LMFDB - Embedded newform 165.4.c.a.34.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,4,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	165.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.73531515095$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 97x^{12} + 3674x^{10} + 68702x^{8} + 656605x^{6} + 2988841x^{4} + 5502384x^{2} + 3385600 $ x^14 + 97x^12 + 3674x^10 + 68702x^8 + 656605x^6 + 2988841x^4 + 5502384x^2 + 3385600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.11
Root			$4.00699i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.4.c.a.34.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00699i q^{2} -3.00000i q^{3} -8.05595 q^{4} +(-2.16823 - 10.9681i) q^{5} +12.0210 q^{6} +26.2766i q^{7} -0.224208i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+4.00699i q^{2} -3.00000i q^{3} -8.05595 q^{4} +(-2.16823 - 10.9681i) q^{5} +12.0210 q^{6} +26.2766i q^{7} -0.224208i q^{8} -9.00000 q^{9} +(43.9490 - 8.68807i) q^{10} -11.0000 q^{11} +24.1679i q^{12} +11.3069i q^{13} -105.290 q^{14} +(-32.9042 + 6.50469i) q^{15} -63.5492 q^{16} +87.6018i q^{17} -36.0629i q^{18} -148.978 q^{19} +(17.4672 + 88.3583i) q^{20} +78.8297 q^{21} -44.0769i q^{22} +12.7783i q^{23} -0.672624 q^{24} +(-115.598 + 47.5627i) q^{25} -45.3065 q^{26} +27.0000i q^{27} -211.683i q^{28} +37.2177 q^{29} +(-26.0642 - 131.847i) q^{30} -30.4121 q^{31} -256.435i q^{32} +33.0000i q^{33} -351.019 q^{34} +(288.204 - 56.9737i) q^{35} +72.5036 q^{36} +122.491i q^{37} -596.955i q^{38} +33.9206 q^{39} +(-2.45913 + 0.486135i) q^{40} +444.960 q^{41} +315.870i q^{42} -36.2510i q^{43} +88.6155 q^{44} +(19.5141 + 98.7127i) q^{45} -51.2025 q^{46} +78.5138i q^{47} +190.648i q^{48} -347.458 q^{49} +(-190.583 - 463.198i) q^{50} +262.805 q^{51} -91.0876i q^{52} +342.345i q^{53} -108.189 q^{54} +(23.8505 + 120.649i) q^{55} +5.89142 q^{56} +446.935i q^{57} +149.131i q^{58} -377.123 q^{59} +(265.075 - 52.4015i) q^{60} -690.244 q^{61} -121.861i q^{62} -236.489i q^{63} +519.137 q^{64} +(124.015 - 24.5159i) q^{65} -132.231 q^{66} -696.564i q^{67} -705.716i q^{68} +38.3349 q^{69} +(228.293 + 1154.83i) q^{70} +1014.66 q^{71} +2.01787i q^{72} +889.198i q^{73} -490.818 q^{74} +(142.688 + 346.793i) q^{75} +1200.16 q^{76} -289.042i q^{77} +135.919i q^{78} +858.251 q^{79} +(137.789 + 697.013i) q^{80} +81.0000 q^{81} +1782.95i q^{82} -115.843i q^{83} -635.048 q^{84} +(960.824 - 189.941i) q^{85} +145.257 q^{86} -111.653i q^{87} +2.46629i q^{88} -553.264 q^{89} +(-395.541 + 78.1927i) q^{90} -297.106 q^{91} -102.941i q^{92} +91.2363i q^{93} -314.604 q^{94} +(323.020 + 1634.01i) q^{95} -769.304 q^{96} +336.110i q^{97} -1392.26i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9}+O(q^{10}) $ 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9	$ 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9} - 28 q^{10} - 154 q^{11} - 284 q^{14} + 362 q^{16} - 52 q^{19} + 226 q^{20} + 300 q^{21} - 126 q^{24} - 366 q^{25} + 952 q^{26} - 1144 q^{29} - 582 q^{30} - 280 q^{31} + 1612 q^{34} - 600 q^{35} + 738 q^{36} - 144 q^{39} + 176 q^{40} + 1792 q^{41} + 902 q^{44} + 126 q^{45} - 688 q^{46} - 590 q^{49} + 388 q^{50} + 228 q^{51} - 162 q^{54} + 154 q^{55} + 3044 q^{56} - 2632 q^{59} - 1140 q^{60} - 772 q^{61} - 1738 q^{64} - 904 q^{65} - 198 q^{66} - 1368 q^{69} + 84 q^{70} + 1608 q^{71} + 1496 q^{74} - 300 q^{75} - 3396 q^{76} + 748 q^{79} - 2606 q^{80} + 1134 q^{81} - 5040 q^{84} + 2508 q^{85} - 5068 q^{86} - 1388 q^{89} + 252 q^{90} - 6752 q^{91} + 5840 q^{94} + 1724 q^{95} + 5946 q^{96} + 1386 q^{99}+O(q^{100}) $ 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9 - 28 * q^10 - 154 * q^11 - 284 * q^14 + 362 * q^16 - 52 * q^19 + 226 * q^20 + 300 * q^21 - 126 * q^24 - 366 * q^25 + 952 * q^26 - 1144 * q^29 - 582 * q^30 - 280 * q^31 + 1612 * q^34 - 600 * q^35 + 738 * q^36 - 144 * q^39 + 176 * q^40 + 1792 * q^41 + 902 * q^44 + 126 * q^45 - 688 * q^46 - 590 * q^49 + 388 * q^50 + 228 * q^51 - 162 * q^54 + 154 * q^55 + 3044 * q^56 - 2632 * q^59 - 1140 * q^60 - 772 * q^61 - 1738 * q^64 - 904 * q^65 - 198 * q^66 - 1368 * q^69 + 84 * q^70 + 1608 * q^71 + 1496 * q^74 - 300 * q^75 - 3396 * q^76 + 748 * q^79 - 2606 * q^80 + 1134 * q^81 - 5040 * q^84 + 2508 * q^85 - 5068 * q^86 - 1388 * q^89 + 252 * q^90 - 6752 * q^91 + 5840 * q^94 + 1724 * q^95 + 5946 * q^96 + 1386 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$			4.00699i			1.41668i	0.705869	+	0.708342i	$0.250557\pi$
$2$			4.00699i			1.41668i	−0.705869	+	0.708342i	$0.749443\pi$
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−8.05595			−1.00699
$5$	−2.16823	−	10.9681i	−0.193932	−	0.981015i
$5$	−2.16823	−	10.9681i	−0.193932	−	0.981015i
$6$	12.0210			0.817923
$7$			26.2766i			1.41880i	0.704805	+	0.709401i	$0.251034\pi$
$7$			26.2766i			1.41880i	−0.704805	+	0.709401i	$0.748966\pi$
$8$		−	0.224208i		−	0.00990869i
$9$	−9.00000			−0.333333
$10$	43.9490	−	8.68807i	1.38979	−	0.274741i
$11$	−11.0000			−0.301511
$11$	−11.0000			−0.301511
$12$			24.1679i			0.581388i
$13$			11.3069i			0.241228i	0.992700	+	0.120614i	$0.0384863\pi$
$13$			11.3069i			0.241228i	−0.992700	+	0.120614i	$0.961514\pi$
$14$	−105.290			−2.00999
$15$	−32.9042	+	6.50469i	−0.566389	+	0.111967i
$16$	−63.5492			−0.992957
$17$			87.6018i			1.24980i	0.780706	+	0.624899i	$0.214860\pi$
$17$			87.6018i			1.24980i	−0.780706	+	0.624899i	$0.785140\pi$
$18$		−	36.0629i		−	0.472228i
$19$	−148.978			−1.79884			−0.899421	−	0.437083i	$-0.856012\pi$
$19$	−148.978			−1.79884			−0.899421	+	0.437083i	$0.856012\pi$
$20$	17.4672	+	88.3583i	0.195289	+	0.987876i
$21$	78.8297			0.819145
$22$		−	44.0769i		−	0.427146i
$23$			12.7783i			0.115846i	0.998321	+	0.0579230i	$0.0184478\pi$
$23$			12.7783i			0.115846i	−0.998321	+	0.0579230i	$0.981552\pi$
$24$	−0.672624			−0.00572078
$25$	−115.598	+	47.5627i	−0.924780	+	0.380501i
$26$	−45.3065			−0.341743
$27$			27.0000i			0.192450i
$28$		−	211.683i		−	1.42872i
$29$	37.2177			0.238315			0.119158	−	0.992875i	$-0.461981\pi$
$29$	37.2177			0.238315			0.119158	+	0.992875i	$0.461981\pi$
$30$	−26.0642	−	131.847i	−0.158622	−	0.802395i
$31$	−30.4121			−0.176199			−0.0880995	−	0.996112i	$-0.528079\pi$
$31$	−30.4121			−0.176199			−0.0880995	+	0.996112i	$0.528079\pi$
$32$		−	256.435i		−	1.41661i
$33$			33.0000i			0.174078i
$34$	−351.019			−1.77057
$35$	288.204	−	56.9737i	1.39187	−	0.275152i
$36$	72.5036			0.335665
$37$			122.491i			0.544252i	0.962262	+	0.272126i	$0.0877267\pi$
$37$			122.491i			0.544252i	−0.962262	+	0.272126i	$0.912273\pi$
$38$		−	596.955i		−	2.54839i
$39$	33.9206			0.139273
$40$	−2.45913	+	0.486135i	−0.00972057	+	0.00192162i
$41$	444.960			1.69490			0.847452	−	0.530871i	$-0.178135\pi$
$41$	444.960			1.69490			0.847452	+	0.530871i	$0.178135\pi$
$42$			315.870i			1.16047i
$43$		−	36.2510i		−	0.128564i	−0.997932	−	0.0642818i	$-0.979524\pi$
$43$		−	36.2510i		−	0.128564i	0.997932	−	0.0642818i	$-0.0204756\pi$
$44$	88.6155			0.303620
$45$	19.5141	+	98.7127i	0.0646441	+	0.327005i
$46$	−51.2025			−0.164117
$47$			78.5138i			0.243668i	0.992550	+	0.121834i	$0.0388776\pi$
$47$			78.5138i			0.243668i	−0.992550	+	0.121834i	$0.961122\pi$
$48$			190.648i			0.573284i
$49$	−347.458			−1.01300
$50$	−190.583	−	463.198i	−0.539050	−	1.31012i
$51$	262.805			0.721571
$52$		−	91.0876i		−	0.242915i
$53$			342.345i			0.887260i	0.896210	+	0.443630i	$0.146309\pi$
$53$			342.345i			0.887260i	−0.896210	+	0.443630i	$0.853691\pi$
$54$	−108.189			−0.272641
$55$	23.8505	+	120.649i	0.0584728	+	0.295787i
$56$	5.89142			0.0140585
$57$			446.935i			1.03856i
$58$			149.131i			0.337618i
$59$	−377.123			−0.832156			−0.416078	−	0.909329i	$-0.636596\pi$
$59$	−377.123			−0.832156			−0.416078	+	0.909329i	$0.636596\pi$
$60$	265.075	−	52.4015i	0.570351	−	0.112750i
$61$	−690.244			−1.44880			−0.724399	−	0.689380i	$-0.757883\pi$
$61$	−690.244			−1.44880			−0.724399	+	0.689380i	$0.757883\pi$
$62$		−	121.861i		−	0.249618i
$63$		−	236.489i		−	0.472934i
$64$	519.137			1.01394
$65$	124.015	−	24.5159i	0.236648	−	0.0467819i
$66$	−132.231			−0.246613
$67$		−	696.564i		−	1.27013i	−0.772458	−	0.635066i	$-0.780973\pi$
$67$		−	696.564i		−	1.27013i	0.772458	−	0.635066i	$-0.219027\pi$
$68$		−	705.716i		−	1.25854i
$69$	38.3349			0.0668837
$70$	228.293	+	1154.83i	0.389803	+	1.97183i
$71$	1014.66			1.69602			0.848011	−	0.529978i	$-0.177800\pi$
$71$	1014.66			1.69602			0.848011	+	0.529978i	$0.177800\pi$
$72$			2.01787i			0.00330290i
$73$			889.198i			1.42565i	0.701339	+	0.712827i	$0.252586\pi$
$73$			889.198i			1.42565i	−0.701339	+	0.712827i	$0.747414\pi$
$74$	−490.818			−0.771033
$75$	142.688	+	346.793i	0.219682	+	0.533922i
$76$	1200.16			1.81142
$77$		−	289.042i		−	0.427785i
$78$			135.919i			0.197306i
$79$	858.251			1.22229			0.611144	−	0.791519i	$-0.290710\pi$
$79$	858.251			1.22229			0.611144	+	0.791519i	$0.290710\pi$
$80$	137.789	+	697.013i	0.192567	+	0.974105i
$81$	81.0000			0.111111
$82$			1782.95i			2.40115i
$83$		−	115.843i		−	0.153198i	−0.997062	−	0.0765989i	$-0.975594\pi$
$83$		−	115.843i		−	0.153198i	0.997062	−	0.0765989i	$-0.0244061\pi$
$84$	−635.048			−0.824875
$85$	960.824	−	189.941i	1.22607	−	0.242376i
$86$	145.257			0.182134
$87$		−	111.653i		−	0.137591i
$88$			2.46629i			0.00298758i
$89$	−553.264			−0.658943			−0.329471	−	0.944166i	$-0.606870\pi$
$89$	−553.264			−0.658943			−0.329471	+	0.944166i	$0.606870\pi$
$90$	−395.541	+	78.1927i	−0.463263	+	0.0915803i
$91$	−297.106			−0.342254
$92$		−	102.941i		−	0.116656i
$93$			91.2363i			0.101729i
$94$	−314.604			−0.345201
$95$	323.020	+	1634.01i	0.348854	+	1.76469i
$96$	−769.304			−0.817883
$97$			336.110i			0.351823i	0.984406	+	0.175911i	$0.0562872\pi$
$97$			336.110i			0.351823i	−0.984406	+	0.175911i	$0.943713\pi$
$98$		−	1392.26i		−	1.43510i
$99$	99.0000			0.100504
$100$	931.249	−	383.163i	0.931249	−	0.383163i
$101$	1277.11			1.25819			0.629097	−	0.777327i	$-0.283425\pi$
$101$	1277.11			1.25819			0.629097	+	0.777327i	$0.283425\pi$
$102$			1053.06i			1.02224i
$103$		−	1075.63i		−	1.02898i	−0.857497	−	0.514490i	$-0.827981\pi$
$103$		−	1075.63i		−	1.02898i	0.857497	−	0.514490i	$-0.172019\pi$
$104$	2.53509			0.00239025
$105$	−170.921	−	864.611i	−0.158859	−	0.803594i
$106$	−1371.77			−1.25697
$107$		−	1903.79i		−	1.72006i	−0.510244	−	0.860030i	$-0.670445\pi$
$107$		−	1903.79i		−	1.72006i	0.510244	−	0.860030i	$-0.329555\pi$
$108$		−	217.511i		−	0.193796i
$109$	894.655			0.786169			0.393084	−	0.919502i	$-0.371408\pi$
$109$	894.655			0.786169			0.393084	+	0.919502i	$0.371408\pi$
$110$	−483.439	+	95.5688i	−0.419037	+	0.0828375i
$111$	367.472			0.314224
$112$		−	1669.86i		−	1.40881i
$113$		−	0.252752i		−	0.000210415i	−1.00000		0.000105208i	$-0.999967\pi$
$113$		−	0.252752i		−	0.000210415i	1.00000		0.000105208i	$-3.34886e-5\pi$
$114$	−1790.87			−1.47131
$115$	140.153	−	27.7063i	0.113647	−	0.0224663i
$116$	−299.824			−0.239982
$117$		−	101.762i		−	0.0804092i
$118$		−	1511.13i		−	1.17890i
$119$	−2301.87			−1.77321
$120$	1.45840	+	7.37739i	0.00110945	+	0.00561217i
$121$	121.000			0.0909091
$122$		−	2765.80i		−	2.05249i
$123$		−	1334.88i		−	0.978554i
$124$	244.998			0.177431
$125$	772.313	+	1164.76i	0.552622	+	0.833432i
$126$	947.609			0.669998
$127$			2393.92i			1.67264i	0.548240	+	0.836321i	$0.315298\pi$
$127$			2393.92i			1.67264i	−0.548240	+	0.836321i	$0.684702\pi$
$128$			28.6979i			0.0198169i
$129$	−108.753			−0.0742262
$130$	98.2348	+	496.925i	0.0662751	+	0.335255i
$131$	−2363.05			−1.57604			−0.788019	−	0.615651i	$-0.788893\pi$
$131$	−2363.05			−1.57604			−0.788019	+	0.615651i	$0.788893\pi$
$132$		−	265.846i		−	0.175295i
$133$		−	3914.64i		−	2.55220i
$134$	2791.12			1.79938
$135$	296.138	−	58.5422i	0.188796	−	0.0373223i
$136$	19.6410			0.0123839
$137$		−	208.264i		−	0.129877i	−0.997889	−	0.0649385i	$-0.979315\pi$
$137$		−	208.264i		−	0.129877i	0.997889	−	0.0649385i	$-0.0206851\pi$
$138$			153.607i			0.0947531i
$139$	612.112			0.373515			0.186758	−	0.982406i	$-0.440202\pi$
$139$	612.112			0.373515			0.186758	+	0.982406i	$0.440202\pi$
$140$	−2321.75	+	458.977i	−1.40160	+	0.277076i
$141$	235.541			0.140682
$142$			4065.72i			2.40273i
$143$		−	124.375i		−	0.0727329i
$144$	571.943			0.330986
$145$	−80.6965	−	408.206i	−0.0462171	−	0.233791i
$146$	−3563.01			−2.01970
$147$			1042.37i			0.584854i
$148$		−	986.778i		−	0.548059i
$149$	2116.42			1.16365			0.581826	−	0.813313i	$-0.302338\pi$
$149$	2116.42			1.16365			0.581826	+	0.813313i	$0.302338\pi$
$150$	−1389.59	+	571.749i	−0.756399	+	0.311221i
$151$	−3405.63			−1.83540			−0.917701	−	0.397271i	$-0.869957\pi$
$151$	−3405.63			−1.83540			−0.917701	+	0.397271i	$0.869957\pi$
$152$			33.4022i			0.0178242i
$153$		−	788.416i		−	0.416599i
$154$	1158.19			0.606036
$155$	65.9404	+	333.562i	0.0341707	+	0.172854i
$156$	−273.263			−0.140247
$157$			294.346i			0.149627i	0.997198	+	0.0748133i	$0.0238361\pi$
$157$			294.346i			0.149627i	−0.997198	+	0.0748133i	$0.976164\pi$
$158$			3439.00i			1.73160i
$159$	1027.04			0.512260
$160$	−2812.60	+	556.010i	−1.38972	+	0.274728i
$161$	−335.770			−0.164362
$162$			324.566i			0.157409i
$163$			2877.76i			1.38284i	0.722452	+	0.691421i	$0.243015\pi$
$163$			2877.76i			1.38284i	−0.722452	+	0.691421i	$0.756985\pi$
$164$	−3584.58			−1.70676
$165$	361.947	−	71.5516i	0.170773	−	0.0337593i
$166$	464.181			0.217033
$167$			2506.59i			1.16147i	0.814093	+	0.580735i	$0.197235\pi$
$167$			2506.59i			1.16147i	−0.814093	+	0.580735i	$0.802765\pi$
$168$		−	17.6742i		−	0.00811665i
$169$	2069.15			0.941809
$170$	761.091	+	3850.01i	0.343371	+	1.73695i
$171$	1340.81			0.599614
$172$			292.037i			0.129463i
$173$		−	3092.28i		−	1.35897i	−0.733689	−	0.679485i	$-0.762203\pi$
$173$		−	3092.28i		−	1.35897i	0.733689	−	0.679485i	$-0.237797\pi$
$174$	447.392			0.194924
$175$	−1249.78	−	3037.51i	−0.539856	−	1.31208i
$176$	699.042			0.299388
$177$			1131.37i			0.480445i
$178$		−	2216.92i		−	0.933514i
$179$	3360.78			1.40333			0.701665	−	0.712507i	$-0.252440\pi$
$179$	3360.78			1.40333			0.701665	+	0.712507i	$0.252440\pi$
$180$	−157.204	−	795.225i	−0.0650963	−	0.329292i
$181$	208.349			0.0855606			0.0427803	−	0.999085i	$-0.486378\pi$
$181$	208.349			0.0855606			0.0427803	+	0.999085i	$0.486378\pi$
$182$		−	1190.50i		−	0.484866i
$183$			2070.73i			0.836464i
$184$	2.86499			0.00114788
$185$	1343.49	−	265.588i	0.533919	−	0.105548i
$186$	−365.583			−0.144117
$187$		−	963.620i		−	0.376828i
$188$		−	632.503i		−	0.245373i
$189$	−709.467			−0.273048
$190$	−6547.45	+	1294.34i	−2.50001	+	0.494216i
$191$	−324.423			−0.122903			−0.0614514	−	0.998110i	$-0.519573\pi$
$191$	−324.423			−0.122903			−0.0614514	+	0.998110i	$0.519573\pi$
$192$		−	1557.41i		−	0.585398i
$193$			3274.46i			1.22125i	0.791920	+	0.610624i	$0.209081\pi$
$193$			3274.46i			1.22125i	−0.791920	+	0.610624i	$0.790919\pi$
$194$	−1346.79			−0.498422
$195$	−73.5476	−	372.044i	−0.0270095	−	0.136629i
$196$	2799.11			1.02008
$197$		−	642.826i		−	0.232484i	−0.993221	−	0.116242i	$-0.962915\pi$
$197$		−	642.826i		−	0.232484i	0.993221	−	0.116242i	$-0.0370849\pi$
$198$			396.692i			0.142382i
$199$	320.513			0.114174			0.0570868	−	0.998369i	$-0.481819\pi$
$199$	320.513			0.114174			0.0570868	+	0.998369i	$0.481819\pi$
$200$	10.6639	+	25.9179i	0.00377027	+	0.00916336i
$201$	−2089.69			−0.733311
$202$			5117.38i			1.78246i
$203$			977.953i			0.338122i
$204$	−2117.15			−0.726618
$205$	−964.776	−	4880.36i	−0.328697	−	1.66273i
$206$	4310.03			1.45774
$207$		−	115.005i		−	0.0386153i
$208$		−	718.542i		−	0.239529i
$209$	1638.76			0.542371
$210$	3464.48	−	684.878i	1.13844	−	0.225053i
$211$	−5158.61			−1.68310			−0.841548	−	0.540182i	$-0.818356\pi$
$211$	−5158.61			−1.68310			−0.841548	+	0.540182i	$0.818356\pi$
$212$		−	2757.92i		−	0.893465i
$213$		−	3043.97i		−	0.979199i
$214$	7628.47			2.43678
$215$	−397.604	+	78.6006i	−0.126123	+	0.0249326i
$216$	6.05361			0.00190693
$217$		−	799.125i		−	0.249992i
$218$			3584.87i			1.11375i
$219$	2667.60			0.823102
$220$	−192.139	−	971.942i	−0.0588818	−	0.297856i
$221$	−990.501			−0.301486
$222$			1472.45i			0.445156i
$223$		−	2948.51i		−	0.885413i	−0.896667	−	0.442706i	$-0.854018\pi$
$223$		−	2948.51i		−	0.885413i	0.896667	−	0.442706i	$-0.145982\pi$
$224$	6738.22			2.00990
$225$	1040.38	−	428.064i	0.308260	−	0.126834i
$226$	1.01277			0.000298092
$227$			2281.12i			0.666974i	0.942755	+	0.333487i	$0.108225\pi$
$227$			2281.12i			0.666974i	−0.942755	+	0.333487i	$0.891775\pi$
$228$		−	3600.49i		−	1.04583i
$229$	−3616.61			−1.04364			−0.521818	−	0.853057i	$-0.674746\pi$
$229$	−3616.61			−1.04364			−0.521818	+	0.853057i	$0.674746\pi$
$230$	111.019	+	561.593i	0.0318276	+	0.161001i
$231$	−867.127			−0.246982
$232$		−	8.34450i		−	0.00236139i
$233$			4571.20i			1.28528i	0.766170	+	0.642638i	$0.222160\pi$
$233$			4571.20i			1.28528i	−0.766170	+	0.642638i	$0.777840\pi$
$234$	407.758			0.113914
$235$	861.145	−	170.236i	0.239042	−	0.0472552i
$236$	3038.08			0.837976
$237$		−	2574.75i		−	0.705688i
$238$		−	9223.59i		−	2.51208i
$239$	−2515.86			−0.680911			−0.340455	−	0.940261i	$-0.610581\pi$
$239$	−2515.86			−0.680911			−0.340455	+	0.940261i	$0.610581\pi$
$240$	2091.04	−	413.368i	0.562400	−	0.111178i
$241$	5325.35			1.42339			0.711693	−	0.702490i	$-0.247929\pi$
$241$	5325.35			1.42339			0.711693	+	0.702490i	$0.247929\pi$
$242$			484.846i			0.128789i
$243$		−	243.000i		−	0.0641500i
$244$	5560.58			1.45893
$245$	753.369	+	3810.95i	0.196453	+	0.993765i
$246$	5348.85			1.38630
$247$		−	1684.48i		−	0.433931i
$248$			6.81863i			0.00174590i
$249$	−347.529			−0.0884488
$250$	−4667.17	+	3094.65i	−1.18071	+	0.782891i
$251$	−4417.05			−1.11076			−0.555382	−	0.831595i	$-0.687428\pi$
$251$	−4417.05			−1.11076			−0.555382	+	0.831595i	$0.687428\pi$
$252$			1905.15i			0.476242i
$253$		−	140.561i		−	0.0349289i
$254$	−9592.39			−2.36961
$255$	−569.823	−	2882.47i	−0.139936	−	0.707872i
$256$	4038.10			0.985865
$257$			1049.24i			0.254668i	0.991860	+	0.127334i	$0.0406421\pi$
$257$			1049.24i			0.254668i	−0.991860	+	0.127334i	$0.959358\pi$
$258$		−	435.772i		−	0.105155i
$259$	−3218.63			−0.772185
$260$	−999.056	+	197.499i	−0.238303	+	0.0471091i
$261$	−334.959			−0.0794385
$262$		−	9468.73i		−	2.23275i
$263$			2773.92i			0.650370i	0.945650	+	0.325185i	$0.105427\pi$
$263$			2773.92i			0.650370i	−0.945650	+	0.325185i	$0.894573\pi$
$264$	7.39886			0.00172488
$265$	3754.87	−	742.284i	0.870415	−	0.172068i
$266$	15685.9			3.61566
$267$			1659.79i			0.380441i
$268$			5611.49i			1.27902i
$269$	1645.90			0.373056			0.186528	−	0.982450i	$-0.440276\pi$
$269$	1645.90			0.373056			0.186528	+	0.982450i	$0.440276\pi$
$270$	234.578	+	1186.62i	0.0528739	+	0.267465i
$271$	−8599.58			−1.92763			−0.963814	−	0.266576i	$-0.914108\pi$
$271$	−8599.58			−1.92763			−0.963814	+	0.266576i	$0.914108\pi$
$272$		−	5567.03i		−	1.24099i
$273$			891.317i			0.197600i
$274$	834.510			0.183995
$275$	1271.57	−	523.189i	0.278832	−	0.114725i
$276$	−308.824			−0.0673515
$277$			3908.67i			0.847832i	0.905701	+	0.423916i	$0.139345\pi$
$277$			3908.67i			0.847832i	−0.905701	+	0.423916i	$0.860655\pi$
$278$			2452.72i			0.529153i
$279$	273.709			0.0587330
$280$	−12.7739	−	64.6175i	−0.00272639	−	0.0137916i
$281$	−1987.21			−0.421875			−0.210938	−	0.977500i	$-0.567652\pi$
$281$	−1987.21			−0.421875			−0.210938	+	0.977500i	$0.567652\pi$
$282$			943.811i			0.199302i
$283$		−	1229.67i		−	0.258291i	−0.991626	−	0.129145i	$-0.958777\pi$
$283$		−	1229.67i		−	0.258291i	0.991626	−	0.129145i	$-0.0412234\pi$
$284$	−8174.03			−1.70789
$285$	4902.02	−	969.059i	1.01885	−	0.201411i
$286$	498.371			0.103040
$287$			11692.0i			2.40473i
$288$			2307.91i			0.472205i
$289$	−2761.08			−0.561994
$290$	1635.68	−	323.350i	0.331208	−	0.0654750i
$291$	1008.33			0.203125
$292$		−	7163.34i		−	1.43563i
$293$			5067.22i			1.01034i	0.863019	+	0.505171i	$0.168571\pi$
$293$			5067.22i			1.01034i	−0.863019	+	0.505171i	$0.831429\pi$
$294$	−4176.78			−0.828554
$295$	817.689	+	4136.31i	0.161382	+	0.816357i
$296$	27.4634			0.00539282
$297$		−	297.000i		−	0.0580259i
$298$			8480.49i			1.64853i
$299$	−144.482			−0.0279453
$300$	−1149.49	−	2793.75i	−0.221219	−	0.537657i
$301$	952.553			0.182406
$302$		−	13646.3i		−	2.60019i
$303$		−	3831.34i		−	0.726419i
$304$	9467.47			1.78617
$305$	1496.61	+	7570.66i	0.280969	+	1.42129i
$306$	3159.17			0.590190
$307$			321.662i			0.0597988i	0.999553	+	0.0298994i	$0.00951869\pi$
$307$			321.662i			0.0597988i	−0.999553	+	0.0298994i	$0.990481\pi$
$308$			2328.51i			0.430777i
$309$	−3226.89			−0.594081
$310$	−1336.58	+	264.222i	−0.244879	+	0.0484091i
$311$	−5135.27			−0.936316			−0.468158	−	0.883645i	$-0.655082\pi$
$311$	−5135.27			−0.936316			−0.468158	+	0.883645i	$0.655082\pi$
$312$		−	7.60526i		−	0.00138001i
$313$			8366.56i			1.51088i	0.655217	+	0.755441i	$0.272577\pi$
$313$			8366.56i			1.51088i	−0.655217	+	0.755441i	$0.727423\pi$
$314$	−1179.44			−0.211974
$315$	−2593.83	+	512.763i	−0.463955	+	0.0917172i
$316$	−6914.03			−1.23084
$317$		−	7744.61i		−	1.37218i	−0.727517	−	0.686089i	$-0.759326\pi$
$317$		−	7744.61i		−	1.37218i	0.727517	−	0.686089i	$-0.240674\pi$
$318$			4115.32i			0.725710i
$319$	−409.394			−0.0718548
$320$	−1125.61	−	5693.94i	−0.196636	−	0.994690i
$321$	−5711.37			−0.993077
$322$		−	1345.43i		−	0.232850i
$323$		−	13050.8i		−	2.24819i
$324$	−652.532			−0.111888
$325$	−537.784	−	1307.05i	−0.0917874	−	0.223083i
$326$	−11531.1			−1.95905
$327$		−	2683.96i		−	0.453895i
$328$		−	99.7636i		−	0.0167943i
$329$	−2063.07			−0.345717
$330$	286.706	+	1450.32i	0.0478263	+	0.241931i
$331$	201.426			0.0334483			0.0167242	−	0.999860i	$-0.494676\pi$
$331$	201.426			0.0334483			0.0167242	+	0.999860i	$0.494676\pi$
$332$			933.225i			0.154269i
$333$		−	1102.41i		−	0.181417i
$334$	−10043.9			−1.64544
$335$	−7639.97	+	1510.31i	−1.24602	+	0.246320i
$336$	−5009.57			−0.813376
$337$			1271.19i			0.205478i	0.994708	+	0.102739i	$0.0327607\pi$
$337$			1271.19i			0.205478i	−0.994708	+	0.102739i	$0.967239\pi$
$338$			8291.08i			1.33425i
$339$	−0.758256			−0.000121483
$340$	−7740.35	+	1530.16i	−1.23465	+	0.244072i
$341$	334.533			0.0531260
$342$			5372.60i			0.849464i
$343$		−	117.142i		−	0.0184405i
$344$	−8.12777			−0.00127390
$345$	−83.1188	−	420.460i	−0.0129709	−	0.0656139i
$346$	12390.7			1.92523
$347$			7274.99i			1.12548i	0.826634	+	0.562740i	$0.190253\pi$
$347$			7274.99i			1.12548i	−0.826634	+	0.562740i	$0.809747\pi$
$348$			899.472i			0.138554i
$349$	−293.092			−0.0449538			−0.0224769	−	0.999747i	$-0.507155\pi$
$349$	−293.092			−0.0449538			−0.0224769	+	0.999747i	$0.507155\pi$
$350$	12171.3	−	5007.87i	1.85880	−	0.764805i
$351$	−305.285			−0.0464243
$352$			2820.78i			0.427125i
$353$		−	1120.68i		−	0.168974i	−0.996425	−	0.0844868i	$-0.973075\pi$
$353$		−	1120.68i		−	0.168974i	0.996425	−	0.0844868i	$-0.0269251\pi$
$354$	−4533.38			−0.680639
$355$	−2200.01	−	11128.8i	−0.328914	−	1.66382i
$356$	4457.07			0.663551
$357$			6905.62i			1.02377i
$358$			13466.6i			1.98808i
$359$	3543.35			0.520921			0.260461	−	0.965484i	$-0.416126\pi$
$359$	3543.35			0.520921			0.260461	+	0.965484i	$0.416126\pi$
$360$	22.1322	−	4.37521i	0.00324019	−	0.000640538i
$361$	15335.6			2.23583
$362$			834.853i			0.121212i
$363$		−	363.000i		−	0.0524864i
$364$	2393.47			0.344648
$365$	9752.80	−	1927.99i	1.39859	−	0.276481i
$366$	−8297.40			−1.18501
$367$		−	5998.09i		−	0.853128i	−0.904457	−	0.426564i	$-0.859724\pi$
$367$		−	5998.09i		−	0.853128i	0.904457	−	0.426564i	$-0.140276\pi$
$368$		−	812.051i		−	0.115030i
$369$	−4004.64			−0.564968
$370$	1064.21	+	5383.33i	0.149528	+	0.756395i
$371$	−8995.66			−1.25885
$372$		−	734.995i		−	0.102440i
$373$		−	4701.91i		−	0.652696i	−0.945250	−	0.326348i	$-0.894182\pi$
$373$		−	4701.91i		−	0.652696i	0.945250	−	0.326348i	$-0.105818\pi$
$374$	3861.21			0.533846
$375$	3494.27	−	2316.94i	0.481182	−	0.319057i
$376$	17.6034			0.00241443
$377$			420.815i			0.0574883i
$378$		−	2842.83i		−	0.386823i
$379$	10784.6			1.46165			0.730826	−	0.682563i	$-0.239135\pi$
$379$	10784.6			1.46165			0.730826	+	0.682563i	$0.239135\pi$
$380$	−2602.23	−	13163.5i	−0.351294	−	1.77703i
$381$	7181.75			0.965701
$382$		−	1299.96i		−	0.174115i
$383$		−	5317.16i		−	0.709385i	−0.934983	−	0.354692i	$-0.884586\pi$
$383$		−	5317.16i		−	0.709385i	0.934983	−	0.354692i	$-0.115414\pi$
$384$	86.0937			0.0114413
$385$	−3170.24	+	626.710i	−0.419663	+	0.0829613i
$386$	−13120.7			−1.73012
$387$			326.259i			0.0428545i
$388$		−	2707.69i		−	0.354284i
$389$	−10677.3			−1.39167			−0.695833	−	0.718203i	$-0.744965\pi$
$389$	−10677.3			−1.39167			−0.695833	+	0.718203i	$0.744965\pi$
$390$	1490.77	−	294.705i	0.193560	−	0.0382640i
$391$	−1119.40			−0.144784
$392$			77.9029i			0.0100375i
$393$			7089.16i			0.909926i
$394$	2575.79			0.329357
$395$	−1860.89	−	9413.36i	−0.237041	−	1.19908i
$396$	−797.539			−0.101207
$397$			8922.89i			1.12803i	0.825765	+	0.564014i	$0.190743\pi$
$397$			8922.89i			1.12803i	−0.825765	+	0.564014i	$0.809257\pi$
$398$			1284.29i			0.161748i
$399$	−11743.9			−1.47351
$400$	7346.14	−	3022.57i	0.918267	−	0.377821i
$401$	−3177.53			−0.395707			−0.197853	−	0.980232i	$-0.563397\pi$
$401$	−3177.53			−0.395707			−0.197853	+	0.980232i	$0.563397\pi$
$402$		−	8373.37i		−	1.03887i
$403$		−	343.865i		−	0.0425041i
$404$	−10288.4			−1.26699
$405$	−175.627	−	888.414i	−0.0215480	−	0.109002i
$406$	−3918.64			−0.479013
$407$		−	1347.40i		−	0.164098i
$408$		−	58.9231i		−	0.00714982i
$409$	2509.89			0.303438			0.151719	−	0.988424i	$-0.451519\pi$
$409$	2509.89			0.303438			0.151719	+	0.988424i	$0.451519\pi$
$410$	19555.5	−	3865.85i	2.35556	−	0.465660i
$411$	−624.791			−0.0749846
$412$			8665.22i			1.03618i
$413$		−	9909.49i		−	1.18066i
$414$	460.822			0.0547057
$415$	−1270.57	+	251.174i	−0.150289	+	0.0297100i
$416$	2899.47			0.341727
$417$		−	1836.34i		−	0.215649i
$418$			6566.51i			0.768369i
$419$	−9452.10			−1.10207			−0.551033	−	0.834484i	$-0.685766\pi$
$419$	−9452.10			−1.10207			−0.551033	+	0.834484i	$0.685766\pi$
$420$	1376.93	+	6965.26i	0.159970	+	0.809214i
$421$	−1824.33			−0.211193			−0.105597	−	0.994409i	$-0.533675\pi$
$421$	−1824.33			−0.211193			−0.105597	+	0.994409i	$0.533675\pi$
$422$		−	20670.5i		−	2.38442i
$423$		−	706.624i		−	0.0812228i
$424$	76.7566			0.00879158
$425$	−4166.57	−	10126.6i	−0.475549	−	1.15579i
$426$	12197.2			1.38722
$427$		−	18137.3i		−	2.05556i
$428$			15336.9i			1.73209i
$429$	−373.126			−0.0419923
$430$	−314.952	−	1593.20i	−0.0353217	−	0.178676i
$431$	15347.3			1.71521			0.857603	−	0.514312i	$-0.171953\pi$
$431$	15347.3			1.71521			0.857603	+	0.514312i	$0.171953\pi$
$432$		−	1715.83i		−	0.191095i
$433$		−	5002.63i		−	0.555222i	−0.960694	−	0.277611i	$-0.910457\pi$
$433$		−	5002.63i		−	0.555222i	0.960694	−	0.277611i	$-0.0895426\pi$
$434$	3202.09			0.354159
$435$	−1224.62	+	242.089i	−0.134979	+	0.0266835i
$436$	−7207.30			−0.791667
$437$		−	1903.69i		−	0.208389i
$438$			10689.0i			1.16608i
$439$	2498.66			0.271651			0.135825	−	0.990733i	$-0.456631\pi$
$439$	2498.66			0.271651			0.135825	+	0.990733i	$0.456631\pi$
$440$	27.0504	−	5.34748i	0.00293086	−	0.000579389i
$441$	3127.12			0.337666
$442$		−	3968.93i		−	0.427110i
$443$			3044.08i			0.326476i	0.986587	+	0.163238i	$0.0521938\pi$
$443$			3044.08i			0.326476i	−0.986587	+	0.163238i	$0.947806\pi$
$444$	−2960.33			−0.316422
$445$	1199.60	+	6068.25i	0.127790	+	0.646433i
$446$	11814.7			1.25435
$447$		−	6349.27i		−	0.671835i
$448$			13641.1i			1.43858i
$449$	−13184.9			−1.38582			−0.692911	−	0.721023i	$-0.743672\pi$
$449$	−13184.9			−1.38582			−0.692911	+	0.721023i	$0.743672\pi$
$450$	1715.25	+	4168.78i	0.179683	+	0.436707i
$451$	−4894.56			−0.511033
$452$			2.03616i			0.000211887i
$453$			10216.9i			1.05967i
$454$	−9140.42			−0.944892
$455$	644.193	+	3258.68i	0.0663742	+	0.335756i
$456$	100.206			0.0102908
$457$			16938.6i			1.73381i	0.498469	+	0.866907i	$0.333896\pi$
$457$			16938.6i			1.73381i	−0.498469	+	0.866907i	$0.666104\pi$
$458$		−	14491.7i		−	1.47850i
$459$	−2365.25			−0.240524
$460$	−1129.07	+	223.201i	−0.114442	+	0.0226234i
$461$	5188.91			0.524234			0.262117	−	0.965036i	$-0.415579\pi$
$461$	5188.91			0.524234			0.262117	+	0.965036i	$0.415579\pi$
$462$		−	3474.57i		−	0.349895i
$463$			15097.9i			1.51546i	0.652569	+	0.757730i	$0.273691\pi$
$463$			15097.9i			1.51546i	−0.652569	+	0.757730i	$0.726309\pi$
$464$	−2365.15			−0.236637
$465$	1000.69	−	197.821i	0.0997973	−	0.0197285i
$466$	−18316.7			−1.82083
$467$			13597.2i			1.34733i	0.739037	+	0.673665i	$0.235281\pi$
$467$			13597.2i			1.34733i	−0.739037	+	0.673665i	$0.764719\pi$
$468$			819.788i			0.0809716i
$469$	18303.3			1.80207
$470$	682.133	+	3450.60i	0.0669457	+	0.338647i
$471$	883.038			0.0863869
$472$			84.5539i			0.00824557i
$473$			398.761i			0.0387634i
$474$	10317.0			0.999738
$475$	17221.5	−	7085.81i	1.66353	−	0.684462i
$476$	18543.8			1.78562
$477$		−	3081.11i		−	0.295753i
$478$		−	10081.0i		−	0.964636i
$479$	6830.32			0.651535			0.325767	−	0.945450i	$-0.394377\pi$
$479$	6830.32			0.651535			0.325767	+	0.945450i	$0.394377\pi$
$480$	1668.03	+	8437.79i	0.158614	+	0.802355i
$481$	−1384.98			−0.131289
$482$			21338.6i			2.01649i
$483$			1007.31i			0.0948947i
$484$	−974.770			−0.0915449
$485$	3686.48	−	728.764i	0.345144	−	0.0682299i
$486$	973.698			0.0908803
$487$		−	762.315i		−	0.0709318i	−0.999371	−	0.0354659i	$-0.988708\pi$
$487$		−	762.315i		−	0.0709318i	0.999371	−	0.0354659i	$-0.0112915\pi$
$488$			154.758i			0.0143557i
$489$	8633.27			0.798384
$490$	−15270.4	+	3018.74i	−1.40785	+	0.278312i
$491$	1478.23			0.135868			0.0679342	−	0.997690i	$-0.478359\pi$
$491$	1478.23			0.135868			0.0679342	+	0.997690i	$0.478359\pi$
$492$			10753.7i			0.985398i
$493$			3260.34i			0.297846i
$494$	6749.69			0.614743
$495$	−214.655	−	1085.84i	−0.0194909	−	0.0985957i
$496$	1932.66			0.174958
$497$			26661.7i			2.40632i
$498$		−	1392.54i		−	0.125304i
$499$	11087.2			0.994648			0.497324	−	0.867565i	$-0.334316\pi$
$499$	11087.2			0.994648			0.497324	+	0.867565i	$0.334316\pi$
$500$	−6221.72	−	9383.22i	−0.556487	−	0.839261i
$501$	7519.76			0.670575
$502$		−	17699.1i		−	1.57360i
$503$			7336.27i			0.650314i	0.945660	+	0.325157i	$0.105417\pi$
$503$			7336.27i			0.650314i	−0.945660	+	0.325157i	$0.894583\pi$
$504$	−53.0227			−0.00468615
$505$	−2769.08	−	14007.5i	−0.244005	−	1.23431i
$506$	563.227			0.0494832
$507$		−	6207.46i		−	0.543754i
$508$		−	19285.3i		−	1.68434i
$509$	15419.2			1.34272			0.671360	−	0.741131i	$-0.265710\pi$
$509$	15419.2			1.34272			0.671360	+	0.741131i	$0.265710\pi$
$510$	11550.0	−	2283.27i	1.00283	−	0.198245i
$511$	−23365.1			−2.02272
$512$			16410.2i			1.41648i
$513$		−	4022.42i		−	0.346187i
$514$	−4204.29			−0.360785
$515$	−11797.6	+	2332.21i	−1.00944	+	0.199552i
$516$	876.110			0.0747454
$517$		−	863.651i		−	0.0734688i
$518$		−	12897.0i		−	1.09394i
$519$	−9276.85			−0.784602
$520$	−5.49666	−	27.8050i	−0.000463547	−	0.00234487i
$521$	20182.9			1.69717			0.848587	−	0.529056i	$-0.177454\pi$
$521$	20182.9			1.69717			0.848587	+	0.529056i	$0.177454\pi$
$522$		−	1342.18i		−	0.112539i
$523$		−	15479.7i		−	1.29422i	−0.762395	−	0.647112i	$-0.775977\pi$
$523$		−	15479.7i		−	1.29422i	0.762395	−	0.647112i	$-0.224023\pi$
$524$	19036.7			1.58706
$525$	−9112.52	+	3749.35i	−0.757530	+	0.311686i
$526$	−11115.1			−0.921369
$527$		−	2664.15i		−	0.220213i
$528$		−	2097.12i		−	0.172852i
$529$	12003.7			0.986580
$530$	2974.32	+	15045.7i	0.243767	+	1.23310i
$531$	3394.10			0.277385
$532$			31536.2i			2.57005i
$533$			5031.10i			0.408858i
$534$	−6650.77			−0.538964
$535$	−20880.9	+	4127.86i	−1.68740	+	0.333575i
$536$	−156.175			−0.0125853
$537$		−	10082.3i		−	0.810213i
$538$			6595.09i			0.528503i
$539$	3822.04			0.305430
$540$	−2385.68	+	471.613i	−0.190117	+	0.0375834i
$541$	−511.002			−0.0406094			−0.0203047	−	0.999794i	$-0.506464\pi$
$541$	−511.002			−0.0406094			−0.0203047	+	0.999794i	$0.506464\pi$
$542$		−	34458.4i		−	2.73084i
$543$		−	625.048i		−	0.0493985i
$544$	22464.1			1.77048
$545$	−1939.82	−	9812.65i	−0.152464	−	0.771243i
$546$	−3571.49			−0.279937
$547$			18912.8i			1.47834i	0.673519	+	0.739170i	$0.264782\pi$
$547$			18912.8i			1.47834i	−0.673519	+	0.739170i	$0.735218\pi$
$548$			1677.76i			0.130785i
$549$	6212.20			0.482933
$550$	2096.41	+	5095.18i	0.162530	+	0.395017i
$551$	−5544.63			−0.428692
$552$		−	8.59498i		−	0.000662730i
$553$			22551.9i			1.73418i
$554$	−15662.0			−1.20111
$555$	−796.763	−	4030.46i	−0.0609382	−	0.308258i
$556$	−4931.14			−0.376128
$557$		−	7869.53i		−	0.598640i	−0.954153	−	0.299320i	$-0.903240\pi$
$557$		−	7869.53i		−	0.598640i	0.954153	−	0.299320i	$-0.0967598\pi$
$558$			1096.75i			0.0832062i
$559$	409.885			0.0310131
$560$	−18315.1	+	3620.63i	−1.38206	+	0.273214i
$561$	−2890.86			−0.217562
$562$		−	7962.72i		−	0.597664i
$563$		−	12877.3i		−	0.963964i	−0.876181	−	0.481982i	$-0.839917\pi$
$563$		−	12877.3i		−	0.963964i	0.876181	−	0.481982i	$-0.160083\pi$
$564$	−1897.51			−0.141666
$565$	−2.77221	+	0.548025i	−0.000206420	+	4.08063e-5i
$566$	4927.28			0.365917
$567$			2128.40i			0.157645i
$568$		−	227.494i		−	0.0168054i
$569$	7070.93			0.520965			0.260482	−	0.965479i	$-0.416118\pi$
$569$	7070.93			0.520965			0.260482	+	0.965479i	$0.416118\pi$
$570$	3883.01	+	19642.4i	0.285336	+	1.44338i
$571$	7455.30			0.546400			0.273200	−	0.961957i	$-0.411918\pi$
$571$	7455.30			0.546400			0.273200	+	0.961957i	$0.411918\pi$
$572$			1001.96i			0.0732416i
$573$			973.270i			0.0709580i
$574$	−46849.8			−3.40675
$575$	−607.769	−	1477.14i	−0.0440795	−	0.107132i
$576$	−4672.23			−0.337980
$577$		−	13840.8i		−	0.998611i	−0.866426	−	0.499306i	$-0.833588\pi$
$577$		−	13840.8i		−	0.998611i	0.866426	−	0.499306i	$-0.166412\pi$
$578$		−	11063.6i		−	0.796168i
$579$	9823.39			0.705088
$580$	650.087	+	3288.49i	0.0465403	+	0.235426i
$581$	3043.95			0.217357
$582$			4040.37i			0.287764i
$583$		−	3765.80i		−	0.267519i
$584$	199.365			0.0141264
$585$	−1116.13	+	220.643i	−0.0788826	+	0.0155940i
$586$	−20304.3			−1.43134
$587$			5382.51i			0.378466i	0.981932	+	0.189233i	$0.0606002\pi$
$587$			5382.51i			0.378466i	−0.981932	+	0.189233i	$0.939400\pi$
$588$		−	8397.32i		−	0.588945i
$589$	4530.75			0.316954
$590$	−16574.1	+	3276.47i	−1.15652	+	0.228627i
$591$	−1928.48			−0.134225
$592$		−	7784.18i		−	0.540419i
$593$		−	17176.5i		−	1.18947i	−0.803922	−	0.594735i	$-0.797257\pi$
$593$		−	17176.5i		−	1.18947i	0.803922	−	0.594735i	$-0.202743\pi$
$594$	1190.08			0.0822044
$595$	4991.00	+	25247.1i	0.343884	+	1.73955i
$596$	−17049.8			−1.17179
$597$		−	961.538i		−	0.0659182i
$598$		−	578.939i		−	0.0395896i
$599$	−4846.64			−0.330598			−0.165299	−	0.986243i	$-0.552859\pi$
$599$	−4846.64			−0.330598			−0.165299	+	0.986243i	$0.552859\pi$
$600$	77.7537	−	31.9918i	0.00529047	−	0.00217676i
$601$	−5837.26			−0.396184			−0.198092	−	0.980183i	$-0.563475\pi$
$601$	−5837.26			−0.396184			−0.198092	+	0.980183i	$0.563475\pi$
$602$			3816.87i			0.258412i
$603$			6269.08i			0.423377i
$604$	27435.6			1.84824
$605$	−262.356	−	1327.14i	−0.0176302	−	0.0891832i
$606$	15352.2			1.02911
$607$		−	22838.2i		−	1.52714i	−0.645723	−	0.763572i	$-0.723444\pi$
$607$		−	22838.2i		−	1.52714i	0.645723	−	0.763572i	$-0.276556\pi$
$608$			38203.3i			2.54827i
$609$	2933.86			0.195215
$610$	−30335.5	+	5996.89i	−2.01352	+	0.398044i
$611$	−887.744			−0.0587795
$612$			6351.45i			0.419513i
$613$		−	22566.4i		−	1.48687i	−0.668811	−	0.743433i	$-0.733196\pi$
$613$		−	22566.4i		−	1.48687i	0.668811	−	0.743433i	$-0.266804\pi$
$614$	−1288.90			−0.0847160
$615$	−14641.1	+	2894.33i	−0.959976	+	0.189773i
$616$	−64.8056			−0.00423878
$617$		−	22553.3i		−	1.47158i	−0.677211	−	0.735789i	$-0.736812\pi$
$617$		−	22553.3i		−	1.47158i	0.677211	−	0.735789i	$-0.263188\pi$
$618$		−	12930.1i		−	0.841626i
$619$	4053.59			0.263211			0.131605	−	0.991302i	$-0.457987\pi$
$619$	4053.59			0.263211			0.131605	+	0.991302i	$0.457987\pi$
$620$	−531.213	−	2687.16i	−0.0344097	−	0.174063i
$621$	−345.014			−0.0222946
$622$		−	20576.9i		−	1.32646i
$623$		−	14537.9i		−	0.934909i
$624$	−2155.63			−0.138292
$625$	11100.6	−	10996.3i	0.710438	−	0.703760i
$626$	−33524.7			−2.14044
$627$		−	4916.29i		−	0.313138i
$628$		−	2371.24i		−	0.150673i
$629$	−10730.4			−0.680205
$630$	−2054.63	−	10393.5i	−0.129934	−	0.657278i
$631$	18912.2			1.19316			0.596580	−	0.802554i	$-0.296526\pi$
$631$	18912.2			1.19316			0.596580	+	0.802554i	$0.296526\pi$
$632$		−	192.427i		−	0.0121113i
$633$			15475.8i			0.971736i
$634$	31032.6			1.94394
$635$	26256.7	−	5190.56i	1.64089	−	0.324380i
$636$	−8273.76			−0.515842
$637$		−	3928.66i		−	0.244363i
$638$		−	1640.44i		−	0.101796i
$639$	−9131.91			−0.565341
$640$	314.761	−	62.2237i	0.0194407	−	0.00384314i
$641$	11120.8			0.685248			0.342624	−	0.939473i	$-0.388684\pi$
$641$	11120.8			0.685248			0.342624	+	0.939473i	$0.388684\pi$
$642$		−	22885.4i		−	1.40688i
$643$			6066.39i			0.372061i	0.982544	+	0.186030i	$0.0595623\pi$
$643$			6066.39i			0.372061i	−0.982544	+	0.186030i	$0.940438\pi$
$644$	2704.94			0.165512
$645$	235.802	+	1192.81i	0.0143949	+	0.0728170i
$646$	52294.3			3.18497
$647$			20954.2i			1.27325i	0.771172	+	0.636627i	$0.219671\pi$
$647$			20954.2i			1.27325i	−0.771172	+	0.636627i	$0.780329\pi$
$648$		−	18.1608i		−	0.00110097i
$649$	4148.35			0.250904
$650$	5237.32	−	2154.90i	0.316038	−	0.130034i
$651$	−2397.38			−0.144333
$652$		−	23183.1i		−	1.39251i
$653$		−	9497.10i		−	0.569142i	−0.958655	−	0.284571i	$-0.908149\pi$
$653$		−	9497.10i		−	0.569142i	0.958655	−	0.284571i	$-0.0918512\pi$
$654$	10754.6			0.643026
$655$	5123.65	+	25918.2i	0.305645	+	1.54612i
$656$	−28276.9			−1.68297
$657$		−	8002.79i		−	0.475218i
$658$		−	8266.71i		−	0.489772i
$659$	21562.5			1.27459			0.637295	−	0.770620i	$-0.280053\pi$
$659$	21562.5			1.27459			0.637295	+	0.770620i	$0.280053\pi$
$660$	−2915.83	+	576.416i	−0.171967	+	0.0339954i
$661$	−15127.3			−0.890141			−0.445070	−	0.895496i	$-0.646821\pi$
$661$	−15127.3			−0.890141			−0.445070	+	0.895496i	$0.646821\pi$
$662$			807.114i			0.0473857i
$663$			2971.50i			0.174063i
$664$	−25.9729			−0.00151799
$665$	−42936.1	+	8487.85i	−2.50375	+	0.494954i
$666$	4417.36			0.257011
$667$			475.578i			0.0276079i
$668$		−	20192.9i		−	1.16959i
$669$	−8845.54			−0.511193
$670$	−6051.80	−	30613.3i	−0.348957	−	1.76522i
$671$	7592.69			0.436829
$672$		−	20214.7i		−	1.16041i
$673$		−	2499.23i		−	0.143148i	−0.997435	−	0.0715738i	$-0.977198\pi$
$673$		−	2499.23i		−	0.143148i	0.997435	−	0.0715738i	$-0.0228021\pi$
$674$	−5093.64			−0.291098
$675$	−1284.19	−	3121.13i	−0.0732275	−	0.177974i
$676$	−16669.0			−0.948397
$677$			32630.0i			1.85240i	0.377036	+	0.926199i	$0.376943\pi$
$677$			32630.0i			1.85240i	−0.377036	+	0.926199i	$0.623057\pi$
$678$		−	3.03832i		−	0.000172103i
$679$	−8831.82			−0.499167
$680$	−42.5863	−	215.424i	−0.00240163	−	0.0121487i
$681$	6843.36			0.385078
$682$			1340.47i			0.0752628i
$683$			9737.59i			0.545532i	0.962080	+	0.272766i	$0.0879385\pi$
$683$			9737.59i			0.545532i	−0.962080	+	0.272766i	$0.912061\pi$
$684$	−10801.5			−0.603808
$685$	−2284.25	+	451.563i	−0.127411	+	0.0251874i
$686$	469.388			0.0261244
$687$			10849.8i			0.602543i
$688$			2303.73i			0.127658i
$689$	−3870.85			−0.214032
$690$	1684.78	−	333.056i	0.0929542	−	0.0183757i
$691$	−8508.21			−0.468404			−0.234202	−	0.972188i	$-0.575248\pi$
$691$	−8508.21			−0.468404			−0.234202	+	0.972188i	$0.575248\pi$
$692$			24911.3i			1.36848i
$693$			2601.38i			0.142595i
$694$	−29150.8			−1.59445
$695$	−1327.20	−	6713.69i	−0.0724367	−	0.366424i
$696$	−25.0335			−0.00136335
$697$			38979.3i			2.11829i
$698$		−	1174.42i		−	0.0636853i
$699$	13713.6			0.742054
$700$	10068.2	+	24470.0i	0.543632	+	1.32126i
$701$	−22843.3			−1.23078			−0.615391	−	0.788222i	$-0.711002\pi$
$701$	−22843.3			−1.23078			−0.615391	+	0.788222i	$0.711002\pi$
$702$		−	1223.27i		−	0.0657685i
$703$		−	18248.5i		−	0.979024i
$704$	−5710.51			−0.305714
$705$	−510.708	−	2583.44i	−0.0272828	−	0.138011i
$706$	4490.54			0.239382
$707$			33558.2i			1.78513i
$708$		−	9114.25i		−	0.483806i
$709$	−8510.36			−0.450794			−0.225397	−	0.974267i	$-0.572368\pi$
$709$	−8510.36			−0.450794			−0.225397	+	0.974267i	$0.572368\pi$
$710$	44593.1	−	8815.41i	2.35711	−	0.465967i
$711$	−7724.26			−0.407429
$712$			124.046i			0.00652926i
$713$		−	388.615i		−	0.0204120i
$714$	−27670.8			−1.45035
$715$	−1364.16	+	269.675i	−0.0713520	+	0.0141053i
$716$	−27074.3			−1.41315
$717$			7547.59i			0.393124i
$718$			14198.2i			0.737981i
$719$	−31326.2			−1.62486			−0.812428	−	0.583062i	$-0.801854\pi$
$719$	−31326.2			−1.62486			−0.812428	+	0.583062i	$0.801854\pi$
$720$	−1240.10	−	6273.12i	−0.0641888	−	0.324702i
$721$	28263.8			1.45992
$722$			61449.5i			3.16747i
$723$		−	15976.1i		−	0.821792i
$724$	−1678.45			−0.0861591
$725$	−4302.27	+	1770.17i	−0.220389	+	0.0906793i
$726$	1454.54			0.0743566
$727$			13516.6i			0.689549i	0.938686	+	0.344774i	$0.112045\pi$
$727$			13516.6i			0.689549i	−0.938686	+	0.344774i	$0.887955\pi$
$728$			66.6134i			0.00339129i
$729$	−729.000			−0.0370370
$730$	7725.42	+	39079.4i	0.391686	+	1.98136i
$731$	3175.66			0.160678
$732$		−	16681.7i		−	0.842315i
$733$		−	9310.89i		−	0.469175i	−0.972095	−	0.234588i	$-0.924626\pi$
$733$		−	9310.89i		−	0.469175i	0.972095	−	0.234588i	$-0.0753740\pi$
$734$	24034.3			1.20861
$735$	11432.8	−	2260.11i	0.573751	−	0.113422i
$736$	3276.80			0.164109
$737$			7662.21i			0.382959i
$738$		−	16046.6i		−	0.800382i
$739$	−14829.0			−0.738149			−0.369074	−	0.929400i	$-0.620325\pi$
$739$	−14829.0			−0.738149			−0.369074	+	0.929400i	$0.620325\pi$
$740$	−10823.1	+	2139.56i	−0.537654	+	0.106286i
$741$	−5053.44			−0.250530
$742$		−	36045.5i		−	1.78339i
$743$		−	7376.85i		−	0.364240i	−0.983276	−	0.182120i	$-0.941704\pi$
$743$		−	7376.85i		−	0.364240i	0.983276	−	0.182120i	$-0.0582960\pi$
$744$	20.4559			0.00100800
$745$	−4588.90	−	23213.1i	−0.225670	−	1.14156i
$746$	18840.5			0.924664
$747$			1042.59i			0.0510659i
$748$			7762.88i			0.379464i
$749$	50025.1			2.44042
$750$	9283.95	+	14001.5i	0.452002	+	0.681683i
$751$	−2568.19			−0.124786			−0.0623932	−	0.998052i	$-0.519873\pi$
$751$	−2568.19			−0.124786			−0.0623932	+	0.998052i	$0.519873\pi$
$752$		−	4989.49i		−	0.241952i
$753$			13251.2i			0.641300i
$754$	−1686.20			−0.0814427
$755$	7384.18	+	37353.2i	0.355944	+	1.80056i
$756$	5715.44			0.274958
$757$			24908.1i			1.19590i	0.801532	+	0.597952i	$0.204019\pi$
$757$			24908.1i			1.19590i	−0.801532	+	0.597952i	$0.795981\pi$
$758$			43213.7i			2.07070i
$759$	−421.684			−0.0201662
$760$	366.358	−	72.4236i	0.0174858	−	0.00345668i
$761$	33333.8			1.58784			0.793922	−	0.608020i	$-0.208036\pi$
$761$	33333.8			1.58784			0.793922	+	0.608020i	$0.208036\pi$
$762$			28777.2i			1.36809i
$763$			23508.5i			1.11542i
$764$	2613.54			0.123763
$765$	−8647.41	+	1709.47i	−0.408690	+	0.0807921i
$766$	21305.8			1.00497
$767$		−	4264.07i		−	0.200739i
$768$		−	12114.3i		−	0.569189i
$769$	27944.9			1.31043			0.655215	−	0.755443i	$-0.272578\pi$
$769$	27944.9			1.31043			0.655215	+	0.755443i	$0.272578\pi$
$770$	−2511.22	−	12703.1i	−0.117530	−	0.594530i
$771$	3147.72			0.147033
$772$		−	26378.9i		−	1.22979i
$773$		−	11831.3i		−	0.550510i	−0.961371	−	0.275255i	$-0.911238\pi$
$773$		−	11831.3i		−	0.550510i	0.961371	−	0.275255i	$-0.0887622\pi$
$774$	−1307.32			−0.0607113
$775$	3515.56	−	1446.48i	0.162945	−	0.0670440i
$776$	75.3586			0.00348610
$777$			9655.89i			0.445821i
$778$		−	42783.6i		−	1.97155i
$779$	−66289.5			−3.04887
$780$	592.496	+	2997.17i	0.0271984	+	0.137584i
$781$	−11161.2			−0.511370
$782$		−	4485.43i		−	0.205113i
$783$			1004.88i			0.0458638i
$784$	22080.7			1.00586
$785$	3228.41	−	638.210i	0.146786	−	0.0290174i
$786$	−28406.2			−1.28908
$787$		−	13469.7i		−	0.610092i	−0.952338	−	0.305046i	$-0.901328\pi$
$787$		−	13469.7i		−	0.610092i	0.952338	−	0.305046i	$-0.0986718\pi$
$788$			5178.57i			0.234110i
$789$	8321.77			0.375491
$790$	37719.2	−	7456.55i	1.69872	−	0.335813i
$791$	6.64146			0.000298537
$792$		−	22.1966i		−	0.000995860i
$793$		−	7804.50i		−	0.349490i
$794$	−35753.9			−1.59806
$795$	−2226.85	−	11264.6i	−0.0993437	−	0.502534i
$796$	−2582.04			−0.114972
$797$		−	897.262i		−	0.0398778i	−0.999801	−	0.0199389i	$-0.993653\pi$
$797$		−	897.262i		−	0.0398778i	0.999801	−	0.0199389i	$-0.00634718\pi$
$798$		−	47057.8i		−	2.08750i
$799$	−6877.95			−0.304536
$800$	12196.7	+	29643.2i	0.539024	+	1.31006i
$801$	4979.38			0.219648
$802$		−	12732.3i		−	0.560591i
$803$		−	9781.18i		−	0.429851i
$804$	16834.5			0.738440
$805$	728.026	+	3682.75i	0.0318752	+	0.161242i
$806$	1377.86			0.0602149
$807$		−	4937.69i		−	0.215384i
$808$		−	286.339i		−	0.0124671i
$809$	5655.30			0.245772			0.122886	−	0.992421i	$-0.460785\pi$
$809$	5655.30			0.245772			0.122886	+	0.992421i	$0.460785\pi$
$810$	3559.87	−	703.734i	0.154421	−	0.0305268i
$811$	9401.84			0.407082			0.203541	−	0.979066i	$-0.434755\pi$
$811$	9401.84			0.407082			0.203541	+	0.979066i	$0.434755\pi$
$812$		−	7878.34i		−	0.340487i
$813$			25798.7i			1.11292i
$814$	5399.00			0.232475
$815$	31563.4	−	6239.64i	1.35659	−	0.268178i
$816$	−16701.1			−0.716489
$817$			5400.63i			0.231266i
$818$			10057.1i			0.429875i
$819$	2673.95			0.114085
$820$	7772.19	+	39315.9i	0.330996	+	1.67436i
$821$	3692.36			0.156960			0.0784800	−	0.996916i	$-0.474993\pi$
$821$	3692.36			0.156960			0.0784800	+	0.996916i	$0.474993\pi$
$822$		−	2503.53i		−	0.106229i
$823$		−	26803.8i		−	1.13526i	−0.823282	−	0.567632i	$-0.807860\pi$
$823$		−	26803.8i		−	1.13526i	0.823282	−	0.567632i	$-0.192140\pi$
$824$	−241.165			−0.0101958
$825$	−1569.57	−	3814.72i	−0.0662368	−	0.160984i
$826$	39707.2			1.67263
$827$		−	11945.5i		−	0.502279i	−0.967951	−	0.251139i	$-0.919195\pi$
$827$		−	11945.5i		−	0.502279i	0.967951	−	0.251139i	$-0.0808052\pi$
$828$			926.472i			0.0388854i
$829$	−41215.0			−1.72673			−0.863364	−	0.504582i	$-0.831646\pi$
$829$	−41215.0			−1.72673			−0.863364	+	0.504582i	$0.831646\pi$
$830$	−1006.45	−	5091.18i	−0.0420897	−	0.212912i
$831$	11726.0			0.489496
$832$			5869.81i			0.244590i
$833$		−	30438.0i		−	1.26604i
$834$	7358.17			0.305507
$835$	27492.4	−	5434.86i	1.13942	−	0.225247i
$836$	−13201.8			−0.546165
$837$		−	821.126i		−	0.0339095i
$838$		−	37874.5i		−	1.56128i
$839$	−11797.4			−0.485447			−0.242724	−	0.970095i	$-0.578041\pi$
$839$	−11797.4			−0.485447			−0.242724	+	0.970095i	$0.578041\pi$
$840$	−193.853	+	38.3218i	−0.00796256	+	0.00157408i
$841$	−23003.8			−0.943206
$842$		−	7310.06i		−	0.299194i
$843$			5961.62i			0.243570i
$844$	41557.5			1.69487
$845$	−4486.40	−	22694.7i	−0.182647	−	0.923929i
$846$	2831.43			0.115067
$847$			3179.46i			0.128982i
$848$		−	21755.8i		−	0.881010i
$849$	−3689.01			−0.149124
$850$	40577.0	−	16695.4i	1.63739	−	0.673703i
$851$	−1565.22			−0.0630494
$852$			24522.1i			0.986048i
$853$			36817.4i			1.47785i	0.673789	+	0.738923i	$0.264666\pi$
$853$			36817.4i			1.47785i	−0.673789	+	0.738923i	$0.735334\pi$
$854$	72675.8			2.91208
$855$	−2907.18	−	14706.1i	−0.116285	−	0.588230i
$856$	−426.845			−0.0170435
$857$		−	42922.8i		−	1.71087i	−0.517911	−	0.855435i	$-0.673290\pi$
$857$		−	42922.8i		−	1.71087i	0.517911	−	0.855435i	$-0.326710\pi$
$858$		−	1495.11i		−	0.0594899i
$859$	−11693.5			−0.464468			−0.232234	−	0.972660i	$-0.574604\pi$
$859$	−11693.5			−0.464468			−0.232234	+	0.972660i	$0.574604\pi$
$860$	3203.08	−	633.203i	0.127005	−	0.0251070i
$861$	35076.1			1.38837
$862$			61496.5i			2.42991i
$863$		−	28640.1i		−	1.12969i	−0.825198	−	0.564844i	$-0.808936\pi$
$863$		−	28640.1i		−	1.12969i	0.825198	−	0.564844i	$-0.191064\pi$
$864$	6923.74			0.272628
$865$	−33916.4	+	6704.78i	−1.33317	+	0.263548i
$866$	20045.5			0.786574
$867$			8283.23i			0.324467i
$868$			6437.72i			0.251740i
$869$	−9440.76			−0.368534
$870$	−970.050	−	4907.03i	−0.0378020	−	0.191223i
$871$	7875.95			0.306391
$872$		−	200.589i		−	0.00778990i
$873$		−	3024.99i		−	0.117274i
$874$	7628.07			0.295221
$875$	−30605.8	+	20293.7i	−1.18247	+	0.784061i
$876$	−21490.0			−0.828859
$877$		−	19344.1i		−	0.744815i	−0.928069	−	0.372407i	$-0.878532\pi$
$877$		−	19344.1i		−	0.744815i	0.928069	−	0.372407i	$-0.121468\pi$
$878$			10012.1i			0.384844i
$879$	15201.7			0.583321
$880$	−1515.68	−	7667.14i	−0.0580610	−	0.293704i
$881$	24160.8			0.923949			0.461974	−	0.886893i	$-0.347141\pi$
$881$	24160.8			0.923949			0.461974	+	0.886893i	$0.347141\pi$
$882$			12530.3i			0.478366i
$883$			30965.1i			1.18014i	0.807354	+	0.590068i	$0.200899\pi$
$883$			30965.1i			1.18014i	−0.807354	+	0.590068i	$0.799101\pi$
$884$	7979.43			0.303594
$885$	12408.9	−	2453.07i	0.471324	−	0.0931739i
$886$	−12197.6			−0.462513
$887$			40432.5i			1.53054i	0.643709	+	0.765270i	$0.277395\pi$
$887$			40432.5i			1.53054i	−0.643709	+	0.765270i	$0.722605\pi$
$888$		−	82.3901i		−	0.00311355i
$889$	−62903.9			−2.37315
$890$	−24315.4	+	4806.80i	−0.915791	+	0.181039i
$891$	−891.000			−0.0335013
$892$			23753.1i			0.891606i
$893$		−	11696.9i		−	0.438321i
$894$	25441.5			0.951778
$895$	−7286.94	−	36861.3i	−0.272151	−	1.37669i
$896$	−754.083			−0.0281162
$897$			433.447i			0.0161342i
$898$		−	52831.7i		−	1.96327i
$899$	−1131.87			−0.0419910
$900$	−8381.24	+	3448.46i	−0.310416	+	0.127721i
$901$	−29990.1			−1.10889
$902$		−	19612.5i		−	0.723972i
$903$		−	2857.66i		−	0.105312i
$904$	−0.0566690			−2.08494e−6
$905$	−451.749	−	2285.19i	−0.0165930	−	0.0839363i
$906$	−40938.9			−1.50122
$907$		−	13270.3i		−	0.485814i	−0.970050	−	0.242907i	$-0.921899\pi$
$907$		−	13270.3i		−	0.485814i	0.970050	−	0.242907i	$-0.0781010\pi$
$908$		−	18376.6i		−	0.671639i
$909$	−11494.0			−0.419398
$910$	−13057.5	+	2581.27i	−0.475661	+	0.0940312i
$911$	43574.4			1.58472			0.792362	−	0.610051i	$-0.208851\pi$
$911$	43574.4			1.58472			0.792362	+	0.610051i	$0.208851\pi$
$912$		−	28402.4i		−	1.03125i
$913$			1274.27i			0.0461909i
$914$	−67872.7			−2.45627
$915$	22712.0	−	4489.83i	0.820584	−	0.162218i
$916$	29135.3			1.05093
$917$		−	62093.0i		−	2.23609i
$918$		−	9477.52i		−	0.340746i
$919$	−41317.7			−1.48307			−0.741537	−	0.670912i	$-0.765903\pi$
$919$	−41317.7			−1.48307			−0.741537	+	0.670912i	$0.765903\pi$
$920$	−6.21197	−	31.4235i	−0.000222611	−	0.00112609i
$921$	964.986			0.0345248
$922$			20791.9i			0.742674i
$923$			11472.6i			0.409128i
$924$	6985.53			0.248709
$925$	−5825.98	−	14159.6i	−0.207089	−	0.503314i
$926$	−60497.0			−2.14693
$927$			9680.66i			0.342993i
$928$		−	9543.90i		−	0.337601i
$929$	27886.3			0.984844			0.492422	−	0.870357i	$-0.336112\pi$
$929$	27886.3			0.984844			0.492422	+	0.870357i	$0.336112\pi$
$930$	792.667	+	4009.74i	0.0279490	+	0.141381i
$931$	51763.8			1.82222
$932$		−	36825.4i		−	1.29427i
$933$			15405.8i			0.540582i
$934$	−54483.8			−1.90874
$935$	−10569.1	+	2089.35i	−0.369674	+	0.0730792i
$936$	−22.8158			−0.000796749
$937$			16036.3i			0.559105i	0.960130	+	0.279553i	$0.0901862\pi$
$937$			16036.3i			0.559105i	−0.960130	+	0.279553i	$0.909814\pi$
$938$			73341.2i			2.55296i
$939$	25099.7			0.872308
$940$	−6937.35	+	1371.41i	−0.240714	+	0.0475857i
$941$	−1506.93			−0.0522046			−0.0261023	−	0.999659i	$-0.508310\pi$
$941$	−1506.93			−0.0522046			−0.0261023	+	0.999659i	$0.508310\pi$
$942$			3538.32i			0.122383i
$943$			5685.83i			0.196348i
$944$	23965.9			0.826294
$945$	1538.29	+	7781.49i	0.0529529	+	0.267865i
$946$	−1597.83			−0.0549154
$947$			7327.03i			0.251422i	0.992067	+	0.125711i	$0.0401212\pi$
$947$			7327.03i			0.251422i	−0.992067	+	0.125711i	$0.959879\pi$
$948$			20742.1i			0.710624i
$949$	−10054.0			−0.343907
$950$	28392.8	+	69006.5i	0.969666	+	2.35670i
$951$	−23233.8			−0.792228
$952$			516.099i			0.0175702i
$953$		−	46874.7i		−	1.59331i	−0.604437	−	0.796653i	$-0.706602\pi$
$953$		−	46874.7i		−	1.59331i	0.604437	−	0.796653i	$-0.293398\pi$
$954$	12346.0			0.418989
$955$	703.425	+	3558.30i	0.0238349	+	0.120570i
$956$	20267.7			0.685673
$957$			1228.18i			0.0414854i
$958$			27369.0i			0.923019i
$959$	5472.45			0.184270
$960$	−17081.8	+	3376.83i	−0.574284	+	0.113528i
$961$	−28866.1			−0.968954
$962$		−	5549.61i		−	0.185994i
$963$			17134.1i			0.573353i
$964$	−42900.8			−1.43334
$965$	35914.6	−	7099.79i	1.19806	−	0.236840i
$966$	−4036.28			−0.134436
$967$		−	2812.90i		−	0.0935437i	−0.998906	−	0.0467719i	$-0.985107\pi$
$967$		−	2812.90i		−	0.0935437i	0.998906	−	0.0467719i	$-0.0148934\pi$
$968$		−	27.1292i		−	0.000900790i
$969$	−39152.4			−1.29799
$970$	2920.15	+	14771.7i	0.0966602	+	0.488959i
$971$	−45216.4			−1.49440			−0.747200	−	0.664599i	$-0.768602\pi$
$971$	−45216.4			−1.49440			−0.747200	+	0.664599i	$0.768602\pi$
$972$			1957.60i			0.0645987i
$973$			16084.2i			0.529944i
$974$	3054.59			0.100488
$975$	−3921.14	+	1613.35i	−0.128797	+	0.0529935i
$976$	43864.5			1.43859
$977$			10647.0i			0.348647i	0.984688	+	0.174323i	$0.0557738\pi$
$977$			10647.0i			0.348647i	−0.984688	+	0.174323i	$0.944226\pi$
$978$			34593.4i			1.13106i
$979$	6085.91			0.198679
$980$	−6069.11	−	30700.8i	−0.197827	−	1.00072i
$981$	−8051.89			−0.262056
$982$			5923.23i			0.192483i
$983$		−	1993.76i		−	0.0646909i	−0.999477	−	0.0323455i	$-0.989702\pi$
$983$		−	1993.76i		−	0.0646909i	0.999477	−	0.0323455i	$-0.0102977\pi$
$984$	−299.291			−0.00969618
$985$	−7050.56	+	1393.79i	−0.228071	+	0.0450863i
$986$	−13064.1			−0.421954
$987$			6189.22i			0.199600i
$988$			13570.1i			0.436966i
$989$	463.226			0.0148936
$990$	4350.95	−	860.119i	0.139679	−	0.0276125i
$991$	−23143.6			−0.741858			−0.370929	−	0.928661i	$-0.620961\pi$
$991$	−23143.6			−0.741858			−0.370929	+	0.928661i	$0.620961\pi$
$992$			7798.71i			0.249606i
$993$		−	604.279i		−	0.0193114i
$994$	−106833.			−3.40899
$995$	−694.946	−	3515.41i	−0.0221420	−	0.112006i
$996$	2799.68			0.0890674
$997$			3506.68i			0.111392i	0.998448	+	0.0556959i	$0.0177377\pi$
$997$			3506.68i			0.111392i	−0.998448	+	0.0556959i	$0.982262\pi$
$998$			44426.1i			1.40910i
$999$	−3307.24			−0.104741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.c.a.34.11	yes	14
3.2	odd	2		495.4.c.c.199.4		14
5.2	odd	4		825.4.a.bb.1.2		7
5.3	odd	4		825.4.a.bc.1.6		7
5.4	even	2	inner	165.4.c.a.34.4	✓	14
15.2	even	4		2475.4.a.br.1.6		7
15.8	even	4		2475.4.a.bq.1.2		7
15.14	odd	2		495.4.c.c.199.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.a.34.4	✓	14	5.4	even	2	inner
165.4.c.a.34.11	yes	14	1.1	even	1	trivial
495.4.c.c.199.4		14	3.2	odd	2
495.4.c.c.199.11		14	15.14	odd	2
825.4.a.bb.1.2		7	5.2	odd	4
825.4.a.bc.1.6		7	5.3	odd	4
2475.4.a.bq.1.2		7	15.8	even	4
2475.4.a.br.1.6		7	15.2	even	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.00699i q^{2} -3.00000i q^{3} -8.05595 q^{4} +(-2.16823 - 10.9681i) q^{5} +12.0210 q^{6} +26.2766i q^{7} -0.224208i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+4.00699i q^{2} -3.00000i q^{3} -8.05595 q^{4} +(-2.16823 - 10.9681i) q^{5} +12.0210 q^{6} +26.2766i q^{7} -0.224208i q^{8} -9.00000 q^{9} +(43.9490 - 8.68807i) q^{10} -11.0000 q^{11} +24.1679i q^{12} +11.3069i q^{13} -105.290 q^{14} +(-32.9042 + 6.50469i) q^{15} -63.5492 q^{16} +87.6018i q^{17} -36.0629i q^{18} -148.978 q^{19} +(17.4672 + 88.3583i) q^{20} +78.8297 q^{21} -44.0769i q^{22} +12.7783i q^{23} -0.672624 q^{24} +(-115.598 + 47.5627i) q^{25} -45.3065 q^{26} +27.0000i q^{27} -211.683i q^{28} +37.2177 q^{29} +(-26.0642 - 131.847i) q^{30} -30.4121 q^{31} -256.435i q^{32} +33.0000i q^{33} -351.019 q^{34} +(288.204 - 56.9737i) q^{35} +72.5036 q^{36} +122.491i q^{37} -596.955i q^{38} +33.9206 q^{39} +(-2.45913 + 0.486135i) q^{40} +444.960 q^{41} +315.870i q^{42} -36.2510i q^{43} +88.6155 q^{44} +(19.5141 + 98.7127i) q^{45} -51.2025 q^{46} +78.5138i q^{47} +190.648i q^{48} -347.458 q^{49} +(-190.583 - 463.198i) q^{50} +262.805 q^{51} -91.0876i q^{52} +342.345i q^{53} -108.189 q^{54} +(23.8505 + 120.649i) q^{55} +5.89142 q^{56} +446.935i q^{57} +149.131i q^{58} -377.123 q^{59} +(265.075 - 52.4015i) q^{60} -690.244 q^{61} -121.861i q^{62} -236.489i q^{63} +519.137 q^{64} +(124.015 - 24.5159i) q^{65} -132.231 q^{66} -696.564i q^{67} -705.716i q^{68} +38.3349 q^{69} +(228.293 + 1154.83i) q^{70} +1014.66 q^{71} +2.01787i q^{72} +889.198i q^{73} -490.818 q^{74} +(142.688 + 346.793i) q^{75} +1200.16 q^{76} -289.042i q^{77} +135.919i q^{78} +858.251 q^{79} +(137.789 + 697.013i) q^{80} +81.0000 q^{81} +1782.95i q^{82} -115.843i q^{83} -635.048 q^{84} +(960.824 - 189.941i) q^{85} +145.257 q^{86} -111.653i q^{87} +2.46629i q^{88} -553.264 q^{89} +(-395.541 + 78.1927i) q^{90} -297.106 q^{91} -102.941i q^{92} +91.2363i q^{93} -314.604 q^{94} +(323.020 + 1634.01i) q^{95} -769.304 q^{96} +336.110i q^{97} -1392.26i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9}+O(q^{10}) \) 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9	\( 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9} - 28 q^{10} - 154 q^{11} - 284 q^{14} + 362 q^{16} - 52 q^{19} + 226 q^{20} + 300 q^{21} - 126 q^{24} - 366 q^{25} + 952 q^{26} - 1144 q^{29} - 582 q^{30} - 280 q^{31} + 1612 q^{34} - 600 q^{35} + 738 q^{36} - 144 q^{39} + 176 q^{40} + 1792 q^{41} + 902 q^{44} + 126 q^{45} - 688 q^{46} - 590 q^{49} + 388 q^{50} + 228 q^{51} - 162 q^{54} + 154 q^{55} + 3044 q^{56} - 2632 q^{59} - 1140 q^{60} - 772 q^{61} - 1738 q^{64} - 904 q^{65} - 198 q^{66} - 1368 q^{69} + 84 q^{70} + 1608 q^{71} + 1496 q^{74} - 300 q^{75} - 3396 q^{76} + 748 q^{79} - 2606 q^{80} + 1134 q^{81} - 5040 q^{84} + 2508 q^{85} - 5068 q^{86} - 1388 q^{89} + 252 q^{90} - 6752 q^{91} + 5840 q^{94} + 1724 q^{95} + 5946 q^{96} + 1386 q^{99}+O(q^{100}) \) 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9 - 28 * q^10 - 154 * q^11 - 284 * q^14 + 362 * q^16 - 52 * q^19 + 226 * q^20 + 300 * q^21 - 126 * q^24 - 366 * q^25 + 952 * q^26 - 1144 * q^29 - 582 * q^30 - 280 * q^31 + 1612 * q^34 - 600 * q^35 + 738 * q^36 - 144 * q^39 + 176 * q^40 + 1792 * q^41 + 902 * q^44 + 126 * q^45 - 688 * q^46 - 590 * q^49 + 388 * q^50 + 228 * q^51 - 162 * q^54 + 154 * q^55 + 3044 * q^56 - 2632 * q^59 - 1140 * q^60 - 772 * q^61 - 1738 * q^64 - 904 * q^65 - 198 * q^66 - 1368 * q^69 + 84 * q^70 + 1608 * q^71 + 1496 * q^74 - 300 * q^75 - 3396 * q^76 + 748 * q^79 - 2606 * q^80 + 1134 * q^81 - 5040 * q^84 + 2508 * q^85 - 5068 * q^86 - 1388 * q^89 + 252 * q^90 - 6752 * q^91 + 5840 * q^94 + 1724 * q^95 + 5946 * q^96 + 1386 * q^99

Introduction

L-functions

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