LMFDB - Embedded newform 1805.2.b.f.1084.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1084,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.b (of order $2$, degree $1$, 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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.4227136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 6x^{4} + 7x^{2} + 1 $ x^6 + 6x^4 + 7x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.3
Root			$-2.11917i$ of defining polynomial
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.f.1084.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.471884i q^{2} -1.04022i q^{3} +1.77733 q^{4} +(0.713538 - 2.11917i) q^{5} -0.490864 q^{6} +1.17540i q^{7} -1.78246i q^{8} +1.91794 q^{9} +O(q^{10})$	\(q-0.471884i q^{2} -1.04022i q^{3} +1.77733 q^{4} +(0.713538 - 2.11917i) q^{5} -0.490864 q^{6} +1.17540i q^{7} -1.78246i q^{8} +1.91794 q^{9} +(-1.00000 - 0.336707i) q^{10} +0.713538 q^{11} -1.84881i q^{12} -4.10315i q^{13} +0.554651 q^{14} +(-2.20440 - 0.742237i) q^{15} +2.71354 q^{16} +2.55233i q^{17} -0.905045i q^{18} +(1.26819 - 3.76645i) q^{20} +1.22267 q^{21} -0.336707i q^{22} +0.607061i q^{23} -1.85415 q^{24} +(-3.98173 - 3.02421i) q^{25} -1.93621 q^{26} -5.11575i q^{27} +2.08907i q^{28} +0.859386 q^{29} +(-0.350250 + 1.04022i) q^{30} +2.50914 q^{31} -4.84539i q^{32} -0.742237i q^{33} +1.20440 q^{34} +(2.49086 + 0.838691i) q^{35} +3.40880 q^{36} +9.38171i q^{37} -4.26819 q^{39} +(-3.77733 - 1.27185i) q^{40} -4.12234 q^{41} -0.576960i q^{42} -10.1239i q^{43} +1.26819 q^{44} +(1.36852 - 4.06443i) q^{45} +0.286462 q^{46} +10.5184i q^{47} -2.82268i q^{48} +5.61844 q^{49} +(-1.42708 + 1.87891i) q^{50} +2.65498 q^{51} -7.29264i q^{52} -4.98057i q^{53} -2.41404 q^{54} +(0.509136 - 1.51211i) q^{55} +2.09510 q^{56} -0.405530i q^{58} +6.24992 q^{59} +(-3.91794 - 1.31920i) q^{60} -4.55465 q^{61} -1.18402i q^{62} +2.25434i q^{63} +3.14061 q^{64} +(-8.69527 - 2.92776i) q^{65} -0.350250 q^{66} -5.18210i q^{67} +4.53632i q^{68} +0.631477 q^{69} +(0.395765 - 1.17540i) q^{70} -13.1679 q^{71} -3.41865i q^{72} +12.3783i q^{73} +4.42708 q^{74} +(-3.14585 + 4.14188i) q^{75} +0.838691i q^{77} +2.01409i q^{78} +5.96345 q^{79} +(1.93621 - 5.75044i) q^{80} +0.432310 q^{81} +1.94527i q^{82} -13.8603i q^{83} +2.17309 q^{84} +(5.40880 + 1.82118i) q^{85} -4.77733 q^{86} -0.893952i q^{87} -1.27185i q^{88} -15.9635 q^{89} +(-1.91794 - 0.645784i) q^{90} +4.82284 q^{91} +1.07894i q^{92} -2.61006i q^{93} +4.96345 q^{94} -5.04028 q^{96} +16.7020i q^{97} -2.65125i q^{98} +1.36852 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} + 2 q^{5} + 12 q^{6} - 8 q^{9}+O(q^{10}) $ 6 * q - 2 * q^4 + 2 * q^5 + 12 * q^6 - 8 * q^9	$ 6 q - 2 q^{4} + 2 q^{5} + 12 q^{6} - 8 q^{9} - 6 q^{10} + 2 q^{11} - 22 q^{14} + 4 q^{15} + 14 q^{16} - 20 q^{20} + 20 q^{21} - 2 q^{24} + 6 q^{25} - 22 q^{26} + 12 q^{29} + 6 q^{30} + 30 q^{31} - 10 q^{34} - 14 q^{36} + 2 q^{39} - 10 q^{40} + 12 q^{41} - 20 q^{44} + 30 q^{45} + 4 q^{46} - 2 q^{49} - 4 q^{50} + 40 q^{51} + 4 q^{54} + 18 q^{55} + 46 q^{56} - 20 q^{59} - 4 q^{60} - 2 q^{61} + 12 q^{64} - 20 q^{65} + 6 q^{66} - 18 q^{69} - 46 q^{70} - 2 q^{71} + 22 q^{74} - 28 q^{75} - 24 q^{79} + 22 q^{80} + 14 q^{81} - 48 q^{84} - 2 q^{85} - 16 q^{86} - 36 q^{89} + 8 q^{90} - 24 q^{91} - 30 q^{94} + 26 q^{96} + 30 q^{99}+O(q^{100}) $ 6 * q - 2 * q^4 + 2 * q^5 + 12 * q^6 - 8 * q^9 - 6 * q^10 + 2 * q^11 - 22 * q^14 + 4 * q^15 + 14 * q^16 - 20 * q^20 + 20 * q^21 - 2 * q^24 + 6 * q^25 - 22 * q^26 + 12 * q^29 + 6 * q^30 + 30 * q^31 - 10 * q^34 - 14 * q^36 + 2 * q^39 - 10 * q^40 + 12 * q^41 - 20 * q^44 + 30 * q^45 + 4 * q^46 - 2 * q^49 - 4 * q^50 + 40 * q^51 + 4 * q^54 + 18 * q^55 + 46 * q^56 - 20 * q^59 - 4 * q^60 - 2 * q^61 + 12 * q^64 - 20 * q^65 + 6 * q^66 - 18 * q^69 - 46 * q^70 - 2 * q^71 + 22 * q^74 - 28 * q^75 - 24 * q^79 + 22 * q^80 + 14 * q^81 - 48 * q^84 - 2 * q^85 - 16 * q^86 - 36 * q^89 + 8 * q^90 - 24 * q^91 - 30 * q^94 + 26 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	0.471884i		−	0.333672i	−0.985985	−	0.166836i	$-0.946645\pi$
$2$		−	0.471884i		−	0.333672i	0.985985	−	0.166836i	$-0.0533551\pi$
$3$		−	1.04022i		−	0.600572i	−0.953849	−	0.300286i	$-0.902918\pi$
$3$		−	1.04022i		−	0.600572i	0.953849	−	0.300286i	$-0.0970821\pi$
$4$	1.77733			0.888663
$5$	0.713538	−	2.11917i	0.319104	−	0.947720i
$5$	0.713538	−	2.11917i	0.319104	−	0.947720i
$6$	−0.490864			−0.200394
$7$			1.17540i			0.444259i	0.975017	+	0.222129i	$0.0713007\pi$
$7$			1.17540i			0.444259i	−0.975017	+	0.222129i	$0.928699\pi$
$8$		−	1.78246i		−	0.630194i
$9$	1.91794			0.639313
$10$	−1.00000	−	0.336707i	−0.316228	−	0.106476i
$11$	0.713538			0.215140			0.107570	−	0.994198i	$-0.465693\pi$
$11$	0.713538			0.215140			0.107570	+	0.994198i	$0.465693\pi$
$12$		−	1.84881i		−	0.533706i
$13$		−	4.10315i		−	1.13801i	−0.822334	−	0.569005i	$-0.807328\pi$
$13$		−	4.10315i		−	1.13801i	0.822334	−	0.569005i	$-0.192672\pi$
$14$	0.554651			0.148237
$15$	−2.20440	−	0.742237i	−0.569174	−	0.191645i
$16$	2.71354			0.678384
$17$			2.55233i			0.619030i	0.950895	+	0.309515i	$0.100167\pi$
$17$			2.55233i			0.619030i	−0.950895	+	0.309515i	$0.899833\pi$
$18$		−	0.905045i		−	0.213321i
$19$		0			0
$19$		0			0
$20$	1.26819	−	3.76645i	0.283576	−	0.842203i
$21$	1.22267			0.266809
$22$		−	0.336707i		−	0.0717862i
$23$			0.607061i			0.126581i	0.997995	+	0.0632904i	$0.0201594\pi$
$23$			0.607061i			0.126581i	−0.997995	+	0.0632904i	$0.979841\pi$
$24$	−1.85415			−0.378477
$25$	−3.98173	−	3.02421i	−0.796345	−	0.604842i
$26$	−1.93621			−0.379722
$27$		−	5.11575i		−	0.984526i
$28$			2.08907i			0.394796i
$29$	0.859386			0.159584			0.0797920	−	0.996812i	$-0.474574\pi$
$29$	0.859386			0.159584			0.0797920	+	0.996812i	$0.474574\pi$
$30$	−0.350250	+	1.04022i	−0.0639466	+	0.189918i
$31$	2.50914			0.450654			0.225327	−	0.974283i	$-0.427655\pi$
$31$	2.50914			0.450654			0.225327	+	0.974283i	$0.427655\pi$
$32$		−	4.84539i		−	0.856552i
$33$		−	0.742237i		−	0.129207i
$34$	1.20440			0.206553
$35$	2.49086	+	0.838691i	0.421033	+	0.141765i
$36$	3.40880			0.568134
$37$			9.38171i			1.54234i	0.636627	+	0.771172i	$0.280329\pi$
$37$			9.38171i			1.54234i	−0.636627	+	0.771172i	$0.719671\pi$
$38$		0			0
$39$	−4.26819			−0.683457
$40$	−3.77733	−	1.27185i	−0.597248	−	0.201097i
$41$	−4.12234			−0.643802			−0.321901	−	0.946773i	$-0.604322\pi$
$41$	−4.12234			−0.643802			−0.321901	+	0.946773i	$0.604322\pi$
$42$		−	0.576960i		−	0.0890269i
$43$		−	10.1239i		−	1.54389i	−0.635691	−	0.771944i	$-0.719285\pi$
$43$		−	10.1239i		−	1.54389i	0.635691	−	0.771944i	$-0.280715\pi$
$44$	1.26819			0.191187
$45$	1.36852	−	4.06443i	0.204007	−	0.605890i
$46$	0.286462			0.0422365
$47$			10.5184i			1.53426i	0.641489	+	0.767132i	$0.278317\pi$
$47$			10.5184i			1.53426i	−0.641489	+	0.767132i	$0.721683\pi$
$48$		−	2.82268i		−	0.407419i
$49$	5.61844			0.802634
$50$	−1.42708	+	1.87891i	−0.201819	+	0.265718i
$51$	2.65498			0.371772
$52$		−	7.29264i		−	1.01131i
$53$		−	4.98057i		−	0.684134i	−0.939676	−	0.342067i	$-0.888873\pi$
$53$		−	4.98057i		−	0.684134i	0.939676	−	0.342067i	$-0.111127\pi$
$54$	−2.41404			−0.328509
$55$	0.509136	−	1.51211i	0.0686519	−	0.203892i
$56$	2.09510			0.279969
$57$		0			0
$58$		−	0.405530i		−	0.0532488i
$59$	6.24992			0.813670			0.406835	−	0.913502i	$-0.366632\pi$
$59$	6.24992			0.813670			0.406835	+	0.913502i	$0.366632\pi$
$60$	−3.91794	−	1.31920i	−0.505804	−	0.170308i
$61$	−4.55465			−0.583163			−0.291582	−	0.956546i	$-0.594182\pi$
$61$	−4.55465			−0.583163			−0.291582	+	0.956546i	$0.594182\pi$
$62$		−	1.18402i		−	0.150371i
$63$			2.25434i			0.284020i
$64$	3.14061			0.392577
$65$	−8.69527	−	2.92776i	−1.07851	−	0.363144i
$66$	−0.350250			−0.0431128
$67$		−	5.18210i		−	0.633094i	−0.948577	−	0.316547i	$-0.897476\pi$
$67$		−	5.18210i		−	0.633094i	0.948577	−	0.316547i	$-0.102524\pi$
$68$			4.53632i			0.550109i
$69$	0.631477			0.0760209
$70$	0.395765	−	1.17540i	0.0473029	−	0.140487i
$71$	−13.1679			−1.56274			−0.781368	−	0.624070i	$-0.785478\pi$
$71$	−13.1679			−1.56274			−0.781368	+	0.624070i	$0.785478\pi$
$72$		−	3.41865i		−	0.402892i
$73$			12.3783i			1.44877i	0.689396	+	0.724384i	$0.257876\pi$
$73$			12.3783i			1.44877i	−0.689396	+	0.724384i	$0.742124\pi$
$74$	4.42708			0.514637
$75$	−3.14585	+	4.14188i	−0.363251	+	0.478263i
$76$		0			0
$77$			0.838691i			0.0955777i
$78$			2.01409i			0.228051i
$79$	5.96345			0.670941			0.335471	−	0.942051i	$-0.391105\pi$
$79$	5.96345			0.670941			0.335471	+	0.942051i	$0.391105\pi$
$80$	1.93621	−	5.75044i	0.216475	−	0.642918i
$81$	0.432310			0.0480345
$82$			1.94527i			0.214819i
$83$		−	13.8603i		−	1.52136i	−0.649124	−	0.760682i	$-0.724864\pi$
$83$		−	13.8603i		−	1.52136i	0.649124	−	0.760682i	$-0.275136\pi$
$84$	2.17309			0.237104
$85$	5.40880	+	1.82118i	0.586667	+	0.197535i
$86$	−4.77733			−0.515152
$87$		−	0.893952i		−	0.0958417i
$88$		−	1.27185i		−	0.135580i
$89$	−15.9635			−1.69212			−0.846061	−	0.533085i	$-0.821032\pi$
$89$	−15.9635			−1.69212			−0.846061	+	0.533085i	$0.821032\pi$
$90$	−1.91794	−	0.645784i	−0.202169	−	0.0680716i
$91$	4.82284			0.505571
$92$			1.07894i			0.112488i
$93$		−	2.61006i		−	0.270650i
$94$	4.96345			0.511941
$95$		0			0
$96$	−5.04028			−0.514421
$97$			16.7020i			1.69583i	0.530133	+	0.847915i	$0.322142\pi$
$97$			16.7020i			1.69583i	−0.530133	+	0.847915i	$0.677858\pi$
$98$		−	2.65125i		−	0.267817i
$99$	1.36852			0.137542
$100$	−7.07683	−	5.37501i	−0.707683	−	0.537501i
$101$	14.0272			1.39576			0.697881	−	0.716213i	$-0.254126\pi$
$101$	14.0272			1.39576			0.697881	+	0.716213i	$0.254126\pi$
$102$		−	1.25284i		−	0.124050i
$103$		−	3.55382i		−	0.350169i	−0.984553	−	0.175084i	$-0.943980\pi$
$103$		−	3.55382i		−	0.350169i	0.984553	−	0.175084i	$-0.0560198\pi$
$104$	−7.31370			−0.717168
$105$	0.872425	−	2.59105i	0.0851399	−	0.252861i
$106$	−2.35025			−0.228276
$107$			3.63127i			0.351048i	0.984475	+	0.175524i	$0.0561620\pi$
$107$			3.63127i			0.351048i	−0.984475	+	0.175524i	$0.943838\pi$
$108$		−	9.09235i		−	0.874911i
$109$	6.22267			0.596024			0.298012	−	0.954562i	$-0.403676\pi$
$109$	6.22267			0.596024			0.298012	+	0.954562i	$0.403676\pi$
$110$	−0.713538	−	0.240253i	−0.0680332	−	0.0229072i
$111$	9.75905			0.926288
$112$			3.18949i			0.301378i
$113$			12.2707i			1.15433i	0.816626	+	0.577167i	$0.195842\pi$
$113$			12.2707i			1.15433i	−0.816626	+	0.577167i	$0.804158\pi$
$114$		0			0
$115$	1.28646	+	0.433161i	0.119963	+	0.0403925i
$116$	1.52741			0.141816
$117$		−	7.86960i		−	0.727545i
$118$		−	2.94923i		−	0.271499i
$119$	−3.00000			−0.275010
$120$	−1.32301	+	3.92925i	−0.120774	+	0.358690i
$121$	−10.4909			−0.953715
$122$			2.14927i			0.194585i
$123$			4.28815i			0.386649i
$124$	4.45955			0.400480
$125$	−9.24992	+	6.28005i	−0.827338	+	0.561705i
$126$	1.06379			0.0947697
$127$			2.15789i			0.191482i	0.995406	+	0.0957408i	$0.0305220\pi$
$127$			2.15789i			0.191482i	−0.995406	+	0.0957408i	$0.969478\pi$
$128$		−	11.1728i		−	0.987544i
$129$	−10.5311			−0.927216
$130$	−1.38156	+	4.10315i	−0.121171	+	0.359870i
$131$	−17.5494			−1.53330			−0.766650	−	0.642065i	$-0.778078\pi$
$131$	−17.5494			−1.53330			−0.766650	+	0.642065i	$0.778078\pi$
$132$		−	1.31920i		−	0.114821i
$133$		0			0
$134$	−2.44535			−0.211246
$135$	−10.8411	−	3.65028i	−0.933054	−	0.314166i
$136$	4.54942			0.390109
$137$			5.07455i			0.433548i	0.976222	+	0.216774i	$0.0695535\pi$
$137$			5.07455i			0.433548i	−0.976222	+	0.216774i	$0.930446\pi$
$138$		−	0.297984i		−	0.0253661i
$139$	−5.98173			−0.507363			−0.253682	−	0.967288i	$-0.581642\pi$
$139$	−5.98173			−0.507363			−0.253682	+	0.967288i	$0.581642\pi$
$140$	4.42708	+	1.49063i	0.374156	+	0.125981i
$141$	10.9414			0.921436
$142$			6.21370i			0.521442i
$143$		−	2.92776i		−	0.244831i
$144$	5.20440			0.433700
$145$	0.613205	−	1.82118i	0.0509239	−	0.151241i
$146$	5.84111			0.483414
$147$		−	5.84442i		−	0.482040i
$148$			16.6744i			1.37062i
$149$	−9.60017			−0.786476			−0.393238	−	0.919437i	$-0.628645\pi$
$149$	−9.60017			−0.786476			−0.393238	+	0.919437i	$0.628645\pi$
$150$	1.95449	+	1.48447i	0.159583	+	0.121207i
$151$	7.53638			0.613302			0.306651	−	0.951822i	$-0.400792\pi$
$151$	7.53638			0.613302			0.306651	+	0.951822i	$0.400792\pi$
$152$		0			0
$153$			4.89521i			0.395754i
$154$	0.395765			0.0318916
$155$	1.79036	−	5.31728i	0.143805	−	0.427094i
$156$	−7.58596			−0.607363
$157$		−	9.85606i		−	0.786599i	−0.919410	−	0.393300i	$-0.871333\pi$
$157$		−	9.85606i		−	0.786599i	0.919410	−	0.393300i	$-0.128667\pi$
$158$		−	2.81406i		−	0.223874i
$159$	−5.18089			−0.410872
$160$	−10.2682	−	3.45737i	−0.811772	−	0.273329i
$161$	−0.713538			−0.0562347
$162$		−	0.204000i		−	0.0160278i
$163$			0.0688234i			0.00539067i	0.999996	+	0.00269533i	$0.000857952\pi$
$163$			0.0688234i			0.00539067i	−0.999996	+	0.00269533i	$0.999142\pi$
$164$	−7.32674			−0.572122
$165$	−1.57292	−	0.529615i	−0.122452	−	0.0412304i
$166$	−6.54045			−0.507637
$167$		−	16.6442i		−	1.28797i	−0.765038	−	0.643985i	$-0.777280\pi$
$167$		−	16.6442i		−	1.28797i	0.765038	−	0.643985i	$-0.222720\pi$
$168$		−	2.17937i		−	0.168142i
$169$	−3.83588			−0.295068
$170$	0.859386	−	2.55233i	0.0659119	−	0.195755i
$171$		0			0
$172$		−	17.9935i		−	1.37200i
$173$		−	12.1356i		−	0.922650i	−0.887231	−	0.461325i	$-0.847374\pi$
$173$		−	12.1356i		−	0.922650i	0.887231	−	0.461325i	$-0.152626\pi$
$174$	−0.421841			−0.0319797
$175$	3.55465	−	4.68011i	0.268706	−	0.353783i
$176$	1.93621			0.145947
$177$		−	6.50130i		−	0.488667i
$178$			7.53290i			0.564614i
$179$	−11.7538			−0.878522			−0.439261	−	0.898360i	$-0.644760\pi$
$179$	−11.7538			−0.878522			−0.439261	+	0.898360i	$0.644760\pi$
$180$	2.43231	−	7.22382i	0.181294	−	0.538432i
$181$	−8.83588			−0.656766			−0.328383	−	0.944545i	$-0.606504\pi$
$181$	−8.83588			−0.656766			−0.328383	+	0.944545i	$0.606504\pi$
$182$		−	2.27582i		−	0.168695i
$183$			4.73785i			0.350232i
$184$	1.08206			0.0797706
$185$	19.8814	+	6.69420i	1.46171	+	0.492168i
$186$	−1.23164			−0.0903085
$187$			1.82118i			0.133178i
$188$			18.6946i			1.36344i
$189$	6.01304			0.437384
$190$		0			0
$191$	14.2447			1.03071			0.515355	−	0.856977i	$-0.327660\pi$
$191$	14.2447			1.03071			0.515355	+	0.856977i	$0.327660\pi$
$192$		−	3.26693i		−	0.235771i
$193$			19.5057i			1.40405i	0.712153	+	0.702024i	$0.247720\pi$
$193$			19.5057i			1.40405i	−0.712153	+	0.702024i	$0.752280\pi$
$194$	7.88139			0.565851
$195$	−3.04551	+	9.04500i	−0.218094	+	0.647726i
$196$	9.98580			0.713271
$197$			4.33232i			0.308665i	0.988019	+	0.154332i	$0.0493226\pi$
$197$			4.33232i			0.308665i	−0.988019	+	0.154332i	$0.950677\pi$
$198$		−	0.645784i		−	0.0458938i
$199$	12.6315			0.895422			0.447711	−	0.894178i	$-0.352239\pi$
$199$	12.6315			0.895422			0.447711	+	0.894178i	$0.352239\pi$
$200$	−5.39053	+	7.09726i	−0.381168	+	0.501852i
$201$	−5.39053			−0.380219
$202$		−	6.61923i		−	0.465727i
$203$			1.01012i			0.0708966i
$204$	4.71877			0.330380
$205$	−2.94145	+	8.73592i	−0.205440	+	0.610143i
$206$	−1.67699			−0.116842
$207$			1.16431i			0.0809248i
$208$		−	11.1341i		−	0.772009i
$209$		0			0
$210$	−1.22267	−	0.411683i	−0.0843725	−	0.0284088i
$211$	22.2447			1.53139			0.765694	−	0.643206i	$-0.222396\pi$
$211$	22.2447			1.53139			0.765694	+	0.643206i	$0.222396\pi$
$212$		−	8.85209i		−	0.607964i
$213$			13.6975i			0.938536i
$214$	1.71354			0.117135
$215$	−21.4543	−	7.22382i	−1.46317	−	0.492660i
$216$	−9.11861			−0.620443
$217$			2.94923i			0.200207i
$218$		−	2.93638i		−	0.198877i
$219$	12.8762			0.870090
$220$	0.904901	−	2.68750i	0.0610084	−	0.181191i
$221$	10.4726			0.704463
$222$		−	4.60514i		−	0.309077i
$223$			13.6225i			0.912231i	0.889921	+	0.456115i	$0.150760\pi$
$223$			13.6225i			0.912231i	−0.889921	+	0.456115i	$0.849240\pi$
$224$	5.69527			0.380531
$225$	−7.63671	−	5.80025i	−0.509114	−	0.386683i
$226$	5.79036			0.385169
$227$		−	6.58913i		−	0.437336i	−0.975799	−	0.218668i	$-0.929829\pi$
$227$		−	6.58913i		−	0.437336i	0.975799	−	0.218668i	$-0.0701711\pi$
$228$		0			0
$229$	0.585962			0.0387215			0.0193607	−	0.999813i	$-0.493837\pi$
$229$	0.585962			0.0387215			0.0193607	+	0.999813i	$0.493837\pi$
$230$	0.204402	−	0.607061i	0.0134778	−	0.0400284i
$231$	0.872425			0.0574013
$232$		−	1.53182i		−	0.100569i
$233$			7.15747i			0.468901i	0.972128	+	0.234451i	$0.0753291\pi$
$233$			7.15747i			0.468901i	−0.972128	+	0.234451i	$0.924671\pi$
$234$	−3.71354			−0.242762
$235$	22.2902	+	7.50527i	1.45405	+	0.489590i
$236$	11.1081			0.723078
$237$		−	6.20331i		−	0.402948i
$238$			1.41565i			0.0917631i
$239$	−3.65498			−0.236421			−0.118211	−	0.992989i	$-0.537716\pi$
$239$	−3.65498			−0.236421			−0.118211	+	0.992989i	$0.537716\pi$
$240$	−5.98173	−	2.01409i	−0.386119	−	0.130009i
$241$	17.2630			1.11200			0.556002	−	0.831181i	$-0.312335\pi$
$241$	17.2630			1.11200			0.556002	+	0.831181i	$0.312335\pi$
$242$			4.95047i			0.318228i
$243$		−	15.7969i		−	1.01337i
$244$	−8.09510			−0.518236
$245$	4.00897	−	11.9064i	0.256124	−	0.760672i
$246$	2.02351			0.129014
$247$		0			0
$248$		−	4.47243i		−	0.284000i
$249$	−14.4178			−0.913689
$250$	2.96345	+	4.36489i	0.187425	+	0.276060i
$251$	−19.4140			−1.22540			−0.612702	−	0.790314i	$-0.709917\pi$
$251$	−19.4140			−1.22540			−0.612702	+	0.790314i	$0.709917\pi$
$252$			4.00670i			0.252398i
$253$			0.433161i			0.0272326i
$254$	1.01827			0.0638921
$255$	1.89443	−	5.62635i	0.118634	−	0.352336i
$256$	1.00897			0.0630606
$257$			13.8929i			0.866613i	0.901247	+	0.433306i	$0.142653\pi$
$257$			13.8929i			0.866613i	−0.901247	+	0.433306i	$0.857347\pi$
$258$			4.96948i			0.309386i
$259$	−11.0272			−0.685199
$260$	−15.4543	−	5.20358i	−0.958436	−	0.322712i
$261$	1.64825			0.102024
$262$			8.28129i			0.511620i
$263$		−	14.9883i		−	0.924221i	−0.886822	−	0.462110i	$-0.847092\pi$
$263$		−	14.9883i		−	0.924221i	0.886822	−	0.462110i	$-0.152908\pi$
$264$	−1.32301			−0.0814255
$265$	−10.5547	−	3.55382i	−0.648367	−	0.218310i
$266$		0			0
$267$			16.6055i			1.01624i
$268$		−	9.21028i		−	0.562607i
$269$	−19.3723			−1.18115			−0.590574	−	0.806984i	$-0.701098\pi$
$269$	−19.3723			−1.18115			−0.590574	+	0.806984i	$0.701098\pi$
$270$	−1.72251	+	5.11575i	−0.104828	+	0.311334i
$271$	11.9179			0.723963			0.361982	−	0.932185i	$-0.382100\pi$
$271$	11.9179			0.723963			0.361982	+	0.932185i	$0.382100\pi$
$272$			6.92583i			0.419940i
$273$		−	5.01682i		−	0.303632i
$274$	2.39460			0.144663
$275$	−2.84111	−	2.15789i	−0.171326	−	0.130126i
$276$	1.12234			0.0675570
$277$		−	10.9824i		−	0.659866i	−0.944004	−	0.329933i	$-0.892974\pi$
$277$		−	10.9824i		−	0.659866i	0.944004	−	0.329933i	$-0.107026\pi$
$278$			2.82268i			0.169293i
$279$	4.81237			0.288109
$280$	1.49493	−	4.43986i	0.0893393	−	0.265332i
$281$	14.6498			0.873931			0.436965	−	0.899478i	$-0.356053\pi$
$281$	14.6498			0.873931			0.436965	+	0.899478i	$0.356053\pi$
$282$		−	5.16309i		−	0.307458i
$283$		−	18.9287i		−	1.12519i	−0.826731	−	0.562597i	$-0.809802\pi$
$283$		−	18.9287i		−	1.12519i	0.826731	−	0.562597i	$-0.190198\pi$
$284$	−23.4036			−1.38875
$285$		0			0
$286$	−1.38156			−0.0816934
$287$		−	4.84539i		−	0.286014i
$288$		−	9.29317i		−	0.547605i
$289$	10.4856			0.616802
$290$	−0.859386	−	0.289361i	−0.0504649	−	0.0169919i
$291$	17.3738			1.01847
$292$			22.0002i			1.28747i
$293$			5.59625i			0.326937i	0.986549	+	0.163468i	$0.0522681\pi$
$293$			5.59625i			0.326937i	−0.986549	+	0.163468i	$0.947732\pi$
$294$	−2.75789			−0.160843
$295$	4.45955	−	13.2446i	0.259645	−	0.771131i
$296$	16.7225			0.971976
$297$		−	3.65028i		−	0.211811i
$298$			4.53016i			0.262425i
$299$	2.49086			0.144050
$300$	−5.59120	+	7.36147i	−0.322808	+	0.425014i
$301$	11.8997			0.685885
$302$		−	3.55629i		−	0.204642i
$303$		−	14.5914i		−	0.838256i
$304$		0			0
$305$	−3.24992	+	9.65206i	−0.186090	+	0.552675i
$306$	2.30997			0.132052
$307$			20.6319i			1.17753i	0.808305	+	0.588764i	$0.200385\pi$
$307$			20.6319i			1.17753i	−0.808305	+	0.588764i	$0.799615\pi$
$308$			1.49063i			0.0849364i
$309$	−3.69676			−0.210302
$310$	−2.50914	−	0.844844i	−0.142509	−	0.0479839i
$311$	−24.6587			−1.39827			−0.699134	−	0.714991i	$-0.746431\pi$
$311$	−24.6587			−1.39827			−0.699134	+	0.714991i	$0.746431\pi$
$312$			7.60787i			0.430711i
$313$		−	3.49856i		−	0.197751i	−0.995100	−	0.0988753i	$-0.968476\pi$
$313$		−	3.49856i		−	0.197751i	0.995100	−	0.0988753i	$-0.0315245\pi$
$314$	−4.65092			−0.262466
$315$	4.77733	+	1.60856i	0.269172	+	0.0906320i
$316$	10.5990			0.596240
$317$			31.3709i			1.76196i	0.473150	+	0.880982i	$0.343117\pi$
$317$			31.3709i			1.76196i	−0.473150	+	0.880982i	$0.656883\pi$
$318$			2.44478i			0.137096i
$319$	0.613205			0.0343329
$320$	2.24095	−	6.65548i	0.125273	−	0.372053i
$321$	3.77733			0.210830
$322$			0.336707i			0.0187639i
$323$		0			0
$324$	0.768356			0.0426865
$325$	−12.4088	+	16.3376i	−0.688317	+	0.906249i
$326$	0.0324767			0.00179872
$327$		−	6.47296i		−	0.357955i
$328$			7.34790i			0.405720i
$329$	−12.3633			−0.681610
$330$	−0.249917	+	0.742237i	−0.0137575	+	0.0408588i
$331$	35.7497			1.96498			0.982492	−	0.186305i	$-0.0596512\pi$
$331$	35.7497			1.96498			0.982492	+	0.186305i	$0.0596512\pi$
$332$		−	24.6343i		−	1.35198i
$333$			17.9935i			0.986040i
$334$	−7.85415			−0.429760
$335$	−10.9817	−	3.69762i	−0.599996	−	0.202023i
$336$	3.31777			0.180999
$337$			26.4892i			1.44296i	0.692435	+	0.721480i	$0.256538\pi$
$337$			26.4892i			1.44296i	−0.692435	+	0.721480i	$0.743462\pi$
$338$			1.81009i			0.0984559i
$339$	12.7643			0.693261
$340$	9.61320	+	3.23683i	0.521349	+	0.175542i
$341$	1.79036			0.0969536
$342$		0			0
$343$			14.8317i			0.800836i
$344$	−18.0455			−0.972949
$345$	0.450583	−	1.33821i	0.0242586	−	0.0720466i
$346$	−5.72658			−0.307863
$347$			34.3398i			1.84346i	0.387835	+	0.921729i	$0.373223\pi$
$347$			34.3398i			1.84346i	−0.387835	+	0.921729i	$0.626777\pi$
$348$		−	1.58884i		−	0.0851710i
$349$	21.4308			1.14717			0.573583	−	0.819148i	$-0.305553\pi$
$349$	21.4308			1.14717			0.573583	+	0.819148i	$0.305553\pi$
$350$	−2.20847	−	1.67738i	−0.118048	−	0.0896599i
$351$	−20.9907			−1.12040
$352$		−	3.45737i		−	0.184279i
$353$		−	19.5659i		−	1.04139i	−0.853744	−	0.520693i	$-0.825674\pi$
$353$		−	19.5659i		−	1.04139i	0.853744	−	0.520693i	$-0.174326\pi$
$354$	−3.06786			−0.163055
$355$	−9.39576	+	27.9049i	−0.498675	+	1.48104i
$356$	−28.3723			−1.50373
$357$			3.12066i			0.165163i
$358$			5.54644i			0.293138i
$359$	16.4726			0.869390			0.434695	−	0.900578i	$-0.356856\pi$
$359$	16.4726			0.869390			0.434695	+	0.900578i	$0.356856\pi$
$360$	−7.24468	−	2.43934i	−0.381828	−	0.128564i
$361$		0			0
$362$			4.16951i			0.219144i
$363$			10.9128i			0.572775i
$364$	8.57176			0.449282
$365$	26.2316	+	8.83238i	1.37303	+	0.462308i
$366$	2.23571			0.116863
$367$			12.7347i			0.664746i	0.943148	+	0.332373i	$0.107849\pi$
$367$			12.7347i			0.664746i	−0.943148	+	0.332373i	$0.892151\pi$
$368$			1.64728i			0.0858705i
$369$	−7.90640			−0.411591
$370$	3.15889	−	9.38171i	0.164223	−	0.487732i
$371$	5.85415			0.303932
$372$		−	4.63892i		−	0.240517i
$373$			19.3342i			1.00109i	0.865711	+	0.500544i	$0.166867\pi$
$373$			19.3342i			1.00109i	−0.865711	+	0.500544i	$0.833133\pi$
$374$	0.859386			0.0444378
$375$	6.53264	+	9.62196i	0.337344	+	0.496876i
$376$	18.7486			0.966884
$377$		−	3.52619i		−	0.181608i
$378$		−	2.83746i		−	0.145943i
$379$	−9.85789			−0.506366			−0.253183	−	0.967418i	$-0.581477\pi$
$379$	−9.85789			−0.506366			−0.253183	+	0.967418i	$0.581477\pi$
$380$		0			0
$381$	2.24468			0.114999
$382$		−	6.72183i		−	0.343919i
$383$			20.3333i			1.03898i	0.854476	+	0.519490i	$0.173878\pi$
$383$			20.3333i			1.03898i	−0.854476	+	0.519490i	$0.826122\pi$
$384$	−11.6222			−0.593092
$385$	1.77733	+	0.598438i	0.0905809	+	0.0304992i
$386$	9.20440			0.468492
$387$		−	19.4171i		−	0.987027i
$388$			29.6849i			1.50702i
$389$	1.00523			0.0509674			0.0254837	−	0.999675i	$-0.491887\pi$
$389$	1.00523			0.0509674			0.0254837	+	0.999675i	$0.491887\pi$
$390$	4.26819	+	1.43713i	0.216128	+	0.0727719i
$391$	−1.54942			−0.0783574
$392$		−	10.0146i		−	0.505816i
$393$			18.2553i			0.920857i
$394$	2.04435			0.102993
$395$	4.25515	−	12.6375i	0.214100	−	0.635864i
$396$	2.43231			0.122228
$397$		−	9.86221i		−	0.494970i	−0.968892	−	0.247485i	$-0.920396\pi$
$397$		−	9.86221i		−	0.494970i	0.968892	−	0.247485i	$-0.0796042\pi$
$398$		−	5.96059i		−	0.298777i
$399$		0			0
$400$	−10.8046	−	8.20631i	−0.540228	−	0.410315i
$401$	29.8318			1.48973			0.744865	−	0.667215i	$-0.232514\pi$
$401$	29.8318			1.48973			0.744865	+	0.667215i	$0.232514\pi$
$402$			2.54370i			0.126868i
$403$		−	10.2954i		−	0.512849i
$404$	24.9310			1.24036
$405$	0.308470	−	0.916137i	0.0153280	−	0.0455232i
$406$	0.476660			0.0236562
$407$			6.69420i			0.331819i
$408$		−	4.73240i		−	0.234289i
$409$	−27.6442			−1.36692			−0.683458	−	0.729989i	$-0.739525\pi$
$409$	−27.6442			−1.36692			−0.683458	+	0.729989i	$0.739525\pi$
$410$	4.12234	+	1.38802i	0.203588	+	0.0685495i
$411$	5.27866			0.260377
$412$		−	6.31630i		−	0.311182i
$413$			7.34614i			0.361480i
$414$	0.549417			0.0270024
$415$	−29.3723	−	9.88984i	−1.44183	−	0.485473i
$416$	−19.8814			−0.974766
$417$			6.22232i			0.304708i
$418$		0			0
$419$	11.2902			0.551562			0.275781	−	0.961220i	$-0.411064\pi$
$419$	11.2902			0.551562			0.275781	+	0.961220i	$0.411064\pi$
$420$	1.55058	−	4.60514i	0.0756607	−	0.224708i
$421$	4.54942			0.221725			0.110863	−	0.993836i	$-0.464639\pi$
$421$	4.54942			0.221725			0.110863	+	0.993836i	$0.464639\pi$
$422$		−	10.4969i		−	0.510981i
$423$			20.1736i			0.980875i
$424$	−8.87766			−0.431137
$425$	7.71877	−	10.1627i	0.374415	−	0.492962i
$426$	6.46362			0.313163
$427$		−	5.35353i		−	0.259075i
$428$			6.45395i			0.311964i
$429$	−3.04551			−0.147039
$430$	−3.40880	+	10.1239i	−0.164387	+	0.488220i
$431$	32.9034			1.58490			0.792451	−	0.609936i	$-0.208805\pi$
$431$	32.9034			1.58490			0.792451	+	0.609936i	$0.208805\pi$
$432$		−	13.8818i		−	0.667887i
$433$			22.3093i			1.07212i	0.844181	+	0.536059i	$0.180088\pi$
$433$			22.3093i			1.07212i	−0.844181	+	0.536059i	$0.819912\pi$
$434$	1.39170			0.0668035
$435$	−1.89443	−	0.637869i	−0.0908311	−	0.0305835i
$436$	11.0597			0.529664
$437$		0			0
$438$		−	6.07605i		−	0.290325i
$439$	−5.70573			−0.272320			−0.136160	−	0.990687i	$-0.543476\pi$
$439$	−5.70573			−0.272320			−0.136160	+	0.990687i	$0.543476\pi$
$440$	−2.69527	−	0.907515i	−0.128492	−	0.0432641i
$441$	10.7758			0.513135
$442$		−	4.94185i		−	0.235060i
$443$			11.5776i			0.550069i	0.961434	+	0.275034i	$0.0886893\pi$
$443$			11.5776i			0.550069i	−0.961434	+	0.275034i	$0.911311\pi$
$444$	17.3450			0.823158
$445$	−11.3905	+	33.8292i	−0.539963	+	1.60366i
$446$	6.42824			0.304386
$447$			9.98630i			0.472336i
$448$			3.69147i			0.174406i
$449$	25.4726			1.20213			0.601063	−	0.799202i	$-0.294744\pi$
$449$	25.4726			1.20213			0.601063	+	0.799202i	$0.294744\pi$
$450$	−2.73705	+	3.60364i	−0.129026	+	0.169877i
$451$	−2.94145			−0.138507
$452$			21.8091i			1.02581i
$453$		−	7.83950i		−	0.368332i
$454$	−3.10930			−0.145927
$455$	3.44128	−	10.2204i	0.161330	−	0.479140i
$456$		0			0
$457$			6.92830i			0.324092i	0.986783	+	0.162046i	$0.0518094\pi$
$457$			6.92830i			0.324092i	−0.986783	+	0.162046i	$0.948191\pi$
$458$		−	0.276506i		−	0.0129203i
$459$	13.0571			0.609451
$460$	2.28646	+	0.769868i	0.106607	+	0.0358953i
$461$	32.4946			1.51342			0.756712	−	0.653748i	$-0.226804\pi$
$461$	32.4946			1.51342			0.756712	+	0.653748i	$0.226804\pi$
$462$		−	0.411683i		−	0.0191532i
$463$			21.5062i			0.999477i	0.866176	+	0.499738i	$0.166571\pi$
$463$			21.5062i			0.999477i	−0.866176	+	0.499738i	$0.833429\pi$
$464$	2.33198			0.108259
$465$	−5.53114	−	1.86237i	−0.256501	−	0.0863656i
$466$	3.37749			0.156459
$467$			16.9509i			0.784392i	0.919882	+	0.392196i	$0.128285\pi$
$467$			16.9509i			0.784392i	−0.919882	+	0.392196i	$0.871715\pi$
$468$		−	13.9868i		−	0.646542i
$469$	6.09103			0.281258
$470$	3.54161	−	10.5184i	0.163362	−	0.485177i
$471$	−10.2525			−0.472410
$472$		−	11.1402i		−	0.512770i
$473$		−	7.22382i		−	0.332152i
$474$	−2.92724			−0.134453
$475$		0			0
$476$	−5.33198			−0.244391
$477$		−	9.55243i		−	0.437376i
$478$			1.72473i			0.0788872i
$479$	−8.85789			−0.404727			−0.202364	−	0.979310i	$-0.564862\pi$
$479$	−8.85789			−0.404727			−0.202364	+	0.979310i	$0.564862\pi$
$480$	−3.59643	+	10.6812i	−0.164154	+	0.487527i
$481$	38.4946			1.75520
$482$		−	8.14611i		−	0.371045i
$483$			0.742237i			0.0337730i
$484$	−18.6457			−0.847531
$485$	35.3943	+	11.9175i	1.60717	+	0.541146i
$486$	−7.45432			−0.338135
$487$			30.0628i			1.36227i	0.732156	+	0.681137i	$0.238514\pi$
$487$			30.0628i			1.36227i	−0.732156	+	0.681137i	$0.761486\pi$
$488$			8.11848i			0.367506i
$489$	0.0715916			0.00323748
$490$	−5.61844	−	1.89177i	−0.253815	−	0.0854614i
$491$	3.10033			0.139916			0.0699580	−	0.997550i	$-0.477713\pi$
$491$	3.10033			0.139916			0.0699580	+	0.997550i	$0.477713\pi$
$492$			7.62143i			0.343601i
$493$			2.19343i			0.0987873i
$494$		0			0
$495$	0.976493	−	2.90013i	0.0438901	−	0.130351i
$496$	6.80864			0.305717
$497$		−	15.4775i		−	0.694260i
$498$			6.80351i			0.304873i
$499$	−32.1391			−1.43874			−0.719372	−	0.694625i	$-0.755570\pi$
$499$	−32.1391			−1.43874			−0.719372	+	0.694625i	$0.755570\pi$
$500$	−16.4401	+	11.1617i	−0.735224	+	0.499166i
$501$	−17.3137			−0.773519
$502$			9.16117i			0.408883i
$503$		−	8.41822i		−	0.375350i	−0.982231	−	0.187675i	$-0.939905\pi$
$503$		−	8.41822i		−	0.375350i	0.982231	−	0.187675i	$-0.0600952\pi$
$504$	4.01827			0.178988
$505$	10.0090	−	29.7261i	0.445393	−	1.32279i
$506$	0.204402			0.00908676
$507$			3.99016i			0.177209i
$508$			3.83527i			0.170163i
$509$	−20.3450			−0.901777			−0.450888	−	0.892580i	$-0.648893\pi$
$509$	−20.3450			−0.901777			−0.450888	+	0.892580i	$0.648893\pi$
$510$	−2.65498	−	0.893952i	−0.117565	−	0.0395849i
$511$	−14.5494			−0.643628
$512$		−	22.8217i		−	1.00859i
$513$		0			0
$514$	6.55582			0.289165
$515$	−7.53114	−	2.53579i	−0.331862	−	0.111740i
$516$	−18.7173			−0.823982
$517$			7.50527i			0.330081i
$518$			5.20358i			0.228632i
$519$	−12.6237			−0.554118
$520$	−5.21861	+	15.4990i	−0.228851	+	0.679674i
$521$	15.3502			0.672507			0.336253	−	0.941772i	$-0.390840\pi$
$521$	15.3502			0.672507			0.336253	+	0.941772i	$0.390840\pi$
$522$		−	0.777783i		−	0.0340426i
$523$		−	13.2367i		−	0.578800i	−0.957208	−	0.289400i	$-0.906544\pi$
$523$		−	13.2367i		−	0.578800i	0.957208	−	0.289400i	$-0.0934558\pi$
$524$	−31.1910			−1.36259
$525$	−4.86836	−	3.69762i	−0.212472	−	0.161378i
$526$	−7.07276			−0.308387
$527$			6.40414i			0.278969i
$528$		−	2.01409i		−	0.0876520i
$529$	22.6315			0.983977
$530$	−1.67699	+	4.98057i	−0.0728439	+	0.216342i
$531$	11.9870			0.520190
$532$		0			0
$533$			16.9146i			0.732653i
$534$	7.83588			0.339092
$535$	7.69527	+	2.59105i	0.332695	+	0.112021i
$536$	−9.23688			−0.398972
$537$			12.2266i			0.527616i
$538$			9.14145i			0.394116i
$539$	4.00897			0.172679
$540$	−19.2682	−	6.48773i	−0.829171	−	0.279188i
$541$	−27.7408			−1.19267			−0.596335	−	0.802736i	$-0.703377\pi$
$541$	−27.7408			−1.19267			−0.596335	+	0.802736i	$0.703377\pi$
$542$		−	5.62388i		−	0.241566i
$543$			9.19127i			0.394435i
$544$	12.3670			0.530232
$545$	4.44011	−	13.1869i	0.190194	−	0.564864i
$546$	−2.36736			−0.101314
$547$			17.0602i			0.729440i	0.931117	+	0.364720i	$0.118835\pi$
$547$			17.0602i			0.729440i	−0.931117	+	0.364720i	$0.881165\pi$
$548$			9.01913i			0.385278i
$549$	−8.73555			−0.372824
$550$	−1.01827	+	1.34068i	−0.0434193	+	0.0571666i
$551$		0			0
$552$		−	1.12558i		−	0.0479080i
$553$			7.00943i			0.298071i
$554$	−5.18239			−0.220179
$555$	6.96345	−	20.6811i	0.295582	−	0.877862i
$556$	−10.6315			−0.450875
$557$		−	26.5415i		−	1.12460i	−0.826933	−	0.562300i	$-0.809917\pi$
$557$		−	26.5415i		−	1.12460i	0.826933	−	0.562300i	$-0.190083\pi$
$558$		−	2.27088i		−	0.0961340i
$559$	−41.5401			−1.75696
$560$	6.75905	+	2.27582i	0.285622	+	0.0961710i
$561$	1.89443			0.0799830
$562$		−	6.91298i		−	0.291606i
$563$		−	35.5594i		−	1.49865i	−0.662203	−	0.749325i	$-0.730378\pi$
$563$		−	35.5594i		−	1.49865i	0.662203	−	0.749325i	$-0.269622\pi$
$564$	19.4465			0.818846
$565$	26.0037	+	8.75564i	1.09399	+	0.368353i
$566$	−8.93214			−0.375446
$567$			0.508137i			0.0213397i
$568$			23.4712i			0.984828i
$569$	14.9713			0.627628			0.313814	−	0.949485i	$-0.398393\pi$
$569$	14.9713			0.627628			0.313814	+	0.949485i	$0.398393\pi$
$570$		0			0
$571$	5.92724			0.248047			0.124024	−	0.992279i	$-0.460420\pi$
$571$	5.92724			0.248047			0.124024	+	0.992279i	$0.460420\pi$
$572$		−	5.20358i		−	0.217572i
$573$		−	14.8176i		−	0.619015i
$574$	−2.28646			−0.0954351
$575$	1.83588	−	2.41715i	0.0765614	−	0.100802i
$576$	6.02351			0.250979
$577$			14.5559i			0.605970i	0.952995	+	0.302985i	$0.0979832\pi$
$577$			14.5559i			0.605970i	−0.952995	+	0.302985i	$0.902017\pi$
$578$		−	4.94800i		−	0.205810i
$579$	20.2902			0.843232
$580$	1.08986	−	3.23683i	0.0452542	−	0.134402i
$581$	16.2914			0.675880
$582$		−	8.19839i		−	0.339834i
$583$		−	3.55382i		−	0.147184i
$584$	22.0638			0.913006
$585$	−16.6770	−	5.61526i	−0.689509	−	0.232162i
$586$	2.64078			0.109090
$587$		−	20.5839i		−	0.849588i	−0.905290	−	0.424794i	$-0.860347\pi$
$587$		−	20.5839i		−	0.849588i	0.905290	−	0.424794i	$-0.139653\pi$
$588$		−	10.3874i		−	0.428371i
$589$		0			0
$590$	−6.24992	−	2.10439i	−0.257305	−	0.0866364i
$591$	4.50657			0.185375
$592$			25.4576i			1.04630i
$593$			14.3322i			0.588552i	0.955720	+	0.294276i	$0.0950785\pi$
$593$			14.3322i			0.588552i	−0.955720	+	0.294276i	$0.904922\pi$
$594$	−1.72251			−0.0706753
$595$	−2.14061	+	6.35750i	−0.0877566	+	0.260632i
$596$	−17.0626			−0.698912
$597$		−	13.1395i		−	0.537765i
$598$		−	1.17540i		−	0.0480656i
$599$	−2.50017			−0.102154			−0.0510770	−	0.998695i	$-0.516265\pi$
$599$	−2.50017			−0.102154			−0.0510770	+	0.998695i	$0.516265\pi$
$600$	7.38273	+	5.60734i	0.301399	+	0.228919i
$601$	14.5259			0.592524			0.296262	−	0.955107i	$-0.404260\pi$
$601$	14.5259			0.592524			0.296262	+	0.955107i	$0.404260\pi$
$602$		−	5.61526i		−	0.228861i
$603$		−	9.93895i		−	0.404745i
$604$	13.3946			0.545019
$605$	−7.48563	+	22.2319i	−0.304334	+	0.903854i
$606$	−6.88546			−0.279703
$607$		−	31.8704i		−	1.29358i	−0.762669	−	0.646789i	$-0.776111\pi$
$607$		−	31.8704i		−	1.29358i	0.762669	−	0.646789i	$-0.223889\pi$
$608$		0			0
$609$	1.05075			0.0425785
$610$	4.55465	+	1.53358i	0.184412	+	0.0620930i
$611$	43.1586			1.74601
$612$			8.70038i			0.351692i
$613$		−	20.0488i		−	0.809765i	−0.914369	−	0.404882i	$-0.867312\pi$
$613$		−	20.0488i		−	0.809765i	0.914369	−	0.404882i	$-0.132688\pi$
$614$	9.73588			0.392908
$615$	9.08729	+	3.05976i	0.366435	+	0.123381i
$616$	1.49493			0.0602325
$617$		−	20.0819i		−	0.808467i	−0.914656	−	0.404234i	$-0.867538\pi$
$617$		−	20.0819i		−	0.808467i	0.914656	−	0.404234i	$-0.132462\pi$
$618$			1.74444i			0.0701718i
$619$	−5.62217			−0.225974			−0.112987	−	0.993596i	$-0.536042\pi$
$619$	−5.62217			−0.225974			−0.112987	+	0.993596i	$0.536042\pi$
$620$	3.18206	−	9.45053i	0.127795	−	0.379542i
$621$	3.10557			0.124622
$622$			11.6361i			0.466563i
$623$		−	18.7634i		−	0.751740i
$624$	−11.5819			−0.463647
$625$	6.70830	+	24.0832i	0.268332	+	0.963326i
$626$	−1.65092			−0.0659839
$627$		0			0
$628$		−	17.5174i		−	0.699022i
$629$	−23.9452			−0.954757
$630$	0.759053	−	2.25434i	0.0302414	−	0.0898152i
$631$	−4.84368			−0.192824			−0.0964120	−	0.995342i	$-0.530737\pi$
$631$	−4.84368			−0.192824			−0.0964120	+	0.995342i	$0.530737\pi$
$632$		−	10.6296i		−	0.422823i
$633$		−	23.1394i		−	0.919708i
$634$	14.8034			0.587918
$635$	4.57292	+	1.53974i	0.181471	+	0.0611025i
$636$	−9.20814			−0.365126
$637$		−	23.0533i		−	0.913406i
$638$		−	0.289361i		−	0.0114559i
$639$	−25.2552			−0.999078
$640$	−23.6770	−	7.97221i	−0.935915	−	0.315129i
$641$	−25.3007			−0.999316			−0.499658	−	0.866223i	$-0.666541\pi$
$641$	−25.3007			−0.999316			−0.499658	+	0.866223i	$0.666541\pi$
$642$		−	1.78246i		−	0.0703480i
$643$		−	13.9457i		−	0.549963i	−0.961450	−	0.274981i	$-0.911328\pi$
$643$		−	13.9457i		−	0.549963i	0.961450	−	0.274981i	$-0.0886717\pi$
$644$	−1.26819			−0.0499737
$645$	−7.51437	+	22.3172i	−0.295878	+	0.878740i
$646$		0			0
$647$		−	2.51360i		−	0.0988200i	−0.998779	−	0.0494100i	$-0.984266\pi$
$647$		−	2.51360i		−	0.0988200i	0.998779	−	0.0494100i	$-0.0157341\pi$
$648$		−	0.770575i		−	0.0302711i
$649$	4.45955			0.175053
$650$	7.70947	+	5.85551i	0.302390	+	0.229672i
$651$	3.06786			0.120239
$652$			0.122322i			0.00479049i
$653$		−	1.92873i		−	0.0754770i	−0.999288	−	0.0377385i	$-0.987985\pi$
$653$		−	1.92873i		−	0.0754770i	0.999288	−	0.0377385i	$-0.0120154\pi$
$654$	−3.05448			−0.119440
$655$	−12.5222	+	37.1901i	−0.489282	+	1.45314i
$656$	−11.1861			−0.436745
$657$			23.7408i			0.926217i
$658$			5.83404i			0.227434i
$659$	−15.8008			−0.615513			−0.307757	−	0.951465i	$-0.599578\pi$
$659$	−15.8008			−0.615513			−0.307757	+	0.951465i	$0.599578\pi$
$660$	−2.79560	−	0.941298i	−0.108819	−	0.0366400i
$661$	16.4036			0.638025			0.319012	−	0.947751i	$-0.396649\pi$
$661$	16.4036			0.638025			0.319012	+	0.947751i	$0.396649\pi$
$662$		−	16.8697i		−	0.655661i
$663$		−	10.8938i		−	0.423081i
$664$	−24.7054			−0.958755
$665$		0			0
$666$	8.49086			0.329014
$667$			0.521700i			0.0202003i
$668$		−	29.5823i		−	1.14457i
$669$	14.1704			0.547860
$670$	−1.74485	+	5.18210i	−0.0674094	+	0.200202i
$671$	−3.24992			−0.125462
$672$		−	5.92434i		−	0.228536i
$673$		−	17.0878i		−	0.658686i	−0.944210	−	0.329343i	$-0.893173\pi$
$673$		−	17.0878i		−	0.658686i	0.944210	−	0.329343i	$-0.106827\pi$
$674$	12.4998			0.481476
$675$	−15.4711	+	20.3695i	−0.595483	+	0.784023i
$676$	−6.81761			−0.262216
$677$		−	4.57680i		−	0.175901i	−0.996125	−	0.0879504i	$-0.971968\pi$
$677$		−	4.57680i		−	0.175901i	0.996125	−	0.0879504i	$-0.0280317\pi$
$678$		−	6.02326i		−	0.231322i
$679$	−19.6315			−0.753387
$680$	3.24618	−	9.64097i	0.124485	−	0.369714i
$681$	−6.85415			−0.262652
$682$		−	0.844844i		−	0.0323507i
$683$			29.0692i			1.11230i	0.831082	+	0.556151i	$0.187722\pi$
$683$			29.0692i			1.11230i	−0.831082	+	0.556151i	$0.812278\pi$
$684$		0			0
$685$	10.7538	+	3.62089i	0.410882	+	0.138347i
$686$	6.99883			0.267217
$687$		−	0.609531i		−	0.0232550i
$688$		−	27.4717i		−	1.04735i
$689$	−20.4360			−0.778551
$690$	−0.631477	−	0.212623i	−0.0240399	−	0.00809441i
$691$	−6.07833			−0.231230			−0.115615	−	0.993294i	$-0.536884\pi$
$691$	−6.07833			−0.231230			−0.115615	+	0.993294i	$0.536884\pi$
$692$		−	21.5689i		−	0.819925i
$693$			1.60856i			0.0611041i
$694$	16.2044			0.615111
$695$	−4.26819	+	12.6763i	−0.161902	+	0.480838i
$696$	−1.59343			−0.0603989
$697$		−	10.5216i		−	0.398533i
$698$		−	10.1129i		−	0.382777i
$699$	7.44535			0.281609
$700$	6.31777	−	8.31809i	0.238789	−	0.314394i
$701$	10.4114			0.393232			0.196616	−	0.980481i	$-0.437005\pi$
$701$	10.4114			0.393232			0.196616	+	0.980481i	$0.437005\pi$
$702$			9.90517i			0.373847i
$703$		0			0
$704$	2.24095			0.0844589
$705$	7.80714	−	23.1867i	0.294034	−	0.873263i
$706$	−9.23281			−0.347481
$707$			16.4876i			0.620080i
$708$		−	11.5549i		−	0.434261i
$709$	0.531144			0.0199475			0.00997377	−	0.999950i	$-0.496825\pi$
$709$	0.531144			0.0199475			0.00997377	+	0.999950i	$0.496825\pi$
$710$	13.1679	+	4.43371i	0.494181	+	0.166394i
$711$	11.4375			0.428941
$712$			28.4542i			1.06637i
$713$			1.52320i			0.0570442i
$714$	1.47259			0.0551103
$715$	−6.20440	−	2.08907i	−0.232031	−	0.0781266i
$716$	−20.8904			−0.780710
$717$			3.80199i			0.141988i
$718$		−	7.77315i		−	0.290091i
$719$	−22.4271			−0.836389			−0.418194	−	0.908358i	$-0.637337\pi$
$719$	−22.4271			−0.836389			−0.418194	+	0.908358i	$0.637337\pi$
$720$	3.71354	−	11.0290i	0.138395	−	0.411026i
$721$	4.17716			0.155566
$722$		0			0
$723$		−	17.9573i		−	0.667839i
$724$	−15.7042			−0.583643
$725$	−3.42184	−	2.59896i	−0.127084	−	0.0965231i
$726$	5.14958			0.191119
$727$		−	45.9734i		−	1.70506i	−0.522679	−	0.852529i	$-0.675067\pi$
$727$		−	45.9734i		−	1.70506i	0.522679	−	0.852529i	$-0.324933\pi$
$728$		−	8.59651i		−	0.318608i
$729$	−15.1354			−0.560570
$730$	4.16786	−	12.3783i	0.154259	−	0.458141i
$731$	25.8396			0.955713
$732$			8.42069i			0.311238i
$733$		−	42.5178i		−	1.57043i	−0.619223	−	0.785215i	$-0.712552\pi$
$733$		−	42.5178i		−	1.57043i	0.619223	−	0.785215i	$-0.287448\pi$
$734$	6.00930			0.221807
$735$	−12.3853	−	4.17022i	−0.456839	−	0.153821i
$736$	2.94145			0.108423
$737$		−	3.69762i		−	0.136204i
$738$			3.73090i			0.137336i
$739$	3.41777			0.125725			0.0628624	−	0.998022i	$-0.479977\pi$
$739$	3.41777			0.125725			0.0628624	+	0.998022i	$0.479977\pi$
$740$	35.3357	+	11.8978i	1.29897	+	0.437371i
$741$		0			0
$742$		−	2.76248i		−	0.101414i
$743$			9.72088i			0.356625i	0.983974	+	0.178312i	$0.0570637\pi$
$743$			9.72088i			0.356625i	−0.983974	+	0.178312i	$0.942936\pi$
$744$	−4.65232			−0.170562
$745$	−6.85008	+	20.3443i	−0.250968	+	0.745359i
$746$	9.12351			0.334035
$747$		−	26.5832i		−	0.972629i
$748$			3.23683i			0.118350i
$749$	−4.26819			−0.155956
$750$	4.54045	−	3.08265i	0.165794	−	0.112562i
$751$	−11.3853			−0.415455			−0.207728	−	0.978187i	$-0.566607\pi$
$751$	−11.3853			−0.415455			−0.207728	+	0.978187i	$0.566607\pi$
$752$			28.5420i			1.04082i
$753$			20.1949i			0.735943i
$754$	−1.66395			−0.0605976
$755$	5.37749	−	15.9708i	0.195707	−	0.581238i
$756$	10.6871			0.388687
$757$			22.7842i			0.828105i	0.910253	+	0.414053i	$0.135887\pi$
$757$			22.7842i			0.828105i	−0.910253	+	0.414053i	$0.864113\pi$
$758$			4.65178i			0.168960i
$759$	0.450583			0.0163551
$760$		0			0
$761$	−36.7665			−1.33279			−0.666393	−	0.745601i	$-0.732163\pi$
$761$	−36.7665			−1.33279			−0.666393	+	0.745601i	$0.732163\pi$
$762$		−	1.05923i		−	0.0383718i
$763$			7.31412i			0.264789i
$764$	25.3174			0.915953
$765$	10.3738	+	3.49292i	0.375064	+	0.126287i
$766$	9.59493			0.346679
$767$		−	25.6444i		−	0.925965i
$768$		−	1.04955i		−	0.0378724i
$769$	20.8008			0.750097			0.375049	−	0.927005i	$-0.377626\pi$
$769$	20.8008			0.750097			0.375049	+	0.927005i	$0.377626\pi$
$770$	0.282393	−	0.838691i	0.0101767	−	0.0302243i
$771$	14.4517			0.520464
$772$			34.6679i			1.24772i
$773$		−	21.0091i		−	0.755646i	−0.925878	−	0.377823i	$-0.876673\pi$
$773$		−	21.0091i		−	0.755646i	0.925878	−	0.377823i	$-0.123327\pi$
$774$	−9.16262			−0.329344
$775$	−9.99070	−	7.58816i	−0.358876	−	0.272575i
$776$	29.7706			1.06870
$777$			11.4708i			0.411512i
$778$		−	0.474354i		−	0.0170064i
$779$		0			0
$780$	−5.41287	+	16.0759i	−0.193812	+	0.575610i
$781$	−9.39576			−0.336207
$782$			0.731145i			0.0261457i
$783$		−	4.39640i		−	0.157115i
$784$	15.2458			0.544495
$785$	−20.8866	−	7.03267i	−0.745476	−	0.251007i
$786$	8.61437			0.307264
$787$		−	18.0606i		−	0.643791i	−0.946775	−	0.321896i	$-0.895680\pi$
$787$		−	18.0606i		−	0.643791i	0.946775	−	0.321896i	$-0.104320\pi$
$788$			7.69994i			0.274299i
$789$	−15.5912			−0.555061
$790$	−5.96345	−	2.00794i	−0.212170	−	0.0714392i
$791$	−14.4230			−0.512823
$792$		−	2.43934i		−	0.0866780i
$793$			18.6884i			0.663646i
$794$	−4.65382			−0.165158
$795$	−3.69676	+	10.9792i	−0.131111	+	0.389391i
$796$	22.4502			0.795728
$797$			24.2571i			0.859229i	0.903012	+	0.429615i	$0.141351\pi$
$797$			24.2571i			0.859229i	−0.903012	+	0.429615i	$0.858649\pi$
$798$		0			0
$799$	−26.8463			−0.949756
$800$	−14.6535	+	19.2930i	−0.518079	+	0.682112i
$801$	−30.6169			−1.08180
$802$		−	14.0771i		−	0.497081i
$803$			8.83238i			0.311688i
$804$	−9.58073			−0.337886
$805$	−0.509136	+	1.51211i	−0.0179447	+	0.0532947i
$806$	−4.85822			−0.171124
$807$			20.1514i			0.709364i
$808$		−	25.0030i		−	0.879602i
$809$	4.27192			0.150193			0.0750964	−	0.997176i	$-0.476074\pi$
$809$	4.27192			0.150193			0.0750964	+	0.997176i	$0.476074\pi$
$810$	−0.432310	−	0.145562i	−0.0151898	−	0.00511452i
$811$	10.1824			0.357552			0.178776	−	0.983890i	$-0.442786\pi$
$811$	10.1824			0.357552			0.178776	+	0.983890i	$0.442786\pi$
$812$			1.79531i			0.0630032i
$813$		−	12.3973i		−	0.434792i
$814$	3.15889			0.110719
$815$	0.145848	+	0.0491081i	0.00510884	+	0.00172018i
$816$	7.20440			0.252205
$817$		0			0
$818$			13.0448i			0.456102i
$819$	9.24992			0.323218
$820$	−5.22791	+	15.5266i	−0.182566	+	0.542212i
$821$	−56.0217			−1.95517			−0.977585	−	0.210541i	$-0.932477\pi$
$821$	−56.0217			−1.95517			−0.977585	+	0.210541i	$0.932477\pi$
$822$		−	2.49091i		−	0.0868806i
$823$			33.5416i			1.16919i	0.811326	+	0.584593i	$0.198746\pi$
$823$			33.5416i			1.16919i	−0.811326	+	0.584593i	$0.801254\pi$
$824$	−6.33455			−0.220674
$825$	−2.24468	+	2.95539i	−0.0781498	+	0.102893i
$826$	3.46652			0.120616
$827$			0.0362530i			0.00126064i	1.00000		0.000630320i	$0.000200637\pi$
$827$			0.0362530i			0.00126064i	−1.00000		0.000630320i	$0.999799\pi$
$828$			2.06935i			0.0719149i
$829$	−39.5662			−1.37419			−0.687095	−	0.726567i	$-0.741115\pi$
$829$	−39.5662			−1.37419			−0.687095	+	0.726567i	$0.741115\pi$
$830$	−4.66686	+	13.8603i	−0.161989	+	0.481098i
$831$	−11.4241			−0.396297
$832$		−	12.8864i		−	0.446756i
$833$			14.3401i			0.496855i
$834$	2.93621			0.101673
$835$	−35.2719	−	11.8763i	−1.22064	−	0.410996i
$836$		0			0
$837$		−	12.8361i		−	0.443681i
$838$		−	5.32766i		−	0.184041i
$839$	−40.1623			−1.38656			−0.693278	−	0.720670i	$-0.743834\pi$
$839$	−40.1623			−1.38656			−0.693278	+	0.720670i	$0.743834\pi$
$840$	−4.61844	−	1.55506i	−0.159351	−	0.0536547i
$841$	−28.2615			−0.974533
$842$		−	2.14680i		−	0.0739835i
$843$		−	15.2390i		−	0.524858i
$844$	39.5360			1.36089
$845$	−2.73705	+	8.12886i	−0.0941572	+	0.279641i
$846$	9.51961			0.327291
$847$		−	12.3309i		−	0.423696i
$848$		−	13.5150i		−	0.464106i
$849$	−19.6900			−0.675760
$850$	−4.79560	−	3.64236i	−0.164488	−	0.124932i
$851$	−5.69527			−0.195231
$852$			24.3449i			0.834042i
$853$			16.4617i			0.563639i	0.959467	+	0.281819i	$0.0909379\pi$
$853$			16.4617i			0.563639i	−0.959467	+	0.281819i	$0.909062\pi$
$854$	−2.52624			−0.0864463
$855$		0			0
$856$	6.47259			0.221229
$857$		−	5.60664i		−	0.191519i	−0.995404	−	0.0957595i	$-0.969472\pi$
$857$		−	5.60664i		−	0.191519i	0.995404	−	0.0957595i	$-0.0305280\pi$
$858$			1.43713i			0.0490628i
$859$	−25.0298			−0.854006			−0.427003	−	0.904250i	$-0.640431\pi$
$859$	−25.0298			−0.854006			−0.427003	+	0.904250i	$0.640431\pi$
$860$	−38.1313	−	12.8391i	−1.30027	−	0.437809i
$861$	−5.04028			−0.171772
$862$		−	15.5266i		−	0.528837i
$863$		−	42.4307i		−	1.44436i	−0.691707	−	0.722178i	$-0.743141\pi$
$863$		−	42.4307i		−	1.44436i	0.691707	−	0.722178i	$-0.256859\pi$
$864$	−24.7878			−0.843298
$865$	−25.7173	−	8.65919i	−0.874414	−	0.294421i
$866$	10.5274			0.357736
$867$		−	10.9074i		−	0.370434i
$868$			5.24175i			0.177917i
$869$	4.25515			0.144346
$870$	−0.301000	+	0.893952i	−0.0102049	+	0.0303078i
$871$	−21.2630			−0.720468
$872$		−	11.0917i		−	0.375611i
$873$			32.0334i			1.08417i
$874$		0			0
$875$	−7.38156	−	10.8723i	−0.249542	−	0.367552i
$876$	22.8851			0.773217
$877$		−	0.557245i		−	0.0188168i	−0.999956	−	0.00940841i	$-0.997005\pi$
$877$		−	0.557245i		−	0.0188168i	0.999956	−	0.00940841i	$-0.00299483\pi$
$878$			2.69244i			0.0908656i
$879$	5.82134			0.196349
$880$	1.38156	−	4.10315i	0.0465724	−	0.138317i
$881$	8.35432			0.281464			0.140732	−	0.990048i	$-0.455054\pi$
$881$	8.35432			0.281464			0.140732	+	0.990048i	$0.455054\pi$
$882$		−	5.08494i		−	0.171219i
$883$			19.4842i			0.655695i	0.944731	+	0.327847i	$0.106323\pi$
$883$			19.4842i			0.655695i	−0.944731	+	0.327847i	$0.893677\pi$
$884$	18.6132			0.626030
$885$	−13.7773	−	4.63892i	−0.463120	−	0.155936i
$886$	5.46329			0.183543
$887$		−	35.9373i		−	1.20666i	−0.797493	−	0.603328i	$-0.793841\pi$
$887$		−	35.9373i		−	1.20666i	0.797493	−	0.603328i	$-0.206159\pi$
$888$		−	17.3951i		−	0.583742i
$889$	−2.53638			−0.0850674
$890$	15.9635	+	5.37501i	0.535096	+	0.180171i
$891$	0.308470			0.0103341
$892$			24.2116i			0.810666i
$893$		0			0
$894$	4.71237			0.157605
$895$	−8.38680	+	24.9083i	−0.280340	+	0.832592i
$896$	13.1325			0.438725
$897$		−	2.59105i		−	0.0865126i
$898$		−	12.0201i		−	0.401116i
$899$	2.15632			0.0719172
$900$	−13.5729	−	10.3089i	−0.452431	−	0.343631i
$901$	12.7120			0.423499
$902$			1.38802i			0.0462160i
$903$		−	12.3783i		−	0.411924i
$904$	21.8721			0.727455
$905$	−6.30473	+	18.7247i	−0.209576	+	0.622430i
$906$	−3.69933			−0.122902
$907$		−	48.9503i		−	1.62537i	−0.582706	−	0.812683i	$-0.698006\pi$
$907$		−	48.9503i		−	1.62537i	0.582706	−	0.812683i	$-0.301994\pi$
$908$		−	11.7110i		−	0.388644i
$909$	26.9034			0.892330
$910$	−4.82284	−	1.62388i	−0.159876	−	0.0538312i
$911$	−19.7811			−0.655376			−0.327688	−	0.944786i	$-0.606269\pi$
$911$	−19.7811			−0.655376			−0.327688	+	0.944786i	$0.606269\pi$
$912$		0			0
$913$		−	9.88984i		−	0.327306i
$914$	3.26935			0.108141
$915$	10.0403	+	3.38063i	0.331921	+	0.111760i
$916$	1.04145			0.0344103
$917$		−	20.6276i		−	0.681182i
$918$		−	6.16141i		−	0.203357i
$919$	−26.0582			−0.859581			−0.429791	−	0.902929i	$-0.641413\pi$
$919$	−26.0582			−0.859581			−0.429791	+	0.902929i	$0.641413\pi$
$920$	0.772091	−	2.29307i	0.0254551	−	0.0756001i
$921$	21.4618			0.707190
$922$		−	15.3337i		−	0.504988i
$923$			54.0298i			1.77841i
$924$	1.55058			0.0510104
$925$	28.3723	−	37.3554i	0.932874	−	1.22824i
$926$	10.1484			0.333498
$927$		−	6.81602i		−	0.223868i
$928$		−	4.16406i		−	0.136692i
$929$	7.97799			0.261749			0.130875	−	0.991399i	$-0.458221\pi$
$929$	7.97799			0.261749			0.130875	+	0.991399i	$0.458221\pi$
$930$	−0.878825	+	2.61006i	−0.0288178	+	0.0855872i
$931$		0			0
$932$			12.7211i			0.416695i
$933$			25.6505i			0.839761i
$934$	7.99883			0.261730
$935$	3.85939	+	1.29948i	0.126215	+	0.0424976i
$936$	−14.0272			−0.458495
$937$			46.6542i			1.52413i	0.647502	+	0.762063i	$0.275814\pi$
$937$			46.6542i			1.52413i	−0.647502	+	0.762063i	$0.724186\pi$
$938$		−	2.87426i		−	0.0938479i
$939$	−3.63928			−0.118763
$940$	39.6169	+	13.3393i	1.29216	+	0.435080i
$941$	−1.40100			−0.0456713			−0.0228356	−	0.999739i	$-0.507269\pi$
$941$	−1.40100			−0.0456713			−0.0228356	+	0.999739i	$0.507269\pi$
$942$			4.83798i			0.157630i
$943$		−	2.50251i		−	0.0814930i
$944$	16.9594			0.551981
$945$	4.29053	−	12.7426i	0.139571	−	0.414518i
$946$	−3.40880			−0.110830
$947$			38.2501i			1.24296i	0.783430	+	0.621480i	$0.213468\pi$
$947$			38.2501i			1.24296i	−0.783430	+	0.621480i	$0.786532\pi$
$948$		−	11.0253i		−	0.358085i
$949$	50.7900			1.64871
$950$		0			0
$951$	32.6326			1.05819
$952$			5.34738i			0.173309i
$953$		−	54.4390i		−	1.76345i	−0.471763	−	0.881726i	$-0.656382\pi$
$953$		−	54.4390i		−	1.76345i	0.471763	−	0.881726i	$-0.343618\pi$
$954$	−4.50764			−0.145940
$955$	10.1641	−	30.1868i	0.328903	−	0.976823i
$956$	−6.49610			−0.210099
$957$		−	0.637869i		−	0.0206194i
$958$			4.17989i			0.135046i
$959$	−5.96462			−0.192608
$960$	−6.92317	−	2.33108i	−0.223444	−	0.0752353i
$961$	−24.7042			−0.796911
$962$		−	18.1650i		−	0.585662i
$963$			6.96456i			0.224430i
$964$	30.6819			0.988197
$965$	41.3357	+	13.9180i	1.33064	+	0.448037i
$966$	0.350250			0.0112691
$967$			4.98919i			0.160442i	0.996777	+	0.0802208i	$0.0255625\pi$
$967$			4.98919i			0.160442i	−0.996777	+	0.0802208i	$0.974437\pi$
$968$			18.6995i			0.601026i
$969$		0			0
$970$	5.62367	−	16.7020i	0.180565	−	0.536268i
$971$	−14.5401			−0.466614			−0.233307	−	0.972403i	$-0.574955\pi$
$971$	−14.5401			−0.466614			−0.233307	+	0.972403i	$0.574955\pi$
$972$		−	28.0763i		−	0.900548i
$973$		−	7.03091i		−	0.225401i
$974$	14.1861			0.454553
$975$	16.9948	+	12.9079i	0.544268	+	0.413384i
$976$	−12.3592			−0.395609
$977$			26.1353i			0.836141i	0.908415	+	0.418071i	$0.137294\pi$
$977$			26.1353i			0.836141i	−0.908415	+	0.418071i	$0.862706\pi$
$978$		−	0.0337829i		−	0.00108026i
$979$	−11.3905			−0.364043
$980$	7.12524	−	21.1616i	0.227608	−	0.675981i
$981$	11.9347			0.381046
$982$		−	1.46300i		−	0.0466861i
$983$		−	46.1160i		−	1.47087i	−0.677595	−	0.735436i	$-0.736978\pi$
$983$		−	46.1160i		−	1.47087i	0.677595	−	0.735436i	$-0.263022\pi$
$984$	7.64345			0.243664
$985$	9.18089	+	3.09127i	0.292528	+	0.0984961i
$986$	1.03505			0.0329626
$987$			12.8606i			0.409356i
$988$		0			0
$989$	6.14585			0.195427
$990$	−1.36852	−	0.460791i	−0.0434945	−	0.0146449i
$991$	−31.3279			−0.995164			−0.497582	−	0.867417i	$-0.665779\pi$
$991$	−31.3279			−0.995164			−0.497582	+	0.867417i	$0.665779\pi$
$992$		−	12.1577i		−	0.386009i
$993$		−	37.1877i		−	1.18011i
$994$	−7.30357			−0.231655
$995$	9.01304	−	26.7682i	0.285733	−	0.848609i
$996$	−25.6251			−0.811962
$997$		−	21.6144i		−	0.684536i	−0.939602	−	0.342268i	$-0.888805\pi$
$997$		−	21.6144i		−	0.684536i	0.939602	−	0.342268i	$-0.111195\pi$
$998$			15.1659i			0.480069i
$999$	47.9944			1.51848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.f.1084.3		6
5.2	odd	4		9025.2.a.bu.1.4		6
5.3	odd	4		9025.2.a.bu.1.3		6
5.4	even	2	inner	1805.2.b.f.1084.4		6
19.7	even	3		95.2.i.b.49.4	yes	12
19.11	even	3		95.2.i.b.64.3	yes	12
19.18	odd	2		1805.2.b.g.1084.4		6
57.11	odd	6		855.2.be.d.64.4		12
57.26	odd	6		855.2.be.d.334.3		12
95.7	odd	12		475.2.e.g.201.3		12
95.18	even	4		9025.2.a.bt.1.4		6
95.37	even	4		9025.2.a.bt.1.3		6
95.49	even	6		95.2.i.b.64.4	yes	12
95.64	even	6		95.2.i.b.49.3	✓	12
95.68	odd	12		475.2.e.g.26.4		12
95.83	odd	12		475.2.e.g.201.4		12
95.87	odd	12		475.2.e.g.26.3		12
95.94	odd	2		1805.2.b.g.1084.3		6
285.239	odd	6		855.2.be.d.64.3		12
285.254	odd	6		855.2.be.d.334.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.i.b.49.3	✓	12	95.64	even	6
95.2.i.b.49.4	yes	12	19.7	even	3
95.2.i.b.64.3	yes	12	19.11	even	3
95.2.i.b.64.4	yes	12	95.49	even	6
475.2.e.g.26.3		12	95.87	odd	12
475.2.e.g.26.4		12	95.68	odd	12
475.2.e.g.201.3		12	95.7	odd	12
475.2.e.g.201.4		12	95.83	odd	12
855.2.be.d.64.3		12	285.239	odd	6
855.2.be.d.64.4		12	57.11	odd	6
855.2.be.d.334.3		12	57.26	odd	6
855.2.be.d.334.4		12	285.254	odd	6
1805.2.b.f.1084.3		6	1.1	even	1	trivial
1805.2.b.f.1084.4		6	5.4	even	2	inner
1805.2.b.g.1084.3		6	95.94	odd	2
1805.2.b.g.1084.4		6	19.18	odd	2
9025.2.a.bt.1.3		6	95.37	even	4
9025.2.a.bt.1.4		6	95.18	even	4
9025.2.a.bu.1.3		6	5.3	odd	4
9025.2.a.bu.1.4		6	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.471884i q^{2} -1.04022i q^{3} +1.77733 q^{4} +(0.713538 - 2.11917i) q^{5} -0.490864 q^{6} +1.17540i q^{7} -1.78246i q^{8} +1.91794 q^{9} +O(q^{10})\)	\(q-0.471884i q^{2} -1.04022i q^{3} +1.77733 q^{4} +(0.713538 - 2.11917i) q^{5} -0.490864 q^{6} +1.17540i q^{7} -1.78246i q^{8} +1.91794 q^{9} +(-1.00000 - 0.336707i) q^{10} +0.713538 q^{11} -1.84881i q^{12} -4.10315i q^{13} +0.554651 q^{14} +(-2.20440 - 0.742237i) q^{15} +2.71354 q^{16} +2.55233i q^{17} -0.905045i q^{18} +(1.26819 - 3.76645i) q^{20} +1.22267 q^{21} -0.336707i q^{22} +0.607061i q^{23} -1.85415 q^{24} +(-3.98173 - 3.02421i) q^{25} -1.93621 q^{26} -5.11575i q^{27} +2.08907i q^{28} +0.859386 q^{29} +(-0.350250 + 1.04022i) q^{30} +2.50914 q^{31} -4.84539i q^{32} -0.742237i q^{33} +1.20440 q^{34} +(2.49086 + 0.838691i) q^{35} +3.40880 q^{36} +9.38171i q^{37} -4.26819 q^{39} +(-3.77733 - 1.27185i) q^{40} -4.12234 q^{41} -0.576960i q^{42} -10.1239i q^{43} +1.26819 q^{44} +(1.36852 - 4.06443i) q^{45} +0.286462 q^{46} +10.5184i q^{47} -2.82268i q^{48} +5.61844 q^{49} +(-1.42708 + 1.87891i) q^{50} +2.65498 q^{51} -7.29264i q^{52} -4.98057i q^{53} -2.41404 q^{54} +(0.509136 - 1.51211i) q^{55} +2.09510 q^{56} -0.405530i q^{58} +6.24992 q^{59} +(-3.91794 - 1.31920i) q^{60} -4.55465 q^{61} -1.18402i q^{62} +2.25434i q^{63} +3.14061 q^{64} +(-8.69527 - 2.92776i) q^{65} -0.350250 q^{66} -5.18210i q^{67} +4.53632i q^{68} +0.631477 q^{69} +(0.395765 - 1.17540i) q^{70} -13.1679 q^{71} -3.41865i q^{72} +12.3783i q^{73} +4.42708 q^{74} +(-3.14585 + 4.14188i) q^{75} +0.838691i q^{77} +2.01409i q^{78} +5.96345 q^{79} +(1.93621 - 5.75044i) q^{80} +0.432310 q^{81} +1.94527i q^{82} -13.8603i q^{83} +2.17309 q^{84} +(5.40880 + 1.82118i) q^{85} -4.77733 q^{86} -0.893952i q^{87} -1.27185i q^{88} -15.9635 q^{89} +(-1.91794 - 0.645784i) q^{90} +4.82284 q^{91} +1.07894i q^{92} -2.61006i q^{93} +4.96345 q^{94} -5.04028 q^{96} +16.7020i q^{97} -2.65125i q^{98} +1.36852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} + 2 q^{5} + 12 q^{6} - 8 q^{9}+O(q^{10}) \) 6 * q - 2 * q^4 + 2 * q^5 + 12 * q^6 - 8 * q^9	\( 6 q - 2 q^{4} + 2 q^{5} + 12 q^{6} - 8 q^{9} - 6 q^{10} + 2 q^{11} - 22 q^{14} + 4 q^{15} + 14 q^{16} - 20 q^{20} + 20 q^{21} - 2 q^{24} + 6 q^{25} - 22 q^{26} + 12 q^{29} + 6 q^{30} + 30 q^{31} - 10 q^{34} - 14 q^{36} + 2 q^{39} - 10 q^{40} + 12 q^{41} - 20 q^{44} + 30 q^{45} + 4 q^{46} - 2 q^{49} - 4 q^{50} + 40 q^{51} + 4 q^{54} + 18 q^{55} + 46 q^{56} - 20 q^{59} - 4 q^{60} - 2 q^{61} + 12 q^{64} - 20 q^{65} + 6 q^{66} - 18 q^{69} - 46 q^{70} - 2 q^{71} + 22 q^{74} - 28 q^{75} - 24 q^{79} + 22 q^{80} + 14 q^{81} - 48 q^{84} - 2 q^{85} - 16 q^{86} - 36 q^{89} + 8 q^{90} - 24 q^{91} - 30 q^{94} + 26 q^{96} + 30 q^{99}+O(q^{100}) \) 6 * q - 2 * q^4 + 2 * q^5 + 12 * q^6 - 8 * q^9 - 6 * q^10 + 2 * q^11 - 22 * q^14 + 4 * q^15 + 14 * q^16 - 20 * q^20 + 20 * q^21 - 2 * q^24 + 6 * q^25 - 22 * q^26 + 12 * q^29 + 6 * q^30 + 30 * q^31 - 10 * q^34 - 14 * q^36 + 2 * q^39 - 10 * q^40 + 12 * q^41 - 20 * q^44 + 30 * q^45 + 4 * q^46 - 2 * q^49 - 4 * q^50 + 40 * q^51 + 4 * q^54 + 18 * q^55 + 46 * q^56 - 20 * q^59 - 4 * q^60 - 2 * q^61 + 12 * q^64 - 20 * q^65 + 6 * q^66 - 18 * q^69 - 46 * q^70 - 2 * q^71 + 22 * q^74 - 28 * q^75 - 24 * q^79 + 22 * q^80 + 14 * q^81 - 48 * q^84 - 2 * q^85 - 16 * q^86 - 36 * q^89 + 8 * q^90 - 24 * q^91 - 30 * q^94 + 26 * q^96 + 30 * q^99

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