LMFDB - Embedded newform 35.5.c.e.34.7

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

$q$-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	$0.357889\pi$
$2$			7.21587i			1.80397i	−0.431770	+	0.901984i	$0.642111\pi$
$3$	−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	$0.0806486\pi$
$19$			180.979i			0.501326i	−0.968074	+	0.250663i	$0.919351\pi$
$20$	−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	$0.399292\pi$
$23$			1005.49i			1.90073i	−0.311131	+	0.950367i	$0.600708\pi$
$24$			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	$0.232899\pi$
$31$			1284.12i			1.33623i	−0.744056	+	0.668117i	$0.767101\pi$
$32$			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	$-0.963587\pi$
$37$		−	312.534i		−	0.228293i	0.993464	−	0.114147i	$-0.0364134\pi$
$38$	−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	$0.0989544\pi$
$41$			1028.41i			0.611783i	−0.952066	+	0.305891i	$0.901046\pi$
$42$	2239.85	+	2496.92i	1.26976	+	1.41549i
$43$		−	2040.07i		−	1.10334i	−0.834063	−	0.551669i	$-0.813991\pi$
$43$		−	2040.07i		−	1.10334i	0.834063	−	0.551669i	$-0.186009\pi$
$44$	−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	$-0.940614\pi$
$53$		−	1042.06i		−	0.370973i	0.982647	−	0.185487i	$-0.0593862\pi$
$54$			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	$-0.940293\pi$
$59$		−	1298.25i		−	0.372953i	0.982459	−	0.186477i	$-0.0597069\pi$
$60$	7611.67	−	3904.02i	2.11435	−	1.08445i
$61$			4523.52i			1.21567i	0.794062	+	0.607837i	$0.207963\pi$
$61$			4523.52i			1.21567i	−0.794062	+	0.607837i	$0.792037\pi$
$62$	−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	$0.181207\pi$
$67$			4839.37i			1.07805i	−0.842290	+	0.539025i	$0.818793\pi$
$68$	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	$0.00644866\pi$
$89$			320.922i			0.0405154i	−0.999795	+	0.0202577i	$0.993551\pi$
$90$	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	$-0.884228\pi$
$101$		−	7257.88i		−	0.711487i	0.934584	−	0.355744i	$-0.115772\pi$
$102$			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	$-0.960547\pi$
$107$		−	2830.84i		−	0.247256i	0.992329	−	0.123628i	$-0.0394530\pi$
$108$	−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	$0.110427\pi$
$113$			8682.94i			0.680002i	−0.940425	+	0.340001i	$0.889573\pi$
$114$	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	$-0.870443\pi$
$127$		−	12770.0i		−	0.791742i	0.918306	−	0.395871i	$-0.129557\pi$
$128$			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	$0.217298\pi$
$131$			21652.4i			1.26172i	−0.775895	+	0.630862i	$0.782702\pi$
$132$	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	$0.0600426\pi$
$137$			7038.86i			0.375026i	−0.982262	+	0.187513i	$0.939957\pi$
$138$	68831.5			3.61434
$139$		−	4008.01i		−	0.207443i	−0.994606	−	0.103721i	$-0.966925\pi$
$139$		−	4008.01i		−	0.207443i	0.994606	−	0.103721i	$-0.0330751\pi$
$140$	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	$0.242497\pi$
$163$			36678.2i			1.38049i	−0.723576	+	0.690245i	$0.757503\pi$
$164$		−	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	$0.129539\pi$
$181$			25934.8i			0.791636i	−0.918329	+	0.395818i	$0.870461\pi$
$182$	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	$-0.681878\pi$
$193$		−	62664.1i		−	1.68230i	0.540799	−	0.841152i	$-0.318122\pi$
$194$			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	$0.0621103\pi$
$197$			15049.3i			0.387779i	−0.981023	+	0.193889i	$0.937890\pi$
$198$			2624.52i			0.0669453i
$199$			14742.7i			0.372281i	0.982523	+	0.186141i	$0.0595980\pi$
$199$			14742.7i			0.372281i	−0.982523	+	0.186141i	$0.940402\pi$
$200$	−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	$0.0582295\pi$
$229$			19079.6i			0.363830i	−0.983314	+	0.181915i	$0.941770\pi$
$230$	−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	$-0.909559\pi$
$233$		−	30436.7i		−	0.560642i	0.959906	−	0.280321i	$-0.0904408\pi$
$234$		−	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	$-0.907681\pi$
$241$		−	33220.0i		−	0.571960i	0.958236	−	0.285980i	$-0.0923191\pi$
$242$		−	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	$0.302695\pi$
$251$			102561.i			1.62793i	−0.580914	+	0.813965i	$0.697305\pi$
$252$	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	$-0.953568\pi$
$263$		−	20107.9i		−	0.290707i	0.989380	−	0.145353i	$-0.0464319\pi$
$264$			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	$0.158525\pi$
$269$			69131.7i			0.955373i	−0.878530	+	0.477686i	$0.841475\pi$
$270$	56234.3	+	109640.i	0.771390	+	1.50398i
$271$		−	57410.7i		−	0.781726i	−0.920449	−	0.390863i	$-0.872177\pi$
$271$		−	57410.7i		−	0.781726i	0.920449	−	0.390863i	$-0.127823\pi$
$272$	−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	$0.235457\pi$
$277$			103442.i			1.34815i	−0.738665	+	0.674073i	$0.764543\pi$
$278$	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	$-0.970759\pi$
$311$		−	17745.1i		−	0.183467i	0.995784	−	0.0917335i	$-0.0292408\pi$
$312$		−	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	$-0.967790\pi$
$317$		−	20302.5i		−	0.202037i	0.994885	−	0.101018i	$-0.0322101\pi$
$318$	−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	$0.163609\pi$
$337$			111674.i			0.983314i	−0.870789	+	0.491657i	$0.836391\pi$
$338$			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	$-0.714372\pi$
$347$		−	188238.i		−	1.56333i	0.623701	−	0.781663i	$-0.285628\pi$
$348$	17203.1			0.142052
$349$			128703.i			1.05667i	0.849036	+	0.528335i	$0.177183\pi$
$349$			128703.i			1.05667i	−0.849036	+	0.528335i	$0.822817\pi$
$350$	−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	$0.263769\pi$
$373$			205082.i			1.47404i	−0.675868	+	0.737022i	$0.736231\pi$
$374$		−	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	$-0.745562\pi$
$409$		−	239846.i		−	1.43379i	0.697180	−	0.716896i	$-0.254438\pi$
$410$	−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	$-0.899399\pi$
$419$		−	109133.i		−	0.621627i	0.950471	−	0.310813i	$-0.100601\pi$
$420$	−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	$0.172932\pi$
$439$			199253.i			1.03390i	−0.856017	+	0.516948i	$0.827068\pi$
$440$	−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	$0.192311\pi$
$443$			222968.i			1.13615i	−0.822978	+	0.568074i	$0.807689\pi$
$444$		−	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	$0.0173881\pi$
$457$			22806.0i			0.109198i	−0.998508	+	0.0545992i	$0.982612\pi$
$458$	−137676.			−0.656337
$459$	−155223.			−0.736767
$460$	−413778.	−	806744.i	−1.95547	−	3.81259i
$461$		−	196170.i		−	0.923063i	−0.887124	−	0.461531i	$-0.847300\pi$
$461$		−	196170.i		−	0.923063i	0.887124	−	0.461531i	$-0.152700\pi$
$462$	90518.6	+	100908.i	0.424086	+	0.472759i
$463$			314624.i			1.46767i	0.679325	+	0.733837i	$0.262273\pi$
$463$			314624.i			1.46767i	−0.679325	+	0.733837i	$0.737727\pi$
$464$	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	$0.108643\pi$
$479$			153599.i			0.669449i	−0.942316	+	0.334725i	$0.891357\pi$
$480$	−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	$0.132922\pi$
$487$			192371.i			0.811112i	−0.914070	+	0.405556i	$0.867078\pi$
$488$	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	$0.0981363\pi$
$509$			157233.i			0.606887i	−0.952849	+	0.303443i	$0.901864\pi$
$510$	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	$0.200706\pi$
$521$			320071.i			1.17916i	−0.807712	+	0.589578i	$0.799294\pi$
$522$			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	$-0.931506\pi$
$547$		−	127776.i		−	0.427046i	0.976938	−	0.213523i	$-0.0684939\pi$
$548$		−	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	$0.309551\pi$
$557$			512709.i			1.65257i	−0.563249	+	0.826287i	$0.690449\pi$
$558$	−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	$-0.661080\pi$
$601$		−	631861.i		−	1.74933i	0.484724	−	0.874667i	$-0.338920\pi$
$602$	−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	$-0.638596\pi$
$613$		−	681417.i		−	1.81339i	0.421783	−	0.906697i	$-0.361404\pi$
$614$		−	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	$0.174217\pi$
$617$			396221.i			1.04080i	−0.853923	+	0.520399i	$0.825783\pi$
$618$			1.11591e6i			2.92181i
$619$		−	80430.5i		−	0.209913i	−0.994477	−	0.104957i	$-0.966530\pi$
$619$		−	80430.5i		−	0.209913i	0.994477	−	0.104957i	$-0.0334704\pi$
$620$	−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	$0.298517\pi$
$653$			687602.i			1.61254i	−0.591548	+	0.806270i	$0.701483\pi$
$654$		−	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	$-0.628283\pi$
$661$		−	803833.i		−	1.83977i	0.392193	−	0.919883i	$-0.371717\pi$
$662$			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	$-0.903945\pi$
$673$		−	269226.i		−	0.594412i	0.954813	−	0.297206i	$-0.0960548\pi$
$674$	−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	$-0.916001\pi$
$683$		−	243356.i		−	0.521676i	0.965383	−	0.260838i	$-0.0839988\pi$
$684$		−	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	$-0.977103\pi$
$691$		−	68635.1i		−	0.143744i	0.997414	−	0.0718721i	$-0.0228973\pi$
$692$	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	$-0.619979\pi$
$719$		−	961341.i		−	1.85960i	0.368064	−	0.929800i	$-0.380021\pi$
$720$	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	$-0.901243\pi$
$743$		−	337081.i		−	0.610599i	0.952256	−	0.305300i	$-0.0987566\pi$
$744$	−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	$-0.751987\pi$
$757$		−	805340.i		−	1.40536i	0.711506	−	0.702680i	$-0.248013\pi$
$758$			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	$-0.785306\pi$
$761$		−	723314.i		−	1.24899i	0.781030	−	0.624493i	$-0.214694\pi$
$762$	−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	$-0.812270\pi$
$769$		−	657795.i		−	1.11234i	0.831068	−	0.556171i	$-0.187730\pi$
$770$	−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	$0.252373\pi$
$811$			937068.i			1.42472i	−0.701815	+	0.712360i	$0.747627\pi$
$812$	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	$0.155009\pi$
$823$			633921.i			0.935912i	−0.883752	+	0.467956i	$0.844991\pi$
$824$			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	$-0.855928\pi$
$827$		−	598189.i		−	0.874636i	0.899307	−	0.437318i	$-0.144072\pi$
$828$		−	326401.i		−	0.476092i
$829$		−	263381.i		−	0.383245i	−0.981469	−	0.191622i	$-0.938625\pi$
$829$		−	263381.i		−	0.383245i	0.981469	−	0.191622i	$-0.0613749\pi$
$830$	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	$-0.935406\pi$
$839$		−	283733.i		−	0.403074i	0.979481	−	0.201537i	$-0.0645937\pi$
$840$	−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	$-0.803957\pi$
$859$		−	852524.i		−	1.15537i	0.816261	−	0.577684i	$-0.196043\pi$
$860$	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	$0.0349397\pi$
$863$			163173.i			0.219092i	−0.993982	+	0.109546i	$0.965060\pi$
$864$			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	$0.254824\pi$
$877$			1.10407e6i			1.43548i	−0.696310	+	0.717741i	$0.745176\pi$
$878$	−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	$0.397127\pi$
$881$			1.47196e6i			1.89646i	−0.317589	+	0.948228i	$0.602873\pi$
$882$	155012.	+	16875.3i	0.199264	+	0.0216927i
$883$		−	731986.i		−	0.938818i	−0.882981	−	0.469409i	$-0.844467\pi$
$883$		−	731986.i		−	0.938818i	0.882981	−	0.469409i	$-0.155533\pi$
$884$	−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	$0.0885596\pi$
$907$			451869.i			0.549286i	−0.961546	+	0.274643i	$0.911440\pi$
$908$	−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	$0.0212980\pi$
$929$			115405.i			0.133719i	−0.997762	+	0.0668597i	$0.978702\pi$
$930$	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	$0.247277\pi$
$941$			1.24150e6i			1.40206i	−0.713131	+	0.701031i	$0.752723\pi$
$942$		−	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	$-0.818195\pi$
$947$		−	969639.i		−	1.08121i	0.841277	−	0.540605i	$-0.181805\pi$
$948$	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	$-0.984489\pi$
$953$		−	88476.8i		−	0.0974189i	0.998813	−	0.0487095i	$-0.0155108\pi$
$954$	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	$0.0902327\pi$
$967$			523076.i			0.559386i	−0.960090	+	0.279693i	$0.909767\pi$
$968$			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	$0.0878445\pi$
$971$			513814.i			0.544964i	−0.962161	+	0.272482i	$0.912155\pi$
$972$	−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	$-0.817400\pi$
$977$		−	1.03606e6i		−	1.08541i	0.839923	−	0.542705i	$-0.182600\pi$
$978$	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.34.7	yes	8
3.2	odd	2		315.5.e.e.244.1		8
4.3	odd	2		560.5.p.g.209.7		8
5.2	odd	4		175.5.d.g.76.2		8
5.3	odd	4		175.5.d.g.76.7		8
5.4	even	2	inner	35.5.c.e.34.2	yes	8
7.6	odd	2	inner	35.5.c.e.34.8	yes	8
15.14	odd	2		315.5.e.e.244.8		8
20.19	odd	2		560.5.p.g.209.1		8
21.20	even	2		315.5.e.e.244.2		8
28.27	even	2		560.5.p.g.209.2		8
35.13	even	4		175.5.d.g.76.8		8
35.27	even	4		175.5.d.g.76.1		8
35.34	odd	2	inner	35.5.c.e.34.1	✓	8
105.104	even	2		315.5.e.e.244.7		8
140.139	even	2		560.5.p.g.209.8		8

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