LMFDB - Embedded newform 1500.2.m.d.301.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(301,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1500.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.m (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.6
Character	$\chi$	$=$	1500.301
Dual form			1500.2.m.d.1201.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{3} +3.54704 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{3} +3.54704 q^{7} +(-0.809017 - 0.587785i) q^{9} +(1.78482 - 1.29675i) q^{11} +(-5.80689 - 4.21895i) q^{13} +(-1.96699 - 6.05378i) q^{17} +(-0.715151 - 2.20101i) q^{19} +(-1.09610 + 3.37344i) q^{21} +(1.76038 - 1.27899i) q^{23} +(0.809017 - 0.587785i) q^{27} +(0.262008 - 0.806379i) q^{29} +(-1.32905 - 4.09040i) q^{31} +(0.681742 + 2.09819i) q^{33} +(-5.84918 - 4.24968i) q^{37} +(5.80689 - 4.21895i) q^{39} +(1.08778 + 0.790317i) q^{41} -8.18973 q^{43} +(-1.87095 + 5.75820i) q^{47} +5.58150 q^{49} +6.36532 q^{51} +(-3.69530 + 11.3730i) q^{53} +2.31428 q^{57} +(10.0896 + 7.33050i) q^{59} +(5.59873 - 4.06772i) q^{61} +(-2.86962 - 2.08490i) q^{63} +(-1.46291 - 4.50239i) q^{67} +(0.672404 + 2.06945i) q^{69} +(4.25799 - 13.1047i) q^{71} +(0.881155 - 0.640196i) q^{73} +(6.33085 - 4.59963i) q^{77} +(-1.80542 + 5.55650i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-3.87127 - 11.9145i) q^{83} +(0.685947 + 0.498370i) q^{87} +(5.68424 - 4.12984i) q^{89} +(-20.5973 - 14.9648i) q^{91} +4.30090 q^{93} +(5.60695 - 17.2564i) q^{97} -2.20616 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9	$ 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9} - 6 q^{11} + 4 q^{17} - 10 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{27} - 4 q^{29} + 6 q^{31} - 4 q^{33} - 8 q^{37} - 10 q^{41} - 56 q^{43} + 26 q^{47} + 56 q^{49} + 16 q^{51} - 32 q^{53} - 20 q^{57} + 36 q^{59} - 12 q^{61} + 4 q^{63} + 36 q^{67} - 4 q^{69} + 40 q^{71} + 32 q^{73} - 46 q^{77} - 8 q^{79} - 6 q^{81} - 6 q^{83} + 4 q^{87} - 30 q^{91} + 4 q^{93} + 48 q^{97} + 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9 - 6 * q^11 + 4 * q^17 - 10 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^27 - 4 * q^29 + 6 * q^31 - 4 * q^33 - 8 * q^37 - 10 * q^41 - 56 * q^43 + 26 * q^47 + 56 * q^49 + 16 * q^51 - 32 * q^53 - 20 * q^57 + 36 * q^59 - 12 * q^61 + 4 * q^63 + 36 * q^67 - 4 * q^69 + 40 * q^71 + 32 * q^73 - 46 * q^77 - 8 * q^79 - 6 * q^81 - 6 * q^83 + 4 * q^87 - 30 * q^91 + 4 * q^93 + 48 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.54704			1.34066			0.670328	−	0.742065i	$-0.266154\pi$
$7$	3.54704			1.34066			0.670328	+	0.742065i	$0.266154\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	1.78482	−	1.29675i	0.538145	−	0.390985i	−0.285251	−	0.958453i	$-0.592077\pi$
$11$	1.78482	−	1.29675i	0.538145	−	0.390985i	0.823396	+	0.567468i	$0.192077\pi$
$12$		0			0
$13$	−5.80689	−	4.21895i	−1.61054	−	1.17013i	−0.861769	−	0.507301i	$-0.830643\pi$
$13$	−5.80689	−	4.21895i	−1.61054	−	1.17013i	−0.748773	−	0.662827i	$-0.769357\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.96699	−	6.05378i	−0.477066	−	1.46826i	−0.843151	−	0.537676i	$-0.819302\pi$
$17$	−1.96699	−	6.05378i	−0.477066	−	1.46826i	0.366086	−	0.930581i	$-0.380698\pi$
$18$		0			0
$19$	−0.715151	−	2.20101i	−0.164067	−	0.504946i	0.834899	−	0.550402i	$-0.185526\pi$
$19$	−0.715151	−	2.20101i	−0.164067	−	0.504946i	−0.998966	+	0.0454566i	$0.985526\pi$
$20$		0			0
$21$	−1.09610	+	3.37344i	−0.239188	+	0.736144i
$22$		0			0
$23$	1.76038	−	1.27899i	0.367064	−	0.266687i	−0.388929	−	0.921268i	$-0.627155\pi$
$23$	1.76038	−	1.27899i	0.367064	−	0.266687i	0.755992	+	0.654580i	$0.227155\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$		0			0
$29$	0.262008	−	0.806379i	0.0486538	−	0.149741i	−0.923778	−	0.382928i	$-0.874916\pi$
$29$	0.262008	−	0.806379i	0.0486538	−	0.149741i	0.972432	+	0.233188i	$0.0749156\pi$
$30$		0			0
$31$	−1.32905	−	4.09040i	−0.238705	−	0.734657i	−0.996608	−	0.0822910i	$-0.973776\pi$
$31$	−1.32905	−	4.09040i	−0.238705	−	0.734657i	0.757904	−	0.652367i	$-0.226224\pi$
$32$		0			0
$33$	0.681742	+	2.09819i	0.118676	+	0.365248i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.84918	−	4.24968i	−0.961599	−	0.698643i	−0.00807756	−	0.999967i	$-0.502571\pi$
$37$	−5.84918	−	4.24968i	−0.961599	−	0.698643i	−0.953522	+	0.301325i	$0.902571\pi$
$38$		0			0
$39$	5.80689	−	4.21895i	0.929847	−	0.675573i
$40$		0			0
$41$	1.08778	+	0.790317i	0.169882	+	0.123427i	0.669478	−	0.742832i	$-0.266518\pi$
$41$	1.08778	+	0.790317i	0.169882	+	0.123427i	−0.499595	+	0.866259i	$0.666518\pi$
$42$		0			0
$43$	−8.18973			−1.24892			−0.624461	−	0.781056i	$-0.714681\pi$
$43$	−8.18973			−1.24892			−0.624461	+	0.781056i	$0.714681\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.87095	+	5.75820i	−0.272907	+	0.839920i	0.716859	+	0.697218i	$0.245579\pi$
$47$	−1.87095	+	5.75820i	−0.272907	+	0.839920i	−0.989766	+	0.142702i	$0.954421\pi$
$48$		0			0
$49$	5.58150			0.797357
$50$		0			0
$51$	6.36532			0.891323
$52$		0			0
$53$	−3.69530	+	11.3730i	−0.507589	+	1.56220i	0.288785	+	0.957394i	$0.406749\pi$
$53$	−3.69530	+	11.3730i	−0.507589	+	1.56220i	−0.796374	+	0.604805i	$0.793251\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.31428			0.306533
$58$		0			0
$59$	10.0896	+	7.33050i	1.31355	+	0.954350i	0.999989	+	0.00478202i	$0.00152217\pi$
$59$	10.0896	+	7.33050i	1.31355	+	0.954350i	0.313561	+	0.949568i	$0.398478\pi$
$60$		0			0
$61$	5.59873	−	4.06772i	0.716844	−	0.520818i	−0.168530	−	0.985696i	$-0.553902\pi$
$61$	5.59873	−	4.06772i	0.716844	−	0.520818i	0.885374	+	0.464879i	$0.153902\pi$
$62$		0			0
$63$	−2.86962	−	2.08490i	−0.361538	−	0.262672i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.46291	−	4.50239i	−0.178723	−	0.550054i	0.821060	−	0.570841i	$-0.193383\pi$
$67$	−1.46291	−	4.50239i	−0.178723	−	0.550054i	−0.999784	+	0.0207870i	$0.993383\pi$
$68$		0			0
$69$	0.672404	+	2.06945i	0.0809479	+	0.249132i
$70$		0			0
$71$	4.25799	−	13.1047i	0.505330	−	1.55525i	−0.294884	−	0.955533i	$-0.595281\pi$
$71$	4.25799	−	13.1047i	0.505330	−	1.55525i	0.800214	−	0.599714i	$-0.204719\pi$
$72$		0			0
$73$	0.881155	−	0.640196i	0.103131	−	0.0749293i	−0.535024	−	0.844837i	$-0.679698\pi$
$73$	0.881155	−	0.640196i	0.103131	−	0.0749293i	0.638156	+	0.769907i	$0.279698\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.33085	−	4.59963i	0.721467	−	0.524176i
$78$		0			0
$79$	−1.80542	+	5.55650i	−0.203125	+	0.625156i	0.796660	+	0.604428i	$0.206598\pi$
$79$	−1.80542	+	5.55650i	−0.203125	+	0.625156i	−0.999785	+	0.0207276i	$0.993402\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−3.87127	−	11.9145i	−0.424927	−	1.30779i	−0.903064	−	0.429505i	$-0.858688\pi$
$83$	−3.87127	−	11.9145i	−0.424927	−	1.30779i	0.478137	−	0.878285i	$-0.341312\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.685947	+	0.498370i	0.0735412	+	0.0534308i
$88$		0			0
$89$	5.68424	−	4.12984i	0.602528	−	0.437762i	−0.244247	−	0.969713i	$-0.578541\pi$
$89$	5.68424	−	4.12984i	0.602528	−	0.437762i	0.846775	+	0.531951i	$0.178541\pi$
$90$		0			0
$91$	−20.5973	−	14.9648i	−2.15918	−	1.56874i
$92$		0			0
$93$	4.30090			0.445983
$94$		0			0
$95$		0			0
$96$		0			0
$97$	5.60695	−	17.2564i	0.569299	−	1.75212i	−0.0855183	−	0.996337i	$-0.527255\pi$
$97$	5.60695	−	17.2564i	0.569299	−	1.75212i	0.654818	−	0.755787i	$-0.272745\pi$
$98$		0			0
$99$	−2.20616			−0.221728
$100$		0			0
$101$	5.97473			0.594508			0.297254	−	0.954798i	$-0.403929\pi$
$101$	5.97473			0.594508			0.297254	+	0.954798i	$0.403929\pi$
$102$		0			0
$103$	0.142014	−	0.437076i	0.0139931	−	0.0430663i	−0.943816	−	0.330471i	$-0.892792\pi$
$103$	0.142014	−	0.437076i	0.0139931	−	0.0430663i	0.957809	+	0.287405i	$0.0927924\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.47862			−0.239617			−0.119809	−	0.992797i	$-0.538228\pi$
$107$	−2.47862			−0.239617			−0.119809	+	0.992797i	$0.538228\pi$
$108$		0			0
$109$	2.70314	+	1.96394i	0.258914	+	0.188112i	0.709668	−	0.704536i	$-0.248845\pi$
$109$	2.70314	+	1.96394i	0.258914	+	0.188112i	−0.450754	+	0.892648i	$0.648845\pi$
$110$		0			0
$111$	5.84918	−	4.24968i	0.555180	−	0.403362i
$112$		0			0
$113$	14.2370	+	10.3438i	1.33930	+	0.973059i	0.999469	+	0.0325728i	$0.0103701\pi$
$113$	14.2370	+	10.3438i	1.33930	+	0.973059i	0.339832	+	0.940486i	$0.389630\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.21804	+	6.82641i	0.205057	+	0.631102i
$118$		0			0
$119$	−6.97700	−	21.4730i	−0.639581	−	1.96843i
$120$		0			0
$121$	−1.89515	+	5.83267i	−0.172286	+	0.530243i
$122$		0			0
$123$	−1.08778	+	0.790317i	−0.0980816	+	0.0712605i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	10.0415	−	7.29555i	0.891036	−	0.647376i	−0.0451118	−	0.998982i	$-0.514364\pi$
$127$	10.0415	−	7.29555i	0.891036	−	0.647376i	0.936148	+	0.351606i	$0.114364\pi$
$128$		0			0
$129$	2.53077	−	7.78890i	0.222822	−	0.685774i
$130$		0			0
$131$	4.88963	+	15.0487i	0.427209	+	1.31481i	0.900863	+	0.434104i	$0.142935\pi$
$131$	4.88963	+	15.0487i	0.427209	+	1.31481i	−0.473654	+	0.880711i	$0.657065\pi$
$132$		0			0
$133$	−2.53667	−	7.80706i	−0.219957	−	0.676958i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.98262	+	4.34663i	0.511130	+	0.371358i	0.813252	−	0.581912i	$-0.197695\pi$
$137$	5.98262	+	4.34663i	0.511130	+	0.371358i	−0.302122	+	0.953269i	$0.597695\pi$
$138$		0			0
$139$	−3.18667	+	2.31525i	−0.270290	+	0.196377i	−0.714671	−	0.699461i	$-0.753424\pi$
$139$	−3.18667	+	2.31525i	−0.270290	+	0.196377i	0.444381	+	0.895838i	$0.353424\pi$
$140$		0			0
$141$	−4.89822	−	3.55876i	−0.412504	−	0.299702i
$142$		0			0
$143$	−15.8352			−1.32421
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.72478	+	5.30832i	−0.142257	+	0.437823i
$148$		0			0
$149$	3.92892			0.321870			0.160935	−	0.986965i	$-0.448549\pi$
$149$	3.92892			0.321870			0.160935	+	0.986965i	$0.448549\pi$
$150$		0			0
$151$	7.93418			0.645674			0.322837	−	0.946455i	$-0.395363\pi$
$151$	7.93418			0.645674			0.322837	+	0.946455i	$0.395363\pi$
$152$		0			0
$153$	−1.96699	+	6.05378i	−0.159022	+	0.489419i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	6.09738			0.486624			0.243312	−	0.969948i	$-0.421766\pi$
$157$	6.09738			0.486624			0.243312	+	0.969948i	$0.421766\pi$
$158$		0			0
$159$	−9.67443	−	7.02889i	−0.767232	−	0.557427i
$160$		0			0
$161$	6.24413	−	4.53662i	0.492106	−	0.357536i
$162$		0			0
$163$	−0.00206811	−	0.00150257i	−0.000161987	−	0.000117690i	0.587704	−	0.809076i	$-0.300032\pi$
$163$	−0.00206811	−	0.00150257i	−0.000161987	−	0.000117690i	−0.587866	+	0.808958i	$0.700032\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.12128	+	9.60630i	0.241532	+	0.743358i	0.996188	+	0.0872372i	$0.0278038\pi$
$167$	3.12128	+	9.60630i	0.241532	+	0.743358i	−0.754656	+	0.656121i	$0.772196\pi$
$168$		0			0
$169$	11.9032	+	36.6343i	0.915631	+	2.81802i
$170$		0			0
$171$	−0.715151	+	2.20101i	−0.0546889	+	0.168315i
$172$		0			0
$173$	−4.99963	+	3.63244i	−0.380115	+	0.276169i	−0.761393	−	0.648291i	$-0.775484\pi$
$173$	−4.99963	+	3.63244i	−0.380115	+	0.276169i	0.381278	+	0.924460i	$0.375484\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−10.0896	+	7.33050i	−0.758378	+	0.550994i
$178$		0			0
$179$	4.45991	−	13.7262i	0.333349	−	1.02594i	−0.634181	−	0.773185i	$-0.718662\pi$
$179$	4.45991	−	13.7262i	0.333349	−	1.02594i	0.967530	−	0.252758i	$-0.0813376\pi$
$180$		0			0
$181$	2.08366	+	6.41283i	0.154877	+	0.476662i	0.998148	−	0.0608258i	$-0.0193734\pi$
$181$	2.08366	+	6.41283i	0.154877	+	0.476662i	−0.843272	+	0.537488i	$0.819373\pi$
$182$		0			0
$183$	2.13853	+	6.58170i	0.158084	+	0.486534i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−11.3610	−	8.25424i	−0.830798	−	0.603610i
$188$		0			0
$189$	2.86962	−	2.08490i	0.208734	−	0.151654i
$190$		0			0
$191$	−12.4512	−	9.04634i	−0.900938	−	0.654570i	0.0377687	−	0.999287i	$-0.487975\pi$
$191$	−12.4512	−	9.04634i	−0.900938	−	0.654570i	−0.938707	+	0.344717i	$0.887975\pi$
$192$		0			0
$193$	−16.3875			−1.17960			−0.589799	−	0.807550i	$-0.700793\pi$
$193$	−16.3875			−1.17960			−0.589799	+	0.807550i	$0.700793\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.04392	+	9.36824i	−0.216871	+	0.667459i	0.782145	+	0.623097i	$0.214126\pi$
$197$	−3.04392	+	9.36824i	−0.216871	+	0.667459i	−0.999015	+	0.0443625i	$0.985874\pi$
$198$		0			0
$199$	−4.96275			−0.351800			−0.175900	−	0.984408i	$-0.556284\pi$
$199$	−4.96275			−0.351800			−0.175900	+	0.984408i	$0.556284\pi$
$200$		0			0
$201$	4.73409			0.333917
$202$		0			0
$203$	0.929355	−	2.86026i	0.0652279	−	0.200751i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−2.17594			−0.151239
$208$		0			0
$209$	−4.13058	−	3.00104i	−0.285718	−	0.207586i
$210$		0			0
$211$	−2.83140	+	2.05713i	−0.194921	+	0.141619i	−0.680965	−	0.732316i	$-0.738440\pi$
$211$	−2.83140	+	2.05713i	−0.194921	+	0.141619i	0.486044	+	0.873934i	$0.338440\pi$
$212$		0			0
$213$	11.1476	+	8.09918i	0.763818	+	0.554947i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−4.71420	−	14.5088i	−0.320021	−	0.984923i
$218$		0			0
$219$	0.336571	+	1.03586i	0.0227434	+	0.0699969i
$220$		0			0
$221$	−14.1185	+	43.4523i	−0.949714	+	2.92292i
$222$		0			0
$223$	18.6710	−	13.5653i	1.25030	−	0.908397i	0.252062	−	0.967711i	$-0.418891\pi$
$223$	18.6710	−	13.5653i	1.25030	−	0.908397i	0.998239	+	0.0593138i	$0.0188913\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.73323	+	3.43889i	−0.314155	+	0.228247i	−0.733677	−	0.679498i	$-0.762198\pi$
$227$	−4.73323	+	3.43889i	−0.314155	+	0.228247i	0.419522	+	0.907745i	$0.362198\pi$
$228$		0			0
$229$	−1.97484	+	6.07793i	−0.130501	+	0.401641i	−0.994863	−	0.101229i	$-0.967723\pi$
$229$	−1.97484	+	6.07793i	−0.130501	+	0.401641i	0.864362	+	0.502870i	$0.167723\pi$
$230$		0			0
$231$	2.41817	+	7.44236i	0.159104	+	0.489671i
$232$		0			0
$233$	−1.40390	−	4.32076i	−0.0919725	−	0.283062i	0.894480	−	0.447107i	$-0.147546\pi$
$233$	−1.40390	−	4.32076i	−0.0919725	−	0.283062i	−0.986453	+	0.164045i	$0.947546\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.72664	−	3.43411i	−0.307029	−	0.223069i
$238$		0			0
$239$	−18.6407	+	13.5432i	−1.20576	+	0.876040i	−0.994839	−	0.101463i	$-0.967648\pi$
$239$	−18.6407	+	13.5432i	−1.20576	+	0.876040i	−0.210926	+	0.977502i	$0.567648\pi$
$240$		0			0
$241$	−13.3064	−	9.66766i	−0.857140	−	0.622749i	0.0699655	−	0.997549i	$-0.477711\pi$
$241$	−13.3064	−	9.66766i	−0.857140	−	0.622749i	−0.927105	+	0.374801i	$0.877711\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.13315	+	15.7982i	−0.326614	+	1.00522i
$248$		0			0
$249$	12.5277			0.793910
$250$		0			0
$251$	4.66327			0.294343			0.147171	−	0.989111i	$-0.452983\pi$
$251$	4.66327			0.294343			0.147171	+	0.989111i	$0.452983\pi$
$252$		0			0
$253$	1.48343	−	4.56554i	0.0932627	−	0.287033i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.78734			0.361004			0.180502	−	0.983575i	$-0.442228\pi$
$257$	5.78734			0.361004			0.180502	+	0.983575i	$0.442228\pi$
$258$		0			0
$259$	−20.7473	−	15.0738i	−1.28917	−	0.936639i
$260$		0			0
$261$	−0.685947	+	0.498370i	−0.0424591	+	0.0308483i
$262$		0			0
$263$	18.5668	+	13.4896i	1.14488	+	0.831803i	0.987792	−	0.155781i	$-0.0497895\pi$
$263$	18.5668	+	13.4896i	1.14488	+	0.831803i	0.157087	+	0.987585i	$0.449790\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.17119	+	6.68222i	0.132874	+	0.408945i
$268$		0			0
$269$	−1.39366	−	4.28923i	−0.0849727	−	0.261519i	0.899538	−	0.436842i	$-0.143903\pi$
$269$	−1.39366	−	4.28923i	−0.0849727	−	0.261519i	−0.984511	+	0.175323i	$0.943903\pi$
$270$		0			0
$271$	−3.06895	+	9.44525i	−0.186425	+	0.573758i	−0.999970	−	0.00774433i	$-0.997535\pi$
$271$	−3.06895	+	9.44525i	−0.186425	+	0.573758i	0.813545	+	0.581502i	$0.197535\pi$
$272$		0			0
$273$	20.5973	−	14.9648i	1.24660	−	0.905711i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−18.6197	+	13.5280i	−1.11875	+	0.812821i	−0.984019	−	0.178061i	$-0.943017\pi$
$277$	−18.6197	+	13.5280i	−1.11875	+	0.812821i	−0.134732	+	0.990882i	$0.543017\pi$
$278$		0			0
$279$	−1.32905	+	4.09040i	−0.0795682	+	0.244886i
$280$		0			0
$281$	0.226820	+	0.698080i	0.0135309	+	0.0416439i	0.957594	−	0.288121i	$-0.0930305\pi$
$281$	0.226820	+	0.698080i	0.0135309	+	0.0416439i	−0.944063	+	0.329765i	$0.893031\pi$
$282$		0			0
$283$	−6.64144	−	20.4402i	−0.394793	−	1.21505i	−0.929123	−	0.369771i	$-0.879436\pi$
$283$	−6.64144	−	20.4402i	−0.394793	−	1.21505i	0.534330	−	0.845276i	$-0.320564\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.85839	+	2.80329i	0.227754	+	0.165473i
$288$		0			0
$289$	−19.0259	+	13.8231i	−1.11917	+	0.813126i
$290$		0			0
$291$	14.6792	+	10.6651i	0.860509	+	0.625196i
$292$		0			0
$293$	26.5961			1.55376			0.776880	−	0.629649i	$-0.216801\pi$
$293$	26.5961			1.55376			0.776880	+	0.629649i	$0.216801\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.681742	−	2.09819i	0.0395587	−	0.121749i
$298$		0			0
$299$	−15.6183			−0.903230
$300$		0			0
$301$	−29.0493			−1.67437
$302$		0			0
$303$	−1.84629	+	5.68231i	−0.106067	+	0.326440i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−12.1736			−0.694785			−0.347393	−	0.937720i	$-0.612933\pi$
$307$	−12.1736			−0.694785			−0.347393	+	0.937720i	$0.612933\pi$
$308$		0			0
$309$	0.371799	+	0.270128i	0.0211509	+	0.0153670i
$310$		0			0
$311$	20.0330	−	14.5548i	1.13597	−	0.825327i	0.149414	−	0.988775i	$-0.452261\pi$
$311$	20.0330	−	14.5548i	1.13597	−	0.825327i	0.986552	+	0.163447i	$0.0522614\pi$
$312$		0			0
$313$	12.0102	+	8.72589i	0.678854	+	0.493216i	0.872977	−	0.487761i	$-0.162186\pi$
$313$	12.0102	+	8.72589i	0.678854	+	0.493216i	−0.194123	+	0.980977i	$0.562186\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.600207	−	1.84725i	−0.0337110	−	0.103752i	0.932785	−	0.360433i	$-0.117371\pi$
$317$	−0.600207	−	1.84725i	−0.0337110	−	0.103752i	−0.966496	+	0.256681i	$0.917371\pi$
$318$		0			0
$319$	−0.578034	−	1.77901i	−0.0323637	−	0.0996052i
$320$		0			0
$321$	0.765935	−	2.35731i	0.0427503	−	0.131572i
$322$		0			0
$323$	−11.9177	+	8.65873i	−0.663120	+	0.481785i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.70314	+	1.96394i	−0.149484	+	0.108606i
$328$		0			0
$329$	−6.63635	+	20.4246i	−0.365874	+	1.12604i
$330$		0			0
$331$	−8.56924	−	26.3734i	−0.471008	−	1.44961i	−0.851266	−	0.524734i	$-0.824165\pi$
$331$	−8.56924	−	26.3734i	−0.471008	−	1.44961i	0.380258	−	0.924880i	$-0.375835\pi$
$332$		0			0
$333$	2.23419	+	6.87612i	0.122433	+	0.376809i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	8.81048	+	6.40119i	0.479937	+	0.348695i	0.801301	−	0.598261i	$-0.204141\pi$
$337$	8.81048	+	6.40119i	0.479937	+	0.348695i	−0.321364	+	0.946956i	$0.604141\pi$
$338$		0			0
$339$	−14.2370	+	10.3438i	−0.773246	+	0.561796i
$340$		0			0
$341$	−7.67636	−	5.57720i	−0.415698	−	0.302022i
$342$		0			0
$343$	−5.03148			−0.271675
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.06224	+	21.7353i	−0.379121	+	1.16681i	0.561536	+	0.827453i	$0.310211\pi$
$347$	−7.06224	+	21.7353i	−0.379121	+	1.16681i	−0.940656	+	0.339361i	$0.889789\pi$
$348$		0			0
$349$	−28.8539			−1.54451			−0.772256	−	0.635311i	$-0.780872\pi$
$349$	−28.8539			−1.54451			−0.772256	+	0.635311i	$0.780872\pi$
$350$		0			0
$351$	−7.17771			−0.383118
$352$		0			0
$353$	8.41799	−	25.9079i	0.448045	−	1.37894i	−0.431065	−	0.902321i	$-0.641862\pi$
$353$	8.41799	−	25.9079i	0.448045	−	1.37894i	0.879110	−	0.476619i	$-0.158138\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	22.5781			1.19496
$358$		0			0
$359$	19.3648	+	14.0694i	1.02204	+	0.742553i	0.966699	−	0.255915i	$-0.0823766\pi$
$359$	19.3648	+	14.0694i	1.02204	+	0.742553i	0.0553373	+	0.998468i	$0.482377\pi$
$360$		0			0
$361$	11.0383	−	8.01981i	0.580965	−	0.422096i
$362$		0			0
$363$	−4.96157	−	3.60479i	−0.260415	−	0.189202i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.07450	+	6.38465i	0.108288	+	0.333276i	0.990488	−	0.137599i	$-0.0439384\pi$
$367$	2.07450	+	6.38465i	0.108288	+	0.333276i	−0.882200	+	0.470875i	$0.843938\pi$
$368$		0			0
$369$	−0.415494	−	1.27876i	−0.0216298	−	0.0665696i
$370$		0			0
$371$	−13.1074	+	40.3404i	−0.680502	+	2.09437i
$372$		0			0
$373$	11.0100	−	7.99923i	0.570076	−	0.414184i	−0.265057	−	0.964233i	$-0.585391\pi$
$373$	11.0100	−	7.99923i	0.570076	−	0.414184i	0.835133	+	0.550048i	$0.185391\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.92353	+	3.57715i	−0.253575	+	0.184233i
$378$		0			0
$379$	0.137272	−	0.422481i	0.00705120	−	0.0217014i	−0.947469	−	0.319848i	$-0.896368\pi$
$379$	0.137272	−	0.422481i	0.00705120	−	0.0217014i	0.954520	+	0.298146i	$0.0963683\pi$
$380$		0			0
$381$	3.83550	+	11.8045i	0.196499	+	0.604760i
$382$		0			0
$383$	−3.16140	−	9.72980i	−0.161540	−	0.497170i	0.837224	−	0.546859i	$-0.184177\pi$
$383$	−3.16140	−	9.72980i	−0.161540	−	0.497170i	−0.998765	+	0.0496897i	$0.984177\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.62563	+	4.81380i	0.336800	+	0.244699i
$388$		0			0
$389$	19.5834	−	14.2282i	0.992919	−	0.721398i	0.0323607	−	0.999476i	$-0.489697\pi$
$389$	19.5834	−	14.2282i	0.992919	−	0.721398i	0.960558	+	0.278078i	$0.0896975\pi$
$390$		0			0
$391$	−11.2054	−	8.14117i	−0.566679	−	0.411717i
$392$		0			0
$393$	−15.8232			−0.798174
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−0.841124	+	2.58871i	−0.0422148	+	0.129924i	−0.969943	−	0.243333i	$-0.921759\pi$
$397$	−0.841124	+	2.58871i	−0.0422148	+	0.129924i	0.927728	+	0.373257i	$0.121759\pi$
$398$		0			0
$399$	8.20883			0.410956
$400$		0			0
$401$	31.3538			1.56573			0.782867	−	0.622189i	$-0.213756\pi$
$401$	31.3538			1.56573			0.782867	+	0.622189i	$0.213756\pi$
$402$		0			0
$403$	−9.53955	+	29.3597i	−0.475199	+	1.46251i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−15.9505			−0.790639
$408$		0			0
$409$	−2.68805	−	1.95298i	−0.132916	−	0.0965688i	0.519341	−	0.854567i	$-0.326177\pi$
$409$	−2.68805	−	1.95298i	−0.132916	−	0.0965688i	−0.652256	+	0.757998i	$0.726177\pi$
$410$		0			0
$411$	−5.98262	+	4.34663i	−0.295101	+	0.214404i
$412$		0			0
$413$	35.7881	+	26.0016i	1.76102	+	1.27945i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.21720	−	3.74615i	−0.0596065	−	0.183450i
$418$		0			0
$419$	−3.41347	−	10.5056i	−0.166759	−	0.513231i	0.832403	−	0.554171i	$-0.186965\pi$
$419$	−3.41347	−	10.5056i	−0.166759	−	0.513231i	−0.999162	+	0.0409399i	$0.986965\pi$
$420$		0			0
$421$	−7.56044	+	23.2686i	−0.368473	+	1.13404i	0.579304	+	0.815111i	$0.303324\pi$
$421$	−7.56044	+	23.2686i	−0.368473	+	1.13404i	−0.947777	+	0.318932i	$0.896676\pi$
$422$		0			0
$423$	4.89822	−	3.55876i	0.238160	−	0.173033i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	19.8589	−	14.4284i	0.961041	−	0.698237i
$428$		0			0
$429$	4.89335	−	15.0602i	0.236253	−	0.727113i
$430$		0			0
$431$	0.354621	+	1.09141i	0.0170815	+	0.0525715i	0.959234	−	0.282613i	$-0.0912013\pi$
$431$	0.354621	+	1.09141i	0.0170815	+	0.0525715i	−0.942152	+	0.335185i	$0.891201\pi$
$432$		0			0
$433$	−1.80916	−	5.56802i	−0.0869427	−	0.267582i	0.898128	−	0.439735i	$-0.144928\pi$
$433$	−1.80916	−	5.56802i	−0.0869427	−	0.267582i	−0.985070	+	0.172153i	$0.944928\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.07400	−	2.95993i	−0.194886	−	0.141593i
$438$		0			0
$439$	16.4473	−	11.9497i	0.784988	−	0.570328i	−0.121484	−	0.992593i	$-0.538765\pi$
$439$	16.4473	−	11.9497i	0.784988	−	0.570328i	0.906472	+	0.422266i	$0.138765\pi$
$440$		0			0
$441$	−4.51553	−	3.28072i	−0.215025	−	0.156225i
$442$		0			0
$443$	17.5912			0.835783			0.417891	−	0.908497i	$-0.362769\pi$
$443$	17.5912			0.835783			0.417891	+	0.908497i	$0.362769\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.21410	+	3.73662i	−0.0574251	+	0.176736i
$448$		0			0
$449$	−2.83956			−0.134007			−0.0670037	−	0.997753i	$-0.521344\pi$
$449$	−2.83956			−0.134007			−0.0670037	+	0.997753i	$0.521344\pi$
$450$		0			0
$451$	2.96634			0.139679
$452$		0			0
$453$	−2.45180	+	7.54585i	−0.115195	+	0.354535i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−8.12004			−0.379840			−0.189920	−	0.981800i	$-0.560823\pi$
$457$	−8.12004			−0.379840			−0.189920	+	0.981800i	$0.560823\pi$
$458$		0			0
$459$	−5.14965	−	3.74144i	−0.240365	−	0.174636i
$460$		0			0
$461$	−14.5629	+	10.5806i	−0.678261	+	0.492786i	−0.872780	−	0.488113i	$-0.837685\pi$
$461$	−14.5629	+	10.5806i	−0.678261	+	0.492786i	0.194519	+	0.980899i	$0.437685\pi$
$462$		0			0
$463$	−23.1960	−	16.8529i	−1.07801	−	0.783219i	−0.100674	−	0.994919i	$-0.532100\pi$
$463$	−23.1960	−	16.8529i	−1.07801	−	0.783219i	−0.977335	+	0.211700i	$0.932100\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.19421	+	19.0638i	0.286634	+	0.882169i	0.985904	+	0.167311i	$0.0535085\pi$
$467$	6.19421	+	19.0638i	0.286634	+	0.882169i	−0.699270	+	0.714858i	$0.746491\pi$
$468$		0			0
$469$	−5.18902	−	15.9702i	−0.239607	−	0.737433i
$470$		0			0
$471$	−1.88419	+	5.79896i	−0.0868191	+	0.267202i
$472$		0			0
$473$	−14.6172	+	10.6200i	−0.672101	+	0.488310i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	9.67443	−	7.02889i	0.442962	−	0.321831i
$478$		0			0
$479$	−4.78232	+	14.7185i	−0.218510	+	0.672505i	0.780376	+	0.625311i	$0.215028\pi$
$479$	−4.78232	+	14.7185i	−0.218510	+	0.672505i	−0.998886	+	0.0471937i	$0.984972\pi$
$480$		0			0
$481$	16.0364	+	49.3548i	0.731195	+	2.25039i
$482$		0			0
$483$	2.38504	+	7.34041i	0.108523	+	0.334000i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	30.3110	+	22.0222i	1.37352	+	0.997923i	0.997453	+	0.0713312i	$0.0227247\pi$
$487$	30.3110	+	22.0222i	1.37352	+	0.997923i	0.376070	+	0.926591i	$0.377275\pi$
$488$		0			0
$489$	0.00206811	−	0.00150257i	9.35232e−5	−	6.79486e-5i
$490$		0			0
$491$	−32.3517	−	23.5049i	−1.46001	−	1.06076i	−0.983360	−	0.181667i	$-0.941851\pi$
$491$	−32.3517	−	23.5049i	−1.46001	−	1.06076i	−0.476651	−	0.879093i	$-0.658149\pi$
$492$		0			0
$493$	−5.39701			−0.243069
$494$		0			0
$495$		0			0
$496$		0			0
$497$	15.1033	−	46.4831i	0.677474	−	2.08505i
$498$		0			0
$499$	28.3040			1.26706			0.633530	−	0.773718i	$-0.281605\pi$
$499$	28.3040			1.26706			0.633530	+	0.773718i	$0.281605\pi$
$500$		0			0
$501$	−10.1007			−0.451264
$502$		0			0
$503$	−10.0998	+	31.0839i	−0.450327	+	1.38596i	0.426208	+	0.904625i	$0.359849\pi$
$503$	−10.0998	+	31.0839i	−0.450327	+	1.38596i	−0.876535	+	0.481338i	$0.840151\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−38.5196			−1.71071
$508$		0			0
$509$	−13.8620	−	10.0713i	−0.614422	−	0.446404i	0.236547	−	0.971620i	$-0.423984\pi$
$509$	−13.8620	−	10.0713i	−0.614422	−	0.446404i	−0.850969	+	0.525217i	$0.823984\pi$
$510$		0			0
$511$	3.12549	−	2.27080i	0.138264	−	0.100454i
$512$		0			0
$513$	−1.87229	−	1.36030i	−0.0826636	−	0.0600586i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	4.12763	+	12.7035i	0.181533	+	0.558701i
$518$		0			0
$519$	−1.90969	−	5.87741i	−0.0838260	−	0.257990i
$520$		0			0
$521$	6.22259	−	19.1512i	0.272617	−	0.839028i	−0.717223	−	0.696843i	$-0.754587\pi$
$521$	6.22259	−	19.1512i	0.272617	−	0.839028i	0.989840	−	0.142185i	$-0.0454128\pi$
$522$		0			0
$523$	22.5777	−	16.4036i	0.987253	−	0.717281i	0.0279349	−	0.999610i	$-0.491107\pi$
$523$	22.5777	−	16.4036i	0.987253	−	0.717281i	0.959318	+	0.282329i	$0.0911069\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−22.1482	+	16.0916i	−0.964789	+	0.700960i
$528$		0			0
$529$	−5.64428	+	17.3713i	−0.245403	+	0.755274i
$530$		0			0
$531$	−3.85387	−	11.8610i	−0.167244	−	0.514724i
$532$		0			0
$533$	−2.98230	−	9.17857i	−0.129178	−	0.397568i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	11.6762	+	8.48325i	0.503865	+	0.366079i
$538$		0			0
$539$	9.96200	−	7.23781i	0.429094	−	0.311755i
$540$		0			0
$541$	9.00089	+	6.53953i	0.386979	+	0.281156i	0.764216	−	0.644960i	$-0.223126\pi$
$541$	9.00089	+	6.53953i	0.386979	+	0.281156i	−0.377238	+	0.926116i	$0.623126\pi$
$542$		0			0
$543$	−6.74285			−0.289363
$544$		0			0
$545$		0			0
$546$		0			0
$547$	8.60009	−	26.4684i	0.367713	−	1.13171i	−0.580551	−	0.814224i	$-0.697163\pi$
$547$	8.60009	−	26.4684i	0.367713	−	1.13171i	0.948264	−	0.317482i	$-0.102837\pi$
$548$		0			0
$549$	−6.92041			−0.295356
$550$		0			0
$551$	−1.96222			−0.0835935
$552$		0			0
$553$	−6.40389	+	19.7091i	−0.272321	+	0.838118i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.36580			−0.269728			−0.134864	−	0.990864i	$-0.543060\pi$
$557$	−6.36580			−0.269728			−0.134864	+	0.990864i	$0.543060\pi$
$558$		0			0
$559$	47.5569	+	34.5521i	2.01144	+	1.46140i
$560$		0			0
$561$	11.3610	−	8.25424i	0.479661	−	0.348494i
$562$		0			0
$563$	−13.8569	−	10.0676i	−0.584000	−	0.424301i	0.256164	−	0.966633i	$-0.417541\pi$
$563$	−13.8569	−	10.0676i	−0.584000	−	0.424301i	−0.840164	+	0.542333i	$0.817541\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.09610	+	3.37344i	0.0460317	+	0.141671i
$568$		0			0
$569$	4.75461	+	14.6332i	0.199324	+	0.613455i	0.999899	+	0.0142229i	$0.00452743\pi$
$569$	4.75461	+	14.6332i	0.199324	+	0.613455i	−0.800575	+	0.599232i	$0.795473\pi$
$570$		0			0
$571$	2.63760	−	8.11770i	0.110380	−	0.339715i	−0.880575	−	0.473906i	$-0.842844\pi$
$571$	2.63760	−	8.11770i	0.110380	−	0.339715i	0.990955	+	0.134191i	$0.0428435\pi$
$572$		0			0
$573$	12.4512	−	9.04634i	0.520157	−	0.377916i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.86491	−	1.35494i	0.0776374	−	0.0564068i	−0.548290	−	0.836289i	$-0.684721\pi$
$577$	1.86491	−	1.35494i	0.0776374	−	0.0564068i	0.625927	+	0.779882i	$0.284721\pi$
$578$		0			0
$579$	5.06402	−	15.5854i	0.210453	−	0.647709i
$580$		0			0
$581$	−13.7315	−	42.2614i	−0.569681	−	1.75330i
$582$		0			0
$583$	8.15245	+	25.0907i	0.337640	+	1.03915i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.743663	−	0.540303i	−0.0306943	−	0.0223007i	0.572332	−	0.820022i	$-0.306039\pi$
$587$	−0.743663	−	0.540303i	−0.0306943	−	0.0223007i	−0.603027	+	0.797721i	$0.706039\pi$
$588$		0			0
$589$	−8.05253	+	5.85051i	−0.331799	+	0.241066i
$590$		0			0
$591$	−7.96910	−	5.78989i	−0.327805	−	0.238164i
$592$		0			0
$593$	−25.5925			−1.05096			−0.525478	−	0.850807i	$-0.676114\pi$
$593$	−25.5925			−1.05096			−0.525478	+	0.850807i	$0.676114\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.53357	−	4.71985i	0.0627650	−	0.193171i
$598$		0			0
$599$	−37.0204			−1.51261			−0.756307	−	0.654217i	$-0.772998\pi$
$599$	−37.0204			−1.51261			−0.756307	+	0.654217i	$0.772998\pi$
$600$		0			0
$601$	33.4191			1.36319			0.681597	−	0.731728i	$-0.261286\pi$
$601$	33.4191			1.36319			0.681597	+	0.731728i	$0.261286\pi$
$602$		0			0
$603$	−1.46291	+	4.50239i	−0.0595745	+	0.183351i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	4.34502			0.176359			0.0881795	−	0.996105i	$-0.471895\pi$
$607$	4.34502			0.176359			0.0881795	+	0.996105i	$0.471895\pi$
$608$		0			0
$609$	2.43308	+	1.76774i	0.0985935	+	0.0716323i
$610$		0			0
$611$	35.1580	−	25.5438i	1.42234	−	1.03339i
$612$		0			0
$613$	−3.20367	−	2.32761i	−0.129395	−	0.0940111i	0.521205	−	0.853431i	$-0.325483\pi$
$613$	−3.20367	−	2.32761i	−0.129395	−	0.0940111i	−0.650600	+	0.759420i	$0.725483\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.26189	+	19.2721i	0.252094	+	0.775866i	0.994388	+	0.105792i	$0.0337377\pi$
$617$	6.26189	+	19.2721i	0.252094	+	0.775866i	−0.742294	+	0.670074i	$0.766262\pi$
$618$		0			0
$619$	−4.65930	−	14.3398i	−0.187273	−	0.576367i	0.812707	−	0.582672i	$-0.197993\pi$
$619$	−4.65930	−	14.3398i	−0.187273	−	0.576367i	−0.999980	+	0.00630532i	$0.997993\pi$
$620$		0			0
$621$	0.672404	−	2.06945i	0.0269826	−	0.0830440i
$622$		0			0
$623$	20.1622	−	14.6487i	0.807782	−	0.586888i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	4.13058	−	3.00104i	0.164959	−	0.119850i
$628$		0			0
$629$	−14.2213	+	43.7687i	−0.567041	+	1.74517i
$630$		0			0
$631$	−0.755761	−	2.32599i	−0.0300864	−	0.0925963i	0.934886	−	0.354949i	$-0.115502\pi$
$631$	−0.755761	−	2.32599i	−0.0300864	−	0.0925963i	−0.964972	+	0.262352i	$0.915502\pi$
$632$		0			0
$633$	−1.08150	−	3.32851i	−0.0429857	−	0.132296i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−32.4112	−	23.5481i	−1.28418	−	0.933009i
$638$		0			0
$639$	−11.1476	+	8.09918i	−0.440991	+	0.320399i
$640$		0			0
$641$	−10.8353	−	7.87228i	−0.427967	−	0.310936i	0.352868	−	0.935673i	$-0.385206\pi$
$641$	−10.8353	−	7.87228i	−0.427967	−	0.310936i	−0.780836	+	0.624737i	$0.785206\pi$
$642$		0			0
$643$	35.4836			1.39934			0.699669	−	0.714467i	$-0.253331\pi$
$643$	35.4836			1.39934			0.699669	+	0.714467i	$0.253331\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.91707	−	21.2886i	0.271938	−	0.836940i	−0.718075	−	0.695966i	$-0.754977\pi$
$647$	6.91707	−	21.2886i	0.271938	−	0.836940i	0.990013	−	0.140974i	$-0.0450234\pi$
$648$		0			0
$649$	27.5140			1.08002
$650$		0			0
$651$	15.2555			0.597909
$652$		0			0
$653$	5.84923	−	18.0021i	0.228898	−	0.704476i	−0.768974	−	0.639279i	$-0.779233\pi$
$653$	5.84923	−	18.0021i	0.228898	−	0.704476i	0.997872	−	0.0651961i	$-0.0207673\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.08917			−0.0424925
$658$		0			0
$659$	−4.58371	−	3.33026i	−0.178556	−	0.129729i	0.494917	−	0.868940i	$-0.335198\pi$
$659$	−4.58371	−	3.33026i	−0.178556	−	0.129729i	−0.673473	+	0.739212i	$0.735198\pi$
$660$		0			0
$661$	20.4225	−	14.8378i	0.794342	−	0.577123i	−0.114907	−	0.993376i	$-0.536657\pi$
$661$	20.4225	−	14.8378i	0.794342	−	0.577123i	0.909249	+	0.416253i	$0.136657\pi$
$662$		0			0
$663$	−36.9627	−	26.8550i	−1.43551	−	1.04296i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.570116	−	1.75464i	−0.0220750	−	0.0679398i
$668$		0			0
$669$	7.13168	+	21.9491i	0.275727	+	0.848600i
$670$		0			0
$671$	4.71794	−	14.5203i	0.182134	−	0.560551i
$672$		0			0
$673$	10.6538	−	7.74044i	0.410674	−	0.298372i	−0.363201	−	0.931711i	$-0.618316\pi$
$673$	10.6538	−	7.74044i	0.410674	−	0.298372i	0.773875	+	0.633339i	$0.218316\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.8139	−	15.8487i	0.838375	−	0.609115i	−0.0835409	−	0.996504i	$-0.526623\pi$
$677$	21.8139	−	15.8487i	0.838375	−	0.609115i	0.921916	+	0.387389i	$0.126623\pi$
$678$		0			0
$679$	19.8881	−	61.2092i	0.763234	−	2.34899i
$680$		0			0
$681$	−1.80793	−	5.56424i	−0.0692801	−	0.213222i
$682$		0			0
$683$	−16.0008	−	49.2454i	−0.612254	−	1.88432i	−0.435897	−	0.899996i	$-0.643569\pi$
$683$	−16.0008	−	49.2454i	−0.612254	−	1.88432i	−0.176356	−	0.984326i	$-0.556431\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−5.17019	−	3.75637i	−0.197255	−	0.143314i
$688$		0			0
$689$	69.4403	−	50.4513i	2.64546	−	1.92204i
$690$		0			0
$691$	3.00647	+	2.18432i	0.114371	+	0.0830956i	0.643501	−	0.765446i	$-0.277481\pi$
$691$	3.00647	+	2.18432i	0.114371	+	0.0830956i	−0.529129	+	0.848541i	$0.677481\pi$
$692$		0			0
$693$	−7.82536			−0.297261
$694$		0			0
$695$		0			0
$696$		0			0
$697$	2.64475	−	8.13972i	0.100177	−	0.308314i
$698$		0			0
$699$	4.54311			0.171836
$700$		0			0
$701$	−28.4299			−1.07378			−0.536890	−	0.843652i	$-0.680401\pi$
$701$	−28.4299			−1.07378			−0.536890	+	0.843652i	$0.680401\pi$
$702$		0			0
$703$	−5.17053	+	15.9132i	−0.195010	+	0.600180i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	21.1926			0.797030
$708$		0			0
$709$	−33.1126	−	24.0577i	−1.24357	−	0.903507i	−0.245740	−	0.969336i	$-0.579031\pi$
$709$	−33.1126	−	24.0577i	−1.24357	−	0.903507i	−0.997831	+	0.0658288i	$0.979031\pi$
$710$		0			0
$711$	4.72664	−	3.43411i	0.177263	−	0.128789i
$712$		0			0
$713$	−7.57120	−	5.50080i	−0.283544	−	0.206007i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−7.12010	−	21.9134i	−0.265905	−	0.818372i
$718$		0			0
$719$	1.46368	+	4.50475i	0.0545861	+	0.167999i	0.974633	−	0.223810i	$-0.0718495\pi$
$719$	1.46368	+	4.50475i	0.0545861	+	0.167999i	−0.920047	+	0.391809i	$0.871849\pi$
$720$		0			0
$721$	0.503731	−	1.55032i	0.0187599	−	0.0577371i
$722$		0			0
$723$	13.3064	−	9.66766i	0.494870	−	0.359544i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−4.50692	+	3.27447i	−0.167153	+	0.121443i	−0.668217	−	0.743967i	$-0.732942\pi$
$727$	−4.50692	+	3.27447i	−0.167153	+	0.121443i	0.501064	+	0.865410i	$0.332942\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	16.1091	+	49.5788i	0.595818	+	1.83374i
$732$		0			0
$733$	9.38166	+	28.8738i	0.346520	+	1.06648i	0.960765	+	0.277363i	$0.0894604\pi$
$733$	9.38166	+	28.8738i	0.346520	+	1.06648i	−0.614246	+	0.789115i	$0.710540\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.44952	−	6.13894i	−0.311242	−	0.226131i
$738$		0			0
$739$	−39.6127	+	28.7803i	−1.45718	+	1.05870i	−0.473089	+	0.881015i	$0.656861\pi$
$739$	−39.6127	+	28.7803i	−1.45718	+	1.05870i	−0.984087	+	0.177686i	$0.943139\pi$
$740$		0			0
$741$	−13.4388	−	9.76383i	−0.493685	−	0.358683i
$742$		0			0
$743$	−45.5953			−1.67273			−0.836364	−	0.548174i	$-0.815323\pi$
$743$	−45.5953			−1.67273			−0.836364	+	0.548174i	$0.815323\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.87127	+	11.9145i	−0.141642	+	0.435930i
$748$		0			0
$749$	−8.79176			−0.321244
$750$		0			0
$751$	−27.9100			−1.01845			−0.509225	−	0.860633i	$-0.670068\pi$
$751$	−27.9100			−1.01845			−0.509225	+	0.860633i	$0.670068\pi$
$752$		0			0
$753$	−1.44103	+	4.43503i	−0.0525140	+	0.161621i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−27.6680			−1.00561			−0.502804	−	0.864400i	$-0.667698\pi$
$757$	−27.6680			−1.00561			−0.502804	+	0.864400i	$0.667698\pi$
$758$		0			0
$759$	3.88368	+	2.82166i	0.140969	+	0.102420i
$760$		0			0
$761$	9.80362	−	7.12275i	0.355381	−	0.258199i	−0.395742	−	0.918362i	$-0.629513\pi$
$761$	9.80362	−	7.12275i	0.355381	−	0.258199i	0.751123	+	0.660162i	$0.229513\pi$
$762$		0			0
$763$	9.58814	+	6.96619i	0.347114	+	0.252193i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−27.6620	−	85.1349i	−0.998817	−	3.07404i
$768$		0			0
$769$	−3.13398	−	9.64540i	−0.113014	−	0.347822i	0.878513	−	0.477718i	$-0.158536\pi$
$769$	−3.13398	−	9.64540i	−0.113014	−	0.347822i	−0.991528	+	0.129896i	$0.958536\pi$
$770$		0			0
$771$	−1.78839	+	5.50409i	−0.0644071	+	0.198225i
$772$		0			0
$773$	−40.5906	+	29.4908i	−1.45994	+	1.06071i	−0.476563	+	0.879140i	$0.658118\pi$
$773$	−40.5906	+	29.4908i	−1.45994	+	1.06071i	−0.983378	+	0.181569i	$0.941882\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	20.7473	−	15.0738i	0.744304	−	0.540769i
$778$		0			0
$779$	0.961568	−	2.95940i	0.0344518	−	0.106032i
$780$		0			0
$781$	−9.39383	−	28.9112i	−0.336138	−	1.03453i
$782$		0			0
$783$	−0.262008	−	0.806379i	−0.00936342	−	0.0288176i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	12.5059	+	9.08606i	0.445787	+	0.323883i	0.787930	−	0.615765i	$-0.211153\pi$
$787$	12.5059	+	9.08606i	0.445787	+	0.323883i	−0.342143	+	0.939648i	$0.611153\pi$
$788$		0			0
$789$	−18.5668	+	13.4896i	−0.660996	+	0.480242i
$790$		0			0
$791$	50.4991	+	36.6897i	1.79554	+	1.30454i
$792$		0			0
$793$	−49.6727			−1.76393
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.77110	+	5.45087i	−0.0627354	+	0.193080i	−0.977512	−	0.210881i	$-0.932367\pi$
$797$	−1.77110	+	5.45087i	−0.0627354	+	0.193080i	0.914776	+	0.403961i	$0.132367\pi$
$798$		0			0
$799$	38.5390			1.36341
$800$		0			0
$801$	−7.02611			−0.248255
$802$		0			0
$803$	0.742531	−	2.28528i	0.0262034	−	0.0806457i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4.50997			0.158758
$808$		0			0
$809$	22.9907	+	16.7038i	0.808312	+	0.587273i	0.913341	−	0.407196i	$-0.133494\pi$
$809$	22.9907	+	16.7038i	0.808312	+	0.587273i	−0.105029	+	0.994469i	$0.533494\pi$
$810$		0			0
$811$	9.86048	−	7.16406i	0.346248	−	0.251564i	−0.401045	−	0.916058i	$-0.631353\pi$
$811$	9.86048	−	7.16406i	0.346248	−	0.251564i	0.747293	+	0.664494i	$0.231353\pi$
$812$		0			0
$813$	−8.03461	−	5.83748i	−0.281786	−	0.204730i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	5.85689	+	18.0257i	0.204907	+	0.630638i
$818$		0			0
$819$	7.86746	+	24.2136i	0.274911	+	0.846090i
$820$		0			0
$821$	4.51854	−	13.9066i	0.157698	−	0.485345i	−0.840726	−	0.541461i	$-0.817872\pi$
$821$	4.51854	−	13.9066i	0.157698	−	0.485345i	0.998424	+	0.0561157i	$0.0178716\pi$
$822$		0			0
$823$	−17.5077	+	12.7201i	−0.610280	+	0.443394i	−0.849513	−	0.527568i	$-0.823104\pi$
$823$	−17.5077	+	12.7201i	−0.610280	+	0.443394i	0.239233	+	0.970962i	$0.423104\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.03038	+	6.56096i	−0.314017	+	0.228147i	−0.733618	−	0.679562i	$-0.762170\pi$
$827$	−9.03038	+	6.56096i	−0.314017	+	0.228147i	0.419601	+	0.907709i	$0.362170\pi$
$828$		0			0
$829$	8.60563	−	26.4854i	0.298886	−	0.919876i	−0.683003	−	0.730416i	$-0.739326\pi$
$829$	8.60563	−	26.4854i	0.298886	−	0.919876i	0.981888	−	0.189460i	$-0.0606738\pi$
$830$		0			0
$831$	−7.11211	−	21.8888i	−0.246716	−	0.759315i
$832$		0			0
$833$	−10.9788	−	33.7892i	−0.380392	−	1.17073i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−3.47950	−	2.52801i	−0.120269	−	0.0873807i
$838$		0			0
$839$	15.3556	−	11.1565i	0.530133	−	0.385164i	−0.290274	−	0.956943i	$-0.593747\pi$
$839$	15.3556	−	11.1565i	0.530133	−	0.385164i	0.820408	+	0.571779i	$0.193747\pi$
$840$		0			0
$841$	22.8799	+	16.6232i	0.788962	+	0.573214i
$842$		0			0
$843$	−0.734004			−0.0252804
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−6.72218	+	20.6887i	−0.230977	+	0.710873i
$848$		0			0
$849$	21.4921			0.737609
$850$		0			0
$851$	−15.7320			−0.539287
$852$		0			0
$853$	−5.10082	+	15.6987i	−0.174649	+	0.537513i	−0.999617	−	0.0276653i	$-0.991193\pi$
$853$	−5.10082	+	15.6987i	−0.174649	+	0.537513i	0.824969	+	0.565179i	$0.191193\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.7615			0.982475			0.491237	−	0.871026i	$-0.336545\pi$
$857$	28.7615			0.982475			0.491237	+	0.871026i	$0.336545\pi$
$858$		0			0
$859$	12.2446	+	8.89622i	0.417780	+	0.303535i	0.776744	−	0.629816i	$-0.216870\pi$
$859$	12.2446	+	8.89622i	0.417780	+	0.303535i	−0.358964	+	0.933351i	$0.616870\pi$
$860$		0			0
$861$	−3.85839	+	2.80329i	−0.131494	+	0.0955357i
$862$		0			0
$863$	34.8258	+	25.3024i	1.18549	+	0.861305i	0.992780	−	0.119951i	$-0.0382738\pi$
$863$	34.8258	+	25.3024i	1.18549	+	0.861305i	0.192705	+	0.981257i	$0.438274\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−7.26725	−	22.3663i	−0.246809	−	0.759600i
$868$		0			0
$869$	3.98305	+	12.2586i	0.135116	+	0.415843i
$870$		0			0
$871$	−10.5004	+	32.3168i	−0.355792	+	1.09501i
$872$		0			0
$873$	−14.6792	+	10.6651i	−0.496815	+	0.360957i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−41.0134	+	29.7980i	−1.38492	+	1.00621i	−0.388523	+	0.921439i	$0.627015\pi$
$877$	−41.0134	+	29.7980i	−1.38492	+	1.00621i	−0.996401	+	0.0847668i	$0.972985\pi$
$878$		0			0
$879$	−8.21864	+	25.2944i	−0.277208	+	0.853158i
$880$		0			0
$881$	−0.818966	−	2.52052i	−0.0275917	−	0.0849184i	0.936312	−	0.351168i	$-0.114215\pi$
$881$	−0.818966	−	2.52052i	−0.0275917	−	0.0849184i	−0.963904	+	0.266250i	$0.914215\pi$
$882$		0			0
$883$	10.4361	+	32.1189i	0.351201	+	1.08089i	0.958179	+	0.286168i	$0.0923816\pi$
$883$	10.4361	+	32.1189i	0.351201	+	1.08089i	−0.606978	+	0.794719i	$0.707618\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.49811	−	2.54153i	−0.117455	−	0.0853361i	0.527507	−	0.849551i	$-0.323127\pi$
$887$	−3.49811	−	2.54153i	−0.117455	−	0.0853361i	−0.644962	+	0.764215i	$0.723127\pi$
$888$		0			0
$889$	35.6175	−	25.8776i	1.19457	−	0.867908i
$890$		0			0
$891$	1.78482	+	1.29675i	0.0597939	+	0.0434428i
$892$		0			0
$893$	14.0119			0.468889
$894$		0			0
$895$		0			0
$896$		0			0
$897$	4.82632	−	14.8539i	0.161146	−	0.495957i
$898$		0			0
$899$	−3.64664			−0.121622
$900$		0			0
$901$	76.1182			2.53586
$902$		0			0
$903$	8.97673	−	27.6275i	0.298727	−	0.919387i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	47.2507			1.56893			0.784467	−	0.620171i	$-0.212937\pi$
$907$	47.2507			1.56893			0.784467	+	0.620171i	$0.212937\pi$
$908$		0			0
$909$	−4.83366	−	3.51186i	−0.160322	−	0.116481i
$910$		0			0
$911$	−41.1586	+	29.9035i	−1.36365	+	0.990747i	−0.365443	+	0.930834i	$0.619082\pi$
$911$	−41.1586	+	29.9035i	−1.36365	+	0.990747i	−0.998204	+	0.0599132i	$0.980918\pi$
$912$		0			0
$913$	−22.3597	−	16.2453i	−0.739999	−	0.537641i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	17.3437	+	53.3785i	0.572740	+	1.76271i
$918$		0			0
$919$	−11.3396	−	34.8998i	−0.374060	−	1.15124i	−0.944111	−	0.329629i	$-0.893076\pi$
$919$	−11.3396	−	34.8998i	−0.374060	−	1.15124i	0.570051	−	0.821610i	$-0.306924\pi$
$920$		0			0
$921$	3.76186	−	11.5778i	0.123957	−	0.381502i
$922$		0			0
$923$	−80.0140	+	58.1336i	−2.63369	+	1.91349i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.371799	+	0.270128i	−0.0122115	+	0.00887215i
$928$		0			0
$929$	14.9269	−	45.9401i	0.489734	−	1.50725i	−0.335271	−	0.942122i	$-0.608828\pi$
$929$	14.9269	−	45.9401i	0.489734	−	1.50725i	0.825005	−	0.565125i	$-0.191172\pi$
$930$		0			0
$931$	−3.99161	−	12.2849i	−0.130820	−	0.402622i
$932$		0			0
$933$	7.65191	+	23.5502i	0.250512	+	0.770998i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	7.67223	+	5.57420i	0.250641	+	0.182101i	0.706011	−	0.708201i	$-0.250493\pi$
$937$	7.67223	+	5.57420i	0.250641	+	0.182101i	−0.455370	+	0.890302i	$0.650493\pi$
$938$		0			0
$939$	−12.0102	+	8.72589i	−0.391937	+	0.284759i
$940$		0			0
$941$	17.2272	+	12.5163i	0.561590	+	0.408019i	0.832041	−	0.554715i	$-0.187173\pi$
$941$	17.2272	+	12.5163i	0.561590	+	0.408019i	−0.270450	+	0.962734i	$0.587173\pi$
$942$		0			0
$943$	2.92570			0.0952740
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.73768	−	29.9695i	0.316432	−	0.973877i	−0.658729	−	0.752380i	$-0.728906\pi$
$947$	9.73768	−	29.9695i	0.316432	−	0.973877i	0.975161	−	0.221497i	$-0.0710943\pi$
$948$		0			0
$949$	−7.81773			−0.253774
$950$		0			0
$951$	1.94231			0.0629837
$952$		0			0
$953$	3.46513	−	10.6646i	0.112247	−	0.345460i	−0.879116	−	0.476608i	$-0.841866\pi$
$953$	3.46513	−	10.6646i	0.112247	−	0.345460i	0.991363	+	0.131148i	$0.0418663\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.87056			0.0604665
$958$		0			0
$959$	21.2206	+	15.4177i	0.685249	+	0.497863i
$960$		0			0
$961$	10.1145	−	7.34864i	0.326275	−	0.237053i
$962$		0			0
$963$	2.00524	+	1.45689i	0.0646181	+	0.0469478i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−11.0077	−	33.8782i	−0.353984	−	1.08945i	−0.956596	−	0.291417i	$-0.905873\pi$
$967$	−11.0077	−	33.8782i	−0.353984	−	1.08945i	0.602612	−	0.798034i	$-0.294127\pi$
$968$		0			0
$969$	−4.55217	−	14.0101i	−0.146237	−	0.450070i
$970$		0			0
$971$	13.2227	−	40.6953i	0.424337	−	1.30598i	−0.479290	−	0.877656i	$-0.659106\pi$
$971$	13.2227	−	40.6953i	0.424337	−	1.30598i	0.903628	−	0.428319i	$-0.140894\pi$
$972$		0			0
$973$	−11.3032	+	8.21228i	−0.362365	+	0.263274i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	32.9119	−	23.9119i	1.05294	−	0.765009i	0.0801740	−	0.996781i	$-0.474452\pi$
$977$	32.9119	−	23.9119i	1.05294	−	0.765009i	0.972770	+	0.231772i	$0.0744524\pi$
$978$		0			0
$979$	4.78999	−	14.7421i	0.153089	−	0.471159i
$980$		0			0
$981$	−1.03251	−	3.17773i	−0.0329654	−	0.101457i
$982$		0			0
$983$	−15.1319	−	46.5713i	−0.482634	−	1.48539i	−0.835379	−	0.549674i	$-0.814752\pi$
$983$	−15.1319	−	46.5713i	−0.482634	−	1.48539i	0.352746	−	0.935719i	$-0.385248\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−17.3742	−	12.6231i	−0.553026	−	0.401797i
$988$		0			0
$989$	−14.4170	+	10.4746i	−0.458434	+	0.333072i
$990$		0			0
$991$	1.99334	+	1.44825i	0.0633206	+	0.0460051i	0.618995	−	0.785395i	$-0.287540\pi$
$991$	1.99334	+	1.44825i	0.0633206	+	0.0460051i	−0.555675	+	0.831400i	$0.687540\pi$
$992$		0			0
$993$	27.7307			0.880006
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−16.7650	+	51.5975i	−0.530954	+	1.63411i	0.221277	+	0.975211i	$0.428977\pi$
$997$	−16.7650	+	51.5975i	−0.530954	+	1.63411i	−0.752232	+	0.658899i	$0.771023\pi$
$998$		0			0
$999$	−7.22998			−0.228747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.m.d.301.6		24
5.2	odd	4		300.2.o.a.289.4	yes	24
5.3	odd	4		1500.2.o.c.949.3		24
5.4	even	2		1500.2.m.c.301.1		24
15.2	even	4		900.2.w.c.289.5		24
25.3	odd	20		7500.2.d.g.1249.2		24
25.4	even	10		7500.2.a.n.1.2		12
25.9	even	10		1500.2.m.c.1201.1		24
25.12	odd	20		1500.2.o.c.49.3		24
25.13	odd	20		300.2.o.a.109.4	✓	24
25.16	even	5	inner	1500.2.m.d.1201.6		24
25.21	even	5		7500.2.a.m.1.11		12
25.22	odd	20		7500.2.d.g.1249.23		24
75.38	even	20		900.2.w.c.109.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.4	✓	24	25.13	odd	20
300.2.o.a.289.4	yes	24	5.2	odd	4
900.2.w.c.109.5		24	75.38	even	20
900.2.w.c.289.5		24	15.2	even	4
1500.2.m.c.301.1		24	5.4	even	2
1500.2.m.c.1201.1		24	25.9	even	10
1500.2.m.d.301.6		24	1.1	even	1	trivial
1500.2.m.d.1201.6		24	25.16	even	5	inner
1500.2.o.c.49.3		24	25.12	odd	20
1500.2.o.c.949.3		24	5.3	odd	4
7500.2.a.m.1.11		12	25.21	even	5
7500.2.a.n.1.2		12	25.4	even	10
7500.2.d.g.1249.2		24	25.3	odd	20
7500.2.d.g.1249.23		24	25.22	odd	20

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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{3} +3.54704 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{3} +3.54704 q^{7} +(-0.809017 - 0.587785i) q^{9} +(1.78482 - 1.29675i) q^{11} +(-5.80689 - 4.21895i) q^{13} +(-1.96699 - 6.05378i) q^{17} +(-0.715151 - 2.20101i) q^{19} +(-1.09610 + 3.37344i) q^{21} +(1.76038 - 1.27899i) q^{23} +(0.809017 - 0.587785i) q^{27} +(0.262008 - 0.806379i) q^{29} +(-1.32905 - 4.09040i) q^{31} +(0.681742 + 2.09819i) q^{33} +(-5.84918 - 4.24968i) q^{37} +(5.80689 - 4.21895i) q^{39} +(1.08778 + 0.790317i) q^{41} -8.18973 q^{43} +(-1.87095 + 5.75820i) q^{47} +5.58150 q^{49} +6.36532 q^{51} +(-3.69530 + 11.3730i) q^{53} +2.31428 q^{57} +(10.0896 + 7.33050i) q^{59} +(5.59873 - 4.06772i) q^{61} +(-2.86962 - 2.08490i) q^{63} +(-1.46291 - 4.50239i) q^{67} +(0.672404 + 2.06945i) q^{69} +(4.25799 - 13.1047i) q^{71} +(0.881155 - 0.640196i) q^{73} +(6.33085 - 4.59963i) q^{77} +(-1.80542 + 5.55650i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-3.87127 - 11.9145i) q^{83} +(0.685947 + 0.498370i) q^{87} +(5.68424 - 4.12984i) q^{89} +(-20.5973 - 14.9648i) q^{91} +4.30090 q^{93} +(5.60695 - 17.2564i) q^{97} -2.20616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9} - 6 q^{11} + 4 q^{17} - 10 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{27} - 4 q^{29} + 6 q^{31} - 4 q^{33} - 8 q^{37} - 10 q^{41} - 56 q^{43} + 26 q^{47} + 56 q^{49} + 16 q^{51} - 32 q^{53} - 20 q^{57} + 36 q^{59} - 12 q^{61} + 4 q^{63} + 36 q^{67} - 4 q^{69} + 40 q^{71} + 32 q^{73} - 46 q^{77} - 8 q^{79} - 6 q^{81} - 6 q^{83} + 4 q^{87} - 30 q^{91} + 4 q^{93} + 48 q^{97} + 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9 - 6 * q^11 + 4 * q^17 - 10 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^27 - 4 * q^29 + 6 * q^31 - 4 * q^33 - 8 * q^37 - 10 * q^41 - 56 * q^43 + 26 * q^47 + 56 * q^49 + 16 * q^51 - 32 * q^53 - 20 * q^57 + 36 * q^59 - 12 * q^61 + 4 * q^63 + 36 * q^67 - 4 * q^69 + 40 * q^71 + 32 * q^73 - 46 * q^77 - 8 * q^79 - 6 * q^81 - 6 * q^83 + 4 * q^87 - 30 * q^91 + 4 * q^93 + 48 * q^97 + 4 * q^99

Introduction

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