LMFDB - Embedded newform 230.5.f.b.47.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,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, 5, names="a")

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
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:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.15
Character	$\chi$	$=$	230.47
Dual form			230.5.f.b.93.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +(4.87410 - 4.87410i) q^{3} +8.00000i q^{4} +(23.2684 - 9.14227i) q^{5} +19.4964 q^{6} +(49.4466 + 49.4466i) q^{7} +(-16.0000 + 16.0000i) q^{8} +33.4862i q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +(4.87410 - 4.87410i) q^{3} +8.00000i q^{4} +(23.2684 - 9.14227i) q^{5} +19.4964 q^{6} +(49.4466 + 49.4466i) q^{7} +(-16.0000 + 16.0000i) q^{8} +33.4862i q^{9} +(64.8214 + 28.2523i) q^{10} +66.9800 q^{11} +(38.9928 + 38.9928i) q^{12} +(-133.414 + 133.414i) q^{13} +197.786i q^{14} +(68.8523 - 157.973i) q^{15} -64.0000 q^{16} +(-145.140 - 145.140i) q^{17} +(-66.9724 + 66.9724i) q^{18} -23.8070i q^{19} +(73.1382 + 186.147i) q^{20} +482.016 q^{21} +(133.960 + 133.960i) q^{22} +(77.9968 - 77.9968i) q^{23} +155.971i q^{24} +(457.838 - 425.452i) q^{25} -533.657 q^{26} +(558.018 + 558.018i) q^{27} +(-395.573 + 395.573i) q^{28} +573.299i q^{29} +(453.651 - 178.242i) q^{30} +244.920 q^{31} +(-128.000 - 128.000i) q^{32} +(326.468 - 326.468i) q^{33} -580.562i q^{34} +(1602.60 + 698.489i) q^{35} -267.890 q^{36} +(-836.705 - 836.705i) q^{37} +(47.6140 - 47.6140i) q^{38} +1300.55i q^{39} +(-226.018 + 518.571i) q^{40} +653.194 q^{41} +(964.031 + 964.031i) q^{42} +(1231.32 - 1231.32i) q^{43} +535.840i q^{44} +(306.140 + 779.171i) q^{45} +311.987 q^{46} +(1571.80 + 1571.80i) q^{47} +(-311.943 + 311.943i) q^{48} +2488.93i q^{49} +(1766.58 + 64.7706i) q^{50} -1414.86 q^{51} +(-1067.31 - 1067.31i) q^{52} +(122.980 - 122.980i) q^{53} +2232.07i q^{54} +(1558.52 - 612.350i) q^{55} -1582.29 q^{56} +(-116.038 - 116.038i) q^{57} +(-1146.60 + 1146.60i) q^{58} -4092.49i q^{59} +(1263.78 + 550.818i) q^{60} -4255.58 q^{61} +(489.840 + 489.840i) q^{62} +(-1655.78 + 1655.78i) q^{63} -512.000i q^{64} +(-1884.63 + 4324.04i) q^{65} +1305.87 q^{66} +(-381.044 - 381.044i) q^{67} +(1161.12 - 1161.12i) q^{68} -760.329i q^{69} +(1808.22 + 4602.17i) q^{70} -216.589 q^{71} +(-535.779 - 535.779i) q^{72} +(6025.51 - 6025.51i) q^{73} -3346.82i q^{74} +(157.849 - 4305.25i) q^{75} +190.456 q^{76} +(3311.93 + 3311.93i) q^{77} +(-2601.10 + 2601.10i) q^{78} -9030.79i q^{79} +(-1489.18 + 585.106i) q^{80} +2727.29 q^{81} +(1306.39 + 1306.39i) q^{82} +(-5707.79 + 5707.79i) q^{83} +3856.12i q^{84} +(-4704.10 - 2050.27i) q^{85} +4925.26 q^{86} +(2794.32 + 2794.32i) q^{87} +(-1071.68 + 1071.68i) q^{88} +7873.14i q^{89} +(-946.061 + 2170.62i) q^{90} -13193.7 q^{91} +(623.974 + 623.974i) q^{92} +(1193.77 - 1193.77i) q^{93} +6287.18i q^{94} +(-217.650 - 553.951i) q^{95} -1247.77 q^{96} +(2815.53 + 2815.53i) q^{97} +(-4977.85 + 4977.85i) q^{98} +2242.91i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8}+O(q^{10}) $ 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8	$ 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8} - 136 q^{10} - 632 q^{11} + 500 q^{13} + 12 q^{15} - 2816 q^{16} + 120 q^{17} + 2648 q^{18} - 736 q^{20} - 856 q^{21} - 1264 q^{22} + 2052 q^{25} + 2000 q^{26} + 588 q^{27} + 640 q^{28} - 1704 q^{30} + 3220 q^{31} - 5632 q^{32} - 2884 q^{33} + 720 q^{35} + 10592 q^{36} + 1856 q^{37} - 1696 q^{38} - 1856 q^{40} - 5156 q^{41} - 1712 q^{42} + 960 q^{43} + 460 q^{45} - 1224 q^{47} + 4456 q^{50} + 3640 q^{51} + 4000 q^{52} + 13556 q^{53} + 12980 q^{55} + 2560 q^{56} - 3072 q^{57} - 3112 q^{58} - 6912 q^{60} - 4864 q^{61} + 6440 q^{62} - 13484 q^{63} - 4100 q^{65} - 11536 q^{66} - 1888 q^{67} - 960 q^{68} + 8824 q^{70} - 1060 q^{71} + 21184 q^{72} + 16616 q^{73} - 11044 q^{75} - 6784 q^{76} + 8892 q^{77} - 23152 q^{78} - 1536 q^{80} - 4044 q^{81} - 10312 q^{82} - 27024 q^{83} - 11068 q^{85} + 3840 q^{86} - 8392 q^{87} + 10112 q^{88} - 7184 q^{90} - 54024 q^{91} + 22528 q^{93} - 25968 q^{95} - 3252 q^{97} - 27984 q^{98}+O(q^{100}) $ 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8 - 136 * q^10 - 632 * q^11 + 500 * q^13 + 12 * q^15 - 2816 * q^16 + 120 * q^17 + 2648 * q^18 - 736 * q^20 - 856 * q^21 - 1264 * q^22 + 2052 * q^25 + 2000 * q^26 + 588 * q^27 + 640 * q^28 - 1704 * q^30 + 3220 * q^31 - 5632 * q^32 - 2884 * q^33 + 720 * q^35 + 10592 * q^36 + 1856 * q^37 - 1696 * q^38 - 1856 * q^40 - 5156 * q^41 - 1712 * q^42 + 960 * q^43 + 460 * q^45 - 1224 * q^47 + 4456 * q^50 + 3640 * q^51 + 4000 * q^52 + 13556 * q^53 + 12980 * q^55 + 2560 * q^56 - 3072 * q^57 - 3112 * q^58 - 6912 * q^60 - 4864 * q^61 + 6440 * q^62 - 13484 * q^63 - 4100 * q^65 - 11536 * q^66 - 1888 * q^67 - 960 * q^68 + 8824 * q^70 - 1060 * q^71 + 21184 * q^72 + 16616 * q^73 - 11044 * q^75 - 6784 * q^76 + 8892 * q^77 - 23152 * q^78 - 1536 * q^80 - 4044 * q^81 - 10312 * q^82 - 27024 * q^83 - 11068 * q^85 + 3840 * q^86 - 8392 * q^87 + 10112 * q^88 - 7184 * q^90 - 54024 * q^91 + 22528 * q^93 - 25968 * q^95 - 3252 * q^97 - 27984 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$	4.87410	−	4.87410i	0.541567	−	0.541567i	−0.382421	−	0.923988i	$-0.624910\pi$
$3$	4.87410	−	4.87410i	0.541567	−	0.541567i	0.923988	+	0.382421i	$0.124910\pi$
$4$			8.00000i			0.500000i
$5$	23.2684	−	9.14227i	0.930736	−	0.365691i
$5$	23.2684	−	9.14227i	0.930736	−	0.365691i
$6$	19.4964			0.541567
$7$	49.4466	+	49.4466i	1.00911	+	1.00911i	0.999958	+	0.00915566i	$0.00291438\pi$
$7$	49.4466	+	49.4466i	1.00911	+	1.00911i	0.00915566	+	0.999958i	$0.497086\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$			33.4862i			0.413410i
$10$	64.8214	+	28.2523i	0.648214	+	0.282523i
$11$	66.9800			0.553554			0.276777	−	0.960934i	$-0.410734\pi$
$11$	66.9800			0.553554			0.276777	+	0.960934i	$0.410734\pi$
$12$	38.9928	+	38.9928i	0.270784	+	0.270784i
$13$	−133.414	+	133.414i	−0.789433	+	0.789433i	−0.981401	−	0.191968i	$-0.938513\pi$
$13$	−133.414	+	133.414i	−0.789433	+	0.789433i	0.191968	+	0.981401i	$0.438513\pi$
$14$			197.786i			1.00911i
$15$	68.8523	−	157.973i	0.306010	−	0.702102i
$16$	−64.0000			−0.250000
$17$	−145.140	−	145.140i	−0.502216	−	0.502216i	0.409910	−	0.912126i	$-0.365560\pi$
$17$	−145.140	−	145.140i	−0.502216	−	0.502216i	−0.912126	+	0.409910i	$0.865560\pi$
$18$	−66.9724	+	66.9724i	−0.206705	+	0.206705i
$19$		−	23.8070i		−	0.0659474i	−0.999456	−	0.0329737i	$-0.989502\pi$
$19$		−	23.8070i		−	0.0659474i	0.999456	−	0.0329737i	$-0.0104978\pi$
$20$	73.1382	+	186.147i	0.182845	+	0.465368i
$21$	482.016			1.09301
$22$	133.960	+	133.960i	0.276777	+	0.276777i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$24$			155.971i			0.270784i
$25$	457.838	−	425.452i	0.732540	−	0.680724i
$26$	−533.657			−0.789433
$27$	558.018	+	558.018i	0.765456	+	0.765456i
$28$	−395.573	+	395.573i	−0.504557	+	0.504557i
$29$			573.299i			0.681688i	0.940120	+	0.340844i	$0.110713\pi$
$29$			573.299i			0.681688i	−0.940120	+	0.340844i	$0.889287\pi$
$30$	453.651	−	178.242i	0.504056	−	0.198046i
$31$	244.920			0.254860			0.127430	−	0.991848i	$-0.459327\pi$
$31$	244.920			0.254860			0.127430	+	0.991848i	$0.459327\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	326.468	−	326.468i	0.299787	−	0.299787i
$34$		−	580.562i		−	0.502216i
$35$	1602.60	+	698.489i	1.30824	+	0.570195i
$36$	−267.890			−0.206705
$37$	−836.705	−	836.705i	−0.611180	−	0.611180i	0.332073	−	0.943254i	$-0.392252\pi$
$37$	−836.705	−	836.705i	−0.611180	−	0.611180i	−0.943254	+	0.332073i	$0.892252\pi$
$38$	47.6140	−	47.6140i	0.0329737	−	0.0329737i
$39$			1300.55i			0.855062i
$40$	−226.018	+	518.571i	−0.141261	+	0.324107i
$41$	653.194			0.388575			0.194287	−	0.980945i	$-0.437761\pi$
$41$	653.194			0.388575			0.194287	+	0.980945i	$0.437761\pi$
$42$	964.031	+	964.031i	0.546503	+	0.546503i
$43$	1231.32	−	1231.32i	0.665936	−	0.665936i	−0.290837	−	0.956773i	$-0.593934\pi$
$43$	1231.32	−	1231.32i	0.665936	−	0.665936i	0.956773	+	0.290837i	$0.0939336\pi$
$44$			535.840i			0.276777i
$45$	306.140	+	779.171i	0.151180	+	0.384776i
$46$	311.987			0.147442
$47$	1571.80	+	1571.80i	0.711542	+	0.711542i	0.966858	−	0.255316i	$-0.0821795\pi$
$47$	1571.80	+	1571.80i	0.711542	+	0.711542i	−0.255316	+	0.966858i	$0.582179\pi$
$48$	−311.943	+	311.943i	−0.135392	+	0.135392i
$49$			2488.93i			1.03662i
$50$	1766.58	+	64.7706i	0.706632	+	0.0259082i
$51$	−1414.86			−0.543968
$52$	−1067.31	−	1067.31i	−0.394716	−	0.394716i
$53$	122.980	−	122.980i	0.0437808	−	0.0437808i	−0.684877	−	0.728658i	$-0.740144\pi$
$53$	122.980	−	122.980i	0.0437808	−	0.0437808i	0.728658	+	0.684877i	$0.240144\pi$
$54$			2232.07i			0.765456i
$55$	1558.52	−	612.350i	0.515213	−	0.202430i
$56$	−1582.29			−0.504557
$57$	−116.038	−	116.038i	−0.0357150	−	0.0357150i
$58$	−1146.60	+	1146.60i	−0.340844	+	0.340844i
$59$		−	4092.49i		−	1.17567i	−0.808982	−	0.587833i	$-0.799981\pi$
$59$		−	4092.49i		−	1.17567i	0.808982	−	0.587833i	$-0.200019\pi$
$60$	1263.78	+	550.818i	0.351051	+	0.153005i
$61$	−4255.58			−1.14367			−0.571833	−	0.820370i	$-0.693767\pi$
$61$	−4255.58			−1.14367			−0.571833	+	0.820370i	$0.693767\pi$
$62$	489.840	+	489.840i	0.127430	+	0.127430i
$63$	−1655.78	+	1655.78i	−0.417178	+	0.417178i
$64$		−	512.000i		−	0.125000i
$65$	−1884.63	+	4324.04i	−0.446065	+	1.02344i
$66$	1305.87			0.299787
$67$	−381.044	−	381.044i	−0.0848839	−	0.0848839i	0.663390	−	0.748274i	$-0.269117\pi$
$67$	−381.044	−	381.044i	−0.0848839	−	0.0848839i	−0.748274	+	0.663390i	$0.769117\pi$
$68$	1161.12	−	1161.12i	0.251108	−	0.251108i
$69$		−	760.329i		−	0.159699i
$70$	1808.22	+	4602.17i	0.369024	+	0.939219i
$71$	−216.589			−0.0429655			−0.0214827	−	0.999769i	$-0.506839\pi$
$71$	−216.589			−0.0429655			−0.0214827	+	0.999769i	$0.506839\pi$
$72$	−535.779	−	535.779i	−0.103353	−	0.103353i
$73$	6025.51	−	6025.51i	1.13070	−	1.13070i	0.140641	−	0.990061i	$-0.455084\pi$
$73$	6025.51	−	6025.51i	1.13070	−	1.13070i	0.990061	−	0.140641i	$-0.0449162\pi$
$74$		−	3346.82i		−	0.611180i
$75$	157.849	−	4305.25i	0.0280621	−	0.765377i
$76$	190.456			0.0329737
$77$	3311.93	+	3311.93i	0.558599	+	0.558599i
$78$	−2601.10	+	2601.10i	−0.427531	+	0.427531i
$79$		−	9030.79i		−	1.44701i	−0.690319	−	0.723505i	$-0.742530\pi$
$79$		−	9030.79i		−	1.44701i	0.690319	−	0.723505i	$-0.257470\pi$
$80$	−1489.18	+	585.106i	−0.232684	+	0.0914227i
$81$	2727.29			0.415682
$82$	1306.39	+	1306.39i	0.194287	+	0.194287i
$83$	−5707.79	+	5707.79i	−0.828537	+	0.828537i	−0.987314	−	0.158777i	$-0.949245\pi$
$83$	−5707.79	+	5707.79i	−0.828537	+	0.828537i	0.158777	+	0.987314i	$0.449245\pi$
$84$			3856.12i			0.546503i
$85$	−4704.10	−	2050.27i	−0.651087	−	0.283775i
$86$	4925.26			0.665936
$87$	2794.32	+	2794.32i	0.369180	+	0.369180i
$88$	−1071.68	+	1071.68i	−0.138389	+	0.138389i
$89$			7873.14i			0.993958i	0.867763	+	0.496979i	$0.165557\pi$
$89$			7873.14i			0.993958i	−0.867763	+	0.496979i	$0.834443\pi$
$90$	−946.061	+	2170.62i	−0.116798	+	0.267978i
$91$	−13193.7			−1.59326
$92$	623.974	+	623.974i	0.0737210	+	0.0737210i
$93$	1193.77	−	1193.77i	0.138024	−	0.138024i
$94$			6287.18i			0.711542i
$95$	−217.650	−	553.951i	−0.0241164	−	0.0613797i
$96$	−1247.77			−0.135392
$97$	2815.53	+	2815.53i	0.299238	+	0.299238i	0.840715	−	0.541477i	$-0.182135\pi$
$97$	2815.53	+	2815.53i	0.299238	+	0.299238i	−0.541477	+	0.840715i	$0.682135\pi$
$98$	−4977.85	+	4977.85i	−0.518311	+	0.518311i
$99$			2242.91i			0.228845i
$100$	3403.62	+	3662.70i	0.340362	+	0.366270i
$101$	0.661641			6.48604e−5			3.24302e−5	−	1.00000i	$-0.499990\pi$
$101$	0.661641			6.48604e−5			3.24302e−5		1.00000i	$0.499990\pi$
$102$	−2829.72	−	2829.72i	−0.271984	−	0.271984i
$103$	4175.30	−	4175.30i	0.393562	−	0.393562i	−0.482393	−	0.875955i	$-0.660232\pi$
$103$	4175.30	−	4175.30i	0.393562	−	0.393562i	0.875955	+	0.482393i	$0.160232\pi$
$104$		−	4269.25i		−	0.394716i
$105$	11215.7	−	4406.72i	1.01730	−	0.399702i
$106$	491.921			0.0437808
$107$	−2031.18	−	2031.18i	−0.177412	−	0.177412i	0.612815	−	0.790226i	$-0.290037\pi$
$107$	−2031.18	−	2031.18i	−0.177412	−	0.177412i	−0.790226	+	0.612815i	$0.790037\pi$
$108$	−4464.14	+	4464.14i	−0.382728	+	0.382728i
$109$		−	4791.87i		−	0.403322i	−0.979455	−	0.201661i	$-0.935366\pi$
$109$		−	4791.87i		−	0.403322i	0.979455	−	0.201661i	$-0.0646340\pi$
$110$	4341.74	+	1892.34i	0.358821	+	0.156392i
$111$	−8156.38			−0.661990
$112$	−3164.58	−	3164.58i	−0.252278	−	0.252278i
$113$	2589.26	−	2589.26i	0.202777	−	0.202777i	−0.598412	−	0.801189i	$-0.704201\pi$
$113$	2589.26	−	2589.26i	0.202777	−	0.202777i	0.801189	+	0.598412i	$0.204201\pi$
$114$		−	464.152i		−	0.0357150i
$115$	1101.79	−	2527.93i	0.0833114	−	0.191148i
$116$	−4586.39			−0.340844
$117$	−4467.54	−	4467.54i	−0.326359	−	0.326359i
$118$	8184.99	−	8184.99i	0.587833	−	0.587833i
$119$		−	14353.4i		−	1.01359i
$120$	1425.93	+	3629.20i	0.0990231	+	0.252028i
$121$	−10154.7			−0.693578
$122$	−8511.16	−	8511.16i	−0.571833	−	0.571833i
$123$	3183.74	−	3183.74i	0.210439	−	0.210439i
$124$			1959.36i			0.127430i
$125$	6763.55	−	14085.3i	0.432867	−	0.901458i
$126$	−6623.11			−0.417178
$127$	−8143.67	−	8143.67i	−0.504908	−	0.504908i	0.408051	−	0.912959i	$-0.366209\pi$
$127$	−8143.67	−	8143.67i	−0.504908	−	0.504908i	−0.912959	+	0.408051i	$0.866209\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$		−	12003.1i		−	0.721298i
$130$	−12417.3	+	4878.84i	−0.734754	+	0.288689i
$131$	25326.5			1.47582			0.737910	−	0.674900i	$-0.235813\pi$
$131$	25326.5			1.47582			0.737910	+	0.674900i	$0.235813\pi$
$132$	2611.74	+	2611.74i	0.149893	+	0.149893i
$133$	1177.18	−	1177.18i	0.0665485	−	0.0665485i
$134$		−	1524.18i		−	0.0848839i
$135$	18085.7	+	7882.63i	0.992359	+	0.432518i
$136$	4644.50			0.251108
$137$	−23880.9	−	23880.9i	−1.27236	−	1.27236i	−0.944848	−	0.327508i	$-0.893791\pi$
$137$	−23880.9	−	23880.9i	−1.27236	−	1.27236i	−0.327508	−	0.944848i	$-0.606209\pi$
$138$	1520.66	−	1520.66i	0.0798497	−	0.0798497i
$139$		−	3414.84i		−	0.176742i	−0.996088	−	0.0883712i	$-0.971834\pi$
$139$		−	3414.84i		−	0.176742i	0.996088	−	0.0883712i	$-0.0281662\pi$
$140$	−5587.91	+	12820.8i	−0.285098	+	0.654121i
$141$	15322.2			0.770695
$142$	−433.178	−	433.178i	−0.0214827	−	0.0214827i
$143$	−8936.09	+	8936.09i	−0.436994	+	0.436994i
$144$		−	2143.12i		−	0.103353i
$145$	5241.26	+	13339.8i	0.249287	+	0.634472i
$146$	24102.0			1.13070
$147$	12131.3	+	12131.3i	0.561400	+	0.561400i
$148$	6693.64	−	6693.64i	0.305590	−	0.305590i
$149$		−	32001.6i		−	1.44145i	−0.693223	−	0.720723i	$-0.743810\pi$
$149$		−	32001.6i		−	1.44145i	0.693223	−	0.720723i	$-0.256190\pi$
$150$	8926.19	−	8294.80i	0.396720	−	0.368658i
$151$	−36878.8			−1.61742			−0.808711	−	0.588206i	$-0.799834\pi$
$151$	−36878.8			−1.61742			−0.808711	+	0.588206i	$0.799834\pi$
$152$	380.912	+	380.912i	0.0164869	+	0.0164869i
$153$	4860.20	−	4860.20i	0.207621	−	0.207621i
$154$			13247.7i			0.558599i
$155$	5698.90	−	2239.13i	0.237207	−	0.0931999i
$156$	−10404.4			−0.427531
$157$	−21028.0	−	21028.0i	−0.853096	−	0.853096i	0.137417	−	0.990513i	$-0.456120\pi$
$157$	−21028.0	−	21028.0i	−0.853096	−	0.853096i	−0.990513	+	0.137417i	$0.956120\pi$
$158$	18061.6	−	18061.6i	0.723505	−	0.723505i
$159$		−	1198.84i		−	0.0474204i
$160$	−4148.57	−	1808.15i	−0.162053	−	0.0706307i
$161$	7713.35			0.297571
$162$	5454.58	+	5454.58i	0.207841	+	0.207841i
$163$	−15942.0	+	15942.0i	−0.600023	+	0.600023i	−0.940318	−	0.340296i	$-0.889473\pi$
$163$	−15942.0	+	15942.0i	−0.600023	+	0.600023i	0.340296	+	0.940318i	$0.389473\pi$
$164$			5225.55i			0.194287i
$165$	4611.73	−	10581.0i	0.169393	−	0.388652i
$166$	−22831.2			−0.828537
$167$	−37393.0	−	37393.0i	−1.34078	−	1.34078i	−0.895284	−	0.445497i	$-0.853027\pi$
$167$	−37393.0	−	37393.0i	−1.34078	−	1.34078i	−0.445497	−	0.895284i	$-0.646973\pi$
$168$	−7712.25	+	7712.25i	−0.273251	+	0.273251i
$169$		−	7037.68i		−	0.246409i
$170$	−5307.66	−	13508.8i	−0.183656	−	0.467431i
$171$	797.207			0.0272633
$172$	9850.53	+	9850.53i	0.332968	+	0.332968i
$173$	−153.064	+	153.064i	−0.00511423	+	0.00511423i	−0.709659	−	0.704545i	$-0.751151\pi$
$173$	−153.064	+	153.064i	−0.00511423	+	0.00511423i	0.704545	+	0.709659i	$0.251151\pi$
$174$			11177.3i			0.369180i
$175$	43675.7	+	1601.34i	1.42614	+	0.0522887i
$176$	−4286.72			−0.138389
$177$	−19947.2	−	19947.2i	−0.636702	−	0.636702i
$178$	−15746.3	+	15746.3i	−0.496979	+	0.496979i
$179$			39349.0i			1.22808i	0.789273	+	0.614042i	$0.210458\pi$
$179$			39349.0i			1.22808i	−0.789273	+	0.614042i	$0.789542\pi$
$180$	−6233.37	+	2449.12i	−0.192388	+	0.0755902i
$181$	16204.5			0.494629			0.247314	−	0.968935i	$-0.420452\pi$
$181$	16204.5			0.494629			0.247314	+	0.968935i	$0.420452\pi$
$182$	−26387.5	−	26387.5i	−0.796628	−	0.796628i
$183$	−20742.1	+	20742.1i	−0.619372	+	0.619372i
$184$			2495.90i			0.0737210i
$185$	−27118.2	−	11819.4i	−0.792351	−	0.345344i
$186$	4775.07			0.138024
$187$	−9721.52	−	9721.52i	−0.278004	−	0.278004i
$188$	−12574.4	+	12574.4i	−0.355771	+	0.355771i
$189$			55184.1i			1.54487i
$190$	672.602	−	1543.20i	0.0186316	−	0.0427480i
$191$	−33385.0			−0.915135			−0.457567	−	0.889175i	$-0.651279\pi$
$191$	−33385.0			−0.915135			−0.457567	+	0.889175i	$0.651279\pi$
$192$	−2495.54	−	2495.54i	−0.0676959	−	0.0676959i
$193$	−9143.14	+	9143.14i	−0.245460	+	0.245460i	−0.819104	−	0.573644i	$-0.805529\pi$
$193$	−9143.14	+	9143.14i	−0.245460	+	0.245460i	0.573644	+	0.819104i	$0.305529\pi$
$194$			11262.1i			0.299238i
$195$	11890.0	+	30261.7i	0.312688	+	0.795837i
$196$	−19911.4			−0.518311
$197$	34385.4	+	34385.4i	0.886017	+	0.886017i	0.994138	−	0.108121i	$-0.0344833\pi$
$197$	34385.4	+	34385.4i	0.886017	+	0.886017i	−0.108121	+	0.994138i	$0.534483\pi$
$198$	−4485.82	+	4485.82i	−0.114422	+	0.114422i
$199$			17385.0i			0.439004i	0.975612	+	0.219502i	$0.0704433\pi$
$199$			17385.0i			0.439004i	−0.975612	+	0.219502i	$0.929557\pi$
$200$	−518.165	+	14132.6i	−0.0129541	+	0.353316i
$201$	−3714.50			−0.0919407
$202$	1.32328	+	1.32328i	3.24302e−5	+	3.24302e-5i
$203$	−28347.7	+	28347.7i	−0.687900	+	0.687900i
$204$		−	11318.9i		−	0.271984i
$205$	15198.8	−	5971.68i	0.361661	−	0.142098i
$206$	16701.2			0.393562
$207$	2611.82	+	2611.82i	0.0609540	+	0.0609540i
$208$	8538.51	−	8538.51i	0.197358	−	0.197358i
$209$		−	1594.60i		−	0.0365055i
$210$	31244.9	+	13618.0i	0.708501	+	0.308799i
$211$	76768.8			1.72433			0.862164	−	0.506630i	$-0.169109\pi$
$211$	76768.8			1.72433			0.862164	+	0.506630i	$0.169109\pi$
$212$	983.841	+	983.841i	0.0218904	+	0.0218904i
$213$	−1055.68	+	1055.68i	−0.0232687	+	0.0232687i
$214$		−	8124.74i		−	0.177412i
$215$	17393.7	−	39907.8i	0.376284	−	0.863338i
$216$	−17856.6			−0.382728
$217$	12110.5	+	12110.5i	0.257182	+	0.257182i
$218$	9583.75	−	9583.75i	0.201661	−	0.201661i
$219$		−	58737.9i		−	1.22470i
$220$	4898.80	+	12468.2i	0.101215	+	0.257606i
$221$	38727.6			0.792932
$222$	−16312.8	−	16312.8i	−0.330995	−	0.330995i
$223$	−65408.4	+	65408.4i	−1.31530	+	1.31530i	−0.397842	+	0.917454i	$0.630241\pi$
$223$	−65408.4	+	65408.4i	−1.31530	+	1.31530i	−0.917454	+	0.397842i	$0.869759\pi$
$224$		−	12658.3i		−	0.252278i
$225$	14246.8	+	15331.2i	0.281418	+	0.302839i
$226$	10357.1			0.202777
$227$	−17946.5	−	17946.5i	−0.348280	−	0.348280i	0.511188	−	0.859469i	$-0.329205\pi$
$227$	−17946.5	−	17946.5i	−0.348280	−	0.348280i	−0.859469	+	0.511188i	$0.829205\pi$
$228$	928.303	−	928.303i	0.0178575	−	0.0178575i
$229$			16859.2i			0.321489i	0.986996	+	0.160744i	$0.0513895\pi$
$229$			16859.2i			0.321489i	−0.986996	+	0.160744i	$0.948611\pi$
$230$	7259.45	−	2852.27i	0.137230	−	0.0539182i
$231$	32285.4			0.605038
$232$	−9172.79	−	9172.79i	−0.170422	−	0.170422i
$233$	−31385.6	+	31385.6i	−0.578120	+	0.578120i	−0.934385	−	0.356265i	$-0.884050\pi$
$233$	−31385.6	+	31385.6i	−0.578120	+	0.578120i	0.356265	+	0.934385i	$0.384050\pi$
$234$		−	17870.1i		−	0.326359i
$235$	50943.0	+	22203.4i	0.922462	+	0.402053i
$236$	32740.0			0.587833
$237$	−44017.0	−	44017.0i	−0.783653	−	0.783653i
$238$	28706.8	−	28706.8i	0.506793	−	0.506793i
$239$			7777.94i			0.136166i	0.997680	+	0.0680830i	$0.0216883\pi$
$239$			7777.94i			0.136166i	−0.997680	+	0.0680830i	$0.978312\pi$
$240$	−4406.54	+	10110.3i	−0.0765025	+	0.175526i
$241$	107256.			1.84666			0.923328	−	0.384012i	$-0.125458\pi$
$241$	107256.			1.84666			0.923328	+	0.384012i	$0.125458\pi$
$242$	−20309.3	−	20309.3i	−0.346789	−	0.346789i
$243$	−31906.3	+	31906.3i	−0.540337	+	0.540337i
$244$		−	34044.6i		−	0.571833i
$245$	22754.5	+	57913.4i	0.379083	+	0.964821i
$246$	12735.0			0.210439
$247$	3176.19	+	3176.19i	0.0520611	+	0.0520611i
$248$	−3918.72	+	3918.72i	−0.0637149	+	0.0637149i
$249$			55640.7i			0.897417i
$250$	41697.7	−	14643.4i	0.667162	−	0.234295i
$251$	−1475.24			−0.0234162			−0.0117081	−	0.999931i	$-0.503727\pi$
$251$	−1475.24			−0.0234162			−0.0117081	+	0.999931i	$0.503727\pi$
$252$	−13246.2	−	13246.2i	−0.208589	−	0.208589i
$253$	5224.23	−	5224.23i	0.0816171	−	0.0816171i
$254$		−	32574.7i		−	0.504908i
$255$	−32921.5	+	12935.0i	−0.506290	+	0.198924i
$256$	4096.00			0.0625000
$257$	−22839.0	−	22839.0i	−0.345788	−	0.345788i	0.512750	−	0.858538i	$-0.328627\pi$
$257$	−22839.0	−	22839.0i	−0.345788	−	0.345788i	−0.858538	+	0.512750i	$0.828627\pi$
$258$	24006.2	−	24006.2i	0.360649	−	0.360649i
$259$		−	82744.4i		−	1.23350i
$260$	−34592.4	−	15077.0i	−0.511721	−	0.223033i
$261$	−19197.6			−0.281817
$262$	50653.1	+	50653.1i	0.737910	+	0.737910i
$263$	−45335.7	+	45335.7i	−0.655434	+	0.655434i	−0.954296	−	0.298862i	$-0.903393\pi$
$263$	−45335.7	+	45335.7i	−0.655434	+	0.655434i	0.298862	+	0.954296i	$0.403393\pi$
$264$			10447.0i			0.149893i
$265$	1737.23	−	3985.87i	0.0247381	−	0.0567586i
$266$	4708.70			0.0665485
$267$	38374.5	+	38374.5i	0.538295	+	0.538295i
$268$	3048.35	−	3048.35i	0.0424420	−	0.0424420i
$269$		−	44524.6i		−	0.615313i	−0.951498	−	0.307656i	$-0.900455\pi$
$269$		−	44524.6i		−	0.615313i	0.951498	−	0.307656i	$-0.0995447\pi$
$270$	20406.2	+	51936.7i	0.279921	+	0.712438i
$271$	52183.3			0.710548			0.355274	−	0.934762i	$-0.384388\pi$
$271$	52183.3			0.710548			0.355274	+	0.934762i	$0.384388\pi$
$272$	9288.99	+	9288.99i	0.125554	+	0.125554i
$273$	−64307.7	+	64307.7i	−0.862855	+	0.862855i
$274$		−	95523.4i		−	1.27236i
$275$	30666.0	−	28496.8i	0.405501	−	0.376817i
$276$	6082.63			0.0798497
$277$	47912.1	+	47912.1i	0.624433	+	0.624433i	0.946662	−	0.322229i	$-0.104432\pi$
$277$	47912.1	+	47912.1i	0.624433	+	0.624433i	−0.322229	+	0.946662i	$0.604432\pi$
$278$	6829.68	−	6829.68i	0.0883712	−	0.0883712i
$279$			8201.45i			0.105362i
$280$	−36817.4	+	14465.7i	−0.469609	+	0.184512i
$281$	76774.1			0.972304			0.486152	−	0.873874i	$-0.338400\pi$
$281$	76774.1			0.972304			0.486152	+	0.873874i	$0.338400\pi$
$282$	30644.4	+	30644.4i	0.385348	+	0.385348i
$283$	−27292.6	+	27292.6i	−0.340778	+	0.340778i	−0.856660	−	0.515882i	$-0.827464\pi$
$283$	−27292.6	+	27292.6i	−0.340778	+	0.340778i	0.515882	+	0.856660i	$0.327464\pi$
$284$		−	1732.71i		−	0.0214827i
$285$	−3760.87	−	1639.17i	−0.0463019	−	0.0201806i
$286$	−35744.3			−0.436994
$287$	32298.2	+	32298.2i	0.392116	+	0.392116i
$288$	4286.23	−	4286.23i	0.0516763	−	0.0516763i
$289$		−	41389.5i		−	0.495558i
$290$	−16197.0	+	37162.0i	−0.192592	+	0.441879i
$291$	27446.4			0.324115
$292$	48204.1	+	48204.1i	0.565351	+	0.565351i
$293$	−67456.0	+	67456.0i	−0.785752	+	0.785752i	−0.980795	−	0.195043i	$-0.937515\pi$
$293$	−67456.0	+	67456.0i	−0.785752	+	0.785752i	0.195043	+	0.980795i	$0.437515\pi$
$294$			48525.2i			0.561400i
$295$	−37414.7	−	95225.8i	−0.429931	−	1.09424i
$296$	26774.6			0.305590
$297$	37376.1	+	37376.1i	0.423722	+	0.423722i
$298$	64003.1	−	64003.1i	0.720723	−	0.720723i
$299$			20811.8i			0.232791i
$300$	34442.0	+	1262.80i	0.382689	+	0.0140311i
$301$	121769.			1.34401
$302$	−73757.7	−	73757.7i	−0.808711	−	0.808711i
$303$	3.22491	−	3.22491i	3.51262e−5	−	3.51262e-5i
$304$			1523.65i			0.0164869i
$305$	−99020.6	+	38905.7i	−1.06445	+	0.418228i
$306$	19440.8			0.207621
$307$	56848.3	+	56848.3i	0.603172	+	0.603172i	0.941153	−	0.337981i	$-0.109744\pi$
$307$	56848.3	+	56848.3i	0.603172	+	0.603172i	−0.337981	+	0.941153i	$0.609744\pi$
$308$	−26495.5	+	26495.5i	−0.279300	+	0.279300i
$309$		−	40701.7i		−	0.426281i
$310$	15876.1	+	6919.55i	0.165204	+	0.0720037i
$311$	−126024.			−1.30297			−0.651485	−	0.758662i	$-0.725853\pi$
$311$	−126024.			−1.30297			−0.651485	+	0.758662i	$0.725853\pi$
$312$	−20808.8	−	20808.8i	−0.213765	−	0.213765i
$313$	−18695.9	+	18695.9i	−0.190834	+	0.190834i	−0.796057	−	0.605222i	$-0.793084\pi$
$313$	−18695.9	+	18695.9i	−0.190834	+	0.190834i	0.605222	+	0.796057i	$0.293084\pi$
$314$		−	84111.9i		−	0.853096i
$315$	−23389.7	+	53664.9i	−0.235724	+	0.540841i
$316$	72246.3			0.723505
$317$	137868.	+	137868.i	1.37197	+	1.37197i	0.857514	+	0.514461i	$0.172008\pi$
$317$	137868.	+	137868.i	1.37197	+	1.37197i	0.514461	+	0.857514i	$0.327992\pi$
$318$	2397.67	−	2397.67i	0.0237102	−	0.0237102i
$319$			38399.6i			0.377351i
$320$	−4680.84	−	11913.4i	−0.0457114	−	0.116342i
$321$	−19800.4			−0.192161
$322$	15426.7	+	15426.7i	0.148786	+	0.148786i
$323$	−3455.36	+	3455.36i	−0.0331199	+	0.0331199i
$324$			21818.3i			0.207841i
$325$	−4320.66	+	117843.i	−0.0409057	+	1.11568i
$326$	−63768.0			−0.600023
$327$	−23356.1	−	23356.1i	−0.218426	−	0.218426i
$328$	−10451.1	+	10451.1i	−0.0971437	+	0.0971437i
$329$			155440.i			1.43605i
$330$	30385.5	−	11938.6i	0.279022	−	0.109629i
$331$	−75996.5			−0.693645			−0.346823	−	0.937931i	$-0.612739\pi$
$331$	−75996.5			−0.693645			−0.346823	+	0.937931i	$0.612739\pi$
$332$	−45662.3	−	45662.3i	−0.414269	−	0.414269i
$333$	28018.1	−	28018.1i	0.252668	−	0.252668i
$334$		−	149572.i		−	1.34078i
$335$	−12349.9	−	5382.68i	−0.110046	−	0.0479633i
$336$	−30849.0			−0.273251
$337$	56927.2	+	56927.2i	0.501257	+	0.501257i	0.911828	−	0.410572i	$-0.134671\pi$
$337$	56927.2	+	56927.2i	0.501257	+	0.501257i	−0.410572	+	0.911828i	$0.634671\pi$
$338$	14075.4	−	14075.4i	0.123204	−	0.123204i
$339$		−	25240.7i		−	0.219635i
$340$	16402.2	−	37632.8i	0.141887	−	0.325543i
$341$	16404.8			0.141079
$342$	1594.41	+	1594.41i	0.0136317	+	0.0136317i
$343$	−4347.70	+	4347.70i	−0.0369549	+	0.0369549i
$344$			39402.1i			0.332968i
$345$	−6951.14	−	17691.6i	−0.0584006	−	0.148638i
$346$	−612.255			−0.00511423
$347$	−72306.8	−	72306.8i	−0.600510	−	0.600510i	0.339938	−	0.940448i	$-0.389594\pi$
$347$	−72306.8	−	72306.8i	−0.600510	−	0.600510i	−0.940448	+	0.339938i	$0.889594\pi$
$348$	−22354.6	+	22354.6i	−0.184590	+	0.184590i
$349$		−	142357.i		−	1.16877i	−0.811478	−	0.584384i	$-0.801336\pi$
$349$		−	142357.i		−	1.16877i	0.811478	−	0.584384i	$-0.198664\pi$
$350$	84148.6	+	90554.0i	0.686928	+	0.739216i
$351$	−148895.			−1.20855
$352$	−8573.45	−	8573.45i	−0.0691943	−	0.0691943i
$353$	−155033.	+	155033.i	−1.24416	+	1.24416i	−0.285895	+	0.958261i	$0.592291\pi$
$353$	−155033.	+	155033.i	−1.24416	+	1.24416i	−0.958261	+	0.285895i	$0.907709\pi$
$354$		−	79789.0i		−	0.636702i
$355$	−5039.68	+	1980.12i	−0.0399895	+	0.0157121i
$356$	−62985.1			−0.496979
$357$	−69960.0	−	69960.0i	−0.548925	−	0.548925i
$358$	−78698.1	+	78698.1i	−0.614042	+	0.614042i
$359$		−	225754.i		−	1.75164i	−0.482635	−	0.875822i	$-0.660320\pi$
$359$		−	225754.i		−	1.75164i	0.482635	−	0.875822i	$-0.339680\pi$
$360$	−17365.0	−	7568.49i	−0.133989	−	0.0583989i
$361$	129754.			0.995651
$362$	32409.1	+	32409.1i	0.247314	+	0.247314i
$363$	−49494.9	+	49494.9i	−0.375619	+	0.375619i
$364$		−	105550.i		−	0.796628i
$365$	85117.1	−	195291.i	0.638897	−	1.46587i
$366$	−82968.6			−0.619372
$367$	−168215.	−	168215.i	−1.24892	−	1.24892i	−0.956199	−	0.292717i	$-0.905441\pi$
$367$	−168215.	−	168215.i	−1.24892	−	1.24892i	−0.292717	−	0.956199i	$-0.594559\pi$
$368$	−4991.79	+	4991.79i	−0.0368605	+	0.0368605i
$369$			21873.0i			0.160641i
$370$	−30597.6	−	77875.2i	−0.223503	−	0.568847i
$371$	12161.9			0.0883595
$372$	9550.13	+	9550.13i	0.0690118	+	0.0690118i
$373$	176630.	−	176630.i	1.26954	−	1.26954i	0.323215	−	0.946326i	$-0.395236\pi$
$373$	176630.	−	176630.i	1.26954	−	1.26954i	0.946326	−	0.323215i	$-0.104764\pi$
$374$		−	38886.1i		−	0.278004i
$375$	−35686.9	−	101619.i	−0.253773	−	0.722627i
$376$	−50297.5			−0.355771
$377$	−76486.3	−	76486.3i	−0.538147	−	0.538147i
$378$	−110368.	+	110368.i	−0.772433	+	0.772433i
$379$			89496.4i			0.623056i	0.950237	+	0.311528i	$0.100841\pi$
$379$			89496.4i			0.623056i	−0.950237	+	0.311528i	$0.899159\pi$
$380$	4431.61	−	1741.20i	0.0306898	−	0.0120582i
$381$	−79386.2			−0.546884
$382$	−66770.1	−	66770.1i	−0.457567	−	0.457567i
$383$	−973.790	+	973.790i	−0.00663847	+	0.00663847i	−0.710418	−	0.703780i	$-0.751494\pi$
$383$	−973.790	+	973.790i	−0.00663847	+	0.00663847i	0.703780	+	0.710418i	$0.251494\pi$
$384$		−	9982.17i		−	0.0676959i
$385$	107342.	+	46784.8i	0.724183	+	0.315634i
$386$	−36572.5			−0.245460
$387$	41232.1	+	41232.1i	0.275305	+	0.275305i
$388$	−22524.2	+	22524.2i	−0.149619	+	0.149619i
$389$			56194.1i			0.371357i	0.982611	+	0.185678i	$0.0594482\pi$
$389$			56194.1i			0.371357i	−0.982611	+	0.185678i	$0.940552\pi$
$390$	−36743.5	+	84303.4i	−0.241574	+	0.554263i
$391$	−22641.0			−0.148095
$392$	−39822.8	−	39822.8i	−0.259155	−	0.259155i
$393$	123444.	−	123444.i	0.799255	−	0.799255i
$394$			137542.i			0.886017i
$395$	−82561.9	−	210132.i	−0.529158	−	1.34678i
$396$	−17943.3			−0.114422
$397$	−132073.	−	132073.i	−0.837980	−	0.837980i	0.150612	−	0.988593i	$-0.451875\pi$
$397$	−132073.	−	132073.i	−0.837980	−	0.837980i	−0.988593	+	0.150612i	$0.951875\pi$
$398$	−34770.0	+	34770.0i	−0.219502	+	0.219502i
$399$		−	11475.4i		−	0.0720809i
$400$	−29301.6	+	27228.9i	−0.183135	+	0.170181i
$401$	236596.			1.47136			0.735679	−	0.677330i	$-0.236863\pi$
$401$	236596.			1.47136			0.735679	+	0.677330i	$0.236863\pi$
$402$	−7428.99	−	7428.99i	−0.0459703	−	0.0459703i
$403$	−32675.8	+	32675.8i	−0.201195	+	0.201195i
$404$			5.29312i			3.24302e-5i
$405$	63459.7	−	24933.6i	0.386890	−	0.152011i
$406$	−113391.			−0.687900
$407$	−56042.6	−	56042.6i	−0.338321	−	0.338321i
$408$	22637.8	−	22637.8i	0.135992	−	0.135992i
$409$		−	23677.5i		−	0.141543i	−0.997493	−	0.0707716i	$-0.977454\pi$
$409$		−	23677.5i		−	0.141543i	0.997493	−	0.0707716i	$-0.0225462\pi$
$410$	42340.9	+	18454.2i	0.251880	+	0.109781i
$411$	−232796.			−1.37813
$412$	33402.4	+	33402.4i	0.196781	+	0.196781i
$413$	202360.	−	202360.i	1.18638	−	1.18638i
$414$			10447.3i			0.0609540i
$415$	−80629.0	+	184993.i	−0.468161	+	1.07414i
$416$	34154.0			0.197358
$417$	−16644.3	−	16644.3i	−0.0957179	−	0.0957179i
$418$	3189.19	−	3189.19i	0.0182527	−	0.0182527i
$419$		−	197470.i		−	1.12479i	−0.826868	−	0.562396i	$-0.809880\pi$
$419$		−	197470.i		−	1.12479i	0.826868	−	0.562396i	$-0.190120\pi$
$420$	35253.7	+	89725.9i	0.199851	+	0.508650i
$421$	233791.			1.31906			0.659530	−	0.751679i	$-0.270756\pi$
$421$	233791.			1.31906			0.659530	+	0.751679i	$0.270756\pi$
$422$	153538.	+	153538.i	0.862164	+	0.862164i
$423$	−52633.5	+	52633.5i	−0.294158	+	0.294158i
$424$			3935.36i			0.0218904i
$425$	−128201.	−	4700.42i	−0.709764	−	0.0260231i
$426$	−4222.71			−0.0232687
$427$	−210424.	−	210424.i	−1.15409	−	1.15409i
$428$	16249.5	−	16249.5i	0.0887058	−	0.0887058i
$429$			87110.8i			0.473323i
$430$	114603.	−	45028.1i	0.619811	−	0.243527i
$431$	88195.3			0.474779			0.237389	−	0.971415i	$-0.423708\pi$
$431$	88195.3			0.474779			0.237389	+	0.971415i	$0.423708\pi$
$432$	−35713.1	−	35713.1i	−0.191364	−	0.191364i
$433$	128806.	−	128806.i	0.687007	−	0.687007i	−0.274562	−	0.961569i	$-0.588533\pi$
$433$	128806.	−	128806.i	0.687007	−	0.687007i	0.961569	+	0.274562i	$0.0885330\pi$
$434$			48441.9i			0.257182i
$435$	90565.9	+	39473.0i	0.478615	+	0.208603i
$436$	38335.0			0.201661
$437$	−1856.87	−	1856.87i	−0.00972342	−	0.00972342i
$438$	117476.	−	117476.i	0.612351	−	0.612351i
$439$		−	216222.i		−	1.12194i	−0.827836	−	0.560971i	$-0.810428\pi$
$439$		−	216222.i		−	1.12194i	0.827836	−	0.560971i	$-0.189572\pi$
$440$	−15138.7	+	34733.9i	−0.0781958	+	0.179411i
$441$	−83344.7			−0.428550
$442$	77455.2	+	77455.2i	0.396466	+	0.396466i
$443$	117107.	−	117107.i	0.596727	−	0.596727i	−0.342713	−	0.939440i	$-0.611346\pi$
$443$	117107.	−	117107.i	0.596727	−	0.596727i	0.939440	+	0.342713i	$0.111346\pi$
$444$		−	65251.0i		−	0.330995i
$445$	71978.4	+	183195.i	0.363481	+	0.925113i
$446$	−261633.			−1.31530
$447$	−155979.	−	155979.i	−0.780640	−	0.780640i
$448$	25316.6	−	25316.6i	0.126139	−	0.126139i
$449$			373382.i			1.85209i	0.377418	+	0.926043i	$0.376812\pi$
$449$			373382.i			1.85209i	−0.377418	+	0.926043i	$0.623188\pi$
$450$	−2168.92	+	59156.1i	−0.0107107	+	0.292129i
$451$	43751.0			0.215097
$452$	20714.1	+	20714.1i	0.101389	+	0.101389i
$453$	−179751.	+	179751.i	−0.875943	+	0.875943i
$454$		−	71786.1i		−	0.348280i
$455$	−306998.	+	120621.i	−1.48290	+	0.582639i
$456$	3713.21			0.0178575
$457$	−95342.7	−	95342.7i	−0.456515	−	0.456515i	0.440995	−	0.897510i	$-0.354626\pi$
$457$	−95342.7	−	95342.7i	−0.456515	−	0.456515i	−0.897510	+	0.440995i	$0.854626\pi$
$458$	−33718.4	+	33718.4i	−0.160744	+	0.160744i
$459$		−	161982.i		−	0.768849i
$460$	20223.4	+	8814.35i	0.0955739	+	0.0416557i
$461$	97649.8			0.459483			0.229742	−	0.973252i	$-0.426212\pi$
$461$	97649.8			0.459483			0.229742	+	0.973252i	$0.426212\pi$
$462$	64570.8	+	64570.8i	0.302519	+	0.302519i
$463$	−107055.	+	107055.i	−0.499396	+	0.499396i	−0.911250	−	0.411854i	$-0.864882\pi$
$463$	−107055.	+	107055.i	−0.499396	+	0.499396i	0.411854	+	0.911250i	$0.364882\pi$
$464$		−	36691.2i		−	0.170422i
$465$	16863.3	−	38690.8i	0.0779896	−	0.178938i
$466$	−125542.			−0.578120
$467$	96323.1	+	96323.1i	0.441669	+	0.441669i	0.892573	−	0.450904i	$-0.148898\pi$
$467$	96323.1	+	96323.1i	0.441669	+	0.441669i	−0.450904	+	0.892573i	$0.648898\pi$
$468$	35740.3	−	35740.3i	0.163180	−	0.163180i
$469$		−	37682.6i		−	0.171315i
$470$	57479.1	+	146293.i	0.260204	+	0.662258i
$471$	−204985.			−0.924018
$472$	65479.9	+	65479.9i	0.293917	+	0.293917i
$473$	82473.6	−	82473.6i	0.368632	−	0.368632i
$474$		−	176068.i		−	0.783653i
$475$	−10128.8	−	10899.8i	−0.0448920	−	0.0483091i
$476$	114827.			0.506793
$477$	4118.14	+	4118.14i	0.0180994	+	0.0180994i
$478$	−15555.9	+	15555.9i	−0.0680830	+	0.0680830i
$479$			131348.i			0.572468i	0.958160	+	0.286234i	$0.0924034\pi$
$479$			131348.i			0.572468i	−0.958160	+	0.286234i	$0.907597\pi$
$480$	−29033.6	+	11407.5i	−0.126014	+	0.0495116i
$481$	223257.			0.964971
$482$	214511.	+	214511.i	0.923328	+	0.923328i
$483$	37595.7	−	37595.7i	0.161155	−	0.161155i
$484$		−	81237.4i		−	0.346789i
$485$	91253.3	+	39772.6i	0.387940	+	0.169083i
$486$	−127625.			−0.540337
$487$	150677.	+	150677.i	0.635316	+	0.635316i	0.949396	−	0.314080i	$-0.101696\pi$
$487$	150677.	+	150677.i	0.635316	+	0.635316i	−0.314080	+	0.949396i	$0.601696\pi$
$488$	68089.3	−	68089.3i	0.285916	−	0.285916i
$489$			155406.i			0.649905i
$490$	−70317.8	+	161336.i	−0.292869	+	0.671952i
$491$	−72117.4			−0.299142			−0.149571	−	0.988751i	$-0.547789\pi$
$491$	−72117.4			−0.299142			−0.149571	+	0.988751i	$0.547789\pi$
$492$	25469.9	+	25469.9i	0.105220	+	0.105220i
$493$	83208.9	−	83208.9i	0.342355	−	0.342355i
$494$			12704.8i			0.0520611i
$495$	20505.3	+	52188.9i	0.0836865	+	0.212994i
$496$	−15674.9			−0.0637149
$497$	−10709.6	−	10709.6i	−0.0433571	−	0.0433571i
$498$	−111281.	+	111281.i	−0.448708	+	0.448708i
$499$		−	31657.7i		−	0.127139i	−0.997977	−	0.0635694i	$-0.979752\pi$
$499$		−	31657.7i		−	0.127139i	0.997977	−	0.0635694i	$-0.0202484\pi$
$500$	112682.	+	54108.4i	0.450729	+	0.216434i
$501$	−364515.			−1.45225
$502$	−2950.49	−	2950.49i	−0.0117081	−	0.0117081i
$503$	−299035.	+	299035.i	−1.18191	+	1.18191i	−0.202664	+	0.979248i	$0.564960\pi$
$503$	−299035.	+	299035.i	−1.18191	+	1.18191i	−0.979248	+	0.202664i	$0.935040\pi$
$504$		−	52984.9i		−	0.208589i
$505$	15.3953	−	6.04890i	6.03679e−5	−	2.37188e-5i
$506$	20896.9			0.0816171
$507$	−34302.4	−	34302.4i	−0.133447	−	0.133447i
$508$	65149.3	−	65149.3i	0.252454	−	0.252454i
$509$			59400.8i			0.229275i	0.993407	+	0.114638i	$0.0365707\pi$
$509$			59400.8i			0.229275i	−0.993407	+	0.114638i	$0.963429\pi$
$510$	−91713.1	−	39973.0i	−0.352607	−	0.153683i
$511$	595881.			2.28201
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	13284.7	−	13284.7i	0.0504799	−	0.0504799i
$514$		−	91355.9i		−	0.345788i
$515$	58980.9	−	135324.i	0.222381	−	0.510225i
$516$	96025.0			0.360649
$517$	105279.	+	105279.i	0.393877	+	0.393877i
$518$	165489.	−	165489.i	0.616750	−	0.616750i
$519$			1492.10i			0.00553939i
$520$	−39030.7	−	99338.7i	−0.144344	−	0.367377i
$521$	185109.			0.681948			0.340974	−	0.940073i	$-0.389243\pi$
$521$	185109.			0.681948			0.340974	+	0.940073i	$0.389243\pi$
$522$	−38395.2	−	38395.2i	−0.140908	−	0.140908i
$523$	−131987.	+	131987.i	−0.482534	+	0.482534i	−0.905940	−	0.423406i	$-0.860834\pi$
$523$	−131987.	+	131987.i	−0.482534	+	0.482534i	0.423406	+	0.905940i	$0.360834\pi$
$524$			202612.i			0.737910i
$525$	220685.	−	205075.i	0.800671	−	0.744035i
$526$	−181343.			−0.655434
$527$	−35547.8	−	35547.8i	−0.127995	−	0.127995i
$528$	−20893.9	+	20893.9i	−0.0749467	+	0.0749467i
$529$		−	12167.0i		−	0.0434783i
$530$	11446.2	−	4497.27i	0.0407483	−	0.0160102i
$531$	137042.			0.486032
$532$	9417.40	+	9417.40i	0.0332742	+	0.0332742i
$533$	−87145.4	+	87145.4i	−0.306754	+	0.306754i
$534$			153498.i			0.538295i
$535$	−65832.1	−	28692.8i	−0.230001	−	0.100246i
$536$	12193.4			0.0424420
$537$	191791.	+	191791.i	0.665090	+	0.665090i
$538$	89049.3	−	89049.3i	0.307656	−	0.307656i
$539$			166708.i			0.573826i
$540$	−63061.1	+	144686.i	−0.216259	+	0.496179i
$541$	415724.			1.42040			0.710200	−	0.704000i	$-0.248604\pi$
$541$	415724.			1.42040			0.710200	+	0.704000i	$0.248604\pi$
$542$	104367.	+	104367.i	0.355274	+	0.355274i
$543$	78982.6	−	78982.6i	0.267875	−	0.267875i
$544$			37156.0i			0.125554i
$545$	−43808.6	−	111499.i	−0.147491	−	0.375387i
$546$	−257231.			−0.862855
$547$	70068.9	+	70068.9i	0.234180	+	0.234180i	0.814435	−	0.580255i	$-0.197047\pi$
$547$	70068.9	+	70068.9i	0.234180	+	0.234180i	−0.580255	+	0.814435i	$0.697047\pi$
$548$	191047.	−	191047.i	0.636178	−	0.636178i
$549$		−	142503.i		−	0.472803i
$550$	118326.	+	4338.34i	0.391159	+	0.0143416i
$551$	13648.5			0.0449556
$552$	12165.3	+	12165.3i	0.0399249	+	0.0399249i
$553$	446541.	−	446541.i	1.46020	−	1.46020i
$554$			191648.i			0.624433i
$555$	−189786.	+	74567.9i	−0.616138	+	0.242084i
$556$	27318.7			0.0883712
$557$	280676.	+	280676.i	0.904678	+	0.904678i	0.995836	−	0.0911581i	$-0.0290569\pi$
$557$	280676.	+	280676.i	0.904678	+	0.904678i	−0.0911581	+	0.995836i	$0.529057\pi$
$558$	−16402.9	+	16402.9i	−0.0526808	+	0.0526808i
$559$			328550.i			1.05142i
$560$	−102566.	−	44703.3i	−0.327061	−	0.142549i
$561$	−94767.4			−0.301115
$562$	153548.	+	153548.i	0.486152	+	0.486152i
$563$	−204179.	+	204179.i	−0.644160	+	0.644160i	−0.951575	−	0.307416i	$-0.900536\pi$
$563$	−204179.	+	204179.i	−0.644160	+	0.644160i	0.307416	+	0.951575i	$0.400536\pi$
$564$			122578.i			0.385348i
$565$	36576.3	−	83919.8i	0.114578	−	0.262886i
$566$	−109170.			−0.340778
$567$	134855.	+	134855.i	0.419471	+	0.419471i
$568$	3465.42	−	3465.42i	0.0107414	−	0.0107414i
$569$			65668.6i			0.202831i	0.994844	+	0.101415i	$0.0323371\pi$
$569$			65668.6i			0.202831i	−0.994844	+	0.101415i	$0.967663\pi$
$570$	−4243.40	−	10800.1i	−0.0130606	−	0.0332412i
$571$	401804.			1.23237			0.616186	−	0.787601i	$-0.288677\pi$
$571$	401804.			1.23237			0.616186	+	0.787601i	$0.288677\pi$
$572$	−71488.7	−	71488.7i	−0.218497	−	0.218497i
$573$	−162722.	+	162722.i	−0.495607	+	0.495607i
$574$			129193.i			0.392116i
$575$	2525.95	−	68893.8i	0.00763993	−	0.208374i
$576$	17144.9			0.0516763
$577$	−333962.	−	333962.i	−1.00310	−	1.00310i	−0.999995	−	0.00310868i	$-0.999010\pi$
$577$	−333962.	−	333962.i	−1.00310	−	1.00310i	−0.00310868	−	0.999995i	$-0.500990\pi$
$578$	82779.0	−	82779.0i	0.247779	−	0.247779i
$579$			89129.2i			0.265866i
$580$	−106718.	+	41930.1i	−0.317236	+	0.124644i
$581$	−564461.			−1.67218
$582$	54892.8	+	54892.8i	0.162057	+	0.162057i
$583$	8237.21	−	8237.21i	0.0242350	−	0.0242350i
$584$			192816.i			0.565351i
$585$	−144796.	−	63109.0i	−0.423101	−	0.184408i
$586$	−269824.			−0.785752
$587$	−298542.	−	298542.i	−0.866422	−	0.866422i	0.125653	−	0.992074i	$-0.459898\pi$
$587$	−298542.	−	298542.i	−0.866422	−	0.866422i	−0.992074	+	0.125653i	$0.959898\pi$
$588$	−97050.3	+	97050.3i	−0.280700	+	0.280700i
$589$		−	5830.82i		−	0.0168073i
$590$	115622.	−	265281.i	0.332152	−	0.762083i
$591$	335196.			0.959675
$592$	53549.2	+	53549.2i	0.152795	+	0.152795i
$593$	291691.	−	291691.i	0.829494	−	0.829494i	−0.157953	−	0.987447i	$-0.550489\pi$
$593$	291691.	−	291691.i	0.829494	−	0.829494i	0.987447	+	0.157953i	$0.0504894\pi$
$594$			149504.i			0.423722i
$595$	−131223.	−	333981.i	−0.370659	−	0.943382i
$596$	256012.			0.720723
$597$	84736.4	+	84736.4i	0.237750	+	0.237750i
$598$	−41623.5	+	41623.5i	−0.116396	+	0.116396i
$599$			345544.i			0.963052i	0.876432	+	0.481526i	$0.159917\pi$
$599$			345544.i			0.963052i	−0.876432	+	0.481526i	$0.840083\pi$
$600$	66358.4	+	71409.6i	0.184329	+	0.198360i
$601$	72905.2			0.201841			0.100921	−	0.994894i	$-0.467821\pi$
$601$	72905.2			0.201841			0.100921	+	0.994894i	$0.467821\pi$
$602$	243537.	+	243537.i	0.672005	+	0.672005i
$603$	12759.7	−	12759.7i	0.0350919	−	0.0350919i
$604$		−	295031.i		−	0.808711i
$605$	−236283.	+	92836.8i	−0.645538	+	0.253635i
$606$	12.8996			3.51262e−5
$607$	312032.	+	312032.i	0.846879	+	0.846879i	0.989742	−	0.142863i	$-0.0456308\pi$
$607$	312032.	+	312032.i	0.846879	+	0.846879i	−0.142863	+	0.989742i	$0.545631\pi$
$608$	−3047.30	+	3047.30i	−0.00824343	+	0.00824343i
$609$			276339.i			0.745089i
$610$	−275853.	−	120230.i	−0.741340	−	0.323112i
$611$	−419400.			−1.12343
$612$	38881.6	+	38881.6i	0.103811	+	0.103811i
$613$	−111509.	+	111509.i	−0.296750	+	0.296750i	−0.839739	−	0.542990i	$-0.817292\pi$
$613$	−111509.	+	111509.i	−0.296750	+	0.296750i	0.542990	+	0.839739i	$0.317292\pi$
$614$			227393.i			0.603172i
$615$	44973.9	−	103187.i	0.118908	−	0.272819i
$616$	−105982.			−0.279300
$617$	1413.62	+	1413.62i	0.00371333	+	0.00371333i	0.708961	−	0.705248i	$-0.249164\pi$
$617$	1413.62	+	1413.62i	0.00371333	+	0.00371333i	−0.705248	+	0.708961i	$0.749164\pi$
$618$	81403.5	−	81403.5i	0.213140	−	0.213140i
$619$		−	13025.6i		−	0.0339952i	−0.999856	−	0.0169976i	$-0.994589\pi$
$619$		−	13025.6i		−	0.0339952i	0.999856	−	0.0169976i	$-0.00541076\pi$
$620$	17913.0	+	45591.2i	0.0466000	+	0.118604i
$621$	87047.2			0.225721
$622$	−252049.	−	252049.i	−0.651485	−	0.651485i
$623$	−389300.	+	389300.i	−1.00302	+	1.00302i
$624$		−	83235.2i		−	0.213765i
$625$	28605.6	−	389576.i	0.0732304	−	0.997315i
$626$	−74783.5			−0.190834
$627$	−7772.22	−	7772.22i	−0.0197702	−	0.0197702i
$628$	168224.	−	168224.i	0.426548	−	0.426548i
$629$			242880.i			0.613889i
$630$	−154109.	+	60550.3i	−0.388282	+	0.152558i
$631$	655022.			1.64512			0.822559	−	0.568679i	$-0.192546\pi$
$631$	655022.			1.64512			0.822559	+	0.568679i	$0.192546\pi$
$632$	144493.	+	144493.i	0.361752	+	0.361752i
$633$	374179.	−	374179.i	0.933839	−	0.933839i
$634$			551473.i			1.37197i
$635$	−263942.	−	115039.i	−0.654577	−	0.285296i
$636$	9590.69			0.0237102
$637$	−332058.	−	332058.i	−0.818343	−	0.818343i
$638$	−76799.2	+	76799.2i	−0.188676	+	0.188676i
$639$		−	7252.74i		−	0.0177624i
$640$	14465.2	−	33188.5i	0.0353153	−	0.0810267i
$641$	−643840.			−1.56697			−0.783487	−	0.621408i	$-0.786561\pi$
$641$	−643840.			−1.56697			−0.783487	+	0.621408i	$0.786561\pi$
$642$	−39600.8	−	39600.8i	−0.0960803	−	0.0960803i
$643$	380239.	−	380239.i	0.919676	−	0.919676i	−0.0773299	−	0.997006i	$-0.524639\pi$
$643$	380239.	−	380239.i	0.919676	−	0.919676i	0.997006	+	0.0773299i	$0.0246395\pi$
$644$			61706.8i			0.148786i
$645$	−109736.	−	279294.i	−0.263772	−	0.671338i
$646$	−13821.4			−0.0331199
$647$	−423413.	−	423413.i	−1.01148	−	1.01148i	−0.999933	−	0.0115431i	$-0.996326\pi$
$647$	−423413.	−	423413.i	−1.01148	−	1.01148i	−0.0115431	−	0.999933i	$-0.503674\pi$
$648$	−43636.7	+	43636.7i	−0.103921	+	0.103921i
$649$		−	274115.i		−	0.650795i
$650$	−244328.	+	227045.i	−0.578291	+	0.537386i
$651$	118055.			0.278563
$652$	−127536.	−	127536.i	−0.300011	−	0.300011i
$653$	−443637.	+	443637.i	−1.04040	+	1.04040i	−0.0412546	+	0.999149i	$0.513135\pi$
$653$	−443637.	+	443637.i	−1.04040	+	1.04040i	−0.999149	+	0.0412546i	$0.986865\pi$
$654$		−	93424.4i		−	0.218426i
$655$	589308.	−	231542.i	1.37360	−	0.539694i
$656$	−41804.4			−0.0971437
$657$	201771.	+	201771.i	0.467443	+	0.467443i
$658$	−310880.	+	310880.i	−0.718027	+	0.718027i
$659$		−	239097.i		−	0.550558i	−0.961364	−	0.275279i	$-0.911230\pi$
$659$		−	239097.i		−	0.550558i	0.961364	−	0.275279i	$-0.0887702\pi$
$660$	84648.3	+	36893.8i	0.194326	+	0.0846965i
$661$	−675145.			−1.54523			−0.772617	−	0.634873i	$-0.781052\pi$
$661$	−675145.			−1.54523			−0.772617	+	0.634873i	$0.781052\pi$
$662$	−151993.	−	151993.i	−0.346823	−	0.346823i
$663$	188762.	−	188762.i	0.429426	−	0.429426i
$664$		−	182649.i		−	0.414269i
$665$	16628.9	−	38153.1i	0.0376029	−	0.0862752i
$666$	112072.			0.252668
$667$	44715.5	+	44715.5i	0.100509	+	0.100509i
$668$	299144.	−	299144.i	0.670390	−	0.670390i
$669$			637614.i			1.42464i
$670$	−13934.4	−	35465.1i	−0.0310413	−	0.0790045i
$671$	−285039.			−0.633081
$672$	−61698.0	−	61698.0i	−0.136626	−	0.136626i
$673$	−75411.5	+	75411.5i	−0.166497	+	0.166497i	−0.785438	−	0.618940i	$-0.787562\pi$
$673$	−75411.5	+	75411.5i	−0.166497	+	0.166497i	0.618940	+	0.785438i	$0.287562\pi$
$674$			227709.i			0.501257i
$675$	492891.	+	18071.6i	1.08179	+	0.0396633i
$676$	56301.5			0.123204
$677$	141263.	+	141263.i	0.308213	+	0.308213i	0.844216	−	0.536003i	$-0.180066\pi$
$677$	141263.	+	141263.i	0.308213	+	0.308213i	−0.536003	+	0.844216i	$0.680066\pi$
$678$	50481.4	−	50481.4i	0.109818	−	0.109818i
$679$			278437.i			0.603930i
$680$	108070.	−	42461.2i	0.233715	−	0.0918280i
$681$	−174947.			−0.377234
$682$	32809.5	+	32809.5i	0.0705393	+	0.0705393i
$683$	569492.	−	569492.i	1.22081	−	1.22081i	0.253459	−	0.967346i	$-0.418432\pi$
$683$	569492.	−	569492.i	1.22081	−	1.22081i	0.967346	−	0.253459i	$-0.0815682\pi$
$684$			6377.66i			0.0136317i
$685$	−773995.	−	337344.i	−1.64952	−	0.718939i
$686$	−17390.8			−0.0369549
$687$	82173.5	+	82173.5i	0.174108	+	0.174108i
$688$	−78804.2	+	78804.2i	−0.166484	+	0.166484i
$689$			32814.6i			0.0691239i
$690$	21481.0	−	49285.6i	0.0451187	−	0.103519i
$691$	332677.			0.696734			0.348367	−	0.937358i	$-0.386736\pi$
$691$	332677.			0.696734			0.348367	+	0.937358i	$0.386736\pi$
$692$	−1224.51	−	1224.51i	−0.00255711	−	0.00255711i
$693$	−110904.	+	110904.i	−0.230930	+	0.230930i
$694$		−	289227.i		−	0.600510i
$695$	−31219.4	−	79457.9i	−0.0646331	−	0.164501i
$696$	−89418.3			−0.184590
$697$	−94804.9	−	94804.9i	−0.195149	−	0.195149i
$698$	284714.	−	284714.i	0.584384	−	0.584384i
$699$			305953.i			0.626182i
$700$	−12810.7	+	349405.i	−0.0261444	+	0.713072i
$701$	99149.2			0.201768			0.100884	−	0.994898i	$-0.467833\pi$
$701$	99149.2			0.201768			0.100884	+	0.994898i	$0.467833\pi$
$702$	−297790.	−	297790.i	−0.604277	−	0.604277i
$703$	−19919.5	+	19919.5i	−0.0403058	+	0.0403058i
$704$		−	34293.8i		−	0.0691943i
$705$	356523.	−	140080.i	0.717314	−	0.281836i
$706$	−620132.			−1.24416
$707$	32.7159	+	32.7159i	6.54515e−5	+	6.54515e-5i
$708$	159578.	−	159578.i	0.318351	−	0.318351i
$709$			352567.i			0.701373i	0.936493	+	0.350687i	$0.114052\pi$
$709$			352567.i			0.701373i	−0.936493	+	0.350687i	$0.885948\pi$
$710$	−14039.6	−	6119.13i	−0.0278508	−	0.0121387i
$711$	302407.			0.598208
$712$	−125970.	−	125970.i	−0.248489	−	0.248489i
$713$	19103.0	−	19103.0i	0.0375770	−	0.0375770i
$714$		−	279840.i		−	0.548925i
$715$	−126232.	+	289625.i	−0.246921	+	0.566531i
$716$	−314792.			−0.614042
$717$	37910.5	+	37910.5i	0.0737431	+	0.0737431i
$718$	451507.	−	451507.i	0.875822	−	0.875822i
$719$			738358.i			1.42827i	0.700010	+	0.714134i	$0.253179\pi$
$719$			738358.i			1.42827i	−0.700010	+	0.714134i	$0.746821\pi$
$720$	−19593.0	−	49866.9i	−0.0377951	−	0.0961939i
$721$	412909.			0.794299
$722$	259508.	+	259508.i	0.497825	+	0.497825i
$723$	522775.	−	522775.i	1.00009	−	1.00009i
$724$			129636.i			0.247314i
$725$	243912.	+	262478.i	0.464041	+	0.499364i
$726$	−197980.			−0.375619
$727$	−339438.	−	339438.i	−0.642232	−	0.642232i	0.308872	−	0.951104i	$-0.400049\pi$
$727$	−339438.	−	339438.i	−0.642232	−	0.642232i	−0.951104	+	0.308872i	$0.900049\pi$
$728$	211100.	−	211100.i	0.398314	−	0.398314i
$729$			531940.i			1.00094i
$730$	560816.	−	220347.i	1.05238	−	0.413487i
$731$	−357427.			−0.668888
$732$	−165937.	−	165937.i	−0.309686	−	0.309686i
$733$	164856.	−	164856.i	0.306830	−	0.306830i	−0.536849	−	0.843678i	$-0.680385\pi$
$733$	164856.	−	164856.i	0.306830	−	0.306830i	0.843678	+	0.536849i	$0.180385\pi$
$734$		−	672861.i		−	1.24892i
$735$	393183.	+	171368.i	0.727814	+	0.317216i
$736$	−19967.2			−0.0368605
$737$	−25522.3	−	25522.3i	−0.0469878	−	0.0469878i
$738$	−43746.0	+	43746.0i	−0.0803204	+	0.0803204i
$739$			149206.i			0.273210i	0.990626	+	0.136605i	$0.0436191\pi$
$739$			149206.i			0.273210i	−0.990626	+	0.136605i	$0.956381\pi$
$740$	94555.3	−	216946.i	0.172672	−	0.396175i
$741$	30962.2			0.0563891
$742$	24323.8	+	24323.8i	0.0441798	+	0.0441798i
$743$	−688486.	+	688486.i	−1.24715	+	1.24715i	−0.290173	+	0.956974i	$0.593713\pi$
$743$	−688486.	+	688486.i	−1.24715	+	1.24715i	−0.956974	+	0.290173i	$0.906287\pi$
$744$			38200.5i			0.0690118i
$745$	−292567.	−	744625.i	−0.527124	−	1.34161i
$746$	706520.			1.26954
$747$	−191132.	−	191132.i	−0.342525	−	0.342525i
$748$	77772.1	−	77772.1i	0.139002	−	0.139002i
$749$		−	200870.i		−	0.358057i
$750$	131865.	−	274612.i	0.234427	−	0.488200i
$751$	−1.03331e6			−1.83210			−0.916052	−	0.401060i	$-0.868642\pi$
$751$	−1.03331e6			−1.83210			−0.916052	+	0.401060i	$0.868642\pi$
$752$	−100595.	−	100595.i	−0.177885	−	0.177885i
$753$	−7190.49	+	7190.49i	−0.0126814	+	0.0126814i
$754$		−	305945.i		−	0.538147i
$755$	−858112.	+	337156.i	−1.50539	+	0.591477i
$756$	−441473.			−0.772433
$757$	501326.	+	501326.i	0.874840	+	0.874840i	0.992995	−	0.118155i	$-0.0376981\pi$
$757$	501326.	+	501326.i	0.874840	+	0.874840i	−0.118155	+	0.992995i	$0.537698\pi$
$758$	−178993.	+	178993.i	−0.311528	+	0.311528i
$759$		−	50926.9i		−	0.0884023i
$760$	12345.6	+	5380.82i	0.0213740	+	0.00931582i
$761$	−523924.			−0.904688			−0.452344	−	0.891844i	$-0.649412\pi$
$761$	−523924.			−0.904688			−0.452344	+	0.891844i	$0.649412\pi$
$762$	−158772.	−	158772.i	−0.273442	−	0.273442i
$763$	236942.	−	236942.i	0.406998	−	0.406998i
$764$		−	267080.i		−	0.457567i
$765$	68655.9	−	157523.i	0.117315	−	0.269166i
$766$	−3895.16			−0.00663847
$767$	545997.	+	545997.i	0.928110	+	0.928110i
$768$	19964.3	−	19964.3i	0.0338479	−	0.0338479i
$769$			376682.i			0.636975i	0.947927	+	0.318487i	$0.103175\pi$
$769$			376682.i			0.636975i	−0.947927	+	0.318487i	$0.896825\pi$
$770$	121114.	+	308254.i	0.204275	+	0.519908i
$771$	−222639.			−0.374535
$772$	−73145.1	−	73145.1i	−0.122730	−	0.122730i
$773$	−488078.	+	488078.i	−0.816827	+	0.816827i	−0.985647	−	0.168820i	$-0.946004\pi$
$773$	−488078.	+	488078.i	−0.816827	+	0.816827i	0.168820	+	0.985647i	$0.446004\pi$
$774$			164928.i			0.275305i
$775$	112134.	−	104202.i	0.186695	−	0.173489i
$776$	−90097.0			−0.149619
$777$	−403305.	−	403305.i	−0.668023	−	0.668023i
$778$	−112388.	+	112388.i	−0.185678	+	0.185678i
$779$		−	15550.6i		−	0.0256255i
$780$	−242094.	+	95119.8i	−0.397919	+	0.156344i
$781$	−14507.1			−0.0237837
$782$	−45282.0	−	45282.0i	−0.0740477	−	0.0740477i
$783$	−319911.	+	319911.i	−0.521802	+	0.521802i
$784$		−	159291.i		−	0.259155i
$785$	−681531.	−	297044.i	−1.10598	−	0.482038i
$786$	493777.			0.799255
$787$	483725.	+	483725.i	0.780996	+	0.780996i	0.979999	−	0.199003i	$-0.0637703\pi$
$787$	483725.	+	483725.i	0.780996	+	0.780996i	−0.199003	+	0.979999i	$0.563770\pi$
$788$	−275083.	+	275083.i	−0.443009	+	0.443009i
$789$			441942.i			0.709924i
$790$	255140.	−	585388.i	0.408813	−	0.937971i
$791$	256060.			0.409251
$792$	−35886.5	−	35886.5i	−0.0572112	−	0.0572112i
$793$	567755.	−	567755.i	0.902848	−	0.902848i
$794$		−	528293.i		−	0.837980i
$795$	−10960.1	−	27895.0i	−0.0173412	−	0.0441359i
$796$	−139080.			−0.219502
$797$	883230.	+	883230.i	1.39045	+	1.39045i	0.824296	+	0.566159i	$0.191571\pi$
$797$	883230.	+	883230.i	1.39045	+	1.39045i	0.566159	+	0.824296i	$0.308429\pi$
$798$	22950.7	−	22950.7i	0.0360405	−	0.0360405i
$799$		−	456262.i		−	0.714695i
$800$	−113061.	−	4145.32i	−0.176658	−	0.00647706i
$801$	−263642.			−0.410912
$802$	473192.	+	473192.i	0.735679	+	0.735679i
$803$	403589.	−	403589.i	0.625904	−	0.625904i
$804$		−	29716.0i		−	0.0459703i
$805$	179477.	−	70517.5i	0.276961	−	0.108819i
$806$	−130703.			−0.201195
$807$	−217018.	−	217018.i	−0.333233	−	0.333233i
$808$	−10.5862	+	10.5862i	−1.62151e−5	+	1.62151e-5i
$809$		−	821626.i		−	1.25539i	−0.778461	−	0.627693i	$-0.784000\pi$
$809$		−	821626.i		−	1.25539i	0.778461	−	0.627693i	$-0.216000\pi$
$810$	176787.	+	77052.1i	0.269451	+	0.117440i
$811$	253907.			0.386040			0.193020	−	0.981195i	$-0.438172\pi$
$811$	253907.			0.386040			0.193020	+	0.981195i	$0.438172\pi$
$812$	−226782.	−	226782.i	−0.343950	−	0.343950i
$813$	254347.	−	254347.i	0.384809	−	0.384809i
$814$		−	224170.i		−	0.338321i
$815$	−225199.	+	516691.i	−0.339040	+	0.777886i
$816$	90551.0			0.135992
$817$	−29314.0	−	29314.0i	−0.0439168	−	0.0439168i
$818$	47355.0	−	47355.0i	0.0707716	−	0.0707716i
$819$		−	441809.i		−	0.658668i
$820$	47773.5	+	121590.i	0.0710492	+	0.180830i
$821$	−564605.			−0.837642			−0.418821	−	0.908069i	$-0.637557\pi$
$821$	−564605.			−0.837642			−0.418821	+	0.908069i	$0.637557\pi$
$822$	−465591.	−	465591.i	−0.689067	−	0.689067i
$823$	−836853.	+	836853.i	−1.23552	+	1.23552i	−0.273706	+	0.961814i	$0.588249\pi$
$823$	−836853.	+	836853.i	−1.23552	+	1.23552i	−0.961814	+	0.273706i	$0.911751\pi$
$824$			133610.i			0.196781i
$825$	10572.8	−	288366.i	0.0155339	−	0.423678i
$826$	809439.			1.18638
$827$	614491.	+	614491.i	0.898472	+	0.898472i	0.995301	−	0.0968291i	$-0.0308700\pi$
$827$	614491.	+	614491.i	0.898472	+	0.898472i	−0.0968291	+	0.995301i	$0.530870\pi$
$828$	−20894.5	+	20894.5i	−0.0304770	+	0.0304770i
$829$			402172.i			0.585199i	0.956235	+	0.292599i	$0.0945202\pi$
$829$			402172.i			0.585199i	−0.956235	+	0.292599i	$0.905480\pi$
$830$	−531245.	+	208729.i	−0.771150	+	0.302989i
$831$	467057.			0.676344
$832$	68308.1	+	68308.1i	0.0986791	+	0.0986791i
$833$	361244.	−	361244.i	0.520608	−	0.520608i
$834$		−	66577.2i		−	0.0957179i
$835$	−1.21193e6	−	528219.i	−1.73822	−	0.757602i
$836$	12756.8			0.0182527
$837$	136670.	+	136670.i	0.195084	+	0.195084i
$838$	394939.	−	394939.i	0.562396	−	0.562396i
$839$		−	848364.i		−	1.20520i	−0.798044	−	0.602599i	$-0.794132\pi$
$839$		−	848364.i		−	1.20520i	0.798044	−	0.602599i	$-0.205868\pi$
$840$	−108944.	+	249959.i	−0.154399	+	0.354251i
$841$	378609.			0.535302
$842$	467583.	+	467583.i	0.659530	+	0.659530i
$843$	374205.	−	374205.i	0.526568	−	0.526568i
$844$			614150.i			0.862164i
$845$	−64340.4	−	163756.i	−0.0901095	−	0.229342i
$846$	−210534.			−0.294158
$847$	−502114.	−	502114.i	−0.699899	−	0.699899i
$848$	−7870.73	+	7870.73i	−0.0109452	+	0.0109452i
$849$			266054.i			0.369108i
$850$	−247001.	−	265803.i	−0.341870	−	0.367894i
$851$	−130521.			−0.180227
$852$	−8445.42	−	8445.42i	−0.0116343	−	0.0116343i
$853$	431174.	−	431174.i	0.592590	−	0.592590i	−0.345740	−	0.938330i	$-0.612372\pi$
$853$	431174.	−	431174.i	0.592590	−	0.592590i	0.938330	+	0.345740i	$0.112372\pi$
$854$		−	841696.i		−	1.15409i
$855$	18549.7	−	7288.28i	0.0253750	−	0.00996995i
$856$	64997.9			0.0887058
$857$	143954.	+	143954.i	0.196002	+	0.196002i	0.798284	−	0.602281i	$-0.205742\pi$
$857$	143954.	+	143954.i	0.196002	+	0.196002i	−0.602281	+	0.798284i	$0.705742\pi$
$858$	−174222.	+	174222.i	−0.236662	+	0.236662i
$859$			581359.i			0.787877i	0.919137	+	0.393938i	$0.128888\pi$
$859$			581359.i			0.787877i	−0.919137	+	0.393938i	$0.871112\pi$
$860$	319262.	+	139150.i	0.431669	+	0.188142i
$861$	314850.			0.424715
$862$	176391.	+	176391.i	0.237389	+	0.237389i
$863$	−355382.	+	355382.i	−0.477170	+	0.477170i	−0.904226	−	0.427055i	$-0.859551\pi$
$863$	−355382.	+	355382.i	−0.477170	+	0.477170i	0.427055	+	0.904226i	$0.359551\pi$
$864$		−	142853.i		−	0.191364i
$865$	−2162.20	+	4960.90i	−0.00288977	+	0.00663022i
$866$	515225.			0.687007
$867$	−201737.	−	201737.i	−0.268378	−	0.268378i
$868$	−96883.7	+	96883.7i	−0.128591	+	0.128591i
$869$		−	604883.i		−	0.800998i
$870$	102186.	+	260078.i	0.135006	+	0.343609i
$871$	101673.			0.134020
$872$	76670.0	+	76670.0i	0.100831	+	0.100831i
$873$	−94281.5	+	94281.5i	−0.123708	+	0.123708i
$874$		−	7427.49i		−	0.00972342i
$875$	1.03090e6	−	362034.i	1.34649	−	0.472861i
$876$	469903.			0.612351
$877$	−777486.	−	777486.i	−1.01087	−	1.01087i	−0.999940	−	0.0109250i	$-0.996522\pi$
$877$	−777486.	−	777486.i	−1.01087	−	1.01087i	−0.0109250	−	0.999940i	$-0.503478\pi$
$878$	432443.	−	432443.i	0.560971	−	0.560971i
$879$			657575.i			0.851075i
$880$	−99745.2	+	39190.4i	−0.128803	+	0.0506074i
$881$	−1.35079e6			−1.74035			−0.870173	−	0.492747i	$-0.835993\pi$
$881$	−1.35079e6			−1.74035			−0.870173	+	0.492747i	$0.835993\pi$
$882$	−166689.	−	166689.i	−0.214275	−	0.214275i
$883$	−909875.	+	909875.i	−1.16697	+	1.16697i	−0.184055	+	0.982916i	$0.558923\pi$
$883$	−909875.	+	909875.i	−1.16697	+	1.16697i	−0.982916	+	0.184055i	$0.941077\pi$
$884$			309821.i			0.396466i
$885$	−646504.	−	281777.i	−0.825438	−	0.359766i
$886$	468428.			0.596727
$887$	−487909.	−	487909.i	−0.620142	−	0.620142i	0.325425	−	0.945568i	$-0.394493\pi$
$887$	−487909.	−	487909.i	−0.620142	−	0.620142i	−0.945568	+	0.325425i	$0.894493\pi$
$888$	130502.	−	130502.i	0.165498	−	0.165498i
$889$		−	805353.i		−	1.01902i
$890$	−222434.	+	510348.i	−0.280816	+	0.644297i
$891$	182674.			0.230103
$892$	−523267.	−	523267.i	−0.657648	−	0.657648i
$893$	37419.8	−	37419.8i	0.0469243	−	0.0469243i
$894$		−	623916.i		−	0.780640i
$895$	359740.	+	915590.i	0.449099	+	1.14302i
$896$	101267.			0.126139
$897$	101439.	+	101439.i	0.126072	+	0.126072i
$898$	−746765.	+	746765.i	−0.926043	+	0.926043i
$899$			140413.i			0.173735i
$900$	−122650.	+	113974.i	−0.151420	+	0.140709i
$901$	−35698.8			−0.0439748
$902$	87502.0	+	87502.0i	0.107549	+	0.107549i
$903$	593513.	−	593513.i	0.727872	−	0.727872i
$904$			82856.4i			0.101389i
$905$	377054.	−	148146.i	0.460369	−	0.180881i
$906$	−719005.			−0.875943
$907$	−719114.	−	719114.i	−0.874144	−	0.874144i	0.118777	−	0.992921i	$-0.462103\pi$
$907$	−719114.	−	719114.i	−0.874144	−	0.874144i	−0.992921	+	0.118777i	$0.962103\pi$
$908$	143572.	−	143572.i	0.174140	−	0.174140i
$909$			22.1558i			2.68139e-5i
$910$	−855237.	−	372753.i	−1.03277	−	0.450131i
$911$	−1.03829e6			−1.25107			−0.625537	−	0.780195i	$-0.715120\pi$
$911$	−1.03829e6			−1.25107			−0.625537	+	0.780195i	$0.715120\pi$
$912$	7426.43	+	7426.43i	0.00892874	+	0.00892874i
$913$	−382308.	+	382308.i	−0.458640	+	0.458640i
$914$		−	381371.i		−	0.456515i
$915$	−293006.	+	672267.i	−0.349973	+	0.802971i
$916$	−134874.			−0.160744
$917$	1.25231e6	+	1.25231e6i	1.48927	+	1.48927i
$918$	323964.	−	323964.i	0.384425	−	0.384425i
$919$		−	363220.i		−	0.430070i	−0.976606	−	0.215035i	$-0.931013\pi$
$919$		−	363220.i		−	0.430070i	0.976606	−	0.215035i	$-0.0689866\pi$
$920$	22818.2	+	58075.6i	0.0269591	+	0.0686148i
$921$	554169.			0.653316
$922$	195300.	+	195300.i	0.229742	+	0.229742i
$923$	28896.0	−	28896.0i	0.0339184	−	0.0339184i
$924$			258283.i			0.302519i
$925$	−739054.	−	27097.0i	−0.863759	−	0.0316692i
$926$	−428220.			−0.499396
$927$	139815.	+	139815.i	0.162703	+	0.162703i
$928$	73382.3	−	73382.3i	0.0852110	−	0.0852110i
$929$		−	1.15614e6i		−	1.33961i	−0.742536	−	0.669806i	$-0.766377\pi$
$929$		−	1.15614e6i		−	1.33961i	0.742536	−	0.669806i	$-0.233623\pi$
$930$	111108.	−	43655.0i	0.128464	−	0.0504740i
$931$	59253.9			0.0683625
$932$	−251085.	−	251085.i	−0.289060	−	0.289060i
$933$	−614256.	+	614256.i	−0.705645	+	0.705645i
$934$			385292.i			0.441669i
$935$	−315081.	−	137327.i	−0.360412	−	0.157085i
$936$	142961.			0.163180
$937$	1.04919e6	+	1.04919e6i	1.19502	+	1.19502i	0.975641	+	0.219375i	$0.0704017\pi$
$937$	1.04919e6	+	1.04919e6i	1.19502	+	1.19502i	0.219375	+	0.975641i	$0.429598\pi$
$938$	75365.3	−	75365.3i	0.0856575	−	0.0856575i
$939$			182251.i			0.206699i
$940$	−177627.	+	407544.i	−0.201027	+	0.461231i
$941$	401501.			0.453427			0.226714	−	0.973961i	$-0.427202\pi$
$941$	401501.			0.453427			0.226714	+	0.973961i	$0.427202\pi$
$942$	−409970.	−	409970.i	−0.462009	−	0.462009i
$943$	50947.1	−	50947.1i	0.0572922	−	0.0572922i
$944$			261920.i			0.293917i
$945$	504508.	+	1.28405e6i	0.564943	+	1.43786i
$946$	329894.			0.368632
$947$	73622.5	+	73622.5i	0.0820939	+	0.0820939i	0.746961	−	0.664867i	$-0.231512\pi$
$947$	73622.5	+	73622.5i	0.0820939	+	0.0820939i	−0.664867	+	0.746961i	$0.731512\pi$
$948$	352136.	−	352136.i	0.391826	−	0.391826i
$949$			1.60778e6i			1.78523i
$950$	1542.00	−	42057.0i	0.00170858	−	0.0466006i
$951$	1.34397e6			1.48603
$952$	229654.	+	229654.i	0.253397	+	0.253397i
$953$	784519.	−	784519.i	0.863809	−	0.863809i	−0.127969	−	0.991778i	$-0.540846\pi$
$953$	784519.	−	784519.i	0.863809	−	0.863809i	0.991778	+	0.127969i	$0.0408458\pi$
$954$			16472.6i			0.0180994i
$955$	−776817.	+	305215.i	−0.851749	+	0.334657i
$956$	−62223.5			−0.0680830
$957$	187164.	+	187164.i	0.204361	+	0.204361i
$958$	−262695.	+	262695.i	−0.286234	+	0.286234i
$959$		−	2.36165e6i		−	2.56791i
$960$	−80882.2	−	35252.4i	−0.0877628	−	0.0382513i
$961$	−863535.			−0.935047
$962$	446513.	+	446513.i	0.482486	+	0.482486i
$963$	68016.7	−	68016.7i	0.0733437	−	0.0733437i
$964$			858045.i			0.923328i
$965$	−129157.	+	296335.i	−0.138696	+	0.318221i
$966$	150383.			0.161155
$967$	986575.	+	986575.i	1.05506	+	1.05506i	0.998393	+	0.0566669i	$0.0180473\pi$
$967$	986575.	+	986575.i	1.05506	+	1.05506i	0.0566669	+	0.998393i	$0.481953\pi$
$968$	162475.	−	162475.i	0.173394	−	0.173394i
$969$			33683.6i			0.0358733i
$970$	102961.	+	262052.i	0.109429	+	0.278512i
$971$	1.01799e6			1.07971			0.539855	−	0.841758i	$-0.318479\pi$
$971$	1.01799e6			1.07971			0.539855	+	0.841758i	$0.318479\pi$
$972$	−255251.	−	255251.i	−0.270168	−	0.270168i
$973$	168852.	−	168852.i	0.178353	−	0.178353i
$974$			602709.i			0.635316i
$975$	553322.	+	595440.i	0.582061	+	0.626367i
$976$	272357.			0.285916
$977$	−569922.	−	569922.i	−0.597071	−	0.597071i	0.342461	−	0.939532i	$-0.388740\pi$
$977$	−569922.	−	569922.i	−0.597071	−	0.597071i	−0.939532	+	0.342461i	$0.888740\pi$
$978$	−310812.	+	310812.i	−0.324953	+	0.324953i
$979$			527343.i			0.550209i
$980$	−463307.	+	182036.i	−0.482410	+	0.189541i
$981$	160462.			0.166737
$982$	−144235.	−	144235.i	−0.149571	−	0.149571i
$983$	−845623.	+	845623.i	−0.875125	+	0.875125i	−0.993025	−	0.117901i	$-0.962384\pi$
$983$	−845623.	+	845623.i	−0.875125	+	0.875125i	0.117901	+	0.993025i	$0.462384\pi$
$984$			101880.i			0.105220i
$985$	1.11446e6	+	485733.i	1.14866	+	0.500640i
$986$	332836.			0.342355
$987$	757630.	+	757630.i	0.777719	+	0.777719i
$988$	−25409.6	+	25409.6i	−0.0260305	+	0.0260305i
$989$		−	192077.i		−	0.196374i
$990$	−63367.2	+	145388.i	−0.0646538	+	0.148340i
$991$	250685.			0.255259			0.127630	−	0.991822i	$-0.459263\pi$
$991$	250685.			0.255259			0.127630	+	0.991822i	$0.459263\pi$
$992$	−31349.8	−	31349.8i	−0.0318575	−	0.0318575i
$993$	−370415.	+	370415.i	−0.375656	+	0.375656i
$994$		−	42838.3i		−	0.0433571i
$995$	158939.	+	404522.i	0.160540	+	0.408597i
$996$	−445126.			−0.448708
$997$	471463.	+	471463.i	0.474305	+	0.474305i	0.903305	−	0.429000i	$-0.141134\pi$
$997$	471463.	+	471463.i	0.474305	+	0.474305i	−0.429000	+	0.903305i	$0.641134\pi$
$998$	63315.3	−	63315.3i	0.0635694	−	0.0635694i
$999$		−	933793.i		−	0.935663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.b.47.15	✓	44
5.3	odd	4	inner	230.5.f.b.93.15	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.b.47.15	✓	44	1.1	even	1	trivial
230.5.f.b.93.15	yes	44	5.3	odd	4	inner

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +(4.87410 - 4.87410i) q^{3} +8.00000i q^{4} +(23.2684 - 9.14227i) q^{5} +19.4964 q^{6} +(49.4466 + 49.4466i) q^{7} +(-16.0000 + 16.0000i) q^{8} +33.4862i q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +(4.87410 - 4.87410i) q^{3} +8.00000i q^{4} +(23.2684 - 9.14227i) q^{5} +19.4964 q^{6} +(49.4466 + 49.4466i) q^{7} +(-16.0000 + 16.0000i) q^{8} +33.4862i q^{9} +(64.8214 + 28.2523i) q^{10} +66.9800 q^{11} +(38.9928 + 38.9928i) q^{12} +(-133.414 + 133.414i) q^{13} +197.786i q^{14} +(68.8523 - 157.973i) q^{15} -64.0000 q^{16} +(-145.140 - 145.140i) q^{17} +(-66.9724 + 66.9724i) q^{18} -23.8070i q^{19} +(73.1382 + 186.147i) q^{20} +482.016 q^{21} +(133.960 + 133.960i) q^{22} +(77.9968 - 77.9968i) q^{23} +155.971i q^{24} +(457.838 - 425.452i) q^{25} -533.657 q^{26} +(558.018 + 558.018i) q^{27} +(-395.573 + 395.573i) q^{28} +573.299i q^{29} +(453.651 - 178.242i) q^{30} +244.920 q^{31} +(-128.000 - 128.000i) q^{32} +(326.468 - 326.468i) q^{33} -580.562i q^{34} +(1602.60 + 698.489i) q^{35} -267.890 q^{36} +(-836.705 - 836.705i) q^{37} +(47.6140 - 47.6140i) q^{38} +1300.55i q^{39} +(-226.018 + 518.571i) q^{40} +653.194 q^{41} +(964.031 + 964.031i) q^{42} +(1231.32 - 1231.32i) q^{43} +535.840i q^{44} +(306.140 + 779.171i) q^{45} +311.987 q^{46} +(1571.80 + 1571.80i) q^{47} +(-311.943 + 311.943i) q^{48} +2488.93i q^{49} +(1766.58 + 64.7706i) q^{50} -1414.86 q^{51} +(-1067.31 - 1067.31i) q^{52} +(122.980 - 122.980i) q^{53} +2232.07i q^{54} +(1558.52 - 612.350i) q^{55} -1582.29 q^{56} +(-116.038 - 116.038i) q^{57} +(-1146.60 + 1146.60i) q^{58} -4092.49i q^{59} +(1263.78 + 550.818i) q^{60} -4255.58 q^{61} +(489.840 + 489.840i) q^{62} +(-1655.78 + 1655.78i) q^{63} -512.000i q^{64} +(-1884.63 + 4324.04i) q^{65} +1305.87 q^{66} +(-381.044 - 381.044i) q^{67} +(1161.12 - 1161.12i) q^{68} -760.329i q^{69} +(1808.22 + 4602.17i) q^{70} -216.589 q^{71} +(-535.779 - 535.779i) q^{72} +(6025.51 - 6025.51i) q^{73} -3346.82i q^{74} +(157.849 - 4305.25i) q^{75} +190.456 q^{76} +(3311.93 + 3311.93i) q^{77} +(-2601.10 + 2601.10i) q^{78} -9030.79i q^{79} +(-1489.18 + 585.106i) q^{80} +2727.29 q^{81} +(1306.39 + 1306.39i) q^{82} +(-5707.79 + 5707.79i) q^{83} +3856.12i q^{84} +(-4704.10 - 2050.27i) q^{85} +4925.26 q^{86} +(2794.32 + 2794.32i) q^{87} +(-1071.68 + 1071.68i) q^{88} +7873.14i q^{89} +(-946.061 + 2170.62i) q^{90} -13193.7 q^{91} +(623.974 + 623.974i) q^{92} +(1193.77 - 1193.77i) q^{93} +6287.18i q^{94} +(-217.650 - 553.951i) q^{95} -1247.77 q^{96} +(2815.53 + 2815.53i) q^{97} +(-4977.85 + 4977.85i) q^{98} +2242.91i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8}+O(q^{10}) \) 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8	\( 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8} - 136 q^{10} - 632 q^{11} + 500 q^{13} + 12 q^{15} - 2816 q^{16} + 120 q^{17} + 2648 q^{18} - 736 q^{20} - 856 q^{21} - 1264 q^{22} + 2052 q^{25} + 2000 q^{26} + 588 q^{27} + 640 q^{28} - 1704 q^{30} + 3220 q^{31} - 5632 q^{32} - 2884 q^{33} + 720 q^{35} + 10592 q^{36} + 1856 q^{37} - 1696 q^{38} - 1856 q^{40} - 5156 q^{41} - 1712 q^{42} + 960 q^{43} + 460 q^{45} - 1224 q^{47} + 4456 q^{50} + 3640 q^{51} + 4000 q^{52} + 13556 q^{53} + 12980 q^{55} + 2560 q^{56} - 3072 q^{57} - 3112 q^{58} - 6912 q^{60} - 4864 q^{61} + 6440 q^{62} - 13484 q^{63} - 4100 q^{65} - 11536 q^{66} - 1888 q^{67} - 960 q^{68} + 8824 q^{70} - 1060 q^{71} + 21184 q^{72} + 16616 q^{73} - 11044 q^{75} - 6784 q^{76} + 8892 q^{77} - 23152 q^{78} - 1536 q^{80} - 4044 q^{81} - 10312 q^{82} - 27024 q^{83} - 11068 q^{85} + 3840 q^{86} - 8392 q^{87} + 10112 q^{88} - 7184 q^{90} - 54024 q^{91} + 22528 q^{93} - 25968 q^{95} - 3252 q^{97} - 27984 q^{98}+O(q^{100}) \) 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8 - 136 * q^10 - 632 * q^11 + 500 * q^13 + 12 * q^15 - 2816 * q^16 + 120 * q^17 + 2648 * q^18 - 736 * q^20 - 856 * q^21 - 1264 * q^22 + 2052 * q^25 + 2000 * q^26 + 588 * q^27 + 640 * q^28 - 1704 * q^30 + 3220 * q^31 - 5632 * q^32 - 2884 * q^33 + 720 * q^35 + 10592 * q^36 + 1856 * q^37 - 1696 * q^38 - 1856 * q^40 - 5156 * q^41 - 1712 * q^42 + 960 * q^43 + 460 * q^45 - 1224 * q^47 + 4456 * q^50 + 3640 * q^51 + 4000 * q^52 + 13556 * q^53 + 12980 * q^55 + 2560 * q^56 - 3072 * q^57 - 3112 * q^58 - 6912 * q^60 - 4864 * q^61 + 6440 * q^62 - 13484 * q^63 - 4100 * q^65 - 11536 * q^66 - 1888 * q^67 - 960 * q^68 + 8824 * q^70 - 1060 * q^71 + 21184 * q^72 + 16616 * q^73 - 11044 * q^75 - 6784 * q^76 + 8892 * q^77 - 23152 * q^78 - 1536 * q^80 - 4044 * q^81 - 10312 * q^82 - 27024 * q^83 - 11068 * q^85 + 3840 * q^86 - 8392 * q^87 + 10112 * q^88 - 7184 * q^90 - 54024 * q^91 + 22528 * q^93 - 25968 * q^95 - 3252 * q^97 - 27984 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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