LMFDB - Embedded newform 3150.2.m.g.1457.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1457,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("3150.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.3
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	3150.1457
Dual form			3150.2.m.g.2843.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.585786i q^{11} +(-3.43916 + 3.43916i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-0.906908 + 0.906908i) q^{17} -2.04989i q^{19} +(0.414214 + 0.414214i) q^{22} +(0.257617 + 0.257617i) q^{23} +4.86370i q^{26} +(-0.707107 + 0.707107i) q^{28} -1.75272 q^{29} +1.47531 q^{31} +(-0.707107 + 0.707107i) q^{32} +1.28256i q^{34} +(4.04989 + 4.04989i) q^{37} +(-1.44949 - 1.44949i) q^{38} +3.84909i q^{41} +(-5.10306 + 5.10306i) q^{43} +0.585786 q^{44} +0.364326 q^{46} +(-5.49938 + 5.49938i) q^{47} +1.00000i q^{49} +(3.43916 + 3.43916i) q^{52} +(5.02494 + 5.02494i) q^{53} +1.00000i q^{56} +(-1.23936 + 1.23936i) q^{58} -11.1562 q^{59} +3.78851 q^{61} +(1.04320 - 1.04320i) q^{62} +1.00000i q^{64} +(6.74202 + 6.74202i) q^{67} +(0.906908 + 0.906908i) q^{68} +10.9282i q^{71} +(-5.97469 + 5.97469i) q^{73} +5.72741 q^{74} -2.04989 q^{76} +(0.414214 - 0.414214i) q^{77} -0.944060i q^{79} +(2.72172 + 2.72172i) q^{82} +(-7.82050 - 7.82050i) q^{83} +7.21682i q^{86} +(0.414214 - 0.414214i) q^{88} -0.0705524 q^{89} +4.86370 q^{91} +(0.257617 - 0.257617i) q^{92} +7.77729i q^{94} +(0.746663 + 0.746663i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 8 q^{13} - 8 q^{14} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 16 q^{37} + 8 q^{38} + 8 q^{43} + 16 q^{44} + 8 q^{46} - 8 q^{47} + 8 q^{52} + 32 q^{53} + 8 q^{58} - 8 q^{59} - 32 q^{61} + 32 q^{62} - 16 q^{67} - 16 q^{74} - 8 q^{77} + 8 q^{82} - 8 q^{83} - 8 q^{88} + 16 q^{89} + 8 q^{91} + 16 q^{92} - 16 q^{97}+O(q^{100}) $ 8 * q - 8 * q^13 - 8 * q^14 - 8 * q^16 - 8 * q^22 + 16 * q^23 + 16 * q^37 + 8 * q^38 + 8 * q^43 + 16 * q^44 + 8 * q^46 - 8 * q^47 + 8 * q^52 + 32 * q^53 + 8 * q^58 - 8 * q^59 - 32 * q^61 + 32 * q^62 - 16 * q^67 - 16 * q^74 - 8 * q^77 + 8 * q^82 - 8 * q^83 - 8 * q^88 + 16 * q^89 + 8 * q^91 + 16 * q^92 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$			0.585786i			0.176621i	0.996093	+	0.0883106i	$0.0281468\pi$
$11$			0.585786i			0.176621i	−0.996093	+	0.0883106i	$0.971853\pi$
$12$		0			0
$13$	−3.43916	+	3.43916i	−0.953851	+	0.953851i	−0.998981	−	0.0451304i	$-0.985630\pi$
$13$	−3.43916	+	3.43916i	−0.953851	+	0.953851i	0.0451304	+	0.998981i	$0.485630\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.906908	+	0.906908i	−0.219957	+	0.219957i	−0.808480	−	0.588523i	$-0.799710\pi$
$17$	−0.906908	+	0.906908i	−0.219957	+	0.219957i	0.588523	+	0.808480i	$0.299710\pi$
$18$		0			0
$19$		−	2.04989i		−	0.470277i	−0.971962	−	0.235138i	$-0.924446\pi$
$19$		−	2.04989i		−	0.470277i	0.971962	−	0.235138i	$-0.0755543\pi$
$20$		0			0
$21$		0			0
$22$	0.414214	+	0.414214i	0.0883106	+	0.0883106i
$23$	0.257617	+	0.257617i	0.0537169	+	0.0537169i	0.733455	−	0.679738i	$-0.237907\pi$
$23$	0.257617	+	0.257617i	0.0537169	+	0.0537169i	−0.679738	+	0.733455i	$0.737907\pi$
$24$		0			0
$25$		0			0
$26$			4.86370i			0.953851i
$27$		0			0
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	−1.75272			−0.325471			−0.162736	−	0.986670i	$-0.552032\pi$
$29$	−1.75272			−0.325471			−0.162736	+	0.986670i	$0.552032\pi$
$30$		0			0
$31$	1.47531			0.264974			0.132487	−	0.991185i	$-0.457704\pi$
$31$	1.47531			0.264974			0.132487	+	0.991185i	$0.457704\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			1.28256i			0.219957i
$35$		0			0
$36$		0			0
$37$	4.04989	+	4.04989i	0.665797	+	0.665797i	0.956740	−	0.290943i	$-0.0939690\pi$
$37$	4.04989	+	4.04989i	0.665797	+	0.665797i	−0.290943	+	0.956740i	$0.593969\pi$
$38$	−1.44949	−	1.44949i	−0.235138	−	0.235138i
$39$		0			0
$40$		0			0
$41$			3.84909i			0.601127i	0.953762	+	0.300564i	$0.0971747\pi$
$41$			3.84909i			0.601127i	−0.953762	+	0.300564i	$0.902825\pi$
$42$		0			0
$43$	−5.10306	+	5.10306i	−0.778209	+	0.778209i	−0.979526	−	0.201317i	$-0.935478\pi$
$43$	−5.10306	+	5.10306i	−0.778209	+	0.778209i	0.201317	+	0.979526i	$0.435478\pi$
$44$	0.585786			0.0883106
$45$		0			0
$46$	0.364326			0.0537169
$47$	−5.49938	+	5.49938i	−0.802167	+	0.802167i	−0.983434	−	0.181267i	$-0.941980\pi$
$47$	−5.49938	+	5.49938i	−0.802167	+	0.802167i	0.181267	+	0.983434i	$0.441980\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		0			0
$52$	3.43916	+	3.43916i	0.476925	+	0.476925i
$53$	5.02494	+	5.02494i	0.690229	+	0.690229i	0.962282	−	0.272053i	$-0.0877026\pi$
$53$	5.02494	+	5.02494i	0.690229	+	0.690229i	−0.272053	+	0.962282i	$0.587703\pi$
$54$		0			0
$55$		0			0
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−1.23936	+	1.23936i	−0.162736	+	0.162736i
$59$	−11.1562			−1.45242			−0.726209	−	0.687474i	$-0.758719\pi$
$59$	−11.1562			−1.45242			−0.726209	+	0.687474i	$0.758719\pi$
$60$		0			0
$61$	3.78851			0.485069			0.242534	−	0.970143i	$-0.422021\pi$
$61$	3.78851			0.485069			0.242534	+	0.970143i	$0.422021\pi$
$62$	1.04320	−	1.04320i	0.132487	−	0.132487i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	6.74202	+	6.74202i	0.823669	+	0.823669i	0.986632	−	0.162963i	$-0.0521053\pi$
$67$	6.74202	+	6.74202i	0.823669	+	0.823669i	−0.162963	+	0.986632i	$0.552105\pi$
$68$	0.906908	+	0.906908i	0.109979	+	0.109979i
$69$		0			0
$70$		0			0
$71$			10.9282i			1.29694i	0.761241	+	0.648470i	$0.224591\pi$
$71$			10.9282i			1.29694i	−0.761241	+	0.648470i	$0.775409\pi$
$72$		0			0
$73$	−5.97469	+	5.97469i	−0.699285	+	0.699285i	−0.964256	−	0.264971i	$-0.914637\pi$
$73$	−5.97469	+	5.97469i	−0.699285	+	0.699285i	0.264971	+	0.964256i	$0.414637\pi$
$74$	5.72741			0.665797
$75$		0			0
$76$	−2.04989			−0.235138
$77$	0.414214	−	0.414214i	0.0472040	−	0.0472040i
$78$		0			0
$79$		−	0.944060i		−	0.106215i	−0.998589	−	0.0531075i	$-0.983087\pi$
$79$		−	0.944060i		−	0.106215i	0.998589	−	0.0531075i	$-0.0169126\pi$
$80$		0			0
$81$		0			0
$82$	2.72172	+	2.72172i	0.300564	+	0.300564i
$83$	−7.82050	−	7.82050i	−0.858411	−	0.858411i	0.132740	−	0.991151i	$-0.457623\pi$
$83$	−7.82050	−	7.82050i	−0.858411	−	0.858411i	−0.991151	+	0.132740i	$0.957623\pi$
$84$		0			0
$85$		0			0
$86$			7.21682i			0.778209i
$87$		0			0
$88$	0.414214	−	0.414214i	0.0441553	−	0.0441553i
$89$	−0.0705524			−0.00747854			−0.00373927	−	0.999993i	$-0.501190\pi$
$89$	−0.0705524			−0.00747854			−0.00373927	+	0.999993i	$0.501190\pi$
$90$		0			0
$91$	4.86370			0.509855
$92$	0.257617	−	0.257617i	0.0268584	−	0.0268584i
$93$		0			0
$94$			7.77729i			0.802167i
$95$		0			0
$96$		0			0
$97$	0.746663	+	0.746663i	0.0758121	+	0.0758121i	0.743996	−	0.668184i	$-0.232928\pi$
$97$	0.746663	+	0.746663i	0.0758121	+	0.0758121i	−0.668184	+	0.743996i	$0.732928\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$		0			0
$101$			4.15696i			0.413633i	0.978380	+	0.206817i	$0.0663103\pi$
$101$			4.15696i			0.413633i	−0.978380	+	0.206817i	$0.933690\pi$
$102$		0			0
$103$	3.14198	−	3.14198i	0.309589	−	0.309589i	−0.535161	−	0.844750i	$-0.679749\pi$
$103$	3.14198	−	3.14198i	0.309589	−	0.309589i	0.844750	+	0.535161i	$0.179749\pi$
$104$	4.86370			0.476925
$105$		0			0
$106$	7.10634			0.690229
$107$	−6.84909	+	6.84909i	−0.662127	+	0.662127i	−0.955881	−	0.293754i	$-0.905095\pi$
$107$	−6.84909	+	6.84909i	−0.662127	+	0.662127i	0.293754	+	0.955881i	$0.405095\pi$
$108$		0			0
$109$		−	19.9335i		−	1.90929i	−0.297753	−	0.954643i	$-0.596237\pi$
$109$		−	19.9335i		−	1.90929i	0.297753	−	0.954643i	$-0.403763\pi$
$110$		0			0
$111$		0			0
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	4.69677	+	4.69677i	0.441835	+	0.441835i	0.892628	−	0.450793i	$-0.148859\pi$
$113$	4.69677	+	4.69677i	0.441835	+	0.441835i	−0.450793	+	0.892628i	$0.648859\pi$
$114$		0			0
$115$		0			0
$116$			1.75272i			0.162736i
$117$		0			0
$118$	−7.88865	+	7.88865i	−0.726209	+	0.726209i
$119$	1.28256			0.117572
$120$		0			0
$121$	10.6569			0.968805
$122$	2.67888	−	2.67888i	0.242534	−	0.242534i
$123$		0			0
$124$		−	1.47531i		−	0.132487i
$125$		0			0
$126$		0			0
$127$	−5.17814	−	5.17814i	−0.459486	−	0.459486i	0.439001	−	0.898487i	$-0.355332\pi$
$127$	−5.17814	−	5.17814i	−0.459486	−	0.459486i	−0.898487	+	0.439001i	$0.855332\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$			9.58630i			0.837559i	0.908088	+	0.418780i	$0.137542\pi$
$131$			9.58630i			0.837559i	−0.908088	+	0.418780i	$0.862458\pi$
$132$		0			0
$133$	−1.44949	+	1.44949i	−0.125687	+	0.125687i
$134$	9.53465			0.823669
$135$		0			0
$136$	1.28256			0.109979
$137$	−2.47015	+	2.47015i	−0.211040	+	0.211040i	−0.804709	−	0.593669i	$-0.797679\pi$
$137$	−2.47015	+	2.47015i	−0.211040	+	0.211040i	0.593669	+	0.804709i	$0.297679\pi$
$138$		0			0
$139$		−	8.33386i		−	0.706869i	−0.935459	−	0.353434i	$-0.885014\pi$
$139$		−	8.33386i		−	0.706869i	0.935459	−	0.353434i	$-0.114986\pi$
$140$		0			0
$141$		0			0
$142$	7.72741	+	7.72741i	0.648470	+	0.648470i
$143$	−2.01461	−	2.01461i	−0.168470	−	0.168470i
$144$		0			0
$145$		0			0
$146$			8.44949i			0.699285i
$147$		0			0
$148$	4.04989	−	4.04989i	0.332899	−	0.332899i
$149$	−13.5799			−1.11251			−0.556254	−	0.831012i	$-0.687762\pi$
$149$	−13.5799			−1.11251			−0.556254	+	0.831012i	$0.687762\pi$
$150$		0			0
$151$	13.1210			1.06777			0.533884	−	0.845558i	$-0.320732\pi$
$151$	13.1210			1.06777			0.533884	+	0.845558i	$0.320732\pi$
$152$	−1.44949	+	1.44949i	−0.117569	+	0.117569i
$153$		0			0
$154$		−	0.585786i		−	0.0472040i
$155$		0			0
$156$		0			0
$157$	16.9988	+	16.9988i	1.35665	+	1.35665i	0.878015	+	0.478634i	$0.158868\pi$
$157$	16.9988	+	16.9988i	1.35665	+	1.35665i	0.478634	+	0.878015i	$0.341132\pi$
$158$	−0.667551	−	0.667551i	−0.0531075	−	0.0531075i
$159$		0			0
$160$		0			0
$161$		−	0.364326i		−	0.0287129i
$162$		0			0
$163$	−0.0884482	+	0.0884482i	−0.00692780	+	0.00692780i	−0.710562	−	0.703634i	$-0.751559\pi$
$163$	−0.0884482	+	0.0884482i	−0.00692780	+	0.00692780i	0.703634	+	0.710562i	$0.251559\pi$
$164$	3.84909			0.300564
$165$		0			0
$166$	−11.0599			−0.858411
$167$	−9.31319	+	9.31319i	−0.720677	+	0.720677i	−0.968743	−	0.248066i	$-0.920205\pi$
$167$	−9.31319	+	9.31319i	−0.720677	+	0.720677i	0.248066	+	0.968743i	$0.420205\pi$
$168$		0			0
$169$		−	10.6556i		−	0.819662i
$170$		0			0
$171$		0			0
$172$	5.10306	+	5.10306i	0.389105	+	0.389105i
$173$	−5.81257	−	5.81257i	−0.441922	−	0.441922i	0.450736	−	0.892657i	$-0.351162\pi$
$173$	−5.81257	−	5.81257i	−0.441922	−	0.441922i	−0.892657	+	0.450736i	$0.851162\pi$
$174$		0			0
$175$		0			0
$176$		−	0.585786i		−	0.0441553i
$177$		0			0
$178$	−0.0498881	+	0.0498881i	−0.00373927	+	0.00373927i
$179$	9.20080			0.687700			0.343850	−	0.939025i	$-0.388269\pi$
$179$	9.20080			0.687700			0.343850	+	0.939025i	$0.388269\pi$
$180$		0			0
$181$	5.24316			0.389721			0.194860	−	0.980831i	$-0.437575\pi$
$181$	5.24316			0.389721			0.194860	+	0.980831i	$0.437575\pi$
$182$	3.43916	−	3.43916i	0.254927	−	0.254927i
$183$		0			0
$184$		−	0.364326i		−	0.0268584i
$185$		0			0
$186$		0			0
$187$	−0.531254	−	0.531254i	−0.0388492	−	0.0388492i
$188$	5.49938	+	5.49938i	0.401083	+	0.401083i
$189$		0			0
$190$		0			0
$191$		−	11.1869i		−	0.809453i	−0.914438	−	0.404727i	$-0.867367\pi$
$191$		−	11.1869i		−	0.809453i	0.914438	−	0.404727i	$-0.132633\pi$
$192$		0			0
$193$	−11.9136	+	11.9136i	−0.857559	+	0.857559i	−0.991050	−	0.133491i	$-0.957381\pi$
$193$	−11.9136	+	11.9136i	−0.857559	+	0.857559i	0.133491	+	0.991050i	$0.457381\pi$
$194$	1.05594			0.0758121
$195$		0			0
$196$	1.00000			0.0714286
$197$	−11.7811	+	11.7811i	−0.839366	+	0.839366i	−0.988775	−	0.149410i	$-0.952263\pi$
$197$	−11.7811	+	11.7811i	−0.839366	+	0.839366i	0.149410	+	0.988775i	$0.452263\pi$
$198$		0			0
$199$			2.11188i			0.149707i	0.997195	+	0.0748536i	$0.0238490\pi$
$199$			2.11188i			0.149707i	−0.997195	+	0.0748536i	$0.976151\pi$
$200$		0			0
$201$		0			0
$202$	2.93942	+	2.93942i	0.206817	+	0.206817i
$203$	1.23936	+	1.23936i	0.0869858	+	0.0869858i
$204$		0			0
$205$		0			0
$206$		−	4.44344i		−	0.309589i
$207$		0			0
$208$	3.43916	−	3.43916i	0.238463	−	0.238463i
$209$	1.20080			0.0830608
$210$		0			0
$211$	15.1968			1.04619			0.523097	−	0.852273i	$-0.324777\pi$
$211$	15.1968			1.04619			0.523097	+	0.852273i	$0.324777\pi$
$212$	5.02494	−	5.02494i	0.345115	−	0.345115i
$213$		0			0
$214$			9.68608i			0.662127i
$215$		0			0
$216$		0			0
$217$	−1.04320	−	1.04320i	−0.0708173	−	0.0708173i
$218$	−14.0951	−	14.0951i	−0.954643	−	0.954643i
$219$		0			0
$220$		0			0
$221$		−	6.23800i		−	0.419613i
$222$		0			0
$223$	−1.39391	+	1.39391i	−0.0933434	+	0.0933434i	−0.752237	−	0.658893i	$-0.771025\pi$
$223$	−1.39391	+	1.39391i	−0.0933434	+	0.0933434i	0.658893	+	0.752237i	$0.271025\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	6.64224			0.441835
$227$	−13.5638	+	13.5638i	−0.900258	+	0.900258i	−0.995458	−	0.0951997i	$-0.969651\pi$
$227$	−13.5638	+	13.5638i	−0.900258	+	0.900258i	0.0951997	+	0.995458i	$0.469651\pi$
$228$		0			0
$229$			10.4336i			0.689474i	0.938699	+	0.344737i	$0.112032\pi$
$229$			10.4336i			0.689474i	−0.938699	+	0.344737i	$0.887968\pi$
$230$		0			0
$231$		0			0
$232$	1.23936	+	1.23936i	0.0813678	+	0.0813678i
$233$	11.3730	+	11.3730i	0.745073	+	0.745073i	0.973549	−	0.228476i	$-0.0733743\pi$
$233$	11.3730	+	11.3730i	0.745073	+	0.745073i	−0.228476	+	0.973549i	$0.573374\pi$
$234$		0			0
$235$		0			0
$236$			11.1562i			0.726209i
$237$		0			0
$238$	0.906908	−	0.906908i	0.0587861	−	0.0587861i
$239$	0.485281			0.0313902			0.0156951	−	0.999877i	$-0.495004\pi$
$239$	0.485281			0.0313902			0.0156951	+	0.999877i	$0.495004\pi$
$240$		0			0
$241$	−12.8897			−0.830298			−0.415149	−	0.909753i	$-0.636271\pi$
$241$	−12.8897			−0.830298			−0.415149	+	0.909753i	$0.636271\pi$
$242$	7.53553	−	7.53553i	0.484402	−	0.484402i
$243$		0			0
$244$		−	3.78851i		−	0.242534i
$245$		0			0
$246$		0			0
$247$	7.04989	+	7.04989i	0.448574	+	0.448574i
$248$	−1.04320	−	1.04320i	−0.0662435	−	0.0662435i
$249$		0			0
$250$		0			0
$251$		−	17.3679i		−	1.09625i	−0.836396	−	0.548126i	$-0.815342\pi$
$251$		−	17.3679i		−	1.09625i	0.836396	−	0.548126i	$-0.184658\pi$
$252$		0			0
$253$	−0.150909	+	0.150909i	−0.00948754	+	0.00948754i
$254$	−7.32300			−0.459486
$255$		0			0
$256$	1.00000			0.0625000
$257$	−21.5212	+	21.5212i	−1.34245	+	1.34245i	−0.448846	+	0.893609i	$0.648165\pi$
$257$	−21.5212	+	21.5212i	−1.34245	+	1.34245i	−0.893609	+	0.448846i	$0.851835\pi$
$258$		0			0
$259$		−	5.72741i		−	0.355884i
$260$		0			0
$261$		0			0
$262$	6.77854	+	6.77854i	0.418780	+	0.418780i
$263$	−12.5708	−	12.5708i	−0.775149	−	0.775149i	0.203852	−	0.979002i	$-0.434654\pi$
$263$	−12.5708	−	12.5708i	−0.775149	−	0.775149i	−0.979002	+	0.203852i	$0.934654\pi$
$264$		0			0
$265$		0			0
$266$			2.04989i			0.125687i
$267$		0			0
$268$	6.74202	−	6.74202i	0.411834	−	0.411834i
$269$	−10.1197			−0.617010			−0.308505	−	0.951223i	$-0.599829\pi$
$269$	−10.1197			−0.617010			−0.308505	+	0.951223i	$0.599829\pi$
$270$		0			0
$271$	1.59310			0.0967740			0.0483870	−	0.998829i	$-0.484592\pi$
$271$	1.59310			0.0967740			0.0483870	+	0.998829i	$0.484592\pi$
$272$	0.906908	−	0.906908i	0.0549894	−	0.0549894i
$273$		0			0
$274$			3.49333i			0.211040i
$275$		0			0
$276$		0			0
$277$	−13.4354	−	13.4354i	−0.807255	−	0.807255i	0.176963	−	0.984218i	$-0.443373\pi$
$277$	−13.4354	−	13.4354i	−0.807255	−	0.807255i	−0.984218	+	0.176963i	$0.943373\pi$
$278$	−5.89293	−	5.89293i	−0.353434	−	0.353434i
$279$		0			0
$280$		0			0
$281$			22.1421i			1.32089i	0.750875	+	0.660445i	$0.229632\pi$
$281$			22.1421i			1.32089i	−0.750875	+	0.660445i	$0.770368\pi$
$282$		0			0
$283$	10.9959	−	10.9959i	0.653637	−	0.653637i	−0.300230	−	0.953867i	$-0.597063\pi$
$283$	10.9959	−	10.9959i	0.653637	−	0.653637i	0.953867	+	0.300230i	$0.0970635\pi$
$284$	10.9282			0.648470
$285$		0			0
$286$	−2.84909			−0.168470
$287$	2.72172	−	2.72172i	0.160658	−	0.160658i
$288$		0			0
$289$			15.3550i			0.903237i
$290$		0			0
$291$		0			0
$292$	5.97469	+	5.97469i	0.349642	+	0.349642i
$293$	−13.4135	−	13.4135i	−0.783624	−	0.783624i	0.196816	−	0.980440i	$-0.436940\pi$
$293$	−13.4135	−	13.4135i	−0.783624	−	0.783624i	−0.980440	+	0.196816i	$0.936940\pi$
$294$		0			0
$295$		0			0
$296$		−	5.72741i		−	0.332899i
$297$		0			0
$298$	−9.60244	+	9.60244i	−0.556254	+	0.556254i
$299$	−1.77197			−0.102476
$300$		0			0
$301$	7.21682			0.415970
$302$	9.27792	−	9.27792i	0.533884	−	0.533884i
$303$		0			0
$304$			2.04989i			0.117569i
$305$		0			0
$306$		0			0
$307$	−6.60091	−	6.60091i	−0.376734	−	0.376734i	0.493188	−	0.869922i	$-0.335831\pi$
$307$	−6.60091	−	6.60091i	−0.376734	−	0.376734i	−0.869922	+	0.493188i	$0.835831\pi$
$308$	−0.414214	−	0.414214i	−0.0236020	−	0.0236020i
$309$		0			0
$310$		0			0
$311$		−	33.0892i		−	1.87632i	−0.346204	−	0.938159i	$-0.612529\pi$
$311$		−	33.0892i		−	1.87632i	0.346204	−	0.938159i	$-0.387471\pi$
$312$		0			0
$313$	−0.803119	+	0.803119i	−0.0453949	+	0.0453949i	−0.729440	−	0.684045i	$-0.760219\pi$
$313$	−0.803119	+	0.803119i	−0.0453949	+	0.0453949i	0.684045	+	0.729440i	$0.260219\pi$
$314$	24.0399			1.35665
$315$		0			0
$316$	−0.944060			−0.0531075
$317$	0.832191	−	0.832191i	0.0467405	−	0.0467405i	−0.683350	−	0.730091i	$-0.739478\pi$
$317$	0.832191	−	0.832191i	0.0467405	−	0.0467405i	0.730091	+	0.683350i	$0.239478\pi$
$318$		0			0
$319$		−	1.02672i		−	0.0574851i
$320$		0			0
$321$		0			0
$322$	−0.257617	−	0.257617i	−0.0143564	−	0.0143564i
$323$	1.85906	+	1.85906i	0.103441	+	0.103441i
$324$		0			0
$325$		0			0
$326$			0.125085i			0.00692780i
$327$		0			0
$328$	2.72172	−	2.72172i	0.150282	−	0.150282i
$329$	7.77729			0.428776
$330$		0			0
$331$	18.5997			1.02233			0.511165	−	0.859483i	$-0.329214\pi$
$331$	18.5997			1.02233			0.511165	+	0.859483i	$0.329214\pi$
$332$	−7.82050	+	7.82050i	−0.429206	+	0.429206i
$333$		0			0
$334$			13.1708i			0.720677i
$335$		0			0
$336$		0			0
$337$	−15.0161	−	15.0161i	−0.817981	−	0.817981i	0.167834	−	0.985815i	$-0.446323\pi$
$337$	−15.0161	−	15.0161i	−0.817981	−	0.817981i	−0.985815	+	0.167834i	$0.946323\pi$
$338$	−7.53465	−	7.53465i	−0.409831	−	0.409831i
$339$		0			0
$340$		0			0
$341$			0.864219i			0.0468001i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	7.21682			0.389105
$345$		0			0
$346$	−8.22022			−0.441922
$347$	25.8218	−	25.8218i	1.38619	−	1.38619i	0.553018	−	0.833169i	$-0.313476\pi$
$347$	25.8218	−	25.8218i	1.38619	−	1.38619i	0.833169	−	0.553018i	$-0.186524\pi$
$348$		0			0
$349$		−	30.1584i		−	1.61434i	−0.590318	−	0.807171i	$-0.700998\pi$
$349$		−	30.1584i		−	1.61434i	0.590318	−	0.807171i	$-0.299002\pi$
$350$		0			0
$351$		0			0
$352$	−0.414214	−	0.414214i	−0.0220777	−	0.0220777i
$353$	8.78710	+	8.78710i	0.467690	+	0.467690i	0.901165	−	0.433475i	$-0.142713\pi$
$353$	8.78710	+	8.78710i	0.467690	+	0.467690i	−0.433475	+	0.901165i	$0.642713\pi$
$354$		0			0
$355$		0			0
$356$			0.0705524i			0.00373927i
$357$		0			0
$358$	6.50595	−	6.50595i	0.343850	−	0.343850i
$359$	7.67360			0.404997			0.202499	−	0.979283i	$-0.435094\pi$
$359$	7.67360			0.404997			0.202499	+	0.979283i	$0.435094\pi$
$360$		0			0
$361$	14.7980			0.778840
$362$	3.70747	−	3.70747i	0.194860	−	0.194860i
$363$		0			0
$364$		−	4.86370i		−	0.254927i
$365$		0			0
$366$		0			0
$367$	13.4146	+	13.4146i	0.700235	+	0.700235i	0.964461	−	0.264226i	$-0.0851164\pi$
$367$	13.4146	+	13.4146i	0.700235	+	0.700235i	−0.264226	+	0.964461i	$0.585116\pi$
$368$	−0.257617	−	0.257617i	−0.0134292	−	0.0134292i
$369$		0			0
$370$		0			0
$371$		−	7.10634i		−	0.368943i
$372$		0			0
$373$	−2.79796	+	2.79796i	−0.144873	+	0.144873i	−0.775823	−	0.630950i	$-0.782665\pi$
$373$	−2.79796	+	2.79796i	−0.144873	+	0.144873i	0.630950	+	0.775823i	$0.282665\pi$
$374$	−0.751307			−0.0388492
$375$		0			0
$376$	7.77729			0.401083
$377$	6.02786	−	6.02786i	0.310451	−	0.310451i
$378$		0			0
$379$		−	13.8539i		−	0.711627i	−0.934557	−	0.355814i	$-0.884204\pi$
$379$		−	13.8539i		−	0.711627i	0.934557	−	0.355814i	$-0.115796\pi$
$380$		0			0
$381$		0			0
$382$	−7.91031	−	7.91031i	−0.404727	−	0.404727i
$383$	−15.6710	−	15.6710i	−0.800748	−	0.800748i	0.182464	−	0.983212i	$-0.441593\pi$
$383$	−15.6710	−	15.6710i	−0.800748	−	0.800748i	−0.983212	+	0.182464i	$0.941593\pi$
$384$		0			0
$385$		0			0
$386$			16.8484i			0.857559i
$387$		0			0
$388$	0.746663	−	0.746663i	0.0379061	−	0.0379061i
$389$	−34.7194			−1.76034			−0.880171	−	0.474657i	$-0.842572\pi$
$389$	−34.7194			−1.76034			−0.880171	+	0.474657i	$0.842572\pi$
$390$		0			0
$391$	−0.467270			−0.0236308
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$			16.6609i			0.839366i
$395$		0			0
$396$		0			0
$397$	−18.9937	−	18.9937i	−0.953269	−	0.953269i	0.0456870	−	0.998956i	$-0.485452\pi$
$397$	−18.9937	−	18.9937i	−0.953269	−	0.953269i	−0.998956	+	0.0456870i	$0.985452\pi$
$398$	1.49333	+	1.49333i	0.0748536	+	0.0748536i
$399$		0			0
$400$		0			0
$401$		−	6.88008i		−	0.343575i	−0.985134	−	0.171787i	$-0.945046\pi$
$401$		−	6.88008i		−	0.343575i	0.985134	−	0.171787i	$-0.0549542\pi$
$402$		0			0
$403$	−5.07384	+	5.07384i	−0.252746	+	0.252746i
$404$	4.15696			0.206817
$405$		0			0
$406$	1.75272			0.0869858
$407$	−2.37237	+	2.37237i	−0.117594	+	0.117594i
$408$		0			0
$409$			26.2722i			1.29908i	0.760329	+	0.649538i	$0.225038\pi$
$409$			26.2722i			1.29908i	−0.760329	+	0.649538i	$0.774962\pi$
$410$		0			0
$411$		0			0
$412$	−3.14198	−	3.14198i	−0.154794	−	0.154794i
$413$	7.88865	+	7.88865i	0.388175	+	0.388175i
$414$		0			0
$415$		0			0
$416$		−	4.86370i		−	0.238463i
$417$		0			0
$418$	0.849091	−	0.849091i	0.0415304	−	0.0415304i
$419$	−2.85690			−0.139569			−0.0697844	−	0.997562i	$-0.522231\pi$
$419$	−2.85690			−0.139569			−0.0697844	+	0.997562i	$0.522231\pi$
$420$		0			0
$421$	−3.99446			−0.194678			−0.0973391	−	0.995251i	$-0.531033\pi$
$421$	−3.99446			−0.194678			−0.0973391	+	0.995251i	$0.531033\pi$
$422$	10.7458	−	10.7458i	0.523097	−	0.523097i
$423$		0			0
$424$		−	7.10634i		−	0.345115i
$425$		0			0
$426$		0			0
$427$	−2.67888	−	2.67888i	−0.129640	−	0.129640i
$428$	6.84909	+	6.84909i	0.331063	+	0.331063i
$429$		0			0
$430$		0			0
$431$		−	15.0871i		−	0.726719i	−0.931649	−	0.363360i	$-0.881630\pi$
$431$		−	15.0871i		−	0.726719i	0.931649	−	0.363360i	$-0.118370\pi$
$432$		0			0
$433$	12.0406	−	12.0406i	0.578634	−	0.578634i	−0.355893	−	0.934527i	$-0.615823\pi$
$433$	12.0406	−	12.0406i	0.578634	−	0.578634i	0.934527	+	0.355893i	$0.115823\pi$
$434$	−1.47531			−0.0708173
$435$		0			0
$436$	−19.9335			−0.954643
$437$	0.528086	−	0.528086i	0.0252618	−	0.0252618i
$438$		0			0
$439$			25.4660i			1.21543i	0.794156	+	0.607714i	$0.207913\pi$
$439$			25.4660i			1.21543i	−0.794156	+	0.607714i	$0.792087\pi$
$440$		0			0
$441$		0			0
$442$	−4.41093	−	4.41093i	−0.209807	−	0.209807i
$443$	0.326397	+	0.326397i	0.0155076	+	0.0155076i	0.714818	−	0.699310i	$-0.246509\pi$
$443$	0.326397	+	0.326397i	0.0155076	+	0.0155076i	−0.699310	+	0.714818i	$0.746509\pi$
$444$		0			0
$445$		0			0
$446$			1.97129i			0.0933434i
$447$		0			0
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	32.0990			1.51485			0.757424	−	0.652924i	$-0.226458\pi$
$449$	32.0990			1.51485			0.757424	+	0.652924i	$0.226458\pi$
$450$		0			0
$451$	−2.25475			−0.106172
$452$	4.69677	−	4.69677i	0.220918	−	0.220918i
$453$		0			0
$454$			19.1821i			0.900258i
$455$		0			0
$456$		0			0
$457$	2.63040	+	2.63040i	0.123045	+	0.123045i	0.765948	−	0.642903i	$-0.222270\pi$
$457$	2.63040	+	2.63040i	0.123045	+	0.123045i	−0.642903	+	0.765948i	$0.722270\pi$
$458$	7.37769	+	7.37769i	0.344737	+	0.344737i
$459$		0			0
$460$		0			0
$461$			20.8005i			0.968774i	0.874854	+	0.484387i	$0.160957\pi$
$461$			20.8005i			0.968774i	−0.874854	+	0.484387i	$0.839043\pi$
$462$		0			0
$463$	12.7214	−	12.7214i	0.591211	−	0.591211i	−0.346747	−	0.937959i	$-0.612714\pi$
$463$	12.7214	−	12.7214i	0.591211	−	0.591211i	0.937959	+	0.346747i	$0.112714\pi$
$464$	1.75272			0.0813678
$465$		0			0
$466$	16.0839			0.745073
$467$	−12.2128	+	12.2128i	−0.565141	+	0.565141i	−0.930763	−	0.365622i	$-0.880856\pi$
$467$	−12.2128	+	12.2128i	−0.565141	+	0.565141i	0.365622	+	0.930763i	$0.380856\pi$
$468$		0			0
$469$		−	9.53465i		−	0.440269i
$470$		0			0
$471$		0			0
$472$	7.88865	+	7.88865i	0.363104	+	0.363104i
$473$	−2.98930	−	2.98930i	−0.137448	−	0.137448i
$474$		0			0
$475$		0			0
$476$		−	1.28256i		−	0.0587861i
$477$		0			0
$478$	0.343146	−	0.343146i	0.0156951	−	0.0156951i
$479$	−32.5054			−1.48521			−0.742606	−	0.669729i	$-0.766410\pi$
$479$	−32.5054			−1.48521			−0.742606	+	0.669729i	$0.766410\pi$
$480$		0			0
$481$	−27.8564			−1.27014
$482$	−9.11439	+	9.11439i	−0.415149	+	0.415149i
$483$		0			0
$484$		−	10.6569i		−	0.484402i
$485$		0			0
$486$		0			0
$487$	−11.1806	−	11.1806i	−0.506644	−	0.506644i	0.406851	−	0.913495i	$-0.366627\pi$
$487$	−11.1806	−	11.1806i	−0.506644	−	0.506644i	−0.913495	+	0.406851i	$0.866627\pi$
$488$	−2.67888	−	2.67888i	−0.121267	−	0.121267i
$489$		0			0
$490$		0			0
$491$		−	29.6889i		−	1.33984i	−0.742433	−	0.669921i	$-0.766328\pi$
$491$		−	29.6889i		−	1.33984i	0.742433	−	0.669921i	$-0.233672\pi$
$492$		0			0
$493$	1.58955	−	1.58955i	0.0715898	−	0.0715898i
$494$	9.97005			0.448574
$495$		0			0
$496$	−1.47531			−0.0662435
$497$	7.72741	−	7.72741i	0.346622	−	0.346622i
$498$		0			0
$499$			38.1119i			1.70612i	0.521810	+	0.853061i	$0.325257\pi$
$499$			38.1119i			1.70612i	−0.521810	+	0.853061i	$0.674743\pi$
$500$		0			0
$501$		0			0
$502$	−12.2810	−	12.2810i	−0.548126	−	0.548126i
$503$	0.0267167	+	0.0267167i	0.00119124	+	0.00119124i	0.707702	−	0.706511i	$-0.249732\pi$
$503$	0.0267167	+	0.0267167i	0.00119124	+	0.00119124i	−0.706511	+	0.707702i	$0.749732\pi$
$504$		0			0
$505$		0			0
$506$			0.213417i			0.00948754i
$507$		0			0
$508$	−5.17814	+	5.17814i	−0.229743	+	0.229743i
$509$	−24.8899			−1.10323			−0.551613	−	0.834100i	$-0.685988\pi$
$509$	−24.8899			−1.10323			−0.551613	+	0.834100i	$0.685988\pi$
$510$		0			0
$511$	8.44949			0.373783
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			30.4356i			1.34245i
$515$		0			0
$516$		0			0
$517$	−3.22146	−	3.22146i	−0.141680	−	0.141680i
$518$	−4.04989	−	4.04989i	−0.177942	−	0.177942i
$519$		0			0
$520$		0			0
$521$		−	32.1495i		−	1.40849i	−0.709956	−	0.704247i	$-0.751285\pi$
$521$		−	32.1495i		−	1.40849i	0.709956	−	0.704247i	$-0.248715\pi$
$522$		0			0
$523$	10.3237	−	10.3237i	0.451423	−	0.451423i	−0.444404	−	0.895827i	$-0.646584\pi$
$523$	10.3237	−	10.3237i	0.451423	−	0.451423i	0.895827	+	0.444404i	$0.146584\pi$
$524$	9.58630			0.418780
$525$		0			0
$526$	−17.7778			−0.775149
$527$	−1.33797	+	1.33797i	−0.0582830	+	0.0582830i
$528$		0			0
$529$		−	22.8673i		−	0.994229i
$530$		0			0
$531$		0			0
$532$	1.44949	+	1.44949i	0.0628434	+	0.0628434i
$533$	−13.2376	−	13.2376i	−0.573385	−	0.573385i
$534$		0			0
$535$		0			0
$536$		−	9.53465i		−	0.411834i
$537$		0			0
$538$	−7.15572	+	7.15572i	−0.308505	+	0.308505i
$539$	−0.585786			−0.0252316
$540$		0			0
$541$	−25.3694			−1.09072			−0.545359	−	0.838203i	$-0.683607\pi$
$541$	−25.3694			−1.09072			−0.545359	+	0.838203i	$0.683607\pi$
$542$	1.12649	−	1.12649i	0.0483870	−	0.0483870i
$543$		0			0
$544$		−	1.28256i		−	0.0549894i
$545$		0			0
$546$		0			0
$547$	−28.9461	−	28.9461i	−1.23765	−	1.23765i	−0.960961	−	0.276685i	$-0.910764\pi$
$547$	−28.9461	−	28.9461i	−1.23765	−	1.23765i	−0.276685	−	0.960961i	$-0.589236\pi$
$548$	2.47015	+	2.47015i	0.105520	+	0.105520i
$549$		0			0
$550$		0			0
$551$			3.59287i			0.153061i
$552$		0			0
$553$	−0.667551	+	0.667551i	−0.0283872	+	0.0283872i
$554$	−19.0005			−0.807255
$555$		0			0
$556$	−8.33386			−0.353434
$557$	1.22073	−	1.22073i	0.0517241	−	0.0517241i	−0.680772	−	0.732496i	$-0.738355\pi$
$557$	1.22073	−	1.22073i	0.0517241	−	0.0517241i	0.732496	+	0.680772i	$0.238355\pi$
$558$		0			0
$559$		−	35.1005i		−	1.48459i
$560$		0			0
$561$		0			0
$562$	15.6569	+	15.6569i	0.660445	+	0.660445i
$563$	6.26999	+	6.26999i	0.264249	+	0.264249i	0.826778	−	0.562529i	$-0.190172\pi$
$563$	6.26999	+	6.26999i	0.264249	+	0.264249i	−0.562529	+	0.826778i	$0.690172\pi$
$564$		0			0
$565$		0			0
$566$		−	15.5505i		−	0.653637i
$567$		0			0
$568$	7.72741	−	7.72741i	0.324235	−	0.324235i
$569$	−23.1192			−0.969207			−0.484604	−	0.874734i	$-0.661036\pi$
$569$	−23.1192			−0.969207			−0.484604	+	0.874734i	$0.661036\pi$
$570$		0			0
$571$	1.94303			0.0813132			0.0406566	−	0.999173i	$-0.487055\pi$
$571$	1.94303			0.0813132			0.0406566	+	0.999173i	$0.487055\pi$
$572$	−2.01461	+	2.01461i	−0.0842352	+	0.0842352i
$573$		0			0
$574$		−	3.84909i		−	0.160658i
$575$		0			0
$576$		0			0
$577$	13.6576	+	13.6576i	0.568573	+	0.568573i	0.931728	−	0.363156i	$-0.118301\pi$
$577$	13.6576	+	13.6576i	0.568573	+	0.568573i	−0.363156	+	0.931728i	$0.618301\pi$
$578$	10.8577	+	10.8577i	0.451619	+	0.451619i
$579$		0			0
$580$		0			0
$581$			11.0599i			0.458840i
$582$		0			0
$583$	−2.94354	+	2.94354i	−0.121909	+	0.121909i
$584$	8.44949			0.349642
$585$		0			0
$586$	−18.9695			−0.783624
$587$	22.9322	−	22.9322i	0.946512	−	0.946512i	−0.0521286	−	0.998640i	$-0.516601\pi$
$587$	22.9322	−	22.9322i	0.946512	−	0.946512i	0.998640	+	0.0521286i	$0.0166006\pi$
$588$		0			0
$589$		−	3.02423i		−	0.124611i
$590$		0			0
$591$		0			0
$592$	−4.04989	−	4.04989i	−0.166449	−	0.166449i
$593$	31.8592	+	31.8592i	1.30830	+	1.30830i	0.922641	+	0.385661i	$0.126027\pi$
$593$	31.8592	+	31.8592i	1.30830	+	1.30830i	0.385661	+	0.922641i	$0.373973\pi$
$594$		0			0
$595$		0			0
$596$			13.5799i			0.556254i
$597$		0			0
$598$	−1.25297	+	1.25297i	−0.0512379	+	0.0512379i
$599$	22.1019			0.903060			0.451530	−	0.892256i	$-0.350878\pi$
$599$	22.1019			0.903060			0.451530	+	0.892256i	$0.350878\pi$
$600$		0			0
$601$	−35.8874			−1.46388			−0.731939	−	0.681371i	$-0.761384\pi$
$601$	−35.8874			−1.46388			−0.731939	+	0.681371i	$0.761384\pi$
$602$	5.10306	−	5.10306i	0.207985	−	0.207985i
$603$		0			0
$604$		−	13.1210i		−	0.533884i
$605$		0			0
$606$		0			0
$607$	−10.7675	−	10.7675i	−0.437039	−	0.437039i	0.453975	−	0.891014i	$-0.350005\pi$
$607$	−10.7675	−	10.7675i	−0.437039	−	0.437039i	−0.891014	+	0.453975i	$0.850005\pi$
$608$	1.44949	+	1.44949i	0.0587846	+	0.0587846i
$609$		0			0
$610$		0			0
$611$		−	37.8265i		−	1.53029i
$612$		0			0
$613$	5.86194	−	5.86194i	0.236762	−	0.236762i	−0.578746	−	0.815508i	$-0.696458\pi$
$613$	5.86194	−	5.86194i	0.236762	−	0.236762i	0.815508	+	0.578746i	$0.196458\pi$
$614$	−9.33510			−0.376734
$615$		0			0
$616$	−0.585786			−0.0236020
$617$	31.6118	−	31.6118i	1.27264	−	1.27264i	0.327945	−	0.944697i	$-0.393644\pi$
$617$	31.6118	−	31.6118i	1.27264	−	1.27264i	0.944697	−	0.327945i	$-0.106356\pi$
$618$		0			0
$619$			32.4856i			1.30571i	0.757484	+	0.652853i	$0.226428\pi$
$619$			32.4856i			1.30571i	−0.757484	+	0.652853i	$0.773572\pi$
$620$		0			0
$621$		0			0
$622$	−23.3976	−	23.3976i	−0.938159	−	0.938159i
$623$	0.0498881	+	0.0498881i	0.00199872	+	0.00199872i
$624$		0			0
$625$		0			0
$626$			1.13578i			0.0453949i
$627$		0			0
$628$	16.9988	−	16.9988i	0.678324	−	0.678324i
$629$	−7.34575			−0.292894
$630$		0			0
$631$	24.5826			0.978617			0.489308	−	0.872111i	$-0.337249\pi$
$631$	24.5826			0.978617			0.489308	+	0.872111i	$0.337249\pi$
$632$	−0.667551	+	0.667551i	−0.0265537	+	0.0265537i
$633$		0			0
$634$		−	1.17690i		−	0.0467405i
$635$		0			0
$636$		0			0
$637$	−3.43916	−	3.43916i	−0.136264	−	0.136264i
$638$	−0.725998	−	0.725998i	−0.0287426	−	0.0287426i
$639$		0			0
$640$		0			0
$641$			7.35255i			0.290408i	0.989402	+	0.145204i	$0.0463839\pi$
$641$			7.35255i			0.290408i	−0.989402	+	0.145204i	$0.953616\pi$
$642$		0			0
$643$	8.73081	−	8.73081i	0.344309	−	0.344309i	−0.513675	−	0.857985i	$-0.671716\pi$
$643$	8.73081	−	8.73081i	0.344309	−	0.344309i	0.857985	+	0.513675i	$0.171716\pi$
$644$	−0.364326			−0.0143564
$645$		0			0
$646$	2.62911			0.103441
$647$	−28.3694	+	28.3694i	−1.11532	+	1.11532i	−0.122898	+	0.992419i	$0.539219\pi$
$647$	−28.3694	+	28.3694i	−1.11532	+	1.11532i	−0.992419	+	0.122898i	$0.960781\pi$
$648$		0			0
$649$		−	6.53517i		−	0.256528i
$650$		0			0
$651$		0			0
$652$	0.0884482	+	0.0884482i	0.00346390	+	0.00346390i
$653$	27.4634	+	27.4634i	1.07472	+	1.07472i	0.996973	+	0.0777521i	$0.0247743\pi$
$653$	27.4634	+	27.4634i	1.07472	+	1.07472i	0.0777521	+	0.996973i	$0.475226\pi$
$654$		0			0
$655$		0			0
$656$		−	3.84909i		−	0.150282i
$657$		0			0
$658$	5.49938	−	5.49938i	0.214388	−	0.214388i
$659$	26.5619			1.03470			0.517352	−	0.855772i	$-0.326918\pi$
$659$	26.5619			1.03470			0.517352	+	0.855772i	$0.326918\pi$
$660$		0			0
$661$	−27.3725			−1.06467			−0.532333	−	0.846535i	$-0.678685\pi$
$661$	−27.3725			−1.06467			−0.532333	+	0.846535i	$0.678685\pi$
$662$	13.1520	−	13.1520i	0.511165	−	0.511165i
$663$		0			0
$664$			11.0599i			0.429206i
$665$		0			0
$666$		0			0
$667$	−0.451529	−	0.451529i	−0.0174833	−	0.0174833i
$668$	9.31319	+	9.31319i	0.360338	+	0.360338i
$669$		0			0
$670$		0			0
$671$			2.21926i			0.0856734i
$672$		0			0
$673$	−12.4095	+	12.4095i	−0.478349	+	0.478349i	−0.904603	−	0.426254i	$-0.859833\pi$
$673$	−12.4095	+	12.4095i	−0.478349	+	0.478349i	0.426254	+	0.904603i	$0.359833\pi$
$674$	−21.2360			−0.817981
$675$		0			0
$676$	−10.6556			−0.409831
$677$	−8.04384	+	8.04384i	−0.309150	+	0.309150i	−0.844580	−	0.535430i	$-0.820150\pi$
$677$	−8.04384	+	8.04384i	−0.309150	+	0.309150i	0.535430	+	0.844580i	$0.320150\pi$
$678$		0			0
$679$		−	1.05594i		−	0.0405233i
$680$		0			0
$681$		0			0
$682$	0.611095	+	0.611095i	0.0234000	+	0.0234000i
$683$	6.88312	+	6.88312i	0.263375	+	0.263375i	0.826424	−	0.563048i	$-0.190372\pi$
$683$	6.88312	+	6.88312i	0.263375	+	0.263375i	−0.563048	+	0.826424i	$0.690372\pi$
$684$		0			0
$685$		0			0
$686$		−	1.00000i		−	0.0381802i
$687$		0			0
$688$	5.10306	−	5.10306i	0.194552	−	0.194552i
$689$	−34.5631			−1.31675
$690$		0			0
$691$	−45.4327			−1.72834			−0.864171	−	0.503199i	$-0.832156\pi$
$691$	−45.4327			−1.72834			−0.864171	+	0.503199i	$0.832156\pi$
$692$	−5.81257	+	5.81257i	−0.220961	+	0.220961i
$693$		0			0
$694$		−	36.5176i		−	1.38619i
$695$		0			0
$696$		0			0
$697$	−3.49077	−	3.49077i	−0.132222	−	0.132222i
$698$	−21.3252	−	21.3252i	−0.807171	−	0.807171i
$699$		0			0
$700$		0			0
$701$			23.9123i			0.903155i	0.892232	+	0.451578i	$0.149139\pi$
$701$			23.9123i			0.903155i	−0.892232	+	0.451578i	$0.850861\pi$
$702$		0			0
$703$	8.30182	−	8.30182i	0.313109	−	0.313109i
$704$	−0.585786			−0.0220777
$705$		0			0
$706$	12.4268			0.467690
$707$	2.93942	−	2.93942i	0.110548	−	0.110548i
$708$		0			0
$709$		−	29.6939i		−	1.11518i	−0.830117	−	0.557589i	$-0.811727\pi$
$709$		−	29.6939i		−	1.11518i	0.830117	−	0.557589i	$-0.188273\pi$
$710$		0			0
$711$		0			0
$712$	0.0498881	+	0.0498881i	0.00186963	+	0.00186963i
$713$	0.380066	+	0.380066i	0.0142336	+	0.0142336i
$714$		0			0
$715$		0			0
$716$		−	9.20080i		−	0.343850i
$717$		0			0
$718$	5.42606	−	5.42606i	0.202499	−	0.202499i
$719$	44.7620			1.66934			0.834670	−	0.550751i	$-0.185659\pi$
$719$	44.7620			1.66934			0.834670	+	0.550751i	$0.185659\pi$
$720$		0			0
$721$	−4.44344			−0.165482
$722$	10.4637	−	10.4637i	0.389420	−	0.389420i
$723$		0			0
$724$		−	5.24316i		−	0.194860i
$725$		0			0
$726$		0			0
$727$	−30.1992	−	30.1992i	−1.12003	−	1.12003i	−0.991737	−	0.128289i	$-0.959051\pi$
$727$	−30.1992	−	30.1992i	−1.12003	−	1.12003i	−0.128289	−	0.991737i	$-0.540949\pi$
$728$	−3.43916	−	3.43916i	−0.127464	−	0.127464i
$729$		0			0
$730$		0			0
$731$		−	9.25601i		−	0.342346i
$732$		0			0
$733$	8.22450	−	8.22450i	0.303779	−	0.303779i	−0.538712	−	0.842490i	$-0.681089\pi$
$733$	8.22450	−	8.22450i	0.303779	−	0.303779i	0.842490	+	0.538712i	$0.181089\pi$
$734$	18.9711			0.700235
$735$		0			0
$736$	−0.364326			−0.0134292
$737$	−3.94938	+	3.94938i	−0.145477	+	0.145477i
$738$		0			0
$739$		−	27.6997i		−	1.01895i	−0.860486	−	0.509474i	$-0.829840\pi$
$739$		−	27.6997i		−	1.01895i	0.860486	−	0.509474i	$-0.170160\pi$
$740$		0			0
$741$		0			0
$742$	−5.02494	−	5.02494i	−0.184471	−	0.184471i
$743$	1.50830	+	1.50830i	0.0553342	+	0.0553342i	0.734232	−	0.678898i	$-0.237542\pi$
$743$	1.50830	+	1.50830i	0.0553342	+	0.0553342i	−0.678898	+	0.734232i	$0.737542\pi$
$744$		0			0
$745$		0			0
$746$			3.95691i			0.144873i
$747$		0			0
$748$	−0.531254	+	0.531254i	−0.0194246	+	0.0194246i
$749$	9.68608			0.353922
$750$		0			0
$751$	−34.5599			−1.26111			−0.630555	−	0.776145i	$-0.717172\pi$
$751$	−34.5599			−1.26111			−0.630555	+	0.776145i	$0.717172\pi$
$752$	5.49938	−	5.49938i	0.200542	−	0.200542i
$753$		0			0
$754$		−	8.52469i		−	0.310451i
$755$		0			0
$756$		0			0
$757$	−26.3636	−	26.3636i	−0.958201	−	0.958201i	0.0409596	−	0.999161i	$-0.486959\pi$
$757$	−26.3636	−	26.3636i	−0.958201	−	0.958201i	−0.999161	+	0.0409596i	$0.986959\pi$
$758$	−9.79619	−	9.79619i	−0.355814	−	0.355814i
$759$		0			0
$760$		0			0
$761$			40.6078i			1.47203i	0.676964	+	0.736016i	$0.263295\pi$
$761$			40.6078i			1.47203i	−0.676964	+	0.736016i	$0.736705\pi$
$762$		0			0
$763$	−14.0951	+	14.0951i	−0.510278	+	0.510278i
$764$	−11.1869			−0.404727
$765$		0			0
$766$	−22.1621			−0.800748
$767$	38.3680	−	38.3680i	1.38539	−	1.38539i
$768$		0			0
$769$			5.37968i			0.193996i	0.995285	+	0.0969982i	$0.0309241\pi$
$769$			5.37968i			0.193996i	−0.995285	+	0.0969982i	$0.969076\pi$
$770$		0			0
$771$		0			0
$772$	11.9136	+	11.9136i	0.428780	+	0.428780i
$773$	25.8174	+	25.8174i	0.928587	+	0.928587i	0.997615	−	0.0690281i	$-0.0219898\pi$
$773$	25.8174	+	25.8174i	0.928587	+	0.928587i	−0.0690281	+	0.997615i	$0.521990\pi$
$774$		0			0
$775$		0			0
$776$		−	1.05594i		−	0.0379061i
$777$		0			0
$778$	−24.5503	+	24.5503i	−0.880171	+	0.880171i
$779$	7.89021			0.282696
$780$		0			0
$781$	−6.40159			−0.229067
$782$	−0.330410	+	0.330410i	−0.0118154	+	0.0118154i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$		0			0
$787$	18.9421	+	18.9421i	0.675212	+	0.675212i	0.958913	−	0.283701i	$-0.0915623\pi$
$787$	18.9421	+	18.9421i	0.675212	+	0.675212i	−0.283701	+	0.958913i	$0.591562\pi$
$788$	11.7811	+	11.7811i	0.419683	+	0.419683i
$789$		0			0
$790$		0			0
$791$		−	6.64224i		−	0.236171i
$792$		0			0
$793$	−13.0293	+	13.0293i	−0.462683	+	0.462683i
$794$	−26.8612			−0.953269
$795$		0			0
$796$	2.11188			0.0748536
$797$	19.5851	−	19.5851i	0.693738	−	0.693738i	−0.269314	−	0.963052i	$-0.586797\pi$
$797$	19.5851	−	19.5851i	0.693738	−	0.693738i	0.963052	+	0.269314i	$0.0867970\pi$
$798$		0			0
$799$		−	9.97486i		−	0.352885i
$800$		0			0
$801$		0			0
$802$	−4.86495	−	4.86495i	−0.171787	−	0.171787i
$803$	−3.49989	−	3.49989i	−0.123509	−	0.123509i
$804$		0			0
$805$		0			0
$806$			7.17549i			0.252746i
$807$		0			0
$808$	2.93942	−	2.93942i	0.103408	−	0.103408i
$809$	20.2933			0.713473			0.356736	−	0.934205i	$-0.383889\pi$
$809$	20.2933			0.713473			0.356736	+	0.934205i	$0.383889\pi$
$810$		0			0
$811$	23.8254			0.836624			0.418312	−	0.908303i	$-0.362622\pi$
$811$	23.8254			0.836624			0.418312	+	0.908303i	$0.362622\pi$
$812$	1.23936	−	1.23936i	0.0434929	−	0.0434929i
$813$		0			0
$814$			3.35504i			0.117594i
$815$		0			0
$816$		0			0
$817$	10.4607	+	10.4607i	0.365974	+	0.365974i
$818$	18.5772	+	18.5772i	0.649538	+	0.649538i
$819$		0			0
$820$		0			0
$821$		−	24.2298i		−	0.845626i	−0.906217	−	0.422813i	$-0.861043\pi$
$821$		−	24.2298i		−	0.845626i	0.906217	−	0.422813i	$-0.138957\pi$
$822$		0			0
$823$	30.9552	−	30.9552i	1.07903	−	1.07903i	0.0824347	−	0.996596i	$-0.473730\pi$
$823$	30.9552	−	30.9552i	1.07903	−	1.07903i	0.996596	−	0.0824347i	$-0.0262696\pi$
$824$	−4.44344			−0.154794
$825$		0			0
$826$	11.1562			0.388175
$827$	−7.83272	+	7.83272i	−0.272370	+	0.272370i	−0.830054	−	0.557683i	$-0.811690\pi$
$827$	−7.83272	+	7.83272i	−0.272370	+	0.272370i	0.557683	+	0.830054i	$0.311690\pi$
$828$		0			0
$829$			53.9816i			1.87486i	0.348176	+	0.937429i	$0.386801\pi$
$829$			53.9816i			1.87486i	−0.348176	+	0.937429i	$0.613199\pi$
$830$		0			0
$831$		0			0
$832$	−3.43916	−	3.43916i	−0.119231	−	0.119231i
$833$	−0.906908	−	0.906908i	−0.0314225	−	0.0314225i
$834$		0			0
$835$		0			0
$836$		−	1.20080i		−	0.0415304i
$837$		0			0
$838$	−2.02014	+	2.02014i	−0.0697844	+	0.0697844i
$839$	−47.5236			−1.64070			−0.820348	−	0.571864i	$-0.806220\pi$
$839$	−47.5236			−1.64070			−0.820348	+	0.571864i	$0.806220\pi$
$840$		0			0
$841$	−25.9280			−0.894069
$842$	−2.82451	+	2.82451i	−0.0973391	+	0.0973391i
$843$		0			0
$844$		−	15.1968i		−	0.523097i
$845$		0			0
$846$		0			0
$847$	−7.53553	−	7.53553i	−0.258924	−	0.258924i
$848$	−5.02494	−	5.02494i	−0.172557	−	0.172557i
$849$		0			0
$850$		0			0
$851$			2.08664i			0.0715291i
$852$		0			0
$853$	−1.07711	+	1.07711i	−0.0368795	+	0.0368795i	−0.725306	−	0.688427i	$-0.758302\pi$
$853$	−1.07711	+	1.07711i	−0.0368795	+	0.0368795i	0.688427	+	0.725306i	$0.258302\pi$
$854$	−3.78851			−0.129640
$855$		0			0
$856$	9.68608			0.331063
$857$	21.5122	−	21.5122i	0.734844	−	0.734844i	−0.236731	−	0.971575i	$-0.576076\pi$
$857$	21.5122	−	21.5122i	0.734844	−	0.734844i	0.971575	+	0.236731i	$0.0760761\pi$
$858$		0			0
$859$			19.1691i			0.654041i	0.945017	+	0.327020i	$0.106045\pi$
$859$			19.1691i			0.654041i	−0.945017	+	0.327020i	$0.893955\pi$
$860$		0			0
$861$		0			0
$862$	−10.6682	−	10.6682i	−0.363360	−	0.363360i
$863$	33.4024	+	33.4024i	1.13703	+	1.13703i	0.988979	+	0.148053i	$0.0473005\pi$
$863$	33.4024	+	33.4024i	1.13703	+	1.13703i	0.148053	+	0.988979i	$0.452699\pi$
$864$		0			0
$865$		0			0
$866$		−	17.0280i		−	0.578634i
$867$		0			0
$868$	−1.04320	+	1.04320i	−0.0354087	+	0.0354087i
$869$	0.553017			0.0187598
$870$		0			0
$871$	−46.3737			−1.57131
$872$	−14.0951	+	14.0951i	−0.477321	+	0.477321i
$873$		0			0
$874$		−	0.746827i		−	0.0252618i
$875$		0			0
$876$		0			0
$877$	5.04257	+	5.04257i	0.170276	+	0.170276i	0.787100	−	0.616825i	$-0.211581\pi$
$877$	5.04257	+	5.04257i	0.170276	+	0.170276i	−0.616825	+	0.787100i	$0.711581\pi$
$878$	18.0072	+	18.0072i	0.607714	+	0.607714i
$879$		0			0
$880$		0			0
$881$			50.3415i			1.69605i	0.529958	+	0.848024i	$0.322208\pi$
$881$			50.3415i			1.69605i	−0.529958	+	0.848024i	$0.677792\pi$
$882$		0			0
$883$	5.32504	−	5.32504i	0.179202	−	0.179202i	−0.611806	−	0.791008i	$-0.709557\pi$
$883$	5.32504	−	5.32504i	0.179202	−	0.179202i	0.791008	+	0.611806i	$0.209557\pi$
$884$	−6.23800			−0.209807
$885$		0			0
$886$	0.461595			0.0155076
$887$	−15.1295	+	15.1295i	−0.507999	+	0.507999i	−0.913912	−	0.405913i	$-0.866954\pi$
$887$	−15.1295	+	15.1295i	−0.507999	+	0.507999i	0.405913	+	0.913912i	$0.366954\pi$
$888$		0			0
$889$			7.32300i			0.245605i
$890$		0			0
$891$		0			0
$892$	1.39391	+	1.39391i	0.0466717	+	0.0466717i
$893$	11.2731	+	11.2731i	0.377240	+	0.377240i
$894$		0			0
$895$		0			0
$896$		−	1.00000i		−	0.0334077i
$897$		0			0
$898$	22.6975	−	22.6975i	0.757424	−	0.757424i
$899$	−2.58580			−0.0862414
$900$		0			0
$901$	−9.11432			−0.303642
$902$	−1.59435	+	1.59435i	−0.0530859	+	0.0530859i
$903$		0			0
$904$		−	6.64224i		−	0.220918i
$905$		0			0
$906$		0			0
$907$	4.50318	+	4.50318i	0.149526	+	0.149526i	0.777906	−	0.628381i	$-0.216282\pi$
$907$	4.50318	+	4.50318i	0.149526	+	0.149526i	−0.628381	+	0.777906i	$0.716282\pi$
$908$	13.5638	+	13.5638i	0.450129	+	0.450129i
$909$		0			0
$910$		0			0
$911$		−	13.7520i		−	0.455624i	−0.973705	−	0.227812i	$-0.926843\pi$
$911$		−	13.7520i		−	0.455624i	0.973705	−	0.227812i	$-0.0731571\pi$
$912$		0			0
$913$	4.58114	−	4.58114i	0.151614	−	0.151614i
$914$	3.71995			0.123045
$915$		0			0
$916$	10.4336			0.344737
$917$	6.77854	−	6.77854i	0.223847	−	0.223847i
$918$		0			0
$919$			43.8245i			1.44564i	0.691039	+	0.722818i	$0.257153\pi$
$919$			43.8245i			1.44564i	−0.691039	+	0.722818i	$0.742847\pi$
$920$		0			0
$921$		0			0
$922$	14.7082	+	14.7082i	0.484387	+	0.484387i
$923$	−37.5838	−	37.5838i	−1.23709	−	1.23709i
$924$		0			0
$925$		0			0
$926$		−	17.9907i		−	0.591211i
$927$		0			0
$928$	1.23936	−	1.23936i	0.0406839	−	0.0406839i
$929$	−9.15215			−0.300272			−0.150136	−	0.988665i	$-0.547971\pi$
$929$	−9.15215			−0.300272			−0.150136	+	0.988665i	$0.547971\pi$
$930$		0			0
$931$	2.04989			0.0671824
$932$	11.3730	−	11.3730i	0.372537	−	0.372537i
$933$		0			0
$934$			17.2715i			0.565141i
$935$		0			0
$936$		0			0
$937$	9.96275	+	9.96275i	0.325469	+	0.325469i	0.850861	−	0.525392i	$-0.176081\pi$
$937$	9.96275	+	9.96275i	0.325469	+	0.325469i	−0.525392	+	0.850861i	$0.676081\pi$
$938$	−6.74202	−	6.74202i	−0.220135	−	0.220135i
$939$		0			0
$940$		0			0
$941$		−	19.9173i		−	0.649287i	−0.945836	−	0.324643i	$-0.894756\pi$
$941$		−	19.9173i		−	0.649287i	0.945836	−	0.324643i	$-0.105244\pi$
$942$		0			0
$943$	−0.991592	+	0.991592i	−0.0322907	+	0.0322907i
$944$	11.1562			0.363104
$945$		0			0
$946$	−4.22751			−0.137448
$947$	−9.40403	+	9.40403i	−0.305590	+	0.305590i	−0.843196	−	0.537606i	$-0.819329\pi$
$947$	−9.40403	+	9.40403i	−0.305590	+	0.305590i	0.537606	+	0.843196i	$0.319329\pi$
$948$		0			0
$949$		−	41.0958i		−	1.33403i
$950$		0			0
$951$		0			0
$952$	−0.906908	−	0.906908i	−0.0293930	−	0.0293930i
$953$	13.5760	+	13.5760i	0.439769	+	0.439769i	0.891934	−	0.452165i	$-0.149348\pi$
$953$	13.5760	+	13.5760i	0.439769	+	0.439769i	−0.452165	+	0.891934i	$0.649348\pi$
$954$		0			0
$955$		0			0
$956$		−	0.485281i		−	0.0156951i
$957$		0			0
$958$	−22.9848	+	22.9848i	−0.742606	+	0.742606i
$959$	3.49333			0.112805
$960$		0			0
$961$	−28.8234			−0.929789
$962$	−19.6975	+	19.6975i	−0.635071	+	0.635071i
$963$		0			0
$964$			12.8897i			0.415149i
$965$		0			0
$966$		0			0
$967$	−14.4331	−	14.4331i	−0.464138	−	0.464138i	0.435871	−	0.900009i	$-0.356440\pi$
$967$	−14.4331	−	14.4331i	−0.464138	−	0.464138i	−0.900009	+	0.435871i	$0.856440\pi$
$968$	−7.53553	−	7.53553i	−0.242201	−	0.242201i
$969$		0			0
$970$		0			0
$971$		−	16.9403i		−	0.543640i	−0.962348	−	0.271820i	$-0.912374\pi$
$971$		−	16.9403i		−	0.543640i	0.962348	−	0.271820i	$-0.0876256\pi$
$972$		0			0
$973$	−5.89293	+	5.89293i	−0.188919	+	0.188919i
$974$	−15.8118			−0.506644
$975$		0			0
$976$	−3.78851			−0.121267
$977$	19.9652	−	19.9652i	0.638745	−	0.638745i	−0.311501	−	0.950246i	$-0.600832\pi$
$977$	19.9652	−	19.9652i	0.638745	−	0.638745i	0.950246	+	0.311501i	$0.100832\pi$
$978$		0			0
$979$		−	0.0413286i		−	0.00132087i
$980$		0			0
$981$		0			0
$982$	−20.9932	−	20.9932i	−0.669921	−	0.669921i
$983$	−40.4112	−	40.4112i	−1.28892	−	1.28892i	−0.935445	−	0.353472i	$-0.885001\pi$
$983$	−40.4112	−	40.4112i	−1.28892	−	1.28892i	−0.353472	−	0.935445i	$-0.614999\pi$
$984$		0			0
$985$		0			0
$986$		−	2.24796i		−	0.0715898i
$987$		0			0
$988$	7.04989	−	7.04989i	0.224287	−	0.224287i
$989$	−2.62927			−0.0836059
$990$		0			0
$991$	16.6002			0.527323			0.263662	−	0.964615i	$-0.415070\pi$
$991$	16.6002			0.527323			0.263662	+	0.964615i	$0.415070\pi$
$992$	−1.04320	+	1.04320i	−0.0331218	+	0.0331218i
$993$		0			0
$994$		−	10.9282i		−	0.346622i
$995$		0			0
$996$		0			0
$997$	38.6264	+	38.6264i	1.22331	+	1.22331i	0.966448	+	0.256862i	$0.0826885\pi$
$997$	38.6264	+	38.6264i	1.22331	+	1.22331i	0.256862	+	0.966448i	$0.417311\pi$
$998$	26.9492	+	26.9492i	0.853061	+	0.853061i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.m.g.1457.3	✓	8
3.2	odd	2		3150.2.m.h.1457.1	yes	8
5.2	odd	4		3150.2.m.l.2843.4	yes	8
5.3	odd	4		3150.2.m.h.2843.1	yes	8
5.4	even	2		3150.2.m.k.1457.2	yes	8
15.2	even	4		3150.2.m.k.2843.2	yes	8
15.8	even	4	inner	3150.2.m.g.2843.3	yes	8
15.14	odd	2		3150.2.m.l.1457.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.m.g.1457.3	✓	8	1.1	even	1	trivial
3150.2.m.g.2843.3	yes	8	15.8	even	4	inner
3150.2.m.h.1457.1	yes	8	3.2	odd	2
3150.2.m.h.2843.1	yes	8	5.3	odd	4
3150.2.m.k.1457.2	yes	8	5.4	even	2
3150.2.m.k.2843.2	yes	8	15.2	even	4
3150.2.m.l.1457.4	yes	8	15.14	odd	2
3150.2.m.l.2843.4	yes	8	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.585786i q^{11} +(-3.43916 + 3.43916i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-0.906908 + 0.906908i) q^{17} -2.04989i q^{19} +(0.414214 + 0.414214i) q^{22} +(0.257617 + 0.257617i) q^{23} +4.86370i q^{26} +(-0.707107 + 0.707107i) q^{28} -1.75272 q^{29} +1.47531 q^{31} +(-0.707107 + 0.707107i) q^{32} +1.28256i q^{34} +(4.04989 + 4.04989i) q^{37} +(-1.44949 - 1.44949i) q^{38} +3.84909i q^{41} +(-5.10306 + 5.10306i) q^{43} +0.585786 q^{44} +0.364326 q^{46} +(-5.49938 + 5.49938i) q^{47} +1.00000i q^{49} +(3.43916 + 3.43916i) q^{52} +(5.02494 + 5.02494i) q^{53} +1.00000i q^{56} +(-1.23936 + 1.23936i) q^{58} -11.1562 q^{59} +3.78851 q^{61} +(1.04320 - 1.04320i) q^{62} +1.00000i q^{64} +(6.74202 + 6.74202i) q^{67} +(0.906908 + 0.906908i) q^{68} +10.9282i q^{71} +(-5.97469 + 5.97469i) q^{73} +5.72741 q^{74} -2.04989 q^{76} +(0.414214 - 0.414214i) q^{77} -0.944060i q^{79} +(2.72172 + 2.72172i) q^{82} +(-7.82050 - 7.82050i) q^{83} +7.21682i q^{86} +(0.414214 - 0.414214i) q^{88} -0.0705524 q^{89} +4.86370 q^{91} +(0.257617 - 0.257617i) q^{92} +7.77729i q^{94} +(0.746663 + 0.746663i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 8 q^{13} - 8 q^{14} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 16 q^{37} + 8 q^{38} + 8 q^{43} + 16 q^{44} + 8 q^{46} - 8 q^{47} + 8 q^{52} + 32 q^{53} + 8 q^{58} - 8 q^{59} - 32 q^{61} + 32 q^{62} - 16 q^{67} - 16 q^{74} - 8 q^{77} + 8 q^{82} - 8 q^{83} - 8 q^{88} + 16 q^{89} + 8 q^{91} + 16 q^{92} - 16 q^{97}+O(q^{100}) \) 8 * q - 8 * q^13 - 8 * q^14 - 8 * q^16 - 8 * q^22 + 16 * q^23 + 16 * q^37 + 8 * q^38 + 8 * q^43 + 16 * q^44 + 8 * q^46 - 8 * q^47 + 8 * q^52 + 32 * q^53 + 8 * q^58 - 8 * q^59 - 32 * q^61 + 32 * q^62 - 16 * q^67 - 16 * q^74 - 8 * q^77 + 8 * q^82 - 8 * q^83 - 8 * q^88 + 16 * q^89 + 8 * q^91 + 16 * q^92 - 16 * q^97

Introduction

L-functions

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