LMFDB - Embedded newform 17.4.c.a.4.1

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			4.1
Root			$-4.93651i$ of defining polynomial
Character	$\chi$	$=$	17.4
Dual form			17.4.c.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.93651i q^{2} +(-0.299807 + 0.299807i) q^{3} -7.49613 q^{4} +(1.37942 - 1.37942i) q^{5} +(1.18019 + 1.18019i) q^{6} +(17.9849 + 17.9849i) q^{7} -1.98349i q^{8} +26.8202i q^{9} +O(q^{10})$	\(q-3.93651i q^{2} +(-0.299807 + 0.299807i) q^{3} -7.49613 q^{4} +(1.37942 - 1.37942i) q^{5} +(1.18019 + 1.18019i) q^{6} +(17.9849 + 17.9849i) q^{7} -1.98349i q^{8} +26.8202i q^{9} +(-5.43011 - 5.43011i) q^{10} +(-22.9317 - 22.9317i) q^{11} +(2.24739 - 2.24739i) q^{12} -54.6855 q^{13} +(70.7978 - 70.7978i) q^{14} +0.827121i q^{15} -67.7771 q^{16} +(58.5003 + 38.6098i) q^{17} +105.578 q^{18} -46.1336i q^{19} +(-10.3403 + 10.3403i) q^{20} -10.7840 q^{21} +(-90.2708 + 90.2708i) q^{22} +(-53.2436 - 53.2436i) q^{23} +(0.594665 + 0.594665i) q^{24} +121.194i q^{25} +215.270i q^{26} +(-16.1357 - 16.1357i) q^{27} +(-134.817 - 134.817i) q^{28} +(111.044 - 111.044i) q^{29} +3.25597 q^{30} +(178.619 - 178.619i) q^{31} +250.937i q^{32} +13.7502 q^{33} +(151.988 - 230.287i) q^{34} +49.6175 q^{35} -201.048i q^{36} +(-159.957 + 159.957i) q^{37} -181.606 q^{38} +(16.3951 - 16.3951i) q^{39} +(-2.73608 - 2.73608i) q^{40} +(-163.457 - 163.457i) q^{41} +42.4513i q^{42} -119.642i q^{43} +(171.899 + 171.899i) q^{44} +(36.9964 + 36.9964i) q^{45} +(-209.594 + 209.594i) q^{46} -188.319 q^{47} +(20.3200 - 20.3200i) q^{48} +303.913i q^{49} +477.083 q^{50} +(-29.1143 + 5.96329i) q^{51} +409.930 q^{52} +468.212i q^{53} +(-63.5183 + 63.5183i) q^{54} -63.2650 q^{55} +(35.6729 - 35.6729i) q^{56} +(13.8312 + 13.8312i) q^{57} +(-437.125 - 437.125i) q^{58} -751.217i q^{59} -6.20021i q^{60} +(341.681 + 341.681i) q^{61} +(-703.136 - 703.136i) q^{62} +(-482.359 + 482.359i) q^{63} +445.601 q^{64} +(-75.4344 + 75.4344i) q^{65} -54.1277i q^{66} +533.879 q^{67} +(-438.526 - 289.424i) q^{68} +31.9256 q^{69} -195.320i q^{70} +(55.2619 - 55.2619i) q^{71} +53.1977 q^{72} +(270.831 - 270.831i) q^{73} +(629.674 + 629.674i) q^{74} +(-36.3349 - 36.3349i) q^{75} +345.824i q^{76} -824.848i q^{77} +(-64.5395 - 64.5395i) q^{78} +(904.285 + 904.285i) q^{79} +(-93.4932 + 93.4932i) q^{80} -714.471 q^{81} +(-643.449 + 643.449i) q^{82} +591.376i q^{83} +80.8382 q^{84} +(133.956 - 27.4373i) q^{85} -470.973 q^{86} +66.5834i q^{87} +(-45.4848 + 45.4848i) q^{88} -609.729 q^{89} +(145.637 - 145.637i) q^{90} +(-983.513 - 983.513i) q^{91} +(399.121 + 399.121i) q^{92} +107.103i q^{93} +741.321i q^{94} +(-63.6378 - 63.6378i) q^{95} +(-75.2328 - 75.2328i) q^{96} +(1125.76 - 1125.76i) q^{97} +1196.36 q^{98} +(615.033 - 615.033i) 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 $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	3.93651i		−	1.39177i	−0.718155	−	0.695884i	$-0.755013\pi$
$2$		−	3.93651i		−	1.39177i	0.718155	−	0.695884i	$-0.244987\pi$
$3$	−0.299807	+	0.299807i	−0.0576979	+	0.0576979i	−0.735367	−	0.677669i	$-0.762990\pi$
$3$	−0.299807	+	0.299807i	−0.0576979	+	0.0576979i	0.677669	+	0.735367i	$0.262990\pi$
$4$	−7.49613			−0.937016
$5$	1.37942	−	1.37942i	0.123379	−	0.123379i	−0.642721	−	0.766100i	$-0.722195\pi$
$5$	1.37942	−	1.37942i	0.123379	−	0.123379i	0.766100	+	0.642721i	$0.222195\pi$
$6$	1.18019	+	1.18019i	0.0803021	+	0.0803021i
$7$	17.9849	+	17.9849i	0.971093	+	0.971093i	0.999594	−	0.0285007i	$-0.00907327\pi$
$7$	17.9849	+	17.9849i	0.971093	+	0.971093i	−0.0285007	+	0.999594i	$0.509073\pi$
$8$		−	1.98349i		−	0.0876588i
$9$			26.8202i			0.993342i
$10$	−5.43011	−	5.43011i	−0.171715	−	0.171715i
$11$	−22.9317	−	22.9317i	−0.628560	−	0.628560i	0.319146	−	0.947706i	$-0.396604\pi$
$11$	−22.9317	−	22.9317i	−0.628560	−	0.628560i	−0.947706	+	0.319146i	$0.896604\pi$
$12$	2.24739	−	2.24739i	0.0540639	−	0.0540639i
$13$	−54.6855			−1.16669			−0.583347	−	0.812223i	$-0.698257\pi$
$13$	−54.6855			−1.16669			−0.583347	+	0.812223i	$0.698257\pi$
$14$	70.7978	−	70.7978i	1.35154	−	1.35154i
$15$			0.827121i			0.0142375i
$16$	−67.7771			−1.05902
$17$	58.5003	+	38.6098i	0.834612	+	0.550839i
$17$	58.5003	+	38.6098i	0.834612	+	0.550839i
$18$	105.578			1.38250
$19$		−	46.1336i		−	0.557041i	−0.960430	−	0.278521i	$-0.910156\pi$
$19$		−	46.1336i		−	0.557041i	0.960430	−	0.278521i	$-0.0898441\pi$
$20$	−10.3403	+	10.3403i	−0.115608	+	0.115608i
$21$	−10.7840			−0.112060
$22$	−90.2708	+	90.2708i	−0.874809	+	0.874809i
$23$	−53.2436	−	53.2436i	−0.482698	−	0.482698i	0.423294	−	0.905992i	$-0.360874\pi$
$23$	−53.2436	−	53.2436i	−0.482698	−	0.482698i	−0.905992	+	0.423294i	$0.860874\pi$
$24$	0.594665	+	0.594665i	0.00505773	+	0.00505773i
$25$			121.194i			0.969555i
$26$			215.270i			1.62377i
$27$	−16.1357	−	16.1357i	−0.115012	−	0.115012i
$28$	−134.817	−	134.817i	−0.909930	−	0.909930i
$29$	111.044	−	111.044i	0.711045	−	0.711045i	−0.255709	−	0.966754i	$-0.582309\pi$
$29$	111.044	−	111.044i	0.711045	−	0.711045i	0.966754	+	0.255709i	$0.0823088\pi$
$30$	3.25597			0.0198152
$31$	178.619	−	178.619i	1.03487	−	1.03487i	0.0354994	−	0.999370i	$-0.488698\pi$
$31$	178.619	−	178.619i	1.03487	−	1.03487i	0.999370	−	0.0354994i	$-0.0113022\pi$
$32$			250.937i			1.38625i
$33$	13.7502			0.0725332
$34$	151.988	−	230.287i	0.766639	−	1.16159i
$35$	49.6175			0.239626
$36$		−	201.048i		−	0.930777i
$37$	−159.957	+	159.957i	−0.710725	+	0.710725i	−0.966687	−	0.255962i	$-0.917608\pi$
$37$	−159.957	+	159.957i	−0.710725	+	0.710725i	0.255962	+	0.966687i	$0.417608\pi$
$38$	−181.606			−0.775272
$39$	16.3951	−	16.3951i	0.0673158	−	0.0673158i
$40$	−2.73608	−	2.73608i	−0.0108153	−	0.0108153i
$41$	−163.457	−	163.457i	−0.622626	−	0.622626i	0.323576	−	0.946202i	$-0.395115\pi$
$41$	−163.457	−	163.457i	−0.622626	−	0.622626i	−0.946202	+	0.323576i	$0.895115\pi$
$42$			42.4513i			0.155962i
$43$		−	119.642i		−	0.424309i	−0.977236	−	0.212154i	$-0.931952\pi$
$43$		−	119.642i		−	0.424309i	0.977236	−	0.212154i	$-0.0680480\pi$
$44$	171.899	+	171.899i	0.588971	+	0.588971i
$45$	36.9964	+	36.9964i	0.122558	+	0.122558i
$46$	−209.594	+	209.594i	−0.671803	+	0.671803i
$47$	−188.319			−0.584451			−0.292225	−	0.956349i	$-0.594396\pi$
$47$	−188.319			−0.584451			−0.292225	+	0.956349i	$0.594396\pi$
$48$	20.3200	−	20.3200i	0.0611031	−	0.0611031i
$49$			303.913i			0.886044i
$50$	477.083			1.34940
$51$	−29.1143	+	5.96329i	−0.0799376	+	0.0163731i
$52$	409.930			1.09321
$53$			468.212i			1.21347i	0.794905	+	0.606734i	$0.207521\pi$
$53$			468.212i			1.21347i	−0.794905	+	0.606734i	$0.792479\pi$
$54$	−63.5183	+	63.5183i	−0.160069	+	0.160069i
$55$	−63.2650			−0.155103
$56$	35.6729	−	35.6729i	0.0851249	−	0.0851249i
$57$	13.8312	+	13.8312i	0.0321401	+	0.0321401i
$58$	−437.125	−	437.125i	−0.989609	−	0.989609i
$59$		−	751.217i		−	1.65763i	−0.559523	−	0.828815i	$-0.689016\pi$
$59$		−	751.217i		−	1.65763i	0.559523	−	0.828815i	$-0.310984\pi$
$60$		−	6.20021i		−	0.0133407i
$61$	341.681	+	341.681i	0.717177	+	0.717177i	0.968026	−	0.250849i	$-0.0807099\pi$
$61$	341.681	+	341.681i	0.717177	+	0.717177i	−0.250849	+	0.968026i	$0.580710\pi$
$62$	−703.136	−	703.136i	−1.44030	−	1.44030i
$63$	−482.359	+	482.359i	−0.964627	+	0.964627i
$64$	445.601			0.870315
$65$	−75.4344	+	75.4344i	−0.143946	+	0.143946i
$66$		−	54.1277i		−	0.100949i
$67$	533.879			0.973487			0.486744	−	0.873545i	$-0.338185\pi$
$67$	533.879			0.973487			0.486744	+	0.873545i	$0.338185\pi$
$68$	−438.526	−	289.424i	−0.782045	−	0.516145i
$69$	31.9256			0.0557013
$70$		−	195.320i		−	0.333503i
$71$	55.2619	−	55.2619i	0.0923715	−	0.0923715i	−0.659411	−	0.751783i	$-0.729194\pi$
$71$	55.2619	−	55.2619i	0.0923715	−	0.0923715i	0.751783	+	0.659411i	$0.229194\pi$
$72$	53.1977			0.0870752
$73$	270.831	−	270.831i	0.434224	−	0.434224i	−0.455839	−	0.890062i	$-0.650661\pi$
$73$	270.831	−	270.831i	0.434224	−	0.434224i	0.890062	+	0.455839i	$0.150661\pi$
$74$	629.674	+	629.674i	0.989164	+	0.989164i
$75$	−36.3349	−	36.3349i	−0.0559413	−	0.0559413i
$76$			345.824i			0.521957i
$77$		−	824.848i		−	1.22078i
$78$	−64.5395	−	64.5395i	−0.0936880	−	0.0936880i
$79$	904.285	+	904.285i	1.28785	+	1.28785i	0.936091	+	0.351757i	$0.114416\pi$
$79$	904.285	+	904.285i	1.28785	+	1.28785i	0.351757	+	0.936091i	$0.385584\pi$
$80$	−93.4932	+	93.4932i	−0.130661	+	0.130661i
$81$	−714.471			−0.980070
$82$	−643.449	+	643.449i	−0.866550	+	0.866550i
$83$			591.376i			0.782071i	0.920376	+	0.391036i	$0.127883\pi$
$83$			591.376i			0.782071i	−0.920376	+	0.391036i	$0.872117\pi$
$84$	80.8382			0.105002
$85$	133.956	−	27.4373i	0.170936	−	0.0350117i
$86$	−470.973			−0.590539
$87$			66.5834i			0.0820516i
$88$	−45.4848	+	45.4848i	−0.0550989	+	0.0550989i
$89$	−609.729			−0.726192			−0.363096	−	0.931752i	$-0.618280\pi$
$89$	−609.729			−0.726192			−0.363096	+	0.931752i	$0.618280\pi$
$90$	145.637	−	145.637i	0.170572	−	0.170572i
$91$	−983.513	−	983.513i	−1.13297	−	1.13297i
$92$	399.121	+	399.121i	0.452296	+	0.452296i
$93$			107.103i			0.119420i
$94$			741.321i			0.813420i
$95$	−63.6378	−	63.6378i	−0.0687274	−	0.0687274i
$96$	−75.2328	−	75.2328i	−0.0799835	−	0.0799835i
$97$	1125.76	−	1125.76i	1.17838	−	1.17838i	0.198226	−	0.980156i	$-0.436482\pi$
$97$	1125.76	−	1125.76i	1.17838	−	1.17838i	0.980156	−	0.198226i	$-0.0635182\pi$
$98$	1196.36			1.23317
$99$	615.033	−	615.033i	0.624375	−	0.624375i
$100$		−	908.489i		−	0.908489i
$101$	−666.897			−0.657017			−0.328508	−	0.944501i	$-0.606546\pi$
$101$	−666.897			−0.657017			−0.328508	+	0.944501i	$0.606546\pi$
$102$	23.4746	+	114.609i	0.0227875	+	0.111255i
$103$	−872.373			−0.834538			−0.417269	−	0.908783i	$-0.637013\pi$
$103$	−872.373			−0.834538			−0.417269	+	0.908783i	$0.637013\pi$
$104$			108.468i			0.102271i
$105$	−14.8757	+	14.8757i	−0.0138259	+	0.0138259i
$106$	1843.12			1.68887
$107$	−244.890	+	244.890i	−0.221256	+	0.221256i	−0.809027	−	0.587771i	$-0.800006\pi$
$107$	−244.890	+	244.890i	−0.221256	+	0.221256i	0.587771	+	0.809027i	$0.300006\pi$
$108$	120.955	+	120.955i	0.107768	+	0.107768i
$109$	−96.0400	−	96.0400i	−0.0843942	−	0.0843942i	0.663649	−	0.748044i	$-0.269007\pi$
$109$	−96.0400	−	96.0400i	−0.0843942	−	0.0843942i	−0.748044	+	0.663649i	$0.769007\pi$
$110$			249.043i			0.215867i
$111$		−	95.9128i		−	0.0820147i
$112$	−1218.96	−	1218.96i	−1.02840	−	1.02840i
$113$	626.459	+	626.459i	0.521525	+	0.521525i	0.918032	−	0.396507i	$-0.129778\pi$
$113$	626.459	+	626.459i	0.521525	+	0.521525i	−0.396507	+	0.918032i	$0.629778\pi$
$114$	54.4467	−	54.4467i	0.0447316	−	0.0447316i
$115$	−146.891			−0.119110
$116$	−832.398	+	832.398i	−0.666261	+	0.666261i
$117$		−	1466.68i		−	1.15893i
$118$	−2957.18			−2.30703
$119$	357.727	+	1746.51i	0.275570	+	1.34540i
$120$	1.64059			0.00124804
$121$		−	279.276i		−	0.209824i
$122$	1345.03	−	1345.03i	0.998143	−	0.998143i
$123$	98.0110			0.0718484
$124$	−1338.95	+	1338.95i	−0.969689	+	0.969689i
$125$	339.606	+	339.606i	0.243002	+	0.243002i
$126$	1898.81	+	1898.81i	1.34254	+	1.34254i
$127$			1971.07i			1.37720i	0.725144	+	0.688598i	$0.241773\pi$
$127$			1971.07i			1.37720i	−0.725144	+	0.688598i	$0.758227\pi$
$128$			253.384i			0.174970i
$129$	35.8696	+	35.8696i	0.0244817	+	0.0244817i
$130$	296.949	+	296.949i	0.200339	+	0.200339i
$131$	177.333	−	177.333i	0.118272	−	0.118272i	−0.645493	−	0.763766i	$-0.723348\pi$
$131$	177.333	−	177.333i	0.118272	−	0.118272i	0.763766	+	0.645493i	$0.223348\pi$
$132$	−103.073			−0.0679648
$133$	829.709	−	829.709i	0.540939	−	0.540939i
$134$		−	2101.62i		−	1.35487i
$135$	−44.5159			−0.0283801
$136$	76.5823	−	116.035i	0.0482859	−	0.0731611i
$137$	436.372			0.272130			0.136065	−	0.990700i	$-0.456554\pi$
$137$	436.372			0.272130			0.136065	+	0.990700i	$0.456554\pi$
$138$		−	125.676i		−	0.0775233i
$139$	−59.2009	+	59.2009i	−0.0361249	+	0.0361249i	−0.724938	−	0.688814i	$-0.758132\pi$
$139$	−59.2009	+	59.2009i	−0.0361249	+	0.0361249i	0.688814	+	0.724938i	$0.258132\pi$
$140$	−371.940			−0.224533
$141$	56.4595	−	56.4595i	0.0337216	−	0.0337216i
$142$	−217.539	−	217.539i	−0.128560	−	0.128560i
$143$	1254.03	+	1254.03i	0.733338	+	0.733338i
$144$		−	1817.80i		−	1.05197i
$145$		−	306.353i		−	0.175457i
$146$	−1066.13	−	1066.13i	−0.604339	−	0.604339i
$147$	−91.1153	−	91.1153i	−0.0511229	−	0.0511229i
$148$	1199.06	−	1199.06i	0.665961	−	0.665961i
$149$	−2357.45			−1.29617			−0.648085	−	0.761568i	$-0.724430\pi$
$149$	−2357.45			−1.29617			−0.648085	+	0.761568i	$0.724430\pi$
$150$	−143.033	+	143.033i	−0.0778573	+	0.0778573i
$151$			149.746i			0.0807031i	0.999186	+	0.0403515i	$0.0128478\pi$
$151$			149.746i			0.0807031i	−0.999186	+	0.0403515i	$0.987152\pi$
$152$	−91.5058			−0.0488296
$153$	−1035.52	+	1568.99i	−0.547171	+	0.829055i
$154$	−3247.02			−1.69904
$155$		−	492.783i		−	0.255363i
$156$	−122.900	+	122.900i	−0.0630760	+	0.0630760i
$157$	−119.280			−0.0606343			−0.0303172	−	0.999540i	$-0.509652\pi$
$157$	−119.280			−0.0606343			−0.0303172	+	0.999540i	$0.509652\pi$
$158$	3559.73	−	3559.73i	1.79238	−	1.79238i
$159$	−140.373	−	140.373i	−0.0700146	−	0.0700146i
$160$	346.149	+	346.149i	0.171034	+	0.171034i
$161$		−	1915.16i		−	0.937489i
$162$			2812.52i			1.36403i
$163$	107.923	+	107.923i	0.0518600	+	0.0518600i	0.732561	−	0.680701i	$-0.238325\pi$
$163$	107.923	+	107.923i	0.0518600	+	0.0518600i	−0.680701	+	0.732561i	$0.738325\pi$
$164$	1225.29	+	1225.29i	0.583410	+	0.583410i
$165$	18.9673	−	18.9673i	0.00894910	−	0.00894910i
$166$	2327.96			1.08846
$167$	−1785.49	+	1785.49i	−0.827339	+	0.827339i	−0.987148	−	0.159809i	$-0.948912\pi$
$167$	−1785.49	+	1785.49i	−0.827339	+	0.827339i	0.159809	+	0.987148i	$0.448912\pi$
$168$			21.3900i			0.00982306i
$169$	793.506			0.361177
$170$	−108.007	−	527.319i	−0.0487281	−	0.237903i
$171$	1237.31			0.553332
$172$			896.854i			0.397584i
$173$	232.125	−	232.125i	0.102012	−	0.102012i	−0.654259	−	0.756271i	$-0.727019\pi$
$173$	232.125	−	232.125i	0.102012	−	0.102012i	0.756271	+	0.654259i	$0.227019\pi$
$174$	262.106			0.114197
$175$	−2179.67	+	2179.67i	−0.941528	+	0.941528i
$176$	1554.24	+	1554.24i	0.665656	+	0.665656i
$177$	225.220	+	225.220i	0.0956417	+	0.0956417i
$178$			2400.20i			1.01069i
$179$		−	4155.11i		−	1.73501i	−0.497427	−	0.867506i	$-0.665722\pi$
$179$		−	4155.11i		−	1.73501i	0.497427	−	0.867506i	$-0.334278\pi$
$180$	−277.330	−	277.330i	−0.114839	−	0.114839i
$181$	675.588	+	675.588i	0.277437	+	0.277437i	0.832085	−	0.554648i	$-0.187147\pi$
$181$	675.588	+	675.588i	0.277437	+	0.277437i	−0.554648	+	0.832085i	$0.687147\pi$
$182$	−3871.61	+	3871.61i	−1.57683	+	1.57683i
$183$	−204.877			−0.0827592
$184$	−105.608	+	105.608i	−0.0423128	+	0.0423128i
$185$			441.298i			0.175378i
$186$	421.611			0.166204
$187$	−456.121	−	2226.90i	−0.178368	−	0.870839i
$188$	1411.67			0.547640
$189$		−	580.397i		−	0.223374i
$190$	−250.511	+	250.511i	−0.0956525	+	0.0956525i
$191$	−889.758			−0.337072			−0.168536	−	0.985696i	$-0.553904\pi$
$191$	−889.758			−0.337072			−0.168536	+	0.985696i	$0.553904\pi$
$192$	−133.594	+	133.594i	−0.0502154	+	0.0502154i
$193$	−1224.76	−	1224.76i	−0.456789	−	0.456789i	0.440811	−	0.897600i	$-0.354691\pi$
$193$	−1224.76	−	1224.76i	−0.456789	−	0.456789i	−0.897600	+	0.440811i	$0.854691\pi$
$194$	−4431.55	−	4431.55i	−1.64003	−	1.64003i
$195$		−	45.2316i		−	0.0166108i
$196$		−	2278.17i		−	0.830237i
$197$	3142.32	+	3142.32i	1.13645	+	1.13645i	0.989082	+	0.147369i	$0.0470805\pi$
$197$	3142.32	+	3142.32i	1.13645	+	1.13645i	0.147369	+	0.989082i	$0.452919\pi$
$198$	−2421.08	−	2421.08i	−0.868985	−	0.868985i
$199$	2205.02	−	2205.02i	0.785478	−	0.785478i	−0.195272	−	0.980749i	$-0.562559\pi$
$199$	2205.02	−	2205.02i	0.785478	−	0.785478i	0.980749	+	0.195272i	$0.0625588\pi$
$200$	240.388			0.0849901
$201$	−160.061	+	160.061i	−0.0561682	+	0.0561682i
$202$			2625.25i			0.914415i
$203$	3994.22			1.38098
$204$	218.245	−	44.7016i	0.0749028	−	0.0153419i
$205$	−450.952			−0.153638
$206$			3434.11i			1.16148i
$207$	1428.01	−	1428.01i	0.479484	−	0.479484i
$208$	3706.42			1.23555
$209$	−1057.92	+	1057.92i	−0.350134	+	0.350134i
$210$	58.5583	+	58.5583i	0.0192424	+	0.0192424i
$211$	−3204.98	−	3204.98i	−1.04569	−	1.04569i	−0.998905	−	0.0467829i	$-0.985103\pi$
$211$	−3204.98	−	3204.98i	−1.04569	−	1.04569i	−0.0467829	−	0.998905i	$-0.514897\pi$
$212$		−	3509.78i		−	1.13704i
$213$			33.1358i			0.0106593i
$214$	964.014	+	964.014i	0.307937	+	0.307937i
$215$	−165.037	−	165.037i	−0.0523509	−	0.0523509i
$216$	−32.0050	+	32.0050i	−0.0100818	+	0.0100818i
$217$	6424.89			2.00991
$218$	−378.063	+	378.063i	−0.117457	+	0.117457i
$219$			162.394i			0.0501076i
$220$	474.242			0.145334
$221$	−3199.12	−	2111.40i	−0.973737	−	0.642661i
$222$	−377.562			−0.114145
$223$			123.574i			0.0371082i	0.999828	+	0.0185541i	$0.00590629\pi$
$223$			123.574i			0.0371082i	−0.999828	+	0.0185541i	$0.994094\pi$
$224$	−4513.08	+	4513.08i	−1.34617	+	1.34617i
$225$	−3250.46			−0.963100
$226$	2466.06	−	2466.06i	0.725841	−	0.725841i
$227$	551.638	+	551.638i	0.161293	+	0.161293i	0.783139	−	0.621846i	$-0.213617\pi$
$227$	551.638	+	551.638i	0.161293	+	0.161293i	−0.621846	+	0.783139i	$0.713617\pi$
$228$	−103.680	−	103.680i	−0.0301158	−	0.0301158i
$229$			2776.64i			0.801247i	0.916243	+	0.400624i	$0.131206\pi$
$229$			2776.64i			0.801247i	−0.916243	+	0.400624i	$0.868794\pi$
$230$			578.237i			0.165773i
$231$	247.295	+	247.295i	0.0704365	+	0.0704365i
$232$	−220.255	−	220.255i	−0.0623294	−	0.0623294i
$233$	−3569.19	+	3569.19i	−1.00354	+	1.00354i	−0.00354906	+	0.999994i	$0.501130\pi$
$233$	−3569.19	+	3569.19i	−1.00354	+	1.00354i	−0.999994	+	0.00354906i	$0.998870\pi$
$234$	−5773.60			−1.61296
$235$	−259.772	+	259.772i	−0.0721091	+	0.0721091i
$236$			5631.22i			1.55323i
$237$	−542.222			−0.148612
$238$	6875.18	−	1408.20i	1.87249	−	0.383529i
$239$	2254.20			0.610092			0.305046	−	0.952338i	$-0.401328\pi$
$239$	2254.20			0.610092			0.305046	+	0.952338i	$0.401328\pi$
$240$		−	56.0599i		−	0.0150777i
$241$	−1222.67	+	1222.67i	−0.326802	+	0.326802i	−0.851369	−	0.524567i	$-0.824227\pi$
$241$	−1222.67	+	1222.67i	−0.326802	+	0.326802i	0.524567	+	0.851369i	$0.324227\pi$
$242$	−1099.37			−0.292027
$243$	649.867	−	649.867i	0.171560	−	0.171560i
$244$	−2561.29	−	2561.29i	−0.672006	−	0.672006i
$245$	419.224	+	419.224i	0.109319	+	0.109319i
$246$		−	385.821i		−	0.0999962i
$247$			2522.84i			0.649897i
$248$	−354.290	−	354.290i	−0.0907154	−	0.0907154i
$249$	−177.299	−	177.299i	−0.0451239	−	0.0451239i
$250$	1336.86	−	1336.86i	0.338203	−	0.338203i
$251$	−1314.25			−0.330496			−0.165248	−	0.986252i	$-0.552842\pi$
$251$	−1314.25			−0.330496			−0.165248	+	0.986252i	$0.552842\pi$
$252$	3615.83	−	3615.83i	0.903872	−	0.903872i
$253$			2441.93i			0.606809i
$254$	7759.13			1.91674
$255$	−31.9350	+	48.3868i	−0.00784254	+	0.0118827i
$256$	4562.26			1.11383
$257$		−	6039.96i		−	1.46600i	−0.680228	−	0.733001i	$-0.738119\pi$
$257$		−	6039.96i		−	1.46600i	0.680228	−	0.733001i	$-0.261881\pi$
$258$	141.201	−	141.201i	0.0340729	−	0.0340729i
$259$	−5753.64			−1.38036
$260$	565.466	−	565.466i	0.134880	−	0.134880i
$261$	2978.22	+	2978.22i	0.706311	+	0.706311i
$262$	−698.074	−	698.074i	−0.164608	−	0.164608i
$263$		−	990.368i		−	0.232201i	−0.993237	−	0.116100i	$-0.962961\pi$
$263$		−	990.368i		−	0.232201i	0.993237	−	0.116100i	$-0.0370394\pi$
$264$		−	27.2733i		−	0.00635818i
$265$	645.862	+	645.862i	0.149717	+	0.149717i
$266$	−3266.16	−	3266.16i	−0.752861	−	0.752861i
$267$	182.801	−	182.801i	0.0418998	−	0.0418998i
$268$	−4002.02			−0.912173
$269$	2397.48	−	2397.48i	0.543409	−	0.543409i	−0.381117	−	0.924527i	$-0.624461\pi$
$269$	2397.48	−	2397.48i	0.543409	−	0.543409i	0.924527	+	0.381117i	$0.124461\pi$
$270$			175.237i			0.0394985i
$271$	−3706.24			−0.830767			−0.415383	−	0.909646i	$-0.636353\pi$
$271$	−3706.24			−0.830767			−0.415383	+	0.909646i	$0.636353\pi$
$272$	−3964.98	−	2616.86i	−0.883868	−	0.583348i
$273$	589.729			0.130740
$274$		−	1717.79i		−	0.378742i
$275$	2779.19	−	2779.19i	0.609424	−	0.609424i
$276$	−239.318			−0.0521930
$277$	−5410.66	+	5410.66i	−1.17363	+	1.17363i	−0.192290	+	0.981338i	$0.561591\pi$
$277$	−5410.66	+	5410.66i	−1.17363	+	1.17363i	−0.981338	+	0.192290i	$0.938409\pi$
$278$	233.045	+	233.045i	0.0502774	+	0.0502774i
$279$	4790.61	+	4790.61i	1.02798	+	1.02798i
$280$		−	98.4161i		−	0.0210053i
$281$			3194.87i			0.678256i	0.940740	+	0.339128i	$0.110132\pi$
$281$			3194.87i			0.678256i	−0.940740	+	0.339128i	$0.889868\pi$
$282$	−222.253	−	222.253i	−0.0469326	−	0.0469326i
$283$	−4235.43	−	4235.43i	−0.889648	−	0.889648i	0.104841	−	0.994489i	$-0.466567\pi$
$283$	−4235.43	−	4235.43i	−0.889648	−	0.889648i	−0.994489	+	0.104841i	$0.966567\pi$
$284$	−414.250	+	414.250i	−0.0865536	+	0.0865536i
$285$	38.1581			0.00793085
$286$	4936.51	−	4936.51i	1.02064	−	1.02064i
$287$		−	5879.50i		−	1.20925i
$288$	−6730.20			−1.37702
$289$	1931.56	+	4517.37i	0.393153	+	0.919473i
$290$	−1205.96			−0.244195
$291$			675.019i			0.135980i
$292$	−2030.18	+	2030.18i	−0.406875	+	0.406875i
$293$	5372.44			1.07120			0.535600	−	0.844472i	$-0.320086\pi$
$293$	5372.44			1.07120			0.535600	+	0.844472i	$0.320086\pi$
$294$	−358.676	+	358.676i	−0.0711511	+	0.0711511i
$295$	−1036.25	−	1036.25i	−0.204517	−	0.204517i
$296$	317.275	+	317.275i	0.0623014	+	0.0623014i
$297$			740.037i			0.144583i
$298$			9280.11i			1.80397i
$299$	2911.65	+	2911.65i	0.563161	+	0.563161i
$300$	272.371	+	272.371i	0.0524179	+	0.0524179i
$301$	2151.75	−	2151.75i	0.412043	−	0.412043i
$302$	589.477			0.112320
$303$	199.940	−	199.940i	0.0379085	−	0.0379085i
$304$			3126.80i			0.589916i
$305$	942.645			0.176970
$306$	6176.35	+	4076.36i	1.15385	+	0.761535i
$307$	7020.91			1.30523			0.652613	−	0.757692i	$-0.273673\pi$
$307$	7020.91			1.30523			0.652613	+	0.757692i	$0.273673\pi$
$308$			6183.16i			1.14389i
$309$	261.544	−	261.544i	0.0481511	−	0.0481511i
$310$	−1939.84			−0.355406
$311$	−725.496	+	725.496i	−0.132280	+	0.132280i	−0.770147	−	0.637867i	$-0.779817\pi$
$311$	−725.496	+	725.496i	−0.132280	+	0.132280i	0.637867	+	0.770147i	$0.279817\pi$
$312$	−32.5196	−	32.5196i	−0.00590083	−	0.00590083i
$313$	−1761.31	−	1761.31i	−0.318067	−	0.318067i	0.529957	−	0.848024i	$-0.322208\pi$
$313$	−1761.31	−	1761.31i	−0.318067	−	0.318067i	−0.848024	+	0.529957i	$0.822208\pi$
$314$			469.548i			0.0843889i
$315$			1330.75i			0.238030i
$316$	−6778.64	−	6778.64i	−1.20673	−	1.20673i
$317$	−1962.35	−	1962.35i	−0.347686	−	0.347686i	0.511561	−	0.859247i	$-0.329067\pi$
$317$	−1962.35	−	1962.35i	−0.347686	−	0.347686i	−0.859247	+	0.511561i	$0.829067\pi$
$318$	−552.581	+	552.581i	−0.0974440	+	0.0974440i
$319$	−5092.84			−0.893869
$320$	614.673	−	614.673i	0.107379	−	0.107379i
$321$		−	146.840i		−	0.0255321i
$322$	−7539.05			−1.30477
$323$	1781.21	−	2698.83i	0.306840	−	0.464913i
$324$	5355.77			0.918341
$325$		−	6627.58i		−	1.13117i
$326$	424.840	−	424.840i	0.0721770	−	0.0721770i
$327$	57.5870			0.00973873
$328$	−324.215	+	324.215i	−0.0545786	+	0.0545786i
$329$	−3386.90	−	3386.90i	−0.567556	−	0.567556i
$330$	−74.6649	−	74.6649i	−0.0124551	−	0.0124551i
$331$			6017.90i			0.999317i	0.866222	+	0.499659i	$0.166541\pi$
$331$			6017.90i			0.999317i	−0.866222	+	0.499659i	$0.833459\pi$
$332$		−	4433.03i		−	0.732813i
$333$	−4290.10	−	4290.10i	−0.705993	−	0.705993i
$334$	7028.61	+	7028.61i	1.15146	+	1.15146i
$335$	736.444	−	736.444i	0.120108	−	0.120108i
$336$	730.908			0.118674
$337$	335.433	−	335.433i	0.0542202	−	0.0542202i	−0.679477	−	0.733697i	$-0.737793\pi$
$337$	335.433	−	335.433i	0.0542202	−	0.0542202i	0.733697	+	0.679477i	$0.237793\pi$
$338$		−	3123.64i		−	0.502674i
$339$	−375.634			−0.0601818
$340$	−1004.15	+	205.674i	−0.160170	+	0.0328065i
$341$	−8192.07			−1.30095
$342$		−	4870.71i		−	0.770110i
$343$	702.976	−	702.976i	0.110662	−	0.110662i
$344$	−237.310			−0.0371944
$345$	44.0389	−	44.0389i	0.00687239	−	0.00687239i
$346$	−913.762	−	913.762i	−0.141977	−	0.141977i
$347$	1043.30	+	1043.30i	0.161405	+	0.161405i	0.783189	−	0.621784i	$-0.213592\pi$
$347$	1043.30	+	1043.30i	0.161405	+	0.161405i	−0.621784	+	0.783189i	$0.713592\pi$
$348$		−	499.118i		−	0.0768837i
$349$		−	6855.25i		−	1.05144i	−0.850657	−	0.525721i	$-0.823796\pi$
$349$		−	6855.25i		−	1.05144i	0.850657	−	0.525721i	$-0.176204\pi$
$350$	8580.29	+	8580.29i	1.31039	+	1.31039i
$351$	882.388	+	882.388i	0.134183	+	0.134183i
$352$	5754.41	−	5754.41i	0.871339	−	0.871339i
$353$	7485.74			1.12868			0.564342	−	0.825541i	$-0.309130\pi$
$353$	7485.74			1.12868			0.564342	+	0.825541i	$0.309130\pi$
$354$	886.582	−	886.582i	0.133111	−	0.133111i
$355$		−	152.459i		−	0.0227935i
$356$	4570.60			0.680454
$357$	−630.867	−	416.368i	−0.0935266	−	0.0617270i
$358$	−16356.6			−2.41473
$359$			7169.54i			1.05402i	0.849859	+	0.527011i	$0.176687\pi$
$359$			7169.54i			1.05402i	−0.849859	+	0.527011i	$0.823313\pi$
$360$	73.3822	−	73.3822i	0.0107433	−	0.0107433i
$361$	4730.69			0.689705
$362$	2659.46	−	2659.46i	0.386127	−	0.386127i
$363$	83.7290	+	83.7290i	0.0121064	+	0.0121064i
$364$	7372.54	+	7372.54i	1.06161	+	1.06161i
$365$		−	747.180i		−	0.107149i
$366$			806.500i			0.115182i
$367$	−4673.13	−	4673.13i	−0.664674	−	0.664674i	0.291804	−	0.956478i	$-0.405744\pi$
$367$	−4673.13	−	4673.13i	−0.664674	−	0.664674i	−0.956478	+	0.291804i	$0.905744\pi$
$368$	3608.69	+	3608.69i	0.511185	+	0.511185i
$369$	4383.95	−	4383.95i	0.618480	−	0.618480i
$370$	1737.17			0.244085
$371$	−8420.74	+	8420.74i	−1.17839	+	1.17839i
$372$		−	802.855i		−	0.111898i
$373$	−1602.91			−0.222508			−0.111254	−	0.993792i	$-0.535487\pi$
$373$	−1602.91			−0.222508			−0.111254	+	0.993792i	$0.535487\pi$
$374$	−8766.21	+	1795.53i	−1.21200	+	0.248247i
$375$	−203.633			−0.0280415
$376$			373.530i			0.0512323i
$377$	−6072.49	+	6072.49i	−0.829573	+	0.829573i
$378$	−2284.74			−0.310885
$379$	1232.54	−	1232.54i	0.167049	−	0.167049i	−0.618632	−	0.785681i	$-0.712313\pi$
$379$	1232.54	−	1232.54i	0.167049	−	0.167049i	0.785681	+	0.618632i	$0.212313\pi$
$380$	477.037	+	477.037i	0.0643986	+	0.0643986i
$381$	−590.940	−	590.940i	−0.0794613	−	0.0794613i
$382$			3502.55i			0.469125i
$383$			1155.24i			0.154125i	0.997026	+	0.0770627i	$0.0245542\pi$
$383$			1155.24i			0.154125i	−0.997026	+	0.0770627i	$0.975446\pi$
$384$	−75.9662	−	75.9662i	−0.0100954	−	0.0100954i
$385$	−1137.81	−	1137.81i	−0.150619	−	0.150619i
$386$	−4821.29	+	4821.29i	−0.635744	+	0.635744i
$387$	3208.83			0.421484
$388$	−8438.81	+	8438.81i	−1.10416	+	1.10416i
$389$			3698.95i			0.482119i	0.970510	+	0.241060i	$0.0774949\pi$
$389$			3698.95i			0.482119i	−0.970510	+	0.241060i	$0.922505\pi$
$390$	−178.055			−0.0231183
$391$	−1059.04	−	5170.49i	−0.136977	−	0.668754i
$392$	602.809			0.0776696
$393$			106.332i			0.0136481i
$394$	12369.8	−	12369.8i	1.58167	−	1.58167i
$395$	2494.78			0.317788
$396$	−4610.37	+	4610.37i	−0.585050	+	0.585050i
$397$	9608.12	+	9608.12i	1.21465	+	1.21465i	0.969479	+	0.245176i	$0.0788458\pi$
$397$	9608.12	+	9608.12i	1.21465	+	1.21465i	0.245176	+	0.969479i	$0.421154\pi$
$398$	−8680.11	−	8680.11i	−1.09320	−	1.09320i
$399$			497.505i			0.0624221i
$400$		−	8214.20i		−	1.02678i
$401$	−1883.98	−	1883.98i	−0.234617	−	0.234617i	0.580000	−	0.814617i	$-0.303053\pi$
$401$	−1883.98	−	1883.98i	−0.234617	−	0.234617i	−0.814617	+	0.580000i	$0.803053\pi$
$402$	630.081	+	630.081i	0.0781730	+	0.0781730i
$403$	−9767.88	+	9767.88i	−1.20738	+	1.20738i
$404$	4999.14			0.615635
$405$	−985.558	+	985.558i	−0.120920	+	0.120920i
$406$		−	15723.3i		−	1.92201i
$407$	7336.19			0.893467
$408$	11.8282	+	57.7480i	0.00143525	+	0.00700724i
$409$	4145.86			0.501222			0.250611	−	0.968088i	$-0.419368\pi$
$409$	4145.86			0.501222			0.250611	+	0.968088i	$0.419368\pi$
$410$			1775.18i			0.213829i
$411$	−130.828	+	130.828i	−0.0157013	+	0.0157013i
$412$	6539.42			0.781976
$413$	13510.6	−	13510.6i	1.60971	−	1.60971i
$414$	−5621.36	−	5621.36i	−0.667330	−	0.667330i
$415$	815.757	+	815.757i	0.0964914	+	0.0964914i
$416$		−	13722.6i		−	1.61733i
$417$		−	35.4977i		−	0.00416866i
$418$	4164.52	+	4164.52i	0.487305	+	0.487305i
$419$	10074.5	+	10074.5i	1.17463	+	1.17463i	0.981092	+	0.193542i	$0.0619975\pi$
$419$	10074.5	+	10074.5i	1.17463	+	1.17463i	0.193542	+	0.981092i	$0.438003\pi$
$420$	111.510	−	111.510i	0.0129551	−	0.0129551i
$421$	−3191.61			−0.369477			−0.184738	−	0.982788i	$-0.559144\pi$
$421$	−3191.61			−0.369477			−0.184738	+	0.982788i	$0.559144\pi$
$422$	−12616.5	+	12616.5i	−1.45535	+	1.45535i
$423$		−	5050.77i		−	0.580560i
$424$	928.695			0.106371
$425$	−4679.29	+	7089.90i	−0.534069	+	0.809202i
$426$	130.439			0.0148352
$427$			12290.2i			1.39289i
$428$	1835.73	−	1835.73i	0.207321	−	0.207321i
$429$	−751.935			−0.0846241
$430$	−649.671	+	649.671i	−0.0728603	+	0.0728603i
$431$	−1159.24	−	1159.24i	−0.129556	−	0.129556i	0.639355	−	0.768911i	$-0.279201\pi$
$431$	−1159.24	−	1159.24i	−0.129556	−	0.129556i	−0.768911	+	0.639355i	$0.779201\pi$
$432$	1093.63	+	1093.63i	0.121799	+	0.121799i
$433$		−	16579.9i		−	1.84013i	−0.391764	−	0.920066i	$-0.628135\pi$
$433$		−	16579.9i		−	1.84013i	0.391764	−	0.920066i	$-0.371865\pi$
$434$		−	25291.7i		−	2.79732i
$435$	91.8467	+	91.8467i	0.0101235	+	0.0101235i
$436$	719.928	+	719.928i	0.0790787	+	0.0790787i
$437$	−2456.32	+	2456.32i	−0.268883	+	0.268883i
$438$	639.266			0.0697382
$439$	5195.18	−	5195.18i	0.564812	−	0.564812i	−0.365859	−	0.930670i	$-0.619225\pi$
$439$	5195.18	−	5195.18i	0.564812	−	0.564812i	0.930670	+	0.365859i	$0.119225\pi$
$440$			125.486i			0.0135961i
$441$	−8151.02			−0.880144
$442$	−8311.55	+	12593.4i	−0.894434	+	1.35522i
$443$	−13325.5			−1.42915			−0.714575	−	0.699559i	$-0.753380\pi$
$443$	−13325.5			−1.42915			−0.714575	+	0.699559i	$0.753380\pi$
$444$			718.974i			0.0768491i
$445$	−841.074	+	841.074i	−0.0895971	+	0.0895971i
$446$	486.451			0.0516460
$447$	706.779	−	706.779i	0.0747863	−	0.0747863i
$448$	8014.09	+	8014.09i	0.845157	+	0.845157i
$449$	−6849.28	−	6849.28i	−0.719906	−	0.719906i	0.248680	−	0.968586i	$-0.420003\pi$
$449$	−6849.28	−	6849.28i	−0.719906	−	0.719906i	−0.968586	+	0.248680i	$0.920003\pi$
$450$			12795.5i			1.34041i
$451$			7496.67i			0.782715i
$452$	−4696.02	−	4696.02i	−0.488677	−	0.488677i
$453$	−44.8949	−	44.8949i	−0.00465640	−	0.00465640i
$454$	2171.53	−	2171.53i	0.224482	−	0.224482i
$455$	−2713.36			−0.279570
$456$	27.4341	−	27.4341i	0.00281736	−	0.00281736i
$457$			698.065i			0.0714532i	0.999362	+	0.0357266i	$0.0113745\pi$
$457$			698.065i			0.0714532i	−0.999362	+	0.0357266i	$0.988625\pi$
$458$	10930.3			1.11515
$459$	−320.946	−	1566.94i	−0.0326372	−	0.159343i
$460$	1101.11			0.111608
$461$			6505.58i			0.657256i	0.944459	+	0.328628i	$0.106586\pi$
$461$			6505.58i			0.657256i	−0.944459	+	0.328628i	$0.893414\pi$
$462$	973.481	−	973.481i	0.0980312	−	0.0980312i
$463$	1181.74			0.118618			0.0593089	−	0.998240i	$-0.481110\pi$
$463$	1181.74			0.118618			0.0593089	+	0.998240i	$0.481110\pi$
$464$	−7526.22	+	7526.22i	−0.753009	+	0.753009i
$465$	147.740	+	147.740i	0.0147339	+	0.0147339i
$466$	14050.2	+	14050.2i	1.39670	+	1.39670i
$467$		−	2950.96i		−	0.292407i	−0.989255	−	0.146204i	$-0.953295\pi$
$467$		−	2950.96i		−	0.292407i	0.989255	−	0.146204i	$-0.0467054\pi$
$468$			10994.4i			1.08593i
$469$	9601.75	+	9601.75i	0.945347	+	0.945347i
$470$	1022.60	+	1022.60i	0.100359	+	0.100359i
$471$	35.7610	−	35.7610i	0.00349847	−	0.00349847i
$472$	−1490.03			−0.145306
$473$	−2743.60	+	2743.60i	−0.266704	+	0.266704i
$474$			2134.46i			0.206834i
$475$	5591.14			0.540082
$476$	−2681.57	−	13092.1i	−0.258213	−	1.26066i
$477$	−12557.5			−1.20539
$478$		−	8873.69i		−	0.849107i
$479$	6286.33	−	6286.33i	0.599644	−	0.599644i	−0.340573	−	0.940218i	$-0.610621\pi$
$479$	6286.33	−	6286.33i	0.599644	−	0.599644i	0.940218	+	0.340573i	$0.110621\pi$
$480$	−207.556			−0.0197366
$481$	8747.36	−	8747.36i	0.829200	−	0.829200i
$482$	4813.07	+	4813.07i	0.454832	+	0.454832i
$483$	574.179	+	574.179i	0.0540912	+	0.0540912i
$484$			2093.49i			0.196609i
$485$		−	3105.78i		−	0.290776i
$486$	−2558.21	−	2558.21i	−0.238771	−	0.238771i
$487$	−5023.62	−	5023.62i	−0.467437	−	0.467437i	0.433646	−	0.901083i	$-0.357227\pi$
$487$	−5023.62	−	5023.62i	−0.467437	−	0.467437i	−0.901083	+	0.433646i	$0.857227\pi$
$488$	677.722	−	677.722i	0.0628669	−	0.0628669i
$489$	−64.7121			−0.00598442
$490$	1650.28	−	1650.28i	0.152147	−	0.152147i
$491$			7638.33i			0.702063i	0.936364	+	0.351031i	$0.114169\pi$
$491$			7638.33i			0.702063i	−0.936364	+	0.351031i	$0.885831\pi$
$492$	−734.703			−0.0673231
$493$	10783.5	−	2208.71i	0.985118	−	0.201775i
$494$	9931.20			0.904505
$495$		−	1696.78i		−	0.154070i
$496$	−12106.3	+	12106.3i	−1.09594	+	1.09594i
$497$	1987.76			0.179403
$498$	−697.938	+	697.938i	−0.0628019	+	0.0628019i
$499$	−14285.4	−	14285.4i	−1.28156	−	1.28156i	−0.939778	−	0.341787i	$-0.888968\pi$
$499$	−14285.4	−	14285.4i	−1.28156	−	1.28156i	−0.341787	−	0.939778i	$-0.611032\pi$
$500$	−2545.73	−	2545.73i	−0.227697	−	0.227697i
$501$		−	1070.61i		−	0.0954714i
$502$			5173.54i			0.459973i
$503$	−14474.1	−	14474.1i	−1.28304	−	1.28304i	−0.938931	−	0.344107i	$-0.888182\pi$
$503$	−14474.1	−	14474.1i	−1.28304	−	1.28304i	−0.344107	−	0.938931i	$-0.611818\pi$
$504$	956.756	+	956.756i	0.0845581	+	0.0845581i
$505$	−919.932	+	919.932i	−0.0810623	+	0.0810623i
$506$	9612.68			0.844537
$507$	−237.899	+	237.899i	−0.0208391	+	0.0208391i
$508$		−	14775.4i		−	1.29045i
$509$	−19503.1			−1.69835			−0.849173	−	0.528116i	$-0.822899\pi$
$509$	−19503.1			−1.69835			−0.849173	+	0.528116i	$0.822899\pi$
$510$	190.475	+	125.713i	0.0165380	+	0.0109150i
$511$	9741.73			0.843344
$512$		−	15932.3i		−	1.37523i
$513$	−744.398	+	744.398i	−0.0640662	+	0.0640662i
$514$	−23776.4			−2.04033
$515$	−1203.37	+	1203.37i	−0.102965	+	0.102965i
$516$	−268.883	−	268.883i	−0.0229398	−	0.0229398i
$517$	4318.48	+	4318.48i	0.367362	+	0.367362i
$518$			22649.3i			1.92114i
$519$			139.185i			0.0117718i
$520$	149.624	+	149.624i	0.0126181	+	0.0126181i
$521$	4923.95	+	4923.95i	0.414054	+	0.414054i	0.883148	−	0.469094i	$-0.155420\pi$
$521$	4923.95	+	4923.95i	0.414054	+	0.414054i	−0.469094	+	0.883148i	$0.655420\pi$
$522$	11723.8	−	11723.8i	0.983020	−	0.983020i
$523$	−2507.22			−0.209623			−0.104812	−	0.994492i	$-0.533424\pi$
$523$	−2507.22			−0.209623			−0.104812	+	0.994492i	$0.533424\pi$
$524$	−1329.31	+	1329.31i	−0.110823	+	0.110823i
$525$		−	1306.96i		−	0.108648i
$526$	−3898.60			−0.323169
$527$	17345.7	−	3552.81i	1.43376	−	0.293668i
$528$	−931.946			−0.0768139
$529$		−	6497.24i		−	0.534005i
$530$	2542.44	−	2542.44i	0.208371	−	0.208371i
$531$	20147.8			1.64659
$532$	−6219.60	+	6219.60i	−0.506868	+	0.506868i
$533$	8938.71	+	8938.71i	0.726414	+	0.726414i
$534$	−719.598	−	719.598i	−0.0583147	−	0.0583147i
$535$			675.614i			0.0545969i
$536$		−	1058.94i		−	0.0853348i
$537$	1245.73	+	1245.73i	0.100107	+	0.100107i
$538$	−9437.72	−	9437.72i	−0.756299	−	0.756299i
$539$	6969.23	−	6969.23i	0.556932	−	0.556932i
$540$	333.697			0.0265926
$541$	13701.0	−	13701.0i	1.08882	−	1.08882i	0.0931705	−	0.995650i	$-0.470300\pi$
$541$	13701.0	−	13701.0i	1.08882	−	1.08882i	0.995650	−	0.0931705i	$-0.0297002\pi$
$542$			14589.6i			1.15623i
$543$	−405.092			−0.0320150
$544$	−9688.65	+	14679.9i	−0.763598	+	1.15698i
$545$	−264.960			−0.0208250
$546$		−	2321.47i		−	0.181960i
$547$	−2090.43	+	2090.43i	−0.163401	+	0.163401i	−0.784071	−	0.620671i	$-0.786860\pi$
$547$	−2090.43	+	2090.43i	−0.163401	+	0.163401i	0.620671	+	0.784071i	$0.286860\pi$
$548$	−3271.10			−0.254990
$549$	−9163.97	+	9163.97i	−0.712402	+	0.712402i
$550$	−10940.3	−	10940.3i	−0.848176	−	0.848176i
$551$	−5122.85	−	5122.85i	−0.396081	−	0.396081i
$552$		−	63.3242i		−	0.00488271i
$553$			32526.9i			2.50124i
$554$	21299.1	+	21299.1i	1.63342	+	1.63342i
$555$	−132.304	−	132.304i	−0.0101189	−	0.0101189i
$556$	443.778	−	443.778i	0.0338496	−	0.0338496i
$557$	−3920.00			−0.298197			−0.149099	−	0.988822i	$-0.547637\pi$
$557$	−3920.00			−0.298197			−0.149099	+	0.988822i	$0.547637\pi$
$558$	18858.3	−	18858.3i	1.43071	−	1.43071i
$559$			6542.70i			0.495039i
$560$	−3362.93			−0.253768
$561$	804.388	+	530.891i	0.0605371	+	0.0399541i
$562$	12576.6			0.943975
$563$			20821.5i			1.55865i	0.626618	+	0.779326i	$0.284439\pi$
$563$			20821.5i			1.55865i	−0.626618	+	0.779326i	$0.715561\pi$
$564$	−423.227	+	423.227i	−0.0315977	+	0.0315977i
$565$	1728.30			0.128691
$566$	−16672.8	+	16672.8i	−1.23818	+	1.23818i
$567$	−12849.7	−	12849.7i	−0.951739	−	0.951739i
$568$	−109.612	−	109.612i	−0.00809718	−	0.00809718i
$569$			7849.66i			0.578339i	0.957278	+	0.289170i	$0.0933791\pi$
$569$			7849.66i			0.578339i	−0.957278	+	0.289170i	$0.906621\pi$
$570$		−	150.210i		−	0.0110379i
$571$	−17349.3	−	17349.3i	−1.27154	−	1.27154i	−0.945282	−	0.326254i	$-0.894214\pi$
$571$	−17349.3	−	17349.3i	−1.27154	−	1.27154i	−0.326254	−	0.945282i	$-0.605786\pi$
$572$	−9400.38	−	9400.38i	−0.687149	−	0.687149i
$573$	266.756	−	266.756i	0.0194483	−	0.0194483i
$574$	−23144.7			−1.68300
$575$	6452.82	−	6452.82i	0.468002	−	0.468002i
$576$			11951.1i			0.864521i
$577$	−7549.37			−0.544687			−0.272343	−	0.962200i	$-0.587799\pi$
$577$	−7549.37			−0.544687			−0.272343	+	0.962200i	$0.587799\pi$
$578$	17782.7	−	7603.62i	1.27969	−	0.547178i
$579$	734.384			0.0527115
$580$			2296.46i			0.164406i
$581$	−10635.8	+	10635.8i	−0.759464	+	0.759464i
$582$	2657.22			0.189253
$583$	10736.9	−	10736.9i	0.762738	−	0.762738i
$584$	−537.191	−	537.191i	−0.0380636	−	0.0380636i
$585$	−2023.17	−	2023.17i	−0.142988	−	0.142988i
$586$		−	21148.7i		−	1.49086i
$587$		−	6451.77i		−	0.453651i	−0.973935	−	0.226826i	$-0.927165\pi$
$587$		−	6451.77i		−	0.453651i	0.973935	−	0.226826i	$-0.0728347\pi$
$588$	683.012	+	683.012i	0.0479029	+	0.0479029i
$589$	−8240.35	−	8240.35i	−0.576465	−	0.576465i
$590$	−4079.19	+	4079.19i	−0.284640	+	0.284640i
$591$	−1884.18			−0.131142
$592$	10841.4	−	10841.4i	0.752670	−	0.752670i
$593$			176.420i			0.0122170i	0.999981	+	0.00610850i	$0.00194441\pi$
$593$			176.420i			0.0122170i	−0.999981	+	0.00610850i	$0.998056\pi$
$594$	2913.16			0.201227
$595$	2902.64	+	1915.72i	0.199994	+	0.131995i
$596$	17671.7			1.21453
$597$			1322.16i			0.0906408i
$598$	11461.8	−	11461.8i	0.783789	−	0.783789i
$599$	−11248.7			−0.767292			−0.383646	−	0.923480i	$-0.625332\pi$
$599$	−11248.7			−0.767292			−0.383646	+	0.923480i	$0.625332\pi$
$600$	−72.0701	+	72.0701i	−0.00490375	+	0.00490375i
$601$	17973.6	+	17973.6i	1.21990	+	1.21990i	0.967668	+	0.252228i	$0.0811632\pi$
$601$	17973.6	+	17973.6i	1.21990	+	1.21990i	0.252228	+	0.967668i	$0.418837\pi$
$602$	−8470.41	−	8470.41i	−0.573469	−	0.573469i
$603$			14318.7i			0.967006i
$604$		−	1122.52i		−	0.0756201i
$605$	−385.240	−	385.240i	−0.0258880	−	0.0258880i
$606$	−787.068	−	787.068i	−0.0527598	−	0.0527598i
$607$	−13916.2	+	13916.2i	−0.930542	+	0.930542i	−0.997740	−	0.0671975i	$-0.978594\pi$
$607$	−13916.2	+	13916.2i	−0.930542	+	0.930542i	0.0671975	+	0.997740i	$0.478594\pi$
$608$	11576.7			0.772196
$609$	−1197.50	+	1197.50i	−0.0796798	+	0.0796798i
$610$		−	3710.74i		−	0.246300i
$611$	10298.3			0.681876
$612$	7762.43	−	11761.4i	0.512708	−	0.776838i
$613$	3619.34			0.238473			0.119236	−	0.992866i	$-0.461955\pi$
$613$	3619.34			0.238473			0.119236	+	0.992866i	$0.461955\pi$
$614$		−	27637.9i		−	1.81657i
$615$	135.199	−	135.199i	0.00886460	−	0.00886460i
$616$	−1636.08			−0.107012
$617$	13961.7	−	13961.7i	0.910985	−	0.910985i	−0.0853644	−	0.996350i	$-0.527205\pi$
$617$	13961.7	−	13961.7i	0.910985	−	0.910985i	0.996350	+	0.0853644i	$0.0272055\pi$
$618$	−1029.57	−	1029.57i	−0.0670151	−	0.0670151i
$619$	13220.0	+	13220.0i	0.858409	+	0.858409i	0.991151	−	0.132741i	$-0.0423780\pi$
$619$	13220.0	+	13220.0i	0.858409	+	0.858409i	−0.132741	+	0.991151i	$0.542378\pi$
$620$			3693.96i			0.239279i
$621$			1718.24i			0.111032i
$622$	2855.93	+	2855.93i	0.184103	+	0.184103i
$623$	−10965.9	−	10965.9i	−0.705200	−	0.705200i
$624$	−1111.21	+	1111.21i	−0.0712886	+	0.0712886i
$625$	−14212.4			−0.909592
$626$	−6933.41	+	6933.41i	−0.442676	+	0.442676i
$627$		−	634.345i		−	0.0404040i
$628$	894.139			0.0568153
$629$	−15533.5	+	3181.62i	−0.984675	+	0.201685i
$630$	5238.53			0.331283
$631$		−	10087.2i		−	0.636394i	−0.948025	−	0.318197i	$-0.896923\pi$
$631$		−	10087.2i		−	0.636394i	0.948025	−	0.318197i	$-0.103077\pi$
$632$	1793.64	−	1793.64i	0.112891	−	0.112891i
$633$	1921.75			0.120668
$634$	−7724.81	+	7724.81i	−0.483898	+	0.483898i
$635$	2718.93	+	2718.93i	0.169917	+	0.169917i
$636$	1052.26	+	1052.26i	0.0656048	+	0.0656048i
$637$		−	16619.6i		−	1.03374i
$638$			20048.0i			1.24406i
$639$	1482.14	+	1482.14i	0.0917565	+	0.0917565i
$640$	349.523	+	349.523i	0.0215877	+	0.0215877i
$641$	7258.52	−	7258.52i	0.447261	−	0.447261i	−0.447182	−	0.894443i	$-0.647572\pi$
$641$	7258.52	−	7258.52i	0.447261	−	0.447261i	0.894443	+	0.447182i	$0.147572\pi$
$642$	−578.036			−0.0355347
$643$	−5500.06	+	5500.06i	−0.337327	+	0.337327i	−0.855360	−	0.518034i	$-0.826664\pi$
$643$	−5500.06	+	5500.06i	−0.337327	+	0.337327i	0.518034	+	0.855360i	$0.326664\pi$
$644$			14356.3i			0.878443i
$645$	98.9587			0.00604108
$646$	−10624.0	−	7011.76i	−0.647051	−	0.427050i
$647$	5015.28			0.304746			0.152373	−	0.988323i	$-0.451308\pi$
$647$	5015.28			0.304746			0.152373	+	0.988323i	$0.451308\pi$
$648$			1417.15i			0.0859118i
$649$	−17226.7	+	17226.7i	−1.04192	+	1.04192i
$650$	−26089.5			−1.57433
$651$	−1926.23	+	1926.23i	−0.115968	+	0.115968i
$652$	−809.004	−	809.004i	−0.0485936	−	0.0485936i
$653$	−10298.2	−	10298.2i	−0.617151	−	0.617151i	0.327649	−	0.944800i	$-0.393744\pi$
$653$	−10298.2	−	10298.2i	−0.617151	−	0.617151i	−0.944800	+	0.327649i	$0.893744\pi$
$654$		−	226.692i		−	0.0135541i
$655$		−	489.235i		−	0.0291847i
$656$	11078.6	+	11078.6i	0.659371	+	0.659371i
$657$	7263.75	+	7263.75i	0.431333	+	0.431333i
$658$	−13332.6	+	13332.6i	−0.789906	+	0.789906i
$659$	6199.21			0.366445			0.183222	−	0.983072i	$-0.441347\pi$
$659$	6199.21			0.366445			0.183222	+	0.983072i	$0.441347\pi$
$660$	−142.181	+	142.181i	−0.00838545	+	0.00838545i
$661$			15131.8i			0.890406i	0.895430	+	0.445203i	$0.146868\pi$
$661$			15131.8i			0.890406i	−0.895430	+	0.445203i	$0.853132\pi$
$662$	23689.6			1.39082
$663$	1592.13	−	326.106i	0.0932628	−	0.0191024i
$664$	1172.99			0.0685554
$665$		−	2289.04i		−	0.133481i
$666$	−16888.0	+	16888.0i	−0.982578	+	0.982578i
$667$	−11824.7			−0.686440
$668$	13384.3	−	13384.3i	0.775230	−	0.775230i
$669$	−37.0484	−	37.0484i	−0.00214107	−	0.00214107i
$670$	−2899.02	−	2899.02i	−0.167163	−	0.167163i
$671$		−	15670.6i		−	0.901577i
$672$		−	2706.11i		−	0.155343i
$673$	19122.8	+	19122.8i	1.09529	+	1.09529i	0.994953	+	0.100337i	$0.0319922\pi$
$673$	19122.8	+	19122.8i	1.09529	+	1.09529i	0.100337	+	0.994953i	$0.468008\pi$
$674$	−1320.44	−	1320.44i	−0.0754619	−	0.0754619i
$675$	1955.55	−	1955.55i	0.111510	−	0.111510i
$676$	−5948.22			−0.338429
$677$	1889.00	−	1889.00i	0.107238	−	0.107238i	−0.651452	−	0.758690i	$-0.725840\pi$
$677$	1889.00	−	1889.00i	0.107238	−	0.107238i	0.758690	+	0.651452i	$0.225840\pi$
$678$			1478.69i			0.0837591i
$679$	40493.2			2.28864
$680$	−54.4217	−	265.701i	−0.00306909	−	0.0149840i
$681$	−330.770			−0.0186125
$682$			32248.2i			1.81063i
$683$	10455.7	−	10455.7i	0.585763	−	0.585763i	−0.350718	−	0.936481i	$-0.614063\pi$
$683$	10455.7	−	10455.7i	0.585763	−	0.585763i	0.936481	+	0.350718i	$0.114063\pi$
$684$	−9275.07			−0.518481
$685$	601.942	−	601.942i	0.0335752	−	0.0335752i
$686$	−2767.27	−	2767.27i	−0.154016	−	0.154016i
$687$	−832.457	−	832.457i	−0.0462303	−	0.0462303i
$688$			8109.01i			0.449350i
$689$		−	25604.4i		−	1.41575i
$690$	−173.360	−	173.360i	−0.00956477	−	0.00956477i
$691$	−13201.7	−	13201.7i	−0.726798	−	0.726798i	0.243182	−	0.969981i	$-0.421809\pi$
$691$	−13201.7	−	13201.7i	−0.726798	−	0.726798i	−0.969981	+	0.243182i	$0.921809\pi$
$692$	−1740.04	+	1740.04i	−0.0955871	+	0.0955871i
$693$	22122.6			1.21265
$694$	4106.98	−	4106.98i	0.224638	−	0.224638i
$695$			163.326i			0.00891413i
$696$	132.068			0.00719255
$697$	−3251.23	−	15873.3i	−0.176684	−	0.862617i
$698$	−26985.8			−1.46336
$699$		−	2140.14i		−	0.115805i
$700$	16339.1	−	16339.1i	0.882227	−	0.882227i
$701$	27668.5			1.49076			0.745381	−	0.666638i	$-0.232267\pi$
$701$	27668.5			1.49076			0.745381	+	0.666638i	$0.232267\pi$
$702$	3473.53	−	3473.53i	0.186752	−	0.186752i
$703$	7379.42	+	7379.42i	0.395903	+	0.395903i
$704$	−10218.4	−	10218.4i	−0.547045	−	0.547045i
$705$		−	155.763i		−	0.00832109i
$706$		−	29467.7i		−	1.57087i
$707$	−11994.1	−	11994.1i	−0.638025	−	0.638025i
$708$	−1688.28	−	1688.28i	−0.0896178	−	0.0896178i
$709$	−7382.12	+	7382.12i	−0.391032	+	0.391032i	−0.875055	−	0.484023i	$-0.839175\pi$
$709$	−7382.12	+	7382.12i	−0.391032	+	0.391032i	0.484023	+	0.875055i	$0.339175\pi$
$710$	−600.157			−0.0317232
$711$	−24253.1	+	24253.1i	−1.27927	+	1.27927i
$712$			1209.39i			0.0636572i
$713$	−19020.6			−0.999059
$714$	−1639.04	+	2483.41i	−0.0859097	+	0.130167i
$715$	3459.68			0.180957
$716$			31147.2i			1.62573i
$717$	−675.825	+	675.825i	−0.0352010	+	0.0352010i
$718$	28223.0			1.46695
$719$	−12597.2	+	12597.2i	−0.653402	+	0.653402i	−0.953811	−	0.300409i	$-0.902877\pi$
$719$	−12597.2	+	12597.2i	−0.653402	+	0.653402i	0.300409	+	0.953811i	$0.402877\pi$
$720$	−2507.51	−	2507.51i	−0.129791	−	0.129791i
$721$	−15689.5	−	15689.5i	−0.810414	−	0.810414i
$722$		−	18622.4i		−	0.959909i
$723$		−	733.132i		−	0.0377116i
$724$	−5064.29	−	5064.29i	−0.259963	−	0.259963i
$725$	13457.9	+	13457.9i	0.689397	+	0.689397i
$726$	329.600	−	329.600i	0.0168493	−	0.0168493i
$727$	−4296.42			−0.219182			−0.109591	−	0.993977i	$-0.534954\pi$
$727$	−4296.42			−0.219182			−0.109591	+	0.993977i	$0.534954\pi$
$728$	−1950.79	+	1950.79i	−0.0993148	+	0.0993148i
$729$		−	18901.0i		−	0.960273i
$730$	−2941.28			−0.149126
$731$	4619.37	−	6999.11i	0.233726	−	0.354133i
$732$	1535.78			0.0775467
$733$		−	28559.1i		−	1.43909i	−0.694445	−	0.719546i	$-0.744350\pi$
$733$		−	28559.1i		−	1.43909i	0.694445	−	0.719546i	$-0.255650\pi$
$734$	−18395.8	+	18395.8i	−0.925071	+	0.925071i
$735$	−251.373			−0.0126150
$736$	13360.8	−	13360.8i	0.669138	−	0.669138i
$737$	−12242.7	−	12242.7i	−0.611895	−	0.611895i
$738$	−17257.5	−	17257.5i	−0.860780	−	0.860780i
$739$			10646.9i			0.529974i	0.964252	+	0.264987i	$0.0853677\pi$
$739$			10646.9i			0.529974i	−0.964252	+	0.264987i	$0.914632\pi$
$740$		−	3308.03i		−	0.164332i
$741$	−756.366	−	756.366i	−0.0374977	−	0.0374977i
$742$	33148.3	+	33148.3i	1.64005	+	1.64005i
$743$	−9874.51	+	9874.51i	−0.487565	+	0.487565i	−0.907537	−	0.419972i	$-0.862040\pi$
$743$	−9874.51	+	9874.51i	−0.487565	+	0.487565i	0.419972	+	0.907537i	$0.362040\pi$
$744$	212.437			0.0104682
$745$	−3251.91	+	3251.91i	−0.159921	+	0.159921i
$746$			6309.87i			0.309679i
$747$	−15860.8			−0.776864
$748$	3419.14	+	16693.1i	0.167134	+	0.815990i
$749$	−8808.65			−0.429721
$750$			801.602i			0.0390272i
$751$	18922.9	−	18922.9i	0.919449	−	0.919449i	−0.0775401	−	0.996989i	$-0.524707\pi$
$751$	18922.9	−	18922.9i	0.919449	−	0.919449i	0.996989	+	0.0775401i	$0.0247066\pi$
$752$	12763.7			0.618943
$753$	394.020	−	394.020i	0.0190689	−	0.0190689i
$754$	23904.4	+	23904.4i	1.15457	+	1.15457i
$755$	206.563	+	206.563i	0.00995709	+	0.00995709i
$756$			4350.73i			0.209305i
$757$			1399.40i			0.0671889i	0.999436	+	0.0335945i	$0.0106955\pi$
$757$			1399.40i			0.0671889i	−0.999436	+	0.0335945i	$0.989305\pi$
$758$	−4851.93	−	4851.93i	−0.232493	−	0.232493i
$759$	−732.108	−	732.108i	−0.0350116	−	0.0350116i
$760$	−126.225	+	126.225i	−0.00602456	+	0.00602456i
$761$	29282.9			1.39488			0.697440	−	0.716644i	$-0.254323\pi$
$761$	29282.9			1.39488			0.697440	+	0.716644i	$0.254323\pi$
$762$	−2326.24	+	2326.24i	−0.110592	+	0.110592i
$763$		−	3454.54i		−	0.163909i
$764$	6669.74			0.315841
$765$	735.875	+	3592.73i	0.0347786	+	0.169798i
$766$	4547.62			0.214507
$767$			41080.7i			1.93395i
$768$	−1367.80	+	1367.80i	−0.0642658	+	0.0642658i
$769$	−11804.9			−0.553571			−0.276786	−	0.960932i	$-0.589269\pi$
$769$	−11804.9			−0.553571			−0.276786	+	0.960932i	$0.589269\pi$
$770$	−4479.02	+	4479.02i	−0.209627	+	0.209627i
$771$	1810.82	+	1810.82i	0.0845852	+	0.0845852i
$772$	9180.97	+	9180.97i	0.428019	+	0.428019i
$773$			18421.7i			0.857155i	0.903505	+	0.428578i	$0.140985\pi$
$773$			18421.7i			0.857155i	−0.903505	+	0.428578i	$0.859015\pi$
$774$		−	12631.6i		−	0.586607i
$775$	21647.6	+	21647.6i	1.00336	+	1.00336i
$776$	−2232.93	−	2232.93i	−0.103296	−	0.103296i
$777$	1724.98	−	1724.98i	0.0796439	−	0.0796439i
$778$	14561.0			0.670998
$779$	−7540.85	+	7540.85i	−0.346828	+	0.346828i
$780$			339.062i			0.0155646i
$781$	−2534.49			−0.116122
$782$	−20353.7	+	4168.92i	−0.930750	+	0.190640i
$783$	−3583.53			−0.163557
$784$		−	20598.3i		−	0.938335i
$785$	−164.538	+	164.538i	−0.00748102	+	0.00748102i
$786$	418.575			0.0189950
$787$	−15833.2	+	15833.2i	−0.717143	+	0.717143i	−0.968019	−	0.250876i	$-0.919281\pi$
$787$	−15833.2	+	15833.2i	−0.717143	+	0.717143i	0.250876	+	0.968019i	$0.419281\pi$
$788$	−23555.2	−	23555.2i	−1.06487	−	1.06487i
$789$	296.919	+	296.919i	0.0133975	+	0.0133975i
$790$		−	9820.74i		−	0.442286i
$791$			22533.6i			1.01290i
$792$	−1219.91	−	1219.91i	−0.0547320	−	0.0547320i
$793$	−18685.0	−	18685.0i	−0.836727	−	0.836727i
$794$	37822.5	−	37822.5i	1.69052	−	1.69052i
$795$	−387.268			−0.0172767
$796$	−16529.2	+	16529.2i	−0.736005	+	0.736005i
$797$		−	13676.1i		−	0.607818i	−0.952701	−	0.303909i	$-0.901708\pi$
$797$		−	13676.1i		−	0.607818i	0.952701	−	0.303909i	$-0.0982919\pi$
$798$	1958.43			0.0868770
$799$	−11016.7	−	7270.98i	−0.487790	−	0.321938i
$800$	−30412.2			−1.34404
$801$		−	16353.1i		−	0.721357i
$802$	−7416.29	+	7416.29i	−0.326532	+	0.326532i
$803$	−12421.2			−0.545872
$804$	1199.83	−	1199.83i	0.0526305	−	0.0526305i
$805$	−2641.82	−	2641.82i	−0.115667	−	0.115667i
$806$	38451.4	+	38451.4i	1.68039	+	1.68039i
$807$			1437.56i			0.0627071i
$808$			1322.79i			0.0575933i
$809$	−71.3327	−	71.3327i	−0.00310003	−	0.00310003i	0.705555	−	0.708655i	$-0.250698\pi$
$809$	−71.3327	−	71.3327i	−0.00310003	−	0.00310003i	−0.708655	+	0.705555i	$0.750698\pi$
$810$	3879.66	+	3879.66i	0.168293	+	0.168293i
$811$	11822.5	−	11822.5i	0.511893	−	0.511893i	−0.403213	−	0.915106i	$-0.632107\pi$
$811$	11822.5	−	11822.5i	0.511893	−	0.511893i	0.915106	+	0.403213i	$0.132107\pi$
$812$	−29941.2			−1.29400
$813$	1111.16	−	1111.16i	0.0479335	−	0.0479335i
$814$		−	28879.0i		−	1.24350i
$815$	297.743			0.0127969
$816$	1973.28	−	404.175i	0.0846552	−	0.0173394i
$817$	−5519.54			−0.236358
$818$		−	16320.2i		−	0.697584i
$819$	26378.1	−	26378.1i	1.12543	−	1.12543i
$820$	3380.39			0.143962
$821$	−3487.82	+	3487.82i	−0.148265	+	0.148265i	−0.777343	−	0.629077i	$-0.783433\pi$
$821$	−3487.82	+	3487.82i	−0.148265	+	0.148265i	0.629077	+	0.777343i	$0.283433\pi$
$822$	515.004	+	515.004i	0.0218526	+	0.0218526i
$823$	18792.3	+	18792.3i	0.795939	+	0.795939i	0.982452	−	0.186513i	$-0.0597187\pi$
$823$	18792.3	+	18792.3i	0.795939	+	0.795939i	−0.186513	+	0.982452i	$0.559719\pi$
$824$			1730.35i			0.0731547i
$825$			1666.44i			0.0703249i
$826$	−53184.5	−	53184.5i	−2.24034	−	2.24034i
$827$	22017.0	+	22017.0i	0.925762	+	0.925762i	0.997429	−	0.0716667i	$-0.0228318\pi$
$827$	22017.0	+	22017.0i	0.925762	+	0.925762i	−0.0716667	+	0.997429i	$0.522832\pi$
$828$	−10704.5	+	10704.5i	−0.449284	+	0.449284i
$829$	17274.9			0.723742			0.361871	−	0.932228i	$-0.382138\pi$
$829$	17274.9			0.723742			0.361871	+	0.932228i	$0.382138\pi$
$830$	3211.24	−	3211.24i	0.134294	−	0.134294i
$831$		−	3244.31i		−	0.135432i
$832$	−24367.9			−1.01539
$833$	−11734.0	+	17779.0i	−0.488067	+	0.739502i
$834$	−139.737			−0.00580180
$835$			4925.90i			0.204153i
$836$	7930.32	−	7930.32i	0.328081	−	0.328081i
$837$	−5764.28			−0.238044
$838$	39658.4	−	39658.4i	1.63482	−	1.63482i
$839$	3970.01	+	3970.01i	0.163361	+	0.163361i	0.784054	−	0.620693i	$-0.213149\pi$
$839$	3970.01	+	3970.01i	0.163361	+	0.163361i	−0.620693	+	0.784054i	$0.713149\pi$
$840$	29.5058	+	29.5058i	0.00121196	+	0.00121196i
$841$		−	272.434i		−	0.0111704i
$842$			12563.8i			0.514226i
$843$	−957.845	−	957.845i	−0.0391340	−	0.0391340i
$844$	24025.0	+	24025.0i	0.979827	+	0.979827i
$845$	1094.58	−	1094.58i	0.0445618	−	0.0445618i
$846$	−19882.4			−0.808004
$847$	5022.76	−	5022.76i	0.203759	−	0.203759i
$848$		−	31734.0i		−	1.28508i
$849$	2539.63			0.102662
$850$	27909.5	+	18420.1i	1.12622	+	0.743299i
$851$	17033.4			0.686132
$852$		−	248.390i		−	0.00998792i
$853$	2686.89	−	2686.89i	0.107851	−	0.107851i	−0.651122	−	0.758973i	$-0.725701\pi$
$853$	2686.89	−	2686.89i	0.107851	−	0.107851i	0.758973	+	0.651122i	$0.225701\pi$
$854$	48380.5			1.93858
$855$	1706.78	−	1706.78i	0.0682698	−	0.0682698i
$856$	485.738	+	485.738i	0.0193951	+	0.0193951i
$857$	29847.2	+	29847.2i	1.18969	+	1.18969i	0.977154	+	0.212532i	$0.0681710\pi$
$857$	29847.2	+	29847.2i	1.18969	+	1.18969i	0.212532	+	0.977154i	$0.431829\pi$
$858$			2960.00i			0.117777i
$859$		−	3132.98i		−	0.124442i	−0.998062	−	0.0622212i	$-0.980182\pi$
$859$		−	3132.98i		−	0.124442i	0.998062	−	0.0622212i	$-0.0198184\pi$
$860$	1237.14	+	1237.14i	0.0490537	+	0.0490537i
$861$	1762.72	+	1762.72i	0.0697715	+	0.0697715i
$862$	−4563.37	+	4563.37i	−0.180312	+	0.180312i
$863$	−31934.9			−1.25965			−0.629824	−	0.776738i	$-0.716873\pi$
$863$	−31934.9			−1.25965			−0.629824	+	0.776738i	$0.716873\pi$
$864$	4049.05	−	4049.05i	0.159434	−	0.159434i
$865$		−	640.396i		−	0.0251724i
$866$	−65266.8			−2.56104
$867$	−1933.44	−	775.244i	−0.0757358	−	0.0303675i
$868$	−48161.8			−1.88332
$869$		−	41473.5i		−	1.61898i
$870$	361.556	−	361.556i	0.0140895	−	0.0140895i
$871$	−29195.4			−1.13576
$872$	−190.495	+	190.495i	−0.00739790	+	0.00739790i
$873$	30193.0	+	30193.0i	1.17054	+	1.17054i
$874$	9669.33	+	9669.33i	0.374222	+	0.374222i
$875$			12215.6i			0.471956i
$876$		−	1217.33i		−	0.0469517i
$877$	−10847.5	−	10847.5i	−0.417667	−	0.417667i	0.466732	−	0.884399i	$-0.345431\pi$
$877$	−10847.5	−	10847.5i	−0.417667	−	0.417667i	−0.884399	+	0.466732i	$0.845431\pi$
$878$	−20450.9	−	20450.9i	−0.786086	−	0.786086i
$879$	−1610.70	+	1610.70i	−0.0618060	+	0.0618060i
$880$	4287.91			0.164256
$881$	32730.5	−	32730.5i	1.25167	−	1.25167i	0.296695	−	0.954972i	$-0.404116\pi$
$881$	32730.5	−	32730.5i	1.25167	−	1.25167i	0.954972	−	0.296695i	$-0.0958845\pi$
$882$			32086.6i			1.22496i
$883$	−26455.9			−1.00828			−0.504140	−	0.863622i	$-0.668190\pi$
$883$	−26455.9			−1.00828			−0.504140	+	0.863622i	$0.668190\pi$
$884$	23981.0	+	15827.3i	0.912407	+	0.602184i
$885$	621.348			0.0236004
$886$			52456.0i			1.98904i
$887$	−12749.8	+	12749.8i	−0.482633	+	0.482633i	−0.905972	−	0.423339i	$-0.860858\pi$
$887$	−12749.8	+	12749.8i	−0.482633	+	0.482633i	0.423339	+	0.905972i	$0.360858\pi$
$888$	−190.242			−0.00718932
$889$	−35449.4	+	35449.4i	−1.33739	+	1.33739i
$890$	3310.90	+	3310.90i	0.124698	+	0.124698i
$891$	16384.0	+	16384.0i	0.616033	+	0.616033i
$892$		−	926.327i		−	0.0347710i
$893$			8687.85i			0.325563i
$894$	−2782.24	−	2782.24i	−0.104085	−	0.104085i
$895$	−5731.65	−	5731.65i	−0.214065	−	0.214065i
$896$	−4557.08	+	4557.08i	−0.169912	+	0.169912i
$897$	−1745.87			−0.0649864
$898$	−26962.3	+	26962.3i	−1.00194	+	1.00194i
$899$		−	39669.1i		−	1.47168i
$900$	24365.9			0.902440
$901$	−18077.6	+	27390.5i	−0.668425	+	1.01277i
$902$	29510.7			1.08936
$903$			1290.22i			0.0475481i
$904$	1242.58	−	1242.58i	0.0457163	−	0.0457163i
$905$	1863.84			0.0684599
$906$	−176.729	+	176.729i	−0.00648062	+	0.00648062i
$907$	−32345.3	−	32345.3i	−1.18413	−	1.18413i	−0.978664	−	0.205467i	$-0.934129\pi$
$907$	−32345.3	−	32345.3i	−1.18413	−	1.18413i	−0.205467	−	0.978664i	$-0.565871\pi$
$908$	−4135.15	−	4135.15i	−0.151134	−	0.151134i
$909$		−	17886.3i		−	0.652642i
$910$			10681.2i			0.389096i
$911$	−1203.07	−	1203.07i	−0.0437534	−	0.0437534i	0.684892	−	0.728645i	$-0.259850\pi$
$911$	−1203.07	−	1203.07i	−0.0437534	−	0.0437534i	−0.728645	+	0.684892i	$0.759850\pi$
$912$	−937.438	−	937.438i	−0.0340369	−	0.0340369i
$913$	13561.2	−	13561.2i	0.491579	−	0.491579i
$914$	2747.94			0.0994462
$915$	−282.612	+	282.612i	−0.0102108	+	0.0102108i
$916$		−	20814.1i		−	0.750782i
$917$	6378.64			0.229707
$918$	−6168.27	+	1263.41i	−0.221768	+	0.0454234i
$919$	30814.5			1.10607			0.553035	−	0.833158i	$-0.313470\pi$
$919$	30814.5			1.10607			0.553035	+	0.833158i	$0.313470\pi$
$920$			291.357i			0.0104410i
$921$	−2104.92	+	2104.92i	−0.0753088	+	0.0753088i
$922$	25609.3			0.914747
$923$	−3022.02	+	3022.02i	−0.107769	+	0.107769i
$924$	−1853.76	−	1853.76i	−0.0660001	−	0.0660001i
$925$	−19385.9	−	19385.9i	−0.689087	−	0.689087i
$926$		−	4651.93i		−	0.165088i
$927$		−	23397.2i		−	0.828982i
$928$	27865.0	+	27865.0i	0.985684	+	0.985684i
$929$	2894.34	+	2894.34i	0.102218	+	0.102218i	0.756366	−	0.654149i	$-0.226973\pi$
$929$	2894.34	+	2894.34i	0.102218	+	0.102218i	−0.654149	+	0.756366i	$0.726973\pi$
$930$	581.579	−	581.579i	0.0205062	−	0.0205062i
$931$	14020.6			0.493563
$932$	26755.1	−	26755.1i	0.940336	−	0.940336i
$933$		−	435.018i		−	0.0152646i
$934$	−11616.5			−0.406963
$935$	−3701.02	−	2442.65i	−0.129450	−	0.0854365i
$936$	−2909.15			−0.101590
$937$		−	16517.3i		−	0.575877i	−0.957649	−	0.287939i	$-0.907030\pi$
$937$		−	16517.3i		−	0.575877i	0.957649	−	0.287939i	$-0.0929699\pi$
$938$	37797.4	−	37797.4i	1.31570	−	1.31570i
$939$	1056.11			0.0367036
$940$	1947.28	−	1947.28i	0.0675674	−	0.0675674i
$941$	−4851.27	−	4851.27i	−0.168063	−	0.168063i	0.618065	−	0.786127i	$-0.287917\pi$
$941$	−4851.27	−	4851.27i	−0.168063	−	0.168063i	−0.786127	+	0.618065i	$0.787917\pi$
$942$	−140.774	−	140.774i	−0.00486906	−	0.00486906i
$943$			17406.0i			0.601080i
$944$			50915.3i			1.75546i
$945$	−800.613	−	800.613i	−0.0275597	−	0.0275597i
$946$	10800.2	+	10800.2i	0.371189	+	0.371189i
$947$	23545.8	−	23545.8i	0.807957	−	0.807957i	−0.176367	−	0.984324i	$-0.556435\pi$
$947$	23545.8	−	23545.8i	0.807957	−	0.807957i	0.984324	+	0.176367i	$0.0564347\pi$
$948$	4064.57			0.139252
$949$	−14810.5	+	14810.5i	−0.506607	+	0.506607i
$950$		−	22009.6i		−	0.751669i
$951$	1176.65			0.0401215
$952$	3464.20	−	709.550i	0.117936	−	0.0241561i
$953$	−24857.5			−0.844925			−0.422462	−	0.906380i	$-0.638834\pi$
$953$	−24857.5			−0.844925			−0.422462	+	0.906380i	$0.638834\pi$
$954$			49432.9i			1.67762i
$955$	−1227.35	+	1227.35i	−0.0415877	+	0.0415877i
$956$	−16897.8			−0.571666
$957$	1526.87	−	1526.87i	0.0515744	−	0.0515744i
$958$	−24746.2	−	24746.2i	−0.834565	−	0.834565i
$959$	7848.11	+	7848.11i	0.264264	+	0.264264i
$960$			368.566i			0.0123911i
$961$		−	34018.6i		−	1.14191i
$962$	−34434.1	−	34434.1i	−1.15405	−	1.15405i
$963$	−6568.01	−	6568.01i	−0.219783	−	0.219783i
$964$	9165.31	−	9165.31i	0.306219	−	0.306219i
$965$	−3378.93			−0.112717
$966$	2260.26	−	2260.26i	0.0752823	−	0.0752823i
$967$			15832.2i			0.526504i	0.964727	+	0.263252i	$0.0847951\pi$
$967$			15832.2i			0.526504i	−0.964727	+	0.263252i	$0.915205\pi$
$968$	−553.943			−0.0183930
$969$	275.108	+	1343.15i	0.00912049	+	0.0445285i
$970$	−12226.0			−0.404693
$971$		−	39521.9i		−	1.30620i	−0.757273	−	0.653098i	$-0.773469\pi$
$971$		−	39521.9i		−	1.30620i	0.757273	−	0.653098i	$-0.226531\pi$
$972$	−4871.49	+	4871.49i	−0.160754	+	0.160754i
$973$	−2129.45			−0.0701612
$974$	−19775.5	+	19775.5i	−0.650564	+	0.650564i
$975$	1986.99	+	1986.99i	0.0652664	+	0.0652664i
$976$	−23158.2	−	23158.2i	−0.759502	−	0.759502i
$977$			11587.3i			0.379438i	0.981838	+	0.189719i	$0.0607577\pi$
$977$			11587.3i			0.379438i	−0.981838	+	0.189719i	$0.939242\pi$
$978$			254.740i			0.00832893i
$979$	13982.1	+	13982.1i	0.456455	+	0.456455i
$980$	−3142.56	−	3142.56i	−0.102434	−	0.102434i
$981$	2575.82	−	2575.82i	0.0838323	−	0.0838323i
$982$	30068.4			0.977108
$983$	−22711.9	+	22711.9i	−0.736925	+	0.736925i	−0.971982	−	0.235057i	$-0.924472\pi$
$983$	−22711.9	+	22711.9i	−0.736925	+	0.736925i	0.235057	+	0.971982i	$0.424472\pi$
$984$		−	194.404i		−	0.00629815i
$985$	8669.17			0.280429
$986$	−8694.61	−	42449.3i	−0.280824	−	1.37105i
$987$	2030.83			0.0654936
$988$		−	18911.5i		−	0.608964i
$989$	−6370.19	+	6370.19i	−0.204813	+	0.204813i
$990$	−6679.40			−0.214429
$991$	−13235.2	+	13235.2i	−0.424247	+	0.424247i	−0.886663	−	0.462416i	$-0.846983\pi$
$991$	−13235.2	+	13235.2i	−0.424247	+	0.424247i	0.462416	+	0.886663i	$0.346983\pi$
$992$	44822.2	+	44822.2i	1.43458	+	1.43458i
$993$	−1804.21	−	1804.21i	−0.0576585	−	0.0576585i
$994$		−	7824.83i		−	0.249687i
$995$		−	6083.32i		−	0.193823i
$996$	1329.05	+	1329.05i	0.0422818	+	0.0422818i
$997$	−8210.42	−	8210.42i	−0.260809	−	0.260809i	0.564574	−	0.825383i	$-0.309041\pi$
$997$	−8210.42	−	8210.42i	−0.260809	−	0.260809i	−0.825383	+	0.564574i	$0.809041\pi$
$998$	−56234.5	+	56234.5i	−1.78364	+	1.78364i
$999$	5162.05			0.163483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.4.c.a.4.1	✓	8
3.2	odd	2		153.4.f.a.55.4		8
4.3	odd	2		272.4.o.e.225.3		8
17.2	even	8		289.4.b.c.288.8		8
17.8	even	8		289.4.a.f.1.2		8
17.9	even	8		289.4.a.f.1.1		8
17.13	even	4	inner	17.4.c.a.13.4	yes	8
17.15	even	8		289.4.b.c.288.7		8
51.47	odd	4		153.4.f.a.64.1		8
68.47	odd	4		272.4.o.e.81.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.c.a.4.1	✓	8	1.1	even	1	trivial
17.4.c.a.13.4	yes	8	17.13	even	4	inner
153.4.f.a.55.4		8	3.2	odd	2
153.4.f.a.64.1		8	51.47	odd	4
272.4.o.e.81.3		8	68.47	odd	4
272.4.o.e.225.3		8	4.3	odd	2
289.4.a.f.1.1		8	17.9	even	8
289.4.a.f.1.2		8	17.8	even	8
289.4.b.c.288.7		8	17.15	even	8
289.4.b.c.288.8		8	17.2	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)

\(f(q)\)	\(=\)	\(q-3.93651i q^{2} +(-0.299807 + 0.299807i) q^{3} -7.49613 q^{4} +(1.37942 - 1.37942i) q^{5} +(1.18019 + 1.18019i) q^{6} +(17.9849 + 17.9849i) q^{7} -1.98349i q^{8} +26.8202i q^{9} +O(q^{10})\)	\(q-3.93651i q^{2} +(-0.299807 + 0.299807i) q^{3} -7.49613 q^{4} +(1.37942 - 1.37942i) q^{5} +(1.18019 + 1.18019i) q^{6} +(17.9849 + 17.9849i) q^{7} -1.98349i q^{8} +26.8202i q^{9} +(-5.43011 - 5.43011i) q^{10} +(-22.9317 - 22.9317i) q^{11} +(2.24739 - 2.24739i) q^{12} -54.6855 q^{13} +(70.7978 - 70.7978i) q^{14} +0.827121i q^{15} -67.7771 q^{16} +(58.5003 + 38.6098i) q^{17} +105.578 q^{18} -46.1336i q^{19} +(-10.3403 + 10.3403i) q^{20} -10.7840 q^{21} +(-90.2708 + 90.2708i) q^{22} +(-53.2436 - 53.2436i) q^{23} +(0.594665 + 0.594665i) q^{24} +121.194i q^{25} +215.270i q^{26} +(-16.1357 - 16.1357i) q^{27} +(-134.817 - 134.817i) q^{28} +(111.044 - 111.044i) q^{29} +3.25597 q^{30} +(178.619 - 178.619i) q^{31} +250.937i q^{32} +13.7502 q^{33} +(151.988 - 230.287i) q^{34} +49.6175 q^{35} -201.048i q^{36} +(-159.957 + 159.957i) q^{37} -181.606 q^{38} +(16.3951 - 16.3951i) q^{39} +(-2.73608 - 2.73608i) q^{40} +(-163.457 - 163.457i) q^{41} +42.4513i q^{42} -119.642i q^{43} +(171.899 + 171.899i) q^{44} +(36.9964 + 36.9964i) q^{45} +(-209.594 + 209.594i) q^{46} -188.319 q^{47} +(20.3200 - 20.3200i) q^{48} +303.913i q^{49} +477.083 q^{50} +(-29.1143 + 5.96329i) q^{51} +409.930 q^{52} +468.212i q^{53} +(-63.5183 + 63.5183i) q^{54} -63.2650 q^{55} +(35.6729 - 35.6729i) q^{56} +(13.8312 + 13.8312i) q^{57} +(-437.125 - 437.125i) q^{58} -751.217i q^{59} -6.20021i q^{60} +(341.681 + 341.681i) q^{61} +(-703.136 - 703.136i) q^{62} +(-482.359 + 482.359i) q^{63} +445.601 q^{64} +(-75.4344 + 75.4344i) q^{65} -54.1277i q^{66} +533.879 q^{67} +(-438.526 - 289.424i) q^{68} +31.9256 q^{69} -195.320i q^{70} +(55.2619 - 55.2619i) q^{71} +53.1977 q^{72} +(270.831 - 270.831i) q^{73} +(629.674 + 629.674i) q^{74} +(-36.3349 - 36.3349i) q^{75} +345.824i q^{76} -824.848i q^{77} +(-64.5395 - 64.5395i) q^{78} +(904.285 + 904.285i) q^{79} +(-93.4932 + 93.4932i) q^{80} -714.471 q^{81} +(-643.449 + 643.449i) q^{82} +591.376i q^{83} +80.8382 q^{84} +(133.956 - 27.4373i) q^{85} -470.973 q^{86} +66.5834i q^{87} +(-45.4848 + 45.4848i) q^{88} -609.729 q^{89} +(145.637 - 145.637i) q^{90} +(-983.513 - 983.513i) q^{91} +(399.121 + 399.121i) q^{92} +107.103i q^{93} +741.321i q^{94} +(-63.6378 - 63.6378i) q^{95} +(-75.2328 - 75.2328i) q^{96} +(1125.76 - 1125.76i) q^{97} +1196.36 q^{98} +(615.033 - 615.033i) 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

L-functions

Modular forms

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