LMFDB - Embedded newform 230.3.f.a.93.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(47,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.f (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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 52 x^{17} + 1020 x^{16} - 1316 x^{15} + 1352 x^{14} - 18724 x^{13} + 250686 x^{12} + \cdots + 88804 $ x^20 - 52x^17 + 1020x^16 - 1316x^15 + 1352x^14 - 18724x^13 + 250686x^12 - 439644x^11 + 460536x^10 - 1833716x^9 + 16970128x^8 - 36894604x^7 + 40544632x^6 - 4380588x^5 + 34721x^4 - 4419956x^3 + 9945800x^2 + 1329080*x + 88804
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			93.10
Root			$2.93330 + 2.93330i$ of defining polynomial
Character	$\chi$	$=$	230.93
Dual form			230.3.f.a.47.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(2.93330 + 2.93330i) q^{3} -2.00000i q^{4} +(0.390531 - 4.98473i) q^{5} -5.86660 q^{6} +(1.49862 - 1.49862i) q^{7} +(2.00000 + 2.00000i) q^{8} +8.20851i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(2.93330 + 2.93330i) q^{3} -2.00000i q^{4} +(0.390531 - 4.98473i) q^{5} -5.86660 q^{6} +(1.49862 - 1.49862i) q^{7} +(2.00000 + 2.00000i) q^{8} +8.20851i q^{9} +(4.59419 + 5.37526i) q^{10} +8.24701 q^{11} +(5.86660 - 5.86660i) q^{12} +(14.8761 + 14.8761i) q^{13} +2.99725i q^{14} +(15.7672 - 13.4762i) q^{15} -4.00000 q^{16} +(8.86691 - 8.86691i) q^{17} +(-8.20851 - 8.20851i) q^{18} +8.33032i q^{19} +(-9.96945 - 0.781063i) q^{20} +8.79183 q^{21} +(-8.24701 + 8.24701i) q^{22} +(3.39116 + 3.39116i) q^{23} +11.7332i q^{24} +(-24.6950 - 3.89338i) q^{25} -29.7522 q^{26} +(2.32167 - 2.32167i) q^{27} +(-2.99725 - 2.99725i) q^{28} +21.2393i q^{29} +(-2.29109 + 29.2434i) q^{30} -38.0320 q^{31} +(4.00000 - 4.00000i) q^{32} +(24.1910 + 24.1910i) q^{33} +17.7338i q^{34} +(-6.88496 - 8.05548i) q^{35} +16.4170 q^{36} +(18.9398 - 18.9398i) q^{37} +(-8.33032 - 8.33032i) q^{38} +87.2722i q^{39} +(10.7505 - 9.18839i) q^{40} +42.1499 q^{41} +(-8.79183 + 8.79183i) q^{42} +(-52.2044 - 52.2044i) q^{43} -16.4940i q^{44} +(40.9172 + 3.20568i) q^{45} -6.78233 q^{46} +(-15.0827 + 15.0827i) q^{47} +(-11.7332 - 11.7332i) q^{48} +44.5083i q^{49} +(28.5884 - 20.8016i) q^{50} +52.0186 q^{51} +(29.7522 - 29.7522i) q^{52} +(27.3408 + 27.3408i) q^{53} +4.64334i q^{54} +(3.22072 - 41.1091i) q^{55} +5.99449 q^{56} +(-24.4354 + 24.4354i) q^{57} +(-21.2393 - 21.2393i) q^{58} -40.1813i q^{59} +(-26.9523 - 31.5345i) q^{60} +9.06197 q^{61} +(38.0320 - 38.0320i) q^{62} +(12.3015 + 12.3015i) q^{63} +8.00000i q^{64} +(79.9629 - 68.3437i) q^{65} -48.3819 q^{66} +(-8.60705 + 8.60705i) q^{67} +(-17.7338 - 17.7338i) q^{68} +19.8946i q^{69} +(14.9404 + 1.17052i) q^{70} -124.620 q^{71} +(-16.4170 + 16.4170i) q^{72} +(-98.5165 - 98.5165i) q^{73} +37.8797i q^{74} +(-61.0173 - 83.8583i) q^{75} +16.6606 q^{76} +(12.3592 - 12.3592i) q^{77} +(-87.2722 - 87.2722i) q^{78} +13.6410i q^{79} +(-1.56213 + 19.9389i) q^{80} +87.4969 q^{81} +(-42.1499 + 42.1499i) q^{82} +(-0.140105 - 0.140105i) q^{83} -17.5837i q^{84} +(-40.7363 - 47.6619i) q^{85} +104.409 q^{86} +(-62.3013 + 62.3013i) q^{87} +(16.4940 + 16.4940i) q^{88} -134.007i q^{89} +(-44.1229 + 37.7115i) q^{90} +44.5873 q^{91} +(6.78233 - 6.78233i) q^{92} +(-111.559 - 111.559i) q^{93} -30.1654i q^{94} +(41.5244 + 3.25325i) q^{95} +23.4664 q^{96} +(-82.0061 + 82.0061i) q^{97} +(-44.5083 - 44.5083i) q^{98} +67.6957i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	$ 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) $ 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	2.93330	+	2.93330i	0.977767	+	0.977767i	0.999758	−	0.0219911i	$-0.00700054\pi$
$3$	2.93330	+	2.93330i	0.977767	+	0.977767i	−0.0219911	+	0.999758i	$0.507001\pi$
$4$		−	2.00000i		−	0.500000i
$5$	0.390531	−	4.98473i	0.0781063	−	0.996945i
$5$	0.390531	−	4.98473i	0.0781063	−	0.996945i
$6$	−5.86660			−0.977767
$7$	1.49862	−	1.49862i	0.214089	−	0.214089i	−0.591913	−	0.806002i	$-0.701627\pi$
$7$	1.49862	−	1.49862i	0.214089	−	0.214089i	0.806002	+	0.591913i	$0.201627\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			8.20851i			0.912057i
$10$	4.59419	+	5.37526i	0.459419	+	0.537526i
$11$	8.24701			0.749728			0.374864	−	0.927080i	$-0.377689\pi$
$11$	8.24701			0.749728			0.374864	+	0.927080i	$0.377689\pi$
$12$	5.86660	−	5.86660i	0.488884	−	0.488884i
$13$	14.8761	+	14.8761i	1.14432	+	1.14432i	0.987652	+	0.156664i	$0.0500739\pi$
$13$	14.8761	+	14.8761i	1.14432	+	1.14432i	0.156664	+	0.987652i	$0.449926\pi$
$14$			2.99725i			0.214089i
$15$	15.7672	−	13.4762i	1.05115	−	0.898410i
$16$	−4.00000			−0.250000
$17$	8.86691	−	8.86691i	0.521583	−	0.521583i	−0.396466	−	0.918049i	$-0.629764\pi$
$17$	8.86691	−	8.86691i	0.521583	−	0.521583i	0.918049	+	0.396466i	$0.129764\pi$
$18$	−8.20851	−	8.20851i	−0.456028	−	0.456028i
$19$			8.33032i			0.438438i	0.975676	+	0.219219i	$0.0703509\pi$
$19$			8.33032i			0.438438i	−0.975676	+	0.219219i	$0.929649\pi$
$20$	−9.96945	−	0.781063i	−0.498473	−	0.0390531i
$21$	8.79183			0.418658
$22$	−8.24701	+	8.24701i	−0.374864	+	0.374864i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$			11.7332i			0.488884i
$25$	−24.6950	−	3.89338i	−0.987799	−	0.155735i
$26$	−29.7522			−1.14432
$27$	2.32167	−	2.32167i	0.0859878	−	0.0859878i
$28$	−2.99725	−	2.99725i	−0.107045	−	0.107045i
$29$			21.2393i			0.732390i	0.930538	+	0.366195i	$0.119340\pi$
$29$			21.2393i			0.732390i	−0.930538	+	0.366195i	$0.880660\pi$
$30$	−2.29109	+	29.2434i	−0.0763698	+	0.974780i
$31$	−38.0320			−1.22684			−0.613419	−	0.789758i	$-0.710206\pi$
$31$	−38.0320			−1.22684			−0.613419	+	0.789758i	$0.710206\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	24.1910	+	24.1910i	0.733059	+	0.733059i
$34$			17.7338i			0.521583i
$35$	−6.88496	−	8.05548i	−0.196713	−	0.230157i
$36$	16.4170			0.456028
$37$	18.9398	−	18.9398i	0.511888	−	0.511888i	−0.403217	−	0.915104i	$-0.632108\pi$
$37$	18.9398	−	18.9398i	0.511888	−	0.511888i	0.915104	+	0.403217i	$0.132108\pi$
$38$	−8.33032	−	8.33032i	−0.219219	−	0.219219i
$39$			87.2722i			2.23775i
$40$	10.7505	−	9.18839i	0.268763	−	0.229710i
$41$	42.1499			1.02805			0.514023	−	0.857776i	$-0.328154\pi$
$41$	42.1499			1.02805			0.514023	+	0.857776i	$0.328154\pi$
$42$	−8.79183	+	8.79183i	−0.209329	+	0.209329i
$43$	−52.2044	−	52.2044i	−1.21406	−	1.21406i	−0.969681	−	0.244374i	$-0.921418\pi$
$43$	−52.2044	−	52.2044i	−1.21406	−	1.21406i	−0.244374	−	0.969681i	$-0.578582\pi$
$44$		−	16.4940i		−	0.374864i
$45$	40.9172	+	3.20568i	0.909271	+	0.0712374i
$46$	−6.78233			−0.147442
$47$	−15.0827	+	15.0827i	−0.320908	+	0.320908i	−0.849115	−	0.528207i	$-0.822864\pi$
$47$	−15.0827	+	15.0827i	−0.320908	+	0.320908i	0.528207	+	0.849115i	$0.322864\pi$
$48$	−11.7332	−	11.7332i	−0.244442	−	0.244442i
$49$			44.5083i			0.908332i
$50$	28.5884	−	20.8016i	0.571767	−	0.416032i
$51$	52.0186			1.01997
$52$	29.7522	−	29.7522i	0.572158	−	0.572158i
$53$	27.3408	+	27.3408i	0.515865	+	0.515865i	0.916317	−	0.400453i	$-0.131147\pi$
$53$	27.3408	+	27.3408i	0.515865	+	0.515865i	−0.400453	+	0.916317i	$0.631147\pi$
$54$			4.64334i			0.0859878i
$55$	3.22072	−	41.1091i	0.0585585	−	0.747438i
$56$	5.99449			0.107045
$57$	−24.4354	+	24.4354i	−0.428690	+	0.428690i
$58$	−21.2393	−	21.2393i	−0.366195	−	0.366195i
$59$		−	40.1813i		−	0.681038i	−0.940238	−	0.340519i	$-0.889397\pi$
$59$		−	40.1813i		−	0.681038i	0.940238	−	0.340519i	$-0.110603\pi$
$60$	−26.9523	−	31.5345i	−0.449205	−	0.525575i
$61$	9.06197			0.148557			0.0742784	−	0.997238i	$-0.476335\pi$
$61$	9.06197			0.148557			0.0742784	+	0.997238i	$0.476335\pi$
$62$	38.0320	−	38.0320i	0.613419	−	0.613419i
$63$	12.3015	+	12.3015i	0.195261	+	0.195261i
$64$			8.00000i			0.125000i
$65$	79.9629	−	68.3437i	1.23020	−	1.05144i
$66$	−48.3819			−0.733059
$67$	−8.60705	+	8.60705i	−0.128463	+	0.128463i	−0.768415	−	0.639952i	$-0.778954\pi$
$67$	−8.60705	+	8.60705i	−0.128463	+	0.128463i	0.639952	+	0.768415i	$0.278954\pi$
$68$	−17.7338	−	17.7338i	−0.260791	−	0.260791i
$69$			19.8946i			0.288328i
$70$	14.9404	+	1.17052i	0.213435	+	0.0167217i
$71$	−124.620			−1.75521			−0.877603	−	0.479389i	$-0.840858\pi$
$71$	−124.620			−1.75521			−0.877603	+	0.479389i	$0.840858\pi$
$72$	−16.4170	+	16.4170i	−0.228014	+	0.228014i
$73$	−98.5165	−	98.5165i	−1.34954	−	1.34954i	−0.886159	−	0.463382i	$-0.846636\pi$
$73$	−98.5165	−	98.5165i	−1.34954	−	1.34954i	−0.463382	−	0.886159i	$-0.653364\pi$
$74$			37.8797i			0.511888i
$75$	−61.0173	−	83.8583i	−0.813564	−	1.11811i
$76$	16.6606			0.219219
$77$	12.3592	−	12.3592i	0.160509	−	0.160509i
$78$	−87.2722	−	87.2722i	−1.11887	−	1.11887i
$79$			13.6410i			0.172671i	0.996266	+	0.0863353i	$0.0275156\pi$
$79$			13.6410i			0.172671i	−0.996266	+	0.0863353i	$0.972484\pi$
$80$	−1.56213	+	19.9389i	−0.0195266	+	0.249236i
$81$	87.4969			1.08021
$82$	−42.1499	+	42.1499i	−0.514023	+	0.514023i
$83$	−0.140105	−	0.140105i	−0.00168801	−	0.00168801i	0.706262	−	0.707950i	$-0.250380\pi$
$83$	−0.140105	−	0.140105i	−0.00168801	−	0.00168801i	−0.707950	+	0.706262i	$0.750380\pi$
$84$		−	17.5837i		−	0.209329i
$85$	−40.7363	−	47.6619i	−0.479251	−	0.560728i
$86$	104.409			1.21406
$87$	−62.3013	+	62.3013i	−0.716107	+	0.716107i
$88$	16.4940	+	16.4940i	0.187432	+	0.187432i
$89$		−	134.007i		−	1.50570i	−0.658193	−	0.752849i	$-0.728679\pi$
$89$		−	134.007i		−	1.50570i	0.658193	−	0.752849i	$-0.271321\pi$
$90$	−44.1229	+	37.7115i	−0.490254	+	0.419017i
$91$	44.5873			0.489971
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	−111.559	−	111.559i	−1.19956	−	1.19956i
$94$		−	30.1654i		−	0.320908i
$95$	41.5244	+	3.25325i	0.437099	+	0.0342448i
$96$	23.4664			0.244442
$97$	−82.0061	+	82.0061i	−0.845423	+	0.845423i	−0.989558	−	0.144135i	$-0.953960\pi$
$97$	−82.0061	+	82.0061i	−0.845423	+	0.845423i	0.144135	+	0.989558i	$0.453960\pi$
$98$	−44.5083	−	44.5083i	−0.454166	−	0.454166i
$99$			67.6957i			0.683795i
$100$	−7.78677	+	49.3899i	−0.0778677	+	0.493899i
$101$	40.5100			0.401089			0.200544	−	0.979685i	$-0.435729\pi$
$101$	40.5100			0.401089			0.200544	+	0.979685i	$0.435729\pi$
$102$	−52.0186	+	52.0186i	−0.509987	+	0.509987i
$103$	−21.6172	−	21.6172i	−0.209876	−	0.209876i	0.594339	−	0.804215i	$-0.297414\pi$
$103$	−21.6172	−	21.6172i	−0.209876	−	0.209876i	−0.804215	+	0.594339i	$0.797414\pi$
$104$			59.5044i			0.572158i
$105$	3.43348	−	43.8248i	0.0326999	−	0.417379i
$106$	−54.6816			−0.515865
$107$	34.6070	−	34.6070i	0.323430	−	0.323430i	−0.526651	−	0.850081i	$-0.676553\pi$
$107$	34.6070	−	34.6070i	0.323430	−	0.323430i	0.850081	+	0.526651i	$0.176553\pi$
$108$	−4.64334	−	4.64334i	−0.0429939	−	0.0429939i
$109$			34.5054i			0.316563i	0.987394	+	0.158282i	$0.0505954\pi$
$109$			34.5054i			0.316563i	−0.987394	+	0.158282i	$0.949405\pi$
$110$	37.8884	+	44.3298i	0.344440	+	0.402998i
$111$	111.113			1.00101
$112$	−5.99449	+	5.99449i	−0.0535223	+	0.0535223i
$113$	−18.9252	−	18.9252i	−0.167479	−	0.167479i	0.618391	−	0.785870i	$-0.287785\pi$
$113$	−18.9252	−	18.9252i	−0.167479	−	0.167479i	−0.785870	+	0.618391i	$0.787785\pi$
$114$		−	48.8707i		−	0.428690i
$115$	18.2284	−	15.5797i	0.158508	−	0.135475i
$116$	42.4786			0.366195
$117$	−122.111	+	122.111i	−1.04368	+	1.04368i
$118$	40.1813	+	40.1813i	0.340519	+	0.340519i
$119$		−	26.5763i		−	0.223330i
$120$	58.4868	+	4.58219i	0.487390	+	0.0381849i
$121$	−52.9869			−0.437908
$122$	−9.06197	+	9.06197i	−0.0742784	+	0.0742784i
$123$	123.638	+	123.638i	1.00519	+	1.00519i
$124$			76.0640i			0.613419i
$125$	−29.0516	+	121.577i	−0.232413	+	0.972617i
$126$	−24.6029			−0.195261
$127$	8.99058	−	8.99058i	0.0707920	−	0.0707920i	−0.670824	−	0.741616i	$-0.734060\pi$
$127$	8.99058	−	8.99058i	0.0707920	−	0.0707920i	0.741616	+	0.670824i	$0.234060\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	306.262i		−	2.37413i
$130$	−11.6192	+	148.307i	−0.0893783	+	1.14082i
$131$	211.736			1.61631			0.808154	−	0.588972i	$-0.200467\pi$
$131$	211.736			1.61631			0.808154	+	0.588972i	$0.200467\pi$
$132$	48.3819	−	48.3819i	0.366530	−	0.366530i
$133$	12.4840	+	12.4840i	0.0938648	+	0.0938648i
$134$		−	17.2141i		−	0.128463i
$135$	−10.6662	−	12.4796i	−0.0790089	−	0.0924413i
$136$	35.4676			0.260791
$137$	147.657	−	147.657i	1.07779	−	1.07779i	0.0810837	−	0.996707i	$-0.474162\pi$
$137$	147.657	−	147.657i	1.07779	−	1.07779i	0.996707	−	0.0810837i	$-0.0258381\pi$
$138$	−19.8946	−	19.8946i	−0.144164	−	0.144164i
$139$			71.3041i			0.512979i	0.966547	+	0.256489i	$0.0825659\pi$
$139$			71.3041i			0.512979i	−0.966547	+	0.256489i	$0.917434\pi$
$140$	−16.1110	+	13.7699i	−0.115078	+	0.0983566i
$141$	−88.4841			−0.627547
$142$	124.620	−	124.620i	0.877603	−	0.877603i
$143$	122.683	+	122.683i	0.857926	+	0.857926i
$144$		−	32.8341i		−	0.228014i
$145$	105.872	+	8.29462i	0.730153	+	0.0572043i
$146$	197.033			1.34954
$147$	−130.556	+	130.556i	−0.888137	+	0.888137i
$148$	−37.8797	−	37.8797i	−0.255944	−	0.255944i
$149$			210.967i			1.41589i	0.706268	+	0.707944i	$0.250377\pi$
$149$			210.967i			1.41589i	−0.706268	+	0.707944i	$0.749623\pi$
$150$	144.876	+	22.8409i	0.965837	+	0.152273i
$151$	−270.221			−1.78954			−0.894772	−	0.446523i	$-0.852662\pi$
$151$	−270.221			−1.78954			−0.894772	+	0.446523i	$0.852662\pi$
$152$	−16.6606	+	16.6606i	−0.109610	+	0.109610i
$153$	72.7841	+	72.7841i	0.475713	+	0.475713i
$154$			24.7183i			0.160509i
$155$	−14.8527	+	189.579i	−0.0958238	+	1.22309i
$156$	174.544			1.11887
$157$	−66.2348	+	66.2348i	−0.421878	+	0.421878i	−0.885850	−	0.463972i	$-0.846424\pi$
$157$	−66.2348	+	66.2348i	−0.421878	+	0.421878i	0.463972	+	0.885850i	$0.346424\pi$
$158$	−13.6410	−	13.6410i	−0.0863353	−	0.0863353i
$159$			160.398i			1.00879i
$160$	−18.3768	−	21.5010i	−0.114855	−	0.134381i
$161$	10.1642			0.0631314
$162$	−87.4969	+	87.4969i	−0.540105	+	0.540105i
$163$	−10.1464	−	10.1464i	−0.0622481	−	0.0622481i	0.675297	−	0.737546i	$-0.264015\pi$
$163$	−10.1464	−	10.1464i	−0.0622481	−	0.0622481i	−0.737546	+	0.675297i	$0.764015\pi$
$164$		−	84.2998i		−	0.514023i
$165$	130.033	−	111.138i	0.788076	−	0.673563i
$166$	0.280210			0.00168801
$167$	−110.018	+	110.018i	−0.658788	+	0.658788i	−0.955093	−	0.296305i	$-0.904245\pi$
$167$	−110.018	+	110.018i	−0.658788	+	0.658788i	0.296305	+	0.955093i	$0.404245\pi$
$168$	17.5837	+	17.5837i	0.104665	+	0.104665i
$169$			273.597i			1.61892i
$170$	88.3982	+	6.92561i	0.519989	+	0.0407389i
$171$	−68.3796			−0.399881
$172$	−104.409	+	104.409i	−0.607028	+	0.607028i
$173$	−186.569	−	186.569i	−1.07844	−	1.07844i	−0.996650	−	0.0817855i	$-0.973938\pi$
$173$	−186.569	−	186.569i	−1.07844	−	1.07844i	−0.0817855	−	0.996650i	$-0.526062\pi$
$174$		−	124.603i		−	0.716107i
$175$	−42.8432	+	31.1737i	−0.244818	+	0.178136i
$176$	−32.9880			−0.187432
$177$	117.864	−	117.864i	0.665897	−	0.665897i
$178$	134.007	+	134.007i	0.752849	+	0.752849i
$179$			115.306i			0.644170i	0.946711	+	0.322085i	$0.104384\pi$
$179$			115.306i			0.644170i	−0.946711	+	0.322085i	$0.895616\pi$
$180$	6.41136	−	81.8344i	0.0356187	−	0.454635i
$181$	−233.419			−1.28961			−0.644803	−	0.764349i	$-0.723061\pi$
$181$	−233.419			−1.28961			−0.644803	+	0.764349i	$0.723061\pi$
$182$	−44.5873	+	44.5873i	−0.244985	+	0.244985i
$183$	26.5815	+	26.5815i	0.145254	+	0.145254i
$184$			13.5647i			0.0737210i
$185$	−87.0133	−	101.807i	−0.470342	−	0.550305i
$186$	223.119			1.19956
$187$	73.1255	−	73.1255i	0.391045	−	0.391045i
$188$	30.1654	+	30.1654i	0.160454	+	0.160454i
$189$		−	6.95862i		−	0.0368181i
$190$	−44.7776	+	38.2711i	−0.235672	+	0.201427i
$191$	−196.087			−1.02664			−0.513318	−	0.858199i	$-0.671584\pi$
$191$	−196.087			−1.02664			−0.513318	+	0.858199i	$0.671584\pi$
$192$	−23.4664	+	23.4664i	−0.122221	+	0.122221i
$193$	−178.951	−	178.951i	−0.927205	−	0.927205i	0.0703198	−	0.997524i	$-0.477598\pi$
$193$	−178.951	−	178.951i	−0.927205	−	0.927205i	−0.997524	+	0.0703198i	$0.977598\pi$
$194$		−	164.012i		−	0.845423i
$195$	435.028	+	34.0825i	2.23091	+	0.174782i
$196$	89.0165			0.454166
$197$	131.643	−	131.643i	0.668240	−	0.668240i	−0.289068	−	0.957308i	$-0.593345\pi$
$197$	131.643	−	131.643i	0.668240	−	0.668240i	0.957308	+	0.289068i	$0.0933455\pi$
$198$	−67.6957	−	67.6957i	−0.341897	−	0.341897i
$199$			11.2591i			0.0565782i	0.999600	+	0.0282891i	$0.00900591\pi$
$199$			11.2591i			0.0565782i	−0.999600	+	0.0282891i	$0.990994\pi$
$200$	−41.6032	−	57.1767i	−0.208016	−	0.285884i
$201$	−50.4941			−0.251215
$202$	−40.5100	+	40.5100i	−0.200544	+	0.200544i
$203$	31.8297	+	31.8297i	0.156797	+	0.156797i
$204$		−	104.037i		−	0.509987i
$205$	16.4609	−	210.106i	0.0802969	−	1.02491i
$206$	43.2344			0.209876
$207$	−27.8364	+	27.8364i	−0.134475	+	0.134475i
$208$	−59.5044	−	59.5044i	−0.286079	−	0.286079i
$209$			68.7003i			0.328709i
$210$	40.3914	+	47.2583i	0.192340	+	0.225040i
$211$	−279.820			−1.32616			−0.663080	−	0.748549i	$-0.730751\pi$
$211$	−279.820			−1.32616			−0.663080	+	0.748549i	$0.730751\pi$
$212$	54.6816	−	54.6816i	0.257932	−	0.257932i
$213$	−365.547	−	365.547i	−1.71618	−	1.71618i
$214$			69.2141i			0.323430i
$215$	−280.612	+	239.837i	−1.30517	+	1.11552i
$216$	9.28668			0.0429939
$217$	−56.9956	+	56.9956i	−0.262653	+	0.262653i
$218$	−34.5054	−	34.5054i	−0.158282	−	0.158282i
$219$		−	577.957i		−	2.63907i
$220$	−82.2181	−	6.44143i	−0.373719	−	0.0292792i
$221$	263.810			1.19371
$222$	−111.113	+	111.113i	−0.500507	+	0.500507i
$223$	213.744	+	213.744i	0.958495	+	0.958495i	0.999172	−	0.0406776i	$-0.0129517\pi$
$223$	213.744	+	213.744i	0.958495	+	0.958495i	−0.0406776	+	0.999172i	$0.512952\pi$
$224$		−	11.9890i		−	0.0535223i
$225$	31.9589	−	202.709i	0.142040	−	0.900929i
$226$	37.8503			0.167479
$227$	84.5320	−	84.5320i	0.372388	−	0.372388i	−0.495959	−	0.868346i	$-0.665183\pi$
$227$	84.5320	−	84.5320i	0.372388	−	0.372388i	0.868346	+	0.495959i	$0.165183\pi$
$228$	48.8707	+	48.8707i	0.214345	+	0.214345i
$229$			146.588i			0.640121i	0.947397	+	0.320060i	$0.103703\pi$
$229$			146.588i			0.640121i	−0.947397	+	0.320060i	$0.896297\pi$
$230$	−2.64871	+	33.8081i	−0.0115161	+	0.146992i
$231$	72.5063			0.313880
$232$	−42.4786	+	42.4786i	−0.183098	+	0.183098i
$233$	−39.9824	−	39.9824i	−0.171598	−	0.171598i	0.616083	−	0.787681i	$-0.288719\pi$
$233$	−39.9824	−	39.9824i	−0.171598	−	0.171598i	−0.787681	+	0.616083i	$0.788719\pi$
$234$		−	244.221i		−	1.04368i
$235$	69.2927	+	81.0733i	0.294863	+	0.344993i
$236$	−80.3625			−0.340519
$237$	−40.0131	+	40.0131i	−0.168832	+	0.168832i
$238$	26.5763	+	26.5763i	0.111665	+	0.111665i
$239$			181.320i			0.758659i	0.925262	+	0.379330i	$0.123845\pi$
$239$			181.320i			0.758659i	−0.925262	+	0.379330i	$0.876155\pi$
$240$	−63.0690	+	53.9046i	−0.262787	+	0.224603i
$241$	193.662			0.803578			0.401789	−	0.915732i	$-0.368389\pi$
$241$	193.662			0.803578			0.401789	+	0.915732i	$0.368389\pi$
$242$	52.9869	−	52.9869i	0.218954	−	0.218954i
$243$	235.760	+	235.760i	0.970205	+	0.970205i
$244$		−	18.1239i		−	0.0742784i
$245$	221.861	+	17.3819i	0.905557	+	0.0709464i
$246$	−247.277			−1.00519
$247$	−123.923	+	123.923i	−0.501712	+	0.501712i
$248$	−76.0640	−	76.0640i	−0.306710	−	0.306710i
$249$		−	0.821942i		−	0.00330097i
$250$	−92.5255	−	150.629i	−0.370102	−	0.602515i
$251$	−390.386			−1.55532			−0.777661	−	0.628684i	$-0.783594\pi$
$251$	−390.386			−1.55532			−0.777661	+	0.628684i	$0.783594\pi$
$252$	24.6029	−	24.6029i	0.0976307	−	0.0976307i
$253$	27.9670	+	27.9670i	0.110541	+	0.110541i
$254$			17.9812i			0.0707920i
$255$	20.3149	−	259.299i	0.0796663	−	1.01686i
$256$	16.0000			0.0625000
$257$	243.584	−	243.584i	0.947799	−	0.947799i	−0.0509047	−	0.998704i	$-0.516210\pi$
$257$	243.584	−	243.584i	0.947799	−	0.947799i	0.998704	+	0.0509047i	$0.0162105\pi$
$258$	306.262	+	306.262i	1.18706	+	1.18706i
$259$		−	56.7674i		−	0.219179i
$260$	−136.687	−	159.926i	−0.525721	−	0.615099i
$261$	−174.343			−0.667981
$262$	−211.736	+	211.736i	−0.808154	+	0.808154i
$263$	207.770	+	207.770i	0.789999	+	0.789999i	0.981494	−	0.191495i	$-0.0613335\pi$
$263$	207.770	+	207.770i	0.789999	+	0.789999i	−0.191495	+	0.981494i	$0.561333\pi$
$264$			96.7638i			0.366530i
$265$	146.964	−	125.609i	0.554581	−	0.473996i
$266$	−24.9680			−0.0938648
$267$	393.083	−	393.083i	1.47222	−	1.47222i
$268$	17.2141	+	17.2141i	0.0642317	+	0.0642317i
$269$			98.1410i			0.364837i	0.983221	+	0.182418i	$0.0583925\pi$
$269$			98.1410i			0.364837i	−0.983221	+	0.182418i	$0.941607\pi$
$270$	23.1458	+	1.81337i	0.0857251	+	0.00671619i
$271$	79.9374			0.294972			0.147486	−	0.989064i	$-0.452882\pi$
$271$	79.9374			0.294972			0.147486	+	0.989064i	$0.452882\pi$
$272$	−35.4676	+	35.4676i	−0.130396	+	0.130396i
$273$	130.788	+	130.788i	0.479077	+	0.479077i
$274$			295.315i			1.07779i
$275$	−203.660	−	32.1088i	−0.740580	−	0.116759i
$276$	39.7892			0.144164
$277$	192.748	−	192.748i	0.695839	−	0.695839i	−0.267671	−	0.963510i	$-0.586254\pi$
$277$	192.748	−	192.748i	0.695839	−	0.695839i	0.963510	+	0.267671i	$0.0862540\pi$
$278$	−71.3041	−	71.3041i	−0.256489	−	0.256489i
$279$		−	312.186i		−	1.11895i
$280$	2.34104	−	29.8809i	0.00836085	−	0.106717i
$281$	−108.185			−0.385002			−0.192501	−	0.981297i	$-0.561660\pi$
$281$	−108.185			−0.385002			−0.192501	+	0.981297i	$0.561660\pi$
$282$	88.4841	−	88.4841i	0.313773	−	0.313773i
$283$	144.938	+	144.938i	0.512149	+	0.512149i	0.915184	−	0.403035i	$-0.132045\pi$
$283$	144.938	+	144.938i	0.512149	+	0.512149i	−0.403035	+	0.915184i	$0.632045\pi$
$284$			249.239i			0.877603i
$285$	112.261	+	131.346i	0.393897	+	0.460864i
$286$	−245.367			−0.857926
$287$	63.1668	−	63.1668i	0.220093	−	0.220093i
$288$	32.8341	+	32.8341i	0.114007	+	0.114007i
$289$			131.756i			0.455903i
$290$	−114.167	+	97.5775i	−0.393678	+	0.336474i
$291$	−481.097			−1.65325
$292$	−197.033	+	197.033i	−0.674770	+	0.674770i
$293$	−284.139	−	284.139i	−0.969758	−	0.969758i	0.0297984	−	0.999556i	$-0.490513\pi$
$293$	−284.139	−	284.139i	−0.969758	−	0.969758i	−0.999556	+	0.0297984i	$0.990513\pi$
$294$		−	261.112i		−	0.888137i
$295$	−200.293	−	15.6920i	−0.678958	−	0.0531934i
$296$	75.7594			0.255944
$297$	19.1468	−	19.1468i	0.0644675	−	0.0644675i
$298$	−210.967	−	210.967i	−0.707944	−	0.707944i
$299$			100.895i			0.337440i
$300$	−167.717	+	122.035i	−0.559055	+	0.406782i
$301$	−156.469			−0.519832
$302$	270.221	−	270.221i	0.894772	−	0.894772i
$303$	118.828	+	118.828i	0.392172	+	0.392172i
$304$		−	33.3213i		−	0.109610i
$305$	3.53898	−	45.1714i	0.0116032	−	0.148103i
$306$	−145.568			−0.475713
$307$	79.7400	−	79.7400i	0.259739	−	0.259739i	−0.565209	−	0.824948i	$-0.691204\pi$
$307$	79.7400	−	79.7400i	0.259739	−	0.259739i	0.824948	+	0.565209i	$0.191204\pi$
$308$	−24.7183	−	24.7183i	−0.0802543	−	0.0802543i
$309$		−	126.819i		−	0.410419i
$310$	−174.726	−	204.432i	−0.563633	−	0.659457i
$311$	−347.931			−1.11875			−0.559374	−	0.828915i	$-0.688958\pi$
$311$	−347.931			−1.11875			−0.559374	+	0.828915i	$0.688958\pi$
$312$	−174.544	+	174.544i	−0.559437	+	0.559437i
$313$	417.790	+	417.790i	1.33479	+	1.33479i	0.901025	+	0.433767i	$0.142816\pi$
$313$	417.790	+	417.790i	1.33479	+	1.33479i	0.433767	+	0.901025i	$0.357184\pi$
$314$		−	132.470i		−	0.421878i
$315$	66.1235	−	56.5153i	0.209916	−	0.179414i
$316$	27.2820			0.0863353
$317$	318.942	−	318.942i	1.00613	−	1.00613i	0.00614481	−	0.999981i	$-0.498044\pi$
$317$	318.942	−	318.942i	1.00613	−	1.00613i	0.999981	−	0.00614481i	$-0.00195597\pi$
$318$	−160.398	−	160.398i	−0.504395	−	0.504395i
$319$			175.161i			0.549093i
$320$	39.8778	+	3.12425i	0.124618	+	0.00976329i
$321$	203.026			0.632479
$322$	−10.1642	+	10.1642i	−0.0315657	+	0.0315657i
$323$	73.8642	+	73.8642i	0.228682	+	0.228682i
$324$		−	174.994i		−	0.540105i
$325$	−309.447	−	425.283i	−0.952143	−	1.30856i
$326$	20.2929			0.0622481
$327$	−101.215	+	101.215i	−0.309525	+	0.309525i
$328$	84.2998	+	84.2998i	0.257012	+	0.257012i
$329$			45.2065i			0.137406i
$330$	−18.8947	+	241.171i	−0.0572565	+	0.730820i
$331$	125.989			0.380632			0.190316	−	0.981723i	$-0.439049\pi$
$331$	125.989			0.380632			0.190316	+	0.981723i	$0.439049\pi$
$332$	−0.280210	+	0.280210i	−0.000844007	+	0.000844007i
$333$	155.468	+	155.468i	0.466871	+	0.466871i
$334$		−	220.035i		−	0.658788i
$335$	39.5424	+	46.2651i	0.118037	+	0.138105i
$336$	−35.1673			−0.104665
$337$	−419.196	+	419.196i	−1.24390	+	1.24390i	−0.285536	+	0.958368i	$0.592172\pi$
$337$	−419.196	+	419.196i	−1.24390	+	1.24390i	−0.958368	+	0.285536i	$0.907828\pi$
$338$	−273.597	−	273.597i	−0.809458	−	0.809458i
$339$		−	111.026i		−	0.327511i
$340$	−95.3238	+	81.4726i	−0.280364	+	0.239625i
$341$	−313.650			−0.919795
$342$	68.3796	−	68.3796i	0.199940	−	0.199940i
$343$	140.134	+	140.134i	0.408553	+	0.408553i
$344$		−	208.817i		−	0.607028i
$345$	99.1692	+	7.76947i	0.287447	+	0.0225202i
$346$	373.139			1.07844
$347$	−364.181	+	364.181i	−1.04951	+	1.04951i	−0.0508046	+	0.998709i	$0.516179\pi$
$347$	−364.181	+	364.181i	−1.04951	+	1.04951i	−0.998709	+	0.0508046i	$0.983821\pi$
$348$	124.603	+	124.603i	0.358053	+	0.358053i
$349$		−	3.69442i		−	0.0105857i	−0.999986	−	0.00529286i	$-0.998315\pi$
$349$		−	3.69442i		−	0.0105857i	0.999986	−	0.00529286i	$-0.00168478\pi$
$350$	11.6694	−	74.0169i	0.0333412	−	0.211477i
$351$	69.0748			0.196794
$352$	32.9880	−	32.9880i	0.0937160	−	0.0937160i
$353$	67.2124	+	67.2124i	0.190403	+	0.190403i	0.795870	−	0.605467i	$-0.207014\pi$
$353$	67.2124	+	67.2124i	0.190403	+	0.190403i	−0.605467	+	0.795870i	$0.707014\pi$
$354$			235.727i			0.665897i
$355$	−48.6679	+	621.194i	−0.137093	+	1.74984i
$356$	−268.014			−0.752849
$357$	77.9563	−	77.9563i	0.218365	−	0.218365i
$358$	−115.306	−	115.306i	−0.322085	−	0.322085i
$359$		−	616.956i		−	1.71854i	−0.511523	−	0.859270i	$-0.670918\pi$
$359$		−	616.956i		−	1.71854i	0.511523	−	0.859270i	$-0.329082\pi$
$360$	75.4230	+	88.2457i	0.209508	+	0.245127i
$361$	291.606			0.807772
$362$	233.419	−	233.419i	0.644803	−	0.644803i
$363$	−155.426	−	155.426i	−0.428172	−	0.428172i
$364$		−	89.1747i		−	0.244985i
$365$	−529.551	+	452.604i	−1.45083	+	1.24001i
$366$	−53.1629			−0.145254
$367$	387.637	−	387.637i	1.05623	−	1.05623i	0.0579085	−	0.998322i	$-0.481557\pi$
$367$	387.637	−	387.637i	1.05623	−	1.05623i	0.998322	−	0.0579085i	$-0.0184432\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$			345.988i			0.937637i
$370$	188.820	+	14.7932i	0.510324	+	0.0399816i
$371$	81.9472			0.220882
$372$	−223.119	+	223.119i	−0.599781	+	0.599781i
$373$	186.795	+	186.795i	0.500792	+	0.500792i	0.911684	−	0.410892i	$-0.134783\pi$
$373$	186.795	+	186.795i	0.500792	+	0.500792i	−0.410892	+	0.911684i	$0.634783\pi$
$374$			146.251i			0.391045i
$375$	−441.840	+	271.405i	−1.17824	+	0.723747i
$376$	−60.3307			−0.160454
$377$	−315.958	+	315.958i	−0.838085	+	0.838085i
$378$	6.95862	+	6.95862i	0.0184090	+	0.0184090i
$379$		−	539.217i		−	1.42274i	−0.702819	−	0.711369i	$-0.748076\pi$
$379$		−	539.217i		−	1.42274i	0.702819	−	0.711369i	$-0.251924\pi$
$380$	6.50651	−	83.0488i	0.0171224	−	0.218549i
$381$	52.7442			0.138436
$382$	196.087	−	196.087i	0.513318	−	0.513318i
$383$	20.4243	+	20.4243i	0.0533271	+	0.0533271i	0.733267	−	0.679940i	$-0.237994\pi$
$383$	20.4243	+	20.4243i	0.0533271	+	0.0533271i	−0.679940	+	0.733267i	$0.737994\pi$
$384$		−	46.9328i		−	0.122221i
$385$	−56.7804	−	66.4336i	−0.147481	−	0.172555i
$386$	357.901			0.927205
$387$	428.520	−	428.520i	1.10729	−	1.10729i
$388$	164.012	+	164.012i	0.422712	+	0.422712i
$389$			706.906i			1.81724i	0.417624	+	0.908620i	$0.362863\pi$
$389$			706.906i			1.81724i	−0.417624	+	0.908620i	$0.637137\pi$
$390$	−469.110	+	400.945i	−1.20285	+	1.02806i
$391$	60.1383			0.153806
$392$	−89.0165	+	89.0165i	−0.227083	+	0.227083i
$393$	621.086	+	621.086i	1.58037	+	1.58037i
$394$			263.287i			0.668240i
$395$	67.9965	+	5.32723i	0.172143	+	0.0134867i
$396$	135.391			0.341897
$397$	427.282	−	427.282i	1.07628	−	1.07628i	0.0794382	−	0.996840i	$-0.474687\pi$
$397$	427.282	−	427.282i	1.07628	−	1.07628i	0.996840	−	0.0794382i	$-0.0253126\pi$
$398$	−11.2591	−	11.2591i	−0.0282891	−	0.0282891i
$399$			73.2388i			0.183556i
$400$	98.7799	+	15.5735i	0.246950	+	0.0389338i
$401$	587.689			1.46556			0.732779	−	0.680467i	$-0.238223\pi$
$401$	587.689			1.46556			0.732779	+	0.680467i	$0.238223\pi$
$402$	50.4941	−	50.4941i	0.125607	−	0.125607i
$403$	−565.768	−	565.768i	−1.40389	−	1.40389i
$404$		−	81.0200i		−	0.200544i
$405$	34.1703	−	436.148i	0.0843711	−	1.07691i
$406$	−63.6594			−0.156797
$407$	156.197	−	156.197i	0.383776	−	0.383776i
$408$	104.037	+	104.037i	0.254993	+	0.254993i
$409$		−	667.696i		−	1.63251i	−0.577694	−	0.816254i	$-0.696047\pi$
$409$		−	667.696i		−	1.63251i	0.577694	−	0.816254i	$-0.303953\pi$
$410$	193.645	+	226.567i	0.472305	+	0.552601i
$411$	866.247			2.10766
$412$	−43.2344	+	43.2344i	−0.104938	+	0.104938i
$413$	−60.2166	−	60.2166i	−0.145803	−	0.145803i
$414$		−	55.6728i		−	0.134475i
$415$	−0.753102	+	0.643671i	−0.00181470	+	0.00155101i
$416$	119.009			0.286079
$417$	−209.156	+	209.156i	−0.501574	+	0.501574i
$418$	−68.7003	−	68.7003i	−0.164355	−	0.164355i
$419$		−	393.072i		−	0.938120i	−0.883166	−	0.469060i	$-0.844593\pi$
$419$		−	393.072i		−	0.938120i	0.883166	−	0.469060i	$-0.155407\pi$
$420$	−87.6497	−	6.86697i	−0.208690	−	0.0163499i
$421$	−67.3773			−0.160041			−0.0800205	−	0.996793i	$-0.525499\pi$
$421$	−67.3773			−0.160041			−0.0800205	+	0.996793i	$0.525499\pi$
$422$	279.820	−	279.820i	0.663080	−	0.663080i
$423$	−123.806	−	123.806i	−0.292686	−	0.292686i
$424$			109.363i			0.257932i
$425$	−253.490	+	184.446i	−0.596448	+	0.433990i
$426$	731.093			1.71618
$427$	13.5805	−	13.5805i	0.0318044	−	0.0318044i
$428$	−69.2141	−	69.2141i	−0.161715	−	0.161715i
$429$			719.734i			1.67770i
$430$	40.7749	−	520.449i	0.0948253	−	1.21035i
$431$	235.521			0.546453			0.273227	−	0.961950i	$-0.411909\pi$
$431$	235.521			0.546453			0.273227	+	0.961950i	$0.411909\pi$
$432$	−9.28668	+	9.28668i	−0.0214969	+	0.0214969i
$433$	391.171	+	391.171i	0.903398	+	0.903398i	0.995728	−	0.0923301i	$-0.0294315\pi$
$433$	391.171	+	391.171i	0.903398	+	0.903398i	−0.0923301	+	0.995728i	$0.529432\pi$
$434$		−	113.991i		−	0.262653i
$435$	286.224	+	334.885i	0.657987	+	0.769852i
$436$	69.0108			0.158282
$437$	−28.2495	+	28.2495i	−0.0646442	+	0.0646442i
$438$	577.957	+	577.957i	1.31954	+	1.31954i
$439$		−	202.665i		−	0.461652i	−0.972995	−	0.230826i	$-0.925857\pi$
$439$		−	202.665i		−	0.461652i	0.972995	−	0.230826i	$-0.0741429\pi$
$440$	88.6596	−	75.7767i	0.201499	−	0.172220i
$441$	−365.347			−0.828450
$442$	−263.810	+	263.810i	−0.596855	+	0.596855i
$443$	456.611	+	456.611i	1.03072	+	1.03072i	0.999513	+	0.0312111i	$0.00993641\pi$
$443$	456.611	+	456.611i	1.03072	+	1.03072i	0.0312111	+	0.999513i	$0.490064\pi$
$444$		−	222.225i		−	0.500507i
$445$	−667.989	−	52.3340i	−1.50110	−	0.117605i
$446$	−427.489			−0.958495
$447$	−618.831	+	618.831i	−1.38441	+	1.38441i
$448$	11.9890	+	11.9890i	0.0267611	+	0.0267611i
$449$			709.974i			1.58123i	0.612312	+	0.790616i	$0.290240\pi$
$449$			709.974i			1.58123i	−0.612312	+	0.790616i	$0.709760\pi$
$450$	170.750	+	234.668i	0.379445	+	0.521484i
$451$	347.611			0.770755
$452$	−37.8503	+	37.8503i	−0.0837396	+	0.0837396i
$453$	−792.640	−	792.640i	−1.74976	−	1.74976i
$454$			169.064i			0.372388i
$455$	17.4128	−	222.256i	0.0382698	−	0.488474i
$456$	−97.7414			−0.214345
$457$	432.714	−	432.714i	0.946859	−	0.946859i	−0.0517988	−	0.998658i	$-0.516495\pi$
$457$	432.714	−	432.714i	0.946859	−	0.946859i	0.998658	+	0.0517988i	$0.0164955\pi$
$458$	−146.588	−	146.588i	−0.320060	−	0.320060i
$459$		−	41.1721i		−	0.0896995i
$460$	−31.1593	−	36.4568i	−0.0677377	−	0.0792538i
$461$	561.628			1.21828			0.609141	−	0.793062i	$-0.291514\pi$
$461$	561.628			1.21828			0.609141	+	0.793062i	$0.291514\pi$
$462$	−72.5063	+	72.5063i	−0.156940	+	0.156940i
$463$	82.5073	+	82.5073i	0.178201	+	0.178201i	0.790571	−	0.612370i	$-0.209784\pi$
$463$	82.5073	+	82.5073i	0.178201	+	0.178201i	−0.612370	+	0.790571i	$0.709784\pi$
$464$		−	84.9572i		−	0.183098i
$465$	−599.660	+	512.525i	−1.28959	+	1.10220i
$466$	79.9648			0.171598
$467$	535.526	−	535.526i	1.14674	−	1.14674i	0.159546	−	0.987190i	$-0.448997\pi$
$467$	535.526	−	535.526i	1.14674	−	1.14674i	0.987190	−	0.159546i	$-0.0510031\pi$
$468$	244.221	+	244.221i	0.521841	+	0.521841i
$469$			25.7974i			0.0550052i
$470$	−150.366	−	11.7805i	−0.319928	−	0.0250649i
$471$	−388.573			−0.824997
$472$	80.3625	−	80.3625i	0.170260	−	0.170260i
$473$	−430.530	−	430.530i	−0.910211	−	0.910211i
$474$		−	80.0262i		−	0.168832i
$475$	32.4331	−	205.717i	0.0682803	−	0.433089i
$476$	−53.1526			−0.111665
$477$	−224.427	+	224.427i	−0.470498	+	0.470498i
$478$	−181.320	−	181.320i	−0.379330	−	0.379330i
$479$			310.478i			0.648180i	0.946026	+	0.324090i	$0.105058\pi$
$479$			310.478i			0.648180i	−0.946026	+	0.324090i	$0.894942\pi$
$480$	9.16437	−	116.974i	0.0190924	−	0.243695i
$481$	563.502			1.17152
$482$	−193.662	+	193.662i	−0.401789	+	0.401789i
$483$	29.8145	+	29.8145i	0.0617278	+	0.0617278i
$484$			105.974i			0.218954i
$485$	376.752	+	440.804i	0.776808	+	0.908873i
$486$	−471.520			−0.970205
$487$	−2.90625	+	2.90625i	−0.00596766	+	0.00596766i	−0.710084	−	0.704117i	$-0.751343\pi$
$487$	−2.90625	+	2.90625i	−0.00596766	+	0.00596766i	0.704117	+	0.710084i	$0.251343\pi$
$488$	18.1239	+	18.1239i	0.0371392	+	0.0371392i
$489$		−	59.5252i		−	0.121728i
$490$	−239.243	+	204.480i	−0.488252	+	0.417305i
$491$	−518.684			−1.05638			−0.528192	−	0.849125i	$-0.677130\pi$
$491$	−518.684			−1.05638			−0.528192	+	0.849125i	$0.677130\pi$
$492$	247.277	−	247.277i	0.502595	−	0.502595i
$493$	188.327	+	188.327i	0.382002	+	0.382002i
$494$		−	247.846i		−	0.501712i
$495$	337.444	+	26.4373i	0.681706	+	0.0534087i
$496$	152.128			0.306710
$497$	−186.758	+	186.758i	−0.375770	+	0.375770i
$498$	0.821942	+	0.821942i	0.00165049	+	0.00165049i
$499$			707.530i			1.41790i	0.705261	+	0.708948i	$0.250830\pi$
$499$			707.530i			1.41790i	−0.705261	+	0.708948i	$0.749170\pi$
$500$	243.154	+	58.1032i	0.486309	+	0.116206i
$501$	−645.429			−1.28828
$502$	390.386	−	390.386i	0.777661	−	0.777661i
$503$	123.616	+	123.616i	0.245758	+	0.245758i	0.819227	−	0.573469i	$-0.194403\pi$
$503$	123.616	+	123.616i	0.245758	+	0.245758i	−0.573469	+	0.819227i	$0.694403\pi$
$504$			49.2059i			0.0976307i
$505$	15.8204	−	201.931i	0.0313276	−	0.399864i
$506$	−55.9339			−0.110541
$507$	−802.542	+	802.542i	−1.58292	+	1.58292i
$508$	−17.9812	−	17.9812i	−0.0353960	−	0.0353960i
$509$		−	453.051i		−	0.890080i	−0.895511	−	0.445040i	$-0.853189\pi$
$509$		−	453.051i		−	0.890080i	0.895511	−	0.445040i	$-0.146811\pi$
$510$	238.984	+	279.613i	0.468595	+	0.548262i
$511$	−295.278			−0.577844
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	19.3403	+	19.3403i	0.0377003	+	0.0377003i
$514$			487.169i			0.947799i
$515$	−116.198	+	99.3136i	−0.225627	+	0.192842i
$516$	−612.525			−1.18706
$517$	−124.387	+	124.387i	−0.240594	+	0.240594i
$518$	56.7674	+	56.7674i	0.109590	+	0.109590i
$519$		−	1094.53i		−	2.10892i
$520$	296.613	+	23.2383i	0.570410	+	0.0446891i
$521$	−157.780			−0.302841			−0.151421	−	0.988469i	$-0.548385\pi$
$521$	−157.780			−0.302841			−0.151421	+	0.988469i	$0.548385\pi$
$522$	174.343	−	174.343i	0.333991	−	0.333991i
$523$	−670.116	−	670.116i	−1.28129	−	1.28129i	−0.939933	−	0.341358i	$-0.889113\pi$
$523$	−670.116	−	670.116i	−1.28129	−	1.28129i	−0.341358	−	0.939933i	$-0.610887\pi$
$524$		−	423.473i		−	0.808154i
$525$	−217.114	−	34.2300i	−0.413550	−	0.0651999i
$526$	−415.539			−0.789999
$527$	−337.226	+	337.226i	−0.639898	+	0.639898i
$528$	−96.7638	−	96.7638i	−0.183265	−	0.183265i
$529$			23.0000i			0.0434783i
$530$	−21.3549	+	272.573i	−0.0402923	+	0.514289i
$531$	329.828			0.621146
$532$	24.9680	−	24.9680i	0.0469324	−	0.0469324i
$533$	627.027	+	627.027i	1.17641	+	1.17641i
$534$			786.167i			1.47222i
$535$	−158.991	−	186.022i	−0.297180	−	0.347704i
$536$	−34.4282			−0.0642317
$537$	−338.228	+	338.228i	−0.629848	+	0.629848i
$538$	−98.1410	−	98.1410i	−0.182418	−	0.182418i
$539$			367.060i			0.681002i
$540$	−24.9591	+	21.3324i	−0.0462206	+	0.0395045i
$541$	132.733			0.245347			0.122673	−	0.992447i	$-0.460853\pi$
$541$	132.733			0.245347			0.122673	+	0.992447i	$0.460853\pi$
$542$	−79.9374	+	79.9374i	−0.147486	+	0.147486i
$543$	−684.687	−	684.687i	−1.26093	−	1.26093i
$544$		−	70.9353i		−	0.130396i
$545$	172.000	+	13.4755i	0.315596	+	0.0247256i
$546$	−261.576			−0.479077
$547$	195.456	−	195.456i	0.357324	−	0.357324i	−0.505501	−	0.862826i	$-0.668692\pi$
$547$	195.456	−	195.456i	0.357324	−	0.357324i	0.862826	+	0.505501i	$0.168692\pi$
$548$	−295.315	−	295.315i	−0.538896	−	0.538896i
$549$			74.3853i			0.135492i
$550$	235.768	−	171.551i	0.428670	−	0.311911i
$551$	−176.930			−0.321108
$552$	−39.7892	+	39.7892i	−0.0720819	+	0.0720819i
$553$	20.4427	+	20.4427i	0.0369669	+	0.0369669i
$554$			385.495i			0.695839i
$555$	43.3929	−	553.865i	0.0781855	−	0.997956i
$556$	142.608			0.256489
$557$	123.892	−	123.892i	0.222428	−	0.222428i	−0.587092	−	0.809520i	$-0.699727\pi$
$557$	123.892	−	123.892i	0.222428	−	0.222428i	0.809520	+	0.587092i	$0.199727\pi$
$558$	312.186	+	312.186i	0.559473	+	0.559473i
$559$		−	1553.20i		−	2.77852i
$560$	27.5399	+	32.2219i	0.0491783	+	0.0575392i
$561$	428.998			0.764702
$562$	108.185	−	108.185i	0.192501	−	0.192501i
$563$	−354.739	−	354.739i	−0.630088	−	0.630088i	0.318002	−	0.948090i	$-0.396988\pi$
$563$	−354.739	−	354.739i	−0.630088	−	0.630088i	−0.948090	+	0.318002i	$0.896988\pi$
$564$			176.968i			0.313773i
$565$	−101.728	+	86.9458i	−0.180049	+	0.153886i
$566$	−289.876			−0.512149
$567$	131.125	−	131.125i	0.231261	−	0.231261i
$568$	−249.239	−	249.239i	−0.438801	−	0.438801i
$569$		−	882.599i		−	1.55114i	−0.631261	−	0.775571i	$-0.717462\pi$
$569$		−	882.599i		−	1.55114i	0.631261	−	0.775571i	$-0.282538\pi$
$570$	−243.607	−	19.0855i	−0.427381	−	0.0334834i
$571$	−833.010			−1.45886			−0.729431	−	0.684054i	$-0.760215\pi$
$571$	−833.010			−1.45886			−0.729431	+	0.684054i	$0.760215\pi$
$572$	245.367	−	245.367i	0.428963	−	0.428963i
$573$	−575.184	−	575.184i	−1.00381	−	1.00381i
$574$			126.334i			0.220093i
$575$	−70.5416	−	96.9478i	−0.122681	−	0.168605i
$576$	−65.6681			−0.114007
$577$	−298.867	+	298.867i	−0.517966	+	0.517966i	−0.916956	−	0.398989i	$-0.869361\pi$
$577$	−298.867	+	298.867i	−0.517966	+	0.517966i	0.398989	+	0.916956i	$0.369361\pi$
$578$	−131.756	−	131.756i	−0.227951	−	0.227951i
$579$		−	1049.83i		−	1.81318i
$580$	16.5892	−	211.744i	0.0286021	−	0.365076i
$581$	−0.419930			−0.000722771
$582$	481.097	−	481.097i	0.826627	−	0.826627i
$583$	225.480	+	225.480i	0.386758	+	0.386758i
$584$		−	394.066i		−	0.674770i
$585$	561.000	+	656.376i	0.958975	+	1.12201i
$586$	568.278			0.969758
$587$	43.0985	−	43.0985i	0.0734217	−	0.0734217i	−0.669442	−	0.742864i	$-0.733467\pi$
$587$	43.0985	−	43.0985i	0.0734217	−	0.0734217i	0.742864	+	0.669442i	$0.233467\pi$
$588$	261.112	+	261.112i	0.444068	+	0.444068i
$589$		−	316.819i		−	0.537893i
$590$	215.985	−	184.600i	0.366076	−	0.312882i
$591$	772.299			1.30677
$592$	−75.7594	+	75.7594i	−0.127972	+	0.127972i
$593$	60.5028	+	60.5028i	0.102028	+	0.102028i	0.756278	−	0.654250i	$-0.227016\pi$
$593$	60.5028	+	60.5028i	0.102028	+	0.102028i	−0.654250	+	0.756278i	$0.727016\pi$
$594$			38.2937i			0.0644675i
$595$	−132.476	−	10.3789i	−0.222648	−	0.0174435i
$596$	421.935			0.707944
$597$	−33.0262	+	33.0262i	−0.0553203	+	0.0553203i
$598$	−100.895	−	100.895i	−0.168720	−	0.168720i
$599$			518.210i			0.865126i	0.901604	+	0.432563i	$0.142391\pi$
$599$			518.210i			0.865126i	−0.901604	+	0.432563i	$0.857609\pi$
$600$	45.6819	−	289.751i	0.0761365	−	0.482919i
$601$	283.917			0.472408			0.236204	−	0.971704i	$-0.424097\pi$
$601$	283.917			0.472408			0.236204	+	0.971704i	$0.424097\pi$
$602$	156.469	−	156.469i	0.259916	−	0.259916i
$603$	−70.6511	−	70.6511i	−0.117166	−	0.117166i
$604$			540.442i			0.894772i
$605$	−20.6930	+	264.125i	−0.0342034	+	0.436570i
$606$	−237.656			−0.392172
$607$	458.034	−	458.034i	0.754587	−	0.754587i	−0.220745	−	0.975332i	$-0.570849\pi$
$607$	458.034	−	458.034i	0.754587	−	0.754587i	0.975332	+	0.220745i	$0.0708488\pi$
$608$	33.3213	+	33.3213i	0.0548048	+	0.0548048i
$609$			186.732i			0.306621i
$610$	41.6324	+	48.7104i	0.0682499	+	0.0798531i
$611$	−448.743			−0.734440
$612$	145.568	−	145.568i	0.237857	−	0.237857i
$613$	−91.5983	−	91.5983i	−0.149426	−	0.149426i	0.628435	−	0.777862i	$-0.283696\pi$
$613$	−91.5983	−	91.5983i	−0.149426	−	0.149426i	−0.777862	+	0.628435i	$0.783696\pi$
$614$			159.480i			0.259739i
$615$	664.588	−	568.019i	1.08063	−	0.923608i
$616$	49.4366			0.0802543
$617$	196.492	−	196.492i	0.318463	−	0.318463i	−0.529714	−	0.848176i	$-0.677701\pi$
$617$	196.492	−	196.492i	0.318463	−	0.318463i	0.848176	+	0.529714i	$0.177701\pi$
$618$	126.819	+	126.819i	0.205210	+	0.205210i
$619$			1132.52i			1.82960i	0.403908	+	0.914800i	$0.367652\pi$
$619$			1132.52i			1.82960i	−0.403908	+	0.914800i	$0.632348\pi$
$620$	379.158	+	29.7054i	0.611545	+	0.0479119i
$621$	15.7463			0.0253564
$622$	347.931	−	347.931i	0.559374	−	0.559374i
$623$	−200.826	−	200.826i	−0.322354	−	0.322354i
$624$		−	349.089i		−	0.559437i
$625$	594.683	+	192.294i	0.951493	+	0.307670i
$626$	−835.580			−1.33479
$627$	−201.519	+	201.519i	−0.321401	+	0.321401i
$628$	132.470	+	132.470i	0.210939	+	0.210939i
$629$		−	335.876i		−	0.533984i
$630$	−9.60822	+	122.639i	−0.0152511	+	0.194665i
$631$	241.839			0.383263			0.191631	−	0.981467i	$-0.438622\pi$
$631$	241.839			0.383263			0.191631	+	0.981467i	$0.438622\pi$
$632$	−27.2820	+	27.2820i	−0.0431676	+	0.0431676i
$633$	−820.795	−	820.795i	−1.29668	−	1.29668i
$634$			637.884i			1.00613i
$635$	−41.3045	−	48.3267i	−0.0650464	−	0.0761050i
$636$	320.795			0.504395
$637$	−662.109	+	662.109i	−1.03942	+	1.03942i
$638$	−175.161	−	175.161i	−0.274547	−	0.274547i
$639$		−	1022.94i		−	1.60085i
$640$	−43.0021	+	36.7536i	−0.0671907	+	0.0574274i
$641$	284.139			0.443275			0.221638	−	0.975129i	$-0.428860\pi$
$641$	284.139			0.443275			0.221638	+	0.975129i	$0.428860\pi$
$642$	−203.026	+	203.026i	−0.316239	+	0.316239i
$643$	851.911	+	851.911i	1.32490	+	1.32490i	0.909755	+	0.415145i	$0.136269\pi$
$643$	851.911	+	851.911i	1.32490	+	1.32490i	0.415145	+	0.909755i	$0.363731\pi$
$644$		−	20.3283i		−	0.0315657i
$645$	−1526.63	−	119.605i	−2.36687	−	0.185434i
$646$	−147.728			−0.228682
$647$	−476.225	+	476.225i	−0.736052	+	0.736052i	−0.971811	−	0.235760i	$-0.924242\pi$
$647$	−476.225	+	476.225i	−0.736052	+	0.736052i	0.235760	+	0.971811i	$0.424242\pi$
$648$	174.994	+	174.994i	0.270052	+	0.270052i
$649$		−	331.375i		−	0.510593i
$650$	734.730	+	115.837i	1.13035	+	0.178210i
$651$	−334.371			−0.513626
$652$	−20.2929	+	20.2929i	−0.0311241	+	0.0311241i
$653$	248.523	+	248.523i	0.380587	+	0.380587i	0.871313	−	0.490727i	$-0.163269\pi$
$653$	248.523	+	248.523i	0.380587	+	0.380587i	−0.490727	+	0.871313i	$0.663269\pi$
$654$		−	202.430i		−	0.309525i
$655$	82.6897	−	1055.45i	0.126244	−	1.61137i
$656$	−168.600			−0.257012
$657$	808.674	−	808.674i	1.23086	−	1.23086i
$658$	−45.2065	−	45.2065i	−0.0687029	−	0.0687029i
$659$			390.353i			0.592341i	0.955135	+	0.296171i	$0.0957097\pi$
$659$			390.353i			0.592341i	−0.955135	+	0.296171i	$0.904290\pi$
$660$	−222.276	−	260.065i	−0.336782	−	0.394038i
$661$	−384.050			−0.581013			−0.290507	−	0.956873i	$-0.593824\pi$
$661$	−384.050			−0.581013			−0.290507	+	0.956873i	$0.593824\pi$
$662$	−125.989	+	125.989i	−0.190316	+	0.190316i
$663$	773.835	+	773.835i	1.16717	+	1.16717i
$664$		−	0.560421i		−	0.000844007i
$665$	67.1048	−	57.3540i	0.100909	−	0.0862466i
$666$	−310.936			−0.466871
$667$	−72.0260	+	72.0260i	−0.107985	+	0.107985i
$668$	220.035	+	220.035i	0.329394	+	0.329394i
$669$			1253.95i			1.87437i
$670$	−85.8075	−	6.72264i	−0.128071	−	0.0100338i
$671$	74.7341			0.111377
$672$	35.1673	−	35.1673i	0.0523323	−	0.0523323i
$673$	220.835	+	220.835i	0.328136	+	0.328136i	0.851877	−	0.523741i	$-0.175464\pi$
$673$	220.835	+	220.835i	0.328136	+	0.328136i	−0.523741	+	0.851877i	$0.675464\pi$
$674$		−	838.392i		−	1.24390i
$675$	−66.3727	+	48.2944i	−0.0983300	+	0.0715473i
$676$	547.194			0.809458
$677$	−485.028	+	485.028i	−0.716437	+	0.716437i	−0.967874	−	0.251437i	$-0.919097\pi$
$677$	−485.028	+	485.028i	−0.716437	+	0.716437i	0.251437	+	0.967874i	$0.419097\pi$
$678$	111.026	+	111.026i	0.163756	+	0.163756i
$679$			245.792i			0.361992i
$680$	13.8512	−	176.796i	0.0203695	−	0.259995i
$681$	495.916			0.728217
$682$	313.650	−	313.650i	0.459898	−	0.459898i
$683$	−565.497	−	565.497i	−0.827960	−	0.827960i	0.159275	−	0.987234i	$-0.449084\pi$
$683$	−565.497	−	565.497i	−0.827960	−	0.827960i	−0.987234	+	0.159275i	$0.949084\pi$
$684$			136.759i			0.199940i
$685$	−678.367	−	793.696i	−0.990316	−	1.15868i
$686$	−280.267			−0.408553
$687$	−429.986	+	429.986i	−0.625889	+	0.625889i
$688$	208.817	+	208.817i	0.303514	+	0.303514i
$689$			813.450i			1.18062i
$690$	−106.939	+	91.3997i	−0.154984	+	0.132463i
$691$	−797.253			−1.15377			−0.576884	−	0.816826i	$-0.695731\pi$
$691$	−797.253			−1.15377			−0.576884	+	0.816826i	$0.695731\pi$
$692$	−373.139	+	373.139i	−0.539218	+	0.539218i
$693$	101.450	+	101.450i	0.146393	+	0.146393i
$694$		−	728.362i		−	1.04951i
$695$	355.431	+	27.8465i	0.511412	+	0.0400669i
$696$	−249.205			−0.358053
$697$	373.739	−	373.739i	0.536212	−	0.536212i
$698$	3.69442	+	3.69442i	0.00529286	+	0.00529286i
$699$		−	234.561i		−	0.335566i
$700$	62.3475	+	85.6863i	0.0890678	+	0.122409i
$701$	−285.085			−0.406684			−0.203342	−	0.979108i	$-0.565180\pi$
$701$	−285.085			−0.406684			−0.203342	+	0.979108i	$0.565180\pi$
$702$	−69.0748	+	69.0748i	−0.0983972	+	0.0983972i
$703$	157.775	+	157.775i	0.224431	+	0.224431i
$704$			65.9761i			0.0937160i
$705$	−34.5558	+	441.069i	−0.0490153	+	0.625629i
$706$	−134.425			−0.190403
$707$	60.7092	−	60.7092i	0.0858687	−	0.0858687i
$708$	−235.727	−	235.727i	−0.332948	−	0.332948i
$709$		−	704.449i		−	0.993581i	−0.867870	−	0.496791i	$-0.834512\pi$
$709$		−	704.449i		−	0.993581i	0.867870	−	0.496791i	$-0.165488\pi$
$710$	−572.526	−	669.862i	−0.806375	−	0.943468i
$711$	−111.972			−0.157485
$712$	268.014	−	268.014i	0.376425	−	0.376425i
$713$	−128.973	−	128.973i	−0.180887	−	0.180887i
$714$			155.913i			0.218365i
$715$	659.454	−	563.631i	0.922314	−	0.788295i
$716$	230.613			0.322085
$717$	−531.865	+	531.865i	−0.741792	+	0.741792i
$718$	616.956	+	616.956i	0.859270	+	0.859270i
$719$			221.172i			0.307610i	0.988101	+	0.153805i	$0.0491528\pi$
$719$			221.172i			0.307610i	−0.988101	+	0.153805i	$0.950847\pi$
$720$	−163.669	−	12.8227i	−0.227318	−	0.0178093i
$721$	−64.7921			−0.0898642
$722$	−291.606	+	291.606i	−0.403886	+	0.403886i
$723$	568.070	+	568.070i	0.785712	+	0.785712i
$724$			466.837i			0.644803i
$725$	82.6928	−	524.504i	0.114059	−	0.723454i
$726$	310.853			0.428172
$727$	−682.913	+	682.913i	−0.939358	+	0.939358i	−0.998264	−	0.0589058i	$-0.981239\pi$
$727$	−682.913	+	682.913i	−0.939358	+	0.939358i	0.0589058	+	0.998264i	$0.481239\pi$
$728$	89.1747	+	89.1747i	0.122493	+	0.122493i
$729$			595.637i			0.817060i
$730$	76.9475	−	982.155i	0.105408	−	1.34542i
$731$	−925.783			−1.26646
$732$	53.1629	−	53.1629i	0.0726270	−	0.0726270i
$733$	771.576	+	771.576i	1.05263	+	1.05263i	0.998536	+	0.0540913i	$0.0172262\pi$
$733$	771.576	+	771.576i	1.05263	+	1.05263i	0.0540913	+	0.998536i	$0.482774\pi$
$734$			775.273i			1.05623i
$735$	599.800	+	701.773i	0.816055	+	0.954793i
$736$	27.1293			0.0368605
$737$	−70.9824	+	70.9824i	−0.0963126	+	0.0963126i
$738$	−345.988	−	345.988i	−0.468819	−	0.468819i
$739$		−	437.300i		−	0.591746i	−0.955227	−	0.295873i	$-0.904389\pi$
$739$		−	437.300i		−	0.591746i	0.955227	−	0.295873i	$-0.0956105\pi$
$740$	−203.613	+	174.027i	−0.275153	+	0.235171i
$741$	−727.006			−0.981114
$742$	−81.9472	+	81.9472i	−0.110441	+	0.110441i
$743$	98.9510	+	98.9510i	0.133178	+	0.133178i	0.770553	−	0.637376i	$-0.219980\pi$
$743$	98.9510	+	98.9510i	0.133178	+	0.133178i	−0.637376	+	0.770553i	$0.719980\pi$
$744$		−	446.237i		−	0.599781i
$745$	1051.61	+	82.3894i	1.41156	+	0.110590i
$746$	−373.591			−0.500792
$747$	1.15006	−	1.15006i	0.00153957	−	0.00153957i
$748$	−146.251	−	146.251i	−0.195523	−	0.195523i
$749$		−	103.726i		−	0.138486i
$750$	170.434	−	713.245i	0.227246	−	0.950993i
$751$	1215.87			1.61900			0.809500	−	0.587120i	$-0.199738\pi$
$751$	1215.87			1.61900			0.809500	+	0.587120i	$0.199738\pi$
$752$	60.3307	−	60.3307i	0.0802270	−	0.0802270i
$753$	−1145.12	−	1145.12i	−1.52074	−	1.52074i
$754$		−	631.916i		−	0.838085i
$755$	−105.530	+	1346.98i	−0.139775	+	1.78408i
$756$	−13.9172			−0.0184090
$757$	−350.412	+	350.412i	−0.462896	+	0.462896i	−0.899604	−	0.436707i	$-0.856145\pi$
$757$	−350.412	+	350.412i	−0.462896	+	0.462896i	0.436707	+	0.899604i	$0.356145\pi$
$758$	539.217	+	539.217i	0.711369	+	0.711369i
$759$			164.071i			0.216167i
$760$	76.5422	+	89.5553i	0.100713	+	0.117836i
$761$	442.067			0.580903			0.290451	−	0.956890i	$-0.406195\pi$
$761$	442.067			0.580903			0.290451	+	0.956890i	$0.406195\pi$
$762$	−52.7442	+	52.7442i	−0.0692181	+	0.0692181i
$763$	51.7106	+	51.7106i	0.0677728	+	0.0677728i
$764$			392.175i			0.513318i
$765$	391.233	−	334.384i	0.511416	−	0.437104i
$766$	−40.8486			−0.0533271
$767$	597.741	−	597.741i	0.779323	−	0.779323i
$768$	46.9328	+	46.9328i	0.0611104	+	0.0611104i
$769$			176.509i			0.229531i	0.993393	+	0.114766i	$0.0366117\pi$
$769$			176.509i			0.229531i	−0.993393	+	0.114766i	$0.963388\pi$
$770$	123.214	+	9.65328i	0.160018	+	0.0125367i
$771$	1429.01			1.85345
$772$	−357.901	+	357.901i	−0.463602	+	0.463602i
$773$	−687.163	−	687.163i	−0.888956	−	0.888956i	0.105467	−	0.994423i	$-0.466366\pi$
$773$	−687.163	−	687.163i	−0.888956	−	0.888956i	−0.994423	+	0.105467i	$0.966366\pi$
$774$			857.040i			1.10729i
$775$	939.199	+	148.073i	1.21187	+	0.191062i
$776$	−328.024			−0.422712
$777$	166.516	−	166.516i	0.214306	−	0.214306i
$778$	−706.906	−	706.906i	−0.908620	−	0.908620i
$779$			351.122i			0.450735i
$780$	68.1651	−	870.056i	0.0873911	−	1.11546i
$781$	−1027.74			−1.31593
$782$	−60.1383	+	60.1383i	−0.0769032	+	0.0769032i
$783$	49.3107	+	49.3107i	0.0629766	+	0.0629766i
$784$		−	178.033i		−	0.227083i
$785$	304.296	+	356.029i	0.387638	+	0.453540i
$786$	−1242.17			−1.58037
$787$	−988.378	+	988.378i	−1.25588	+	1.25588i	−0.302839	+	0.953042i	$0.597935\pi$
$787$	−988.378	+	988.378i	−1.25588	+	1.25588i	−0.953042	+	0.302839i	$0.902065\pi$
$788$	−263.287	−	263.287i	−0.334120	−	0.334120i
$789$			1218.90i			1.54487i
$790$	−73.3237	+	62.6693i	−0.0928149	+	0.0793282i
$791$	−56.7233			−0.0717109
$792$	−135.391	+	135.391i	−0.170949	+	0.170949i
$793$	134.807	+	134.807i	0.169996	+	0.169996i
$794$			854.565i			1.07628i
$795$	799.539	+	62.6404i	1.00571	+	0.0787929i
$796$	22.5181			0.0282891
$797$	546.758	−	546.758i	0.686020	−	0.686020i	−0.275330	−	0.961350i	$-0.588787\pi$
$797$	546.758	−	546.758i	0.686020	−	0.686020i	0.961350	+	0.275330i	$0.0887870\pi$
$798$	−73.2388	−	73.2388i	−0.0917779	−	0.0917779i
$799$			267.473i			0.334760i
$800$	−114.353	+	83.2063i	−0.142942	+	0.104008i
$801$	1100.00			1.37328
$802$	−587.689	+	587.689i	−0.732779	+	0.732779i
$803$	−812.466	−	812.466i	−1.01179	−	1.01179i
$804$			100.988i			0.125607i
$805$	3.96942	−	50.6655i	0.00493096	−	0.0629385i
$806$	1131.54			1.40389
$807$	−287.877	+	287.877i	−0.356725	+	0.356725i
$808$	81.0200	+	81.0200i	0.100272	+	0.100272i
$809$			507.535i			0.627361i	0.949529	+	0.313680i	$0.101562\pi$
$809$			507.535i			0.627361i	−0.949529	+	0.313680i	$0.898438\pi$
$810$	401.978	+	470.318i	0.496269	+	0.580640i
$811$	425.796			0.525026			0.262513	−	0.964929i	$-0.415449\pi$
$811$	425.796			0.525026			0.262513	+	0.964929i	$0.415449\pi$
$812$	63.6594	−	63.6594i	0.0783983	−	0.0783983i
$813$	234.481	+	234.481i	0.288414	+	0.288414i
$814$			312.394i			0.383776i
$815$	−54.5398	+	46.6147i	−0.0669199	+	0.0571960i
$816$	−208.075			−0.254993
$817$	434.879	−	434.879i	0.532288	−	0.532288i
$818$	667.696	+	667.696i	0.816254	+	0.816254i
$819$			365.996i			0.446881i
$820$	−420.211	−	32.9217i	−0.512453	−	0.0401485i
$821$	699.302			0.851768			0.425884	−	0.904778i	$-0.359963\pi$
$821$	699.302			0.851768			0.425884	+	0.904778i	$0.359963\pi$
$822$	−866.247	+	866.247i	−1.05383	+	1.05383i
$823$	1034.27	+	1034.27i	1.25671	+	1.25671i	0.952656	+	0.304049i	$0.0983386\pi$
$823$	1034.27	+	1034.27i	1.25671	+	1.25671i	0.304049	+	0.952656i	$0.401661\pi$
$824$		−	86.4688i		−	0.104938i
$825$	−503.210	−	691.580i	−0.609952	−	0.838278i
$826$	120.433			0.145803
$827$	1036.48	−	1036.48i	1.25330	−	1.25330i	0.299071	−	0.954231i	$-0.403323\pi$
$827$	1036.48	−	1036.48i	1.25330	−	1.25330i	0.954231	−	0.299071i	$-0.0966766\pi$
$828$	55.6728	+	55.6728i	0.0672377	+	0.0672377i
$829$		−	253.518i		−	0.305811i	−0.988241	−	0.152906i	$-0.951137\pi$
$829$		−	253.518i		−	0.305811i	0.988241	−	0.152906i	$-0.0488631\pi$
$830$	0.109431	−	1.39677i	0.000131845	−	0.00168286i
$831$	1130.77			1.36074
$832$	−119.009	+	119.009i	−0.143039	+	0.143039i
$833$	394.651	+	394.651i	0.473770	+	0.473770i
$834$		−	418.313i		−	0.501574i
$835$	505.442	+	591.373i	0.605320	+	0.708231i
$836$	137.401			0.164355
$837$	−88.2977	+	88.2977i	−0.105493	+	0.105493i
$838$	393.072	+	393.072i	0.469060	+	0.469060i
$839$			803.555i			0.957754i	0.877882	+	0.478877i	$0.158956\pi$
$839$			803.555i			0.957754i	−0.877882	+	0.478877i	$0.841044\pi$
$840$	94.5166	−	80.7827i	0.112520	−	0.0961699i
$841$	389.892			0.463605
$842$	67.3773	−	67.3773i	0.0800205	−	0.0800205i
$843$	−317.341	−	317.341i	−0.376442	−	0.376442i
$844$			559.639i			0.663080i
$845$	1363.81	+	106.848i	1.61397	+	0.126448i
$846$	247.613			0.292686
$847$	−79.4073	+	79.4073i	−0.0937513	+	0.0937513i
$848$	−109.363	−	109.363i	−0.128966	−	0.128966i
$849$			850.295i			1.00152i
$850$	69.0446	−	437.936i	0.0812289	−	0.515219i
$851$	128.456			0.150947
$852$	−731.093	+	731.093i	−0.858091	+	0.858091i
$853$	−217.664	−	217.664i	−0.255175	−	0.255175i	0.567914	−	0.823088i	$-0.307751\pi$
$853$	−217.664	−	217.664i	−0.255175	−	0.255175i	−0.823088	+	0.567914i	$0.807751\pi$
$854$			27.1609i			0.0318044i
$855$	−26.7044	+	340.853i	−0.0312332	+	0.398659i
$856$	138.428			0.161715
$857$	931.024	−	931.024i	1.08638	−	1.08638i	0.0904773	−	0.995899i	$-0.471161\pi$
$857$	931.024	−	931.024i	1.08638	−	1.08638i	0.995899	−	0.0904773i	$-0.0288392\pi$
$858$	−719.734	−	719.734i	−0.838851	−	0.838851i
$859$		−	197.133i		−	0.229492i	−0.993395	−	0.114746i	$-0.963395\pi$
$859$		−	197.133i		−	0.229492i	0.993395	−	0.114746i	$-0.0366054\pi$
$860$	479.674	+	561.224i	0.557760	+	0.652586i
$861$	370.575			0.430400
$862$	−235.521	+	235.521i	−0.273227	+	0.273227i
$863$	−584.780	−	584.780i	−0.677613	−	0.677613i	0.281846	−	0.959460i	$-0.409053\pi$
$863$	−584.780	−	584.780i	−0.677613	−	0.677613i	−0.959460	+	0.281846i	$0.909053\pi$
$864$		−	18.5734i		−	0.0214969i
$865$	−1002.86	+	857.136i	−1.15937	+	0.990908i
$866$	−782.343			−0.903398
$867$	−386.480	+	386.480i	−0.445767	+	0.445767i
$868$	113.991	+	113.991i	0.131326	+	0.131326i
$869$			112.497i			0.129456i
$870$	−621.110	−	48.6612i	−0.713919	−	0.0559324i
$871$	−256.079			−0.294005
$872$	−69.0108	+	69.0108i	−0.0791409	+	0.0791409i
$873$	−673.148	−	673.148i	−0.771074	−	0.771074i
$874$		−	56.4990i		−	0.0646442i
$875$	138.661	+	225.736i	0.158470	+	0.257984i
$876$	−1155.91			−1.31954
$877$	429.031	−	429.031i	0.489203	−	0.489203i	−0.418852	−	0.908055i	$-0.637567\pi$
$877$	429.031	−	429.031i	0.489203	−	0.489203i	0.908055	+	0.418852i	$0.137567\pi$
$878$	202.665	+	202.665i	0.230826	+	0.230826i
$879$		−	1666.93i		−	1.89639i
$880$	−12.8829	+	164.436i	−0.0146396	+	0.186859i
$881$	651.488			0.739487			0.369743	−	0.929134i	$-0.379446\pi$
$881$	651.488			0.739487			0.369743	+	0.929134i	$0.379446\pi$
$882$	365.347	−	365.347i	0.414225	−	0.414225i
$883$	−1003.05	−	1003.05i	−1.13596	−	1.13596i	−0.989167	−	0.146793i	$-0.953105\pi$
$883$	−1003.05	−	1003.05i	−1.13596	−	1.13596i	−0.146793	−	0.989167i	$-0.546895\pi$
$884$		−	527.620i		−	0.596855i
$885$	−541.489	−	633.548i	−0.611852	−	0.715873i
$886$	−913.221			−1.03072
$887$	−615.433	+	615.433i	−0.693836	+	0.693836i	−0.963074	−	0.269237i	$-0.913228\pi$
$887$	−615.433	+	615.433i	−0.693836	+	0.693836i	0.269237	+	0.963074i	$0.413228\pi$
$888$	222.225	+	222.225i	0.250253	+	0.250253i
$889$		−	26.9470i		−	0.0303116i
$890$	720.323	−	615.655i	0.809352	−	0.691747i
$891$	721.588			0.809863
$892$	427.489	−	427.489i	0.479247	−	0.479247i
$893$	−125.644	−	125.644i	−0.140698	−	0.140698i
$894$		−	1237.66i		−	1.38441i
$895$	574.771	+	45.0308i	0.642202	+	0.0503137i
$896$	−23.9780			−0.0267611
$897$	−295.954	+	295.954i	−0.329938	+	0.329938i
$898$	−709.974	−	709.974i	−0.790616	−	0.790616i
$899$		−	807.773i		−	0.898524i
$900$	−405.418	−	63.9178i	−0.450464	−	0.0710198i
$901$	484.857			0.538132
$902$	−347.611	+	347.611i	−0.385378	+	0.385378i
$903$	−458.972	−	458.972i	−0.508274	−	0.508274i
$904$		−	75.7006i		−	0.0837396i
$905$	−91.1573	+	1163.53i	−0.100726	+	1.28567i
$906$	1585.28			1.74976
$907$	342.093	−	342.093i	0.377170	−	0.377170i	−0.492910	−	0.870080i	$-0.664067\pi$
$907$	342.093	−	342.093i	0.377170	−	0.377170i	0.870080	+	0.492910i	$0.164067\pi$
$908$	−169.064	−	169.064i	−0.186194	−	0.186194i
$909$			332.527i			0.365816i
$910$	204.843	+	239.668i	0.225102	+	0.263372i
$911$	−191.082			−0.209749			−0.104875	−	0.994485i	$-0.533444\pi$
$911$	−191.082			−0.209749			−0.104875	+	0.994485i	$0.533444\pi$
$912$	97.7414	−	97.7414i	0.107173	−	0.107173i
$913$	−1.15545	−	1.15545i	−0.00126555	−	0.00126555i
$914$			865.429i			0.946859i
$915$	142.882	−	122.120i	0.156155	−	0.133465i
$916$	293.175			0.320060
$917$	317.313	−	317.313i	0.346034	−	0.346034i
$918$	41.1721	+	41.1721i	0.0448498	+	0.0448498i
$919$		−	801.645i		−	0.872301i	−0.899874	−	0.436151i	$-0.856341\pi$
$919$		−	801.645i		−	0.872301i	0.899874	−	0.436151i	$-0.143659\pi$
$920$	67.6161	+	5.29743i	0.0734958	+	0.00575807i
$921$	467.803			0.507929
$922$	−561.628	+	561.628i	−0.609141	+	0.609141i
$923$	−1853.85	−	1853.85i	−2.00851	−	2.00851i
$924$		−	145.013i		−	0.156940i
$925$	−541.459	+	393.979i	−0.585361	+	0.425923i
$926$	−165.015			−0.178201
$927$	177.445	−	177.445i	0.191419	−	0.191419i
$928$	84.9572	+	84.9572i	0.0915488	+	0.0915488i
$929$			1361.18i			1.46521i	0.680655	+	0.732604i	$0.261695\pi$
$929$			1361.18i			1.46521i	−0.680655	+	0.732604i	$0.738305\pi$
$930$	87.1348	−	1112.18i	0.0936933	−	1.19590i
$931$	−370.768			−0.398247
$932$	−79.9648	+	79.9648i	−0.0857992	+	0.0857992i
$933$	−1020.59	−	1020.59i	−1.09388	−	1.09388i
$934$			1071.05i			1.14674i
$935$	−335.953	−	393.068i	−0.359308	−	0.420394i
$936$	−488.443			−0.521841
$937$	177.056	−	177.056i	0.188960	−	0.188960i	−0.606286	−	0.795247i	$-0.707341\pi$
$937$	177.056	−	177.056i	0.188960	−	0.188960i	0.795247	+	0.606286i	$0.207341\pi$
$938$	−25.7974	−	25.7974i	−0.0275026	−	0.0275026i
$939$			2451.01i			2.61023i
$940$	162.147	−	138.585i	0.172496	−	0.147431i
$941$	657.970			0.699224			0.349612	−	0.936895i	$-0.386313\pi$
$941$	657.970			0.699224			0.349612	+	0.936895i	$0.386313\pi$
$942$	388.573	−	388.573i	0.412498	−	0.412498i
$943$	142.937	+	142.937i	0.151577	+	0.151577i
$944$			160.725i			0.170260i
$945$	−34.6868	−	2.71756i	−0.0367056	−	0.00287572i
$946$	861.060			0.910211
$947$	−427.809	+	427.809i	−0.451752	+	0.451752i	−0.895936	−	0.444183i	$-0.853494\pi$
$947$	−427.809	+	427.809i	−0.451752	+	0.451752i	0.444183	+	0.895936i	$0.353494\pi$
$948$	80.0262	+	80.0262i	0.0844158	+	0.0844158i
$949$		−	2931.08i		−	3.08860i
$950$	173.284	+	238.150i	0.182404	+	0.250684i
$951$	1871.11			1.96751
$952$	53.1526	−	53.1526i	0.0558326	−	0.0558326i
$953$	−383.309	−	383.309i	−0.402213	−	0.402213i	0.476799	−	0.879012i	$-0.341797\pi$
$953$	−383.309	−	383.309i	−0.402213	−	0.402213i	−0.879012	+	0.476799i	$0.841797\pi$
$954$		−	448.855i		−	0.470498i
$955$	−76.5783	+	977.442i	−0.0801867	+	1.02350i
$956$	362.639			0.379330
$957$	−513.799	+	513.799i	−0.536885	+	0.536885i
$958$	−310.478	−	310.478i	−0.324090	−	0.324090i
$959$		−	442.565i		−	0.461486i
$960$	107.809	+	126.138i	0.112301	+	0.131394i
$961$	485.432			0.505132
$962$	−563.502	+	563.502i	−0.585761	+	0.585761i
$963$	284.072	+	284.072i	0.294987	+	0.294987i
$964$		−	387.324i		−	0.401789i
$965$	−961.905	+	822.133i	−0.996793	+	0.851952i
$966$	−59.6291			−0.0617278
$967$	1075.83	−	1075.83i	1.11255	−	1.11255i	0.119742	−	0.992805i	$-0.461793\pi$
$967$	1075.83	−	1075.83i	1.11255	−	1.11255i	0.992805	−	0.119742i	$-0.0382068\pi$
$968$	−105.974	−	105.974i	−0.109477	−	0.109477i
$969$			433.332i			0.447195i
$970$	−817.555	−	64.0519i	−0.842841	−	0.0660329i
$971$	−1782.45			−1.83568			−0.917840	−	0.396951i	$-0.870068\pi$
$971$	−1782.45			−1.83568			−0.917840	+	0.396951i	$0.870068\pi$
$972$	471.520	−	471.520i	0.485103	−	0.485103i
$973$	106.858	+	106.858i	0.109823	+	0.109823i
$974$		−	5.81250i		−	0.00596766i
$975$	339.784	−	2155.18i	0.348497	−	2.21045i
$976$	−36.2479			−0.0371392
$977$	702.040	−	702.040i	0.718567	−	0.718567i	−0.249744	−	0.968312i	$-0.580347\pi$
$977$	702.040	−	702.040i	0.718567	−	0.718567i	0.968312	+	0.249744i	$0.0803466\pi$
$978$	59.5252	+	59.5252i	0.0608642	+	0.0608642i
$979$		−	1105.16i		−	1.12886i
$980$	34.7637	−	443.723i	0.0354732	−	0.452778i
$981$	−283.238			−0.288724
$982$	518.684	−	518.684i	0.528192	−	0.528192i
$983$	1002.66	+	1002.66i	1.02000	+	1.02000i	0.999796	+	0.0202076i	$0.00643270\pi$
$983$	1002.66	+	1002.66i	1.02000	+	1.02000i	0.0202076	+	0.999796i	$0.493567\pi$
$984$			494.554i			0.502595i
$985$	−604.795	−	707.617i	−0.614005	−	0.718393i
$986$	−376.654			−0.382002
$987$	−132.604	+	132.604i	−0.134351	+	0.134351i
$988$	247.846	+	247.846i	0.250856	+	0.250856i
$989$		−	354.067i		−	0.358005i
$990$	−363.882	+	311.007i	−0.367557	+	0.314149i
$991$	190.889			0.192622			0.0963111	−	0.995351i	$-0.469296\pi$
$991$	190.889			0.192622			0.0963111	+	0.995351i	$0.469296\pi$
$992$	−152.128	+	152.128i	−0.153355	+	0.153355i
$993$	369.565	+	369.565i	0.372170	+	0.372170i
$994$		−	373.515i		−	0.375770i
$995$	56.1234	+	4.39702i	0.0564054	+	0.00441912i
$996$	−1.64388			−0.00165049
$997$	−1085.66	+	1085.66i	−1.08893	+	1.08893i	−0.0932882	+	0.995639i	$0.529738\pi$
$997$	−1085.66	+	1085.66i	−1.08893	+	1.08893i	−0.995639	+	0.0932882i	$0.970262\pi$
$998$	−707.530	−	707.530i	−0.708948	−	0.708948i
$999$		−	87.9441i		−	0.0880322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.a.93.10	yes	20
5.2	odd	4	inner	230.3.f.a.47.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.a.47.10	✓	20	5.2	odd	4	inner
230.3.f.a.93.10	yes	20	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(2.93330 + 2.93330i) q^{3} -2.00000i q^{4} +(0.390531 - 4.98473i) q^{5} -5.86660 q^{6} +(1.49862 - 1.49862i) q^{7} +(2.00000 + 2.00000i) q^{8} +8.20851i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(2.93330 + 2.93330i) q^{3} -2.00000i q^{4} +(0.390531 - 4.98473i) q^{5} -5.86660 q^{6} +(1.49862 - 1.49862i) q^{7} +(2.00000 + 2.00000i) q^{8} +8.20851i q^{9} +(4.59419 + 5.37526i) q^{10} +8.24701 q^{11} +(5.86660 - 5.86660i) q^{12} +(14.8761 + 14.8761i) q^{13} +2.99725i q^{14} +(15.7672 - 13.4762i) q^{15} -4.00000 q^{16} +(8.86691 - 8.86691i) q^{17} +(-8.20851 - 8.20851i) q^{18} +8.33032i q^{19} +(-9.96945 - 0.781063i) q^{20} +8.79183 q^{21} +(-8.24701 + 8.24701i) q^{22} +(3.39116 + 3.39116i) q^{23} +11.7332i q^{24} +(-24.6950 - 3.89338i) q^{25} -29.7522 q^{26} +(2.32167 - 2.32167i) q^{27} +(-2.99725 - 2.99725i) q^{28} +21.2393i q^{29} +(-2.29109 + 29.2434i) q^{30} -38.0320 q^{31} +(4.00000 - 4.00000i) q^{32} +(24.1910 + 24.1910i) q^{33} +17.7338i q^{34} +(-6.88496 - 8.05548i) q^{35} +16.4170 q^{36} +(18.9398 - 18.9398i) q^{37} +(-8.33032 - 8.33032i) q^{38} +87.2722i q^{39} +(10.7505 - 9.18839i) q^{40} +42.1499 q^{41} +(-8.79183 + 8.79183i) q^{42} +(-52.2044 - 52.2044i) q^{43} -16.4940i q^{44} +(40.9172 + 3.20568i) q^{45} -6.78233 q^{46} +(-15.0827 + 15.0827i) q^{47} +(-11.7332 - 11.7332i) q^{48} +44.5083i q^{49} +(28.5884 - 20.8016i) q^{50} +52.0186 q^{51} +(29.7522 - 29.7522i) q^{52} +(27.3408 + 27.3408i) q^{53} +4.64334i q^{54} +(3.22072 - 41.1091i) q^{55} +5.99449 q^{56} +(-24.4354 + 24.4354i) q^{57} +(-21.2393 - 21.2393i) q^{58} -40.1813i q^{59} +(-26.9523 - 31.5345i) q^{60} +9.06197 q^{61} +(38.0320 - 38.0320i) q^{62} +(12.3015 + 12.3015i) q^{63} +8.00000i q^{64} +(79.9629 - 68.3437i) q^{65} -48.3819 q^{66} +(-8.60705 + 8.60705i) q^{67} +(-17.7338 - 17.7338i) q^{68} +19.8946i q^{69} +(14.9404 + 1.17052i) q^{70} -124.620 q^{71} +(-16.4170 + 16.4170i) q^{72} +(-98.5165 - 98.5165i) q^{73} +37.8797i q^{74} +(-61.0173 - 83.8583i) q^{75} +16.6606 q^{76} +(12.3592 - 12.3592i) q^{77} +(-87.2722 - 87.2722i) q^{78} +13.6410i q^{79} +(-1.56213 + 19.9389i) q^{80} +87.4969 q^{81} +(-42.1499 + 42.1499i) q^{82} +(-0.140105 - 0.140105i) q^{83} -17.5837i q^{84} +(-40.7363 - 47.6619i) q^{85} +104.409 q^{86} +(-62.3013 + 62.3013i) q^{87} +(16.4940 + 16.4940i) q^{88} -134.007i q^{89} +(-44.1229 + 37.7115i) q^{90} +44.5873 q^{91} +(6.78233 - 6.78233i) q^{92} +(-111.559 - 111.559i) q^{93} -30.1654i q^{94} +(41.5244 + 3.25325i) q^{95} +23.4664 q^{96} +(-82.0061 + 82.0061i) q^{97} +(-44.5083 - 44.5083i) q^{98} +67.6957i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8	\( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^5 + 8 * q^7 + 40 * q^8 + 4 * q^10 + 56 * q^11 - 4 * q^13 - 48 * q^15 - 80 * q^16 - 72 * q^17 - 28 * q^18 - 16 * q^20 + 8 * q^21 - 56 * q^22 + 36 * q^25 + 8 * q^26 + 156 * q^27 - 16 * q^28 + 84 * q^30 - 212 * q^31 + 80 * q^32 - 100 * q^33 + 56 * q^36 + 72 * q^37 + 88 * q^38 + 24 * q^40 - 12 * q^41 - 8 * q^42 + 120 * q^43 - 32 * q^45 + 8 * q^47 - 28 * q^50 + 64 * q^51 - 8 * q^52 - 244 * q^53 + 68 * q^55 + 32 * q^56 - 384 * q^57 - 188 * q^58 - 72 * q^60 + 328 * q^61 + 212 * q^62 + 172 * q^63 + 20 * q^65 + 200 * q^66 + 56 * q^67 + 144 * q^68 - 28 * q^70 - 92 * q^71 - 56 * q^72 + 144 * q^73 - 124 * q^75 - 176 * q^76 + 292 * q^77 - 208 * q^78 - 16 * q^80 - 84 * q^81 + 12 * q^82 - 72 * q^83 - 20 * q^85 - 240 * q^86 - 208 * q^87 + 112 * q^88 - 56 * q^90 - 192 * q^91 + 256 * q^93 - 96 * q^95 - 276 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more