LMFDB - Embedded newform 1150.2.e.e.1057.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(643,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("1150.643");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{12} + 326x^{8} - 275x^{4} + 81 $ x^16 + 20x^12 + 326x^8 - 275*x^4 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.6
Root			$-0.119323 + 0.826430i$ of defining polynomial
Character	$\chi$	$=$	1150.1057
Dual form			1150.2.e.e.643.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.62831 + 1.62831i) q^{3} +1.00000i q^{4} -2.30278 q^{6} +(3.12361 - 3.12361i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.30278i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.62831 + 1.62831i) q^{3} +1.00000i q^{4} -2.30278 q^{6} +(3.12361 - 3.12361i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.30278i q^{9} -3.07995i q^{11} +(-1.62831 - 1.62831i) q^{12} +(-3.74963 + 3.74963i) q^{13} +4.41745 q^{14} -1.00000 q^{16} +(-4.06936 + 4.06936i) q^{17} +(1.62831 - 1.62831i) q^{18} -7.09244 q^{19} +10.1724i q^{21} +(2.17786 - 2.17786i) q^{22} +(-4.20237 + 2.31086i) q^{23} -2.30278i q^{24} -5.30278 q^{26} +(-1.13530 - 1.13530i) q^{27} +(3.12361 + 3.12361i) q^{28} -2.00000i q^{29} -3.90833 q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.01512 + 5.01512i) q^{33} -5.75495 q^{34} +2.30278 q^{36} +(-6.24722 + 6.24722i) q^{37} +(-5.01512 - 5.01512i) q^{38} -12.2111i q^{39} -4.30278 q^{41} +(-7.19297 + 7.19297i) q^{42} +(8.13873 + 8.13873i) q^{43} +3.07995 q^{44} +(-4.60555 - 1.33750i) q^{46} +(6.51323 + 6.51323i) q^{47} +(1.62831 - 1.62831i) q^{48} -12.5139i q^{49} -13.2524i q^{51} +(-3.74963 - 3.74963i) q^{52} +(-4.35571 - 4.35571i) q^{53} -1.60555i q^{54} +4.41745i q^{56} +(11.5487 - 11.5487i) q^{57} +(1.41421 - 1.41421i) q^{58} +3.39445i q^{59} -3.07995i q^{61} +(-2.76360 - 2.76360i) q^{62} +(-7.19297 - 7.19297i) q^{63} -1.00000i q^{64} +7.09244i q^{66} +(3.78301 - 3.78301i) q^{67} +(-4.06936 - 4.06936i) q^{68} +(3.07995 - 10.6056i) q^{69} +4.30278 q^{71} +(1.62831 + 1.62831i) q^{72} +(0.986024 - 0.986024i) q^{73} -8.83490 q^{74} -7.09244i q^{76} +(-9.62058 - 9.62058i) q^{77} +(8.63455 - 8.63455i) q^{78} +6.15991 q^{79} +10.6056 q^{81} +(-3.04252 - 3.04252i) q^{82} -10.1724 q^{84} +11.5099i q^{86} +(3.25662 + 3.25662i) q^{87} +(2.17786 + 2.17786i) q^{88} +23.4248i q^{91} +(-2.31086 - 4.20237i) q^{92} +(6.36396 - 6.36396i) q^{93} +9.21110i q^{94} +2.30278 q^{96} +(-0.286351 + 0.286351i) q^{97} +(8.84865 - 8.84865i) q^{98} -7.09244 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{6}+O(q^{10}) $ 16 * q - 8 * q^6	$ 16 q - 8 q^{6} - 16 q^{16} - 56 q^{26} + 24 q^{31} + 8 q^{36} - 40 q^{41} - 16 q^{46} + 40 q^{71} + 112 q^{81} + 8 q^{96}+O(q^{100}) $ 16 * q - 8 * q^6 - 16 * q^16 - 56 * q^26 + 24 * q^31 + 8 * q^36 - 40 * q^41 - 16 * q^46 + 40 * q^71 + 112 * q^81 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.62831	+	1.62831i	−0.940104	+	0.940104i	−0.998305	−	0.0582007i	$-0.981464\pi$
$3$	−1.62831	+	1.62831i	−0.940104	+	0.940104i	0.0582007	+	0.998305i	$0.481464\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−2.30278			−0.940104
$7$	3.12361	−	3.12361i	1.18061	−	1.18061i	0.201028	−	0.979585i	$-0.435572\pi$
$7$	3.12361	−	3.12361i	1.18061	−	1.18061i	0.979585	−	0.201028i	$-0.0644283\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	2.30278i		−	0.767592i
$10$		0			0
$11$		−	3.07995i		−	0.928641i	−0.885667	−	0.464321i	$-0.846299\pi$
$11$		−	3.07995i		−	0.928641i	0.885667	−	0.464321i	$-0.153701\pi$
$12$	−1.62831	−	1.62831i	−0.470052	−	0.470052i
$13$	−3.74963	+	3.74963i	−1.03996	+	1.03996i	−0.0407922	+	0.999168i	$0.512988\pi$
$13$	−3.74963	+	3.74963i	−1.03996	+	1.03996i	−0.999168	+	0.0407922i	$0.987012\pi$
$14$	4.41745			1.18061
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.06936	+	4.06936i	−0.986965	+	0.986965i	−0.999916	−	0.0129507i	$-0.995878\pi$
$17$	−4.06936	+	4.06936i	−0.986965	+	0.986965i	0.0129507	+	0.999916i	$0.495878\pi$
$18$	1.62831	−	1.62831i	0.383796	−	0.383796i
$19$	−7.09244			−1.62712			−0.813559	−	0.581482i	$-0.802473\pi$
$19$	−7.09244			−1.62712			−0.813559	+	0.581482i	$0.802473\pi$
$20$		0			0
$21$			10.1724i			2.21980i
$22$	2.17786	−	2.17786i	0.464321	−	0.464321i
$23$	−4.20237	+	2.31086i	−0.876255	+	0.481848i
$23$	−4.20237	+	2.31086i	−0.876255	+	0.481848i
$24$		−	2.30278i		−	0.470052i
$25$		0			0
$26$	−5.30278			−1.03996
$27$	−1.13530	−	1.13530i	−0.218488	−	0.218488i
$28$	3.12361	+	3.12361i	0.590307	+	0.590307i
$29$		−	2.00000i		−	0.371391i	−0.982607	−	0.185695i	$-0.940546\pi$
$29$		−	2.00000i		−	0.371391i	0.982607	−	0.185695i	$-0.0594537\pi$
$30$		0			0
$31$	−3.90833			−0.701956			−0.350978	−	0.936384i	$-0.614151\pi$
$31$	−3.90833			−0.701956			−0.350978	+	0.936384i	$0.614151\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	5.01512	+	5.01512i	0.873020	+	0.873020i
$34$	−5.75495			−0.986965
$35$		0			0
$36$	2.30278			0.383796
$37$	−6.24722	+	6.24722i	−1.02704	+	1.02704i	−0.0274124	+	0.999624i	$0.508727\pi$
$37$	−6.24722	+	6.24722i	−1.02704	+	1.02704i	−0.999624	+	0.0274124i	$0.991273\pi$
$38$	−5.01512	−	5.01512i	−0.813559	−	0.813559i
$39$		−	12.2111i		−	1.95534i
$40$		0			0
$41$	−4.30278			−0.671981			−0.335990	−	0.941865i	$-0.609071\pi$
$41$	−4.30278			−0.671981			−0.335990	+	0.941865i	$0.609071\pi$
$42$	−7.19297	+	7.19297i	−1.10990	+	1.10990i
$43$	8.13873	+	8.13873i	1.24114	+	1.24114i	0.959527	+	0.281617i	$0.0908708\pi$
$43$	8.13873	+	8.13873i	1.24114	+	1.24114i	0.281617	+	0.959527i	$0.409129\pi$
$44$	3.07995			0.464321
$45$		0			0
$46$	−4.60555	−	1.33750i	−0.679051	−	0.197203i
$47$	6.51323	+	6.51323i	0.950053	+	0.950053i	0.998811	−	0.0487579i	$-0.0155263\pi$
$47$	6.51323	+	6.51323i	0.950053	+	0.950053i	−0.0487579	+	0.998811i	$0.515526\pi$
$48$	1.62831	−	1.62831i	0.235026	−	0.235026i
$49$		−	12.5139i		−	1.78770i
$50$		0			0
$51$		−	13.2524i		−	1.85570i
$52$	−3.74963	−	3.74963i	−0.519980	−	0.519980i
$53$	−4.35571	−	4.35571i	−0.598303	−	0.598303i	0.341558	−	0.939861i	$-0.389046\pi$
$53$	−4.35571	−	4.35571i	−0.598303	−	0.598303i	−0.939861	+	0.341558i	$0.889046\pi$
$54$		−	1.60555i		−	0.218488i
$55$		0			0
$56$			4.41745i			0.590307i
$57$	11.5487	−	11.5487i	1.52966	−	1.52966i
$58$	1.41421	−	1.41421i	0.185695	−	0.185695i
$59$			3.39445i			0.441920i	0.975283	+	0.220960i	$0.0709190\pi$
$59$			3.39445i			0.441920i	−0.975283	+	0.220960i	$0.929081\pi$
$60$		0			0
$61$		−	3.07995i		−	0.394348i	−0.980369	−	0.197174i	$-0.936824\pi$
$61$		−	3.07995i		−	0.394348i	0.980369	−	0.197174i	$-0.0631764\pi$
$62$	−2.76360	−	2.76360i	−0.350978	−	0.350978i
$63$	−7.19297	−	7.19297i	−0.906229	−	0.906229i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$			7.09244i			0.873020i
$67$	3.78301	−	3.78301i	0.462168	−	0.462168i	−0.437197	−	0.899366i	$-0.644029\pi$
$67$	3.78301	−	3.78301i	0.462168	−	0.462168i	0.899366	+	0.437197i	$0.144029\pi$
$68$	−4.06936	−	4.06936i	−0.493483	−	0.493483i
$69$	3.07995	−	10.6056i	0.370783	−	1.27676i
$70$		0			0
$71$	4.30278			0.510646			0.255323	−	0.966856i	$-0.417818\pi$
$71$	4.30278			0.510646			0.255323	+	0.966856i	$0.417818\pi$
$72$	1.62831	+	1.62831i	0.191898	+	0.191898i
$73$	0.986024	−	0.986024i	0.115405	−	0.115405i	−0.647046	−	0.762451i	$-0.723996\pi$
$73$	0.986024	−	0.986024i	0.115405	−	0.115405i	0.762451	+	0.647046i	$0.223996\pi$
$74$	−8.83490			−1.02704
$75$		0			0
$76$		−	7.09244i		−	0.813559i
$77$	−9.62058	−	9.62058i	−1.09637	−	1.09637i
$78$	8.63455	−	8.63455i	0.977671	−	0.977671i
$79$	6.15991			0.693044			0.346522	−	0.938042i	$-0.387363\pi$
$79$	6.15991			0.693044			0.346522	+	0.938042i	$0.387363\pi$
$80$		0			0
$81$	10.6056			1.17839
$82$	−3.04252	−	3.04252i	−0.335990	−	0.335990i
$83$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$83$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$84$	−10.1724			−1.10990
$85$		0			0
$86$			11.5099i			1.24114i
$87$	3.25662	+	3.25662i	0.349146	+	0.349146i
$88$	2.17786	+	2.17786i	0.232160	+	0.232160i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$			23.4248i			2.45558i
$92$	−2.31086	−	4.20237i	−0.240924	−	0.438127i
$93$	6.36396	−	6.36396i	0.659912	−	0.659912i
$94$			9.21110i			0.950053i
$95$		0			0
$96$	2.30278			0.235026
$97$	−0.286351	+	0.286351i	−0.0290745	+	0.0290745i	−0.721495	−	0.692420i	$-0.756545\pi$
$97$	−0.286351	+	0.286351i	−0.0290745	+	0.0290745i	0.692420	+	0.721495i	$0.256545\pi$
$98$	8.84865	−	8.84865i	0.893848	−	0.893848i
$99$	−7.09244			−0.712818
$100$		0			0
$101$	−17.8167			−1.77282			−0.886412	−	0.462898i	$-0.846810\pi$
$101$	−17.8167			−1.77282			−0.886412	+	0.462898i	$0.846810\pi$
$102$	9.37083	−	9.37083i	0.927850	−	0.927850i
$103$	−8.42508	−	8.42508i	−0.830147	−	0.830147i	0.157389	−	0.987537i	$-0.449692\pi$
$103$	−8.42508	−	8.42508i	−0.830147	−	0.830147i	−0.987537	+	0.157389i	$0.949692\pi$
$104$		−	5.30278i		−	0.519980i
$105$		0			0
$106$		−	6.15991i		−	0.598303i
$107$	−10.6029	+	10.6029i	−1.02502	+	1.02502i	−0.0253455	+	0.999679i	$0.508069\pi$
$107$	−10.6029	+	10.6029i	−1.02502	+	1.02502i	−0.999679	+	0.0253455i	$0.991931\pi$
$108$	1.13530	−	1.13530i	0.109244	−	0.109244i
$109$	13.2524			1.26935			0.634673	−	0.772781i	$-0.281135\pi$
$109$	13.2524			1.26935			0.634673	+	0.772781i	$0.281135\pi$
$110$		0			0
$111$		−	20.3448i		−	1.93104i
$112$	−3.12361	+	3.12361i	−0.295153	+	0.295153i
$113$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$113$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$114$	16.3323			1.52966
$115$		0			0
$116$	2.00000			0.185695
$117$	8.63455	+	8.63455i	0.798265	+	0.798265i
$118$	−2.40024	+	2.40024i	−0.220960	+	0.220960i
$119$			25.4222i			2.33045i
$120$		0			0
$121$	1.51388			0.137625
$122$	2.17786	−	2.17786i	0.197174	−	0.197174i
$123$	7.00625	−	7.00625i	0.631732	−	0.631732i
$124$		−	3.90833i		−	0.350978i
$125$		0			0
$126$		−	10.1724i		−	0.906229i
$127$	5.52721	+	5.52721i	0.490460	+	0.490460i	0.908451	−	0.417991i	$-0.137266\pi$
$127$	5.52721	+	5.52721i	0.490460	+	0.490460i	−0.417991	+	0.908451i	$0.637266\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−26.5047			−2.33361
$130$		0			0
$131$	−0.605551			−0.0529073			−0.0264536	−	0.999650i	$-0.508421\pi$
$131$	−0.605551			−0.0529073			−0.0264536	+	0.999650i	$0.508421\pi$
$132$	−5.01512	+	5.01512i	−0.436510	+	0.436510i
$133$	−22.1540	+	22.1540i	−1.92100	+	1.92100i
$134$	5.34999			0.462168
$135$		0			0
$136$		−	5.75495i		−	0.493483i
$137$	1.23210	−	1.23210i	0.105266	−	0.105266i	−0.652512	−	0.757778i	$-0.726285\pi$
$137$	1.23210	−	1.23210i	0.105266	−	0.105266i	0.757778	+	0.652512i	$0.226285\pi$
$138$	9.67711	−	5.32140i	0.823771	−	0.452988i
$139$			10.6056i			0.899551i	0.893142	+	0.449776i	$0.148496\pi$
$139$			10.6056i			0.899551i	−0.893142	+	0.449776i	$0.851504\pi$
$140$		0			0
$141$	−21.2111			−1.78630
$142$	3.04252	+	3.04252i	0.255323	+	0.255323i
$143$	11.5487	+	11.5487i	0.965750	+	0.965750i
$144$			2.30278i			0.191898i
$145$		0			0
$146$	1.39445			0.115405
$147$	20.3765	+	20.3765i	1.68062	+	1.68062i
$148$	−6.24722	−	6.24722i	−0.513518	−	0.513518i
$149$	0.932535			0.0763963			0.0381981	−	0.999270i	$-0.487838\pi$
$149$	0.932535			0.0763963			0.0381981	+	0.999270i	$0.487838\pi$
$150$		0			0
$151$	8.30278			0.675670			0.337835	−	0.941205i	$-0.390305\pi$
$151$	8.30278			0.675670			0.337835	+	0.941205i	$0.390305\pi$
$152$	5.01512	−	5.01512i	0.406780	−	0.406780i
$153$	9.37083	+	9.37083i	0.757587	+	0.757587i
$154$		−	13.6056i		−	1.09637i
$155$		0			0
$156$	12.2111			0.977671
$157$	8.13873	−	8.13873i	0.649541	−	0.649541i	−0.303341	−	0.952882i	$-0.598102\pi$
$157$	8.13873	−	8.13873i	0.649541	−	0.649541i	0.952882	+	0.303341i	$0.0981021\pi$
$158$	4.35571	+	4.35571i	0.346522	+	0.346522i
$159$	14.1849			1.12493
$160$		0			0
$161$	−5.90833	+	20.3448i	−0.465641	+	1.60339i
$162$	7.49926	+	7.49926i	0.589197	+	0.589197i
$163$	5.03420	−	5.03420i	0.394309	−	0.394309i	−0.481911	−	0.876220i	$-0.660057\pi$
$163$	5.03420	−	5.03420i	0.394309	−	0.394309i	0.876220	+	0.481911i	$0.160057\pi$
$164$		−	4.30278i		−	0.335990i
$165$		0			0
$166$		0			0
$167$	−12.7279	−	12.7279i	−0.984916	−	0.984916i	0.0149717	−	0.999888i	$-0.495234\pi$
$167$	−12.7279	−	12.7279i	−0.984916	−	0.984916i	−0.999888	+	0.0149717i	$0.995234\pi$
$168$	−7.19297	−	7.19297i	−0.554950	−	0.554950i
$169$		−	15.1194i		−	1.16303i
$170$		0			0
$171$			16.3323i			1.24896i
$172$	−8.13873	+	8.13873i	−0.620572	+	0.620572i
$173$	−10.1136	+	10.1136i	−0.768922	+	0.768922i	−0.977917	−	0.208995i	$-0.932981\pi$
$173$	−10.1136	+	10.1136i	−0.768922	+	0.768922i	0.208995	+	0.977917i	$0.432981\pi$
$174$			4.60555i			0.349146i
$175$		0			0
$176$			3.07995i			0.232160i
$177$	−5.52721	−	5.52721i	−0.415450	−	0.415450i
$178$		0			0
$179$			25.6333i			1.91592i	0.286896	+	0.957962i	$0.407377\pi$
$179$			25.6333i			1.91592i	−0.286896	+	0.957962i	$0.592623\pi$
$180$		0			0
$181$		−	0.932535i		−	0.0693148i	−0.999399	−	0.0346574i	$-0.988966\pi$
$181$		−	0.932535i		−	0.0693148i	0.999399	−	0.0346574i	$-0.0110340\pi$
$182$	−16.5638	+	16.5638i	−1.22779	+	1.22779i
$183$	5.01512	+	5.01512i	0.370728	+	0.370728i
$184$	1.33750	−	4.60555i	0.0986016	−	0.339526i
$185$		0			0
$186$	9.00000			0.659912
$187$	12.5335	+	12.5335i	0.916537	+	0.916537i
$188$	−6.51323	+	6.51323i	−0.475026	+	0.475026i
$189$	−7.09244			−0.515899
$190$		0			0
$191$		−	12.3198i		−	0.891431i	−0.895175	−	0.445715i	$-0.852949\pi$
$191$		−	12.3198i		−	0.891431i	0.895175	−	0.445715i	$-0.147051\pi$
$192$	1.62831	+	1.62831i	0.117513	+	0.117513i
$193$	3.25662	−	3.25662i	0.234416	−	0.234416i	−0.580117	−	0.814533i	$-0.696993\pi$
$193$	3.25662	−	3.25662i	0.234416	−	0.234416i	0.814533	+	0.580117i	$0.196993\pi$
$194$	−0.404961			−0.0290745
$195$		0			0
$196$	12.5139			0.893848
$197$	−2.91288	−	2.91288i	−0.207534	−	0.207534i	0.595685	−	0.803218i	$-0.296881\pi$
$197$	−2.91288	−	2.91288i	−0.207534	−	0.207534i	−0.803218	+	0.595685i	$0.796881\pi$
$198$	−5.01512	−	5.01512i	−0.356409	−	0.356409i
$199$	20.3448			1.44220			0.721102	−	0.692829i	$-0.243636\pi$
$199$	20.3448			1.44220			0.721102	+	0.692829i	$0.243636\pi$
$200$		0			0
$201$			12.3198i			0.868973i
$202$	−12.5983	−	12.5983i	−0.886412	−	0.886412i
$203$	−6.24722	−	6.24722i	−0.438469	−	0.438469i
$204$	13.2524			0.927850
$205$		0			0
$206$		−	11.9149i		−	0.830147i
$207$	5.32140	+	9.67711i	0.369863	+	0.672606i
$208$	3.74963	−	3.74963i	0.259990	−	0.259990i
$209$			21.8444i			1.51101i
$210$		0			0
$211$	0.422205			0.0290658			0.0145329	−	0.999894i	$-0.495374\pi$
$211$	0.422205			0.0290658			0.0145329	+	0.999894i	$0.495374\pi$
$212$	4.35571	−	4.35571i	0.299152	−	0.299152i
$213$	−7.00625	+	7.00625i	−0.480060	+	0.480060i
$214$	−14.9948			−1.02502
$215$		0			0
$216$	1.60555			0.109244
$217$	−12.2081	+	12.2081i	−0.828739	+	0.828739i
$218$	9.37083	+	9.37083i	0.634673	+	0.634673i
$219$			3.21110i			0.216986i
$220$		0			0
$221$		−	30.5172i		−	2.05281i
$222$	14.3859	−	14.3859i	0.965521	−	0.965521i
$223$	−5.52721	+	5.52721i	−0.370129	+	0.370129i	−0.867524	−	0.497395i	$-0.834290\pi$
$223$	−5.52721	+	5.52721i	−0.370129	+	0.370129i	0.497395	+	0.867524i	$0.334290\pi$
$224$	−4.41745			−0.295153
$225$		0			0
$226$		0			0
$227$	18.7417	−	18.7417i	1.24393	−	1.24393i	0.285570	−	0.958358i	$-0.407817\pi$
$227$	18.7417	−	18.7417i	1.24393	−	1.24393i	0.958358	−	0.285570i	$-0.0921828\pi$
$228$	11.5487	+	11.5487i	0.764830	+	0.764830i
$229$	−12.3198			−0.814117			−0.407058	−	0.913402i	$-0.633445\pi$
$229$	−12.3198			−0.814117			−0.407058	+	0.913402i	$0.633445\pi$
$230$		0			0
$231$	31.3305			2.06140
$232$	1.41421	+	1.41421i	0.0928477	+	0.0928477i
$233$	−7.49926	+	7.49926i	−0.491293	+	0.491293i	−0.908713	−	0.417421i	$-0.862934\pi$
$233$	−7.49926	+	7.49926i	−0.491293	+	0.491293i	0.417421	+	0.908713i	$0.362934\pi$
$234$			12.2111i			0.798265i
$235$		0			0
$236$	−3.39445			−0.220960
$237$	−10.0302	+	10.0302i	−0.651534	+	0.651534i
$238$	−17.9762	+	17.9762i	−1.16522	+	1.16522i
$239$		−	14.4222i		−	0.932895i	−0.884549	−	0.466447i	$-0.845534\pi$
$239$		−	14.4222i		−	0.932895i	0.884549	−	0.466447i	$-0.154466\pi$
$240$		0			0
$241$		−	20.3448i		−	1.31052i	−0.755402	−	0.655262i	$-0.772558\pi$
$241$		−	20.3448i		−	1.31052i	0.755402	−	0.655262i	$-0.227442\pi$
$242$	1.07047	+	1.07047i	0.0688126	+	0.0688126i
$243$	−13.8632	+	13.8632i	−0.889326	+	0.889326i
$244$	3.07995			0.197174
$245$		0			0
$246$	9.90833			0.631732
$247$	26.5940	−	26.5940i	1.69214	−	1.69214i
$248$	2.76360	−	2.76360i	0.175489	−	0.175489i
$249$		0			0
$250$		0			0
$251$			19.4123i			1.22529i	0.790358	+	0.612646i	$0.209895\pi$
$251$			19.4123i			1.22529i	−0.790358	+	0.612646i	$0.790105\pi$
$252$	7.19297	−	7.19297i	0.453115	−	0.453115i
$253$	7.11736	+	12.9431i	0.447464	+	0.813726i
$254$			7.81665i			0.490460i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−15.2971	−	15.2971i	−0.954204	−	0.954204i	0.0447920	−	0.998996i	$-0.485737\pi$
$257$	−15.2971	−	15.2971i	−0.954204	−	0.954204i	−0.998996	+	0.0447920i	$0.985737\pi$
$258$	−18.7417	−	18.7417i	−1.16680	−	1.16680i
$259$			39.0278i			2.42507i
$260$		0			0
$261$	−4.60555			−0.285076
$262$	−0.428189	−	0.428189i	−0.0264536	−	0.0264536i
$263$	−7.85237	−	7.85237i	−0.484198	−	0.484198i	0.422271	−	0.906469i	$-0.361233\pi$
$263$	−7.85237	−	7.85237i	−0.484198	−	0.484198i	−0.906469	+	0.422271i	$0.861233\pi$
$264$	−7.09244			−0.436510
$265$		0			0
$266$	−31.3305			−1.92100
$267$		0			0
$268$	3.78301	+	3.78301i	0.231084	+	0.231084i
$269$			22.4222i			1.36711i	0.729901	+	0.683553i	$0.239566\pi$
$269$			22.4222i			1.36711i	−0.729901	+	0.683553i	$0.760434\pi$
$270$		0			0
$271$	17.1194			1.03993			0.519966	−	0.854187i	$-0.325945\pi$
$271$	17.1194			1.03993			0.519966	+	0.854187i	$0.325945\pi$
$272$	4.06936	−	4.06936i	0.246741	−	0.246741i
$273$	−38.1427	−	38.1427i	−2.30850	−	2.30850i
$274$	1.74246			0.105266
$275$		0			0
$276$	10.6056	+	3.07995i	0.638379	+	0.185391i
$277$	12.7279	+	12.7279i	0.764747	+	0.764747i	0.977176	−	0.212430i	$-0.0681376\pi$
$277$	12.7279	+	12.7279i	0.764747	+	0.764747i	−0.212430	+	0.977176i	$0.568138\pi$
$278$	−7.49926	+	7.49926i	−0.449776	+	0.449776i
$279$			9.00000i			0.538816i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−14.9985	−	14.9985i	−0.893149	−	0.893149i
$283$	10.6029	+	10.6029i	0.630279	+	0.630279i	0.948138	−	0.317859i	$-0.102964\pi$
$283$	10.6029	+	10.6029i	0.630279	+	0.630279i	−0.317859	+	0.948138i	$0.602964\pi$
$284$			4.30278i			0.255323i
$285$		0			0
$286$			16.3323i			0.965750i
$287$	−13.4402	+	13.4402i	−0.793349	+	0.793349i
$288$	−1.62831	+	1.62831i	−0.0959490	+	0.0959490i
$289$		−	16.1194i		−	0.948202i
$290$		0			0
$291$		−	0.932535i		−	0.0546662i
$292$	0.986024	+	0.986024i	0.0577027	+	0.0577027i
$293$	11.9217	+	11.9217i	0.696475	+	0.696475i	0.963649	−	0.267173i	$-0.0860896\pi$
$293$	11.9217	+	11.9217i	0.696475	+	0.696475i	−0.267173	+	0.963649i	$0.586090\pi$
$294$			28.8167i			1.68062i
$295$		0			0
$296$		−	8.83490i		−	0.513518i
$297$	−3.49666	+	3.49666i	−0.202897	+	0.202897i
$298$	0.659402	+	0.659402i	0.0381981	+	0.0381981i
$299$	7.09244	−	24.4222i	0.410167	−	1.41237i
$300$		0			0
$301$	50.8444			2.93062
$302$	5.87095	+	5.87095i	0.337835	+	0.337835i
$303$	29.0110	−	29.0110i	1.66664	−	1.66664i
$304$	7.09244			0.406780
$305$		0			0
$306$			13.2524i			0.757587i
$307$	−21.8555	−	21.8555i	−1.24736	−	1.24736i	−0.956882	−	0.290476i	$-0.906186\pi$
$307$	−21.8555	−	21.8555i	−1.24736	−	1.24736i	−0.290476	−	0.956882i	$-0.593814\pi$
$308$	9.62058	−	9.62058i	0.548183	−	0.548183i
$309$	27.4372			1.56085
$310$		0			0
$311$	1.57779			0.0894685			0.0447343	−	0.998999i	$-0.485756\pi$
$311$	1.57779			0.0894685			0.0447343	+	0.998999i	$0.485756\pi$
$312$	8.63455	+	8.63455i	0.488835	+	0.488835i
$313$	11.2623	+	11.2623i	0.636585	+	0.636585i	0.949711	−	0.313127i	$-0.101376\pi$
$313$	11.2623	+	11.2623i	0.636585	+	0.636585i	−0.313127	+	0.949711i	$0.601376\pi$
$314$	11.5099			0.649541
$315$		0			0
$316$			6.15991i			0.346522i
$317$	−19.7342	−	19.7342i	−1.10838	−	1.10838i	−0.993363	−	0.115018i	$-0.963307\pi$
$317$	−19.7342	−	19.7342i	−1.10838	−	1.10838i	−0.115018	−	0.993363i	$-0.536693\pi$
$318$	10.0302	+	10.0302i	0.562467	+	0.562467i
$319$	−6.15991			−0.344889
$320$		0			0
$321$		−	34.5297i		−	1.92726i
$322$	−18.5638	+	10.2081i	−1.03452	+	0.568877i
$323$	28.8617	−	28.8617i	1.60591	−	1.60591i
$324$			10.6056i			0.589197i
$325$		0			0
$326$	7.11943			0.394309
$327$	−21.5789	+	21.5789i	−1.19332	+	1.19332i
$328$	3.04252	−	3.04252i	0.167995	−	0.167995i
$329$	40.6896			2.24329
$330$		0			0
$331$	−23.8167			−1.30908			−0.654541	−	0.756027i	$-0.727138\pi$
$331$	−23.8167			−1.30908			−0.654541	+	0.756027i	$0.727138\pi$
$332$		0			0
$333$	14.3859	+	14.3859i	0.788345	+	0.788345i
$334$		−	18.0000i		−	0.984916i
$335$		0			0
$336$		−	10.1724i		−	0.554950i
$337$	−8.79813	+	8.79813i	−0.479265	+	0.479265i	−0.904896	−	0.425632i	$-0.860052\pi$
$337$	−8.79813	+	8.79813i	−0.479265	+	0.479265i	0.425632	+	0.904896i	$0.360052\pi$
$338$	10.6911	−	10.6911i	0.581517	−	0.581517i
$339$		0			0
$340$		0			0
$341$			12.0375i			0.651866i
$342$	−11.5487	+	11.5487i	−0.624481	+	0.624481i
$343$	−17.2232	−	17.2232i	−0.929966	−	0.929966i
$344$	−11.5099			−0.620572
$345$		0			0
$346$	−14.3028			−0.768922
$347$	3.60036	+	3.60036i	0.193277	+	0.193277i	0.797111	−	0.603833i	$-0.206361\pi$
$347$	3.60036	+	3.60036i	0.193277	+	0.193277i	−0.603833	+	0.797111i	$0.706361\pi$
$348$	−3.25662	+	3.25662i	−0.174573	+	0.174573i
$349$			14.4222i			0.772003i	0.922498	+	0.386001i	$0.126144\pi$
$349$			14.4222i			0.772003i	−0.922498	+	0.386001i	$0.873856\pi$
$350$		0			0
$351$	8.51388			0.454437
$352$	−2.17786	+	2.17786i	−0.116080	+	0.116080i
$353$	9.76985	−	9.76985i	0.519997	−	0.519997i	−0.397574	−	0.917570i	$-0.630148\pi$
$353$	9.76985	−	9.76985i	0.519997	−	0.519997i	0.917570	+	0.397574i	$0.130148\pi$
$354$		−	7.81665i		−	0.415450i
$355$		0			0
$356$		0			0
$357$	−41.3952	−	41.3952i	−2.19087	−	2.19087i
$358$	−18.1255	+	18.1255i	−0.957962	+	0.957962i
$359$	8.02498			0.423542			0.211771	−	0.977319i	$-0.432077\pi$
$359$	8.02498			0.423542			0.211771	+	0.977319i	$0.432077\pi$
$360$		0			0
$361$	31.3028			1.64751
$362$	0.659402	−	0.659402i	0.0346574	−	0.0346574i
$363$	−2.46506	+	2.46506i	−0.129382	+	0.129382i
$364$	−23.4248			−1.22779
$365$		0			0
$366$			7.09244i			0.370728i
$367$	−19.3144	+	19.3144i	−1.00820	+	1.00820i	−0.00823538	+	0.999966i	$0.502621\pi$
$367$	−19.3144	+	19.3144i	−1.00820	+	1.00820i	−0.999966	+	0.00823538i	$0.997379\pi$
$368$	4.20237	−	2.31086i	0.219064	−	0.120462i
$369$			9.90833i			0.515807i
$370$		0			0
$371$	−27.2111			−1.41273
$372$	6.36396	+	6.36396i	0.329956	+	0.329956i
$373$	−12.4944	−	12.4944i	−0.646938	−	0.646938i	0.305314	−	0.952252i	$-0.401239\pi$
$373$	−12.4944	−	12.4944i	−0.646938	−	0.646938i	−0.952252	+	0.305314i	$0.901239\pi$
$374$			17.7250i			0.916537i
$375$		0			0
$376$	−9.21110			−0.475026
$377$	7.49926	+	7.49926i	0.386231	+	0.386231i
$378$	−5.01512	−	5.01512i	−0.257950	−	0.257950i
$379$	−31.4497			−1.61546			−0.807732	−	0.589550i	$-0.799305\pi$
$379$	−31.4497			−1.61546			−0.807732	+	0.589550i	$0.799305\pi$
$380$		0			0
$381$	−18.0000			−0.922168
$382$	8.71143	−	8.71143i	0.445715	−	0.445715i
$383$	1.89151	+	1.89151i	0.0966514	+	0.0966514i	0.753779	−	0.657128i	$-0.228229\pi$
$383$	1.89151	+	1.89151i	0.0966514	+	0.0966514i	−0.657128	+	0.753779i	$0.728229\pi$
$384$			2.30278i			0.117513i
$385$		0			0
$386$	4.60555			0.234416
$387$	18.7417	−	18.7417i	0.952692	−	0.952692i
$388$	−0.286351	−	0.286351i	−0.0145373	−	0.0145373i
$389$	−37.6096			−1.90688			−0.953442	−	0.301575i	$-0.902488\pi$
$389$	−37.6096			−1.90688			−0.953442	+	0.301575i	$0.902488\pi$
$390$		0			0
$391$	7.69722	−	26.5047i	0.389265	−	1.34040i
$392$	8.84865	+	8.84865i	0.446924	+	0.446924i
$393$	0.986024	−	0.986024i	0.0497383	−	0.0497383i
$394$		−	4.11943i		−	0.207534i
$395$		0			0
$396$		−	7.09244i		−	0.356409i
$397$	−2.31579	−	2.31579i	−0.116226	−	0.116226i	0.646602	−	0.762828i	$-0.276190\pi$
$397$	−2.31579	−	2.31579i	−0.116226	−	0.116226i	−0.762828	+	0.646602i	$0.776190\pi$
$398$	14.3859	+	14.3859i	0.721102	+	0.721102i
$399$		−	72.1472i		−	3.61188i
$400$		0			0
$401$			8.02498i			0.400748i	0.979719	+	0.200374i	$0.0642158\pi$
$401$			8.02498i			0.400748i	−0.979719	+	0.200374i	$0.935784\pi$
$402$	−8.71143	+	8.71143i	−0.434487	+	0.434487i
$403$	14.6548	−	14.6548i	0.730006	−	0.730006i
$404$		−	17.8167i		−	0.886412i
$405$		0			0
$406$		−	8.83490i		−	0.438469i
$407$	19.2412	+	19.2412i	0.953749	+	0.953749i
$408$	9.37083	+	9.37083i	0.463925	+	0.463925i
$409$			26.9361i			1.33190i	0.745995	+	0.665952i	$0.231974\pi$
$409$			26.9361i			1.33190i	−0.745995	+	0.665952i	$0.768026\pi$
$410$		0			0
$411$			4.01249i			0.197922i
$412$	8.42508	−	8.42508i	0.415074	−	0.415074i
$413$	10.6029	+	10.6029i	0.521736	+	0.521736i
$414$	−3.07995	+	10.6056i	−0.151372	+	0.521234i
$415$		0			0
$416$	5.30278			0.259990
$417$	−17.2691	−	17.2691i	−0.845672	−	0.845672i
$418$	−15.4463	+	15.4463i	−0.755505	+	0.755505i
$419$	8.02498			0.392046			0.196023	−	0.980599i	$-0.437197\pi$
$419$	8.02498			0.392046			0.196023	+	0.980599i	$0.437197\pi$
$420$		0			0
$421$			25.5722i			1.24631i	0.782098	+	0.623156i	$0.214150\pi$
$421$			25.5722i			1.24631i	−0.782098	+	0.623156i	$0.785850\pi$
$422$	0.298544	+	0.298544i	0.0145329	+	0.0145329i
$423$	14.9985	−	14.9985i	0.729253	−	0.729253i
$424$	6.15991			0.299152
$425$		0			0
$426$	−9.90833			−0.480060
$427$	−9.62058	−	9.62058i	−0.465572	−	0.465572i
$428$	−10.6029	−	10.6029i	−0.512512	−	0.512512i
$429$	−37.6096			−1.81581
$430$		0			0
$431$			8.02498i			0.386550i	0.981145	+	0.193275i	$0.0619109\pi$
$431$			8.02498i			0.386550i	−0.981145	+	0.193275i	$0.938089\pi$
$432$	1.13530	+	1.13530i	0.0546220	+	0.0546220i
$433$	−17.5096	−	17.5096i	−0.841456	−	0.841456i	0.147593	−	0.989048i	$-0.452848\pi$
$433$	−17.5096	−	17.5096i	−0.841456	−	0.841456i	−0.989048	+	0.147593i	$0.952848\pi$
$434$	−17.2648			−0.828739
$435$		0			0
$436$			13.2524i			0.634673i
$437$	29.8051	−	16.3897i	1.42577	−	0.784024i
$438$	−2.27059	+	2.27059i	−0.108493	+	0.108493i
$439$		−	20.0917i		−	0.958923i	−0.877563	−	0.479462i	$-0.840832\pi$
$439$		−	20.0917i		−	0.958923i	0.877563	−	0.479462i	$-0.159168\pi$
$440$		0			0
$441$	−28.8167			−1.37222
$442$	21.5789	−	21.5789i	1.02640	−	1.02640i
$443$	−22.0048	+	22.0048i	−1.04548	+	1.04548i	−0.0465623	+	0.998915i	$0.514827\pi$
$443$	−22.0048	+	22.0048i	−1.04548	+	1.04548i	−0.998915	+	0.0465623i	$0.985173\pi$
$444$	20.3448			0.965521
$445$		0			0
$446$	−7.81665			−0.370129
$447$	−1.51845	+	1.51845i	−0.0718205	+	0.0718205i
$448$	−3.12361	−	3.12361i	−0.147577	−	0.147577i
$449$		−	3.30278i		−	0.155868i	−0.996959	−	0.0779338i	$-0.975168\pi$
$449$		−	3.30278i		−	0.155868i	0.996959	−	0.0779338i	$-0.0248323\pi$
$450$		0			0
$451$			13.2524i			0.624029i
$452$		0			0
$453$	−13.5195	+	13.5195i	−0.635200	+	0.635200i
$454$	26.5047			1.24393
$455$		0			0
$456$			16.3323i			0.764830i
$457$	−16.2775	+	16.2775i	−0.761427	+	0.761427i	−0.976580	−	0.215153i	$-0.930975\pi$
$457$	−16.2775	+	16.2775i	−0.761427	+	0.761427i	0.215153	+	0.976580i	$0.430975\pi$
$458$	−8.71143	−	8.71143i	−0.407058	−	0.407058i
$459$	9.23986			0.431280
$460$		0			0
$461$	−7.63331			−0.355519			−0.177759	−	0.984074i	$-0.556885\pi$
$461$	−7.63331			−0.355519			−0.177759	+	0.984074i	$0.556885\pi$
$462$	22.1540	+	22.1540i	1.03070	+	1.03070i
$463$	0.298544	−	0.298544i	0.0138745	−	0.0138745i	−0.700135	−	0.714010i	$-0.746877\pi$
$463$	0.298544	−	0.298544i	0.0138745	−	0.0138745i	0.714010	+	0.700135i	$0.246877\pi$
$464$			2.00000i			0.0928477i
$465$		0			0
$466$	−10.6056			−0.491293
$467$	1.31880	−	1.31880i	0.0610270	−	0.0610270i	−0.675935	−	0.736962i	$-0.736260\pi$
$467$	1.31880	−	1.31880i	0.0610270	−	0.0610270i	0.736962	+	0.675935i	$0.236260\pi$
$468$	−8.63455	+	8.63455i	−0.399132	+	0.399132i
$469$		−	23.6333i		−	1.09128i
$470$		0			0
$471$			26.5047i			1.22127i
$472$	−2.40024	−	2.40024i	−0.110480	−	0.110480i
$473$	25.0669	−	25.0669i	1.15258	−	1.15258i
$474$	−14.1849			−0.651534
$475$		0			0
$476$	−25.4222			−1.16522
$477$	−10.0302	+	10.0302i	−0.459253	+	0.459253i
$478$	10.1980	−	10.1980i	0.466447	−	0.466447i
$479$	26.5047			1.21103			0.605516	−	0.795833i	$-0.292967\pi$
$479$	26.5047			1.21103			0.605516	+	0.795833i	$0.292967\pi$
$480$		0			0
$481$		−	46.8495i		−	2.13615i
$482$	14.3859	−	14.3859i	0.655262	−	0.655262i
$483$	−23.5070	−	42.7482i	−1.06961	−	1.94511i
$484$			1.51388i			0.0688126i
$485$		0			0
$486$	−19.6056			−0.889326
$487$	28.7125	+	28.7125i	1.30109	+	1.30109i	0.927660	+	0.373426i	$0.121817\pi$
$487$	28.7125	+	28.7125i	1.30109	+	1.30109i	0.373426	+	0.927660i	$0.378183\pi$
$488$	2.17786	+	2.17786i	0.0985870	+	0.0985870i
$489$			16.3944i			0.741383i
$490$		0			0
$491$	−19.6333			−0.886039			−0.443019	−	0.896512i	$-0.646093\pi$
$491$	−19.6333			−0.886039			−0.443019	+	0.896512i	$0.646093\pi$
$492$	7.00625	+	7.00625i	0.315866	+	0.315866i
$493$	8.13873	+	8.13873i	0.366550	+	0.366550i
$494$	37.6096			1.69214
$495$		0			0
$496$	3.90833			0.175489
$497$	13.4402	−	13.4402i	0.602875	−	0.602875i
$498$		0			0
$499$			0.788897i			0.0353159i	0.999844	+	0.0176580i	$0.00562099\pi$
$499$			0.788897i			0.0353159i	−0.999844	+	0.0176580i	$0.994379\pi$
$500$		0			0
$501$	41.4500			1.85185
$502$	−13.7265	+	13.7265i	−0.612646	+	0.612646i
$503$	18.0823	+	18.0823i	0.806248	+	0.806248i	0.984064	−	0.177816i	$-0.0569031\pi$
$503$	18.0823	+	18.0823i	0.806248	+	0.806248i	−0.177816	+	0.984064i	$0.556903\pi$
$504$	10.1724			0.453115
$505$		0			0
$506$	−4.11943	+	14.1849i	−0.183131	+	0.630595i
$507$	24.6191	+	24.6191i	1.09337	+	1.09337i
$508$	−5.52721	+	5.52721i	−0.245230	+	0.245230i
$509$			4.97224i			0.220391i	0.993910	+	0.110195i	$0.0351477\pi$
$509$			4.97224i			0.220391i	−0.993910	+	0.110195i	$0.964852\pi$
$510$		0			0
$511$		−	6.15991i		−	0.272498i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	8.05203	+	8.05203i	0.355506	+	0.355506i
$514$		−	21.6333i		−	0.954204i
$515$		0			0
$516$		−	26.5047i		−	1.16680i
$517$	20.0605	−	20.0605i	0.882258	−	0.882258i
$518$	−27.5968	+	27.5968i	−1.21253	+	1.21253i
$519$		−	32.9361i		−	1.44573i
$520$		0			0
$521$			22.2099i			0.973032i	0.873672	+	0.486516i	$0.161732\pi$
$521$			22.2099i			0.973032i	−0.873672	+	0.486516i	$0.838268\pi$
$522$	−3.25662	−	3.25662i	−0.142538	−	0.142538i
$523$	11.1756	+	11.1756i	0.488676	+	0.488676i	0.907888	−	0.419212i	$-0.137694\pi$
$523$	11.1756	+	11.1756i	0.488676	+	0.488676i	−0.419212	+	0.907888i	$0.637694\pi$
$524$		−	0.605551i		−	0.0264536i
$525$		0			0
$526$		−	11.1049i		−	0.484198i
$527$	15.9044	−	15.9044i	0.692807	−	0.692807i
$528$	−5.01512	−	5.01512i	−0.218255	−	0.218255i
$529$	12.3198	−	19.4222i	0.535644	−	0.844444i
$530$		0			0
$531$	7.81665			0.339214
$532$	−22.1540	−	22.1540i	−0.960499	−	0.960499i
$533$	16.1338	−	16.1338i	0.698833	−	0.698833i
$534$		0			0
$535$		0			0
$536$			5.34999i			0.231084i
$537$	−41.7389	−	41.7389i	−1.80117	−	1.80117i
$538$	−15.8549	+	15.8549i	−0.683553	+	0.683553i
$539$	−38.5422			−1.66013
$540$		0			0
$541$	14.7889			0.635824			0.317912	−	0.948120i	$-0.397018\pi$
$541$	14.7889			0.635824			0.317912	+	0.948120i	$0.397018\pi$
$542$	12.1053	+	12.1053i	0.519966	+	0.519966i
$543$	1.51845	+	1.51845i	0.0651631	+	0.0651631i
$544$	5.75495			0.246741
$545$		0			0
$546$		−	53.9420i		−	2.30850i
$547$	25.5599	+	25.5599i	1.09286	+	1.09286i	0.995222	+	0.0976416i	$0.0311299\pi$
$547$	25.5599	+	25.5599i	1.09286	+	1.09286i	0.0976416	+	0.995222i	$0.468870\pi$
$548$	1.23210	+	1.23210i	0.0526329	+	0.0526329i
$549$	−7.09244			−0.302698
$550$		0			0
$551$			14.1849i			0.604297i
$552$	5.32140	+	9.67711i	0.226494	+	0.411885i
$553$	19.2412	−	19.2412i	0.818217	−	0.818217i
$554$			18.0000i			0.764747i
$555$		0			0
$556$	−10.6056			−0.449776
$557$	−7.56602	+	7.56602i	−0.320583	+	0.320583i	−0.848991	−	0.528408i	$-0.822789\pi$
$557$	−7.56602	+	7.56602i	−0.320583	+	0.320583i	0.528408	+	0.848991i	$0.322789\pi$
$558$	−6.36396	+	6.36396i	−0.269408	+	0.269408i
$559$	−61.0344			−2.58148
$560$		0			0
$561$	−40.8167			−1.72328
$562$		0			0
$563$	−28.1992	−	28.1992i	−1.18845	−	1.18845i	−0.977495	−	0.210959i	$-0.932341\pi$
$563$	−28.1992	−	28.1992i	−1.18845	−	1.18845i	−0.210959	−	0.977495i	$-0.567659\pi$
$564$		−	21.2111i		−	0.893149i
$565$		0			0
$566$			14.9948i			0.630279i
$567$	33.1276	−	33.1276i	1.39123	−	1.39123i
$568$	−3.04252	+	3.04252i	−0.127661	+	0.127661i
$569$	−26.5047			−1.11114			−0.555568	−	0.831471i	$-0.687499\pi$
$569$	−26.5047			−1.11114			−0.555568	+	0.831471i	$0.687499\pi$
$570$		0			0
$571$			21.5597i			0.902245i	0.892462	+	0.451122i	$0.148976\pi$
$571$			21.5597i			0.902245i	−0.892462	+	0.451122i	$0.851024\pi$
$572$	−11.5487	+	11.5487i	−0.482875	+	0.482875i
$573$	20.0605	+	20.0605i	0.838038	+	0.838038i
$574$	−19.0073			−0.793349
$575$		0			0
$576$	−2.30278			−0.0959490
$577$	10.4573	+	10.4573i	0.435344	+	0.435344i	0.890442	−	0.455097i	$-0.150396\pi$
$577$	10.4573	+	10.4573i	0.435344	+	0.435344i	−0.455097	+	0.890442i	$0.650396\pi$
$578$	11.3982	−	11.3982i	0.474101	−	0.474101i
$579$			10.6056i			0.440752i
$580$		0			0
$581$		0			0
$582$	0.659402	−	0.659402i	0.0273331	−	0.0273331i
$583$	−13.4154	+	13.4154i	−0.555609	+	0.555609i
$584$			1.39445i			0.0577027i
$585$		0			0
$586$			16.8599i			0.696475i
$587$	−0.343740	−	0.343740i	−0.0141877	−	0.0141877i	0.699977	−	0.714165i	$-0.253193\pi$
$587$	−0.343740	−	0.343740i	−0.0141877	−	0.0141877i	−0.714165	+	0.699977i	$0.753193\pi$
$588$	−20.3765	+	20.3765i	−0.840311	+	0.840311i
$589$	27.7196			1.14217
$590$		0			0
$591$	9.48612			0.390207
$592$	6.24722	−	6.24722i	0.256759	−	0.256759i
$593$	−18.2551	+	18.2551i	−0.749648	+	0.749648i	−0.974413	−	0.224765i	$-0.927839\pi$
$593$	−18.2551	+	18.2551i	−0.749648	+	0.749648i	0.224765	+	0.974413i	$0.427839\pi$
$594$	−4.94503			−0.202897
$595$		0			0
$596$			0.932535i			0.0381981i
$597$	−33.1276	+	33.1276i	−1.35582	+	1.35582i
$598$	22.2842	−	12.2540i	0.911270	−	0.501103i
$599$			9.51388i			0.388727i	0.980930	+	0.194363i	$0.0622641\pi$
$599$			9.51388i			0.388727i	−0.980930	+	0.194363i	$0.937736\pi$
$600$		0			0
$601$	0.513878			0.0209615			0.0104808	−	0.999945i	$-0.496664\pi$
$601$	0.513878			0.0209615			0.0104808	+	0.999945i	$0.496664\pi$
$602$	35.9524	+	35.9524i	1.46531	+	1.46531i
$603$	−8.71143	−	8.71143i	−0.354757	−	0.354757i
$604$			8.30278i			0.337835i
$605$		0			0
$606$	41.0278			1.66664
$607$	13.7139	+	13.7139i	0.556632	+	0.556632i	0.928347	−	0.371715i	$-0.121230\pi$
$607$	13.7139	+	13.7139i	0.556632	+	0.556632i	−0.371715	+	0.928347i	$0.621230\pi$
$608$	5.01512	+	5.01512i	0.203390	+	0.203390i
$609$	20.3448			0.824413
$610$		0			0
$611$	−48.8444			−1.97603
$612$	−9.37083	+	9.37083i	−0.378793	+	0.378793i
$613$	−22.5247	−	22.5247i	−0.909763	−	0.909763i	0.0864898	−	0.996253i	$-0.472435\pi$
$613$	−22.5247	−	22.5247i	−0.909763	−	0.909763i	−0.996253	+	0.0864898i	$0.972435\pi$
$614$		−	30.9083i		−	1.24736i
$615$		0			0
$616$	13.6056			0.548183
$617$	−32.2686	+	32.2686i	−1.29908	+	1.29908i	−0.370085	+	0.928998i	$0.620672\pi$
$617$	−32.2686	+	32.2686i	−1.29908	+	1.29908i	−0.928998	+	0.370085i	$0.879328\pi$
$618$	19.4011	+	19.4011i	0.780425	+	0.780425i
$619$	33.5972			1.35038			0.675192	−	0.737642i	$-0.264061\pi$
$619$	33.5972			1.35038			0.675192	+	0.737642i	$0.264061\pi$
$620$		0			0
$621$	7.39445	+	2.14742i	0.296729	+	0.0861730i
$622$	1.11567	+	1.11567i	0.0447343	+	0.0447343i
$623$		0			0
$624$			12.2111i			0.488835i
$625$		0			0
$626$			15.9273i			0.636585i
$627$	−35.5694	−	35.5694i	−1.42051	−	1.42051i
$628$	8.13873	+	8.13873i	0.324771	+	0.324771i
$629$		−	50.8444i		−	2.02730i
$630$		0			0
$631$		−	40.6896i		−	1.61983i	−0.586549	−	0.809914i	$-0.699514\pi$
$631$		−	40.6896i		−	1.61983i	0.586549	−	0.809914i	$-0.300486\pi$
$632$	−4.35571	+	4.35571i	−0.173261	+	0.173261i
$633$	−0.687480	+	0.687480i	−0.0273249	+	0.0273249i
$634$		−	27.9083i		−	1.10838i
$635$		0			0
$636$			14.1849i			0.562467i
$637$	46.9224	+	46.9224i	1.85913	+	1.85913i
$638$	−4.35571	−	4.35571i	−0.172444	−	0.172444i
$639$		−	9.90833i		−	0.391967i
$640$		0			0
$641$			8.02498i			0.316968i	0.987362	+	0.158484i	$0.0506606\pi$
$641$			8.02498i			0.316968i	−0.987362	+	0.158484i	$0.949339\pi$
$642$	24.4162	−	24.4162i	0.963630	−	0.963630i
$643$	−13.8132	−	13.8132i	−0.544741	−	0.544741i	0.380174	−	0.924915i	$-0.375864\pi$
$643$	−13.8132	−	13.8132i	−0.544741	−	0.544741i	−0.924915	+	0.380174i	$0.875864\pi$
$644$	−20.3448	−	5.90833i	−0.801697	−	0.232821i
$645$		0			0
$646$	40.8167			1.60591
$647$	−6.21469	−	6.21469i	−0.244325	−	0.244325i	0.574312	−	0.818637i	$-0.305270\pi$
$647$	−6.21469	−	6.21469i	−0.244325	−	0.244325i	−0.818637	+	0.574312i	$0.805270\pi$
$648$	−7.49926	+	7.49926i	−0.294599	+	0.294599i
$649$	10.4547			0.410385
$650$		0			0
$651$		−	39.7571i		−	1.55820i
$652$	5.03420	+	5.03420i	0.197154	+	0.197154i
$653$	−20.3313	+	20.3313i	−0.795624	+	0.795624i	−0.982402	−	0.186779i	$-0.940195\pi$
$653$	−20.3313	+	20.3313i	−0.795624	+	0.795624i	0.186779	+	0.982402i	$0.440195\pi$
$654$	−30.5172			−1.19332
$655$		0			0
$656$	4.30278			0.167995
$657$	−2.27059	−	2.27059i	−0.0885842	−	0.0885842i
$658$	28.7719	+	28.7719i	1.12165	+	1.12165i
$659$	−20.3448			−0.792521			−0.396260	−	0.918138i	$-0.629692\pi$
$659$	−20.3448			−0.792521			−0.396260	+	0.918138i	$0.629692\pi$
$660$		0			0
$661$		−	15.3998i		−	0.598982i	−0.954099	−	0.299491i	$-0.903183\pi$
$661$		−	15.3998i		−	0.598982i	0.954099	−	0.299491i	$-0.0968168\pi$
$662$	−16.8409	−	16.8409i	−0.654541	−	0.654541i
$663$	49.6914	+	49.6914i	1.92985	+	1.92985i
$664$		0			0
$665$		0			0
$666$			20.3448i			0.788345i
$667$	4.62173	+	8.40474i	0.178954	+	0.325433i
$668$	12.7279	−	12.7279i	0.492458	−	0.492458i
$669$		−	18.0000i		−	0.695920i
$670$		0			0
$671$	−9.48612			−0.366208
$672$	7.19297	−	7.19297i	0.277475	−	0.277475i
$673$	2.27059	−	2.27059i	0.0875249	−	0.0875249i	−0.661989	−	0.749514i	$-0.730287\pi$
$673$	2.27059	−	2.27059i	0.0875249	−	0.0875249i	0.749514	+	0.661989i	$0.230287\pi$
$674$	−12.4424			−0.479265
$675$		0			0
$676$	15.1194			0.581517
$677$	−8.71143	+	8.71143i	−0.334807	+	0.334807i	−0.854409	−	0.519601i	$-0.826080\pi$
$677$	−8.71143	+	8.71143i	−0.334807	+	0.334807i	0.519601	+	0.854409i	$0.326080\pi$
$678$		0			0
$679$			1.78890i			0.0686516i
$680$		0			0
$681$			61.0344i			2.33884i
$682$	−8.51178	+	8.51178i	−0.325933	+	0.325933i
$683$	−17.0746	+	17.0746i	−0.653343	+	0.653343i	−0.953796	−	0.300454i	$-0.902862\pi$
$683$	−17.0746	+	17.0746i	−0.653343	+	0.653343i	0.300454	+	0.953796i	$0.402862\pi$
$684$	−16.3323			−0.624481
$685$		0			0
$686$		−	24.3573i		−	0.929966i
$687$	20.0605	−	20.0605i	0.765354	−	0.765354i
$688$	−8.13873	−	8.13873i	−0.310286	−	0.310286i
$689$	32.6646			1.24442
$690$		0			0
$691$	−25.8167			−0.982112			−0.491056	−	0.871128i	$-0.663389\pi$
$691$	−25.8167			−0.982112			−0.491056	+	0.871128i	$0.663389\pi$
$692$	−10.1136	−	10.1136i	−0.384461	−	0.384461i
$693$	−22.1540	+	22.1540i	−0.841562	+	0.841562i
$694$			5.09167i			0.193277i
$695$		0			0
$696$	−4.60555			−0.174573
$697$	17.5096	−	17.5096i	0.663222	−	0.663222i
$698$	−10.1980	+	10.1980i	−0.386001	+	0.386001i
$699$		−	24.4222i		−	0.923733i
$700$		0			0
$701$		−	13.2524i		−	0.500535i	−0.968177	−	0.250267i	$-0.919482\pi$
$701$		−	13.2524i		−	0.500535i	0.968177	−	0.250267i	$-0.0805185\pi$
$702$	6.02022	+	6.02022i	0.227219	+	0.227219i
$703$	44.3081	−	44.3081i	1.67111	−	1.67111i
$704$	−3.07995			−0.116080
$705$		0			0
$706$	13.8167			0.519997
$707$	−55.6523	+	55.6523i	−2.09302	+	2.09302i
$708$	5.52721	−	5.52721i	0.207725	−	0.207725i
$709$	31.4497			1.18112			0.590560	−	0.806994i	$-0.298907\pi$
$709$	31.4497			1.18112			0.590560	+	0.806994i	$0.298907\pi$
$710$		0			0
$711$		−	14.1849i		−	0.531975i
$712$		0			0
$713$	16.4242	−	9.03161i	0.615092	−	0.338236i
$714$		−	58.5416i		−	2.19087i
$715$		0			0
$716$	−25.6333			−0.957962
$717$	23.4838	+	23.4838i	0.877018	+	0.877018i
$718$	5.67452	+	5.67452i	0.211771	+	0.211771i
$719$			26.3305i			0.981963i	0.871170	+	0.490982i	$0.163362\pi$
$719$			26.3305i			0.981963i	−0.871170	+	0.490982i	$0.836638\pi$
$720$		0			0
$721$	−52.6333			−1.96017
$722$	22.1344	+	22.1344i	0.823757	+	0.823757i
$723$	33.1276	+	33.1276i	1.23203	+	1.23203i
$724$	0.932535			0.0346574
$725$		0			0
$726$	−3.48612			−0.129382
$727$	−15.9911	+	15.9911i	−0.593077	+	0.593077i	−0.938461	−	0.345384i	$-0.887749\pi$
$727$	−15.9911	+	15.9911i	−0.593077	+	0.593077i	0.345384	+	0.938461i	$0.387749\pi$
$728$	−16.5638	−	16.5638i	−0.613895	−	0.613895i
$729$		−	13.3305i		−	0.493723i
$730$		0			0
$731$	−66.2389			−2.44993
$732$	−5.01512	+	5.01512i	−0.185364	+	0.185364i
$733$	3.21031	+	3.21031i	0.118576	+	0.118576i	0.763905	−	0.645329i	$-0.223280\pi$
$733$	3.21031	+	3.21031i	0.118576	+	0.118576i	−0.645329	+	0.763905i	$0.723280\pi$
$734$	−27.3146			−1.00820
$735$		0			0
$736$	4.60555	+	1.33750i	0.169763	+	0.0493008i
$737$	−11.6515	−	11.6515i	−0.429189	−	0.429189i
$738$	−7.00625	+	7.00625i	−0.257903	+	0.257903i
$739$		−	49.2666i		−	1.81230i	−0.422955	−	0.906151i	$-0.639007\pi$
$739$		−	49.2666i		−	1.81230i	0.422955	−	0.906151i	$-0.360993\pi$
$740$		0			0
$741$			86.6066i			3.18157i
$742$	−19.2412	−	19.2412i	−0.706365	−	0.706365i
$743$	−33.0409	−	33.0409i	−1.21215	−	1.21215i	−0.970317	−	0.241836i	$-0.922250\pi$
$743$	−33.0409	−	33.0409i	−1.21215	−	1.21215i	−0.241836	−	0.970317i	$-0.577750\pi$
$744$			9.00000i			0.329956i
$745$		0			0
$746$		−	17.6698i		−	0.646938i
$747$		0			0
$748$	−12.5335	+	12.5335i	−0.458268	+	0.458268i
$749$			66.2389i			2.42032i
$750$		0			0
$751$		−	22.2099i		−	0.810450i	−0.914217	−	0.405225i	$-0.867193\pi$
$751$		−	22.2099i		−	0.810450i	0.914217	−	0.405225i	$-0.132807\pi$
$752$	−6.51323	−	6.51323i	−0.237513	−	0.237513i
$753$	−31.6092	−	31.6092i	−1.15190	−	1.15190i
$754$			10.6056i			0.386231i
$755$		0			0
$756$		−	7.09244i		−	0.257950i
$757$	30.6634	−	30.6634i	1.11448	−	1.11448i	0.121943	−	0.992537i	$-0.461087\pi$
$757$	30.6634	−	30.6634i	1.11448	−	1.11448i	0.992537	−	0.121943i	$-0.0389125\pi$
$758$	−22.2383	−	22.2383i	−0.807732	−	0.807732i
$759$	−32.6646	−	9.48612i	−1.18565	−	0.344324i
$760$		0			0
$761$	11.4861			0.416372			0.208186	−	0.978089i	$-0.433244\pi$
$761$	11.4861			0.416372			0.208186	+	0.978089i	$0.433244\pi$
$762$	−12.7279	−	12.7279i	−0.461084	−	0.461084i
$763$	41.3952	−	41.3952i	1.49861	−	1.49861i
$764$	12.3198			0.445715
$765$		0			0
$766$			2.67499i			0.0966514i
$767$	−12.7279	−	12.7279i	−0.459579	−	0.459579i
$768$	−1.62831	+	1.62831i	−0.0587565	+	0.0587565i
$769$	−30.7995			−1.11066			−0.555330	−	0.831630i	$-0.687408\pi$
$769$	−30.7995			−1.11066			−0.555330	+	0.831630i	$0.687408\pi$
$770$		0			0
$771$	49.8167			1.79410
$772$	3.25662	+	3.25662i	0.117208	+	0.117208i
$773$	−25.5616	−	25.5616i	−0.919386	−	0.919386i	0.0775985	−	0.996985i	$-0.475275\pi$
$773$	−25.5616	−	25.5616i	−0.919386	−	0.919386i	−0.996985	+	0.0775985i	$0.975275\pi$
$774$	26.5047			0.952692
$775$		0			0
$776$		−	0.404961i		−	0.0145373i
$777$	−63.5492	−	63.5492i	−2.27982	−	2.27982i
$778$	−26.5940	−	26.5940i	−0.953442	−	0.953442i
$779$	30.5172			1.09339
$780$		0			0
$781$		−	13.2524i		−	0.474207i
$782$	24.1844	−	13.2989i	0.864833	−	0.475568i
$783$	−2.27059	+	2.27059i	−0.0811444	+	0.0811444i
$784$			12.5139i			0.446924i
$785$		0			0
$786$	1.39445			0.0497383
$787$	18.1690	−	18.1690i	0.647653	−	0.647653i	−0.304772	−	0.952425i	$-0.598580\pi$
$787$	18.1690	−	18.1690i	0.647653	−	0.647653i	0.952425	+	0.304772i	$0.0985802\pi$
$788$	2.91288	−	2.91288i	0.103767	−	0.103767i
$789$	25.5722			0.910394
$790$		0			0
$791$		0			0
$792$	5.01512	−	5.01512i	0.178204	−	0.178204i
$793$	11.5487	+	11.5487i	0.410106	+	0.410106i
$794$		−	3.27502i		−	0.116226i
$795$		0			0
$796$			20.3448i			0.721102i
$797$	1.89151	−	1.89151i	0.0670006	−	0.0670006i	−0.672812	−	0.739813i	$-0.734914\pi$
$797$	1.89151	−	1.89151i	0.0670006	−	0.0670006i	0.739813	+	0.672812i	$0.234914\pi$
$798$	51.0158	−	51.0158i	1.80594	−	1.80594i
$799$	−53.0094			−1.87534
$800$		0			0
$801$		0			0
$802$	−5.67452	+	5.67452i	−0.200374	+	0.200374i
$803$	−3.03691	−	3.03691i	−0.107170	−	0.107170i
$804$	−12.3198			−0.434487
$805$		0			0
$806$	20.7250			0.730006
$807$	−36.5103	−	36.5103i	−1.28522	−	1.28522i
$808$	12.5983	−	12.5983i	0.443206	−	0.443206i
$809$			23.6972i			0.833150i	0.909101	+	0.416575i	$0.136770\pi$
$809$			23.6972i			0.833150i	−0.909101	+	0.416575i	$0.863230\pi$
$810$		0			0
$811$	−30.7889			−1.08114			−0.540572	−	0.841298i	$-0.681792\pi$
$811$	−30.7889			−1.08114			−0.540572	+	0.841298i	$0.681792\pi$
$812$	6.24722	−	6.24722i	0.219234	−	0.219234i
$813$	−27.8757	+	27.8757i	−0.977644	+	0.977644i
$814$			27.2111i			0.953749i
$815$		0			0
$816$			13.2524i			0.463925i
$817$	−57.7235	−	57.7235i	−2.01949	−	2.01949i
$818$	−19.0467	+	19.0467i	−0.665952	+	0.665952i
$819$	53.9420			1.88488
$820$		0			0
$821$	−15.8167			−0.552005			−0.276003	−	0.961157i	$-0.589010\pi$
$821$	−15.8167			−0.552005			−0.276003	+	0.961157i	$0.589010\pi$
$822$	−2.83726	+	2.83726i	−0.0989608	+	0.0989608i
$823$	10.7559	−	10.7559i	0.374926	−	0.374926i	−0.494342	−	0.869268i	$-0.664591\pi$
$823$	10.7559	−	10.7559i	0.374926	−	0.374926i	0.869268	+	0.494342i	$0.164591\pi$
$824$	11.9149			0.415074
$825$		0			0
$826$			14.9948i			0.521736i
$827$	31.8088	−	31.8088i	1.10610	−	1.10610i	0.112442	−	0.993658i	$-0.464133\pi$
$827$	31.8088	−	31.8088i	1.10610	−	1.10610i	0.993658	−	0.112442i	$-0.0358673\pi$
$828$	−9.67711	+	5.32140i	−0.336303	+	0.184931i
$829$			13.3944i			0.465208i	0.972571	+	0.232604i	$0.0747247\pi$
$829$			13.3944i			0.465208i	−0.972571	+	0.232604i	$0.925275\pi$
$830$		0			0
$831$	−41.4500			−1.43788
$832$	3.74963	+	3.74963i	0.129995	+	0.129995i
$833$	50.9235	+	50.9235i	1.76440	+	1.76440i
$834$		−	24.4222i		−	0.845672i
$835$		0			0
$836$	−21.8444			−0.755505
$837$	4.43711	+	4.43711i	0.153369	+	0.153369i
$838$	5.67452	+	5.67452i	0.196023	+	0.196023i
$839$	38.8245			1.34037			0.670186	−	0.742193i	$-0.266214\pi$
$839$	38.8245			1.34037			0.670186	+	0.742193i	$0.266214\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$	−18.0823	+	18.0823i	−0.623156	+	0.623156i
$843$		0			0
$844$			0.422205i			0.0145329i
$845$		0			0
$846$	21.2111			0.729253
$847$	4.72876	−	4.72876i	0.162482	−	0.162482i
$848$	4.35571	+	4.35571i	0.149576	+	0.149576i
$849$	−34.5297			−1.18506
$850$		0			0
$851$	11.8167	−	40.6896i	0.405070	−	1.39482i
$852$	−7.00625	−	7.00625i	−0.240030	−	0.240030i
$853$	17.7621	−	17.7621i	0.608163	−	0.608163i	−0.334302	−	0.942466i	$-0.608501\pi$
$853$	17.7621	−	17.7621i	0.608163	−	0.608163i	0.942466	+	0.334302i	$0.108501\pi$
$854$		−	13.6056i		−	0.465572i
$855$		0			0
$856$		−	14.9948i		−	0.512512i
$857$	−8.18674	−	8.18674i	−0.279654	−	0.279654i	0.553317	−	0.832971i	$-0.313362\pi$
$857$	−8.18674	−	8.18674i	−0.279654	−	0.279654i	−0.832971	+	0.553317i	$0.813362\pi$
$858$	−26.5940	−	26.5940i	−0.907905	−	0.907905i
$859$			30.0555i			1.02548i	0.858544	+	0.512740i	$0.171370\pi$
$859$			30.0555i			1.02548i	−0.858544	+	0.512740i	$0.828630\pi$
$860$		0			0
$861$		−	43.7696i		−	1.49166i
$862$	−5.67452	+	5.67452i	−0.193275	+	0.193275i
$863$	7.79780	−	7.79780i	0.265440	−	0.265440i	−0.561820	−	0.827260i	$-0.689898\pi$
$863$	7.79780	−	7.79780i	0.265440	−	0.265440i	0.827260	+	0.561820i	$0.189898\pi$
$864$			1.60555i			0.0546220i
$865$		0			0
$866$		−	24.7623i		−	0.841456i
$867$	26.2474	+	26.2474i	0.891408	+	0.891408i
$868$	−12.2081	−	12.2081i	−0.414370	−	0.414370i
$869$		−	18.9722i		−	0.643589i
$870$		0			0
$871$			28.3698i			0.961273i
$872$	−9.37083	+	9.37083i	−0.317336	+	0.317336i
$873$	0.659402	+	0.659402i	0.0223174	+	0.0223174i
$874$	32.6646	+	9.48612i	1.10490	+	0.320873i
$875$		0			0
$876$	−3.21110			−0.108493
$877$	−8.14154	−	8.14154i	−0.274920	−	0.274920i	0.556157	−	0.831077i	$-0.312275\pi$
$877$	−8.14154	−	8.14154i	−0.274920	−	0.274920i	−0.831077	+	0.556157i	$0.812275\pi$
$878$	14.2070	−	14.2070i	0.479462	−	0.479462i
$879$	−38.8245			−1.30952
$880$		0			0
$881$			10.4547i			0.352229i	0.984370	+	0.176115i	$0.0563530\pi$
$881$			10.4547i			0.352229i	−0.984370	+	0.176115i	$0.943647\pi$
$882$	−20.3765	−	20.3765i	−0.686111	−	0.686111i
$883$	20.4216	−	20.4216i	0.687243	−	0.687243i	−0.274379	−	0.961622i	$-0.588472\pi$
$883$	20.4216	−	20.4216i	0.687243	−	0.687243i	0.961622	+	0.274379i	$0.0884721\pi$
$884$	30.5172			1.02640
$885$		0			0
$886$	−31.1194			−1.04548
$887$	−26.7404	−	26.7404i	−0.897855	−	0.897855i	0.0973910	−	0.995246i	$-0.468950\pi$
$887$	−26.7404	−	26.7404i	−0.897855	−	0.897855i	−0.995246	+	0.0973910i	$0.968950\pi$
$888$	14.3859	+	14.3859i	0.482761	+	0.482761i
$889$	34.5297			1.15809
$890$		0			0
$891$		−	32.6646i		−	1.09431i
$892$	−5.52721	−	5.52721i	−0.185065	−	0.185065i
$893$	−46.1947	−	46.1947i	−1.54585	−	1.54585i
$894$	−2.14742			−0.0718205
$895$		0			0
$896$		−	4.41745i		−	0.147577i
$897$	28.2182	+	51.3156i	0.942178	+	1.71338i
$898$	2.33542	−	2.33542i	0.0779338	−	0.0779338i
$899$			7.81665i			0.260700i
$900$		0			0
$901$	35.4500			1.18101
$902$	−9.37083	+	9.37083i	−0.312015	+	0.312015i
$903$	−82.7904	+	82.7904i	−2.75509	+	2.75509i
$904$		0			0
$905$		0			0
$906$	−19.1194			−0.635200
$907$	−3.78301	+	3.78301i	−0.125613	+	0.125613i	−0.767118	−	0.641506i	$-0.778310\pi$
$907$	−3.78301	+	3.78301i	−0.125613	+	0.125613i	0.641506	+	0.767118i	$0.278310\pi$
$908$	18.7417	+	18.7417i	0.621964	+	0.621964i
$909$			41.0278i			1.36080i
$910$		0			0
$911$			34.5297i			1.14402i	0.820247	+	0.572010i	$0.193836\pi$
$911$			34.5297i			1.14402i	−0.820247	+	0.572010i	$0.806164\pi$
$912$	−11.5487	+	11.5487i	−0.382415	+	0.382415i
$913$		0			0
$914$	−23.0198			−0.761427
$915$		0			0
$916$		−	12.3198i		−	0.407058i
$917$	−1.89151	+	1.89151i	−0.0624630	+	0.0624630i
$918$	6.53357	+	6.53357i	0.215640	+	0.215640i
$919$	−26.5047			−0.874310			−0.437155	−	0.899386i	$-0.644014\pi$
$919$	−26.5047			−0.874310			−0.437155	+	0.899386i	$0.644014\pi$
$920$		0			0
$921$	71.1749			2.34529
$922$	−5.39756	−	5.39756i	−0.177759	−	0.177759i
$923$	−16.1338	+	16.1338i	−0.531051	+	0.531051i
$924$			31.3305i			1.03070i
$925$		0			0
$926$	0.422205			0.0138745
$927$	−19.4011	+	19.4011i	−0.637214	+	0.637214i
$928$	−1.41421	+	1.41421i	−0.0464238	+	0.0464238i
$929$			13.6333i			0.447294i	0.974670	+	0.223647i	$0.0717963\pi$
$929$			13.6333i			0.447294i	−0.974670	+	0.223647i	$0.928204\pi$
$930$		0			0
$931$			88.7540i			2.90879i
$932$	−7.49926	−	7.49926i	−0.245646	−	0.245646i
$933$	−2.56914	+	2.56914i	−0.0841098	+	0.0841098i
$934$	1.86507			0.0610270
$935$		0			0
$936$	−12.2111			−0.399132
$937$	11.2623	−	11.2623i	0.367924	−	0.367924i	−0.498795	−	0.866720i	$-0.666224\pi$
$937$	11.2623	−	11.2623i	0.367924	−	0.367924i	0.866720	+	0.498795i	$0.166224\pi$
$938$	16.7113	−	16.7113i	0.545642	−	0.545642i
$939$	−36.6771			−1.19691
$940$		0			0
$941$			12.9700i			0.422810i	0.977399	+	0.211405i	$0.0678039\pi$
$941$			12.9700i			0.422810i	−0.977399	+	0.211405i	$0.932196\pi$
$942$	−18.7417	+	18.7417i	−0.610636	+	0.610636i
$943$	18.0819	−	9.94313i	0.588826	−	0.323793i
$944$		−	3.39445i		−	0.110480i
$945$		0			0
$946$	35.4500			1.15258
$947$	24.9628	+	24.9628i	0.811183	+	0.811183i	0.984811	−	0.173628i	$-0.0555491\pi$
$947$	24.9628	+	24.9628i	0.811183	+	0.811183i	−0.173628	+	0.984811i	$0.555549\pi$
$948$	−10.0302	−	10.0302i	−0.325767	−	0.325767i
$949$			7.39445i			0.240034i
$950$		0			0
$951$	64.2666			2.08399
$952$	−17.9762	−	17.9762i	−0.582612	−	0.582612i
$953$	−20.9195	−	20.9195i	−0.677650	−	0.677650i	0.281818	−	0.959468i	$-0.409062\pi$
$953$	−20.9195	−	20.9195i	−0.677650	−	0.677650i	−0.959468	+	0.281818i	$0.909062\pi$
$954$	−14.1849			−0.459253
$955$		0			0
$956$	14.4222			0.466447
$957$	10.0302	−	10.0302i	0.324231	−	0.324231i
$958$	18.7417	+	18.7417i	0.605516	+	0.605516i
$959$		−	7.69722i		−	0.248556i
$960$		0			0
$961$	−15.7250			−0.507257
$962$	33.1276	−	33.1276i	1.06808	−	1.06808i
$963$	24.4162	+	24.4162i	0.786800	+	0.786800i
$964$	20.3448			0.655262
$965$		0			0
$966$	13.6056	−	46.8495i	0.437751	−	1.50736i
$967$	27.4279	+	27.4279i	0.882022	+	0.882022i	0.993740	−	0.111718i	$-0.0356354\pi$
$967$	27.4279	+	27.4279i	0.882022	+	0.882022i	−0.111718	+	0.993740i	$0.535635\pi$
$968$	−1.07047	+	1.07047i	−0.0344063	+	0.0344063i
$969$			93.9916i			3.01945i
$970$		0			0
$971$		−	37.6096i		−	1.20695i	−0.797382	−	0.603475i	$-0.793782\pi$
$971$		−	37.6096i		−	1.20695i	0.797382	−	0.603475i	$-0.206218\pi$
$972$	−13.8632	−	13.8632i	−0.444663	−	0.444663i
$973$	33.1276	+	33.1276i	1.06202	+	1.06202i
$974$			40.6056i			1.30109i
$975$		0			0
$976$			3.07995i			0.0985870i
$977$	−0.0867001	+	0.0867001i	−0.00277378	+	0.00277378i	−0.708492	−	0.705719i	$-0.750624\pi$
$977$	−0.0867001	+	0.0867001i	−0.00277378	+	0.00277378i	0.705719	+	0.708492i	$0.250624\pi$
$978$	−11.5926	+	11.5926i	−0.370691	+	0.370691i
$979$		0			0
$980$		0			0
$981$		−	30.5172i		−	0.974339i
$982$	−13.8828	−	13.8828i	−0.443019	−	0.443019i
$983$	7.27967	+	7.27967i	0.232186	+	0.232186i	0.813604	−	0.581419i	$-0.197502\pi$
$983$	7.27967	+	7.27967i	0.232186	+	0.232186i	−0.581419	+	0.813604i	$0.697502\pi$
$984$			9.90833i			0.315866i
$985$		0			0
$986$			11.5099i			0.366550i
$987$	−66.2552	+	66.2552i	−2.10893	+	2.10893i
$988$	26.5940	+	26.5940i	0.846069	+	0.846069i
$989$	−53.0094	−	15.3944i	−1.68560	−	0.489515i
$990$		0			0
$991$	−17.5139			−0.556347			−0.278173	−	0.960531i	$-0.589729\pi$
$991$	−17.5139			−0.556347			−0.278173	+	0.960531i	$0.589729\pi$
$992$	2.76360	+	2.76360i	0.0877445	+	0.0877445i
$993$	38.7809	−	38.7809i	1.23067	−	1.23067i
$994$	19.0073			0.602875
$995$		0			0
$996$		0			0
$997$	19.8382	+	19.8382i	0.628283	+	0.628283i	0.947636	−	0.319353i	$-0.103465\pi$
$997$	19.8382	+	19.8382i	0.628283	+	0.628283i	−0.319353	+	0.947636i	$0.603465\pi$
$998$	−0.557835	+	0.557835i	−0.0176580	+	0.0176580i
$999$	14.1849			0.448790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.e.e.1057.6	yes	16
5.2	odd	4	inner	1150.2.e.e.643.4	yes	16
5.3	odd	4	inner	1150.2.e.e.643.5	yes	16
5.4	even	2	inner	1150.2.e.e.1057.3	yes	16
23.22	odd	2	inner	1150.2.e.e.1057.5	yes	16
115.22	even	4	inner	1150.2.e.e.643.3	✓	16
115.68	even	4	inner	1150.2.e.e.643.6	yes	16
115.114	odd	2	inner	1150.2.e.e.1057.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.2.e.e.643.3	✓	16	115.22	even	4	inner
1150.2.e.e.643.4	yes	16	5.2	odd	4	inner
1150.2.e.e.643.5	yes	16	5.3	odd	4	inner
1150.2.e.e.643.6	yes	16	115.68	even	4	inner
1150.2.e.e.1057.3	yes	16	5.4	even	2	inner
1150.2.e.e.1057.4	yes	16	115.114	odd	2	inner
1150.2.e.e.1057.5	yes	16	23.22	odd	2	inner
1150.2.e.e.1057.6	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.62831 + 1.62831i) q^{3} +1.00000i q^{4} -2.30278 q^{6} +(3.12361 - 3.12361i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.30278i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.62831 + 1.62831i) q^{3} +1.00000i q^{4} -2.30278 q^{6} +(3.12361 - 3.12361i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.30278i q^{9} -3.07995i q^{11} +(-1.62831 - 1.62831i) q^{12} +(-3.74963 + 3.74963i) q^{13} +4.41745 q^{14} -1.00000 q^{16} +(-4.06936 + 4.06936i) q^{17} +(1.62831 - 1.62831i) q^{18} -7.09244 q^{19} +10.1724i q^{21} +(2.17786 - 2.17786i) q^{22} +(-4.20237 + 2.31086i) q^{23} -2.30278i q^{24} -5.30278 q^{26} +(-1.13530 - 1.13530i) q^{27} +(3.12361 + 3.12361i) q^{28} -2.00000i q^{29} -3.90833 q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.01512 + 5.01512i) q^{33} -5.75495 q^{34} +2.30278 q^{36} +(-6.24722 + 6.24722i) q^{37} +(-5.01512 - 5.01512i) q^{38} -12.2111i q^{39} -4.30278 q^{41} +(-7.19297 + 7.19297i) q^{42} +(8.13873 + 8.13873i) q^{43} +3.07995 q^{44} +(-4.60555 - 1.33750i) q^{46} +(6.51323 + 6.51323i) q^{47} +(1.62831 - 1.62831i) q^{48} -12.5139i q^{49} -13.2524i q^{51} +(-3.74963 - 3.74963i) q^{52} +(-4.35571 - 4.35571i) q^{53} -1.60555i q^{54} +4.41745i q^{56} +(11.5487 - 11.5487i) q^{57} +(1.41421 - 1.41421i) q^{58} +3.39445i q^{59} -3.07995i q^{61} +(-2.76360 - 2.76360i) q^{62} +(-7.19297 - 7.19297i) q^{63} -1.00000i q^{64} +7.09244i q^{66} +(3.78301 - 3.78301i) q^{67} +(-4.06936 - 4.06936i) q^{68} +(3.07995 - 10.6056i) q^{69} +4.30278 q^{71} +(1.62831 + 1.62831i) q^{72} +(0.986024 - 0.986024i) q^{73} -8.83490 q^{74} -7.09244i q^{76} +(-9.62058 - 9.62058i) q^{77} +(8.63455 - 8.63455i) q^{78} +6.15991 q^{79} +10.6056 q^{81} +(-3.04252 - 3.04252i) q^{82} -10.1724 q^{84} +11.5099i q^{86} +(3.25662 + 3.25662i) q^{87} +(2.17786 + 2.17786i) q^{88} +23.4248i q^{91} +(-2.31086 - 4.20237i) q^{92} +(6.36396 - 6.36396i) q^{93} +9.21110i q^{94} +2.30278 q^{96} +(-0.286351 + 0.286351i) q^{97} +(8.84865 - 8.84865i) q^{98} -7.09244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{6}+O(q^{10}) \) 16 * q - 8 * q^6	\( 16 q - 8 q^{6} - 16 q^{16} - 56 q^{26} + 24 q^{31} + 8 q^{36} - 40 q^{41} - 16 q^{46} + 40 q^{71} + 112 q^{81} + 8 q^{96}+O(q^{100}) \) 16 * q - 8 * q^6 - 16 * q^16 - 56 * q^26 + 24 * q^31 + 8 * q^36 - 40 * q^41 - 16 * q^46 + 40 * q^71 + 112 * q^81 + 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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