LMFDB - Embedded newform 108.4.b.a.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(107,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("108.107");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 12x^{10} + 112x^{8} - 368x^{6} + 928x^{4} - 256x^{2} + 64 $ x^12 - 12x^10 + 112x^8 - 368x^6 + 928x^4 - 256*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.2
Root			$-1.61829 + 0.934317i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.4.b.a.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.72087 + 0.772562i) q^{2} +(6.80630 - 4.20408i) q^{4} +3.33155i q^{5} -16.9016i q^{7} +(-15.2712 + 16.6971i) q^{8} +O(q^{10})$	\(q+(-2.72087 + 0.772562i) q^{2} +(6.80630 - 4.20408i) q^{4} +3.33155i q^{5} -16.9016i q^{7} +(-15.2712 + 16.6971i) q^{8} +(-2.57383 - 9.06473i) q^{10} -16.8325 q^{11} +25.0775 q^{13} +(13.0575 + 45.9871i) q^{14} +(28.6514 - 57.2285i) q^{16} -116.919i q^{17} -85.4801i q^{19} +(14.0061 + 22.6755i) q^{20} +(45.7990 - 13.0041i) q^{22} +158.740 q^{23} +113.901 q^{25} +(-68.2328 + 19.3739i) q^{26} +(-71.0557 - 115.037i) q^{28} -269.955i q^{29} +36.0884i q^{31} +(-33.7442 + 177.846i) q^{32} +(90.3269 + 318.121i) q^{34} +56.3085 q^{35} -353.780 q^{37} +(66.0386 + 232.580i) q^{38} +(-55.6272 - 50.8767i) q^{40} -144.415i q^{41} +368.186i q^{43} +(-114.567 + 70.7651i) q^{44} +(-431.911 + 122.636i) q^{46} -397.333 q^{47} +57.3363 q^{49} +(-309.909 + 87.9954i) q^{50} +(170.685 - 105.428i) q^{52} +96.0857i q^{53} -56.0783i q^{55} +(282.207 + 258.107i) q^{56} +(208.557 + 734.514i) q^{58} +294.902 q^{59} +146.724 q^{61} +(-27.8805 - 98.1920i) q^{62} +(-45.5837 - 509.967i) q^{64} +83.5471i q^{65} +301.433i q^{67} +(-491.536 - 795.784i) q^{68} +(-153.208 + 43.5018i) q^{70} +687.794 q^{71} -312.138 q^{73} +(962.590 - 273.317i) q^{74} +(-359.365 - 581.803i) q^{76} +284.496i q^{77} -602.063i q^{79} +(190.660 + 95.4535i) q^{80} +(111.569 + 392.934i) q^{82} -1334.44 q^{83} +389.521 q^{85} +(-284.446 - 1001.79i) q^{86} +(257.051 - 281.053i) q^{88} +856.292i q^{89} -423.850i q^{91} +(1080.43 - 667.355i) q^{92} +(1081.09 - 306.964i) q^{94} +284.781 q^{95} +218.564 q^{97} +(-156.005 + 44.2959i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4}+O(q^{10}) $ 12 * q - 12 * q^4	$ 12 q - 12 q^{4} + 24 q^{10} + 36 q^{13} + 24 q^{16} + 120 q^{22} - 132 q^{25} + 420 q^{28} - 360 q^{34} + 516 q^{37} - 1152 q^{40} - 696 q^{46} - 720 q^{49} + 204 q^{52} + 2832 q^{58} - 972 q^{61} + 2496 q^{64} - 1848 q^{70} + 660 q^{73} - 5004 q^{76} - 3888 q^{82} + 1056 q^{85} + 3168 q^{88} + 7608 q^{94} + 2532 q^{97}+O(q^{100}) $ 12 * q - 12 * q^4 + 24 * q^10 + 36 * q^13 + 24 * q^16 + 120 * q^22 - 132 * q^25 + 420 * q^28 - 360 * q^34 + 516 * q^37 - 1152 * q^40 - 696 * q^46 - 720 * q^49 + 204 * q^52 + 2832 * q^58 - 972 * q^61 + 2496 * q^64 - 1848 * q^70 + 660 * q^73 - 5004 * q^76 - 3888 * q^82 + 1056 * q^85 + 3168 * q^88 + 7608 * q^94 + 2532 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.72087	+	0.772562i	−0.961974	+	0.273142i
$2$	−2.72087	+	0.772562i	−0.961974	+	0.273142i
$3$		0			0
$3$		0			0
$4$	6.80630	−	4.20408i	0.850787	−	0.525510i
$5$			3.33155i			0.297983i	0.988838	+	0.148992i	$0.0476027\pi$
$5$			3.33155i			0.297983i	−0.988838	+	0.148992i	$0.952397\pi$
$6$		0			0
$7$		−	16.9016i		−	0.912600i	−0.889826	−	0.456300i	$-0.849174\pi$
$7$		−	16.9016i		−	0.912600i	0.889826	−	0.456300i	$-0.150826\pi$
$8$	−15.2712	+	16.6971i	−0.674896	+	0.737913i
$9$		0			0
$10$	−2.57383	−	9.06473i	−0.0813917	−	0.286652i
$11$	−16.8325			−0.461380			−0.230690	−	0.973027i	$-0.574098\pi$
$11$	−16.8325			−0.461380			−0.230690	+	0.973027i	$0.574098\pi$
$12$		0			0
$13$	25.0775			0.535020			0.267510	−	0.963555i	$-0.413799\pi$
$13$	25.0775			0.535020			0.267510	+	0.963555i	$0.413799\pi$
$14$	13.0575	+	45.9871i	0.249269	+	0.877897i
$15$		0			0
$16$	28.6514	−	57.2285i	0.447677	−	0.894195i
$17$		−	116.919i		−	1.66806i	−0.551722	−	0.834028i	$-0.686029\pi$
$17$		−	116.919i		−	1.66806i	0.551722	−	0.834028i	$-0.313971\pi$
$18$		0			0
$19$		−	85.4801i		−	1.03213i	−0.856549	−	0.516065i	$-0.827396\pi$
$19$		−	85.4801i		−	1.03213i	0.856549	−	0.516065i	$-0.172604\pi$
$20$	14.0061	+	22.6755i	0.156593	+	0.253520i
$21$		0			0
$22$	45.7990	−	13.0041i	0.443836	−	0.126022i
$23$	158.740			1.43911			0.719555	−	0.694436i	$-0.244346\pi$
$23$	158.740			1.43911			0.719555	+	0.694436i	$0.244346\pi$
$24$		0			0
$25$	113.901			0.911206
$26$	−68.2328	+	19.3739i	−0.514675	+	0.146136i
$27$		0			0
$28$	−71.0557	−	115.037i	−0.479581	−	0.776428i
$29$		−	269.955i		−	1.72860i	−0.502976	−	0.864300i	$-0.667762\pi$
$29$		−	269.955i		−	1.72860i	0.502976	−	0.864300i	$-0.332238\pi$
$30$		0			0
$31$			36.0884i			0.209086i	0.994520	+	0.104543i	$0.0333380\pi$
$31$			36.0884i			0.209086i	−0.994520	+	0.104543i	$0.966662\pi$
$32$	−33.7442	+	177.846i	−0.186412	+	0.982472i
$33$		0			0
$34$	90.3269	+	318.121i	0.455616	+	1.60463i
$35$	56.3085			0.271939
$36$		0			0
$37$	−353.780			−1.57192			−0.785960	−	0.618277i	$-0.787831\pi$
$37$	−353.780			−1.57192			−0.785960	+	0.618277i	$0.787831\pi$
$38$	66.0386	+	232.580i	0.281918	+	0.992882i
$39$		0			0
$40$	−55.6272	−	50.8767i	−0.219886	−	0.201108i
$41$		−	144.415i		−	0.550093i	−0.961431	−	0.275046i	$-0.911307\pi$
$41$		−	144.415i		−	0.550093i	0.961431	−	0.275046i	$-0.0886932\pi$
$42$		0			0
$43$			368.186i			1.30576i	0.757460	+	0.652881i	$0.226440\pi$
$43$			368.186i			1.30576i	−0.757460	+	0.652881i	$0.773560\pi$
$44$	−114.567	+	70.7651i	−0.392536	+	0.242460i
$45$		0			0
$46$	−431.911	+	122.636i	−1.38439	+	0.393081i
$47$	−397.333			−1.23313			−0.616563	−	0.787305i	$-0.711476\pi$
$47$	−397.333			−1.23313			−0.616563	+	0.787305i	$0.711476\pi$
$48$		0			0
$49$	57.3363			0.167161
$50$	−309.909	+	87.9954i	−0.876556	+	0.248888i
$51$		0			0
$52$	170.685	−	105.428i	0.455188	−	0.281158i
$53$			96.0857i			0.249026i	0.992218	+	0.124513i	$0.0397369\pi$
$53$			96.0857i			0.249026i	−0.992218	+	0.124513i	$0.960263\pi$
$54$		0			0
$55$		−	56.0783i		−	0.137484i
$56$	282.207	+	258.107i	0.673419	+	0.615910i
$57$		0			0
$58$	208.557	+	734.514i	0.472153	+	1.66287i
$59$	294.902			0.650727			0.325364	−	0.945589i	$-0.394513\pi$
$59$	294.902			0.650727			0.325364	+	0.945589i	$0.394513\pi$
$60$		0			0
$61$	146.724			0.307969			0.153984	−	0.988073i	$-0.450789\pi$
$61$	146.724			0.307969			0.153984	+	0.988073i	$0.450789\pi$
$62$	−27.8805	−	98.1920i	−0.0571102	−	0.201135i
$63$		0			0
$64$	−45.5837	−	509.967i	−0.0890307	−	0.996029i
$65$			83.5471i			0.159427i
$66$		0			0
$67$			301.433i			0.549641i	0.961496	+	0.274820i	$0.0886184\pi$
$67$			301.433i			0.549641i	−0.961496	+	0.274820i	$0.911382\pi$
$68$	−491.536	−	795.784i	−0.876581	−	1.41916i
$69$		0			0
$70$	−153.208	+	43.5018i	−0.261599	+	0.0742780i
$71$	687.794			1.14966			0.574832	−	0.818272i	$-0.305067\pi$
$71$	687.794			1.14966			0.574832	+	0.818272i	$0.305067\pi$
$72$		0			0
$73$	−312.138			−0.500452			−0.250226	−	0.968187i	$-0.580505\pi$
$73$	−312.138			−0.500452			−0.250226	+	0.968187i	$0.580505\pi$
$74$	962.590	−	273.317i	1.51215	−	0.429357i
$75$		0			0
$76$	−359.365	−	581.803i	−0.542395	−	0.878123i
$77$			284.496i			0.421056i
$78$		0			0
$79$		−	602.063i		−	0.857436i	−0.903438	−	0.428718i	$-0.858965\pi$
$79$		−	602.063i		−	0.857436i	0.903438	−	0.428718i	$-0.141035\pi$
$80$	190.660	+	95.4535i	0.266455	+	0.133400i
$81$		0			0
$82$	111.569	+	392.934i	0.150253	+	0.529175i
$83$	−1334.44			−1.76475			−0.882373	−	0.470551i	$-0.844055\pi$
$83$	−1334.44			−1.76475			−0.882373	+	0.470551i	$0.844055\pi$
$84$		0			0
$85$	389.521			0.497053
$86$	−284.446	−	1001.79i	−0.356658	−	1.25611i
$87$		0			0
$88$	257.051	−	281.053i	0.311384	−	0.340458i
$89$			856.292i			1.01985i	0.860218	+	0.509926i	$0.170327\pi$
$89$			856.292i			1.01985i	−0.860218	+	0.509926i	$0.829673\pi$
$90$		0			0
$91$		−	423.850i		−	0.488259i
$92$	1080.43	−	667.355i	1.22438	−	0.756267i
$93$		0			0
$94$	1081.09	−	306.964i	1.18624	−	0.336818i
$95$	284.781			0.307557
$96$		0			0
$97$	218.564			0.228782			0.114391	−	0.993436i	$-0.463508\pi$
$97$	218.564			0.228782			0.114391	+	0.993436i	$0.463508\pi$
$98$	−156.005	+	44.2959i	−0.160805	+	0.0456587i
$99$		0			0
$100$	775.242	−	478.848i	0.775242	−	0.478848i
$101$			793.625i			0.781868i	0.920419	+	0.390934i	$0.127848\pi$
$101$			793.625i			0.781868i	−0.920419	+	0.390934i	$0.872152\pi$
$102$		0			0
$103$		−	1245.59i		−	1.19157i	−0.803145	−	0.595784i	$-0.796841\pi$
$103$		−	1245.59i		−	1.19157i	0.803145	−	0.595784i	$-0.203159\pi$
$104$	−382.963	+	418.721i	−0.361083	+	0.394798i
$105$		0			0
$106$	−74.2321	−	261.437i	−0.0680194	−	0.239557i
$107$	−95.7189			−0.0864813			−0.0432406	−	0.999065i	$-0.513768\pi$
$107$	−95.7189			−0.0864813			−0.0432406	+	0.999065i	$0.513768\pi$
$108$		0			0
$109$	1349.09			1.18550			0.592749	−	0.805387i	$-0.298043\pi$
$109$	1349.09			1.18550			0.592749	+	0.805387i	$0.298043\pi$
$110$	43.3239	+	152.582i	0.0375525	+	0.132256i
$111$		0			0
$112$	−967.252	−	484.253i	−0.816042	−	0.408550i
$113$			1885.41i			1.56960i	0.619750	+	0.784799i	$0.287234\pi$
$113$			1885.41i			1.56960i	−0.619750	+	0.784799i	$0.712766\pi$
$114$		0			0
$115$			528.850i			0.428831i
$116$	−1134.91	−	1837.40i	−0.908398	−	1.47067i
$117$		0			0
$118$	−802.390	+	227.830i	−0.625983	+	0.177741i
$119$	−1976.11			−1.52227
$120$		0			0
$121$	−1047.67			−0.787128
$122$	−399.217	+	113.353i	−0.296258	+	0.0841191i
$123$		0			0
$124$	151.719	+	245.629i	0.109877	+	0.177888i
$125$			795.911i			0.569507i
$126$		0			0
$127$			714.330i			0.499106i	0.968361	+	0.249553i	$0.0802838\pi$
$127$			714.330i			0.499106i	−0.968361	+	0.249553i	$0.919716\pi$
$128$	518.008	+	1352.34i	0.357702	+	0.933836i
$129$		0			0
$130$	−64.5453	−	227.321i	−0.0435461	−	0.153364i
$131$	2153.89			1.43654			0.718268	−	0.695766i	$-0.244935\pi$
$131$	2153.89			1.43654			0.718268	+	0.695766i	$0.244935\pi$
$132$		0			0
$133$	−1444.75			−0.941922
$134$	−232.876	−	820.161i	−0.150130	−	0.528740i
$135$		0			0
$136$	1952.20	+	1785.48i	1.23088	+	1.12576i
$137$		−	2053.68i		−	1.28071i	−0.768079	−	0.640356i	$-0.778787\pi$
$137$		−	2053.68i		−	1.28071i	0.768079	−	0.640356i	$-0.221213\pi$
$138$		0			0
$139$			2000.40i			1.22066i	0.792148	+	0.610329i	$0.208963\pi$
$139$			2000.40i			1.22066i	−0.792148	+	0.610329i	$0.791037\pi$
$140$	383.253	−	236.726i	0.231363	−	0.142907i
$141$		0			0
$142$	−1871.40	+	531.363i	−1.10595	+	0.314021i
$143$	−422.117			−0.246847
$144$		0			0
$145$	899.370			0.515094
$146$	849.287	−	241.146i	0.481421	−	0.136694i
$147$		0			0
$148$	−2407.93	+	1487.32i	−1.33737	+	0.826060i
$149$		−	988.026i		−	0.543236i	−0.962405	−	0.271618i	$-0.912441\pi$
$149$		−	988.026i		−	0.543236i	0.962405	−	0.271618i	$-0.0875588\pi$
$150$		0			0
$151$		−	1630.56i		−	0.878764i	−0.898300	−	0.439382i	$-0.855197\pi$
$151$		−	1630.56i		−	0.878764i	0.898300	−	0.439382i	$-0.144803\pi$
$152$	1427.27	+	1305.38i	0.761622	+	0.696580i
$153$		0			0
$154$	−219.790	−	774.076i	−0.115008	−	0.405044i
$155$	−120.231			−0.0623042
$156$		0			0
$157$	−690.002			−0.350752			−0.175376	−	0.984501i	$-0.556114\pi$
$157$	−690.002			−0.350752			−0.175376	+	0.984501i	$0.556114\pi$
$158$	465.131	+	1638.14i	0.234202	+	0.824831i
$159$		0			0
$160$	−592.505	−	112.420i	−0.292760	−	0.0555476i
$161$		−	2682.95i		−	1.31333i
$162$		0			0
$163$			3414.58i			1.64080i	0.571790	+	0.820400i	$0.306249\pi$
$163$			3414.58i			1.64080i	−0.571790	+	0.820400i	$0.693751\pi$
$164$	−607.132	−	982.930i	−0.289080	−	0.468012i
$165$		0			0
$166$	3630.84	−	1030.94i	1.69764	−	0.482026i
$167$	1372.95			0.636180			0.318090	−	0.948061i	$-0.396959\pi$
$167$	1372.95			0.636180			0.318090	+	0.948061i	$0.396959\pi$
$168$		0			0
$169$	−1568.12			−0.713754
$170$	−1059.84	+	300.929i	−0.478152	+	0.135766i
$171$		0			0
$172$	1547.88	+	2505.98i	0.686192	+	1.11093i
$173$		−	1118.25i		−	0.491441i	−0.969341	−	0.245721i	$-0.920975\pi$
$173$		−	1118.25i		−	0.491441i	0.969341	−	0.245721i	$-0.0790246\pi$
$174$		0			0
$175$		−	1925.10i		−	0.831567i
$176$	−482.273	+	963.297i	−0.206549	+	0.412564i
$177$		0			0
$178$	−661.539	−	2329.86i	−0.278564	−	0.981071i
$179$	1755.59			0.733067			0.366534	−	0.930405i	$-0.380544\pi$
$179$	1755.59			0.733067			0.366534	+	0.930405i	$0.380544\pi$
$180$		0			0
$181$	312.973			0.128525			0.0642626	−	0.997933i	$-0.479530\pi$
$181$	312.973			0.128525			0.0642626	+	0.997933i	$0.479530\pi$
$182$	327.450	+	1153.24i	0.133364	+	0.469692i
$183$		0			0
$184$	−2424.14	+	2650.49i	−0.971249	+	1.06194i
$185$		−	1178.64i		−	0.468406i
$186$		0			0
$187$			1968.03i			0.769608i
$188$	−2704.36	+	1670.42i	−1.04913	+	0.648021i
$189$		0			0
$190$	−774.854	+	220.011i	−0.295862	+	0.0840068i
$191$	2024.40			0.766915			0.383457	−	0.923559i	$-0.374733\pi$
$191$	2024.40			0.766915			0.383457	+	0.923559i	$0.374733\pi$
$192$		0			0
$193$	1138.00			0.424431			0.212216	−	0.977223i	$-0.431932\pi$
$193$	1138.00			0.424431			0.212216	+	0.977223i	$0.431932\pi$
$194$	−594.686	+	168.854i	−0.220082	+	0.0624899i
$195$		0			0
$196$	390.248	−	241.047i	0.142219	−	0.0878450i
$197$		−	2345.77i		−	0.848370i	−0.905576	−	0.424185i	$-0.860561\pi$
$197$		−	2345.77i		−	0.848370i	0.905576	−	0.424185i	$-0.139439\pi$
$198$		0			0
$199$		−	2839.16i		−	1.01137i	−0.862718	−	0.505686i	$-0.831240\pi$
$199$		−	2839.16i		−	1.01137i	0.862718	−	0.505686i	$-0.168760\pi$
$200$	−1739.40	+	1901.81i	−0.614969	+	0.672391i
$201$		0			0
$202$	−613.124	−	2159.35i	−0.213561	−	0.752136i
$203$	−4562.67			−1.57752
$204$		0			0
$205$	481.126			0.163918
$206$	962.294	+	3389.09i	0.325467	+	1.14626i
$207$		0			0
$208$	718.505	−	1435.15i	0.239516	−	0.478412i
$209$			1438.84i			0.476204i
$210$		0			0
$211$			256.564i			0.0837091i	0.999124	+	0.0418545i	$0.0133266\pi$
$211$			256.564i			0.0837091i	−0.999124	+	0.0418545i	$0.986673\pi$
$212$	403.952	+	653.988i	0.130866	+	0.211868i
$213$		0			0
$214$	260.439	−	73.9488i	0.0831927	−	0.0236217i
$215$	−1226.63			−0.389095
$216$		0			0
$217$	609.952			0.190812
$218$	−3670.70	+	1042.25i	−1.14042	+	0.323809i
$219$		0			0
$220$	−235.758	−	381.685i	−0.0722490	−	0.116969i
$221$		−	2932.03i		−	0.892443i
$222$		0			0
$223$		−	4020.58i		−	1.20734i	−0.797233	−	0.603672i	$-0.793704\pi$
$223$		−	4020.58i		−	1.20734i	0.797233	−	0.603672i	$-0.206296\pi$
$224$	3005.89	+	570.330i	0.896604	+	0.170120i
$225$		0			0
$226$	−1456.60	−	5129.97i	−0.428723	−	1.50991i
$227$	2958.44			0.865016			0.432508	−	0.901630i	$-0.357629\pi$
$227$	2958.44			0.865016			0.432508	+	0.901630i	$0.357629\pi$
$228$		0			0
$229$	226.069			0.0652360			0.0326180	−	0.999468i	$-0.489616\pi$
$229$	226.069			0.0652360			0.0326180	+	0.999468i	$0.489616\pi$
$230$	−408.569	−	1438.93i	−0.117132	−	0.412524i
$231$		0			0
$232$	4507.46	+	4122.53i	1.27556	+	1.16663i
$233$			2356.56i			0.662591i	0.943527	+	0.331295i	$0.107486\pi$
$233$			2356.56i			0.662591i	−0.943527	+	0.331295i	$0.892514\pi$
$234$		0			0
$235$		−	1323.74i		−	0.367451i
$236$	2007.19	−	1239.79i	0.553630	−	0.341964i
$237$		0			0
$238$	5376.75	−	1526.67i	1.46438	−	0.415795i
$239$	−2191.70			−0.593176			−0.296588	−	0.955006i	$-0.595849\pi$
$239$	−2191.70			−0.593176			−0.296588	+	0.955006i	$0.595849\pi$
$240$		0			0
$241$	6532.08			1.74593			0.872963	−	0.487787i	$-0.162196\pi$
$241$	6532.08			1.74593			0.872963	+	0.487787i	$0.162196\pi$
$242$	2850.57	−	809.388i	0.757197	−	0.214998i
$243$		0			0
$244$	998.647	−	616.840i	0.262016	−	0.161841i
$245$			191.019i			0.0498113i
$246$		0			0
$247$		−	2143.63i		−	0.552210i
$248$	−602.571	−	551.112i	−0.154287	−	0.141111i
$249$		0			0
$250$	−614.890	−	2165.57i	−0.155556	−	0.547851i
$251$	−34.6697			−0.00871844			−0.00435922	−	0.999990i	$-0.501388\pi$
$251$	−34.6697			−0.00871844			−0.00435922	+	0.999990i	$0.501388\pi$
$252$		0			0
$253$	−2671.98			−0.663977
$254$	−551.864	−	1943.60i	−0.136327	−	0.480127i
$255$		0			0
$256$	−2454.20	−	3279.35i	−0.599170	−	0.800622i
$257$		−	3945.92i		−	0.957742i	−0.877885	−	0.478871i	$-0.841046\pi$
$257$		−	3945.92i		−	0.957742i	0.877885	−	0.478871i	$-0.158954\pi$
$258$		0			0
$259$			5979.44i			1.43453i
$260$	351.239	+	568.647i	0.0837805	+	0.135638i
$261$		0			0
$262$	−5860.46	+	1664.01i	−1.38191	+	0.392378i
$263$	6558.79			1.53777			0.768883	−	0.639390i	$-0.220813\pi$
$263$	6558.79			1.53777			0.768883	+	0.639390i	$0.220813\pi$
$264$		0			0
$265$	−320.115			−0.0742056
$266$	3930.98	−	1116.16i	0.906104	−	0.257278i
$267$		0			0
$268$	1267.25	+	2051.64i	0.288842	+	0.467627i
$269$			3741.27i			0.847991i	0.905664	+	0.423995i	$0.139373\pi$
$269$			3741.27i			0.847991i	−0.905664	+	0.423995i	$0.860627\pi$
$270$		0			0
$271$		−	6011.98i		−	1.34761i	−0.738910	−	0.673804i	$-0.764659\pi$
$271$		−	6011.98i		−	1.34761i	0.738910	−	0.673804i	$-0.235341\pi$
$272$	−6691.08	−	3349.88i	−1.49157	−	0.746751i
$273$		0			0
$274$	1586.59	+	5587.79i	0.349816	+	1.23201i
$275$	−1917.23			−0.420412
$276$		0			0
$277$	−4524.48			−0.981407			−0.490704	−	0.871327i	$-0.663260\pi$
$277$	−4524.48			−0.981407			−0.490704	+	0.871327i	$0.663260\pi$
$278$	−1545.43	−	5442.83i	−0.333413	−	1.17424i
$279$		0			0
$280$	−859.896	+	940.187i	−0.183531	+	0.200668i
$281$			4251.22i			0.902514i	0.892394	+	0.451257i	$0.149024\pi$
$281$			4251.22i			0.902514i	−0.892394	+	0.451257i	$0.850976\pi$
$282$		0			0
$283$			4433.04i			0.931154i	0.885007	+	0.465577i	$0.154153\pi$
$283$			4433.04i			0.931154i	−0.885007	+	0.465577i	$0.845847\pi$
$284$	4681.33	−	2891.54i	0.978119	−	0.604160i
$285$		0			0
$286$	1148.53	−	326.111i	0.237461	−	0.0674243i
$287$	−2440.84			−0.502015
$288$		0			0
$289$	−8756.99			−1.78241
$290$	−2447.07	+	694.819i	−0.495507	+	0.140694i
$291$		0			0
$292$	−2124.50	+	1312.25i	−0.425778	+	0.262993i
$293$			7734.73i			1.54221i	0.636708	+	0.771105i	$0.280296\pi$
$293$			7734.73i			1.54221i	−0.636708	+	0.771105i	$0.719704\pi$
$294$		0			0
$295$			982.480i			0.193906i
$296$	5402.63	−	5907.08i	1.06088	−	1.15994i
$297$		0			0
$298$	763.311	+	2688.29i	0.148381	+	0.522579i
$299$	3980.80			0.769952
$300$		0			0
$301$	6222.92			1.19164
$302$	1259.71	+	4436.56i	0.240027	+	0.845348i
$303$		0			0
$304$	−4891.89	−	2449.12i	−0.922926	−	0.462061i
$305$			488.819i			0.0917694i
$306$		0			0
$307$			8510.18i			1.58209i	0.611759	+	0.791045i	$0.290462\pi$
$307$			8510.18i			1.58209i	−0.611759	+	0.791045i	$0.709538\pi$
$308$	1196.04	+	1936.36i	0.221269	+	0.358229i
$309$		0			0
$310$	327.132	−	92.8855i	0.0599350	−	0.0170179i
$311$	−8133.65			−1.48301			−0.741507	−	0.670945i	$-0.765888\pi$
$311$	−8133.65			−1.48301			−0.741507	+	0.670945i	$0.765888\pi$
$312$		0			0
$313$	5066.73			0.914979			0.457489	−	0.889215i	$-0.348749\pi$
$313$	5066.73			0.914979			0.457489	+	0.889215i	$0.348749\pi$
$314$	1877.41	−	533.069i	0.337415	−	0.0958052i
$315$		0			0
$316$	−2531.13	−	4097.82i	−0.450591	−	0.729495i
$317$			4122.54i			0.730425i	0.930924	+	0.365212i	$0.119004\pi$
$317$			4122.54i			0.730425i	−0.930924	+	0.365212i	$0.880996\pi$
$318$		0			0
$319$			4544.01i			0.797542i
$320$	1698.98	−	151.865i	0.296800	−	0.0265296i
$321$		0			0
$322$	2072.75	+	7299.98i	0.358726	+	1.26339i
$323$	−9994.22			−1.72165
$324$		0			0
$325$	2856.35			0.487513
$326$	−2637.97	−	9290.63i	−0.448171	−	1.57841i
$327$		0			0
$328$	2411.30	+	2205.38i	0.405921	+	0.371256i
$329$			6715.55i			1.12535i
$330$		0			0
$331$		−	3819.96i		−	0.634332i	−0.948370	−	0.317166i	$-0.897269\pi$
$331$		−	3819.96i		−	0.634332i	0.948370	−	0.317166i	$-0.102731\pi$
$332$	−9082.60	+	5610.10i	−1.50142	+	0.927392i
$333$		0			0
$334$	−3735.62	+	1060.69i	−0.611988	+	0.173767i
$335$	−1004.24			−0.163784
$336$		0			0
$337$	−9712.35			−1.56993			−0.784963	−	0.619542i	$-0.787318\pi$
$337$	−9712.35			−1.56993			−0.784963	+	0.619542i	$0.787318\pi$
$338$	4266.65	−	1211.47i	0.686613	−	0.194956i
$339$		0			0
$340$	2651.20	−	1637.58i	0.422886	−	0.261206i
$341$		−	607.457i		−	0.0964682i
$342$		0			0
$343$		−	6766.32i		−	1.06515i
$344$	−6147.62	−	5622.62i	−0.963539	−	0.881254i
$345$		0			0
$346$	863.921	+	3042.63i	0.134233	+	0.472754i
$347$	3315.20			0.512880			0.256440	−	0.966560i	$-0.417450\pi$
$347$	3315.20			0.512880			0.256440	+	0.966560i	$0.417450\pi$
$348$		0			0
$349$	−2864.88			−0.439408			−0.219704	−	0.975567i	$-0.570509\pi$
$349$	−2864.88			−0.439408			−0.219704	+	0.975567i	$0.570509\pi$
$350$	1487.26	+	5237.96i	0.227136	+	0.799945i
$351$		0			0
$352$	567.998	−	2993.59i	0.0860068	−	0.453293i
$353$			4904.72i			0.739523i	0.929127	+	0.369762i	$0.120561\pi$
$353$			4904.72i			0.739523i	−0.929127	+	0.369762i	$0.879439\pi$
$354$		0			0
$355$			2291.42i			0.342580i
$356$	3599.92	+	5828.18i	0.535943	+	0.867677i
$357$		0			0
$358$	−4776.74	+	1356.30i	−0.705191	+	0.200231i
$359$	4185.24			0.615288			0.307644	−	0.951501i	$-0.400459\pi$
$359$	4185.24			0.615288			0.307644	+	0.951501i	$0.400459\pi$
$360$		0			0
$361$	−447.841			−0.0652924
$362$	−851.559	+	241.791i	−0.123638	+	0.0351056i
$363$		0			0
$364$	−1781.90	−	2884.85i	−0.256585	−	0.415404i
$365$		−	1039.90i		−	0.149126i
$366$		0			0
$367$			4979.97i			0.708317i	0.935185	+	0.354158i	$0.115233\pi$
$367$			4979.97i			0.708317i	−0.935185	+	0.354158i	$0.884767\pi$
$368$	4548.11	−	9084.44i	0.644257	−	1.28684i
$369$		0			0
$370$	910.569	+	3206.92i	0.127941	+	0.450594i
$371$	1624.00			0.227261
$372$		0			0
$373$	6411.84			0.890060			0.445030	−	0.895516i	$-0.353193\pi$
$373$	6411.84			0.890060			0.445030	+	0.895516i	$0.353193\pi$
$374$	−1520.43	−	5354.76i	−0.210212	−	0.740343i
$375$		0			0
$376$	6067.73	−	6634.29i	0.832232	−	0.909940i
$377$		−	6769.81i		−	0.924835i
$378$		0			0
$379$			5294.51i			0.717574i	0.933419	+	0.358787i	$0.116810\pi$
$379$			5294.51i			0.717574i	−0.933419	+	0.358787i	$0.883190\pi$
$380$	1938.31	−	1197.24i	0.261666	−	0.161625i
$381$		0			0
$382$	−5508.14	+	1563.98i	−0.737752	+	0.209476i
$383$	5923.23			0.790242			0.395121	−	0.918629i	$-0.370703\pi$
$383$	5923.23			0.790242			0.395121	+	0.918629i	$0.370703\pi$
$384$		0			0
$385$	−947.812			−0.125467
$386$	−3096.36	+	879.177i	−0.408292	+	0.115930i
$387$		0			0
$388$	1487.61	−	918.863i	0.194645	−	0.120227i
$389$		−	4084.92i		−	0.532426i	−0.963914	−	0.266213i	$-0.914228\pi$
$389$		−	4084.92i		−	0.532426i	0.963914	−	0.266213i	$-0.0857724\pi$
$390$		0			0
$391$		−	18559.6i		−	2.40052i
$392$	−875.592	+	957.348i	−0.112817	+	0.123350i
$393$		0			0
$394$	1812.25	+	6382.53i	0.231725	+	0.816110i
$395$	2005.81			0.255501
$396$		0			0
$397$	2821.56			0.356700			0.178350	−	0.983967i	$-0.442924\pi$
$397$	2821.56			0.356700			0.178350	+	0.983967i	$0.442924\pi$
$398$	2193.43	+	7725.00i	0.276248	+	0.972912i
$399$		0			0
$400$	3263.41	−	6518.37i	0.407926	−	0.814796i
$401$		−	4215.14i		−	0.524923i	−0.964942	−	0.262461i	$-0.915466\pi$
$401$		−	4215.14i		−	0.524923i	0.964942	−	0.262461i	$-0.0845343\pi$
$402$		0			0
$403$			905.009i			0.111865i
$404$	3336.47	+	5401.65i	0.410880	+	0.665203i
$405$		0			0
$406$	12414.4	−	3524.94i	1.51753	−	0.430887i
$407$	5954.99			0.725253
$408$		0			0
$409$	605.285			0.0731771			0.0365885	−	0.999330i	$-0.488351\pi$
$409$	605.285			0.0731771			0.0365885	+	0.999330i	$0.488351\pi$
$410$	−1309.08	+	371.699i	−0.157685	+	0.0447730i
$411$		0			0
$412$	−5236.56	−	8477.85i	−0.626181	−	1.01377i
$413$		−	4984.30i		−	0.593854i
$414$		0			0
$415$		−	4445.76i		−	0.525865i
$416$	−846.220	+	4459.95i	−0.0997340	+	0.525642i
$417$		0			0
$418$	−1111.59	−	3914.90i	−0.130071	−	0.458096i
$419$	−6479.90			−0.755523			−0.377761	−	0.925903i	$-0.623306\pi$
$419$	−6479.90			−0.755523			−0.377761	+	0.925903i	$0.623306\pi$
$420$		0			0
$421$	−363.812			−0.0421166			−0.0210583	−	0.999778i	$-0.506704\pi$
$421$	−363.812			−0.0421166			−0.0210583	+	0.999778i	$0.506704\pi$
$422$	−198.212	−	698.079i	−0.0228645	−	0.0805260i
$423$		0			0
$424$	−1604.35	−	1467.34i	−0.183760	−	0.168067i
$425$		−	13317.1i		−	1.51994i
$426$		0			0
$427$		−	2479.87i		−	0.281052i
$428$	−651.491	+	402.410i	−0.0735772	+	0.0454468i
$429$		0			0
$430$	3337.50	−	947.647i	0.374299	−	0.106278i
$431$	−1486.97			−0.166182			−0.0830912	−	0.996542i	$-0.526479\pi$
$431$	−1486.97			−0.166182			−0.0830912	+	0.996542i	$0.526479\pi$
$432$		0			0
$433$	12322.8			1.36765			0.683827	−	0.729644i	$-0.260314\pi$
$433$	12322.8			1.36765			0.683827	+	0.729644i	$0.260314\pi$
$434$	−1659.60	+	471.225i	−0.183556	+	0.0521188i
$435$		0			0
$436$	9182.30	−	5671.69i	1.00861	−	0.622992i
$437$		−	13569.1i		−	1.48535i
$438$		0			0
$439$		−	10918.0i		−	1.18698i	−0.804840	−	0.593492i	$-0.797749\pi$
$439$		−	10918.0i		−	1.18698i	0.804840	−	0.593492i	$-0.202251\pi$
$440$	936.343	+	856.380i	0.101451	+	0.0927871i
$441$		0			0
$442$	2265.18	+	7977.69i	0.243763	+	0.858507i
$443$	−3934.04			−0.421923			−0.210961	−	0.977494i	$-0.567659\pi$
$443$	−3934.04			−0.421923			−0.210961	+	0.977494i	$0.567659\pi$
$444$		0			0
$445$	−2852.78			−0.303899
$446$	3106.14	+	10939.5i	0.329776	+	1.16143i
$447$		0			0
$448$	−8619.25	+	770.437i	−0.908976	+	0.0812494i
$449$			9560.84i			1.00491i	0.864604	+	0.502454i	$0.167570\pi$
$449$			9560.84i			1.00491i	−0.864604	+	0.502454i	$0.832430\pi$
$450$		0			0
$451$			2430.86i			0.253802i
$452$	7926.43	+	12832.7i	0.824840	+	1.33539i
$453$		0			0
$454$	−8049.54	+	2285.58i	−0.832123	+	0.236272i
$455$	1412.08			0.145493
$456$		0			0
$457$	6479.90			0.663276			0.331638	−	0.943407i	$-0.392399\pi$
$457$	6479.90			0.663276			0.331638	+	0.943407i	$0.392399\pi$
$458$	−615.105	+	174.652i	−0.0627553	+	0.0178187i
$459$		0			0
$460$	2223.33	+	3599.51i	0.225355	+	0.364843i
$461$			3560.77i			0.359743i	0.983690	+	0.179872i	$0.0575682\pi$
$461$			3560.77i			0.359743i	−0.983690	+	0.179872i	$0.942432\pi$
$462$		0			0
$463$			15775.3i			1.58346i	0.610874	+	0.791728i	$0.290818\pi$
$463$			15775.3i			1.58346i	−0.610874	+	0.791728i	$0.709182\pi$
$464$	−15449.1	−	7734.58i	−1.54571	−	0.773856i
$465$		0			0
$466$	−1820.59	−	6411.91i	−0.180981	−	0.637395i
$467$	14291.6			1.41614			0.708071	−	0.706141i	$-0.249566\pi$
$467$	14291.6			1.41614			0.708071	+	0.706141i	$0.249566\pi$
$468$		0			0
$469$	5094.70			0.501602
$470$	1022.67	+	3601.72i	0.100366	+	0.353478i
$471$		0			0
$472$	−4503.49	+	4923.99i	−0.439173	+	0.480180i
$473$		−	6197.48i		−	0.602453i
$474$		0			0
$475$		−	9736.24i		−	0.940483i
$476$	−13450.0	+	8307.74i	−1.29513	+	0.799968i
$477$		0			0
$478$	5963.32	−	1693.22i	0.570619	−	0.162021i
$479$	−14630.0			−1.39553			−0.697766	−	0.716326i	$-0.745822\pi$
$479$	−14630.0			−1.39553			−0.697766	+	0.716326i	$0.745822\pi$
$480$		0			0
$481$	−8871.92			−0.841008
$482$	−17772.9	+	5046.43i	−1.67953	+	0.476885i
$483$		0			0
$484$	−7130.74	+	4404.48i	−0.669679	+	0.413644i
$485$			728.159i			0.0681732i
$486$		0			0
$487$			16742.7i			1.55787i	0.627102	+	0.778937i	$0.284241\pi$
$487$			16742.7i			1.55787i	−0.627102	+	0.778937i	$0.715759\pi$
$488$	−2240.64	+	2449.86i	−0.207847	+	0.227254i
$489$		0			0
$490$	−147.574	−	519.739i	−0.0136055	−	0.0479171i
$491$	7342.23			0.674847			0.337424	−	0.941353i	$-0.390445\pi$
$491$	7342.23			0.674847			0.337424	+	0.941353i	$0.390445\pi$
$492$		0			0
$493$	−31562.8			−2.88340
$494$	1656.09	+	5832.54i	0.150832	+	0.531211i
$495$		0			0
$496$	2065.29	+	1033.98i	0.186964	+	0.0936032i
$497$		−	11624.8i		−	1.04918i
$498$		0			0
$499$			1565.06i			0.140404i	0.997533	+	0.0702020i	$0.0223644\pi$
$499$			1565.06i			0.140404i	−0.997533	+	0.0702020i	$0.977636\pi$
$500$	3346.07	+	5417.20i	0.299282	+	0.484529i
$501$		0			0
$502$	94.3317	−	26.7844i	0.00838691	−	0.00238137i
$503$	−1257.87			−0.111503			−0.0557513	−	0.998445i	$-0.517755\pi$
$503$	−1257.87			−0.111503			−0.0557513	+	0.998445i	$0.517755\pi$
$504$		0			0
$505$	−2644.00			−0.232983
$506$	7270.12	−	2064.27i	0.638728	−	0.181360i
$507$		0			0
$508$	3003.10	+	4861.94i	0.262286	+	0.424633i
$509$			3160.96i			0.275260i	0.990484	+	0.137630i	$0.0439484\pi$
$509$			3160.96i			0.275260i	−0.990484	+	0.137630i	$0.956052\pi$
$510$		0			0
$511$			5275.63i			0.456712i
$512$	9211.06	+	7026.67i	0.795069	+	0.606519i
$513$		0			0
$514$	3048.47	+	10736.3i	0.261599	+	0.921323i
$515$	4149.75			0.355067
$516$		0			0
$517$	6688.09			0.568940
$518$	−4619.49	−	16269.3i	−0.391831	−	1.37998i
$519$		0			0
$520$	−1394.99	−	1275.86i	−0.117643	−	0.107597i
$521$			2973.62i			0.250051i	0.992154	+	0.125026i	$0.0399013\pi$
$521$			2973.62i			0.250051i	−0.992154	+	0.125026i	$0.960099\pi$
$522$		0			0
$523$		−	8019.43i		−	0.670488i	−0.942131	−	0.335244i	$-0.891181\pi$
$523$		−	8019.43i		−	0.670488i	0.942131	−	0.335244i	$-0.108819\pi$
$524$	14660.0	−	9055.14i	1.22219	−	0.754915i
$525$		0			0
$526$	−17845.6	+	5067.07i	−1.47929	+	0.420028i
$527$	4219.41			0.348768
$528$		0			0
$529$	13031.3			1.07104
$530$	870.991	−	247.308i	0.0713838	−	0.0202687i
$531$		0			0
$532$	−9833.39	+	6073.84i	−0.801375	+	0.494990i
$533$		−	3621.57i		−	0.294311i
$534$		0			0
$535$		−	318.893i		−	0.0257700i
$536$	−5033.05	−	4603.23i	−0.405587	−	0.370950i
$537$		0			0
$538$	−2890.36	−	10179.5i	−0.231622	−	0.815745i
$539$	−965.112			−0.0771249
$540$		0			0
$541$	11815.3			0.938961			0.469480	−	0.882943i	$-0.344441\pi$
$541$	11815.3			0.938961			0.469480	+	0.882943i	$0.344441\pi$
$542$	4644.63	+	16357.8i	0.368088	+	1.29636i
$543$		0			0
$544$	20793.6	+	3945.32i	1.63882	+	0.310946i
$545$			4494.56i			0.353259i
$546$		0			0
$547$			15596.6i			1.21913i	0.792737	+	0.609564i	$0.208655\pi$
$547$			15596.6i			1.21913i	−0.792737	+	0.609564i	$0.791345\pi$
$548$	−8633.83	−	13977.9i	−0.673027	−	1.08961i
$549$		0			0
$550$	5216.54	−	1481.18i	0.404426	−	0.114832i
$551$	−23075.8			−1.78414
$552$		0			0
$553$	−10175.8			−0.782496
$554$	12310.5	−	3495.44i	0.944088	−	0.268063i
$555$		0			0
$556$	8409.84	+	13615.3i	0.641469	+	1.03852i
$557$		−	19104.3i		−	1.45327i	−0.687022	−	0.726637i	$-0.741082\pi$
$557$		−	19104.3i		−	1.45327i	0.687022	−	0.726637i	$-0.258918\pi$
$558$		0			0
$559$			9233.19i			0.698608i
$560$	1613.32	−	3222.45i	0.121741	−	0.243167i
$561$		0			0
$562$	−3284.33	−	11567.0i	−0.246514	−	0.868195i
$563$	13747.5			1.02911			0.514555	−	0.857458i	$-0.327957\pi$
$563$	13747.5			1.02911			0.514555	+	0.857458i	$0.327957\pi$
$564$		0			0
$565$	−6281.35			−0.467714
$566$	−3424.79	−	12061.7i	−0.254337	−	0.895746i
$567$		0			0
$568$	−10503.4	+	11484.1i	−0.775903	+	0.848352i
$569$			18303.4i			1.34854i	0.738486	+	0.674269i	$0.235541\pi$
$569$			18303.4i			1.34854i	−0.738486	+	0.674269i	$0.764459\pi$
$570$		0			0
$571$		−	8345.58i		−	0.611649i	−0.952088	−	0.305824i	$-0.901068\pi$
$571$		−	8345.58i		−	0.611649i	0.952088	−	0.305824i	$-0.0989320\pi$
$572$	−2873.05	+	1774.61i	−0.210015	+	0.129721i
$573$		0			0
$574$	6641.22	−	1885.70i	0.482925	−	0.137121i
$575$	18080.6			1.31133
$576$		0			0
$577$	−21336.5			−1.53943			−0.769713	−	0.638390i	$-0.779601\pi$
$577$	−21336.5			−1.53943			−0.769713	+	0.638390i	$0.779601\pi$
$578$	23826.6	−	6765.31i	1.71463	−	0.486851i
$579$		0			0
$580$	6121.38	−	3781.03i	0.438235	−	0.270687i
$581$			22554.2i			1.61051i
$582$		0			0
$583$		−	1617.36i		−	0.114896i
$584$	4766.71	−	5211.78i	0.337753	−	0.369290i
$585$		0			0
$586$	−5975.55	−	21045.2i	−0.421242	−	1.48357i
$587$	−26431.2			−1.85849			−0.929244	−	0.369467i	$-0.879540\pi$
$587$	−26431.2			−1.85849			−0.929244	+	0.369467i	$0.879540\pi$
$588$		0			0
$589$	3084.84			0.215804
$590$	−759.027	−	2673.20i	−0.0529638	−	0.186532i
$591$		0			0
$592$	−10136.3	+	20246.3i	−0.703713	+	1.40560i
$593$		−	248.904i		−	0.0172366i	−0.999963	−	0.00861828i	$-0.997257\pi$
$593$		−	248.904i		−	0.0172366i	0.999963	−	0.00861828i	$-0.00274332\pi$
$594$		0			0
$595$		−	6583.52i		−	0.453610i
$596$	−4153.74	−	6724.80i	−0.285476	−	0.462179i
$597$		0			0
$598$	−10831.3	+	3075.41i	−0.740674	+	0.210306i
$599$	14995.9			1.02290			0.511449	−	0.859313i	$-0.329109\pi$
$599$	14995.9			1.02290			0.511449	+	0.859313i	$0.329109\pi$
$600$		0			0
$601$	23747.1			1.61175			0.805876	−	0.592085i	$-0.201695\pi$
$601$	23747.1			1.61175			0.805876	+	0.592085i	$0.201695\pi$
$602$	−16931.8	+	4807.59i	−1.14633	+	0.325486i
$603$		0			0
$604$	−6855.03	−	11098.1i	−0.461800	−	0.747641i
$605$		−	3490.36i		−	0.234551i
$606$		0			0
$607$			6539.02i			0.437250i	0.975809	+	0.218625i	$0.0701571\pi$
$607$			6539.02i			0.437250i	−0.975809	+	0.218625i	$0.929843\pi$
$608$	15202.3	+	2884.45i	1.01404	+	0.192401i
$609$		0			0
$610$	−377.643	−	1330.01i	−0.0250661	−	0.0882798i
$611$	−9964.12			−0.659747
$612$		0			0
$613$	−5985.95			−0.394405			−0.197202	−	0.980363i	$-0.563186\pi$
$613$	−5985.95			−0.394405			−0.197202	+	0.980363i	$0.563186\pi$
$614$	−6574.64	−	23155.1i	−0.432135	−	1.52193i
$615$		0			0
$616$	−4750.24	−	4344.57i	−0.310702	−	0.284169i
$617$			6168.16i			0.402465i	0.979544	+	0.201232i	$0.0644947\pi$
$617$			6168.16i			0.402465i	−0.979544	+	0.201232i	$0.935505\pi$
$618$		0			0
$619$		−	6667.31i		−	0.432927i	−0.976291	−	0.216464i	$-0.930548\pi$
$619$		−	6667.31i		−	0.432927i	0.976291	−	0.216464i	$-0.0694523\pi$
$620$	−818.325	+	505.459i	−0.0530076	+	0.0327415i
$621$		0			0
$622$	22130.6	−	6283.75i	1.42662	−	0.405073i
$623$	14472.7			0.930717
$624$		0			0
$625$	11586.0			0.741502
$626$	−13785.9	+	3914.36i	−0.880186	+	0.249919i
$627$		0			0
$628$	−4696.36	+	2900.83i	−0.298416	+	0.184324i
$629$			41363.5i			2.62205i
$630$		0			0
$631$		−	8168.49i		−	0.515344i	−0.966232	−	0.257672i	$-0.917045\pi$
$631$		−	8168.49i		−	0.515344i	0.966232	−	0.257672i	$-0.0829554\pi$
$632$	10052.7	+	9194.20i	0.632713	+	0.578680i
$633$		0			0
$634$	−3184.91	−	11216.9i	−0.199510	−	0.702649i
$635$	−2379.83			−0.148725
$636$		0			0
$637$	1437.85			0.0894346
$638$	−3510.53	−	12363.7i	−0.217842	−	0.767215i
$639$		0			0
$640$	−4505.39	+	1725.77i	−0.278267	+	0.106589i
$641$			6332.36i			0.390192i	0.980784	+	0.195096i	$0.0625018\pi$
$641$			6332.36i			0.390192i	−0.980784	+	0.195096i	$0.937498\pi$
$642$		0			0
$643$		−	9433.98i		−	0.578600i	−0.957239	−	0.289300i	$-0.906578\pi$
$643$		−	9433.98i		−	0.578600i	0.957239	−	0.289300i	$-0.0934225\pi$
$644$	−11279.4	−	18261.0i	−0.690169	−	1.11737i
$645$		0			0
$646$	27193.0	−	7721.15i	1.65618	−	0.470255i
$647$	−20479.8			−1.24442			−0.622212	−	0.782848i	$-0.713766\pi$
$647$	−20479.8			−1.24442			−0.622212	+	0.782848i	$0.713766\pi$
$648$		0			0
$649$	−4963.92			−0.300233
$650$	−7771.76	+	2206.71i	−0.468975	+	0.133160i
$651$		0			0
$652$	14355.2	+	23240.6i	0.862258	+	1.39597i
$653$			24435.7i			1.46438i	0.681099	+	0.732192i	$0.261502\pi$
$653$			24435.7i			1.46438i	−0.681099	+	0.732192i	$0.738498\pi$
$654$		0			0
$655$			7175.80i			0.428064i
$656$	−8264.64	−	4137.68i	−0.491890	−	0.246264i
$657$		0			0
$658$	−5188.18	−	18272.2i	−0.307380	−	1.08256i
$659$	−32183.0			−1.90238			−0.951192	−	0.308601i	$-0.900139\pi$
$659$	−32183.0			−1.90238			−0.951192	+	0.308601i	$0.900139\pi$
$660$		0			0
$661$	13990.4			0.823245			0.411622	−	0.911355i	$-0.364962\pi$
$661$	13990.4			0.823245			0.411622	+	0.911355i	$0.364962\pi$
$662$	2951.15	+	10393.6i	0.173263	+	0.610211i
$663$		0			0
$664$	20378.5	−	22281.2i	1.19102	−	1.30223i
$665$		−	4813.26i		−	0.280677i
$666$		0			0
$667$		−	42852.6i		−	2.48765i
$668$	9344.71	−	5772.00i	0.541254	−	0.334319i
$669$		0			0
$670$	2732.41	−	775.838i	0.157556	−	0.0447362i
$671$	−2469.73			−0.142091
$672$		0			0
$673$	12289.9			0.703923			0.351961	−	0.936014i	$-0.385515\pi$
$673$	12289.9			0.703923			0.351961	+	0.936014i	$0.385515\pi$
$674$	26426.1	−	7503.39i	1.51023	−	0.428813i
$675$		0			0
$676$	−10673.1	+	6592.50i	−0.607253	+	0.375085i
$677$		−	16303.5i		−	0.925548i	−0.886476	−	0.462774i	$-0.846854\pi$
$677$		−	16303.5i		−	0.925548i	0.886476	−	0.462774i	$-0.153146\pi$
$678$		0			0
$679$		−	3694.09i		−	0.208786i
$680$	−5948.43	+	6503.86i	−0.335459	+	0.366782i
$681$		0			0
$682$	469.298	+	1652.81i	0.0263495	+	0.0927999i
$683$	9720.93			0.544599			0.272299	−	0.962213i	$-0.412216\pi$
$683$	9720.93			0.544599			0.272299	+	0.962213i	$0.412216\pi$
$684$		0			0
$685$	6841.93			0.381630
$686$	5227.40	+	18410.3i	0.290937	+	1.02465i
$687$		0			0
$688$	21070.7	+	10549.0i	1.16761	+	0.584560i
$689$			2409.59i			0.133234i
$690$		0			0
$691$		−	80.4083i		−	0.00442674i	−0.999998	−	0.00221337i	$-0.999295\pi$
$691$		−	80.4083i		−	0.00442674i	0.999998	−	0.00221337i	$-0.000704538\pi$
$692$	−4701.24	−	7611.17i	−0.258257	−	0.418112i
$693$		0			0
$694$	−9020.24	+	2561.20i	−0.493377	+	0.140089i
$695$	−6664.43			−0.363736
$696$		0			0
$697$	−16884.8			−0.917586
$698$	7794.97	−	2213.29i	0.422699	−	0.120021i
$699$		0			0
$700$	−8093.30	−	13102.8i	−0.436997	−	0.707486i
$701$			4285.46i			0.230898i	0.993313	+	0.115449i	$0.0368307\pi$
$701$			4285.46i			0.230898i	−0.993313	+	0.115449i	$0.963169\pi$
$702$		0			0
$703$			30241.1i			1.62243i
$704$	767.287	+	8584.00i	0.0410770	+	0.459548i
$705$		0			0
$706$	−3789.19	−	13345.1i	−0.201995	−	0.711402i
$707$	13413.5			0.713532
$708$		0			0
$709$	−8587.44			−0.454878			−0.227439	−	0.973792i	$-0.573035\pi$
$709$	−8587.44			−0.454878			−0.227439	+	0.973792i	$0.573035\pi$
$710$	−1770.26	−	6234.67i	−0.0935730	−	0.329553i
$711$		0			0
$712$	−14297.6	−	13076.6i	−0.752562	−	0.688294i
$713$			5728.67i			0.300898i
$714$		0			0
$715$		−	1406.30i		−	0.0735564i
$716$	11949.1	−	7380.65i	0.623684	−	0.385234i
$717$		0			0
$718$	−11387.5	+	3233.36i	−0.591891	+	0.168061i
$719$	−665.197			−0.0345030			−0.0172515	−	0.999851i	$-0.505492\pi$
$719$	−665.197			−0.0345030			−0.0172515	+	0.999851i	$0.505492\pi$
$720$		0			0
$721$	−21052.4			−1.08742
$722$	1218.52	−	345.984i	0.0628096	−	0.0178341i
$723$		0			0
$724$	2130.18	−	1315.76i	0.109348	−	0.0675414i
$725$		−	30748.1i		−	1.57511i
$726$		0			0
$727$		−	1269.94i		−	0.0647860i	−0.999475	−	0.0323930i	$-0.989687\pi$
$727$		−	1269.94i		−	0.0647860i	0.999475	−	0.0323930i	$-0.0103128\pi$
$728$	7077.05	+	6472.68i	0.360292	+	0.329524i
$729$		0			0
$730$	803.390	+	2829.45i	0.0407326	+	0.143455i
$731$	43047.8			2.17809
$732$		0			0
$733$	26425.0			1.33155			0.665777	−	0.746151i	$-0.268100\pi$
$733$	26425.0			1.33155			0.665777	+	0.746151i	$0.268100\pi$
$734$	−3847.33	−	13549.9i	−0.193471	−	0.681382i
$735$		0			0
$736$	−5356.54	+	28231.3i	−0.268267	+	1.41388i
$737$		−	5073.87i		−	0.253593i
$738$		0			0
$739$			4732.65i			0.235579i	0.993039	+	0.117790i	$0.0375809\pi$
$739$			4732.65i			0.235579i	−0.993039	+	0.117790i	$0.962419\pi$
$740$	−4955.09	−	8022.15i	−0.246152	−	0.398514i
$741$		0			0
$742$	−4418.70	+	1254.64i	−0.218619	+	0.0620745i
$743$	−14771.2			−0.729346			−0.364673	−	0.931136i	$-0.618819\pi$
$743$	−14771.2			−0.729346			−0.364673	+	0.931136i	$0.618819\pi$
$744$		0			0
$745$	3291.66			0.161875
$746$	−17445.8	+	4953.54i	−0.856214	+	0.243113i
$747$		0			0
$748$	8273.77	+	13395.0i	0.404437	+	0.654773i
$749$			1617.80i			0.0789228i
$750$		0			0
$751$			27071.9i			1.31540i	0.753280	+	0.657700i	$0.228471\pi$
$751$			27071.9i			1.31540i	−0.753280	+	0.657700i	$0.771529\pi$
$752$	−11384.1	+	22738.8i	−0.552043	+	1.10266i
$753$		0			0
$754$	5230.09	+	18419.8i	0.252611	+	0.889667i
$755$	5432.31			0.261857
$756$		0			0
$757$	−12404.5			−0.595576			−0.297788	−	0.954632i	$-0.596249\pi$
$757$	−12404.5			−0.595576			−0.297788	+	0.954632i	$0.596249\pi$
$758$	−4090.33	−	14405.7i	−0.196000	−	0.690288i
$759$		0			0
$760$	−4348.94	+	4755.01i	−0.207569	+	0.226951i
$761$		−	8564.67i		−	0.407975i	−0.978973	−	0.203988i	$-0.934610\pi$
$761$		−	8564.67i		−	0.407975i	0.978973	−	0.203988i	$-0.0653902\pi$
$762$		0			0
$763$		−	22801.8i		−	1.08189i
$764$	13778.7	−	8510.76i	0.652481	−	0.403022i
$765$		0			0
$766$	−16116.4	+	4576.06i	−0.760193	+	0.215848i
$767$	7395.40			0.348152
$768$		0			0
$769$	−19117.5			−0.896483			−0.448241	−	0.893913i	$-0.647949\pi$
$769$	−19117.5			−0.896483			−0.448241	+	0.893913i	$0.647949\pi$
$770$	2578.88	−	732.243i	0.120696	−	0.0342704i
$771$		0			0
$772$	7745.58	−	4784.26i	0.361101	−	0.223043i
$773$		−	28145.2i		−	1.30959i	−0.755807	−	0.654794i	$-0.772755\pi$
$773$		−	28145.2i		−	1.30959i	0.755807	−	0.654794i	$-0.227245\pi$
$774$		0			0
$775$			4110.50i			0.190521i
$776$	−3337.73	+	3649.38i	−0.154404	+	0.168821i
$777$		0			0
$778$	3155.85	+	11114.5i	0.145428	+	0.512180i
$779$	−12344.6			−0.567767
$780$		0			0
$781$	−11577.3			−0.530432
$782$	14338.5	+	50498.4i	0.655681	+	2.30923i
$783$		0			0
$784$	1642.76	−	3281.27i	0.0748344	−	0.149475i
$785$		−	2298.78i		−	0.104518i
$786$		0			0
$787$			15895.3i			0.719959i	0.932960	+	0.359979i	$0.117216\pi$
$787$			15895.3i			0.719959i	−0.932960	+	0.359979i	$0.882784\pi$
$788$	−9861.80	−	15966.0i	−0.445827	−	0.721782i
$789$		0			0
$790$	−5457.54	+	1549.61i	−0.245786	+	0.0697881i
$791$	31866.4			1.43242
$792$		0			0
$793$	3679.47			0.164769
$794$	−7677.09	+	2179.83i	−0.343136	+	0.0974296i
$795$		0			0
$796$	−11936.1	−	19324.2i	−0.531486	−	0.860461i
$797$		−	39051.2i		−	1.73559i	−0.496924	−	0.867794i	$-0.665537\pi$
$797$		−	39051.2i		−	1.73559i	0.496924	−	0.867794i	$-0.334463\pi$
$798$		0			0
$799$			46455.6i			2.05692i
$800$	−3843.49	+	20256.8i	−0.169860	+	0.895234i
$801$		0			0
$802$	3256.46	+	11468.9i	0.143378	+	0.504962i
$803$	5254.05			0.230898
$804$		0			0
$805$	8938.40			0.391351
$806$	−699.175	−	2462.41i	−0.0305551	−	0.107611i
$807$		0			0
$808$	−13251.2	−	12119.6i	−0.576950	−	0.527679i
$809$		−	67.6844i		−	0.00294148i	−0.999999	−	0.00147074i	$-0.999532\pi$
$809$		−	67.6844i		−	0.00294148i	0.999999	−	0.00147074i	$-0.000468151\pi$
$810$		0			0
$811$		−	26390.7i		−	1.14267i	−0.820718	−	0.571334i	$-0.806426\pi$
$811$		−	26390.7i		−	1.14267i	0.820718	−	0.571334i	$-0.193574\pi$
$812$	−31054.9	+	19181.9i	−1.34213	+	0.829004i
$813$		0			0
$814$	−16202.8	+	4600.60i	−0.697674	+	0.198097i
$815$	−11375.9			−0.488931
$816$		0			0
$817$	31472.5			1.34772
$818$	−1646.90	+	467.620i	−0.0703944	+	0.0199877i
$819$		0			0
$820$	3274.69	−	2022.69i	0.139460	−	0.0861409i
$821$			15840.6i			0.673374i	0.941617	+	0.336687i	$0.109306\pi$
$821$			15840.6i			0.673374i	−0.941617	+	0.336687i	$0.890694\pi$
$822$		0			0
$823$			227.779i			0.00964747i	0.999988	+	0.00482373i	$0.00153545\pi$
$823$			227.779i			0.00964747i	−0.999988	+	0.00482373i	$0.998465\pi$
$824$	20797.7	+	19021.6i	0.879273	+	0.804185i
$825$		0			0
$826$	3850.68	+	13561.7i	0.162206	+	0.571272i
$827$	−11468.2			−0.482209			−0.241105	−	0.970499i	$-0.577510\pi$
$827$	−11468.2			−0.482209			−0.241105	+	0.970499i	$0.577510\pi$
$828$		0			0
$829$	15188.4			0.636327			0.318164	−	0.948036i	$-0.396934\pi$
$829$	15188.4			0.636327			0.318164	+	0.948036i	$0.396934\pi$
$830$	3434.62	+	12096.3i	0.143636	+	0.505868i
$831$		0			0
$832$	−1143.13	−	12788.7i	−0.0476332	−	0.532895i
$833$		−	6703.69i		−	0.278835i
$834$		0			0
$835$			4574.06i			0.189571i
$836$	6049.01	+	9793.18i	0.250250	+	0.405149i
$837$		0			0
$838$	17631.0	−	5006.12i	0.726793	−	0.206365i
$839$	28109.4			1.15667			0.578334	−	0.815800i	$-0.303703\pi$
$839$	28109.4			1.15667			0.578334	+	0.815800i	$0.303703\pi$
$840$		0			0
$841$	−48486.8			−1.98806
$842$	989.886	−	281.067i	0.0405151	−	0.0115038i
$843$		0			0
$844$	1078.62	+	1746.25i	0.0439900	+	0.0712186i
$845$		−	5224.27i		−	0.212687i
$846$		0			0
$847$			17707.2i			0.718333i
$848$	5498.84	+	2752.99i	0.222678	+	0.111483i
$849$		0			0
$850$	10288.3	+	36234.2i	0.415160	+	1.46215i
$851$	−56158.9			−2.26217
$852$		0			0
$853$	−41817.8			−1.67856			−0.839281	−	0.543699i	$-0.817023\pi$
$853$	−41817.8			−1.67856			−0.839281	+	0.543699i	$0.817023\pi$
$854$	1915.85	+	6747.41i	0.0767671	+	0.270365i
$855$		0			0
$856$	1461.74	−	1598.22i	0.0583659	−	0.0638156i
$857$		−	38510.6i		−	1.53500i	−0.641048	−	0.767501i	$-0.721500\pi$
$857$		−	38510.6i		−	1.53500i	0.641048	−	0.767501i	$-0.278500\pi$
$858$		0			0
$859$		−	43912.4i		−	1.74421i	−0.489322	−	0.872103i	$-0.662756\pi$
$859$		−	43912.4i		−	1.74421i	0.489322	−	0.872103i	$-0.337244\pi$
$860$	−8348.81	+	5156.86i	−0.331037	+	0.204474i
$861$		0			0
$862$	4045.84	−	1148.77i	0.159863	−	0.0453913i
$863$	−40298.8			−1.58956			−0.794779	−	0.606899i	$-0.792413\pi$
$863$	−40298.8			−1.58956			−0.794779	+	0.606899i	$0.792413\pi$
$864$		0			0
$865$	3725.52			0.146441
$866$	−33528.7	+	9520.09i	−1.31565	+	0.373563i
$867$		0			0
$868$	4151.51	−	2564.29i	0.162340	−	0.100274i
$869$			10134.2i			0.395604i
$870$		0			0
$871$			7559.20i			0.294069i
$872$	−20602.2	+	22525.8i	−0.800088	+	0.874795i
$873$		0			0
$874$	10483.0	+	36919.7i	0.405711	+	1.42887i
$875$	13452.2			0.519732
$876$		0			0
$877$	17806.9			0.685629			0.342814	−	0.939403i	$-0.388620\pi$
$877$	17806.9			0.685629			0.342814	+	0.939403i	$0.388620\pi$
$878$	8434.79	+	29706.4i	0.324215	+	1.14185i
$879$		0			0
$880$	−3209.28	−	1606.72i	−0.122937	−	0.0615483i
$881$		−	4232.13i		−	0.161843i	−0.996720	−	0.0809217i	$-0.974214\pi$
$881$		−	4232.13i		−	0.161843i	0.996720	−	0.0809217i	$-0.0257864\pi$
$882$		0			0
$883$			36881.3i			1.40561i	0.711382	+	0.702806i	$0.248070\pi$
$883$			36881.3i			1.40561i	−0.711382	+	0.702806i	$0.751930\pi$
$884$	−12326.5	−	19956.3i	−0.468988	−	0.759279i
$885$		0			0
$886$	10704.0	−	3039.29i	0.405879	−	0.115245i
$887$	31760.2			1.20226			0.601128	−	0.799152i	$-0.294718\pi$
$887$	31760.2			1.20226			0.601128	+	0.799152i	$0.294718\pi$
$888$		0			0
$889$	12073.3			0.455485
$890$	7762.06	−	2203.95i	0.292343	−	0.0830074i
$891$		0			0
$892$	−16902.8	−	27365.3i	−0.634472	−	1.02719i
$893$			33964.0i			1.27275i
$894$		0			0
$895$			5848.84i			0.218442i
$896$	22856.7	−	8755.16i	0.852218	−	0.326439i
$897$		0			0
$898$	−7386.34	−	26013.8i	−0.274483	−	0.966696i
$899$	9742.26			0.361427
$900$		0			0
$901$	11234.2			0.415390
$902$	−1877.99	−	6614.06i	−0.0693239	−	0.244151i
$903$		0			0
$904$	−31480.8	−	28792.4i	−1.15823	−	1.05932i
$905$			1042.68i			0.0382984i
$906$		0			0
$907$		−	50257.3i		−	1.83987i	−0.392066	−	0.919937i	$-0.628240\pi$
$907$		−	50257.3i		−	1.83987i	0.392066	−	0.919937i	$-0.371760\pi$
$908$	20136.0	−	12437.5i	0.735945	−	0.454575i
$909$		0			0
$910$	−3842.09	+	1090.92i	−0.139960	+	0.0397402i
$911$	22485.6			0.817763			0.408881	−	0.912588i	$-0.365919\pi$
$911$	22485.6			0.817763			0.408881	+	0.912588i	$0.365919\pi$
$912$		0			0
$913$	22461.9			0.814219
$914$	−17631.0	+	5006.13i	−0.638054	+	0.181168i
$915$		0			0
$916$	1538.69	−	950.412i	0.0555020	−	0.0342822i
$917$		−	36404.2i		−	1.31098i
$918$		0			0
$919$		−	26918.9i		−	0.966240i	−0.875554	−	0.483120i	$-0.839504\pi$
$919$		−	26918.9i		−	0.966240i	0.875554	−	0.483120i	$-0.160496\pi$
$920$	−8830.24	−	8076.15i	−0.316440	−	0.289416i
$921$		0			0
$922$	−2750.91	−	9688.40i	−0.0982609	−	0.346063i
$923$	17248.2			0.615093
$924$		0			0
$925$	−40295.8			−1.43234
$926$	−12187.4	−	42922.6i	−0.432508	−	1.52324i
$927$		0			0
$928$	48010.5	+	9109.41i	1.69830	+	0.322232i
$929$		−	11212.4i		−	0.395983i	−0.980204	−	0.197991i	$-0.936558\pi$
$929$		−	11212.4i		−	0.395983i	0.980204	−	0.197991i	$-0.0634418\pi$
$930$		0			0
$931$		−	4901.11i		−	0.172532i
$932$	9907.19	+	16039.5i	0.348198	+	0.563724i
$933$		0			0
$934$	−38885.8	+	11041.2i	−1.36229	+	0.386808i
$935$	−6556.60			−0.229330
$936$		0			0
$937$	38358.1			1.33736			0.668679	−	0.743551i	$-0.266860\pi$
$937$	38358.1			1.33736			0.668679	+	0.743551i	$0.266860\pi$
$938$	−13862.0	+	3935.97i	−0.482528	+	0.137008i
$939$		0			0
$940$	−5565.09	−	9009.74i	−0.193099	−	0.312623i
$941$		−	7558.00i		−	0.261832i	−0.991393	−	0.130916i	$-0.958208\pi$
$941$		−	7558.00i		−	0.261832i	0.991393	−	0.130916i	$-0.0417918\pi$
$942$		0			0
$943$		−	22924.4i		−	0.791644i
$944$	8449.33	−	16876.8i	0.291316	−	0.581877i
$945$		0			0
$946$	4787.93	+	16862.5i	0.164555	+	0.579544i
$947$	50708.7			1.74003			0.870016	−	0.493023i	$-0.164108\pi$
$947$	50708.7			1.74003			0.870016	+	0.493023i	$0.164108\pi$
$948$		0			0
$949$	−7827.65			−0.267751
$950$	7521.85	+	26491.1i	0.256885	+	0.904720i
$951$		0			0
$952$	30177.5	−	32995.3i	1.02737	−	1.12330i
$953$			16440.9i			0.558837i	0.960169	+	0.279419i	$0.0901417\pi$
$953$			16440.9i			0.558837i	−0.960169	+	0.279419i	$0.909858\pi$
$954$		0			0
$955$			6744.41i			0.228528i
$956$	−14917.3	+	9214.07i	−0.504666	+	0.311720i
$957$		0			0
$958$	39806.2	−	11302.5i	1.34247	−	0.381178i
$959$	−34710.4			−1.16878
$960$		0			0
$961$	28488.6			0.956283
$962$	24139.4	−	6854.11i	0.809028	−	0.229714i
$963$		0			0
$964$	44459.3	−	27461.4i	1.48541	−	0.917502i
$965$			3791.32i			0.126473i
$966$		0			0
$967$		−	488.917i		−	0.0162591i	−0.999967	−	0.00812953i	$-0.997412\pi$
$967$		−	488.917i		−	0.0162591i	0.999967	−	0.00812953i	$-0.00258774\pi$
$968$	15999.1	−	17493.0i	0.531230	−	0.580832i
$969$		0			0
$970$	−562.548	−	1981.23i	−0.0186209	−	0.0655808i
$971$	−31950.1			−1.05595			−0.527975	−	0.849260i	$-0.677049\pi$
$971$	−31950.1			−1.05595			−0.527975	+	0.849260i	$0.677049\pi$
$972$		0			0
$973$	33809.9			1.11397
$974$	−12934.8	−	45554.8i	−0.425521	−	1.49863i
$975$		0			0
$976$	4203.84	−	8396.79i	0.137871	−	0.275384i
$977$			5271.73i			0.172628i	0.996268	+	0.0863140i	$0.0275088\pi$
$977$			5271.73i			0.172628i	−0.996268	+	0.0863140i	$0.972491\pi$
$978$		0			0
$979$		−	14413.5i		−	0.470539i
$980$	803.060	+	1300.13i	0.0261763	+	0.0423788i
$981$		0			0
$982$	−19977.3	+	5672.32i	−0.649185	+	0.184329i
$983$	−11052.1			−0.358603			−0.179302	−	0.983794i	$-0.557384\pi$
$983$	−11052.1			−0.358603			−0.179302	+	0.983794i	$0.557384\pi$
$984$		0			0
$985$	7815.04			0.252800
$986$	85878.4	−	24384.2i	2.77376	−	0.787578i
$987$		0			0
$988$	−9011.99	−	14590.2i	−0.290192	−	0.469813i
$989$			58445.7i			1.87914i
$990$		0			0
$991$			41203.4i			1.32076i	0.750933	+	0.660378i	$0.229604\pi$
$991$			41203.4i			1.32076i	−0.750933	+	0.660378i	$0.770396\pi$
$992$	−6418.20	−	1217.77i	−0.205421	−	0.0389762i
$993$		0			0
$994$	8980.88	+	31629.6i	0.286576	+	1.00929i
$995$	9458.82			0.301372
$996$		0			0
$997$	−14951.3			−0.474938			−0.237469	−	0.971395i	$-0.576318\pi$
$997$	−14951.3			−0.474938			−0.237469	+	0.971395i	$0.576318\pi$
$998$	−1209.10	−	4258.32i	−0.0383502	−	0.135065i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.b.a.107.2	yes	12
3.2	odd	2	inner	108.4.b.a.107.11	yes	12
4.3	odd	2	inner	108.4.b.a.107.12	yes	12
8.3	odd	2		1728.4.c.i.1727.6		12
8.5	even	2		1728.4.c.i.1727.5		12
12.11	even	2	inner	108.4.b.a.107.1	✓	12
24.5	odd	2		1728.4.c.i.1727.7		12
24.11	even	2		1728.4.c.i.1727.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.b.a.107.1	✓	12	12.11	even	2	inner
108.4.b.a.107.2	yes	12	1.1	even	1	trivial
108.4.b.a.107.11	yes	12	3.2	odd	2	inner
108.4.b.a.107.12	yes	12	4.3	odd	2	inner
1728.4.c.i.1727.5		12	8.5	even	2
1728.4.c.i.1727.6		12	8.3	odd	2
1728.4.c.i.1727.7		12	24.5	odd	2
1728.4.c.i.1727.8		12	24.11	even	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.72087 + 0.772562i) q^{2} +(6.80630 - 4.20408i) q^{4} +3.33155i q^{5} -16.9016i q^{7} +(-15.2712 + 16.6971i) q^{8} +O(q^{10})\)	\(q+(-2.72087 + 0.772562i) q^{2} +(6.80630 - 4.20408i) q^{4} +3.33155i q^{5} -16.9016i q^{7} +(-15.2712 + 16.6971i) q^{8} +(-2.57383 - 9.06473i) q^{10} -16.8325 q^{11} +25.0775 q^{13} +(13.0575 + 45.9871i) q^{14} +(28.6514 - 57.2285i) q^{16} -116.919i q^{17} -85.4801i q^{19} +(14.0061 + 22.6755i) q^{20} +(45.7990 - 13.0041i) q^{22} +158.740 q^{23} +113.901 q^{25} +(-68.2328 + 19.3739i) q^{26} +(-71.0557 - 115.037i) q^{28} -269.955i q^{29} +36.0884i q^{31} +(-33.7442 + 177.846i) q^{32} +(90.3269 + 318.121i) q^{34} +56.3085 q^{35} -353.780 q^{37} +(66.0386 + 232.580i) q^{38} +(-55.6272 - 50.8767i) q^{40} -144.415i q^{41} +368.186i q^{43} +(-114.567 + 70.7651i) q^{44} +(-431.911 + 122.636i) q^{46} -397.333 q^{47} +57.3363 q^{49} +(-309.909 + 87.9954i) q^{50} +(170.685 - 105.428i) q^{52} +96.0857i q^{53} -56.0783i q^{55} +(282.207 + 258.107i) q^{56} +(208.557 + 734.514i) q^{58} +294.902 q^{59} +146.724 q^{61} +(-27.8805 - 98.1920i) q^{62} +(-45.5837 - 509.967i) q^{64} +83.5471i q^{65} +301.433i q^{67} +(-491.536 - 795.784i) q^{68} +(-153.208 + 43.5018i) q^{70} +687.794 q^{71} -312.138 q^{73} +(962.590 - 273.317i) q^{74} +(-359.365 - 581.803i) q^{76} +284.496i q^{77} -602.063i q^{79} +(190.660 + 95.4535i) q^{80} +(111.569 + 392.934i) q^{82} -1334.44 q^{83} +389.521 q^{85} +(-284.446 - 1001.79i) q^{86} +(257.051 - 281.053i) q^{88} +856.292i q^{89} -423.850i q^{91} +(1080.43 - 667.355i) q^{92} +(1081.09 - 306.964i) q^{94} +284.781 q^{95} +218.564 q^{97} +(-156.005 + 44.2959i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4}+O(q^{10}) \) 12 * q - 12 * q^4	\( 12 q - 12 q^{4} + 24 q^{10} + 36 q^{13} + 24 q^{16} + 120 q^{22} - 132 q^{25} + 420 q^{28} - 360 q^{34} + 516 q^{37} - 1152 q^{40} - 696 q^{46} - 720 q^{49} + 204 q^{52} + 2832 q^{58} - 972 q^{61} + 2496 q^{64} - 1848 q^{70} + 660 q^{73} - 5004 q^{76} - 3888 q^{82} + 1056 q^{85} + 3168 q^{88} + 7608 q^{94} + 2532 q^{97}+O(q^{100}) \) 12 * q - 12 * q^4 + 24 * q^10 + 36 * q^13 + 24 * q^16 + 120 * q^22 - 132 * q^25 + 420 * q^28 - 360 * q^34 + 516 * q^37 - 1152 * q^40 - 696 * q^46 - 720 * q^49 + 204 * q^52 + 2832 * q^58 - 972 * q^61 + 2496 * q^64 - 1848 * q^70 + 660 * q^73 - 5004 * q^76 - 3888 * q^82 + 1056 * q^85 + 3168 * q^88 + 7608 * q^94 + 2532 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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