LMFDB - Embedded newform 276.2.k.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(5,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

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

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

chi := DirichletCharacter("276.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.k (of order $22$, degree $10$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	276.17
Dual form			276.2.k.a.65.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38578 - 1.03904i) q^{3} +(-0.998768 + 0.641869i) q^{5} +(3.17327 + 0.456247i) q^{7} +(0.840791 - 2.87977i) q^{9} +O(q^{10})$	\(q+(1.38578 - 1.03904i) q^{3} +(-0.998768 + 0.641869i) q^{5} +(3.17327 + 0.456247i) q^{7} +(0.840791 - 2.87977i) q^{9} +(0.407017 + 0.891242i) q^{11} +(-0.0854275 - 0.594161i) q^{13} +(-0.717148 + 1.92725i) q^{15} +(2.34297 - 2.70393i) q^{17} +(1.37294 - 1.18966i) q^{19} +(4.87152 - 2.66489i) q^{21} +(-4.70450 + 0.931481i) q^{23} +(-1.49153 + 3.26600i) q^{25} +(-1.82704 - 4.86435i) q^{27} +(-1.18589 - 1.02758i) q^{29} +(-6.25083 + 1.83541i) q^{31} +(1.49007 + 0.812162i) q^{33} +(-3.46221 + 1.58114i) q^{35} +(-0.682962 + 1.06271i) q^{37} +(-0.735741 - 0.734616i) q^{39} +(5.38229 + 8.37501i) q^{41} +(2.14779 - 7.31472i) q^{43} +(1.00868 + 3.41590i) q^{45} +10.6227i q^{47} +(3.14503 + 0.923464i) q^{49} +(0.437356 - 6.18151i) q^{51} +(-0.462019 + 3.21341i) q^{53} +(-0.978575 - 0.628892i) q^{55} +(0.666494 - 3.07515i) q^{57} +(-12.0862 + 1.73774i) q^{59} +(1.10580 + 3.76602i) q^{61} +(3.98194 - 8.75468i) q^{63} +(0.466696 + 0.538596i) q^{65} +(-8.09530 - 3.69700i) q^{67} +(-5.55158 + 6.17900i) q^{69} +(6.35593 + 2.90266i) q^{71} +(-3.39175 - 3.91429i) q^{73} +(1.32657 + 6.07574i) q^{75} +(0.884947 + 3.01385i) q^{77} +(-14.0661 + 2.02240i) q^{79} +(-7.58614 - 4.84257i) q^{81} +(-7.75693 - 4.98507i) q^{83} +(-0.604513 + 4.20448i) q^{85} +(-2.71107 - 0.191815i) q^{87} +(1.88871 + 0.554576i) q^{89} -1.92441i q^{91} +(-6.75523 + 9.03834i) q^{93} +(-0.607643 + 2.06944i) q^{95} +(1.22310 + 1.90318i) q^{97} +(2.90879 - 0.422765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + 6 * q^9	$ 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{7}{22}\right)$	$1$	$-1$

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
$3$	1.38578	−	1.03904i	0.800082	−	0.599890i
$3$	1.38578	−	1.03904i	0.800082	−	0.599890i
$4$		0			0
$5$	−0.998768	+	0.641869i	−0.446662	+	0.287053i	−0.744573	−	0.667541i	$-0.767347\pi$
$5$	−0.998768	+	0.641869i	−0.446662	+	0.287053i	0.297910	+	0.954594i	$0.403710\pi$
$6$		0			0
$7$	3.17327	+	0.456247i	1.19938	+	0.172445i	0.712913	−	0.701252i	$-0.247375\pi$
$7$	3.17327	+	0.456247i	1.19938	+	0.172445i	0.486470	+	0.873697i	$0.338284\pi$
$8$		0			0
$9$	0.840791	−	2.87977i	0.280264	−	0.959923i
$10$		0			0
$11$	0.407017	+	0.891242i	0.122720	+	0.268720i	0.961014	−	0.276499i	$-0.0891741\pi$
$11$	0.407017	+	0.891242i	0.122720	+	0.268720i	−0.838294	+	0.545218i	$0.816447\pi$
$12$		0			0
$13$	−0.0854275	−	0.594161i	−0.0236933	−	0.164791i	0.974539	−	0.224216i	$-0.0719822\pi$
$13$	−0.0854275	−	0.594161i	−0.0236933	−	0.164791i	−0.998233	+	0.0594256i	$0.981073\pi$
$14$		0			0
$15$	−0.717148	+	1.92725i	−0.185167	+	0.497614i
$16$		0			0
$17$	2.34297	−	2.70393i	0.568254	−	0.655800i	−0.396784	−	0.917912i	$-0.629874\pi$
$17$	2.34297	−	2.70393i	0.568254	−	0.655800i	0.965037	+	0.262112i	$0.0844191\pi$
$18$		0			0
$19$	1.37294	−	1.18966i	0.314974	−	0.272927i	−0.482997	−	0.875622i	$-0.660452\pi$
$19$	1.37294	−	1.18966i	0.314974	−	0.272927i	0.797972	+	0.602695i	$0.205906\pi$
$20$		0			0
$21$	4.87152	−	2.66489i	1.06305	−	0.581528i
$22$		0			0
$23$	−4.70450	+	0.931481i	−0.980957	+	0.194227i
$23$	−4.70450	+	0.931481i	−0.980957	+	0.194227i
$24$		0			0
$25$	−1.49153	+	3.26600i	−0.298307	+	0.653201i
$26$		0			0
$27$	−1.82704	−	4.86435i	−0.351614	−	0.936145i
$28$		0			0
$29$	−1.18589	−	1.02758i	−0.220214	−	0.190816i	0.537767	−	0.843094i	$-0.319268\pi$
$29$	−1.18589	−	1.02758i	−0.220214	−	0.190816i	−0.757980	+	0.652278i	$0.773814\pi$
$30$		0			0
$31$	−6.25083	+	1.83541i	−1.12268	+	0.329649i	−0.789827	−	0.613329i	$-0.789830\pi$
$31$	−6.25083	+	1.83541i	−1.12268	+	0.329649i	−0.332854	+	0.942978i	$0.608012\pi$
$32$		0			0
$33$	1.49007	+	0.812162i	0.259388	+	0.141379i
$34$		0			0
$35$	−3.46221	+	1.58114i	−0.585220	+	0.267261i
$36$		0			0
$37$	−0.682962	+	1.06271i	−0.112278	+	0.174708i	−0.892845	−	0.450364i	$-0.851294\pi$
$37$	−0.682962	+	1.06271i	−0.112278	+	0.174708i	0.780567	+	0.625072i	$0.214931\pi$
$38$		0			0
$39$	−0.735741	−	0.734616i	−0.117813	−	0.117633i
$40$		0			0
$41$	5.38229	+	8.37501i	0.840573	+	1.30796i	0.949455	+	0.313902i	$0.101636\pi$
$41$	5.38229	+	8.37501i	0.840573	+	1.30796i	−0.108883	+	0.994055i	$0.534727\pi$
$42$		0			0
$43$	2.14779	−	7.31472i	0.327536	−	1.11548i	−0.616969	−	0.786987i	$-0.711640\pi$
$43$	2.14779	−	7.31472i	0.327536	−	1.11548i	0.944505	−	0.328497i	$-0.106542\pi$
$44$		0			0
$45$	1.00868	+	3.41590i	0.150365	+	0.509212i
$46$		0			0
$47$			10.6227i			1.54948i	0.632282	+	0.774738i	$0.282118\pi$
$47$			10.6227i			1.54948i	−0.632282	+	0.774738i	$0.717882\pi$
$48$		0			0
$49$	3.14503	+	0.923464i	0.449290	+	0.131923i
$50$		0			0
$51$	0.437356	−	6.18151i	0.0612420	−	0.865584i
$52$		0			0
$53$	−0.462019	+	3.21341i	−0.0634631	+	0.441396i	0.933172	+	0.359430i	$0.117029\pi$
$53$	−0.462019	+	3.21341i	−0.0634631	+	0.441396i	−0.996635	+	0.0819657i	$0.973880\pi$
$54$		0			0
$55$	−0.978575	−	0.628892i	−0.131951	−	0.0847998i
$56$		0			0
$57$	0.666494	−	3.07515i	0.0882793	−	0.407314i
$58$		0			0
$59$	−12.0862	+	1.73774i	−1.57349	+	0.226234i	−0.873106	−	0.487531i	$-0.837898\pi$
$59$	−12.0862	+	1.73774i	−1.57349	+	0.226234i	−0.700386	+	0.713765i	$0.746989\pi$
$60$		0			0
$61$	1.10580	+	3.76602i	0.141584	+	0.482189i	0.999501	−	0.0315989i	$-0.0100599\pi$
$61$	1.10580	+	3.76602i	0.141584	+	0.482189i	−0.857917	+	0.513788i	$0.828242\pi$
$62$		0			0
$63$	3.98194	−	8.75468i	0.501678	−	1.10299i
$64$		0			0
$65$	0.466696	+	0.538596i	0.0578865	+	0.0668046i
$66$		0			0
$67$	−8.09530	−	3.69700i	−0.988998	−	0.451660i	−0.145830	−	0.989310i	$-0.546585\pi$
$67$	−8.09530	−	3.69700i	−0.988998	−	0.451660i	−0.843168	+	0.537649i	$0.819312\pi$
$68$		0			0
$69$	−5.55158	+	6.17900i	−0.668331	+	0.743864i
$70$		0			0
$71$	6.35593	+	2.90266i	0.754311	+	0.344482i	0.755180	−	0.655517i	$-0.227549\pi$
$71$	6.35593	+	2.90266i	0.754311	+	0.344482i	−0.000869334		1.00000i	$0.500277\pi$
$72$		0			0
$73$	−3.39175	−	3.91429i	−0.396974	−	0.458133i	0.521711	−	0.853122i	$-0.325294\pi$
$73$	−3.39175	−	3.91429i	−0.396974	−	0.458133i	−0.918686	+	0.394989i	$0.870748\pi$
$74$		0			0
$75$	1.32657	+	6.07574i	0.153179	+	0.701566i
$76$		0			0
$77$	0.884947	+	3.01385i	0.100849	+	0.343460i
$78$		0			0
$79$	−14.0661	+	2.02240i	−1.58256	+	0.227538i	−0.876779	−	0.480894i	$-0.840312\pi$
$79$	−14.0661	+	2.02240i	−1.58256	+	0.227538i	−0.705780	+	0.708431i	$0.749403\pi$
$80$		0			0
$81$	−7.58614	−	4.84257i	−0.842905	−	0.538063i
$82$		0			0
$83$	−7.75693	−	4.98507i	−0.851433	−	0.547183i	0.0405883	−	0.999176i	$-0.487077\pi$
$83$	−7.75693	−	4.98507i	−0.851433	−	0.547183i	−0.892021	+	0.451993i	$0.850713\pi$
$84$		0			0
$85$	−0.604513	+	4.20448i	−0.0655686	+	0.456040i
$86$		0			0
$87$	−2.71107	−	0.191815i	−0.290658	−	0.0205647i
$88$		0			0
$89$	1.88871	+	0.554576i	0.200203	+	0.0587850i	0.380297	−	0.924865i	$-0.375822\pi$
$89$	1.88871	+	0.554576i	0.200203	+	0.0587850i	−0.180094	+	0.983649i	$0.557640\pi$
$90$		0			0
$91$		−	1.92441i		−	0.201733i
$92$		0			0
$93$	−6.75523	+	9.03834i	−0.700485	+	0.937232i
$94$		0			0
$95$	−0.607643	+	2.06944i	−0.0623428	+	0.212320i
$96$		0			0
$97$	1.22310	+	1.90318i	0.124187	+	0.193239i	0.897780	−	0.440444i	$-0.145179\pi$
$97$	1.22310	+	1.90318i	0.124187	+	0.193239i	−0.773593	+	0.633683i	$0.781543\pi$
$98$		0			0
$99$	2.90879	−	0.422765i	0.292344	−	0.0424895i
$100$		0			0
$101$	7.63710	−	11.8836i	0.759919	−	1.18246i	−0.218502	−	0.975837i	$-0.570117\pi$
$101$	7.63710	−	11.8836i	0.759919	−	1.18246i	0.978421	−	0.206621i	$-0.0662468\pi$
$102$		0			0
$103$	11.7777	−	5.37872i	1.16050	−	0.529981i	0.260326	−	0.965521i	$-0.416170\pi$
$103$	11.7777	−	5.37872i	1.16050	−	0.529981i	0.900169	+	0.435540i	$0.143443\pi$
$104$		0			0
$105$	−3.15501	+	5.78849i	−0.307897	+	0.564899i
$106$		0			0
$107$	−1.02908	+	0.302165i	−0.0994849	+	0.0292114i	−0.331096	−	0.943597i	$-0.607418\pi$
$107$	−1.02908	+	0.302165i	−0.0994849	+	0.0292114i	0.231611	+	0.972808i	$0.425600\pi$
$108$		0			0
$109$	6.75635	+	5.85441i	0.647141	+	0.560751i	0.915375	−	0.402603i	$-0.131895\pi$
$109$	6.75635	+	5.85441i	0.647141	+	0.560751i	−0.268234	+	0.963354i	$0.586440\pi$
$110$		0			0
$111$	0.157761	+	2.18231i	0.0149740	+	0.207136i
$112$		0			0
$113$	5.28602	−	11.5748i	0.497267	−	1.08886i	−0.480082	−	0.877224i	$-0.659393\pi$
$113$	5.28602	−	11.5748i	0.497267	−	1.08886i	0.977348	−	0.211638i	$-0.0678798\pi$
$114$		0			0
$115$	4.10082	−	3.95001i	0.382403	−	0.368340i
$116$		0			0
$117$	−1.78287	−	0.253554i	−0.164827	−	0.0234411i
$118$		0			0
$119$	8.66854	−	7.51133i	0.794644	−	0.688563i
$120$		0			0
$121$	6.57482	−	7.58775i	0.597711	−	0.689795i
$122$		0			0
$123$	16.1607	+	6.01353i	1.45716	+	0.542222i
$124$		0			0
$125$	−1.45146	−	10.0951i	−0.129822	−	0.902934i
$126$		0			0
$127$	6.67608	+	14.6186i	0.592406	+	1.29719i	0.933977	+	0.357333i	$0.116314\pi$
$127$	6.67608	+	14.6186i	0.592406	+	1.29719i	−0.341571	+	0.939856i	$0.610959\pi$
$128$		0			0
$129$	−4.62391	−	12.3683i	−0.407112	−	1.08896i
$130$		0			0
$131$	−20.0840	−	2.88765i	−1.75475	−	0.252295i	−0.811495	−	0.584360i	$-0.801346\pi$
$131$	−20.0840	−	2.88765i	−1.75475	−	0.252295i	−0.943257	+	0.332065i	$0.892255\pi$
$132$		0			0
$133$	4.89949	−	3.14871i	0.424840	−	0.273028i
$134$		0			0
$135$	4.94707	+	3.68564i	0.425776	+	0.317209i
$136$		0			0
$137$	22.5562			1.92711			0.963555	−	0.267512i	$-0.0862015\pi$
$137$	22.5562			1.92711			0.963555	+	0.267512i	$0.0862015\pi$
$138$		0			0
$139$	5.05590			0.428836			0.214418	−	0.976742i	$-0.431215\pi$
$139$	5.05590			0.428836			0.214418	+	0.976742i	$0.431215\pi$
$140$		0			0
$141$	11.0374	+	14.7207i	0.929516	+	1.23971i
$142$		0			0
$143$	0.494771	−	0.317970i	0.0413748	−	0.0265900i
$144$		0			0
$145$	1.84399	+	0.265126i	0.153135	+	0.0220175i
$146$		0			0
$147$	5.31785	−	1.98809i	0.438609	−	0.163975i
$148$		0			0
$149$	0.521518	+	1.14197i	0.0427244	+	0.0935534i	0.929791	−	0.368089i	$-0.119988\pi$
$149$	0.521518	+	1.14197i	0.0427244	+	0.0935534i	−0.887066	+	0.461642i	$0.847260\pi$
$150$		0			0
$151$	−0.0581307	−	0.404308i	−0.00473061	−	0.0329021i	0.987319	−	0.158746i	$-0.0507452\pi$
$151$	−0.0581307	−	0.404308i	−0.00473061	−	0.0329021i	−0.992050	+	0.125844i	$0.959836\pi$
$152$		0			0
$153$	−5.81675	−	9.02066i	−0.470257	−	0.729277i
$154$		0			0
$155$	5.06503	−	5.84536i	0.406833	−	0.469511i
$156$		0			0
$157$	−16.8454	+	14.5967i	−1.34441	+	1.16494i	−0.372922	+	0.927863i	$0.621644\pi$
$157$	−16.8454	+	14.5967i	−1.34441	+	1.16494i	−0.971491	+	0.237078i	$0.923810\pi$
$158$		0			0
$159$	2.69860	+	4.93315i	0.214013	+	0.391224i
$160$		0			0
$161$	−15.3536	+	0.809424i	−1.21004	+	0.0637915i
$162$		0			0
$163$	2.84235	−	6.22388i	0.222630	−	0.487492i	−0.765051	−	0.643969i	$-0.777286\pi$
$163$	2.84235	−	6.22388i	0.222630	−	0.487492i	0.987682	+	0.156477i	$0.0500137\pi$
$164$		0			0
$165$	−2.00954	+	0.145271i	−0.156442	+	0.0113093i
$166$		0			0
$167$	7.34774	+	6.36685i	0.568585	+	0.492682i	0.891053	−	0.453899i	$-0.149967\pi$
$167$	7.34774	+	6.36685i	0.568585	+	0.492682i	−0.322468	+	0.946580i	$0.604513\pi$
$168$		0			0
$169$	12.1277	−	3.56101i	0.932898	−	0.273924i
$170$		0			0
$171$	−2.27159	−	4.95401i	−0.173713	−	0.378842i
$172$		0			0
$173$	13.9739	−	6.38167i	1.06242	−	0.485190i	0.193988	−	0.981004i	$-0.437858\pi$
$173$	13.9739	−	6.38167i	1.06242	−	0.485190i	0.868429	+	0.495814i	$0.165130\pi$
$174$		0			0
$175$	−6.22315	+	9.68340i	−0.470426	+	0.731997i
$176$		0			0
$177$	−14.9433	+	14.9662i	−1.12321	+	1.12493i
$178$		0			0
$179$	−5.85090	−	9.10418i	−0.437317	−	0.680478i	0.550721	−	0.834689i	$-0.314353\pi$
$179$	−5.85090	−	9.10418i	−0.437317	−	0.680478i	−0.988038	+	0.154211i	$0.950716\pi$
$180$		0			0
$181$	4.20279	−	14.3134i	0.312391	−	1.06391i	−0.642336	−	0.766423i	$-0.722035\pi$
$181$	4.20279	−	14.3134i	0.312391	−	1.06391i	0.954727	−	0.297483i	$-0.0961471\pi$
$182$		0			0
$183$	5.44545	+	4.06991i	0.402539	+	0.300857i
$184$		0			0
$185$		−	1.49977i		−	0.110265i
$186$		0			0
$187$	3.36349	+	0.987608i	0.245962	+	0.0722211i
$188$		0			0
$189$	−3.57835	−	16.2695i	−0.260287	−	1.18343i
$190$		0			0
$191$	3.04742	−	21.1953i	0.220504	−	1.53364i	−0.515637	−	0.856807i	$-0.672445\pi$
$191$	3.04742	−	21.1953i	0.220504	−	1.53364i	0.736141	−	0.676829i	$-0.236646\pi$
$192$		0			0
$193$	−8.65786	−	5.56407i	−0.623206	−	0.400510i	0.190582	−	0.981671i	$-0.438962\pi$
$193$	−8.65786	−	5.56407i	−0.623206	−	0.400510i	−0.813789	+	0.581161i	$0.802599\pi$
$194$		0			0
$195$	1.20636	+	0.261461i	0.0863894	+	0.0187236i
$196$		0			0
$197$	−9.53119	+	1.37038i	−0.679069	+	0.0976354i	−0.473215	−	0.880947i	$-0.656906\pi$
$197$	−9.53119	+	1.37038i	−0.679069	+	0.0976354i	−0.205855	+	0.978583i	$0.565997\pi$
$198$		0			0
$199$	2.10016	+	7.15249i	0.148876	+	0.507027i	0.999834	−	0.0182074i	$-0.00579592\pi$
$199$	2.10016	+	7.15249i	0.148876	+	0.507027i	−0.850958	+	0.525234i	$0.823978\pi$
$200$		0			0
$201$	−15.0597	+	3.28810i	−1.06223	+	0.231925i
$202$		0			0
$203$	−3.29431	−	3.80183i	−0.231215	−	0.266836i
$204$		0			0
$205$	−10.7513	−	4.90996i	−0.750904	−	0.342927i
$206$		0			0
$207$	−1.27305	+	14.3311i	−0.0884834	+	0.996078i
$208$		0			0
$209$	1.61908	+	0.739411i	0.111994	+	0.0511461i
$210$		0			0
$211$	7.96499	+	9.19209i	0.548333	+	0.632809i	0.960494	−	0.278301i	$-0.0897714\pi$
$211$	7.96499	+	9.19209i	0.548333	+	0.632809i	−0.412161	+	0.911111i	$0.635226\pi$
$212$		0			0
$213$	11.8239	−	2.58162i	0.810162	−	0.176889i
$214$		0			0
$215$	2.54994	+	8.68431i	0.173905	+	0.592265i
$216$		0			0
$217$	−20.6730	+	2.97232i	−1.40337	+	0.201774i
$218$		0			0
$219$	−8.76734	−	1.90019i	−0.592442	−	0.128403i
$220$		0			0
$221$	−1.80673	−	1.16111i	−0.121534	−	0.0781049i
$222$		0			0
$223$	−2.14569	+	14.9236i	−0.143686	+	0.999358i	0.782597	+	0.622529i	$0.213895\pi$
$223$	−2.14569	+	14.9236i	−0.143686	+	0.999358i	−0.926283	+	0.376829i	$0.877014\pi$
$224$		0			0
$225$	8.15127	+	7.04130i	0.543418	+	0.469420i
$226$		0			0
$227$	27.6507	+	8.11899i	1.83524	+	0.538876i	0.999940	−	0.0109130i	$-0.00347380\pi$
$227$	27.6507	+	8.11899i	1.83524	+	0.538876i	0.835303	+	0.549789i	$0.185292\pi$
$228$		0			0
$229$		−	20.3189i		−	1.34271i	−0.741135	−	0.671356i	$-0.765712\pi$
$229$		−	20.3189i		−	1.34271i	0.741135	−	0.671356i	$-0.234288\pi$
$230$		0			0
$231$	4.35786	+	3.25705i	0.286726	+	0.214298i
$232$		0			0
$233$	−5.84352	+	19.9012i	−0.382822	+	1.30377i	0.512629	+	0.858610i	$0.328672\pi$
$233$	−5.84352	+	19.9012i	−0.382822	+	1.30377i	−0.895451	+	0.445161i	$0.853147\pi$
$234$		0			0
$235$	−6.81837	−	10.6096i	−0.444781	−	0.692093i
$236$		0			0
$237$	−17.3912	+	17.4178i	−1.12968	+	1.13141i
$238$		0			0
$239$	0.163180	−	0.253913i	0.0105552	−	0.0164243i	−0.835936	−	0.548827i	$-0.815074\pi$
$239$	0.163180	−	0.253913i	0.0105552	−	0.0164243i	0.846491	+	0.532403i	$0.178711\pi$
$240$		0			0
$241$	2.32125	−	1.06008i	0.149525	−	0.0682858i	−0.339247	−	0.940697i	$-0.610172\pi$
$241$	2.32125	−	1.06008i	0.149525	−	0.0682858i	0.488772	+	0.872412i	$0.337445\pi$
$242$		0			0
$243$	−15.5444	+	1.17155i	−0.997172	+	0.0751552i
$244$		0			0
$245$	−3.73390	+	1.09637i	−0.238550	+	0.0700446i
$246$		0			0
$247$	−0.824136	−	0.714118i	−0.0524385	−	0.0454383i
$248$		0			0
$249$	−15.9291	+	1.15153i	−1.00947	+	0.0729749i
$250$		0			0
$251$	−2.93765	+	6.43255i	−0.185423	+	0.406019i	−0.979400	−	0.201928i	$-0.935279\pi$
$251$	−2.93765	+	6.43255i	−0.185423	+	0.406019i	0.793978	+	0.607947i	$0.208007\pi$
$252$		0			0
$253$	−2.74498	−	3.81372i	−0.172576	−	0.239767i
$254$		0			0
$255$	3.53090	+	6.45461i	0.221114	+	0.404203i
$256$		0			0
$257$	5.00768	−	4.33918i	0.312371	−	0.270671i	−0.484538	−	0.874770i	$-0.661012\pi$
$257$	5.00768	−	4.33918i	0.312371	−	0.270671i	0.796909	+	0.604099i	$0.206467\pi$
$258$		0			0
$259$	−2.65208	+	3.06066i	−0.164792	+	0.190180i
$260$		0			0
$261$	−3.95626	+	2.55110i	−0.244887	+	0.157909i
$262$		0			0
$263$	−4.00363	−	27.8459i	−0.246874	−	1.71705i	−0.616064	−	0.787696i	$-0.711274\pi$
$263$	−4.00363	−	27.8459i	−0.246874	−	1.71705i	0.369190	−	0.929354i	$-0.379635\pi$
$264$		0			0
$265$	−1.60114	−	3.50601i	−0.0983572	−	0.215372i
$266$		0			0
$267$	3.19357	−	1.19393i	0.195444	−	0.0730671i
$268$		0			0
$269$	−19.9467	−	2.86790i	−1.21617	−	0.174859i	−0.495793	−	0.868440i	$-0.665123\pi$
$269$	−19.9467	−	2.86790i	−1.21617	−	0.174859i	−0.720378	+	0.693581i	$0.756032\pi$
$270$		0			0
$271$	−10.9257	+	7.02150i	−0.663687	+	0.426526i	−0.828645	−	0.559775i	$-0.810888\pi$
$271$	−10.9257	+	7.02150i	−0.663687	+	0.426526i	0.164958	+	0.986301i	$0.447251\pi$
$272$		0			0
$273$	−1.99954	−	2.66682i	−0.121018	−	0.161403i
$274$		0			0
$275$	−3.51788			−0.212136
$276$		0			0
$277$	0.692059			0.0415818			0.0207909	−	0.999784i	$-0.493382\pi$
$277$	0.692059			0.0415818			0.0207909	+	0.999784i	$0.493382\pi$
$278$		0			0
$279$	0.0299125	+	19.5441i	0.00179082	+	1.17008i
$280$		0			0
$281$	17.9297	−	11.5227i	1.06959	−	0.687386i	0.117463	−	0.993077i	$-0.462524\pi$
$281$	17.9297	−	11.5227i	1.06959	−	0.687386i	0.952131	+	0.305691i	$0.0988876\pi$
$282$		0			0
$283$	18.7628	+	2.69768i	1.11533	+	0.160361i	0.675245	−	0.737594i	$-0.264038\pi$
$283$	18.7628	+	2.69768i	1.11533	+	0.160361i	0.440088	+	0.897954i	$0.354947\pi$
$284$		0			0
$285$	1.30817	+	3.49916i	0.0774894	+	0.207273i
$286$		0			0
$287$	13.2584	+	29.0318i	0.782618	+	1.71369i
$288$		0			0
$289$	0.597614	+	4.15650i	0.0351538	+	0.244500i
$290$		0			0
$291$	3.67243	+	1.36655i	0.215282	+	0.0801083i
$292$		0			0
$293$	−8.37273	+	9.66264i	−0.489140	+	0.564498i	−0.945636	−	0.325228i	$-0.894559\pi$
$293$	−8.37273	+	9.66264i	−0.489140	+	0.564498i	0.456496	+	0.889726i	$0.349104\pi$
$294$		0			0
$295$	10.9559	−	9.49336i	0.637879	−	0.552725i
$296$		0			0
$297$	3.59168	−	3.60821i	0.208410	−	0.209369i
$298$		0			0
$299$	0.955344	+	2.71566i	0.0552490	+	0.157051i
$300$		0			0
$301$	10.1529	−	22.2316i	0.585201	−	1.28141i
$302$		0			0
$303$	−1.76413	−	24.4033i	−0.101347	−	1.40193i
$304$		0			0
$305$	−3.52173	−	3.05160i	−0.201654	−	0.174734i
$306$		0			0
$307$	−4.15366	+	1.21962i	−0.237062	+	0.0696076i	−0.398105	−	0.917340i	$-0.630332\pi$
$307$	−4.15366	+	1.21962i	−0.237062	+	0.0696076i	0.161044	+	0.986947i	$0.448514\pi$
$308$		0			0
$309$	10.7327	−	19.6913i	0.610562	−	1.12020i
$310$		0			0
$311$	−19.7936	+	9.03945i	−1.12239	+	0.512580i	−0.888130	−	0.459593i	$-0.847995\pi$
$311$	−19.7936	+	9.03945i	−1.12239	+	0.512580i	−0.234264	+	0.972173i	$0.575268\pi$
$312$		0			0
$313$	−15.3200	+	23.8384i	−0.865937	+	1.34742i	0.0708359	+	0.997488i	$0.477433\pi$
$313$	−15.3200	+	23.8384i	−0.865937	+	1.34742i	−0.936773	+	0.349937i	$0.886203\pi$
$314$		0			0
$315$	1.64232	+	11.2998i	0.0925341	+	0.636670i
$316$		0			0
$317$	3.18874	+	4.96178i	0.179098	+	0.278681i	0.919182	−	0.393832i	$-0.128851\pi$
$317$	3.18874	+	4.96178i	0.179098	+	0.278681i	−0.740085	+	0.672514i	$0.765215\pi$
$318$		0			0
$319$	0.433144	−	1.47515i	0.0242514	−	0.0825926i
$320$		0			0
$321$	−1.11212	+	1.48799i	−0.0620725	+	0.0830515i
$322$		0			0
$323$		−	6.49968i		−	0.361652i
$324$		0			0
$325$	2.06795	+	0.607205i	0.114709	+	0.0336817i
$326$		0			0
$327$	15.4458	+	1.09283i	0.854155	+	0.0604334i
$328$		0			0
$329$	−4.84657	+	33.7086i	−0.267200	+	1.85842i
$330$		0			0
$331$	−18.3164	−	11.7712i	−1.00676	−	0.647006i	−0.0702076	−	0.997532i	$-0.522366\pi$
$331$	−18.3164	−	11.7712i	−1.00676	−	0.647006i	−0.936553	+	0.350527i	$0.886003\pi$
$332$		0			0
$333$	2.48613	+	2.86029i	0.136239	+	0.156743i
$334$		0			0
$335$	10.4583	−	1.50368i	0.571399	−	0.0821547i
$336$		0			0
$337$	6.13057	+	20.8788i	0.333953	+	1.13734i	0.939790	+	0.341752i	$0.111020\pi$
$337$	6.13057	+	20.8788i	0.333953	+	1.13734i	−0.605837	+	0.795589i	$0.707162\pi$
$338$		0			0
$339$	−4.70137	−	21.5325i	−0.255343	−	1.16948i
$340$		0			0
$341$	−4.17998	−	4.82396i	−0.226359	−	0.261232i
$342$		0			0
$343$	−10.8546	−	4.95714i	−0.586095	−	0.267661i
$344$		0			0
$345$	1.57863	−	9.73477i	0.0849904	−	0.524102i
$346$		0			0
$347$	−8.87465	−	4.05292i	−0.476416	−	0.217572i	0.162710	−	0.986674i	$-0.447977\pi$
$347$	−8.87465	−	4.05292i	−0.476416	−	0.217572i	−0.639126	+	0.769102i	$0.720704\pi$
$348$		0			0
$349$	−11.2370	−	12.9682i	−0.601504	−	0.694173i	0.370581	−	0.928800i	$-0.379159\pi$
$349$	−11.2370	−	12.9682i	−0.601504	−	0.694173i	−0.972085	+	0.234627i	$0.924613\pi$
$350$		0			0
$351$	−2.73413	+	1.50111i	−0.145937	+	0.0801231i
$352$		0			0
$353$	1.97937	+	6.74112i	0.105351	+	0.358793i	0.995248	−	0.0973676i	$-0.0310423\pi$
$353$	1.97937	+	6.74112i	0.105351	+	0.358793i	−0.889897	+	0.456161i	$0.849224\pi$
$354$		0			0
$355$	−8.21123	+	1.18060i	−0.435807	+	0.0626595i
$356$		0			0
$357$	4.20814	−	19.4160i	0.222719	−	1.02761i
$358$		0			0
$359$	0.433032	+	0.278292i	0.0228545	+	0.0146877i	0.552018	−	0.833832i	$-0.313858\pi$
$359$	0.433032	+	0.278292i	0.0228545	+	0.0146877i	−0.529164	+	0.848520i	$0.677494\pi$
$360$		0			0
$361$	−2.23431	+	15.5399i	−0.117595	+	0.817892i
$362$		0			0
$363$	1.22730	−	17.3465i	0.0644167	−	0.910454i
$364$		0			0
$365$	5.90003	+	1.73241i	0.308822	+	0.0906783i
$366$		0			0
$367$			1.07761i			0.0562508i	0.999604	+	0.0281254i	$0.00895377\pi$
$367$			1.07761i			0.0562508i	−0.999604	+	0.0281254i	$0.991046\pi$
$368$		0			0
$369$	28.6435	−	8.45812i	1.49112	−	0.440312i
$370$		0			0
$371$	−2.93222	+	9.98622i	−0.152233	+	0.518459i
$372$		0			0
$373$	7.18198	+	11.1754i	0.371869	+	0.578640i	0.975872	−	0.218342i	$-0.0700649\pi$
$373$	7.18198	+	11.1754i	0.371869	+	0.578640i	−0.604003	+	0.796982i	$0.706429\pi$
$374$		0			0
$375$	−12.5006	−	12.4815i	−0.645530	−	0.644543i
$376$		0			0
$377$	−0.509239	+	0.792391i	−0.0262271	+	0.0408102i
$378$		0			0
$379$	29.4813	−	13.4636i	1.51435	−	0.691581i	0.526962	−	0.849889i	$-0.323331\pi$
$379$	29.4813	−	13.4636i	1.51435	−	0.691581i	0.987390	+	0.158308i	$0.0506038\pi$
$380$		0			0
$381$	24.4409	+	13.3215i	1.25214	+	0.682479i
$382$		0			0
$383$	−18.2807	+	5.36769i	−0.934098	+	0.274276i	−0.713151	−	0.701010i	$-0.752733\pi$
$383$	−18.2807	+	5.36769i	−0.934098	+	0.274276i	−0.220947	+	0.975286i	$0.570915\pi$
$384$		0			0
$385$	−2.81835	−	2.44212i	−0.143637	−	0.124462i
$386$		0			0
$387$	−19.2588	−	12.3353i	−0.978982	−	0.627039i
$388$		0			0
$389$	11.5054	−	25.1933i	0.583346	−	1.27735i	−0.356035	−	0.934473i	$-0.615872\pi$
$389$	11.5054	−	25.1933i	0.583346	−	1.27735i	0.939381	−	0.342876i	$-0.111401\pi$
$390$		0			0
$391$	−8.50385	+	14.9031i	−0.430058	+	0.753682i
$392$		0			0
$393$	−30.8325	+	16.8665i	−1.55529	+	0.850801i
$394$		0			0
$395$	12.7506	−	11.0485i	0.641554	−	0.555910i
$396$		0			0
$397$	−3.93976	+	4.54673i	−0.197731	+	0.228194i	−0.845953	−	0.533258i	$-0.820968\pi$
$397$	−3.93976	+	4.54673i	−0.197731	+	0.228194i	0.648222	+	0.761452i	$0.275513\pi$
$398$		0			0
$399$	3.51799	−	9.45420i	0.176120	−	0.473302i
$400$		0			0
$401$	−1.10183	−	7.66342i	−0.0550230	−	0.382693i	−0.998662	−	0.0517162i	$-0.983531\pi$
$401$	−1.10183	−	7.66342i	−0.0550230	−	0.382693i	0.943639	−	0.330977i	$-0.107378\pi$
$402$		0			0
$403$	1.62452	+	3.55720i	0.0809232	+	0.177197i
$404$		0			0
$405$	10.6851	−	0.0327074i	0.530946	−	0.00162524i
$406$		0			0
$407$	−1.22511	−	0.176144i	−0.0607263	−	0.00873113i
$408$		0			0
$409$	17.7258	−	11.3917i	0.876487	−	0.563284i	−0.0232438	−	0.999730i	$-0.507399\pi$
$409$	17.7258	−	11.3917i	0.876487	−	0.563284i	0.899730	+	0.436446i	$0.143763\pi$
$410$		0			0
$411$	31.2581	−	23.4368i	1.54185	−	1.15605i
$412$		0			0
$413$	−39.1457			−1.92623
$414$		0			0
$415$	10.9471			0.537373
$416$		0			0
$417$	7.00638	−	5.25328i	0.343104	−	0.257254i
$418$		0			0
$419$	−3.84442	+	2.47066i	−0.187812	+	0.120700i	−0.631168	−	0.775646i	$-0.717424\pi$
$419$	−3.84442	+	2.47066i	−0.187812	+	0.120700i	0.443356	+	0.896346i	$0.353788\pi$
$420$		0			0
$421$	37.7553	+	5.42839i	1.84008	+	0.264564i	0.972529	−	0.232782i	$-0.0747828\pi$
$421$	37.7553	+	5.42839i	1.84008	+	0.264564i	0.867552	+	0.497346i	$0.165692\pi$
$422$		0			0
$423$	30.5909	+	8.93145i	1.48738	+	0.434262i
$424$		0			0
$425$	5.33643	+	11.6852i	0.258855	+	0.566813i
$426$		0			0
$427$	1.79077	+	12.4551i	0.0866617	+	0.602745i
$428$		0			0
$429$	0.355262	−	0.954724i	0.0171522	−	0.0460945i
$430$		0			0
$431$	1.40540	−	1.62191i	0.0676956	−	0.0781248i	−0.720892	−	0.693048i	$-0.756267\pi$
$431$	1.40540	−	1.62191i	0.0676956	−	0.0781248i	0.788587	+	0.614923i	$0.210813\pi$
$432$		0			0
$433$	21.9919	−	19.0561i	1.05686	−	0.915778i	0.0602648	−	0.998182i	$-0.480806\pi$
$433$	21.9919	−	19.0561i	1.05686	−	0.915778i	0.996599	+	0.0824048i	$0.0262600\pi$
$434$		0			0
$435$	2.83085	−	1.54858i	0.135729	−	0.0742485i
$436$		0			0
$437$	−5.35086	+	6.87562i	−0.255966	+	0.328906i
$438$		0			0
$439$	6.74802	−	14.7761i	0.322066	−	0.705225i	−0.677475	−	0.735546i	$-0.736926\pi$
$439$	6.74802	−	14.7761i	0.322066	−	0.705225i	0.999540	+	0.0303208i	$0.00965289\pi$
$440$		0			0
$441$	5.30368	−	8.28052i	0.252556	−	0.394310i
$442$		0			0
$443$	11.3532	+	9.83763i	0.539408	+	0.467400i	0.881445	−	0.472287i	$-0.156571\pi$
$443$	11.3532	+	9.83763i	0.539408	+	0.467400i	−0.342037	+	0.939687i	$0.611117\pi$
$444$		0			0
$445$	−2.24235	+	0.658414i	−0.106298	+	0.0312118i
$446$		0			0
$447$	1.90926	+	1.04064i	0.0903049	+	0.0492205i
$448$		0			0
$449$	19.8224	−	9.05257i	0.935475	−	0.427217i	0.111449	−	0.993770i	$-0.464451\pi$
$449$	19.8224	−	9.05257i	0.935475	−	0.427217i	0.824025	+	0.566553i	$0.191723\pi$
$450$		0			0
$451$	−5.27348	+	8.20569i	−0.248318	+	0.386391i
$452$		0			0
$453$	−0.500649	−	0.499883i	−0.0235225	−	0.0234866i
$454$		0			0
$455$	1.23522	+	1.92204i	0.0579080	+	0.0901065i
$456$		0			0
$457$	−3.47801	+	11.8450i	−0.162695	+	0.554087i	0.837279	+	0.546776i	$0.184145\pi$
$457$	−3.47801	+	11.8450i	−0.162695	+	0.554087i	−0.999973	+	0.00731055i	$0.997673\pi$
$458$		0			0
$459$	−17.4336	−	6.45684i	−0.813730	−	0.301379i
$460$		0			0
$461$		−	3.85499i		−	0.179545i	−0.995962	−	0.0897724i	$-0.971386\pi$
$461$		−	3.85499i		−	0.179545i	0.995962	−	0.0897724i	$-0.0286140\pi$
$462$		0			0
$463$	23.5968	+	6.92865i	1.09664	+	0.322002i	0.779515	−	0.626383i	$-0.215466\pi$
$463$	23.5968	+	6.92865i	1.09664	+	0.322002i	0.317122	+	0.948385i	$0.397284\pi$
$464$		0			0
$465$	0.945475	−	13.3632i	0.0438454	−	0.619702i
$466$		0			0
$467$	−3.65294	+	25.4068i	−0.169038	+	1.17569i	0.711840	+	0.702342i	$0.247862\pi$
$467$	−3.65294	+	25.4068i	−0.169038	+	1.17569i	−0.880878	+	0.473343i	$0.843047\pi$
$468$		0			0
$469$	−24.0018	−	15.4250i	−1.10830	−	0.712262i
$470$		0			0
$471$	−8.17762	+	37.7309i	−0.376805	+	1.73855i
$472$		0			0
$473$	7.39337	−	1.06301i	0.339947	−	0.0488771i
$474$		0			0
$475$	1.83765	+	6.25845i	0.0843170	+	0.287157i
$476$		0			0
$477$	8.86542	+	4.03231i	0.405920	+	0.184627i
$478$		0			0
$479$	−18.7067	−	21.5887i	−0.854730	−	0.986411i	0.145265	−	0.989393i	$-0.453596\pi$
$479$	−18.7067	−	21.5887i	−0.854730	−	0.986411i	−0.999996	+	0.00298133i	$0.999051\pi$
$480$		0			0
$481$	0.689764	+	0.315005i	0.0314505	+	0.0143630i
$482$		0			0
$483$	−20.4358	+	17.0747i	−0.929861	+	0.776927i
$484$		0			0
$485$	−2.44318	−	1.11577i	−0.110939	−	0.0506643i
$486$		0			0
$487$	4.04814	+	4.67180i	0.183439	+	0.211699i	0.840020	−	0.542556i	$-0.182543\pi$
$487$	4.04814	+	4.67180i	0.183439	+	0.211699i	−0.656581	+	0.754256i	$0.727998\pi$
$488$		0			0
$489$	−2.52798	−	11.5783i	−0.114319	−	0.523588i
$490$		0			0
$491$	−6.88771	−	23.4574i	−0.310838	−	1.05862i	−0.955706	−	0.294323i	$-0.904906\pi$
$491$	−6.88771	−	23.4574i	−0.310838	−	1.05862i	0.644868	−	0.764294i	$-0.276912\pi$
$492$		0			0
$493$	−5.55699	+	0.798975i	−0.250274	+	0.0359840i
$494$		0			0
$495$	−2.63384	+	2.28930i	−0.118382	+	0.102897i
$496$		0			0
$497$	18.8448	+	12.1108i	0.845303	+	0.543243i
$498$		0			0
$499$	5.61365	−	39.0438i	0.251301	−	1.74784i	−0.339118	−	0.940744i	$-0.610129\pi$
$499$	5.61365	−	39.0438i	0.251301	−	1.74784i	0.590420	−	0.807096i	$-0.298962\pi$
$500$		0			0
$501$	16.7978	+	1.18848i	0.750470	+	0.0530975i
$502$		0			0
$503$	9.15427	+	2.68794i	0.408169	+	0.119849i	0.479370	−	0.877613i	$-0.340865\pi$
$503$	9.15427	+	2.68794i	0.408169	+	0.119849i	−0.0712013	+	0.997462i	$0.522683\pi$
$504$		0			0
$505$			16.7709i			0.746296i
$506$		0			0
$507$	13.1063	−	17.5359i	0.582071	−	0.778798i
$508$		0			0
$509$	−5.60336	+	19.0833i	−0.248365	+	0.845853i	0.737073	+	0.675814i	$0.236208\pi$
$509$	−5.60336	+	19.0833i	−0.248365	+	0.845853i	−0.985437	+	0.170039i	$0.945611\pi$
$510$		0			0
$511$	−8.97706	−	13.9686i	−0.397122	−	0.617933i
$512$		0			0
$513$	−8.29534	−	4.50491i	−0.366248	−	0.198897i
$514$		0			0
$515$	−8.31080	+	12.9319i	−0.366218	+	0.569846i
$516$		0			0
$517$	−9.46737	+	4.32360i	−0.416375	+	0.190152i
$518$		0			0
$519$	12.7340	−	23.3631i	0.558961	−	1.02552i
$520$		0			0
$521$	−16.7797	+	4.92696i	−0.735131	+	0.215854i	−0.627806	−	0.778370i	$-0.716047\pi$
$521$	−16.7797	+	4.92696i	−0.735131	+	0.215854i	−0.107325	+	0.994224i	$0.534229\pi$
$522$		0			0
$523$	−18.0751	−	15.6621i	−0.790367	−	0.684857i	0.163014	−	0.986624i	$-0.447878\pi$
$523$	−18.0751	−	15.6621i	−0.790367	−	0.684857i	−0.953382	+	0.301766i	$0.902424\pi$
$524$		0			0
$525$	1.43751	+	19.8852i	0.0627382	+	0.867861i
$526$		0			0
$527$	−9.68268	+	21.2021i	−0.421784	+	0.923579i
$528$		0			0
$529$	21.2647	−	8.76431i	0.924552	−	0.381057i
$530$		0			0
$531$	−5.15771	+	36.2666i	−0.223825	+	1.57384i
$532$		0			0
$533$	4.51631	−	3.91340i	0.195623	−	0.169508i
$534$		0			0
$535$	0.833861	−	0.962327i	0.0360510	−	0.0416050i
$536$		0			0
$537$	−17.5677	−	6.53710i	−0.758102	−	0.282097i
$538$		0			0
$539$	0.457049	+	3.17885i	0.0196865	+	0.136923i
$540$		0			0
$541$	13.0937	+	28.6711i	0.562940	+	1.23267i	0.950472	+	0.310811i	$0.100601\pi$
$541$	13.0937	+	28.6711i	0.562940	+	1.23267i	−0.387531	+	0.921857i	$0.626672\pi$
$542$		0			0
$543$	−9.04803	−	24.2021i	−0.388288	−	1.03861i
$544$		0			0
$545$	−10.5058	−	1.51050i	−0.450018	−	0.0647029i
$546$		0			0
$547$	−22.1398	+	14.2284i	−0.946630	+	0.608362i	−0.920267	−	0.391290i	$-0.872029\pi$
$547$	−22.1398	+	14.2284i	−0.946630	+	0.608362i	−0.0263630	+	0.999652i	$0.508393\pi$
$548$		0			0
$549$	11.7750	−	0.0180218i	0.502545	−	0.000769151i
$550$		0			0
$551$	−2.85062			−0.121440
$552$		0			0
$553$	−45.5582			−1.93733
$554$		0			0
$555$	−1.55832	−	2.07836i	−0.0661471	−	0.0882214i
$556$		0			0
$557$	24.1510	−	15.5209i	1.02331	−	0.657643i	0.0825066	−	0.996591i	$-0.473707\pi$
$557$	24.1510	−	15.5209i	1.02331	−	0.657643i	0.940805	+	0.338948i	$0.110071\pi$
$558$		0			0
$559$	−4.52960	−	0.651258i	−0.191582	−	0.0275453i
$560$		0			0
$561$	5.68723	−	2.12618i	0.240115	−	0.0897676i
$562$		0			0
$563$	14.0634	+	30.7945i	0.592701	+	1.29783i	0.933796	+	0.357806i	$0.116475\pi$
$563$	14.0634	+	30.7945i	0.592701	+	1.29783i	−0.341095	+	0.940029i	$0.610798\pi$
$564$		0			0
$565$	2.14998	+	14.9534i	0.0904503	+	0.629095i
$566$		0			0
$567$	−21.8635	−	18.8279i	−0.918179	−	0.790699i
$568$		0			0
$569$	−8.64607	+	9.97809i	−0.362462	+	0.418303i	−0.907463	−	0.420132i	$-0.861984\pi$
$569$	−8.64607	+	9.97809i	−0.362462	+	0.418303i	0.545001	+	0.838435i	$0.316529\pi$
$570$		0			0
$571$	−13.5119	+	11.7081i	−0.565453	+	0.489968i	−0.890037	−	0.455889i	$-0.849321\pi$
$571$	−13.5119	+	11.7081i	−0.565453	+	0.489968i	0.324583	+	0.945857i	$0.394776\pi$
$572$		0			0
$573$	−17.7997	−	32.5384i	−0.743592	−	1.35931i
$574$		0			0
$575$	3.97470	−	16.7543i	0.165757	−	0.698701i
$576$		0			0
$577$	14.4970	−	31.7441i	0.603519	−	1.32152i	−0.323401	−	0.946262i	$-0.604826\pi$
$577$	14.4970	−	31.7441i	0.603519	−	1.32152i	0.926920	−	0.375260i	$-0.122447\pi$
$578$		0			0
$579$	−17.7792	+	1.28527i	−0.738879	+	0.0534140i
$580$		0			0
$581$	−22.3404	−	19.3581i	−0.926836	−	0.803108i
$582$		0			0
$583$	−3.05197	+	0.896141i	−0.126400	+	0.0371143i
$584$		0			0
$585$	1.94343	−	0.891130i	0.0803507	−	0.0368437i
$586$		0			0
$587$	−12.0394	+	5.49819i	−0.496918	+	0.226935i	−0.648077	−	0.761575i	$-0.724427\pi$
$587$	−12.0394	+	5.49819i	−0.496918	+	0.226935i	0.151159	+	0.988509i	$0.451699\pi$
$588$		0			0
$589$	−6.39850	+	9.95626i	−0.263646	+	0.410241i
$590$		0			0
$591$	−11.7843	+	11.8023i	−0.484741	+	0.485483i
$592$		0			0
$593$	8.02636	+	12.4893i	0.329603	+	0.512873i	0.966018	−	0.258474i	$-0.0832197\pi$
$593$	8.02636	+	12.4893i	0.329603	+	0.512873i	−0.636415	+	0.771347i	$0.719583\pi$
$594$		0			0
$595$	−3.83657	+	13.0661i	−0.157284	+	0.535660i
$596$		0			0
$597$	10.3421	+	7.72965i	0.423274	+	0.316354i
$598$		0			0
$599$			19.9952i			0.816982i	0.912762	+	0.408491i	$0.133945\pi$
$599$			19.9952i			0.816982i	−0.912762	+	0.408491i	$0.866055\pi$
$600$		0			0
$601$	−35.7201	−	10.4884i	−1.45705	−	0.427829i	−0.545185	−	0.838316i	$-0.683541\pi$
$601$	−35.7201	−	10.4884i	−1.45705	−	0.427829i	−0.911866	+	0.410487i	$0.865359\pi$
$602$		0			0
$603$	−17.4530	+	20.2042i	−0.710739	+	0.822778i
$604$		0			0
$605$	−1.69638	+	11.7986i	−0.0689676	+	0.479680i
$606$		0			0
$607$	−38.5483	−	24.7735i	−1.56463	−	1.00553i	−0.981116	−	0.193421i	$-0.938042\pi$
$607$	−38.5483	−	24.7735i	−1.56463	−	1.00553i	−0.583512	−	0.812105i	$-0.698322\pi$
$608$		0			0
$609$	−8.51546	−	1.84560i	−0.345064	−	0.0747875i
$610$		0			0
$611$	6.31158	−	0.907469i	0.255339	−	0.0367122i
$612$		0			0
$613$	4.90529	+	16.7059i	0.198123	+	0.674744i	0.997286	+	0.0736296i	$0.0234582\pi$
$613$	4.90529	+	16.7059i	0.198123	+	0.674744i	−0.799163	+	0.601114i	$0.794724\pi$
$614$		0			0
$615$	−20.0006	+	4.36691i	−0.806504	+	0.176091i
$616$		0			0
$617$	−1.67795	−	1.93645i	−0.0675516	−	0.0779587i	0.720968	−	0.692968i	$-0.243698\pi$
$617$	−1.67795	−	1.93645i	−0.0675516	−	0.0779587i	−0.788519	+	0.615010i	$0.789152\pi$
$618$		0			0
$619$	7.16320	+	3.27132i	0.287913	+	0.131486i	0.554136	−	0.832426i	$-0.313049\pi$
$619$	7.16320	+	3.27132i	0.287913	+	0.131486i	−0.266223	+	0.963911i	$0.585776\pi$
$620$		0			0
$621$	13.1264	+	21.1825i	0.526743	+	0.850024i
$622$		0			0
$623$	5.74037	+	2.62154i	0.229983	+	0.105030i
$624$		0			0
$625$	−3.82687	−	4.41644i	−0.153075	−	0.176658i
$626$		0			0
$627$	3.01198	−	0.657630i	0.120287	−	0.0262632i
$628$		0			0
$629$	1.27333	+	4.33658i	0.0507712	+	0.172911i
$630$		0			0
$631$	−18.0466	+	2.59471i	−0.718424	+	0.103294i	−0.491825	−	0.870694i	$-0.663670\pi$
$631$	−18.0466	+	2.59471i	−0.718424	+	0.103294i	−0.226599	+	0.973988i	$0.572761\pi$
$632$		0			0
$633$	20.5887	+	4.46230i	0.818327	+	0.177360i
$634$		0			0
$635$	−16.0511	−	10.3154i	−0.636967	−	0.409354i
$636$		0			0
$637$	0.280015	−	1.94754i	0.0110946	−	0.0771645i
$638$		0			0
$639$	13.7030	−	15.8631i	0.542082	−	0.627534i
$640$		0			0
$641$	−9.60559	−	2.82046i	−0.379398	−	0.111401i	0.0864724	−	0.996254i	$-0.472441\pi$
$641$	−9.60559	−	2.82046i	−0.379398	−	0.111401i	−0.465870	+	0.884853i	$0.654259\pi$
$642$		0			0
$643$		−	28.0371i		−	1.10567i	−0.833289	−	0.552837i	$-0.813545\pi$
$643$		−	28.0371i		−	1.10567i	0.833289	−	0.552837i	$-0.186455\pi$
$644$		0			0
$645$	12.5570	+	9.38507i	0.494432	+	0.369537i
$646$		0			0
$647$	−1.17952	+	4.01707i	−0.0463717	+	0.157927i	−0.979424	−	0.201813i	$-0.935317\pi$
$647$	−1.17952	+	4.01707i	−0.0463717	+	0.157927i	0.933052	+	0.359741i	$0.117135\pi$
$648$		0			0
$649$	−6.46803	−	10.0645i	−0.253892	−	0.395064i
$650$		0			0
$651$	−25.5599	+	25.5990i	−1.00177	+	1.00331i
$652$		0			0
$653$	−8.85137	+	13.7730i	−0.346381	+	0.538979i	−0.970111	−	0.242660i	$-0.921980\pi$
$653$	−8.85137	+	13.7730i	−0.346381	+	0.538979i	0.623730	+	0.781640i	$0.285616\pi$
$654$		0			0
$655$	21.9128	−	10.0072i	0.856203	−	0.391015i
$656$		0			0
$657$	−14.1240	+	6.47636i	−0.551030	+	0.252667i
$658$		0			0
$659$	42.2936	−	12.4185i	1.64752	−	0.483757i	0.679304	−	0.733857i	$-0.262282\pi$
$659$	42.2936	−	12.4185i	1.64752	−	0.483757i	0.968220	+	0.250100i	$0.0804635\pi$
$660$		0			0
$661$	29.0891	+	25.2059i	1.13144	+	0.980394i	0.999940	−	0.0109226i	$-0.00347684\pi$
$661$	29.0891	+	25.2059i	1.13144	+	0.980394i	0.131495	+	0.991317i	$0.458022\pi$
$662$		0			0
$663$	−3.71017	+	0.268211i	−0.144091	+	0.0104164i
$664$		0			0
$665$	−2.87239	+	6.28966i	−0.111387	+	0.243903i
$666$		0			0
$667$	6.53617	+	3.72960i	0.253082	+	0.144411i
$668$		0			0
$669$	12.5328	+	22.9103i	0.484544	+	0.885764i
$670$		0			0
$671$	−2.90635	+	2.51837i	−0.112199	+	0.0972206i
$672$		0			0
$673$	8.65998	−	9.99415i	0.333818	−	0.385246i	−0.563881	−	0.825856i	$-0.690692\pi$
$673$	8.65998	−	9.99415i	0.333818	−	0.385246i	0.897699	+	0.440610i	$0.145238\pi$
$674$		0			0
$675$	18.6121	+	1.28822i	0.716380	+	0.0495837i
$676$		0			0
$677$	−0.631871	−	4.39476i	−0.0242848	−	0.168904i	0.974070	−	0.226248i	$-0.0726460\pi$
$677$	−0.631871	−	4.39476i	−0.0242848	−	0.168904i	−0.998354	+	0.0573437i	$0.981737\pi$
$678$		0			0
$679$	3.01290	+	6.59734i	0.115625	+	0.253183i
$680$		0			0
$681$	46.7539	−	17.4791i	1.79161	−	0.669799i
$682$		0			0
$683$	31.1905	+	4.48452i	1.19347	+	0.171595i	0.710280	−	0.703919i	$-0.248568\pi$
$683$	31.1905	+	4.48452i	1.19347	+	0.171595i	0.483192	+	0.875514i	$0.339477\pi$
$684$		0			0
$685$	−22.5284	+	14.4781i	−0.860767	+	0.553182i
$686$		0			0
$687$	−21.1122	−	28.1576i	−0.805479	−	1.07428i
$688$		0			0
$689$	1.94875			0.0742416
$690$		0			0
$691$	−8.80715			−0.335040			−0.167520	−	0.985869i	$-0.553576\pi$
$691$	−8.80715			−0.335040			−0.167520	+	0.985869i	$0.553576\pi$
$692$		0			0
$693$	9.42325	−	0.0144224i	0.357960	−	0.000547861i
$694$		0			0
$695$	−5.04967	+	3.24523i	−0.191545	+	0.123098i
$696$		0			0
$697$	35.2560	+	5.06905i	1.33542	+	0.192004i
$698$		0			0
$699$	12.5803	+	33.6504i	0.475830	+	1.27278i
$700$		0			0
$701$	−18.6663	−	40.8735i	−0.705016	−	1.54377i	−0.833781	−	0.552095i	$-0.813829\pi$
$701$	−18.6663	−	40.8735i	−0.705016	−	1.54377i	0.128765	−	0.991675i	$-0.458899\pi$
$702$		0			0
$703$	0.326596	+	2.27153i	0.0123178	+	0.0856723i
$704$		0			0
$705$	−20.4726	−	7.61803i	−0.771041	−	0.286912i
$706$		0			0
$707$	29.6564	−	34.2253i	1.11534	−	1.28718i
$708$		0			0
$709$	5.49805	−	4.76408i	0.206483	−	0.178919i	−0.545480	−	0.838124i	$-0.683653\pi$
$709$	5.49805	−	4.76408i	0.206483	−	0.178919i	0.751963	+	0.659205i	$0.229107\pi$
$710$		0			0
$711$	−6.00260	+	42.2075i	−0.225115	+	1.58291i
$712$		0			0
$713$	27.6974	−	14.4572i	1.03728	−	0.541427i
$714$		0			0
$715$	−0.290066	+	0.635156i	−0.0108479	+	0.0237535i
$716$		0			0
$717$	−0.0376937	−	0.521419i	−0.00140770	−	0.0194727i
$718$		0			0
$719$	−2.59413	−	2.24783i	−0.0967448	−	0.0838299i	0.605146	−	0.796115i	$-0.293115\pi$
$719$	−2.59413	−	2.24783i	−0.0967448	−	0.0838299i	−0.701890	+	0.712285i	$0.747660\pi$
$720$		0			0
$721$	39.8280	−	11.6946i	1.48327	−	0.435528i
$722$		0			0
$723$	2.11529	−	3.88091i	0.0786683	−	0.144333i
$724$		0			0
$725$	5.12486	−	2.34044i	0.190332	−	0.0869219i
$726$		0			0
$727$	2.33517	−	3.63359i	0.0866066	−	0.134763i	−0.795247	−	0.606285i	$-0.792659\pi$
$727$	2.33517	−	3.63359i	0.0866066	−	0.134763i	0.881854	+	0.471523i	$0.156295\pi$
$728$		0			0
$729$	−20.3238	+	17.7747i	−0.752735	+	0.658324i
$730$		0			0
$731$	−14.7463	−	22.9457i	−0.545411	−	0.848676i
$732$		0			0
$733$	−7.63952	+	26.0178i	−0.282172	+	0.960990i	0.689427	+	0.724355i	$0.257862\pi$
$733$	−7.63952	+	26.0178i	−0.282172	+	0.960990i	−0.971599	+	0.236634i	$0.923956\pi$
$734$		0			0
$735$	−4.03520	+	5.39900i	−0.148841	+	0.199145i
$736$		0			0
$737$		−	8.71961i		−	0.321191i
$738$		0			0
$739$	−7.05908	−	2.07273i	−0.259673	−	0.0762467i	0.149305	−	0.988791i	$-0.452296\pi$
$739$	−7.05908	−	2.07273i	−0.259673	−	0.0762467i	−0.408978	+	0.912544i	$0.634115\pi$
$740$		0			0
$741$	−1.88407	−	0.133302i	−0.0692131	−	0.00489699i
$742$		0			0
$743$	6.30855	−	43.8769i	0.231438	−	1.60969i	−0.460451	−	0.887685i	$-0.652312\pi$
$743$	6.30855	−	43.8769i	0.231438	−	1.60969i	0.691889	−	0.722004i	$-0.256779\pi$
$744$		0			0
$745$	−1.25387	−	0.805812i	−0.0459382	−	0.0295227i
$746$		0			0
$747$	−20.8778	+	18.1467i	−0.763879	+	0.663955i
$748$		0			0
$749$	−3.40341	+	0.489336i	−0.124358	+	0.0178800i
$750$		0			0
$751$	−8.45959	−	28.8107i	−0.308695	−	1.05132i	−0.957036	−	0.289969i	$-0.906355\pi$
$751$	−8.45959	−	28.8107i	−0.308695	−	1.05132i	0.648341	−	0.761350i	$-0.275463\pi$
$752$		0			0
$753$	2.61274	+	11.9665i	0.0952134	+	0.436082i
$754$		0			0
$755$	0.317572	+	0.366497i	0.0115576	+	0.0133382i
$756$		0			0
$757$	3.82490	+	1.74677i	0.139018	+	0.0634875i	0.483710	−	0.875229i	$-0.339289\pi$
$757$	3.82490	+	1.74677i	0.139018	+	0.0634875i	−0.344691	+	0.938716i	$0.612016\pi$
$758$		0			0
$759$	−7.76656	−	2.43284i	−0.281908	−	0.0883066i
$760$		0			0
$761$	−10.1592	−	4.63956i	−0.368271	−	0.168184i	0.222679	−	0.974892i	$-0.428520\pi$
$761$	−10.1592	−	4.63956i	−0.368271	−	0.168184i	−0.590950	+	0.806708i	$0.701247\pi$
$762$		0			0
$763$	18.7687	+	21.6602i	0.679471	+	0.784151i
$764$		0			0
$765$	11.5997	+	5.27595i	0.419387	+	0.190752i
$766$		0			0
$767$	2.06499	+	7.03271i	0.0745625	+	0.253936i
$768$		0			0
$769$	−24.6862	+	3.54934i	−0.890208	+	0.127993i	−0.572218	−	0.820101i	$-0.693917\pi$
$769$	−24.6862	+	3.54934i	−0.890208	+	0.127993i	−0.317990	+	0.948094i	$0.603008\pi$
$770$		0			0
$771$	2.43098	−	11.2163i	0.0875496	−	0.403947i
$772$		0			0
$773$	−12.2244	−	7.85616i	−0.439682	−	0.282566i	0.302013	−	0.953304i	$-0.402341\pi$
$773$	−12.2244	−	7.85616i	−0.439682	−	0.282566i	−0.741695	+	0.670737i	$0.765978\pi$
$774$		0			0
$775$	3.32887	−	23.1528i	0.119577	−	0.831673i
$776$		0			0
$777$	−0.495056	+	6.99703i	−0.0177600	+	0.251017i
$778$		0			0
$779$	17.3530	+	5.09529i	0.621735	+	0.182558i
$780$		0			0
$781$			6.84610i			0.244973i
$782$		0			0
$783$	−2.83183	+	7.64599i	−0.101201	+	0.273245i
$784$		0			0
$785$	7.45554	−	25.3912i	0.266100	−	0.906252i
$786$		0			0
$787$	15.5856	+	24.2516i	0.555565	+	0.864476i	0.999501	−	0.0315822i	$-0.0100546\pi$
$787$	15.5856	+	24.2516i	0.555565	+	0.864476i	−0.443936	+	0.896059i	$0.646418\pi$
$788$		0			0
$789$	−34.4811	−	34.4284i	−1.22756	−	1.22568i
$790$		0			0
$791$	22.0549	−	34.3181i	0.784182	−	1.22021i
$792$		0			0
$793$	2.14316	−	0.978747i	0.0761057	−	0.0347563i
$794$		0			0
$795$	−5.86171	−	3.19492i	−0.207893	−	0.113312i
$796$		0			0
$797$	−5.91931	+	1.73807i	−0.209673	+	0.0615654i	−0.384882	−	0.922966i	$-0.625758\pi$
$797$	−5.91931	+	1.73807i	−0.209673	+	0.0615654i	0.175209	+	0.984531i	$0.443940\pi$
$798$		0			0
$799$	28.7230	+	24.8886i	1.01615	+	0.880496i
$800$		0			0
$801$	3.18507	−	4.97278i	0.112539	−	0.175704i
$802$		0			0
$803$	2.10808	−	4.61605i	0.0743925	−	0.162897i
$804$		0			0
$805$	14.8152	−	10.6635i	0.522166	−	0.375837i
$806$		0			0
$807$	−30.6217	+	16.7511i	−1.07793	+	0.589668i
$808$		0			0
$809$	−15.1208	+	13.1022i	−0.531619	+	0.460650i	−0.878829	−	0.477137i	$-0.841675\pi$
$809$	−15.1208	+	13.1022i	−0.531619	+	0.460650i	0.347210	+	0.937787i	$0.387129\pi$
$810$		0			0
$811$	−14.7447	+	17.0163i	−0.517756	+	0.597522i	−0.953067	−	0.302758i	$-0.902093\pi$
$811$	−14.7447	+	17.0163i	−0.517756	+	0.597522i	0.435312	+	0.900280i	$0.356638\pi$
$812$		0			0
$813$	−7.84498	+	21.0825i	−0.275136	+	0.739395i
$814$		0			0
$815$	1.15607	+	8.04063i	0.0404953	+	0.281651i
$816$		0			0
$817$	−5.75323	−	12.5978i	−0.201280	−	0.440742i
$818$		0			0
$819$	−5.54186	−	1.61803i	−0.193648	−	0.0565384i
$820$		0			0
$821$	−36.6014	−	5.26249i	−1.27740	−	0.183662i	−0.529977	−	0.848012i	$-0.677799\pi$
$821$	−36.6014	−	5.26249i	−1.27740	−	0.183662i	−0.747422	+	0.664350i	$0.768708\pi$
$822$		0			0
$823$	1.55845	−	1.00156i	0.0543242	−	0.0349121i	−0.513197	−	0.858271i	$-0.671539\pi$
$823$	1.55845	−	1.00156i	0.0543242	−	0.0349121i	0.567521	+	0.823359i	$0.307903\pi$
$824$		0			0
$825$	−4.87502	+	3.65522i	−0.169726	+	0.127258i
$826$		0			0
$827$	40.9130			1.42269			0.711343	−	0.702845i	$-0.248087\pi$
$827$	40.9130			1.42269			0.711343	+	0.702845i	$0.248087\pi$
$828$		0			0
$829$	−5.80044			−0.201458			−0.100729	−	0.994914i	$-0.532117\pi$
$829$	−5.80044			−0.201458			−0.100729	+	0.994914i	$0.532117\pi$
$830$		0			0
$831$	0.959044	−	0.719077i	0.0332689	−	0.0249445i
$832$		0			0
$833$	9.86570	−	6.34030i	0.341826	−	0.219678i
$834$		0			0
$835$	−11.4254	−	1.64272i	−0.395391	−	0.0568487i
$836$		0			0
$837$	20.3486	+	27.0529i	0.703350	+	0.935084i
$838$		0			0
$839$	−16.0425	−	35.1282i	−0.553850	−	1.21276i	−0.954961	−	0.296732i	$-0.904103\pi$
$839$	−16.0425	−	35.1282i	−0.553850	−	1.21276i	0.401111	−	0.916029i	$-0.368624\pi$
$840$		0			0
$841$	−3.77672	−	26.2676i	−0.130232	−	0.905781i
$842$		0			0
$843$	12.8741	−	34.5976i	0.443407	−	1.19160i
$844$		0			0
$845$	−9.82703	+	11.3410i	−0.338060	+	0.390142i
$846$		0			0
$847$	24.3256	−	21.0782i	0.835836	−	0.724256i
$848$		0			0
$849$	28.8042	−	15.7569i	0.988557	−	0.540776i
$850$		0			0
$851$	2.22310	−	5.63568i	0.0762069	−	0.193189i
$852$		0			0
$853$	17.5346	−	38.3954i	0.600373	−	1.31463i	−0.328594	−	0.944471i	$-0.606575\pi$
$853$	17.5346	−	38.3954i	0.600373	−	1.31463i	0.928967	−	0.370162i	$-0.120698\pi$
$854$		0			0
$855$	5.44861	+	3.48984i	0.186339	+	0.119350i
$856$		0			0
$857$	43.0400	+	37.2943i	1.47022	+	1.27395i	0.887113	+	0.461553i	$0.152708\pi$
$857$	43.0400	+	37.2943i	1.47022	+	1.27395i	0.583104	+	0.812397i	$0.301838\pi$
$858$		0			0
$859$	−19.5241	+	5.73280i	−0.666154	+	0.195600i	−0.597290	−	0.802026i	$-0.703756\pi$
$859$	−19.5241	+	5.73280i	−0.666154	+	0.195600i	−0.0688643	+	0.997626i	$0.521938\pi$
$860$		0			0
$861$	48.5385	+	26.4558i	1.65419	+	0.901612i
$862$		0			0
$863$	−2.67618	+	1.22217i	−0.0910983	+	0.0416032i	−0.460443	−	0.887689i	$-0.652309\pi$
$863$	−2.67618	+	1.22217i	−0.0910983	+	0.0416032i	0.369345	+	0.929292i	$0.379582\pi$
$864$		0			0
$865$	−9.86049	+	15.3432i	−0.335267	+	0.521685i
$866$		0			0
$867$	5.14693	+	5.13906i	0.174799	+	0.174532i
$868$		0			0
$869$	−7.52758	−	11.7131i	−0.255356	−	0.397341i
$870$		0			0
$871$	−1.50505	+	5.12574i	−0.0509967	+	0.173679i
$872$		0			0
$873$	6.50909	−	1.92207i	0.220299	−	0.0650521i
$874$		0			0
$875$		−	32.6967i		−	1.10535i
$876$		0			0
$877$	5.95554	+	1.74870i	0.201104	+	0.0590495i	0.380733	−	0.924685i	$-0.375672\pi$
$877$	5.95554	+	1.74870i	0.201104	+	0.0590495i	−0.179629	+	0.983734i	$0.557490\pi$
$878$		0			0
$879$	−1.56291	+	22.0899i	−0.0527157	+	0.745075i
$880$		0			0
$881$	2.28417	−	15.8867i	0.0769556	−	0.535238i	−0.914479	−	0.404634i	$-0.867399\pi$
$881$	2.28417	−	15.8867i	0.0769556	−	0.535238i	0.991435	−	0.130605i	$-0.0416918\pi$
$882$		0			0
$883$	39.1846	+	25.1824i	1.31867	+	0.847456i	0.995112	−	0.0987529i	$-0.0314854\pi$
$883$	39.1846	+	25.1824i	1.31867	+	0.847456i	0.323556	+	0.946209i	$0.395122\pi$
$884$		0			0
$885$	5.31855	−	24.5394i	0.178781	−	0.824882i
$886$		0			0
$887$	24.1686	−	3.47491i	0.811501	−	0.116676i	0.275942	−	0.961174i	$-0.411010\pi$
$887$	24.1686	−	3.47491i	0.811501	−	0.116676i	0.535559	+	0.844498i	$0.320101\pi$
$888$		0			0
$889$	14.5153	+	49.4346i	0.486828	+	1.65798i
$890$		0			0
$891$	1.22822	−	8.73209i	0.0411468	−	0.292536i
$892$		0			0
$893$	12.6374	+	14.5843i	0.422893	+	0.488045i
$894$		0			0
$895$	11.6874	+	5.33745i	0.390666	+	0.178411i
$896$		0			0
$897$	4.14558	+	2.77067i	0.138417	+	0.0925101i
$898$		0			0
$899$	9.29879	+	4.24662i	0.310132	+	0.141633i
$900$		0			0
$901$	7.60635	+	8.77819i	0.253404	+	0.292444i
$902$		0			0
$903$	−9.02992	−	41.3575i	−0.300497	−	1.37629i
$904$		0			0
$905$	4.98971	+	16.9934i	0.165864	+	0.564879i
$906$		0			0
$907$	5.74067	−	0.825384i	0.190616	−	0.0274064i	−0.0463457	−	0.998925i	$-0.514758\pi$
$907$	5.74067	−	0.825384i	0.190616	−	0.0274064i	0.236961	+	0.971519i	$0.423848\pi$
$908$		0			0
$909$	−27.8007	−	31.9847i	−0.922091	−	1.06086i
$910$		0			0
$911$	−9.30969	−	5.98297i	−0.308444	−	0.198225i	0.377256	−	0.926109i	$-0.376868\pi$
$911$	−9.30969	−	5.98297i	−0.308444	−	0.198225i	−0.685700	+	0.727884i	$0.740504\pi$
$912$		0			0
$913$	1.28571	−	8.94230i	0.0425508	−	0.295947i
$914$		0			0
$915$	−8.05109	−	0.569633i	−0.266161	−	0.0188315i
$916$		0			0
$917$	−62.4146	−	18.3266i	−2.06111	−	0.605197i
$918$		0			0
$919$		−	25.0966i		−	0.827859i	−0.910309	−	0.413930i	$-0.864156\pi$
$919$		−	25.0966i		−	0.827859i	0.910309	−	0.413930i	$-0.135844\pi$
$920$		0			0
$921$	−4.48883	+	6.00595i	−0.147912	+	0.197903i
$922$		0			0
$923$	1.18168	−	4.02442i	0.0388953	−	0.132465i
$924$		0			0
$925$	−2.45215	−	3.81562i	−0.0806263	−	0.125457i
$926$		0			0
$927$	−5.58684	−	38.4396i	−0.183496	−	1.26252i
$928$		0			0
$929$	4.14453	−	6.44902i	0.135978	−	0.211585i	−0.766586	−	0.642142i	$-0.778046\pi$
$929$	4.14453	−	6.44902i	0.135978	−	0.211585i	0.902564	+	0.430556i	$0.141683\pi$
$930$		0			0
$931$	5.41655	−	2.47365i	0.177520	−	0.0810707i
$932$		0			0
$933$	−18.0373	+	33.0931i	−0.590516	+	1.08342i
$934$		0			0
$935$	−3.99326	+	1.17253i	−0.130593	+	0.0383457i
$936$		0			0
$937$	−9.73747	−	8.43756i	−0.318109	−	0.275643i	0.481139	−	0.876644i	$-0.340223\pi$
$937$	−9.73747	−	8.43756i	−0.318109	−	0.275643i	−0.799248	+	0.601001i	$0.794769\pi$
$938$		0			0
$939$	3.53884	+	48.9529i	0.115486	+	1.59752i
$940$		0			0
$941$	7.22981	−	15.8311i	0.235685	−	0.516078i	−0.754422	−	0.656389i	$-0.772083\pi$
$941$	7.22981	−	15.8311i	0.235685	−	0.516078i	0.990108	+	0.140311i	$0.0448102\pi$
$942$		0			0
$943$	−33.1222	−	34.3867i	−1.07861	−	1.11979i
$944$		0			0
$945$	14.0168	+	13.9526i	0.455967	+	0.453878i
$946$		0			0
$947$	−42.6323	+	36.9411i	−1.38536	+	1.20042i	−0.430788	+	0.902453i	$0.641764\pi$
$947$	−42.6323	+	36.9411i	−1.38536	+	1.20042i	−0.954575	+	0.297971i	$0.903690\pi$
$948$		0			0
$949$	−2.03597	+	2.34963i	−0.0660904	+	0.0762724i
$950$		0			0
$951$	9.57440	+	3.56272i	0.310471	+	0.115529i
$952$		0			0
$953$	5.16501	+	35.9235i	0.167311	+	1.16368i	0.884412	+	0.466706i	$0.154559\pi$
$953$	5.16501	+	35.9235i	0.167311	+	1.16368i	−0.717101	+	0.696969i	$0.754531\pi$
$954$		0			0
$955$	10.5609	+	23.1252i	0.341743	+	0.748314i
$956$		0			0
$957$	−0.932499	−	2.49429i	−0.0301434	−	0.0806291i
$958$		0			0
$959$	71.5770	+	10.2912i	2.31134	+	0.332321i
$960$		0			0
$961$	9.62526	−	6.18578i	0.310492	−	0.199541i
$962$		0			0
$963$	0.00492453	+	3.21757i	0.000158691	+	0.103685i
$964$		0			0
$965$	12.2186			0.393330
$966$		0			0
$967$	−27.7083			−0.891040			−0.445520	−	0.895272i	$-0.646981\pi$
$967$	−27.7083			−0.891040			−0.445520	+	0.895272i	$0.646981\pi$
$968$		0			0
$969$	−6.75342	−	9.00714i	−0.216951	−	0.289351i
$970$		0			0
$971$	−32.4010	+	20.8228i	−1.03980	+	0.668237i	−0.944936	−	0.327254i	$-0.893877\pi$
$971$	−32.4010	+	20.8228i	−1.03980	+	0.668237i	−0.0948602	+	0.995491i	$0.530240\pi$
$972$		0			0
$973$	16.0437	+	2.30674i	0.514338	+	0.0739507i
$974$		0			0
$975$	3.49664	−	1.30723i	0.111982	−	0.0418648i
$976$		0			0
$977$	−14.4958	−	31.7413i	−0.463761	−	1.01549i	−0.986614	−	0.163072i	$-0.947860\pi$
$977$	−14.4958	−	31.7413i	−0.463761	−	1.01549i	0.522853	−	0.852423i	$-0.324868\pi$
$978$		0			0
$979$	0.274476	+	1.90902i	0.00877229	+	0.0610126i
$980$		0			0
$981$	22.5400	−	14.5344i	0.719647	−	0.464047i
$982$		0			0
$983$	−8.34269	+	9.62798i	−0.266090	+	0.307085i	−0.873033	−	0.487661i	$-0.837850\pi$
$983$	−8.34269	+	9.62798i	−0.266090	+	0.307085i	0.606943	+	0.794746i	$0.292396\pi$
$984$		0			0
$985$	8.63984	−	7.48646i	0.275288	−	0.238539i
$986$		0			0
$987$	28.3083	+	51.7486i	0.901064	+	1.64718i
$988$		0			0
$989$	−3.29079	+	36.4127i	−0.104641	+	1.15786i
$990$		0			0
$991$	13.2852	−	29.0906i	0.422019	−	0.924093i	−0.572536	−	0.819880i	$-0.694040\pi$
$991$	13.2852	−	29.0906i	0.422019	−	0.924093i	0.994555	−	0.104213i	$-0.0332324\pi$
$992$		0			0
$993$	−37.6133	+	2.71909i	−1.19362	+	0.0862878i
$994$		0			0
$995$	−6.68854	−	5.79565i	−0.212041	−	0.183734i
$996$		0			0
$997$	−27.2963	+	8.01493i	−0.864484	+	0.253835i	−0.683767	−	0.729700i	$-0.739660\pi$
$997$	−27.2963	+	8.01493i	−0.864484	+	0.253835i	−0.180716	+	0.983535i	$0.557842\pi$
$998$		0			0
$999$	6.41719	+	1.38055i	0.203031	+	0.0436788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.k.a.17.7	yes	80
3.2	odd	2	inner	276.2.k.a.17.5	✓	80
23.19	odd	22	inner	276.2.k.a.65.5	yes	80
69.65	even	22	inner	276.2.k.a.65.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.k.a.17.5	✓	80	3.2	odd	2	inner
276.2.k.a.17.7	yes	80	1.1	even	1	trivial
276.2.k.a.65.5	yes	80	23.19	odd	22	inner
276.2.k.a.65.7	yes	80	69.65	even	22	inner

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38578 - 1.03904i) q^{3} +(-0.998768 + 0.641869i) q^{5} +(3.17327 + 0.456247i) q^{7} +(0.840791 - 2.87977i) q^{9} +O(q^{10})\)	\(q+(1.38578 - 1.03904i) q^{3} +(-0.998768 + 0.641869i) q^{5} +(3.17327 + 0.456247i) q^{7} +(0.840791 - 2.87977i) q^{9} +(0.407017 + 0.891242i) q^{11} +(-0.0854275 - 0.594161i) q^{13} +(-0.717148 + 1.92725i) q^{15} +(2.34297 - 2.70393i) q^{17} +(1.37294 - 1.18966i) q^{19} +(4.87152 - 2.66489i) q^{21} +(-4.70450 + 0.931481i) q^{23} +(-1.49153 + 3.26600i) q^{25} +(-1.82704 - 4.86435i) q^{27} +(-1.18589 - 1.02758i) q^{29} +(-6.25083 + 1.83541i) q^{31} +(1.49007 + 0.812162i) q^{33} +(-3.46221 + 1.58114i) q^{35} +(-0.682962 + 1.06271i) q^{37} +(-0.735741 - 0.734616i) q^{39} +(5.38229 + 8.37501i) q^{41} +(2.14779 - 7.31472i) q^{43} +(1.00868 + 3.41590i) q^{45} +10.6227i q^{47} +(3.14503 + 0.923464i) q^{49} +(0.437356 - 6.18151i) q^{51} +(-0.462019 + 3.21341i) q^{53} +(-0.978575 - 0.628892i) q^{55} +(0.666494 - 3.07515i) q^{57} +(-12.0862 + 1.73774i) q^{59} +(1.10580 + 3.76602i) q^{61} +(3.98194 - 8.75468i) q^{63} +(0.466696 + 0.538596i) q^{65} +(-8.09530 - 3.69700i) q^{67} +(-5.55158 + 6.17900i) q^{69} +(6.35593 + 2.90266i) q^{71} +(-3.39175 - 3.91429i) q^{73} +(1.32657 + 6.07574i) q^{75} +(0.884947 + 3.01385i) q^{77} +(-14.0661 + 2.02240i) q^{79} +(-7.58614 - 4.84257i) q^{81} +(-7.75693 - 4.98507i) q^{83} +(-0.604513 + 4.20448i) q^{85} +(-2.71107 - 0.191815i) q^{87} +(1.88871 + 0.554576i) q^{89} -1.92441i q^{91} +(-6.75523 + 9.03834i) q^{93} +(-0.607643 + 2.06944i) q^{95} +(1.22310 + 1.90318i) q^{97} +(2.90879 - 0.422765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + 6 * q^9	\( 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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