LMFDB - Embedded newform 17.4.c.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,4,Mod(4,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("17.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	17.c (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:	$1.00303247010$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 46x^{6} + 561x^{4} + 836x^{2} + 256 $ x^8 + 46x^6 + 561x^4 + 836*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.1
Root			$-4.46767i$ of defining polynomial
Character	$\chi$	$=$	17.13
Dual form			17.4.c.a.4.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.46767i q^{2} +(3.94546 + 3.94546i) q^{3} -21.8954 q^{4} +(4.79064 + 4.79064i) q^{5} +(21.5725 - 21.5725i) q^{6} +(3.33761 - 3.33761i) q^{7} +75.9757i q^{8} +4.13329i q^{9} +O(q^{10})$	\(q-5.46767i q^{2} +(3.94546 + 3.94546i) q^{3} -21.8954 q^{4} +(4.79064 + 4.79064i) q^{5} +(21.5725 - 21.5725i) q^{6} +(3.33761 - 3.33761i) q^{7} +75.9757i q^{8} +4.13329i q^{9} +(26.1937 - 26.1937i) q^{10} +(-6.70048 + 6.70048i) q^{11} +(-86.3876 - 86.3876i) q^{12} -33.7223 q^{13} +(-18.2490 - 18.2490i) q^{14} +37.8026i q^{15} +240.247 q^{16} +(-56.0931 + 42.0305i) q^{17} +22.5994 q^{18} -27.4317i q^{19} +(-104.893 - 104.893i) q^{20} +26.3368 q^{21} +(36.6360 + 36.6360i) q^{22} +(58.6134 - 58.6134i) q^{23} +(-299.759 + 299.759i) q^{24} -79.0995i q^{25} +184.382i q^{26} +(90.2197 - 90.2197i) q^{27} +(-73.0784 + 73.0784i) q^{28} +(147.098 + 147.098i) q^{29} +206.692 q^{30} +(-158.115 - 158.115i) q^{31} -705.786i q^{32} -52.8729 q^{33} +(229.809 + 306.699i) q^{34} +31.9786 q^{35} -90.5001i q^{36} +(122.947 + 122.947i) q^{37} -149.988 q^{38} +(-133.050 - 133.050i) q^{39} +(-363.973 + 363.973i) q^{40} +(-60.9335 + 60.9335i) q^{41} -144.001i q^{42} -258.362i q^{43} +(146.710 - 146.710i) q^{44} +(-19.8011 + 19.8011i) q^{45} +(-320.479 - 320.479i) q^{46} +88.9429 q^{47} +(947.884 + 947.884i) q^{48} +320.721i q^{49} -432.490 q^{50} +(-387.143 - 55.4832i) q^{51} +738.364 q^{52} +541.310i q^{53} +(-493.292 - 493.292i) q^{54} -64.1992 q^{55} +(253.577 + 253.577i) q^{56} +(108.231 - 108.231i) q^{57} +(804.282 - 804.282i) q^{58} -13.5759i q^{59} -827.704i q^{60} +(-112.176 + 112.176i) q^{61} +(-864.520 + 864.520i) q^{62} +(13.7953 + 13.7953i) q^{63} -1937.03 q^{64} +(-161.551 - 161.551i) q^{65} +289.092i q^{66} +357.758 q^{67} +(1228.18 - 920.277i) q^{68} +462.513 q^{69} -174.848i q^{70} +(679.278 + 679.278i) q^{71} -314.029 q^{72} +(-635.175 - 635.175i) q^{73} +(672.233 - 672.233i) q^{74} +(312.084 - 312.084i) q^{75} +600.630i q^{76} +44.7272i q^{77} +(-727.473 + 727.473i) q^{78} +(-319.090 + 319.090i) q^{79} +(1150.94 + 1150.94i) q^{80} +823.515 q^{81} +(333.164 + 333.164i) q^{82} -559.916i q^{83} -576.656 q^{84} +(-470.075 - 67.3686i) q^{85} -1412.64 q^{86} +1160.74i q^{87} +(-509.074 - 509.074i) q^{88} -602.266 q^{89} +(108.266 + 108.266i) q^{90} +(-112.552 + 112.552i) q^{91} +(-1283.37 + 1283.37i) q^{92} -1247.67i q^{93} -486.311i q^{94} +(131.416 - 131.416i) q^{95} +(2784.65 - 2784.65i) q^{96} +(-580.502 - 580.502i) q^{97} +1753.60 q^{98} +(-27.6950 - 27.6950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7}+O(q^{10}) $ 8 * q - 36 * q^4 + 14 * q^5 + 22 * q^6 + 2 * q^7	$ 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7} + 78 q^{10} - 108 q^{11} - 174 q^{12} - 88 q^{13} + 108 q^{14} + 420 q^{16} - 10 q^{17} + 428 q^{18} - 306 q^{20} - 260 q^{21} + 30 q^{22} - 22 q^{23} - 862 q^{24} + 540 q^{27} - 764 q^{28} + 46 q^{29} - 120 q^{30} + 610 q^{31} + 816 q^{33} + 1002 q^{34} + 1172 q^{35} - 574 q^{37} - 768 q^{38} - 844 q^{39} - 342 q^{40} - 968 q^{41} + 550 q^{44} - 1154 q^{45} - 944 q^{46} - 368 q^{47} + 2494 q^{48} + 468 q^{50} + 296 q^{51} + 2564 q^{52} - 1592 q^{54} - 1996 q^{55} + 684 q^{56} - 300 q^{57} + 266 q^{58} + 1258 q^{61} - 2516 q^{62} + 122 q^{63} - 3044 q^{64} + 628 q^{65} + 764 q^{67} + 1914 q^{68} + 1812 q^{69} + 1266 q^{71} + 1404 q^{72} - 1732 q^{73} + 1538 q^{74} + 1292 q^{75} - 2836 q^{78} + 914 q^{79} + 498 q^{80} + 280 q^{81} - 280 q^{82} - 2952 q^{84} - 2498 q^{85} - 4244 q^{86} + 442 q^{88} - 2156 q^{89} + 2478 q^{90} - 1632 q^{91} - 1768 q^{92} + 1484 q^{95} + 3998 q^{96} + 1836 q^{97} + 6728 q^{98} - 2088 q^{99}+O(q^{100}) $ 8 * q - 36 * q^4 + 14 * q^5 + 22 * q^6 + 2 * q^7 + 78 * q^10 - 108 * q^11 - 174 * q^12 - 88 * q^13 + 108 * q^14 + 420 * q^16 - 10 * q^17 + 428 * q^18 - 306 * q^20 - 260 * q^21 + 30 * q^22 - 22 * q^23 - 862 * q^24 + 540 * q^27 - 764 * q^28 + 46 * q^29 - 120 * q^30 + 610 * q^31 + 816 * q^33 + 1002 * q^34 + 1172 * q^35 - 574 * q^37 - 768 * q^38 - 844 * q^39 - 342 * q^40 - 968 * q^41 + 550 * q^44 - 1154 * q^45 - 944 * q^46 - 368 * q^47 + 2494 * q^48 + 468 * q^50 + 296 * q^51 + 2564 * q^52 - 1592 * q^54 - 1996 * q^55 + 684 * q^56 - 300 * q^57 + 266 * q^58 + 1258 * q^61 - 2516 * q^62 + 122 * q^63 - 3044 * q^64 + 628 * q^65 + 764 * q^67 + 1914 * q^68 + 1812 * q^69 + 1266 * q^71 + 1404 * q^72 - 1732 * q^73 + 1538 * q^74 + 1292 * q^75 - 2836 * q^78 + 914 * q^79 + 498 * q^80 + 280 * q^81 - 280 * q^82 - 2952 * q^84 - 2498 * q^85 - 4244 * q^86 + 442 * q^88 - 2156 * q^89 + 2478 * q^90 - 1632 * q^91 - 1768 * q^92 + 1484 * q^95 + 3998 * q^96 + 1836 * q^97 + 6728 * q^98 - 2088 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		−	5.46767i		−	1.93311i	−0.256451	−	0.966557i	$-0.582553\pi$
$2$		−	5.46767i		−	1.93311i	0.256451	−	0.966557i	$-0.417447\pi$
$3$	3.94546	+	3.94546i	0.759304	+	0.759304i	0.976196	−	0.216892i	$-0.0695919\pi$
$3$	3.94546	+	3.94546i	0.759304	+	0.759304i	−0.216892	+	0.976196i	$0.569592\pi$
$4$	−21.8954			−2.73693
$5$	4.79064	+	4.79064i	0.428488	+	0.428488i	0.888113	−	0.459625i	$-0.152016\pi$
$5$	4.79064	+	4.79064i	0.428488	+	0.428488i	−0.459625	+	0.888113i	$0.652016\pi$
$6$	21.5725	−	21.5725i	1.46782	−	1.46782i
$7$	3.33761	−	3.33761i	0.180214	−	0.180214i	−0.611235	−	0.791449i	$-0.709327\pi$
$7$	3.33761	−	3.33761i	0.180214	−	0.180214i	0.791449	+	0.611235i	$0.209327\pi$
$8$			75.9757i			3.35769i
$9$			4.13329i			0.153085i
$10$	26.1937	−	26.1937i	0.828316	−	0.828316i
$11$	−6.70048	+	6.70048i	−0.183661	+	0.183661i	−0.792949	−	0.609288i	$-0.791455\pi$
$11$	−6.70048	+	6.70048i	−0.183661	+	0.183661i	0.609288	+	0.792949i	$0.291455\pi$
$12$	−86.3876	−	86.3876i	−2.07816	−	2.07816i
$13$	−33.7223			−0.719452			−0.359726	−	0.933058i	$-0.617130\pi$
$13$	−33.7223			−0.719452			−0.359726	+	0.933058i	$0.617130\pi$
$14$	−18.2490	−	18.2490i	−0.348374	−	0.348374i
$15$			37.8026i			0.650705i
$16$	240.247			3.75386
$17$	−56.0931	+	42.0305i	−0.800269	+	0.599641i
$17$	−56.0931	+	42.0305i	−0.800269	+	0.599641i
$18$	22.5994			0.295930
$19$		−	27.4317i		−	0.331225i	−0.986191	−	0.165612i	$-0.947040\pi$
$19$		−	27.4317i		−	0.331225i	0.986191	−	0.165612i	$-0.0529601\pi$
$20$	−104.893	−	104.893i	−1.17274	−	1.17274i
$21$	26.3368			0.273674
$22$	36.6360	+	36.6360i	0.355038	+	0.355038i
$23$	58.6134	−	58.6134i	0.531380	−	0.531380i	−0.389603	−	0.920983i	$-0.627388\pi$
$23$	58.6134	−	58.6134i	0.531380	−	0.531380i	0.920983	+	0.389603i	$0.127388\pi$
$24$	−299.759	+	299.759i	−2.54950	+	2.54950i
$25$		−	79.0995i		−	0.632796i
$26$			184.382i			1.39078i
$27$	90.2197	−	90.2197i	0.643066	−	0.643066i
$28$	−73.0784	+	73.0784i	−0.493233	+	0.493233i
$29$	147.098	+	147.098i	0.941908	+	0.941908i	0.998403	−	0.0564944i	$-0.0179923\pi$
$29$	147.098	+	147.098i	0.941908	+	0.941908i	−0.0564944	+	0.998403i	$0.517992\pi$
$30$	206.692			1.25789
$31$	−158.115	−	158.115i	−0.916072	−	0.916072i	0.0806685	−	0.996741i	$-0.474294\pi$
$31$	−158.115	−	158.115i	−0.916072	−	0.916072i	−0.996741	+	0.0806685i	$0.974294\pi$
$32$		−	705.786i		−	3.89895i
$33$	−52.8729			−0.278909
$34$	229.809	+	306.699i	1.15918	+	1.54701i
$35$	31.9786			0.154439
$36$		−	90.5001i		−	0.418982i
$37$	122.947	+	122.947i	0.546279	+	0.546279i	0.925363	−	0.379083i	$-0.123761\pi$
$37$	122.947	+	122.947i	0.546279	+	0.546279i	−0.379083	+	0.925363i	$0.623761\pi$
$38$	−149.988			−0.640296
$39$	−133.050	−	133.050i	−0.546282	−	0.546282i
$40$	−363.973	+	363.973i	−1.43873	+	1.43873i
$41$	−60.9335	+	60.9335i	−0.232103	+	0.232103i	−0.813570	−	0.581467i	$-0.802479\pi$
$41$	−60.9335	+	60.9335i	−0.232103	+	0.232103i	0.581467	+	0.813570i	$0.302479\pi$
$42$		−	144.001i		−	0.529044i
$43$		−	258.362i		−	0.916274i	−0.888882	−	0.458137i	$-0.848517\pi$
$43$		−	258.362i		−	0.916274i	0.888882	−	0.458137i	$-0.151483\pi$
$44$	146.710	−	146.710i	0.502667	−	0.502667i
$45$	−19.8011	+	19.8011i	−0.0655949	+	0.0655949i
$46$	−320.479	−	320.479i	−1.02722	−	1.02722i
$47$	88.9429			0.276035			0.138018	−	0.990430i	$-0.455927\pi$
$47$	88.9429			0.276035			0.138018	+	0.990430i	$0.455927\pi$
$48$	947.884	+	947.884i	2.85032	+	2.85032i
$49$			320.721i			0.935046i
$50$	−432.490			−1.22327
$51$	−387.143	−	55.4832i	−1.06296	−	0.152337i
$52$	738.364			1.96909
$53$			541.310i			1.40292i	0.712710	+	0.701458i	$0.247467\pi$
$53$			541.310i			1.40292i	−0.712710	+	0.701458i	$0.752533\pi$
$54$	−493.292	−	493.292i	−1.24312	−	1.24312i
$55$	−64.1992			−0.157393
$56$	253.577	+	253.577i	0.605102	+	0.605102i
$57$	108.231	−	108.231i	0.251500	−	0.251500i
$58$	804.282	−	804.282i	1.82082	−	1.82082i
$59$		−	13.5759i		−	0.0299564i	−0.999888	−	0.0149782i	$-0.995232\pi$
$59$		−	13.5759i		−	0.0299564i	0.999888	−	0.0149782i	$-0.00476789\pi$
$60$		−	827.704i		−	1.78093i
$61$	−112.176	+	112.176i	−0.235453	+	0.235453i	−0.814964	−	0.579511i	$-0.803243\pi$
$61$	−112.176	+	112.176i	−0.235453	+	0.235453i	0.579511	+	0.814964i	$0.303243\pi$
$62$	−864.520	+	864.520i	−1.77087	+	1.77087i
$63$	13.7953	+	13.7953i	0.0275880	+	0.0275880i
$64$	−1937.03			−3.78326
$65$	−161.551	−	161.551i	−0.308276	−	0.308276i
$66$			289.092i			0.539163i
$67$	357.758			0.652345			0.326172	−	0.945310i	$-0.394241\pi$
$67$	357.758			0.652345			0.326172	+	0.945310i	$0.394241\pi$
$68$	1228.18	−	920.277i	2.19028	−	1.64118i
$69$	462.513			0.806957
$70$		−	174.848i		−	0.298548i
$71$	679.278	+	679.278i	1.13543	+	1.13543i	0.989259	+	0.146170i	$0.0466948\pi$
$71$	679.278	+	679.278i	1.13543	+	1.13543i	0.146170	+	0.989259i	$0.453305\pi$
$72$	−314.029			−0.514010
$73$	−635.175	−	635.175i	−1.01838	−	1.01838i	−0.999828	−	0.0185509i	$-0.994095\pi$
$73$	−635.175	−	635.175i	−1.01838	−	1.01838i	−0.0185509	−	0.999828i	$-0.505905\pi$
$74$	672.233	−	672.233i	1.05602	−	1.05602i
$75$	312.084	−	312.084i	0.480484	−	0.480484i
$76$			600.630i			0.906540i
$77$			44.7272i			0.0661965i
$78$	−727.473	+	727.473i	−1.05603	+	1.05603i
$79$	−319.090	+	319.090i	−0.454436	+	0.454436i	−0.896824	−	0.442388i	$-0.854132\pi$
$79$	−319.090	+	319.090i	−0.454436	+	0.454436i	0.442388	+	0.896824i	$0.354132\pi$
$80$	1150.94	+	1150.94i	1.60848	+	1.60848i
$81$	823.515			1.12965
$82$	333.164	+	333.164i	0.448681	+	0.448681i
$83$		−	559.916i		−	0.740467i	−0.928939	−	0.370234i	$-0.879278\pi$
$83$		−	559.916i		−	0.740467i	0.928939	−	0.370234i	$-0.120722\pi$
$84$	−576.656			−0.749028
$85$	−470.075	−	67.3686i	−0.599845	−	0.0859664i
$86$	−1412.64			−1.77126
$87$			1160.74i			1.43039i
$88$	−509.074	−	509.074i	−0.616676	−	0.616676i
$89$	−602.266			−0.717304			−0.358652	−	0.933471i	$-0.616763\pi$
$89$	−602.266			−0.717304			−0.358652	+	0.933471i	$0.616763\pi$
$90$	108.266	+	108.266i	0.126802	+	0.126802i
$91$	−112.552	+	112.552i	−0.129655	+	0.129655i
$92$	−1283.37	+	1283.37i	−1.45435	+	1.45435i
$93$		−	1247.67i		−	1.39115i
$94$		−	486.311i		−	0.533608i
$95$	131.416	−	131.416i	0.141926	−	0.141926i
$96$	2784.65	−	2784.65i	2.96049	−	2.96049i
$97$	−580.502	−	580.502i	−0.607640	−	0.607640i	0.334689	−	0.942329i	$-0.391369\pi$
$97$	−580.502	−	580.502i	−0.607640	−	0.607640i	−0.942329	+	0.334689i	$0.891369\pi$
$98$	1753.60			1.80755
$99$	−27.6950	−	27.6950i	−0.0281157	−	0.0281157i
$100$			1731.92i			1.73192i
$101$	246.217			0.242570			0.121285	−	0.992618i	$-0.461299\pi$
$101$	246.217			0.242570			0.121285	+	0.992618i	$0.461299\pi$
$102$	−303.364	+	2116.77i	−0.294485	+	2.05482i
$103$	−102.854			−0.0983931			−0.0491965	−	0.998789i	$-0.515666\pi$
$103$	−102.854			−0.0983931			−0.0491965	+	0.998789i	$0.515666\pi$
$104$		−	2562.07i		−	2.41569i
$105$	126.170	+	126.170i	0.117266	+	0.117266i
$106$	2959.70			2.71200
$107$	−1445.44	−	1445.44i	−1.30594	−	1.30594i	−0.924317	−	0.381625i	$-0.875365\pi$
$107$	−1445.44	−	1445.44i	−1.30594	−	1.30594i	−0.381625	−	0.924317i	$-0.624635\pi$
$108$	−1975.40	+	1975.40i	−1.76003	+	1.76003i
$109$	−185.564	+	185.564i	−0.163063	+	0.163063i	−0.783922	−	0.620859i	$-0.786784\pi$
$109$	−185.564	+	185.564i	−0.163063	+	0.163063i	0.620859	+	0.783922i	$0.286784\pi$
$110$			351.020i			0.304259i
$111$			970.163i			0.829584i
$112$	801.850	−	801.850i	0.676498	−	0.676498i
$113$	211.740	−	211.740i	0.176273	−	0.176273i	−0.613456	−	0.789729i	$-0.710221\pi$
$113$	211.740	−	211.740i	0.176273	−	0.176273i	0.789729	+	0.613456i	$0.210221\pi$
$114$	−591.771	−	591.771i	−0.486179	−	0.486179i
$115$	561.591			0.455380
$116$	−3220.77	−	3220.77i	−2.57794	−	2.57794i
$117$		−	139.384i		−	0.110137i
$118$	−74.2284			−0.0579092
$119$	−46.9353	+	327.498i	−0.0361559	+	0.252283i
$120$	−2872.08			−2.18486
$121$			1241.21i			0.932537i
$122$	613.340	+	613.340i	0.455157	+	0.455157i
$123$	−480.821			−0.352473
$124$	3461.99	+	3461.99i	2.50723	+	2.50723i
$125$	977.768	−	977.768i	0.699634	−	0.699634i
$126$	75.4281	−	75.4281i	0.0533307	−	0.0533307i
$127$			761.059i			0.531757i	0.964007	+	0.265878i	$0.0856619\pi$
$127$			761.059i			0.531757i	−0.964007	+	0.265878i	$0.914338\pi$
$128$			4944.76i			3.41452i
$129$	1019.35	−	1019.35i	0.695730	−	0.695730i
$130$	−883.309	+	883.309i	−0.595933	+	0.595933i
$131$	1024.15	+	1024.15i	0.683054	+	0.683054i	0.960687	−	0.277633i	$-0.0895500\pi$
$131$	1024.15	+	1024.15i	0.683054	+	0.683054i	−0.277633	+	0.960687i	$0.589550\pi$
$132$	1157.68			0.763354
$133$	−91.5565	−	91.5565i	−0.0596914	−	0.0596914i
$134$		−	1956.10i		−	1.26106i
$135$	864.420			0.551092
$136$	−3193.30	−	4261.71i	−2.01341	−	2.68705i
$137$	1902.77			1.18660			0.593301	−	0.804981i	$-0.297824\pi$
$137$	1902.77			1.18660			0.593301	+	0.804981i	$0.297824\pi$
$138$		−	2528.87i		−	1.55994i
$139$	−437.312	−	437.312i	−0.266851	−	0.266851i	0.560979	−	0.827830i	$-0.310425\pi$
$139$	−437.312	−	437.312i	−0.266851	−	0.266851i	−0.827830	+	0.560979i	$0.810425\pi$
$140$	−700.185			−0.422689
$141$	350.920	+	350.920i	0.209595	+	0.209595i
$142$	3714.07	−	3714.07i	2.19492	−	2.19492i
$143$	225.955	−	225.955i	0.132135	−	0.132135i
$144$			993.009i			0.574658i
$145$			1409.38i			0.807193i
$146$	−3472.93	+	3472.93i	−1.96864	+	1.96864i
$147$	−1265.39	+	1265.39i	−0.709984	+	0.709984i
$148$	−2691.97	−	2691.97i	−1.49513	−	1.49513i
$149$	−1398.00			−0.768647			−0.384323	−	0.923199i	$-0.625565\pi$
$149$	−1398.00			−0.768647			−0.384323	+	0.923199i	$0.625565\pi$
$150$	−1706.37	−	1706.37i	−0.928831	−	0.928831i
$151$			2503.54i			1.34924i	0.738166	+	0.674619i	$0.235692\pi$
$151$			2503.54i			1.34924i	−0.738166	+	0.674619i	$0.764308\pi$
$152$	2084.15			1.11215
$153$	−173.724	−	231.849i	−0.0917959	−	0.122509i
$154$	244.553			0.127965
$155$		−	1514.94i		−	0.785052i
$156$	2913.18	+	2913.18i	1.49514	+	1.49514i
$157$	−2715.22			−1.38024			−0.690121	−	0.723694i	$-0.742443\pi$
$157$	−2715.22			−1.38024			−0.690121	+	0.723694i	$0.742443\pi$
$158$	1744.68	+	1744.68i	0.878478	+	0.878478i
$159$	−2135.71	+	2135.71i	−1.06524	+	1.06524i
$160$	3381.17	−	3381.17i	1.67065	−	1.67065i
$161$		−	391.257i		−	0.191524i
$162$		−	4502.71i		−	2.18374i
$163$	2340.59	−	2340.59i	1.12472	−	1.12472i	0.133697	−	0.991022i	$-0.457315\pi$
$163$	2340.59	−	2340.59i	1.12472	−	1.12472i	0.991022	−	0.133697i	$-0.0426850\pi$
$164$	1334.17	−	1334.17i	0.635249	−	0.635249i
$165$	−253.295	−	253.295i	−0.119509	−	0.119509i
$166$	−3061.44			−1.43141
$167$	247.639	+	247.639i	0.114748	+	0.114748i	0.762149	−	0.647401i	$-0.224144\pi$
$167$	247.639	+	247.639i	0.114748	+	0.114748i	−0.647401	+	0.762149i	$0.724144\pi$
$168$			2000.96i			0.918912i
$169$	−1059.81			−0.482389
$170$	−368.349	+	2570.22i	−0.166183	+	1.15957i
$171$	113.383			0.0507055
$172$			5656.94i			2.50778i
$173$	−1478.19	−	1478.19i	−0.649622	−	0.649622i	0.303279	−	0.952902i	$-0.401919\pi$
$173$	−1478.19	−	1478.19i	−0.649622	−	0.649622i	−0.952902	+	0.303279i	$0.901919\pi$
$174$	6346.52			2.76511
$175$	−264.003	−	264.003i	−0.114039	−	0.114039i
$176$	−1609.77	+	1609.77i	−0.689437	+	0.689437i
$177$	53.5630	−	53.5630i	0.0227460	−	0.0227460i
$178$			3292.99i			1.38663i
$179$		−	739.046i		−	0.308597i	−0.988024	−	0.154299i	$-0.950688\pi$
$179$		−	739.046i		−	0.308597i	0.988024	−	0.154299i	$-0.0493118\pi$
$180$	433.554	−	433.554i	0.179529	−	0.179529i
$181$	2306.67	−	2306.67i	0.947258	−	0.947258i	−0.0514191	−	0.998677i	$-0.516374\pi$
$181$	2306.67	−	2306.67i	0.947258	−	0.947258i	0.998677	+	0.0514191i	$0.0163744\pi$
$182$	615.396	+	615.396i	0.250638	+	0.250638i
$183$	−885.169			−0.357560
$184$	4453.19	+	4453.19i	1.78421	+	1.78421i
$185$			1177.99i			0.468148i
$186$	−6821.85			−2.68926
$187$	94.2257	−	657.475i	0.0368474	−	0.257109i
$188$	−1947.44			−0.755489
$189$		−	602.236i		−	0.231779i
$190$	−718.538	−	718.538i	−0.274359	−	0.274359i
$191$	−265.840			−0.100710			−0.0503548	−	0.998731i	$-0.516035\pi$
$191$	−265.840			−0.100710			−0.0503548	+	0.998731i	$0.516035\pi$
$192$	−7642.47	−	7642.47i	−2.87264	−	2.87264i
$193$	25.1722	−	25.1722i	0.00938825	−	0.00938825i	−0.702397	−	0.711785i	$-0.747887\pi$
$193$	25.1722	−	25.1722i	0.00938825	−	0.00938825i	0.711785	+	0.702397i	$0.247887\pi$
$194$	−3174.00	+	3174.00i	−1.17464	+	1.17464i
$195$		−	1274.79i		−	0.468151i
$196$		−	7022.32i		−	2.55916i
$197$	446.683	−	446.683i	0.161547	−	0.161547i	−0.621704	−	0.783252i	$-0.713559\pi$
$197$	446.683	−	446.683i	0.161547	−	0.161547i	0.783252	+	0.621704i	$0.213559\pi$
$198$	−151.427	+	151.427i	−0.0543508	+	0.0543508i
$199$	2696.51	+	2696.51i	0.960554	+	0.960554i	0.999251	−	0.0386973i	$-0.0123208\pi$
$199$	2696.51	+	2696.51i	0.960554	+	0.960554i	−0.0386973	+	0.999251i	$0.512321\pi$
$200$	6009.64			2.12473
$201$	1411.52	+	1411.52i	0.495328	+	0.495328i
$202$		−	1346.24i		−	0.468915i
$203$	981.909			0.339490
$204$	8476.66	+	1214.83i	2.90924	+	0.416936i
$205$	−583.821			−0.198906
$206$			562.371i			0.190205i
$207$	242.266	+	242.266i	0.0813461	+	0.0813461i
$208$	−8101.67			−2.70072
$209$	183.806	+	183.806i	0.0608331	+	0.0608331i
$210$	689.857	−	689.857i	0.226689	−	0.226689i
$211$	1667.04	−	1667.04i	0.543903	−	0.543903i	−0.380768	−	0.924671i	$-0.624340\pi$
$211$	1667.04	−	1667.04i	0.543903	−	0.543903i	0.924671	+	0.380768i	$0.124340\pi$
$212$		−	11852.2i		−	3.83969i
$213$			5360.13i			1.72427i
$214$	−7903.18	+	7903.18i	−2.52454	+	2.52454i
$215$	1237.72	−	1237.72i	0.392612	−	0.392612i
$216$	6854.51	+	6854.51i	2.15921	+	2.15921i
$217$	−1055.45			−0.330178
$218$	1014.61	+	1014.61i	0.315219	+	0.315219i
$219$		−	5012.12i		−	1.54652i
$220$	1405.67			0.430774
$221$	1891.59	−	1417.36i	0.575755	−	0.431413i
$222$	5304.53			1.60368
$223$		−	5273.08i		−	1.58346i	−0.610871	−	0.791730i	$-0.709181\pi$
$223$		−	5273.08i		−	1.58346i	0.610871	−	0.791730i	$-0.290819\pi$
$224$	−2355.64	−	2355.64i	−0.702645	−	0.702645i
$225$	326.941			0.0968714
$226$	−1157.72	−	1157.72i	−0.340755	−	0.340755i
$227$	−2472.24	+	2472.24i	−0.722857	+	0.722857i	−0.969186	−	0.246329i	$-0.920776\pi$
$227$	−2472.24	+	2472.24i	−0.722857	+	0.722857i	0.246329	+	0.969186i	$0.420776\pi$
$228$	−2369.76	+	2369.76i	−0.688339	+	0.688339i
$229$			1982.99i			0.572226i	0.958196	+	0.286113i	$0.0923633\pi$
$229$			1982.99i			0.572226i	−0.958196	+	0.286113i	$0.907637\pi$
$230$		−	3070.60i		−	0.880301i
$231$	−176.469	+	176.469i	−0.0502633	+	0.0502633i
$232$	−11175.9	+	11175.9i	−3.16263	+	3.16263i
$233$	−10.2611	−	10.2611i	−0.00288509	−	0.00288509i	0.705663	−	0.708548i	$-0.250649\pi$
$233$	−10.2611	−	10.2611i	−0.00288509	−	0.00288509i	−0.708548	+	0.705663i	$0.750649\pi$
$234$	−762.104			−0.212907
$235$	426.094	+	426.094i	0.118278	+	0.118278i
$236$			297.250i			0.0819886i
$237$	−2517.92			−0.690111
$238$	1790.65	+	256.627i	0.487693	+	0.0698934i
$239$	−5365.31			−1.45210			−0.726052	−	0.687640i	$-0.758647\pi$
$239$	−5365.31			−1.45210			−0.726052	+	0.687640i	$0.758647\pi$
$240$			9081.95i			2.44265i
$241$	−119.928	−	119.928i	−0.0320551	−	0.0320551i	0.690898	−	0.722953i	$-0.257216\pi$
$241$	−119.928	−	119.928i	−0.0320551	−	0.0320551i	−0.722953	+	0.690898i	$0.757216\pi$
$242$	6786.51			1.80270
$243$	813.212	+	813.212i	0.214681	+	0.214681i
$244$	2456.14	−	2456.14i	0.644418	−	0.644418i
$245$	−1536.46	+	1536.46i	−0.400656	+	0.400656i
$246$			2628.97i			0.681371i
$247$			925.060i			0.238300i
$248$	12012.9	−	12012.9i	3.07588	−	3.07588i
$249$	2209.13	−	2209.13i	0.562239	−	0.562239i
$250$	−5346.11	−	5346.11i	−1.35247	−	1.35247i
$251$	−4824.87			−1.21332			−0.606659	−	0.794962i	$-0.707491\pi$
$251$	−4824.87			−1.21332			−0.606659	+	0.794962i	$0.707491\pi$
$252$	−302.054	−	302.054i	−0.0755064	−	0.0755064i
$253$			785.475i			0.195187i
$254$	4161.22			1.02795
$255$	−1588.86	−	2120.46i	−0.390190	−	0.520739i
$256$	11540.1			2.81740
$257$			5583.38i			1.35518i	0.735439	+	0.677591i	$0.236976\pi$
$257$			5583.38i			1.35518i	−0.735439	+	0.677591i	$0.763024\pi$
$258$	−5573.50	−	5573.50i	−1.34493	−	1.34493i
$259$	820.697			0.196894
$260$	3537.24	+	3537.24i	0.843731	+	0.843731i
$261$	−607.996	+	607.996i	−0.144192	+	0.144192i
$262$	5599.69	−	5599.69i	1.32042	−	1.32042i
$263$			4116.11i			0.965059i	0.875880	+	0.482529i	$0.160282\pi$
$263$			4116.11i			0.965059i	−0.875880	+	0.482529i	$0.839718\pi$
$264$		−	4017.06i		−	0.936488i
$265$	−2593.22	+	2593.22i	−0.601133	+	0.601133i
$266$	−500.601	+	500.601i	−0.115390	+	0.115390i
$267$	−2376.21	−	2376.21i	−0.544652	−	0.544652i
$268$	−7833.27			−1.78542
$269$	4277.93	+	4277.93i	0.969629	+	0.969629i	0.999552	−	0.0299232i	$-0.00952628\pi$
$269$	4277.93	+	4277.93i	0.969629	+	0.969629i	−0.0299232	+	0.999552i	$0.509526\pi$
$270$		−	4726.37i		−	1.06532i
$271$	6555.61			1.46947			0.734733	−	0.678357i	$-0.237308\pi$
$271$	6555.61			1.46947			0.734733	+	0.678357i	$0.237308\pi$
$272$	−13476.2	+	10097.7i	−3.00410	+	2.25097i
$273$	−888.136			−0.196895
$274$		−	10403.7i		−	2.29384i
$275$	530.005	+	530.005i	0.116220	+	0.116220i
$276$	−10126.9			−2.20859
$277$	1725.33	+	1725.33i	0.374241	+	0.374241i	0.869019	−	0.494778i	$-0.164751\pi$
$277$	1725.33	+	1725.33i	0.374241	+	0.374241i	−0.494778	+	0.869019i	$0.664751\pi$
$278$	−2391.08	+	2391.08i	−0.515854	+	0.515854i
$279$	653.533	−	653.533i	0.140237	−	0.140237i
$280$			2429.60i			0.518558i
$281$			519.764i			0.110343i	0.998477	+	0.0551717i	$0.0175706\pi$
$281$			519.764i			0.110343i	−0.998477	+	0.0551717i	$0.982429\pi$
$282$	1918.72	−	1918.72i	0.405170	−	0.405170i
$283$	3290.24	−	3290.24i	0.691112	−	0.691112i	−0.271365	−	0.962477i	$-0.587475\pi$
$283$	3290.24	−	3290.24i	0.691112	−	0.691112i	0.962477	+	0.271365i	$0.0874749\pi$
$284$	−14873.1	−	14873.1i	−3.10759	−	3.10759i
$285$	1036.99			0.215530
$286$	−1235.45	−	1235.45i	−0.255432	−	0.255432i
$287$			406.744i			0.0836563i
$288$	2917.21			0.596870
$289$	1379.87	−	4715.25i	0.280860	−	0.959749i
$290$	7706.05			1.56040
$291$		−	4580.69i		−	0.922766i
$292$	13907.4	+	13907.4i	2.78723	+	2.78723i
$293$	1856.79			0.370220			0.185110	−	0.982718i	$-0.440736\pi$
$293$	1856.79			0.370220			0.185110	+	0.982718i	$0.440736\pi$
$294$	6918.74	+	6918.74i	1.37248	+	1.37248i
$295$	65.0371	−	65.0371i	0.0128360	−	0.0128360i
$296$	−9340.97	+	9340.97i	−1.83423	+	1.83423i
$297$			1209.03i			0.236212i
$298$			7643.79i			1.48588i
$299$	−1976.58	+	1976.58i	−0.382302	+	0.382302i
$300$	−6833.21	+	6833.21i	−1.31505	+	1.31505i
$301$	−862.310	−	862.310i	−0.165125	−	0.165125i
$302$	13688.5			2.60823
$303$	971.440	+	971.440i	0.184184	+	0.184184i
$304$		−	6590.39i		−	1.24337i
$305$	−1074.79			−0.201777
$306$	−1267.67	+	949.867i	−0.236824	+	0.177452i
$307$	759.641			0.141221			0.0706107	−	0.997504i	$-0.477505\pi$
$307$	759.641			0.141221			0.0706107	+	0.997504i	$0.477505\pi$
$308$		−	979.321i		−	0.181175i
$309$	−405.805	−	405.805i	−0.0747102	−	0.0747102i
$310$	−8283.21			−1.51760
$311$	−722.960	−	722.960i	−0.131818	−	0.131818i	0.638120	−	0.769937i	$-0.279713\pi$
$311$	−722.960	−	722.960i	−0.131818	−	0.131818i	−0.769937	+	0.638120i	$0.779713\pi$
$312$	10108.6	−	10108.6i	1.83424	−	1.83424i
$313$	−2786.70	+	2786.70i	−0.503238	+	0.503238i	−0.912443	−	0.409205i	$-0.865806\pi$
$313$	−2786.70	+	2786.70i	−0.503238	+	0.503238i	0.409205	+	0.912443i	$0.365806\pi$
$314$			14845.9i			2.66817i
$315$			132.177i			0.0236422i
$316$	6986.63	−	6986.63i	1.24376	−	1.24376i
$317$	3806.81	−	3806.81i	0.674485	−	0.674485i	−0.284262	−	0.958747i	$-0.591748\pi$
$317$	3806.81	−	3806.81i	0.674485	−	0.674485i	0.958747	+	0.284262i	$0.0917485\pi$
$318$	11677.4	+	11677.4i	2.05923	+	2.05923i
$319$	−1971.25			−0.345984
$320$	−9279.61	−	9279.61i	−1.62108	−	1.62108i
$321$		−	11405.8i		−	1.98321i
$322$	−2139.27			−0.370238
$323$	1152.97	+	1538.73i	0.198616	+	0.265069i
$324$	−18031.2			−3.09177
$325$			2667.41i			0.455266i
$326$	−12797.6	−	12797.6i	−2.17421	−	2.17421i
$327$	−1464.27			−0.247628
$328$	−4629.47	−	4629.47i	−0.779328	−	0.779328i
$329$	296.857	−	296.857i	0.0497454	−	0.0497454i
$330$	−1384.94	+	1384.94i	−0.231025	+	0.231025i
$331$		−	1697.70i		−	0.281915i	−0.990016	−	0.140958i	$-0.954982\pi$
$331$		−	1697.70i		−	0.281915i	0.990016	−	0.140958i	$-0.0450181\pi$
$332$			12259.6i			2.02661i
$333$	−508.174	+	508.174i	−0.0836269	+	0.0836269i
$334$	1354.01	−	1354.01i	0.221820	−	0.221820i
$335$	1713.89	+	1713.89i	0.279522	+	0.279522i
$336$	6327.33			1.02733
$337$	−7987.91	−	7987.91i	−1.29119	−	1.29119i	−0.934054	−	0.357131i	$-0.883755\pi$
$337$	−7987.91	−	7987.91i	−1.29119	−	1.29119i	−0.357131	−	0.934054i	$-0.616245\pi$
$338$			5794.69i			0.932514i
$339$	1670.82			0.267689
$340$	10292.5	+	1475.06i	1.64173	+	0.235284i
$341$	2118.89			0.336493
$342$		−	619.942i		−	0.0980194i
$343$	2215.24	+	2215.24i	0.348722	+	0.348722i
$344$	19629.2			3.07656
$345$	2215.74	+	2215.74i	0.345772	+	0.345772i
$346$	−8082.26	+	8082.26i	−1.25579	+	1.25579i
$347$	−2544.06	+	2544.06i	−0.393580	+	0.393580i	−0.875961	−	0.482381i	$-0.839772\pi$
$347$	−2544.06	+	2544.06i	−0.393580	+	0.393580i	0.482381	+	0.875961i	$0.339772\pi$
$348$		−	25414.8i		−	3.91488i
$349$		−	3741.37i		−	0.573842i	−0.957954	−	0.286921i	$-0.907368\pi$
$349$		−	3741.37i		−	0.573842i	0.957954	−	0.286921i	$-0.0926318\pi$
$350$	−1443.48	+	1443.48i	−0.220450	+	0.220450i
$351$	−3042.41	+	3042.41i	−0.462655	+	0.462655i
$352$	4729.10	+	4729.10i	0.716085	+	0.716085i
$353$	−5726.82			−0.863478			−0.431739	−	0.901999i	$-0.642100\pi$
$353$	−5726.82			−0.863478			−0.431739	+	0.901999i	$0.642100\pi$
$354$	−292.865	−	292.865i	−0.0439706	−	0.0439706i
$355$			6508.36i			0.973036i
$356$	13186.9			1.96321
$357$	−1477.31	+	1106.95i	−0.219013	+	0.164106i
$358$	−4040.86			−0.596554
$359$		−	6048.82i		−	0.889260i	−0.895714	−	0.444630i	$-0.853335\pi$
$359$		−	6048.82i		−	0.889260i	0.895714	−	0.444630i	$-0.146665\pi$
$360$	−1504.40	−	1504.40i	−0.220247	−	0.220247i
$361$	6106.50			0.890290
$362$	−12612.1	−	12612.1i	−1.83116	−	1.83116i
$363$	−4897.13	+	4897.13i	−0.708079	+	0.708079i
$364$	2464.37	−	2464.37i	0.354857	−	0.354857i
$365$		−	6085.79i		−	0.872726i
$366$			4839.81i			0.691205i
$367$	−2432.09	+	2432.09i	−0.345924	+	0.345924i	−0.858589	−	0.512665i	$-0.828658\pi$
$367$	−2432.09	+	2432.09i	−0.345924	+	0.345924i	0.512665	+	0.858589i	$0.328658\pi$
$368$	14081.7	−	14081.7i	1.99472	−	1.99472i
$369$	−251.855	−	251.855i	−0.0355314	−	0.0355314i
$370$	6440.85			0.904984
$371$	1806.68	+	1806.68i	0.252825	+	0.252825i
$372$			27318.3i			3.80749i
$373$	−6816.14			−0.946184			−0.473092	−	0.881013i	$-0.656862\pi$
$373$	−6816.14			−0.946184			−0.473092	+	0.881013i	$0.656862\pi$
$374$	−3594.86	−	515.195i	−0.497021	−	0.0712303i
$375$	7715.48			1.06247
$376$			6757.50i			0.926839i
$377$	−4960.46	−	4960.46i	−0.677658	−	0.677658i
$378$	−3292.83			−0.448055
$379$	4184.48	+	4184.48i	0.567130	+	0.567130i	0.931323	−	0.364193i	$-0.118655\pi$
$379$	4184.48	+	4184.48i	0.567130	+	0.567130i	−0.364193	+	0.931323i	$0.618655\pi$
$380$	−2877.40	+	2877.40i	−0.388441	+	0.388441i
$381$	−3002.73	+	3002.73i	−0.403765	+	0.403765i
$382$			1453.53i			0.194683i
$383$		−	7584.88i		−	1.01193i	−0.862554	−	0.505965i	$-0.831137\pi$
$383$		−	7584.88i		−	1.01193i	0.862554	−	0.505965i	$-0.168863\pi$
$384$	−19509.3	+	19509.3i	−2.59266	+	2.59266i
$385$	−214.272	+	214.272i	−0.0283644	+	0.0283644i
$386$	−137.633	−	137.633i	−0.0181486	−	0.0181486i
$387$	1067.88			0.140267
$388$	12710.3	+	12710.3i	1.66307	+	1.66307i
$389$			1389.74i			0.181137i	0.995890	+	0.0905687i	$0.0288685\pi$
$389$			1389.74i			0.181137i	−0.995890	+	0.0905687i	$0.971132\pi$
$390$	−6970.12			−0.904989
$391$	−824.253	+	5751.36i	−0.106609	+	0.743884i
$392$	−24367.0			−3.13959
$393$			8081.45i			1.03729i
$394$	−2442.32	−	2442.32i	−0.312290	−	0.312290i
$395$	−3057.30			−0.389441
$396$	606.394	+	606.394i	0.0769506	+	0.0769506i
$397$	9672.31	−	9672.31i	1.22277	−	1.22277i	0.256126	−	0.966643i	$-0.417554\pi$
$397$	9672.31	−	9672.31i	1.22277	−	1.22277i	0.966643	−	0.256126i	$-0.0824461\pi$
$398$	14743.6	−	14743.6i	1.85686	−	1.85686i
$399$		−	722.464i		−	0.0906478i
$400$		−	19003.4i		−	2.37543i
$401$	9399.33	−	9399.33i	1.17052	−	1.17052i	0.188439	−	0.982085i	$-0.439657\pi$
$401$	9399.33	−	9399.33i	1.17052	−	1.17052i	0.982085	−	0.188439i	$-0.0603427\pi$
$402$	7717.73	−	7717.73i	0.957525	−	0.957525i
$403$	5331.99	+	5331.99i	0.659070	+	0.659070i
$404$	−5391.04			−0.663897
$405$	3945.16	+	3945.16i	0.484041	+	0.484041i
$406$		−	5368.76i		−	0.656273i
$407$	−1647.60			−0.200660
$408$	4215.37	−	29413.5i	0.511500	−	3.56908i
$409$	−6570.02			−0.794295			−0.397147	−	0.917755i	$-0.630000\pi$
$409$	−6570.02			−0.794295			−0.397147	+	0.917755i	$0.630000\pi$
$410$			3192.14i			0.384509i
$411$	7507.29	+	7507.29i	0.900991	+	0.900991i
$412$	2252.03			0.269295
$413$	−45.3110	−	45.3110i	−0.00539856	−	0.00539856i
$414$	1324.63	−	1324.63i	0.157251	−	0.157251i
$415$	2682.36	−	2682.36i	0.317281	−	0.317281i
$416$			23800.7i			2.80511i
$417$		−	3450.80i		−	0.405243i
$418$	1004.99	−	1004.99i	0.117597	−	0.117597i
$419$	−9830.40	+	9830.40i	−1.14617	+	1.14617i	−0.158874	+	0.987299i	$0.550786\pi$
$419$	−9830.40	+	9830.40i	−1.14617	+	1.14617i	−0.987299	+	0.158874i	$0.949214\pi$
$420$	−2762.55	−	2762.55i	−0.320949	−	0.320949i
$421$	3041.18			0.352062			0.176031	−	0.984385i	$-0.443674\pi$
$421$	3041.18			0.352062			0.176031	+	0.984385i	$0.443674\pi$
$422$	−9114.80	−	9114.80i	−1.05143	−	1.05143i
$423$			367.626i			0.0422567i
$424$	−41126.4			−4.71055
$425$	3324.60	+	4436.93i	0.379451	+	0.506407i
$426$	29307.4			3.33322
$427$			748.797i			0.0848638i
$428$	31648.5	+	31648.5i	3.57427	+	3.57427i
$429$	1782.99			0.200661
$430$	−6767.43	−	6767.43i	−0.758964	−	0.758964i
$431$	4422.43	−	4422.43i	0.494248	−	0.494248i	−0.415394	−	0.909642i	$-0.636356\pi$
$431$	4422.43	−	4422.43i	0.494248	−	0.494248i	0.909642	+	0.415394i	$0.136356\pi$
$432$	21675.0	−	21675.0i	2.41398	−	2.41398i
$433$			10180.7i			1.12992i	0.825119	+	0.564959i	$0.191108\pi$
$433$			10180.7i			1.12992i	−0.825119	+	0.564959i	$0.808892\pi$
$434$			5770.86i			0.638272i
$435$	−5560.67	+	5560.67i	−0.612905	+	0.612905i
$436$	4063.01	−	4063.01i	0.446292	−	0.446292i
$437$	−1607.87	−	1607.87i	−0.176006	−	0.176006i
$438$	−27404.6			−2.98960
$439$	−7042.71	−	7042.71i	−0.765672	−	0.765672i	0.211669	−	0.977341i	$-0.432110\pi$
$439$	−7042.71	−	7042.71i	−0.765672	−	0.765672i	−0.977341	+	0.211669i	$0.932110\pi$
$440$		−	4877.58i		−	0.528476i
$441$	−1325.63			−0.143141
$442$	−7749.69	−	10342.6i	−0.833971	−	1.11300i
$443$	6833.02			0.732836			0.366418	−	0.930450i	$-0.380584\pi$
$443$	6833.02			0.732836			0.366418	+	0.930450i	$0.380584\pi$
$444$		−	21242.1i		−	2.27051i
$445$	−2885.24	−	2885.24i	−0.307356	−	0.307356i
$446$	−28831.5			−3.06101
$447$	−5515.74	−	5515.74i	−0.583636	−	0.583636i
$448$	−6465.05	+	6465.05i	−0.681796	+	0.681796i
$449$	4645.28	−	4645.28i	0.488251	−	0.488251i	−0.419503	−	0.907754i	$-0.637796\pi$
$449$	4645.28	−	4645.28i	0.488251	−	0.488251i	0.907754	+	0.419503i	$0.137796\pi$
$450$		−	1787.61i		−	0.187263i
$451$		−	816.567i		−	0.0852564i
$452$	−4636.14	+	4636.14i	−0.482446	+	0.482446i
$453$	−9877.60	+	9877.60i	−1.02448	+	1.02448i
$454$	13517.4	+	13517.4i	1.39737	+	1.39737i
$455$	−1078.39			−0.111111
$456$	8222.92	+	8222.92i	0.844459	+	0.844459i
$457$			10031.6i			1.02682i	0.858144	+	0.513410i	$0.171618\pi$
$457$			10031.6i			1.02682i	−0.858144	+	0.513410i	$0.828382\pi$
$458$	10842.4			1.10618
$459$	−1268.72	+	8852.68i	−0.129017	+	0.900235i
$460$	−12296.3			−1.24634
$461$		−	1359.04i		−	0.137304i	−0.997641	−	0.0686518i	$-0.978130\pi$
$461$		−	1359.04i		−	0.137304i	0.997641	−	0.0686518i	$-0.0218698\pi$
$462$	964.876	+	964.876i	0.0971647	+	0.0971647i
$463$	81.1156			0.00814203			0.00407102	−	0.999992i	$-0.498704\pi$
$463$	81.1156			0.00814203			0.00407102	+	0.999992i	$0.498704\pi$
$464$	35339.8	+	35339.8i	3.53579	+	3.53579i
$465$	5977.14	−	5977.14i	0.596093	−	0.596093i
$466$	−56.1043	+	56.1043i	−0.00557721	+	0.00557721i
$467$		−	10790.7i		−	1.06924i	−0.845094	−	0.534618i	$-0.820455\pi$
$467$		−	10790.7i		−	1.06924i	0.845094	−	0.534618i	$-0.179545\pi$
$468$			3051.87i			0.301437i
$469$	1194.06	−	1194.06i	0.117562	−	0.117562i
$470$	2329.74	−	2329.74i	0.228644	−	0.228644i
$471$	−10712.8	−	10712.8i	−1.04802	−	1.04802i
$472$	1031.44			0.100584
$473$	1731.15	+	1731.15i	0.168284	+	0.168284i
$474$			13767.1i			1.33406i
$475$	−2169.84			−0.209598
$476$	1027.67	−	7170.72i	0.0989561	−	0.690482i
$477$	−2237.39			−0.214765
$478$			29335.7i			2.80708i
$479$	−1974.01	−	1974.01i	−0.188298	−	0.188298i	0.606662	−	0.794960i	$-0.292508\pi$
$479$	−1974.01	−	1974.01i	−0.188298	−	0.188298i	−0.794960	+	0.606662i	$0.792508\pi$
$480$	26680.5			2.53707
$481$	−4146.04	−	4146.04i	−0.393021	−	0.393021i
$482$	−655.729	+	655.729i	−0.0619661	+	0.0619661i
$483$	1543.69	−	1543.69i	0.145425	−	0.145425i
$484$		−	27176.8i		−	2.55229i
$485$		−	5561.95i		−	0.520733i
$486$	4446.38	−	4446.38i	0.415003	−	0.415003i
$487$	4575.10	−	4575.10i	0.425703	−	0.425703i	−0.461459	−	0.887162i	$-0.652674\pi$
$487$	4575.10	−	4575.10i	0.425703	−	0.425703i	0.887162	+	0.461459i	$0.152674\pi$
$488$	−8522.63	−	8522.63i	−0.790576	−	0.790576i
$489$	18469.4			1.70801
$490$	8400.85	+	8400.85i	0.774514	+	0.774514i
$491$		−	221.719i		−	0.0203789i	−0.999948	−	0.0101895i	$-0.996757\pi$
$491$		−	221.719i		−	0.0203789i	0.999948	−	0.0101895i	$-0.00324346\pi$
$492$	10527.8			0.964694
$493$	−14433.8	−	2068.57i	−1.31859	−	0.188973i
$494$	5057.93			0.460662
$495$		−	265.354i		−	0.0240945i
$496$	−37986.6	−	37986.6i	−3.43881	−	3.43881i
$497$	4534.33			0.409241
$498$	−12078.8	−	12078.8i	−1.08687	−	1.08687i
$499$	−5125.17	+	5125.17i	−0.459788	+	0.459788i	−0.898586	−	0.438798i	$-0.855404\pi$
$499$	−5125.17	+	5125.17i	−0.459788	+	0.459788i	0.438798	+	0.898586i	$0.355404\pi$
$500$	−21408.7	+	21408.7i	−1.91485	+	1.91485i
$501$			1954.10i			0.174257i
$502$			26380.8i			2.34548i
$503$	−5194.90	+	5194.90i	−0.460495	+	0.460495i	−0.898818	−	0.438323i	$-0.855573\pi$
$503$	−5194.90	+	5194.90i	−0.460495	+	0.460495i	0.438323	+	0.898818i	$0.355573\pi$
$504$	−1048.11	+	1048.11i	−0.0926318	+	0.0926318i
$505$	1179.54	+	1179.54i	0.103938	+	0.103938i
$506$	4294.72			0.377320
$507$	−4181.43	−	4181.43i	−0.366280	−	0.366280i
$508$		−	16663.7i		−	1.45538i
$509$	−1656.30			−0.144232			−0.0721162	−	0.997396i	$-0.522975\pi$
$509$	−1656.30			−0.144232			−0.0721162	+	0.997396i	$0.522975\pi$
$510$	−11594.0	+	8687.38i	−1.00665	+	0.754281i
$511$	−4239.93			−0.367052
$512$		−	23539.3i		−	2.03184i
$513$	−2474.88	−	2474.88i	−0.213000	−	0.213000i
$514$	30528.1			2.61972
$515$	−492.736	−	492.736i	−0.0421602	−	0.0421602i
$516$	−22319.2	+	22319.2i	−1.90416	+	1.90416i
$517$	−595.960	+	595.960i	−0.0506969	+	0.0506969i
$518$		−	4487.30i		−	0.380619i
$519$		−	11664.3i		−	0.986522i
$520$	12274.0	−	12274.0i	1.03510	−	1.03510i
$521$	−12169.0	+	12169.0i	−1.02329	+	1.02329i	−0.0235669	+	0.999722i	$0.507502\pi$
$521$	−12169.0	+	12169.0i	−1.02329	+	1.02329i	−0.999722	+	0.0235669i	$0.992498\pi$
$522$	3324.33	+	3324.33i	0.278739	+	0.278739i
$523$	22280.9			1.86286			0.931429	−	0.363922i	$-0.118563\pi$
$523$	22280.9			1.86286			0.931429	+	0.363922i	$0.118563\pi$
$524$	−22424.1	−	22424.1i	−1.86947	−	1.86947i
$525$		−	2083.23i		−	0.173180i
$526$	22505.6			1.86557
$527$	15514.8	+	2223.49i	1.28242	+	0.183789i
$528$	−12702.6			−1.04698
$529$			5295.94i			0.435271i
$530$	14178.9	+	14178.9i	1.16206	+	1.16206i
$531$	56.1130			0.00458587
$532$	2004.67	+	2004.67i	0.163371	+	0.163371i
$533$	2054.81	−	2054.81i	0.166987	−	0.166987i
$534$	−12992.4	+	12992.4i	−1.05287	+	1.05287i
$535$		−	13849.2i		−	1.11916i
$536$			27180.9i			2.19037i
$537$	2915.88	−	2915.88i	0.234319	−	0.234319i
$538$	23390.3	−	23390.3i	1.87440	−	1.87440i
$539$	−2148.98	−	2148.98i	−0.171731	−	0.171731i
$540$	−18926.9			−1.50830
$541$	−6005.23	−	6005.23i	−0.477237	−	0.477237i	0.427010	−	0.904247i	$-0.359567\pi$
$541$	−6005.23	−	6005.23i	−0.477237	−	0.477237i	−0.904247	+	0.427010i	$0.859567\pi$
$542$		−	35843.9i		−	2.84064i
$543$	18201.8			1.43851
$544$	29664.6	+	39589.7i	2.33797	+	3.12021i
$545$	−1777.94			−0.139741
$546$			4856.04i			0.380621i
$547$	8851.45	+	8851.45i	0.691885	+	0.691885i	0.962646	−	0.270762i	$-0.0872756\pi$
$547$	8851.45	+	8851.45i	0.691885	+	0.691885i	−0.270762	+	0.962646i	$0.587276\pi$
$548$	−41662.0			−3.24765
$549$	−463.654	−	463.654i	−0.0360442	−	0.0360442i
$550$	2897.89	−	2897.89i	0.224666	−	0.224666i
$551$	4035.15	−	4035.15i	0.311984	−	0.311984i
$552$			35139.8i			2.70951i
$553$			2130.00i			0.163792i
$554$	9433.52	−	9433.52i	0.723451	−	0.723451i
$555$	−4647.70	+	4647.70i	−0.355467	+	0.355467i
$556$	9575.15	+	9575.15i	0.730354	+	0.730354i
$557$	21449.2			1.63165			0.815827	−	0.578295i	$-0.196282\pi$
$557$	21449.2			1.63165			0.815827	+	0.578295i	$0.196282\pi$
$558$	−3573.31	−	3573.31i	−0.271093	−	0.271093i
$559$			8712.53i			0.659215i
$560$	7682.76			0.579742
$561$	2965.81	−	2222.28i	0.223202	−	0.167245i
$562$	2841.90			0.213306
$563$		−	9661.93i		−	0.723271i	−0.932319	−	0.361636i	$-0.882218\pi$
$563$		−	9661.93i		−	0.723271i	0.932319	−	0.361636i	$-0.117782\pi$
$564$	−7683.56	−	7683.56i	−0.573646	−	0.573646i
$565$	2028.74			0.151061
$566$	−17990.0	−	17990.0i	−1.33600	−	1.33600i
$567$	2748.57	−	2748.57i	0.203579	−	0.203579i
$568$	−51608.7	+	51608.7i	−3.81242	+	3.81242i
$569$			22571.3i			1.66298i	0.555537	+	0.831492i	$0.312513\pi$
$569$			22571.3i			1.66298i	−0.555537	+	0.831492i	$0.687487\pi$
$570$		−	5669.92i		−	0.416644i
$571$	−12344.5	+	12344.5i	−0.904732	+	0.904732i	−0.995841	−	0.0911089i	$-0.970959\pi$
$571$	−12344.5	+	12344.5i	−0.904732	+	0.904732i	0.0911089	+	0.995841i	$0.470959\pi$
$572$	−4947.39	+	4947.39i	−0.361645	+	0.361645i
$573$	−1048.86	−	1048.86i	−0.0764692	−	0.0764692i
$574$	2223.94			0.161717
$575$	−4636.29	−	4636.29i	−0.336255	−	0.336255i
$576$		−	8006.29i		−	0.579159i
$577$	−22153.0			−1.59834			−0.799168	−	0.601108i	$-0.794726\pi$
$577$	−22153.0			−1.59834			−0.799168	+	0.601108i	$0.794726\pi$
$578$	−25781.4	−	7544.66i	−1.85530	−	0.542935i
$579$	198.631			0.0142571
$580$		−	30859.1i		−	2.20923i
$581$	−1868.78	−	1868.78i	−0.133443	−	0.133443i
$582$	−25045.7			−1.78381
$583$	−3627.03	−	3627.03i	−0.257661	−	0.257661i
$584$	48257.9	−	48257.9i	3.41940	−	3.41940i
$585$	667.737	−	667.737i	0.0471924	−	0.0471924i
$586$		−	10152.3i		−	0.715678i
$587$			16152.5i			1.13575i	0.823116	+	0.567873i	$0.192234\pi$
$587$			16152.5i			1.13575i	−0.823116	+	0.567873i	$0.807766\pi$
$588$	27706.3	−	27706.3i	1.94318	−	1.94318i
$589$	−4337.36	+	4337.36i	−0.303426	+	0.303426i
$590$	−355.602	−	355.602i	−0.0248134	−	0.0248134i
$591$	3524.74			0.245327
$592$	29537.6	+	29537.6i	2.05065	+	2.05065i
$593$		−	8336.26i		−	0.577284i	−0.957437	−	0.288642i	$-0.906796\pi$
$593$		−	8336.26i		−	0.577284i	0.957437	−	0.288642i	$-0.0932037\pi$
$594$	6610.58			0.456625
$595$	−1793.78	+	1344.08i	−0.123593	+	0.0926080i
$596$	30609.8			2.10373
$597$			21277.9i			1.45870i
$598$	10807.3	+	10807.3i	0.739033	+	0.739033i
$599$	−9798.73			−0.668390			−0.334195	−	0.942504i	$-0.608464\pi$
$599$	−9798.73			−0.668390			−0.334195	+	0.942504i	$0.608464\pi$
$600$	23710.8	+	23710.8i	1.61332	+	1.61332i
$601$	−5458.38	+	5458.38i	−0.370469	+	0.370469i	−0.867648	−	0.497179i	$-0.834369\pi$
$601$	−5458.38	+	5458.38i	−0.370469	+	0.370469i	0.497179	+	0.867648i	$0.334369\pi$
$602$	−4714.83	+	4714.83i	−0.319206	+	0.319206i
$603$			1478.72i			0.0998640i
$604$		−	54816.1i		−	3.69277i
$605$	−5946.18	+	5946.18i	−0.399581	+	0.399581i
$606$	5311.52	−	5311.52i	0.356049	−	0.356049i
$607$	−17165.0	−	17165.0i	−1.14779	−	1.14779i	−0.986987	−	0.160799i	$-0.948593\pi$
$607$	−17165.0	−	17165.0i	−1.14779	−	1.14779i	−0.160799	−	0.986987i	$-0.551407\pi$
$608$	−19360.9			−1.29143
$609$	3874.08	+	3874.08i	0.257776	+	0.257776i
$610$			5876.58i			0.390059i
$611$	−2999.36			−0.198594
$612$	3803.77	+	5076.43i	0.251239	+	0.335298i
$613$	−12662.6			−0.834318			−0.417159	−	0.908833i	$-0.636974\pi$
$613$	−12662.6			−0.834318			−0.417159	+	0.908833i	$0.636974\pi$
$614$		−	4153.47i		−	0.272997i
$615$	−2303.44	−	2303.44i	−0.151030	−	0.151030i
$616$	−3398.18			−0.222267
$617$	13203.5	+	13203.5i	0.861514	+	0.861514i	0.991514	−	0.130000i	$-0.0414978\pi$
$617$	13203.5	+	13203.5i	0.861514	+	0.861514i	−0.130000	+	0.991514i	$0.541498\pi$
$618$	−2218.81	+	2218.81i	−0.144423	+	0.144423i
$619$	13686.4	−	13686.4i	0.888697	−	0.888697i	−0.105701	−	0.994398i	$-0.533709\pi$
$619$	13686.4	−	13686.4i	0.888697	−	0.888697i	0.994398	+	0.105701i	$0.0337087\pi$
$620$			33170.3i			2.14863i
$621$		−	10576.2i		−	0.683425i
$622$	−3952.91	+	3952.91i	−0.254819	+	0.254819i
$623$	−2010.13	+	2010.13i	−0.129268	+	0.129268i
$624$	−31964.8	−	31964.8i	−2.05067	−	2.05067i
$625$	−519.171			−0.0332269
$626$	15236.8	+	15236.8i	0.972816	+	0.972816i
$627$			1450.40i			0.0923816i
$628$	59450.9			3.77763
$629$	−12064.0	−	1728.94i	−0.764742	−	0.109599i
$630$	722.698			0.0457032
$631$		−	6088.34i		−	0.384109i	−0.981384	−	0.192055i	$-0.938485\pi$
$631$		−	6088.34i		−	0.384109i	0.981384	−	0.192055i	$-0.0615151\pi$
$632$	−24243.1	−	24243.1i	−1.52585	−	1.52585i
$633$	13154.4			0.825975
$634$	−20814.4	−	20814.4i	−1.30386	−	1.30386i
$635$	−3645.96	+	3645.96i	−0.227851	+	0.227851i
$636$	46762.4	−	46762.4i	2.91549	−	2.91549i
$637$		−	10815.4i		−	0.672720i
$638$			10778.1i			0.668826i
$639$	−2807.65	+	2807.65i	−0.173817	+	0.173817i
$640$	−23688.6	+	23688.6i	−1.46308	+	1.46308i
$641$	6462.87	+	6462.87i	0.398234	+	0.398234i	0.877610	−	0.479376i	$-0.159137\pi$
$641$	6462.87	+	6462.87i	0.398234	+	0.398234i	−0.479376	+	0.877610i	$0.659137\pi$
$642$	−62363.4			−3.83378
$643$	−17003.8	−	17003.8i	−1.04287	−	1.04287i	−0.999039	−	0.0438299i	$-0.986044\pi$
$643$	−17003.8	−	17003.8i	−1.04287	−	1.04287i	−0.0438299	−	0.999039i	$-0.513956\pi$
$644$			8566.75i			0.524188i
$645$	9766.73			0.596224
$646$	8413.28	−	6304.07i	0.512409	−	0.383948i
$647$	22785.1			1.38451			0.692253	−	0.721655i	$-0.256618\pi$
$647$	22785.1			1.38451			0.692253	+	0.721655i	$0.256618\pi$
$648$			62567.1i			3.79301i
$649$	90.9649	+	90.9649i	0.00550182	+	0.00550182i
$650$	14584.5			0.880082
$651$	−4164.24	−	4164.24i	−0.250705	−	0.250705i
$652$	−51248.3	+	51248.3i	−3.07828	+	3.07828i
$653$	−5235.78	+	5235.78i	−0.313770	+	0.313770i	−0.846368	−	0.532598i	$-0.821216\pi$
$653$	−5235.78	+	5235.78i	−0.313770	+	0.313770i	0.532598	+	0.846368i	$0.321216\pi$
$654$			8006.17i			0.478694i
$655$			9812.63i			0.585361i
$656$	−14639.1	+	14639.1i	−0.871281	+	0.871281i
$657$	2625.36	−	2625.36i	0.155898	−	0.155898i
$658$	−1623.11	−	1623.11i	−0.0961635	−	0.0961635i
$659$	−18416.5			−1.08863			−0.544314	−	0.838882i	$-0.683210\pi$
$659$	−18416.5			−1.08863			−0.544314	+	0.838882i	$0.683210\pi$
$660$	5546.01	+	5546.01i	0.327088	+	0.327088i
$661$			23526.7i			1.38439i	0.721709	+	0.692197i	$0.243357\pi$
$661$			23526.7i			1.38439i	−0.721709	+	0.692197i	$0.756643\pi$
$662$	−9282.45			−0.544974
$663$	13055.3	+	1871.02i	0.764746	+	0.109599i
$664$	42540.0			2.48626
$665$		−	877.228i		−	0.0511541i
$666$	2778.53	+	2778.53i	0.161660	+	0.161660i
$667$	17243.8			1.00102
$668$	−5422.16	−	5422.16i	−0.314057	−	0.314057i
$669$	20804.7	−	20804.7i	1.20233	−	1.20233i
$670$	9370.99	−	9370.99i	0.540348	−	0.540348i
$671$		−	1503.26i		−	0.0864870i
$672$		−	18588.1i		−	1.06704i
$673$	14333.6	−	14333.6i	0.820979	−	0.820979i	−0.165269	−	0.986248i	$-0.552849\pi$
$673$	14333.6	−	14333.6i	0.820979	−	0.820979i	0.986248	+	0.165269i	$0.0528493\pi$
$674$	−43675.3	+	43675.3i	−2.49601	+	2.49601i
$675$	−7136.33	−	7136.33i	−0.406930	−	0.406930i
$676$	23205.0			1.32027
$677$	23854.8	+	23854.8i	1.35423	+	1.35423i	0.880866	+	0.473366i	$0.156961\pi$
$677$	23854.8	+	23854.8i	1.35423	+	1.35423i	0.473366	+	0.880866i	$0.343039\pi$
$678$		−	9135.51i		−	0.517474i
$679$	−3874.98			−0.219010
$680$	5118.38	−	35714.3i	0.288648	−	2.01409i
$681$	−19508.3			−1.09774
$682$		−	11585.4i		−	0.650480i
$683$	466.809	+	466.809i	0.0261522	+	0.0261522i	0.720062	−	0.693910i	$-0.244113\pi$
$683$	466.809	+	466.809i	0.0261522	+	0.0261522i	−0.693910	+	0.720062i	$0.744113\pi$
$684$	−2482.58			−0.138777
$685$	9115.48	+	9115.48i	0.508445	+	0.508445i
$686$	12112.2	−	12112.2i	0.674120	−	0.674120i
$687$	−7823.81	+	7823.81i	−0.434494	+	0.434494i
$688$		−	62070.6i		−	3.43956i
$689$		−	18254.2i		−	1.00933i
$690$	12114.9	−	12114.9i	0.668416	−	0.668416i
$691$	15237.1	−	15237.1i	0.838850	−	0.838850i	−0.149858	−	0.988708i	$-0.547882\pi$
$691$	15237.1	−	15237.1i	0.838850	−	0.838850i	0.988708	+	0.149858i	$0.0478815\pi$
$692$	32365.6	+	32365.6i	1.77797	+	1.77797i
$693$	−184.870			−0.0101337
$694$	13910.1	+	13910.1i	0.760836	+	0.760836i
$695$		−	4190.01i		−	0.228685i
$696$	−88187.7			−4.80280
$697$	856.879	−	5979.01i	0.0465662	−	0.324923i
$698$	−20456.6			−1.10930
$699$		−	80.9694i		−	0.00438132i
$700$	5780.47	+	5780.47i	0.312116	+	0.312116i
$701$	−13156.7			−0.708878			−0.354439	−	0.935079i	$-0.615328\pi$
$701$	−13156.7			−0.708878			−0.354439	+	0.935079i	$0.615328\pi$
$702$	16634.9	+	16634.9i	0.894365	+	0.894365i
$703$	3372.65	−	3372.65i	0.180941	−	0.180941i
$704$	12979.0	−	12979.0i	0.694837	−	0.694837i
$705$			3362.27i			0.179618i
$706$			31312.4i			1.66920i
$707$	821.777	−	821.777i	0.0437145	−	0.0437145i
$708$	−1172.79	+	1172.79i	−0.0622543	+	0.0622543i
$709$	23107.7	+	23107.7i	1.22402	+	1.22402i	0.966191	+	0.257828i	$0.0830069\pi$
$709$	23107.7	+	23107.7i	1.22402	+	1.22402i	0.257828	+	0.966191i	$0.416993\pi$
$710$	35585.6			1.88099
$711$	−1318.89	−	1318.89i	−0.0695672	−	0.0695672i
$712$		−	45757.6i		−	2.40848i
$713$	−18535.3			−0.973565
$714$	6052.44	+	8077.46i	0.317236	+	0.423377i
$715$	2164.94			0.113237
$716$			16181.7i			0.844609i
$717$	−21168.6	−	21168.6i	−1.10259	−	1.10259i
$718$	−33073.0			−1.71904
$719$	9521.59	+	9521.59i	0.493874	+	0.493874i	0.909524	−	0.415650i	$-0.136446\pi$
$719$	9521.59	+	9521.59i	0.493874	+	0.493874i	−0.415650	+	0.909524i	$0.636446\pi$
$720$	−4757.15	+	4757.15i	−0.246234	+	0.246234i
$721$	−343.286	+	343.286i	−0.0177318	+	0.0177318i
$722$		−	33388.3i		−	1.72103i
$723$		−	946.345i		−	0.0486791i
$724$	−50505.6	+	50505.6i	−2.59258	+	2.59258i
$725$	11635.4	−	11635.4i	0.596036	−	0.596036i
$726$	26775.9	+	26775.9i	1.36880	+	1.36880i
$727$	−32562.8			−1.66119			−0.830596	−	0.556875i	$-0.812000\pi$
$727$	−32562.8			−1.66119			−0.830596	+	0.556875i	$0.812000\pi$
$728$	−8551.20	−	8551.20i	−0.435341	−	0.435341i
$729$		−	15817.9i		−	0.803633i
$730$	−33275.1			−1.68708
$731$	10859.1	+	14492.3i	0.549436	+	0.733265i
$732$	19381.2			0.978618
$733$		−	36291.9i		−	1.82875i	−0.404869	−	0.914375i	$-0.632683\pi$
$733$		−	36291.9i		−	1.82875i	0.404869	−	0.914375i	$-0.367317\pi$
$734$	13297.9	+	13297.9i	0.668710	+	0.668710i
$735$	−12124.1			−0.608439
$736$	−41368.5	−	41368.5i	−2.07182	−	2.07182i
$737$	−2397.15	+	2397.15i	−0.119810	+	0.119810i
$738$	−1377.06	+	1377.06i	−0.0686862	+	0.0686862i
$739$		−	13314.8i		−	0.662776i	−0.943495	−	0.331388i	$-0.892483\pi$
$739$		−	13314.8i		−	0.662776i	0.943495	−	0.331388i	$-0.107517\pi$
$740$		−	25792.6i		−	1.28129i
$741$	−3649.79	+	3649.79i	−0.180942	+	0.180942i
$742$	9878.34	−	9878.34i	0.488740	−	0.488740i
$743$	2986.28	+	2986.28i	0.147451	+	0.147451i	0.776978	−	0.629527i	$-0.216751\pi$
$743$	2986.28	+	2986.28i	0.147451	+	0.147451i	−0.629527	+	0.776978i	$0.716751\pi$
$744$	94792.7			4.67106
$745$	−6697.30	−	6697.30i	−0.329356	−	0.329356i
$746$			37268.4i			1.82908i
$747$	2314.29			0.113354
$748$	−2063.11	+	14395.7i	−0.100849	+	0.703689i
$749$	−9648.62			−0.470698
$750$		−	42185.7i		−	2.05387i
$751$	25948.6	+	25948.6i	1.26082	+	1.26082i	0.950695	+	0.310129i	$0.100372\pi$
$751$	25948.6	+	25948.6i	1.26082	+	1.26082i	0.310129	+	0.950695i	$0.399628\pi$
$752$	21368.3			1.03620
$753$	−19036.3	−	19036.3i	−0.921277	−	0.921277i
$754$	−27122.2	+	27122.2i	−1.30999	+	1.30999i
$755$	−11993.5	+	11993.5i	−0.578132	+	0.578132i
$756$			13186.2i			0.634363i
$757$			8664.38i			0.416000i	0.978129	+	0.208000i	$0.0666955\pi$
$757$			8664.38i			0.416000i	−0.978129	+	0.208000i	$0.933305\pi$
$758$	22879.4	−	22879.4i	1.09633	−	1.09633i
$759$	−3099.06	+	3099.06i	−0.148207	+	0.148207i
$760$	9984.40	+	9984.40i	0.476543	+	0.476543i
$761$	−30593.6			−1.45731			−0.728657	−	0.684879i	$-0.759855\pi$
$761$	−30593.6			−1.45731			−0.728657	+	0.684879i	$0.759855\pi$
$762$	16417.9	+	16417.9i	0.780524	+	0.780524i
$763$			1238.68i			0.0587724i
$764$	5820.69			0.275635
$765$	278.454	−	1942.95i	0.0131601	−	0.0918270i
$766$	−41471.6			−1.95618
$767$			457.809i			0.0215522i
$768$	45530.9	+	45530.9i	2.13926	+	2.13926i
$769$	24560.3			1.15171			0.575857	−	0.817550i	$-0.304668\pi$
$769$	24560.3			1.15171			0.575857	+	0.817550i	$0.304668\pi$
$770$	1171.57	+	1171.57i	0.0548317	+	0.0548317i
$771$	−22029.0	+	22029.0i	−1.02900	+	1.02900i
$772$	−551.156	+	551.156i	−0.0256950	+	0.0256950i
$773$		−	4421.49i		−	0.205731i	−0.994695	−	0.102865i	$-0.967199\pi$
$773$		−	4421.49i		−	0.205731i	0.994695	−	0.102865i	$-0.0328011\pi$
$774$		−	5838.83i		−	0.271153i
$775$	−12506.8	+	12506.8i	−0.579687	+	0.579687i
$776$	44104.1	−	44104.1i	2.04026	−	2.04026i
$777$	3238.02	+	3238.02i	0.149503	+	0.149503i
$778$	7598.63			0.350159
$779$	1671.51	+	1671.51i	0.0768782	+	0.0768782i
$780$			27912.0i			1.28130i
$781$	−9102.98			−0.417068
$782$	31446.5	+	4506.74i	1.43801	+	0.206088i
$783$	26542.2			1.21142
$784$			77052.2i			3.51003i
$785$	−13007.6	−	13007.6i	−0.591417	−	0.591417i
$786$	44186.7			2.00520
$787$	18102.6	+	18102.6i	0.819932	+	0.819932i	0.986098	−	0.166166i	$-0.0531387\pi$
$787$	18102.6	+	18102.6i	0.819932	+	0.819932i	−0.166166	+	0.986098i	$0.553139\pi$
$788$	−9780.33	+	9780.33i	−0.442144	+	0.442144i
$789$	−16240.0	+	16240.0i	−0.732773	+	0.732773i
$790$			16716.3i			0.752834i
$791$		−	1413.41i		−	0.0635336i
$792$	2104.15	−	2104.15i	0.0944036	−	0.0944036i
$793$	3782.82	−	3782.82i	0.169397	−	0.169397i
$794$	−52885.0	−	52885.0i	−2.36375	−	2.36375i
$795$	−20462.9			−0.912885
$796$	−59041.2	−	59041.2i	−2.62897	−	2.62897i
$797$		−	29252.2i		−	1.30008i	−0.759899	−	0.650042i	$-0.774751\pi$
$797$		−	29252.2i		−	1.30008i	0.759899	−	0.650042i	$-0.225249\pi$
$798$	−3950.20			−0.175232
$799$	−4989.08	+	3738.32i	−0.220902	+	0.165522i
$800$	−55827.3			−2.46724
$801$		−	2489.34i		−	0.109808i
$802$	−51392.4	−	51392.4i	−2.26276	−	2.26276i
$803$	8511.96			0.374073
$804$	−30905.8	−	30905.8i	−1.35568	−	1.35568i
$805$	1874.37	−	1874.37i	0.0820658	−	0.0820658i
$806$	29153.6	−	29153.6i	1.27406	−	1.27406i
$807$			33756.8i			1.47249i
$808$			18706.5i			0.814473i
$809$	21127.9	−	21127.9i	0.918191	−	0.918191i	−0.0787072	−	0.996898i	$-0.525079\pi$
$809$	21127.9	−	21127.9i	0.918191	−	0.918191i	0.996898	+	0.0787072i	$0.0250792\pi$
$810$	21570.9	−	21570.9i	0.935707	−	0.935707i
$811$	5743.99	+	5743.99i	0.248704	+	0.248704i	0.820439	−	0.571735i	$-0.193729\pi$
$811$	5743.99	+	5743.99i	0.248704	+	0.248704i	−0.571735	+	0.820439i	$0.693729\pi$
$812$	−21499.3			−0.929161
$813$	25864.9	+	25864.9i	1.11577	+	1.11577i
$814$			9008.56i			0.387899i
$815$	22425.9			0.963858
$816$	−93009.8	−	13329.7i	−3.99019	−	0.571852i
$817$	−7087.31			−0.303493
$818$			35922.7i			1.53546i
$819$	−465.208	−	465.208i	−0.0198482	−	0.0198482i
$820$	12783.0			0.544393
$821$	19490.2	+	19490.2i	0.828518	+	0.828518i	0.987312	−	0.158794i	$-0.0507605\pi$
$821$	19490.2	+	19490.2i	0.828518	+	0.828518i	−0.158794	+	0.987312i	$0.550760\pi$
$822$	41047.4	−	41047.4i	1.74172	−	1.74172i
$823$	13917.8	−	13917.8i	0.589483	−	0.589483i	−0.348008	−	0.937491i	$-0.613142\pi$
$823$	13917.8	−	13917.8i	0.589483	−	0.589483i	0.937491	+	0.348008i	$0.113142\pi$
$824$		−	7814.39i		−	0.330373i
$825$			4182.22i			0.176492i
$826$	−247.745	+	247.745i	−0.0104360	+	0.0104360i
$827$	21762.7	−	21762.7i	0.915071	−	0.915071i	−0.0815942	−	0.996666i	$-0.526001\pi$
$827$	21762.7	−	21762.7i	0.915071	−	0.915071i	0.996666	+	0.0815942i	$0.0260012\pi$
$828$	−5304.52	−	5304.52i	−0.222639	−	0.222639i
$829$	29861.7			1.25108			0.625538	−	0.780194i	$-0.284880\pi$
$829$	29861.7			1.25108			0.625538	+	0.780194i	$0.284880\pi$
$830$	−14666.2	−	14666.2i	−0.613341	−	0.613341i
$831$			13614.4i			0.568326i
$832$	65321.0			2.72187
$833$	−13480.1	−	17990.2i	−0.560692	−	0.748288i
$834$	−18867.8			−0.783380
$835$			2372.70i			0.0983361i
$836$	−4024.51	−	4024.51i	−0.166496	−	0.166496i
$837$	−28530.1			−1.17819
$838$	53749.4	+	53749.4i	2.21568	+	2.21568i
$839$	−20354.4	+	20354.4i	−0.837558	+	0.837558i	−0.988537	−	0.150979i	$-0.951758\pi$
$839$	−20354.4	+	20354.4i	−0.837558	+	0.837558i	0.150979	+	0.988537i	$0.451758\pi$
$840$	−9585.87	+	9585.87i	−0.393743	+	0.393743i
$841$			18886.4i			0.774383i
$842$		−	16628.2i		−	0.680576i
$843$	−2050.71	+	2050.71i	−0.0837842	+	0.0837842i
$844$	−36500.5	+	36500.5i	−1.48862	+	1.48862i
$845$	−5077.17	−	5077.17i	−0.206698	−	0.206698i
$846$	2010.06			0.0816871
$847$	4142.66	+	4142.66i	0.168056	+	0.168056i
$848$			130048.i			5.26635i
$849$	25963.0			1.04953
$850$	24259.7	−	18177.8i	0.978942	−	0.733522i
$851$	14412.7			0.580563
$852$		−	117362.i		−	4.71921i
$853$	1527.89	+	1527.89i	0.0613293	+	0.0613293i	0.737106	−	0.675777i	$-0.236192\pi$
$853$	1527.89	+	1527.89i	0.0613293	+	0.0613293i	−0.675777	+	0.737106i	$0.736192\pi$
$854$	4094.18			0.164051
$855$	543.178	+	543.178i	0.0217267	+	0.0217267i
$856$	109818.	−	109818.i	4.38494	−	4.38494i
$857$	−17938.8	+	17938.8i	−0.715025	+	0.715025i	−0.967582	−	0.252557i	$-0.918729\pi$
$857$	−17938.8	+	17938.8i	−0.715025	+	0.715025i	0.252557	+	0.967582i	$0.418729\pi$
$858$		−	9748.83i		−	0.387902i
$859$			4878.89i			0.193790i	0.995295	+	0.0968951i	$0.0308911\pi$
$859$			4878.89i			0.193790i	−0.995295	+	0.0968951i	$0.969109\pi$
$860$	−27100.4	+	27100.4i	−1.07455	+	1.07455i
$861$	−1604.79	+	1604.79i	−0.0635206	+	0.0635206i
$862$	−24180.4	−	24180.4i	−0.955438	−	0.955438i
$863$	−39426.2			−1.55514			−0.777569	−	0.628797i	$-0.783548\pi$
$863$	−39426.2			−1.55514			−0.777569	+	0.628797i	$0.783548\pi$
$864$	−63675.7	−	63675.7i	−2.50728	−	2.50728i
$865$		−	14163.0i		−	0.556711i
$866$	55664.9			2.18426
$867$	24048.0	−	13159.6i	0.941999	−	0.515482i
$868$	23109.6			0.903674
$869$		−	4276.12i		−	0.166924i
$870$	30403.9	+	30403.9i	1.18481	+	1.18481i
$871$	−12064.4			−0.469330
$872$	−14098.4	−	14098.4i	−0.547514	−	0.547514i
$873$	2399.38	−	2399.38i	0.0930203	−	0.0930203i
$874$	−8791.29	+	8791.29i	−0.340240	+	0.340240i
$875$		−	6526.81i		−	0.252167i
$876$			109743.i			4.23271i
$877$	1781.74	−	1781.74i	0.0686034	−	0.0686034i	−0.671973	−	0.740576i	$-0.734553\pi$
$877$	1781.74	−	1781.74i	0.0686034	−	0.0686034i	0.740576	+	0.671973i	$0.234553\pi$
$878$	−38507.2	+	38507.2i	−1.48013	+	1.48013i
$879$	7325.87	+	7325.87i	0.281110	+	0.281110i
$880$	−15423.7			−0.590831
$881$	−2784.04	−	2784.04i	−0.106466	−	0.106466i	0.651867	−	0.758333i	$-0.273986\pi$
$881$	−2784.04	−	2784.04i	−0.106466	−	0.106466i	−0.758333	+	0.651867i	$0.773986\pi$
$882$			7248.11i			0.276708i
$883$	−8794.76			−0.335184			−0.167592	−	0.985856i	$-0.553599\pi$
$883$	−8794.76			−0.335184			−0.167592	+	0.985856i	$0.553599\pi$
$884$	−41417.1	+	31033.8i	−1.57580	+	1.18075i
$885$	513.203			0.0194928
$886$		−	37360.7i		−	1.41666i
$887$	−385.409	−	385.409i	−0.0145894	−	0.0145894i	0.699774	−	0.714364i	$-0.253284\pi$
$887$	−385.409	−	385.409i	−0.0145894	−	0.0145894i	−0.714364	+	0.699774i	$0.753284\pi$
$888$	−73708.8			−2.78548
$889$	2540.12	+	2540.12i	0.0958300	+	0.0958300i
$890$	−15775.5	+	15775.5i	−0.594154	+	0.594154i
$891$	−5517.94	+	5517.94i	−0.207473	+	0.207473i
$892$			115456.i			4.33382i
$893$		−	2439.86i		−	0.0914298i
$894$	−30158.2	+	30158.2i	−1.12824	+	1.12824i
$895$	3540.51	−	3540.51i	0.132230	−	0.132230i
$896$	16503.7	+	16503.7i	0.615345	+	0.615345i
$897$	−15597.0			−0.580567
$898$	−25398.9	−	25398.9i	−0.943844	−	0.943844i
$899$		−	46516.6i		−	1.72571i
$900$	−7158.51			−0.265130
$901$	−22751.5	−	30363.7i	−0.841247	−	1.12271i
$902$	−4464.72			−0.164810
$903$		−	6804.42i		−	0.250761i
$904$	16087.1	+	16087.1i	0.591868	+	0.591868i
$905$	22100.9			0.811777
$906$	54007.5	+	54007.5i	1.98044	+	1.98044i
$907$	1870.27	−	1870.27i	0.0684688	−	0.0684688i	−0.672043	−	0.740512i	$-0.734583\pi$
$907$	1870.27	−	1870.27i	0.0684688	−	0.0684688i	0.740512	+	0.672043i	$0.234583\pi$
$908$	54130.9	−	54130.9i	1.97841	−	1.97841i
$909$			1017.69i			0.0371337i
$910$			5896.28i			0.214791i
$911$	−576.131	+	576.131i	−0.0209529	+	0.0209529i	−0.717506	−	0.696553i	$-0.754716\pi$
$911$	−576.131	+	576.131i	−0.0209529	+	0.0209529i	0.696553	+	0.717506i	$0.254716\pi$
$912$	26002.1	−	26002.1i	0.944097	−	0.944097i
$913$	3751.71	+	3751.71i	0.135995	+	0.135995i
$914$	54849.3			1.98496
$915$	−4240.53	−	4240.53i	−0.153210	−	0.153210i
$916$		−	43418.5i		−	1.56614i
$917$	6836.40			0.246192
$918$	48403.6	+	6936.93i	1.74026	+	0.249404i
$919$	−44667.9			−1.60333			−0.801664	−	0.597774i	$-0.796052\pi$
$919$	−44667.9			−1.60333			−0.801664	+	0.597774i	$0.796052\pi$
$920$			42667.3i			1.52902i
$921$	2997.13	+	2997.13i	0.107230	+	0.107230i
$922$	−7430.81			−0.265424
$923$	−22906.8	−	22906.8i	−0.816887	−	0.816887i
$924$	3863.87	−	3863.87i	0.137567	−	0.137567i
$925$	9725.03	−	9725.03i	0.345683	−	0.345683i
$926$		−	443.514i		−	0.0157395i
$927$		−	425.124i		−	0.0150625i
$928$	103819.	−	103819.i	3.67246	−	3.67246i
$929$	4929.53	−	4929.53i	0.174093	−	0.174093i	−0.614682	−	0.788775i	$-0.710716\pi$
$929$	4929.53	−	4929.53i	0.174093	−	0.174093i	0.788775	+	0.614682i	$0.210716\pi$
$930$	−32681.1	−	32681.1i	−1.15232	−	1.15232i
$931$	8797.93			0.309711
$932$	224.671	+	224.671i	0.00789629	+	0.00789629i
$933$		−	5704.82i		−	0.200179i
$934$	−59000.0			−2.06696
$935$	3601.13	−	2698.33i	0.125957	−	0.0943794i
$936$	10589.8			0.369805
$937$			46241.3i			1.61221i	0.591776	+	0.806103i	$0.298427\pi$
$937$			46241.3i			1.61221i	−0.591776	+	0.806103i	$0.701573\pi$
$938$	−6528.71	−	6528.71i	−0.227260	−	0.227260i
$939$	−21989.6			−0.764221
$940$	−9329.51	−	9329.51i	−0.323718	−	0.323718i
$941$	−21810.5	+	21810.5i	−0.755582	+	0.755582i	−0.975515	−	0.219933i	$-0.929416\pi$
$941$	−21810.5	+	21810.5i	−0.755582	+	0.755582i	0.219933	+	0.975515i	$0.429416\pi$
$942$	−58574.0	+	58574.0i	−2.02595	+	2.02595i
$943$			7143.03i			0.246669i
$944$		−	3261.56i		−	0.112452i
$945$	2885.10	−	2885.10i	0.0993145	−	0.0993145i
$946$	9465.34	−	9465.34i	0.325312	−	0.325312i
$947$	−17699.8	−	17699.8i	−0.607355	−	0.607355i	0.334899	−	0.942254i	$-0.391298\pi$
$947$	−17699.8	−	17699.8i	−0.607355	−	0.607355i	−0.942254	+	0.334899i	$0.891298\pi$
$948$	55130.9			1.88879
$949$	21419.5	+	21419.5i	0.732674	+	0.732674i
$950$			11864.0i			0.405177i
$951$	30039.2			1.02428
$952$	−24881.9	−	3565.94i	−0.847088	−	0.121400i
$953$	−8104.79			−0.275488			−0.137744	−	0.990468i	$-0.543985\pi$
$953$	−8104.79			−0.275488			−0.137744	+	0.990468i	$0.543985\pi$
$954$			12233.3i			0.415165i
$955$	−1273.55	−	1273.55i	−0.0431528	−	0.0431528i
$956$	117476.			3.97431
$957$	−7777.48	−	7777.48i	−0.262707	−	0.262707i
$958$	−10793.2	+	10793.2i	−0.364001	+	0.364001i
$959$	6350.70	−	6350.70i	0.213842	−	0.213842i
$960$		−	73224.7i		−	2.46179i
$961$			20209.5i			0.678377i
$962$	−22669.2	+	22669.2i	−0.759755	+	0.759755i
$963$	5974.41	−	5974.41i	0.199920	−	0.199920i
$964$	2625.89	+	2625.89i	0.0877325	+	0.0877325i
$965$	241.182			0.00804550
$966$	−8440.38	−	8440.38i	−0.281123	−	0.281123i
$967$			12592.3i			0.418759i	0.977834	+	0.209379i	$0.0671443\pi$
$967$			12592.3i			0.418759i	−0.977834	+	0.209379i	$0.932856\pi$
$968$	−94301.6			−3.13117
$969$	−1522.00	+	10620.0i	−0.0504579	+	0.352078i
$970$	−30410.9			−1.00664
$971$		−	43998.8i		−	1.45416i	−0.686553	−	0.727080i	$-0.740877\pi$
$971$		−	43998.8i		−	1.45416i	0.686553	−	0.727080i	$-0.259123\pi$
$972$	−17805.6	−	17805.6i	−0.587568	−	0.587568i
$973$	−2919.16			−0.0961807
$974$	−25015.1	−	25015.1i	−0.822933	−	0.822933i
$975$	−10524.2	+	10524.2i	−0.345685	+	0.345685i
$976$	−26949.9	+	26949.9i	−0.883856	+	0.883856i
$977$			8709.69i			0.285207i	0.989780	+	0.142604i	$0.0455474\pi$
$977$			8709.69i			0.285207i	−0.989780	+	0.142604i	$0.954453\pi$
$978$		−	100985.i		−	3.30177i
$979$	4035.47	−	4035.47i	0.131741	−	0.131741i
$980$	33641.4	−	33641.4i	1.09657	−	1.09657i
$981$	−766.991	−	766.991i	−0.0249624	−	0.0249624i
$982$	−1212.29			−0.0393948
$983$	24475.0	+	24475.0i	0.794132	+	0.794132i	0.982163	−	0.188031i	$-0.0602107\pi$
$983$	24475.0	+	24475.0i	0.794132	+	0.794132i	−0.188031	+	0.982163i	$0.560211\pi$
$984$		−	36530.7i		−	1.18349i
$985$	4279.80			0.138442
$986$	−11310.2	+	78919.0i	−0.365306	+	2.54898i
$987$	2342.47			0.0755437
$988$		−	20254.6i		−	0.652212i
$989$	−15143.4	−	15143.4i	−0.486889	−	0.486889i
$990$	−1450.87			−0.0465773
$991$	−20930.6	−	20930.6i	−0.670919	−	0.670919i	0.287009	−	0.957928i	$-0.407339\pi$
$991$	−20930.6	−	20930.6i	−0.670919	−	0.670919i	−0.957928	+	0.287009i	$0.907339\pi$
$992$	−111595.	+	111595.i	−3.57172	+	3.57172i
$993$	6698.19	−	6698.19i	0.214059	−	0.214059i
$994$		−	24792.2i		−	0.791109i
$995$			25836.0i			0.823171i
$996$	−48369.8	+	48369.8i	−1.53881	+	1.53881i
$997$	25813.9	−	25813.9i	0.819993	−	0.819993i	−0.166114	−	0.986107i	$-0.553122\pi$
$997$	25813.9	−	25813.9i	0.819993	−	0.819993i	0.986107	+	0.166114i	$0.0531219\pi$
$998$	28022.7	+	28022.7i	0.888822	+	0.888822i
$999$	22184.4			0.702587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.4.c.a.13.1	yes	8
3.2	odd	2		153.4.f.a.64.4		8
4.3	odd	2		272.4.o.e.81.1		8
17.2	even	8		289.4.a.f.1.8		8
17.4	even	4	inner	17.4.c.a.4.4	✓	8
17.8	even	8		289.4.b.c.288.1		8
17.9	even	8		289.4.b.c.288.2		8
17.15	even	8		289.4.a.f.1.7		8
51.38	odd	4		153.4.f.a.55.1		8
68.55	odd	4		272.4.o.e.225.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.c.a.4.4	✓	8	17.4	even	4	inner
17.4.c.a.13.1	yes	8	1.1	even	1	trivial
153.4.f.a.55.1		8	51.38	odd	4
153.4.f.a.64.4		8	3.2	odd	2
272.4.o.e.81.1		8	4.3	odd	2
272.4.o.e.225.1		8	68.55	odd	4
289.4.a.f.1.7		8	17.15	even	8
289.4.a.f.1.8		8	17.2	even	8
289.4.b.c.288.1		8	17.8	even	8
289.4.b.c.288.2		8	17.9	even	8

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-5.46767i q^{2} +(3.94546 + 3.94546i) q^{3} -21.8954 q^{4} +(4.79064 + 4.79064i) q^{5} +(21.5725 - 21.5725i) q^{6} +(3.33761 - 3.33761i) q^{7} +75.9757i q^{8} +4.13329i q^{9} +O(q^{10})\)	\(q-5.46767i q^{2} +(3.94546 + 3.94546i) q^{3} -21.8954 q^{4} +(4.79064 + 4.79064i) q^{5} +(21.5725 - 21.5725i) q^{6} +(3.33761 - 3.33761i) q^{7} +75.9757i q^{8} +4.13329i q^{9} +(26.1937 - 26.1937i) q^{10} +(-6.70048 + 6.70048i) q^{11} +(-86.3876 - 86.3876i) q^{12} -33.7223 q^{13} +(-18.2490 - 18.2490i) q^{14} +37.8026i q^{15} +240.247 q^{16} +(-56.0931 + 42.0305i) q^{17} +22.5994 q^{18} -27.4317i q^{19} +(-104.893 - 104.893i) q^{20} +26.3368 q^{21} +(36.6360 + 36.6360i) q^{22} +(58.6134 - 58.6134i) q^{23} +(-299.759 + 299.759i) q^{24} -79.0995i q^{25} +184.382i q^{26} +(90.2197 - 90.2197i) q^{27} +(-73.0784 + 73.0784i) q^{28} +(147.098 + 147.098i) q^{29} +206.692 q^{30} +(-158.115 - 158.115i) q^{31} -705.786i q^{32} -52.8729 q^{33} +(229.809 + 306.699i) q^{34} +31.9786 q^{35} -90.5001i q^{36} +(122.947 + 122.947i) q^{37} -149.988 q^{38} +(-133.050 - 133.050i) q^{39} +(-363.973 + 363.973i) q^{40} +(-60.9335 + 60.9335i) q^{41} -144.001i q^{42} -258.362i q^{43} +(146.710 - 146.710i) q^{44} +(-19.8011 + 19.8011i) q^{45} +(-320.479 - 320.479i) q^{46} +88.9429 q^{47} +(947.884 + 947.884i) q^{48} +320.721i q^{49} -432.490 q^{50} +(-387.143 - 55.4832i) q^{51} +738.364 q^{52} +541.310i q^{53} +(-493.292 - 493.292i) q^{54} -64.1992 q^{55} +(253.577 + 253.577i) q^{56} +(108.231 - 108.231i) q^{57} +(804.282 - 804.282i) q^{58} -13.5759i q^{59} -827.704i q^{60} +(-112.176 + 112.176i) q^{61} +(-864.520 + 864.520i) q^{62} +(13.7953 + 13.7953i) q^{63} -1937.03 q^{64} +(-161.551 - 161.551i) q^{65} +289.092i q^{66} +357.758 q^{67} +(1228.18 - 920.277i) q^{68} +462.513 q^{69} -174.848i q^{70} +(679.278 + 679.278i) q^{71} -314.029 q^{72} +(-635.175 - 635.175i) q^{73} +(672.233 - 672.233i) q^{74} +(312.084 - 312.084i) q^{75} +600.630i q^{76} +44.7272i q^{77} +(-727.473 + 727.473i) q^{78} +(-319.090 + 319.090i) q^{79} +(1150.94 + 1150.94i) q^{80} +823.515 q^{81} +(333.164 + 333.164i) q^{82} -559.916i q^{83} -576.656 q^{84} +(-470.075 - 67.3686i) q^{85} -1412.64 q^{86} +1160.74i q^{87} +(-509.074 - 509.074i) q^{88} -602.266 q^{89} +(108.266 + 108.266i) q^{90} +(-112.552 + 112.552i) q^{91} +(-1283.37 + 1283.37i) q^{92} -1247.67i q^{93} -486.311i q^{94} +(131.416 - 131.416i) q^{95} +(2784.65 - 2784.65i) q^{96} +(-580.502 - 580.502i) q^{97} +1753.60 q^{98} +(-27.6950 - 27.6950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7}+O(q^{10}) \) 8 * q - 36 * q^4 + 14 * q^5 + 22 * q^6 + 2 * q^7	\( 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7} + 78 q^{10} - 108 q^{11} - 174 q^{12} - 88 q^{13} + 108 q^{14} + 420 q^{16} - 10 q^{17} + 428 q^{18} - 306 q^{20} - 260 q^{21} + 30 q^{22} - 22 q^{23} - 862 q^{24} + 540 q^{27} - 764 q^{28} + 46 q^{29} - 120 q^{30} + 610 q^{31} + 816 q^{33} + 1002 q^{34} + 1172 q^{35} - 574 q^{37} - 768 q^{38} - 844 q^{39} - 342 q^{40} - 968 q^{41} + 550 q^{44} - 1154 q^{45} - 944 q^{46} - 368 q^{47} + 2494 q^{48} + 468 q^{50} + 296 q^{51} + 2564 q^{52} - 1592 q^{54} - 1996 q^{55} + 684 q^{56} - 300 q^{57} + 266 q^{58} + 1258 q^{61} - 2516 q^{62} + 122 q^{63} - 3044 q^{64} + 628 q^{65} + 764 q^{67} + 1914 q^{68} + 1812 q^{69} + 1266 q^{71} + 1404 q^{72} - 1732 q^{73} + 1538 q^{74} + 1292 q^{75} - 2836 q^{78} + 914 q^{79} + 498 q^{80} + 280 q^{81} - 280 q^{82} - 2952 q^{84} - 2498 q^{85} - 4244 q^{86} + 442 q^{88} - 2156 q^{89} + 2478 q^{90} - 1632 q^{91} - 1768 q^{92} + 1484 q^{95} + 3998 q^{96} + 1836 q^{97} + 6728 q^{98} - 2088 q^{99}+O(q^{100}) \) 8 * q - 36 * q^4 + 14 * q^5 + 22 * q^6 + 2 * q^7 + 78 * q^10 - 108 * q^11 - 174 * q^12 - 88 * q^13 + 108 * q^14 + 420 * q^16 - 10 * q^17 + 428 * q^18 - 306 * q^20 - 260 * q^21 + 30 * q^22 - 22 * q^23 - 862 * q^24 + 540 * q^27 - 764 * q^28 + 46 * q^29 - 120 * q^30 + 610 * q^31 + 816 * q^33 + 1002 * q^34 + 1172 * q^35 - 574 * q^37 - 768 * q^38 - 844 * q^39 - 342 * q^40 - 968 * q^41 + 550 * q^44 - 1154 * q^45 - 944 * q^46 - 368 * q^47 + 2494 * q^48 + 468 * q^50 + 296 * q^51 + 2564 * q^52 - 1592 * q^54 - 1996 * q^55 + 684 * q^56 - 300 * q^57 + 266 * q^58 + 1258 * q^61 - 2516 * q^62 + 122 * q^63 - 3044 * q^64 + 628 * q^65 + 764 * q^67 + 1914 * q^68 + 1812 * q^69 + 1266 * q^71 + 1404 * q^72 - 1732 * q^73 + 1538 * q^74 + 1292 * q^75 - 2836 * q^78 + 914 * q^79 + 498 * q^80 + 280 * q^81 - 280 * q^82 - 2952 * q^84 - 2498 * q^85 - 4244 * q^86 + 442 * q^88 - 2156 * q^89 + 2478 * q^90 - 1632 * q^91 - 1768 * q^92 + 1484 * q^95 + 3998 * q^96 + 1836 * q^97 + 6728 * q^98 - 2088 * q^99

Introduction

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