LMFDB - Embedded newform 1520.2.q.i.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,2,Mod(881,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1520.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.q (of order $3$, degree $2$, not 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:	$12.1372611072$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.2
Root			$1.09935 + 1.90412i$ of defining polynomial
Character	$\chi$	$=$	1520.961
Dual form			1520.2.q.i.881.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.182224 + 0.315621i) q^{3} +(0.500000 - 0.866025i) q^{5} -0.635552 q^{7} +(1.43359 + 2.48305i) q^{9} -1.63555 q^{11} +(0.500000 + 0.866025i) q^{13} +(0.182224 + 0.315621i) q^{15} +(3.29804 - 5.71237i) q^{17} +(-0.0466721 + 4.35865i) q^{19} +(0.115813 - 0.200594i) q^{21} +(0.433589 + 0.750998i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.13828 q^{27} +(4.54940 + 7.87979i) q^{29} +1.86718 q^{31} +(0.298037 - 0.516215i) q^{33} +(-0.317776 + 0.550404i) q^{35} +0.635552 q^{37} -0.364448 q^{39} +(-0.953328 + 1.65121i) q^{41} +(1.98026 - 3.42991i) q^{43} +2.86718 q^{45} +(4.54940 + 7.87979i) q^{47} -6.59607 q^{49} +(1.20196 + 2.08186i) q^{51} +(4.93359 + 8.54523i) q^{53} +(-0.817776 + 1.41643i) q^{55} +(-1.36718 - 0.808981i) q^{57} +(4.54940 - 7.87979i) q^{59} +(-1.13555 - 1.96683i) q^{61} +(-0.911120 - 1.57811i) q^{63} +1.00000 q^{65} +(6.23163 + 10.7935i) q^{67} -0.316041 q^{69} +(1.25136 - 2.16743i) q^{71} +(0.201963 - 0.349810i) q^{73} +0.364448 q^{75} +1.03948 q^{77} +(5.36445 - 9.29150i) q^{79} +(-3.91112 + 6.77426i) q^{81} +15.8672 q^{83} +(-3.29804 - 5.71237i) q^{85} -3.31604 q^{87} +(-0.271104 - 0.469566i) q^{89} +(-0.317776 - 0.550404i) q^{91} +(-0.340245 + 0.589321i) q^{93} +(3.75136 + 2.21974i) q^{95} +(3.68495 - 6.38253i) q^{97} +(-2.34471 - 4.06116i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 3 q^{5} - 4 q^{7} - 8 q^{9} - 10 q^{11} + 3 q^{13} + q^{15} + 3 q^{17} - 16 q^{21} - 14 q^{23} - 3 q^{25} + 20 q^{27} - 6 q^{29} - 22 q^{31} - 15 q^{33} - 2 q^{35} + 4 q^{37} - 2 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q - q^3 + 3 * q^5 - 4 * q^7 - 8 * q^9 - 10 * q^11 + 3 * q^13 + q^15 + 3 * q^17 - 16 * q^21 - 14 * q^23 - 3 * q^25 + 20 * q^27 - 6 * q^29 - 22 * q^31 - 15 * q^33 - 2 * q^35 + 4 * q^37 - 2 * q^39 - 6 * q^41 - 5 * q^43 - 16 * q^45 - 6 * q^47 - 6 * q^49 + 24 * q^51 + 13 * q^53 - 5 * q^55 + 25 * q^57 - 6 * q^59 - 7 * q^61 - 5 * q^63 + 6 * q^65 + 4 * q^67 + 30 * q^69 - 9 * q^71 + 18 * q^73 + 2 * q^75 + 40 * q^77 + 32 * q^79 - 23 * q^81 + 62 * q^83 - 3 * q^85 + 12 * q^87 - 2 * q^89 - 2 * q^91 + 14 * q^93 + 6 * q^95 - 11 * q^97 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.182224	+	0.315621i	−0.105207	+	0.182224i	−0.913823	−	0.406113i	$-0.866884\pi$
$3$	−0.182224	+	0.315621i	−0.105207	+	0.182224i	0.808616	+	0.588337i	$0.200217\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−0.635552			−0.240216			−0.120108	−	0.992761i	$-0.538324\pi$
$7$	−0.635552			−0.240216			−0.120108	+	0.992761i	$0.538324\pi$
$8$		0			0
$9$	1.43359	+	2.48305i	0.477863	+	0.827683i
$10$		0			0
$11$	−1.63555			−0.493137			−0.246569	−	0.969125i	$-0.579303\pi$
$11$	−1.63555			−0.493137			−0.246569	+	0.969125i	$0.579303\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$	0.182224	+	0.315621i	0.0470500	+	0.0814931i
$16$		0			0
$17$	3.29804	−	5.71237i	0.799891	−	1.38545i	−0.119795	−	0.992799i	$-0.538224\pi$
$17$	3.29804	−	5.71237i	0.799891	−	1.38545i	0.919686	−	0.392654i	$-0.128443\pi$
$18$		0			0
$19$	−0.0466721	+	4.35865i	−0.0107073	+	0.999943i
$19$	−0.0466721	+	4.35865i	−0.0107073	+	0.999943i
$20$		0			0
$21$	0.115813	−	0.200594i	0.0252724	−	0.0437731i
$22$		0			0
$23$	0.433589	+	0.750998i	0.0904095	+	0.156594i	0.907684	−	0.419655i	$-0.137849\pi$
$23$	0.433589	+	0.750998i	0.0904095	+	0.156594i	−0.817274	+	0.576249i	$0.804516\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−2.13828			−0.411512
$28$		0			0
$29$	4.54940	+	7.87979i	0.844803	+	1.46324i	0.885792	+	0.464082i	$0.153616\pi$
$29$	4.54940	+	7.87979i	0.844803	+	1.46324i	−0.0409898	+	0.999160i	$0.513051\pi$
$30$		0			0
$31$	1.86718			0.335355			0.167677	−	0.985842i	$-0.446373\pi$
$31$	1.86718			0.335355			0.167677	+	0.985842i	$0.446373\pi$
$32$		0			0
$33$	0.298037	−	0.516215i	0.0518816	−	0.0898615i
$34$		0			0
$35$	−0.317776	+	0.550404i	−0.0537139	+	0.0930353i
$36$		0			0
$37$	0.635552			0.104484			0.0522420	−	0.998634i	$-0.483363\pi$
$37$	0.635552			0.104484			0.0522420	+	0.998634i	$0.483363\pi$
$38$		0			0
$39$	−0.364448			−0.0583584
$40$		0			0
$41$	−0.953328	+	1.65121i	−0.148885	+	0.257876i	−0.930816	−	0.365489i	$-0.880902\pi$
$41$	−0.953328	+	1.65121i	−0.148885	+	0.257876i	0.781931	+	0.623365i	$0.214235\pi$
$42$		0			0
$43$	1.98026	−	3.42991i	0.301987	−	0.523057i	−0.674599	−	0.738184i	$-0.735683\pi$
$43$	1.98026	−	3.42991i	0.301987	−	0.523057i	0.976586	+	0.215128i	$0.0690168\pi$
$44$		0			0
$45$	2.86718			0.427414
$46$		0			0
$47$	4.54940	+	7.87979i	0.663598	+	1.14939i	0.979663	+	0.200649i	$0.0643049\pi$
$47$	4.54940	+	7.87979i	0.663598	+	1.14939i	−0.316065	+	0.948738i	$0.602362\pi$
$48$		0			0
$49$	−6.59607			−0.942296
$50$		0			0
$51$	1.20196	+	2.08186i	0.168309	+	0.291519i
$52$		0			0
$53$	4.93359	+	8.54523i	0.677681	+	1.17378i	0.975678	+	0.219210i	$0.0703481\pi$
$53$	4.93359	+	8.54523i	0.677681	+	1.17378i	−0.297997	+	0.954567i	$0.596319\pi$
$54$		0			0
$55$	−0.817776	+	1.41643i	−0.110269	+	0.190991i
$56$		0			0
$57$	−1.36718	−	0.808981i	−0.181087	−	0.107152i
$58$		0			0
$59$	4.54940	−	7.87979i	0.592282	−	1.02586i	−0.401643	−	0.915796i	$-0.631561\pi$
$59$	4.54940	−	7.87979i	0.592282	−	1.02586i	0.993924	−	0.110065i	$-0.0351060\pi$
$60$		0			0
$61$	−1.13555	−	1.96683i	−0.145393	−	0.251827i	0.784127	−	0.620601i	$-0.213111\pi$
$61$	−1.13555	−	1.96683i	−0.145393	−	0.251827i	−0.929519	+	0.368773i	$0.879778\pi$
$62$		0			0
$63$	−0.911120	−	1.57811i	−0.114790	−	0.198823i
$64$		0			0
$65$	1.00000			0.124035
$66$		0			0
$67$	6.23163	+	10.7935i	0.761314	+	1.31863i	0.942173	+	0.335126i	$0.108779\pi$
$67$	6.23163	+	10.7935i	0.761314	+	1.31863i	−0.180859	+	0.983509i	$0.557888\pi$
$68$		0			0
$69$	−0.316041			−0.0380469
$70$		0			0
$71$	1.25136	−	2.16743i	0.148510	−	0.257226i	−0.782167	−	0.623069i	$-0.785886\pi$
$71$	1.25136	−	2.16743i	0.148510	−	0.257226i	0.930677	+	0.365842i	$0.119219\pi$
$72$		0			0
$73$	0.201963	−	0.349810i	0.0236380	−	0.0409422i	−0.853964	−	0.520331i	$-0.825808\pi$
$73$	0.201963	−	0.349810i	0.0236380	−	0.0409422i	0.877602	+	0.479389i	$0.159142\pi$
$74$		0			0
$75$	0.364448			0.0420828
$76$		0			0
$77$	1.03948			0.118460
$78$		0			0
$79$	5.36445	−	9.29150i	0.603548	−	1.04538i	−0.388732	−	0.921351i	$-0.627087\pi$
$79$	5.36445	−	9.29150i	0.603548	−	1.04538i	0.992279	−	0.124024i	$-0.0395800\pi$
$80$		0			0
$81$	−3.91112	+	6.77426i	−0.434569	+	0.752695i
$82$		0			0
$83$	15.8672			1.74165			0.870825	−	0.491594i	$-0.163586\pi$
$83$	15.8672			1.74165			0.870825	+	0.491594i	$0.163586\pi$
$84$		0			0
$85$	−3.29804	−	5.71237i	−0.357722	−	0.619593i
$86$		0			0
$87$	−3.31604			−0.355517
$88$		0			0
$89$	−0.271104	−	0.469566i	−0.0287370	−	0.0497739i	0.851299	−	0.524680i	$-0.175815\pi$
$89$	−0.271104	−	0.469566i	−0.0287370	−	0.0497739i	−0.880036	+	0.474907i	$0.842482\pi$
$90$		0			0
$91$	−0.317776	−	0.550404i	−0.0333120	−	0.0576980i
$92$		0			0
$93$	−0.340245	+	0.589321i	−0.0352817	+	0.0611097i
$94$		0			0
$95$	3.75136	+	2.21974i	0.384882	+	0.227741i
$96$		0			0
$97$	3.68495	−	6.38253i	0.374150	−	0.648047i	−0.616049	−	0.787708i	$-0.711268\pi$
$97$	3.68495	−	6.38253i	0.374150	−	0.648047i	0.990199	+	0.139660i	$0.0446011\pi$
$98$		0			0
$99$	−2.34471	−	4.06116i	−0.235652	−	0.408161i
$100$		0			0
$101$	4.66248	+	8.07566i	0.463935	+	0.803558i	0.999153	−	0.0411556i	$-0.0131039\pi$
$101$	4.66248	+	8.07566i	0.463935	+	0.803558i	−0.535218	+	0.844714i	$0.679771\pi$
$102$		0			0
$103$	10.8672			1.07077			0.535387	−	0.844607i	$-0.320166\pi$
$103$	10.8672			1.07077			0.535387	+	0.844607i	$0.320166\pi$
$104$		0			0
$105$	−0.115813	−	0.200594i	−0.0113022	−	0.0195759i
$106$		0			0
$107$	−11.3304			−1.09535			−0.547677	−	0.836690i	$-0.684488\pi$
$107$	−11.3304			−1.09535			−0.547677	+	0.836690i	$0.684488\pi$
$108$		0			0
$109$	−6.61581	+	11.4589i	−0.633680	+	1.09757i	0.353113	+	0.935581i	$0.385123\pi$
$109$	−6.61581	+	11.4589i	−0.633680	+	1.09757i	−0.986793	+	0.161985i	$0.948210\pi$
$110$		0			0
$111$	−0.115813	+	0.200594i	−0.0109925	+	0.0190395i
$112$		0			0
$113$	7.09334			0.667286			0.333643	−	0.942700i	$-0.391722\pi$
$113$	7.09334			0.667286			0.333643	+	0.942700i	$0.391722\pi$
$114$		0			0
$115$	0.867178			0.0808647
$116$		0			0
$117$	−1.43359	+	2.48305i	−0.132535	+	0.229558i
$118$		0			0
$119$	−2.09607	+	3.63051i	−0.192147	+	0.332808i
$120$		0			0
$121$	−8.32497			−0.756815
$122$		0			0
$123$	−0.347439	−	0.601781i	−0.0313275	−	0.0542608i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	8.13828	+	14.0959i	0.722156	+	1.25081i	0.960134	+	0.279540i	$0.0901819\pi$
$127$	8.13828	+	14.0959i	0.722156	+	1.25081i	−0.237978	+	0.971270i	$0.576485\pi$
$128$		0			0
$129$	0.721702	+	1.25002i	0.0635423	+	0.110059i
$130$		0			0
$131$	−5.31778	+	9.21066i	−0.464616	+	0.804739i	−0.999184	−	0.0403866i	$-0.987141\pi$
$131$	−5.31778	+	9.21066i	−0.464616	+	0.804739i	0.534568	+	0.845126i	$0.320474\pi$
$132$		0			0
$133$	0.0296625	−	2.77015i	0.00257207	−	0.240202i
$134$		0			0
$135$	−1.06914	+	1.85181i	−0.0920170	+	0.159378i
$136$		0			0
$137$	−1.74864	−	3.02873i	−0.149396	−	0.258761i	0.781608	−	0.623769i	$-0.214400\pi$
$137$	−1.74864	−	3.02873i	−0.149396	−	0.258761i	−0.931004	+	0.365008i	$0.881066\pi$
$138$		0			0
$139$	0.367178	+	0.635970i	0.0311436	+	0.0539423i	0.881177	−	0.472786i	$-0.156752\pi$
$139$	0.367178	+	0.635970i	0.0311436	+	0.0539423i	−0.850034	+	0.526729i	$0.823418\pi$
$140$		0			0
$141$	−3.31604			−0.279261
$142$		0			0
$143$	−0.817776	−	1.41643i	−0.0683859	−	0.118448i
$144$		0			0
$145$	9.09880			0.755614
$146$		0			0
$147$	1.20196	−	2.08186i	0.0991362	−	0.171709i
$148$		0			0
$149$	−5.06914	+	8.78001i	−0.415280	+	0.719286i	−0.995458	−	0.0952036i	$-0.969650\pi$
$149$	−5.06914	+	8.78001i	−0.415280	+	0.719286i	0.580178	+	0.814490i	$0.302983\pi$
$150$		0			0
$151$	−2.81331			−0.228944			−0.114472	−	0.993426i	$-0.536518\pi$
$151$	−2.81331			−0.228944			−0.114472	+	0.993426i	$0.536518\pi$
$152$		0			0
$153$	18.9121			1.52895
$154$		0			0
$155$	0.933589	−	1.61702i	0.0749877	−	0.129882i
$156$		0			0
$157$	−0.480261	+	0.831836i	−0.0383290	+	0.0663878i	−0.884554	−	0.466439i	$-0.845537\pi$
$157$	−0.480261	+	0.831836i	−0.0383290	+	0.0663878i	0.846225	+	0.532826i	$0.178870\pi$
$158$		0			0
$159$	−3.59607			−0.285187
$160$		0			0
$161$	−0.275568	−	0.477298i	−0.0217178	−	0.0376164i
$162$		0			0
$163$	−3.13828			−0.245809			−0.122905	−	0.992418i	$-0.539221\pi$
$163$	−3.13828			−0.245809			−0.122905	+	0.992418i	$0.539221\pi$
$164$		0			0
$165$	−0.298037	−	0.516215i	−0.0232021	−	0.0401873i
$166$		0			0
$167$	−5.31778	−	9.21066i	−0.411502	−	0.712742i	0.583552	−	0.812076i	$-0.301662\pi$
$167$	−5.31778	−	9.21066i	−0.411502	−	0.712742i	−0.995054	+	0.0993334i	$0.968329\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	−10.8896	+	6.13262i	−0.832752	+	0.468973i
$172$		0			0
$173$	−6.18495	+	10.7127i	−0.470233	+	0.814468i	−0.999421	−	0.0340371i	$-0.989164\pi$
$173$	−6.18495	+	10.7127i	−0.470233	+	0.814468i	0.529187	+	0.848505i	$0.322497\pi$
$174$		0			0
$175$	0.317776	+	0.550404i	0.0240216	+	0.0416066i
$176$		0			0
$177$	1.65802	+	2.87178i	0.124624	+	0.215856i
$178$		0			0
$179$	0.324970			0.0242894			0.0121447	−	0.999926i	$-0.496134\pi$
$179$	0.324970			0.0242894			0.0121447	+	0.999926i	$0.496134\pi$
$180$		0			0
$181$	−4.40666	−	7.63255i	−0.327544	−	0.567323i	0.654480	−	0.756079i	$-0.272888\pi$
$181$	−4.40666	−	7.63255i	−0.327544	−	0.567323i	−0.982024	+	0.188756i	$0.939554\pi$
$182$		0			0
$183$	0.827699			0.0611853
$184$		0			0
$185$	0.317776	−	0.550404i	0.0233634	−	0.0404665i
$186$		0			0
$187$	−5.39411	+	9.34287i	−0.394456	+	0.683219i
$188$		0			0
$189$	1.35899			0.0988519
$190$		0			0
$191$	−25.1921			−1.82284			−0.911420	−	0.411478i	$-0.865013\pi$
$191$	−25.1921			−1.82284			−0.911420	+	0.411478i	$0.865013\pi$
$192$		0			0
$193$	9.43632	−	16.3442i	0.679241	−	1.17648i	−0.295969	−	0.955198i	$-0.595642\pi$
$193$	9.43632	−	16.3442i	0.679241	−	1.17648i	0.975210	−	0.221282i	$-0.0710243\pi$
$194$		0			0
$195$	−0.182224	+	0.315621i	−0.0130493	+	0.0226021i
$196$		0			0
$197$	−7.36445			−0.524695			−0.262348	−	0.964973i	$-0.584497\pi$
$197$	−7.36445			−0.524695			−0.262348	+	0.964973i	$0.584497\pi$
$198$		0			0
$199$	1.38419	+	2.39748i	0.0981224	+	0.169953i	0.910907	−	0.412611i	$-0.135383\pi$
$199$	1.38419	+	2.39748i	0.0981224	+	0.169953i	−0.812785	+	0.582564i	$0.802050\pi$
$200$		0			0
$201$	−4.54221			−0.320383
$202$		0			0
$203$	−2.89138	−	5.00802i	−0.202935	−	0.351494i
$204$		0			0
$205$	0.953328	+	1.65121i	0.0665833	+	0.115326i
$206$		0			0
$207$	−1.24318	+	2.15324i	−0.0864067	+	0.149661i
$208$		0			0
$209$	0.0763346	−	7.12880i	0.00528018	−	0.493109i
$210$		0			0
$211$	8.46325	−	14.6588i	0.582634	−	1.00915i	−0.412532	−	0.910943i	$-0.635355\pi$
$211$	8.46325	−	14.6588i	0.582634	−	1.00915i	0.995166	−	0.0982088i	$-0.0313113\pi$
$212$		0			0
$213$	0.456057	+	0.789915i	0.0312485	+	0.0541241i
$214$		0			0
$215$	−1.98026	−	3.42991i	−0.135053	−	0.233918i
$216$		0			0
$217$	−1.18669			−0.0805577
$218$		0			0
$219$	0.0736051	+	0.127488i	0.00497377	+	0.00861482i
$220$		0			0
$221$	6.59607			0.443700
$222$		0			0
$223$	4.32051	−	7.48334i	0.289322	−	0.501121i	−0.684326	−	0.729176i	$-0.739903\pi$
$223$	4.32051	−	7.48334i	0.289322	−	0.501121i	0.973648	+	0.228055i	$0.0732367\pi$
$224$		0			0
$225$	1.43359	−	2.48305i	0.0955726	−	0.165537i
$226$		0			0
$227$	−20.9265			−1.38894			−0.694470	−	0.719521i	$-0.744361\pi$
$227$	−20.9265			−1.38894			−0.694470	+	0.719521i	$0.744361\pi$
$228$		0			0
$229$	22.3754			1.47861			0.739303	−	0.673373i	$-0.235155\pi$
$229$	22.3754			1.47861			0.739303	+	0.673373i	$0.235155\pi$
$230$		0			0
$231$	−0.189418	+	0.328081i	−0.0124628	+	0.0215862i
$232$		0			0
$233$	9.61854	−	16.6598i	0.630132	−	1.09142i	−0.357393	−	0.933954i	$-0.616334\pi$
$233$	9.61854	−	16.6598i	0.630132	−	1.09142i	0.987524	−	0.157466i	$-0.0503324\pi$
$234$		0			0
$235$	9.09880			0.593540
$236$		0			0
$237$	1.95506	+	3.38627i	0.126995	+	0.219962i
$238$		0			0
$239$	2.13282			0.137961			0.0689804	−	0.997618i	$-0.478025\pi$
$239$	2.13282			0.137961			0.0689804	+	0.997618i	$0.478025\pi$
$240$		0			0
$241$	−12.2316	−	21.1858i	−0.787908	−	1.36470i	−0.927246	−	0.374452i	$-0.877831\pi$
$241$	−12.2316	−	21.1858i	−0.787908	−	1.36470i	0.139338	−	0.990245i	$-0.455503\pi$
$242$		0			0
$243$	−4.63282	−	8.02428i	−0.297196	−	0.514758i
$244$		0			0
$245$	−3.29804	+	5.71237i	−0.210704	+	0.364950i
$246$		0			0
$247$	−3.79804	+	2.13891i	−0.241663	+	0.136095i
$248$		0			0
$249$	−2.89138	+	5.00802i	−0.183234	+	0.317370i
$250$		0			0
$251$	1.64002	+	2.84059i	0.103517	+	0.179297i	0.913131	−	0.407666i	$-0.133657\pi$
$251$	1.64002	+	2.84059i	0.103517	+	0.179297i	−0.809614	+	0.586962i	$0.800324\pi$
$252$		0			0
$253$	−0.709157	−	1.22830i	−0.0445843	−	0.0772223i
$254$		0			0
$255$	2.40393			0.150540
$256$		0			0
$257$	3.81778	+	6.61258i	0.238146	+	0.412482i	0.960182	−	0.279374i	$-0.0901269\pi$
$257$	3.81778	+	6.61258i	0.238146	+	0.412482i	−0.722036	+	0.691855i	$0.756794\pi$
$258$		0			0
$259$	−0.403926			−0.0250988
$260$		0			0
$261$	−13.0439	+	22.5928i	−0.807400	+	1.39846i
$262$		0			0
$263$	7.36445	−	12.7556i	0.454111	−	0.786544i	−0.544525	−	0.838744i	$-0.683290\pi$
$263$	7.36445	−	12.7556i	0.454111	−	0.786544i	0.998637	+	0.0522005i	$0.0166235\pi$
$264$		0			0
$265$	9.86718			0.606136
$266$		0			0
$267$	0.197607			0.0120933
$268$		0			0
$269$	6.73163	−	11.6595i	0.410434	−	0.710893i	−0.584503	−	0.811392i	$-0.698710\pi$
$269$	6.73163	−	11.6595i	0.410434	−	0.710893i	0.994937	+	0.100498i	$0.0320437\pi$
$270$		0			0
$271$	1.93086	−	3.34435i	0.117291	−	0.203155i	−0.801402	−	0.598126i	$-0.795912\pi$
$271$	1.93086	−	3.34435i	0.117291	−	0.203155i	0.918693	+	0.394971i	$0.129246\pi$
$272$		0			0
$273$	0.231626			0.0140186
$274$		0			0
$275$	0.817776	+	1.41643i	0.0493137	+	0.0854139i
$276$		0			0
$277$	−24.2766			−1.45864			−0.729319	−	0.684174i	$-0.760163\pi$
$277$	−24.2766			−1.45864			−0.729319	+	0.684174i	$0.760163\pi$
$278$		0			0
$279$	2.67676	+	4.63629i	0.160254	+	0.277568i
$280$		0			0
$281$	−0.248635	−	0.430649i	−0.0148323	−	0.0256904i	0.858514	−	0.512790i	$-0.171388\pi$
$281$	−0.248635	−	0.430649i	−0.0148323	−	0.0256904i	−0.873346	+	0.487100i	$0.838055\pi$
$282$		0			0
$283$	−7.57906	+	13.1273i	−0.450529	+	0.780338i	−0.998419	−	0.0562118i	$-0.982098\pi$
$283$	−7.57906	+	13.1273i	−0.450529	+	0.780338i	0.547890	+	0.836550i	$0.315431\pi$
$284$		0			0
$285$	−1.38419	+	0.779520i	−0.0819922	+	0.0461748i
$286$		0			0
$287$	0.605889	−	1.04943i	0.0357645	−	0.0619460i
$288$		0			0
$289$	−13.2541	−	22.9568i	−0.779653	−	1.35040i
$290$		0			0
$291$	1.34297	+	2.32610i	0.0787265	+	0.136358i
$292$		0			0
$293$	−13.4094			−0.783385			−0.391692	−	0.920096i	$-0.628110\pi$
$293$	−13.4094			−0.783385			−0.391692	+	0.920096i	$0.628110\pi$
$294$		0			0
$295$	−4.54940	−	7.87979i	−0.264876	−	0.458779i
$296$		0			0
$297$	3.49727			0.202932
$298$		0			0
$299$	−0.433589	+	0.750998i	−0.0250751	+	0.0434313i
$300$		0			0
$301$	−1.25856	+	2.17989i	−0.0725421	+	0.125647i
$302$		0			0
$303$	−3.39847			−0.195237
$304$		0			0
$305$	−2.27110			−0.130043
$306$		0			0
$307$	16.1033	−	27.8917i	0.919062	−	1.59186i	0.118219	−	0.992988i	$-0.462281\pi$
$307$	16.1033	−	27.8917i	0.919062	−	1.59186i	0.800843	−	0.598875i	$-0.204385\pi$
$308$		0			0
$309$	−1.98026	+	3.42991i	−0.112653	+	0.195121i
$310$		0			0
$311$	−12.3699			−0.701433			−0.350717	−	0.936482i	$-0.614062\pi$
$311$	−12.3699			−0.701433			−0.350717	+	0.936482i	$0.614062\pi$
$312$		0			0
$313$	−12.3941	−	21.4672i	−0.700557	−	1.21340i	−0.968271	−	0.249901i	$-0.919602\pi$
$313$	−12.3941	−	21.4672i	−0.700557	−	1.21340i	0.267715	−	0.963498i	$-0.413732\pi$
$314$		0			0
$315$	−1.82224			−0.102672
$316$		0			0
$317$	−3.65529	−	6.33115i	−0.205302	−	0.355593i	0.744927	−	0.667146i	$-0.232484\pi$
$317$	−3.65529	−	6.33115i	−0.205302	−	0.355593i	−0.950229	+	0.311553i	$0.899151\pi$
$318$		0			0
$319$	−7.44078	−	12.8878i	−0.416604	−	0.721579i
$320$		0			0
$321$	2.06468	−	3.57612i	0.115239	−	0.199600i
$322$		0			0
$323$	24.7443	+	14.6416i	1.37681	+	0.814680i
$324$		0			0
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$		0			0
$327$	−2.41112	−	4.17618i	−0.133335	−	0.230943i
$328$		0			0
$329$	−2.89138	−	5.00802i	−0.159407	−	0.276101i
$330$		0			0
$331$	−18.4722			−1.01532			−0.507661	−	0.861557i	$-0.669490\pi$
$331$	−18.4722			−1.01532			−0.507661	+	0.861557i	$0.669490\pi$
$332$		0			0
$333$	0.911120	+	1.57811i	0.0499291	+	0.0864797i
$334$		0			0
$335$	12.4633			0.680940
$336$		0			0
$337$	−15.2316	+	26.3819i	−0.829720	+	1.43712i	0.0685388	+	0.997648i	$0.478166\pi$
$337$	−15.2316	+	26.3819i	−0.829720	+	1.43712i	−0.898258	+	0.439468i	$0.855167\pi$
$338$		0			0
$339$	−1.29258	+	2.23881i	−0.0702032	+	0.121595i
$340$		0			0
$341$	−3.05387			−0.165376
$342$		0			0
$343$	8.64101			0.466571
$344$		0			0
$345$	−0.158021	+	0.273700i	−0.00850754	+	0.0147355i
$346$		0			0
$347$	11.6608	−	20.1970i	0.625982	−	1.08423i	−0.362368	−	0.932035i	$-0.618032\pi$
$347$	11.6608	−	20.1970i	0.625982	−	1.08423i	0.988350	−	0.152197i	$-0.0486349\pi$
$348$		0			0
$349$	−17.6894			−0.946893			−0.473446	−	0.880823i	$-0.656990\pi$
$349$	−17.6894			−0.946893			−0.473446	+	0.880823i	$0.656990\pi$
$350$		0			0
$351$	−1.06914	−	1.85181i	−0.0570665	−	0.0988421i
$352$		0			0
$353$	−7.13828			−0.379932			−0.189966	−	0.981791i	$-0.560838\pi$
$353$	−7.13828			−0.379932			−0.189966	+	0.981791i	$0.560838\pi$
$354$		0			0
$355$	−1.25136	−	2.16743i	−0.0664155	−	0.115035i
$356$		0			0
$357$	−0.763910	−	1.32313i	−0.0404304	−	0.0700275i
$358$		0			0
$359$	−15.0719	+	26.1052i	−0.795463	+	1.37778i	0.127082	+	0.991892i	$0.459439\pi$
$359$	−15.0719	+	26.1052i	−0.795463	+	1.37778i	−0.922545	+	0.385890i	$0.873894\pi$
$360$		0			0
$361$	−18.9956	−	0.406855i	−0.999771	−	0.0214134i
$362$		0			0
$363$	1.51701	−	2.62754i	0.0796224	−	0.137910i
$364$		0			0
$365$	−0.201963	−	0.349810i	−0.0105712	−	0.0183099i
$366$		0			0
$367$	−15.1015	−	26.1566i	−0.788294	−	1.36536i	−0.927012	−	0.375033i	$-0.877631\pi$
$367$	−15.1015	−	26.1566i	−0.788294	−	1.36536i	0.138718	−	0.990332i	$-0.455702\pi$
$368$		0			0
$369$	−5.46672			−0.284586
$370$		0			0
$371$	−3.13555	−	5.43094i	−0.162790	−	0.281960i
$372$		0			0
$373$	29.0449			1.50389			0.751945	−	0.659226i	$-0.229116\pi$
$373$	29.0449			1.50389			0.751945	+	0.659226i	$0.229116\pi$
$374$		0			0
$375$	0.182224	−	0.315621i	0.00941001	−	0.0162986i
$376$		0			0
$377$	−4.54940	+	7.87979i	−0.234306	+	0.405830i
$378$		0			0
$379$	−2.76837			−0.142202			−0.0711009	−	0.997469i	$-0.522651\pi$
$379$	−2.76837			−0.142202			−0.0711009	+	0.997469i	$0.522651\pi$
$380$		0			0
$381$	−5.93196			−0.303904
$382$		0			0
$383$	13.3052	−	23.0453i	0.679866	−	1.17756i	−0.295156	−	0.955449i	$-0.595371\pi$
$383$	13.3052	−	23.0453i	0.679866	−	1.17756i	0.975021	−	0.222112i	$-0.0712952\pi$
$384$		0			0
$385$	0.519739	−	0.900215i	0.0264884	−	0.0458792i
$386$		0			0
$387$	11.3555			0.577233
$388$		0			0
$389$	2.77830	+	4.81215i	0.140865	+	0.243986i	0.927823	−	0.373021i	$-0.121678\pi$
$389$	2.77830	+	4.81215i	0.140865	+	0.243986i	−0.786957	+	0.617007i	$0.788345\pi$
$390$		0			0
$391$	5.71997			0.289271
$392$		0			0
$393$	−1.93805	−	3.35681i	−0.0977618	−	0.169328i
$394$		0			0
$395$	−5.36445	−	9.29150i	−0.269915	−	0.467506i
$396$		0			0
$397$	−1.35725	+	2.35083i	−0.0681186	+	0.117985i	−0.898073	−	0.439846i	$-0.855033\pi$
$397$	−1.35725	+	2.35083i	−0.0681186	+	0.117985i	0.829955	+	0.557831i	$0.188366\pi$
$398$		0			0
$399$	0.868912	+	0.514150i	0.0435000	+	0.0257397i
$400$		0			0
$401$	8.94078	−	15.4859i	0.446481	−	0.773328i	−0.551673	−	0.834061i	$-0.686010\pi$
$401$	8.94078	−	15.4859i	0.446481	−	0.773328i	0.998154	+	0.0607322i	$0.0193436\pi$
$402$		0			0
$403$	0.933589	+	1.61702i	0.0465054	+	0.0805497i
$404$		0			0
$405$	3.91112	+	6.77426i	0.194345	+	0.336616i
$406$		0			0
$407$	−1.03948			−0.0515250
$408$		0			0
$409$	−13.1625	−	22.7981i	−0.650843	−	1.12729i	−0.982919	−	0.184040i	$-0.941082\pi$
$409$	−13.1625	−	22.7981i	−0.650843	−	1.12729i	0.332076	−	0.943253i	$-0.392251\pi$
$410$		0			0
$411$	1.27457			0.0628701
$412$		0			0
$413$	−2.89138	+	5.00802i	−0.142276	+	0.246428i
$414$		0			0
$415$	7.93359	−	13.7414i	0.389445	−	0.674538i
$416$		0			0
$417$	−0.267634			−0.0131061
$418$		0			0
$419$	−15.3250			−0.748674			−0.374337	−	0.927293i	$-0.622130\pi$
$419$	−15.3250			−0.748674			−0.374337	+	0.927293i	$0.622130\pi$
$420$		0			0
$421$	−10.9166	+	18.9081i	−0.532042	+	0.921523i	0.467259	+	0.884121i	$0.345242\pi$
$421$	−10.9166	+	18.9081i	−0.532042	+	0.921523i	−0.999300	+	0.0374023i	$0.988092\pi$
$422$		0			0
$423$	−13.0439	+	22.5928i	−0.634218	+	1.09850i
$424$		0			0
$425$	−6.59607			−0.319957
$426$		0			0
$427$	0.721702	+	1.25002i	0.0349256	+	0.0604929i
$428$		0			0
$429$	0.596074			0.0287787
$430$		0			0
$431$	11.6427	+	20.1658i	0.560811	+	0.971354i	0.997426	+	0.0717050i	$0.0228440\pi$
$431$	11.6427	+	20.1658i	0.560811	+	0.971354i	−0.436615	+	0.899649i	$0.643823\pi$
$432$		0			0
$433$	1.95060	+	3.37854i	0.0937398	+	0.162362i	0.909082	−	0.416617i	$-0.136784\pi$
$433$	1.95060	+	3.37854i	0.0937398	+	0.162362i	−0.815342	+	0.578979i	$0.803451\pi$
$434$		0			0
$435$	−1.65802	+	2.87178i	−0.0794960	+	0.137691i
$436$		0			0
$437$	−3.29357	+	1.85481i	−0.157553	+	0.0887276i
$438$		0			0
$439$	−9.73882	+	16.8681i	−0.464808	+	0.805072i	−0.999193	−	0.0401697i	$-0.987210\pi$
$439$	−9.73882	+	16.8681i	−0.464808	+	0.805072i	0.534384	+	0.845242i	$0.320543\pi$
$440$		0			0
$441$	−9.45606	−	16.3784i	−0.450288	−	0.779922i
$442$		0			0
$443$	0.953328	+	1.65121i	0.0452940	+	0.0784515i	0.887784	−	0.460261i	$-0.152244\pi$
$443$	0.953328	+	1.65121i	0.0452940	+	0.0784515i	−0.842490	+	0.538713i	$0.818911\pi$
$444$		0			0
$445$	−0.542208			−0.0257031
$446$		0			0
$447$	−1.84744	−	3.19986i	−0.0873808	−	0.151348i
$448$		0			0
$449$	−8.05933			−0.380343			−0.190172	−	0.981751i	$-0.560904\pi$
$449$	−8.05933			−0.380343			−0.190172	+	0.981751i	$0.560904\pi$
$450$		0			0
$451$	1.55922	−	2.70064i	0.0734207	−	0.127168i
$452$		0			0
$453$	0.512653	−	0.887941i	0.0240865	−	0.0417191i
$454$		0			0
$455$	−0.635552			−0.0297951
$456$		0			0
$457$	11.3250			0.529760			0.264880	−	0.964281i	$-0.414668\pi$
$457$	11.3250			0.529760			0.264880	+	0.964281i	$0.414668\pi$
$458$		0			0
$459$	−7.05213	+	12.2146i	−0.329165	+	0.570131i
$460$		0			0
$461$	−10.0521	+	17.4108i	−0.468174	+	0.810902i	−0.999338	−	0.0363671i	$-0.988421\pi$
$461$	−10.0521	+	17.4108i	−0.468174	+	0.810902i	0.531164	+	0.847269i	$0.321755\pi$
$462$		0			0
$463$	−1.33043			−0.0618303			−0.0309151	−	0.999522i	$-0.509842\pi$
$463$	−1.33043			−0.0618303			−0.0309151	+	0.999522i	$0.509842\pi$
$464$		0			0
$465$	0.340245	+	0.589321i	0.0157785	+	0.0273291i
$466$		0			0
$467$	−10.0844			−0.466651			−0.233326	−	0.972399i	$-0.574961\pi$
$467$	−10.0844			−0.466651			−0.233326	+	0.972399i	$0.574961\pi$
$468$		0			0
$469$	−3.96052	−	6.85982i	−0.182880	−	0.316757i
$470$		0			0
$471$	−0.175030	−	0.303161i	−0.00806496	−	0.0139689i
$472$		0			0
$473$	−3.23882	+	5.60980i	−0.148921	+	0.257939i
$474$		0			0
$475$	3.79804	−	2.13891i	0.174266	−	0.0981397i
$476$		0			0
$477$	−14.1455	+	24.5007i	−0.647677	+	1.12181i
$478$		0			0
$479$	4.44078	+	7.69166i	0.202905	+	0.351441i	0.949463	−	0.313879i	$-0.101629\pi$
$479$	4.44078	+	7.69166i	0.202905	+	0.351441i	−0.746559	+	0.665320i	$0.768295\pi$
$480$		0			0
$481$	0.317776	+	0.550404i	0.0144893	+	0.0250963i
$482$		0			0
$483$	0.200861			0.00913947
$484$		0			0
$485$	−3.68495	−	6.38253i	−0.167325	−	0.289816i
$486$		0			0
$487$	−5.32497			−0.241297			−0.120649	−	0.992695i	$-0.538497\pi$
$487$	−5.32497			−0.241297			−0.120649	+	0.992695i	$0.538497\pi$
$488$		0			0
$489$	0.571870	−	0.990508i	0.0258609	−	0.0447923i
$490$		0			0
$491$	−9.70469	+	16.8090i	−0.437967	+	0.758580i	−0.997533	−	0.0702054i	$-0.977635\pi$
$491$	−9.70469	+	16.8090i	−0.437967	+	0.758580i	0.559566	+	0.828786i	$0.310968\pi$
$492$		0			0
$493$	60.0164			2.70300
$494$		0			0
$495$	−4.68942			−0.210774
$496$		0			0
$497$	−0.795307	+	1.37751i	−0.0356744	+	0.0617899i
$498$		0			0
$499$	5.79357	−	10.0348i	0.259356	−	0.449218i	−0.706714	−	0.707500i	$-0.749823\pi$
$499$	5.79357	−	10.0348i	0.259356	−	0.449218i	0.966070	+	0.258282i	$0.0831564\pi$
$500$		0			0
$501$	3.87611			0.173172
$502$		0			0
$503$	17.5521	+	30.4012i	0.782611	+	1.35552i	0.930416	+	0.366505i	$0.119446\pi$
$503$	17.5521	+	30.4012i	0.782611	+	1.35552i	−0.147805	+	0.989017i	$0.547221\pi$
$504$		0			0
$505$	9.32497			0.414956
$506$		0			0
$507$	2.18669	+	3.78746i	0.0971142	+	0.168207i
$508$		0			0
$509$	7.93359	+	13.7414i	0.351650	+	0.609076i	0.986539	−	0.163528i	$-0.0522873\pi$
$509$	7.93359	+	13.7414i	0.351650	+	0.609076i	−0.634889	+	0.772604i	$0.718954\pi$
$510$		0			0
$511$	−0.128358	+	0.222323i	−0.00567823	+	0.00983498i
$512$		0			0
$513$	0.0997981	−	9.32002i	0.00440619	−	0.411489i
$514$		0			0
$515$	5.43359	−	9.41125i	0.239433	−	0.414709i
$516$		0			0
$517$	−7.44078	−	12.8878i	−0.327245	−	0.566805i
$518$		0			0
$519$	−2.25409	−	3.90421i	−0.0989438	−	0.171376i
$520$		0			0
$521$	36.6949			1.60763			0.803816	−	0.594878i	$-0.202800\pi$
$521$	36.6949			1.60763			0.803816	+	0.594878i	$0.202800\pi$
$522$		0			0
$523$	−15.5127	−	26.8687i	−0.678321	−	1.17489i	−0.975486	−	0.220060i	$-0.929375\pi$
$523$	−15.5127	−	26.8687i	−0.678321	−	1.17489i	0.297165	−	0.954826i	$-0.403959\pi$
$524$		0			0
$525$	−0.231626			−0.0101090
$526$		0			0
$527$	6.15802	−	10.6660i	0.268248	−	0.464618i
$528$		0			0
$529$	11.1240	−	19.2673i	0.483652	−	0.837710i
$530$		0			0
$531$	26.0879			1.13212
$532$		0			0
$533$	−1.90666			−0.0825864
$534$		0			0
$535$	−5.66521	+	9.81244i	−0.244929	+	0.424229i
$536$		0			0
$537$	−0.0592173	+	0.102567i	−0.00255542	+	0.00442611i
$538$		0			0
$539$	10.7882			0.464682
$540$		0			0
$541$	3.79357	+	6.57066i	0.163098	+	0.282495i	0.935978	−	0.352058i	$-0.114518\pi$
$541$	3.79357	+	6.57066i	0.163098	+	0.282495i	−0.772880	+	0.634552i	$0.781185\pi$
$542$		0			0
$543$	3.21199			0.137840
$544$		0			0
$545$	6.61581	+	11.4589i	0.283390	+	0.490846i
$546$		0			0
$547$	−15.3914	−	26.6587i	−0.658088	−	1.13984i	−0.981110	−	0.193450i	$-0.938032\pi$
$547$	−15.3914	−	26.6587i	−0.658088	−	1.13984i	0.323022	−	0.946391i	$-0.395301\pi$
$548$		0			0
$549$	3.25583	−	5.63926i	0.138955	−	0.240678i
$550$		0			0
$551$	−34.5576	+	19.4615i	−1.47220	+	0.829087i
$552$		0			0
$553$	−3.40939	+	5.90523i	−0.144982	+	0.251116i
$554$		0			0
$555$	0.115813	+	0.200594i	0.00491598	+	0.00851473i
$556$		0			0
$557$	−15.5369	−	26.9106i	−0.658318	−	1.14024i	−0.981051	−	0.193750i	$-0.937935\pi$
$557$	−15.5369	−	26.9106i	−0.658318	−	1.14024i	0.322733	−	0.946490i	$-0.395398\pi$
$558$		0			0
$559$	3.96052			0.167512
$560$		0			0
$561$	−1.96587	−	3.40499i	−0.0829992	−	0.143759i
$562$		0			0
$563$	23.2766			0.980990			0.490495	−	0.871444i	$-0.336816\pi$
$563$	23.2766			0.980990			0.490495	+	0.871444i	$0.336816\pi$
$564$		0			0
$565$	3.54667	−	6.14302i	0.149210	−	0.258439i
$566$		0			0
$567$	2.48572	−	4.30539i	0.104390	−	0.180810i
$568$		0			0
$569$	24.1976			1.01442			0.507208	−	0.861824i	$-0.330678\pi$
$569$	24.1976			1.01442			0.507208	+	0.861824i	$0.330678\pi$
$570$		0			0
$571$	−29.8475			−1.24908			−0.624540	−	0.780992i	$-0.714714\pi$
$571$	−29.8475			−1.24908			−0.624540	+	0.780992i	$0.714714\pi$
$572$		0			0
$573$	4.59061	−	7.95118i	0.191776	−	0.332165i
$574$		0			0
$575$	0.433589	−	0.750998i	0.0180819	−	0.0313188i
$576$		0			0
$577$	33.7882			1.40662			0.703311	−	0.710882i	$-0.251704\pi$
$577$	33.7882			1.40662			0.703311	+	0.710882i	$0.251704\pi$
$578$		0			0
$579$	3.43905	+	5.95661i	0.142922	+	0.247548i
$580$		0			0
$581$	−10.0844			−0.418372
$582$		0			0
$583$	−8.06914	−	13.9762i	−0.334190	−	0.578833i
$584$		0			0
$585$	1.43359	+	2.48305i	0.0592716	+	0.102661i
$586$		0			0
$587$	−15.3474	+	26.5825i	−0.633457	+	1.09718i	0.353383	+	0.935479i	$0.385031\pi$
$587$	−15.3474	+	26.5825i	−0.633457	+	1.09718i	−0.986840	+	0.161700i	$0.948302\pi$
$588$		0			0
$589$	−0.0871451	+	8.13837i	−0.00359075	+	0.335336i
$590$		0			0
$591$	1.34198	−	2.32438i	0.0552017	−	0.0956121i
$592$		0			0
$593$	−3.49727	−	6.05745i	−0.143616	−	0.248750i	0.785240	−	0.619192i	$-0.212540\pi$
$593$	−3.49727	−	6.05745i	−0.143616	−	0.248750i	−0.928856	+	0.370442i	$0.879206\pi$
$594$		0			0
$595$	2.09607	+	3.63051i	0.0859306	+	0.148836i
$596$		0			0
$597$	−1.00893			−0.0412927
$598$		0			0
$599$	−2.26837	−	3.92894i	−0.0926833	−	0.160532i	0.815956	−	0.578114i	$-0.196211\pi$
$599$	−2.26837	−	3.92894i	−0.0926833	−	0.160532i	−0.908639	+	0.417582i	$0.862878\pi$
$600$		0			0
$601$	16.0790			0.655874			0.327937	−	0.944700i	$-0.393647\pi$
$601$	16.0790			0.655874			0.327937	+	0.944700i	$0.393647\pi$
$602$		0			0
$603$	−17.8672	+	30.9469i	−0.727608	+	1.26025i
$604$		0			0
$605$	−4.16248	+	7.20964i	−0.169229	+	0.293113i
$606$		0			0
$607$	34.0702			1.38287			0.691434	−	0.722439i	$-0.256979\pi$
$607$	34.0702			1.38287			0.691434	+	0.722439i	$0.256979\pi$
$608$		0			0
$609$	2.10752			0.0854009
$610$		0			0
$611$	−4.54940	+	7.87979i	−0.184049	+	0.318782i
$612$		0			0
$613$	19.7191	−	34.1544i	0.796446	−	1.37949i	−0.125471	−	0.992097i	$-0.540044\pi$
$613$	19.7191	−	34.1544i	0.796446	−	1.37949i	0.921917	−	0.387388i	$-0.126623\pi$
$614$		0			0
$615$	−0.694877			−0.0280201
$616$		0			0
$617$	19.6257	+	33.9928i	0.790102	+	1.36850i	0.925903	+	0.377761i	$0.123306\pi$
$617$	19.6257	+	33.9928i	0.790102	+	1.36850i	−0.135801	+	0.990736i	$0.543361\pi$
$618$		0			0
$619$	−24.3644			−0.979290			−0.489645	−	0.871922i	$-0.662874\pi$
$619$	−24.3644			−0.979290			−0.489645	+	0.871922i	$0.662874\pi$
$620$		0			0
$621$	−0.927135	−	1.60584i	−0.0372046	−	0.0644403i
$622$		0			0
$623$	0.172301	+	0.298433i	0.00690308	+	0.0119565i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	2.23609	+	1.32313i	0.0893008	+	0.0528408i
$628$		0			0
$629$	2.09607	−	3.63051i	0.0835759	−	0.144758i
$630$		0			0
$631$	−17.6949	−	30.6484i	−0.704422	−	1.22009i	−0.966900	−	0.255157i	$-0.917873\pi$
$631$	−17.6949	−	30.6484i	−0.704422	−	1.22009i	0.262478	−	0.964938i	$-0.415460\pi$
$632$		0			0
$633$	3.08442	+	5.34236i	0.122595	+	0.212340i
$634$		0			0
$635$	16.2766			0.645916
$636$		0			0
$637$	−3.29804	−	5.71237i	−0.130673	−	0.226332i
$638$		0			0
$639$	7.17577			0.283869
$640$		0			0
$641$	−17.8546	+	30.9251i	−0.705216	+	1.22147i	0.261398	+	0.965231i	$0.415816\pi$
$641$	−17.8546	+	30.9251i	−0.705216	+	1.22147i	−0.966614	+	0.256238i	$0.917517\pi$
$642$		0			0
$643$	10.5549	−	18.2816i	0.416243	−	0.720954i	−0.579315	−	0.815104i	$-0.696680\pi$
$643$	10.5549	−	18.2816i	0.416243	−	0.720954i	0.995558	+	0.0941496i	$0.0300132\pi$
$644$		0			0
$645$	1.44340			0.0568340
$646$		0			0
$647$	−43.7058			−1.71825			−0.859126	−	0.511764i	$-0.828992\pi$
$647$	−43.7058			−1.71825			−0.859126	+	0.511764i	$0.828992\pi$
$648$		0			0
$649$	−7.44078	+	12.8878i	−0.292076	+	0.505891i
$650$		0			0
$651$	0.216243	−	0.374544i	0.00847524	−	0.0146795i
$652$		0			0
$653$	−24.1887			−0.946576			−0.473288	−	0.880908i	$-0.656933\pi$
$653$	−24.1887			−0.946576			−0.473288	+	0.880908i	$0.656933\pi$
$654$		0			0
$655$	5.31778	+	9.21066i	0.207783	+	0.359890i
$656$		0			0
$657$	1.15813			0.0451829
$658$		0			0
$659$	16.9956	+	29.4373i	0.662056	+	1.14672i	0.980074	+	0.198630i	$0.0636494\pi$
$659$	16.9956	+	29.4373i	0.662056	+	1.14672i	−0.318018	+	0.948085i	$0.603017\pi$
$660$		0			0
$661$	−2.27830	−	3.94613i	−0.0886155	−	0.153487i	0.818311	−	0.574776i	$-0.194911\pi$
$661$	−2.27830	−	3.94613i	−0.0886155	−	0.153487i	−0.906926	+	0.421290i	$0.861578\pi$
$662$		0			0
$663$	−1.20196	+	2.08186i	−0.0466804	+	0.0808528i
$664$		0			0
$665$	−2.38419	−	1.41076i	−0.0924548	−	0.0547070i
$666$		0			0
$667$	−3.94514	+	6.83318i	−0.152756	+	0.264582i
$668$		0			0
$669$	1.57460	+	2.72729i	0.0608775	+	0.105443i
$670$		0			0
$671$	1.85725	+	3.21686i	0.0716985	+	0.124185i
$672$		0			0
$673$	−22.7487			−0.876900			−0.438450	−	0.898756i	$-0.644472\pi$
$673$	−22.7487			−0.876900			−0.438450	+	0.898756i	$0.644472\pi$
$674$		0			0
$675$	1.06914	+	1.85181i	0.0411512	+	0.0712760i
$676$		0			0
$677$	−15.6949			−0.603203			−0.301602	−	0.953434i	$-0.597521\pi$
$677$	−15.6949			−0.603203			−0.301602	+	0.953434i	$0.597521\pi$
$678$		0			0
$679$	−2.34198	+	4.05643i	−0.0898769	+	0.155671i
$680$		0			0
$681$	3.81331	−	6.60485i	0.146126	−	0.253098i
$682$		0			0
$683$	8.82770			0.337783			0.168891	−	0.985635i	$-0.445981\pi$
$683$	8.82770			0.337783			0.168891	+	0.985635i	$0.445981\pi$
$684$		0			0
$685$	−3.49727			−0.133624
$686$		0			0
$687$	−4.07733	+	7.06214i	−0.155560	+	0.269438i
$688$		0			0
$689$	−4.93359	+	8.54523i	−0.187955	+	0.325547i
$690$		0			0
$691$	23.0198			0.875716			0.437858	−	0.899044i	$-0.355737\pi$
$691$	23.0198			0.875716			0.437858	+	0.899044i	$0.355737\pi$
$692$		0			0
$693$	1.49018	+	2.58107i	0.0566074	+	0.0980469i
$694$		0			0
$695$	0.734355			0.0278557
$696$		0			0
$697$	6.28822	+	10.8915i	0.238183	+	0.412546i
$698$		0			0
$699$	3.50546	+	6.07163i	0.132589	+	0.229650i
$700$		0			0
$701$	4.95606	−	8.58414i	0.187188	−	0.324219i	−0.757124	−	0.653271i	$-0.773396\pi$
$701$	4.95606	−	8.58414i	0.187188	−	0.324219i	0.944312	+	0.329053i	$0.106729\pi$
$702$		0			0
$703$	−0.0296625	+	2.77015i	−0.00111874	+	0.104478i
$704$		0			0
$705$	−1.65802	+	2.87178i	−0.0624447	+	0.108157i
$706$		0			0
$707$	−2.96325	−	5.13250i	−0.111445	−	0.193028i
$708$		0			0
$709$	18.0521	+	31.2672i	0.677962	+	1.17426i	0.975594	+	0.219584i	$0.0704700\pi$
$709$	18.0521	+	31.2672i	0.677962	+	1.17426i	−0.297632	+	0.954681i	$0.596197\pi$
$710$		0			0
$711$	30.7617			1.15365
$712$		0			0
$713$	0.809587	+	1.40225i	0.0303193	+	0.0525145i
$714$		0			0
$715$	−1.63555			−0.0611662
$716$		0			0
$717$	−0.388651	+	0.673164i	−0.0145145	+	0.0251398i
$718$		0			0
$719$	−9.50546	+	16.4639i	−0.354494	+	0.614001i	−0.987031	−	0.160529i	$-0.948680\pi$
$719$	−9.50546	+	16.4639i	−0.354494	+	0.614001i	0.632537	+	0.774530i	$0.282013\pi$
$720$		0			0
$721$	−6.90666			−0.257217
$722$		0			0
$723$	8.91558			0.331574
$724$		0			0
$725$	4.54940	−	7.87979i	0.168961	−	0.292648i
$726$		0			0
$727$	−1.44351	+	2.50024i	−0.0535369	+	0.0927286i	−0.891552	−	0.452919i	$-0.850383\pi$
$727$	−1.44351	+	2.50024i	−0.0535369	+	0.0927286i	0.838015	+	0.545647i	$0.183716\pi$
$728$		0			0
$729$	−20.0899			−0.744069
$730$		0			0
$731$	−13.0619	−	22.6240i	−0.483114	−	0.836777i
$732$		0			0
$733$	44.9463			1.66013			0.830066	−	0.557666i	$-0.188303\pi$
$733$	44.9463			1.66013			0.830066	+	0.557666i	$0.188303\pi$
$734$		0			0
$735$	−1.20196	−	2.08186i	−0.0443351	−	0.0767906i
$736$		0			0
$737$	−10.1921	−	17.6533i	−0.375433	−	0.650268i
$738$		0			0
$739$	25.4956	−	44.1597i	0.937872	−	1.62444i	0.168442	−	0.985711i	$-0.446126\pi$
$739$	25.4956	−	44.1597i	0.937872	−	1.62444i	0.769430	−	0.638731i	$-0.220540\pi$
$740$		0			0
$741$	0.0170096	−	1.58850i	0.000624862	−	0.0583550i
$742$		0			0
$743$	9.43805	−	16.3472i	0.346249	−	0.599720i	−0.639331	−	0.768931i	$-0.720789\pi$
$743$	9.43805	−	16.3472i	0.346249	−	0.599720i	0.985580	+	0.169211i	$0.0541220\pi$
$744$		0			0
$745$	5.06914	+	8.78001i	0.185719	+	0.321675i
$746$		0			0
$747$	22.7470	+	39.3990i	0.832270	+	1.44153i
$748$		0			0
$749$	7.20108			0.263122
$750$		0			0
$751$	13.0127	+	22.5386i	0.474838	+	0.822444i	0.999585	−	0.0288143i	$-0.00917315\pi$
$751$	13.0127	+	22.5386i	0.474838	+	0.822444i	−0.524746	+	0.851259i	$0.675840\pi$
$752$		0			0
$753$	−1.19540			−0.0435629
$754$		0			0
$755$	−1.40666	+	2.43640i	−0.0511934	+	0.0886697i
$756$		0			0
$757$	5.95779	−	10.3192i	0.216540	−	0.375058i	−0.737208	−	0.675666i	$-0.763856\pi$
$757$	5.95779	−	10.3192i	0.216540	−	0.375058i	0.953748	+	0.300608i	$0.0971896\pi$
$758$		0			0
$759$	0.516902			0.0187623
$760$		0			0
$761$	−2.39500			−0.0868186			−0.0434093	−	0.999057i	$-0.513822\pi$
$761$	−2.39500			−0.0868186			−0.0434093	+	0.999057i	$0.513822\pi$
$762$		0			0
$763$	4.20469	−	7.28274i	0.152220	−	0.263653i
$764$		0			0
$765$	9.45606	−	16.3784i	0.341884	−	0.592161i
$766$		0			0
$767$	9.09880			0.328539
$768$		0			0
$769$	−2.66248	−	4.61156i	−0.0960117	−	0.166297i	0.814019	−	0.580839i	$-0.197275\pi$
$769$	−2.66248	−	4.61156i	−0.0960117	−	0.166297i	−0.910030	+	0.414542i	$0.863942\pi$
$770$		0			0
$771$	−2.78276			−0.100219
$772$		0			0
$773$	12.2486	+	21.2153i	0.440553	+	0.763060i	0.997731	−	0.0673334i	$-0.0214491\pi$
$773$	12.2486	+	21.2153i	0.440553	+	0.763060i	−0.557178	+	0.830393i	$0.688116\pi$
$774$		0			0
$775$	−0.933589	−	1.61702i	−0.0335355	−	0.0580852i
$776$		0			0
$777$	0.0736051	−	0.127488i	0.00264057	−	0.00457360i
$778$		0			0
$779$	−7.15256	−	4.23229i	−0.256267	−	0.151637i
$780$		0			0
$781$	−2.04667	+	3.54494i	−0.0732357	+	0.126848i
$782$		0			0
$783$	−9.72790	−	16.8492i	−0.347647	−	0.602142i
$784$		0			0
$785$	0.480261	+	0.831836i	0.0171412	+	0.0296895i
$786$		0			0
$787$	20.5171			0.731356			0.365678	−	0.930741i	$-0.380837\pi$
$787$	20.5171			0.731356			0.365678	+	0.930741i	$0.380837\pi$
$788$		0			0
$789$	2.68396	+	4.64875i	0.0955515	+	0.165500i
$790$		0			0
$791$	−4.50819			−0.160293
$792$		0			0
$793$	1.13555	−	1.96683i	0.0403246	−	0.0698443i
$794$		0			0
$795$	−1.79804	+	3.11429i	−0.0637698	+	0.110453i
$796$		0			0
$797$	−23.0144			−0.815211			−0.407606	−	0.913158i	$-0.633636\pi$
$797$	−23.0144			−0.815211			−0.407606	+	0.913158i	$0.633636\pi$
$798$		0			0
$799$	60.0164			2.12323
$800$		0			0
$801$	0.777303	−	1.34633i	0.0274647	−	0.0475702i
$802$		0			0
$803$	−0.330321	+	0.572133i	−0.0116568	+	0.0201901i
$804$		0			0
$805$	−0.551136			−0.0194250
$806$		0			0
$807$	2.45333	+	4.24929i	0.0863612	+	0.149582i
$808$		0			0
$809$	−28.3195			−0.995661			−0.497830	−	0.867274i	$-0.665870\pi$
$809$	−28.3195			−0.995661			−0.497830	+	0.867274i	$0.665870\pi$
$810$		0			0
$811$	19.7766	+	34.2540i	0.694449	+	1.20282i	0.970366	+	0.241640i	$0.0776852\pi$
$811$	19.7766	+	34.2540i	0.694449	+	1.20282i	−0.275917	+	0.961181i	$0.588981\pi$
$812$		0			0
$813$	0.703698	+	1.21884i	0.0246798	+	0.0427466i
$814$		0			0
$815$	−1.56914	+	2.71783i	−0.0549646	+	0.0952015i
$816$		0			0
$817$	14.8574	+	8.79134i	0.519793	+	0.307570i
$818$		0			0
$819$	0.911120	−	1.57811i	0.0318371	−	0.0551435i
$820$		0			0
$821$	−15.4013	−	26.6758i	−0.537509	−	0.930993i	−0.999037	−	0.0438677i	$-0.986032\pi$
$821$	−15.4013	−	26.6758i	−0.537509	−	0.930993i	0.461528	−	0.887126i	$-0.347301\pi$
$822$		0			0
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	0.692240	−	0.721668i	$-0.256624\pi$
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	−0.971102	+	0.238664i	$0.923291\pi$
$824$		0			0
$825$	−0.596074			−0.0207526
$826$		0			0
$827$	10.1427	+	17.5678i	0.352698	+	0.610891i	0.986721	−	0.162423i	$-0.0519310\pi$
$827$	10.1427	+	17.5678i	0.352698	+	0.610891i	−0.634023	+	0.773314i	$0.718598\pi$
$828$		0			0
$829$	44.0792			1.53093			0.765466	−	0.643476i	$-0.222508\pi$
$829$	44.0792			1.53093			0.765466	+	0.643476i	$0.222508\pi$
$830$		0			0
$831$	4.42377	−	7.66220i	0.153459	−	0.265799i
$832$		0			0
$833$	−21.7541	+	37.6792i	−0.753735	+	1.30551i
$834$		0			0
$835$	−10.6356			−0.368058
$836$		0			0
$837$	−3.99255			−0.138003
$838$		0			0
$839$	26.9534	−	46.6847i	0.930536	−	1.61174i	0.148129	−	0.988968i	$-0.452675\pi$
$839$	26.9534	−	46.6847i	0.930536	−	1.61174i	0.782407	−	0.622767i	$-0.213992\pi$
$840$		0			0
$841$	−26.8941	+	46.5820i	−0.927383	+	1.60627i
$842$		0			0
$843$	0.181229			0.00624187
$844$		0			0
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$	5.29095			0.181799
$848$		0			0
$849$	−2.76218	−	4.78423i	−0.0947976	−	0.164194i
$850$		0			0
$851$	0.275568	+	0.477298i	0.00944636	+	0.0163616i
$852$		0			0
$853$	−13.5324	+	23.4388i	−0.463340	+	0.802529i	−0.999125	−	0.0418258i	$-0.986683\pi$
$853$	−13.5324	+	23.4388i	−0.463340	+	0.802529i	0.535785	+	0.844355i	$0.320016\pi$
$854$		0			0
$855$	−0.133817	+	12.4970i	−0.00457645	+	0.427389i
$856$		0			0
$857$	1.67676	−	2.90424i	0.0572772	−	0.0992070i	−0.835965	−	0.548783i	$-0.815091\pi$
$857$	1.67676	−	2.90424i	0.0572772	−	0.0992070i	0.893242	+	0.449576i	$0.148425\pi$
$858$		0			0
$859$	−26.8529	−	46.5106i	−0.916209	−	1.58692i	−0.805121	−	0.593110i	$-0.797900\pi$
$859$	−26.8529	−	46.5106i	−0.916209	−	1.58692i	−0.111088	−	0.993811i	$-0.535433\pi$
$860$		0			0
$861$	0.220815	+	0.382463i	0.00752536	+	0.0130343i
$862$		0			0
$863$	39.1527			1.33277			0.666386	−	0.745607i	$-0.267840\pi$
$863$	39.1527			1.33277			0.666386	+	0.745607i	$0.267840\pi$
$864$		0			0
$865$	6.18495	+	10.7127i	0.210295	+	0.364241i
$866$		0			0
$867$	9.66086			0.328100
$868$		0			0
$869$	−8.77383	+	15.1967i	−0.297632	+	0.515514i
$870$		0			0
$871$	−6.23163	+	10.7935i	−0.211151	+	0.365724i
$872$		0			0
$873$	21.1308			0.715170
$874$		0			0
$875$	0.635552			0.0214856
$876$		0			0
$877$	14.8260	−	25.6793i	0.500637	−	0.867129i	−0.499362	−	0.866393i	$-0.666432\pi$
$877$	14.8260	−	25.6793i	0.500637	−	0.867129i	1.00000		0.000735993i	$-0.000234274\pi$
$878$		0			0
$879$	2.44351	−	4.23229i	0.0824176	−	0.142752i
$880$		0			0
$881$	43.2820			1.45821			0.729104	−	0.684403i	$-0.239937\pi$
$881$	43.2820			1.45821			0.729104	+	0.684403i	$0.239937\pi$
$882$		0			0
$883$	28.4830	+	49.3340i	0.958529	+	1.66022i	0.726078	+	0.687613i	$0.241341\pi$
$883$	28.4830	+	49.3340i	0.958529	+	1.66022i	0.232451	+	0.972608i	$0.425325\pi$
$884$		0			0
$885$	3.31604			0.111468
$886$		0			0
$887$	10.1158	+	17.5211i	0.339656	+	0.588301i	0.984368	−	0.176124i	$-0.0563561\pi$
$887$	10.1158	+	17.5211i	0.339656	+	0.588301i	−0.644712	+	0.764425i	$0.723023\pi$
$888$		0			0
$889$	−5.17230	−	8.95869i	−0.173473	−	0.300465i
$890$		0			0
$891$	6.39684	−	11.0797i	0.214302	−	0.371182i
$892$		0			0
$893$	−34.5576	+	19.4615i	−1.15643	+	0.651254i
$894$		0			0
$895$	0.162485	−	0.281432i	0.00543127	−	0.00940724i
$896$		0			0
$897$	−0.158021	−	0.273700i	−0.00527615	−	0.00913857i
$898$		0			0
$899$	8.49454	+	14.7130i	0.283309	+	0.490705i
$900$		0			0
$901$	65.0846			2.16828
$902$		0			0
$903$	−0.458679	−	0.794456i	−0.0152639	−	0.0264378i
$904$		0			0
$905$	−8.81331			−0.292964
$906$		0			0
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	−0.937018	−	0.349281i	$-0.886426\pi$
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	0.770996	+	0.636841i	$0.219759\pi$
$908$		0			0
$909$	−13.3682	+	23.1544i	−0.443394	+	0.767981i
$910$		0			0
$911$	55.0109			1.82259			0.911297	−	0.411751i	$-0.135083\pi$
$911$	55.0109			1.82259			0.911297	+	0.411751i	$0.135083\pi$
$912$		0			0
$913$	−25.9516			−0.858872
$914$		0			0
$915$	0.413850	−	0.716809i	0.0136814	−	0.0236970i
$916$		0			0
$917$	3.37972	−	5.85385i	0.111608	−	0.193311i
$918$		0			0
$919$	−48.6159			−1.60369			−0.801846	−	0.597531i	$-0.796148\pi$
$919$	−48.6159			−1.60369			−0.801846	+	0.597531i	$0.796148\pi$
$920$		0			0
$921$	5.86880	+	10.1651i	0.193384	+	0.334950i
$922$		0			0
$923$	2.50273			0.0823783
$924$		0			0
$925$	−0.317776	−	0.550404i	−0.0104484	−	0.0180972i
$926$		0			0
$927$	15.5791	+	26.9837i	0.511684	+	0.886262i
$928$		0			0
$929$	−5.66075	+	9.80471i	−0.185723	+	0.321682i	−0.943820	−	0.330460i	$-0.892796\pi$
$929$	−5.66075	+	9.80471i	−0.185723	+	0.321682i	0.758097	+	0.652142i	$0.226129\pi$
$930$		0			0
$931$	0.307853	−	28.7500i	0.0100895	−	0.942242i
$932$		0			0
$933$	2.25409	−	3.90421i	0.0737957	−	0.127818i
$934$		0			0
$935$	5.39411	+	9.34287i	0.176406	+	0.305545i
$936$		0			0
$937$	5.24864	+	9.09090i	0.171465	+	0.296987i	0.938932	−	0.344102i	$-0.111816\pi$
$937$	5.24864	+	9.09090i	0.171465	+	0.296987i	−0.767467	+	0.641088i	$0.778483\pi$
$938$		0			0
$939$	9.03402			0.294814
$940$		0			0
$941$	1.40939	+	2.44113i	0.0459447	+	0.0795785i	0.888083	−	0.459683i	$-0.152037\pi$
$941$	1.40939	+	2.44113i	0.0459447	+	0.0795785i	−0.842139	+	0.539261i	$0.818704\pi$
$942$		0			0
$943$	−1.65341			−0.0538424
$944$		0			0
$945$	0.679494	−	1.17692i	0.0221040	−	0.0382852i
$946$		0			0
$947$	−22.7568	+	39.4160i	−0.739497	+	1.28085i	0.213224	+	0.977003i	$0.431603\pi$
$947$	−22.7568	+	39.4160i	−0.739497	+	1.28085i	−0.952722	+	0.303844i	$0.901730\pi$
$948$		0			0
$949$	0.403926			0.0131120
$950$		0			0
$951$	2.66433			0.0863967
$952$		0			0
$953$	10.3600	−	17.9440i	0.335593	−	0.581264i	−0.648006	−	0.761635i	$-0.724397\pi$
$953$	10.3600	−	17.9440i	0.335593	−	0.581264i	0.983599	+	0.180372i	$0.0577301\pi$
$954$		0			0
$955$	−12.5961	+	21.8170i	−0.407599	+	0.705983i
$956$		0			0
$957$	5.42356			0.175319
$958$		0			0
$959$	1.11135	+	1.92491i	0.0358873	+	0.0621587i
$960$		0			0
$961$	−27.5136			−0.887537
$962$		0			0
$963$	−16.2432	−	28.1340i	−0.523429	−	0.906606i
$964$		0			0
$965$	−9.43632	−	16.3442i	−0.303766	−	0.526138i
$966$		0			0
$967$	−6.73436	+	11.6642i	−0.216562	+	0.375097i	−0.953755	−	0.300586i	$-0.902818\pi$
$967$	−6.73436	+	11.6642i	−0.216562	+	0.375097i	0.737192	+	0.675683i	$0.236151\pi$
$968$		0			0
$969$	−9.13020	+	5.14177i	−0.293304	+	0.165177i
$970$		0			0
$971$	−23.5252	+	40.7468i	−0.754960	+	1.30763i	0.190435	+	0.981700i	$0.439010\pi$
$971$	−23.5252	+	40.7468i	−0.754960	+	1.30763i	−0.945394	+	0.325928i	$0.894323\pi$
$972$		0			0
$973$	−0.233360	−	0.404192i	−0.00748119	−	0.0129578i
$974$		0			0
$975$	0.182224	+	0.315621i	0.00583584	+	0.0101080i
$976$		0			0
$977$	43.0648			1.37776			0.688882	−	0.724873i	$-0.258102\pi$
$977$	43.0648			1.37776			0.688882	+	0.724873i	$0.258102\pi$
$978$		0			0
$979$	0.443404	+	0.767999i	0.0141713	+	0.0245454i
$980$		0			0
$981$	−37.9374			−1.21125
$982$		0			0
$983$	−27.0396	+	46.8339i	−0.862429	+	1.49377i	0.00714884	+	0.999974i	$0.497724\pi$
$983$	−27.0396	+	46.8339i	−0.862429	+	1.49377i	−0.869578	+	0.493796i	$0.835609\pi$
$984$		0			0
$985$	−3.68222	+	6.37780i	−0.117325	+	0.203214i
$986$		0			0
$987$	2.10752			0.0670830
$988$		0			0
$989$	3.43448			0.109210
$990$		0			0
$991$	20.6356	−	35.7418i	0.655510	−	1.13538i	−0.326256	−	0.945282i	$-0.605787\pi$
$991$	20.6356	−	35.7418i	0.655510	−	1.13538i	0.981766	−	0.190095i	$-0.0608796\pi$
$992$		0			0
$993$	3.36608	−	5.83021i	0.106819	−	0.185016i
$994$		0			0
$995$	2.76837			0.0877634
$996$		0			0
$997$	0.544937	+	0.943859i	0.0172583	+	0.0298923i	0.874526	−	0.484979i	$-0.161173\pi$
$997$	0.544937	+	0.943859i	0.0172583	+	0.0298923i	−0.857267	+	0.514872i	$0.827840\pi$
$998$		0			0
$999$	−1.35899			−0.0429965

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.2.q.i.961.2		6
4.3	odd	2		380.2.i.b.201.2	yes	6
12.11	even	2		3420.2.t.v.3241.2		6
19.7	even	3	inner	1520.2.q.i.881.2		6
20.3	even	4		1900.2.s.c.49.4		12
20.7	even	4		1900.2.s.c.49.3		12
20.19	odd	2		1900.2.i.c.201.2		6
76.7	odd	6		380.2.i.b.121.2	✓	6
76.11	odd	6		7220.2.a.n.1.2		3
76.27	even	6		7220.2.a.o.1.2		3
228.83	even	6		3420.2.t.v.1261.2		6
380.7	even	12		1900.2.s.c.349.4		12
380.83	even	12		1900.2.s.c.349.3		12
380.159	odd	6		1900.2.i.c.501.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.b.121.2	✓	6	76.7	odd	6
380.2.i.b.201.2	yes	6	4.3	odd	2
1520.2.q.i.881.2		6	19.7	even	3	inner
1520.2.q.i.961.2		6	1.1	even	1	trivial
1900.2.i.c.201.2		6	20.19	odd	2
1900.2.i.c.501.2		6	380.159	odd	6
1900.2.s.c.49.3		12	20.7	even	4
1900.2.s.c.49.4		12	20.3	even	4
1900.2.s.c.349.3		12	380.83	even	12
1900.2.s.c.349.4		12	380.7	even	12
3420.2.t.v.1261.2		6	228.83	even	6
3420.2.t.v.3241.2		6	12.11	even	2
7220.2.a.n.1.2		3	76.11	odd	6
7220.2.a.o.1.2		3	76.27	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:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.182224 + 0.315621i) q^{3} +(0.500000 - 0.866025i) q^{5} -0.635552 q^{7} +(1.43359 + 2.48305i) q^{9} -1.63555 q^{11} +(0.500000 + 0.866025i) q^{13} +(0.182224 + 0.315621i) q^{15} +(3.29804 - 5.71237i) q^{17} +(-0.0466721 + 4.35865i) q^{19} +(0.115813 - 0.200594i) q^{21} +(0.433589 + 0.750998i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.13828 q^{27} +(4.54940 + 7.87979i) q^{29} +1.86718 q^{31} +(0.298037 - 0.516215i) q^{33} +(-0.317776 + 0.550404i) q^{35} +0.635552 q^{37} -0.364448 q^{39} +(-0.953328 + 1.65121i) q^{41} +(1.98026 - 3.42991i) q^{43} +2.86718 q^{45} +(4.54940 + 7.87979i) q^{47} -6.59607 q^{49} +(1.20196 + 2.08186i) q^{51} +(4.93359 + 8.54523i) q^{53} +(-0.817776 + 1.41643i) q^{55} +(-1.36718 - 0.808981i) q^{57} +(4.54940 - 7.87979i) q^{59} +(-1.13555 - 1.96683i) q^{61} +(-0.911120 - 1.57811i) q^{63} +1.00000 q^{65} +(6.23163 + 10.7935i) q^{67} -0.316041 q^{69} +(1.25136 - 2.16743i) q^{71} +(0.201963 - 0.349810i) q^{73} +0.364448 q^{75} +1.03948 q^{77} +(5.36445 - 9.29150i) q^{79} +(-3.91112 + 6.77426i) q^{81} +15.8672 q^{83} +(-3.29804 - 5.71237i) q^{85} -3.31604 q^{87} +(-0.271104 - 0.469566i) q^{89} +(-0.317776 - 0.550404i) q^{91} +(-0.340245 + 0.589321i) q^{93} +(3.75136 + 2.21974i) q^{95} +(3.68495 - 6.38253i) q^{97} +(-2.34471 - 4.06116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 3 q^{5} - 4 q^{7} - 8 q^{9} - 10 q^{11} + 3 q^{13} + q^{15} + 3 q^{17} - 16 q^{21} - 14 q^{23} - 3 q^{25} + 20 q^{27} - 6 q^{29} - 22 q^{31} - 15 q^{33} - 2 q^{35} + 4 q^{37} - 2 q^{39}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q - q^3 + 3 * q^5 - 4 * q^7 - 8 * q^9 - 10 * q^11 + 3 * q^13 + q^15 + 3 * q^17 - 16 * q^21 - 14 * q^23 - 3 * q^25 + 20 * q^27 - 6 * q^29 - 22 * q^31 - 15 * q^33 - 2 * q^35 + 4 * q^37 - 2 * q^39 - 6 * q^41 - 5 * q^43 - 16 * q^45 - 6 * q^47 - 6 * q^49 + 24 * q^51 + 13 * q^53 - 5 * q^55 + 25 * q^57 - 6 * q^59 - 7 * q^61 - 5 * q^63 + 6 * q^65 + 4 * q^67 + 30 * q^69 - 9 * q^71 + 18 * q^73 + 2 * q^75 + 40 * q^77 + 32 * q^79 - 23 * q^81 + 62 * q^83 - 3 * q^85 + 12 * q^87 - 2 * q^89 - 2 * q^91 + 14 * q^93 + 6 * q^95 - 11 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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