LMFDB - Embedded newform 252.2.i.b.25.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(25,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.i (of order $3$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.7
Root			$-0.674693 + 1.59524i$ of defining polynomial
Character	$\chi$	$=$	252.25
Dual form			252.2.i.b.121.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71886 - 0.213318i) q^{3} +(-2.07260 + 3.58985i) q^{5} +(2.19013 - 1.48437i) q^{7} +(2.90899 - 0.733330i) q^{9} +O(q^{10})$	\(q+(1.71886 - 0.213318i) q^{3} +(-2.07260 + 3.58985i) q^{5} +(2.19013 - 1.48437i) q^{7} +(2.90899 - 0.733330i) q^{9} +(-0.434429 - 0.752453i) q^{11} +(2.86231 + 4.95766i) q^{13} +(-2.79674 + 6.61258i) q^{15} +(-1.44613 + 2.50478i) q^{17} +(-2.00703 - 3.47627i) q^{19} +(3.44789 - 3.01862i) q^{21} +(2.91488 - 5.04873i) q^{23} +(-6.09133 - 10.5505i) q^{25} +(4.84373 - 1.88104i) q^{27} +(-0.900417 + 1.55957i) q^{29} -2.96091 q^{31} +(-0.907237 - 1.20069i) q^{33} +(0.789399 + 10.9387i) q^{35} +(-2.64925 - 4.58864i) q^{37} +(5.97748 + 7.91097i) q^{39} +(-5.89325 - 10.2074i) q^{41} +(-2.00703 + 3.47627i) q^{43} +(-3.39663 + 11.9627i) q^{45} +2.34436 q^{47} +(2.59331 - 6.50190i) q^{49} +(-1.95139 + 4.61386i) q^{51} +(-1.09116 + 1.88995i) q^{53} +3.60159 q^{55} +(-4.19136 - 5.54711i) q^{57} -3.05430 q^{59} +5.63318 q^{61} +(5.28253 - 5.92410i) q^{63} -23.7297 q^{65} -2.51078 q^{67} +(3.93331 - 9.29988i) q^{69} -1.09143 q^{71} +(0.723285 - 1.25277i) q^{73} +(-12.7208 - 16.8355i) q^{75} +(-2.06837 - 1.00312i) q^{77} -2.12928 q^{79} +(7.92445 - 4.26650i) q^{81} +(2.18784 - 3.78946i) q^{83} +(-5.99451 - 10.3828i) q^{85} +(-1.21501 + 2.87276i) q^{87} +(5.83373 + 10.1043i) q^{89} +(13.6278 + 6.60919i) q^{91} +(-5.08940 + 0.631616i) q^{93} +16.6391 q^{95} +(-3.98779 + 6.90706i) q^{97} +(-1.81555 - 1.87030i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	$ 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) $ 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.71886	−	0.213318i	0.992387	−	0.123159i
$3$	1.71886	−	0.213318i	0.992387	−	0.123159i
$4$		0			0
$5$	−2.07260	+	3.58985i	−0.926894	+	1.60543i	−0.138409	+	0.990375i	$0.544199\pi$
$5$	−2.07260	+	3.58985i	−0.926894	+	1.60543i	−0.788486	+	0.615053i	$0.789135\pi$
$6$		0			0
$7$	2.19013	−	1.48437i	0.827790	−	0.561038i
$7$	2.19013	−	1.48437i	0.827790	−	0.561038i
$8$		0			0
$9$	2.90899	−	0.733330i	0.969664	−	0.244443i
$10$		0			0
$11$	−0.434429	−	0.752453i	−0.130985	−	0.226873i	0.793071	−	0.609129i	$-0.208481\pi$
$11$	−0.434429	−	0.752453i	−0.130985	−	0.226873i	−0.924057	+	0.382256i	$0.875147\pi$
$12$		0			0
$13$	2.86231	+	4.95766i	0.793861	+	1.37501i	0.923560	+	0.383455i	$0.125266\pi$
$13$	2.86231	+	4.95766i	0.793861	+	1.37501i	−0.129698	+	0.991554i	$0.541401\pi$
$14$		0			0
$15$	−2.79674	+	6.61258i	−0.722115	+	1.70736i
$16$		0			0
$17$	−1.44613	+	2.50478i	−0.350739	+	0.607498i	−0.986379	−	0.164488i	$-0.947403\pi$
$17$	−1.44613	+	2.50478i	−0.350739	+	0.607498i	0.635640	+	0.771986i	$0.280736\pi$
$18$		0			0
$19$	−2.00703	−	3.47627i	−0.460444	−	0.797512i	0.538539	−	0.842600i	$-0.318976\pi$
$19$	−2.00703	−	3.47627i	−0.460444	−	0.797512i	−0.998983	+	0.0450884i	$0.985643\pi$
$20$		0			0
$21$	3.44789	−	3.01862i	0.752391	−	0.658717i
$22$		0			0
$23$	2.91488	−	5.04873i	0.607795	−	1.05273i	−0.383808	−	0.923413i	$-0.625387\pi$
$23$	2.91488	−	5.04873i	0.607795	−	1.05273i	0.991603	−	0.129319i	$-0.0412792\pi$
$24$		0			0
$25$	−6.09133	−	10.5505i	−1.21827	−	2.11010i
$26$		0			0
$27$	4.84373	−	1.88104i	0.932176	−	0.362005i
$28$		0			0
$29$	−0.900417	+	1.55957i	−0.167203	+	0.289604i	−0.937435	−	0.348159i	$-0.886807\pi$
$29$	−0.900417	+	1.55957i	−0.167203	+	0.289604i	0.770232	+	0.637763i	$0.220140\pi$
$30$		0			0
$31$	−2.96091			−0.531795			−0.265898	−	0.964001i	$-0.585668\pi$
$31$	−2.96091			−0.531795			−0.265898	+	0.964001i	$0.585668\pi$
$32$		0			0
$33$	−0.907237	−	1.20069i	−0.157930	−	0.209014i
$34$		0			0
$35$	0.789399	+	10.9387i	0.133433	+	1.84898i
$36$		0			0
$37$	−2.64925	−	4.58864i	−0.435535	−	0.754368i	0.561804	−	0.827270i	$-0.310107\pi$
$37$	−2.64925	−	4.58864i	−0.435535	−	0.754368i	−0.997339	+	0.0729017i	$0.976774\pi$
$38$		0			0
$39$	5.97748	+	7.91097i	0.957163	+	1.26677i
$40$		0			0
$41$	−5.89325	−	10.2074i	−0.920371	−	1.59413i	−0.798842	−	0.601541i	$-0.794554\pi$
$41$	−5.89325	−	10.2074i	−0.920371	−	1.59413i	−0.121528	−	0.992588i	$-0.538780\pi$
$42$		0			0
$43$	−2.00703	+	3.47627i	−0.306069	+	0.530127i	−0.977499	−	0.210941i	$-0.932347\pi$
$43$	−2.00703	+	3.47627i	−0.306069	+	0.530127i	0.671430	+	0.741068i	$0.265680\pi$
$44$		0			0
$45$	−3.39663	+	11.9627i	−0.506340	+	1.78330i
$46$		0			0
$47$	2.34436			0.341961			0.170980	−	0.985274i	$-0.445307\pi$
$47$	2.34436			0.341961			0.170980	+	0.985274i	$0.445307\pi$
$48$		0			0
$49$	2.59331	−	6.50190i	0.370472	−	0.928844i
$50$		0			0
$51$	−1.95139	+	4.61386i	−0.273250	+	0.646070i
$52$		0			0
$53$	−1.09116	+	1.88995i	−0.149883	+	0.259605i	−0.931184	−	0.364549i	$-0.881223\pi$
$53$	−1.09116	+	1.88995i	−0.149883	+	0.259605i	0.781301	+	0.624154i	$0.214556\pi$
$54$		0			0
$55$	3.60159			0.485638
$56$		0			0
$57$	−4.19136	−	5.54711i	−0.555159	−	0.734733i
$58$		0			0
$59$	−3.05430			−0.397636			−0.198818	−	0.980036i	$-0.563710\pi$
$59$	−3.05430			−0.397636			−0.198818	+	0.980036i	$0.563710\pi$
$60$		0			0
$61$	5.63318			0.721255			0.360628	−	0.932710i	$-0.382563\pi$
$61$	5.63318			0.721255			0.360628	+	0.932710i	$0.382563\pi$
$62$		0			0
$63$	5.28253	−	5.92410i	0.665536	−	0.746366i
$64$		0			0
$65$	−23.7297			−2.94330
$66$		0			0
$67$	−2.51078			−0.306740			−0.153370	−	0.988169i	$-0.549013\pi$
$67$	−2.51078			−0.306740			−0.153370	+	0.988169i	$0.549013\pi$
$68$		0			0
$69$	3.93331	−	9.29988i	0.473514	−	1.11957i
$70$		0			0
$71$	−1.09143			−0.129529			−0.0647647	−	0.997901i	$-0.520630\pi$
$71$	−1.09143			−0.129529			−0.0647647	+	0.997901i	$0.520630\pi$
$72$		0			0
$73$	0.723285	−	1.25277i	0.0846541	−	0.146625i	−0.820590	−	0.571518i	$-0.806355\pi$
$73$	0.723285	−	1.25277i	0.0846541	−	0.146625i	0.905244	+	0.424893i	$0.139688\pi$
$74$		0			0
$75$	−12.7208	−	16.8355i	−1.46887	−	1.94399i
$76$		0			0
$77$	−2.06837	−	1.00312i	−0.235713	−	0.114316i
$78$		0			0
$79$	−2.12928			−0.239563			−0.119781	−	0.992800i	$-0.538219\pi$
$79$	−2.12928			−0.239563			−0.119781	+	0.992800i	$0.538219\pi$
$80$		0			0
$81$	7.92445	−	4.26650i	0.880495	−	0.474055i
$82$		0			0
$83$	2.18784	−	3.78946i	0.240147	−	0.415947i	−0.720609	−	0.693342i	$-0.756138\pi$
$83$	2.18784	−	3.78946i	0.240147	−	0.415947i	0.960756	+	0.277395i	$0.0894710\pi$
$84$		0			0
$85$	−5.99451	−	10.3828i	−0.650196	−	1.12617i
$86$		0			0
$87$	−1.21501	+	2.87276i	−0.130263	+	0.307992i
$88$		0			0
$89$	5.83373	+	10.1043i	0.618374	+	1.07105i	0.989783	+	0.142585i	$0.0455415\pi$
$89$	5.83373	+	10.1043i	0.618374	+	1.07105i	−0.371409	+	0.928469i	$0.621125\pi$
$90$		0			0
$91$	13.6278	+	6.60919i	1.42858	+	0.692831i
$92$		0			0
$93$	−5.08940	+	0.631616i	−0.527747	+	0.0654955i
$94$		0			0
$95$	16.6391			1.70713
$96$		0			0
$97$	−3.98779	+	6.90706i	−0.404899	+	0.701306i	−0.994310	−	0.106528i	$-0.966027\pi$
$97$	−3.98779	+	6.90706i	−0.404899	+	0.701306i	0.589411	+	0.807834i	$0.299360\pi$
$98$		0			0
$99$	−1.81555	−	1.87030i	−0.182469	−	0.187972i
$100$		0			0
$101$	1.88185	+	3.25946i	0.187251	+	0.324329i	0.944333	−	0.328992i	$-0.106709\pi$
$101$	1.88185	+	3.25946i	0.187251	+	0.324329i	−0.757082	+	0.653320i	$0.773376\pi$
$102$		0			0
$103$	−5.42778	+	9.40119i	−0.534815	+	0.926327i	0.464357	+	0.885648i	$0.346285\pi$
$103$	−5.42778	+	9.40119i	−0.534815	+	0.926327i	−0.999172	+	0.0406786i	$0.987048\pi$
$104$		0			0
$105$	3.69030	+	18.6338i	0.360136	+	1.81847i
$106$		0			0
$107$	−4.82343	−	8.35442i	−0.466298	−	0.807653i	0.532961	−	0.846140i	$-0.321079\pi$
$107$	−4.82343	−	8.35442i	−0.466298	−	0.807653i	−0.999259	+	0.0384875i	$0.987746\pi$
$108$		0			0
$109$	−5.86131	+	10.1521i	−0.561412	+	0.972394i	0.435962	+	0.899965i	$0.356408\pi$
$109$	−5.86131	+	10.1521i	−0.561412	+	0.972394i	−0.997374	+	0.0724288i	$0.976925\pi$
$110$		0			0
$111$	−5.53255	−	7.32212i	−0.525127	−	0.694985i
$112$		0			0
$113$	2.88981	+	5.00530i	0.271851	+	0.470859i	0.969336	−	0.245740i	$-0.0790310\pi$
$113$	2.88981	+	5.00530i	0.271851	+	0.470859i	−0.697485	+	0.716599i	$0.745698\pi$
$114$		0			0
$115$	12.0828	+	20.9280i	1.12672	+	1.95154i
$116$		0			0
$117$	11.9620	+	12.3228i	1.10589	+	1.13924i
$118$		0			0
$119$	0.550795	+	7.63237i	0.0504913	+	0.699659i
$120$		0			0
$121$	5.12254	−	8.87250i	0.465686	−	0.806591i
$122$		0			0
$123$	−12.3071	−	16.2880i	−1.10970	−	1.46864i
$124$		0			0
$125$	29.7736			2.66303
$126$		0			0
$127$	6.47468			0.574535			0.287268	−	0.957850i	$-0.407253\pi$
$127$	6.47468			0.574535			0.287268	+	0.957850i	$0.407253\pi$
$128$		0			0
$129$	−2.70826	+	6.40338i	−0.238449	+	0.563786i
$130$		0			0
$131$	8.86514	−	15.3549i	0.774551	−	1.34156i	−0.160495	−	0.987037i	$-0.551309\pi$
$131$	8.86514	−	15.3549i	0.774551	−	1.34156i	0.935046	−	0.354525i	$-0.115357\pi$
$132$		0			0
$133$	−9.55571	−	4.63431i	−0.828585	−	0.401846i
$134$		0			0
$135$	−3.28648	+	21.2869i	−0.282855	+	1.83208i
$136$		0			0
$137$	−1.36116	−	2.35760i	−0.116292	−	0.201423i	0.802004	−	0.597319i	$-0.203767\pi$
$137$	−1.36116	−	2.35760i	−0.116292	−	0.201423i	−0.918295	+	0.395896i	$0.870434\pi$
$138$		0			0
$139$	8.65431	+	14.9897i	0.734049	+	1.27141i	0.955139	+	0.296157i	$0.0957051\pi$
$139$	8.65431	+	14.9897i	0.734049	+	1.27141i	−0.221090	+	0.975253i	$0.570962\pi$
$140$		0			0
$141$	4.02964	−	0.500095i	0.339357	−	0.0421156i
$142$		0			0
$143$	2.48694	−	4.30751i	0.207968	−	0.360212i
$144$		0			0
$145$	−3.73241	−	6.46472i	−0.309959	−	0.536865i
$146$		0			0
$147$	3.07057	−	11.7291i	0.253256	−	0.967399i
$148$		0			0
$149$	3.42343	−	5.92955i	0.280458	−	0.485767i	−0.691040	−	0.722817i	$-0.742847\pi$
$149$	3.42343	−	5.92955i	0.280458	−	0.485767i	0.971498	+	0.237049i	$0.0761803\pi$
$150$		0			0
$151$	−4.64083	−	8.03816i	−0.377666	−	0.654136i	0.613057	−	0.790039i	$-0.289940\pi$
$151$	−4.64083	−	8.03816i	−0.377666	−	0.654136i	−0.990722	+	0.135903i	$0.956606\pi$
$152$		0			0
$153$	−2.36996	+	8.34687i	−0.191600	+	0.674804i
$154$		0			0
$155$	6.13678	−	10.6292i	0.492918	−	0.853759i
$156$		0			0
$157$	13.6768			1.09153			0.545764	−	0.837939i	$-0.316240\pi$
$157$	13.6768			1.09153			0.545764	+	0.837939i	$0.316240\pi$
$158$		0			0
$159$	−1.47240	+	3.48134i	−0.116769	+	0.276088i
$160$		0			0
$161$	−1.11020	−	15.3841i	−0.0874963	−	1.21244i
$162$		0			0
$163$	−1.65003	−	2.85793i	−0.129240	−	0.223850i	0.794142	−	0.607732i	$-0.207920\pi$
$163$	−1.65003	−	2.85793i	−0.129240	−	0.223850i	−0.923382	+	0.383882i	$0.874587\pi$
$164$		0			0
$165$	6.19064	−	0.768284i	0.481941	−	0.0598108i
$166$		0			0
$167$	5.96228	+	10.3270i	0.461375	+	0.799125i	0.999030	−	0.0440399i	$-0.0140229\pi$
$167$	5.96228	+	10.3270i	0.461375	+	0.799125i	−0.537655	+	0.843165i	$0.680690\pi$
$168$		0			0
$169$	−9.88562	+	17.1224i	−0.760432	+	1.31711i
$170$		0			0
$171$	−8.38768	−	8.64064i	−0.641422	−	0.660766i
$172$		0			0
$173$	−9.63389			−0.732451			−0.366225	−	0.930526i	$-0.619350\pi$
$173$	−9.63389			−0.732451			−0.366225	+	0.930526i	$0.619350\pi$
$174$		0			0
$175$	−29.0016	−	14.0651i	−2.19231	−	1.06322i
$176$		0			0
$177$	−5.24993	+	0.651538i	−0.394609	+	0.0489726i
$178$		0			0
$179$	−11.5285	+	19.9680i	−0.861682	+	1.49248i	0.00862183	+	0.999963i	$0.497256\pi$
$179$	−11.5285	+	19.9680i	−0.861682	+	1.49248i	−0.870304	+	0.492515i	$0.836078\pi$
$180$		0			0
$181$	−11.8325			−0.879504			−0.439752	−	0.898119i	$-0.644934\pi$
$181$	−11.8325			−0.879504			−0.439752	+	0.898119i	$0.644934\pi$
$182$		0			0
$183$	9.68268	−	1.20166i	0.715764	−	0.0888292i
$184$		0			0
$185$	21.9634			1.61478
$186$		0			0
$187$	2.51297			0.183767
$188$		0			0
$189$	7.81623	−	11.3096i	0.568547	−	0.822651i
$190$		0			0
$191$	−6.28508			−0.454772			−0.227386	−	0.973805i	$-0.573018\pi$
$191$	−6.28508			−0.454772			−0.227386	+	0.973805i	$0.573018\pi$
$192$		0			0
$193$	13.7312			0.988392			0.494196	−	0.869351i	$-0.335463\pi$
$193$	13.7312			0.988392			0.494196	+	0.869351i	$0.335463\pi$
$194$		0			0
$195$	−40.7881	+	5.06197i	−2.92090	+	0.362495i
$196$		0			0
$197$	−0.161495			−0.0115061			−0.00575303	−	0.999983i	$-0.501831\pi$
$197$	−0.161495			−0.0115061			−0.00575303	+	0.999983i	$0.501831\pi$
$198$		0			0
$199$	−12.4140	+	21.5016i	−0.880003	+	1.52421i	−0.0286672	+	0.999589i	$0.509126\pi$
$199$	−12.4140	+	21.5016i	−0.880003	+	1.52421i	−0.851336	+	0.524621i	$0.824207\pi$
$200$		0			0
$201$	−4.31569	+	0.535594i	−0.304405	+	0.0377779i
$202$		0			0
$203$	0.342945	+	4.75220i	0.0240700	+	0.333539i
$204$		0			0
$205$	48.8573			3.41235
$206$		0			0
$207$	4.77699	−	16.8243i	0.332024	−	1.16937i
$208$		0			0
$209$	−1.74382	+	3.02039i	−0.120623	+	0.208925i
$210$		0			0
$211$	9.44607	+	16.3611i	0.650295	+	1.12634i	0.983051	+	0.183331i	$0.0586879\pi$
$211$	9.44607	+	16.3611i	0.650295	+	1.12634i	−0.332757	+	0.943013i	$0.607979\pi$
$212$		0			0
$213$	−1.87603	+	0.232823i	−0.128543	+	0.0159527i
$214$		0			0
$215$	−8.31953	−	14.4098i	−0.567387	−	0.982743i
$216$		0			0
$217$	−6.48477	+	4.39508i	−0.440215	+	0.298357i
$218$		0			0
$219$	0.975992	−	2.30763i	0.0659514	−	0.155935i
$220$		0			0
$221$	−16.5571			−1.11375
$222$		0			0
$223$	7.04717	−	12.2061i	0.471914	−	0.817378i	−0.527570	−	0.849512i	$-0.676897\pi$
$223$	7.04717	−	12.2061i	0.471914	−	0.817378i	0.999484	+	0.0321333i	$0.0102301\pi$
$224$		0			0
$225$	−25.4566	−	26.2243i	−1.69711	−	1.74829i
$226$		0			0
$227$	−12.9891	−	22.4978i	−0.862118	−	1.49323i	−0.869881	−	0.493262i	$-0.835804\pi$
$227$	−12.9891	−	22.4978i	−0.862118	−	1.49323i	0.00776306	−	0.999970i	$-0.497529\pi$
$228$		0			0
$229$	−12.4579	+	21.5777i	−0.823239	+	1.42589i	0.0800190	+	0.996793i	$0.474502\pi$
$229$	−12.4579	+	21.5777i	−0.823239	+	1.42589i	−0.903258	+	0.429098i	$0.858831\pi$
$230$		0			0
$231$	−3.76923	−	1.28300i	−0.247997	−	0.0844151i
$232$		0			0
$233$	−3.05923	−	5.29874i	−0.200417	−	0.347132i	0.748246	−	0.663421i	$-0.230896\pi$
$233$	−3.05923	−	5.29874i	−0.200417	−	0.347132i	−0.948663	+	0.316289i	$0.897563\pi$
$234$		0			0
$235$	−4.85893	+	8.41591i	−0.316961	+	0.548993i
$236$		0			0
$237$	−3.65995	+	0.454214i	−0.237739	+	0.0295044i
$238$		0			0
$239$	−7.71988	−	13.3712i	−0.499357	−	0.864912i	0.500643	−	0.865654i	$-0.333097\pi$
$239$	−7.71988	−	13.3712i	−0.499357	−	0.864912i	−1.00000		0.000742080i	$0.999764\pi$
$240$		0			0
$241$	−4.92259	−	8.52617i	−0.317092	−	0.549219i	0.662788	−	0.748807i	$-0.269373\pi$
$241$	−4.92259	−	8.52617i	−0.317092	−	0.549219i	−0.979880	+	0.199588i	$0.936040\pi$
$242$		0			0
$243$	12.7109	−	9.02396i	0.815407	−	0.578888i
$244$		0			0
$245$	17.9660	+	22.7854i	1.14780	+	1.45571i
$246$		0			0
$247$	11.4895	−	19.9003i	0.731057	−	1.26623i
$248$		0			0
$249$	2.95225	−	6.98027i	0.187091	−	0.442357i
$250$		0			0
$251$	26.8843			1.69692			0.848461	−	0.529258i	$-0.177530\pi$
$251$	26.8843			1.69692			0.848461	+	0.529258i	$0.177530\pi$
$252$		0			0
$253$	−5.06524			−0.318449
$254$		0			0
$255$	−12.5186	−	16.5679i	−0.783945	−	1.03752i
$256$		0			0
$257$	−5.50636	+	9.53729i	−0.343477	+	0.594920i	−0.985076	−	0.172121i	$-0.944938\pi$
$257$	−5.50636	+	9.53729i	−0.343477	+	0.594920i	0.641599	+	0.767040i	$0.278271\pi$
$258$		0			0
$259$	−12.6134	−	6.11724i	−0.783761	−	0.380107i
$260$		0			0
$261$	−1.47563	+	5.19707i	−0.0913390	+	0.321691i
$262$		0			0
$263$	3.65547	+	6.33146i	0.225406	+	0.390415i	0.956441	−	0.291925i	$-0.0942958\pi$
$263$	3.65547	+	6.33146i	0.225406	+	0.390415i	−0.731035	+	0.682340i	$0.760962\pi$
$264$		0			0
$265$	−4.52309	−	7.83423i	−0.277851	−	0.481253i
$266$		0			0
$267$	12.1828	+	16.1235i	0.745576	+	0.986742i
$268$		0			0
$269$	−2.08048	+	3.60349i	−0.126849	+	0.219709i	−0.922454	−	0.386107i	$-0.873820\pi$
$269$	−2.08048	+	3.60349i	−0.126849	+	0.219709i	0.795605	+	0.605815i	$0.207153\pi$
$270$		0			0
$271$	−4.18300	−	7.24516i	−0.254099	−	0.440112i	0.710551	−	0.703645i	$-0.248446\pi$
$271$	−4.18300	−	7.24516i	−0.254099	−	0.440112i	−0.964650	+	0.263533i	$0.915112\pi$
$272$		0			0
$273$	24.8342	+	8.45325i	1.50304	+	0.511614i
$274$		0			0
$275$	−5.29250	+	9.16689i	−0.319150	+	0.552784i
$276$		0			0
$277$	1.39928	+	2.42362i	0.0840745	+	0.145621i	0.904996	−	0.425419i	$-0.139873\pi$
$277$	1.39928	+	2.42362i	0.0840745	+	0.145621i	−0.820922	+	0.571040i	$0.806540\pi$
$278$		0			0
$279$	−8.61326	+	2.17132i	−0.515662	+	0.129994i
$280$		0			0
$281$	−5.44314	+	9.42779i	−0.324710	+	0.562415i	−0.981454	−	0.191699i	$-0.938600\pi$
$281$	−5.44314	+	9.42779i	−0.324710	+	0.562415i	0.656743	+	0.754114i	$0.271933\pi$
$282$		0			0
$283$	−2.02424			−0.120328			−0.0601642	−	0.998188i	$-0.519162\pi$
$283$	−2.02424			−0.120328			−0.0601642	+	0.998188i	$0.519162\pi$
$284$		0			0
$285$	28.6003	−	3.54941i	1.69413	−	0.210249i
$286$		0			0
$287$	−28.0585	−	13.6078i	−1.65624	−	0.803241i
$288$		0			0
$289$	4.31739	+	7.47794i	0.253964	+	0.439879i
$290$		0			0
$291$	−5.38108	+	12.7230i	−0.315444	+	0.745834i
$292$		0			0
$293$	−9.65448	−	16.7220i	−0.564021	−	0.976912i	−0.997140	−	0.0755757i	$-0.975921\pi$
$293$	−9.65448	−	16.7220i	−0.564021	−	0.976912i	0.433120	−	0.901336i	$-0.357413\pi$
$294$		0			0
$295$	6.33035	−	10.9645i	0.368567	−	0.638377i
$296$		0			0
$297$	−3.51965	−	2.82750i	−0.204231	−	0.164068i
$298$		0			0
$299$	33.3732			1.93002
$300$		0			0
$301$	0.764425	+	10.5926i	0.0440607	+	0.610550i
$302$		0			0
$303$	3.92995	+	5.20114i	0.225770	+	0.298798i
$304$		0			0
$305$	−11.6753	+	20.2223i	−0.668527	+	1.15792i
$306$		0			0
$307$	−13.1378			−0.749813			−0.374907	−	0.927063i	$-0.622325\pi$
$307$	−13.1378			−0.749813			−0.374907	+	0.927063i	$0.622325\pi$
$308$		0			0
$309$	−7.32417	+	17.3172i	−0.416658	+	0.985142i
$310$		0			0
$311$	−13.5321			−0.767336			−0.383668	−	0.923471i	$-0.625339\pi$
$311$	−13.5321			−0.767336			−0.383668	+	0.923471i	$0.625339\pi$
$312$		0			0
$313$	−25.2000			−1.42439			−0.712194	−	0.701983i	$-0.752298\pi$
$313$	−25.2000			−1.42439			−0.712194	+	0.701983i	$0.752298\pi$
$314$		0			0
$315$	10.3180	+	31.2417i	0.581356	+	1.76027i
$316$		0			0
$317$	−12.2978			−0.690711			−0.345356	−	0.938472i	$-0.612242\pi$
$317$	−12.2978			−0.690711			−0.345356	+	0.938472i	$0.612242\pi$
$318$		0			0
$319$	1.56467			0.0876047
$320$		0			0
$321$	−10.0730	−	13.3312i	−0.562218	−	0.744075i
$322$		0			0
$323$	11.6097			0.645982
$324$		0			0
$325$	34.8705	−	60.3975i	1.93427	−	3.35025i
$326$		0			0
$327$	−7.90918	+	18.7004i	−0.437379	+	1.03413i
$328$		0			0
$329$	5.13445	−	3.47990i	0.283072	−	0.191853i
$330$		0			0
$331$	−19.9257			−1.09522			−0.547608	−	0.836735i	$-0.684461\pi$
$331$	−19.9257			−1.09522			−0.547608	+	0.836735i	$0.684461\pi$
$332$		0			0
$333$	−11.0716	−	11.4055i	−0.606723	−	0.625020i
$334$		0			0
$335$	5.20383	−	9.01330i	0.284316	−	0.492449i
$336$		0			0
$337$	−0.966380	−	1.67382i	−0.0526421	−	0.0911788i	0.838504	−	0.544896i	$-0.183431\pi$
$337$	−0.966380	−	1.67382i	−0.0526421	−	0.0911788i	−0.891146	+	0.453717i	$0.850098\pi$
$338$		0			0
$339$	6.03492	+	7.98698i	0.327772	+	0.433793i
$340$		0			0
$341$	1.28631	+	2.22795i	0.0696574	+	0.120650i
$342$		0			0
$343$	−3.97155	−	18.0894i	−0.214444	−	0.976736i
$344$		0			0
$345$	25.2330	+	33.3949i	1.35850	+	1.79792i
$346$		0			0
$347$	16.9648			0.910720			0.455360	−	0.890307i	$-0.349511\pi$
$347$	16.9648			0.910720			0.455360	+	0.890307i	$0.349511\pi$
$348$		0			0
$349$	−6.25767	+	10.8386i	−0.334966	+	0.580177i	−0.983478	−	0.181027i	$-0.942058\pi$
$349$	−6.25767	+	10.8386i	−0.334966	+	0.580177i	0.648513	+	0.761204i	$0.275391\pi$
$350$		0			0
$351$	23.1898	+	18.6295i	1.23778	+	0.994368i
$352$		0			0
$353$	−16.1929	−	28.0468i	−0.861859	−	1.49278i	−0.870133	−	0.492817i	$-0.835967\pi$
$353$	−16.1929	−	28.0468i	−0.861859	−	1.49278i	0.00827416	−	0.999966i	$-0.497366\pi$
$354$		0			0
$355$	2.26211	−	3.91808i	0.120060	−	0.207950i
$356$		0			0
$357$	2.57486	+	13.0015i	0.136276	+	0.688113i
$358$		0			0
$359$	8.98559	+	15.5635i	0.474242	+	0.821410i	0.999565	−	0.0294922i	$-0.00938902\pi$
$359$	8.98559	+	15.5635i	0.474242	+	0.821410i	−0.525323	+	0.850903i	$0.676056\pi$
$360$		0			0
$361$	1.44368	−	2.50052i	0.0759830	−	0.131606i
$362$		0			0
$363$	6.91229	−	16.3434i	0.362801	−	0.857804i
$364$		0			0
$365$	2.99816	+	5.19297i	0.156931	+	0.271812i
$366$		0			0
$367$	−4.08420	−	7.07404i	−0.213194	−	0.369262i	0.739519	−	0.673136i	$-0.235053\pi$
$367$	−4.08420	−	7.07404i	−0.213194	−	0.369262i	−0.952712	+	0.303874i	$0.901720\pi$
$368$		0			0
$369$	−24.6288	−	25.3715i	−1.28212	−	1.32079i
$370$		0			0
$371$	0.415596	+	5.75892i	0.0215767	+	0.298988i
$372$		0			0
$373$	2.58080	−	4.47008i	0.133629	−	0.231452i	−0.791444	−	0.611242i	$-0.790670\pi$
$373$	2.58080	−	4.47008i	0.133629	−	0.231452i	0.925073	+	0.379790i	$0.124004\pi$
$374$		0			0
$375$	51.1767	−	6.35124i	2.64275	−	0.327977i
$376$		0			0
$377$	−10.3091			−0.530945
$378$		0			0
$379$	21.0017			1.07878			0.539392	−	0.842055i	$-0.318654\pi$
$379$	21.0017			1.07878			0.539392	+	0.842055i	$0.318654\pi$
$380$		0			0
$381$	11.1291	−	1.38117i	0.570161	−	0.0707593i
$382$		0			0
$383$	−14.7794	+	25.5988i	−0.755194	+	1.30804i	0.190083	+	0.981768i	$0.439124\pi$
$383$	−14.7794	+	25.5988i	−0.755194	+	1.30804i	−0.945278	+	0.326267i	$0.894209\pi$
$384$		0			0
$385$	7.88794	−	5.34608i	0.402006	−	0.272462i
$386$		0			0
$387$	−3.28917	+	11.5843i	−0.167198	+	0.588861i
$388$		0			0
$389$	8.26895	+	14.3222i	0.419252	+	0.726166i	0.995864	−	0.0908518i	$-0.0289589\pi$
$389$	8.26895	+	14.3222i	0.419252	+	0.726166i	−0.576612	+	0.817018i	$0.695626\pi$
$390$		0			0
$391$	8.43063	+	14.6023i	0.426355	+	0.738469i
$392$		0			0
$393$	11.9625	−	28.2840i	0.603429	−	1.42674i
$394$		0			0
$395$	4.41315	−	7.64379i	0.222049	−	0.384601i
$396$		0			0
$397$	15.4394	+	26.7418i	0.774881	+	1.34213i	0.934861	+	0.355014i	$0.115524\pi$
$397$	15.4394	+	26.7418i	0.774881	+	1.34213i	−0.159980	+	0.987120i	$0.551143\pi$
$398$		0			0
$399$	−17.4136	−	5.92735i	−0.871768	−	0.296739i
$400$		0			0
$401$	−5.31614	+	9.20782i	−0.265475	+	0.459817i	−0.967688	−	0.252150i	$-0.918862\pi$
$401$	−5.31614	+	9.20782i	−0.265475	+	0.459817i	0.702213	+	0.711967i	$0.252196\pi$
$402$		0			0
$403$	−8.47504	−	14.6792i	−0.422172	−	0.731223i
$404$		0			0
$405$	−1.10814	+	37.2903i	−0.0550638	+	1.85297i
$406$		0			0
$407$	−2.30183	+	3.98688i	−0.114097	+	0.197622i
$408$		0			0
$409$	−14.7956			−0.731598			−0.365799	−	0.930694i	$-0.619204\pi$
$409$	−14.7956			−0.731598			−0.365799	+	0.930694i	$0.619204\pi$
$410$		0			0
$411$	−2.84257	−	3.76203i	−0.140214	−	0.185567i
$412$		0			0
$413$	−6.68931	+	4.53371i	−0.329159	+	0.223089i
$414$		0			0
$415$	9.06904	+	15.7080i	0.445182	+	0.771078i
$416$		0			0
$417$	18.0732	+	23.9191i	0.885046	+	1.17133i
$418$		0			0
$419$	−1.56134	−	2.70432i	−0.0762765	−	0.132115i	0.825364	−	0.564601i	$-0.190970\pi$
$419$	−1.56134	−	2.70432i	−0.0762765	−	0.132115i	−0.901641	+	0.432486i	$0.857637\pi$
$420$		0			0
$421$	−0.644580	+	1.11645i	−0.0314149	+	0.0544122i	−0.881305	−	0.472547i	$-0.843335\pi$
$421$	−0.644580	+	1.11645i	−0.0314149	+	0.0544122i	0.849891	+	0.526959i	$0.176668\pi$
$422$		0			0
$423$	6.81973	−	1.71919i	0.331587	−	0.0835900i
$424$		0			0
$425$	35.2355			1.70917
$426$		0			0
$427$	12.3374	−	8.36171i	0.597048	−	0.404652i
$428$		0			0
$429$	3.35584	−	7.93453i	0.162022	−	0.383083i
$430$		0			0
$431$	−11.5916	+	20.0773i	−0.558350	+	0.967090i	0.439285	+	0.898348i	$0.355232\pi$
$431$	−11.5916	+	20.0773i	−0.558350	+	0.967090i	−0.997634	+	0.0687421i	$0.978101\pi$
$432$		0			0
$433$	35.6437			1.71293			0.856464	−	0.516207i	$-0.172657\pi$
$433$	35.6437			1.71293			0.856464	+	0.516207i	$0.172657\pi$
$434$		0			0
$435$	−7.79454	−	10.3158i	−0.373720	−	0.494604i
$436$		0			0
$437$	−23.4010			−1.11942
$438$		0			0
$439$	16.0124			0.764230			0.382115	−	0.924115i	$-0.375196\pi$
$439$	16.0124			0.764230			0.382115	+	0.924115i	$0.375196\pi$
$440$		0			0
$441$	2.77586	−	20.8157i	0.132184	−	0.991225i
$442$		0			0
$443$	14.3556			0.682054			0.341027	−	0.940054i	$-0.389225\pi$
$443$	14.3556			0.682054			0.341027	+	0.940054i	$0.389225\pi$
$444$		0			0
$445$	−48.3639			−2.29267
$446$		0			0
$447$	4.61953	−	10.9224i	0.218496	−	0.516610i
$448$		0			0
$449$	5.72475			0.270168			0.135084	−	0.990834i	$-0.456870\pi$
$449$	5.72475			0.270168			0.135084	+	0.990834i	$0.456870\pi$
$450$		0			0
$451$	−5.12040	+	8.86879i	−0.241110	+	0.417615i
$452$		0			0
$453$	−9.69164	−	12.8265i	−0.455353	−	0.602643i
$454$		0			0
$455$	−51.9710	+	35.2235i	−2.43644	+	1.65131i
$456$		0			0
$457$	14.6635			0.685930			0.342965	−	0.939348i	$-0.388569\pi$
$457$	14.6635			0.685930			0.342965	+	0.939348i	$0.388569\pi$
$458$		0			0
$459$	−2.29311	+	14.8527i	−0.107033	+	0.693264i
$460$		0			0
$461$	−12.9720	+	22.4681i	−0.604164	+	1.04644i	0.388018	+	0.921652i	$0.373160\pi$
$461$	−12.9720	+	22.4681i	−0.604164	+	1.04644i	−0.992183	+	0.124792i	$0.960174\pi$
$462$		0			0
$463$	−6.46277	−	11.1939i	−0.300351	−	0.520223i	0.675865	−	0.737026i	$-0.263770\pi$
$463$	−6.46277	−	11.1939i	−0.300351	−	0.520223i	−0.976215	+	0.216803i	$0.930437\pi$
$464$		0			0
$465$	8.28089	−	19.5793i	0.384017	−	0.907967i
$466$		0			0
$467$	−16.3104	−	28.2504i	−0.754755	−	1.30727i	−0.945496	−	0.325633i	$-0.894423\pi$
$467$	−16.3104	−	28.2504i	−0.754755	−	1.30727i	0.190741	−	0.981640i	$-0.438911\pi$
$468$		0			0
$469$	−5.49892	+	3.72692i	−0.253916	+	0.172093i
$470$		0			0
$471$	23.5086	−	2.91751i	1.08322	−	0.134432i
$472$		0			0
$473$	3.48765			0.160362
$474$		0			0
$475$	−24.4509	+	42.3503i	−1.12189	+	1.94316i
$476$		0			0
$477$	−1.78823	+	6.29804i	−0.0818774	+	0.288367i
$478$		0			0
$479$	12.6739	+	21.9518i	0.579084	+	1.00300i	0.995585	+	0.0938679i	$0.0299231\pi$
$479$	12.6739	+	21.9518i	0.579084	+	1.00300i	−0.416500	+	0.909136i	$0.636744\pi$
$480$		0			0
$481$	15.1660	−	26.2682i	0.691509	−	1.19773i
$482$		0			0
$483$	−5.19000	−	26.2064i	−0.236153	−	1.19243i
$484$		0			0
$485$	−16.5302	−	28.6311i	−0.750597	−	1.30007i
$486$		0			0
$487$	17.7383	−	30.7236i	0.803799	−	1.39222i	−0.113299	−	0.993561i	$-0.536142\pi$
$487$	17.7383	−	30.7236i	0.803799	−	1.39222i	0.917099	−	0.398660i	$-0.130525\pi$
$488$		0			0
$489$	−3.44582	−	4.56041i	−0.155825	−	0.206229i
$490$		0			0
$491$	13.2554	+	22.9590i	0.598208	+	1.03613i	0.993085	+	0.117393i	$0.0374538\pi$
$491$	13.2554	+	22.9590i	0.598208	+	1.03613i	−0.394877	+	0.918734i	$0.629213\pi$
$492$		0			0
$493$	−2.60425	−	4.51069i	−0.117289	−	0.203151i
$494$		0			0
$495$	10.4770	−	2.64115i	0.470906	−	0.118711i
$496$		0			0
$497$	−2.39038	+	1.62009i	−0.107223	+	0.0726710i
$498$		0			0
$499$	3.00130	−	5.19841i	0.134357	−	0.232713i	−0.790995	−	0.611823i	$-0.790437\pi$
$499$	3.00130	−	5.19841i	0.134357	−	0.232713i	0.925352	+	0.379110i	$0.123770\pi$
$500$		0			0
$501$	12.4513	+	16.4788i	0.556282	+	0.736219i
$502$		0			0
$503$	−22.9460			−1.02311			−0.511556	−	0.859250i	$-0.670931\pi$
$503$	−22.9460			−1.02311			−0.511556	+	0.859250i	$0.670931\pi$
$504$		0			0
$505$	−15.6013			−0.694248
$506$		0			0
$507$	−13.3395	+	31.5399i	−0.592429	+	1.40073i
$508$		0			0
$509$	−14.9348	+	25.8679i	−0.661975	+	1.14657i	0.318121	+	0.948050i	$0.396948\pi$
$509$	−14.9348	+	25.8679i	−0.661975	+	1.14657i	−0.980096	+	0.198524i	$0.936385\pi$
$510$		0			0
$511$	−0.275480	−	3.81734i	−0.0121865	−	0.168869i
$512$		0			0
$513$	−16.2605	−	13.0628i	−0.717918	−	0.576738i
$514$		0			0
$515$	−22.4992	−	38.9698i	−0.991434	−	1.71721i
$516$		0			0
$517$	−1.01846	−	1.76402i	−0.0447918	−	0.0775817i
$518$		0			0
$519$	−16.5593	+	2.05508i	−0.726875	+	0.0902081i
$520$		0			0
$521$	15.5980	−	27.0166i	0.683362	−	1.18362i	−0.290587	−	0.956849i	$-0.593851\pi$
$521$	15.5980	−	27.0166i	0.683362	−	1.18362i	0.973949	−	0.226769i	$-0.0728162\pi$
$522$		0			0
$523$	−3.07911	−	5.33318i	−0.134640	−	0.233203i	0.790820	−	0.612049i	$-0.209654\pi$
$523$	−3.07911	−	5.33318i	−0.134640	−	0.233203i	−0.925460	+	0.378846i	$0.876321\pi$
$524$		0			0
$525$	−52.8502	−	17.9895i	−2.30657	−	0.785127i
$526$		0			0
$527$	4.28187	−	7.41642i	0.186521	−	0.323064i
$528$		0			0
$529$	−5.49310	−	9.51433i	−0.238830	−	0.413666i
$530$		0			0
$531$	−8.88494	+	2.23981i	−0.385574	+	0.0971995i
$532$		0			0
$533$	33.7366	−	58.4335i	1.46129	−	2.53103i
$534$		0			0
$535$	39.9881			1.72884
$536$		0			0
$537$	−15.5564	+	36.7815i	−0.671310	+	1.58724i
$538$		0			0
$539$	−6.01899	+	0.873275i	−0.259256	+	0.0376146i
$540$		0			0
$541$	−13.5137	−	23.4064i	−0.580999	−	1.00632i	−0.995361	−	0.0962083i	$-0.969329\pi$
$541$	−13.5137	−	23.4064i	−0.580999	−	1.00632i	0.414362	−	0.910112i	$-0.364005\pi$
$542$		0			0
$543$	−20.3385	+	2.52409i	−0.872808	+	0.108319i
$544$		0			0
$545$	−24.2963	−	42.0824i	−1.04074	−	1.80261i
$546$		0			0
$547$	14.9426	−	25.8814i	0.638900	−	1.10661i	−0.346775	−	0.937948i	$-0.612723\pi$
$547$	14.9426	−	25.8814i	0.638900	−	1.10661i	0.985675	−	0.168658i	$-0.0539434\pi$
$548$		0			0
$549$	16.3869	−	4.13098i	0.699375	−	0.176306i
$550$		0			0
$551$	7.22865			0.307951
$552$		0			0
$553$	−4.66339	+	3.16064i	−0.198308	+	0.134404i
$554$		0			0
$555$	37.7521	−	4.68518i	1.60249	−	0.198875i
$556$		0			0
$557$	10.6650	−	18.4722i	0.451889	−	0.782694i	−0.546615	−	0.837384i	$-0.684084\pi$
$557$	10.6650	−	18.4722i	0.451889	−	0.782694i	0.998503	+	0.0546900i	$0.0174171\pi$
$558$		0			0
$559$	−22.9789			−0.971905
$560$		0			0
$561$	4.31946	−	0.536062i	0.182368	−	0.0226326i
$562$		0			0
$563$	31.4635			1.32603			0.663014	−	0.748607i	$-0.269277\pi$
$563$	31.4635			1.32603			0.663014	+	0.748607i	$0.269277\pi$
$564$		0			0
$565$	−23.9577			−1.00791
$566$		0			0
$567$	11.0225	−	21.1070i	0.462902	−	0.886410i
$568$		0			0
$569$	29.3391			1.22996			0.614980	−	0.788543i	$-0.289164\pi$
$569$	29.3391			1.22996			0.614980	+	0.788543i	$0.289164\pi$
$570$		0			0
$571$	−27.4947			−1.15062			−0.575308	−	0.817937i	$-0.695118\pi$
$571$	−27.4947			−1.15062			−0.575308	+	0.817937i	$0.695118\pi$
$572$		0			0
$573$	−10.8032	+	1.34072i	−0.451310	+	0.0560094i
$574$		0			0
$575$	−71.0221			−2.96183
$576$		0			0
$577$	−20.2293	+	35.0381i	−0.842156	+	1.45866i	0.0459122	+	0.998945i	$0.485381\pi$
$577$	−20.2293	+	35.0381i	−0.842156	+	1.45866i	−0.888068	+	0.459712i	$0.847953\pi$
$578$		0			0
$579$	23.6020	−	2.92911i	0.980867	−	0.121730i
$580$		0			0
$581$	−0.833292	−	11.5470i	−0.0345708	−	0.479048i
$582$		0			0
$583$	1.89613			0.0785299
$584$		0			0
$585$	−69.0294	+	17.4017i	−2.85401	+	0.719471i
$586$		0			0
$587$	−13.6559	+	23.6528i	−0.563641	+	0.976255i	0.433533	+	0.901137i	$0.357267\pi$
$587$	−13.6559	+	23.6528i	−0.563641	+	0.976255i	−0.997175	+	0.0751177i	$0.976067\pi$
$588$		0			0
$589$	5.94263	+	10.2929i	0.244862	+	0.424113i
$590$		0			0
$591$	−0.277589	+	0.0344499i	−0.0114185	+	0.00141708i
$592$		0			0
$593$	14.2898	+	24.7507i	0.586813	+	1.01639i	0.994647	+	0.103334i	$0.0329512\pi$
$593$	14.2898	+	24.7507i	0.586813	+	1.01639i	−0.407833	+	0.913056i	$0.633716\pi$
$594$		0			0
$595$	−28.5406	−	13.8416i	−1.17005	−	0.567449i
$596$		0			0
$597$	−16.7512	+	39.6065i	−0.685583	+	1.62099i
$598$		0			0
$599$	39.9838			1.63370			0.816848	−	0.576854i	$-0.195720\pi$
$599$	39.9838			1.63370			0.816848	+	0.576854i	$0.195720\pi$
$600$		0			0
$601$	−12.6948	+	21.9880i	−0.517831	+	0.896910i	0.481954	+	0.876196i	$0.339927\pi$
$601$	−12.6948	+	21.9880i	−0.517831	+	0.896910i	−0.999785	+	0.0207133i	$0.993406\pi$
$602$		0			0
$603$	−7.30383	+	1.84123i	−0.297435	+	0.0749806i
$604$		0			0
$605$	21.2340	+	36.7783i	0.863283	+	1.49525i
$606$		0			0
$607$	18.6469	−	32.2975i	0.756856	−	1.31091i	−0.187590	−	0.982247i	$-0.560068\pi$
$607$	18.6469	−	32.2975i	0.756856	−	1.31091i	0.944446	−	0.328666i	$-0.106599\pi$
$608$		0			0
$609$	1.60321	+	8.09523i	0.0649652	+	0.328035i
$610$		0			0
$611$	6.71029	+	11.6226i	0.271469	+	0.470199i
$612$		0			0
$613$	−11.7319	+	20.3203i	−0.473848	+	0.820729i	−0.999552	−	0.0299390i	$-0.990469\pi$
$613$	−11.7319	+	20.3203i	−0.473848	+	0.820729i	0.525704	+	0.850668i	$0.323802\pi$
$614$		0			0
$615$	83.9792	−	10.4222i	3.38637	−	0.420262i
$616$		0			0
$617$	6.56888	+	11.3776i	0.264453	+	0.458047i	0.967420	−	0.253176i	$-0.0814752\pi$
$617$	6.56888	+	11.3776i	0.264453	+	0.458047i	−0.702967	+	0.711223i	$0.748142\pi$
$618$		0			0
$619$	−10.7776	−	18.6674i	−0.433190	−	0.750308i	0.563956	−	0.825805i	$-0.309279\pi$
$619$	−10.7776	−	18.6674i	−0.433190	−	0.750308i	−0.997146	+	0.0754975i	$0.975946\pi$
$620$		0			0
$621$	4.62207	−	29.9377i	0.185477	−	1.20136i
$622$		0			0
$623$	27.7751	+	13.4703i	1.11279	+	0.539677i
$624$		0			0
$625$	−31.2520	+	54.1300i	−1.25008	+	2.16520i
$626$		0			0
$627$	−2.35309	+	5.56363i	−0.0939734	+	0.222190i
$628$		0			0
$629$	15.3247			0.611036
$630$		0			0
$631$	−6.15223			−0.244916			−0.122458	−	0.992474i	$-0.539078\pi$
$631$	−6.15223			−0.244916			−0.122458	+	0.992474i	$0.539078\pi$
$632$		0			0
$633$	19.7266	+	26.1075i	0.784063	+	1.03768i
$634$		0			0
$635$	−13.4194	+	23.2431i	−0.532533	+	0.922375i
$636$		0			0
$637$	39.6571	−	5.75372i	1.57127	−	0.227971i
$638$		0			0
$639$	−3.17497	+	0.800381i	−0.125600	+	0.0316626i
$640$		0			0
$641$	2.23682	+	3.87429i	0.0883491	+	0.153025i	0.906813	−	0.421532i	$-0.138508\pi$
$641$	2.23682	+	3.87429i	0.0883491	+	0.153025i	−0.818464	+	0.574557i	$0.805174\pi$
$642$		0			0
$643$	8.98009	+	15.5540i	0.354140	+	0.613389i	0.986970	−	0.160902i	$-0.0514402\pi$
$643$	8.98009	+	15.5540i	0.354140	+	0.613389i	−0.632830	+	0.774291i	$0.718107\pi$
$644$		0			0
$645$	−17.3740	−	22.9939i	−0.684101	−	0.905383i
$646$		0			0
$647$	6.02992	−	10.4441i	0.237061	−	0.410601i	−0.722809	−	0.691048i	$-0.757149\pi$
$647$	6.02992	−	10.4441i	0.237061	−	0.410601i	0.959870	+	0.280447i	$0.0904826\pi$
$648$		0			0
$649$	1.32688	+	2.29822i	0.0520845	+	0.0902131i
$650$		0			0
$651$	−10.2089	+	8.93786i	−0.400118	+	0.350302i
$652$		0			0
$653$	24.1366	−	41.8059i	0.944540	−	1.63599i	0.187870	−	0.982194i	$-0.439842\pi$
$653$	24.1366	−	41.8059i	0.944540	−	1.63599i	0.756670	−	0.653797i	$-0.226825\pi$
$654$		0			0
$655$	36.7478	+	63.6490i	1.43585	+	2.48697i
$656$		0			0
$657$	1.18534	−	4.17469i	0.0462445	−	0.162870i
$658$		0			0
$659$	14.5795	−	25.2525i	0.567937	−	0.983696i	−0.428832	−	0.903384i	$-0.641075\pi$
$659$	14.5795	−	25.2525i	0.567937	−	0.983696i	0.996770	−	0.0803122i	$-0.0255917\pi$
$660$		0			0
$661$	−14.5486			−0.565873			−0.282937	−	0.959139i	$-0.591309\pi$
$661$	−14.5486			−0.565873			−0.282937	+	0.959139i	$0.591309\pi$
$662$		0			0
$663$	−28.4595	+	3.53193i	−1.10527	+	0.137169i
$664$		0			0
$665$	36.4416	−	24.6985i	1.41315	−	0.957766i
$666$		0			0
$667$	5.24922	+	9.09192i	0.203251	+	0.352040i
$668$		0			0
$669$	9.50936	−	22.4839i	0.367653	−	0.869276i
$670$		0			0
$671$	−2.44722	−	4.23871i	−0.0944738	−	0.163633i
$672$		0			0
$673$	11.6825	−	20.2348i	0.450329	−	0.779993i	−0.548077	−	0.836428i	$-0.684640\pi$
$673$	11.6825	−	20.2348i	0.450329	−	0.779993i	0.998406	+	0.0564349i	$0.0179733\pi$
$674$		0			0
$675$	−49.3506	−	39.6457i	−1.89951	−	1.52596i
$676$		0			0
$677$	−17.7175			−0.680939			−0.340469	−	0.940256i	$-0.610586\pi$
$677$	−17.7175			−0.680939			−0.340469	+	0.940256i	$0.610586\pi$
$678$		0			0
$679$	1.51885	+	21.0467i	0.0582880	+	0.807698i
$680$		0			0
$681$	−27.1257	−	35.8999i	−1.03946	−	1.37569i
$682$		0			0
$683$	21.7769	−	37.7186i	0.833269	−	1.44326i	−0.0621637	−	0.998066i	$-0.519800\pi$
$683$	21.7769	−	37.7186i	0.833269	−	1.44326i	0.895432	−	0.445198i	$-0.146867\pi$
$684$		0			0
$685$	11.2846			0.431161
$686$		0			0
$687$	−16.8105	+	39.7466i	−0.641360	+	1.51643i
$688$		0			0
$689$	−12.4930			−0.475945
$690$		0			0
$691$	23.5344			0.895291			0.447645	−	0.894211i	$-0.352263\pi$
$691$	23.5344			0.895291			0.447645	+	0.894211i	$0.352263\pi$
$692$		0			0
$693$	−6.75249	−	1.40125i	−0.256506	−	0.0532292i
$694$		0			0
$695$	−71.7476			−2.72154
$696$		0			0
$697$	34.0897			1.29124
$698$		0			0
$699$	−6.38872	−	8.45523i	−0.241644	−	0.319806i
$700$		0			0
$701$	45.1804			1.70644			0.853219	−	0.521552i	$-0.174647\pi$
$701$	45.1804			1.70644			0.853219	+	0.521552i	$0.174647\pi$
$702$		0			0
$703$	−10.6343	+	18.4191i	−0.401079	+	0.694689i
$704$		0			0
$705$	−6.55657	+	15.5023i	−0.246935	+	0.583850i
$706$		0			0
$707$	8.95973	+	4.34527i	0.336965	+	0.163421i
$708$		0			0
$709$	−27.0127			−1.01448			−0.507242	−	0.861804i	$-0.669335\pi$
$709$	−27.0127			−1.01448			−0.507242	+	0.861804i	$0.669335\pi$
$710$		0			0
$711$	−6.19406	+	1.56147i	−0.232295	+	0.0585595i
$712$		0			0
$713$	−8.63071	+	14.9488i	−0.323223	+	0.559838i
$714$		0			0
$715$	10.3089	+	17.8555i	0.385529	+	0.667757i
$716$		0			0
$717$	−16.1217	−	21.3365i	−0.602077	−	0.796827i
$718$		0			0
$719$	−11.2096	−	19.4156i	−0.418048	−	0.724080i	0.577695	−	0.816253i	$-0.303952\pi$
$719$	−11.2096	−	19.4156i	−0.418048	−	0.724080i	−0.995743	+	0.0921724i	$0.970619\pi$
$720$		0			0
$721$	2.06730	+	28.6466i	0.0769902	+	1.06686i
$722$		0			0
$723$	−10.2800	−	13.6053i	−0.382319	−	0.505985i
$724$		0			0
$725$	21.9389			0.814792
$726$		0			0
$727$	21.9820	−	38.0740i	0.815268	−	1.41208i	−0.0938680	−	0.995585i	$-0.529923\pi$
$727$	21.9820	−	38.0740i	0.815268	−	1.41208i	0.909136	−	0.416500i	$-0.136744\pi$
$728$		0			0
$729$	19.9234	−	18.2224i	0.737904	−	0.674905i
$730$		0			0
$731$	−5.80486	−	10.0543i	−0.214701	−	0.371872i
$732$		0			0
$733$	−0.433386	+	0.750646i	−0.0160075	+	0.0277257i	−0.873918	−	0.486073i	$-0.838429\pi$
$733$	−0.433386	+	0.750646i	−0.0160075	+	0.0277257i	0.857911	+	0.513799i	$0.171762\pi$
$734$		0			0
$735$	35.7416	+	35.3326i	1.31835	+	1.30326i
$736$		0			0
$737$	1.09075	+	1.88924i	0.0401785	+	0.0695911i
$738$		0			0
$739$	13.0442	−	22.5932i	0.479838	−	0.831103i	−0.519895	−	0.854230i	$-0.674029\pi$
$739$	13.0442	−	22.5932i	0.479838	−	0.831103i	0.999733	+	0.0231270i	$0.00736222\pi$
$740$		0			0
$741$	15.5037	−	36.6569i	0.569544	−	1.34662i
$742$		0			0
$743$	22.5842	+	39.1170i	0.828533	+	1.43506i	0.899189	+	0.437561i	$0.144158\pi$
$743$	22.5842	+	39.1170i	0.828533	+	1.43506i	−0.0706551	+	0.997501i	$0.522509\pi$
$744$		0			0
$745$	14.1908	+	24.5791i	0.519910	+	0.900510i
$746$		0			0
$747$	3.58550	−	12.6279i	0.131186	−	0.462031i
$748$		0			0
$749$	−22.9650	−	11.1375i	−0.839121	−	0.406955i
$750$		0			0
$751$	10.2994	−	17.8391i	0.375831	−	0.650958i	−0.614620	−	0.788823i	$-0.710691\pi$
$751$	10.2994	−	17.8391i	0.375831	−	0.650958i	0.990451	+	0.137865i	$0.0440241\pi$
$752$		0			0
$753$	46.2105	−	5.73491i	1.68400	−	0.208992i
$754$		0			0
$755$	38.4743			1.40022
$756$		0			0
$757$	−39.0856			−1.42059			−0.710294	−	0.703905i	$-0.751438\pi$
$757$	−39.0856			−1.42059			−0.710294	+	0.703905i	$0.751438\pi$
$758$		0			0
$759$	−8.70647	+	1.08051i	−0.316025	+	0.0392200i
$760$		0			0
$761$	14.4436	−	25.0171i	0.523581	−	0.906868i	−0.476043	−	0.879422i	$-0.657929\pi$
$761$	14.4436	−	25.0171i	0.523581	−	0.906868i	0.999623	−	0.0274459i	$-0.00873741\pi$
$762$		0			0
$763$	2.23242	+	30.9347i	0.0808191	+	1.11991i
$764$		0			0
$765$	−25.0520	−	25.8075i	−0.905757	−	0.933072i
$766$		0			0
$767$	−8.74236	−	15.1422i	−0.315668	−	0.546753i
$768$		0			0
$769$	−11.1407	−	19.2962i	−0.401742	−	0.695838i	0.592194	−	0.805796i	$-0.298262\pi$
$769$	−11.1407	−	19.2962i	−0.401742	−	0.695838i	−0.993936	+	0.109957i	$0.964929\pi$
$770$		0			0
$771$	−7.43021	+	17.5679i	−0.267592	+	0.632693i
$772$		0			0
$773$	−21.3593	+	36.9955i	−0.768242	+	1.33063i	0.170273	+	0.985397i	$0.445535\pi$
$773$	−21.3593	+	36.9955i	−0.768242	+	1.33063i	−0.938515	+	0.345238i	$0.887798\pi$
$774$		0			0
$775$	18.0359	+	31.2391i	0.647868	+	1.12214i
$776$		0			0
$777$	−22.9857	−	7.82404i	−0.824608	−	0.280686i
$778$		0			0
$779$	−23.6558	+	40.9731i	−0.847558	+	1.46801i
$780$		0			0
$781$	0.474151	+	0.821254i	0.0169665	+	0.0293868i
$782$		0			0
$783$	−1.42777	+	9.24784i	−0.0510245	+	0.330491i
$784$		0			0
$785$	−28.3465	+	49.0976i	−1.01173	+	1.75237i
$786$		0			0
$787$	−0.286769			−0.0102222			−0.00511110	−	0.999987i	$-0.501627\pi$
$787$	−0.286769			−0.0102222			−0.00511110	+	0.999987i	$0.501627\pi$
$788$		0			0
$789$	7.63388	+	10.1032i	0.271773	+	0.359682i
$790$		0			0
$791$	13.7588	+	6.67270i	0.489205	+	0.237254i
$792$		0			0
$793$	16.1239	+	27.9274i	0.572577	+	0.991732i
$794$		0			0
$795$	−9.44576	−	12.5011i	−0.335007	−	0.443369i
$796$		0			0
$797$	−0.457746	−	0.792840i	−0.0162142	−	0.0280838i	0.857804	−	0.513976i	$-0.171828\pi$
$797$	−0.457746	−	0.792840i	−0.0162142	−	0.0280838i	−0.874019	+	0.485892i	$0.838495\pi$
$798$		0			0
$799$	−3.39026	+	5.87211i	−0.119939	+	0.207740i
$800$		0			0
$801$	24.3800	+	25.1153i	0.861426	+	0.887405i
$802$		0			0
$803$	−1.25687			−0.0443538
$804$		0			0
$805$	57.5276	+	27.8996i	2.02758	+	0.983333i
$806$		0			0
$807$	−2.80737	+	6.63771i	−0.0988239	+	0.233659i
$808$		0			0
$809$	−14.3721	+	24.8932i	−0.505297	+	0.875199i	0.494685	+	0.869073i	$0.335284\pi$
$809$	−14.3721	+	24.8932i	−0.505297	+	0.875199i	−0.999981	+	0.00612685i	$0.998050\pi$
$810$		0			0
$811$	14.3005			0.502157			0.251079	−	0.967967i	$-0.419215\pi$
$811$	14.3005			0.502157			0.251079	+	0.967967i	$0.419215\pi$
$812$		0			0
$813$	−8.73553	−	11.5611i	−0.306368	−	0.405467i
$814$		0			0
$815$	13.6794			0.479167
$816$		0			0
$817$	16.1126			0.563710
$818$		0			0
$819$	44.4899	+	9.23239i	1.55460	+	0.322606i
$820$		0			0
$821$	35.6250			1.24332			0.621660	−	0.783287i	$-0.286458\pi$
$821$	35.6250			1.24332			0.621660	+	0.783287i	$0.286458\pi$
$822$		0			0
$823$	−22.4313			−0.781907			−0.390953	−	0.920411i	$-0.627855\pi$
$823$	−22.4313			−0.781907			−0.390953	+	0.920411i	$0.627855\pi$
$824$		0			0
$825$	−7.14164	+	16.8856i	−0.248640	+	0.587882i
$826$		0			0
$827$	−26.6728			−0.927505			−0.463753	−	0.885965i	$-0.653497\pi$
$827$	−26.6728			−0.927505			−0.463753	+	0.885965i	$0.653497\pi$
$828$		0			0
$829$	−16.0078	+	27.7263i	−0.555973	+	0.962973i	0.441854	+	0.897087i	$0.354321\pi$
$829$	−16.0078	+	27.7263i	−0.555973	+	0.962973i	−0.997827	+	0.0658866i	$0.979012\pi$
$830$		0			0
$831$	2.92217	+	3.86739i	0.101369	+	0.134158i
$832$		0			0
$833$	12.5356	+	15.8983i	0.434331	+	0.550843i
$834$		0			0
$835$	−49.4297			−1.71058
$836$		0			0
$837$	−14.3418	+	5.56958i	−0.495727	+	0.192513i
$838$		0			0
$839$	9.10375	−	15.7682i	0.314296	−	0.544377i	−0.664991	−	0.746851i	$-0.731565\pi$
$839$	9.10375	−	15.7682i	0.314296	−	0.544377i	0.979288	+	0.202474i	$0.0648982\pi$
$840$		0			0
$841$	12.8785	+	22.3062i	0.444086	+	0.769180i
$842$		0			0
$843$	−7.34490	+	17.3662i	−0.252972	+	0.598124i
$844$		0			0
$845$	−40.9778	−	70.9757i	−1.40968	−	2.44164i
$846$		0			0
$847$	−1.95104	−	27.0356i	−0.0670386	−	0.928956i
$848$		0			0
$849$	−3.47939	+	0.431807i	−0.119412	+	0.0148196i
$850$		0			0
$851$	−30.8891			−1.05886
$852$		0			0
$853$	20.9242	−	36.2419i	0.716432	−	1.24090i	−0.245972	−	0.969277i	$-0.579107\pi$
$853$	20.9242	−	36.2419i	0.716432	−	1.24090i	0.962404	−	0.271621i	$-0.0875596\pi$
$854$		0			0
$855$	48.4029	−	12.2019i	1.65534	−	0.417297i
$856$		0			0
$857$	−7.85704	−	13.6088i	−0.268391	−	0.464867i	0.700055	−	0.714089i	$-0.253159\pi$
$857$	−7.85704	−	13.6088i	−0.268391	−	0.464867i	−0.968447	+	0.249221i	$0.919825\pi$
$858$		0			0
$859$	−12.1023	+	20.9618i	−0.412924	+	0.715206i	−0.995208	−	0.0977797i	$-0.968826\pi$
$859$	−12.1023	+	20.9618i	−0.412924	+	0.715206i	0.582284	+	0.812986i	$0.302159\pi$
$860$		0			0
$861$	−51.1315	−	17.4045i	−1.74256	−	0.593144i
$862$		0			0
$863$	26.0542	+	45.1272i	0.886896	+	1.53615i	0.843525	+	0.537090i	$0.180477\pi$
$863$	26.0542	+	45.1272i	0.886896	+	1.53615i	0.0433714	+	0.999059i	$0.486190\pi$
$864$		0			0
$865$	19.9672	−	34.5842i	0.678904	−	1.17590i
$866$		0			0
$867$	9.01619	+	11.9326i	0.306206	+	0.405252i
$868$		0			0
$869$	0.925022	+	1.60219i	0.0313792	+	0.0543504i
$870$		0			0
$871$	−7.18662	−	12.4476i	−0.243509	−	0.421770i
$872$		0			0
$873$	−6.53530	+	23.0169i	−0.221186	+	0.779006i
$874$		0			0
$875$	65.2078	−	44.1949i	2.20443	−	1.49406i
$876$		0			0
$877$	6.98841	−	12.1043i	0.235982	−	0.408733i	−0.723576	−	0.690245i	$-0.757503\pi$
$877$	6.98841	−	12.1043i	0.235982	−	0.408733i	0.959558	+	0.281512i	$0.0908360\pi$
$878$		0			0
$879$	−20.1619	−	26.6835i	−0.680042	−	0.900011i
$880$		0			0
$881$	28.1210			0.947421			0.473710	−	0.880681i	$-0.342914\pi$
$881$	28.1210			0.947421			0.473710	+	0.880681i	$0.342914\pi$
$882$		0			0
$883$	−35.1633			−1.18334			−0.591670	−	0.806180i	$-0.701531\pi$
$883$	−35.1633			−1.18334			−0.591670	+	0.806180i	$0.701531\pi$
$884$		0			0
$885$	8.54208	−	20.1968i	0.287139	−	0.678909i
$886$		0			0
$887$	13.4610	−	23.3151i	0.451975	−	0.782844i	−0.546533	−	0.837437i	$-0.684053\pi$
$887$	13.4610	−	23.3151i	0.451975	−	0.782844i	0.998509	+	0.0545932i	$0.0173862\pi$
$888$		0			0
$889$	14.1804	−	9.61081i	0.475594	−	0.322336i
$890$		0			0
$891$	−6.65296	−	4.10929i	−0.222882	−	0.137666i
$892$		0			0
$893$	−4.70520	−	8.14965i	−0.157454	−	0.272718i
$894$		0			0
$895$	−47.7880	−	82.7713i	−1.59738	−	2.76674i
$896$		0			0
$897$	57.3640	−	7.11911i	1.91533	−	0.237700i
$898$		0			0
$899$	2.66605	−	4.61774i	0.0889179	−	0.154010i
$900$		0			0
$901$	−3.15594	−	5.46625i	−0.105140	−	0.182107i
$902$		0			0
$903$	3.57355	+	18.0443i	0.118920	+	0.600475i
$904$		0			0
$905$	24.5241	−	42.4769i	0.815207	−	1.41198i
$906$		0			0
$907$	22.3571	+	38.7236i	0.742355	+	1.28580i	0.951420	+	0.307895i	$0.0996246\pi$
$907$	22.3571	+	38.7236i	0.742355	+	1.28580i	−0.209065	+	0.977902i	$0.567042\pi$
$908$		0			0
$909$	7.86455	+	8.10173i	0.260851	+	0.268717i
$910$		0			0
$911$	−13.7822	+	23.8715i	−0.456626	+	0.790899i	−0.998780	−	0.0493800i	$-0.984275\pi$
$911$	−13.7822	+	23.8715i	−0.456626	+	0.790899i	0.542154	+	0.840279i	$0.317609\pi$
$912$		0			0
$913$	−3.80185			−0.125823
$914$		0			0
$915$	−15.7545	+	37.2499i	−0.520829	+	1.23144i
$916$		0			0
$917$	−3.37650	−	46.7882i	−0.111502	−	1.54508i
$918$		0			0
$919$	−21.3836	−	37.0376i	−0.705381	−	1.22176i	−0.966554	−	0.256464i	$-0.917442\pi$
$919$	−21.3836	−	37.0376i	−0.705381	−	1.22176i	0.261173	−	0.965292i	$-0.415891\pi$
$920$		0			0
$921$	−22.5821	+	2.80253i	−0.744105	+	0.0923464i
$922$		0			0
$923$	−3.12402	−	5.41096i	−0.102828	−	0.178104i
$924$		0			0
$925$	−32.2750	+	55.9019i	−1.06119	+	1.83804i
$926$		0			0
$927$	−8.89519	+	31.3283i	−0.292156	+	1.02896i
$928$		0			0
$929$	47.9497			1.57318			0.786589	−	0.617477i	$-0.211845\pi$
$929$	47.9497			1.57318			0.786589	+	0.617477i	$0.211845\pi$
$930$		0			0
$931$	−27.8072	+	4.03446i	−0.911346	+	0.132224i
$932$		0			0
$933$	−23.2599	+	2.88665i	−0.761495	+	0.0945046i
$934$		0			0
$935$	−5.20838	+	9.02118i	−0.170332	+	0.295024i
$936$		0			0
$937$	33.9136			1.10791			0.553955	−	0.832547i	$-0.313118\pi$
$937$	33.9136			1.10791			0.553955	+	0.832547i	$0.313118\pi$
$938$		0			0
$939$	−43.3154	+	5.37562i	−1.41354	+	0.175427i
$940$		0			0
$941$	−8.54790			−0.278654			−0.139327	−	0.990246i	$-0.544494\pi$
$941$	−8.54790			−0.278654			−0.139327	+	0.990246i	$0.544494\pi$
$942$		0			0
$943$	−68.7125			−2.23759
$944$		0			0
$945$	24.3997	+	51.4993i	0.793724	+	1.67527i
$946$		0			0
$947$	0.823127			0.0267480			0.0133740	−	0.999911i	$-0.495743\pi$
$947$	0.823127			0.0267480			0.0133740	+	0.999911i	$0.495743\pi$
$948$		0			0
$949$	8.28106			0.268815
$950$		0			0
$951$	−21.1382	+	2.62334i	−0.685453	+	0.0850675i
$952$		0			0
$953$	−44.6726			−1.44709			−0.723544	−	0.690278i	$-0.757488\pi$
$953$	−44.6726			−1.44709			−0.723544	+	0.690278i	$0.757488\pi$
$954$		0			0
$955$	13.0264	−	22.5625i	0.421526	−	0.730104i
$956$		0			0
$957$	2.68945	−	0.333772i	0.0869377	−	0.0107893i
$958$		0			0
$959$	−6.48065	−	3.14298i	−0.209271	−	0.101492i
$960$		0			0
$961$	−22.2330			−0.717194
$962$		0			0
$963$	−20.1579	−	20.7658i	−0.649578	−	0.669168i
$964$		0			0
$965$	−28.4592	+	49.2928i	−0.916135	+	1.58679i
$966$		0			0
$967$	−18.2289	−	31.5735i	−0.586203	−	1.01533i	−0.994724	−	0.102585i	$-0.967289\pi$
$967$	−18.2289	−	31.5735i	−0.586203	−	1.01533i	0.408521	−	0.912749i	$-0.366045\pi$
$968$		0			0
$969$	19.9555	−	2.47656i	0.641064	−	0.0795587i
$970$		0			0
$971$	8.63674	+	14.9593i	0.277166	+	0.480066i	0.970679	−	0.240378i	$-0.0772714\pi$
$971$	8.63674	+	14.9593i	0.277166	+	0.480066i	−0.693513	+	0.720444i	$0.743938\pi$
$972$		0			0
$973$	41.2043	+	19.9832i	1.32095	+	0.640631i
$974$		0			0
$975$	47.0538	−	111.254i	1.50693	−	3.56297i
$976$		0			0
$977$	9.03550			0.289071			0.144536	−	0.989500i	$-0.453831\pi$
$977$	9.03550			0.289071			0.144536	+	0.989500i	$0.453831\pi$
$978$		0			0
$979$	5.06868	−	8.77921i	0.161996	−	0.280585i
$980$		0			0
$981$	−9.60567	+	33.8306i	−0.306686	+	1.08013i
$982$		0			0
$983$	11.4286	+	19.7950i	0.364517	+	0.631362i	0.988698	−	0.149918i	$-0.0479008\pi$
$983$	11.4286	+	19.7950i	0.364517	+	0.631362i	−0.624182	+	0.781279i	$0.714568\pi$
$984$		0			0
$985$	0.334715	−	0.579743i	0.0106649	−	0.0184722i
$986$		0			0
$987$	8.08310	−	7.07675i	0.257288	−	0.225255i
$988$		0			0
$989$	11.7005	+	20.2659i	0.372055	+	0.644417i
$990$		0			0
$991$	−4.37884	+	7.58437i	−0.139098	+	0.240925i	−0.927156	−	0.374677i	$-0.877754\pi$
$991$	−4.37884	+	7.58437i	−0.139098	+	0.240925i	0.788057	+	0.615602i	$0.211087\pi$
$992$		0			0
$993$	−34.2496	+	4.25051i	−1.08688	+	0.134886i
$994$		0			0
$995$	−51.4584	−	89.1285i	−1.63134	−	2.82556i
$996$		0			0
$997$	−3.46535	−	6.00216i	−0.109749	−	0.190090i	0.805920	−	0.592025i	$-0.201671\pi$
$997$	−3.46535	−	6.00216i	−0.109749	−	0.190090i	−0.915668	+	0.401934i	$0.868338\pi$
$998$		0			0
$999$	−21.4637	−	17.2428i	−0.679081	−	0.545538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.i.b.25.7	✓	14
3.2	odd	2		756.2.i.b.613.7		14
4.3	odd	2		1008.2.q.j.529.1		14
7.2	even	3		252.2.l.b.205.3	yes	14
7.3	odd	6		1764.2.j.h.1177.5		14
7.4	even	3		1764.2.j.g.1177.3		14
7.5	odd	6		1764.2.l.i.961.5		14
7.6	odd	2		1764.2.i.i.1537.1		14
9.2	odd	6		2268.2.k.f.1621.7		14
9.4	even	3		252.2.l.b.193.3	yes	14
9.5	odd	6		756.2.l.b.361.1		14
9.7	even	3		2268.2.k.e.1621.1		14
12.11	even	2		3024.2.q.j.2881.7		14
21.2	odd	6		756.2.l.b.289.1		14
21.5	even	6		5292.2.l.i.3313.7		14
21.11	odd	6		5292.2.j.h.3529.7		14
21.17	even	6		5292.2.j.g.3529.1		14
21.20	even	2		5292.2.i.i.2125.1		14
28.23	odd	6		1008.2.t.j.961.5		14
36.23	even	6		3024.2.t.j.1873.1		14
36.31	odd	6		1008.2.t.j.193.5		14
63.2	odd	6		2268.2.k.f.1297.7		14
63.4	even	3		1764.2.j.g.589.3		14
63.5	even	6		5292.2.i.i.1549.1		14
63.13	odd	6		1764.2.l.i.949.5		14
63.16	even	3		2268.2.k.e.1297.1		14
63.23	odd	6		756.2.i.b.37.7		14
63.31	odd	6		1764.2.j.h.589.5		14
63.32	odd	6		5292.2.j.h.1765.7		14
63.40	odd	6		1764.2.i.i.373.1		14
63.41	even	6		5292.2.l.i.361.7		14
63.58	even	3	inner	252.2.i.b.121.7	yes	14
63.59	even	6		5292.2.j.g.1765.1		14
84.23	even	6		3024.2.t.j.289.1		14
252.23	even	6		3024.2.q.j.2305.7		14
252.247	odd	6		1008.2.q.j.625.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.7	✓	14	1.1	even	1	trivial
252.2.i.b.121.7	yes	14	63.58	even	3	inner
252.2.l.b.193.3	yes	14	9.4	even	3
252.2.l.b.205.3	yes	14	7.2	even	3
756.2.i.b.37.7		14	63.23	odd	6
756.2.i.b.613.7		14	3.2	odd	2
756.2.l.b.289.1		14	21.2	odd	6
756.2.l.b.361.1		14	9.5	odd	6
1008.2.q.j.529.1		14	4.3	odd	2
1008.2.q.j.625.1		14	252.247	odd	6
1008.2.t.j.193.5		14	36.31	odd	6
1008.2.t.j.961.5		14	28.23	odd	6
1764.2.i.i.373.1		14	63.40	odd	6
1764.2.i.i.1537.1		14	7.6	odd	2
1764.2.j.g.589.3		14	63.4	even	3
1764.2.j.g.1177.3		14	7.4	even	3
1764.2.j.h.589.5		14	63.31	odd	6
1764.2.j.h.1177.5		14	7.3	odd	6
1764.2.l.i.949.5		14	63.13	odd	6
1764.2.l.i.961.5		14	7.5	odd	6
2268.2.k.e.1297.1		14	63.16	even	3
2268.2.k.e.1621.1		14	9.7	even	3
2268.2.k.f.1297.7		14	63.2	odd	6
2268.2.k.f.1621.7		14	9.2	odd	6
3024.2.q.j.2305.7		14	252.23	even	6
3024.2.q.j.2881.7		14	12.11	even	2
3024.2.t.j.289.1		14	84.23	even	6
3024.2.t.j.1873.1		14	36.23	even	6
5292.2.i.i.1549.1		14	63.5	even	6
5292.2.i.i.2125.1		14	21.20	even	2
5292.2.j.g.1765.1		14	63.59	even	6
5292.2.j.g.3529.1		14	21.17	even	6
5292.2.j.h.1765.7		14	63.32	odd	6
5292.2.j.h.3529.7		14	21.11	odd	6
5292.2.l.i.361.7		14	63.41	even	6
5292.2.l.i.3313.7		14	21.5	even	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71886 - 0.213318i) q^{3} +(-2.07260 + 3.58985i) q^{5} +(2.19013 - 1.48437i) q^{7} +(2.90899 - 0.733330i) q^{9} +O(q^{10})\)	\(q+(1.71886 - 0.213318i) q^{3} +(-2.07260 + 3.58985i) q^{5} +(2.19013 - 1.48437i) q^{7} +(2.90899 - 0.733330i) q^{9} +(-0.434429 - 0.752453i) q^{11} +(2.86231 + 4.95766i) q^{13} +(-2.79674 + 6.61258i) q^{15} +(-1.44613 + 2.50478i) q^{17} +(-2.00703 - 3.47627i) q^{19} +(3.44789 - 3.01862i) q^{21} +(2.91488 - 5.04873i) q^{23} +(-6.09133 - 10.5505i) q^{25} +(4.84373 - 1.88104i) q^{27} +(-0.900417 + 1.55957i) q^{29} -2.96091 q^{31} +(-0.907237 - 1.20069i) q^{33} +(0.789399 + 10.9387i) q^{35} +(-2.64925 - 4.58864i) q^{37} +(5.97748 + 7.91097i) q^{39} +(-5.89325 - 10.2074i) q^{41} +(-2.00703 + 3.47627i) q^{43} +(-3.39663 + 11.9627i) q^{45} +2.34436 q^{47} +(2.59331 - 6.50190i) q^{49} +(-1.95139 + 4.61386i) q^{51} +(-1.09116 + 1.88995i) q^{53} +3.60159 q^{55} +(-4.19136 - 5.54711i) q^{57} -3.05430 q^{59} +5.63318 q^{61} +(5.28253 - 5.92410i) q^{63} -23.7297 q^{65} -2.51078 q^{67} +(3.93331 - 9.29988i) q^{69} -1.09143 q^{71} +(0.723285 - 1.25277i) q^{73} +(-12.7208 - 16.8355i) q^{75} +(-2.06837 - 1.00312i) q^{77} -2.12928 q^{79} +(7.92445 - 4.26650i) q^{81} +(2.18784 - 3.78946i) q^{83} +(-5.99451 - 10.3828i) q^{85} +(-1.21501 + 2.87276i) q^{87} +(5.83373 + 10.1043i) q^{89} +(13.6278 + 6.60919i) q^{91} +(-5.08940 + 0.631616i) q^{93} +16.6391 q^{95} +(-3.98779 + 6.90706i) q^{97} +(-1.81555 - 1.87030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9	\( 14 q + 3 q^{3} - 2 q^{5} + 6 q^{7} - 5 q^{9} + 2 q^{11} + 2 q^{13} + 7 q^{15} + 2 q^{17} + 7 q^{19} - 11 q^{21} + 11 q^{23} - 9 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 4 q^{33} - 19 q^{35} + 10 q^{37} - 2 q^{39} - 33 q^{41} + 7 q^{43} - 10 q^{45} + 6 q^{47} - 4 q^{49} - 13 q^{51} - 15 q^{53} - 28 q^{55} - 18 q^{57} + 28 q^{59} + 20 q^{61} + 33 q^{63} - 30 q^{65} - 12 q^{67} - 43 q^{69} + 2 q^{71} + 21 q^{73} - 44 q^{75} - 47 q^{77} + 20 q^{79} - 29 q^{81} - 25 q^{83} + 8 q^{85} + 28 q^{87} - 6 q^{89} + 2 q^{91} + 22 q^{93} + 56 q^{95} - 18 q^{97} + 7 q^{99}+O(q^{100}) \) 14 * q + 3 * q^3 - 2 * q^5 + 6 * q^7 - 5 * q^9 + 2 * q^11 + 2 * q^13 + 7 * q^15 + 2 * q^17 + 7 * q^19 - 11 * q^21 + 11 * q^23 - 9 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 4 * q^33 - 19 * q^35 + 10 * q^37 - 2 * q^39 - 33 * q^41 + 7 * q^43 - 10 * q^45 + 6 * q^47 - 4 * q^49 - 13 * q^51 - 15 * q^53 - 28 * q^55 - 18 * q^57 + 28 * q^59 + 20 * q^61 + 33 * q^63 - 30 * q^65 - 12 * q^67 - 43 * q^69 + 2 * q^71 + 21 * q^73 - 44 * q^75 - 47 * q^77 + 20 * q^79 - 29 * q^81 - 25 * q^83 + 8 * q^85 + 28 * q^87 - 6 * q^89 + 2 * q^91 + 22 * q^93 + 56 * q^95 - 18 * q^97 + 7 * q^99

Introduction

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