LMFDB - Embedded newform 35.5.c.e.34.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(34,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("35.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.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:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$8$
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} + 110x^{6} + 7113x^{4} + 190880x^{2} + 4177936 $ x^8 + 110x^6 + 7113x^4 + 190880*x^2 + 4177936
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.1
Root			$-3.16228 - 7.21587i$ of defining polynomial
Character	$\chi$	$=$	35.34
Dual form			35.5.c.e.34.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.21587i q^{2} -9.48683 q^{3} -36.0688 q^{4} +(22.2447 + 11.4093i) q^{5} +68.4558i q^{6} +(-36.4750 - 32.7197i) q^{7} +144.814i q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-7.21587i q^{2} -9.48683 q^{3} -36.0688 q^{4} +(22.2447 + 11.4093i) q^{5} +68.4558i q^{6} +(-36.4750 - 32.7197i) q^{7} +144.814i q^{8} +9.00000 q^{9} +(82.3280 - 160.515i) q^{10} +40.4128 q^{11} +342.179 q^{12} -222.012 q^{13} +(-236.101 + 263.199i) q^{14} +(-211.032 - 108.238i) q^{15} +467.858 q^{16} -227.249 q^{17} -64.9428i q^{18} -180.979i q^{19} +(-802.341 - 411.520i) q^{20} +(346.032 + 310.406i) q^{21} -291.614i q^{22} -1005.49i q^{23} -1373.83i q^{24} +(364.656 + 507.593i) q^{25} +1602.01i q^{26} +683.052 q^{27} +(1315.61 + 1180.16i) q^{28} +50.2752 q^{29} +(-781.032 + 1522.78i) q^{30} -1284.12i q^{31} -1058.98i q^{32} -383.390 q^{33} +1639.80i q^{34} +(-438.068 - 1143.99i) q^{35} -324.619 q^{36} +312.534i q^{37} -1305.92 q^{38} +2106.19 q^{39} +(-1652.22 + 3221.35i) q^{40} -1028.41i q^{41} +(2239.85 - 2496.92i) q^{42} +2040.07i q^{43} -1457.64 q^{44} +(200.203 + 102.684i) q^{45} -7255.48 q^{46} -794.384 q^{47} -4438.49 q^{48} +(259.848 + 2386.90i) q^{49} +(3662.73 - 2631.31i) q^{50} +2155.87 q^{51} +8007.71 q^{52} +1042.06i q^{53} -4928.82i q^{54} +(898.972 + 461.082i) q^{55} +(4738.26 - 5282.08i) q^{56} +1716.92i q^{57} -362.779i q^{58} +1298.25i q^{59} +(7611.67 + 3904.02i) q^{60} -4523.52i q^{61} -9266.05 q^{62} +(-328.275 - 294.477i) q^{63} -155.730 q^{64} +(-4938.60 - 2533.00i) q^{65} +2766.49i q^{66} -4839.37i q^{67} +8196.59 q^{68} +9538.90i q^{69} +(-8254.91 + 3161.04i) q^{70} -4932.66 q^{71} +1303.33i q^{72} +1959.68 q^{73} +2255.20 q^{74} +(-3459.43 - 4815.45i) q^{75} +6527.69i q^{76} +(-1474.06 - 1322.29i) q^{77} -15198.0i q^{78} +1894.04 q^{79} +(10407.4 + 5337.93i) q^{80} -7209.00 q^{81} -7420.85 q^{82} +77.7515 q^{83} +(-12481.0 - 11196.0i) q^{84} +(-5055.09 - 2592.75i) q^{85} +14720.9 q^{86} -476.953 q^{87} +5852.34i q^{88} -320.922i q^{89} +(740.952 - 1444.64i) q^{90} +(8097.89 + 7264.16i) q^{91} +36266.8i q^{92} +12182.2i q^{93} +5732.18i q^{94} +(2064.84 - 4025.82i) q^{95} +10046.4i q^{96} +12653.8 q^{97} +(17223.5 - 1875.03i) q^{98} +363.715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 172 q^{4} + 72 q^{9}+O(q^{10}) $ 8 * q - 172 * q^4 + 72 * q^9	$ 8 q - 172 q^{4} + 72 q^{9} - 376 q^{11} - 24 q^{14} + 60 q^{15} + 596 q^{16} + 1020 q^{21} + 3500 q^{25} - 64 q^{29} - 4500 q^{30} - 4160 q^{35} - 1548 q^{36} + 6360 q^{39} - 2104 q^{44} - 28440 q^{46} - 7828 q^{49} + 7740 q^{50} + 24240 q^{51} + 27300 q^{56} + 24180 q^{60} - 5092 q^{64} - 24940 q^{65} - 10620 q^{70} - 18016 q^{71} + 39720 q^{74} - 8624 q^{79} - 57672 q^{81} - 47400 q^{84} + 19000 q^{85} + 18000 q^{86} + 34480 q^{91} + 25260 q^{95} - 3384 q^{99}+O(q^{100}) $ 8 * q - 172 * q^4 + 72 * q^9 - 376 * q^11 - 24 * q^14 + 60 * q^15 + 596 * q^16 + 1020 * q^21 + 3500 * q^25 - 64 * q^29 - 4500 * q^30 - 4160 * q^35 - 1548 * q^36 + 6360 * q^39 - 2104 * q^44 - 28440 * q^46 - 7828 * q^49 + 7740 * q^50 + 24240 * q^51 + 27300 * q^56 + 24180 * q^60 - 5092 * q^64 - 24940 * q^65 - 10620 * q^70 - 18016 * q^71 + 39720 * q^74 - 8624 * q^79 - 57672 * q^81 - 47400 * q^84 + 19000 * q^85 + 18000 * q^86 + 34480 * q^91 + 25260 * q^95 - 3384 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	7.21587i		−	1.80397i	−0.431770	−	0.901984i	$-0.642111\pi$
$2$		−	7.21587i		−	1.80397i	0.431770	−	0.901984i	$-0.357889\pi$
$3$	−9.48683			−1.05409			−0.527046	−	0.849837i	$-0.676701\pi$
$3$	−9.48683			−1.05409			−0.527046	+	0.849837i	$0.676701\pi$
$4$	−36.0688			−2.25430
$5$	22.2447	+	11.4093i	0.889789	+	0.456372i
$5$	22.2447	+	11.4093i	0.889789	+	0.456372i
$6$			68.4558i			1.90155i
$7$	−36.4750	−	32.7197i	−0.744387	−	0.667748i
$7$	−36.4750	−	32.7197i	−0.744387	−	0.667748i
$8$			144.814i			2.26272i
$9$	9.00000			0.111111
$10$	82.3280	−	160.515i	0.823280	−	1.60515i
$11$	40.4128			0.333990			0.166995	−	0.985958i	$-0.446594\pi$
$11$	40.4128			0.333990			0.166995	+	0.985958i	$0.446594\pi$
$12$	342.179			2.37624
$13$	−222.012			−1.31368			−0.656841	−	0.754029i	$-0.728108\pi$
$13$	−222.012			−1.31368			−0.656841	+	0.754029i	$0.728108\pi$
$14$	−236.101	+	263.199i	−1.20460	+	1.34285i
$15$	−211.032	−	108.238i	−0.937920	−	0.481058i
$16$	467.858			1.82757
$17$	−227.249			−0.786328			−0.393164	−	0.919468i	$-0.628620\pi$
$17$	−227.249			−0.786328			−0.393164	+	0.919468i	$0.628620\pi$
$18$		−	64.9428i		−	0.200441i
$19$		−	180.979i		−	0.501326i	−0.968074	−	0.250663i	$-0.919351\pi$
$19$		−	180.979i		−	0.501326i	0.968074	−	0.250663i	$-0.0806486\pi$
$20$	−802.341	−	411.520i	−2.00585	−	1.02880i
$21$	346.032	+	310.406i	0.784653	+	0.703868i
$22$		−	291.614i		−	0.602508i
$23$		−	1005.49i		−	1.90073i	−0.311131	−	0.950367i	$-0.600708\pi$
$23$		−	1005.49i		−	1.90073i	0.311131	−	0.950367i	$-0.399292\pi$
$24$		−	1373.83i		−	2.38511i
$25$	364.656	+	507.593i	0.583450	+	0.812149i
$26$			1602.01i			2.36984i
$27$	683.052			0.936971
$28$	1315.61	+	1180.16i	1.67807	+	1.50530i
$29$	50.2752			0.0597803			0.0298901	−	0.999553i	$-0.490484\pi$
$29$	50.2752			0.0597803			0.0298901	+	0.999553i	$0.490484\pi$
$30$	−781.032	+	1522.78i	−0.867813	+	1.69198i
$31$		−	1284.12i		−	1.33623i	−0.744056	−	0.668117i	$-0.767101\pi$
$31$		−	1284.12i		−	1.33623i	0.744056	−	0.668117i	$-0.232899\pi$
$32$		−	1058.98i		−	1.03416i
$33$	−383.390			−0.352057
$34$			1639.80i			1.41851i
$35$	−438.068	−	1143.99i	−0.357606	−	0.933872i
$36$	−324.619			−0.250478
$37$			312.534i			0.228293i	0.993464	+	0.114147i	$0.0364134\pi$
$37$			312.534i			0.228293i	−0.993464	+	0.114147i	$0.963587\pi$
$38$	−1305.92			−0.904376
$39$	2106.19			1.38474
$40$	−1652.22	+	3221.35i	−1.03264	+	2.01334i
$41$		−	1028.41i		−	0.611783i	−0.952066	−	0.305891i	$-0.901046\pi$
$41$		−	1028.41i		−	0.611783i	0.952066	−	0.305891i	$-0.0989544\pi$
$42$	2239.85	−	2496.92i	1.26976	−	1.41549i
$43$			2040.07i			1.10334i	0.834063	+	0.551669i	$0.186009\pi$
$43$			2040.07i			1.10334i	−0.834063	+	0.551669i	$0.813991\pi$
$44$	−1457.64			−0.752914
$45$	200.203	+	102.684i	0.0988655	+	0.0507080i
$46$	−7255.48			−3.42886
$47$	−794.384			−0.359613			−0.179806	−	0.983702i	$-0.557547\pi$
$47$	−794.384			−0.359613			−0.179806	+	0.983702i	$0.557547\pi$
$48$	−4438.49			−1.92643
$49$	259.848	+	2386.90i	0.108225	+	0.994126i
$50$	3662.73	−	2631.31i	1.46509	−	1.05252i
$51$	2155.87			0.828863
$52$	8007.71			2.96143
$53$			1042.06i			0.370973i	0.982647	+	0.185487i	$0.0593862\pi$
$53$			1042.06i			0.370973i	−0.982647	+	0.185487i	$0.940614\pi$
$54$		−	4928.82i		−	1.69027i
$55$	898.972	+	461.082i	0.297181	+	0.152424i
$56$	4738.26	−	5282.08i	1.51093	−	1.68434i
$57$			1716.92i			0.528444i
$58$		−	362.779i		−	0.107842i
$59$			1298.25i			0.372953i	0.982459	+	0.186477i	$0.0597069\pi$
$59$			1298.25i			0.372953i	−0.982459	+	0.186477i	$0.940293\pi$
$60$	7611.67	+	3904.02i	2.11435	+	1.08445i
$61$		−	4523.52i		−	1.21567i	−0.794062	−	0.607837i	$-0.792037\pi$
$61$		−	4523.52i		−	1.21567i	0.794062	−	0.607837i	$-0.207963\pi$
$62$	−9266.05			−2.41052
$63$	−328.275	−	294.477i	−0.0827097	−	0.0741942i
$64$	−155.730			−0.0380199
$65$	−4938.60	−	2533.00i	−1.16890	−	0.599527i
$66$			2766.49i			0.635099i
$67$		−	4839.37i		−	1.07805i	−0.842290	−	0.539025i	$-0.818793\pi$
$67$		−	4839.37i		−	1.07805i	0.842290	−	0.539025i	$-0.181207\pi$
$68$	8196.59			1.77262
$69$			9538.90i			2.00355i
$70$	−8254.91	+	3161.04i	−1.68468	+	0.645110i
$71$	−4932.66			−0.978508			−0.489254	−	0.872141i	$-0.662731\pi$
$71$	−4932.66			−0.978508			−0.489254	+	0.872141i	$0.662731\pi$
$72$			1303.33i			0.251413i
$73$	1959.68			0.367739			0.183870	−	0.982951i	$-0.441138\pi$
$73$	1959.68			0.367739			0.183870	+	0.982951i	$0.441138\pi$
$74$	2255.20			0.411834
$75$	−3459.43	−	4815.45i	−0.615010	−	0.856081i
$76$			6527.69i			1.13014i
$77$	−1474.06	−	1322.29i	−0.248618	−	0.223021i
$78$		−	15198.0i		−	2.49803i
$79$	1894.04			0.303483			0.151741	−	0.988420i	$-0.451512\pi$
$79$	1894.04			0.303483			0.151741	+	0.988420i	$0.451512\pi$
$80$	10407.4	+	5337.93i	1.62615	+	0.834051i
$81$	−7209.00			−1.09877
$82$	−7420.85			−1.10364
$83$	77.7515			0.0112863			0.00564316	−	0.999984i	$-0.498204\pi$
$83$	77.7515			0.0112863			0.00564316	+	0.999984i	$0.498204\pi$
$84$	−12481.0	−	11196.0i	−1.76884	−	1.58673i
$85$	−5055.09	−	2592.75i	−0.699666	−	0.358858i
$86$	14720.9			1.99039
$87$	−476.953			−0.0630139
$88$			5852.34i			0.755725i
$89$		−	320.922i		−	0.0405154i	−0.999795	−	0.0202577i	$-0.993551\pi$
$89$		−	320.922i		−	0.0405154i	0.999795	−	0.0202577i	$-0.00644866\pi$
$90$	740.952	−	1444.64i	0.0914756	−	0.178350i
$91$	8097.89	+	7264.16i	0.977888	+	0.877208i
$92$			36266.8i			4.28483i
$93$			12182.2i			1.40851i
$94$			5732.18i			0.648730i
$95$	2064.84	−	4025.82i	0.228791	−	0.446075i
$96$			10046.4i			1.09010i
$97$	12653.8			1.34487			0.672433	−	0.740158i	$-0.265249\pi$
$97$	12653.8			1.34487			0.672433	+	0.740158i	$0.265249\pi$
$98$	17223.5	−	1875.03i	1.79337	−	0.195234i
$99$	363.715			0.0371100
$100$	−13152.7	−	18308.3i	−1.31527	−	1.83083i
$101$			7257.88i			0.711487i	0.934584	+	0.355744i	$0.115772\pi$
$101$			7257.88i			0.711487i	−0.934584	+	0.355744i	$0.884228\pi$
$102$		−	15556.5i		−	1.49524i
$103$	−16301.2			−1.53654			−0.768271	−	0.640125i	$-0.778883\pi$
$103$	−16301.2			−1.53654			−0.768271	+	0.640125i	$0.778883\pi$
$104$		−	32150.4i		−	2.97249i
$105$	4155.88	+	10852.9i	0.376950	+	0.984388i
$106$	7519.40			0.669224
$107$			2830.84i			0.247256i	0.992329	+	0.123628i	$0.0394530\pi$
$107$			2830.84i			0.247256i	−0.992329	+	0.123628i	$0.960547\pi$
$108$	−24636.9			−2.11221
$109$	6579.49			0.553783			0.276891	−	0.960901i	$-0.410696\pi$
$109$	6579.49			0.553783			0.276891	+	0.960901i	$0.410696\pi$
$110$	3327.11	−	6486.87i	0.274967	−	0.536105i
$111$		−	2964.95i		−	0.240642i
$112$	−17065.1	−	15308.1i	−1.36042	−	1.22036i
$113$		−	8682.94i		−	0.680002i	−0.940425	−	0.340001i	$-0.889573\pi$
$113$		−	8682.94i		−	0.680002i	0.940425	−	0.340001i	$-0.110427\pi$
$114$	12389.0			0.953296
$115$	11471.9	−	22366.8i	0.867442	−	1.69125i
$116$	−1813.37			−0.134763
$117$	−1998.11			−0.145965
$118$	9368.01			0.672796
$119$	8288.90	+	7435.50i	0.585333	+	0.525069i
$120$	15674.4	−	30560.4i	1.08850	−	2.12225i
$121$	−13007.8			−0.888451
$122$	−32641.2			−2.19304
$123$			9756.32i			0.644875i
$124$			46316.7i			3.01227i
$125$	2320.39	+	15451.7i	0.148505	+	0.988912i
$126$	−2124.91	+	2368.79i	−0.133844	+	0.149206i
$127$			12770.0i			0.791742i	0.918306	+	0.395871i	$0.129557\pi$
$127$			12770.0i			0.791742i	−0.918306	+	0.395871i	$0.870443\pi$
$128$		−	15819.9i		−	0.965572i
$129$		−	19353.8i		−	1.16302i
$130$	−18277.8	+	35636.3i	−1.08153	+	2.10866i
$131$		−	21652.4i		−	1.26172i	−0.775895	−	0.630862i	$-0.782702\pi$
$131$		−	21652.4i		−	1.26172i	0.775895	−	0.630862i	$-0.217298\pi$
$132$	13828.4			0.793641
$133$	−5921.56	+	6601.20i	−0.334760	+	0.373181i
$134$	−34920.3			−1.94477
$135$	15194.3	+	7793.14i	0.833707	+	0.427607i
$136$		−	32908.8i		−	1.77924i
$137$		−	7038.86i		−	0.375026i	−0.982262	−	0.187513i	$-0.939957\pi$
$137$		−	7038.86i		−	0.375026i	0.982262	−	0.187513i	$-0.0600426\pi$
$138$	68831.5			3.61434
$139$			4008.01i			0.207443i	0.994606	+	0.103721i	$0.0330751\pi$
$139$			4008.01i			0.207443i	−0.994606	+	0.103721i	$0.966925\pi$
$140$	15800.6	+	41262.5i	0.806152	+	2.10523i
$141$	7536.19			0.379065
$142$			35593.4i			1.76520i
$143$	−8972.14			−0.438757
$144$	4210.72			0.203063
$145$	1118.36	+	573.605i	0.0531918	+	0.0272820i
$146$		−	14140.8i		−	0.663390i
$147$	−2465.14	−	22644.1i	−0.114079	−	1.04790i
$148$		−	11272.7i		−	0.514642i
$149$	−1042.33			−0.0469499			−0.0234750	−	0.999724i	$-0.507473\pi$
$149$	−1042.33			−0.0469499			−0.0234750	+	0.999724i	$0.507473\pi$
$150$	−34747.7	+	24962.8i	−1.54434	+	1.10946i
$151$	18103.3			0.793968			0.396984	−	0.917826i	$-0.370057\pi$
$151$	18103.3			0.793968			0.396984	+	0.917826i	$0.370057\pi$
$152$	26208.2			1.13436
$153$	−2045.24			−0.0873698
$154$	−9541.50	+	10636.6i	−0.402323	+	0.448499i
$155$	14650.9	−	28564.9i	0.609820	−	1.18897i
$156$	−75967.8			−3.12162
$157$	29215.7			1.18527			0.592635	−	0.805471i	$-0.298088\pi$
$157$	29215.7			1.18527			0.592635	+	0.805471i	$0.298088\pi$
$158$		−	13667.1i		−	0.547473i
$159$		−	9885.89i		−	0.391040i
$160$	12082.2	−	23556.7i	0.471961	−	0.920183i
$161$	−32899.2	+	36675.2i	−1.26921	+	1.41488i
$162$			52019.2i			1.98214i
$163$		−	36678.2i		−	1.38049i	−0.723576	−	0.690245i	$-0.757503\pi$
$163$		−	36678.2i		−	1.38049i	0.723576	−	0.690245i	$-0.242497\pi$
$164$			37093.4i			1.37914i
$165$	−8528.40	−	4374.21i	−0.313256	−	0.160669i
$166$		−	561.045i		−	0.0203602i
$167$	−22317.8			−0.800238			−0.400119	−	0.916463i	$-0.631031\pi$
$167$	−22317.8			−0.800238			−0.400119	+	0.916463i	$0.631031\pi$
$168$	−44951.1	+	50110.2i	−1.59265	+	1.77545i
$169$	20728.4			0.725759
$170$	−18708.9	+	36476.9i	−0.647368	+	1.26218i
$171$		−	1628.81i		−	0.0557029i
$172$		−	73582.9i		−	2.48725i
$173$	−44748.9			−1.49517			−0.747585	−	0.664166i	$-0.768787\pi$
$173$	−44748.9			−1.49517			−0.747585	+	0.664166i	$0.768787\pi$
$174$			3441.63i			0.113675i
$175$	3307.46	−	30445.9i	0.107999	−	0.994151i
$176$	18907.4			0.610390
$177$		−	12316.3i		−	0.393127i
$178$	−2315.73			−0.0730884
$179$	−45407.4			−1.41716			−0.708582	−	0.705628i	$-0.750665\pi$
$179$	−45407.4			−1.41716			−0.708582	+	0.705628i	$0.750665\pi$
$180$	−7221.07	−	3703.68i	−0.222872	−	0.114311i
$181$		−	25934.8i		−	0.791636i	−0.918329	−	0.395818i	$-0.870461\pi$
$181$		−	25934.8i		−	0.791636i	0.918329	−	0.395818i	$-0.129539\pi$
$182$	52417.3	−	58433.3i	1.58246	−	1.76408i
$183$			42913.9i			1.28143i
$184$	145609.			4.30082
$185$	−3565.79	+	6952.23i	−0.104187	+	0.203133i
$186$	87905.5			2.54091
$187$	−9183.77			−0.262626
$188$	28652.5			0.810675
$189$	−24914.3	−	22349.2i	−0.697469	−	0.625661i
$190$	−29049.8	−	14899.6i	−0.804704	−	0.412732i
$191$	11732.3			0.321599			0.160800	−	0.986987i	$-0.448593\pi$
$191$	11732.3			0.321599			0.160800	+	0.986987i	$0.448593\pi$
$192$	1477.38			0.0400765
$193$			62664.1i			1.68230i	0.540799	+	0.841152i	$0.318122\pi$
$193$			62664.1i			1.68230i	−0.540799	+	0.841152i	$0.681878\pi$
$194$		−	91308.5i		−	2.42609i
$195$	46851.7	+	24030.2i	1.23213	+	0.631957i
$196$	−9372.41	−	86092.5i	−0.243972	−	2.24106i
$197$		−	15049.3i		−	0.387779i	−0.981023	−	0.193889i	$-0.937890\pi$
$197$		−	15049.3i		−	0.387779i	0.981023	−	0.193889i	$-0.0621103\pi$
$198$		−	2624.52i		−	0.0669453i
$199$		−	14742.7i		−	0.372281i	−0.982523	−	0.186141i	$-0.940402\pi$
$199$		−	14742.7i		−	0.372281i	0.982523	−	0.186141i	$-0.0595980\pi$
$200$	−73506.6	+	52807.3i	−1.83766	+	1.32018i
$201$			45910.3i			1.13636i
$202$	52371.9			1.28350
$203$	−1833.79	−	1644.99i	−0.0444997	−	0.0399182i
$204$	−77759.7			−1.86851
$205$	11733.4	−	22876.6i	0.279200	−	0.544358i
$206$			117627.i			2.77187i
$207$		−	9049.40i		−	0.211193i
$208$	−103870.			−2.40084
$209$		−	7313.86i		−	0.167438i
$210$	78313.0	−	29988.3i	1.77580	−	0.680006i
$211$	17553.8			0.394281			0.197140	−	0.980375i	$-0.436835\pi$
$211$	17553.8			0.394281			0.197140	+	0.980375i	$0.436835\pi$
$212$		−	37586.0i		−	0.836285i
$213$	46795.3			1.03144
$214$	20427.0			0.446043
$215$	−23275.8	+	45380.8i	−0.503532	+	0.981738i
$216$			98915.4i			2.12010i
$217$	−42016.0	+	46838.3i	−0.892268	+	0.994676i
$218$		−	47476.8i		−	0.999006i
$219$	−18591.2			−0.387631
$220$	−32424.8	−	16630.7i	−0.669935	−	0.343609i
$221$	50452.0			1.03298
$222$	−21394.7			−0.434111
$223$	23623.6			0.475047			0.237524	−	0.971382i	$-0.423664\pi$
$223$	23623.6			0.475047			0.237524	+	0.971382i	$0.423664\pi$
$224$	−34649.4	+	38626.2i	−0.690557	+	0.769815i
$225$	3281.90	+	4568.34i	0.0648277	+	0.0902388i
$226$	−62655.0			−1.22670
$227$	62724.9			1.21727			0.608637	−	0.793449i	$-0.291716\pi$
$227$	62724.9			1.21727			0.608637	+	0.793449i	$0.291716\pi$
$228$		−	61927.1i		−	1.19127i
$229$		−	19079.6i		−	0.363830i	−0.983314	−	0.181915i	$-0.941770\pi$
$229$		−	19079.6i		−	0.363830i	0.983314	−	0.181915i	$-0.0582295\pi$
$230$	−161396.	−	82779.9i	−3.05097	−	1.56484i
$231$	13984.1	+	12544.4i	0.262066	+	0.235085i
$232$			7280.55i			0.135266i
$233$			30436.7i			0.560642i	0.959906	+	0.280321i	$0.0904408\pi$
$233$			30436.7i			0.560642i	−0.959906	+	0.280321i	$0.909559\pi$
$234$			14418.1i			0.263315i
$235$	−17670.9	−	9063.37i	−0.319979	−	0.164117i
$236$		−	46826.3i		−	0.840749i
$237$	−17968.4			−0.319899
$238$	53653.6	−	59811.6i	0.947208	−	1.05592i
$239$	−77595.8			−1.35845			−0.679223	−	0.733932i	$-0.737683\pi$
$239$	−77595.8			−1.35845			−0.679223	+	0.733932i	$0.737683\pi$
$240$	−98733.0	−	50640.0i	−1.71411	−	0.879167i
$241$			33220.0i			0.571960i	0.958236	+	0.285980i	$0.0923191\pi$
$241$			33220.0i			0.571960i	−0.958236	+	0.285980i	$0.907681\pi$
$242$			93862.6i			1.60274i
$243$	13063.4			0.221229
$244$			163158.i			2.74049i
$245$	−21452.6	+	56060.6i	−0.357394	+	0.933954i
$246$	70400.4			1.16333
$247$			40179.5i			0.658583i
$248$	185959.			3.02352
$249$	−737.616			−0.0118968
$250$	111498.	−	16743.6i	1.78396	−	0.267898i
$251$		−	102561.i		−	1.62793i	−0.580914	−	0.813965i	$-0.697305\pi$
$251$		−	102561.i		−	1.62793i	0.580914	−	0.813965i	$-0.302695\pi$
$252$	11840.5	+	10621.4i	0.186452	+	0.167256i
$253$		−	40634.6i		−	0.634827i
$254$	92146.8			1.42828
$255$	47956.8	+	24597.0i	0.737513	+	0.378270i
$256$	−116646.			−1.77988
$257$	98512.0			1.49150			0.745749	−	0.666227i	$-0.232092\pi$
$257$	98512.0			1.49150			0.745749	+	0.666227i	$0.232092\pi$
$258$	−139655.			−2.09805
$259$	10226.0	−	11399.7i	0.152442	−	0.169939i
$260$	178129.	+	91362.4i	2.63505	+	1.35151i
$261$	452.477			0.00664225
$262$	−156241.			−2.27611
$263$			20107.9i			0.290707i	0.989380	+	0.145353i	$0.0464319\pi$
$263$			20107.9i			0.290707i	−0.989380	+	0.145353i	$0.953568\pi$
$264$		−	55520.1i		−	0.796604i
$265$	−11889.2	+	23180.4i	−0.169302	+	0.330088i
$266$	47633.4	+	42729.2i	0.673206	+	0.603896i
$267$			3044.54i			0.0427069i
$268$			174550.i			2.43025i
$269$		−	69131.7i		−	0.955373i	−0.878530	−	0.477686i	$-0.841475\pi$
$269$		−	69131.7i		−	0.955373i	0.878530	−	0.477686i	$-0.158525\pi$
$270$	56234.3	−	109640.i	0.771390	−	1.50398i
$271$			57410.7i			0.781726i	0.920449	+	0.390863i	$0.127823\pi$
$271$			57410.7i			0.781726i	−0.920449	+	0.390863i	$0.872177\pi$
$272$	−106320.			−1.43707
$273$	−76823.3	−	68913.9i	−1.03078	−	0.924659i
$274$	−50791.5			−0.676534
$275$	14736.8	+	20513.3i	0.194866	+	0.271250i
$276$		−	344057.i		−	4.51660i
$277$		−	103442.i		−	1.34815i	−0.738665	−	0.674073i	$-0.764543\pi$
$277$		−	103442.i		−	1.34815i	0.738665	−	0.674073i	$-0.235457\pi$
$278$	28921.3			0.374220
$279$		−	11557.1i		−	0.148470i
$280$	165666.	−	63438.3i	2.11309	−	0.809162i
$281$	−34831.4			−0.441122			−0.220561	−	0.975373i	$-0.570789\pi$
$281$	−34831.4			−0.441122			−0.220561	+	0.975373i	$0.570789\pi$
$282$		−	54380.2i		−	0.683821i
$283$	−52532.0			−0.655920			−0.327960	−	0.944692i	$-0.606361\pi$
$283$	−52532.0			−0.655920			−0.327960	+	0.944692i	$0.606361\pi$
$284$	177915.			2.20585
$285$	−19588.8	+	38192.3i	−0.241167	+	0.470204i
$286$			64741.8i			0.791503i
$287$	−33649.1	+	37511.1i	−0.408517	+	0.455403i
$288$		−	9530.81i		−	0.114907i
$289$	−31879.0			−0.381688
$290$	4139.06	−	8069.93i	0.0492159	−	0.0959564i
$291$	−120045.			−1.41761
$292$	−70683.4			−0.828994
$293$	−41519.3			−0.483632			−0.241816	−	0.970322i	$-0.577743\pi$
$293$	−41519.3			−0.483632			−0.241816	+	0.970322i	$0.577743\pi$
$294$	−163397.	+	17788.1i	−1.89038	+	0.205795i
$295$	−14812.1	+	28879.2i	−0.170205	+	0.331850i
$296$	−45259.2			−0.516563
$297$	27604.1			0.312939
$298$			7521.35i			0.0846961i
$299$			223231.i			2.49696i
$300$	124778.	+	173688.i	1.38642	+	1.92986i
$301$	66750.4	−	74411.6i	0.736752	−	0.821311i
$302$		−	130631.i		−	1.43229i
$303$		−	68854.3i		−	0.749973i
$304$		−	84672.3i		−	0.916208i
$305$	51610.2	−	100625.i	0.554799	−	1.08169i
$306$			14758.2i			0.157612i
$307$	−90825.2			−0.963673			−0.481836	−	0.876261i	$-0.660030\pi$
$307$	−90825.2			−0.963673			−0.481836	+	0.876261i	$0.660030\pi$
$308$	53167.5	+	47693.5i	0.560460	+	0.502757i
$309$	154647.			1.61966
$310$	−206121.	−	105719.i	−2.14486	−	1.10009i
$311$			17745.1i			0.183467i	0.995784	+	0.0917335i	$0.0292408\pi$
$311$			17745.1i			0.183467i	−0.995784	+	0.0917335i	$0.970759\pi$
$312$			305006.i			3.13328i
$313$	−2438.59			−0.0248915			−0.0124457	−	0.999923i	$-0.503962\pi$
$313$	−2438.59			−0.0248915			−0.0124457	+	0.999923i	$0.503962\pi$
$314$		−	210817.i		−	2.13819i
$315$	−3942.61	−	10295.9i	−0.0397340	−	0.103764i
$316$	−68315.6			−0.684141
$317$			20302.5i			0.202037i	0.994885	+	0.101018i	$0.0322101\pi$
$317$			20302.5i			0.202037i	−0.994885	+	0.101018i	$0.967790\pi$
$318$	−71335.3			−0.705424
$319$	2031.76			0.0199660
$320$	−3464.16	−	1776.76i	−0.0338297	−	0.0173512i
$321$		−	26855.7i		−	0.260631i
$322$	264643.	+	237397.i	2.55240	+	2.28962i
$323$			41127.2i			0.394207i
$324$	260020.			2.47695
$325$	−80958.1	−	112692.i	−0.766467	−	1.06691i
$326$	−264665.			−2.49036
$327$	−62418.5			−0.583738
$328$	148928.			1.38429
$329$	28975.2	+	25992.0i	0.267691	+	0.240131i
$330$	−31563.7	+	61539.8i	−0.289841	+	0.565104i
$331$	128190.			1.17003			0.585015	−	0.811022i	$-0.301088\pi$
$331$	128190.			1.17003			0.585015	+	0.811022i	$0.301088\pi$
$332$	−2804.40			−0.0254428
$333$			2812.80i			0.0253659i
$334$			161043.i			1.44360i
$335$	55213.8	−	107650.i	0.491992	−	0.959237i
$336$	161894.	+	145226.i	1.43401	+	1.28637i
$337$		−	111674.i		−	0.983314i	−0.870789	−	0.491657i	$-0.836391\pi$
$337$		−	111674.i		−	0.983314i	0.870789	−	0.491657i	$-0.163609\pi$
$338$		−	149573.i		−	1.30925i
$339$			82373.6i			0.716785i
$340$	182331.	+	93517.4i	1.57726	+	0.808974i
$341$		−	51894.9i		−	0.446289i
$342$	−11753.3			−0.100486
$343$	68620.5	−	95564.2i	0.583265	−	0.812282i
$344$	−295431.			−2.49654
$345$	−108832.	+	212190.i	−0.914364	+	1.78274i
$346$			322903.i			2.69724i
$347$			188238.i			1.56333i	0.623701	+	0.781663i	$0.285628\pi$
$347$			188238.i			1.56333i	−0.623701	+	0.781663i	$0.714372\pi$
$348$	17203.1			0.142052
$349$		−	128703.i		−	1.05667i	−0.849036	−	0.528335i	$-0.822817\pi$
$349$		−	128703.i		−	1.05667i	0.849036	−	0.528335i	$-0.177183\pi$
$350$	−219694.	−	23866.2i	−1.79342	−	0.194826i
$351$	−151646.			−1.23088
$352$		−	42796.3i		−	0.345399i
$353$	161707.			1.29771			0.648857	−	0.760910i	$-0.275247\pi$
$353$	161707.			1.29771			0.648857	+	0.760910i	$0.275247\pi$
$354$	−88872.7			−0.709189
$355$	−109726.	−	56278.2i	−0.870666	−	0.446564i
$356$			11575.3i			0.0913338i
$357$	−78635.4	−	70539.4i	−0.616995	−	0.553471i
$358$			327654.i			2.55652i
$359$	−1212.72			−0.00940965			−0.00470482	−	0.999989i	$-0.501498\pi$
$359$	−1212.72			−0.00940965			−0.00470482	+	0.999989i	$0.501498\pi$
$360$	−14870.0	+	28992.1i	−0.114738	+	0.223705i
$361$	97567.7			0.748672
$362$	−187142.			−1.42809
$363$	123403.			0.936509
$364$	−292081.	−	262010.i	−2.20445	−	1.97749i
$365$	43592.6	+	22358.6i	0.327210	+	0.167826i
$366$	309661.			2.31166
$367$	5671.18			0.0421057			0.0210529	−	0.999778i	$-0.493298\pi$
$367$	5671.18			0.0421057			0.0210529	+	0.999778i	$0.493298\pi$
$368$		−	470425.i		−	3.47372i
$369$		−	9255.66i		−	0.0679758i
$370$	50166.4	+	25730.3i	0.366445	+	0.187949i
$371$	34096.0	−	38009.3i	0.247717	−	0.276148i
$372$		−	439399.i		−	3.17521i
$373$		−	205082.i		−	1.47404i	−0.675868	−	0.737022i	$-0.736231\pi$
$373$		−	205082.i		−	1.47404i	0.675868	−	0.737022i	$-0.263769\pi$
$374$			66268.9i			0.473769i
$375$	−22013.2	−	146588.i	−0.156538	−	1.04240i
$376$		−	115038.i		−	0.813702i
$377$	−11161.7			−0.0785322
$378$	−161269.	+	179778.i	−1.12867	+	1.25821i
$379$	21930.2			0.152673			0.0763367	−	0.997082i	$-0.475678\pi$
$379$	21930.2			0.152673			0.0763367	+	0.997082i	$0.475678\pi$
$380$	−74476.3	+	145207.i	−0.515764	+	1.00559i
$381$		−	121147.i		−	0.834570i
$382$		−	84658.5i		−	0.580155i
$383$	109992.			0.749830			0.374915	−	0.927059i	$-0.377672\pi$
$383$	109992.			0.749830			0.374915	+	0.927059i	$0.377672\pi$
$384$			150081.i			1.01780i
$385$	−17703.6	−	46232.0i	−0.119437	−	0.311904i
$386$	452176.			3.03482
$387$			18360.6i			0.122593i
$388$	−456409.			−3.03173
$389$	291930.			1.92921			0.964604	−	0.263703i	$-0.0849440\pi$
$389$	291930.			1.92921			0.964604	+	0.263703i	$0.0849440\pi$
$390$	173399.	−	338076.i	1.14003	−	2.22272i
$391$			228496.i			1.49460i
$392$	−345656.	+	37629.6i	−2.24943	+	0.244883i
$393$			205413.i			1.32997i
$394$	−108594.			−0.699541
$395$	42132.3	+	21609.6i	0.270036	+	0.138501i
$396$	−13118.8			−0.0836571
$397$	289165.			1.83470			0.917350	−	0.398081i	$-0.130324\pi$
$397$	289165.			1.83470			0.917350	+	0.398081i	$0.130324\pi$
$398$	−106381.			−0.671583
$399$	56176.9	−	62624.4i	0.352868	−	0.393367i
$400$	170607.	+	237481.i	1.06629	+	1.48426i
$401$	−183963.			−1.14404			−0.572021	−	0.820239i	$-0.693841\pi$
$401$	−183963.			−1.14404			−0.572021	+	0.820239i	$0.693841\pi$
$402$	331283.			2.04997
$403$			285090.i			1.75539i
$404$		−	261783.i		−	1.60391i
$405$	−160362.	−	82249.6i	−0.977670	−	0.501446i
$406$	−11870.0	+	13232.4i	−0.0720111	+	0.0802760i
$407$			12630.4i			0.0762478i
$408$			312200.i			1.87548i
$409$			239846.i			1.43379i	0.697180	+	0.716896i	$0.254438\pi$
$409$			239846.i			1.43379i	−0.697180	+	0.716896i	$0.745562\pi$
$410$	−165075.	−	84666.7i	−0.982003	−	0.503668i
$411$			66776.4i			0.395312i
$412$	587964.			3.46383
$413$	42478.3	−	47353.7i	0.249039	−	0.277622i
$414$	−65299.3			−0.380985
$415$	1729.56	+	887.090i	0.0100425	+	0.00515076i
$416$			235106.i			1.35855i
$417$		−	38023.3i		−	0.218664i
$418$	−52775.9			−0.302053
$419$			109133.i			0.621627i	0.950471	+	0.310813i	$0.100601\pi$
$419$			109133.i			0.621627i	−0.950471	+	0.310813i	$0.899399\pi$
$420$	−149897.	−	391450.i	−0.849759	−	2.21911i
$421$	−96025.3			−0.541778			−0.270889	−	0.962611i	$-0.587318\pi$
$421$	−96025.3			−0.541778			−0.270889	+	0.962611i	$0.587318\pi$
$422$		−	126666.i		−	0.711270i
$423$	−7149.46			−0.0399570
$424$	−150905.			−0.839408
$425$	−82867.7	−	115350.i	−0.458783	−	0.638616i
$426$		−	337669.i		−	1.86068i
$427$	−148008.	+	164995.i	−0.811764	+	0.904932i
$428$		−	102105.i		−	0.557390i
$429$	85117.2			0.462490
$430$	327462.	+	167955.i	1.77102	+	0.908356i
$431$	−65006.1			−0.349945			−0.174972	−	0.984573i	$-0.555984\pi$
$431$	−65006.1			−0.349945			−0.174972	+	0.984573i	$0.555984\pi$
$432$	319571.			1.71238
$433$	−48797.7			−0.260270			−0.130135	−	0.991496i	$-0.541541\pi$
$433$	−48797.7			−0.260270			−0.130135	+	0.991496i	$0.541541\pi$
$434$	337979.	+	303182.i	1.79436	+	1.60962i
$435$	−10609.7	−	5441.69i	−0.0560691	−	0.0287578i
$436$	−237314.			−1.24839
$437$	−181972.			−0.952888
$438$			134152.i			0.699274i
$439$		−	199253.i		−	1.03390i	−0.856017	−	0.516948i	$-0.827068\pi$
$439$		−	199253.i		−	1.03390i	0.856017	−	0.516948i	$-0.172932\pi$
$440$	−66771.0	+	130184.i	−0.344892	+	0.672436i
$441$	2338.63	+	21482.1i	0.0120250	+	0.110458i
$442$		−	364055.i		−	1.86347i
$443$		−	222968.i		−	1.13615i	−0.822978	−	0.568074i	$-0.807689\pi$
$443$		−	222968.i		−	1.13615i	0.822978	−	0.568074i	$-0.192311\pi$
$444$			106942.i			0.542480i
$445$	3661.50	−	7138.83i	0.0184901	−	0.0360501i
$446$		−	170465.i		−	0.856970i
$447$	9888.46			0.0494895
$448$	5680.23	+	5095.42i	0.0283015	+	0.0253877i
$449$	−199767.			−0.990904			−0.495452	−	0.868635i	$-0.664998\pi$
$449$	−199767.			−0.990904			−0.495452	+	0.868635i	$0.664998\pi$
$450$	32964.6	−	23681.8i	0.162788	−	0.116947i
$451$		−	41560.8i		−	0.204329i
$452$			313183.i			1.53293i
$453$	−171743.			−0.836916
$454$		−	452615.i		−	2.19592i
$455$	97256.4	+	253981.i	0.469781	+	1.22681i
$456$	−248633.			−1.19572
$457$		−	22806.0i		−	0.109198i	−0.998508	−	0.0545992i	$-0.982612\pi$
$457$		−	22806.0i		−	0.109198i	0.998508	−	0.0545992i	$-0.0173881\pi$
$458$	−137676.			−0.656337
$459$	−155223.			−0.736767
$460$	−413778.	+	806744.i	−1.95547	+	3.81259i
$461$			196170.i			0.923063i	0.887124	+	0.461531i	$0.152700\pi$
$461$			196170.i			0.923063i	−0.887124	+	0.461531i	$0.847300\pi$
$462$	90518.6	−	100908.i	0.424086	−	0.472759i
$463$		−	314624.i		−	1.46767i	−0.679325	−	0.733837i	$-0.737727\pi$
$463$		−	314624.i		−	1.46767i	0.679325	−	0.733837i	$-0.262273\pi$
$464$	23521.6			0.109253
$465$	−138991.	+	270991.i	−0.642806	+	1.25328i
$466$	219627.			1.01138
$467$	−160539.			−0.736117			−0.368059	−	0.929803i	$-0.619977\pi$
$467$	−160539.			−0.736117			−0.368059	+	0.929803i	$0.619977\pi$
$468$	72069.4			0.329048
$469$	−158342.	+	176516.i	−0.719866	+	0.802487i
$470$	−65400.1	+	127511.i	−0.296062	+	0.577233i
$471$	−277165.			−1.24938
$472$	−188005.			−0.843888
$473$			82445.0i			0.368504i
$474$			129658.i			0.577087i
$475$	91863.6	−	65995.0i	0.407152	−	0.292499i
$476$	−298971.	−	268190.i	−1.31952	−	1.18366i
$477$			9378.58i			0.0412193i
$478$			559921.i			2.45059i
$479$		−	153599.i		−	0.669449i	−0.942316	−	0.334725i	$-0.891357\pi$
$479$		−	153599.i		−	0.669449i	0.942316	−	0.334725i	$-0.108643\pi$
$480$	−114622.	+	223478.i	−0.497490	+	0.969958i
$481$		−	69386.3i		−	0.299905i
$482$	239711.			1.03180
$483$	312110.	−	347931.i	1.33787	−	1.49142i
$484$	469176.			2.00283
$485$	281481.	+	144371.i	1.19665	+	0.613759i
$486$		−	94263.6i		−	0.399091i
$487$		−	192371.i		−	0.811112i	−0.914070	−	0.405556i	$-0.867078\pi$
$487$		−	192371.i		−	0.811112i	0.914070	−	0.405556i	$-0.132922\pi$
$488$	655069.			2.75073
$489$			347960.i			1.45516i
$490$	404526.	+	154799.i	1.68482	+	0.644727i
$491$	59857.4			0.248287			0.124144	−	0.992264i	$-0.460382\pi$
$491$	59857.4			0.248287			0.124144	+	0.992264i	$0.460382\pi$
$492$		−	351899.i		−	1.45374i
$493$	−11425.0			−0.0470069
$494$	289930.			1.18806
$495$	8090.75	+	4149.74i	0.0330201	+	0.0169360i
$496$		−	600786.i		−	2.44206i
$497$	179919.	+	161395.i	0.728389	+	0.653397i
$498$			5322.54i			0.0214615i
$499$	182889.			0.734493			0.367247	−	0.930124i	$-0.380301\pi$
$499$	182889.			0.734493			0.367247	+	0.930124i	$0.380301\pi$
$500$	−83693.8	−	557326.i	−0.334775	−	2.22930i
$501$	211726.			0.843525
$502$	−740069.			−2.93673
$503$	213254.			0.842870			0.421435	−	0.906859i	$-0.361526\pi$
$503$	213254.			0.842870			0.421435	+	0.906859i	$0.361526\pi$
$504$	42644.3	−	47538.8i	0.167881	−	0.187149i
$505$	−82807.3	+	161450.i	−0.324703	+	0.633074i
$506$	−293214.			−1.14521
$507$	−196647.			−0.765017
$508$		−	460599.i		−	1.78482i
$509$		−	157233.i		−	0.606887i	−0.952849	−	0.303443i	$-0.901864\pi$
$509$		−	157233.i		−	0.606887i	0.952849	−	0.303443i	$-0.0981363\pi$
$510$	177489.	−	346050.i	0.682386	−	1.33045i
$511$	−71479.4	−	64120.1i	−0.273740	−	0.245557i
$512$			588586.i			2.24528i
$513$		−	123618.i		−	0.469728i
$514$		−	710850.i		−	2.69062i
$515$	−362615.	−	185985.i	−1.36720	−	0.701234i
$516$			698069.i			2.62180i
$517$	−32103.3			−0.120107
$518$	−82258.5	−	73789.5i	−0.306564	−	0.275001i
$519$	424526.			1.57605
$520$	366814.	−	715178.i	1.35656	−	2.64489i
$521$		−	320071.i		−	1.17916i	−0.807712	−	0.589578i	$-0.799294\pi$
$521$		−	320071.i		−	1.17916i	0.807712	−	0.589578i	$-0.200706\pi$
$522$		−	3265.02i		−	0.0119824i
$523$	−138391.			−0.505947			−0.252974	−	0.967473i	$-0.581409\pi$
$523$	−138391.			−0.505947			−0.252974	+	0.967473i	$0.581409\pi$
$524$			780977.i			2.84430i
$525$	−31377.3	+	288835.i	−0.113841	+	1.04793i
$526$	145096.			0.524426
$527$			291815.i			1.05072i
$528$	−179372.			−0.643408
$529$	−731166.			−2.61279
$530$	167267.	+	85791.1i	0.595468	+	0.305415i
$531$			11684.3i			0.0414393i
$532$	213584.	−	238097.i	0.754649	−	0.841262i
$533$			228319.i			0.803687i
$534$	21969.0			0.0770420
$535$	−32297.9	+	62971.2i	−0.112841	+	0.220006i
$536$	700808.			2.43932
$537$	430772.			1.49382
$538$	−498846.			−1.72346
$539$	10501.2	+	96461.2i	0.0361461	+	0.332028i
$540$	−548040.	−	281089.i	−1.87943	−	0.963955i
$541$	313055.			1.06961			0.534806	−	0.844975i	$-0.320385\pi$
$541$	313055.			1.06961			0.534806	+	0.844975i	$0.320385\pi$
$542$	414268.			1.41021
$543$			246039.i			0.834458i
$544$			240652.i			0.813188i
$545$	146359.	+	75067.4i	0.492750	+	0.252731i
$546$	−497274.	+	554347.i	−1.66805	+	1.85950i
$547$			127776.i			0.427046i	0.976938	+	0.213523i	$0.0684939\pi$
$547$			127776.i			0.427046i	−0.976938	+	0.213523i	$0.931506\pi$
$548$			253883.i			0.845420i
$549$		−	40711.7i		−	0.135075i
$550$	148021.	−	106339.i	0.489326	−	0.351533i
$551$		−	9098.74i		−	0.0299694i
$552$	−1.38137e6			−4.53347
$553$	−69084.9	−	61972.2i	−0.225909	−	0.202650i
$554$	−746423.			−2.43201
$555$	33828.0	−	65954.6i	0.109822	−	0.214121i
$556$		−	144564.i		−	0.467639i
$557$		−	512709.i		−	1.65257i	−0.563249	−	0.826287i	$-0.690449\pi$
$557$		−	512709.i		−	1.65257i	0.563249	−	0.826287i	$-0.309551\pi$
$558$	−83394.5			−0.267836
$559$		−	452921.i		−	1.44943i
$560$	−204953.	−	535226.i	−0.653550	−	1.70672i
$561$	87124.8			0.276832
$562$			251339.i			0.795769i
$563$	−505215.			−1.59390			−0.796948	−	0.604048i	$-0.793553\pi$
$563$	−505215.			−1.59390			−0.796948	+	0.604048i	$0.793553\pi$
$564$	−271821.			−0.854526
$565$	99066.3	−	193150.i	0.310334	−	0.605058i
$566$			379064.i			1.18326i
$567$	262948.	+	235876.i	0.817907	+	0.733699i
$568$		−	714318.i		−	2.21409i
$569$	−279119.			−0.862115			−0.431057	−	0.902325i	$-0.641859\pi$
$569$	−279119.			−0.862115			−0.431057	+	0.902325i	$0.641859\pi$
$570$	275591.	+	141350.i	0.848233	+	0.435058i
$571$	596534.			1.82963			0.914814	−	0.403875i	$-0.132337\pi$
$571$	596534.			1.82963			0.914814	+	0.403875i	$0.132337\pi$
$572$	323614.			0.989089
$573$	−111302.			−0.338995
$574$	270675.	+	242808.i	0.821533	+	0.736951i
$575$	510379.	−	366657.i	1.54368	−	1.10898i
$576$	−1401.57			−0.00422443
$577$	350643.			1.05321			0.526604	−	0.850111i	$-0.323465\pi$
$577$	350643.			1.05321			0.526604	+	0.850111i	$0.323465\pi$
$578$			230034.i			0.688553i
$579$		−	594484.i		−	1.77330i
$580$	−40337.8	−	20689.2i	−0.119910	−	0.0615019i
$581$	−2835.98	−	2544.00i	−0.00840140	−	0.00753642i
$582$			866228.i			2.55733i
$583$			42112.8i			0.123901i
$584$			283789.i			0.832090i
$585$	−44447.4	−	22797.0i	−0.129878	−	0.0666141i
$586$			299598.i			0.872456i
$587$	−252470.			−0.732712			−0.366356	−	0.930475i	$-0.619395\pi$
$587$	−252470.			−0.732712			−0.366356	+	0.930475i	$0.619395\pi$
$588$	88914.5	+	816746.i	0.257169	+	2.36228i
$589$	−232399.			−0.669889
$590$	208389.	+	106882.i	0.598646	+	0.307045i
$591$			142770.i			0.408755i
$592$			146221.i			0.417222i
$593$	546727.			1.55475			0.777376	−	0.629036i	$-0.216550\pi$
$593$	546727.			1.55475			0.777376	+	0.629036i	$0.216550\pi$
$594$		−	199187.i		−	0.564532i
$595$	99550.4	+	259971.i	0.281196	+	0.734330i
$596$	37595.8			0.105839
$597$			139862.i			0.392419i
$598$	1.61080e6			4.50443
$599$	393929.			1.09791			0.548953	−	0.835853i	$-0.315027\pi$
$599$	393929.			1.09791			0.548953	+	0.835853i	$0.315027\pi$
$600$	697345.	−	500974.i	1.93707	−	1.39159i
$601$			631861.i			1.74933i	0.484724	+	0.874667i	$0.338920\pi$
$601$			631861.i			1.74933i	−0.484724	+	0.874667i	$0.661080\pi$
$602$	−536944.	−	481663.i	−1.48162	−	1.32908i
$603$		−	43554.3i		−	0.119783i
$604$	−652963.			−1.78984
$605$	−289355.	−	148410.i	−0.790534	−	0.405464i
$606$	−496844.			−1.35293
$607$	−539383.			−1.46393			−0.731964	−	0.681343i	$-0.761396\pi$
$607$	−539383.			−1.46393			−0.731964	+	0.681343i	$0.761396\pi$
$608$	−191653.			−0.518451
$609$	17396.8	+	15605.7i	0.0469068	+	0.0420774i
$610$	−726094.	−	372413.i	−1.95134	−	1.00084i
$611$	176363.			0.472416
$612$	73769.3			0.196958
$613$			681417.i			1.81339i	0.421783	+	0.906697i	$0.361404\pi$
$613$			681417.i			1.81339i	−0.421783	+	0.906697i	$0.638596\pi$
$614$			655383.i			1.73843i
$615$	−111313.	+	217027.i	−0.294303	+	0.573803i
$616$	191486.	−	213464.i	0.504634	−	0.562552i
$617$		−	396221.i		−	1.04080i	−0.853923	−	0.520399i	$-0.825783\pi$
$617$		−	396221.i		−	1.04080i	0.853923	−	0.520399i	$-0.174217\pi$
$618$		−	1.11591e6i		−	2.92181i
$619$			80430.5i			0.209913i	0.994477	+	0.104957i	$0.0334704\pi$
$619$			80430.5i			0.209913i	−0.994477	+	0.104957i	$0.966530\pi$
$620$	−528441.	+	1.03030e6i	−1.37472	+	2.68029i
$621$		−	686801.i		−	1.78093i
$622$	128047.			0.330969
$623$	−10500.5	+	11705.6i	−0.0270541	+	0.0301591i
$624$	985398.			2.53071
$625$	−124677.	+	370194.i	−0.319173	+	0.947696i
$626$			17596.6i			0.0449034i
$627$			69385.4i			0.176495i
$628$	−1.05378e6			−2.67195
$629$		−	71022.9i		−	0.179514i
$630$	−74294.2	+	28449.4i	−0.187186	+	0.0716789i
$631$	−41636.8			−0.104573			−0.0522863	−	0.998632i	$-0.516651\pi$
$631$	−41636.8			−0.104573			−0.0522863	+	0.998632i	$0.516651\pi$
$632$			274283.i			0.686696i
$633$	−166530.			−0.415609
$634$	146500.			0.364468
$635$	−145697.	+	284065.i	−0.361329	+	0.704484i
$636$			356572.i			0.881522i
$637$	−57689.5	−	529920.i	−0.142173	−	1.30597i
$638$		−	14660.9i		−	0.0360181i
$639$	−44393.9			−0.108723
$640$	180494.	−	351910.i	0.440660	−	0.859155i
$641$	−302758.			−0.736852			−0.368426	−	0.929657i	$-0.620103\pi$
$641$	−302758.			−0.736852			−0.368426	+	0.929657i	$0.620103\pi$
$642$	−193787.			−0.470170
$643$	531006.			1.28433			0.642166	−	0.766565i	$-0.278036\pi$
$643$	531006.			1.28433			0.642166	+	0.766565i	$0.278036\pi$
$644$	1.18664e6	−	1.32283e6i	2.86118	−	3.18957i
$645$	220813.	−	430520.i	0.530770	−	1.03484i
$646$	296769.			0.711137
$647$	−732226.			−1.74919			−0.874594	−	0.484856i	$-0.838872\pi$
$647$	−732226.			−1.74919			−0.874594	+	0.484856i	$0.838872\pi$
$648$		−	1.04396e6i		−	2.48620i
$649$			52466.0i			0.124563i
$650$	−813170.	+	584183.i	−1.92466	+	1.38268i
$651$	398599.	−	444347.i	0.940533	−	1.04848i
$652$			1.32294e6i			3.11204i
$653$		−	687602.i		−	1.61254i	−0.591548	−	0.806270i	$-0.701483\pi$
$653$		−	687602.i		−	1.61254i	0.591548	−	0.806270i	$-0.298517\pi$
$654$			450404.i			1.05305i
$655$	247039.	−	481653.i	0.575815	−	1.12267i
$656$		−	481148.i		−	1.11807i
$657$	17637.1			0.0408599
$658$	187555.	−	209081.i	0.433188	−	0.482906i
$659$	−210169.			−0.483947			−0.241973	−	0.970283i	$-0.577795\pi$
$659$	−210169.			−0.483947			−0.241973	+	0.970283i	$0.577795\pi$
$660$	307609.	+	157772.i	0.706173	+	0.362195i
$661$			803833.i			1.83977i	0.392193	+	0.919883i	$0.371717\pi$
$661$			803833.i			1.83977i	−0.392193	+	0.919883i	$0.628283\pi$
$662$		−	925001.i		−	2.11070i
$663$	−478630.			−1.08886
$664$			11259.5i			0.0255378i
$665$	−207039.	+	79281.0i	−0.468175	+	0.179277i
$666$	20296.8			0.0457593
$667$		−	50551.1i		−	0.113626i
$668$	804978.			1.80398
$669$	−224113.			−0.500744
$670$	−776792.	−	398415.i	−1.73043	−	0.887537i
$671$		−	182808.i		−	0.406023i
$672$	328713.	−	366440.i	0.727911	−	0.811456i
$673$			269226.i			0.594412i	0.954813	+	0.297206i	$0.0960548\pi$
$673$			269226.i			0.594412i	−0.954813	+	0.297206i	$0.903945\pi$
$674$	−805825.			−1.77387
$675$	249079.	+	346713.i	0.546675	+	0.760961i
$676$	−747648.			−1.63608
$677$	364515.			0.795313			0.397657	−	0.917534i	$-0.369824\pi$
$677$	364515.			0.795313			0.397657	+	0.917534i	$0.369824\pi$
$678$	594398.			1.29306
$679$	−461548.	−	414029.i	−1.00110	−	0.898031i
$680$	375466.	−	732047.i	0.811994	−	1.58315i
$681$	−595061.			−1.28312
$682$	−374467.			−0.805091
$683$			243356.i			0.521676i	0.965383	+	0.260838i	$0.0839988\pi$
$683$			243356.i			0.521676i	−0.965383	+	0.260838i	$0.916001\pi$
$684$			58749.2i			0.125571i
$685$	80308.4	−	156577.i	0.171151	−	0.333694i
$686$	−689579.	−	495157.i	−1.46533	−	1.05219i
$687$			181005.i			0.383510i
$688$			954463.i			2.01643i
$689$		−	231351.i		−	0.487341i
$690$	1.53114e6	+	785319.i	3.21600	+	1.64948i
$691$			68635.1i			0.143744i	0.997414	+	0.0718721i	$0.0228973\pi$
$691$			68635.1i			0.143744i	−0.997414	+	0.0718721i	$0.977103\pi$
$692$	1.61404e6			3.37056
$693$	−13266.5	−	11900.6i	−0.0276242	−	0.0247801i
$694$	1.35830e6			2.82019
$695$	−45728.5	+	89157.0i	−0.0946711	+	0.184581i
$696$		−	69069.4i		−	0.142583i
$697$			233704.i			0.481062i
$698$	−928708.			−1.90620
$699$		−	288748.i		−	0.590968i
$700$	−119296.	+	1.09815e6i	−0.243462	+	2.24111i
$701$	−604095.			−1.22933			−0.614666	−	0.788787i	$-0.710709\pi$
$701$	−604095.			−1.22933			−0.614666	+	0.788787i	$0.710709\pi$
$702$			1.09426e6i			2.22047i
$703$	56562.0			0.114449
$704$	−6293.47			−0.0126983
$705$	167641.	+	85982.6i	0.337288	+	0.172995i
$706$		−	1.16686e6i		−	2.34104i
$707$	237475.	−	264731.i	0.475094	−	0.529622i
$708$			444234.i			0.886227i
$709$	261511.			0.520232			0.260116	−	0.965577i	$-0.416239\pi$
$709$	261511.			0.520232			0.260116	+	0.965577i	$0.416239\pi$
$710$	−406096.	+	791766.i	−0.805586	+	1.57065i
$711$	17046.3			0.0337203
$712$	46474.0			0.0916748
$713$	−1.29117e6			−2.53983
$714$	−509003.	+	567423.i	−0.998445	+	1.11304i
$715$	−199583.	−	102366.i	−0.390401	−	0.200236i
$716$	1.63779e6			3.19471
$717$	736138.			1.43193
$718$			8750.86i			0.0169747i
$719$			961341.i			1.85960i	0.368064	+	0.929800i	$0.380021\pi$
$719$			961341.i			1.85960i	−0.368064	+	0.929800i	$0.619979\pi$
$720$	93666.3	+	48041.3i	0.180683	+	0.0926723i
$721$	594585.	+	533369.i	1.14378	+	1.02602i
$722$		−	704036.i		−	1.35058i
$723$		−	315153.i		−	0.602899i
$724$			935437.i			1.78459i
$725$	18333.2	+	25519.4i	0.0348788	+	0.0485505i
$726$		−	890459.i		−	1.68943i
$727$	342294.			0.647635			0.323818	−	0.946120i	$-0.395034\pi$
$727$	342294.			0.647635			0.323818	+	0.946120i	$0.395034\pi$
$728$	−1.05195e6	+	1.17269e6i	−1.98487	+	2.21268i
$729$	459999.			0.865569
$730$	161337.	−	314559.i	0.302752	−	0.590277i
$731$		−	463604.i		−	0.867586i
$732$		−	1.54785e6i		−	2.88873i
$733$	487173.			0.906725			0.453362	−	0.891326i	$-0.350224\pi$
$733$	487173.			0.906725			0.453362	+	0.891326i	$0.350224\pi$
$734$		−	40922.5i		−	0.0759574i
$735$	203517.	−	531837.i	0.376726	−	0.984474i
$736$	−1.06479e6			−1.96566
$737$		−	195572.i		−	0.360058i
$738$	−66787.6			−0.122626
$739$	323468.			0.592300			0.296150	−	0.955141i	$-0.404297\pi$
$739$	323468.			0.592300			0.296150	+	0.955141i	$0.404297\pi$
$740$	128614.	−	250758.i	0.234868	−	0.457923i
$741$		−	381176.i		−	0.694207i
$742$	−274270.	−	246032.i	−0.498162	−	0.446873i
$743$			337081.i			0.610599i	0.952256	+	0.305300i	$0.0987566\pi$
$743$			337081.i			0.610599i	−0.952256	+	0.305300i	$0.901243\pi$
$744$	−1.76416e6			−3.18707
$745$	−23186.5	−	11892.3i	−0.0417755	−	0.0214266i
$746$	−1.47985e6			−2.65913
$747$	699.764			0.00125404
$748$	331247.			0.592038
$749$	92624.1	−	103255.i	0.165105	−	0.184055i
$750$	−1.05776e6	+	158844.i	−1.88046	+	0.282390i
$751$	−191215.			−0.339033			−0.169517	−	0.985527i	$-0.554221\pi$
$751$	−191215.			−0.339033			−0.169517	+	0.985527i	$0.554221\pi$
$752$	−371659.			−0.657217
$753$			972981.i			1.71599i
$754$			80541.4i			0.141670i
$755$	402702.	+	206545.i	0.706464	+	0.362345i
$756$	898629.	+	806110.i	1.57231	+	1.41043i
$757$			805340.i			1.40536i	0.711506	+	0.702680i	$0.248013\pi$
$757$			805340.i			1.40536i	−0.711506	+	0.702680i	$0.751987\pi$
$758$		−	158245.i		−	0.275418i
$759$			385494.i			0.669166i
$760$	582995.	+	299018.i	1.00934	+	0.517690i
$761$			723314.i			1.24899i	0.781030	+	0.624493i	$0.214694\pi$
$761$			723314.i			1.24899i	−0.781030	+	0.624493i	$0.785306\pi$
$762$	−874181.			−1.50554
$763$	−239987.	−	215279.i	−0.412229	−	0.369787i
$764$	−423169.			−0.724981
$765$	−45495.8	−	23334.7i	−0.0777407	−	0.0398731i
$766$		−	793687.i		−	1.35267i
$767$		−	288227.i		−	0.489942i
$768$	1.10660e6			1.87616
$769$			657795.i			1.11234i	0.831068	+	0.556171i	$0.187730\pi$
$769$			657795.i			1.11234i	−0.831068	+	0.556171i	$0.812270\pi$
$770$	−333604.	+	127747.i	−0.562665	+	0.215461i
$771$	−934567.			−1.57218
$772$		−	2.26022e6i		−	3.79242i
$773$	−313235.			−0.524217			−0.262109	−	0.965038i	$-0.584418\pi$
$773$	−313235.			−0.524217			−0.262109	+	0.965038i	$0.584418\pi$
$774$	132488.			0.221154
$775$	651811.	−	468262.i	1.08522	−	0.779625i
$776$			1.83245e6i			3.04305i
$777$	−97012.3	+	108147.i	−0.160688	+	0.179131i
$778$		−	2.10653e6i		−	3.48023i
$779$	−186120.			−0.306703
$780$	−1.68988e6	−	866739.i	−2.77759	−	1.42462i
$781$	−199343.			−0.326812
$782$	1.64880e6			2.69621
$783$	34340.6			0.0560124
$784$	121572.	+	1.11673e6i	0.197789	+	1.81683i
$785$	649896.	+	333331.i	1.05464	+	0.540924i
$786$	1.48223e6			2.39923
$787$	−251880.			−0.406671			−0.203336	−	0.979109i	$-0.565178\pi$
$787$	−251880.			−0.406671			−0.203336	+	0.979109i	$0.565178\pi$
$788$			542811.i			0.874170i
$789$		−	190760.i		−	0.306432i
$790$	155932.	−	304021.i	0.249851	−	0.487136i
$791$	−284103.	+	316710.i	−0.454070	+	0.506185i
$792$			52671.0i			0.0839695i
$793$			1.00428e6i			1.59701i
$794$		−	2.08658e6i		−	3.30974i
$795$	112791.	−	219909.i	0.178460	−	0.347943i
$796$			531752.i			0.839233i
$797$	−230487.			−0.362853			−0.181426	−	0.983405i	$-0.558071\pi$
$797$	−230487.			−0.362853			−0.181426	+	0.983405i	$0.558071\pi$
$798$	−451890.	−	405365.i	−0.709622	−	0.636562i
$799$	180523.			0.282774
$800$	537530.	−	386163.i	0.839891	−	0.603379i
$801$		−	2888.30i		−	0.00450171i
$802$			1.32745e6i			2.06382i
$803$	79196.3			0.122821
$804$		−	1.65593e6i		−	2.56171i
$805$	−1.15027e6	+	440472.i	−1.77504	+	0.679715i
$806$	2.05718e6			3.16666
$807$			655841.i			1.00705i
$808$	−1.05104e6			−1.60989
$809$	194215.			0.296746			0.148373	−	0.988931i	$-0.452596\pi$
$809$	194215.			0.296746			0.148373	+	0.988931i	$0.452596\pi$
$810$	−593503.	+	1.15715e6i	−0.904592	+	1.76368i
$811$		−	937068.i		−	1.42472i	−0.701815	−	0.712360i	$-0.747627\pi$
$811$		−	937068.i		−	1.42472i	0.701815	−	0.712360i	$-0.252373\pi$
$812$	66142.5	+	59332.7i	0.100316	+	0.0899875i
$813$		−	544646.i		−	0.824011i
$814$	91139.1			0.137549
$815$	418473.	−	815898.i	0.630017	−	1.22835i
$816$	1.00864e6			1.51480
$817$	369210.			0.553132
$818$	1.73070e6			2.58652
$819$	72881.0	+	65377.5i	0.108654	+	0.0974676i
$820$	−423209.	+	825132.i	−0.629401	+	1.22715i
$821$	937068.			1.39022			0.695112	−	0.718901i	$-0.255355\pi$
$821$	937068.			1.39022			0.695112	+	0.718901i	$0.255355\pi$
$822$	481850.			0.713130
$823$		−	633921.i		−	0.935912i	−0.883752	−	0.467956i	$-0.844991\pi$
$823$		−	633921.i		−	0.935912i	0.883752	−	0.467956i	$-0.155009\pi$
$824$		−	2.36064e6i		−	3.47676i
$825$	−139805.	−	194606.i	−0.205407	−	0.285923i
$826$	−341698.	−	306518.i	−0.500821	−	0.449258i
$827$			598189.i			0.874636i	0.899307	+	0.437318i	$0.144072\pi$
$827$			598189.i			0.874636i	−0.899307	+	0.437318i	$0.855928\pi$
$828$			326401.i			0.476092i
$829$			263381.i			0.383245i	0.981469	+	0.191622i	$0.0613749\pi$
$829$			263381.i			0.383245i	−0.981469	+	0.191622i	$0.938625\pi$
$830$	6401.13	−	12480.3i	0.00929181	−	0.0181163i
$831$			981336.i			1.42107i
$832$	34573.8			0.0499460
$833$	−59050.2	−	542420.i	−0.0851004	−	0.781710i
$834$	−274371.			−0.394463
$835$	−496454.	−	254631.i	−0.712043	−	0.365206i
$836$			263802.i			0.377456i
$837$		−	877121.i		−	1.25201i
$838$	787493.			1.12139
$839$			283733.i			0.403074i	0.979481	+	0.201537i	$0.0645937\pi$
$839$			283733.i			0.403074i	−0.979481	+	0.201537i	$0.935406\pi$
$840$	−1.57165e6	+	601829.i	−2.22739	+	0.852932i
$841$	−704753.			−0.996426
$842$			692906.i			0.977350i
$843$	330440.			0.464983
$844$	−633144.			−0.888827
$845$	461098.	+	236496.i	0.645772	+	0.331216i
$846$			51589.6i			0.0720811i
$847$	474459.	+	425611.i	0.661351	+	0.593261i
$848$			487538.i			0.677980i
$849$	498362.			0.691401
$850$	−832351.	+	597962.i	−1.15204	+	0.827630i
$851$	314249.			0.433925
$852$	−1.68785e6			−2.32517
$853$	−715024.			−0.982703			−0.491352	−	0.870961i	$-0.663497\pi$
$853$	−715024.			−0.982703			−0.491352	+	0.870961i	$0.663497\pi$
$854$	1.19059e6	+	1.06801e6i	1.63247	+	1.46440i
$855$	18583.6	−	36232.4i	0.0254212	−	0.0495638i
$856$	−409945.			−0.559471
$857$	−35913.1			−0.0488980			−0.0244490	−	0.999701i	$-0.507783\pi$
$857$	−35913.1			−0.0488980			−0.0244490	+	0.999701i	$0.507783\pi$
$858$		−	614194.i		−	0.834317i
$859$			852524.i			1.15537i	0.816261	+	0.577684i	$0.196043\pi$
$859$			852524.i			1.15537i	−0.816261	+	0.577684i	$0.803957\pi$
$860$	839529.	−	1.63683e6i	1.13511	−	2.21313i
$861$	319223.	−	355862.i	0.430614	−	0.480037i
$862$			469075.i			0.631289i
$863$		−	163173.i		−	0.219092i	−0.993982	−	0.109546i	$-0.965060\pi$
$863$		−	163173.i		−	0.219092i	0.993982	−	0.109546i	$-0.0349397\pi$
$864$		−	723337.i		−	0.968977i
$865$	−995428.	−	510554.i	−1.33039	−	0.682353i
$866$			352118.i			0.469518i
$867$	302430.			0.402334
$868$	1.51547e6	−	1.68940e6i	2.01144	−	2.24230i
$869$	76543.3			0.101360
$870$	−39266.5	+	76558.1i	−0.0518781	+	0.101147i
$871$			1.07440e6i			1.41621i
$872$			952802.i			1.25305i
$873$	113885.			0.149429
$874$			1.31309e6i			1.71898i
$875$	420940.	−	639524.i	0.549799	−	0.835297i
$876$	670561.			0.873837
$877$		−	1.10407e6i		−	1.43548i	−0.696310	−	0.717741i	$-0.745176\pi$
$877$		−	1.10407e6i		−	1.43548i	0.696310	−	0.717741i	$-0.254824\pi$
$878$	−1.43779e6			−1.86511
$879$	393887.			0.509793
$880$	420591.	+	215721.i	0.543119	+	0.278565i
$881$		−	1.47196e6i		−	1.89646i	−0.317589	−	0.948228i	$-0.602873\pi$
$881$		−	1.47196e6i		−	1.89646i	0.317589	−	0.948228i	$-0.397127\pi$
$882$	155012.	−	16875.3i	0.199264	−	0.0216927i
$883$			731986.i			0.938818i	0.882981	+	0.469409i	$0.155533\pi$
$883$			731986.i			0.938818i	−0.882981	+	0.469409i	$0.844467\pi$
$884$	−1.81974e6			−2.32866
$885$	140520.	−	273972.i	0.179412	−	0.349800i
$886$	−1.60891e6			−2.04957
$887$	−1.29241e6			−1.64268			−0.821338	−	0.570442i	$-0.806772\pi$
$887$	−1.29241e6			−1.64268			−0.821338	+	0.570442i	$0.806772\pi$
$888$	429367.			0.544506
$889$	417830.	−	465786.i	0.528684	−	0.589363i
$890$	−51512.9	−	26420.9i	−0.0650333	−	0.0333555i
$891$	−291336.			−0.366977
$892$	−852076.			−1.07090
$893$			143767.i			0.180283i
$894$		−	71353.8i		−	0.0892776i
$895$	−1.01007e6	−	518066.i	−1.26098	−	0.646754i
$896$	−517623.	+	577032.i	−0.644759	+	0.718759i
$897$		−	2.11775e6i		−	2.63203i
$898$			1.44150e6i			1.78756i
$899$		−	64559.4i		−	0.0798804i
$900$	−118374.	−	164775.i	−0.146141	−	0.203425i
$901$		−	236808.i		−	0.291707i
$902$	−299897.			−0.368604
$903$	−633250.	+	705930.i	−0.776604	+	0.865737i
$904$	1.25741e6			1.53865
$905$	295898.	−	576913.i	0.361281	−	0.704390i
$906$			1.23927e6i			1.50977i
$907$		−	451869.i		−	0.549286i	−0.961546	−	0.274643i	$-0.911440\pi$
$907$		−	451869.i		−	0.549286i	0.961546	−	0.274643i	$-0.0885596\pi$
$908$	−2.26241e6			−2.74410
$909$			65320.9i			0.0790541i
$910$	1.83269e6	−	701790.i	2.21313	−	0.847470i
$911$	−620131.			−0.747217			−0.373609	−	0.927586i	$-0.621880\pi$
$911$	−620131.			−0.747217			−0.373609	+	0.927586i	$0.621880\pi$
$912$			803272.i			0.965768i
$913$	3142.16			0.00376952
$914$	−164565.			−0.196991
$915$	−489617.	+	954608.i	−0.584810	+	1.14020i
$916$			688178.i			0.820181i
$917$	−708460.	+	789772.i	−0.842513	+	0.939211i
$918$			1.12007e6i			1.32910i
$919$	−231493.			−0.274099			−0.137049	−	0.990564i	$-0.543762\pi$
$919$	−231493.			−0.274099			−0.137049	+	0.990564i	$0.543762\pi$
$920$	3.23903e6	+	1.66129e6i	3.82683	+	1.96277i
$921$	861644.			1.01580
$922$	1.41554e6			1.66518
$923$	1.09511e6			1.28545
$924$	−504391.	−	452461.i	−0.590776	−	0.529952i
$925$	−158640.	+	113967.i	−0.185408	+	0.133198i
$926$	−2.27029e6			−2.64764
$927$	−146711.			−0.170727
$928$		−	53240.4i		−	0.0618223i
$929$		−	115405.i		−	0.133719i	−0.997762	−	0.0668597i	$-0.978702\pi$
$929$		−	115405.i		−	0.133719i	0.997762	−	0.0668597i	$-0.0212980\pi$
$930$	1.95543e6	+	1.00294e6i	2.26088	+	1.15960i
$931$	431978.	−	47027.0i	0.498382	−	0.0542560i
$932$		−	1.09781e6i		−	1.26385i
$933$		−	168345.i		−	0.193391i
$934$			1.15843e6i			1.32793i
$935$	−204290.	−	104780.i	−0.233682	−	0.119855i
$936$		−	289354.i		−	0.330277i
$937$	1.19051e6			1.35598			0.677988	−	0.735073i	$-0.262852\pi$
$937$	1.19051e6			1.35598			0.677988	+	0.735073i	$0.262852\pi$
$938$	1.27372e6	+	1.14258e6i	1.44766	+	1.29862i
$939$	23134.5			0.0262379
$940$	637367.	+	326905.i	0.721330	+	0.369969i
$941$		−	1.24150e6i		−	1.40206i	−0.713131	−	0.701031i	$-0.752723\pi$
$941$		−	1.24150e6i		−	1.40206i	0.713131	−	0.701031i	$-0.247277\pi$
$942$			1.99998e6i			2.25385i
$943$	−1.03405e6			−1.16284
$944$			607397.i			0.681598i
$945$	−299223.	−	781407.i	−0.335067	−	0.875012i
$946$	594913.			0.664769
$947$			969639.i			1.08121i	0.841277	+	0.540605i	$0.181805\pi$
$947$			969639.i			1.08121i	−0.841277	+	0.540605i	$0.818195\pi$
$948$	648099.			0.721148
$949$	−435073.			−0.483092
$950$	−476211.	−	662876.i	−0.527658	−	0.734489i
$951$		−	192606.i		−	0.212965i
$952$	−1.07676e6	+	1.20035e6i	−1.18808	+	1.32444i
$953$			88476.8i			0.0974189i	0.998813	+	0.0487095i	$0.0155108\pi$
$953$			88476.8i			0.0974189i	−0.998813	+	0.0487095i	$0.984489\pi$
$954$	67674.6			0.0743582
$955$	260981.	+	133857.i	0.286156	+	0.146769i
$956$	2.79879e6			3.06235
$957$	−19275.0			−0.0210460
$958$	−1.10835e6			−1.20767
$959$	−230309.	+	256742.i	−0.250423	+	0.279164i
$960$	32863.9	+	16855.9i	0.0356596	+	0.0182898i
$961$	−725445.			−0.785521
$962$	−500682.			−0.541019
$963$			25477.5i			0.0274729i
$964$		−	1.19821e6i		−	1.28937i
$965$	−714954.	+	1.39395e6i	−0.767756	+	1.49690i
$966$	−2.51063e6	−	2.25214e6i	−2.69047	−	2.41347i
$967$		−	523076.i		−	0.559386i	−0.960090	−	0.279693i	$-0.909767\pi$
$967$		−	523076.i		−	0.559386i	0.960090	−	0.279693i	$-0.0902327\pi$
$968$		−	1.88371e6i		−	2.01031i
$969$		−	390167.i		−	0.415531i
$970$	1.04177e6	−	2.03113e6i	1.10720	−	2.15871i
$971$		−	513814.i		−	0.544964i	−0.962161	−	0.272482i	$-0.912155\pi$
$971$		−	513814.i		−	0.544964i	0.962161	−	0.272482i	$-0.0878445\pi$
$972$	−471180.			−0.498717
$973$	131141.	−	146192.i	0.138520	−	0.154418i
$974$	−1.38812e6			−1.46322
$975$	768036.	+	1.06909e6i	0.807927	+	1.12462i
$976$		−	2.11636e6i		−	2.22173i
$977$			1.03606e6i			1.08541i	0.839923	+	0.542705i	$0.182600\pi$
$977$			1.03606e6i			1.08541i	−0.839923	+	0.542705i	$0.817400\pi$
$978$	2.51084e6			2.62507
$979$		−	12969.4i		−	0.0135317i
$980$	773768.	−	2.02204e6i	0.805673	−	2.10541i
$981$	59215.4			0.0615314
$982$		−	431923.i		−	0.447902i
$983$	1.06902e6			1.10632			0.553158	−	0.833077i	$-0.313423\pi$
$983$	1.06902e6			1.10632			0.553158	+	0.833077i	$0.313423\pi$
$984$	−1.41285e6			−1.45917
$985$	171702.	−	334768.i	0.176971	−	0.345042i
$986$			82441.2i			0.0847990i
$987$	−274882.	−	246582.i	−0.282171	−	0.253120i
$988$		−	1.44923e6i		−	1.48464i
$989$	2.05127e6			2.09715
$990$	29944.0	−	58381.8i	0.0305519	−	0.0595672i
$991$	1.26809e6			1.29123			0.645613	−	0.763664i	$-0.276602\pi$
$991$	1.26809e6			1.29123			0.645613	+	0.763664i	$0.276602\pi$
$992$	−1.35986e6			−1.38188
$993$	−1.21611e6			−1.23332
$994$	1.16461e6	−	1.29827e6i	1.17871	−	1.31399i
$995$	168204.	−	327947.i	0.169899	−	0.331252i
$996$	26604.9			0.0268190
$997$	326572.			0.328541			0.164270	−	0.986415i	$-0.447473\pi$
$997$	326572.			0.328541			0.164270	+	0.986415i	$0.447473\pi$
$998$		−	1.31971e6i		−	1.32500i
$999$			213477.i			0.213904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.c.e.34.1	✓	8
3.2	odd	2		315.5.e.e.244.7		8
4.3	odd	2		560.5.p.g.209.8		8
5.2	odd	4		175.5.d.g.76.8		8
5.3	odd	4		175.5.d.g.76.1		8
5.4	even	2	inner	35.5.c.e.34.8	yes	8
7.6	odd	2	inner	35.5.c.e.34.2	yes	8
15.14	odd	2		315.5.e.e.244.2		8
20.19	odd	2		560.5.p.g.209.2		8
21.20	even	2		315.5.e.e.244.8		8
28.27	even	2		560.5.p.g.209.1		8
35.13	even	4		175.5.d.g.76.2		8
35.27	even	4		175.5.d.g.76.7		8
35.34	odd	2	inner	35.5.c.e.34.7	yes	8
105.104	even	2		315.5.e.e.244.1		8
140.139	even	2		560.5.p.g.209.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.c.e.34.1	✓	8	1.1	even	1	trivial
35.5.c.e.34.2	yes	8	7.6	odd	2	inner
35.5.c.e.34.7	yes	8	35.34	odd	2	inner
35.5.c.e.34.8	yes	8	5.4	even	2	inner
175.5.d.g.76.1		8	5.3	odd	4
175.5.d.g.76.2		8	35.13	even	4
175.5.d.g.76.7		8	35.27	even	4
175.5.d.g.76.8		8	5.2	odd	4
315.5.e.e.244.1		8	105.104	even	2
315.5.e.e.244.2		8	15.14	odd	2
315.5.e.e.244.7		8	3.2	odd	2
315.5.e.e.244.8		8	21.20	even	2
560.5.p.g.209.1		8	28.27	even	2
560.5.p.g.209.2		8	20.19	odd	2
560.5.p.g.209.7		8	140.139	even	2
560.5.p.g.209.8		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-7.21587i q^{2} -9.48683 q^{3} -36.0688 q^{4} +(22.2447 + 11.4093i) q^{5} +68.4558i q^{6} +(-36.4750 - 32.7197i) q^{7} +144.814i q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-7.21587i q^{2} -9.48683 q^{3} -36.0688 q^{4} +(22.2447 + 11.4093i) q^{5} +68.4558i q^{6} +(-36.4750 - 32.7197i) q^{7} +144.814i q^{8} +9.00000 q^{9} +(82.3280 - 160.515i) q^{10} +40.4128 q^{11} +342.179 q^{12} -222.012 q^{13} +(-236.101 + 263.199i) q^{14} +(-211.032 - 108.238i) q^{15} +467.858 q^{16} -227.249 q^{17} -64.9428i q^{18} -180.979i q^{19} +(-802.341 - 411.520i) q^{20} +(346.032 + 310.406i) q^{21} -291.614i q^{22} -1005.49i q^{23} -1373.83i q^{24} +(364.656 + 507.593i) q^{25} +1602.01i q^{26} +683.052 q^{27} +(1315.61 + 1180.16i) q^{28} +50.2752 q^{29} +(-781.032 + 1522.78i) q^{30} -1284.12i q^{31} -1058.98i q^{32} -383.390 q^{33} +1639.80i q^{34} +(-438.068 - 1143.99i) q^{35} -324.619 q^{36} +312.534i q^{37} -1305.92 q^{38} +2106.19 q^{39} +(-1652.22 + 3221.35i) q^{40} -1028.41i q^{41} +(2239.85 - 2496.92i) q^{42} +2040.07i q^{43} -1457.64 q^{44} +(200.203 + 102.684i) q^{45} -7255.48 q^{46} -794.384 q^{47} -4438.49 q^{48} +(259.848 + 2386.90i) q^{49} +(3662.73 - 2631.31i) q^{50} +2155.87 q^{51} +8007.71 q^{52} +1042.06i q^{53} -4928.82i q^{54} +(898.972 + 461.082i) q^{55} +(4738.26 - 5282.08i) q^{56} +1716.92i q^{57} -362.779i q^{58} +1298.25i q^{59} +(7611.67 + 3904.02i) q^{60} -4523.52i q^{61} -9266.05 q^{62} +(-328.275 - 294.477i) q^{63} -155.730 q^{64} +(-4938.60 - 2533.00i) q^{65} +2766.49i q^{66} -4839.37i q^{67} +8196.59 q^{68} +9538.90i q^{69} +(-8254.91 + 3161.04i) q^{70} -4932.66 q^{71} +1303.33i q^{72} +1959.68 q^{73} +2255.20 q^{74} +(-3459.43 - 4815.45i) q^{75} +6527.69i q^{76} +(-1474.06 - 1322.29i) q^{77} -15198.0i q^{78} +1894.04 q^{79} +(10407.4 + 5337.93i) q^{80} -7209.00 q^{81} -7420.85 q^{82} +77.7515 q^{83} +(-12481.0 - 11196.0i) q^{84} +(-5055.09 - 2592.75i) q^{85} +14720.9 q^{86} -476.953 q^{87} +5852.34i q^{88} -320.922i q^{89} +(740.952 - 1444.64i) q^{90} +(8097.89 + 7264.16i) q^{91} +36266.8i q^{92} +12182.2i q^{93} +5732.18i q^{94} +(2064.84 - 4025.82i) q^{95} +10046.4i q^{96} +12653.8 q^{97} +(17223.5 - 1875.03i) q^{98} +363.715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 172 q^{4} + 72 q^{9}+O(q^{10}) \) 8 * q - 172 * q^4 + 72 * q^9	\( 8 q - 172 q^{4} + 72 q^{9} - 376 q^{11} - 24 q^{14} + 60 q^{15} + 596 q^{16} + 1020 q^{21} + 3500 q^{25} - 64 q^{29} - 4500 q^{30} - 4160 q^{35} - 1548 q^{36} + 6360 q^{39} - 2104 q^{44} - 28440 q^{46} - 7828 q^{49} + 7740 q^{50} + 24240 q^{51} + 27300 q^{56} + 24180 q^{60} - 5092 q^{64} - 24940 q^{65} - 10620 q^{70} - 18016 q^{71} + 39720 q^{74} - 8624 q^{79} - 57672 q^{81} - 47400 q^{84} + 19000 q^{85} + 18000 q^{86} + 34480 q^{91} + 25260 q^{95} - 3384 q^{99}+O(q^{100}) \) 8 * q - 172 * q^4 + 72 * q^9 - 376 * q^11 - 24 * q^14 + 60 * q^15 + 596 * q^16 + 1020 * q^21 + 3500 * q^25 - 64 * q^29 - 4500 * q^30 - 4160 * q^35 - 1548 * q^36 + 6360 * q^39 - 2104 * q^44 - 28440 * q^46 - 7828 * q^49 + 7740 * q^50 + 24240 * q^51 + 27300 * q^56 + 24180 * q^60 - 5092 * q^64 - 24940 * q^65 - 10620 * q^70 - 18016 * q^71 + 39720 * q^74 - 8624 * q^79 - 57672 * q^81 - 47400 * q^84 + 19000 * q^85 + 18000 * q^86 + 34480 * q^91 + 25260 * q^95 - 3384 * q^99

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