LMFDB - Embedded newform 225.3.g.a.118.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,3,Mod(82,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("225.82");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.g (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:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.1
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	225.118
Dual form			225.3.g.a.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22474 + 2.22474i) q^{2} -5.89898i q^{4} +(1.44949 - 1.44949i) q^{7} +(4.22474 + 4.22474i) q^{8} +O(q^{10})$	\(q+(-2.22474 + 2.22474i) q^{2} -5.89898i q^{4} +(1.44949 - 1.44949i) q^{7} +(4.22474 + 4.22474i) q^{8} +3.34847 q^{11} +(10.4495 + 10.4495i) q^{13} +6.44949i q^{14} +4.79796 q^{16} +(-2.65153 + 2.65153i) q^{17} +20.6969i q^{19} +(-7.44949 + 7.44949i) q^{22} +(16.4495 + 16.4495i) q^{23} -46.4949 q^{26} +(-8.55051 - 8.55051i) q^{28} +0.853572i q^{29} -18.6969 q^{31} +(-27.5732 + 27.5732i) q^{32} -11.7980i q^{34} +(-38.0454 + 38.0454i) q^{37} +(-46.0454 - 46.0454i) q^{38} +28.6969 q^{41} +(-22.4949 - 22.4949i) q^{43} -19.7526i q^{44} -73.1918 q^{46} +(19.7526 - 19.7526i) q^{47} +44.7980i q^{49} +(61.6413 - 61.6413i) q^{52} +(28.6969 + 28.6969i) q^{53} +12.2474 q^{56} +(-1.89898 - 1.89898i) q^{58} +111.934i q^{59} +94.0908 q^{61} +(41.5959 - 41.5959i) q^{62} -103.495i q^{64} +(54.8990 - 54.8990i) q^{67} +(15.6413 + 15.6413i) q^{68} +68.0000 q^{71} +(39.7878 + 39.7878i) q^{73} -169.283i q^{74} +122.091 q^{76} +(4.85357 - 4.85357i) q^{77} -24.4949i q^{79} +(-63.8434 + 63.8434i) q^{82} +(-21.1464 - 21.1464i) q^{83} +100.091 q^{86} +(14.1464 + 14.1464i) q^{88} -94.1816i q^{89} +30.2929 q^{91} +(97.0352 - 97.0352i) q^{92} +87.8888i q^{94} +(-14.5959 + 14.5959i) q^{97} +(-99.6640 - 99.6640i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{7} + 12 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^7 + 12 * q^8	$ 4 q - 4 q^{2} - 4 q^{7} + 12 q^{8} - 16 q^{11} + 32 q^{13} - 20 q^{16} - 40 q^{17} - 20 q^{22} + 56 q^{23} - 88 q^{26} - 44 q^{28} - 16 q^{31} - 76 q^{32} - 64 q^{37} - 96 q^{38} + 56 q^{41} + 8 q^{43} - 136 q^{46} + 128 q^{47} + 80 q^{52} + 56 q^{53} + 12 q^{58} + 200 q^{61} + 88 q^{62} + 200 q^{67} - 104 q^{68} + 272 q^{71} - 76 q^{73} + 312 q^{76} + 88 q^{77} - 128 q^{82} - 16 q^{83} + 224 q^{86} - 12 q^{88} - 16 q^{91} + 104 q^{92} + 20 q^{97} - 188 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^7 + 12 * q^8 - 16 * q^11 + 32 * q^13 - 20 * q^16 - 40 * q^17 - 20 * q^22 + 56 * q^23 - 88 * q^26 - 44 * q^28 - 16 * q^31 - 76 * q^32 - 64 * q^37 - 96 * q^38 + 56 * q^41 + 8 * q^43 - 136 * q^46 + 128 * q^47 + 80 * q^52 + 56 * q^53 + 12 * q^58 + 200 * q^61 + 88 * q^62 + 200 * q^67 - 104 * q^68 + 272 * q^71 - 76 * q^73 + 312 * q^76 + 88 * q^77 - 128 * q^82 - 16 * q^83 + 224 * q^86 - 12 * q^88 - 16 * q^91 + 104 * q^92 + 20 * q^97 - 188 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−2.22474	+	2.22474i	−1.11237	+	1.11237i	−0.119543	+	0.992829i	$0.538143\pi$
$2$	−2.22474	+	2.22474i	−1.11237	+	1.11237i	−0.992829	+	0.119543i	$0.961857\pi$
$3$		0			0
$3$		0			0
$4$		−	5.89898i		−	1.47474i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.44949	−	1.44949i	0.207070	−	0.207070i	−0.595951	−	0.803021i	$-0.703225\pi$
$7$	1.44949	−	1.44949i	0.207070	−	0.207070i	0.803021	+	0.595951i	$0.203225\pi$
$8$	4.22474	+	4.22474i	0.528093	+	0.528093i
$9$		0			0
$10$		0			0
$11$	3.34847			0.304406			0.152203	−	0.988349i	$-0.451363\pi$
$11$	3.34847			0.304406			0.152203	+	0.988349i	$0.451363\pi$
$12$		0			0
$13$	10.4495	+	10.4495i	0.803807	+	0.803807i	0.983688	−	0.179881i	$-0.0575714\pi$
$13$	10.4495	+	10.4495i	0.803807	+	0.803807i	−0.179881	+	0.983688i	$0.557571\pi$
$14$			6.44949i			0.460678i
$15$		0			0
$16$	4.79796			0.299872
$17$	−2.65153	+	2.65153i	−0.155972	+	0.155972i	−0.780779	−	0.624807i	$-0.785178\pi$
$17$	−2.65153	+	2.65153i	−0.155972	+	0.155972i	0.624807	+	0.780779i	$0.285178\pi$
$18$		0			0
$19$			20.6969i			1.08931i	0.838659	+	0.544656i	$0.183340\pi$
$19$			20.6969i			1.08931i	−0.838659	+	0.544656i	$0.816660\pi$
$20$		0			0
$21$		0			0
$22$	−7.44949	+	7.44949i	−0.338613	+	0.338613i
$23$	16.4495	+	16.4495i	0.715195	+	0.715195i	0.967617	−	0.252422i	$-0.0812271\pi$
$23$	16.4495	+	16.4495i	0.715195	+	0.715195i	−0.252422	+	0.967617i	$0.581227\pi$
$24$		0			0
$25$		0			0
$26$	−46.4949			−1.78827
$27$		0			0
$28$	−8.55051	−	8.55051i	−0.305375	−	0.305375i
$29$			0.853572i			0.0294335i	0.999892	+	0.0147168i	$0.00468466\pi$
$29$			0.853572i			0.0294335i	−0.999892	+	0.0147168i	$0.995315\pi$
$30$		0			0
$31$	−18.6969			−0.603127			−0.301564	−	0.953446i	$-0.597509\pi$
$31$	−18.6969			−0.603127			−0.301564	+	0.953446i	$0.597509\pi$
$32$	−27.5732	+	27.5732i	−0.861663	+	0.861663i
$33$		0			0
$34$		−	11.7980i		−	0.346999i
$35$		0			0
$36$		0			0
$37$	−38.0454	+	38.0454i	−1.02825	+	1.02825i	−0.0286652	+	0.999589i	$0.509126\pi$
$37$	−38.0454	+	38.0454i	−1.02825	+	1.02825i	−0.999589	+	0.0286652i	$0.990874\pi$
$38$	−46.0454	−	46.0454i	−1.21172	−	1.21172i
$39$		0			0
$40$		0			0
$41$	28.6969			0.699925			0.349963	−	0.936764i	$-0.386194\pi$
$41$	28.6969			0.699925			0.349963	+	0.936764i	$0.386194\pi$
$42$		0			0
$43$	−22.4949	−	22.4949i	−0.523137	−	0.523137i	0.395380	−	0.918517i	$-0.370613\pi$
$43$	−22.4949	−	22.4949i	−0.523137	−	0.523137i	−0.918517	+	0.395380i	$0.870613\pi$
$44$		−	19.7526i		−	0.448922i
$45$		0			0
$46$	−73.1918			−1.59113
$47$	19.7526	−	19.7526i	0.420267	−	0.420267i	−0.465029	−	0.885296i	$-0.653956\pi$
$47$	19.7526	−	19.7526i	0.420267	−	0.420267i	0.885296	+	0.465029i	$0.153956\pi$
$48$		0			0
$49$			44.7980i			0.914244i
$50$		0			0
$51$		0			0
$52$	61.6413	−	61.6413i	1.18541	−	1.18541i
$53$	28.6969	+	28.6969i	0.541452	+	0.541452i	0.923954	−	0.382503i	$-0.124938\pi$
$53$	28.6969	+	28.6969i	0.541452	+	0.541452i	−0.382503	+	0.923954i	$0.624938\pi$
$54$		0			0
$55$		0			0
$56$	12.2474			0.218704
$57$		0			0
$58$	−1.89898	−	1.89898i	−0.0327410	−	0.0327410i
$59$			111.934i			1.89719i	0.316493	+	0.948595i	$0.397495\pi$
$59$			111.934i			1.89719i	−0.316493	+	0.948595i	$0.602505\pi$
$60$		0			0
$61$	94.0908			1.54247			0.771236	−	0.636549i	$-0.219639\pi$
$61$	94.0908			1.54247			0.771236	+	0.636549i	$0.219639\pi$
$62$	41.5959	−	41.5959i	0.670902	−	0.670902i
$63$		0			0
$64$		−	103.495i		−	1.61711i
$65$		0			0
$66$		0			0
$67$	54.8990	−	54.8990i	0.819388	−	0.819388i	−0.166631	−	0.986019i	$-0.553289\pi$
$67$	54.8990	−	54.8990i	0.819388	−	0.819388i	0.986019	+	0.166631i	$0.0532890\pi$
$68$	15.6413	+	15.6413i	0.230019	+	0.230019i
$69$		0			0
$70$		0			0
$71$	68.0000			0.957746			0.478873	−	0.877884i	$-0.341045\pi$
$71$	68.0000			0.957746			0.478873	+	0.877884i	$0.341045\pi$
$72$		0			0
$73$	39.7878	+	39.7878i	0.545038	+	0.545038i	0.925001	−	0.379964i	$-0.124064\pi$
$73$	39.7878	+	39.7878i	0.545038	+	0.545038i	−0.379964	+	0.925001i	$0.624064\pi$
$74$		−	169.283i		−	2.28760i
$75$		0			0
$76$	122.091			1.60646
$77$	4.85357	−	4.85357i	0.0630334	−	0.0630334i
$78$		0			0
$79$		−	24.4949i		−	0.310062i	−0.987910	−	0.155031i	$-0.950452\pi$
$79$		−	24.4949i		−	0.310062i	0.987910	−	0.155031i	$-0.0495477\pi$
$80$		0			0
$81$		0			0
$82$	−63.8434	+	63.8434i	−0.778578	+	0.778578i
$83$	−21.1464	−	21.1464i	−0.254776	−	0.254776i	0.568149	−	0.822926i	$-0.307660\pi$
$83$	−21.1464	−	21.1464i	−0.254776	−	0.254776i	−0.822926	+	0.568149i	$0.807660\pi$
$84$		0			0
$85$		0			0
$86$	100.091			1.16385
$87$		0			0
$88$	14.1464	+	14.1464i	0.160755	+	0.160755i
$89$		−	94.1816i		−	1.05822i	−0.848553	−	0.529110i	$-0.822526\pi$
$89$		−	94.1816i		−	1.05822i	0.848553	−	0.529110i	$-0.177474\pi$
$90$		0			0
$91$	30.2929			0.332889
$92$	97.0352	−	97.0352i	1.05473	−	1.05473i
$93$		0			0
$94$			87.8888i			0.934987i
$95$		0			0
$96$		0			0
$97$	−14.5959	+	14.5959i	−0.150473	+	0.150473i	−0.778329	−	0.627856i	$-0.783933\pi$
$97$	−14.5959	+	14.5959i	−0.150473	+	0.150473i	0.627856	+	0.778329i	$0.283933\pi$
$98$	−99.6640	−	99.6640i	−1.01698	−	1.01698i
$99$		0			0
$100$		0			0
$101$	−173.621			−1.71902			−0.859509	−	0.511120i	$-0.829231\pi$
$101$	−173.621			−1.71902			−0.859509	+	0.511120i	$0.829231\pi$
$102$		0			0
$103$	64.7526	+	64.7526i	0.628666	+	0.628666i	0.947732	−	0.319067i	$-0.103369\pi$
$103$	64.7526	+	64.7526i	0.628666	+	0.628666i	−0.319067	+	0.947732i	$0.603369\pi$
$104$			88.2929i			0.848970i
$105$		0			0
$106$	−127.687			−1.20459
$107$	−4.74235	+	4.74235i	−0.0443210	+	0.0443210i	−0.728920	−	0.684599i	$-0.759977\pi$
$107$	−4.74235	+	4.74235i	−0.0443210	+	0.0443210i	0.684599	+	0.728920i	$0.259977\pi$
$108$		0			0
$109$		−	39.3031i		−	0.360579i	−0.983614	−	0.180289i	$-0.942297\pi$
$109$		−	39.3031i		−	0.360579i	0.983614	−	0.180289i	$-0.0577034\pi$
$110$		0			0
$111$		0			0
$112$	6.95459	−	6.95459i	0.0620946	−	0.0620946i
$113$	14.3587	+	14.3587i	0.127068	+	0.127068i	0.767781	−	0.640713i	$-0.221361\pi$
$113$	14.3587	+	14.3587i	0.127068	+	0.127068i	−0.640713	+	0.767781i	$0.721361\pi$
$114$		0			0
$115$		0			0
$116$	5.03520			0.0434069
$117$		0			0
$118$	−249.025	−	249.025i	−2.11038	−	2.11038i
$119$			7.68673i			0.0645944i
$120$		0			0
$121$	−109.788			−0.907337
$122$	−209.328	+	209.328i	−1.71580	+	1.71580i
$123$		0			0
$124$			110.293i			0.889459i
$125$		0			0
$126$		0			0
$127$	114.621	−	114.621i	0.902527	−	0.902527i	−0.0931273	−	0.995654i	$-0.529686\pi$
$127$	114.621	−	114.621i	0.902527	−	0.902527i	0.995654	+	0.0931273i	$0.0296864\pi$
$128$	119.957	+	119.957i	0.937163	+	0.937163i
$129$		0			0
$130$		0			0
$131$	26.1362			0.199513			0.0997566	−	0.995012i	$-0.468194\pi$
$131$	26.1362			0.199513			0.0997566	+	0.995012i	$0.468194\pi$
$132$		0			0
$133$	30.0000	+	30.0000i	0.225564	+	0.225564i
$134$			244.272i			1.82293i
$135$		0			0
$136$	−22.4041			−0.164736
$137$	14.6311	−	14.6311i	0.106796	−	0.106796i	−0.651689	−	0.758486i	$-0.725939\pi$
$137$	14.6311	−	14.6311i	0.106796	−	0.106796i	0.758486	+	0.651689i	$0.225939\pi$
$138$		0			0
$139$		−	83.1714i		−	0.598356i	−0.954197	−	0.299178i	$-0.903288\pi$
$139$		−	83.1714i		−	0.598356i	0.954197	−	0.299178i	$-0.0967124\pi$
$140$		0			0
$141$		0			0
$142$	−151.283	+	151.283i	−1.06537	+	1.06537i
$143$	34.9898	+	34.9898i	0.244684	+	0.244684i
$144$		0			0
$145$		0			0
$146$	−177.035			−1.21257
$147$		0			0
$148$	224.429	+	224.429i	1.51641	+	1.51641i
$149$			119.146i			0.799640i	0.916594	+	0.399820i	$0.130927\pi$
$149$			119.146i			0.799640i	−0.916594	+	0.399820i	$0.869073\pi$
$150$		0			0
$151$	−144.969			−0.960062			−0.480031	−	0.877251i	$-0.659375\pi$
$151$	−144.969			−0.960062			−0.480031	+	0.877251i	$0.659375\pi$
$152$	−87.4393	+	87.4393i	−0.575258	+	0.575258i
$153$		0			0
$154$			21.5959i			0.140233i
$155$		0			0
$156$		0			0
$157$	−51.1464	+	51.1464i	−0.325773	+	0.325773i	−0.850977	−	0.525203i	$-0.823989\pi$
$157$	−51.1464	+	51.1464i	−0.325773	+	0.325773i	0.525203	+	0.850977i	$0.323989\pi$
$158$	54.4949	+	54.4949i	0.344904	+	0.344904i
$159$		0			0
$160$		0			0
$161$	47.6867			0.296191
$162$		0			0
$163$	−189.394	−	189.394i	−1.16193	−	1.16193i	−0.984054	−	0.177872i	$-0.943079\pi$
$163$	−189.394	−	189.394i	−1.16193	−	1.16193i	−0.177872	−	0.984054i	$-0.556921\pi$
$164$		−	169.283i		−	1.03221i
$165$		0			0
$166$	94.0908			0.566812
$167$	97.0352	−	97.0352i	0.581049	−	0.581049i	−0.354142	−	0.935192i	$-0.615227\pi$
$167$	97.0352	−	97.0352i	0.581049	−	0.581049i	0.935192	+	0.354142i	$0.115227\pi$
$168$		0			0
$169$			49.3837i			0.292211i
$170$		0			0
$171$		0			0
$172$	−132.697	+	132.697i	−0.771494	+	0.771494i
$173$	−34.6311	−	34.6311i	−0.200180	−	0.200180i	0.599897	−	0.800077i	$-0.295208\pi$
$173$	−34.6311	−	34.6311i	−0.200180	−	0.200180i	−0.800077	+	0.599897i	$0.795208\pi$
$174$		0			0
$175$		0			0
$176$	16.0658			0.0912831
$177$		0			0
$178$	209.530	+	209.530i	1.17714	+	1.17714i
$179$		−	183.712i		−	1.02632i	−0.858292	−	0.513161i	$-0.828474\pi$
$179$		−	183.712i		−	1.02632i	0.858292	−	0.513161i	$-0.171526\pi$
$180$		0			0
$181$	−21.7276			−0.120042			−0.0600209	−	0.998197i	$-0.519117\pi$
$181$	−21.7276			−0.120042			−0.0600209	+	0.998197i	$0.519117\pi$
$182$	−67.3939	+	67.3939i	−0.370296	+	0.370296i
$183$		0			0
$184$			138.990i			0.755379i
$185$		0			0
$186$		0			0
$187$	−8.87857	+	8.87857i	−0.0474790	+	0.0474790i
$188$	−116.520	−	116.520i	−0.619787	−	0.619787i
$189$		0			0
$190$		0			0
$191$	40.0908			0.209900			0.104950	−	0.994478i	$-0.466532\pi$
$191$	40.0908			0.209900			0.104950	+	0.994478i	$0.466532\pi$
$192$		0			0
$193$	−77.5653	−	77.5653i	−0.401893	−	0.401893i	0.477007	−	0.878900i	$-0.341722\pi$
$193$	−77.5653	−	77.5653i	−0.401893	−	0.401893i	−0.878900	+	0.477007i	$0.841722\pi$
$194$		−	64.9444i		−	0.334765i
$195$		0			0
$196$	264.262			1.34828
$197$	−67.3031	+	67.3031i	−0.341640	+	0.341640i	−0.856984	−	0.515344i	$-0.827664\pi$
$197$	−67.3031	+	67.3031i	−0.341640	+	0.341640i	0.515344	+	0.856984i	$0.327664\pi$
$198$		0			0
$199$		−	251.394i		−	1.26329i	−0.775259	−	0.631643i	$-0.782381\pi$
$199$		−	251.394i		−	1.26329i	0.775259	−	0.631643i	$-0.217619\pi$
$200$		0			0
$201$		0			0
$202$	386.262	−	386.262i	1.91219	−	1.91219i
$203$	1.23724	+	1.23724i	0.00609480	+	0.00609480i
$204$		0			0
$205$		0			0
$206$	−288.116			−1.39862
$207$		0			0
$208$	50.1362	+	50.1362i	0.241040	+	0.241040i
$209$			69.3031i			0.331594i
$210$		0			0
$211$	264.788			1.25492			0.627459	−	0.778649i	$-0.284095\pi$
$211$	264.788			1.25492			0.627459	+	0.778649i	$0.284095\pi$
$212$	169.283	−	169.283i	0.798503	−	0.798503i
$213$		0			0
$214$		−	21.1010i		−	0.0986029i
$215$		0			0
$216$		0			0
$217$	−27.1010	+	27.1010i	−0.124889	+	0.124889i
$218$	87.4393	+	87.4393i	0.401098	+	0.401098i
$219$		0			0
$220$		0			0
$221$	−55.4143			−0.250743
$222$		0			0
$223$	33.4291	+	33.4291i	0.149906	+	0.149906i	0.778076	−	0.628170i	$-0.216196\pi$
$223$	33.4291	+	33.4291i	0.149906	+	0.149906i	−0.628170	+	0.778076i	$0.716196\pi$
$224$			79.9342i			0.356849i
$225$		0			0
$226$	−63.8888			−0.282694
$227$	−21.1714	+	21.1714i	−0.0932662	+	0.0932662i	−0.752200	−	0.658934i	$-0.771008\pi$
$227$	−21.1714	+	21.1714i	−0.0932662	+	0.0932662i	0.658934	+	0.752200i	$0.271008\pi$
$228$		0			0
$229$			243.798i			1.06462i	0.846550	+	0.532310i	$0.178676\pi$
$229$			243.798i			1.06462i	−0.846550	+	0.532310i	$0.821324\pi$
$230$		0			0
$231$		0			0
$232$	−3.60612	+	3.60612i	−0.0155436	+	0.0155436i
$233$	161.712	+	161.712i	0.694042	+	0.694042i	0.963119	−	0.269077i	$-0.0867186\pi$
$233$	161.712	+	161.712i	0.694042	+	0.694042i	−0.269077	+	0.963119i	$0.586719\pi$
$234$		0			0
$235$		0			0
$236$	660.297			2.79787
$237$		0			0
$238$	−17.1010	−	17.1010i	−0.0718530	−	0.0718530i
$239$		−	326.202i		−	1.36486i	−0.730950	−	0.682431i	$-0.760923\pi$
$239$		−	326.202i		−	1.36486i	0.730950	−	0.682431i	$-0.239077\pi$
$240$		0			0
$241$	−133.576			−0.554255			−0.277128	−	0.960833i	$-0.589382\pi$
$241$	−133.576			−0.554255			−0.277128	+	0.960833i	$0.589382\pi$
$242$	244.250	−	244.250i	1.00930	−	1.00930i
$243$		0			0
$244$		−	555.040i		−	2.27475i
$245$		0			0
$246$		0			0
$247$	−216.272	+	216.272i	−0.875597	+	0.875597i
$248$	−78.9898	−	78.9898i	−0.318507	−	0.318507i
$249$		0			0
$250$		0			0
$251$	404.742			1.61252			0.806260	−	0.591562i	$-0.201488\pi$
$251$	404.742			1.61252			0.806260	+	0.591562i	$0.201488\pi$
$252$		0			0
$253$	55.0806	+	55.0806i	0.217710	+	0.217710i
$254$			510.005i			2.00789i
$255$		0			0
$256$	−119.767			−0.467841
$257$	−89.2372	+	89.2372i	−0.347227	+	0.347227i	−0.859076	−	0.511849i	$-0.828961\pi$
$257$	−89.2372	+	89.2372i	−0.347227	+	0.347227i	0.511849	+	0.859076i	$0.328961\pi$
$258$		0			0
$259$			110.293i			0.425841i
$260$		0			0
$261$		0			0
$262$	−58.1464	+	58.1464i	−0.221933	+	0.221933i
$263$	−341.843	−	341.843i	−1.29978	−	1.29978i	−0.928532	−	0.371253i	$-0.878928\pi$
$263$	−341.843	−	341.843i	−1.29978	−	1.29978i	−0.371253	−	0.928532i	$-0.621072\pi$
$264$		0			0
$265$		0			0
$266$	−133.485			−0.501822
$267$		0			0
$268$	−323.848	−	323.848i	−1.20839	−	1.20839i
$269$		−	3.50052i		−	0.0130131i	−0.999979	−	0.00650653i	$-0.997929\pi$
$269$		−	3.50052i		−	0.0130131i	0.999979	−	0.00650653i	$-0.00207111\pi$
$270$		0			0
$271$	−103.576			−0.382197			−0.191099	−	0.981571i	$-0.561205\pi$
$271$	−103.576			−0.382197			−0.191099	+	0.981571i	$0.561205\pi$
$272$	−12.7219	+	12.7219i	−0.0467718	+	0.0467718i
$273$		0			0
$274$			65.1010i			0.237595i
$275$		0			0
$276$		0			0
$277$	285.510	−	285.510i	1.03072	−	1.03072i	0.0312080	−	0.999513i	$-0.490065\pi$
$277$	285.510	−	285.510i	1.03072	−	1.03072i	0.999513	−	0.0312080i	$-0.00993542\pi$
$278$	185.035	+	185.035i	0.665594	+	0.665594i
$279$		0			0
$280$		0			0
$281$	−372.697			−1.32632			−0.663162	−	0.748476i	$-0.730786\pi$
$281$	−372.697			−1.32632			−0.663162	+	0.748476i	$0.730786\pi$
$282$		0			0
$283$	77.1918	+	77.1918i	0.272763	+	0.272763i	0.830211	−	0.557449i	$-0.188220\pi$
$283$	77.1918	+	77.1918i	0.272763	+	0.272763i	−0.557449	+	0.830211i	$0.688220\pi$
$284$		−	401.131i		−	1.41243i
$285$		0			0
$286$	−155.687			−0.544359
$287$	41.5959	−	41.5959i	0.144934	−	0.144934i
$288$		0			0
$289$			274.939i			0.951345i
$290$		0			0
$291$		0			0
$292$	234.707	−	234.707i	0.803792	−	0.803792i
$293$	−236.565	−	236.565i	−0.807390	−	0.807390i	0.176848	−	0.984238i	$-0.443410\pi$
$293$	−236.565	−	236.565i	−0.807390	−	0.807390i	−0.984238	+	0.176848i	$0.943410\pi$
$294$		0			0
$295$		0			0
$296$	−321.464			−1.08603
$297$		0			0
$298$	−265.070	−	265.070i	−0.889498	−	0.889498i
$299$			343.778i			1.14976i
$300$		0			0
$301$	−65.2122			−0.216652
$302$	322.520	−	322.520i	1.06795	−	1.06795i
$303$		0			0
$304$			99.3031i			0.326655i
$305$		0			0
$306$		0			0
$307$	−168.969	+	168.969i	−0.550389	+	0.550389i	−0.926553	−	0.376164i	$-0.877243\pi$
$307$	−168.969	+	168.969i	−0.550389	+	0.550389i	0.376164	+	0.926553i	$0.377243\pi$
$308$	−28.6311	−	28.6311i	−0.0929582	−	0.0929582i
$309$		0			0
$310$		0			0
$311$	−354.302			−1.13923			−0.569617	−	0.821910i	$-0.692909\pi$
$311$	−354.302			−1.13923			−0.569617	+	0.821910i	$0.692909\pi$
$312$		0			0
$313$	−152.373	−	152.373i	−0.486816	−	0.486816i	0.420484	−	0.907300i	$-0.361860\pi$
$313$	−152.373	−	152.373i	−0.486816	−	0.486816i	−0.907300	+	0.420484i	$0.861860\pi$
$314$		−	227.576i		−	0.724763i
$315$		0			0
$316$	−144.495			−0.457262
$317$	−427.217	+	427.217i	−1.34769	+	1.34769i	−0.459519	+	0.888168i	$0.651978\pi$
$317$	−427.217	+	427.217i	−1.34769	+	1.34769i	−0.888168	+	0.459519i	$0.848022\pi$
$318$		0			0
$319$			2.85816i			0.00895975i
$320$		0			0
$321$		0			0
$322$	−106.091	+	106.091i	−0.329475	+	0.329475i
$323$	−54.8786	−	54.8786i	−0.169903	−	0.169903i
$324$		0			0
$325$		0			0
$326$	842.706			2.58499
$327$		0			0
$328$	121.237	+	121.237i	0.369626	+	0.369626i
$329$		−	57.2622i		−	0.174049i
$330$		0			0
$331$	489.423			1.47862			0.739310	−	0.673365i	$-0.235152\pi$
$331$	489.423			1.47862			0.739310	+	0.673365i	$0.235152\pi$
$332$	−124.742	+	124.742i	−0.375730	+	0.375730i
$333$		0			0
$334$			431.757i			1.29269i
$335$		0			0
$336$		0			0
$337$	−292.192	+	292.192i	−0.867038	+	0.867038i	−0.992143	−	0.125105i	$-0.960073\pi$
$337$	−292.192	+	292.192i	−0.867038	+	0.867038i	0.125105	+	0.992143i	$0.460073\pi$
$338$	−109.866	−	109.866i	−0.325048	−	0.325048i
$339$		0			0
$340$		0			0
$341$	−62.6061			−0.183596
$342$		0			0
$343$	135.959	+	135.959i	0.396382	+	0.396382i
$344$		−	190.070i		−	0.552530i
$345$		0			0
$346$	154.091			0.445349
$347$	320.050	−	320.050i	0.922334	−	0.922334i	−0.0748598	−	0.997194i	$-0.523851\pi$
$347$	320.050	−	320.050i	0.922334	−	0.922334i	0.997194	+	0.0748598i	$0.0238509\pi$
$348$		0			0
$349$		−	574.009i		−	1.64473i	−0.568964	−	0.822363i	$-0.692655\pi$
$349$		−	574.009i		−	1.64473i	0.568964	−	0.822363i	$-0.307345\pi$
$350$		0			0
$351$		0			0
$352$	−92.3281	+	92.3281i	−0.262296	+	0.262296i
$353$	266.520	+	266.520i	0.755014	+	0.755014i	0.975410	−	0.220396i	$-0.0707351\pi$
$353$	266.520	+	266.520i	0.755014	+	0.755014i	−0.220396	+	0.975410i	$0.570735\pi$
$354$		0			0
$355$		0			0
$356$	−555.576			−1.56061
$357$		0			0
$358$	408.712	+	408.712i	1.14165	+	1.14165i
$359$		−	216.272i		−	0.602430i	−0.953556	−	0.301215i	$-0.902608\pi$
$359$		−	216.272i		−	0.602430i	0.953556	−	0.301215i	$-0.0973922\pi$
$360$		0			0
$361$	−67.3633			−0.186602
$362$	48.3383	−	48.3383i	0.133531	−	0.133531i
$363$		0			0
$364$		−	178.697i		−	0.490926i
$365$		0			0
$366$		0			0
$367$	240.510	−	240.510i	0.655340	−	0.655340i	−0.298934	−	0.954274i	$-0.596631\pi$
$367$	240.510	−	240.510i	0.655340	−	0.655340i	0.954274	+	0.298934i	$0.0966311\pi$
$368$	78.9240	+	78.9240i	0.214467	+	0.214467i
$369$		0			0
$370$		0			0
$371$	83.1918			0.224237
$372$		0			0
$373$	330.207	+	330.207i	0.885272	+	0.885272i	0.994065	−	0.108792i	$-0.0346983\pi$
$373$	330.207	+	330.207i	0.885272	+	0.885272i	−0.108792	+	0.994065i	$0.534698\pi$
$374$		−	39.5051i		−	0.105629i
$375$		0			0
$376$	166.899			0.443880
$377$	−8.91939	+	8.91939i	−0.0236589	+	0.0236589i
$378$		0			0
$379$			210.000i			0.554090i	0.960857	+	0.277045i	$0.0893551\pi$
$379$			210.000i			0.554090i	−0.960857	+	0.277045i	$0.910645\pi$
$380$		0			0
$381$		0			0
$382$	−89.1918	+	89.1918i	−0.233486	+	0.233486i
$383$	170.631	+	170.631i	0.445512	+	0.445512i	0.893859	−	0.448347i	$-0.147987\pi$
$383$	170.631	+	170.631i	0.445512	+	0.445512i	−0.448347	+	0.893859i	$0.647987\pi$
$384$		0			0
$385$		0			0
$386$	345.126			0.894109
$387$		0			0
$388$	86.1010	+	86.1010i	0.221910	+	0.221910i
$389$			547.337i			1.40704i	0.710677	+	0.703518i	$0.248389\pi$
$389$			547.337i			1.40704i	−0.710677	+	0.703518i	$0.751611\pi$
$390$		0			0
$391$	−87.2327			−0.223101
$392$	−189.260	+	189.260i	−0.482806	+	0.482806i
$393$		0			0
$394$		−	299.464i		−	0.760062i
$395$		0			0
$396$		0			0
$397$	−45.2577	+	45.2577i	−0.113999	+	0.113999i	−0.761805	−	0.647806i	$-0.775687\pi$
$397$	−45.2577	+	45.2577i	−0.113999	+	0.113999i	0.647806	+	0.761805i	$0.275687\pi$
$398$	559.287	+	559.287i	1.40524	+	1.40524i
$399$		0			0
$400$		0			0
$401$	520.302			1.29751			0.648756	−	0.760997i	$-0.275290\pi$
$401$	520.302			1.29751			0.648756	+	0.760997i	$0.275290\pi$
$402$		0			0
$403$	−195.373	−	195.373i	−0.484798	−	0.484798i
$404$			1024.19i			2.53511i
$405$		0			0
$406$	−5.50510			−0.0135594
$407$	−127.394	+	127.394i	−0.313007	+	0.313007i
$408$		0			0
$409$		−	347.110i		−	0.848680i	−0.905503	−	0.424340i	$-0.860506\pi$
$409$		−	347.110i		−	0.848680i	0.905503	−	0.424340i	$-0.139494\pi$
$410$		0			0
$411$		0			0
$412$	381.974	−	381.974i	0.927121	−	0.927121i
$413$	162.247	+	162.247i	0.392851	+	0.392851i
$414$		0			0
$415$		0			0
$416$	−576.252			−1.38522
$417$		0			0
$418$	−154.182	−	154.182i	−0.368856	−	0.368856i
$419$		−	583.398i		−	1.39236i	−0.717868	−	0.696180i	$-0.754882\pi$
$419$		−	583.398i		−	1.39236i	0.717868	−	0.696180i	$-0.245118\pi$
$420$		0			0
$421$	213.151			0.506297			0.253148	−	0.967427i	$-0.418534\pi$
$421$	213.151			0.506297			0.253148	+	0.967427i	$0.418534\pi$
$422$	−589.085	+	589.085i	−1.39594	+	1.39594i
$423$		0			0
$424$			242.474i			0.571874i
$425$		0			0
$426$		0			0
$427$	136.384	−	136.384i	0.319400	−	0.319400i
$428$	27.9750	+	27.9750i	0.0653622	+	0.0653622i
$429$		0			0
$430$		0			0
$431$	−187.364			−0.434720			−0.217360	−	0.976092i	$-0.569745\pi$
$431$	−187.364			−0.434720			−0.217360	+	0.976092i	$0.569745\pi$
$432$		0			0
$433$	−154.848	−	154.848i	−0.357617	−	0.357617i	0.505317	−	0.862934i	$-0.331376\pi$
$433$	−154.848	−	154.848i	−0.357617	−	0.357617i	−0.862934	+	0.505317i	$0.831376\pi$
$434$		−	120.586i		−	0.277847i
$435$		0			0
$436$	−231.848			−0.531761
$437$	−340.454	+	340.454i	−0.779071	+	0.779071i
$438$		0			0
$439$			252.929i			0.576147i	0.957608	+	0.288074i	$0.0930148\pi$
$439$			252.929i			0.576147i	−0.957608	+	0.288074i	$0.906985\pi$
$440$		0			0
$441$		0			0
$442$	123.283	−	123.283i	0.278920	−	0.278920i
$443$	−421.131	−	421.131i	−0.950633	−	0.950633i	0.0482041	−	0.998838i	$-0.484650\pi$
$443$	−421.131	−	421.131i	−0.950633	−	0.950633i	−0.998838	+	0.0482041i	$0.984650\pi$
$444$		0			0
$445$		0			0
$446$	−148.742			−0.333503
$447$		0			0
$448$	−150.015	−	150.015i	−0.334854	−	0.334854i
$449$			297.909i			0.663495i	0.943368	+	0.331747i	$0.107638\pi$
$449$			297.909i			0.663495i	−0.943368	+	0.331747i	$0.892362\pi$
$450$		0			0
$451$	96.0908			0.213062
$452$	84.7015	−	84.7015i	0.187393	−	0.187393i
$453$		0			0
$454$		−	94.2020i		−	0.207493i
$455$		0			0
$456$		0			0
$457$	−285.747	+	285.747i	−0.625267	+	0.625267i	−0.946873	−	0.321607i	$-0.895777\pi$
$457$	−285.747	+	285.747i	−0.625267	+	0.625267i	0.321607	+	0.946873i	$0.395777\pi$
$458$	−542.388	−	542.388i	−1.18425	−	1.18425i
$459$		0			0
$460$		0			0
$461$	−526.620			−1.14234			−0.571171	−	0.820831i	$-0.693511\pi$
$461$	−526.620			−1.14234			−0.571171	+	0.820831i	$0.693511\pi$
$462$		0			0
$463$	−335.702	−	335.702i	−0.725057	−	0.725057i	0.244573	−	0.969631i	$-0.421352\pi$
$463$	−335.702	−	335.702i	−0.725057	−	0.725057i	−0.969631	+	0.244573i	$0.921352\pi$
$464$			4.09540i			0.00882630i
$465$		0			0
$466$	−719.535			−1.54407
$467$	488.742	−	488.742i	1.04656	−	1.04656i	0.0476956	−	0.998862i	$-0.484812\pi$
$467$	488.742	−	488.742i	1.04656	−	1.04656i	0.998862	−	0.0476956i	$-0.0151877\pi$
$468$		0			0
$469$		−	159.151i		−	0.339341i
$470$		0			0
$471$		0			0
$472$	−472.893	+	472.893i	−1.00189	+	1.00189i
$473$	−75.3235	−	75.3235i	−0.159246	−	0.159246i
$474$		0			0
$475$		0			0
$476$	45.3439			0.0952603
$477$		0			0
$478$	725.716	+	725.716i	1.51823	+	1.51823i
$479$		−	184.949i		−	0.386115i	−0.981187	−	0.193057i	$-0.938160\pi$
$479$		−	184.949i		−	0.386115i	0.981187	−	0.193057i	$-0.0618404\pi$
$480$		0			0
$481$	−795.110			−1.65304
$482$	297.171	−	297.171i	0.616538	−	0.616538i
$483$		0			0
$484$			647.636i			1.33809i
$485$		0			0
$486$		0			0
$487$	120.682	−	120.682i	0.247807	−	0.247807i	−0.572263	−	0.820070i	$-0.693934\pi$
$487$	120.682	−	120.682i	0.247807	−	0.247807i	0.820070	+	0.572263i	$0.193934\pi$
$488$	397.510	+	397.510i	0.814569	+	0.814569i
$489$		0			0
$490$		0			0
$491$	105.682			0.215239			0.107619	−	0.994192i	$-0.465677\pi$
$491$	105.682			0.215239			0.107619	+	0.994192i	$0.465677\pi$
$492$		0			0
$493$	−2.26327	−	2.26327i	−0.00459082	−	0.00459082i
$494$		−	962.302i		−	1.94798i
$495$		0			0
$496$	−89.7071			−0.180861
$497$	98.5653	−	98.5653i	0.198321	−	0.198321i
$498$		0			0
$499$			739.585i			1.48213i	0.671431	+	0.741067i	$0.265680\pi$
$499$			739.585i			1.48213i	−0.671431	+	0.741067i	$0.734320\pi$
$500$		0			0
$501$		0			0
$502$	−900.448	+	900.448i	−1.79372	+	1.79372i
$503$	−406.409	−	406.409i	−0.807970	−	0.807970i	0.176357	−	0.984326i	$-0.443569\pi$
$503$	−406.409	−	406.409i	−0.807970	−	0.807970i	−0.984326	+	0.176357i	$0.943569\pi$
$504$		0			0
$505$		0			0
$506$	−245.081			−0.484349
$507$		0			0
$508$	−676.146	−	676.146i	−1.33100	−	1.33100i
$509$			194.511i			0.382143i	0.981576	+	0.191071i	$0.0611962\pi$
$509$			194.511i			0.382143i	−0.981576	+	0.191071i	$0.938804\pi$
$510$		0			0
$511$	115.344			0.225722
$512$	−213.376	+	213.376i	−0.416750	+	0.416750i
$513$		0			0
$514$		−	397.060i		−	0.772491i
$515$		0			0
$516$		0			0
$517$	66.1408	−	66.1408i	0.127932	−	0.127932i
$518$	−245.373	−	245.373i	−0.473694	−	0.473694i
$519$		0			0
$520$		0			0
$521$	589.605			1.13168			0.565840	−	0.824515i	$-0.308552\pi$
$521$	589.605			1.13168			0.565840	+	0.824515i	$0.308552\pi$
$522$		0			0
$523$	141.546	+	141.546i	0.270642	+	0.270642i	0.829359	−	0.558716i	$-0.188706\pi$
$523$	141.546	+	141.546i	0.270642	+	0.270642i	−0.558716	+	0.829359i	$0.688706\pi$
$524$		−	154.177i		−	0.294231i
$525$		0			0
$526$	1521.03			2.89169
$527$	49.5755	−	49.5755i	0.0940712	−	0.0940712i
$528$		0			0
$529$			12.1714i			0.0230084i
$530$		0			0
$531$		0			0
$532$	176.969	−	176.969i	0.332649	−	0.332649i
$533$	299.868	+	299.868i	0.562605	+	0.562605i
$534$		0			0
$535$		0			0
$536$	463.868			0.865426
$537$		0			0
$538$	7.78775	+	7.78775i	0.0144754	+	0.0144754i
$539$			150.005i			0.278302i
$540$		0			0
$541$	431.303			0.797233			0.398617	−	0.917118i	$-0.369490\pi$
$541$	431.303			0.797233			0.398617	+	0.917118i	$0.369490\pi$
$542$	230.429	−	230.429i	0.425146	−	0.425146i
$543$		0			0
$544$		−	146.222i		−	0.268791i
$545$		0			0
$546$		0			0
$547$	446.222	−	446.222i	0.815763	−	0.815763i	−0.169728	−	0.985491i	$-0.554289\pi$
$547$	446.222	−	446.222i	0.815763	−	0.815763i	0.985491	+	0.169728i	$0.0542889\pi$
$548$	−86.3087	−	86.3087i	−0.157498	−	0.157498i
$549$		0			0
$550$		0			0
$551$	−17.6663			−0.0320623
$552$		0			0
$553$	−35.5051	−	35.5051i	−0.0642045	−	0.0642045i
$554$			1270.37i			2.29309i
$555$		0			0
$556$	−490.627			−0.882422
$557$	214.091	−	214.091i	0.384364	−	0.384364i	−0.488308	−	0.872672i	$-0.662386\pi$
$557$	214.091	−	214.091i	0.384364	−	0.384364i	0.872672	+	0.488308i	$0.162386\pi$
$558$		0			0
$559$		−	470.120i		−	0.841003i
$560$		0			0
$561$		0			0
$562$	829.156	−	829.156i	1.47537	−	1.47537i
$563$	672.009	+	672.009i	1.19362	+	1.19362i	0.976043	+	0.217579i	$0.0698161\pi$
$563$	672.009	+	672.009i	1.19362	+	1.19362i	0.217579	+	0.976043i	$0.430184\pi$
$564$		0			0
$565$		0			0
$566$	−343.464			−0.606827
$567$		0			0
$568$	287.283	+	287.283i	0.505779	+	0.505779i
$569$		−	972.161i		−	1.70854i	−0.519827	−	0.854272i	$-0.674003\pi$
$569$		−	972.161i		−	1.70854i	0.519827	−	0.854272i	$-0.325997\pi$
$570$		0			0
$571$	−924.030			−1.61827			−0.809133	−	0.587626i	$-0.800063\pi$
$571$	−924.030			−1.61827			−0.809133	+	0.587626i	$0.800063\pi$
$572$	206.404	−	206.404i	0.360846	−	0.360846i
$573$		0			0
$574$			185.081i			0.322440i
$575$		0			0
$576$		0			0
$577$	497.879	−	497.879i	0.862874	−	0.862874i	−0.128797	−	0.991671i	$-0.541111\pi$
$577$	497.879	−	497.879i	0.862874	−	0.862874i	0.991671	+	0.128797i	$0.0411114\pi$
$578$	−611.669	−	611.669i	−1.05825	−	1.05825i
$579$		0			0
$580$		0			0
$581$	−61.3031			−0.105513
$582$		0			0
$583$	96.0908	+	96.0908i	0.164821	+	0.164821i
$584$			336.186i			0.575661i
$585$		0			0
$586$	1052.59			1.79624
$587$	292.783	−	292.783i	0.498779	−	0.498779i	−0.412279	−	0.911058i	$-0.635267\pi$
$587$	292.783	−	292.783i	0.498779	−	0.498779i	0.911058	+	0.412279i	$0.135267\pi$
$588$		0			0
$589$		−	386.969i		−	0.656994i
$590$		0			0
$591$		0			0
$592$	−182.540	+	182.540i	−0.308345	+	0.308345i
$593$	451.258	+	451.258i	0.760974	+	0.760974i	0.976498	−	0.215524i	$-0.0691461\pi$
$593$	451.258	+	451.258i	0.760974	+	0.760974i	−0.215524	+	0.976498i	$0.569146\pi$
$594$		0			0
$595$		0			0
$596$	702.842			1.17927
$597$		0			0
$598$	−764.817	−	764.817i	−1.27896	−	1.27896i
$599$			32.8582i			0.0548550i	0.999624	+	0.0274275i	$0.00873154\pi$
$599$			32.8582i			0.0548550i	−0.999624	+	0.0274275i	$0.991268\pi$
$600$		0			0
$601$	−184.484			−0.306961			−0.153481	−	0.988152i	$-0.549048\pi$
$601$	−184.484			−0.306961			−0.153481	+	0.988152i	$0.549048\pi$
$602$	145.081	−	145.081i	0.240998	−	0.240998i
$603$		0			0
$604$			855.171i			1.41585i
$605$		0			0
$606$		0			0
$607$	−136.389	+	136.389i	−0.224694	+	0.224694i	−0.810472	−	0.585778i	$-0.800789\pi$
$607$	−136.389	+	136.389i	−0.224694	+	0.224694i	0.585778	+	0.810472i	$0.300789\pi$
$608$	−570.681	−	570.681i	−0.938620	−	0.938620i
$609$		0			0
$610$		0			0
$611$	412.808			0.675627
$612$		0			0
$613$	12.7128	+	12.7128i	0.0207386	+	0.0207386i	0.717400	−	0.696661i	$-0.245332\pi$
$613$	12.7128	+	12.7128i	0.0207386	+	0.0207386i	−0.696661	+	0.717400i	$0.745332\pi$
$614$		−	751.828i		−	1.22447i
$615$		0			0
$616$	41.0102			0.0665750
$617$	−398.752	+	398.752i	−0.646275	+	0.646275i	−0.952091	−	0.305816i	$-0.901071\pi$
$617$	−398.752	+	398.752i	−0.646275	+	0.646275i	0.305816	+	0.952091i	$0.401071\pi$
$618$		0			0
$619$		−	819.131i		−	1.32331i	−0.749807	−	0.661656i	$-0.769854\pi$
$619$		−	819.131i		−	1.32331i	0.749807	−	0.661656i	$-0.230146\pi$
$620$		0			0
$621$		0			0
$622$	788.232	−	788.232i	1.26725	−	1.26725i
$623$	−136.515	−	136.515i	−0.219126	−	0.219126i
$624$		0			0
$625$		0			0
$626$	677.984			1.08304
$627$		0			0
$628$	301.712	+	301.712i	0.480433	+	0.480433i
$629$		−	201.757i		−	0.320759i
$630$		0			0
$631$	105.485			0.167171			0.0835853	−	0.996501i	$-0.473363\pi$
$631$	105.485			0.167171			0.0835853	+	0.996501i	$0.473363\pi$
$632$	103.485	−	103.485i	0.163742	−	0.163742i
$633$		0			0
$634$		−	1900.90i		−	2.99826i
$635$		0			0
$636$		0			0
$637$	−468.116	+	468.116i	−0.734876	+	0.734876i
$638$	−6.35867	−	6.35867i	−0.00996657	−	0.00996657i
$639$		0			0
$640$		0			0
$641$	−164.788			−0.257079			−0.128540	−	0.991704i	$-0.541029\pi$
$641$	−164.788			−0.257079			−0.128540	+	0.991704i	$0.541029\pi$
$642$		0			0
$643$	764.372	+	764.372i	1.18876	+	1.18876i	0.977411	+	0.211349i	$0.0677856\pi$
$643$	764.372	+	764.372i	1.18876	+	1.18876i	0.211349	+	0.977411i	$0.432214\pi$
$644$		−	281.303i		−	0.436806i
$645$		0			0
$646$	244.182			0.377990
$647$	321.287	−	321.287i	0.496580	−	0.496580i	−0.413792	−	0.910372i	$-0.635796\pi$
$647$	321.287	−	321.287i	0.496580	−	0.496580i	0.910372	+	0.413792i	$0.135796\pi$
$648$		0			0
$649$			374.808i			0.577516i
$650$		0			0
$651$		0			0
$652$	−1117.23	+	1117.23i	−1.71354	+	1.71354i
$653$	−169.823	−	169.823i	−0.260066	−	0.260066i	0.565015	−	0.825081i	$-0.308870\pi$
$653$	−169.823	−	169.823i	−0.260066	−	0.260066i	−0.825081	+	0.565015i	$0.808870\pi$
$654$		0			0
$655$		0			0
$656$	137.687			0.209888
$657$		0			0
$658$	127.394	+	127.394i	0.193608	+	0.193608i
$659$			958.763i			1.45488i	0.686174	+	0.727438i	$0.259289\pi$
$659$			958.763i			1.45488i	−0.686174	+	0.727438i	$0.740711\pi$
$660$		0			0
$661$	396.393			0.599687			0.299843	−	0.953988i	$-0.403066\pi$
$661$	396.393			0.599687			0.299843	+	0.953988i	$0.403066\pi$
$662$	−1088.84	+	1088.84i	−1.64478	+	1.64478i
$663$		0			0
$664$		−	178.677i		−	0.269091i
$665$		0			0
$666$		0			0
$667$	−14.0408	+	14.0408i	−0.0210507	+	0.0210507i
$668$	−572.409	−	572.409i	−0.856899	−	0.856899i
$669$		0			0
$670$		0			0
$671$	315.060			0.469538
$672$		0			0
$673$	−164.707	−	164.707i	−0.244736	−	0.244736i	0.574070	−	0.818806i	$-0.305364\pi$
$673$	−164.707	−	164.707i	−0.244736	−	0.244736i	−0.818806	+	0.574070i	$0.805364\pi$
$674$		−	1300.10i		−	1.92894i
$675$		0			0
$676$	291.313			0.430937
$677$	544.388	−	544.388i	0.804119	−	0.804119i	−0.179618	−	0.983736i	$-0.557486\pi$
$677$	544.388	−	544.388i	0.804119	−	0.804119i	0.983736	+	0.179618i	$0.0574861\pi$
$678$		0			0
$679$			42.3133i			0.0623170i
$680$		0			0
$681$		0			0
$682$	139.283	−	139.283i	0.204227	−	0.204227i
$683$	786.590	+	786.590i	1.15167	+	1.15167i	0.986218	+	0.165452i	$0.0529082\pi$
$683$	786.590	+	786.590i	1.15167	+	1.15167i	0.165452	+	0.986218i	$0.447092\pi$
$684$		0			0
$685$		0			0
$686$	−604.949			−0.881850
$687$		0			0
$688$	−107.930	−	107.930i	−0.156874	−	0.156874i
$689$			599.737i			0.870445i
$690$		0			0
$691$	356.879			0.516467			0.258233	−	0.966083i	$-0.416860\pi$
$691$	356.879			0.516467			0.258233	+	0.966083i	$0.416860\pi$
$692$	−204.288	+	204.288i	−0.295214	+	0.295214i
$693$		0			0
$694$			1424.06i			2.05196i
$695$		0			0
$696$		0			0
$697$	−76.0908	+	76.0908i	−0.109169	+	0.109169i
$698$	1277.02	+	1277.02i	1.82955	+	1.82955i
$699$		0			0
$700$		0			0
$701$	−885.680			−1.26345			−0.631726	−	0.775192i	$-0.717653\pi$
$701$	−885.680			−1.26345			−0.631726	+	0.775192i	$0.717653\pi$
$702$		0			0
$703$	−787.423	−	787.423i	−1.12009	−	1.12009i
$704$		−	346.549i		−	0.492258i
$705$		0			0
$706$	−1185.88			−1.67971
$707$	−251.662	+	251.662i	−0.355957	+	0.355957i
$708$		0			0
$709$			731.049i			1.03110i	0.856860	+	0.515549i	$0.172412\pi$
$709$			731.049i			1.03110i	−0.856860	+	0.515549i	$0.827588\pi$
$710$		0			0
$711$		0			0
$712$	397.893	−	397.893i	0.558839	−	0.558839i
$713$	−307.555	−	307.555i	−0.431354	−	0.431354i
$714$		0			0
$715$		0			0
$716$	−1083.71			−1.51356
$717$		0			0
$718$	481.151	+	481.151i	0.670127	+	0.670127i
$719$			629.271i			0.875204i	0.899169	+	0.437602i	$0.144172\pi$
$719$			629.271i			0.875204i	−0.899169	+	0.437602i	$0.855828\pi$
$720$		0			0
$721$	187.716			0.260356
$722$	149.866	−	149.866i	0.207571	−	0.207571i
$723$		0			0
$724$			128.170i			0.177031i
$725$		0			0
$726$		0			0
$727$	15.8740	−	15.8740i	0.0218349	−	0.0218349i	−0.696105	−	0.717940i	$-0.745085\pi$
$727$	15.8740	−	15.8740i	0.0218349	−	0.0218349i	0.717940	+	0.696105i	$0.245085\pi$
$728$	127.980	+	127.980i	0.175796	+	0.175796i
$729$		0			0
$730$		0			0
$731$	119.292			0.163190
$732$		0			0
$733$	393.237	+	393.237i	0.536476	+	0.536476i	0.922492	−	0.386016i	$-0.126149\pi$
$733$	393.237	+	393.237i	0.536476	+	0.536476i	−0.386016	+	0.922492i	$0.626149\pi$
$734$			1070.15i			1.45796i
$735$		0			0
$736$	−907.131			−1.23251
$737$	183.828	−	183.828i	0.249427	−	0.249427i
$738$		0			0
$739$			192.334i			0.260262i	0.991497	+	0.130131i	$0.0415398\pi$
$739$			192.334i			0.260262i	−0.991497	+	0.130131i	$0.958460\pi$
$740$		0			0
$741$		0			0
$742$	−185.081	+	185.081i	−0.249435	+	0.249435i
$743$	−44.7015	−	44.7015i	−0.0601636	−	0.0601636i	0.676385	−	0.736548i	$-0.263546\pi$
$743$	−44.7015	−	44.7015i	−0.0601636	−	0.0601636i	−0.736548	+	0.676385i	$0.763546\pi$
$744$		0			0
$745$		0			0
$746$	−1469.25			−1.96951
$747$		0			0
$748$	52.3745	+	52.3745i	0.0700194	+	0.0700194i
$749$			13.7480i			0.0183551i
$750$		0			0
$751$	227.787			0.303311			0.151656	−	0.988433i	$-0.451540\pi$
$751$	227.787			0.303311			0.151656	+	0.988433i	$0.451540\pi$
$752$	94.7719	−	94.7719i	0.126027	−	0.126027i
$753$		0			0
$754$		−	39.6867i		−	0.0526349i
$755$		0			0
$756$		0			0
$757$	235.925	−	235.925i	0.311658	−	0.311658i	−0.533894	−	0.845552i	$-0.679272\pi$
$757$	235.925	−	235.925i	0.311658	−	0.311658i	0.845552	+	0.533894i	$0.179272\pi$
$758$	−467.196	−	467.196i	−0.616354	−	0.616354i
$759$		0			0
$760$		0			0
$761$	881.242			1.15801			0.579003	−	0.815326i	$-0.303442\pi$
$761$	881.242			1.15801			0.579003	+	0.815326i	$0.303442\pi$
$762$		0			0
$763$	−56.9694	−	56.9694i	−0.0746650	−	0.0746650i
$764$		−	236.495i		−	0.309548i
$765$		0			0
$766$	−759.221			−0.991151
$767$	−1169.66	+	1169.66i	−1.52497	+	1.52497i
$768$		0			0
$769$			1208.40i			1.57139i	0.618612	+	0.785697i	$0.287696\pi$
$769$			1208.40i			1.57139i	−0.618612	+	0.785697i	$0.712304\pi$
$770$		0			0
$771$		0			0
$772$	−457.556	+	457.556i	−0.592689	+	0.592689i
$773$	−815.226	−	815.226i	−1.05463	−	1.05463i	−0.998419	−	0.0562070i	$-0.982099\pi$
$773$	−815.226	−	815.226i	−1.05463	−	1.05463i	−0.0562070	−	0.998419i	$-0.517901\pi$
$774$		0			0
$775$		0			0
$776$	−123.328			−0.158928
$777$		0			0
$778$	−1217.69	−	1217.69i	−1.56515	−	1.56515i
$779$			593.939i			0.762437i
$780$		0			0
$781$	227.696			0.291544
$782$	194.070	−	194.070i	0.248172	−	0.248172i
$783$		0			0
$784$			214.939i			0.274157i
$785$		0			0
$786$		0			0
$787$	−813.010	+	813.010i	−1.03305	+	1.03305i	−0.0336150	+	0.999435i	$0.510702\pi$
$787$	−813.010	+	813.010i	−1.03305	+	1.03305i	−0.999435	+	0.0336150i	$0.989298\pi$
$788$	397.019	+	397.019i	0.503832	+	0.503832i
$789$		0			0
$790$		0			0
$791$	41.6255			0.0526239
$792$		0			0
$793$	983.201	+	983.201i	1.23985	+	1.23985i
$794$		−	201.373i		−	0.253619i
$795$		0			0
$796$	−1482.97			−1.86302
$797$	311.217	−	311.217i	0.390485	−	0.390485i	−0.484375	−	0.874860i	$-0.660953\pi$
$797$	311.217	−	311.217i	0.390485	−	0.390485i	0.874860	+	0.484375i	$0.160953\pi$
$798$		0			0
$799$			104.749i			0.131100i
$800$		0			0
$801$		0			0
$802$	−1157.54	+	1157.54i	−1.44332	+	1.44332i
$803$	133.228	+	133.228i	0.165913	+	0.165913i
$804$		0			0
$805$		0			0
$806$	869.312			1.07855
$807$		0			0
$808$	−733.504	−	733.504i	−0.907802	−	0.907802i
$809$		−	150.000i		−	0.185414i	−0.995693	−	0.0927070i	$-0.970448\pi$
$809$		−	150.000i		−	0.185414i	0.995693	−	0.0927070i	$-0.0295520\pi$
$810$		0			0
$811$	−132.847			−0.163806			−0.0819032	−	0.996640i	$-0.526100\pi$
$811$	−132.847			−0.163806			−0.0819032	+	0.996640i	$0.526100\pi$
$812$	7.29847	−	7.29847i	0.00898827	−	0.00898827i
$813$		0			0
$814$		−	566.838i		−	0.696361i
$815$		0			0
$816$		0			0
$817$	465.576	−	465.576i	0.569860	−	0.569860i
$818$	772.232	+	772.232i	0.944048	+	0.944048i
$819$		0			0
$820$		0			0
$821$	−509.893			−0.621064			−0.310532	−	0.950563i	$-0.600507\pi$
$821$	−509.893			−0.621064			−0.310532	+	0.950563i	$0.600507\pi$
$822$		0			0
$823$	−300.369	−	300.369i	−0.364968	−	0.364968i	0.500670	−	0.865638i	$-0.333087\pi$
$823$	−300.369	−	300.369i	−0.364968	−	0.364968i	−0.865638	+	0.500670i	$0.833087\pi$
$824$			547.126i			0.663988i
$825$		0			0
$826$	−721.918			−0.873993
$827$	−1030.76	+	1030.76i	−1.24638	+	1.24638i	−0.289073	+	0.957307i	$0.593347\pi$
$827$	−1030.76	+	1030.76i	−1.24638	+	1.24638i	−0.957307	+	0.289073i	$0.906653\pi$
$828$		0			0
$829$		−	37.4235i		−	0.0451429i	−0.999745	−	0.0225714i	$-0.992815\pi$
$829$		−	37.4235i		−	0.0451429i	0.999745	−	0.0225714i	$-0.00718533\pi$
$830$		0			0
$831$		0			0
$832$	1081.47	−	1081.47i	1.29984	−	1.29984i
$833$	−118.783	−	118.783i	−0.142597	−	0.142597i
$834$		0			0
$835$		0			0
$836$	408.817			0.489016
$837$		0			0
$838$	1297.91	+	1297.91i	1.54882	+	1.54882i
$839$		−	1152.37i		−	1.37351i	−0.726890	−	0.686754i	$-0.759035\pi$
$839$		−	1152.37i		−	1.37351i	0.726890	−	0.686754i	$-0.240965\pi$
$840$		0			0
$841$	840.271			0.999134
$842$	−474.207	+	474.207i	−0.563191	+	0.563191i
$843$		0			0
$844$		−	1561.98i		−	1.85068i
$845$		0			0
$846$		0			0
$847$	−159.136	+	159.136i	−0.187882	+	0.187882i
$848$	137.687	+	137.687i	0.162366	+	0.162366i
$849$		0			0
$850$		0			0
$851$	−1251.66			−1.47081
$852$		0			0
$853$	−694.570	−	694.570i	−0.814267	−	0.814267i	0.171003	−	0.985270i	$-0.445299\pi$
$853$	−694.570	−	694.570i	−0.814267	−	0.814267i	−0.985270	+	0.171003i	$0.945299\pi$
$854$			606.838i			0.710583i
$855$		0			0
$856$	−40.0704			−0.0468112
$857$	417.176	−	417.176i	0.486786	−	0.486786i	−0.420504	−	0.907291i	$-0.638147\pi$
$857$	417.176	−	417.176i	0.486786	−	0.486786i	0.907291	+	0.420504i	$0.138147\pi$
$858$		0			0
$859$		−	486.867i		−	0.566784i	−0.959004	−	0.283392i	$-0.908540\pi$
$859$		−	486.867i		−	0.566784i	0.959004	−	0.283392i	$-0.0914597\pi$
$860$		0			0
$861$		0			0
$862$	416.838	−	416.838i	0.483570	−	0.483570i
$863$	−411.319	−	411.319i	−0.476615	−	0.476615i	0.427432	−	0.904047i	$-0.359418\pi$
$863$	−411.319	−	411.319i	−0.476615	−	0.476615i	−0.904047	+	0.427432i	$0.859418\pi$
$864$		0			0
$865$		0			0
$866$	688.994			0.795606
$867$		0			0
$868$	159.868	+	159.868i	0.184180	+	0.184180i
$869$		−	82.0204i		−	0.0943848i
$870$		0			0
$871$	1147.33			1.31726
$872$	166.045	−	166.045i	0.190419	−	0.190419i
$873$		0			0
$874$		−	1514.85i		−	1.73323i
$875$		0			0
$876$		0			0
$877$	−332.540	+	332.540i	−0.379179	+	0.379179i	−0.870806	−	0.491627i	$-0.836402\pi$
$877$	−332.540	+	332.540i	−0.379179	+	0.379179i	0.491627	+	0.870806i	$0.336402\pi$
$878$	−562.702	−	562.702i	−0.640890	−	0.640890i
$879$		0			0
$880$		0			0
$881$	−533.151			−0.605166			−0.302583	−	0.953123i	$-0.597849\pi$
$881$	−533.151			−0.605166			−0.302583	+	0.953123i	$0.597849\pi$
$882$		0			0
$883$	745.939	+	745.939i	0.844778	+	0.844778i	0.989476	−	0.144698i	$-0.0462211\pi$
$883$	745.939	+	745.939i	0.844778	+	0.844778i	−0.144698	+	0.989476i	$0.546221\pi$
$884$			326.888i			0.369783i
$885$		0			0
$886$	1873.82			2.11492
$887$	−386.207	+	386.207i	−0.435408	+	0.435408i	−0.890463	−	0.455055i	$-0.849619\pi$
$887$	−386.207	+	386.207i	−0.435408	+	0.435408i	0.455055	+	0.890463i	$0.349619\pi$
$888$		0			0
$889$		−	332.284i		−	0.373772i
$890$		0			0
$891$		0			0
$892$	197.197	−	197.197i	0.221073	−	0.221073i
$893$	408.817	+	408.817i	0.457802	+	0.457802i
$894$		0			0
$895$		0			0
$896$	347.753			0.388117
$897$		0			0
$898$	−662.772	−	662.772i	−0.738053	−	0.738053i
$899$		−	15.9592i		−	0.0177521i
$900$		0			0
$901$	−152.182			−0.168903
$902$	−213.778	+	213.778i	−0.237004	+	0.237004i
$903$		0			0
$904$			121.323i			0.134207i
$905$		0			0
$906$		0			0
$907$	947.342	−	947.342i	1.04448	−	1.04448i	0.0455146	−	0.998964i	$-0.485507\pi$
$907$	947.342	−	947.342i	1.04448	−	1.04448i	0.998964	−	0.0455146i	$-0.0144928\pi$
$908$	124.890	+	124.890i	0.137544	+	0.137544i
$909$		0			0
$910$		0			0
$911$	1149.36			1.26165			0.630824	−	0.775926i	$-0.282717\pi$
$911$	1149.36			1.26165			0.630824	+	0.775926i	$0.282717\pi$
$912$		0			0
$913$	−70.8082	−	70.8082i	−0.0775555	−	0.0775555i
$914$		−	1271.43i		−	1.39106i
$915$		0			0
$916$	1438.16			1.57004
$917$	37.8842	−	37.8842i	0.0413132	−	0.0413132i
$918$		0			0
$919$		−	412.577i		−	0.448941i	−0.974481	−	0.224470i	$-0.927935\pi$
$919$		−	412.577i		−	0.448941i	0.974481	−	0.224470i	$-0.0720652\pi$
$920$		0			0
$921$		0			0
$922$	1171.59	−	1171.59i	1.27071	−	1.27071i
$923$	710.565	+	710.565i	0.769843	+	0.769843i
$924$		0			0
$925$		0			0
$926$	1493.70			1.61307
$927$		0			0
$928$	−23.5357	−	23.5357i	−0.0253618	−	0.0253618i
$929$		−	151.707i		−	0.163302i	−0.996661	−	0.0816508i	$-0.973981\pi$
$929$		−	151.707i		−	0.163302i	0.996661	−	0.0816508i	$-0.0260192\pi$
$930$		0			0
$931$	−927.181			−0.995898
$932$	953.934	−	953.934i	1.02353	−	1.02353i
$933$		0			0
$934$			2174.65i			2.32832i
$935$		0			0
$936$		0			0
$937$	−662.090	+	662.090i	−0.706606	+	0.706606i	−0.965820	−	0.259214i	$-0.916537\pi$
$937$	−662.090	+	662.090i	−0.706606	+	0.706606i	0.259214	+	0.965820i	$0.416537\pi$
$938$	354.070	+	354.070i	0.377474	+	0.377474i
$939$		0			0
$940$		0			0
$941$	1533.77			1.62994			0.814969	−	0.579505i	$-0.196754\pi$
$941$	1533.77			1.62994			0.814969	+	0.579505i	$0.196754\pi$
$942$		0			0
$943$	472.050	+	472.050i	0.500583	+	0.500583i
$944$			537.056i			0.568915i
$945$		0			0
$946$	335.151			0.354282
$947$	1173.19	−	1173.19i	1.23885	−	1.23885i	0.278377	−	0.960472i	$-0.410204\pi$
$947$	1173.19	−	1173.19i	1.23885	−	1.23885i	0.960472	−	0.278377i	$-0.0897964\pi$
$948$		0			0
$949$			831.523i			0.876210i
$950$		0			0
$951$		0			0
$952$	−32.4745	+	32.4745i	−0.0341119	+	0.0341119i
$953$	−145.501	−	145.501i	−0.152676	−	0.152676i	0.626636	−	0.779312i	$-0.284431\pi$
$953$	−145.501	−	145.501i	−0.152676	−	0.152676i	−0.779312	+	0.626636i	$0.784431\pi$
$954$		0			0
$955$		0			0
$956$	−1924.26			−2.01282
$957$		0			0
$958$	411.464	+	411.464i	0.429503	+	0.429503i
$959$		−	42.4153i		−	0.0442287i
$960$		0			0
$961$	−611.424			−0.636238
$962$	1768.92	−	1768.92i	1.83879	−	1.83879i
$963$		0			0
$964$			787.959i			0.817385i
$965$		0			0
$966$		0			0
$967$	−1151.69	+	1151.69i	−1.19099	+	1.19099i	−0.214204	+	0.976789i	$0.568716\pi$
$967$	−1151.69	+	1151.69i	−1.19099	+	1.19099i	−0.976789	+	0.214204i	$0.931284\pi$
$968$	−463.825	−	463.825i	−0.479158	−	0.479158i
$969$		0			0
$970$		0			0
$971$	−72.4383			−0.0746017			−0.0373009	−	0.999304i	$-0.511876\pi$
$971$	−72.4383			−0.0746017			−0.0373009	+	0.999304i	$0.511876\pi$
$972$		0			0
$973$	−120.556	−	120.556i	−0.123901	−	0.123901i
$974$			536.974i			0.551308i
$975$		0			0
$976$	451.444			0.462545
$977$	706.338	−	706.338i	0.722966	−	0.722966i	−0.246242	−	0.969208i	$-0.579196\pi$
$977$	706.338	−	706.338i	0.722966	−	0.722966i	0.969208	+	0.246242i	$0.0791958\pi$
$978$		0			0
$979$		−	315.364i		−	0.322129i
$980$		0			0
$981$		0			0
$982$	−235.116	+	235.116i	−0.239425	+	0.239425i
$983$	−134.663	−	134.663i	−0.136992	−	0.136992i	0.635286	−	0.772277i	$-0.280882\pi$
$983$	−134.663	−	134.663i	−0.136992	−	0.136992i	−0.772277	+	0.635286i	$0.780882\pi$
$984$		0			0
$985$		0			0
$986$	10.0704			0.0102134
$987$		0			0
$988$	1275.79	+	1275.79i	1.29128	+	1.29128i
$989$		−	740.059i		−	0.748290i
$990$		0			0
$991$	−1131.94			−1.14222			−0.571109	−	0.820874i	$-0.693487\pi$
$991$	−1131.94			−1.14222			−0.571109	+	0.820874i	$0.693487\pi$
$992$	515.535	−	515.535i	0.519692	−	0.519692i
$993$		0			0
$994$			438.565i			0.441213i
$995$		0			0
$996$		0			0
$997$	1115.27	−	1115.27i	1.11862	−	1.11862i	0.126679	−	0.991944i	$-0.459568\pi$
$997$	1115.27	−	1115.27i	1.11862	−	1.11862i	0.991944	−	0.126679i	$-0.0404318\pi$
$998$	−1645.39	−	1645.39i	−1.64868	−	1.64868i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.g.a.118.1		4
3.2	odd	2		75.3.f.c.43.2		4
5.2	odd	4	inner	225.3.g.a.82.1		4
5.3	odd	4		45.3.g.b.37.2		4
5.4	even	2		45.3.g.b.28.2		4
12.11	even	2		1200.3.bg.k.193.2		4
15.2	even	4		75.3.f.c.7.2		4
15.8	even	4		15.3.f.a.7.1	✓	4
15.14	odd	2		15.3.f.a.13.1	yes	4
20.3	even	4		720.3.bh.k.577.1		4
20.19	odd	2		720.3.bh.k.433.1		4
45.4	even	6		405.3.l.f.298.2		8
45.13	odd	12		405.3.l.f.217.1		8
45.14	odd	6		405.3.l.h.298.1		8
45.23	even	12		405.3.l.h.217.2		8
45.29	odd	6		405.3.l.h.28.2		8
45.34	even	6		405.3.l.f.28.1		8
45.38	even	12		405.3.l.h.352.1		8
45.43	odd	12		405.3.l.f.352.2		8
60.23	odd	4		240.3.bg.a.97.1		4
60.47	odd	4		1200.3.bg.k.1057.2		4
60.59	even	2		240.3.bg.a.193.1		4
120.29	odd	2		960.3.bg.i.193.1		4
120.53	even	4		960.3.bg.i.577.1		4
120.59	even	2		960.3.bg.h.193.2		4
120.83	odd	4		960.3.bg.h.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.1	✓	4	15.8	even	4
15.3.f.a.13.1	yes	4	15.14	odd	2
45.3.g.b.28.2		4	5.4	even	2
45.3.g.b.37.2		4	5.3	odd	4
75.3.f.c.7.2		4	15.2	even	4
75.3.f.c.43.2		4	3.2	odd	2
225.3.g.a.82.1		4	5.2	odd	4	inner
225.3.g.a.118.1		4	1.1	even	1	trivial
240.3.bg.a.97.1		4	60.23	odd	4
240.3.bg.a.193.1		4	60.59	even	2
405.3.l.f.28.1		8	45.34	even	6
405.3.l.f.217.1		8	45.13	odd	12
405.3.l.f.298.2		8	45.4	even	6
405.3.l.f.352.2		8	45.43	odd	12
405.3.l.h.28.2		8	45.29	odd	6
405.3.l.h.217.2		8	45.23	even	12
405.3.l.h.298.1		8	45.14	odd	6
405.3.l.h.352.1		8	45.38	even	12
720.3.bh.k.433.1		4	20.19	odd	2
720.3.bh.k.577.1		4	20.3	even	4
960.3.bg.h.193.2		4	120.59	even	2
960.3.bg.h.577.2		4	120.83	odd	4
960.3.bg.i.193.1		4	120.29	odd	2
960.3.bg.i.577.1		4	120.53	even	4
1200.3.bg.k.193.2		4	12.11	even	2
1200.3.bg.k.1057.2		4	60.47	odd	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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.22474 + 2.22474i) q^{2} -5.89898i q^{4} +(1.44949 - 1.44949i) q^{7} +(4.22474 + 4.22474i) q^{8} +O(q^{10})\)	\(q+(-2.22474 + 2.22474i) q^{2} -5.89898i q^{4} +(1.44949 - 1.44949i) q^{7} +(4.22474 + 4.22474i) q^{8} +3.34847 q^{11} +(10.4495 + 10.4495i) q^{13} +6.44949i q^{14} +4.79796 q^{16} +(-2.65153 + 2.65153i) q^{17} +20.6969i q^{19} +(-7.44949 + 7.44949i) q^{22} +(16.4495 + 16.4495i) q^{23} -46.4949 q^{26} +(-8.55051 - 8.55051i) q^{28} +0.853572i q^{29} -18.6969 q^{31} +(-27.5732 + 27.5732i) q^{32} -11.7980i q^{34} +(-38.0454 + 38.0454i) q^{37} +(-46.0454 - 46.0454i) q^{38} +28.6969 q^{41} +(-22.4949 - 22.4949i) q^{43} -19.7526i q^{44} -73.1918 q^{46} +(19.7526 - 19.7526i) q^{47} +44.7980i q^{49} +(61.6413 - 61.6413i) q^{52} +(28.6969 + 28.6969i) q^{53} +12.2474 q^{56} +(-1.89898 - 1.89898i) q^{58} +111.934i q^{59} +94.0908 q^{61} +(41.5959 - 41.5959i) q^{62} -103.495i q^{64} +(54.8990 - 54.8990i) q^{67} +(15.6413 + 15.6413i) q^{68} +68.0000 q^{71} +(39.7878 + 39.7878i) q^{73} -169.283i q^{74} +122.091 q^{76} +(4.85357 - 4.85357i) q^{77} -24.4949i q^{79} +(-63.8434 + 63.8434i) q^{82} +(-21.1464 - 21.1464i) q^{83} +100.091 q^{86} +(14.1464 + 14.1464i) q^{88} -94.1816i q^{89} +30.2929 q^{91} +(97.0352 - 97.0352i) q^{92} +87.8888i q^{94} +(-14.5959 + 14.5959i) q^{97} +(-99.6640 - 99.6640i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{7} + 12 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^7 + 12 * q^8	\( 4 q - 4 q^{2} - 4 q^{7} + 12 q^{8} - 16 q^{11} + 32 q^{13} - 20 q^{16} - 40 q^{17} - 20 q^{22} + 56 q^{23} - 88 q^{26} - 44 q^{28} - 16 q^{31} - 76 q^{32} - 64 q^{37} - 96 q^{38} + 56 q^{41} + 8 q^{43} - 136 q^{46} + 128 q^{47} + 80 q^{52} + 56 q^{53} + 12 q^{58} + 200 q^{61} + 88 q^{62} + 200 q^{67} - 104 q^{68} + 272 q^{71} - 76 q^{73} + 312 q^{76} + 88 q^{77} - 128 q^{82} - 16 q^{83} + 224 q^{86} - 12 q^{88} - 16 q^{91} + 104 q^{92} + 20 q^{97} - 188 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^7 + 12 * q^8 - 16 * q^11 + 32 * q^13 - 20 * q^16 - 40 * q^17 - 20 * q^22 + 56 * q^23 - 88 * q^26 - 44 * q^28 - 16 * q^31 - 76 * q^32 - 64 * q^37 - 96 * q^38 + 56 * q^41 + 8 * q^43 - 136 * q^46 + 128 * q^47 + 80 * q^52 + 56 * q^53 + 12 * q^58 + 200 * q^61 + 88 * q^62 + 200 * q^67 - 104 * q^68 + 272 * q^71 - 76 * q^73 + 312 * q^76 + 88 * q^77 - 128 * q^82 - 16 * q^83 + 224 * q^86 - 12 * q^88 - 16 * q^91 + 104 * q^92 + 20 * q^97 - 188 * q^98

Introduction

L-functions

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