0.925334i	$-0.623784\pi$
$59$	−343.654			−0.758304			−0.379152	+	0.925334i	$0.623784\pi$
$60$		0			0
$61$	110.000			0.230886			0.115443	−	0.993314i	$-0.463171\pi$
$61$	110.000			0.230886			0.115443	+	0.993314i	$0.463171\pi$
$62$	333.754	−	333.754i	0.683659	−	0.683659i
$63$		0			0
$64$			64.0000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−702.000	−	702.000i	−1.28004	−	1.28004i	−0.940641	−	0.339403i	$-0.889775\pi$
$67$	−702.000	−	702.000i	−1.28004	−	1.28004i	−0.339403	−	0.940641i	$-0.610225\pi$
$68$	−220.617	−	220.617i	−0.393438	−	0.393438i
$69$		0			0
$70$		0			0
$71$			76.3675i			0.127650i	0.997961	+	0.0638251i	$0.0203300\pi$
$71$			76.3675i			0.127650i	−0.997961	+	0.0638251i	$0.979670\pi$
$72$		0			0
$73$	−378.000	+	378.000i	−0.606049	+	0.606049i	−0.941911	−	0.335862i	$-0.890972\pi$
$73$	−378.000	+	378.000i	−0.606049	+	0.606049i	0.335862	+	0.941911i	$0.390972\pi$
$74$	789.131			1.23966
$75$		0			0
$76$	152.000			0.229416
$77$	343.654	−	343.654i	0.508610	−	0.508610i
$78$		0			0
$79$		−	272.000i		−	0.387372i	−0.981064	−	0.193686i	$-0.937956\pi$
$79$		−	272.000i		−	0.387372i	0.981064	−	0.193686i	$-0.0620443\pi$
$80$		0			0
$81$		0			0
$82$	−486.000	−	486.000i	−0.654509	−	0.654509i
$83$	59.3970	+	59.3970i	0.0785502	+	0.0785502i	0.745290	−	0.666740i	$-0.232311\pi$
$83$	59.3970	+	59.3970i	0.0785502	+	0.0785502i	−0.666740	+	0.745290i	$0.732311\pi$
$84$		0			0
$85$		0			0
$86$		−	1018.23i		−	1.27673i
$87$		0			0
$88$	−216.000	+	216.000i	−0.261655	+	0.261655i
$89$	−1489.17			−1.77361			−0.886805	−	0.462143i	$-0.847081\pi$
$89$	−1489.17			−1.77361			−0.886805	+	0.462143i	$0.847081\pi$
$90$		0			0
$91$	−162.000			−0.186618
$92$	−118.794	+	118.794i	−0.134621	+	0.134621i
$93$		0			0
$94$			720.000i			0.790025i
$95$		0			0
$96$		0			0
$97$	−684.000	−	684.000i	−0.715976	−	0.715976i	0.251803	−	0.967779i	$-0.418977\pi$
$97$	−684.000	−	684.000i	−0.715976	−	0.715976i	−0.967779	+	0.251803i	$0.918977\pi$
$98$	255.973	+	255.973i	0.263848	+	0.263848i
$99$		0			0
$100$		0			0
$101$		−	840.043i		−	0.827598i	−0.910368	−	0.413799i	$-0.864202\pi$
$101$		−	840.043i		−	0.827598i	0.910368	−	0.413799i	$-0.135798\pi$
$102$		0			0
$103$	81.0000	−	81.0000i	0.0774871	−	0.0774871i	−0.667301	−	0.744788i	$-0.732551\pi$
$103$	81.0000	−	81.0000i	0.0774871	−	0.0774871i	0.744788	+	0.667301i	$0.232551\pi$
$104$	101.823			0.0960058
$105$		0			0
$106$	996.000			0.912642
$107$	1018.23	−	1018.23i	0.919966	−	0.919966i	−0.0770603	−	0.997026i	$-0.524553\pi$
$107$	1018.23	−	1018.23i	0.919966	−	0.919966i	0.997026	+	0.0770603i	$0.0245534\pi$
$108$		0			0
$109$		−	1658.00i		−	1.45695i	−0.685072	−	0.728475i	$-0.740229\pi$
$109$		−	1658.00i		−	1.45695i	0.685072	−	0.728475i	$-0.259771\pi$
$110$		0			0
$111$		0			0
$112$	144.000	+	144.000i	0.121489	+	0.121489i
$113$	−470.933	−	470.933i	−0.392050	−	0.392050i	0.483367	−	0.875418i	$-0.339414\pi$
$113$	−470.933	−	470.933i	−0.392050	−	0.392050i	−0.875418	+	0.483367i	$0.839414\pi$
$114$		0			0
$115$		0			0
$116$		−	305.470i		−	0.244502i
$117$		0			0
$118$	486.000	−	486.000i	0.379152	−	0.379152i
$119$	−992.778			−0.764771
$120$		0			0
$121$	−127.000			−0.0954170
$122$	−155.563	+	155.563i	−0.115443	+	0.115443i
$123$		0			0
$124$			944.000i			0.683659i
$125$		0			0
$126$		0			0
$127$	747.000	+	747.000i	0.521933	+	0.521933i	0.918155	−	0.396222i	$-0.129679\pi$
$127$	747.000	+	747.000i	0.521933	+	0.521933i	−0.396222	+	0.918155i	$0.629679\pi$
$128$	−90.5097	−	90.5097i	−0.0625000	−	0.0625000i
$129$		0			0
$130$		0			0
$131$			1718.27i			1.14600i	0.819556	+	0.573000i	$0.194220\pi$
$131$			1718.27i			1.14600i	−0.819556	+	0.573000i	$0.805780\pi$
$132$		0			0
$133$	342.000	−	342.000i	0.222971	−	0.222971i
$134$	1985.56			1.28004
$135$		0			0
$136$	624.000			0.393438
$137$	−963.079	+	963.079i	−0.600594	+	0.600594i	−0.940470	−	0.339876i	$-0.889615\pi$
$137$	−963.079	+	963.079i	−0.600594	+	0.600594i	0.339876	+	0.940470i	$0.389615\pi$
$138$		0			0
$139$		−	1636.00i		−	0.998300i	−0.866516	−	0.499150i	$-0.833646\pi$
$139$		−	1636.00i		−	0.998300i	0.866516	−	0.499150i	$-0.166354\pi$
$140$		0			0
$141$		0			0
$142$	−108.000	−	108.000i	−0.0638251	−	0.0638251i
$143$	343.654	+	343.654i	0.200964	+	0.200964i
$144$		0			0
$145$		0			0
$146$		−	1069.15i		−	0.606049i
$147$		0			0
$148$	−1116.00	+	1116.00i	−0.619829	+	0.619829i
$149$	−1527.35			−0.839768			−0.419884	−	0.907578i	$-0.637929\pi$
$149$	−1527.35			−0.839768			−0.419884	+	0.907578i	$0.637929\pi$
$150$		0			0
$151$	−128.000			−0.0689834			−0.0344917	−	0.999405i	$-0.510981\pi$
$151$	−128.000			−0.0689834			−0.0344917	+	0.999405i	$0.510981\pi$
$152$	−214.960	+	214.960i	−0.114708	+	0.114708i
$153$		0			0
$154$			972.000i			0.508610i
$155$		0			0
$156$		0			0
$157$	1683.00	+	1683.00i	0.855529	+	0.855529i	0.990808	−	0.135279i	$-0.0431930\pi$
$157$	1683.00	+	1683.00i	0.855529	+	0.855529i	−0.135279	+	0.990808i	$0.543193\pi$
$158$	384.666	+	384.666i	0.193686	+	0.193686i
$159$		0			0
$160$		0			0
$161$			534.573i			0.261678i
$162$		0			0
$163$	198.000	−	198.000i	0.0951445	−	0.0951445i	−0.657932	−	0.753077i	$-0.728569\pi$
$163$	198.000	−	198.000i	0.0951445	−	0.0951445i	0.753077	+	0.657932i	$0.228569\pi$
$164$	1374.62			0.654509
$165$		0			0
$166$	−168.000			−0.0785502
$167$	−2982.58	+	2982.58i	−1.38203	+	1.38203i	−0.541015	+	0.841013i	$0.681960\pi$
$167$	−2982.58	+	2982.58i	−1.38203	+	1.38203i	−0.841013	+	0.541015i	$0.818040\pi$
$168$		0			0
$169$			2035.00i			0.926263i
$170$		0			0
$171$		0			0
$172$	1440.00	+	1440.00i	0.638366	+	0.638366i
$173$	1684.33	+	1684.33i	0.740215	+	0.740215i	0.972619	−	0.232405i	$-0.0746594\pi$
$173$	1684.33	+	1684.33i	0.740215	+	0.740215i	−0.232405	+	0.972619i	$0.574659\pi$
$174$		0			0
$175$		0			0
$176$		−	610.940i		−	0.261655i
$177$		0			0
$178$	2106.00	−	2106.00i	0.886805	−	0.886805i
$179$	343.654			0.143497			0.0717483	−	0.997423i	$-0.477142\pi$
$179$	343.654			0.143497			0.0717483	+	0.997423i	$0.477142\pi$
$180$		0			0
$181$	−2522.00			−1.03568			−0.517842	−	0.855476i	$-0.673264\pi$
$181$	−2522.00			−1.03568			−0.517842	+	0.855476i	$0.673264\pi$
$182$	229.103	−	229.103i	0.0933089	−	0.0933089i
$183$		0			0
$184$		−	336.000i		−	0.134621i
$185$		0			0
$186$		0			0
$187$	2106.00	+	2106.00i	0.823561	+	0.823561i
$188$	−1018.23	−	1018.23i	−0.395012	−	0.395012i
$189$		0			0
$190$		0			0
$191$			4505.68i			1.70691i	0.521166	+	0.853455i	$0.325497\pi$
$191$			4505.68i			1.70691i	−0.521166	+	0.853455i	$0.674503\pi$
$192$		0			0
$193$	1458.00	−	1458.00i	0.543778	−	0.543778i	−0.380856	−	0.924634i	$-0.624371\pi$
$193$	1458.00	−	1458.00i	0.543778	−	0.543778i	0.924634	+	0.380856i	$0.124371\pi$
$194$	1934.64			0.715976
$195$		0			0
$196$	−724.000			−0.263848
$197$	110.309	−	110.309i	0.0398942	−	0.0398942i	−0.686878	−	0.726772i	$-0.741019\pi$
$197$	110.309	−	110.309i	0.0398942	−	0.0398942i	0.726772	+	0.686878i	$0.241019\pi$
$198$		0			0
$199$			700.000i			0.249355i	0.992197	+	0.124678i	$0.0397897\pi$
$199$			700.000i			0.249355i	−0.992197	+	0.124678i	$0.960210\pi$
$200$		0			0
$201$		0			0
$202$	1188.00	+	1188.00i	0.413799	+	0.413799i
$203$	−687.308	−	687.308i	−0.237633	−	0.237633i
$204$		0			0
$205$		0			0
$206$			229.103i			0.0774871i
$207$		0			0
$208$	−144.000	+	144.000i	−0.0480029	+	0.0480029i
$209$	−1450.98			−0.480223
$210$		0			0
$211$	−4084.00			−1.33248			−0.666242	−	0.745736i	$-0.732098\pi$
$211$	−4084.00			−1.33248			−0.666242	+	0.745736i	$0.732098\pi$
$212$	−1408.56	+	1408.56i	−0.456321	+	0.456321i
$213$		0			0
$214$			2880.00i			0.919966i
$215$		0			0
$216$		0			0
$217$	2124.00	+	2124.00i	0.664454	+	0.664454i
$218$	2344.77	+	2344.77i	0.728475	+	0.728475i
$219$		0			0
$220$		0			0
$221$		−	992.778i		−	0.302179i
$222$		0			0
$223$	2637.00	−	2637.00i	0.791868	−	0.791868i	−0.189930	−	0.981798i	$-0.560826\pi$
$223$	2637.00	−	2637.00i	0.791868	−	0.791868i	0.981798	+	0.189930i	$0.0608260\pi$
$224$	−407.294			−0.121489
$225$		0			0
$226$	1332.00			0.392050
$227$	−1671.60	+	1671.60i	−0.488758	+	0.488758i	−0.907914	−	0.419156i	$-0.862326\pi$
$227$	−1671.60	+	1671.60i	−0.488758	+	0.488758i	0.419156	+	0.907914i	$0.362326\pi$
$228$		0			0
$229$		−	5434.00i		−	1.56807i	−0.620714	−	0.784037i	$-0.713157\pi$
$229$		−	5434.00i		−	1.56807i	0.620714	−	0.784037i	$-0.286843\pi$
$230$		0			0
$231$		0			0
$232$	432.000	+	432.000i	0.122251	+	0.122251i
$233$	4034.75	+	4034.75i	1.13444	+	1.13444i	0.989430	+	0.145014i	$0.0463227\pi$
$233$	4034.75	+	4034.75i	1.13444	+	1.13444i	0.145014	+	0.989430i	$0.453677\pi$
$234$		0			0
$235$		0			0
$236$			1374.62i			0.379152i
$237$		0			0
$238$	1404.00	−	1404.00i	0.382386	−	0.382386i
$239$	3589.27			0.971426			0.485713	−	0.874118i	$-0.338560\pi$
$239$	3589.27			0.971426			0.485713	+	0.874118i	$0.338560\pi$
$240$		0			0
$241$	6212.00			1.66037			0.830187	−	0.557485i	$-0.188234\pi$
$241$	6212.00			1.66037			0.830187	+	0.557485i	$0.188234\pi$
$242$	179.605	−	179.605i	0.0477085	−	0.0477085i
$243$		0			0
$244$		−	440.000i		−	0.115443i
$245$		0			0
$246$		0			0
$247$	342.000	+	342.000i	0.0881010	+	0.0881010i
$248$	−1335.02	−	1335.02i	−0.341829	−	0.341829i
$249$		0			0
$250$		0			0
$251$			1641.90i			0.412892i	0.978458	+	0.206446i	$0.0661898\pi$
$251$			1641.90i			0.412892i	−0.978458	+	0.206446i	$0.933810\pi$
$252$		0			0
$253$	1134.00	−	1134.00i	0.281794	−	0.281794i
$254$	−2112.84			−0.521933
$255$		0			0
$256$	256.000			0.0625000
$257$	−1981.31	+	1981.31i	−0.480899	+	0.480899i	−0.905419	−	0.424520i	$-0.860443\pi$
$257$	−1981.31	+	1981.31i	−0.480899	+	0.480899i	0.424520	+	0.905419i	$0.360443\pi$
$258$		0			0
$259$			5022.00i			1.20483i
$260$		0			0
$261$		0			0
$262$	−2430.00	−	2430.00i	−0.573000	−	0.573000i
$263$	420.021	+	420.021i	0.0984777	+	0.0984777i	0.754629	−	0.656152i	$-0.227817\pi$
$263$	420.021	+	420.021i	0.0984777	+	0.0984777i	−0.656152	+	0.754629i	$0.727817\pi$
$264$		0			0
$265$		0			0
$266$			967.322i			0.222971i
$267$		0			0
$268$	−2808.00	+	2808.00i	−0.640022	+	0.640022i
$269$	−76.3675			−0.0173093			−0.00865467	−	0.999963i	$-0.502755\pi$
$269$	−76.3675			−0.0173093			−0.00865467	+	0.999963i	$0.502755\pi$
$270$		0			0
$271$	−3580.00			−0.802471			−0.401235	−	0.915975i	$-0.631419\pi$
$271$	−3580.00			−0.802471			−0.401235	+	0.915975i	$0.631419\pi$
$272$	−882.469	+	882.469i	−0.196719	+	0.196719i
$273$		0			0
$274$		−	2724.00i		−	0.600594i
$275$		0			0
$276$		0			0
$277$	2277.00	+	2277.00i	0.493905	+	0.493905i	0.909534	−	0.415629i	$-0.136439\pi$
$277$	2277.00	+	2277.00i	0.493905	+	0.493905i	−0.415629	+	0.909534i	$0.636439\pi$
$278$	2313.65	+	2313.65i	0.499150	+	0.499150i
$279$		0			0
$280$		0			0
$281$		−	5613.01i		−	1.19162i	−0.803127	−	0.595808i	$-0.796832\pi$
$281$		−	5613.01i		−	1.19162i	0.803127	−	0.595808i	$-0.203168\pi$
$282$		0			0
$283$	1206.00	−	1206.00i	0.253319	−	0.253319i	−0.569011	−	0.822330i	$-0.692674\pi$
$283$	1206.00	−	1206.00i	0.253319	−	0.253319i	0.822330	+	0.569011i	$0.192674\pi$
$284$	305.470			0.0638251
$285$		0			0
$286$	−972.000			−0.200964
$287$	3092.89	−	3092.89i	0.636123	−	0.636123i
$288$		0			0
$289$		−	1171.00i		−	0.238347i
$290$		0			0
$291$		0			0
$292$	1512.00	+	1512.00i	0.303024	+	0.303024i
$293$	−6932.47	−	6932.47i	−1.38225	−	1.38225i	−0.840610	−	0.541641i	$-0.817803\pi$
$293$	−6932.47	−	6932.47i	−1.38225	−	1.38225i	−0.541641	−	0.840610i	$-0.682197\pi$
$294$		0			0
$295$		0			0
$296$		−	3156.52i		−	0.619829i
$297$		0			0
$298$	2160.00	−	2160.00i	0.419884	−	0.419884i
$299$	−534.573			−0.103395
$300$		0			0
$301$	6480.00			1.24087
$302$	181.019	−	181.019i	0.0344917	−	0.0344917i
$303$		0			0
$304$		−	608.000i		−	0.114708i
$305$		0			0
$306$		0			0
$307$	−2160.00	−	2160.00i	−0.401556	−	0.401556i	0.477225	−	0.878781i	$-0.341643\pi$
$307$	−2160.00	−	2160.00i	−0.401556	−	0.401556i	−0.878781	+	0.477225i	$0.841643\pi$
$308$	−1374.62	−	1374.62i	−0.254305	−	0.254305i
$309$		0			0
$310$		0			0
$311$		−	4658.42i		−	0.849372i	−0.905341	−	0.424686i	$-0.860384\pi$
$311$		−	4658.42i		−	0.849372i	0.905341	−	0.424686i	$-0.139616\pi$
$312$		0			0
$313$	−5742.00	+	5742.00i	−1.03692	+	1.03692i	−0.0376317	+	0.999292i	$0.511981\pi$
$313$	−5742.00	+	5742.00i	−1.03692	+	1.03692i	−0.999292	+	0.0376317i	$0.988019\pi$
$314$	−4760.24			−0.855529
$315$		0			0
$316$	−1088.00			−0.193686
$317$	4183.24	−	4183.24i	0.741181	−	0.741181i	−0.231624	−	0.972805i	$-0.574404\pi$
$317$	4183.24	−	4183.24i	0.741181	−	0.741181i	0.972805	+	0.231624i	$0.0744040\pi$
$318$		0			0
$319$			2916.00i			0.511801i
$320$		0			0
$321$		0			0
$322$	−756.000	−	756.000i	−0.130839	−	0.130839i
$323$	2095.86	+	2095.86i	0.361043	+	0.361043i
$324$		0			0
$325$		0			0
$326$			560.029i			0.0951445i
$327$		0			0
$328$	−1944.00	+	1944.00i	−0.327254	+	0.327254i
$329$	−4582.05			−0.767832
$330$		0			0
$331$	2126.00			0.353038			0.176519	−	0.984297i	$-0.443516\pi$
$331$	2126.00			0.353038			0.176519	+	0.984297i	$0.443516\pi$
$332$	237.588	−	237.588i	0.0392751	−	0.0392751i
$333$		0			0
$334$		−	8436.00i		−	1.38203i
$335$		0			0
$336$		0			0
$337$	−5958.00	−	5958.00i	−0.963065	−	0.963065i	0.0362767	−	0.999342i	$-0.488450\pi$
$337$	−5958.00	−	5958.00i	−0.963065	−	0.963065i	−0.999342	+	0.0362767i	$0.988450\pi$
$338$	−2877.92	−	2877.92i	−0.463132	−	0.463132i
$339$		0			0
$340$		0			0
$341$		−	9011.37i		−	1.43106i
$342$		0			0
$343$	−4716.00	+	4716.00i	−0.742391	+	0.742391i
$344$	−4072.94			−0.638366
$345$		0			0
$346$	−4764.00			−0.740215
$347$	−2112.84	+	2112.84i	−0.326867	+	0.326867i	−0.851394	−	0.524527i	$-0.824242\pi$
$347$	−2112.84	+	2112.84i	−0.326867	+	0.326867i	0.524527	+	0.851394i	$0.324242\pi$
$348$		0			0
$349$			2594.00i			0.397861i	0.980014	+	0.198931i	$0.0637469\pi$
$349$			2594.00i			0.397861i	−0.980014	+	0.198931i	$0.936253\pi$
$350$		0			0
$351$		0			0
$352$	864.000	+	864.000i	0.130828	+	0.130828i
$353$	980.050	+	980.050i	0.147770	+	0.147770i	0.777121	−	0.629351i	$-0.216679\pi$
$353$	980.050	+	980.050i	0.147770	+	0.147770i	−0.629351	+	0.777121i	$0.716679\pi$
$354$		0			0
$355$		0			0
$356$			5956.67i			0.886805i
$357$		0			0
$358$	−486.000	+	486.000i	−0.0717483	+	0.0717483i
$359$	9011.37			1.32480			0.662398	−	0.749152i	$-0.269539\pi$
$359$	9011.37			1.32480			0.662398	+	0.749152i	$0.269539\pi$
$360$		0			0
$361$	5415.00			0.789474
$362$	3566.65	−	3566.65i	0.517842	−	0.517842i
$363$		0			0
$364$			648.000i			0.0933089i
$365$		0			0
$366$		0			0
$367$	−5751.00	−	5751.00i	−0.817983	−	0.817983i	0.167833	−	0.985816i	$-0.446323\pi$
$367$	−5751.00	−	5751.00i	−0.817983	−	0.817983i	−0.985816	+	0.167833i	$0.946323\pi$
$368$	475.176	+	475.176i	0.0673105	+	0.0673105i
$369$		0			0
$370$		0			0
$371$			6338.51i			0.887005i
$372$		0			0
$373$	−2205.00	+	2205.00i	−0.306087	+	0.306087i	−0.843390	−	0.537302i	$-0.819443\pi$
$373$	−2205.00	+	2205.00i	−0.306087	+	0.306087i	0.537302	+	0.843390i	$0.319443\pi$
$374$	−5956.67			−0.823561
$375$		0			0
$376$	2880.00			0.395012
$377$	687.308	−	687.308i	0.0938943	−	0.0938943i
$378$		0			0
$379$			740.000i			0.100294i	0.998742	+	0.0501468i	$0.0159689\pi$
$379$			740.000i			0.100294i	−0.998742	+	0.0501468i	$0.984031\pi$
$380$		0			0
$381$		0			0
$382$	−6372.00	−	6372.00i	−0.853455	−	0.853455i
$383$	−8281.63	−	8281.63i	−1.10489	−	1.10489i	−0.993812	−	0.111075i	$-0.964571\pi$
$383$	−8281.63	−	8281.63i	−1.10489	−	1.10489i	−0.111075	−	0.993812i	$-0.535429\pi$
$384$		0			0
$385$		0			0
$386$			4123.85i			0.543778i
$387$		0			0
$388$	−2736.00	+	2736.00i	−0.357988	+	0.357988i
$389$	6109.40			0.796296			0.398148	−	0.917321i	$-0.369653\pi$
$389$	6109.40			0.796296			0.398148	+	0.917321i	$0.369653\pi$
$390$		0			0
$391$	−3276.00			−0.423720
$392$	1023.89	−	1023.89i	0.131924	−	0.131924i
$393$		0			0
$394$			312.000i			0.0398942i
$395$		0			0
$396$		0			0
$397$	−6849.00	−	6849.00i	−0.865847	−	0.865847i	0.126162	−	0.992010i	$-0.459734\pi$
$397$	−6849.00	−	6849.00i	−0.865847	−	0.865847i	−0.992010	+	0.126162i	$0.959734\pi$
$398$	−989.949	−	989.949i	−0.124678	−	0.124678i
$399$		0			0
$400$		0			0
$401$		−	11722.4i		−	1.45982i	−0.683541	−	0.729912i	$-0.739561\pi$
$401$		−	11722.4i		−	1.45982i	0.683541	−	0.729912i	$-0.260439\pi$
$402$		0			0
$403$	−2124.00	+	2124.00i	−0.262541	+	0.262541i
$404$	−3360.17			−0.413799
$405$		0			0
$406$	1944.00			0.237633
$407$	10653.3	−	10653.3i	1.29745	−	1.29745i
$408$		0			0
$409$		−	4354.00i		−	0.526385i	−0.964743	−	0.263192i	$-0.915225\pi$
$409$		−	4354.00i		−	0.526385i	0.964743	−	0.263192i	$-0.0847754\pi$
$410$		0			0
$411$		0			0
$412$	−324.000	−	324.000i	−0.0387435	−	0.0387435i
$413$	3092.89	+	3092.89i	0.368501	+	0.368501i
$414$		0			0
$415$		0			0
$416$		−	407.294i		−	0.0480029i
$417$		0			0
$418$	2052.00	−	2052.00i	0.240111	−	0.240111i
$419$	13708.0			1.59828			0.799139	−	0.601147i	$-0.205289\pi$
$419$	13708.0			1.59828			0.799139	+	0.601147i	$0.205289\pi$
$420$		0			0
$421$	8530.00			0.987474			0.493737	−	0.869611i	$-0.335630\pi$
$421$	8530.00			0.987474			0.493737	+	0.869611i	$0.335630\pi$
$422$	5775.65	−	5775.65i	0.666242	−	0.666242i
$423$		0			0
$424$		−	3984.00i		−	0.456321i
$425$		0			0
$426$		0			0
$427$	−990.000	−	990.000i	−0.112200	−	0.112200i
$428$	−4072.94	−	4072.94i	−0.459983	−	0.459983i
$429$		0			0
$430$		0			0
$431$			13593.4i			1.51919i	0.650395	+	0.759596i	$0.274603\pi$
$431$			13593.4i			1.51919i	−0.650395	+	0.759596i	$0.725397\pi$
$432$		0			0
$433$	4626.00	−	4626.00i	0.513421	−	0.513421i	−0.402152	−	0.915573i	$-0.631738\pi$
$433$	4626.00	−	4626.00i	0.513421	−	0.513421i	0.915573	+	0.402152i	$0.131738\pi$
$434$	−6007.58			−0.664454
$435$		0			0
$436$	−6632.00			−0.728475
$437$	1128.54	−	1128.54i	0.123537	−	0.123537i
$438$		0			0
$439$			14092.0i			1.53206i	0.642805	+	0.766030i	$0.277771\pi$
$439$			14092.0i			1.53206i	−0.642805	+	0.766030i	$0.722229\pi$
$440$		0			0
$441$		0			0
$442$	1404.00	+	1404.00i	0.151089	+	0.151089i
$443$	2664.38	+	2664.38i	0.285753	+	0.285753i	0.835398	−	0.549645i	$-0.185237\pi$
$443$	2664.38	+	2664.38i	0.285753	+	0.285753i	−0.549645	+	0.835398i	$0.685237\pi$
$444$		0			0
$445$		0			0
$446$			7458.56i			0.791868i
$447$		0			0
$448$	576.000	−	576.000i	0.0607443	−	0.0607443i
$449$	−1260.06			−0.132441			−0.0662206	−	0.997805i	$-0.521094\pi$
$449$	−1260.06			−0.132441			−0.0662206	+	0.997805i	$0.521094\pi$
$450$		0			0
$451$	−13122.0			−1.37005
$452$	−1883.73	+	1883.73i	−0.196025	+	0.196025i
$453$		0			0
$454$		−	4728.00i		−	0.488758i
$455$		0			0
$456$		0			0
$457$	−8280.00	−	8280.00i	−0.847532	−	0.847532i	0.142293	−	0.989825i	$-0.454553\pi$
$457$	−8280.00	−	8280.00i	−0.847532	−	0.847532i	−0.989825	+	0.142293i	$0.954553\pi$
$458$	7684.84	+	7684.84i	0.784037	+	0.784037i
$459$		0			0
$460$		0			0
$461$		−	12371.5i		−	1.24989i	−0.780668	−	0.624946i	$-0.785121\pi$
$461$		−	12371.5i		−	1.24989i	0.780668	−	0.624946i	$-0.214879\pi$
$462$		0			0
$463$	−8847.00	+	8847.00i	−0.888024	+	0.888024i	−0.994333	−	0.106309i	$-0.966097\pi$
$463$	−8847.00	+	8847.00i	−0.888024	+	0.888024i	0.106309	+	0.994333i	$0.466097\pi$
$464$	−1221.88			−0.122251
$465$		0			0
$466$	−11412.0			−1.13444
$467$	4946.92	−	4946.92i	0.490184	−	0.490184i	−0.418180	−	0.908364i	$-0.637332\pi$
$467$	4946.92	−	4946.92i	0.490184	−	0.490184i	0.908364	+	0.418180i	$0.137332\pi$
$468$		0			0
$469$			12636.0i			1.24409i
$470$		0			0
$471$		0			0
$472$	−1944.00	−	1944.00i	−0.189576	−	0.189576i
$473$	−13746.2	−	13746.2i	−1.33626	−	1.33626i
$474$		0			0
$475$		0			0
$476$			3971.11i			0.382386i
$477$		0			0
$478$	−5076.00	+	5076.00i	−0.485713	+	0.485713i
$479$	12906.1			1.23110			0.615548	−	0.788099i	$-0.288935\pi$
$479$	12906.1			1.23110			0.615548	+	0.788099i	$0.288935\pi$
$480$		0			0
$481$	−5022.00			−0.476057
$482$	−8785.09	+	8785.09i	−0.830187	+	0.830187i
$483$		0			0
$484$			508.000i			0.0477085i
$485$		0			0
$486$		0			0
$487$	−369.000	−	369.000i	−0.0343347	−	0.0343347i	0.689731	−	0.724066i	$-0.257729\pi$
$487$	−369.000	−	369.000i	−0.0343347	−	0.0343347i	−0.724066	+	0.689731i	$0.757729\pi$
$488$	622.254	+	622.254i	0.0577215	+	0.0577215i
$489$		0			0
$490$		0			0
$491$			19817.4i			1.82148i	0.412983	+	0.910739i	$0.364487\pi$
$491$			19817.4i			1.82148i	−0.412983	+	0.910739i	$0.635513\pi$
$492$		0			0
$493$	4212.00	−	4212.00i	0.384785	−	0.384785i
$494$	−967.322			−0.0881010
$495$		0			0
$496$	3776.00			0.341829
$497$	687.308	−	687.308i	0.0620321	−	0.0620321i
$498$		0			0
$499$			3058.00i			0.274338i	0.990548	+	0.137169i	$0.0438004\pi$
$499$			3058.00i			0.274338i	−0.990548	+	0.137169i	$0.956200\pi$
$500$		0			0
$501$		0			0
$502$	−2322.00	−	2322.00i	−0.206446	−	0.206446i
$503$	11336.3	+	11336.3i	1.00490	+	1.00490i	0.999988	+	0.00490714i	$0.00156200\pi$
$503$	11336.3	+	11336.3i	1.00490	+	1.00490i	0.00490714	+	0.999988i	$0.498438\pi$
$504$		0			0
$505$		0			0
$506$			3207.44i			0.281794i
$507$		0			0
$508$	2988.00	−	2988.00i	0.260967	−	0.260967i
$509$	−13517.1			−1.17708			−0.588539	−	0.808469i	$-0.700297\pi$
$509$	−13517.1			−1.17708			−0.588539	+	0.808469i	$0.700297\pi$
$510$		0			0
$511$	6804.00			0.589024
$512$	−362.039	+	362.039i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	5604.00i		−	0.480899i
$515$		0			0
$516$		0			0
$517$	9720.00	+	9720.00i	0.826857	+	0.826857i
$518$	−7102.18	−	7102.18i	−0.602417	−	0.602417i
$519$		0			0
$520$		0			0
$521$		−	8667.71i		−	0.728867i	−0.931229	−	0.364433i	$-0.881263\pi$
$521$		−	8667.71i		−	0.728867i	0.931229	−	0.364433i	$-0.118737\pi$
$522$		0			0
$523$	1242.00	−	1242.00i	0.103841	−	0.103841i	−0.653278	−	0.757119i	$-0.726606\pi$
$523$	1242.00	−	1242.00i	0.103841	−	0.103841i	0.757119	+	0.653278i	$0.226606\pi$
$524$	6873.08			0.573000
$525$		0			0
$526$	−1188.00			−0.0984777
$527$	−13016.4	+	13016.4i	−1.07591	+	1.07591i
$528$		0			0
$529$		−	10403.0i		−	0.855018i
$530$		0			0
$531$		0			0
$532$	−1368.00	−	1368.00i	−0.111486	−	0.111486i
$533$	3092.89	+	3092.89i	0.251347	+	0.251347i
$534$		0			0
$535$		0			0
$536$		−	7942.22i		−	0.640022i
$537$		0			0
$538$	108.000	−	108.000i	0.00865467	−	0.00865467i
$539$	6911.26			0.552299
$540$		0			0
$541$	3242.00			0.257642			0.128821	−	0.991668i	$-0.458881\pi$
$541$	3242.00			0.257642			0.128821	+	0.991668i	$0.458881\pi$
$542$	5062.88	−	5062.88i	0.401235	−	0.401235i
$543$		0			0
$544$		−	2496.00i		−	0.196719i
$545$		0			0
$546$		0			0
$547$	10476.0	+	10476.0i	0.818869	+	0.818869i	0.985944	−	0.167075i	$-0.0534322\pi$
$547$	10476.0	+	10476.0i	0.818869	+	0.818869i	−0.167075	+	0.985944i	$0.553432\pi$
$548$	3852.32	+	3852.32i	0.300297	+	0.300297i
$549$		0			0
$550$		0			0
$551$			2901.97i			0.224370i
$552$		0			0
$553$	−2448.00	+	2448.00i	−0.188245	+	0.188245i
$554$	−6440.33			−0.493905
$555$		0			0
$556$	−6544.00			−0.499150
$557$	165.463	−	165.463i	0.0125869	−	0.0125869i	−0.700785	−	0.713372i	$-0.747167\pi$
$557$	165.463	−	165.463i	0.0125869	−	0.0125869i	0.713372	+	0.700785i	$0.247167\pi$
$558$		0			0
$559$			6480.00i			0.490295i
$560$		0			0
$561$		0			0
$562$	7938.00	+	7938.00i	0.595808	+	0.595808i
$563$	−14586.2	−	14586.2i	−1.09189	−	1.09189i	−0.995327	−	0.0965649i	$-0.969214\pi$
$563$	−14586.2	−	14586.2i	−1.09189	−	1.09189i	−0.0965649	−	0.995327i	$-0.530786\pi$
$564$		0			0
$565$		0			0
$566$			3411.08i			0.253319i
$567$		0			0
$568$	−432.000	+	432.000i	−0.0319125	+	0.0319125i
$569$	7216.73			0.531707			0.265853	−	0.964013i	$-0.414346\pi$
$569$	7216.73			0.531707			0.265853	+	0.964013i	$0.414346\pi$
$570$		0			0
$571$	−1762.00			−0.129137			−0.0645687	−	0.997913i	$-0.520567\pi$
$571$	−1762.00			−0.129137			−0.0645687	+	0.997913i	$0.520567\pi$
$572$	1374.62	−	1374.62i	0.100482	−	0.100482i
$573$		0			0
$574$			8748.00i			0.636123i
$575$		0			0
$576$		0			0
$577$	14688.0	+	14688.0i	1.05974	+	1.05974i	0.998098	+	0.0616407i	$0.0196333\pi$
$577$	14688.0	+	14688.0i	1.05974	+	1.05974i	0.0616407	+	0.998098i	$0.480367\pi$
$578$	1656.04	+	1656.04i	0.119174	+	0.119174i
$579$		0			0
$580$		0			0
$581$		−	1069.15i		−	0.0763436i
$582$		0			0
$583$	13446.0	−	13446.0i	0.955191	−	0.955191i
$584$	−4276.58			−0.303024
$585$		0			0
$586$	19608.0			1.38225
$587$	−2324.97	+	2324.97i	−0.163478	+	0.163478i	−0.784106	−	0.620627i	$-0.786878\pi$
$587$	−2324.97	+	2324.97i	−0.163478	+	0.163478i	0.620627	+	0.784106i	$0.286878\pi$
$588$		0			0
$589$		−	8968.00i		−	0.627368i
$590$		0			0
$591$		0			0
$592$	4464.00	+	4464.00i	0.309914	+	0.309914i
$593$	15625.6	+	15625.6i	1.08207	+	1.08207i	0.996316	+	0.0857552i	$0.0273303\pi$
$593$	15625.6	+	15625.6i	1.08207	+	1.08207i	0.0857552	+	0.996316i	$0.472670\pi$
$594$		0			0
$595$		0			0
$596$			6109.40i			0.419884i
$597$		0			0
$598$	756.000	−	756.000i	0.0516976	−	0.0516976i
$599$	9011.37			0.614682			0.307341	−	0.951599i	$-0.400561\pi$
$599$	9011.37			0.614682			0.307341	+	0.951599i	$0.400561\pi$
$600$		0			0
$601$	15388.0			1.04441			0.522204	−	0.852820i	$-0.325110\pi$
$601$	15388.0			1.04441			0.522204	+	0.852820i	$0.325110\pi$
$602$	−9164.10	+	9164.10i	−0.620434	+	0.620434i
$603$		0			0
$604$			512.000i			0.0344917i
$605$		0			0
$606$		0			0
$607$	3177.00	+	3177.00i	0.212439	+	0.212439i	0.805303	−	0.592864i	$-0.202003\pi$
$607$	3177.00	+	3177.00i	0.212439	+	0.212439i	−0.592864	+	0.805303i	$0.702003\pi$
$608$	859.842	+	859.842i	0.0573539	+	0.0573539i
$609$		0			0
$610$		0			0
$611$		−	4582.05i		−	0.303388i
$612$		0			0
$613$	−1701.00	+	1701.00i	−0.112076	+	0.112076i	−0.760921	−	0.648845i	$-0.775253\pi$
$613$	−1701.00	+	1701.00i	−0.112076	+	0.112076i	0.648845	+	0.760921i	$0.275253\pi$
$614$	6109.40			0.401556
$615$		0			0
$616$	3888.00			0.254305
$617$	−18782.2	+	18782.2i	−1.22551	+	1.22551i	−0.259870	+	0.965644i	$0.583680\pi$
$617$	−18782.2	+	18782.2i	−1.22551	+	1.22551i	−0.965644	+	0.259870i	$0.916320\pi$
$618$		0			0
$619$		−	12548.0i		−	0.814777i	−0.913255	−	0.407388i	$-0.866440\pi$
$619$		−	12548.0i		−	0.814777i	0.913255	−	0.407388i	$-0.133560\pi$
$620$		0			0
$621$		0			0
$622$	6588.00	+	6588.00i	0.424686	+	0.424686i
$623$	13402.5	+	13402.5i	0.861894	+	0.861894i
$624$		0			0
$625$		0			0
$626$		−	16240.8i		−	1.03692i
$627$		0			0
$628$	6732.00	−	6732.00i	0.427764	−	0.427764i
$629$	−30776.1			−1.95091
$630$		0			0
$631$	−27340.0			−1.72486			−0.862431	−	0.506174i	$-0.831059\pi$
$631$	−27340.0			−1.72486			−0.862431	+	0.506174i	$0.831059\pi$
$632$	1538.66	−	1538.66i	0.0968430	−	0.0968430i
$633$		0			0
$634$			11832.0i			0.741181i
$635$		0			0
$636$		0			0
$637$	−1629.00	−	1629.00i	−0.101324	−	0.101324i
$638$	−4123.85	−	4123.85i	−0.255901	−	0.255901i
$639$		0			0
$640$		0			0
$641$		−	21039.3i		−	1.29641i	−0.761465	−	0.648206i	$-0.775519\pi$
$641$		−	21039.3i		−	1.29641i	0.761465	−	0.648206i	$-0.224481\pi$
$642$		0			0
$643$	11394.0	−	11394.0i	0.698811	−	0.698811i	−0.265343	−	0.964154i	$-0.585485\pi$
$643$	11394.0	−	11394.0i	0.698811	−	0.698811i	0.964154	+	0.265343i	$0.0854852\pi$
$644$	2138.29			0.130839
$645$		0			0
$646$	−5928.00			−0.361043
$647$	−6584.58	+	6584.58i	−0.400103	+	0.400103i	−0.878269	−	0.478166i	$-0.841302\pi$
$647$	−6584.58	+	6584.58i	−0.400103	+	0.400103i	0.478166	+	0.878269i	$0.341302\pi$
$648$		0			0
$649$		−	13122.0i		−	0.793657i
$650$		0			0
$651$		0			0
$652$	−792.000	−	792.000i	−0.0475723	−	0.0475723i
$653$	−7008.84	−	7008.84i	−0.420026	−	0.420026i	0.465186	−	0.885213i	$-0.345987\pi$
$653$	−7008.84	−	7008.84i	−0.420026	−	0.420026i	−0.885213	+	0.465186i	$0.845987\pi$
$654$		0			0
$655$		0			0
$656$		−	5498.46i		−	0.327254i
$657$		0			0
$658$	6480.00	−	6480.00i	0.383916	−	0.383916i
$659$	−32112.5			−1.89822			−0.949110	−	0.314944i	$-0.898014\pi$
$659$	−32112.5			−1.89822			−0.949110	+	0.314944i	$0.898014\pi$
$660$		0			0
$661$	31822.0			1.87251			0.936257	−	0.351315i	$-0.114265\pi$
$661$	31822.0			1.87251			0.936257	+	0.351315i	$0.114265\pi$
$662$	−3006.62	+	3006.62i	−0.176519	+	0.176519i
$663$		0			0
$664$			672.000i			0.0392751i
$665$		0			0
$666$		0			0
$667$	−2268.00	−	2268.00i	−0.131660	−	0.131660i
$668$	11930.3	+	11930.3i	0.691014	+	0.691014i
$669$		0			0
$670$		0			0
$671$			4200.21i			0.241650i
$672$		0			0
$673$	3330.00	−	3330.00i	0.190731	−	0.190731i	−0.605281	−	0.796012i	$-0.706939\pi$
$673$	3330.00	−	3330.00i	0.190731	−	0.190731i	0.796012	+	0.605281i	$0.206939\pi$
$674$	16851.8			0.963065
$675$		0			0
$676$	8140.00			0.463132
$677$	−5600.29	+	5600.29i	−0.317927	+	0.317927i	−0.847970	−	0.530044i	$-0.822176\pi$
$677$	−5600.29	+	5600.29i	−0.317927	+	0.317927i	0.530044	+	0.847970i	$0.322176\pi$
$678$		0			0
$679$			12312.0i			0.695863i
$680$		0			0
$681$		0			0
$682$	12744.0	+	12744.0i	0.715532	+	0.715532i
$683$	17581.5	+	17581.5i	0.984974	+	0.984974i	0.999889	−	0.0149144i	$-0.00474757\pi$
$683$	17581.5	+	17581.5i	0.984974	+	0.984974i	−0.0149144	+	0.999889i	$0.504748\pi$
$684$		0			0
$685$		0			0
$686$		−	13338.9i		−	0.742391i
$687$		0			0
$688$	5760.00	−	5760.00i	0.319183	−	0.319183i
$689$	−6338.51			−0.350476
$690$		0			0
$691$	−23330.0			−1.28439			−0.642196	−	0.766540i	$-0.721977\pi$
$691$	−23330.0			−1.28439			−0.642196	+	0.766540i	$0.721977\pi$
$692$	6737.31	−	6737.31i	0.370107	−	0.370107i
$693$		0			0
$694$		−	5976.00i		−	0.326867i
$695$		0			0
$696$		0			0
$697$	18954.0	+	18954.0i	1.03003	+	1.03003i
$698$	−3668.47	−	3668.47i	−0.198931	−	0.198931i
$699$		0			0
$700$		0			0
$701$		−	8018.59i		−	0.432037i	−0.976389	−	0.216019i	$-0.930693\pi$
$701$		−	8018.59i		−	0.432037i	0.976389	−	0.216019i	$-0.0693072\pi$
$702$		0			0
$703$	10602.0	−	10602.0i	0.568794	−	0.568794i
$704$	−2443.76			−0.130828
$705$		0			0
$706$	−2772.00			−0.147770
$707$	−7560.39	+	7560.39i	−0.402175	+	0.402175i
$708$		0			0
$709$		−	25414.0i		−	1.34618i	−0.739560	−	0.673091i	$-0.764966\pi$
$709$		−	25414.0i		−	1.34618i	0.739560	−	0.673091i	$-0.235034\pi$
$710$		0			0
$711$		0			0
$712$	−8424.00	−	8424.00i	−0.443403	−	0.443403i
$713$	7008.84	+	7008.84i	0.368139	+	0.368139i
$714$		0			0
$715$		0			0
$716$		−	1374.62i		−	0.0717483i
$717$		0			0
$718$	−12744.0	+	12744.0i	−0.662398	+	0.662398i
$719$	10386.0			0.538709			0.269355	−	0.963041i	$-0.413190\pi$
$719$	10386.0			0.538709			0.269355	+	0.963041i	$0.413190\pi$
$720$		0			0
$721$	−1458.00			−0.0753103
$722$	−7657.97	+	7657.97i	−0.394737	+	0.394737i
$723$		0			0
$724$			10088.0i			0.517842i
$725$		0			0
$726$		0			0
$727$	22707.0	+	22707.0i	1.15840	+	1.15840i	0.984820	+	0.173579i	$0.0555332\pi$
$727$	22707.0	+	22707.0i	1.15840	+	1.15840i	0.173579	+	0.984820i	$0.444467\pi$
$728$	−916.410	−	916.410i	−0.0466544	−	0.0466544i
$729$		0			0
$730$		0			0
$731$			39711.1i			2.00926i
$732$		0			0
$733$	12573.0	−	12573.0i	0.633553	−	0.633553i	−0.315404	−	0.948957i	$-0.602140\pi$
$733$	12573.0	−	12573.0i	0.633553	−	0.633553i	0.948957	+	0.315404i	$0.102140\pi$
$734$	16266.3			0.817983
$735$		0			0
$736$	−1344.00			−0.0673105
$737$	26805.0	−	26805.0i	1.33972	−	1.33972i
$738$		0			0
$739$			14402.0i			0.716896i	0.933550	+	0.358448i	$0.116694\pi$
$739$			14402.0i			0.716896i	−0.933550	+	0.358448i	$0.883306\pi$
$740$		0			0
$741$		0			0
$742$	−8964.00	−	8964.00i	−0.443502	−	0.443502i
$743$	−22146.6	−	22146.6i	−1.09351	−	1.09351i	−0.995151	−	0.0983612i	$-0.968640\pi$
$743$	−22146.6	−	22146.6i	−1.09351	−	1.09351i	−0.0983612	−	0.995151i	$-0.531360\pi$
$744$		0			0
$745$		0			0
$746$		−	6236.68i		−	0.306087i
$747$		0			0
$748$	8424.00	−	8424.00i	0.411781	−	0.411781i
$749$	−18328.2			−0.894123
$750$		0			0
$751$	15208.0			0.738945			0.369473	−	0.929242i	$-0.379538\pi$
$751$	15208.0			0.738945			0.369473	+	0.929242i	$0.379538\pi$
$752$	−4072.94	+	4072.94i	−0.197506	+	0.197506i
$753$		0			0
$754$			1944.00i			0.0938943i
$755$		0			0
$756$		0			0
$757$	−1485.00	−	1485.00i	−0.0712989	−	0.0712989i	0.670558	−	0.741857i	$-0.266055\pi$
$757$	−1485.00	−	1485.00i	−0.0712989	−	0.0712989i	−0.741857	+	0.670558i	$0.766055\pi$
$758$	−1046.52	−	1046.52i	−0.0501468	−	0.0501468i
$759$		0			0
$760$		0			0
$761$			2176.47i			0.103676i	0.998656	+	0.0518378i	$0.0165079\pi$
$761$			2176.47i			0.103676i	−0.998656	+	0.0518378i	$0.983492\pi$
$762$		0			0
$763$	−14922.0	+	14922.0i	−0.708011	+	0.708011i
$764$	18022.7			0.853455
$765$		0			0
$766$	23424.0			1.10489
$767$	−3092.89	+	3092.89i	−0.145603	+	0.145603i
$768$		0			0
$769$		−	5960.00i		−	0.279484i	−0.990188	−	0.139742i	$-0.955373\pi$
$769$		−	5960.00i		−	0.279484i	0.990188	−	0.139742i	$-0.0446273\pi$
$770$		0			0
$771$		0			0
$772$	−5832.00	−	5832.00i	−0.271889	−	0.271889i
$773$	14569.2	+	14569.2i	0.677903	+	0.677903i	0.959525	−	0.281623i	$-0.0908726\pi$
$773$	14569.2	+	14569.2i	0.677903	+	0.677903i	−0.281623	+	0.959525i	$0.590873\pi$
$774$		0			0
$775$		0			0
$776$		−	7738.58i		−	0.357988i
$777$		0			0
$778$	−8640.00	+	8640.00i	−0.398148	+	0.398148i
$779$	−13058.8			−0.600618
$780$		0			0
$781$	−2916.00			−0.133601
$782$	4632.96	−	4632.96i	0.211860	−	0.211860i
$783$		0			0
$784$			2896.00i			0.131924i
$785$		0			0
$786$		0			0
$787$	−21330.0	−	21330.0i	−0.966115	−	0.966115i	0.0333296	−	0.999444i	$-0.489389\pi$
$787$	−21330.0	−	21330.0i	−0.966115	−	0.966115i	−0.999444	+	0.0333296i	$0.989389\pi$
$788$	−441.235	−	441.235i	−0.0199471	−	0.0199471i
$789$		0			0
$790$		0			0
$791$			8476.80i			0.381037i
$792$		0			0
$793$	990.000	−	990.000i	0.0443328	−	0.0443328i
$794$	19371.9			0.865847
$795$		0			0
$796$	2800.00			0.124678
$797$	−21107.1	+	21107.1i	−0.938084	+	0.938084i	−0.998192	−	0.0601076i	$-0.980856\pi$
$797$	−21107.1	+	21107.1i	−0.938084	+	0.938084i	0.0601076	+	0.998192i	$0.480856\pi$
$798$		0			0
$799$		−	28080.0i		−	1.24330i
$800$		0			0
$801$		0			0
$802$	16578.0	+	16578.0i	0.729912	+	0.729912i
$803$	−14433.5	−	14433.5i	−0.634304	−	0.634304i
$804$		0			0
$805$		0			0
$806$		−	6007.58i		−	0.262541i
$807$		0			0
$808$	4752.00	−	4752.00i	0.206899	−	0.206899i
$809$	−3321.99			−0.144369			−0.0721847	−	0.997391i	$-0.522997\pi$
$809$	−3321.99			−0.144369			−0.0721847	+	0.997391i	$0.522997\pi$
$810$		0			0
$811$	−27380.0			−1.18550			−0.592751	−	0.805386i	$-0.701958\pi$
$811$	−27380.0			−1.18550			−0.592751	+	0.805386i	$0.701958\pi$
$812$	−2749.23	+	2749.23i	−0.118817	+	0.118817i
$813$		0			0
$814$			30132.0i			1.29745i
$815$		0			0
$816$		0			0
$817$	−13680.0	−	13680.0i	−0.585805	−	0.585805i
$818$	6157.49	+	6157.49i	0.263192	+	0.263192i
$819$		0			0
$820$		0			0
$821$			14586.2i			0.620051i	0.950728	+	0.310025i	$0.100338\pi$
$821$			14586.2i			0.620051i	−0.950728	+	0.310025i	$0.899662\pi$
$822$		0			0
$823$	−11079.0	+	11079.0i	−0.469246	+	0.469246i	−0.901670	−	0.432424i	$-0.857658\pi$
$823$	−11079.0	+	11079.0i	−0.469246	+	0.469246i	0.432424	+	0.901670i	$0.357658\pi$
$824$	916.410			0.0387435
$825$		0			0
$826$	−8748.00			−0.368501
$827$	12286.7	−	12286.7i	0.516626	−	0.516626i	−0.399923	−	0.916549i	$-0.630963\pi$
$827$	12286.7	−	12286.7i	0.516626	−	0.516626i	0.916549	+	0.399923i	$0.130963\pi$
$828$		0			0
$829$			12854.0i			0.538526i	0.963067	+	0.269263i	$0.0867801\pi$
$829$			12854.0i			0.538526i	−0.963067	+	0.269263i	$0.913220\pi$
$830$		0			0
$831$		0			0
$832$	576.000	+	576.000i	0.0240015	+	0.0240015i
$833$	−9982.93	−	9982.93i	−0.415232	−	0.415232i
$834$		0			0
$835$		0			0
$836$			5803.93i			0.240111i
$837$		0			0
$838$	−19386.0	+	19386.0i	−0.799139	+	0.799139i
$839$	18480.9			0.760468			0.380234	−	0.924890i	$-0.375843\pi$
$839$	18480.9			0.760468			0.380234	+	0.924890i	$0.375843\pi$
$840$		0			0
$841$	−18557.0			−0.760876
$842$	−12063.2	+	12063.2i	−0.493737	+	0.493737i
$843$		0			0
$844$			16336.0i			0.666242i
$845$		0			0
$846$		0			0
$847$	1143.00	+	1143.00i	0.0463683	+	0.0463683i
$848$	5634.23	+	5634.23i	0.228161	+	0.228161i
$849$		0			0
$850$		0			0
$851$			16571.8i			0.667535i
$852$		0			0
$853$	−28377.0	+	28377.0i	−1.13905	+	1.13905i	−0.150430	+	0.988621i	$0.548066\pi$
$853$	−28377.0	+	28377.0i	−1.13905	+	1.13905i	−0.988621	+	0.150430i	$0.951934\pi$
$854$	2800.14			0.112200
$855$		0			0
$856$	11520.0			0.459983
$857$	19732.5	−	19732.5i	0.786523	−	0.786523i	−0.194400	−	0.980922i	$-0.562276\pi$
$857$	19732.5	−	19732.5i	0.786523	−	0.786523i	0.980922	+	0.194400i	$0.0622758\pi$
$858$		0			0
$859$		−	17084.0i		−	0.678578i	−0.940682	−	0.339289i	$-0.889814\pi$
$859$		−	17084.0i		−	0.678578i	0.940682	−	0.339289i	$-0.110186\pi$
$860$		0			0
$861$		0			0
$862$	−19224.0	−	19224.0i	−0.759596	−	0.759596i
$863$	−17280.3	−	17280.3i	−0.681608	−	0.681608i	0.278755	−	0.960362i	$-0.410078\pi$
$863$	−17280.3	−	17280.3i	−0.681608	−	0.681608i	−0.960362	+	0.278755i	$0.910078\pi$
$864$		0			0
$865$		0			0
$866$			13084.3i			0.513421i
$867$		0			0
$868$	8496.00	−	8496.00i	0.332227	−	0.332227i
$869$	10386.0			0.405432
$870$		0			0
$871$	−12636.0			−0.491567
$872$	9379.06	−	9379.06i	0.364238	−	0.364238i
$873$		0			0
$874$			3192.00i			0.123537i
$875$		0			0
$876$		0			0
$877$	−14805.0	−	14805.0i	−0.570045	−	0.570045i	0.362096	−	0.932141i	$-0.382061\pi$
$877$	−14805.0	−	14805.0i	−0.570045	−	0.570045i	−0.932141	+	0.362096i	$0.882061\pi$
$878$	−19929.1	−	19929.1i	−0.766030	−	0.766030i
$879$		0			0
$880$		0			0
$881$			23635.8i			0.903869i	0.892051	+	0.451935i	$0.149266\pi$
$881$			23635.8i			0.903869i	−0.892051	+	0.451935i	$0.850734\pi$
$882$		0			0
$883$	−5958.00	+	5958.00i	−0.227070	+	0.227070i	−0.811467	−	0.584398i	$-0.801331\pi$
$883$	−5958.00	+	5958.00i	−0.227070	+	0.227070i	0.584398	+	0.811467i	$0.301331\pi$
$884$	−3971.11			−0.151089
$885$		0			0
$886$	−7536.00			−0.285753
$887$	13164.9	−	13164.9i	0.498348	−	0.498348i	−0.412576	−	0.910923i	$-0.635371\pi$
$887$	13164.9	−	13164.9i	0.498348	−	0.498348i	0.910923	+	0.412576i	$0.135371\pi$
$888$		0			0
$889$		−	13446.0i		−	0.507272i
$890$		0			0
$891$		0			0
$892$	−10548.0	−	10548.0i	−0.395934	−	0.395934i
$893$	9673.22	+	9673.22i	0.362488	+	0.362488i
$894$		0			0
$895$		0			0
$896$			1629.17i			0.0607443i
$897$		0			0
$898$	1782.00	−	1782.00i	0.0662206	−	0.0662206i
$899$	−18022.7			−0.668623
$900$		0			0
$901$	−38844.0			−1.43627
$902$	18557.3	−	18557.3i	0.685023	−	0.685023i
$903$		0			0
$904$		−	5328.00i		−	0.196025i
$905$		0			0
$906$		0			0
$907$	−11088.0	−	11088.0i	−0.405922	−	0.405922i	0.474392	−	0.880314i	$-0.342668\pi$
$907$	−11088.0	−	11088.0i	−0.405922	−	0.405922i	−0.880314	+	0.474392i	$0.842668\pi$
$908$	6686.40	+	6686.40i	0.244379	+	0.244379i
$909$		0			0
$910$		0			0
$911$		−	3207.44i		−	0.116649i	−0.998298	−	0.0583244i	$-0.981424\pi$
$911$		−	3207.44i		−	0.116649i	0.998298	−	0.0583244i	$-0.0185758\pi$
$912$		0			0
$913$	−2268.00	+	2268.00i	−0.0822123	+	0.0822123i
$914$	23419.4			0.847532
$915$		0			0
$916$	−21736.0			−0.784037
$917$	15464.4	−	15464.4i	0.556903	−	0.556903i
$918$		0			0
$919$			46820.0i			1.68058i	0.542140	+	0.840288i	$0.317614\pi$
$919$			46820.0i			1.68058i	−0.542140	+	0.840288i	$0.682386\pi$
$920$		0			0
$921$		0			0
$922$	17496.0	+	17496.0i	0.624946	+	0.624946i
$923$	687.308	+	687.308i	0.0245103	+	0.0245103i
$924$		0			0
$925$		0			0
$926$		−	25023.1i		−	0.888024i
$927$		0			0
$928$	1728.00	−	1728.00i	0.0611254	−	0.0611254i
$929$	−44331.4			−1.56562			−0.782812	−	0.622258i	$-0.786215\pi$
$929$	−44331.4			−1.56562			−0.782812	+	0.622258i	$0.786215\pi$
$930$		0			0
$931$	6878.00			0.242124
$932$	16139.0	−	16139.0i	0.567222	−	0.567222i
$933$		0			0
$934$			13992.0i			0.490184i
$935$		0			0
$936$		0			0
$937$	−23688.0	−	23688.0i	−0.825884	−	0.825884i	0.161061	−	0.986945i	$-0.448509\pi$
$937$	−23688.0	−	23688.0i	−0.825884	−	0.825884i	−0.986945	+	0.161061i	$0.948509\pi$
$938$	−17870.0	−	17870.0i	−0.622043	−	0.622043i
$939$		0			0
$940$		0			0
$941$		−	17259.1i		−	0.597906i	−0.954268	−	0.298953i	$-0.903363\pi$
$941$		−	17259.1i		−	0.597906i	0.954268	−	0.298953i	$-0.0966373\pi$
$942$		0			0
$943$	10206.0	−	10206.0i	0.352442	−	0.352442i
$944$	5498.46			0.189576
$945$		0			0
$946$	38880.0			1.33626
$947$	−441.235	+	441.235i	−0.0151407	+	0.0151407i	−0.714637	−	0.699496i	$-0.753408\pi$
$947$	−441.235	+	441.235i	−0.0151407	+	0.0151407i	0.699496	+	0.714637i	$0.253408\pi$
$948$		0			0
$949$			6804.00i			0.232737i
$950$		0			0
$951$		0			0
$952$	−5616.00	−	5616.00i	−0.191193	−	0.191193i
$953$	−29414.2	−	29414.2i	−0.999811	−	0.999811i	0.000188542	−	1.00000i	$-0.499940\pi$
$953$	−29414.2	−	29414.2i	−0.999811	−	0.999811i	−1.00000		0.000188542i	$0.999940\pi$
$954$		0			0
$955$		0			0
$956$		−	14357.1i		−	0.485713i
$957$		0			0
$958$	−18252.0	+	18252.0i	−0.615548	+	0.615548i
$959$	17335.4			0.583723
$960$		0			0
$961$	25905.0			0.869558
$962$	7102.18	−	7102.18i	0.238029	−	0.238029i
$963$		0			0
$964$		−	24848.0i		−	0.830187i
$965$		0			0
$966$		0			0
$967$	−33075.0	−	33075.0i	−1.09992	−	1.09992i	−0.994420	−	0.105498i	$-0.966356\pi$
$967$	−33075.0	−	33075.0i	−1.09992	−	1.09992i	−0.105498	−	0.994420i	$-0.533644\pi$
$968$	−718.420	−	718.420i	−0.0238542	−	0.0238542i
$969$		0			0
$970$		0			0
$971$			35396.4i			1.16985i	0.811088	+	0.584924i	$0.198876\pi$
$971$			35396.4i			1.16985i	−0.811088	+	0.584924i	$0.801124\pi$
$972$		0			0
$973$	−14724.0	+	14724.0i	−0.485128	+	0.485128i
$974$	1043.69			0.0343347
$975$		0			0
$976$	−1760.00			−0.0577215
$977$	−2711.05	+	2711.05i	−0.0887759	+	0.0887759i	−0.750100	−	0.661324i	$-0.769995\pi$
$977$	−2711.05	+	2711.05i	−0.0887759	+	0.0887759i	0.661324	+	0.750100i	$0.269995\pi$
$978$		0			0
$979$		−	56862.0i		−	1.85630i
$980$		0			0
$981$		0			0
$982$	−28026.0	−	28026.0i	−0.910739	−	0.910739i
$983$	38166.8	+	38166.8i	1.23838	+	1.23838i	0.960661	+	0.277723i	$0.0895798\pi$
$983$	38166.8	+	38166.8i	1.23838	+	1.23838i	0.277723	+	0.960661i	$0.410420\pi$
$984$		0			0
$985$		0			0
$986$			11913.3i			0.384785i
$987$		0			0
$988$	1368.00	−	1368.00i	0.0440505	−	0.0440505i
$989$	21382.9			0.687499
$990$		0			0
$991$	27308.0			0.875345			0.437673	−	0.899134i	$-0.355803\pi$
$991$	27308.0			0.875345			0.437673	+	0.899134i	$0.355803\pi$
$992$	−5340.07	+	5340.07i	−0.170915	+	0.170915i
$993$		0			0
$994$			1944.00i			0.0620321i
$995$		0			0
$996$		0			0
$997$	−14391.0	−	14391.0i	−0.457139	−	0.457139i	0.440576	−	0.897715i	$-0.354774\pi$
$997$	−14391.0	−	14391.0i	−0.457139	−	0.457139i	−0.897715	+	0.440576i	$0.854774\pi$
$998$	−4324.67	−	4324.67i	−0.137169	−	0.137169i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.4.f.a.107.1	✓	4
3.2	odd	2	inner	450.4.f.a.107.2	yes	4
5.2	odd	4		450.4.f.c.143.1	yes	4
5.3	odd	4	inner	450.4.f.a.143.2	yes	4
5.4	even	2		450.4.f.c.107.2	yes	4
15.2	even	4		450.4.f.c.143.2	yes	4
15.8	even	4	inner	450.4.f.a.143.1	yes	4
15.14	odd	2		450.4.f.c.107.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.4.f.a.107.1	✓	4	1.1	even	1	trivial
450.4.f.a.107.2	yes	4	3.2	odd	2	inner
450.4.f.a.143.1	yes	4	15.8	even	4	inner
450.4.f.a.143.2	yes	4	5.3	odd	4	inner
450.4.f.c.107.1	yes	4	15.14	odd	2
450.4.f.c.107.2	yes	4	5.4	even	2
450.4.f.c.143.1	yes	4	5.2	odd	4
450.4.f.c.143.2	yes	4	15.2	even	4

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	450.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 + 1.41421i) q^{2} -4.00000i q^{4} +(-9.00000 - 9.00000i) q^{7} +(5.65685 + 5.65685i) q^{8} +O(q^{10})\)	\(q+(-1.41421 + 1.41421i) q^{2} -4.00000i q^{4} +(-9.00000 - 9.00000i) q^{7} +(5.65685 + 5.65685i) q^{8} +38.1838i q^{11} +(9.00000 - 9.00000i) q^{13} +25.4558 q^{14} -16.0000 q^{16} +(55.1543 - 55.1543i) q^{17} +38.0000i q^{19} +(-54.0000 - 54.0000i) q^{22} +(-29.6985 - 29.6985i) q^{23} +25.4558i q^{26} +(-36.0000 + 36.0000i) q^{28} +76.3675 q^{29} -236.000 q^{31} +(22.6274 - 22.6274i) q^{32} +156.000i q^{34} +(-279.000 - 279.000i) q^{37} +(-53.7401 - 53.7401i) q^{38} +343.654i q^{41} +(-360.000 + 360.000i) q^{43} +152.735 q^{44} +84.0000 q^{46} +(254.558 - 254.558i) q^{47} -181.000i q^{49} +(-36.0000 - 36.0000i) q^{52} +(-352.139 - 352.139i) q^{53} -101.823i q^{56} +(-108.000 + 108.000i) q^{58} -343.654 q^{59} +110.000 q^{61} +(333.754 - 333.754i) q^{62} +64.0000i q^{64} +(-702.000 - 702.000i) q^{67} +(-220.617 - 220.617i) q^{68} +76.3675i q^{71} +(-378.000 + 378.000i) q^{73} +789.131 q^{74} +152.000 q^{76} +(343.654 - 343.654i) q^{77} -272.000i q^{79} +(-486.000 - 486.000i) q^{82} +(59.3970 + 59.3970i) q^{83} -1018.23i q^{86} +(-216.000 + 216.000i) q^{88} -1489.17 q^{89} -162.000 q^{91} +(-118.794 + 118.794i) q^{92} +720.000i q^{94} +(-684.000 - 684.000i) q^{97} +(255.973 + 255.973i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 36 q^{7}+O(q^{10}) \) 4 * q - 36 * q^7	\( 4 q - 36 q^{7} + 36 q^{13} - 64 q^{16} - 216 q^{22} - 144 q^{28} - 944 q^{31} - 1116 q^{37} - 1440 q^{43} + 336 q^{46} - 144 q^{52} - 432 q^{58} + 440 q^{61} - 2808 q^{67} - 1512 q^{73} + 608 q^{76} - 1944 q^{82} - 864 q^{88} - 648 q^{91} - 2736 q^{97}+O(q^{100}) \) 4 * q - 36 * q^7 + 36 * q^13 - 64 * q^16 - 216 * q^22 - 144 * q^28 - 944 * q^31 - 1116 * q^37 - 1440 * q^43 + 336 * q^46 - 144 * q^52 - 432 * q^58 + 440 * q^61 - 2808 * q^67 - 1512 * q^73 + 608 * q^76 - 1944 * q^82 - 864 * q^88 - 648 * q^91 - 2736 * q^97

Introduction

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