LMFDB - Embedded newform 315.3.w.c.271.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(136,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("315.136");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.w (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 19 x^{10} - 26 x^{9} + 244 x^{8} - 338 x^{7} + 1249 x^{6} - 986 x^{5} + 3532 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 19x^10 - 26x^9 + 244x^8 - 338x^7 + 1249x^6 - 986x^5 + 3532x^4 - 3618x^3 + 3579x^2 - 1386*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.5
Root			$1.18241 + 2.04800i$ of defining polynomial
Character	$\chi$	$=$	315.271
Dual form			315.3.w.c.136.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18241 - 2.04800i) q^{2} +(-0.796202 - 1.37906i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-1.42520 + 6.85338i) q^{7} +5.69355 q^{8} +O(q^{10})$	\(q+(1.18241 - 2.04800i) q^{2} +(-0.796202 - 1.37906i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-1.42520 + 6.85338i) q^{7} +5.69355 q^{8} +(4.57947 - 2.64396i) q^{10} +(6.86467 + 11.8900i) q^{11} +6.14666i q^{13} +(12.3505 + 11.0223i) q^{14} +(9.91693 - 17.1766i) q^{16} +(1.74292 - 1.00628i) q^{17} +(-2.08213 - 1.20212i) q^{19} -3.56072i q^{20} +32.4675 q^{22} +(8.02550 - 13.9006i) q^{23} +(2.50000 + 4.33013i) q^{25} +(12.5884 + 7.26789i) q^{26} +(10.5860 - 3.49123i) q^{28} -15.9780 q^{29} +(17.9557 - 10.3667i) q^{31} +(-12.0647 - 20.8967i) q^{32} -4.75934i q^{34} +(-10.4222 + 11.6781i) q^{35} +(-6.51335 + 11.2814i) q^{37} +(-4.92387 + 2.84279i) q^{38} +(11.0255 + 6.36558i) q^{40} -55.2974i q^{41} +54.7172 q^{43} +(10.9313 - 18.9336i) q^{44} +(-18.9789 - 32.8724i) q^{46} +(-61.9889 - 35.7893i) q^{47} +(-44.9376 - 19.5349i) q^{49} +11.8241 q^{50} +(8.47662 - 4.89398i) q^{52} +(33.6897 + 58.3523i) q^{53} +30.6997i q^{55} +(-8.11445 + 39.0200i) q^{56} +(-18.8926 + 32.7230i) q^{58} +(-18.2612 + 10.5431i) q^{59} +(-22.8803 - 13.2100i) q^{61} -49.0311i q^{62} +22.2735 q^{64} +(-6.87217 + 11.9029i) q^{65} +(-37.2194 - 64.4659i) q^{67} +(-2.77544 - 1.60240i) q^{68} +(11.5934 + 35.1530i) q^{70} +66.7438 q^{71} +(-108.278 + 62.5145i) q^{73} +(15.4029 + 26.6787i) q^{74} +3.82851i q^{76} +(-91.2699 + 30.1006i) q^{77} +(49.0504 - 84.9577i) q^{79} +(38.4081 - 22.1749i) q^{80} +(-113.249 - 65.3844i) q^{82} +78.1877i q^{83} +4.50020 q^{85} +(64.6983 - 112.061i) q^{86} +(39.0843 + 67.6960i) q^{88} +(-38.7285 - 22.3599i) q^{89} +(-42.1254 - 8.76023i) q^{91} -25.5597 q^{92} +(-146.593 + 84.6355i) q^{94} +(-2.68801 - 4.65577i) q^{95} +31.6777i q^{97} +(-93.1423 + 68.9339i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 10 q^{4} - 2 q^{7} + 4 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 10 * q^4 - 2 * q^7 + 4 * q^8	$ 12 q + 2 q^{2} - 10 q^{4} - 2 q^{7} + 4 q^{8} + 14 q^{11} + 2 q^{14} - 22 q^{16} - 48 q^{17} - 30 q^{19} - 88 q^{22} + 14 q^{23} + 30 q^{25} - 66 q^{26} + 202 q^{28} - 64 q^{29} + 132 q^{31} + 54 q^{32} - 30 q^{35} + 44 q^{37} + 300 q^{38} - 4 q^{43} - 6 q^{44} - 214 q^{46} - 204 q^{47} - 24 q^{49} + 20 q^{50} + 252 q^{52} - 196 q^{53} + 460 q^{56} + 158 q^{58} - 72 q^{59} + 72 q^{61} - 140 q^{64} - 30 q^{65} - 138 q^{67} + 348 q^{68} + 240 q^{70} + 8 q^{71} - 528 q^{73} - 50 q^{74} + 176 q^{77} - 12 q^{79} + 240 q^{80} - 378 q^{82} + 40 q^{86} + 604 q^{88} - 204 q^{89} - 480 q^{91} - 732 q^{92} - 42 q^{94} - 60 q^{95} - 898 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 - 10 * q^4 - 2 * q^7 + 4 * q^8 + 14 * q^11 + 2 * q^14 - 22 * q^16 - 48 * q^17 - 30 * q^19 - 88 * q^22 + 14 * q^23 + 30 * q^25 - 66 * q^26 + 202 * q^28 - 64 * q^29 + 132 * q^31 + 54 * q^32 - 30 * q^35 + 44 * q^37 + 300 * q^38 - 4 * q^43 - 6 * q^44 - 214 * q^46 - 204 * q^47 - 24 * q^49 + 20 * q^50 + 252 * q^52 - 196 * q^53 + 460 * q^56 + 158 * q^58 - 72 * q^59 + 72 * q^61 - 140 * q^64 - 30 * q^65 - 138 * q^67 + 348 * q^68 + 240 * q^70 + 8 * q^71 - 528 * q^73 - 50 * q^74 + 176 * q^77 - 12 * q^79 + 240 * q^80 - 378 * q^82 + 40 * q^86 + 604 * q^88 - 204 * q^89 - 480 * q^91 - 732 * q^92 - 42 * q^94 - 60 * q^95 - 898 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	1.18241	−	2.04800i	0.591207	−	1.02400i	−0.402864	−	0.915260i	$-0.631985\pi$
$2$	1.18241	−	2.04800i	0.591207	−	1.02400i	0.994070	−	0.108740i	$-0.0346816\pi$
$3$		0			0
$3$		0			0
$4$	−0.796202	−	1.37906i	−0.199051	−	0.344766i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$		0			0
$7$	−1.42520	+	6.85338i	−0.203600	+	0.979054i
$7$	−1.42520	+	6.85338i	−0.203600	+	0.979054i
$8$	5.69355			0.711693
$9$		0			0
$10$	4.57947	−	2.64396i	0.457947	−	0.264396i
$11$	6.86467	+	11.8900i	0.624061	+	1.08091i	0.988722	+	0.149765i	$0.0478516\pi$
$11$	6.86467	+	11.8900i	0.624061	+	1.08091i	−0.364661	+	0.931140i	$0.618815\pi$
$12$		0			0
$13$			6.14666i			0.472820i	0.971653	+	0.236410i	$0.0759708\pi$
$13$			6.14666i			0.472820i	−0.971653	+	0.236410i	$0.924029\pi$
$14$	12.3505	+	11.0223i	0.882181	+	0.787310i
$15$		0			0
$16$	9.91693	−	17.1766i	0.619808	−	1.07354i
$17$	1.74292	−	1.00628i	0.102525	−	0.0591927i	−0.447861	−	0.894103i	$-0.647814\pi$
$17$	1.74292	−	1.00628i	0.102525	−	0.0591927i	0.550386	+	0.834911i	$0.314481\pi$
$18$		0			0
$19$	−2.08213	−	1.20212i	−0.109586	−	0.0632692i	0.444205	−	0.895925i	$-0.353486\pi$
$19$	−2.08213	−	1.20212i	−0.109586	−	0.0632692i	−0.553791	+	0.832656i	$0.686819\pi$
$20$		−	3.56072i		−	0.178036i
$21$		0			0
$22$	32.4675			1.47580
$23$	8.02550	−	13.9006i	0.348935	−	0.604373i	−0.637126	−	0.770760i	$-0.719877\pi$
$23$	8.02550	−	13.9006i	0.348935	−	0.604373i	0.986061	+	0.166387i	$0.0532101\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	12.5884	+	7.26789i	0.484167	+	0.279534i
$27$		0			0
$28$	10.5860	−	3.49123i	0.378071	−	0.124687i
$29$	−15.9780			−0.550966			−0.275483	−	0.961306i	$-0.588838\pi$
$29$	−15.9780			−0.550966			−0.275483	+	0.961306i	$0.588838\pi$
$30$		0			0
$31$	17.9557	−	10.3667i	0.579217	−	0.334411i	−0.181605	−	0.983371i	$-0.558129\pi$
$31$	17.9557	−	10.3667i	0.579217	−	0.334411i	0.760822	+	0.648961i	$0.224796\pi$
$32$	−12.0647	−	20.8967i	−0.377023	−	0.653023i
$33$		0			0
$34$		−	4.75934i		−	0.139981i
$35$	−10.4222	+	11.6781i	−0.297777	+	0.333660i
$36$		0			0
$37$	−6.51335	+	11.2814i	−0.176036	+	0.304904i	−0.940519	−	0.339740i	$-0.889661\pi$
$37$	−6.51335	+	11.2814i	−0.176036	+	0.304904i	0.764483	+	0.644644i	$0.222994\pi$
$38$	−4.92387	+	2.84279i	−0.129575	+	0.0748104i
$39$		0			0
$40$	11.0255	+	6.36558i	0.275638	+	0.159139i
$41$		−	55.2974i		−	1.34872i	−0.738404	−	0.674358i	$-0.764420\pi$
$41$		−	55.2974i		−	1.34872i	0.738404	−	0.674358i	$-0.235580\pi$
$42$		0			0
$43$	54.7172			1.27249			0.636246	−	0.771486i	$-0.280486\pi$
$43$	54.7172			1.27249			0.636246	+	0.771486i	$0.280486\pi$
$44$	10.9313	−	18.9336i	0.248439	−	0.430310i
$45$		0			0
$46$	−18.9789	−	32.8724i	−0.412585	−	0.714618i
$47$	−61.9889	−	35.7893i	−1.31891	−	0.761475i	−0.335359	−	0.942090i	$-0.608858\pi$
$47$	−61.9889	−	35.7893i	−1.31891	−	0.761475i	−0.983554	+	0.180615i	$0.942191\pi$
$48$		0			0
$49$	−44.9376	−	19.5349i	−0.917094	−	0.398671i
$50$	11.8241			0.236483
$51$		0			0
$52$	8.47662	−	4.89398i	0.163012	−	0.0941150i
$53$	33.6897	+	58.3523i	0.635655	+	1.10099i	0.986376	+	0.164507i	$0.0526033\pi$
$53$	33.6897	+	58.3523i	0.635655	+	1.10099i	−0.350721	+	0.936480i	$0.614063\pi$
$54$		0			0
$55$			30.6997i			0.558177i
$56$	−8.11445	+	39.0200i	−0.144901	+	0.696786i
$57$		0			0
$58$	−18.8926	+	32.7230i	−0.325735	+	0.564189i
$59$	−18.2612	+	10.5431i	−0.309511	+	0.178696i	−0.646708	−	0.762738i	$-0.723855\pi$
$59$	−18.2612	+	10.5431i	−0.309511	+	0.178696i	0.337196	+	0.941434i	$0.390521\pi$
$60$		0			0
$61$	−22.8803	−	13.2100i	−0.375088	−	0.216557i	0.300591	−	0.953753i	$-0.402816\pi$
$61$	−22.8803	−	13.2100i	−0.375088	−	0.216557i	−0.675679	+	0.737196i	$0.736149\pi$
$62$		−	49.0311i		−	0.790824i
$63$		0			0
$64$	22.2735			0.348023
$65$	−6.87217	+	11.9029i	−0.105726	+	0.183122i
$66$		0			0
$67$	−37.2194	−	64.4659i	−0.555513	−	0.962177i	−0.997863	−	0.0653349i	$-0.979188\pi$
$67$	−37.2194	−	64.4659i	−0.555513	−	0.962177i	0.442350	−	0.896843i	$-0.354145\pi$
$68$	−2.77544	−	1.60240i	−0.0408152	−	0.0235647i
$69$		0			0
$70$	11.5934	+	35.1530i	0.165620	+	0.502186i
$71$	66.7438			0.940053			0.470027	−	0.882652i	$-0.344244\pi$
$71$	66.7438			0.940053			0.470027	+	0.882652i	$0.344244\pi$
$72$		0			0
$73$	−108.278	+	62.5145i	−1.48327	+	0.856363i	−0.999819	−	0.0190109i	$-0.993948\pi$
$73$	−108.278	+	62.5145i	−1.48327	+	0.856363i	−0.483446	+	0.875374i	$0.660615\pi$
$74$	15.4029	+	26.6787i	0.208148	+	0.360522i
$75$		0			0
$76$			3.82851i			0.0503751i
$77$	−91.2699	+	30.1006i	−1.18532	+	0.390917i
$78$		0			0
$79$	49.0504	−	84.9577i	0.620891	−	1.07541i	−0.368430	−	0.929656i	$-0.620104\pi$
$79$	49.0504	−	84.9577i	0.620891	−	1.07541i	0.989320	−	0.145758i	$-0.0465622\pi$
$80$	38.4081	−	22.1749i	0.480101	−	0.277187i
$81$		0			0
$82$	−113.249	−	65.3844i	−1.38109	−	0.797370i
$83$			78.1877i			0.942020i	0.882128	+	0.471010i	$0.156110\pi$
$83$			78.1877i			0.942020i	−0.882128	+	0.471010i	$0.843890\pi$
$84$		0			0
$85$	4.50020			0.0529436
$86$	64.6983	−	112.061i	0.752306	−	1.30303i
$87$		0			0
$88$	39.0843	+	67.6960i	0.444140	+	0.769273i
$89$	−38.7285	−	22.3599i	−0.435151	−	0.251235i	0.266388	−	0.963866i	$-0.414170\pi$
$89$	−38.7285	−	22.3599i	−0.435151	−	0.251235i	−0.701539	+	0.712631i	$0.747503\pi$
$90$		0			0
$91$	−42.1254	−	8.76023i	−0.462916	−	0.0962662i
$92$	−25.5597			−0.277823
$93$		0			0
$94$	−146.593	+	84.6355i	−1.55950	+	0.900378i
$95$	−2.68801	−	4.65577i	−0.0282949	−	0.0490081i
$96$		0			0
$97$			31.6777i			0.326574i	0.986579	+	0.163287i	$0.0522096\pi$
$97$			31.6777i			0.326574i	−0.986579	+	0.163287i	$0.947790\pi$
$98$	−93.1423	+	68.9339i	−0.950431	+	0.703407i
$99$		0			0
$100$	3.98101	−	6.89531i	0.0398101	−	0.0689531i
$101$	63.7153	−	36.7861i	0.630845	−	0.364218i	−0.150234	−	0.988650i	$-0.548003\pi$
$101$	63.7153	−	36.7861i	0.630845	−	0.364218i	0.781079	+	0.624432i	$0.214670\pi$
$102$		0			0
$103$	23.9642	+	13.8358i	0.232663	+	0.134328i	0.611800	−	0.791013i	$-0.290446\pi$
$103$	23.9642	+	13.8358i	0.232663	+	0.134328i	−0.379137	+	0.925340i	$0.623779\pi$
$104$			34.9963i			0.336503i
$105$		0			0
$106$	159.341			1.50321
$107$	−41.1422	+	71.2603i	−0.384506	+	0.665984i	−0.991701	−	0.128569i	$-0.958962\pi$
$107$	−41.1422	+	71.2603i	−0.384506	+	0.665984i	0.607194	+	0.794553i	$0.292295\pi$
$108$		0			0
$109$	16.9306	+	29.3247i	0.155327	+	0.269034i	0.933178	−	0.359415i	$-0.117024\pi$
$109$	16.9306	+	29.3247i	0.155327	+	0.269034i	−0.777851	+	0.628449i	$0.783690\pi$
$110$	62.8731	+	36.2998i	0.571573	+	0.329998i
$111$		0			0
$112$	103.584	+	92.4447i	0.924860	+	0.825399i
$113$	36.7538			0.325255			0.162628	−	0.986688i	$-0.448003\pi$
$113$	36.7538			0.325255			0.162628	+	0.986688i	$0.448003\pi$
$114$		0			0
$115$	31.0826	−	17.9456i	0.270284	−	0.156048i
$116$	12.7217	+	22.0347i	0.109670	+	0.189954i
$117$		0			0
$118$			49.8652i			0.422586i
$119$	4.41238	+	13.3790i	0.0370788	+	0.112429i
$120$		0			0
$121$	−33.7474	+	58.4522i	−0.278904	+	0.483076i
$122$	−54.1081	+	31.2393i	−0.443509	+	0.256060i
$123$		0			0
$124$	−28.5928	−	16.5080i	−0.230587	−	0.133129i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−181.035			−1.42547			−0.712737	−	0.701431i	$-0.752545\pi$
$127$	−181.035			−1.42547			−0.712737	+	0.701431i	$0.752545\pi$
$128$	74.5954	−	129.203i	0.582776	−	1.00940i
$129$		0			0
$130$	16.2515	+	28.1484i	0.125011	+	0.216526i
$131$	−37.0813	−	21.4089i	−0.283063	−	0.163427i	0.351746	−	0.936095i	$-0.385588\pi$
$131$	−37.0813	−	21.4089i	−0.283063	−	0.163427i	−0.634809	+	0.772669i	$0.718921\pi$
$132$		0			0
$133$	11.2060	−	12.5563i	0.0842557	−	0.0944085i
$134$	−176.035			−1.31369
$135$		0			0
$136$	9.92340	−	5.72928i	0.0729662	−	0.0421271i
$137$	50.5297	+	87.5200i	0.368830	+	0.638832i	0.989383	−	0.145332i	$-0.0464251\pi$
$137$	50.5297	+	87.5200i	0.368830	+	0.638832i	−0.620553	+	0.784165i	$0.713092\pi$
$138$		0			0
$139$		−	132.591i		−	0.953895i	−0.878932	−	0.476947i	$-0.841743\pi$
$139$		−	132.591i		−	0.953895i	0.878932	−	0.476947i	$-0.158257\pi$
$140$	24.4030	+	5.07475i	0.174307	+	0.0362482i
$141$		0			0
$142$	78.9187	−	136.691i	0.555766	−	0.962615i
$143$	−73.0835	+	42.1948i	−0.511073	+	0.295068i
$144$		0			0
$145$	−30.9413	−	17.8640i	−0.213388	−	0.123200i
$146$			295.672i			2.02515i
$147$		0			0
$148$	20.7438			0.140161
$149$	71.8152	−	124.388i	0.481981	−	0.834816i	−0.517805	−	0.855499i	$-0.673251\pi$
$149$	71.8152	−	124.388i	0.481981	−	0.834816i	0.999786	+	0.0206830i	$0.00658408\pi$
$150$		0			0
$151$	−73.0209	−	126.476i	−0.483582	−	0.837588i	0.516240	−	0.856444i	$-0.327331\pi$
$151$	−73.0209	−	126.476i	−0.483582	−	0.837588i	−0.999822	+	0.0188554i	$0.993998\pi$
$152$	−11.8547	−	6.84430i	−0.0779913	−	0.0450283i
$153$		0			0
$154$	−46.2727	+	222.512i	−0.300472	+	1.44488i
$155$	46.3615			0.299106
$156$		0			0
$157$	−172.624	+	99.6646i	−1.09952	+	0.634807i	−0.936094	−	0.351749i	$-0.885587\pi$
$157$	−172.624	+	99.6646i	−1.09952	+	0.634807i	−0.163423	+	0.986556i	$0.552254\pi$
$158$	−115.996	−	200.910i	−0.734149	−	1.27158i
$159$		0			0
$160$		−	53.9551i		−	0.337220i
$161$	83.8279	+	74.8129i	0.520670	+	0.464676i
$162$		0			0
$163$	64.0489	−	110.936i	0.392938	−	0.680589i	−0.599897	−	0.800077i	$-0.704792\pi$
$163$	64.0489	−	110.936i	0.392938	−	0.680589i	0.992836	+	0.119488i	$0.0381253\pi$
$164$	−76.2585	+	44.0279i	−0.464991	+	0.268463i
$165$		0			0
$166$	160.128	+	92.4501i	0.964629	+	0.556929i
$167$		−	300.506i		−	1.79944i	−0.436469	−	0.899719i	$-0.643771\pi$
$167$		−	300.506i		−	1.79944i	0.436469	−	0.899719i	$-0.356229\pi$
$168$		0			0
$169$	131.219			0.776442
$170$	5.32110	−	9.21642i	0.0313006	−	0.0542142i
$171$		0			0
$172$	−43.5659	−	75.4584i	−0.253290	−	0.438712i
$173$	−96.8042	−	55.8899i	−0.559562	−	0.323063i	0.193408	−	0.981118i	$-0.438046\pi$
$173$	−96.8042	−	55.8899i	−0.559562	−	0.323063i	−0.752970	+	0.658055i	$0.771379\pi$
$174$		0			0
$175$	−33.2390	+	10.9621i	−0.189937	+	0.0626408i
$176$	272.306			1.54719
$177$		0			0
$178$	−91.5861	+	52.8772i	−0.514529	+	0.297063i
$179$	−176.173	−	305.141i	−0.984207	−	1.70470i	−0.645407	−	0.763839i	$-0.723312\pi$
$179$	−176.173	−	305.141i	−0.984207	−	1.70470i	−0.338800	−	0.940858i	$-0.610021\pi$
$180$		0			0
$181$			153.980i			0.850718i	0.905025	+	0.425359i	$0.139852\pi$
$181$			153.980i			0.850718i	−0.905025	+	0.425359i	$0.860148\pi$
$182$	−67.7505	+	75.9145i	−0.372256	+	0.417113i
$183$		0			0
$184$	45.6936	−	79.1436i	0.248335	−	0.430128i
$185$	−25.2261	+	14.5643i	−0.136357	+	0.0787259i
$186$		0			0
$187$	23.9292	+	13.8155i	0.127963	+	0.0738797i
$188$			113.982i			0.606288i
$189$		0			0
$190$	−12.7134			−0.0669124
$191$	−38.4323	+	66.5667i	−0.201216	+	0.348517i	−0.948921	−	0.315515i	$-0.897823\pi$
$191$	−38.4323	+	66.5667i	−0.201216	+	0.348517i	0.747704	+	0.664032i	$0.231156\pi$
$192$		0			0
$193$	−166.261	−	287.973i	−0.861456	−	1.49209i	−0.870523	−	0.492127i	$-0.836220\pi$
$193$	−166.261	−	287.973i	−0.861456	−	1.49209i	0.00906705	−	0.999959i	$-0.497114\pi$
$194$	64.8759	+	37.4561i	0.334412	+	0.193073i
$195$		0			0
$196$	8.83957	+	77.5255i	0.0450998	+	0.395538i
$197$	122.760			0.623146			0.311573	−	0.950222i	$-0.399144\pi$
$197$	122.760			0.623146			0.311573	+	0.950222i	$0.399144\pi$
$198$		0			0
$199$	73.5085	−	42.4402i	0.369390	−	0.213267i	−0.303802	−	0.952735i	$-0.598256\pi$
$199$	73.5085	−	42.4402i	0.369390	−	0.213267i	0.673192	+	0.739468i	$0.264923\pi$
$200$	14.2339	+	24.6538i	0.0711693	+	0.123269i
$201$		0			0
$202$		−	173.985i		−	0.861313i
$203$	22.7719	−	109.503i	0.112177	−	0.539426i
$204$		0			0
$205$	61.8243	−	107.083i	0.301582	−	0.522356i
$206$	56.6713	−	32.7192i	0.275103	−	0.158831i
$207$		0			0
$208$	105.579	+	60.9560i	0.507591	+	0.293058i
$209$		−	33.0085i		−	0.157935i
$210$		0			0
$211$	142.536			0.675527			0.337763	−	0.941231i	$-0.390330\pi$
$211$	142.536			0.675527			0.337763	+	0.941231i	$0.390330\pi$
$212$	53.6477	−	92.9205i	0.253055	−	0.438304i
$213$		0			0
$214$	97.2941	+	168.518i	0.454645	+	0.787469i
$215$	105.959	+	61.1756i	0.492834	+	0.284538i
$216$		0			0
$217$	45.4567	+	137.832i	0.209478	+	0.635171i
$218$	80.0760			0.367321
$219$		0			0
$220$	42.3369	−	24.4432i	0.192440	−	0.111105i
$221$	6.18523	+	10.7131i	0.0279875	+	0.0484757i
$222$		0			0
$223$		−	229.951i		−	1.03117i	−0.856838	−	0.515585i	$-0.827575\pi$
$223$		−	229.951i		−	1.03117i	0.856838	−	0.515585i	$-0.172425\pi$
$224$	160.408	−	52.9021i	0.716107	−	0.236170i
$225$		0			0
$226$	43.4582	−	75.2719i	0.192293	−	0.333061i
$227$	−297.681	+	171.866i	−1.31137	+	0.757121i	−0.982323	−	0.187192i	$-0.940061\pi$
$227$	−297.681	+	171.866i	−1.31137	+	0.757121i	−0.329048	+	0.944313i	$0.606728\pi$
$228$		0			0
$229$	0.761259	+	0.439513i	0.00332428	+	0.00191927i	0.501661	−	0.865064i	$-0.332722\pi$
$229$	0.761259	+	0.439513i	0.00332428	+	0.00191927i	−0.498337	+	0.866983i	$0.666056\pi$
$230$		−	84.8763i		−	0.369027i
$231$		0			0
$232$	−90.9716			−0.392119
$233$	51.9301	−	89.9455i	0.222876	−	0.386032i	−0.732804	−	0.680440i	$-0.761789\pi$
$233$	51.9301	−	89.9455i	0.222876	−	0.386032i	0.955680	+	0.294407i	$0.0951222\pi$
$234$		0			0
$235$	−80.0274	−	138.611i	−0.340542	−	0.589836i
$236$	29.0792	+	16.7889i	0.123217	+	0.0711393i
$237$		0			0
$238$	32.6175	+	6.78302i	0.137048	+	0.0285001i
$239$	159.924			0.669140			0.334570	−	0.942371i	$-0.391409\pi$
$239$	159.924			0.669140			0.334570	+	0.942371i	$0.391409\pi$
$240$		0			0
$241$	223.306	−	128.926i	0.926583	−	0.534963i	0.0408535	−	0.999165i	$-0.486992\pi$
$241$	223.306	−	128.926i	0.926583	−	0.534963i	0.885729	+	0.464202i	$0.153659\pi$
$242$	79.8067	+	138.229i	0.329780	+	0.571195i
$243$		0			0
$244$			42.0712i			0.172423i
$245$	−65.1806	−	88.0709i	−0.266043	−	0.359473i
$246$		0			0
$247$	7.38899	−	12.7981i	0.0299149	−	0.0518142i
$248$	102.232	−	59.0235i	0.412225	−	0.237998i
$249$		0			0
$250$	22.8973	+	13.2198i	0.0915893	+	0.0528791i
$251$		−	148.025i		−	0.589740i	−0.955537	−	0.294870i	$-0.904724\pi$
$251$		−	148.025i		−	0.589740i	0.955537	−	0.294870i	$-0.0952763\pi$
$252$		0			0
$253$	220.370			0.871026
$254$	−214.059	+	370.760i	−0.842750	+	1.45969i
$255$		0			0
$256$	−131.858	−	228.385i	−0.515071	−	0.892129i
$257$	−59.0535	−	34.0946i	−0.229780	−	0.132664i	0.380690	−	0.924703i	$-0.375686\pi$
$257$	−59.0535	−	34.0946i	−0.229780	−	0.132664i	−0.610471	+	0.792039i	$0.709020\pi$
$258$		0			0
$259$	−68.0332	−	60.7168i	−0.262676	−	0.234428i
$260$	21.8865			0.0841790
$261$		0			0
$262$	−87.6909	+	50.6283i	−0.334698	+	0.193238i
$263$	137.599	+	238.329i	0.523191	+	0.906193i	0.999636	+	0.0269887i	$0.00859180\pi$
$263$	137.599	+	238.329i	0.523191	+	0.906193i	−0.476445	+	0.879204i	$0.658075\pi$
$264$		0			0
$265$			150.665i			0.568547i
$266$	−12.4652	−	37.7967i	−0.0468618	−	0.142093i
$267$		0			0
$268$	−59.2683	+	102.656i	−0.221151	+	0.383044i
$269$	−198.847	+	114.804i	−0.739207	+	0.426782i	−0.821781	−	0.569803i	$-0.807019\pi$
$269$	−198.847	+	114.804i	−0.739207	+	0.426782i	0.0825736	+	0.996585i	$0.473686\pi$
$270$		0			0
$271$	451.013	+	260.393i	1.66425	+	0.960858i	0.970648	+	0.240504i	$0.0773128\pi$
$271$	451.013	+	260.393i	1.66425	+	0.960858i	0.693607	+	0.720354i	$0.256021\pi$
$272$		−	39.9167i		−	0.146753i
$273$		0			0
$274$	238.988			0.872219
$275$	−34.3233	+	59.4498i	−0.124812	+	0.216181i
$276$		0			0
$277$	193.738	+	335.564i	0.699414	+	1.21142i	0.968670	+	0.248352i	$0.0798891\pi$
$277$	193.738	+	335.564i	0.699414	+	1.21142i	−0.269255	+	0.963069i	$0.586778\pi$
$278$	−271.547	−	156.778i	−0.976788	−	0.563949i
$279$		0			0
$280$	−59.3393	+	66.4897i	−0.211926	+	0.237463i
$281$	157.972			0.562180			0.281090	−	0.959681i	$-0.409304\pi$
$281$	157.972			0.562180			0.281090	+	0.959681i	$0.409304\pi$
$282$		0			0
$283$	−39.0701	+	22.5571i	−0.138057	+	0.0797072i	−0.567438	−	0.823416i	$-0.692065\pi$
$283$	−39.0701	+	22.5571i	−0.138057	+	0.0797072i	0.429381	+	0.903124i	$0.358732\pi$
$284$	−53.1415	−	92.0439i	−0.187118	−	0.324098i
$285$		0			0
$286$			199.567i			0.697785i
$287$	378.974	+	78.8099i	1.32047	+	0.274599i
$288$		0			0
$289$	−142.475	+	246.774i	−0.492992	+	0.853888i
$290$	−73.1708	+	42.2452i	−0.252313	+	0.145673i
$291$		0			0
$292$	172.423	+	99.5484i	0.590489	+	0.340919i
$293$			54.4900i			0.185973i	0.995667	+	0.0929864i	$0.0296413\pi$
$293$			54.4900i			0.185973i	−0.995667	+	0.0929864i	$0.970359\pi$
$294$		0			0
$295$	−47.1501			−0.159831
$296$	−37.0840	+	64.2314i	−0.125284	+	0.216998i
$297$		0			0
$298$	−169.830	−	294.155i	−0.569901	−	0.987097i
$299$	85.4420	+	49.3300i	0.285759	+	0.164983i
$300$		0			0
$301$	−77.9830	+	374.997i	−0.259080	+	1.24584i
$302$	−345.363			−1.14359
$303$		0			0
$304$	−41.2966	+	23.8426i	−0.135844	+	0.0784296i
$305$	−29.5384	−	51.1620i	−0.0968472	−	0.167744i
$306$		0			0
$307$		−	176.942i		−	0.576357i	−0.957577	−	0.288178i	$-0.906950\pi$
$307$		−	176.942i		−	0.576357i	0.957577	−	0.288178i	$-0.0930496\pi$
$308$	114.180	+	101.901i	0.370714	+	0.330847i
$309$		0			0
$310$	54.8184	−	94.9483i	0.176834	−	0.306285i
$311$	189.438	−	109.372i	0.609125	−	0.351678i	−0.163498	−	0.986544i	$-0.552278\pi$
$311$	189.438	−	109.372i	0.609125	−	0.351678i	0.772623	+	0.634865i	$0.218944\pi$
$312$		0			0
$313$	132.570	+	76.5394i	0.423547	+	0.244535i	0.696594	−	0.717466i	$-0.254698\pi$
$313$	132.570	+	76.5394i	0.423547	+	0.244535i	−0.273047	+	0.962001i	$0.588031\pi$
$314$			471.379i			1.50121i
$315$		0			0
$316$	−156.216			−0.494354
$317$	−64.6285	+	111.940i	−0.203875	+	0.353122i	−0.949774	−	0.312937i	$-0.898687\pi$
$317$	−64.6285	+	111.940i	−0.203875	+	0.353122i	0.745898	+	0.666060i	$0.232020\pi$
$318$		0			0
$319$	−109.684	−	189.978i	−0.343836	−	0.595542i
$320$	43.1324	+	24.9025i	0.134789	+	0.0778203i
$321$		0			0
$322$	252.336	−	83.2198i	0.783652	−	0.258447i
$323$	−4.83864			−0.0149803
$324$		0			0
$325$	−26.6158	+	15.3666i	−0.0818948	+	0.0472820i
$326$	−151.465	−	262.344i	−0.464615	−	0.804737i
$327$		0			0
$328$		−	314.838i		−	0.959872i
$329$	333.624	−	373.827i	1.01406	−	1.13625i
$330$		0			0
$331$	−289.516	+	501.457i	−0.874672	+	1.51498i	−0.0175606	+	0.999846i	$0.505590\pi$
$331$	−289.516	+	501.457i	−0.874672	+	1.51498i	−0.857112	+	0.515131i	$0.827743\pi$
$332$	107.826	−	62.2532i	0.324776	−	0.187510i
$333$		0			0
$334$	−615.437	−	355.323i	−1.84262	−	1.06384i
$335$		−	166.450i		−	0.496866i
$336$		0			0
$337$	−14.2685			−0.0423397			−0.0211698	−	0.999776i	$-0.506739\pi$
$337$	−14.2685			−0.0423397			−0.0211698	+	0.999776i	$0.506739\pi$
$338$	155.155	−	268.736i	0.459037	−	0.795076i
$339$		0			0
$340$	−3.58307	−	6.20606i	−0.0105384	−	0.0182531i
$341$	246.520	+	142.328i	0.722933	+	0.417385i
$342$		0			0
$343$	197.925	−	280.133i	0.577041	−	0.816715i
$344$	311.535			0.905624
$345$		0			0
$346$	−228.925	+	132.170i	−0.661633	+	0.381994i
$347$	−94.0286	−	162.862i	−0.270976	−	0.469344i	0.698136	−	0.715965i	$-0.254013\pi$
$347$	−94.0286	−	162.862i	−0.270976	−	0.469344i	−0.969112	+	0.246621i	$0.920680\pi$
$348$		0			0
$349$		−	297.734i		−	0.853106i	−0.904463	−	0.426553i	$-0.859728\pi$
$349$		−	297.734i		−	0.853106i	0.904463	−	0.426553i	$-0.140272\pi$
$350$	−16.8518	+	81.0353i	−0.0481479	+	0.231529i
$351$		0			0
$352$	165.641	−	286.898i	0.470571	−	0.815052i
$353$	−384.830	+	222.182i	−1.09017	+	0.629410i	−0.933622	−	0.358260i	$-0.883370\pi$
$353$	−384.830	+	222.182i	−1.09017	+	0.629410i	−0.156549	+	0.987670i	$0.550037\pi$
$354$		0			0
$355$	129.249	+	74.6218i	0.364081	+	0.210202i
$356$			71.2120i			0.200034i
$357$		0			0
$358$	−833.238			−2.32748
$359$	−208.158	+	360.540i	−0.579827	+	1.00429i	0.415672	+	0.909515i	$0.363547\pi$
$359$	−208.158	+	360.540i	−0.579827	+	1.00429i	−0.995499	+	0.0947753i	$0.969787\pi$
$360$		0			0
$361$	−177.610	−	307.629i	−0.491994	−	0.852159i
$362$	315.351	+	182.068i	0.871135	+	0.502950i
$363$		0			0
$364$	21.4594	+	65.0684i	0.0589544	+	0.178759i
$365$	−279.573			−0.765955
$366$		0			0
$367$	−460.868	+	266.082i	−1.25577	+	0.725019i	−0.972249	−	0.233947i	$-0.924836\pi$
$367$	−460.868	+	266.082i	−1.25577	+	0.725019i	−0.283521	+	0.958966i	$0.591503\pi$
$368$	−159.177	−	275.702i	−0.432545	−	0.749191i
$369$		0			0
$370$			68.8840i			0.186173i
$371$	−447.925	+	147.725i	−1.20735	+	0.398180i
$372$		0			0
$373$	−254.610	+	440.997i	−0.682600	+	1.18230i	0.291584	+	0.956545i	$0.405818\pi$
$373$	−254.610	+	440.997i	−0.682600	+	1.18230i	−0.974185	+	0.225753i	$0.927516\pi$
$374$	56.5883	−	32.6713i	0.151306	−	0.0873564i
$375$		0			0
$376$	−352.937	−	203.768i	−0.938662	−	0.541937i
$377$		−	98.2114i		−	0.260508i
$378$		0			0
$379$	166.742			0.439953			0.219976	−	0.975505i	$-0.429402\pi$
$379$	166.742			0.439953			0.219976	+	0.975505i	$0.429402\pi$
$380$	−4.28040	+	7.41387i	−0.0112642	+	0.0195102i
$381$		0			0
$382$	90.8858	+	157.419i	0.237921	+	0.412091i
$383$	295.194	+	170.430i	0.770742	+	0.444988i	0.833139	−	0.553063i	$-0.186541\pi$
$383$	295.194	+	170.430i	0.770742	+	0.444988i	−0.0623972	+	0.998051i	$0.519875\pi$
$384$		0			0
$385$	−210.397	−	43.7533i	−0.546485	−	0.113645i
$386$	−786.357			−2.03719
$387$		0			0
$388$	43.6855	−	25.2218i	0.112591	−	0.0650047i
$389$	−14.9678	−	25.9249i	−0.0384775	−	0.0666450i	0.846145	−	0.532952i	$-0.178917\pi$
$389$	−14.9678	−	25.9249i	−0.0384775	−	0.0666450i	−0.884623	+	0.466307i	$0.845584\pi$
$390$		0			0
$391$		−	32.3035i		−	0.0826176i
$392$	−255.854	−	111.223i	−0.652690	−	0.283732i
$393$		0			0
$394$	145.153	−	251.412i	0.368408	−	0.638102i
$395$	189.971	−	109.680i	0.480940	−	0.277671i
$396$		0			0
$397$	415.166	+	239.696i	1.04576	+	0.603769i	0.921459	−	0.388476i	$-0.126998\pi$
$397$	415.166	+	239.696i	1.04576	+	0.603769i	0.124300	+	0.992245i	$0.460332\pi$
$398$		−	200.727i		−	0.504340i
$399$		0			0
$400$	99.1693			0.247923
$401$	−304.548	+	527.492i	−0.759470	+	1.31544i	0.183651	+	0.982991i	$0.441208\pi$
$401$	−304.548	+	527.492i	−0.759470	+	1.31544i	−0.943121	+	0.332449i	$0.892125\pi$
$402$		0			0
$403$	63.7208	+	110.368i	0.158116	+	0.273865i
$404$	−101.461	−	58.5783i	−0.251140	−	0.144996i
$405$		0			0
$406$	−197.337	−	176.115i	−0.486052	−	0.433781i
$407$	−178.848			−0.439430
$408$		0			0
$409$	−438.488	+	253.161i	−1.07210	+	0.618976i	−0.928754	−	0.370696i	$-0.879119\pi$
$409$	−438.488	+	253.161i	−1.07210	+	0.618976i	−0.143344	+	0.989673i	$0.545786\pi$
$410$	−146.204	−	253.232i	−0.356595	−	0.617640i
$411$		0			0
$412$		−	44.0643i		−	0.106952i
$413$	−46.2300	−	140.177i	−0.111937	−	0.339411i
$414$		0			0
$415$	−87.4165	+	151.410i	−0.210642	+	0.364843i
$416$	128.445	−	74.1578i	0.308762	−	0.178264i
$417$		0			0
$418$	−67.6014	−	39.0297i	−0.161726	−	0.0933725i
$419$		−	600.983i		−	1.43433i	−0.696905	−	0.717163i	$-0.745440\pi$
$419$		−	600.983i		−	1.43433i	0.696905	−	0.717163i	$-0.254560\pi$
$420$		0			0
$421$	−277.147			−0.658307			−0.329153	−	0.944276i	$-0.606763\pi$
$421$	−277.147			−0.658307			−0.329153	+	0.944276i	$0.606763\pi$
$422$	168.537	−	291.914i	0.399376	−	0.691739i
$423$		0			0
$424$	191.814	+	332.232i	0.452392	+	0.783565i
$425$	8.71461	+	5.03138i	0.0205050	+	0.0118385i
$426$		0			0
$427$	123.142	−	137.981i	0.288389	−	0.323140i
$428$	131.030			0.306145
$429$		0			0
$430$	250.575	−	144.670i	0.582733	−	0.336441i
$431$	−203.623	−	352.686i	−0.472444	−	0.818296i	0.527059	−	0.849829i	$-0.323295\pi$
$431$	−203.623	−	352.686i	−0.472444	−	0.818296i	−0.999503	+	0.0315322i	$0.989961\pi$
$432$		0			0
$433$			312.356i			0.721377i	0.932686	+	0.360689i	$0.117458\pi$
$433$			312.356i			0.721377i	−0.932686	+	0.360689i	$0.882542\pi$
$434$	336.028	+	69.8792i	0.774259	+	0.161012i
$435$		0			0
$436$	26.9604	−	46.6968i	0.0618358	−	0.107103i
$437$	−33.4202	+	19.2952i	−0.0764764	+	0.0441537i
$438$		0			0
$439$	−184.053	−	106.263i	−0.419255	−	0.242057i	0.275504	−	0.961300i	$-0.411155\pi$
$439$	−184.053	−	106.263i	−0.419255	−	0.242057i	−0.694758	+	0.719243i	$0.744489\pi$
$440$			174.790i			0.397251i
$441$		0			0
$442$	29.2540			0.0661855
$443$	−185.709	+	321.658i	−0.419208	+	0.726089i	−0.995860	−	0.0909005i	$-0.971025\pi$
$443$	−185.709	+	321.658i	−0.419208	+	0.726089i	0.576652	+	0.816990i	$0.304359\pi$
$444$		0			0
$445$	−49.9982	−	86.5995i	−0.112356	−	0.194606i
$446$	−470.940	−	271.897i	−1.05592	−	0.609635i
$447$		0			0
$448$	−31.7442	+	152.648i	−0.0708575	+	0.340733i
$449$	−4.22975			−0.00942037			−0.00471018	−	0.999989i	$-0.501499\pi$
$449$	−4.22975			−0.00942037			−0.00471018	+	0.999989i	$0.501499\pi$
$450$		0			0
$451$	657.483	−	379.598i	1.45783	−	0.841681i
$452$	−29.2635	−	50.6859i	−0.0647422	−	0.112137i
$453$		0			0
$454$			812.869i			1.79046i
$455$	−71.7812	−	64.0617i	−0.157761	−	0.140795i
$456$		0			0
$457$	−250.605	+	434.061i	−0.548371	+	0.949806i	0.450016	+	0.893021i	$0.351418\pi$
$457$	−250.605	+	434.061i	−0.548371	+	0.949806i	−0.998386	+	0.0567855i	$0.981915\pi$
$458$	1.80025	−	1.03937i	0.00393067	−	0.00226937i
$459$		0			0
$460$	−49.4961	−	28.5766i	−0.107600	−	0.0621230i
$461$			300.121i			0.651022i	0.945538	+	0.325511i	$0.105536\pi$
$461$			300.121i			0.651022i	−0.945538	+	0.325511i	$0.894464\pi$
$462$		0			0
$463$	571.548			1.23444			0.617222	−	0.786789i	$-0.288258\pi$
$463$	571.548			1.23444			0.617222	+	0.786789i	$0.288258\pi$
$464$	−158.453	+	274.449i	−0.341493	+	0.591484i
$465$		0			0
$466$	−122.806	−	212.706i	−0.263531	−	0.456450i
$467$	771.238	+	445.274i	1.65147	+	0.953478i	0.976467	+	0.215665i	$0.0691918\pi$
$467$	771.238	+	445.274i	1.65147	+	0.953478i	0.675005	+	0.737813i	$0.264142\pi$
$468$		0			0
$469$	494.854	−	163.202i	1.05513	−	0.347978i
$470$	−378.502			−0.805323
$471$		0			0
$472$	−103.971	+	60.0276i	−0.220277	+	0.127177i
$473$	375.615	+	650.585i	0.794112	+	1.37544i
$474$		0			0
$475$		−	12.0212i		−	0.0253077i
$476$	14.9374	−	16.7374i	0.0313811	−	0.0351625i
$477$		0			0
$478$	189.097	−	327.525i	0.395600	−	0.685199i
$479$	28.6660	−	16.5503i	0.0598456	−	0.0345519i	−0.469779	−	0.882784i	$-0.655666\pi$
$479$	28.6660	−	16.5503i	0.0598456	−	0.0345519i	0.529624	+	0.848232i	$0.322333\pi$
$480$		0			0
$481$	−69.3432	−	40.0353i	−0.144165	−	0.0832335i
$482$		−	609.775i		−	1.26509i
$483$		0			0
$484$	107.479			0.222064
$485$	−35.4167	+	61.3435i	−0.0730241	+	0.126482i
$486$		0			0
$487$	307.943	+	533.374i	0.632327	+	1.09522i	0.987075	+	0.160261i	$0.0512335\pi$
$487$	307.943	+	533.374i	0.632327	+	1.09522i	−0.354747	+	0.934962i	$0.615433\pi$
$488$	−130.270	−	75.2116i	−0.266947	−	0.154122i
$489$		0			0
$490$	−257.440	+	29.3536i	−0.525387	+	0.0599054i
$491$	223.560			0.455316			0.227658	−	0.973741i	$-0.426893\pi$
$491$	223.560			0.455316			0.227658	+	0.973741i	$0.426893\pi$
$492$		0			0
$493$	−27.8484	+	16.0783i	−0.0564877	+	0.0326132i
$494$	−17.4737	−	30.2653i	−0.0353718	−	0.0612658i
$495$		0			0
$496$		−	411.225i		−	0.829083i
$497$	−95.1234	+	457.420i	−0.191395	+	0.920363i
$498$		0			0
$499$	410.782	−	711.496i	0.823211	−	1.42584i	−0.0800672	−	0.996789i	$-0.525513\pi$
$499$	410.782	−	711.496i	0.823211	−	1.42584i	0.903279	−	0.429054i	$-0.141153\pi$
$500$	15.4184	−	8.90181i	0.0308368	−	0.0178036i
$501$		0			0
$502$	−303.155	−	175.026i	−0.603893	−	0.348658i
$503$			173.706i			0.345340i	0.984980	+	0.172670i	$0.0552394\pi$
$503$			173.706i			0.345340i	−0.984980	+	0.172670i	$0.944761\pi$
$504$		0			0
$505$	164.512			0.325767
$506$	260.568	−	451.317i	0.514956	−	0.891931i
$507$		0			0
$508$	144.141	+	249.659i	0.283742	+	0.491455i
$509$	397.384	+	229.430i	0.780715	+	0.450746i	0.836684	−	0.547686i	$-0.184491\pi$
$509$	397.384	+	229.430i	0.780715	+	0.450746i	−0.0559685	+	0.998433i	$0.517825\pi$
$510$		0			0
$511$	−274.117	−	831.168i	−0.536433	−	1.62655i
$512$	−26.8805			−0.0525010
$513$		0			0
$514$	−139.651	+	80.6278i	−0.271695	+	0.156863i
$515$	30.9377	+	53.5857i	0.0600732	+	0.104050i
$516$		0			0
$517$		−	982.727i		−	1.90083i
$518$	−204.791	+	67.5397i	−0.395350	+	0.130385i
$519$		0			0
$520$	−39.1270	+	67.7700i	−0.0752443	+	0.130327i
$521$	−388.712	+	224.423i	−0.746089	+	0.430755i	−0.824279	−	0.566184i	$-0.808419\pi$
$521$	−388.712	+	224.423i	−0.746089	+	0.430755i	0.0781902	+	0.996938i	$0.475086\pi$
$522$		0			0
$523$	330.871	+	191.028i	0.632640	+	0.365255i	0.781774	−	0.623562i	$-0.214315\pi$
$523$	330.871	+	191.028i	0.632640	+	0.365255i	−0.149134	+	0.988817i	$0.547649\pi$
$524$			68.1833i			0.130121i
$525$		0			0
$526$	650.796			1.23726
$527$	20.8636	−	36.1368i	0.0395894	−	0.0685708i
$528$		0			0
$529$	135.683	+	235.009i	0.256489	+	0.444252i
$530$	308.562	+	178.148i	0.582192	+	0.336129i
$531$		0			0
$532$	−26.2382	−	5.45640i	−0.0493200	−	0.0102564i
$533$	339.894			0.637700
$534$		0			0
$535$	−159.343	+	91.9967i	−0.297837	+	0.171956i
$536$	−211.910	−	367.040i	−0.395355	−	0.684775i
$537$		0			0
$538$			542.984i			1.00926i
$539$	−76.2127	−	668.407i	−0.141396	−	1.24009i
$540$		0			0
$541$	−102.522	+	177.573i	−0.189504	+	0.328231i	−0.945085	−	0.326825i	$-0.894021\pi$
$541$	−102.522	+	177.573i	−0.189504	+	0.328231i	0.755581	+	0.655055i	$0.227355\pi$
$542$	1066.57	−	615.783i	1.96784	−	1.13613i
$543$		0			0
$544$	−42.0558	−	24.2809i	−0.0773084	−	0.0446340i
$545$			75.7161i			0.138929i
$546$		0			0
$547$	−182.754			−0.334102			−0.167051	−	0.985948i	$-0.553424\pi$
$547$	−182.754			−0.334102			−0.167051	+	0.985948i	$0.553424\pi$
$548$	80.4637	−	139.367i	0.146832	−	0.254320i
$549$		0			0
$550$	81.1688	+	140.588i	0.147580	+	0.255615i
$551$	33.2682	+	19.2074i	0.0603779	+	0.0348592i
$552$		0			0
$553$	512.341	+	457.243i	0.926475	+	0.826840i
$554$	916.312			1.65399
$555$		0			0
$556$	−182.852	+	105.570i	−0.328870	+	0.189873i
$557$	405.832	+	702.922i	0.728604	+	1.26198i	0.957473	+	0.288522i	$0.0931637\pi$
$557$	405.832	+	702.922i	0.728604	+	1.26198i	−0.228870	+	0.973457i	$0.573503\pi$
$558$		0			0
$559$			336.328i			0.601659i
$560$	97.2339	+	294.829i	0.173632	+	0.526481i
$561$		0			0
$562$	186.789	−	323.528i	0.332364	−	0.575672i
$563$	275.702	−	159.176i	0.489701	−	0.282729i	−0.234749	−	0.972056i	$-0.575427\pi$
$563$	275.702	−	159.176i	0.489701	−	0.282729i	0.724450	+	0.689327i	$0.242094\pi$
$564$		0			0
$565$	71.1735	+	41.0921i	0.125971	+	0.0727293i
$566$			106.687i			0.188494i
$567$		0			0
$568$	380.009			0.669030
$569$	299.181	−	518.196i	0.525801	−	0.910714i	−0.473747	−	0.880661i	$-0.657099\pi$
$569$	299.181	−	518.196i	0.525801	−	0.910714i	0.999548	−	0.0300533i	$-0.00956769\pi$
$570$		0			0
$571$	−436.429	−	755.917i	−0.764324	−	1.32385i	−0.940603	−	0.339508i	$-0.889740\pi$
$571$	−436.429	−	755.917i	−0.764324	−	1.32385i	0.176279	−	0.984340i	$-0.443594\pi$
$572$	116.378	+	67.1911i	0.203459	+	0.117467i
$573$		0			0
$574$	609.506	−	682.953i	1.06186	−	1.18981i
$575$	80.2550			0.139574
$576$		0			0
$577$	639.833	−	369.408i	1.10890	−	0.640222i	0.170353	−	0.985383i	$-0.445509\pi$
$577$	639.833	−	369.408i	1.10890	−	0.640222i	0.938543	+	0.345162i	$0.112176\pi$
$578$	336.928	+	583.577i	0.582921	+	1.00965i
$579$		0			0
$580$			56.8933i			0.0980919i
$581$	−535.850	−	111.433i	−0.922289	−	0.191796i
$582$		0			0
$583$	−462.538	+	801.139i	−0.793375	+	1.37417i
$584$	−616.488	+	355.929i	−1.05563	+	0.609468i
$585$		0			0
$586$	111.596	+	64.4297i	0.190436	+	0.109948i
$587$		−	149.507i		−	0.254697i	−0.991858	−	0.127349i	$-0.959353\pi$
$587$		−	149.507i		−	0.254697i	0.991858	−	0.127349i	$-0.0406467\pi$
$588$		0			0
$589$	−49.8481			−0.0846317
$590$	−55.7510	+	96.5635i	−0.0944931	+	0.163667i
$591$		0			0
$592$	129.185	+	223.755i	0.218218	+	0.377964i
$593$	219.713	+	126.851i	0.370511	+	0.213914i	0.673682	−	0.739022i	$-0.264712\pi$
$593$	219.713	+	126.851i	0.370511	+	0.213914i	−0.303171	+	0.952936i	$0.598045\pi$
$594$		0			0
$595$	−6.41370	+	30.8416i	−0.0107793	+	0.0518346i
$596$	−228.718			−0.383754
$597$		0			0
$598$	202.056	−	116.657i	0.337886	−	0.195078i
$599$	261.282	+	452.554i	0.436197	+	0.755515i	0.997392	−	0.0721679i	$-0.0229918\pi$
$599$	261.282	+	452.554i	0.436197	+	0.755515i	−0.561196	+	0.827683i	$0.689658\pi$
$600$		0			0
$601$			956.828i			1.59206i	0.605258	+	0.796030i	$0.293070\pi$
$601$			956.828i			1.59206i	−0.605258	+	0.796030i	$0.706930\pi$
$602$	675.786	+	603.111i	1.12257	+	1.00185i
$603$		0			0
$604$	−116.279	+	201.401i	−0.192514	+	0.333445i
$605$	−130.703	+	75.4614i	−0.216038	+	0.124730i
$606$		0			0
$607$	−239.609	−	138.338i	−0.394743	−	0.227905i	0.289470	−	0.957187i	$-0.406521\pi$
$607$	−239.609	−	138.338i	−0.394743	−	0.227905i	−0.684213	+	0.729282i	$0.739854\pi$
$608$			58.0128i			0.0954158i
$609$		0			0
$610$	−139.706			−0.229027
$611$	219.985	−	381.025i	0.360040	−	0.623608i
$612$		0			0
$613$	107.119	+	185.535i	0.174745	+	0.302668i	0.940073	−	0.340973i	$-0.110756\pi$
$613$	107.119	+	185.535i	0.174745	+	0.302668i	−0.765328	+	0.643641i	$0.777423\pi$
$614$	−362.376	−	209.218i	−0.590189	−	0.340746i
$615$		0			0
$616$	−519.649	+	171.379i	−0.843587	+	0.278213i
$617$	−1133.85			−1.83769			−0.918844	−	0.394620i	$-0.870876\pi$
$617$	−1133.85			−1.83769			−0.918844	+	0.394620i	$0.870876\pi$
$618$		0			0
$619$	646.950	−	373.517i	1.04515	−	0.603420i	0.123865	−	0.992299i	$-0.460471\pi$
$619$	646.950	−	373.517i	1.04515	−	0.603420i	0.921289	+	0.388879i	$0.127138\pi$
$620$	−36.9131	−	63.9354i	−0.0595372	−	0.103122i
$621$		0			0
$622$		−	517.292i		−	0.831658i
$623$	208.437	−	233.553i	0.334569	−	0.374885i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	313.505	−	181.002i	0.500807	−	0.289141i
$627$		0			0
$628$	274.888	+	158.706i	0.437719	+	0.252717i
$629$			26.2169i			0.0416803i
$630$		0			0
$631$	−879.471			−1.39377			−0.696887	−	0.717181i	$-0.745432\pi$
$631$	−879.471			−1.39377			−0.696887	+	0.717181i	$0.745432\pi$
$632$	279.270	−	483.711i	0.441884	−	0.765365i
$633$		0			0
$634$	152.835	+	264.718i	0.241065	+	0.417537i
$635$	−350.573	−	202.404i	−0.552084	−	0.318746i
$636$		0			0
$637$	120.074	−	276.216i	0.188500	−	0.433620i
$638$	−518.766			−0.813114
$639$		0			0
$640$	288.907	−	166.800i	0.451417	−	0.260625i
$641$	−146.735	−	254.153i	−0.228916	−	0.396494i	0.728571	−	0.684970i	$-0.240185\pi$
$641$	−146.735	−	254.153i	−0.228916	−	0.396494i	−0.957487	+	0.288476i	$0.906851\pi$
$642$		0			0
$643$			401.514i			0.624439i	0.950010	+	0.312219i	$0.101072\pi$
$643$			401.514i			0.624439i	−0.950010	+	0.312219i	$0.898928\pi$
$644$	36.4277	−	175.170i	0.0565648	−	0.272003i
$645$		0			0
$646$	−5.72127	+	9.90954i	−0.00885646	+	0.0153398i
$647$	783.686	−	452.461i	1.21126	−	0.699322i	0.248227	−	0.968702i	$-0.420152\pi$
$647$	783.686	−	452.461i	1.21126	−	0.699322i	0.963034	+	0.269380i	$0.0868189\pi$
$648$		0			0
$649$	−250.714	−	144.750i	−0.386308	−	0.223035i
$650$			72.6789i			0.111814i
$651$		0			0
$652$	−203.984			−0.312858
$653$	−216.459	+	374.918i	−0.331484	+	0.574148i	−0.982803	−	0.184657i	$-0.940883\pi$
$653$	−216.459	+	374.918i	−0.331484	+	0.574148i	0.651319	+	0.758804i	$0.274216\pi$
$654$		0			0
$655$	−47.8718	−	82.9163i	−0.0730867	−	0.126590i
$656$	−949.823	−	548.380i	−1.44790	−	0.835946i
$657$		0			0
$658$	−371.115	−	1125.28i	−0.564004	−	1.71015i
$659$	−358.497			−0.544002			−0.272001	−	0.962297i	$-0.587685\pi$
$659$	−358.497			−0.544002			−0.272001	+	0.962297i	$0.587685\pi$
$660$		0			0
$661$	804.899	−	464.709i	1.21770	−	0.703039i	0.253274	−	0.967395i	$-0.418492\pi$
$661$	804.899	−	464.709i	1.21770	−	0.703039i	0.964425	+	0.264355i	$0.0851592\pi$
$662$	684.656	+	1185.86i	1.03422	+	1.79133i
$663$		0			0
$664$			445.165i			0.670429i
$665$	35.7387	−	11.7865i	0.0537425	−	0.0177241i
$666$		0			0
$667$	−128.232	+	222.104i	−0.192251	+	0.332989i
$668$	−414.417	+	239.264i	−0.620385	+	0.358179i
$669$		0			0
$670$	−340.890	−	196.813i	−0.508791	−	0.293751i
$671$		−	362.728i		−	0.540579i
$672$		0			0
$673$	−853.958			−1.26888			−0.634442	−	0.772971i	$-0.718770\pi$
$673$	−853.958			−1.26888			−0.634442	+	0.772971i	$0.718770\pi$
$674$	−16.8712	+	29.2218i	−0.0250315	+	0.0433558i
$675$		0			0
$676$	−104.477	−	180.959i	−0.154551	−	0.267690i
$677$	−321.116	−	185.396i	−0.474321	−	0.273850i	0.243726	−	0.969844i	$-0.421630\pi$
$677$	−321.116	−	185.396i	−0.474321	−	0.273850i	−0.718047	+	0.695995i	$0.754964\pi$
$678$		0			0
$679$	−217.099	−	45.1471i	−0.319734	−	0.0664905i
$680$	25.6221			0.0376796
$681$		0			0
$682$	582.977	−	336.582i	0.854805	−	0.493522i
$683$	−364.738	−	631.744i	−0.534023	−	0.924955i	−0.999210	−	0.0397422i	$-0.987346\pi$
$683$	−364.738	−	631.744i	−0.534023	−	0.924955i	0.465187	−	0.885212i	$-0.345987\pi$
$684$		0			0
$685$			225.976i			0.329892i
$686$	−339.683	−	736.584i	−0.495165	−	1.07374i
$687$		0			0
$688$	542.626	−	939.856i	0.788701	−	1.36607i
$689$	−358.672	+	207.079i	−0.520568	+	0.300550i
$690$		0			0
$691$	4.35725	+	2.51566i	0.00630572	+	0.00364061i	0.503150	−	0.864199i	$-0.332174\pi$
$691$	4.35725	+	2.51566i	0.00630572	+	0.00364061i	−0.496844	+	0.867840i	$0.665508\pi$
$692$			177.999i			0.257224i
$693$		0			0
$694$	−444.723			−0.640811
$695$	148.242	−	256.762i	0.213297	−	0.369442i
$696$		0			0
$697$	−55.6444	−	96.3790i	−0.0798342	−	0.138277i
$698$	−609.759	−	352.045i	−0.873581	−	0.504362i
$699$		0			0
$700$	41.5824	+	37.1106i	0.0594035	+	0.0530151i
$701$	132.748			0.189370			0.0946850	−	0.995507i	$-0.469816\pi$
$701$	132.748			0.189370			0.0946850	+	0.995507i	$0.469816\pi$
$702$		0			0
$703$	27.1232	−	15.6596i	0.0385821	−	0.0222754i
$704$	152.900	+	264.830i	0.217187	+	0.376180i
$705$		0			0
$706$			1050.84i			1.48845i
$707$	161.302	+	489.093i	0.228149	+	0.691786i
$708$		0			0
$709$	81.9066	−	141.866i	0.115524	−	0.200094i	−0.802465	−	0.596699i	$-0.796479\pi$
$709$	81.9066	−	141.866i	0.115524	−	0.200094i	0.917989	+	0.396606i	$0.129812\pi$
$710$	305.651	−	176.468i	0.430494	−	0.248546i
$711$		0			0
$712$	−220.502	−	127.307i	−0.309694	−	0.178802i
$713$		−	332.793i		−	0.466750i
$714$		0			0
$715$	−188.701			−0.263917
$716$	−280.539	+	485.908i	−0.391814	+	0.678642i
$717$		0			0
$718$	492.257	+	852.615i	0.685595	+	1.18749i
$719$	−1229.91	−	710.091i	−1.71059	−	0.987609i	−0.933762	−	0.357895i	$-0.883495\pi$
$719$	−1229.91	−	710.091i	−1.71059	−	0.987609i	−0.776827	−	0.629714i	$-0.783172\pi$
$720$		0			0
$721$	−128.976	+	144.517i	−0.178884	+	0.200440i
$722$	−840.033			−1.16348
$723$		0			0
$724$	212.348	−	122.599i	0.293298	−	0.169336i
$725$	−39.9451	−	69.1869i	−0.0550966	−	0.0954302i
$726$		0			0
$727$		−	1115.52i		−	1.53441i	−0.641403	−	0.767204i	$-0.721647\pi$
$727$		−	1115.52i		−	1.53441i	0.641403	−	0.767204i	$-0.278353\pi$
$728$	−239.843	−	49.8767i	−0.329454	−	0.0685120i
$729$		0			0
$730$	−330.571	+	572.566i	−0.452838	+	0.784338i
$731$	95.3677	−	55.0606i	0.130462	−	0.0753223i
$732$		0			0
$733$	−532.598	−	307.496i	−0.726600	−	0.419503i	0.0905770	−	0.995889i	$-0.471129\pi$
$733$	−532.598	−	307.496i	−0.726600	−	0.419503i	−0.817177	+	0.576387i	$0.804462\pi$
$734$			1258.48i			1.71454i
$735$		0			0
$736$	−387.302			−0.526226
$737$	510.998	−	885.074i	0.693348	−	1.20091i
$738$		0			0
$739$	169.560	+	293.687i	0.229446	+	0.397412i	0.957644	−	0.287955i	$-0.0929753\pi$
$739$	169.560	+	293.687i	0.229446	+	0.397412i	−0.728198	+	0.685367i	$0.759642\pi$
$740$	40.1701	+	23.1922i	0.0542839	+	0.0313409i
$741$		0			0
$742$	−227.093	+	1092.02i	−0.306055	+	1.47173i
$743$	1032.93			1.39021			0.695105	−	0.718909i	$-0.255358\pi$
$743$	1032.93			1.39021			0.695105	+	0.718909i	$0.255358\pi$
$744$		0			0
$745$	278.139	−	160.584i	0.373341	−	0.215548i
$746$	602.108	+	1042.88i	0.807115	+	1.39796i
$747$		0			0
$748$		−	43.9997i		−	0.0588232i
$749$	−429.738	−	383.523i	−0.573749	−	0.512047i
$750$		0			0
$751$	273.235	−	473.257i	0.363829	−	0.630170i	−0.624759	−	0.780818i	$-0.714803\pi$
$751$	273.235	−	473.257i	0.363829	−	0.630170i	0.988587	+	0.150648i	$0.0481361\pi$
$752$	−1229.48	+	709.841i	−1.63495	+	0.943937i
$753$		0			0
$754$	−201.137	−	116.126i	−0.266760	−	0.154014i
$755$		−	326.559i		−	0.432529i
$756$		0			0
$757$	191.558			0.253049			0.126524	−	0.991964i	$-0.459618\pi$
$757$	191.558			0.253049			0.126524	+	0.991964i	$0.459618\pi$
$758$	197.158	−	341.488i	0.260103	−	0.450511i
$759$		0			0
$760$	−15.3043	−	26.5079i	−0.0201373	−	0.0348788i
$761$	471.813	+	272.401i	0.619990	+	0.357952i	0.776865	−	0.629667i	$-0.216809\pi$
$761$	471.813	+	272.401i	0.619990	+	0.357952i	−0.156875	+	0.987618i	$0.550142\pi$
$762$		0			0
$763$	−225.103	+	74.2384i	−0.295024	+	0.0972980i
$764$	122.400			0.160209
$765$		0			0
$766$	698.083	−	403.038i	0.911336	−	0.526160i
$767$	−64.8048	−	112.245i	−0.0844912	−	0.146343i
$768$		0			0
$769$		−	120.495i		−	0.156691i	−0.996926	−	0.0783453i	$-0.975036\pi$
$769$		−	120.495i		−	0.156691i	0.996926	−	0.0783453i	$-0.0249637\pi$
$770$	−338.383	+	379.158i	−0.439458	+	0.492413i
$771$		0			0
$772$	−264.755	+	458.569i	−0.342947	+	0.594001i
$773$	1146.74	−	662.070i	1.48349	−	0.856495i	0.483668	−	0.875251i	$-0.339304\pi$
$773$	1146.74	−	662.070i	1.48349	−	0.856495i	0.999824	+	0.0187565i	$0.00597072\pi$
$774$		0			0
$775$	89.7786	+	51.8337i	0.115843	+	0.0668822i
$776$			180.358i			0.232420i
$777$		0			0
$778$	−70.7923			−0.0909926
$779$	−66.4738	+	115.136i	−0.0853323	+	0.147800i
$780$		0			0
$781$	458.174	+	793.581i	0.586650	+	1.01611i
$782$	−66.1575	−	38.1961i	−0.0846004	−	0.0488441i
$783$		0			0
$784$	−781.187	+	578.150i	−0.996412	+	0.737437i
$785$	−445.714			−0.567788
$786$		0			0
$787$	−1131.71	+	653.396i	−1.43801	+	0.830236i	−0.997712	−	0.0676145i	$-0.978461\pi$
$787$	−1131.71	+	653.396i	−1.43801	+	0.830236i	−0.440300	+	0.897851i	$0.645128\pi$
$788$	−97.7416	−	169.293i	−0.124038	−	0.214839i
$789$		0			0
$790$		−	518.748i		−	0.656643i
$791$	−52.3817	+	251.888i	−0.0662221	+	0.318443i
$792$		0			0
$793$	81.1972	−	140.638i	0.102392	−	0.177349i
$794$	981.796	−	566.840i	1.23652	−	0.713904i
$795$		0			0
$796$	−117.055	−	67.5819i	−0.147054	−	0.0849019i
$797$		−	263.263i		−	0.330317i	−0.986267	−	0.165159i	$-0.947186\pi$
$797$		−	263.263i		−	0.330317i	0.986267	−	0.165159i	$-0.0528136\pi$
$798$		0			0
$799$	−144.056			−0.180295
$800$	60.3237	−	104.484i	0.0754046	−	0.130605i
$801$		0			0
$802$	720.202	+	1247.43i	0.898007	+	1.55539i
$803$	−1486.59	−	858.283i	−1.85130	−	1.06885i
$804$		0			0
$805$	78.6887	+	238.597i	0.0977500	+	0.296394i
$806$	301.377			0.373917
$807$		0			0
$808$	362.766	−	209.443i	0.448968	−	0.259212i
$809$	−296.062	−	512.795i	−0.365961	−	0.633863i	0.622969	−	0.782247i	$-0.285926\pi$
$809$	−296.062	−	512.795i	−0.365961	−	0.633863i	−0.988930	+	0.148384i	$0.952593\pi$
$810$		0			0
$811$			34.9609i			0.0431083i	0.999768	+	0.0215542i	$0.00686144\pi$
$811$			34.9609i			0.0431083i	−0.999768	+	0.0215542i	$0.993139\pi$
$812$	−169.143	+	55.7830i	−0.208304	+	0.0686983i
$813$		0			0
$814$	−211.472	+	366.280i	−0.259794	+	0.449976i
$815$	248.060	−	143.218i	0.304369	−	0.175727i
$816$		0			0
$817$	−113.928	−	65.7763i	−0.139447	−	0.0805096i
$818$			1197.37i			1.46377i
$819$		0			0
$820$	−196.899			−0.240120
$821$	−412.442	+	714.371i	−0.502365	+	0.870122i	0.497631	+	0.867389i	$0.334203\pi$
$821$	−412.442	+	714.371i	−0.502365	+	0.870122i	−0.999996	+	0.00273351i	$0.999130\pi$
$822$		0			0
$823$	−421.891	−	730.737i	−0.512626	−	0.887894i	−0.999893	−	0.0146410i	$-0.995339\pi$
$823$	−421.891	−	730.737i	−0.512626	−	0.887894i	0.487267	−	0.873253i	$-0.337994\pi$
$824$	136.442	+	78.7745i	0.165584	+	0.0956002i
$825$		0			0
$826$	−341.745	−	71.0679i	−0.413735	−	0.0860387i
$827$	−359.972			−0.435274			−0.217637	−	0.976030i	$-0.569835\pi$
$827$	−359.972			−0.435274			−0.217637	+	0.976030i	$0.569835\pi$
$828$		0			0
$829$	−1290.05	+	744.811i	−1.55615	+	0.898446i	−0.558534	+	0.829481i	$0.688636\pi$
$829$	−1290.05	+	744.811i	−1.55615	+	0.898446i	−0.997619	+	0.0689641i	$0.978031\pi$
$830$	206.725	+	358.058i	0.249066	+	0.431395i
$831$		0			0
$832$			136.907i			0.164552i
$833$	−97.9802	+	11.1718i	−0.117623	+	0.0134116i
$834$		0			0
$835$	335.976	−	581.928i	0.402367	−	0.696920i
$836$	−45.5208	+	26.2814i	−0.0544507	+	0.0314371i
$837$		0			0
$838$	−1230.81	−	710.610i	−1.46875	−	0.847983i
$839$			778.799i			0.928247i	0.885770	+	0.464124i	$0.153631\pi$
$839$			778.799i			0.928247i	−0.885770	+	0.464124i	$0.846369\pi$
$840$		0			0
$841$	−585.703			−0.696436
$842$	−327.703	+	567.597i	−0.389195	+	0.674106i
$843$		0			0
$844$	−113.488	−	196.566i	−0.134464	−	0.232898i
$845$	254.104	+	146.707i	0.300715	+	0.173618i
$846$		0			0
$847$	−352.498	−	314.590i	−0.416172	−	0.371416i
$848$	1336.40			1.57594
$849$		0			0
$850$	20.6085	−	11.8983i	0.0242453	−	0.0139981i
$851$	104.546	+	181.078i	0.122850	+	0.212783i
$852$		0			0
$853$		−	496.640i		−	0.582228i	−0.956688	−	0.291114i	$-0.905974\pi$
$853$		−	496.640i		−	0.582228i	0.956688	−	0.291114i	$-0.0940259\pi$
$854$	−136.980	−	415.345i	−0.160398	−	0.486353i
$855$		0			0
$856$	−234.245	+	405.724i	−0.273650	+	0.473977i
$857$	112.697	−	65.0654i	0.131501	−	0.0759223i	−0.432806	−	0.901487i	$-0.642477\pi$
$857$	112.697	−	65.0654i	0.131501	−	0.0759223i	0.564307	+	0.825565i	$0.309143\pi$
$858$		0			0
$859$	762.753	+	440.376i	0.887954	+	0.512661i	0.873273	−	0.487232i	$-0.161993\pi$
$859$	762.753	+	440.376i	0.887954	+	0.512661i	0.0146815	+	0.999892i	$0.495327\pi$
$860$		−	194.833i		−	0.226550i
$861$		0			0
$862$	−963.067			−1.11725
$863$	−389.409	+	674.477i	−0.451227	+	0.781549i	−0.998463	−	0.0554301i	$-0.982347\pi$
$863$	−389.409	+	674.477i	−0.451227	+	0.781549i	0.547235	+	0.836979i	$0.315680\pi$
$864$		0			0
$865$	−124.974	−	216.461i	−0.144478	−	0.250244i
$866$	639.706	+	369.334i	0.738690	+	0.426483i
$867$		0			0
$868$	153.886	−	172.430i	0.177288	−	0.198652i
$869$	1346.86			1.54989
$870$		0			0
$871$	396.250	−	228.775i	0.454936	−	0.262658i
$872$	96.3953	+	166.962i	0.110545	+	0.191470i
$873$		0			0
$874$			91.2594i			0.104416i
$875$	−76.6231	−	15.9342i	−0.0875693	−	0.0182106i
$876$		0			0
$877$	31.3183	−	54.2449i	0.0357107	−	0.0618528i	−0.847618	−	0.530607i	$-0.821964\pi$
$877$	31.3183	−	54.2449i	0.0357107	−	0.0618528i	0.883328	+	0.468755i	$0.155297\pi$
$878$	−435.253	+	251.293i	−0.495732	+	0.286211i
$879$		0			0
$880$	527.318	+	304.447i	0.599225	+	0.345963i
$881$			1073.96i			1.21902i	0.792777	+	0.609512i	$0.208635\pi$
$881$			1073.96i			1.21902i	−0.792777	+	0.609512i	$0.791365\pi$
$882$		0			0
$883$	61.5102			0.0696605			0.0348303	−	0.999393i	$-0.488911\pi$
$883$	61.5102			0.0696605			0.0348303	+	0.999393i	$0.488911\pi$
$884$	9.84939	−	17.0597i	0.0111418	−	0.0192982i
$885$		0			0
$886$	439.170	+	760.664i	0.495677	+	0.858538i
$887$	−112.273	−	64.8207i	−0.126576	−	0.0730786i	0.435375	−	0.900249i	$-0.356616\pi$
$887$	−112.273	−	64.8207i	−0.126576	−	0.0730786i	−0.561951	+	0.827171i	$0.689949\pi$
$888$		0			0
$889$	258.012	−	1240.70i	0.290227	−	1.39562i
$890$	−236.474			−0.265701
$891$		0			0
$892$	−317.117	+	183.087i	−0.355512	+	0.205255i
$893$	86.0458	+	149.036i	0.0963559	+	0.166893i
$894$		0			0
$895$		−	787.870i		−	0.880302i
$896$	779.163	+	695.371i	0.869602	+	0.776083i
$897$		0			0
$898$	−5.00131	+	8.66252i	−0.00556938	+	0.00964646i
$899$	−286.897	+	165.640i	−0.319129	+	0.184249i
$900$		0			0
$901$	117.437	+	67.8023i	0.130341	+	0.0752523i
$902$		−	1795.37i		−	1.99043i
$903$		0			0
$904$	209.260			0.231482
$905$	−172.155	+	298.181i	−0.190226	+	0.329482i
$906$		0			0
$907$	700.954	+	1214.09i	0.772827	+	1.33858i	0.936008	+	0.351979i	$0.114491\pi$
$907$	700.954	+	1214.09i	0.772827	+	1.33858i	−0.163181	+	0.986596i	$0.552175\pi$
$908$	474.029	+	273.681i	0.522059	+	0.301411i
$909$		0			0
$910$	−216.073	+	71.2605i	−0.237443	+	0.0783082i
$911$	1235.23			1.35590			0.677950	−	0.735108i	$-0.262868\pi$
$911$	1235.23			1.35590			0.677950	+	0.735108i	$0.262868\pi$
$912$		0			0
$913$	−929.648	+	536.732i	−1.01823	+	0.587878i
$914$	592.639	+	1026.48i	0.648401	+	1.12306i
$915$		0			0
$916$		−	1.39977i		−	0.00152813i
$917$	199.572	−	223.620i	0.217635	−	0.243861i
$918$		0			0
$919$	−341.200	+	590.976i	−0.371273	+	0.643064i	−0.989762	−	0.142730i	$-0.954412\pi$
$919$	−341.200	+	590.976i	−0.371273	+	0.643064i	0.618488	+	0.785794i	$0.287745\pi$
$920$	176.970	−	102.174i	0.192359	−	0.111059i
$921$		0			0
$922$	614.648	+	354.867i	0.666646	+	0.384889i
$923$			410.251i			0.444476i
$924$		0			0
$925$	−65.1335			−0.0704146
$926$	675.805	−	1170.53i	0.729811	−	1.26407i
$927$		0			0
$928$	192.771	+	333.888i	0.207727	+	0.359794i
$929$	−109.020	−	62.9427i	−0.117352	−	0.0677531i	0.440175	−	0.897912i	$-0.354916\pi$
$929$	−109.020	−	62.9427i	−0.117352	−	0.0677531i	−0.557527	+	0.830159i	$0.688250\pi$
$930$		0			0
$931$	70.0825	+	94.6943i	0.0752766	+	0.101712i
$932$	−165.387			−0.177454
$933$		0			0
$934$	1823.84	−	1053.00i	1.95272	−	1.12740i
$935$	30.8924	+	53.5072i	0.0330400	+	0.0572270i
$936$		0			0
$937$			235.260i			0.251078i	0.992089	+	0.125539i	$0.0400660\pi$
$937$			235.260i			0.251078i	−0.992089	+	0.125539i	$0.959934\pi$
$938$	250.885	−	1206.43i	0.267468	−	1.28618i
$939$		0			0
$940$	−127.436	+	220.725i	−0.135570	+	0.234814i
$941$	−300.317	+	173.388i	−0.319147	+	0.184260i	−0.651012	−	0.759067i	$-0.725655\pi$
$941$	−300.317	+	173.388i	−0.319147	+	0.184260i	0.331865	+	0.943327i	$0.392322\pi$
$942$		0			0
$943$	−768.665	−	443.789i	−0.815128	−	0.470614i
$944$			418.221i			0.443030i
$945$		0			0
$946$	1776.53			1.87794
$947$	−347.003	+	601.027i	−0.366424	+	0.634665i	−0.989004	−	0.147892i	$-0.952751\pi$
$947$	−347.003	+	601.027i	−0.366424	+	0.634665i	0.622580	+	0.782556i	$0.286085\pi$
$948$		0			0
$949$	−384.255	−	665.550i	−0.404906	−	0.701317i
$950$	−24.6193	−	14.2140i	−0.0259151	−	0.0149621i
$951$		0			0
$952$	25.1221	+	76.1742i	0.0263887	+	0.0800149i
$953$	−1530.11			−1.60557			−0.802786	−	0.596267i	$-0.796650\pi$
$953$	−1530.11			−1.60557			−0.802786	+	0.596267i	$0.796650\pi$
$954$		0			0
$955$	−148.848	+	85.9373i	−0.155861	+	0.0899867i
$956$	−127.332	−	220.546i	−0.133193	−	0.230696i
$957$		0			0
$958$		−	78.2774i		−	0.0817091i
$959$	−671.823	+	221.566i	−0.700545	+	0.231038i
$960$		0			0
$961$	−265.562	+	459.966i	−0.276339	+	0.478633i
$962$	−163.985	+	94.6765i	−0.170462	+	0.0984164i
$963$		0			0
$964$	−355.594	−	205.302i	−0.368874	−	0.212969i
$965$		−	743.542i		−	0.770510i
$966$		0			0
$967$	66.4870			0.0687560			0.0343780	−	0.999409i	$-0.489055\pi$
$967$	66.4870			0.0687560			0.0343780	+	0.999409i	$0.489055\pi$
$968$	−192.142	+	332.800i	−0.198494	+	0.343802i
$969$		0			0
$970$	83.7544	+	145.067i	0.0863447	+	0.149553i
$971$	527.453	+	304.525i	0.543206	+	0.313620i	0.746377	−	0.665523i	$-0.231792\pi$
$971$	527.453	+	304.525i	0.543206	+	0.313620i	−0.203171	+	0.979143i	$0.565125\pi$
$972$		0			0
$973$	908.699	+	188.969i	0.933915	+	0.194213i
$974$	1456.47			1.49534
$975$		0			0
$976$	−453.806	+	262.005i	−0.464965	+	0.268448i
$977$	−635.780	−	1101.20i	−0.650748	−	1.12713i	−0.982942	−	0.183917i	$-0.941122\pi$
$977$	−635.780	−	1101.20i	−0.650748	−	1.12713i	0.332194	−	0.943211i	$-0.392211\pi$
$978$		0			0
$979$		−	613.973i		−	0.627143i
$980$	−69.5584	+	160.010i	−0.0709779	+	0.163276i
$981$		0			0
$982$	264.340	−	457.851i	0.269186	−	0.466243i
$983$	−147.832	+	85.3509i	−0.150389	+	0.0868270i	−0.573306	−	0.819341i	$-0.694339\pi$
$983$	−147.832	+	85.3509i	−0.150389	+	0.0868270i	0.422917	+	0.906168i	$0.361006\pi$
$984$		0			0
$985$	237.723	+	137.250i	0.241343	+	0.139340i
$986$			76.0448i			0.0771245i
$987$		0			0
$988$	−23.5325			−0.0238183
$989$	439.133	−	760.600i	0.444017	−	0.769060i
$990$		0			0
$991$	11.7052	+	20.2740i	0.0118115	+	0.0204581i	0.871871	−	0.489736i	$-0.162907\pi$
$991$	11.7052	+	20.2740i	0.0118115	+	0.0204581i	−0.860059	+	0.510194i	$0.829574\pi$
$992$	−433.262	−	250.144i	−0.436756	−	0.252161i
$993$		0			0
$994$	824.322	+	735.673i	0.829298	+	0.740113i
$995$	189.798			0.190752
$996$		0			0
$997$	1576.72	−	910.318i	1.58146	−	0.913057i	0.586815	−	0.809721i	$-0.300382\pi$
$997$	1576.72	−	910.318i	1.58146	−	0.913057i	0.994647	−	0.103336i	$-0.0329516\pi$
$998$	−971.429	−	1682.56i	−0.973376	−	1.68594i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.w.c.271.5		12
3.2	odd	2		35.3.h.a.26.2	✓	12
7.3	odd	6	inner	315.3.w.c.136.5		12
12.11	even	2		560.3.bx.c.481.1		12
15.2	even	4		175.3.j.b.124.3		24
15.8	even	4		175.3.j.b.124.10		24
15.14	odd	2		175.3.i.d.26.5		12
21.2	odd	6		245.3.d.a.146.10		12
21.5	even	6		245.3.d.a.146.9		12
21.11	odd	6		245.3.h.c.31.2		12
21.17	even	6		35.3.h.a.31.2	yes	12
21.20	even	2		245.3.h.c.166.2		12
84.59	odd	6		560.3.bx.c.241.1		12
105.17	odd	12		175.3.j.b.24.10		24
105.38	odd	12		175.3.j.b.24.3		24
105.59	even	6		175.3.i.d.101.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.h.a.26.2	✓	12	3.2	odd	2
35.3.h.a.31.2	yes	12	21.17	even	6
175.3.i.d.26.5		12	15.14	odd	2
175.3.i.d.101.5		12	105.59	even	6
175.3.j.b.24.3		24	105.38	odd	12
175.3.j.b.24.10		24	105.17	odd	12
175.3.j.b.124.3		24	15.2	even	4
175.3.j.b.124.10		24	15.8	even	4
245.3.d.a.146.9		12	21.5	even	6
245.3.d.a.146.10		12	21.2	odd	6
245.3.h.c.31.2		12	21.11	odd	6
245.3.h.c.166.2		12	21.20	even	2
315.3.w.c.136.5		12	7.3	odd	6	inner
315.3.w.c.271.5		12	1.1	even	1	trivial
560.3.bx.c.241.1		12	84.59	odd	6
560.3.bx.c.481.1		12	12.11	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18241 - 2.04800i) q^{2} +(-0.796202 - 1.37906i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-1.42520 + 6.85338i) q^{7} +5.69355 q^{8} +O(q^{10})\)	\(q+(1.18241 - 2.04800i) q^{2} +(-0.796202 - 1.37906i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-1.42520 + 6.85338i) q^{7} +5.69355 q^{8} +(4.57947 - 2.64396i) q^{10} +(6.86467 + 11.8900i) q^{11} +6.14666i q^{13} +(12.3505 + 11.0223i) q^{14} +(9.91693 - 17.1766i) q^{16} +(1.74292 - 1.00628i) q^{17} +(-2.08213 - 1.20212i) q^{19} -3.56072i q^{20} +32.4675 q^{22} +(8.02550 - 13.9006i) q^{23} +(2.50000 + 4.33013i) q^{25} +(12.5884 + 7.26789i) q^{26} +(10.5860 - 3.49123i) q^{28} -15.9780 q^{29} +(17.9557 - 10.3667i) q^{31} +(-12.0647 - 20.8967i) q^{32} -4.75934i q^{34} +(-10.4222 + 11.6781i) q^{35} +(-6.51335 + 11.2814i) q^{37} +(-4.92387 + 2.84279i) q^{38} +(11.0255 + 6.36558i) q^{40} -55.2974i q^{41} +54.7172 q^{43} +(10.9313 - 18.9336i) q^{44} +(-18.9789 - 32.8724i) q^{46} +(-61.9889 - 35.7893i) q^{47} +(-44.9376 - 19.5349i) q^{49} +11.8241 q^{50} +(8.47662 - 4.89398i) q^{52} +(33.6897 + 58.3523i) q^{53} +30.6997i q^{55} +(-8.11445 + 39.0200i) q^{56} +(-18.8926 + 32.7230i) q^{58} +(-18.2612 + 10.5431i) q^{59} +(-22.8803 - 13.2100i) q^{61} -49.0311i q^{62} +22.2735 q^{64} +(-6.87217 + 11.9029i) q^{65} +(-37.2194 - 64.4659i) q^{67} +(-2.77544 - 1.60240i) q^{68} +(11.5934 + 35.1530i) q^{70} +66.7438 q^{71} +(-108.278 + 62.5145i) q^{73} +(15.4029 + 26.6787i) q^{74} +3.82851i q^{76} +(-91.2699 + 30.1006i) q^{77} +(49.0504 - 84.9577i) q^{79} +(38.4081 - 22.1749i) q^{80} +(-113.249 - 65.3844i) q^{82} +78.1877i q^{83} +4.50020 q^{85} +(64.6983 - 112.061i) q^{86} +(39.0843 + 67.6960i) q^{88} +(-38.7285 - 22.3599i) q^{89} +(-42.1254 - 8.76023i) q^{91} -25.5597 q^{92} +(-146.593 + 84.6355i) q^{94} +(-2.68801 - 4.65577i) q^{95} +31.6777i q^{97} +(-93.1423 + 68.9339i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 10 q^{4} - 2 q^{7} + 4 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 10 * q^4 - 2 * q^7 + 4 * q^8	\( 12 q + 2 q^{2} - 10 q^{4} - 2 q^{7} + 4 q^{8} + 14 q^{11} + 2 q^{14} - 22 q^{16} - 48 q^{17} - 30 q^{19} - 88 q^{22} + 14 q^{23} + 30 q^{25} - 66 q^{26} + 202 q^{28} - 64 q^{29} + 132 q^{31} + 54 q^{32} - 30 q^{35} + 44 q^{37} + 300 q^{38} - 4 q^{43} - 6 q^{44} - 214 q^{46} - 204 q^{47} - 24 q^{49} + 20 q^{50} + 252 q^{52} - 196 q^{53} + 460 q^{56} + 158 q^{58} - 72 q^{59} + 72 q^{61} - 140 q^{64} - 30 q^{65} - 138 q^{67} + 348 q^{68} + 240 q^{70} + 8 q^{71} - 528 q^{73} - 50 q^{74} + 176 q^{77} - 12 q^{79} + 240 q^{80} - 378 q^{82} + 40 q^{86} + 604 q^{88} - 204 q^{89} - 480 q^{91} - 732 q^{92} - 42 q^{94} - 60 q^{95} - 898 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 - 10 * q^4 - 2 * q^7 + 4 * q^8 + 14 * q^11 + 2 * q^14 - 22 * q^16 - 48 * q^17 - 30 * q^19 - 88 * q^22 + 14 * q^23 + 30 * q^25 - 66 * q^26 + 202 * q^28 - 64 * q^29 + 132 * q^31 + 54 * q^32 - 30 * q^35 + 44 * q^37 + 300 * q^38 - 4 * q^43 - 6 * q^44 - 214 * q^46 - 204 * q^47 - 24 * q^49 + 20 * q^50 + 252 * q^52 - 196 * q^53 + 460 * q^56 + 158 * q^58 - 72 * q^59 + 72 * q^61 - 140 * q^64 - 30 * q^65 - 138 * q^67 + 348 * q^68 + 240 * q^70 + 8 * q^71 - 528 * q^73 - 50 * q^74 + 176 * q^77 - 12 * q^79 + 240 * q^80 - 378 * q^82 + 40 * q^86 + 604 * q^88 - 204 * q^89 - 480 * q^91 - 732 * q^92 - 42 * q^94 - 60 * q^95 - 898 * q^98

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