LMFDB - Embedded newform 1500.2.o.c.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(49,1500)]

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, 7]))

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

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

chi := DirichletCharacter("1500.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.o (of order $10$, 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 $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	1500.49
Dual form			1500.2.o.c.949.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{3} +3.54704i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{3} +3.54704i q^{7} +(0.809017 - 0.587785i) q^{9} +(1.78482 + 1.29675i) q^{11} +(4.21895 + 5.80689i) q^{13} +(-6.05378 - 1.96699i) q^{17} +(0.715151 - 2.20101i) q^{19} +(-1.09610 - 3.37344i) q^{21} +(1.27899 - 1.76038i) q^{23} +(-0.587785 + 0.809017i) q^{27} +(-0.262008 - 0.806379i) q^{29} +(-1.32905 + 4.09040i) q^{31} +(-2.09819 - 0.681742i) q^{33} +(-4.24968 - 5.84918i) q^{37} +(-5.80689 - 4.21895i) q^{39} +(1.08778 - 0.790317i) q^{41} +8.18973i q^{43} +(5.75820 - 1.87095i) q^{47} -5.58150 q^{49} +6.36532 q^{51} +(-11.3730 + 3.69530i) q^{53} +2.31428i q^{57} +(-10.0896 + 7.33050i) q^{59} +(5.59873 + 4.06772i) q^{61} +(2.08490 + 2.86962i) q^{63} +(-4.50239 - 1.46291i) q^{67} +(-0.672404 + 2.06945i) q^{69} +(4.25799 + 13.1047i) q^{71} +(0.640196 - 0.881155i) q^{73} +(-4.59963 + 6.33085i) q^{77} +(1.80542 + 5.55650i) q^{79} +(0.309017 - 0.951057i) q^{81} +(11.9145 + 3.87127i) q^{83} +(0.498370 + 0.685947i) q^{87} +(-5.68424 - 4.12984i) q^{89} +(-20.5973 + 14.9648i) q^{91} -4.30090i q^{93} +(-17.2564 + 5.60695i) q^{97} +2.20616 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^9	$ 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63} - 20 q^{67} + 4 q^{69} + 40 q^{71} - 60 q^{73} + 40 q^{77} + 8 q^{79} - 6 q^{81} + 50 q^{83} + 20 q^{87} - 30 q^{91} + 40 q^{97} - 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$	$1$

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
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			3.54704i			1.34066i	0.742065	+	0.670328i	$0.233846\pi$
$7$			3.54704i			1.34066i	−0.742065	+	0.670328i	$0.766154\pi$
$8$		0			0
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	1.78482	+	1.29675i	0.538145	+	0.390985i	0.823396	−	0.567468i	$-0.192077\pi$
$11$	1.78482	+	1.29675i	0.538145	+	0.390985i	−0.285251	+	0.958453i	$0.592077\pi$
$12$		0			0
$13$	4.21895	+	5.80689i	1.17013	+	1.61054i	0.662827	+	0.748773i	$0.269357\pi$
$13$	4.21895	+	5.80689i	1.17013	+	1.61054i	0.507301	+	0.861769i	$0.330643\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.05378	−	1.96699i	−1.46826	−	0.477066i	−0.537676	−	0.843151i	$-0.680698\pi$
$17$	−6.05378	−	1.96699i	−1.46826	−	0.477066i	−0.930581	+	0.366086i	$0.880698\pi$
$18$		0			0
$19$	0.715151	−	2.20101i	0.164067	−	0.504946i	−0.834899	−	0.550402i	$-0.814474\pi$
$19$	0.715151	−	2.20101i	0.164067	−	0.504946i	0.998966	+	0.0454566i	$0.0144743\pi$
$20$		0			0
$21$	−1.09610	−	3.37344i	−0.239188	−	0.736144i
$22$		0			0
$23$	1.27899	−	1.76038i	0.266687	−	0.367064i	−0.654580	−	0.755992i	$-0.727155\pi$
$23$	1.27899	−	1.76038i	0.266687	−	0.367064i	0.921268	+	0.388929i	$0.127155\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$		0			0
$29$	−0.262008	−	0.806379i	−0.0486538	−	0.149741i	0.923778	−	0.382928i	$-0.125084\pi$
$29$	−0.262008	−	0.806379i	−0.0486538	−	0.149741i	−0.972432	+	0.233188i	$0.925084\pi$
$30$		0			0
$31$	−1.32905	+	4.09040i	−0.238705	+	0.734657i	0.757904	+	0.652367i	$0.226224\pi$
$31$	−1.32905	+	4.09040i	−0.238705	+	0.734657i	−0.996608	+	0.0822910i	$0.973776\pi$
$32$		0			0
$33$	−2.09819	−	0.681742i	−0.365248	−	0.118676i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.24968	−	5.84918i	−0.698643	−	0.961599i	−0.999967	−	0.00807756i	$-0.997429\pi$
$37$	−4.24968	−	5.84918i	−0.698643	−	0.961599i	0.301325	−	0.953522i	$-0.402571\pi$
$38$		0			0
$39$	−5.80689	−	4.21895i	−0.929847	−	0.675573i
$40$		0			0
$41$	1.08778	−	0.790317i	0.169882	−	0.123427i	−0.499595	−	0.866259i	$-0.666518\pi$
$41$	1.08778	−	0.790317i	0.169882	−	0.123427i	0.669478	+	0.742832i	$0.266518\pi$
$42$		0			0
$43$			8.18973i			1.24892i	0.781056	+	0.624461i	$0.214681\pi$
$43$			8.18973i			1.24892i	−0.781056	+	0.624461i	$0.785319\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.75820	−	1.87095i	0.839920	−	0.272907i	0.142702	−	0.989766i	$-0.454421\pi$
$47$	5.75820	−	1.87095i	0.839920	−	0.272907i	0.697218	+	0.716859i	$0.254421\pi$
$48$		0			0
$49$	−5.58150			−0.797357
$50$		0			0
$51$	6.36532			0.891323
$52$		0			0
$53$	−11.3730	+	3.69530i	−1.56220	+	0.507589i	−0.957394	−	0.288785i	$-0.906749\pi$
$53$	−11.3730	+	3.69530i	−1.56220	+	0.507589i	−0.604805	+	0.796374i	$0.706749\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			2.31428i			0.306533i
$58$		0			0
$59$	−10.0896	+	7.33050i	−1.31355	+	0.954350i	−0.313561	+	0.949568i	$0.601522\pi$
$59$	−10.0896	+	7.33050i	−1.31355	+	0.954350i	−0.999989	+	0.00478202i	$0.998478\pi$
$60$		0			0
$61$	5.59873	+	4.06772i	0.716844	+	0.520818i	0.885374	−	0.464879i	$-0.153902\pi$
$61$	5.59873	+	4.06772i	0.716844	+	0.520818i	−0.168530	+	0.985696i	$0.553902\pi$
$62$		0			0
$63$	2.08490	+	2.86962i	0.262672	+	0.361538i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.50239	−	1.46291i	−0.550054	−	0.178723i	0.0207870	−	0.999784i	$-0.493383\pi$
$67$	−4.50239	−	1.46291i	−0.550054	−	0.178723i	−0.570841	+	0.821060i	$0.693383\pi$
$68$		0			0
$69$	−0.672404	+	2.06945i	−0.0809479	+	0.249132i
$70$		0			0
$71$	4.25799	+	13.1047i	0.505330	+	1.55525i	0.800214	+	0.599714i	$0.204719\pi$
$71$	4.25799	+	13.1047i	0.505330	+	1.55525i	−0.294884	+	0.955533i	$0.595281\pi$
$72$		0			0
$73$	0.640196	−	0.881155i	0.0749293	−	0.103131i	−0.769907	−	0.638156i	$-0.779698\pi$
$73$	0.640196	−	0.881155i	0.0749293	−	0.103131i	0.844837	+	0.535024i	$0.179698\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.59963	+	6.33085i	−0.524176	+	0.721467i
$78$		0			0
$79$	1.80542	+	5.55650i	0.203125	+	0.625156i	0.999785	+	0.0207276i	$0.00659828\pi$
$79$	1.80542	+	5.55650i	0.203125	+	0.625156i	−0.796660	+	0.604428i	$0.793402\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	11.9145	+	3.87127i	1.30779	+	0.424927i	0.878285	−	0.478137i	$-0.158688\pi$
$83$	11.9145	+	3.87127i	1.30779	+	0.424927i	0.429505	+	0.903064i	$0.358688\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.498370	+	0.685947i	0.0534308	+	0.0735412i
$88$		0			0
$89$	−5.68424	−	4.12984i	−0.602528	−	0.437762i	0.244247	−	0.969713i	$-0.421459\pi$
$89$	−5.68424	−	4.12984i	−0.602528	−	0.437762i	−0.846775	+	0.531951i	$0.821459\pi$
$90$		0			0
$91$	−20.5973	+	14.9648i	−2.15918	+	1.56874i
$92$		0			0
$93$		−	4.30090i		−	0.445983i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−17.2564	+	5.60695i	−1.75212	+	0.569299i	−0.996337	−	0.0855183i	$-0.972745\pi$
$97$	−17.2564	+	5.60695i	−1.75212	+	0.569299i	−0.755787	+	0.654818i	$0.772745\pi$
$98$		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
$103$	0.437076	−	0.142014i	0.0430663	−	0.0139931i	−0.287405	−	0.957809i	$-0.592792\pi$
$103$	0.437076	−	0.142014i	0.0430663	−	0.0139931i	0.330471	+	0.943816i	$0.392792\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	2.47862i		−	0.239617i	−0.992797	−	0.119809i	$-0.961772\pi$
$107$		−	2.47862i		−	0.239617i	0.992797	−	0.119809i	$-0.0382281\pi$
$108$		0			0
$109$	−2.70314	+	1.96394i	−0.258914	+	0.188112i	−0.709668	−	0.704536i	$-0.751155\pi$
$109$	−2.70314	+	1.96394i	−0.258914	+	0.188112i	0.450754	+	0.892648i	$0.351155\pi$
$110$		0			0
$111$	5.84918	+	4.24968i	0.555180	+	0.403362i
$112$		0			0
$113$	−10.3438	−	14.2370i	−0.973059	−	1.33930i	−0.940486	−	0.339832i	$-0.889630\pi$
$113$	−10.3438	−	14.2370i	−0.973059	−	1.33930i	−0.0325728	−	0.999469i	$-0.510370\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6.82641	+	2.21804i	0.631102	+	0.205057i
$118$		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
$123$	−0.790317	+	1.08778i	−0.0712605	+	0.0980816i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−7.29555	+	10.0415i	−0.647376	+	0.891036i	−0.998982	−	0.0451118i	$-0.985636\pi$
$127$	−7.29555	+	10.0415i	−0.647376	+	0.891036i	0.351606	+	0.936148i	$0.385636\pi$
$128$		0			0
$129$	−2.53077	−	7.78890i	−0.222822	−	0.685774i
$130$		0			0
$131$	4.88963	−	15.0487i	0.427209	−	1.31481i	−0.473654	−	0.880711i	$-0.657065\pi$
$131$	4.88963	−	15.0487i	0.427209	−	1.31481i	0.900863	−	0.434104i	$-0.142935\pi$
$132$		0			0
$133$	7.80706	+	2.53667i	0.676958	+	0.219957i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.34663	+	5.98262i	0.371358	+	0.511130i	0.953269	−	0.302122i	$-0.0976950\pi$
$137$	4.34663	+	5.98262i	0.371358	+	0.511130i	−0.581912	+	0.813252i	$0.697695\pi$
$138$		0			0
$139$	3.18667	+	2.31525i	0.270290	+	0.196377i	0.714671	−	0.699461i	$-0.246576\pi$
$139$	3.18667	+	2.31525i	0.270290	+	0.196377i	−0.444381	+	0.895838i	$0.646576\pi$
$140$		0			0
$141$	−4.89822	+	3.55876i	−0.412504	+	0.299702i
$142$		0			0
$143$			15.8352i			1.32421i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.30832	−	1.72478i	0.437823	−	0.142257i
$148$		0			0
$149$	−3.92892			−0.321870			−0.160935	−	0.986965i	$-0.551451\pi$
$149$	−3.92892			−0.321870			−0.160935	+	0.986965i	$0.551451\pi$
$150$		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
$153$	−6.05378	+	1.96699i	−0.489419	+	0.159022i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			6.09738i			0.486624i	0.969948	+	0.243312i	$0.0782339\pi$
$157$			6.09738i			0.486624i	−0.969948	+	0.243312i	$0.921766\pi$
$158$		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
$163$	0.00150257	+	0.00206811i	0.000117690	+	0.000161987i	0.809076	−	0.587704i	$-0.199968\pi$
$163$	0.00150257	+	0.00206811i	0.000117690	+	0.000161987i	−0.808958	+	0.587866i	$0.799968\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.60630	+	3.12128i	0.743358	+	0.241532i	0.656121	−	0.754656i	$-0.272196\pi$
$167$	9.60630	+	3.12128i	0.743358	+	0.241532i	0.0872372	+	0.996188i	$0.472196\pi$
$168$		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
$173$	−3.63244	+	4.99963i	−0.276169	+	0.380115i	−0.924460	−	0.381278i	$-0.875484\pi$
$173$	−3.63244	+	4.99963i	−0.276169	+	0.380115i	0.648291	+	0.761393i	$0.275484\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	7.33050	−	10.0896i	0.550994	−	0.758378i
$178$		0			0
$179$	−4.45991	−	13.7262i	−0.333349	−	1.02594i	−0.967530	−	0.252758i	$-0.918662\pi$
$179$	−4.45991	−	13.7262i	−0.333349	−	1.02594i	0.634181	−	0.773185i	$-0.281338\pi$
$180$		0			0
$181$	2.08366	−	6.41283i	0.154877	−	0.476662i	−0.843272	−	0.537488i	$-0.819373\pi$
$181$	2.08366	−	6.41283i	0.154877	−	0.476662i	0.998148	+	0.0608258i	$0.0193734\pi$
$182$		0			0
$183$	−6.58170	−	2.13853i	−0.486534	−	0.158084i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−8.25424	−	11.3610i	−0.603610	−	0.830798i
$188$		0			0
$189$	−2.86962	−	2.08490i	−0.208734	−	0.151654i
$190$		0			0
$191$	−12.4512	+	9.04634i	−0.900938	+	0.654570i	−0.938707	−	0.344717i	$-0.887975\pi$
$191$	−12.4512	+	9.04634i	−0.900938	+	0.654570i	0.0377687	+	0.999287i	$0.487975\pi$
$192$		0			0
$193$			16.3875i			1.17960i	0.807550	+	0.589799i	$0.200793\pi$
$193$			16.3875i			1.17960i	−0.807550	+	0.589799i	$0.799207\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.36824	−	3.04392i	0.667459	−	0.216871i	0.0443625	−	0.999015i	$-0.485874\pi$
$197$	9.36824	−	3.04392i	0.667459	−	0.216871i	0.623097	+	0.782145i	$0.285874\pi$
$198$		0			0
$199$	4.96275			0.351800			0.175900	−	0.984408i	$-0.443716\pi$
$199$	4.96275			0.351800			0.175900	+	0.984408i	$0.443716\pi$
$200$		0			0
$201$	4.73409			0.333917
$202$		0			0
$203$	2.86026	−	0.929355i	0.200751	−	0.0652279i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	2.17594i		−	0.151239i
$208$		0			0
$209$	4.13058	−	3.00104i	0.285718	−	0.207586i
$210$		0			0
$211$	−2.83140	−	2.05713i	−0.194921	−	0.141619i	0.486044	−	0.873934i	$-0.338440\pi$
$211$	−2.83140	−	2.05713i	−0.194921	−	0.141619i	−0.680965	+	0.732316i	$0.738440\pi$
$212$		0			0
$213$	−8.09918	−	11.1476i	−0.554947	−	0.763818i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−14.5088	−	4.71420i	−0.984923	−	0.320021i
$218$		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
$223$	13.5653	−	18.6710i	0.908397	−	1.25030i	−0.0593138	−	0.998239i	$-0.518891\pi$
$223$	13.5653	−	18.6710i	0.908397	−	1.25030i	0.967711	−	0.252062i	$-0.0811087\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.43889	−	4.73323i	0.228247	−	0.314155i	−0.679498	−	0.733677i	$-0.737802\pi$
$227$	3.43889	−	4.73323i	0.228247	−	0.314155i	0.907745	+	0.419522i	$0.137802\pi$
$228$		0			0
$229$	1.97484	+	6.07793i	0.130501	+	0.401641i	0.994863	−	0.101229i	$-0.0322775\pi$
$229$	1.97484	+	6.07793i	0.130501	+	0.401641i	−0.864362	+	0.502870i	$0.832277\pi$
$230$		0			0
$231$	2.41817	−	7.44236i	0.159104	−	0.489671i
$232$		0			0
$233$	4.32076	+	1.40390i	0.283062	+	0.0919725i	0.447107	−	0.894480i	$-0.352454\pi$
$233$	4.32076	+	1.40390i	0.283062	+	0.0919725i	−0.164045	+	0.986453i	$0.552454\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−3.43411	−	4.72664i	−0.223069	−	0.307029i
$238$		0			0
$239$	18.6407	+	13.5432i	1.20576	+	0.876040i	0.994839	−	0.101463i	$-0.0323522\pi$
$239$	18.6407	+	13.5432i	1.20576	+	0.876040i	0.210926	+	0.977502i	$0.432352\pi$
$240$		0			0
$241$	−13.3064	+	9.66766i	−0.857140	+	0.622749i	−0.927105	−	0.374801i	$-0.877711\pi$
$241$	−13.3064	+	9.66766i	−0.857140	+	0.622749i	0.0699655	+	0.997549i	$0.477711\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	15.7982	−	5.13315i	1.00522	−	0.326614i
$248$		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
$253$	4.56554	−	1.48343i	0.287033	−	0.0932627i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			5.78734i			0.361004i	0.983575	+	0.180502i	$0.0577723\pi$
$257$			5.78734i			0.361004i	−0.983575	+	0.180502i	$0.942228\pi$
$258$		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
$263$	−13.4896	−	18.5668i	−0.831803	−	1.14488i	−0.987585	−	0.157087i	$-0.949790\pi$
$263$	−13.4896	−	18.5668i	−0.831803	−	1.14488i	0.155781	−	0.987792i	$-0.450210\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	6.68222	+	2.17119i	0.408945	+	0.132874i
$268$		0			0
$269$	1.39366	−	4.28923i	0.0849727	−	0.261519i	−0.899538	−	0.436842i	$-0.856097\pi$
$269$	1.39366	−	4.28923i	0.0849727	−	0.261519i	0.984511	+	0.175323i	$0.0560969\pi$
$270$		0			0
$271$	−3.06895	−	9.44525i	−0.186425	−	0.573758i	0.813545	−	0.581502i	$-0.197535\pi$
$271$	−3.06895	−	9.44525i	−0.186425	−	0.573758i	−0.999970	+	0.00774433i	$0.997535\pi$
$272$		0			0
$273$	14.9648	−	20.5973i	0.905711	−	1.24660i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	13.5280	−	18.6197i	0.812821	−	1.11875i	−0.178061	−	0.984019i	$-0.556983\pi$
$277$	13.5280	−	18.6197i	0.812821	−	1.11875i	0.990882	−	0.134732i	$-0.0430175\pi$
$278$		0			0
$279$	1.32905	+	4.09040i	0.0795682	+	0.244886i
$280$		0			0
$281$	0.226820	−	0.698080i	0.0135309	−	0.0416439i	−0.944063	−	0.329765i	$-0.893031\pi$
$281$	0.226820	−	0.698080i	0.0135309	−	0.0416439i	0.957594	+	0.288121i	$0.0930305\pi$
$282$		0			0
$283$	20.4402	+	6.64144i	1.21505	+	0.394793i	0.845276	−	0.534330i	$-0.179436\pi$
$283$	20.4402	+	6.64144i	1.21505	+	0.394793i	0.369771	+	0.929123i	$0.379436\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.80329	+	3.85839i	0.165473	+	0.227754i
$288$		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
$293$		−	26.5961i		−	1.55376i	−0.629649	−	0.776880i	$-0.716801\pi$
$293$		−	26.5961i		−	1.55376i	0.629649	−	0.776880i	$-0.283199\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.09819	+	0.681742i	−0.121749	+	0.0395587i
$298$		0			0
$299$	15.6183			0.903230
$300$		0			0
$301$	−29.0493			−1.67437
$302$		0			0
$303$	−5.68231	+	1.84629i	−0.326440	+	0.106067i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	12.1736i		−	0.694785i	−0.937720	−	0.347393i	$-0.887067\pi$
$307$		−	12.1736i		−	0.694785i	0.937720	−	0.347393i	$-0.112933\pi$
$308$		0			0
$309$	−0.371799	+	0.270128i	−0.0211509	+	0.0153670i
$310$		0			0
$311$	20.0330	+	14.5548i	1.13597	+	0.825327i	0.986552	−	0.163447i	$-0.0522614\pi$
$311$	20.0330	+	14.5548i	1.13597	+	0.825327i	0.149414	+	0.988775i	$0.452261\pi$
$312$		0			0
$313$	−8.72589	−	12.0102i	−0.493216	−	0.678854i	0.487761	−	0.872977i	$-0.337814\pi$
$313$	−8.72589	−	12.0102i	−0.493216	−	0.678854i	−0.980977	+	0.194123i	$0.937814\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.84725	−	0.600207i	−0.103752	−	0.0337110i	0.256681	−	0.966496i	$-0.417371\pi$
$317$	−1.84725	−	0.600207i	−0.103752	−	0.0337110i	−0.360433	+	0.932785i	$0.617371\pi$
$318$		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
$323$	−8.65873	+	11.9177i	−0.481785	+	0.663120i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.96394	−	2.70314i	0.108606	−	0.149484i
$328$		0			0
$329$	6.63635	+	20.4246i	0.365874	+	1.12604i
$330$		0			0
$331$	−8.56924	+	26.3734i	−0.471008	+	1.44961i	0.380258	+	0.924880i	$0.375835\pi$
$331$	−8.56924	+	26.3734i	−0.471008	+	1.44961i	−0.851266	+	0.524734i	$0.824165\pi$
$332$		0			0
$333$	−6.87612	−	2.23419i	−0.376809	−	0.122433i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	6.40119	+	8.81048i	0.348695	+	0.479937i	0.946956	−	0.321364i	$-0.104141\pi$
$337$	6.40119	+	8.81048i	0.348695	+	0.479937i	−0.598261	+	0.801301i	$0.704141\pi$
$338$		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
$343$			5.03148i			0.271675i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	21.7353	−	7.06224i	1.16681	−	0.379121i	0.339361	−	0.940656i	$-0.389789\pi$
$347$	21.7353	−	7.06224i	1.16681	−	0.379121i	0.827453	+	0.561536i	$0.189789\pi$
$348$		0			0
$349$	28.8539			1.54451			0.772256	−	0.635311i	$-0.219128\pi$
$349$	28.8539			1.54451			0.772256	+	0.635311i	$0.219128\pi$
$350$		0			0
$351$	−7.17771			−0.383118
$352$		0			0
$353$	25.9079	−	8.41799i	1.37894	−	0.448045i	0.476619	−	0.879110i	$-0.341862\pi$
$353$	25.9079	−	8.41799i	1.37894	−	0.448045i	0.902321	+	0.431065i	$0.141862\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			22.5781i			1.19496i
$358$		0			0
$359$	−19.3648	+	14.0694i	−1.02204	+	0.742553i	−0.966699	−	0.255915i	$-0.917623\pi$
$359$	−19.3648	+	14.0694i	−1.02204	+	0.742553i	−0.0553373	+	0.998468i	$0.517623\pi$
$360$		0			0
$361$	11.0383	+	8.01981i	0.580965	+	0.422096i
$362$		0			0
$363$	3.60479	+	4.96157i	0.189202	+	0.260415i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	6.38465	+	2.07450i	0.333276	+	0.108288i	0.470875	−	0.882200i	$-0.343938\pi$
$367$	6.38465	+	2.07450i	0.333276	+	0.108288i	−0.137599	+	0.990488i	$0.543938\pi$
$368$		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
$373$	7.99923	−	11.0100i	0.414184	−	0.570076i	−0.550048	−	0.835133i	$-0.685391\pi$
$373$	7.99923	−	11.0100i	0.414184	−	0.570076i	0.964233	+	0.265057i	$0.0853908\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.57715	−	4.92353i	0.184233	−	0.253575i
$378$		0			0
$379$	−0.137272	−	0.422481i	−0.00705120	−	0.0217014i	0.947469	−	0.319848i	$-0.103632\pi$
$379$	−0.137272	−	0.422481i	−0.00705120	−	0.0217014i	−0.954520	+	0.298146i	$0.903632\pi$
$380$		0			0
$381$	3.83550	−	11.8045i	0.196499	−	0.604760i
$382$		0			0
$383$	9.72980	+	3.16140i	0.497170	+	0.161540i	0.546859	−	0.837224i	$-0.315823\pi$
$383$	9.72980	+	3.16140i	0.497170	+	0.161540i	−0.0496897	+	0.998765i	$0.515823\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.81380	+	6.62563i	0.244699	+	0.336800i
$388$		0			0
$389$	−19.5834	−	14.2282i	−0.992919	−	0.721398i	−0.0323607	−	0.999476i	$-0.510303\pi$
$389$	−19.5834	−	14.2282i	−0.992919	−	0.721398i	−0.960558	+	0.278078i	$0.910303\pi$
$390$		0			0
$391$	−11.2054	+	8.14117i	−0.566679	+	0.411717i
$392$		0			0
$393$			15.8232i			0.798174i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	2.58871	−	0.841124i	0.129924	−	0.0422148i	−0.243333	−	0.969943i	$-0.578241\pi$
$397$	2.58871	−	0.841124i	0.129924	−	0.0422148i	0.373257	+	0.927728i	$0.378241\pi$
$398$		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
$403$	−29.3597	+	9.53955i	−1.46251	+	0.475199i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	15.9505i		−	0.790639i
$408$		0			0
$409$	2.68805	−	1.95298i	0.132916	−	0.0965688i	−0.519341	−	0.854567i	$-0.673823\pi$
$409$	2.68805	−	1.95298i	0.132916	−	0.0965688i	0.652256	+	0.757998i	$0.273823\pi$
$410$		0			0
$411$	−5.98262	−	4.34663i	−0.295101	−	0.214404i
$412$		0			0
$413$	−26.0016	−	35.7881i	−1.27945	−	1.76102i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−3.74615	−	1.21720i	−0.183450	−	0.0596065i
$418$		0			0
$419$	3.41347	−	10.5056i	0.166759	−	0.513231i	−0.832403	−	0.554171i	$-0.813035\pi$
$419$	3.41347	−	10.5056i	0.166759	−	0.513231i	0.999162	+	0.0409399i	$0.0130352\pi$
$420$		0			0
$421$	−7.56044	−	23.2686i	−0.368473	−	1.13404i	−0.947777	−	0.318932i	$-0.896676\pi$
$421$	−7.56044	−	23.2686i	−0.368473	−	1.13404i	0.579304	−	0.815111i	$-0.303324\pi$
$422$		0			0
$423$	3.55876	−	4.89822i	0.173033	−	0.238160i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−14.4284	+	19.8589i	−0.698237	+	0.961041i
$428$		0			0
$429$	−4.89335	−	15.0602i	−0.236253	−	0.727113i
$430$		0			0
$431$	0.354621	−	1.09141i	0.0170815	−	0.0525715i	−0.942152	−	0.335185i	$-0.891201\pi$
$431$	0.354621	−	1.09141i	0.0170815	−	0.0525715i	0.959234	+	0.282613i	$0.0912013\pi$
$432$		0			0
$433$	5.56802	+	1.80916i	0.267582	+	0.0869427i	0.439735	−	0.898128i	$-0.355072\pi$
$433$	5.56802	+	1.80916i	0.267582	+	0.0869427i	−0.172153	+	0.985070i	$0.555072\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.95993	−	4.07400i	−0.141593	−	0.194886i
$438$		0			0
$439$	−16.4473	−	11.9497i	−0.784988	−	0.570328i	0.121484	−	0.992593i	$-0.461235\pi$
$439$	−16.4473	−	11.9497i	−0.784988	−	0.570328i	−0.906472	+	0.422266i	$0.861235\pi$
$440$		0			0
$441$	−4.51553	+	3.28072i	−0.215025	+	0.156225i
$442$		0			0
$443$		−	17.5912i		−	0.835783i	−0.908497	−	0.417891i	$-0.862769\pi$
$443$		−	17.5912i		−	0.835783i	0.908497	−	0.417891i	$-0.137231\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	3.73662	−	1.21410i	0.176736	−	0.0574251i
$448$		0			0
$449$	2.83956			0.134007			0.0670037	−	0.997753i	$-0.478656\pi$
$449$	2.83956			0.134007			0.0670037	+	0.997753i	$0.478656\pi$
$450$		0			0
$451$	2.96634			0.139679
$452$		0			0
$453$	−7.54585	+	2.45180i	−0.354535	+	0.115195i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	8.12004i		−	0.379840i	−0.981800	−	0.189920i	$-0.939177\pi$
$457$		−	8.12004i		−	0.379840i	0.981800	−	0.189920i	$-0.0608228\pi$
$458$		0			0
$459$	5.14965	−	3.74144i	0.240365	−	0.174636i
$460$		0			0
$461$	−14.5629	−	10.5806i	−0.678261	−	0.492786i	0.194519	−	0.980899i	$-0.437685\pi$
$461$	−14.5629	−	10.5806i	−0.678261	−	0.492786i	−0.872780	+	0.488113i	$0.837685\pi$
$462$		0			0
$463$	16.8529	+	23.1960i	0.783219	+	1.07801i	0.994919	+	0.100674i	$0.0320999\pi$
$463$	16.8529	+	23.1960i	0.783219	+	1.07801i	−0.211700	+	0.977335i	$0.567900\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.0638	+	6.19421i	0.882169	+	0.286634i	0.714858	−	0.699270i	$-0.246491\pi$
$467$	19.0638	+	6.19421i	0.882169	+	0.286634i	0.167311	+	0.985904i	$0.446491\pi$
$468$		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
$473$	−10.6200	+	14.6172i	−0.488310	+	0.672101i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.02889	+	9.67443i	−0.321831	+	0.442962i
$478$		0			0
$479$	4.78232	+	14.7185i	0.218510	+	0.672505i	0.998886	+	0.0471937i	$0.0150278\pi$
$479$	4.78232	+	14.7185i	0.218510	+	0.672505i	−0.780376	+	0.625311i	$0.784972\pi$
$480$		0			0
$481$	16.0364	−	49.3548i	0.731195	−	2.25039i
$482$		0			0
$483$	−7.34041	−	2.38504i	−0.334000	−	0.108523i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	22.0222	+	30.3110i	0.997923	+	1.37352i	0.926591	+	0.376070i	$0.122725\pi$
$487$	22.0222	+	30.3110i	0.997923	+	1.37352i	0.0713312	+	0.997453i	$0.477275\pi$
$488$		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	−0.476651	+	0.879093i	$0.658149\pi$
$491$	−32.3517	+	23.5049i	−1.46001	+	1.06076i	−0.983360	+	0.181667i	$0.941851\pi$
$492$		0			0
$493$			5.39701i			0.243069i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−46.4831	+	15.1033i	−2.08505	+	0.677474i
$498$		0			0
$499$	−28.3040			−1.26706			−0.633530	−	0.773718i	$-0.718395\pi$
$499$	−28.3040			−1.26706			−0.633530	+	0.773718i	$0.718395\pi$
$500$		0			0
$501$	−10.1007			−0.451264
$502$		0			0
$503$	−31.0839	+	10.0998i	−1.38596	+	0.450327i	−0.904625	−	0.426208i	$-0.859849\pi$
$503$	−31.0839	+	10.0998i	−1.38596	+	0.450327i	−0.481338	+	0.876535i	$0.659849\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	38.5196i		−	1.71071i
$508$		0			0
$509$	13.8620	−	10.0713i	0.614422	−	0.446404i	−0.236547	−	0.971620i	$-0.576016\pi$
$509$	13.8620	−	10.0713i	0.614422	−	0.446404i	0.850969	+	0.525217i	$0.176016\pi$
$510$		0			0
$511$	3.12549	+	2.27080i	0.138264	+	0.100454i
$512$		0			0
$513$	1.36030	+	1.87229i	0.0600586	+	0.0826636i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	12.7035	+	4.12763i	0.558701	+	0.181533i
$518$		0			0
$519$	1.90969	−	5.87741i	0.0838260	−	0.257990i
$520$		0			0
$521$	6.22259	+	19.1512i	0.272617	+	0.839028i	0.989840	+	0.142185i	$0.0454128\pi$
$521$	6.22259	+	19.1512i	0.272617	+	0.839028i	−0.717223	+	0.696843i	$0.754587\pi$
$522$		0			0
$523$	16.4036	−	22.5777i	0.717281	−	0.987253i	−0.282329	−	0.959318i	$-0.591107\pi$
$523$	16.4036	−	22.5777i	0.717281	−	0.987253i	0.999610	−	0.0279349i	$-0.00889312\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	16.0916	−	22.1482i	0.700960	−	0.964789i
$528$		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
$533$	9.17857	+	2.98230i	0.397568	+	0.129178i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	8.48325	+	11.6762i	0.366079	+	0.503865i
$538$		0			0
$539$	−9.96200	−	7.23781i	−0.429094	−	0.311755i
$540$		0			0
$541$	9.00089	−	6.53953i	0.386979	−	0.281156i	−0.377238	−	0.926116i	$-0.623126\pi$
$541$	9.00089	−	6.53953i	0.386979	−	0.281156i	0.764216	+	0.644960i	$0.223126\pi$
$542$		0			0
$543$			6.74285i			0.289363i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−26.4684	+	8.60009i	−1.13171	+	0.367713i	−0.814224	−	0.580551i	$-0.802837\pi$
$547$	−26.4684	+	8.60009i	−1.13171	+	0.367713i	−0.317482	+	0.948264i	$0.602837\pi$
$548$		0			0
$549$	6.92041			0.295356
$550$		0			0
$551$	−1.96222			−0.0835935
$552$		0			0
$553$	−19.7091	+	6.40389i	−0.838118	+	0.272321i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	6.36580i		−	0.269728i	−0.990864	−	0.134864i	$-0.956940\pi$
$557$		−	6.36580i		−	0.269728i	0.990864	−	0.134864i	$-0.0430597\pi$
$558$		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
$563$	10.0676	+	13.8569i	0.424301	+	0.584000i	0.966633	−	0.256164i	$-0.0824587\pi$
$563$	10.0676	+	13.8569i	0.424301	+	0.584000i	−0.542333	+	0.840164i	$0.682459\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	3.37344	+	1.09610i	0.141671	+	0.0460317i
$568$		0			0
$569$	−4.75461	+	14.6332i	−0.199324	+	0.613455i	0.800575	+	0.599232i	$0.204527\pi$
$569$	−4.75461	+	14.6332i	−0.199324	+	0.613455i	−0.999899	+	0.0142229i	$0.995473\pi$
$570$		0			0
$571$	2.63760	+	8.11770i	0.110380	+	0.339715i	0.990955	−	0.134191i	$-0.0428435\pi$
$571$	2.63760	+	8.11770i	0.110380	+	0.339715i	−0.880575	+	0.473906i	$0.842844\pi$
$572$		0			0
$573$	9.04634	−	12.4512i	0.377916	−	0.520157i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−1.35494	+	1.86491i	−0.0564068	+	0.0776374i	−0.836289	−	0.548290i	$-0.815279\pi$
$577$	−1.35494	+	1.86491i	−0.0564068	+	0.0776374i	0.779882	+	0.625927i	$0.215279\pi$
$578$		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
$583$	−25.0907	−	8.15245i	−1.03915	−	0.337640i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.540303	−	0.743663i	−0.0223007	−	0.0306943i	0.797721	−	0.603027i	$-0.206039\pi$
$587$	−0.540303	−	0.743663i	−0.0223007	−	0.0306943i	−0.820022	+	0.572332i	$0.806039\pi$
$588$		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
$593$			25.5925i			1.05096i	0.850807	+	0.525478i	$0.176114\pi$
$593$			25.5925i			1.05096i	−0.850807	+	0.525478i	$0.823886\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.71985	+	1.53357i	−0.193171	+	0.0627650i
$598$		0			0
$599$	37.0204			1.51261			0.756307	−	0.654217i	$-0.227002\pi$
$599$	37.0204			1.51261			0.756307	+	0.654217i	$0.227002\pi$
$600$		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
$603$	−4.50239	+	1.46291i	−0.183351	+	0.0595745i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			4.34502i			0.176359i	0.996105	+	0.0881795i	$0.0281049\pi$
$607$			4.34502i			0.176359i	−0.996105	+	0.0881795i	$0.971895\pi$
$608$		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
$613$	2.32761	+	3.20367i	0.0940111	+	0.129395i	0.853431	−	0.521205i	$-0.174517\pi$
$613$	2.32761	+	3.20367i	0.0940111	+	0.129395i	−0.759420	+	0.650600i	$0.774517\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	19.2721	+	6.26189i	0.775866	+	0.252094i	0.670074	−	0.742294i	$-0.266262\pi$
$617$	19.2721	+	6.26189i	0.775866	+	0.252094i	0.105792	+	0.994388i	$0.466262\pi$
$618$		0			0
$619$	4.65930	−	14.3398i	0.187273	−	0.576367i	−0.812707	−	0.582672i	$-0.802007\pi$
$619$	4.65930	−	14.3398i	0.187273	−	0.576367i	0.999980	+	0.00630532i	$0.00200706\pi$
$620$		0			0
$621$	0.672404	+	2.06945i	0.0269826	+	0.0830440i
$622$		0			0
$623$	14.6487	−	20.1622i	0.586888	−	0.807782i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−3.00104	+	4.13058i	−0.119850	+	0.164959i
$628$		0			0
$629$	14.2213	+	43.7687i	0.567041	+	1.74517i
$630$		0			0
$631$	−0.755761	+	2.32599i	−0.0300864	+	0.0925963i	−0.964972	−	0.262352i	$-0.915502\pi$
$631$	−0.755761	+	2.32599i	−0.0300864	+	0.0925963i	0.934886	+	0.354949i	$0.115502\pi$
$632$		0			0
$633$	3.32851	+	1.08150i	0.132296	+	0.0429857i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−23.5481	−	32.4112i	−0.933009	−	1.28418i
$638$		0			0
$639$	11.1476	+	8.09918i	0.440991	+	0.320399i
$640$		0			0
$641$	−10.8353	+	7.87228i	−0.427967	+	0.310936i	−0.780836	−	0.624737i	$-0.785206\pi$
$641$	−10.8353	+	7.87228i	−0.427967	+	0.310936i	0.352868	+	0.935673i	$0.385206\pi$
$642$		0			0
$643$		−	35.4836i		−	1.39934i	−0.714467	−	0.699669i	$-0.753331\pi$
$643$		−	35.4836i		−	1.39934i	0.714467	−	0.699669i	$-0.246669\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−21.2886	+	6.91707i	−0.836940	+	0.271938i	−0.695966	−	0.718075i	$-0.745023\pi$
$647$	−21.2886	+	6.91707i	−0.836940	+	0.271938i	−0.140974	+	0.990013i	$0.545023\pi$
$648$		0			0
$649$	−27.5140			−1.08002
$650$		0			0
$651$	15.2555			0.597909
$652$		0			0
$653$	18.0021	−	5.84923i	0.704476	−	0.228898i	0.0651961	−	0.997872i	$-0.479233\pi$
$653$	18.0021	−	5.84923i	0.704476	−	0.228898i	0.639279	+	0.768974i	$0.279233\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	1.08917i		−	0.0424925i
$658$		0			0
$659$	4.58371	−	3.33026i	0.178556	−	0.129729i	−0.494917	−	0.868940i	$-0.664802\pi$
$659$	4.58371	−	3.33026i	0.178556	−	0.129729i	0.673473	+	0.739212i	$0.264802\pi$
$660$		0			0
$661$	20.4225	+	14.8378i	0.794342	+	0.577123i	0.909249	−	0.416253i	$-0.136657\pi$
$661$	20.4225	+	14.8378i	0.794342	+	0.577123i	−0.114907	+	0.993376i	$0.536657\pi$
$662$		0			0
$663$	26.8550	+	36.9627i	1.04296	+	1.43551i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.75464	−	0.570116i	−0.0679398	−	0.0220750i
$668$		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
$673$	7.74044	−	10.6538i	0.298372	−	0.410674i	−0.633339	−	0.773875i	$-0.718316\pi$
$673$	7.74044	−	10.6538i	0.298372	−	0.410674i	0.931711	+	0.363201i	$0.118316\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−15.8487	+	21.8139i	−0.609115	+	0.838375i	−0.996504	−	0.0835409i	$-0.973377\pi$
$677$	−15.8487	+	21.8139i	−0.609115	+	0.838375i	0.387389	+	0.921916i	$0.373377\pi$
$678$		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
$683$	49.2454	+	16.0008i	1.88432	+	0.612254i	0.984326	+	0.176356i	$0.0564311\pi$
$683$	49.2454	+	16.0008i	1.88432	+	0.612254i	0.899996	+	0.435897i	$0.143569\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−3.75637	−	5.17019i	−0.143314	−	0.197255i
$688$		0			0
$689$	−69.4403	−	50.4513i	−2.64546	−	1.92204i
$690$		0			0
$691$	3.00647	−	2.18432i	0.114371	−	0.0830956i	−0.529129	−	0.848541i	$-0.677481\pi$
$691$	3.00647	−	2.18432i	0.114371	−	0.0830956i	0.643501	+	0.765446i	$0.277481\pi$
$692$		0			0
$693$			7.82536i			0.297261i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−8.13972	+	2.64475i	−0.308314	+	0.100177i
$698$		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
$703$	−15.9132	+	5.17053i	−0.600180	+	0.195010i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			21.1926i			0.797030i
$708$		0			0
$709$	33.1126	−	24.0577i	1.24357	−	0.903507i	0.245740	−	0.969336i	$-0.420969\pi$
$709$	33.1126	−	24.0577i	1.24357	−	0.903507i	0.997831	+	0.0658288i	$0.0209691\pi$
$710$		0			0
$711$	4.72664	+	3.43411i	0.177263	+	0.128789i
$712$		0			0
$713$	5.50080	+	7.57120i	0.206007	+	0.283544i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−21.9134	−	7.12010i	−0.818372	−	0.265905i
$718$		0			0
$719$	−1.46368	+	4.50475i	−0.0545861	+	0.167999i	−0.974633	−	0.223810i	$-0.928151\pi$
$719$	−1.46368	+	4.50475i	−0.0545861	+	0.167999i	0.920047	+	0.391809i	$0.128151\pi$
$720$		0			0
$721$	0.503731	+	1.55032i	0.0187599	+	0.0577371i
$722$		0			0
$723$	9.66766	−	13.3064i	0.359544	−	0.494870i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	3.27447	−	4.50692i	0.121443	−	0.167153i	−0.743967	−	0.668217i	$-0.767058\pi$
$727$	3.27447	−	4.50692i	0.121443	−	0.167153i	0.865410	+	0.501064i	$0.167058\pi$
$728$		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
$733$	−28.8738	−	9.38166i	−1.06648	−	0.346520i	−0.277363	−	0.960765i	$-0.589460\pi$
$733$	−28.8738	−	9.38166i	−1.06648	−	0.346520i	−0.789115	+	0.614246i	$0.789460\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.13894	−	8.44952i	−0.226131	−	0.311242i
$738$		0			0
$739$	39.6127	+	28.7803i	1.45718	+	1.05870i	0.984087	+	0.177686i	$0.0568611\pi$
$739$	39.6127	+	28.7803i	1.45718	+	1.05870i	0.473089	+	0.881015i	$0.343139\pi$
$740$		0			0
$741$	−13.4388	+	9.76383i	−0.493685	+	0.358683i
$742$		0			0
$743$			45.5953i			1.67273i	0.548174	+	0.836364i	$0.315323\pi$
$743$			45.5953i			1.67273i	−0.548174	+	0.836364i	$0.684677\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	11.9145	−	3.87127i	0.435930	−	0.141642i
$748$		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
$753$	−4.43503	+	1.44103i	−0.161621	+	0.0525140i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	27.6680i		−	1.00561i	−0.864400	−	0.502804i	$-0.832302\pi$
$757$		−	27.6680i		−	1.00561i	0.864400	−	0.502804i	$-0.167698\pi$
$758$		0			0
$759$	−3.88368	+	2.82166i	−0.140969	+	0.102420i
$760$		0			0
$761$	9.80362	+	7.12275i	0.355381	+	0.258199i	0.751123	−	0.660162i	$-0.229513\pi$
$761$	9.80362	+	7.12275i	0.355381	+	0.258199i	−0.395742	+	0.918362i	$0.629513\pi$
$762$		0			0
$763$	−6.96619	−	9.58814i	−0.252193	−	0.347114i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−85.1349	−	27.6620i	−3.07404	−	0.998817i
$768$		0			0
$769$	3.13398	−	9.64540i	0.113014	−	0.347822i	−0.878513	−	0.477718i	$-0.841464\pi$
$769$	3.13398	−	9.64540i	0.113014	−	0.347822i	0.991528	+	0.129896i	$0.0414642\pi$
$770$		0			0
$771$	−1.78839	−	5.50409i	−0.0644071	−	0.198225i
$772$		0			0
$773$	−29.4908	+	40.5906i	−1.06071	+	1.45994i	−0.181569	+	0.983378i	$0.558118\pi$
$773$	−29.4908	+	40.5906i	−1.06071	+	1.45994i	−0.879140	+	0.476563i	$0.841882\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−15.0738	+	20.7473i	−0.540769	+	0.744304i
$778$		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
$783$	0.806379	+	0.262008i	0.0288176	+	0.00936342i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	9.08606	+	12.5059i	0.323883	+	0.445787i	0.939648	−	0.342143i	$-0.111153\pi$
$787$	9.08606	+	12.5059i	0.323883	+	0.445787i	−0.615765	+	0.787930i	$0.711153\pi$
$788$		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
$793$			49.6727i			1.76393i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.45087	−	1.77110i	0.193080	−	0.0627354i	−0.210881	−	0.977512i	$-0.567633\pi$
$797$	5.45087	−	1.77110i	0.193080	−	0.0627354i	0.403961	+	0.914776i	$0.367633\pi$
$798$		0			0
$799$	−38.5390			−1.36341
$800$		0			0
$801$	−7.02611			−0.248255
$802$		0			0
$803$	2.28528	−	0.742531i	0.0806457	−	0.0262034i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			4.50997i			0.158758i
$808$		0			0
$809$	−22.9907	+	16.7038i	−0.808312	+	0.587273i	−0.913341	−	0.407196i	$-0.866506\pi$
$809$	−22.9907	+	16.7038i	−0.808312	+	0.587273i	0.105029	+	0.994469i	$0.466506\pi$
$810$		0			0
$811$	9.86048	+	7.16406i	0.346248	+	0.251564i	0.747293	−	0.664494i	$-0.231353\pi$
$811$	9.86048	+	7.16406i	0.346248	+	0.251564i	−0.401045	+	0.916058i	$0.631353\pi$
$812$		0			0
$813$	5.83748	+	8.03461i	0.204730	+	0.281786i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	18.0257	+	5.85689i	0.630638	+	0.204907i
$818$		0			0
$819$	−7.86746	+	24.2136i	−0.274911	+	0.846090i
$820$		0			0
$821$	4.51854	+	13.9066i	0.157698	+	0.485345i	0.998424	−	0.0561157i	$-0.0178716\pi$
$821$	4.51854	+	13.9066i	0.157698	+	0.485345i	−0.840726	+	0.541461i	$0.817872\pi$
$822$		0			0
$823$	−12.7201	+	17.5077i	−0.443394	+	0.610280i	−0.970962	−	0.239233i	$-0.923104\pi$
$823$	−12.7201	+	17.5077i	−0.443394	+	0.610280i	0.527568	+	0.849513i	$0.323104\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.56096	−	9.03038i	0.228147	−	0.314017i	−0.679562	−	0.733618i	$-0.737830\pi$
$827$	6.56096	−	9.03038i	0.228147	−	0.314017i	0.907709	+	0.419601i	$0.137830\pi$
$828$		0			0
$829$	−8.60563	−	26.4854i	−0.298886	−	0.919876i	−0.981888	−	0.189460i	$-0.939326\pi$
$829$	−8.60563	−	26.4854i	−0.298886	−	0.919876i	0.683003	−	0.730416i	$-0.260674\pi$
$830$		0			0
$831$	−7.11211	+	21.8888i	−0.246716	+	0.759315i
$832$		0			0
$833$	33.7892	+	10.9788i	1.17073	+	0.380392i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−2.52801	−	3.47950i	−0.0873807	−	0.120269i
$838$		0			0
$839$	−15.3556	−	11.1565i	−0.530133	−	0.385164i	0.290274	−	0.956943i	$-0.406253\pi$
$839$	−15.3556	−	11.1565i	−0.530133	−	0.385164i	−0.820408	+	0.571779i	$0.806253\pi$
$840$		0			0
$841$	22.8799	−	16.6232i	0.788962	−	0.573214i
$842$		0			0
$843$			0.734004i			0.0252804i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	20.6887	−	6.72218i	0.710873	−	0.230977i
$848$		0			0
$849$	−21.4921			−0.737609
$850$		0			0
$851$	−15.7320			−0.539287
$852$		0			0
$853$	−15.6987	+	5.10082i	−0.537513	+	0.174649i	−0.565179	−	0.824969i	$-0.691193\pi$
$853$	−15.6987	+	5.10082i	−0.537513	+	0.174649i	0.0276653	+	0.999617i	$0.491193\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			28.7615i			0.982475i	0.871026	+	0.491237i	$0.163455\pi$
$857$			28.7615i			0.982475i	−0.871026	+	0.491237i	$0.836545\pi$
$858$		0			0
$859$	−12.2446	+	8.89622i	−0.417780	+	0.303535i	−0.776744	−	0.629816i	$-0.783130\pi$
$859$	−12.2446	+	8.89622i	−0.417780	+	0.303535i	0.358964	+	0.933351i	$0.383130\pi$
$860$		0			0
$861$	−3.85839	−	2.80329i	−0.131494	−	0.0955357i
$862$		0			0
$863$	−25.3024	−	34.8258i	−0.861305	−	1.18549i	−0.981257	−	0.192705i	$-0.938274\pi$
$863$	−25.3024	−	34.8258i	−0.861305	−	1.18549i	0.119951	−	0.992780i	$-0.461726\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−22.3663	−	7.26725i	−0.759600	−	0.246809i
$868$		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
$873$	−10.6651	+	14.6792i	−0.360957	+	0.496815i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	29.7980	−	41.0134i	1.00621	−	1.38492i	0.0847668	−	0.996401i	$-0.472985\pi$
$877$	29.7980	−	41.0134i	1.00621	−	1.38492i	0.921439	−	0.388523i	$-0.127015\pi$
$878$		0			0
$879$	8.21864	+	25.2944i	0.277208	+	0.853158i
$880$		0			0
$881$	−0.818966	+	2.52052i	−0.0275917	+	0.0849184i	−0.963904	−	0.266250i	$-0.914215\pi$
$881$	−0.818966	+	2.52052i	−0.0275917	+	0.0849184i	0.936312	+	0.351168i	$0.114215\pi$
$882$		0			0
$883$	−32.1189	−	10.4361i	−1.08089	−	0.351201i	−0.286168	−	0.958179i	$-0.592382\pi$
$883$	−32.1189	−	10.4361i	−1.08089	−	0.351201i	−0.794719	+	0.606978i	$0.792382\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.54153	−	3.49811i	−0.0853361	−	0.117455i	0.764215	−	0.644962i	$-0.223127\pi$
$887$	−2.54153	−	3.49811i	−0.0853361	−	0.117455i	−0.849551	+	0.527507i	$0.823127\pi$
$888$		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
$893$		−	14.0119i		−	0.468889i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−14.8539	+	4.82632i	−0.495957	+	0.161146i
$898$		0			0
$899$	3.64664			0.121622
$900$		0			0
$901$	76.1182			2.53586
$902$		0			0
$903$	27.6275	−	8.97673i	0.919387	−	0.298727i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			47.2507i			1.56893i	0.620171	+	0.784467i	$0.287063\pi$
$907$			47.2507i			1.56893i	−0.620171	+	0.784467i	$0.712937\pi$
$908$		0			0
$909$	4.83366	−	3.51186i	0.160322	−	0.116481i
$910$		0			0
$911$	−41.1586	−	29.9035i	−1.36365	−	0.990747i	−0.998204	−	0.0599132i	$-0.980918\pi$
$911$	−41.1586	−	29.9035i	−1.36365	−	0.990747i	−0.365443	−	0.930834i	$-0.619082\pi$
$912$		0			0
$913$	16.2453	+	22.3597i	0.537641	+	0.739999i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	53.3785	+	17.3437i	1.76271	+	0.572740i
$918$		0			0
$919$	11.3396	−	34.8998i	0.374060	−	1.15124i	−0.570051	−	0.821610i	$-0.693076\pi$
$919$	11.3396	−	34.8998i	0.374060	−	1.15124i	0.944111	−	0.329629i	$-0.106924\pi$
$920$		0			0
$921$	3.76186	+	11.5778i	0.123957	+	0.381502i
$922$		0			0
$923$	−58.1336	+	80.0140i	−1.91349	+	2.63369i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.270128	−	0.371799i	0.00887215	−	0.0122115i
$928$		0			0
$929$	−14.9269	−	45.9401i	−0.489734	−	1.50725i	−0.825005	−	0.565125i	$-0.808828\pi$
$929$	−14.9269	−	45.9401i	−0.489734	−	1.50725i	0.335271	−	0.942122i	$-0.391172\pi$
$930$		0			0
$931$	−3.99161	+	12.2849i	−0.130820	+	0.402622i
$932$		0			0
$933$	−23.5502	−	7.65191i	−0.770998	−	0.250512i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	5.57420	+	7.67223i	0.182101	+	0.250641i	0.890302	−	0.455370i	$-0.150493\pi$
$937$	5.57420	+	7.67223i	0.182101	+	0.250641i	−0.708201	+	0.706011i	$0.750493\pi$
$938$		0			0
$939$	12.0102	+	8.72589i	0.391937	+	0.284759i
$940$		0			0
$941$	17.2272	−	12.5163i	0.561590	−	0.408019i	−0.270450	−	0.962734i	$-0.587173\pi$
$941$	17.2272	−	12.5163i	0.561590	−	0.408019i	0.832041	+	0.554715i	$0.187173\pi$
$942$		0			0
$943$		−	2.92570i		−	0.0952740i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.9695	+	9.73768i	−0.973877	+	0.316432i	−0.752380	−	0.658729i	$-0.771094\pi$
$947$	−29.9695	+	9.73768i	−0.973877	+	0.316432i	−0.221497	+	0.975161i	$0.571094\pi$
$948$		0			0
$949$	7.81773			0.253774
$950$		0			0
$951$	1.94231			0.0629837
$952$		0			0
$953$	10.6646	−	3.46513i	0.345460	−	0.112247i	−0.131148	−	0.991363i	$-0.541866\pi$
$953$	10.6646	−	3.46513i	0.345460	−	0.112247i	0.476608	+	0.879116i	$0.341866\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			1.87056i			0.0604665i
$958$		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
$963$	−1.45689	−	2.00524i	−0.0469478	−	0.0646181i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−33.8782	−	11.0077i	−1.08945	−	0.353984i	−0.291417	−	0.956596i	$-0.594127\pi$
$967$	−33.8782	−	11.0077i	−1.08945	−	0.353984i	−0.798034	+	0.602612i	$0.794127\pi$
$968$		0			0
$969$	4.55217	−	14.0101i	0.146237	−	0.450070i
$970$		0			0
$971$	13.2227	+	40.6953i	0.424337	+	1.30598i	0.903628	+	0.428319i	$0.140894\pi$
$971$	13.2227	+	40.6953i	0.424337	+	1.30598i	−0.479290	+	0.877656i	$0.659106\pi$
$972$		0			0
$973$	−8.21228	+	11.3032i	−0.263274	+	0.362365i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.9119	+	32.9119i	−0.765009	+	1.05294i	0.231772	+	0.972770i	$0.425548\pi$
$977$	−23.9119	+	32.9119i	−0.765009	+	1.05294i	−0.996781	+	0.0801740i	$0.974452\pi$
$978$		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
$983$	46.5713	+	15.1319i	1.48539	+	0.482634i	0.935719	−	0.352746i	$-0.114752\pi$
$983$	46.5713	+	15.1319i	1.48539	+	0.482634i	0.549674	+	0.835379i	$0.314752\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−12.6231	−	17.3742i	−0.401797	−	0.553026i
$988$		0			0
$989$	14.4170	+	10.4746i	0.458434	+	0.333072i
$990$		0			0
$991$	1.99334	−	1.44825i	0.0633206	−	0.0460051i	−0.555675	−	0.831400i	$-0.687540\pi$
$991$	1.99334	−	1.44825i	0.0633206	−	0.0460051i	0.618995	+	0.785395i	$0.287540\pi$
$992$		0			0
$993$		−	27.7307i		−	0.880006i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	51.5975	−	16.7650i	1.63411	−	0.530954i	0.658899	−	0.752232i	$-0.271023\pi$
$997$	51.5975	−	16.7650i	1.63411	−	0.530954i	0.975211	+	0.221277i	$0.0710226\pi$
$998$		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.o.c.49.3		24
5.2	odd	4		1500.2.m.c.1201.1		24
5.3	odd	4		1500.2.m.d.1201.6		24
5.4	even	2		300.2.o.a.109.4	✓	24
15.14	odd	2		900.2.w.c.109.5		24
25.2	odd	20		1500.2.m.c.301.1		24
25.6	even	5		7500.2.d.g.1249.23		24
25.8	odd	20		7500.2.a.m.1.11		12
25.11	even	5		300.2.o.a.289.4	yes	24
25.14	even	10	inner	1500.2.o.c.949.3		24
25.17	odd	20		7500.2.a.n.1.2		12
25.19	even	10		7500.2.d.g.1249.2		24
25.23	odd	20		1500.2.m.d.301.6		24
75.11	odd	10		900.2.w.c.289.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.4	✓	24	5.4	even	2
300.2.o.a.289.4	yes	24	25.11	even	5
900.2.w.c.109.5		24	15.14	odd	2
900.2.w.c.289.5		24	75.11	odd	10
1500.2.m.c.301.1		24	25.2	odd	20
1500.2.m.c.1201.1		24	5.2	odd	4
1500.2.m.d.301.6		24	25.23	odd	20
1500.2.m.d.1201.6		24	5.3	odd	4
1500.2.o.c.49.3		24	1.1	even	1	trivial
1500.2.o.c.949.3		24	25.14	even	10	inner
7500.2.a.m.1.11		12	25.8	odd	20
7500.2.a.n.1.2		12	25.17	odd	20
7500.2.d.g.1249.2		24	25.19	even	10
7500.2.d.g.1249.23		24	25.6	even	5

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.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{3} +3.54704i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{3} +3.54704i q^{7} +(0.809017 - 0.587785i) q^{9} +(1.78482 + 1.29675i) q^{11} +(4.21895 + 5.80689i) q^{13} +(-6.05378 - 1.96699i) q^{17} +(0.715151 - 2.20101i) q^{19} +(-1.09610 - 3.37344i) q^{21} +(1.27899 - 1.76038i) q^{23} +(-0.587785 + 0.809017i) q^{27} +(-0.262008 - 0.806379i) q^{29} +(-1.32905 + 4.09040i) q^{31} +(-2.09819 - 0.681742i) q^{33} +(-4.24968 - 5.84918i) q^{37} +(-5.80689 - 4.21895i) q^{39} +(1.08778 - 0.790317i) q^{41} +8.18973i q^{43} +(5.75820 - 1.87095i) q^{47} -5.58150 q^{49} +6.36532 q^{51} +(-11.3730 + 3.69530i) q^{53} +2.31428i q^{57} +(-10.0896 + 7.33050i) q^{59} +(5.59873 + 4.06772i) q^{61} +(2.08490 + 2.86962i) q^{63} +(-4.50239 - 1.46291i) q^{67} +(-0.672404 + 2.06945i) q^{69} +(4.25799 + 13.1047i) q^{71} +(0.640196 - 0.881155i) q^{73} +(-4.59963 + 6.33085i) q^{77} +(1.80542 + 5.55650i) q^{79} +(0.309017 - 0.951057i) q^{81} +(11.9145 + 3.87127i) q^{83} +(0.498370 + 0.685947i) q^{87} +(-5.68424 - 4.12984i) q^{89} +(-20.5973 + 14.9648i) q^{91} -4.30090i q^{93} +(-17.2564 + 5.60695i) q^{97} +2.20616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^9	\( 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63} - 20 q^{67} + 4 q^{69} + 40 q^{71} - 60 q^{73} + 40 q^{77} + 8 q^{79} - 6 q^{81} + 50 q^{83} + 20 q^{87} - 30 q^{91} + 40 q^{97} - 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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