LMFDB - Embedded newform 450.4.f.e.107.3

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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.12745506816.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 71x^{4} + 625 $ x^8 + 71*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{7}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.3
Root			$1.97374 + 1.97374i$ of defining polynomial
Character	$\chi$	$=$	450.107
Dual form			450.4.f.e.143.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41421 - 1.41421i) q^{2} -4.00000i q^{4} +(-21.9129 - 21.9129i) q^{7} +(-5.65685 - 5.65685i) q^{8} +O(q^{10})$	\(q+(1.41421 - 1.41421i) q^{2} -4.00000i q^{4} +(-21.9129 - 21.9129i) q^{7} +(-5.65685 - 5.65685i) q^{8} +64.9306i q^{11} +(-13.0871 + 13.0871i) q^{13} -61.9790 q^{14} -16.0000 q^{16} +(5.53365 - 5.53365i) q^{17} +103.826i q^{19} +(91.8258 + 91.8258i) q^{22} +(-19.7990 - 19.7990i) q^{23} +37.0160i q^{26} +(-87.6515 + 87.6515i) q^{28} +184.646 q^{29} +19.8258 q^{31} +(-22.6274 + 22.6274i) q^{32} -15.6515i q^{34} +(254.739 + 254.739i) q^{37} +(146.832 + 146.832i) q^{38} -63.1468i q^{41} +(-104.174 + 104.174i) q^{43} +259.722 q^{44} -56.0000 q^{46} +(-185.567 + 185.567i) q^{47} +617.348i q^{49} +(52.3485 + 52.3485i) q^{52} +(-259.476 - 259.476i) q^{53} +247.916i q^{56} +(261.129 - 261.129i) q^{58} -255.539 q^{59} -894.083 q^{61} +(28.0379 - 28.0379i) q^{62} +64.0000i q^{64} +(100.523 + 100.523i) q^{67} +(-22.1346 - 22.1346i) q^{68} +491.653i q^{71} +(-603.780 + 603.780i) q^{73} +720.510 q^{74} +415.303 q^{76} +(1422.82 - 1422.82i) q^{77} +698.780i q^{79} +(-89.3030 - 89.3030i) q^{82} +(707.101 + 707.101i) q^{83} +294.649i q^{86} +(367.303 - 367.303i) q^{88} +389.648 q^{89} +573.553 q^{91} +(-79.1960 + 79.1960i) q^{92} +524.864i q^{94} +(29.2576 + 29.2576i) q^{97} +(873.063 + 873.063i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{7}+O(q^{10}) $ 8 * q + 8 * q^7	$ 8 q + 8 q^{7} - 288 q^{13} - 128 q^{16} + 368 q^{22} + 32 q^{28} - 208 q^{31} + 1488 q^{37} - 1200 q^{43} - 448 q^{46} + 1152 q^{52} + 256 q^{58} - 3120 q^{61} + 1904 q^{67} - 2264 q^{73} + 1856 q^{76} + 752 q^{82} + 1472 q^{88} - 8976 q^{91} - 3432 q^{97}+O(q^{100}) $ 8 * q + 8 * q^7 - 288 * q^13 - 128 * q^16 + 368 * q^22 + 32 * q^28 - 208 * q^31 + 1488 * q^37 - 1200 * q^43 - 448 * q^46 + 1152 * q^52 + 256 * q^58 - 3120 * q^61 + 1904 * q^67 - 2264 * q^73 + 1856 * q^76 + 752 * q^82 + 1472 * q^88 - 8976 * q^91 - 3432 * 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
$7$	−21.9129	−	21.9129i	−1.18318	−	1.18318i	−0.978915	−	0.204270i	$-0.934518\pi$
$7$	−21.9129	−	21.9129i	−1.18318	−	1.18318i	−0.204270	−	0.978915i	$-0.565482\pi$
$8$	−5.65685	−	5.65685i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$			64.9306i			1.77976i	0.456198	+	0.889878i	$0.349211\pi$
$11$			64.9306i			1.77976i	−0.456198	+	0.889878i	$0.650789\pi$
$12$		0			0
$13$	−13.0871	+	13.0871i	−0.279209	+	0.279209i	−0.832793	−	0.553584i	$-0.813260\pi$
$13$	−13.0871	+	13.0871i	−0.279209	+	0.279209i	0.553584	+	0.832793i	$0.313260\pi$
$14$	−61.9790			−1.18318
$15$		0			0
$16$	−16.0000			−0.250000
$17$	5.53365	−	5.53365i	0.0789474	−	0.0789474i	−0.666530	−	0.745478i	$-0.732221\pi$
$17$	5.53365	−	5.53365i	0.0789474	−	0.0789474i	0.745478	+	0.666530i	$0.232221\pi$
$18$		0			0
$19$			103.826i			1.25365i	0.779162	+	0.626823i	$0.215645\pi$
$19$			103.826i			1.25365i	−0.779162	+	0.626823i	$0.784355\pi$
$20$		0			0
$21$		0			0
$22$	91.8258	+	91.8258i	0.889878	+	0.889878i
$23$	−19.7990	−	19.7990i	−0.179495	−	0.179495i	0.611641	−	0.791135i	$-0.290510\pi$
$23$	−19.7990	−	19.7990i	−0.179495	−	0.179495i	−0.791135	+	0.611641i	$0.790510\pi$
$24$		0			0
$25$		0			0
$26$			37.0160i			0.279209i
$27$		0			0
$28$	−87.6515	+	87.6515i	−0.591592	+	0.591592i
$29$	184.646			1.18234			0.591171	−	0.806547i	$-0.298666\pi$
$29$	184.646			1.18234			0.591171	+	0.806547i	$0.298666\pi$
$30$		0			0
$31$	19.8258			0.114865			0.0574324	−	0.998349i	$-0.481709\pi$
$31$	19.8258			0.114865			0.0574324	+	0.998349i	$0.481709\pi$
$32$	−22.6274	+	22.6274i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	15.6515i		−	0.0789474i
$35$		0			0
$36$		0			0
$37$	254.739	+	254.739i	1.13186	+	1.13186i	0.989868	+	0.141991i	$0.0453503\pi$
$37$	254.739	+	254.739i	1.13186	+	1.13186i	0.141991	+	0.989868i	$0.454650\pi$
$38$	146.832	+	146.832i	0.626823	+	0.626823i
$39$		0			0
$40$		0			0
$41$		−	63.1468i		−	0.240533i	−0.992742	−	0.120267i	$-0.961625\pi$
$41$		−	63.1468i		−	0.240533i	0.992742	−	0.120267i	$-0.0383750\pi$
$42$		0			0
$43$	−104.174	+	104.174i	−0.369452	+	0.369452i	−0.867277	−	0.497826i	$-0.834132\pi$
$43$	−104.174	+	104.174i	−0.369452	+	0.369452i	0.497826	+	0.867277i	$0.334132\pi$
$44$	259.722			0.889878
$45$		0			0
$46$	−56.0000			−0.179495
$47$	−185.567	+	185.567i	−0.575910	+	0.575910i	−0.933774	−	0.357864i	$-0.883505\pi$
$47$	−185.567	+	185.567i	−0.575910	+	0.575910i	0.357864	+	0.933774i	$0.383505\pi$
$48$		0			0
$49$			617.348i			1.79985i
$50$		0			0
$51$		0			0
$52$	52.3485	+	52.3485i	0.139604	+	0.139604i
$53$	−259.476	−	259.476i	−0.672486	−	0.672486i	0.285802	−	0.958289i	$-0.407740\pi$
$53$	−259.476	−	259.476i	−0.672486	−	0.672486i	−0.958289	+	0.285802i	$0.907740\pi$
$54$		0			0
$55$		0			0
$56$			247.916i			0.591592i
$57$		0			0
$58$	261.129	−	261.129i	0.591171	−	0.591171i
$59$	−255.539			−0.563870			−0.281935	−	0.959434i	$-0.590976\pi$
$59$	−255.539			−0.563870			−0.281935	+	0.959434i	$0.590976\pi$
$60$		0			0
$61$	−894.083			−1.87665			−0.938325	−	0.345755i	$-0.887623\pi$
$61$	−894.083			−1.87665			−0.938325	+	0.345755i	$0.887623\pi$
$62$	28.0379	−	28.0379i	0.0574324	−	0.0574324i
$63$		0			0
$64$			64.0000i			0.125000i
$65$		0			0
$66$		0			0
$67$	100.523	+	100.523i	0.183296	+	0.183296i	0.792790	−	0.609495i	$-0.208628\pi$
$67$	100.523	+	100.523i	0.183296	+	0.183296i	−0.609495	+	0.792790i	$0.708628\pi$
$68$	−22.1346	−	22.1346i	−0.0394737	−	0.0394737i
$69$		0			0
$70$		0			0
$71$			491.653i			0.821810i	0.911678	+	0.410905i	$0.134787\pi$
$71$			491.653i			0.821810i	−0.911678	+	0.410905i	$0.865213\pi$
$72$		0			0
$73$	−603.780	+	603.780i	−0.968043	+	0.968043i	−0.999505	−	0.0314620i	$-0.989984\pi$
$73$	−603.780	+	603.780i	−0.968043	+	0.968043i	0.0314620	+	0.999505i	$0.489984\pi$
$74$	720.510			1.13186
$75$		0			0
$76$	415.303			0.626823
$77$	1422.82	−	1422.82i	2.10578	−	2.10578i
$78$		0			0
$79$			698.780i			0.995176i	0.867413	+	0.497588i	$0.165781\pi$
$79$			698.780i			0.995176i	−0.867413	+	0.497588i	$0.834219\pi$
$80$		0			0
$81$		0			0
$82$	−89.3030	−	89.3030i	−0.120267	−	0.120267i
$83$	707.101	+	707.101i	0.935114	+	0.935114i	0.998019	−	0.0629055i	$-0.0200367\pi$
$83$	707.101	+	707.101i	0.935114	+	0.935114i	−0.0629055	+	0.998019i	$0.520037\pi$
$84$		0			0
$85$		0			0
$86$			294.649i			0.369452i
$87$		0			0
$88$	367.303	−	367.303i	0.444939	−	0.444939i
$89$	389.648			0.464074			0.232037	−	0.972707i	$-0.425461\pi$
$89$	389.648			0.464074			0.232037	+	0.972707i	$0.425461\pi$
$90$		0			0
$91$	573.553			0.660711
$92$	−79.1960	+	79.1960i	−0.0897473	+	0.0897473i
$93$		0			0
$94$			524.864i			0.575910i
$95$		0			0
$96$		0			0
$97$	29.2576	+	29.2576i	0.0306253	+	0.0306253i	0.722254	−	0.691628i	$-0.243106\pi$
$97$	29.2576	+	29.2576i	0.0306253	+	0.0306253i	−0.691628	+	0.722254i	$0.743106\pi$
$98$	873.063	+	873.063i	0.899925	+	0.899925i
$99$		0			0
$100$		0			0
$101$		−	386.204i		−	0.380482i	−0.981737	−	0.190241i	$-0.939073\pi$
$101$		−	386.204i		−	0.380482i	0.981737	−	0.190241i	$-0.0609269\pi$
$102$		0			0
$103$	−793.564	+	793.564i	−0.759148	+	0.759148i	−0.976167	−	0.217019i	$-0.930366\pi$
$103$	−793.564	+	793.564i	−0.759148	+	0.759148i	0.217019	+	0.976167i	$0.430366\pi$
$104$	148.064			0.139604
$105$		0			0
$106$	−733.909			−0.672486
$107$	501.494	−	501.494i	0.453096	−	0.453096i	−0.443285	−	0.896381i	$-0.646187\pi$
$107$	501.494	−	501.494i	0.453096	−	0.453096i	0.896381	+	0.443285i	$0.146187\pi$
$108$		0			0
$109$		−	875.295i		−	0.769157i	−0.923092	−	0.384578i	$-0.874347\pi$
$109$		−	875.295i		−	0.769157i	0.923092	−	0.384578i	$-0.125653\pi$
$110$		0			0
$111$		0			0
$112$	350.606	+	350.606i	0.295796	+	0.295796i
$113$	−943.768	−	943.768i	−0.785683	−	0.785683i	0.195100	−	0.980783i	$-0.437497\pi$
$113$	−943.768	−	943.768i	−0.785683	−	0.785683i	−0.980783	+	0.195100i	$0.937497\pi$
$114$		0			0
$115$		0			0
$116$		−	738.584i		−	0.591171i
$117$		0			0
$118$	−361.386	+	361.386i	−0.281935	+	0.281935i
$119$	−242.516			−0.186819
$120$		0			0
$121$	−2884.98			−2.16753
$122$	−1264.42	+	1264.42i	−0.938325	+	0.938325i
$123$		0			0
$124$		−	79.3030i		−	0.0574324i
$125$		0			0
$126$		0			0
$127$	−535.822	−	535.822i	−0.374382	−	0.374382i	0.494688	−	0.869070i	$-0.335282\pi$
$127$	−535.822	−	535.822i	−0.374382	−	0.374382i	−0.869070	+	0.494688i	$0.835282\pi$
$128$	90.5097	+	90.5097i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	1852.00i		−	1.23519i	−0.786495	−	0.617597i	$-0.788106\pi$
$131$		−	1852.00i		−	1.23519i	0.786495	−	0.617597i	$-0.211894\pi$
$132$		0			0
$133$	2275.12	−	2275.12i	1.48329	−	1.48329i
$134$	284.321			0.183296
$135$		0			0
$136$	−62.6061			−0.0394737
$137$	−888.796	+	888.796i	−0.554270	+	0.554270i	−0.927670	−	0.373401i	$-0.878192\pi$
$137$	−888.796	+	888.796i	−0.554270	+	0.554270i	0.373401	+	0.927670i	$0.378192\pi$
$138$		0			0
$139$			252.348i			0.153985i	0.997032	+	0.0769925i	$0.0245318\pi$
$139$			252.348i			0.153985i	−0.997032	+	0.0769925i	$0.975468\pi$
$140$		0			0
$141$		0			0
$142$	695.303	+	695.303i	0.410905	+	0.410905i
$143$	−849.755	−	849.755i	−0.496924	−	0.496924i
$144$		0			0
$145$		0			0
$146$			1707.75i			0.968043i
$147$		0			0
$148$	1018.95	−	1018.95i	0.565929	−	0.565929i
$149$	169.025			0.0929335			0.0464668	−	0.998920i	$-0.485204\pi$
$149$	169.025			0.0929335			0.0464668	+	0.998920i	$0.485204\pi$
$150$		0			0
$151$	2783.65			1.50020			0.750100	−	0.661324i	$-0.230005\pi$
$151$	2783.65			1.50020			0.750100	+	0.661324i	$0.230005\pi$
$152$	587.327	−	587.327i	0.313411	−	0.313411i
$153$		0			0
$154$		−	4024.33i		−	2.10578i
$155$		0			0
$156$		0			0
$157$	−2018.22	−	2018.22i	−1.02593	−	1.02593i	−0.999655	−	0.0262763i	$-0.991635\pi$
$157$	−2018.22	−	2018.22i	−1.02593	−	1.02593i	−0.0262763	−	0.999655i	$-0.508365\pi$
$158$	988.225	+	988.225i	0.497588	+	0.497588i
$159$		0			0
$160$		0			0
$161$			867.706i			0.424750i
$162$		0			0
$163$	−2132.69	+	2132.69i	−1.02482	+	1.02482i	−0.0251326	+	0.999684i	$0.508001\pi$
$163$	−2132.69	+	2132.69i	−1.02482	+	1.02482i	−0.999684	+	0.0251326i	$0.991999\pi$
$164$	−252.587			−0.120267
$165$		0			0
$166$	1999.98			0.935114
$167$	−1027.95	+	1027.95i	−0.476319	+	0.476319i	−0.903952	−	0.427633i	$-0.859347\pi$
$167$	−1027.95	+	1027.95i	−0.476319	+	0.476319i	0.427633	+	0.903952i	$0.359347\pi$
$168$		0			0
$169$			1854.45i			0.844085i
$170$		0			0
$171$		0			0
$172$	416.697	+	416.697i	0.184726	+	0.184726i
$173$	−868.268	−	868.268i	−0.381579	−	0.381579i	0.490092	−	0.871671i	$-0.336963\pi$
$173$	−868.268	−	868.268i	−0.381579	−	0.381579i	−0.871671	+	0.490092i	$0.836963\pi$
$174$		0			0
$175$		0			0
$176$		−	1038.89i		−	0.444939i
$177$		0			0
$178$	551.045	−	551.045i	0.232037	−	0.232037i
$179$	−3448.21			−1.43984			−0.719920	−	0.694057i	$-0.755822\pi$
$179$	−3448.21			−1.43984			−0.719920	+	0.694057i	$0.755822\pi$
$180$		0			0
$181$	3511.81			1.44216			0.721080	−	0.692852i	$-0.243646\pi$
$181$	3511.81			1.44216			0.721080	+	0.692852i	$0.243646\pi$
$182$	811.126	−	811.126i	0.330355	−	0.330355i
$183$		0			0
$184$			224.000i			0.0897473i
$185$		0			0
$186$		0			0
$187$	359.303	+	359.303i	0.140507	+	0.140507i
$188$	742.269	+	742.269i	0.287955	+	0.287955i
$189$		0			0
$190$		0			0
$191$		−	2037.43i		−	0.771850i	−0.922530	−	0.385925i	$-0.873882\pi$
$191$		−	2037.43i		−	0.771850i	0.922530	−	0.385925i	$-0.126118\pi$
$192$		0			0
$193$	−1127.78	+	1127.78i	−0.420619	+	0.420619i	−0.885417	−	0.464798i	$-0.846127\pi$
$193$	−1127.78	+	1127.78i	−0.420619	+	0.420619i	0.464798	+	0.885417i	$0.346127\pi$
$194$	82.7529			0.0306253
$195$		0			0
$196$	2469.39			0.899925
$197$	257.810	−	257.810i	0.0932396	−	0.0932396i	−0.658948	−	0.752188i	$-0.728998\pi$
$197$	257.810	−	257.810i	0.0932396	−	0.0932396i	0.752188	+	0.658948i	$0.228998\pi$
$198$		0			0
$199$			513.030i			0.182753i	0.995816	+	0.0913763i	$0.0291266\pi$
$199$			513.030i			0.182753i	−0.995816	+	0.0913763i	$0.970873\pi$
$200$		0			0
$201$		0			0
$202$	−546.174	−	546.174i	−0.190241	−	0.190241i
$203$	−4046.12	−	4046.12i	−1.39893	−	1.39893i
$204$		0			0
$205$		0			0
$206$			2244.54i			0.759148i
$207$		0			0
$208$	209.394	−	209.394i	0.0698022	−	0.0698022i
$209$	−6741.47			−2.23118
$210$		0			0
$211$	−1610.24			−0.525373			−0.262686	−	0.964881i	$-0.584608\pi$
$211$	−1610.24			−0.525373			−0.262686	+	0.964881i	$0.584608\pi$
$212$	−1037.90	+	1037.90i	−0.336243	+	0.336243i
$213$		0			0
$214$		−	1418.44i		−	0.453096i
$215$		0			0
$216$		0			0
$217$	−434.439	−	434.439i	−0.135906	−	0.135906i
$218$	−1237.85	−	1237.85i	−0.384578	−	0.384578i
$219$		0			0
$220$		0			0
$221$			144.839i			0.0440856i
$222$		0			0
$223$	2339.82	−	2339.82i	0.702628	−	0.702628i	−0.262346	−	0.964974i	$-0.584496\pi$
$223$	2339.82	−	2339.82i	0.702628	−	0.702628i	0.964974	+	0.262346i	$0.0844961\pi$
$224$	991.664			0.295796
$225$		0			0
$226$	−2669.38			−0.785683
$227$	−1601.14	+	1601.14i	−0.468155	+	0.468155i	−0.901316	−	0.433162i	$-0.857398\pi$
$227$	−1601.14	+	1601.14i	−0.468155	+	0.468155i	0.433162	+	0.901316i	$0.357398\pi$
$228$		0			0
$229$		−	6303.36i		−	1.81894i	−0.415766	−	0.909472i	$-0.636486\pi$
$229$		−	6303.36i		−	1.81894i	0.415766	−	0.909472i	$-0.363514\pi$
$230$		0			0
$231$		0			0
$232$	−1044.52	−	1044.52i	−0.295585	−	0.295585i
$233$	2681.95	+	2681.95i	0.754080	+	0.754080i	0.975238	−	0.221158i	$-0.0709836\pi$
$233$	2681.95	+	2681.95i	0.754080	+	0.754080i	−0.221158	+	0.975238i	$0.570984\pi$
$234$		0			0
$235$		0			0
$236$			1022.15i			0.281935i
$237$		0			0
$238$	−342.970	+	342.970i	−0.0934093	+	0.0934093i
$239$	2314.62			0.626444			0.313222	−	0.949680i	$-0.398592\pi$
$239$	2314.62			0.626444			0.313222	+	0.949680i	$0.398592\pi$
$240$		0			0
$241$	1476.59			0.394670			0.197335	−	0.980336i	$-0.436771\pi$
$241$	1476.59			0.394670			0.197335	+	0.980336i	$0.436771\pi$
$242$	−4079.98	+	4079.98i	−1.08377	+	1.08377i
$243$		0			0
$244$			3576.33i			0.938325i
$245$		0			0
$246$		0			0
$247$	−1358.78	−	1358.78i	−0.350029	−	0.350029i
$248$	−112.151	−	112.151i	−0.0287162	−	0.0287162i
$249$		0			0
$250$		0			0
$251$			4021.54i			1.01130i	0.862738	+	0.505652i	$0.168748\pi$
$251$			4021.54i			1.01130i	−0.862738	+	0.505652i	$0.831252\pi$
$252$		0			0
$253$	1285.56	−	1285.56i	0.319457	−	0.319457i
$254$	−1515.53			−0.374382
$255$		0			0
$256$	256.000			0.0625000
$257$	−371.183	+	371.183i	−0.0900924	+	0.0900924i	−0.750717	−	0.660624i	$-0.770292\pi$
$257$	−371.183	+	371.183i	−0.0900924	+	0.0900924i	0.660624	+	0.750717i	$0.270292\pi$
$258$		0			0
$259$		−	11164.1i		−	2.67839i
$260$		0			0
$261$		0			0
$262$	−2619.13	−	2619.13i	−0.617597	−	0.617597i
$263$	181.405	+	181.405i	0.0425320	+	0.0425320i	0.728053	−	0.685521i	$-0.240425\pi$
$263$	181.405	+	181.405i	0.0425320	+	0.0425320i	−0.685521	+	0.728053i	$0.740425\pi$
$264$		0			0
$265$		0			0
$266$		−	6435.01i		−	1.48329i
$267$		0			0
$268$	402.091	−	402.091i	0.0916478	−	0.0916478i
$269$	3301.79			0.748377			0.374189	−	0.927353i	$-0.377921\pi$
$269$	3301.79			0.748377			0.374189	+	0.927353i	$0.377921\pi$
$270$		0			0
$271$	−3894.23			−0.872906			−0.436453	−	0.899727i	$-0.643765\pi$
$271$	−3894.23			−0.872906			−0.436453	+	0.899727i	$0.643765\pi$
$272$	−88.5383	+	88.5383i	−0.0197369	+	0.0197369i
$273$		0			0
$274$			2513.89i			0.554270i
$275$		0			0
$276$		0			0
$277$	1417.53	+	1417.53i	0.307476	+	0.307476i	0.843930	−	0.536454i	$-0.180236\pi$
$277$	1417.53	+	1417.53i	0.307476	+	0.307476i	−0.536454	+	0.843930i	$0.680236\pi$
$278$	356.875	+	356.875i	0.0769925	+	0.0769925i
$279$		0			0
$280$		0			0
$281$		−	8119.33i		−	1.72370i	−0.507166	−	0.861848i	$-0.669307\pi$
$281$		−	8119.33i		−	1.72370i	0.507166	−	0.861848i	$-0.330693\pi$
$282$		0			0
$283$	−1166.94	+	1166.94i	−0.245114	+	0.245114i	−0.818962	−	0.573848i	$-0.805450\pi$
$283$	−1166.94	+	1166.94i	−0.245114	+	0.245114i	0.573848	+	0.818962i	$0.305450\pi$
$284$	1966.61			0.410905
$285$		0			0
$286$	−2403.47			−0.496924
$287$	−1383.73	+	1383.73i	−0.284595	+	0.284595i
$288$		0			0
$289$			4851.76i			0.987535i
$290$		0			0
$291$		0			0
$292$	2415.12	+	2415.12i	0.484021	+	0.484021i
$293$	4826.44	+	4826.44i	0.962333	+	0.962333i	0.999316	−	0.0369831i	$-0.0117748\pi$
$293$	4826.44	+	4826.44i	0.962333	+	0.962333i	−0.0369831	+	0.999316i	$0.511775\pi$
$294$		0			0
$295$		0			0
$296$		−	2882.04i		−	0.565929i
$297$		0			0
$298$	239.038	−	239.038i	0.0464668	−	0.0464668i
$299$	518.224			0.100233
$300$		0			0
$301$	4565.52			0.874259
$302$	3936.68	−	3936.68i	0.750100	−	0.750100i
$303$		0			0
$304$		−	1661.21i		−	0.313411i
$305$		0			0
$306$		0			0
$307$	4161.89	+	4161.89i	0.773718	+	0.773718i	0.978754	−	0.205036i	$-0.0657313\pi$
$307$	4161.89	+	4161.89i	0.773718	+	0.773718i	−0.205036	+	0.978754i	$0.565731\pi$
$308$	−5691.27	−	5691.27i	−1.05289	−	1.05289i
$309$		0			0
$310$		0			0
$311$			3984.60i			0.726514i	0.931689	+	0.363257i	$0.118335\pi$
$311$			3984.60i			0.726514i	−0.931689	+	0.363257i	$0.881665\pi$
$312$		0			0
$313$	−2427.14	+	2427.14i	−0.438308	+	0.438308i	−0.891442	−	0.453135i	$-0.850306\pi$
$313$	−2427.14	+	2427.14i	−0.438308	+	0.438308i	0.453135	+	0.891442i	$0.350306\pi$
$314$	−5708.38			−1.02593
$315$		0			0
$316$	2795.12			0.497588
$317$	7132.54	−	7132.54i	1.26373	−	1.26373i	0.314464	−	0.949269i	$-0.398175\pi$
$317$	7132.54	−	7132.54i	1.26373	−	1.26373i	0.949269	−	0.314464i	$-0.101825\pi$
$318$		0			0
$319$			11989.2i			2.10428i
$320$		0			0
$321$		0			0
$322$	1227.12	+	1227.12i	0.212375	+	0.212375i
$323$	574.535	+	574.535i	0.0989721	+	0.0989721i
$324$		0			0
$325$		0			0
$326$			6032.16i			1.02482i
$327$		0			0
$328$	−357.212	+	357.212i	−0.0601334	+	0.0601334i
$329$	8132.63			1.36282
$330$		0			0
$331$	−1793.22			−0.297777			−0.148889	−	0.988854i	$-0.547570\pi$
$331$	−1793.22			−0.297777			−0.148889	+	0.988854i	$0.547570\pi$
$332$	2828.41	−	2828.41i	0.467557	−	0.467557i
$333$		0			0
$334$			2907.48i			0.476319i
$335$		0			0
$336$		0			0
$337$	−4438.46	−	4438.46i	−0.717443	−	0.717443i	0.250638	−	0.968081i	$-0.419360\pi$
$337$	−4438.46	−	4438.46i	−0.717443	−	0.717443i	−0.968081	+	0.250638i	$0.919360\pi$
$338$	2622.59	+	2622.59i	0.422042	+	0.422042i
$339$		0			0
$340$		0			0
$341$			1287.30i			0.204431i
$342$		0			0
$343$	6011.77	−	6011.77i	0.946370	−	0.946370i
$344$	1178.60			0.184726
$345$		0			0
$346$	−2455.83			−0.381579
$347$	4669.58	−	4669.58i	0.722410	−	0.722410i	−0.246685	−	0.969096i	$-0.579341\pi$
$347$	4669.58	−	4669.58i	0.722410	−	0.722410i	0.969096	+	0.246685i	$0.0793414\pi$
$348$		0			0
$349$		−	1244.02i		−	0.190805i	−0.995439	−	0.0954026i	$-0.969586\pi$
$349$		−	1244.02i		−	0.190805i	0.995439	−	0.0954026i	$-0.0304138\pi$
$350$		0			0
$351$		0			0
$352$	−1469.21	−	1469.21i	−0.222470	−	0.222470i
$353$	5341.19	+	5341.19i	0.805334	+	0.805334i	0.983924	−	0.178590i	$-0.0571535\pi$
$353$	5341.19	+	5341.19i	0.805334	+	0.805334i	−0.178590	+	0.983924i	$0.557153\pi$
$354$		0			0
$355$		0			0
$356$		−	1558.59i		−	0.232037i
$357$		0			0
$358$	−4876.51	+	4876.51i	−0.719920	+	0.719920i
$359$	1040.64			0.152988			0.0764940	−	0.997070i	$-0.475627\pi$
$359$	1040.64			0.152988			0.0764940	+	0.997070i	$0.475627\pi$
$360$		0			0
$361$	−3920.79			−0.571627
$362$	4966.45	−	4966.45i	0.721080	−	0.721080i
$363$		0			0
$364$		−	2294.21i		−	0.330355i
$365$		0			0
$366$		0			0
$367$	1447.50	+	1447.50i	0.205883	+	0.205883i	0.802515	−	0.596632i	$-0.203495\pi$
$367$	1447.50	+	1447.50i	0.205883	+	0.205883i	−0.596632	+	0.802515i	$0.703495\pi$
$368$	316.784	+	316.784i	0.0448736	+	0.0448736i
$369$		0			0
$370$		0			0
$371$			11371.7i			1.59135i
$372$		0			0
$373$	−106.398	+	106.398i	−0.0147696	+	0.0147696i	−0.714453	−	0.699683i	$-0.753324\pi$
$373$	−106.398	+	106.398i	−0.0147696	+	0.0147696i	0.699683	+	0.714453i	$0.253324\pi$
$374$	1016.26			0.140507
$375$		0			0
$376$	2099.45			0.287955
$377$	−2416.48	+	2416.48i	−0.330120	+	0.330120i
$378$		0			0
$379$			9384.86i			1.27195i	0.771711	+	0.635974i	$0.219401\pi$
$379$			9384.86i			1.27195i	−0.771711	+	0.635974i	$0.780599\pi$
$380$		0			0
$381$		0			0
$382$	−2881.36	−	2881.36i	−0.385925	−	0.385925i
$383$	−8015.85	−	8015.85i	−1.06943	−	1.06943i	−0.997403	−	0.0720253i	$-0.977054\pi$
$383$	−8015.85	−	8015.85i	−1.06943	−	1.06943i	−0.0720253	−	0.997403i	$-0.522946\pi$
$384$		0			0
$385$		0			0
$386$			3189.84i			0.420619i
$387$		0			0
$388$	117.030	−	117.030i	0.0153127	−	0.0153127i
$389$	8892.72			1.15907			0.579536	−	0.814947i	$-0.303234\pi$
$389$	8892.72			1.15907			0.579536	+	0.814947i	$0.303234\pi$
$390$		0			0
$391$	−219.121			−0.0283413
$392$	3492.25	−	3492.25i	0.449962	−	0.449962i
$393$		0			0
$394$		−	729.197i		−	0.0932396i
$395$		0			0
$396$		0			0
$397$	−3248.62	−	3248.62i	−0.410689	−	0.410689i	0.471290	−	0.881978i	$-0.343789\pi$
$397$	−3248.62	−	3248.62i	−0.410689	−	0.410689i	−0.881978	+	0.471290i	$0.843789\pi$
$398$	725.534	+	725.534i	0.0913763	+	0.0913763i
$399$		0			0
$400$		0			0
$401$		−	12012.4i		−	1.49594i	−0.663731	−	0.747971i	$-0.731028\pi$
$401$		−	12012.4i		−	1.49594i	0.663731	−	0.747971i	$-0.268972\pi$
$402$		0			0
$403$	−259.462	+	259.462i	−0.0320713	+	0.0320713i
$404$	−1544.81			−0.190241
$405$		0			0
$406$	−11444.2			−1.39893
$407$	−16540.3	+	16540.3i	−2.01443	+	2.01443i
$408$		0			0
$409$		−	1710.61i		−	0.206807i	−0.994639	−	0.103403i	$-0.967027\pi$
$409$		−	1710.61i		−	0.206807i	0.994639	−	0.103403i	$-0.0329733\pi$
$410$		0			0
$411$		0			0
$412$	3174.26	+	3174.26i	0.379574	+	0.379574i
$413$	5599.59	+	5599.59i	0.667162	+	0.667162i
$414$		0			0
$415$		0			0
$416$		−	592.256i		−	0.0698022i
$417$		0			0
$418$	−9533.88	+	9533.88i	−1.11559	+	1.11559i
$419$	−2905.88			−0.338811			−0.169405	−	0.985546i	$-0.554185\pi$
$419$	−2905.88			−0.338811			−0.169405	+	0.985546i	$0.554185\pi$
$420$		0			0
$421$	−9062.85			−1.04916			−0.524580	−	0.851361i	$-0.675778\pi$
$421$	−9062.85			−1.04916			−0.524580	+	0.851361i	$0.675778\pi$
$422$	−2277.23	+	2277.23i	−0.262686	+	0.262686i
$423$		0			0
$424$			2935.64i			0.336243i
$425$		0			0
$426$		0			0
$427$	19591.9	+	19591.9i	2.22042	+	2.22042i
$428$	−2005.98	−	2005.98i	−0.226548	−	0.226548i
$429$		0			0
$430$		0			0
$431$			10334.6i			1.15498i	0.816396	+	0.577492i	$0.195969\pi$
$431$			10334.6i			1.15498i	−0.816396	+	0.577492i	$0.804031\pi$
$432$		0			0
$433$	3105.17	−	3105.17i	0.344631	−	0.344631i	−0.513474	−	0.858105i	$-0.671642\pi$
$433$	3105.17	−	3105.17i	0.344631	−	0.344631i	0.858105	+	0.513474i	$0.171642\pi$
$434$	−1228.78			−0.135906
$435$		0			0
$436$	−3501.18			−0.384578
$437$	2055.65	−	2055.65i	0.225023	−	0.225023i
$438$		0			0
$439$			4940.17i			0.537087i	0.963268	+	0.268544i	$0.0865423\pi$
$439$			4940.17i			0.537087i	−0.963268	+	0.268544i	$0.913458\pi$
$440$		0			0
$441$		0			0
$442$	204.833	+	204.833i	0.0220428	+	0.0220428i
$443$	11835.5	+	11835.5i	1.26935	+	1.26935i	0.946423	+	0.322931i	$0.104668\pi$
$443$	11835.5	+	11835.5i	1.26935	+	1.26935i	0.322931	+	0.946423i	$0.395332\pi$
$444$		0			0
$445$		0			0
$446$		−	6618.02i		−	0.702628i
$447$		0			0
$448$	1402.42	−	1402.42i	0.147898	−	0.147898i
$449$	3384.05			0.355687			0.177843	−	0.984059i	$-0.443088\pi$
$449$	3384.05			0.355687			0.177843	+	0.984059i	$0.443088\pi$
$450$		0			0
$451$	4100.16			0.428091
$452$	−3775.07	+	3775.07i	−0.392842	+	0.392842i
$453$		0			0
$454$			4528.70i			0.468155i
$455$		0			0
$456$		0			0
$457$	3509.05	+	3509.05i	0.359182	+	0.359182i	0.863511	−	0.504329i	$-0.168260\pi$
$457$	3509.05	+	3509.05i	0.359182	+	0.359182i	−0.504329	+	0.863511i	$0.668260\pi$
$458$	−8914.30	−	8914.30i	−0.909472	−	0.909472i
$459$		0			0
$460$		0			0
$461$			8838.05i			0.892904i	0.894807	+	0.446452i	$0.147313\pi$
$461$			8838.05i			0.892904i	−0.894807	+	0.446452i	$0.852687\pi$
$462$		0			0
$463$	−6343.49	+	6343.49i	−0.636732	+	0.636732i	−0.949748	−	0.313016i	$-0.898661\pi$
$463$	−6343.49	+	6343.49i	−0.636732	+	0.636732i	0.313016	+	0.949748i	$0.398661\pi$
$464$	−2954.33			−0.295585
$465$		0			0
$466$	7585.71			0.754080
$467$	−226.322	+	226.322i	−0.0224260	+	0.0224260i	−0.718231	−	0.695805i	$-0.755048\pi$
$467$	−226.322	+	226.322i	−0.0224260	+	0.0224260i	0.695805	+	0.718231i	$0.255048\pi$
$468$		0			0
$469$		−	4405.48i		−	0.433745i
$470$		0			0
$471$		0			0
$472$	1445.55	+	1445.55i	0.140967	+	0.140967i
$473$	−6764.10	−	6764.10i	−0.657534	−	0.657534i
$474$		0			0
$475$		0			0
$476$			970.065i			0.0934093i
$477$		0			0
$478$	3273.36	−	3273.36i	0.313222	−	0.313222i
$479$	15546.2			1.48293			0.741465	−	0.670991i	$-0.234131\pi$
$479$	15546.2			1.48293			0.741465	+	0.670991i	$0.234131\pi$
$480$		0			0
$481$	−6667.59			−0.632050
$482$	2088.21	−	2088.21i	0.197335	−	0.197335i
$483$		0			0
$484$			11539.9i			1.08377i
$485$		0			0
$486$		0			0
$487$	3464.88	+	3464.88i	0.322399	+	0.322399i	0.849687	−	0.527288i	$-0.176791\pi$
$487$	3464.88	+	3464.88i	0.322399	+	0.322399i	−0.527288	+	0.849687i	$0.676791\pi$
$488$	5057.70	+	5057.70i	0.469162	+	0.469162i
$489$		0			0
$490$		0			0
$491$		−	2614.21i		−	0.240280i	−0.992757	−	0.120140i	$-0.961666\pi$
$491$		−	2614.21i		−	0.240280i	0.992757	−	0.120140i	$-0.0383344\pi$
$492$		0			0
$493$	1021.77	−	1021.77i	0.0933428	−	0.0933428i
$494$	−3843.21			−0.350029
$495$		0			0
$496$	−317.212			−0.0287162
$497$	10773.5	−	10773.5i	0.972353	−	0.972353i
$498$		0			0
$499$		−	3762.23i		−	0.337517i	−0.985657	−	0.168758i	$-0.946024\pi$
$499$		−	3762.23i		−	0.337517i	0.985657	−	0.168758i	$-0.0539757\pi$
$500$		0			0
$501$		0			0
$502$	5687.31	+	5687.31i	0.505652	+	0.505652i
$503$	7204.69	+	7204.69i	0.638651	+	0.638651i	0.950223	−	0.311572i	$-0.100855\pi$
$503$	7204.69	+	7204.69i	0.638651	+	0.638651i	−0.311572	+	0.950223i	$0.600855\pi$
$504$		0			0
$505$		0			0
$506$		−	3636.11i		−	0.319457i
$507$		0			0
$508$	−2143.29	+	2143.29i	−0.187191	+	0.187191i
$509$	15219.2			1.32530			0.662652	−	0.748928i	$-0.269431\pi$
$509$	15219.2			1.32530			0.662652	+	0.748928i	$0.269431\pi$
$510$		0			0
$511$	26461.1			2.29075
$512$	362.039	−	362.039i	0.0312500	−	0.0312500i
$513$		0			0
$514$			1049.86i			0.0900924i
$515$		0			0
$516$		0			0
$517$	−12049.0	−	12049.0i	−1.02498	−	1.02498i
$518$	−15788.4	−	15788.4i	−1.33920	−	1.33920i
$519$		0			0
$520$		0			0
$521$			4041.49i			0.339848i	0.985457	+	0.169924i	$0.0543523\pi$
$521$			4041.49i			0.339848i	−0.985457	+	0.169924i	$0.945648\pi$
$522$		0			0
$523$	−14873.0	+	14873.0i	−1.24350	+	1.24350i	−0.284958	+	0.958540i	$0.591980\pi$
$523$	−14873.0	+	14873.0i	−1.24350	+	1.24350i	−0.958540	+	0.284958i	$0.908020\pi$
$524$	−7408.01			−0.617597
$525$		0			0
$526$	513.091			0.0425320
$527$	109.709	−	109.709i	0.00906829	−	0.00906829i
$528$		0			0
$529$		−	11383.0i		−	0.935563i
$530$		0			0
$531$		0			0
$532$	−9100.48	−	9100.48i	−0.741647	−	0.741647i
$533$	826.410	+	826.410i	0.0671590	+	0.0671590i
$534$		0			0
$535$		0			0
$536$		−	1137.28i		−	0.0916478i
$537$		0			0
$538$	4669.43	−	4669.43i	0.374189	−	0.374189i
$539$	−40084.8			−3.20329
$540$		0			0
$541$	−8356.96			−0.664129			−0.332065	−	0.943257i	$-0.607745\pi$
$541$	−8356.96			−0.664129			−0.332065	+	0.943257i	$0.607745\pi$
$542$	−5507.27	+	5507.27i	−0.436453	+	0.436453i
$543$		0			0
$544$			250.424i			0.0197369i
$545$		0			0
$546$		0			0
$547$	−5395.94	−	5395.94i	−0.421780	−	0.421780i	0.464036	−	0.885816i	$-0.346401\pi$
$547$	−5395.94	−	5395.94i	−0.421780	−	0.421780i	−0.885816	+	0.464036i	$0.846401\pi$
$548$	3555.18	+	3555.18i	0.277135	+	0.277135i
$549$		0			0
$550$		0			0
$551$			19171.0i			1.48224i
$552$		0			0
$553$	15312.3	−	15312.3i	1.17748	−	1.17748i
$554$	4009.37			0.307476
$555$		0			0
$556$	1009.39			0.0769925
$557$	−4120.65	+	4120.65i	−0.313461	+	0.313461i	−0.846249	−	0.532788i	$-0.821144\pi$
$557$	−4120.65	+	4120.65i	−0.313461	+	0.313461i	0.532788	+	0.846249i	$0.321144\pi$
$558$		0			0
$559$		−	2726.68i		−	0.206308i
$560$		0			0
$561$		0			0
$562$	−11482.5	−	11482.5i	−0.861848	−	0.861848i
$563$	−10494.4	−	10494.4i	−0.785590	−	0.785590i	0.195177	−	0.980768i	$-0.437472\pi$
$563$	−10494.4	−	10494.4i	−0.785590	−	0.785590i	−0.980768	+	0.195177i	$0.937472\pi$
$564$		0			0
$565$		0			0
$566$			3300.60i			0.245114i
$567$		0			0
$568$	2781.21	−	2781.21i	0.205453	−	0.205453i
$569$	−25399.7			−1.87137			−0.935687	−	0.352832i	$-0.885219\pi$
$569$	−25399.7			−1.87137			−0.935687	+	0.352832i	$0.885219\pi$
$570$		0			0
$571$	15700.6			1.15070			0.575351	−	0.817907i	$-0.304865\pi$
$571$	15700.6			1.15070			0.575351	+	0.817907i	$0.304865\pi$
$572$	−3399.02	+	3399.02i	−0.248462	+	0.248462i
$573$		0			0
$574$			3913.77i			0.284595i
$575$		0			0
$576$		0			0
$577$	5627.77	+	5627.77i	0.406044	+	0.406044i	0.880356	−	0.474313i	$-0.157303\pi$
$577$	5627.77	+	5627.77i	0.406044	+	0.406044i	−0.474313	+	0.880356i	$0.657303\pi$
$578$	6861.42	+	6861.42i	0.493767	+	0.493767i
$579$		0			0
$580$		0			0
$581$		−	30989.3i		−	2.21282i
$582$		0			0
$583$	16847.9	−	16847.9i	1.19686	−	1.19686i
$584$	6830.99			0.484021
$585$		0			0
$586$	13651.2			0.962333
$587$	−10563.0	+	10563.0i	−0.742731	+	0.742731i	−0.973103	−	0.230372i	$-0.926006\pi$
$587$	−10563.0	+	10563.0i	−0.742731	+	0.742731i	0.230372	+	0.973103i	$0.426006\pi$
$588$		0			0
$589$			2058.42i			0.144000i
$590$		0			0
$591$		0			0
$592$	−4075.82	−	4075.82i	−0.282965	−	0.282965i
$593$	−4080.58	−	4080.58i	−0.282579	−	0.282579i	0.551558	−	0.834137i	$-0.314034\pi$
$593$	−4080.58	−	4080.58i	−0.282579	−	0.282579i	−0.834137	+	0.551558i	$0.814034\pi$
$594$		0			0
$595$		0			0
$596$		−	676.101i		−	0.0464668i
$597$		0			0
$598$	732.879	−	732.879i	0.0501165	−	0.0501165i
$599$	10431.0			0.711515			0.355758	−	0.934578i	$-0.384223\pi$
$599$	10431.0			0.711515			0.355758	+	0.934578i	$0.384223\pi$
$600$		0			0
$601$	−13534.1			−0.918584			−0.459292	−	0.888285i	$-0.651897\pi$
$601$	−13534.1			−0.918584			−0.459292	+	0.888285i	$0.651897\pi$
$602$	6456.61	−	6456.61i	0.437129	−	0.437129i
$603$		0			0
$604$		−	11134.6i		−	0.750100i
$605$		0			0
$606$		0			0
$607$	−8819.49	−	8819.49i	−0.589740	−	0.589740i	0.347821	−	0.937561i	$-0.386922\pi$
$607$	−8819.49	−	8819.49i	−0.589740	−	0.589740i	−0.937561	+	0.347821i	$0.886922\pi$
$608$	−2349.31	−	2349.31i	−0.156706	−	0.156706i
$609$		0			0
$610$		0			0
$611$		−	4857.08i		−	0.321598i
$612$		0			0
$613$	−6914.61	+	6914.61i	−0.455593	+	0.455593i	−0.897206	−	0.441613i	$-0.854406\pi$
$613$	−6914.61	+	6914.61i	−0.455593	+	0.455593i	0.441613	+	0.897206i	$0.354406\pi$
$614$	11771.6			0.773718
$615$		0			0
$616$	−16097.3			−1.05289
$617$	14354.7	−	14354.7i	0.936629	−	0.936629i	−0.0614791	−	0.998108i	$-0.519582\pi$
$617$	14354.7	−	14354.7i	0.936629	−	0.936629i	0.998108	+	0.0614791i	$0.0195818\pi$
$618$		0			0
$619$		−	15236.3i		−	0.989334i	−0.869083	−	0.494667i	$-0.835290\pi$
$619$		−	15236.3i		−	0.989334i	0.869083	−	0.494667i	$-0.164710\pi$
$620$		0			0
$621$		0			0
$622$	5635.08	+	5635.08i	0.363257	+	0.363257i
$623$	−8538.31	−	8538.31i	−0.549085	−	0.549085i
$624$		0			0
$625$		0			0
$626$			6865.00i			0.438308i
$627$		0			0
$628$	−8072.86	+	8072.86i	−0.512965	+	0.512965i
$629$	2819.27			0.178715
$630$		0			0
$631$	2894.27			0.182597			0.0912986	−	0.995824i	$-0.470898\pi$
$631$	2894.27			0.182597			0.0912986	+	0.995824i	$0.470898\pi$
$632$	3952.90	−	3952.90i	0.248794	−	0.248794i
$633$		0			0
$634$		−	20173.9i		−	1.26373i
$635$		0			0
$636$		0			0
$637$	−8079.31	−	8079.31i	−0.502534	−	0.502534i
$638$	16955.3	+	16955.3i	1.05214	+	1.05214i
$639$		0			0
$640$		0			0
$641$		−	345.840i		−	0.0213102i	−0.999943	−	0.0106551i	$-0.996608\pi$
$641$		−	345.840i		−	0.0213102i	0.999943	−	0.0106551i	$-0.00339169\pi$
$642$		0			0
$643$	1161.24	−	1161.24i	0.0712207	−	0.0712207i	−0.670599	−	0.741820i	$-0.733963\pi$
$643$	1161.24	−	1161.24i	0.0712207	−	0.0712207i	0.741820	+	0.670599i	$0.233963\pi$
$644$	3470.82			0.212375
$645$		0			0
$646$	1625.03			0.0989721
$647$	−15317.4	+	15317.4i	−0.930738	+	0.930738i	−0.997752	−	0.0670144i	$-0.978653\pi$
$647$	−15317.4	+	15317.4i	−0.930738	+	0.930738i	0.0670144	+	0.997752i	$0.478653\pi$
$648$		0			0
$649$		−	16592.3i		−	1.00355i
$650$		0			0
$651$		0			0
$652$	8530.76	+	8530.76i	0.512408	+	0.512408i
$653$	9594.72	+	9594.72i	0.574993	+	0.574993i	0.933520	−	0.358527i	$-0.116721\pi$
$653$	9594.72	+	9594.72i	0.574993	+	0.574993i	−0.358527	+	0.933520i	$0.616721\pi$
$654$		0			0
$655$		0			0
$656$			1010.35i			0.0601334i
$657$		0			0
$658$	11501.3	−	11501.3i	0.681408	−	0.681408i
$659$	1554.04			0.0918618			0.0459309	−	0.998945i	$-0.485375\pi$
$659$	1554.04			0.0918618			0.0459309	+	0.998945i	$0.485375\pi$
$660$		0			0
$661$	2698.57			0.158793			0.0793965	−	0.996843i	$-0.474701\pi$
$661$	2698.57			0.158793			0.0793965	+	0.996843i	$0.474701\pi$
$662$	−2536.00	+	2536.00i	−0.148889	+	0.148889i
$663$		0			0
$664$		−	7999.94i		−	0.467557i
$665$		0			0
$666$		0			0
$667$	−3655.80	−	3655.80i	−0.212224	−	0.212224i
$668$	4111.80	+	4111.80i	0.238159	+	0.238159i
$669$		0			0
$670$		0			0
$671$		−	58053.4i		−	3.33998i
$672$		0			0
$673$	8704.87	−	8704.87i	0.498586	−	0.498586i	−0.412412	−	0.910997i	$-0.635314\pi$
$673$	8704.87	−	8704.87i	0.498586	−	0.498586i	0.910997	+	0.412412i	$0.135314\pi$
$674$	−12553.9			−0.717443
$675$		0			0
$676$	7417.82			0.422042
$677$	8512.59	−	8512.59i	0.483258	−	0.483258i	−0.422913	−	0.906170i	$-0.638992\pi$
$677$	8512.59	−	8512.59i	0.483258	−	0.483258i	0.906170	+	0.422913i	$0.138992\pi$
$678$		0			0
$679$		−	1282.24i		−	0.0724708i
$680$		0			0
$681$		0			0
$682$	1820.52	+	1820.52i	0.102216	+	0.102216i
$683$	−4988.15	−	4988.15i	−0.279453	−	0.279453i	0.553438	−	0.832891i	$-0.313316\pi$
$683$	−4988.15	−	4988.15i	−0.279453	−	0.279453i	−0.832891	+	0.553438i	$0.813316\pi$
$684$		0			0
$685$		0			0
$686$		−	17003.8i		−	0.946370i
$687$		0			0
$688$	1666.79	−	1666.79i	0.0923629	−	0.0923629i
$689$	6791.59			0.375528
$690$		0			0
$691$	−24712.4			−1.36050			−0.680250	−	0.732980i	$-0.738129\pi$
$691$	−24712.4			−1.36050			−0.680250	+	0.732980i	$0.738129\pi$
$692$	−3473.07	+	3473.07i	−0.190790	+	0.190790i
$693$		0			0
$694$		−	13207.6i		−	0.722410i
$695$		0			0
$696$		0			0
$697$	−349.432	−	349.432i	−0.0189895	−	0.0189895i
$698$	−1759.31	−	1759.31i	−0.0954026	−	0.0954026i
$699$		0			0
$700$		0			0
$701$			9481.12i			0.510837i	0.966831	+	0.255419i	$0.0822133\pi$
$701$			9481.12i			0.510837i	−0.966831	+	0.255419i	$0.917787\pi$
$702$		0			0
$703$	−26448.4	+	26448.4i	−1.41895	+	1.41895i
$704$	−4155.56			−0.222470
$705$		0			0
$706$	15107.2			0.805334
$707$	−8462.83	+	8462.83i	−0.450180	+	0.450180i
$708$		0			0
$709$			33090.6i			1.75281i	0.481571	+	0.876407i	$0.340066\pi$
$709$			33090.6i			1.75281i	−0.481571	+	0.876407i	$0.659934\pi$
$710$		0			0
$711$		0			0
$712$	−2204.18	−	2204.18i	−0.116019	−	0.116019i
$713$	−392.530	−	392.530i	−0.0206176	−	0.0206176i
$714$		0			0
$715$		0			0
$716$			13792.8i			0.719920i
$717$		0			0
$718$	1471.68	−	1471.68i	0.0764940	−	0.0764940i
$719$	−19996.8			−1.03721			−0.518605	−	0.855014i	$-0.673549\pi$
$719$	−19996.8			−1.03721			−0.518605	+	0.855014i	$0.673549\pi$
$720$		0			0
$721$	34778.6			1.79642
$722$	−5544.83	+	5544.83i	−0.285813	+	0.285813i
$723$		0			0
$724$		−	14047.2i		−	0.721080i
$725$		0			0
$726$		0			0
$727$	−25556.9	−	25556.9i	−1.30379	−	1.30379i	−0.925818	−	0.377969i	$-0.876623\pi$
$727$	−25556.9	−	25556.9i	−1.30379	−	1.30379i	−0.377969	−	0.925818i	$-0.623377\pi$
$728$	−3244.51	−	3244.51i	−0.165178	−	0.165178i
$729$		0			0
$730$		0			0
$731$			1152.93i			0.0583345i
$732$		0			0
$733$	18981.4	−	18981.4i	0.956474	−	0.956474i	−0.0426176	−	0.999091i	$-0.513570\pi$
$733$	18981.4	−	18981.4i	0.956474	−	0.956474i	0.999091	+	0.0426176i	$0.0135697\pi$
$734$	4094.16			0.205883
$735$		0			0
$736$	896.000			0.0448736
$737$	−6527.00	+	6527.00i	−0.326221	+	0.326221i
$738$		0			0
$739$		−	4651.19i		−	0.231525i	−0.993277	−	0.115762i	$-0.963069\pi$
$739$		−	4651.19i		−	0.231525i	0.993277	−	0.115762i	$-0.0369311\pi$
$740$		0			0
$741$		0			0
$742$	16082.1	+	16082.1i	0.795675	+	0.795675i
$743$	−9737.08	−	9737.08i	−0.480779	−	0.480779i	0.424601	−	0.905380i	$-0.360414\pi$
$743$	−9737.08	−	9737.08i	−0.480779	−	0.480779i	−0.905380	+	0.424601i	$0.860414\pi$
$744$		0			0
$745$		0			0
$746$			300.938i			0.0147696i
$747$		0			0
$748$	1437.21	−	1437.21i	0.0702536	−	0.0702536i
$749$	−21978.4			−1.07219
$750$		0			0
$751$	−7800.89			−0.379039			−0.189520	−	0.981877i	$-0.560693\pi$
$751$	−7800.89			−0.379039			−0.189520	+	0.981877i	$0.560693\pi$
$752$	2969.08	−	2969.08i	0.143978	−	0.143978i
$753$		0			0
$754$			6834.85i			0.330120i
$755$		0			0
$756$		0			0
$757$	−1497.47	−	1497.47i	−0.0718974	−	0.0718974i	0.670244	−	0.742141i	$-0.266190\pi$
$757$	−1497.47	−	1497.47i	−0.0718974	−	0.0718974i	−0.742141	+	0.670244i	$0.766190\pi$
$758$	13272.2	+	13272.2i	0.635974	+	0.635974i
$759$		0			0
$760$		0			0
$761$			22037.0i			1.04973i	0.851187	+	0.524863i	$0.175884\pi$
$761$			22037.0i			1.04973i	−0.851187	+	0.524863i	$0.824116\pi$
$762$		0			0
$763$	−19180.2	+	19180.2i	−0.910054	+	0.910054i
$764$	−8149.73			−0.385925
$765$		0			0
$766$	−22672.3			−1.06943
$767$	3344.27	−	3344.27i	0.157437	−	0.157437i
$768$		0			0
$769$		−	6827.73i		−	0.320174i	−0.987103	−	0.160087i	$-0.948822\pi$
$769$		−	6827.73i		−	0.320174i	0.987103	−	0.160087i	$-0.0511775\pi$
$770$		0			0
$771$		0			0
$772$	4511.12	+	4511.12i	0.210309	+	0.210309i
$773$	2717.78	+	2717.78i	0.126457	+	0.126457i	0.767503	−	0.641045i	$-0.221499\pi$
$773$	2717.78	+	2717.78i	0.126457	+	0.126457i	−0.641045	+	0.767503i	$0.721499\pi$
$774$		0			0
$775$		0			0
$776$		−	331.012i		−	0.0153127i
$777$		0			0
$778$	12576.2	−	12576.2i	0.579536	−	0.579536i
$779$	6556.26			0.301544
$780$		0			0
$781$	−31923.4			−1.46262
$782$	−309.884	+	309.884i	−0.0141706	+	0.0141706i
$783$		0			0
$784$		−	9877.58i		−	0.449962i
$785$		0			0
$786$		0			0
$787$	−18023.9	−	18023.9i	−0.816370	−	0.816370i	0.169210	−	0.985580i	$-0.445878\pi$
$787$	−18023.9	−	18023.9i	−0.816370	−	0.816370i	−0.985580	+	0.169210i	$0.945878\pi$
$788$	−1031.24	−	1031.24i	−0.0466198	−	0.0466198i
$789$		0			0
$790$		0			0
$791$			41361.3i			1.85922i
$792$		0			0
$793$	11701.0	−	11701.0i	0.523977	−	0.523977i
$794$	−9188.48			−0.410689
$795$		0			0
$796$	2052.12			0.0913763
$797$	21477.8	−	21477.8i	0.954557	−	0.954557i	−0.0444541	−	0.999011i	$-0.514155\pi$
$797$	21477.8	−	21477.8i	0.954557	−	0.954557i	0.999011	+	0.0444541i	$0.0141549\pi$
$798$		0			0
$799$			2053.73i			0.0909332i
$800$		0			0
$801$		0			0
$802$	−16988.2	−	16988.2i	−0.747971	−	0.747971i
$803$	−39203.8	−	39203.8i	−1.72288	−	1.72288i
$804$		0			0
$805$		0			0
$806$			733.870i			0.0320713i
$807$		0			0
$808$	−2184.70	+	2184.70i	−0.0951205	+	0.0951205i
$809$	36819.3			1.60012			0.800060	−	0.599920i	$-0.204801\pi$
$809$	36819.3			1.60012			0.800060	+	0.599920i	$0.204801\pi$
$810$		0			0
$811$	38040.8			1.64709			0.823546	−	0.567249i	$-0.191992\pi$
$811$	38040.8			1.64709			0.823546	+	0.567249i	$0.191992\pi$
$812$	−16184.5	+	16184.5i	−0.699464	+	0.699464i
$813$		0			0
$814$			46783.1i			2.01443i
$815$		0			0
$816$		0			0
$817$	−10816.0	−	10816.0i	−0.463161	−	0.463161i
$818$	−2419.16	−	2419.16i	−0.103403	−	0.103403i
$819$		0			0
$820$		0			0
$821$			2824.53i			0.120069i	0.998196	+	0.0600346i	$0.0191211\pi$
$821$			2824.53i			0.120069i	−0.998196	+	0.0600346i	$0.980879\pi$
$822$		0			0
$823$	14878.3	−	14878.3i	0.630164	−	0.630164i	−0.317945	−	0.948109i	$-0.602993\pi$
$823$	14878.3	−	14878.3i	0.630164	−	0.630164i	0.948109	+	0.317945i	$0.102993\pi$
$824$	8978.16			0.379574
$825$		0			0
$826$	15838.0			0.667162
$827$	31885.6	−	31885.6i	1.34072	−	1.34072i	0.445369	−	0.895347i	$-0.353072\pi$
$827$	31885.6	−	31885.6i	1.34072	−	1.34072i	0.895347	−	0.445369i	$-0.146928\pi$
$828$		0			0
$829$		−	6395.67i		−	0.267950i	−0.990985	−	0.133975i	$-0.957226\pi$
$829$		−	6395.67i		−	0.267950i	0.990985	−	0.133975i	$-0.0427743\pi$
$830$		0			0
$831$		0			0
$832$	−837.576	−	837.576i	−0.0349011	−	0.0349011i
$833$	3416.19	+	3416.19i	0.142094	+	0.142094i
$834$		0			0
$835$		0			0
$836$			26965.9i			1.11559i
$837$		0			0
$838$	−4109.54	+	4109.54i	−0.169405	+	0.169405i
$839$	−19006.7			−0.782104			−0.391052	−	0.920369i	$-0.627889\pi$
$839$	−19006.7			−0.782104			−0.391052	+	0.920369i	$0.627889\pi$
$840$		0			0
$841$	9705.12			0.397930
$842$	−12816.8	+	12816.8i	−0.524580	+	0.524580i
$843$		0			0
$844$			6440.97i			0.262686i
$845$		0			0
$846$		0			0
$847$	63218.3	+	63218.3i	2.56459	+	2.56459i
$848$	4151.62	+	4151.62i	0.168122	+	0.168122i
$849$		0			0
$850$		0			0
$851$		−	10087.1i		−	0.406325i
$852$		0			0
$853$	−31885.3	+	31885.3i	−1.27987	+	1.27987i	−0.339133	+	0.940738i	$0.610134\pi$
$853$	−31885.3	+	31885.3i	−1.27987	+	1.27987i	−0.940738	+	0.339133i	$0.889866\pi$
$854$	55414.4			2.22042
$855$		0			0
$856$	−5673.76			−0.226548
$857$	14082.6	−	14082.6i	0.561322	−	0.561322i	−0.368361	−	0.929683i	$-0.620081\pi$
$857$	14082.6	−	14082.6i	0.561322	−	0.561322i	0.929683	+	0.368361i	$0.120081\pi$
$858$		0			0
$859$			24821.7i			0.985920i	0.870052	+	0.492960i	$0.164085\pi$
$859$			24821.7i			0.985920i	−0.870052	+	0.492960i	$0.835915\pi$
$860$		0			0
$861$		0			0
$862$	14615.3	+	14615.3i	0.577492	+	0.577492i
$863$	31772.4	+	31772.4i	1.25324	+	1.25324i	0.954260	+	0.298976i	$0.0966452\pi$
$863$	31772.4	+	31772.4i	1.25324	+	1.25324i	0.298976	+	0.954260i	$0.403355\pi$
$864$		0			0
$865$		0			0
$866$		−	8782.76i		−	0.344631i
$867$		0			0
$868$	−1737.76	+	1737.76i	−0.0679532	+	0.0679532i
$869$	−45372.2			−1.77117
$870$		0			0
$871$	−2631.11			−0.102355
$872$	−4951.42	+	4951.42i	−0.192289	+	0.192289i
$873$		0			0
$874$		−	5814.24i		−	0.225023i
$875$		0			0
$876$		0			0
$877$	30277.2	+	30277.2i	1.16578	+	1.16578i	0.983189	+	0.182592i	$0.0584488\pi$
$877$	30277.2	+	30277.2i	1.16578	+	1.16578i	0.182592	+	0.983189i	$0.441551\pi$
$878$	6986.45	+	6986.45i	0.268544	+	0.268544i
$879$		0			0
$880$		0			0
$881$		−	32069.6i		−	1.22639i	−0.789930	−	0.613197i	$-0.789883\pi$
$881$		−	32069.6i		−	1.22639i	0.789930	−	0.613197i	$-0.210117\pi$
$882$		0			0
$883$	−7061.36	+	7061.36i	−0.269121	+	0.269121i	−0.828746	−	0.559625i	$-0.810945\pi$
$883$	−7061.36	+	7061.36i	−0.269121	+	0.269121i	0.559625	+	0.828746i	$0.310945\pi$
$884$	579.356			0.0220428
$885$		0			0
$886$	33476.0			1.26935
$887$	−18324.6	+	18324.6i	−0.693664	+	0.693664i	−0.963036	−	0.269372i	$-0.913184\pi$
$887$	−18324.6	+	18324.6i	−0.693664	+	0.693664i	0.269372	+	0.963036i	$0.413184\pi$
$888$		0			0
$889$			23482.8i			0.885926i
$890$		0			0
$891$		0			0
$892$	−9359.29	−	9359.29i	−0.351314	−	0.351314i
$893$	−19266.7	−	19266.7i	−0.721987	−	0.721987i
$894$		0			0
$895$		0			0
$896$		−	3966.65i		−	0.147898i
$897$		0			0
$898$	4785.77	−	4785.77i	0.177843	−	0.177843i
$899$	3660.75			0.135809
$900$		0			0
$901$	−2871.70			−0.106182
$902$	5798.50	−	5798.50i	0.214045	−	0.214045i
$903$		0			0
$904$			10677.5i			0.392842i
$905$		0			0
$906$		0			0
$907$	18445.0	+	18445.0i	0.675256	+	0.675256i	0.958923	−	0.283667i	$-0.0915511\pi$
$907$	18445.0	+	18445.0i	0.675256	+	0.675256i	−0.283667	+	0.958923i	$0.591551\pi$
$908$	6404.54	+	6404.54i	0.234077	+	0.234077i
$909$		0			0
$910$		0			0
$911$			7421.18i			0.269895i	0.990853	+	0.134948i	$0.0430866\pi$
$911$			7421.18i			0.269895i	−0.990853	+	0.134948i	$0.956913\pi$
$912$		0			0
$913$	−45912.5	+	45912.5i	−1.66427	+	1.66427i
$914$	9925.08			0.359182
$915$		0			0
$916$	−25213.5			−0.909472
$917$	−40582.7	+	40582.7i	−1.46146	+	1.46146i
$918$		0			0
$919$			36117.6i			1.29642i	0.761462	+	0.648209i	$0.224482\pi$
$919$			36117.6i			1.29642i	−0.761462	+	0.648209i	$0.775518\pi$
$920$		0			0
$921$		0			0
$922$	12498.9	+	12498.9i	0.446452	+	0.446452i
$923$	−6434.33	−	6434.33i	−0.229457	−	0.229457i
$924$		0			0
$925$		0			0
$926$			17942.1i			0.636732i
$927$		0			0
$928$	−4178.06	+	4178.06i	−0.147793	+	0.147793i
$929$	11654.8			0.411606			0.205803	−	0.978593i	$-0.434019\pi$
$929$	11654.8			0.411606			0.205803	+	0.978593i	$0.434019\pi$
$930$		0			0
$931$	−64096.7			−2.25637
$932$	10727.8	−	10727.8i	0.377040	−	0.377040i
$933$		0			0
$934$			640.137i			0.0224260i
$935$		0			0
$936$		0			0
$937$	−16788.2	−	16788.2i	−0.585323	−	0.585323i	0.351038	−	0.936361i	$-0.385829\pi$
$937$	−16788.2	−	16788.2i	−0.585323	−	0.585323i	−0.936361	+	0.351038i	$0.885829\pi$
$938$	−6230.30	−	6230.30i	−0.216872	−	0.216872i
$939$		0			0
$940$		0			0
$941$		−	27834.5i		−	0.964271i	−0.876097	−	0.482136i	$-0.839861\pi$
$941$		−	27834.5i		−	0.964271i	0.876097	−	0.482136i	$-0.160139\pi$
$942$		0			0
$943$	−1250.24	+	1250.24i	−0.0431744	+	0.0431744i
$944$	4088.62			0.140967
$945$		0			0
$946$	−19131.8			−0.657534
$947$	4017.43	−	4017.43i	0.137855	−	0.137855i	−0.634812	−	0.772667i	$-0.718922\pi$
$947$	4017.43	−	4017.43i	0.137855	−	0.137855i	0.772667	+	0.634812i	$0.218922\pi$
$948$		0			0
$949$		−	15803.5i		−	0.540572i
$950$		0			0
$951$		0			0
$952$	1371.88	+	1371.88i	0.0467047	+	0.0467047i
$953$	14545.6	+	14545.6i	0.494416	+	0.494416i	0.909694	−	0.415278i	$-0.136316\pi$
$953$	14545.6	+	14545.6i	0.494416	+	0.494416i	−0.415278	+	0.909694i	$0.636316\pi$
$954$		0			0
$955$		0			0
$956$		−	9258.47i		−	0.313222i
$957$		0			0
$958$	21985.6	−	21985.6i	0.741465	−	0.741465i
$959$	38952.1			1.31161
$960$		0			0
$961$	−29397.9			−0.986806
$962$	−9429.40	+	9429.40i	−0.316025	+	0.316025i
$963$		0			0
$964$		−	5906.36i		−	0.197335i
$965$		0			0
$966$		0			0
$967$	24630.8	+	24630.8i	0.819105	+	0.819105i	0.985978	−	0.166874i	$-0.0533672\pi$
$967$	24630.8	+	24630.8i	0.819105	+	0.819105i	−0.166874	+	0.985978i	$0.553367\pi$
$968$	16319.9	+	16319.9i	0.541883	+	0.541883i
$969$		0			0
$970$		0			0
$971$			17813.2i			0.588727i	0.955693	+	0.294364i	$0.0951077\pi$
$971$			17813.2i			0.588727i	−0.955693	+	0.294364i	$0.904892\pi$
$972$		0			0
$973$	5529.68	−	5529.68i	0.182193	−	0.182193i
$974$	9800.15			0.322399
$975$		0			0
$976$	14305.3			0.469162
$977$	2909.26	−	2909.26i	0.0952665	−	0.0952665i	−0.657867	−	0.753134i	$-0.728541\pi$
$977$	2909.26	−	2909.26i	0.0952665	−	0.0952665i	0.753134	+	0.657867i	$0.228541\pi$
$978$		0			0
$979$			25300.1i			0.825939i
$980$		0			0
$981$		0			0
$982$	−3697.05	−	3697.05i	−0.120140	−	0.120140i
$983$	10412.0	+	10412.0i	0.337834	+	0.337834i	0.855552	−	0.517718i	$-0.173218\pi$
$983$	10412.0	+	10412.0i	0.337834	+	0.337834i	−0.517718	+	0.855552i	$0.673218\pi$
$984$		0			0
$985$		0			0
$986$		−	2889.99i		−	0.0933428i
$987$		0			0
$988$	−5435.12	+	5435.12i	−0.175014	+	0.175014i
$989$	4125.09			0.132629
$990$		0			0
$991$	−12712.1			−0.407482			−0.203741	−	0.979025i	$-0.565310\pi$
$991$	−12712.1			−0.407482			−0.203741	+	0.979025i	$0.565310\pi$
$992$	−448.606	+	448.606i	−0.0143581	+	0.0143581i
$993$		0			0
$994$		−	30472.2i		−	0.972353i
$995$		0			0
$996$		0			0
$997$	−7747.71	−	7747.71i	−0.246111	−	0.246111i	0.573262	−	0.819372i	$-0.305678\pi$
$997$	−7747.71	−	7747.71i	−0.246111	−	0.246111i	−0.819372	+	0.573262i	$0.805678\pi$
$998$	−5320.60	−	5320.60i	−0.168758	−	0.168758i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.4.f.e.107.3		8
3.2	odd	2	inner	450.4.f.e.107.1		8
5.2	odd	4		90.4.f.b.53.4	yes	8
5.3	odd	4	inner	450.4.f.e.143.1		8
5.4	even	2		90.4.f.b.17.1	✓	8
15.2	even	4		90.4.f.b.53.1	yes	8
15.8	even	4	inner	450.4.f.e.143.3		8
15.14	odd	2		90.4.f.b.17.4	yes	8
20.7	even	4		720.4.w.c.593.3		8
20.19	odd	2		720.4.w.c.17.2		8
60.47	odd	4		720.4.w.c.593.2		8
60.59	even	2		720.4.w.c.17.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.4.f.b.17.1	✓	8	5.4	even	2
90.4.f.b.17.4	yes	8	15.14	odd	2
90.4.f.b.53.1	yes	8	15.2	even	4
90.4.f.b.53.4	yes	8	5.2	odd	4
450.4.f.e.107.1		8	3.2	odd	2	inner
450.4.f.e.107.3		8	1.1	even	1	trivial
450.4.f.e.143.1		8	5.3	odd	4	inner
450.4.f.e.143.3		8	15.8	even	4	inner
720.4.w.c.17.2		8	20.19	odd	2
720.4.w.c.17.3		8	60.59	even	2
720.4.w.c.593.2		8	60.47	odd	4
720.4.w.c.593.3		8	20.7	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)

\(f(q)\)	\(=\)	\(q+(1.41421 - 1.41421i) q^{2} -4.00000i q^{4} +(-21.9129 - 21.9129i) q^{7} +(-5.65685 - 5.65685i) q^{8} +O(q^{10})\)	\(q+(1.41421 - 1.41421i) q^{2} -4.00000i q^{4} +(-21.9129 - 21.9129i) q^{7} +(-5.65685 - 5.65685i) q^{8} +64.9306i q^{11} +(-13.0871 + 13.0871i) q^{13} -61.9790 q^{14} -16.0000 q^{16} +(5.53365 - 5.53365i) q^{17} +103.826i q^{19} +(91.8258 + 91.8258i) q^{22} +(-19.7990 - 19.7990i) q^{23} +37.0160i q^{26} +(-87.6515 + 87.6515i) q^{28} +184.646 q^{29} +19.8258 q^{31} +(-22.6274 + 22.6274i) q^{32} -15.6515i q^{34} +(254.739 + 254.739i) q^{37} +(146.832 + 146.832i) q^{38} -63.1468i q^{41} +(-104.174 + 104.174i) q^{43} +259.722 q^{44} -56.0000 q^{46} +(-185.567 + 185.567i) q^{47} +617.348i q^{49} +(52.3485 + 52.3485i) q^{52} +(-259.476 - 259.476i) q^{53} +247.916i q^{56} +(261.129 - 261.129i) q^{58} -255.539 q^{59} -894.083 q^{61} +(28.0379 - 28.0379i) q^{62} +64.0000i q^{64} +(100.523 + 100.523i) q^{67} +(-22.1346 - 22.1346i) q^{68} +491.653i q^{71} +(-603.780 + 603.780i) q^{73} +720.510 q^{74} +415.303 q^{76} +(1422.82 - 1422.82i) q^{77} +698.780i q^{79} +(-89.3030 - 89.3030i) q^{82} +(707.101 + 707.101i) q^{83} +294.649i q^{86} +(367.303 - 367.303i) q^{88} +389.648 q^{89} +573.553 q^{91} +(-79.1960 + 79.1960i) q^{92} +524.864i q^{94} +(29.2576 + 29.2576i) q^{97} +(873.063 + 873.063i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{7}+O(q^{10}) \) 8 * q + 8 * q^7	\( 8 q + 8 q^{7} - 288 q^{13} - 128 q^{16} + 368 q^{22} + 32 q^{28} - 208 q^{31} + 1488 q^{37} - 1200 q^{43} - 448 q^{46} + 1152 q^{52} + 256 q^{58} - 3120 q^{61} + 1904 q^{67} - 2264 q^{73} + 1856 q^{76} + 752 q^{82} + 1472 q^{88} - 8976 q^{91} - 3432 q^{97}+O(q^{100}) \) 8 * q + 8 * q^7 - 288 * q^13 - 128 * q^16 + 368 * q^22 + 32 * q^28 - 208 * q^31 + 1488 * q^37 - 1200 * q^43 - 448 * q^46 + 1152 * q^52 + 256 * q^58 - 3120 * q^61 + 1904 * q^67 - 2264 * q^73 + 1856 * q^76 + 752 * q^82 + 1472 * q^88 - 8976 * q^91 - 3432 * q^97

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