LMFDB - Embedded newform 315.3.o.b.127.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(127,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("315.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.11
Character	$\chi$	$=$	315.127
Dual form			315.3.o.b.253.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.59930 + 1.59930i) q^{2} +1.11554i q^{4} +(1.35929 + 4.81169i) q^{5} +(1.87083 + 1.87083i) q^{7} +(4.61313 - 4.61313i) q^{8} +O(q^{10})$	\(q+(1.59930 + 1.59930i) q^{2} +1.11554i q^{4} +(1.35929 + 4.81169i) q^{5} +(1.87083 + 1.87083i) q^{7} +(4.61313 - 4.61313i) q^{8} +(-5.52142 + 9.86926i) q^{10} +13.7143 q^{11} +(-16.4959 + 16.4959i) q^{13} +5.98404i q^{14} +19.2177 q^{16} +(3.05243 + 3.05243i) q^{17} -4.66410i q^{19} +(-5.36761 + 1.51634i) q^{20} +(21.9333 + 21.9333i) q^{22} +(4.61681 - 4.61681i) q^{23} +(-21.3046 + 13.0810i) q^{25} -52.7638 q^{26} +(-2.08698 + 2.08698i) q^{28} +50.3467i q^{29} +11.0632 q^{31} +(12.2824 + 12.2824i) q^{32} +9.76351i q^{34} +(-6.45883 + 11.5448i) q^{35} +(-44.4533 - 44.4533i) q^{37} +(7.45931 - 7.45931i) q^{38} +(28.4675 + 15.9263i) q^{40} +20.5922 q^{41} +(41.9068 - 41.9068i) q^{43} +15.2988i q^{44} +14.7673 q^{46} +(-20.4247 - 20.4247i) q^{47} +7.00000i q^{49} +(-54.9930 - 13.1521i) q^{50} +(-18.4017 - 18.4017i) q^{52} +(46.1212 - 46.1212i) q^{53} +(18.6417 + 65.9888i) q^{55} +17.2608 q^{56} +(-80.5197 + 80.5197i) q^{58} -47.2598i q^{59} +33.7814 q^{61} +(17.6934 + 17.6934i) q^{62} -37.5843i q^{64} +(-101.796 - 56.9502i) q^{65} +(-63.1243 - 63.1243i) q^{67} +(-3.40509 + 3.40509i) q^{68} +(-28.7933 + 8.13407i) q^{70} +31.1884 q^{71} +(-19.0978 + 19.0978i) q^{73} -142.189i q^{74} +5.20297 q^{76} +(25.6570 + 25.6570i) q^{77} -53.2345i q^{79} +(26.1225 + 92.4696i) q^{80} +(32.9332 + 32.9332i) q^{82} +(-97.3590 + 97.3590i) q^{83} +(-10.5382 + 18.8365i) q^{85} +134.043 q^{86} +(63.2657 - 63.2657i) q^{88} -156.139i q^{89} -61.7219 q^{91} +(5.15021 + 5.15021i) q^{92} -65.3306i q^{94} +(22.4422 - 6.33989i) q^{95} +(-76.2395 - 76.2395i) q^{97} +(-11.1951 + 11.1951i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) $ 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8	$ 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) $ 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8 - 40 * q^10 + 64 * q^13 - 184 * q^16 - 24 * q^17 - 72 * q^20 + 8 * q^22 - 8 * q^23 - 136 * q^25 + 80 * q^26 + 96 * q^31 - 56 * q^32 + 8 * q^37 - 56 * q^38 + 232 * q^40 - 320 * q^41 - 112 * q^43 + 320 * q^46 - 64 * q^47 + 256 * q^50 + 96 * q^52 + 72 * q^53 - 80 * q^55 + 336 * q^56 - 512 * q^58 - 496 * q^61 + 776 * q^62 - 312 * q^65 - 192 * q^67 - 568 * q^68 + 112 * q^70 + 144 * q^71 + 224 * q^73 + 416 * q^76 - 112 * q^77 + 528 * q^80 + 352 * q^82 + 32 * q^83 + 24 * q^85 - 240 * q^86 + 216 * q^88 - 1304 * q^92 - 376 * q^95 - 816 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	1.59930	+	1.59930i	0.799651	+	0.799651i	0.983040	−	0.183389i	$-0.0587069\pi$
$2$	1.59930	+	1.59930i	0.799651	+	0.799651i	−0.183389	+	0.983040i	$0.558707\pi$
$3$		0			0
$3$		0			0
$4$			1.11554i			0.278884i
$5$	1.35929	+	4.81169i	0.271859	+	0.962337i
$5$	1.35929	+	4.81169i	0.271859	+	0.962337i
$6$		0			0
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$8$	4.61313	−	4.61313i	0.576641	−	0.576641i
$9$		0			0
$10$	−5.52142	+	9.86926i	−0.552142	+	0.986926i
$11$	13.7143			1.24675			0.623376	−	0.781922i	$-0.285761\pi$
$11$	13.7143			1.24675			0.623376	+	0.781922i	$0.285761\pi$
$12$		0			0
$13$	−16.4959	+	16.4959i	−1.26891	+	1.26891i	−0.322263	+	0.946650i	$0.604443\pi$
$13$	−16.4959	+	16.4959i	−1.26891	+	1.26891i	−0.946650	+	0.322263i	$0.895557\pi$
$14$			5.98404i			0.427432i
$15$		0			0
$16$	19.2177			1.20111
$17$	3.05243	+	3.05243i	0.179555	+	0.179555i	0.791162	−	0.611607i	$-0.209477\pi$
$17$	3.05243	+	3.05243i	0.179555	+	0.179555i	−0.611607	+	0.791162i	$0.709477\pi$
$18$		0			0
$19$		−	4.66410i		−	0.245479i	−0.992439	−	0.122740i	$-0.960832\pi$
$19$		−	4.66410i		−	0.245479i	0.992439	−	0.122740i	$-0.0391680\pi$
$20$	−5.36761	+	1.51634i	−0.268380	+	0.0758171i
$21$		0			0
$22$	21.9333	+	21.9333i	0.996966	+	0.996966i
$23$	4.61681	−	4.61681i	0.200731	−	0.200731i	−0.599582	−	0.800313i	$-0.704667\pi$
$23$	4.61681	−	4.61681i	0.200731	−	0.200731i	0.800313	+	0.599582i	$0.204667\pi$
$24$		0			0
$25$	−21.3046	+	13.0810i	−0.852186	+	0.523240i
$26$	−52.7638			−2.02938
$27$		0			0
$28$	−2.08698	+	2.08698i	−0.0745349	+	0.0745349i
$29$			50.3467i			1.73609i	0.496481	+	0.868047i	$0.334625\pi$
$29$			50.3467i			1.73609i	−0.496481	+	0.868047i	$0.665375\pi$
$30$		0			0
$31$	11.0632			0.356877			0.178438	−	0.983951i	$-0.442896\pi$
$31$	11.0632			0.356877			0.178438	+	0.983951i	$0.442896\pi$
$32$	12.2824	+	12.2824i	0.383826	+	0.383826i
$33$		0			0
$34$			9.76351i			0.287162i
$35$	−6.45883	+	11.5448i	−0.184538	+	0.329853i
$36$		0			0
$37$	−44.4533	−	44.4533i	−1.20144	−	1.20144i	−0.973729	−	0.227712i	$-0.926876\pi$
$37$	−44.4533	−	44.4533i	−1.20144	−	1.20144i	−0.227712	−	0.973729i	$-0.573124\pi$
$38$	7.45931	−	7.45931i	0.196298	−	0.196298i
$39$		0			0
$40$	28.4675	+	15.9263i	0.711688	+	0.398158i
$41$	20.5922			0.502249			0.251124	−	0.967955i	$-0.419200\pi$
$41$	20.5922			0.502249			0.251124	+	0.967955i	$0.419200\pi$
$42$		0			0
$43$	41.9068	−	41.9068i	0.974578	−	0.974578i	−0.0251070	−	0.999685i	$-0.507993\pi$
$43$	41.9068	−	41.9068i	0.974578	−	0.974578i	0.999685	+	0.0251070i	$0.00799264\pi$
$44$			15.2988i			0.347699i
$45$		0			0
$46$	14.7673			0.321029
$47$	−20.4247	−	20.4247i	−0.434569	−	0.434569i	0.455610	−	0.890179i	$-0.349421\pi$
$47$	−20.4247	−	20.4247i	−0.434569	−	0.434569i	−0.890179	+	0.455610i	$0.849421\pi$
$48$		0			0
$49$			7.00000i			0.142857i
$50$	−54.9930	−	13.1521i	−1.09986	−	0.263042i
$51$		0			0
$52$	−18.4017	−	18.4017i	−0.353879	−	0.353879i
$53$	46.1212	−	46.1212i	0.870212	−	0.870212i	−0.122283	−	0.992495i	$-0.539022\pi$
$53$	46.1212	−	46.1212i	0.870212	−	0.870212i	0.992495	+	0.122283i	$0.0390216\pi$
$54$		0			0
$55$	18.6417	+	65.9888i	0.338941	+	1.19980i
$56$	17.2608			0.308228
$57$		0			0
$58$	−80.5197	+	80.5197i	−1.38827	+	1.38827i
$59$		−	47.2598i		−	0.801014i	−0.916294	−	0.400507i	$-0.868834\pi$
$59$		−	47.2598i		−	0.801014i	0.916294	−	0.400507i	$-0.131166\pi$
$60$		0			0
$61$	33.7814			0.553793			0.276896	−	0.960900i	$-0.410694\pi$
$61$	33.7814			0.553793			0.276896	+	0.960900i	$0.410694\pi$
$62$	17.6934	+	17.6934i	0.285377	+	0.285377i
$63$		0			0
$64$		−	37.5843i		−	0.587254i
$65$	−101.796	−	56.9502i	−1.56609	−	0.876157i
$66$		0			0
$67$	−63.1243	−	63.1243i	−0.942154	−	0.942154i	0.0562621	−	0.998416i	$-0.482082\pi$
$67$	−63.1243	−	63.1243i	−0.942154	−	0.942154i	−0.998416	+	0.0562621i	$0.982082\pi$
$68$	−3.40509	+	3.40509i	−0.0500749	+	0.0500749i
$69$		0			0
$70$	−28.7933	+	8.13407i	−0.411333	+	0.116201i
$71$	31.1884			0.439273			0.219637	−	0.975582i	$-0.429513\pi$
$71$	31.1884			0.439273			0.219637	+	0.975582i	$0.429513\pi$
$72$		0			0
$73$	−19.0978	+	19.0978i	−0.261614	+	0.261614i	−0.825709	−	0.564096i	$-0.809225\pi$
$73$	−19.0978	+	19.0978i	−0.261614	+	0.261614i	0.564096	+	0.825709i	$0.309225\pi$
$74$		−	142.189i		−	1.92147i
$75$		0			0
$76$	5.20297			0.0684601
$77$	25.6570	+	25.6570i	0.333208	+	0.333208i
$78$		0			0
$79$		−	53.2345i		−	0.673854i	−0.941531	−	0.336927i	$-0.890612\pi$
$79$		−	53.2345i		−	0.673854i	0.941531	−	0.336927i	$-0.109388\pi$
$80$	26.1225	+	92.4696i	0.326532	+	1.15587i
$81$		0			0
$82$	32.9332	+	32.9332i	0.401624	+	0.401624i
$83$	−97.3590	+	97.3590i	−1.17300	+	1.17300i	−0.191510	+	0.981491i	$0.561338\pi$
$83$	−97.3590	+	97.3590i	−1.17300	+	1.17300i	−0.981491	+	0.191510i	$0.938662\pi$
$84$		0			0
$85$	−10.5382	+	18.8365i	−0.123979	+	0.221606i
$86$	134.043			1.55864
$87$		0			0
$88$	63.2657	−	63.2657i	0.718929	−	0.718929i
$89$		−	156.139i		−	1.75437i	−0.480154	−	0.877184i	$-0.659419\pi$
$89$		−	156.139i		−	1.75437i	0.480154	−	0.877184i	$-0.340581\pi$
$90$		0			0
$91$	−61.7219			−0.678263
$92$	5.15021	+	5.15021i	0.0559806	+	0.0559806i
$93$		0			0
$94$		−	65.3306i		−	0.695007i
$95$	22.4422	−	6.33989i	0.236234	−	0.0667356i
$96$		0			0
$97$	−76.2395	−	76.2395i	−0.785974	−	0.785974i	0.194857	−	0.980832i	$-0.437576\pi$
$97$	−76.2395	−	76.2395i	−0.785974	−	0.785974i	−0.980832	+	0.194857i	$0.937576\pi$
$98$	−11.1951	+	11.1951i	−0.114236	+	0.114236i
$99$		0			0
$100$	−14.5923	−	23.7661i	−0.145923	−	0.237661i
$101$	70.4622			0.697646			0.348823	−	0.937189i	$-0.386582\pi$
$101$	70.4622			0.697646			0.348823	+	0.937189i	$0.386582\pi$
$102$		0			0
$103$	60.8151	−	60.8151i	0.590438	−	0.590438i	−0.347312	−	0.937750i	$-0.612905\pi$
$103$	60.8151	−	60.8151i	0.590438	−	0.590438i	0.937750	+	0.347312i	$0.112905\pi$
$104$			152.195i			1.46342i
$105$		0			0
$106$	147.524			1.39173
$107$	52.5369	+	52.5369i	0.490999	+	0.490999i	0.908621	−	0.417622i	$-0.137136\pi$
$107$	52.5369	+	52.5369i	0.490999	+	0.490999i	−0.417622	+	0.908621i	$0.637136\pi$
$108$		0			0
$109$			38.7375i			0.355390i	0.984086	+	0.177695i	$0.0568640\pi$
$109$			38.7375i			0.355390i	−0.984086	+	0.177695i	$0.943136\pi$
$110$	−75.7222	+	135.350i	−0.688384	+	1.23045i
$111$		0			0
$112$	35.9531	+	35.9531i	0.321010	+	0.321010i
$113$	40.5307	−	40.5307i	0.358679	−	0.358679i	−0.504647	−	0.863326i	$-0.668377\pi$
$113$	40.5307	−	40.5307i	0.358679	−	0.358679i	0.863326	+	0.504647i	$0.168377\pi$
$114$		0			0
$115$	28.4902	+	15.9390i	0.247741	+	0.138600i
$116$	−56.1636			−0.484169
$117$		0			0
$118$	75.5827	−	75.5827i	0.640532	−	0.640532i
$119$			11.4211i			0.0959760i
$120$		0			0
$121$	67.0812			0.554390
$122$	54.0266	+	54.0266i	0.442841	+	0.442841i
$123$		0			0
$124$			12.3414i			0.0995271i
$125$	−91.9009	−	84.7303i	−0.735207	−	0.677842i
$126$		0			0
$127$	−3.98961	−	3.98961i	−0.0314143	−	0.0314143i	0.691225	−	0.722639i	$-0.257071\pi$
$127$	−3.98961	−	3.98961i	−0.0314143	−	0.0314143i	−0.722639	+	0.691225i	$0.757071\pi$
$128$	109.238	−	109.238i	0.853424	−	0.853424i
$129$		0			0
$130$	−71.7215	−	253.883i	−0.551704	−	1.95294i
$131$	72.5637			0.553921			0.276961	−	0.960881i	$-0.410673\pi$
$131$	72.5637			0.553921			0.276961	+	0.960881i	$0.410673\pi$
$132$		0			0
$133$	8.72573	−	8.72573i	0.0656070	−	0.0656070i
$134$		−	201.910i		−	1.50679i
$135$		0			0
$136$	28.1625			0.207077
$137$	−67.6559	−	67.6559i	−0.493838	−	0.493838i	0.415675	−	0.909513i	$-0.363545\pi$
$137$	−67.6559	−	67.6559i	−0.493838	−	0.493838i	−0.909513	+	0.415675i	$0.863545\pi$
$138$		0			0
$139$			132.992i			0.956777i	0.878148	+	0.478388i	$0.158779\pi$
$139$			132.992i			0.956777i	−0.878148	+	0.478388i	$0.841221\pi$
$140$	−12.8787	−	7.20506i	−0.0919906	−	0.0514647i
$141$		0			0
$142$	49.8797	+	49.8797i	0.351265	+	0.351265i
$143$	−226.229	+	226.229i	−1.58202	+	1.58202i
$144$		0			0
$145$	−242.253	+	68.4361i	−1.67071	+	0.471973i
$146$	−61.0863			−0.418399
$147$		0			0
$148$	49.5892	−	49.5892i	0.335062	−	0.335062i
$149$			46.6022i			0.312767i	0.987696	+	0.156383i	$0.0499835\pi$
$149$			46.6022i			0.312767i	−0.987696	+	0.156383i	$0.950016\pi$
$150$		0			0
$151$	162.417			1.07561			0.537803	−	0.843071i	$-0.319254\pi$
$151$	162.417			1.07561			0.537803	+	0.843071i	$0.319254\pi$
$152$	−21.5161	−	21.5161i	−0.141553	−	0.141553i
$153$		0			0
$154$			82.0667i			0.532901i
$155$	15.0381	+	53.2325i	0.0970201	+	0.343436i
$156$		0			0
$157$	108.835	+	108.835i	0.693219	+	0.693219i	0.962939	−	0.269720i	$-0.0869312\pi$
$157$	108.835	+	108.835i	0.693219	+	0.693219i	−0.269720	+	0.962939i	$0.586931\pi$
$158$	85.1380	−	85.1380i	0.538848	−	0.538848i
$159$		0			0
$160$	−42.4037	+	75.7946i	−0.265023	+	0.473716i
$161$	17.2745			0.107295
$162$		0			0
$163$	−201.498	+	201.498i	−1.23619	+	1.23619i	−0.274638	+	0.961548i	$0.588558\pi$
$163$	−201.498	+	201.498i	−1.23619	+	1.23619i	−0.961548	+	0.274638i	$0.911442\pi$
$164$			22.9713i			0.140069i
$165$		0			0
$166$	−311.413			−1.87598
$167$	41.4832	+	41.4832i	0.248402	+	0.248402i	0.820315	−	0.571912i	$-0.193798\pi$
$167$	41.4832	+	41.4832i	0.248402	+	0.248402i	−0.571912	+	0.820315i	$0.693798\pi$
$168$		0			0
$169$		−	375.227i		−	2.22028i
$170$	−46.9790	+	13.2715i	−0.276347	+	0.0780676i
$171$		0			0
$172$	46.7486	+	46.7486i	0.271794	+	0.271794i
$173$	−130.020	+	130.020i	−0.751561	+	0.751561i	−0.974771	−	0.223209i	$-0.928347\pi$
$173$	−130.020	+	130.020i	−0.751561	+	0.751561i	0.223209	+	0.974771i	$0.428347\pi$
$174$		0			0
$175$	−64.3296	−	15.3850i	−0.367598	−	0.0879144i
$176$	263.557			1.49748
$177$		0			0
$178$	249.713	−	249.713i	1.40288	−	1.40288i
$179$		−	95.2857i		−	0.532322i	−0.963929	−	0.266161i	$-0.914245\pi$
$179$		−	95.2857i		−	0.532322i	0.963929	−	0.266161i	$-0.0857553\pi$
$180$		0			0
$181$	−189.309			−1.04590			−0.522952	−	0.852362i	$-0.675169\pi$
$181$	−189.309			−1.04590			−0.522952	+	0.852362i	$0.675169\pi$
$182$	−98.7120	−	98.7120i	−0.542373	−	0.542373i
$183$		0			0
$184$		−	42.5959i		−	0.231499i
$185$	153.470	−	274.320i	0.829569	−	1.48281i
$186$		0			0
$187$	41.8618	+	41.8618i	0.223860	+	0.223860i
$188$	22.7845	−	22.7845i	0.121194	−	0.121194i
$189$		0			0
$190$	46.0312	+	25.7524i	0.242270	+	0.135539i
$191$	−324.784			−1.70044			−0.850219	−	0.526430i	$-0.823530\pi$
$191$	−324.784			−1.70044			−0.850219	+	0.526430i	$0.823530\pi$
$192$		0			0
$193$	−24.7283	+	24.7283i	−0.128126	+	0.128126i	−0.768262	−	0.640136i	$-0.778878\pi$
$193$	−24.7283	+	24.7283i	−0.128126	+	0.128126i	0.640136	+	0.768262i	$0.278878\pi$
$194$		−	243.860i		−	1.25701i
$195$		0			0
$196$	−7.80875			−0.0398406
$197$	−9.08901	−	9.08901i	−0.0461371	−	0.0461371i	0.683662	−	0.729799i	$-0.260386\pi$
$197$	−9.08901	−	9.08901i	−0.0461371	−	0.0461371i	−0.729799	+	0.683662i	$0.760386\pi$
$198$		0			0
$199$			119.192i			0.598953i	0.954104	+	0.299476i	$0.0968120\pi$
$199$			119.192i			0.598953i	−0.954104	+	0.299476i	$0.903188\pi$
$200$	−37.9367	+	158.625i	−0.189684	+	0.793127i
$201$		0			0
$202$	112.690	+	112.690i	0.557873	+	0.557873i
$203$	−94.1901	+	94.1901i	−0.463991	+	0.463991i
$204$		0			0
$205$	27.9909	+	99.0832i	0.136541	+	0.483333i
$206$	194.524			0.944289
$207$		0			0
$208$	−317.013	+	317.013i	−1.52410	+	1.52410i
$209$		−	63.9647i		−	0.306051i
$210$		0			0
$211$	−35.9417			−0.170340			−0.0851699	−	0.996366i	$-0.527143\pi$
$211$	−35.9417			−0.170340			−0.0851699	+	0.996366i	$0.527143\pi$
$212$	51.4499	+	51.4499i	0.242688	+	0.242688i
$213$		0			0
$214$			168.045i			0.785256i
$215$	258.606	+	144.679i	1.20282	+	0.672925i
$216$		0			0
$217$	20.6973	+	20.6973i	0.0953793	+	0.0953793i
$218$	−61.9529	+	61.9529i	−0.284188	+	0.284188i
$219$		0			0
$220$	−73.6128	+	20.7955i	−0.334604	+	0.0945251i
$221$	−100.705			−0.455678
$222$		0			0
$223$	−230.412	+	230.412i	−1.03324	+	1.03324i	−0.0338071	+	0.999428i	$0.510763\pi$
$223$	−230.412	+	230.412i	−1.03324	+	1.03324i	−0.999428	+	0.0338071i	$0.989237\pi$
$224$			45.9566i			0.205164i
$225$		0			0
$226$	129.642			0.573636
$227$	−99.4972	−	99.4972i	−0.438314	−	0.438314i	0.453130	−	0.891444i	$-0.350307\pi$
$227$	−99.4972	−	99.4972i	−0.438314	−	0.438314i	−0.891444	+	0.453130i	$0.850307\pi$
$228$		0			0
$229$		−	12.3627i		−	0.0539854i	−0.999636	−	0.0269927i	$-0.991407\pi$
$229$		−	12.3627i		−	0.0539854i	0.999636	−	0.0269927i	$-0.00859309\pi$
$230$	20.0732	+	71.0558i	0.0872746	+	0.308938i
$231$		0			0
$232$	232.256	+	232.256i	1.00110	+	1.00110i
$233$	−214.583	+	214.583i	−0.920959	+	0.920959i	−0.997097	−	0.0761385i	$-0.975741\pi$
$233$	−214.583	+	214.583i	−0.920959	+	0.920959i	0.0761385	+	0.997097i	$0.475741\pi$
$234$		0			0
$235$	70.5142	−	126.041i	0.300060	−	0.536343i
$236$	52.7200			0.223390
$237$		0			0
$238$	−18.2659	+	18.2659i	−0.0767473	+	0.0767473i
$239$			10.6709i			0.0446481i	0.999751	+	0.0223240i	$0.00710655\pi$
$239$			10.6709i			0.0446481i	−0.999751	+	0.0223240i	$0.992893\pi$
$240$		0			0
$241$	−217.027			−0.900526			−0.450263	−	0.892896i	$-0.648670\pi$
$241$	−217.027			−0.900526			−0.450263	+	0.892896i	$0.648670\pi$
$242$	107.283	+	107.283i	0.443318	+	0.443318i
$243$		0			0
$244$			37.6843i			0.154444i
$245$	−33.6818	+	9.51506i	−0.137477	+	0.0388370i
$246$		0			0
$247$	76.9384	+	76.9384i	0.311492	+	0.311492i
$248$	51.0359	−	51.0359i	0.205790	−	0.205790i
$249$		0			0
$250$	−11.4680	−	282.487i	−0.0458719	−	1.12995i
$251$	59.6693			0.237726			0.118863	−	0.992911i	$-0.462075\pi$
$251$	59.6693			0.237726			0.118863	+	0.992911i	$0.462075\pi$
$252$		0			0
$253$	63.3161	−	63.3161i	0.250261	−	0.250261i
$254$		−	12.7612i		−	0.0502409i
$255$		0			0
$256$	199.073			0.777629
$257$	224.525	+	224.525i	0.873639	+	0.873639i	0.992867	−	0.119228i	$-0.0380419\pi$
$257$	224.525	+	224.525i	0.873639	+	0.873639i	−0.119228	+	0.992867i	$0.538042\pi$
$258$		0			0
$259$		−	166.329i		−	0.642197i
$260$	63.5300	−	113.557i	0.244346	−	0.436757i
$261$		0			0
$262$	116.051	+	116.051i	0.442944	+	0.442944i
$263$	0.00150876	−	0.00150876i	5.73673e−6	−	5.73673e-6i	−0.707104	−	0.707110i	$-0.749999\pi$
$263$	0.00150876	−	0.00150876i	5.73673e−6	−	5.73673e-6i	0.707110	+	0.707104i	$0.249999\pi$
$264$		0			0
$265$	284.613	+	159.229i	1.07401	+	0.600862i
$266$	27.9102			0.104925
$267$		0			0
$268$	70.4174	−	70.4174i	0.262752	−	0.262752i
$269$		−	10.8410i		−	0.0403011i	−0.999797	−	0.0201506i	$-0.993585\pi$
$269$		−	10.8410i		−	0.0403011i	0.999797	−	0.0201506i	$-0.00641456\pi$
$270$		0			0
$271$	423.331			1.56211			0.781054	−	0.624464i	$-0.214682\pi$
$271$	423.331			1.56211			0.781054	+	0.624464i	$0.214682\pi$
$272$	58.6607	+	58.6607i	0.215664	+	0.215664i
$273$		0			0
$274$		−	216.404i		−	0.789797i
$275$	−292.178	+	179.396i	−1.06246	+	0.652350i
$276$		0			0
$277$	43.6341	+	43.6341i	0.157524	+	0.157524i	0.781469	−	0.623945i	$-0.214471\pi$
$277$	43.6341	+	43.6341i	0.157524	+	0.157524i	−0.623945	+	0.781469i	$0.714471\pi$
$278$	−212.694	+	212.694i	−0.765088	+	0.765088i
$279$		0			0
$280$	23.4624	+	83.0533i	0.0837944	+	0.296619i
$281$	173.395			0.617065			0.308532	−	0.951214i	$-0.400162\pi$
$281$	173.395			0.617065			0.308532	+	0.951214i	$0.400162\pi$
$282$		0			0
$283$	205.636	−	205.636i	0.726630	−	0.726630i	−0.243317	−	0.969947i	$-0.578235\pi$
$283$	205.636	−	205.636i	0.726630	−	0.726630i	0.969947	+	0.243317i	$0.0782354\pi$
$284$			34.7918i			0.122506i
$285$		0			0
$286$	−723.616			−2.53013
$287$	38.5245	+	38.5245i	0.134232	+	0.134232i
$288$		0			0
$289$		−	270.365i		−	0.935520i
$290$	−496.885	−	277.985i	−1.71340	−	0.958570i
$291$		0			0
$292$	−21.3043	−	21.3043i	−0.0729598	−	0.0729598i
$293$	240.660	−	240.660i	0.821366	−	0.821366i	−0.164938	−	0.986304i	$-0.552742\pi$
$293$	240.660	−	240.660i	0.821366	−	0.821366i	0.986304	+	0.164938i	$0.0527423\pi$
$294$		0			0
$295$	227.399	−	64.2400i	0.770845	−	0.217763i
$296$	−410.138			−1.38560
$297$		0			0
$298$	−74.5311	+	74.5311i	−0.250104	+	0.250104i
$299$			152.316i			0.509420i
$300$		0			0
$301$	156.801			0.520934
$302$	259.753	+	259.753i	0.860110	+	0.860110i
$303$		0			0
$304$		−	89.6334i		−	0.294847i
$305$	45.9188	+	162.545i	0.150554	+	0.532936i
$306$		0			0
$307$	−334.742	−	334.742i	−1.09037	−	1.09037i	−0.995489	−	0.0948775i	$-0.969754\pi$
$307$	−334.742	−	334.742i	−1.09037	−	1.09037i	−0.0948775	−	0.995489i	$-0.530246\pi$
$308$	−28.6214	+	28.6214i	−0.0929265	+	0.0929265i
$309$		0			0
$310$	−61.0844	+	109.185i	−0.197046	+	0.352211i
$311$	29.4564			0.0947151			0.0473575	−	0.998878i	$-0.484920\pi$
$311$	29.4564			0.0947151			0.0473575	+	0.998878i	$0.484920\pi$
$312$		0			0
$313$	−375.133	+	375.133i	−1.19851	+	1.19851i	−0.223895	+	0.974613i	$0.571877\pi$
$313$	−375.133	+	375.133i	−1.19851	+	1.19851i	−0.974613	+	0.223895i	$0.928123\pi$
$314$			348.121i			1.10867i
$315$		0			0
$316$	59.3850			0.187927
$317$	409.594	+	409.594i	1.29209	+	1.29209i	0.933489	+	0.358605i	$0.116748\pi$
$317$	409.594	+	409.594i	1.29209	+	1.29209i	0.358605	+	0.933489i	$0.383252\pi$
$318$		0			0
$319$			690.469i			2.16448i
$320$	180.844	−	51.0881i	0.565136	−	0.159650i
$321$		0			0
$322$	27.6272	+	27.6272i	0.0857987	+	0.0857987i
$323$	14.2368	−	14.2368i	0.0440769	−	0.0440769i
$324$		0			0
$325$	135.656	−	567.221i	0.417403	−	1.74530i
$326$	−644.513			−1.97703
$327$		0			0
$328$	94.9945	−	94.9945i	0.289617	−	0.289617i
$329$		−	76.4224i		−	0.232287i
$330$		0			0
$331$	−71.9385			−0.217337			−0.108668	−	0.994078i	$-0.534659\pi$
$331$	−71.9385			−0.217337			−0.108668	+	0.994078i	$0.534659\pi$
$332$	−108.607	−	108.607i	−0.327131	−	0.327131i
$333$		0			0
$334$			132.688i			0.397270i
$335$	217.930	−	389.539i	0.650537	−	1.16280i
$336$		0			0
$337$	−302.137	−	302.137i	−0.896548	−	0.896548i	0.0985809	−	0.995129i	$-0.468570\pi$
$337$	−302.137	−	302.137i	−0.896548	−	0.896548i	−0.995129	+	0.0985809i	$0.968570\pi$
$338$	600.102	−	600.102i	1.77545	−	1.77545i
$339$		0			0
$340$	−21.0128	−	11.7557i	−0.0618022	−	0.0345756i
$341$	151.723			0.444937
$342$		0			0
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$		−	386.643i		−	1.12396i
$345$		0			0
$346$	−415.883			−1.20197
$347$	346.764	+	346.764i	0.999320	+	0.999320i	1.00000		0.000679298i	$-0.000216227\pi$
$347$	346.764	+	346.764i	0.999320	+	0.999320i	−0.000679298		1.00000i	$0.500216\pi$
$348$		0			0
$349$			29.7025i			0.0851075i	0.999094	+	0.0425537i	$0.0135494\pi$
$349$			29.7025i			0.0851075i	−0.999094	+	0.0425537i	$0.986451\pi$
$350$	−78.2772	−	127.488i	−0.223649	−	0.364251i
$351$		0			0
$352$	168.444	+	168.444i	0.478535	+	0.478535i
$353$	368.835	−	368.835i	1.04486	−	1.04486i	0.0459136	−	0.998945i	$-0.485380\pi$
$353$	368.835	−	368.835i	1.04486	−	1.04486i	0.998945	−	0.0459136i	$-0.0146199\pi$
$354$		0			0
$355$	42.3942	+	150.069i	0.119420	+	0.422729i
$356$	174.178			0.489265
$357$		0			0
$358$	152.391	−	152.391i	0.425672	−	0.425672i
$359$		−	610.662i		−	1.70101i	−0.525969	−	0.850504i	$-0.676297\pi$
$359$		−	610.662i		−	1.70101i	0.525969	−	0.850504i	$-0.323703\pi$
$360$		0			0
$361$	339.246			0.939740
$362$	−302.762	−	302.762i	−0.836358	−	0.836358i
$363$		0			0
$364$		−	68.8530i		−	0.189157i
$365$	−117.852	−	65.9331i	−0.322882	−	0.180639i
$366$		0			0
$367$	72.5232	+	72.5232i	0.197611	+	0.197611i	0.798975	−	0.601364i	$-0.205376\pi$
$367$	72.5232	+	72.5232i	0.197611	+	0.197611i	−0.601364	+	0.798975i	$0.705376\pi$
$368$	88.7245	−	88.7245i	0.241099	−	0.241099i
$369$		0			0
$370$	684.167	−	193.276i	1.84910	−	0.522368i
$371$	172.570			0.465148
$372$		0			0
$373$	6.51685	−	6.51685i	0.0174714	−	0.0174714i	−0.698317	−	0.715789i	$-0.746067\pi$
$373$	6.51685	−	6.51685i	0.0174714	−	0.0174714i	0.715789	+	0.698317i	$0.246067\pi$
$374$			133.899i			0.358020i
$375$		0			0
$376$	−188.444			−0.501181
$377$	−830.513	−	830.513i	−2.20295	−	2.20295i
$378$		0			0
$379$		−	224.357i		−	0.591970i	−0.955193	−	0.295985i	$-0.904352\pi$
$379$		−	224.357i		−	0.591970i	0.955193	−	0.295985i	$-0.0956479\pi$
$380$	7.07237	+	25.0351i	0.0186115	+	0.0658817i
$381$		0			0
$382$	−519.427	−	519.427i	−1.35976	−	1.35976i
$383$	−82.5720	+	82.5720i	−0.215593	+	0.215593i	−0.806638	−	0.591045i	$-0.798715\pi$
$383$	−82.5720	+	82.5720i	−0.215593	+	0.215593i	0.591045	+	0.806638i	$0.298715\pi$
$384$		0			0
$385$	−88.5782	+	158.329i	−0.230073	+	0.411244i
$386$	−79.0961			−0.204912
$387$		0			0
$388$	85.0479	−	85.0479i	0.219196	−	0.219196i
$389$			711.444i			1.82891i	0.404693	+	0.914453i	$0.367378\pi$
$389$			711.444i			1.82891i	−0.404693	+	0.914453i	$0.632622\pi$
$390$		0			0
$391$	28.1850			0.0720843
$392$	32.2919	+	32.2919i	0.0823773	+	0.0823773i
$393$		0			0
$394$		−	29.0721i		−	0.0737871i
$395$	256.148	−	72.3613i	0.648475	−	0.183193i
$396$		0			0
$397$	−333.858	−	333.858i	−0.840951	−	0.840951i	0.148032	−	0.988983i	$-0.452706\pi$
$397$	−333.858	−	333.858i	−0.840951	−	0.840951i	−0.988983	+	0.148032i	$0.952706\pi$
$398$	−190.623	+	190.623i	−0.478953	+	0.478953i
$399$		0			0
$400$	−409.427	+	251.387i	−1.02357	+	0.628467i
$401$	125.123			0.312027			0.156014	−	0.987755i	$-0.450136\pi$
$401$	125.123			0.312027			0.156014	+	0.987755i	$0.450136\pi$
$402$		0			0
$403$	−182.497	+	182.497i	−0.452845	+	0.452845i
$404$			78.6031i			0.194562i
$405$		0			0
$406$	−301.277			−0.742062
$407$	−609.645	−	609.645i	−1.49790	−	1.49790i
$408$		0			0
$409$		−	313.700i		−	0.766993i	−0.923542	−	0.383496i	$-0.874720\pi$
$409$		−	313.700i		−	0.766993i	0.923542	−	0.383496i	$-0.125280\pi$
$410$	−113.698	+	203.230i	−0.277313	+	0.495683i
$411$		0			0
$412$	67.8414	+	67.8414i	0.164664	+	0.164664i
$413$	88.4150	−	88.4150i	0.214080	−	0.214080i
$414$		0			0
$415$	−600.801	−	336.121i	−1.44771	−	0.809931i
$416$	−405.219			−0.974083
$417$		0			0
$418$	102.299	−	102.299i	0.244734	−	0.244734i
$419$			182.061i			0.434514i	0.976114	+	0.217257i	$0.0697110\pi$
$419$			182.061i			0.434514i	−0.976114	+	0.217257i	$0.930289\pi$
$420$		0			0
$421$	444.013			1.05466			0.527331	−	0.849660i	$-0.323193\pi$
$421$	444.013			1.05466			0.527331	+	0.849660i	$0.323193\pi$
$422$	−57.4817	−	57.4817i	−0.136212	−	0.136212i
$423$		0			0
$424$		−	425.527i		−	1.00360i
$425$	−104.960	−	25.1021i	−0.246964	−	0.0590637i
$426$		0			0
$427$	63.1992	+	63.1992i	0.148007	+	0.148007i
$428$	−58.6068	+	58.6068i	−0.136932	+	0.136932i
$429$		0			0
$430$	182.204	+	644.975i	0.423731	+	1.49994i
$431$	209.687			0.486514			0.243257	−	0.969962i	$-0.421784\pi$
$431$	209.687			0.486514			0.243257	+	0.969962i	$0.421784\pi$
$432$		0			0
$433$	593.138	−	593.138i	1.36983	−	1.36983i	0.509167	−	0.860668i	$-0.329954\pi$
$433$	593.138	−	593.138i	1.36983	−	1.36983i	0.860668	−	0.509167i	$-0.170046\pi$
$434$			66.2025i			0.152540i
$435$		0			0
$436$	−43.2130			−0.0991124
$437$	−21.5333	−	21.5333i	−0.0492752	−	0.0492752i
$438$		0			0
$439$		−	91.5547i		−	0.208553i	−0.994548	−	0.104276i	$-0.966747\pi$
$439$		−	91.5547i		−	0.208553i	0.994548	−	0.104276i	$-0.0332527\pi$
$440$	390.411	+	218.418i	0.887299	+	0.496405i
$441$		0			0
$442$	−161.058	−	161.058i	−0.364384	−	0.364384i
$443$	−302.352	+	302.352i	−0.682511	+	0.682511i	−0.960565	−	0.278054i	$-0.910311\pi$
$443$	−302.352	+	302.352i	−0.682511	+	0.682511i	0.278054	+	0.960565i	$0.410311\pi$
$444$		0			0
$445$	751.291	−	212.239i	1.68829	−	0.476941i
$446$	−736.995			−1.65246
$447$		0			0
$448$	70.3137	−	70.3137i	0.156950	−	0.156950i
$449$			190.141i			0.423477i	0.977326	+	0.211738i	$0.0679125\pi$
$449$			190.141i			0.423477i	−0.977326	+	0.211738i	$0.932088\pi$
$450$		0			0
$451$	282.407			0.626180
$452$	45.2135	+	45.2135i	0.100030	+	0.100030i
$453$		0			0
$454$		−	318.252i		−	0.700996i
$455$	−83.8982	−	296.986i	−0.184392	−	0.652717i
$456$		0			0
$457$	−83.0275	−	83.0275i	−0.181680	−	0.181680i	0.610408	−	0.792087i	$-0.291006\pi$
$457$	−83.0275	−	83.0275i	−0.181680	−	0.181680i	−0.792087	+	0.610408i	$0.791006\pi$
$458$	19.7716	−	19.7716i	0.0431695	−	0.0431695i
$459$		0			0
$460$	−17.7806	+	31.7819i	−0.0386534	+	0.0690910i
$461$	−231.095			−0.501290			−0.250645	−	0.968079i	$-0.580643\pi$
$461$	−231.095			−0.501290			−0.250645	+	0.968079i	$0.580643\pi$
$462$		0			0
$463$	−584.068	+	584.068i	−1.26149	+	1.26149i	−0.311112	+	0.950373i	$0.600701\pi$
$463$	−584.068	+	584.068i	−1.26149	+	1.26149i	−0.950373	+	0.311112i	$0.899299\pi$
$464$			967.550i			2.08524i
$465$		0			0
$466$	−686.367			−1.47289
$467$	50.5678	+	50.5678i	0.108282	+	0.108282i	0.759172	−	0.650890i	$-0.225604\pi$
$467$	50.5678	+	50.5678i	0.108282	+	0.108282i	−0.650890	+	0.759172i	$0.725604\pi$
$468$		0			0
$469$		−	236.190i		−	0.503602i
$470$	314.351	−	88.8036i	0.668831	−	0.188944i
$471$		0			0
$472$	−218.016	−	218.016i	−0.461898	−	0.461898i
$473$	574.722	−	574.722i	1.21506	−	1.21506i
$474$		0			0
$475$	61.0111	+	99.3670i	0.128444	+	0.209194i
$476$	−12.7407			−0.0267662
$477$		0			0
$478$	−17.0660	+	17.0660i	−0.0357029	+	0.0357029i
$479$			479.014i			1.00003i	0.866017	+	0.500015i	$0.166672\pi$
$479$			479.014i			1.00003i	−0.866017	+	0.500015i	$0.833328\pi$
$480$		0			0
$481$	1466.59			3.04905
$482$	−347.092	−	347.092i	−0.720107	−	0.720107i
$483$		0			0
$484$			74.8314i			0.154610i
$485$	263.209	−	470.473i	0.542698	−	0.970046i
$486$		0			0
$487$	533.369	+	533.369i	1.09521	+	1.09521i	0.994962	+	0.100250i	$0.0319644\pi$
$487$	533.369	+	533.369i	1.09521	+	1.09521i	0.100250	+	0.994962i	$0.468036\pi$
$488$	155.838	−	155.838i	0.319340	−	0.319340i
$489$		0			0
$490$	−69.0848	−	38.6499i	−0.140989	−	0.0788774i
$491$	348.294			0.709356			0.354678	−	0.934989i	$-0.384591\pi$
$491$	348.294			0.709356			0.354678	+	0.934989i	$0.384591\pi$
$492$		0			0
$493$	−153.680	+	153.680i	−0.311724	+	0.311724i
$494$			246.096i			0.498169i
$495$		0			0
$496$	212.609			0.428647
$497$	58.3481	+	58.3481i	0.117401	+	0.117401i
$498$		0			0
$499$			665.697i			1.33406i	0.745030	+	0.667031i	$0.232435\pi$
$499$			665.697i			1.33406i	−0.745030	+	0.667031i	$0.767565\pi$
$500$	94.5197	−	102.519i	0.189039	−	0.205037i
$501$		0			0
$502$	95.4292	+	95.4292i	0.190098	+	0.190098i
$503$	−462.086	+	462.086i	−0.918660	+	0.918660i	−0.996932	−	0.0782724i	$-0.975060\pi$
$503$	−462.086	+	462.086i	−0.918660	+	0.918660i	0.0782724	+	0.996932i	$0.475060\pi$
$504$		0			0
$505$	95.7789	+	339.042i	0.189661	+	0.671370i
$506$	202.523			0.400244
$507$		0			0
$508$	4.45055	−	4.45055i	0.00876093	−	0.00876093i
$509$		−	75.7747i		−	0.148870i	−0.997226	−	0.0744348i	$-0.976285\pi$
$509$		−	75.7747i		−	0.148870i	0.997226	−	0.0744348i	$-0.0237153\pi$
$510$		0			0
$511$	−71.4574			−0.139838
$512$	−118.575	−	118.575i	−0.231592	−	0.231592i
$513$		0			0
$514$			718.167i			1.39721i
$515$	375.289	+	209.958i	0.728716	+	0.407685i
$516$		0			0
$517$	−280.110	−	280.110i	−0.541799	−	0.541799i
$518$	266.010	−	266.010i	0.513534	−	0.513534i
$519$		0			0
$520$	−732.315	+	206.878i	−1.40830	+	0.397842i
$521$	493.508			0.947231			0.473616	−	0.880732i	$-0.342949\pi$
$521$	493.508			0.947231			0.473616	+	0.880732i	$0.342949\pi$
$522$		0			0
$523$	88.8615	−	88.8615i	0.169907	−	0.169907i	−0.617031	−	0.786939i	$-0.711665\pi$
$523$	88.8615	−	88.8615i	0.169907	−	0.169907i	0.786939	+	0.617031i	$0.211665\pi$
$524$			80.9474i			0.154480i
$525$		0			0
$526$	0.00482592			9.17476e−6
$527$	33.7696	+	33.7696i	0.0640789	+	0.0640789i
$528$		0			0
$529$			486.370i			0.919414i
$530$	200.528	+	709.837i	0.378355	+	1.33932i
$531$		0			0
$532$	9.73387	+	9.73387i	0.0182967	+	0.0182967i
$533$	−339.686	+	339.686i	−0.637310	+	0.637310i
$534$		0			0
$535$	−181.378	+	324.204i	−0.339024	+	0.605989i
$536$	−582.401			−1.08657
$537$		0			0
$538$	17.3380	−	17.3380i	0.0322268	−	0.0322268i
$539$			95.9999i			0.178107i
$540$		0			0
$541$	95.0854			0.175759			0.0878793	−	0.996131i	$-0.471991\pi$
$541$	95.0854			0.175759			0.0878793	+	0.996131i	$0.471991\pi$
$542$	677.035	+	677.035i	1.24914	+	1.24914i
$543$		0			0
$544$			74.9825i			0.137835i
$545$	−186.392	+	52.6556i	−0.342005	+	0.0966158i
$546$		0			0
$547$	638.590	+	638.590i	1.16744	+	1.16744i	0.982807	+	0.184634i	$0.0591100\pi$
$547$	638.590	+	638.590i	1.16744	+	1.16744i	0.184634	+	0.982807i	$0.440890\pi$
$548$	75.4725	−	75.4725i	0.137724	−	0.137724i
$549$		0			0
$550$	−754.189	−	180.371i	−1.37125	−	0.327948i
$551$	234.822			0.426175
$552$		0			0
$553$	99.5926	−	99.5926i	0.180095	−	0.180095i
$554$			139.568i			0.251928i
$555$		0			0
$556$	−148.357			−0.266830
$557$	−368.475	−	368.475i	−0.661534	−	0.661534i	0.294207	−	0.955742i	$-0.404944\pi$
$557$	−368.475	−	368.475i	−0.661534	−	0.661534i	−0.955742	+	0.294207i	$0.904944\pi$
$558$		0			0
$559$			1382.58i			2.47331i
$560$	−124.124	+	221.866i	−0.221650	+	0.396189i
$561$		0			0
$562$	277.311	+	277.311i	0.493436	+	0.493436i
$563$	229.051	−	229.051i	0.406840	−	0.406840i	−0.473795	−	0.880635i	$-0.657116\pi$
$563$	229.051	−	229.051i	0.406840	−	0.406840i	0.880635	+	0.473795i	$0.157116\pi$
$564$		0			0
$565$	250.114	+	139.928i	0.442680	+	0.247660i
$566$	657.749			1.16210
$567$		0			0
$568$	143.876	−	143.876i	0.253303	−	0.253303i
$569$			156.076i			0.274298i	0.990550	+	0.137149i	$0.0437940\pi$
$569$			156.076i			0.274298i	−0.990550	+	0.137149i	$0.956206\pi$
$570$		0			0
$571$	−689.495			−1.20752			−0.603761	−	0.797166i	$-0.706332\pi$
$571$	−689.495			−1.20752			−0.603761	+	0.797166i	$0.706332\pi$
$572$	−252.366	−	252.366i	−0.441200	−	0.441200i
$573$		0			0
$574$			123.225i			0.214677i
$575$	−37.9670	+	158.752i	−0.0660295	+	0.276090i
$576$		0			0
$577$	−613.020	−	613.020i	−1.06243	−	1.06243i	−0.997917	−	0.0645083i	$-0.979452\pi$
$577$	−613.020	−	613.020i	−1.06243	−	1.06243i	−0.0645083	−	0.997917i	$-0.520548\pi$
$578$	432.396	−	432.396i	0.748090	−	0.748090i
$579$		0			0
$580$	−76.3429	−	270.242i	−0.131626	−	0.465934i
$581$	−364.284			−0.626995
$582$		0			0
$583$	632.519	−	632.519i	1.08494	−	1.08494i
$584$			176.201i			0.301714i
$585$		0			0
$586$	769.777			1.31361
$587$	100.105	+	100.105i	0.170536	+	0.170536i	0.787215	−	0.616679i	$-0.211522\pi$
$587$	100.105	+	100.105i	0.170536	+	0.170536i	−0.616679	+	0.787215i	$0.711522\pi$
$588$		0			0
$589$		−	51.5998i		−	0.0876057i
$590$	466.420	+	260.941i	0.790542	+	0.442273i
$591$		0			0
$592$	−854.291	−	854.291i	−1.44306	−	1.44306i
$593$	−436.401	+	436.401i	−0.735920	+	0.735920i	−0.971786	−	0.235866i	$-0.924207\pi$
$593$	−436.401	+	436.401i	−0.735920	+	0.735920i	0.235866	+	0.971786i	$0.424207\pi$
$594$		0			0
$595$	−54.9549	+	15.5247i	−0.0923613	+	0.0260919i
$596$	−51.9865			−0.0872256
$597$		0			0
$598$	−243.600	+	243.600i	−0.407358	+	0.407358i
$599$		−	30.2472i		−	0.0504962i	−0.999681	−	0.0252481i	$-0.991962\pi$
$599$		−	30.2472i		−	0.0504962i	0.999681	−	0.0252481i	$-0.00803757\pi$
$600$		0			0
$601$	−880.877			−1.46569			−0.732843	−	0.680398i	$-0.761807\pi$
$601$	−880.877			−1.46569			−0.732843	+	0.680398i	$0.761807\pi$
$602$	250.772	+	250.772i	0.416565	+	0.416565i
$603$		0			0
$604$			181.181i			0.299969i
$605$	91.1831	+	322.773i	0.150716	+	0.533510i
$606$		0			0
$607$	313.283	+	313.283i	0.516117	+	0.516117i	0.916394	−	0.400277i	$-0.131086\pi$
$607$	313.283	+	313.283i	0.516117	+	0.516117i	−0.400277	+	0.916394i	$0.631086\pi$
$608$	57.2865	−	57.2865i	0.0942212	−	0.0942212i
$609$		0			0
$610$	−186.521	+	333.397i	−0.305772	+	0.546553i
$611$	673.847			1.10286
$612$		0			0
$613$	−83.0520	+	83.0520i	−0.135485	+	0.135485i	−0.771597	−	0.636112i	$-0.780542\pi$
$613$	−83.0520	+	83.0520i	−0.135485	+	0.135485i	0.636112	+	0.771597i	$0.280542\pi$
$614$		−	1070.71i		−	1.74383i
$615$		0			0
$616$	236.719			0.384283
$617$	−238.533	−	238.533i	−0.386602	−	0.386602i	0.486872	−	0.873473i	$-0.338138\pi$
$617$	−238.533	−	238.533i	−0.386602	−	0.386602i	−0.873473	+	0.486872i	$0.838138\pi$
$618$		0			0
$619$		−	26.3818i		−	0.0426201i	−0.999773	−	0.0213100i	$-0.993216\pi$
$619$		−	26.3818i		−	0.0426201i	0.999773	−	0.0213100i	$-0.00678371\pi$
$620$	−59.3828	+	16.7756i	−0.0957787	+	0.0270573i
$621$		0			0
$622$	47.1097	+	47.1097i	0.0757390	+	0.0757390i
$623$	292.109	−	292.109i	0.468875	−	0.468875i
$624$		0			0
$625$	282.775	−	557.372i	0.452440	−	0.891795i
$626$	−1199.90			−1.91678
$627$		0			0
$628$	−121.410	+	121.410i	−0.193328	+	0.193328i
$629$		−	271.381i		−	0.431448i
$630$		0			0
$631$	−672.112			−1.06515			−0.532577	−	0.846382i	$-0.678776\pi$
$631$	−672.112			−1.06515			−0.532577	+	0.846382i	$0.678776\pi$
$632$	−245.578	−	245.578i	−0.388572	−	0.388572i
$633$		0			0
$634$			1310.13i			2.06645i
$635$	13.7737	−	24.6198i	0.0216909	−	0.0387713i
$636$		0			0
$637$	−115.471	−	115.471i	−0.181273	−	0.181273i
$638$	−1104.27	+	1104.27i	−1.73083	+	1.73083i
$639$		0			0
$640$	674.107	+	377.133i	1.05329	+	0.589271i
$641$	−582.851			−0.909284			−0.454642	−	0.890674i	$-0.650233\pi$
$641$	−582.851			−0.909284			−0.454642	+	0.890674i	$0.650233\pi$
$642$		0			0
$643$	488.888	−	488.888i	0.760324	−	0.760324i	−0.216057	−	0.976381i	$-0.569320\pi$
$643$	488.888	−	488.888i	0.760324	−	0.760324i	0.976381	+	0.216057i	$0.0693196\pi$
$644$			19.2703i			0.0299229i
$645$		0			0
$646$	45.5380			0.0704923
$647$	−501.243	−	501.243i	−0.774718	−	0.774718i	0.204209	−	0.978927i	$-0.434538\pi$
$647$	−501.243	−	501.243i	−0.774718	−	0.774718i	−0.978927	+	0.204209i	$0.934538\pi$
$648$		0			0
$649$		−	648.134i		−	0.998665i
$650$	1124.11	−	690.202i	1.72940	−	1.06185i
$651$		0			0
$652$	−224.778	−	224.778i	−0.344752	−	0.344752i
$653$	−385.795	+	385.795i	−0.590805	+	0.590805i	−0.937849	−	0.347044i	$-0.887185\pi$
$653$	−385.795	+	385.795i	−0.590805	+	0.590805i	0.347044	+	0.937849i	$0.387185\pi$
$654$		0			0
$655$	98.6354	+	349.154i	0.150588	+	0.533059i
$656$	395.735			0.603255
$657$		0			0
$658$	122.222	−	122.222i	0.185748	−	0.185748i
$659$			232.235i			0.352405i	0.984354	+	0.176203i	$0.0563814\pi$
$659$			232.235i			0.352405i	−0.984354	+	0.176203i	$0.943619\pi$
$660$		0			0
$661$	−1126.09			−1.70361			−0.851804	−	0.523860i	$-0.824491\pi$
$661$	−1126.09			−1.70361			−0.851804	+	0.523860i	$0.824491\pi$
$662$	−115.051	−	115.051i	−0.173794	−	0.173794i
$663$		0			0
$664$			898.260i			1.35280i
$665$	53.8463	+	30.1246i	0.0809719	+	0.0453002i
$666$		0			0
$667$	232.441	+	232.441i	0.348488	+	0.348488i
$668$	−46.2760	+	46.2760i	−0.0692754	+	0.0692754i
$669$		0			0
$670$	971.526	−	274.455i	1.45004	−	0.409634i
$671$	463.287			0.690442
$672$		0			0
$673$	146.969	−	146.969i	0.218379	−	0.218379i	−0.589436	−	0.807815i	$-0.700650\pi$
$673$	146.969	−	146.969i	0.218379	−	0.218379i	0.807815	+	0.589436i	$0.200650\pi$
$674$		−	966.416i		−	1.43385i
$675$		0			0
$676$	418.580			0.619200
$677$	−312.515	−	312.515i	−0.461617	−	0.461617i	0.437568	−	0.899185i	$-0.355840\pi$
$677$	−312.515	−	312.515i	−0.461617	−	0.461617i	−0.899185	+	0.437568i	$0.855840\pi$
$678$		0			0
$679$		−	285.262i		−	0.420121i
$680$	38.2811	+	135.509i	0.0562958	+	0.199278i
$681$		0			0
$682$	242.652	+	242.652i	0.355794	+	0.355794i
$683$	660.747	−	660.747i	0.967419	−	0.967419i	−0.0320664	−	0.999486i	$-0.510209\pi$
$683$	660.747	−	660.747i	0.967419	−	0.967419i	0.999486	+	0.0320664i	$0.0102088\pi$
$684$		0			0
$685$	233.575	−	417.503i	0.340985	−	0.609493i
$686$	−41.8883			−0.0610616
$687$		0			0
$688$	805.354	−	805.354i	1.17057	−	1.17057i
$689$			1521.62i			2.20845i
$690$		0			0
$691$	−1000.24			−1.44752			−0.723759	−	0.690053i	$-0.757587\pi$
$691$	−1000.24			−1.44752			−0.723759	+	0.690053i	$0.757587\pi$
$692$	−145.042	−	145.042i	−0.209598	−	0.209598i
$693$		0			0
$694$			1109.16i			1.59822i
$695$	−639.916	+	180.775i	−0.920742	+	0.260108i
$696$		0			0
$697$	62.8562	+	62.8562i	0.0901811	+	0.0901811i
$698$	−47.5033	+	47.5033i	−0.0680563	+	0.0680563i
$699$		0			0
$700$	17.1625	−	71.7620i	0.0245179	−	0.102517i
$701$	−440.221			−0.627989			−0.313995	−	0.949425i	$-0.601667\pi$
$701$	−440.221			−0.627989			−0.313995	+	0.949425i	$0.601667\pi$
$702$		0			0
$703$	−207.335	+	207.335i	−0.294928	+	0.294928i
$704$		−	515.441i		−	0.732160i
$705$		0			0
$706$	1179.76			1.67105
$707$	131.823	+	131.823i	0.186454	+	0.186454i
$708$		0			0
$709$		−	63.2033i		−	0.0891443i	−0.999006	−	0.0445721i	$-0.985808\pi$
$709$		−	63.2033i		−	0.0891443i	0.999006	−	0.0445721i	$-0.0141925\pi$
$710$	−172.204	+	307.806i	−0.242541	+	0.433530i
$711$		0			0
$712$	−720.289	−	720.289i	−1.01164	−	1.01164i
$713$	51.0766	−	51.0766i	0.0716361	−	0.0716361i
$714$		0			0
$715$	−1396.05	−	781.030i	−1.95252	−	1.09235i
$716$	106.295			0.148456
$717$		0			0
$718$	976.633	−	976.633i	1.36021	−	1.36021i
$719$		−	934.275i		−	1.29941i	−0.760187	−	0.649704i	$-0.774893\pi$
$719$		−	934.275i		−	1.29941i	0.760187	−	0.649704i	$-0.225107\pi$
$720$		0			0
$721$	227.549			0.315602
$722$	542.557	+	542.557i	0.751464	+	0.751464i
$723$		0			0
$724$		−	211.180i		−	0.291686i
$725$	−658.586	−	1072.62i	−0.908394	−	1.47947i
$726$		0			0
$727$	−584.907	−	584.907i	−0.804548	−	0.804548i	0.179254	−	0.983803i	$-0.442631\pi$
$727$	−584.907	−	584.907i	−0.804548	−	0.804548i	−0.983803	+	0.179254i	$0.942631\pi$
$728$	−284.731	+	284.731i	−0.391114	+	0.391114i
$729$		0			0
$730$	−83.0342	−	293.928i	−0.113746	−	0.402641i
$731$	255.835			0.349980
$732$		0			0
$733$	−281.681	+	281.681i	−0.384285	+	0.384285i	−0.872643	−	0.488358i	$-0.837596\pi$
$733$	−281.681	+	281.681i	−0.384285	+	0.384285i	0.488358	+	0.872643i	$0.337596\pi$
$734$			231.973i			0.316040i
$735$		0			0
$736$	113.411			0.154091
$737$	−865.704	−	865.704i	−1.17463	−	1.17463i
$738$		0			0
$739$		−	892.992i		−	1.20838i	−0.796841	−	0.604189i	$-0.793497\pi$
$739$		−	892.992i		−	1.20838i	0.796841	−	0.604189i	$-0.206503\pi$
$740$	306.014	+	171.201i	0.413533	+	0.231353i
$741$		0			0
$742$	275.991	+	275.991i	0.371956	+	0.371956i
$743$	−305.538	+	305.538i	−0.411222	+	0.411222i	−0.882164	−	0.470942i	$-0.843914\pi$
$743$	−305.538	+	305.538i	−0.411222	+	0.411222i	0.470942	+	0.882164i	$0.343914\pi$
$744$		0			0
$745$	−224.235	+	63.3462i	−0.300987	+	0.0850284i
$746$	20.8448			0.0279421
$747$		0			0
$748$	−46.6984	+	46.6984i	−0.0624310	+	0.0624310i
$749$			196.575i			0.262450i
$750$		0			0
$751$	562.121			0.748496			0.374248	−	0.927329i	$-0.377901\pi$
$751$	562.121			0.748496			0.374248	+	0.927329i	$0.377901\pi$
$752$	−392.517	−	392.517i	−0.521964	−	0.521964i
$753$		0			0
$754$		−	2656.48i		−	3.52319i
$755$	220.772	+	781.497i	0.292413	+	1.03510i
$756$		0			0
$757$	370.109	+	370.109i	0.488915	+	0.488915i	0.907964	−	0.419048i	$-0.137636\pi$
$757$	370.109	+	370.109i	0.488915	+	0.488915i	−0.419048	+	0.907964i	$0.637636\pi$
$758$	358.814	−	358.814i	0.473370	−	0.473370i
$759$		0			0
$760$	74.2820	−	132.775i	0.0977395	−	0.174705i
$761$	466.002			0.612354			0.306177	−	0.951975i	$-0.400950\pi$
$761$	466.002			0.612354			0.306177	+	0.951975i	$0.400950\pi$
$762$		0			0
$763$	−72.4712	+	72.4712i	−0.0949819	+	0.0949819i
$764$		−	362.308i		−	0.474225i
$765$		0			0
$766$	−264.115			−0.344798
$767$	779.592	+	779.592i	1.01642	+	1.01642i
$768$		0			0
$769$		−	216.013i		−	0.280901i	−0.990088	−	0.140451i	$-0.955145\pi$
$769$		−	216.013i		−	0.280901i	0.990088	−	0.140451i	$-0.0448551\pi$
$770$	−394.879	+	111.553i	−0.512830	+	0.144874i
$771$		0			0
$772$	−27.5853	−	27.5853i	−0.0357323	−	0.0357323i
$773$	290.907	−	290.907i	0.376335	−	0.376335i	−0.493443	−	0.869778i	$-0.664262\pi$
$773$	290.907	−	290.907i	0.376335	−	0.376335i	0.869778	+	0.493443i	$0.164262\pi$
$774$		0			0
$775$	−235.697	+	144.717i	−0.304125	+	0.186732i
$776$	−703.406			−0.906451
$777$		0			0
$778$	−1137.81	+	1137.81i	−1.46249	+	1.46249i
$779$		−	96.0441i		−	0.123292i
$780$		0			0
$781$	427.726			0.547665
$782$	45.0763	+	45.0763i	0.0576423	+	0.0576423i
$783$		0			0
$784$			134.524i			0.171587i
$785$	−375.742	+	671.621i	−0.478652	+	0.855568i
$786$		0			0
$787$	310.573	+	310.573i	0.394629	+	0.394629i	0.876334	−	0.481705i	$-0.159982\pi$
$787$	310.573	+	310.573i	0.394629	+	0.394629i	−0.481705	+	0.876334i	$0.659982\pi$
$788$	10.1391	−	10.1391i	0.0128669	−	0.0128669i
$789$		0			0
$790$	525.385	+	293.930i	0.665044	+	0.372063i
$791$	151.652			0.191722
$792$		0			0
$793$	−557.253	+	557.253i	−0.702715	+	0.702715i
$794$		−	1067.88i		−	1.34494i
$795$		0			0
$796$	−132.962			−0.167038
$797$	762.912	+	762.912i	0.957230	+	0.957230i	0.999122	−	0.0418921i	$-0.0133386\pi$
$797$	762.912	+	762.912i	0.957230	+	0.957230i	−0.0418921	+	0.999122i	$0.513339\pi$
$798$		0			0
$799$		−	124.690i		−	0.156058i
$800$	−422.339	−	101.006i	−0.527924	−	0.126258i
$801$		0			0
$802$	200.109	+	200.109i	0.249513	+	0.249513i
$803$	−261.912	+	261.912i	−0.326167	+	0.326167i
$804$		0			0
$805$	23.4811	+	83.1195i	0.0291691	+	0.103254i
$806$	−583.735			−0.724237
$807$		0			0
$808$	325.051	−	325.051i	0.402291	−	0.402291i
$809$			1212.68i			1.49898i	0.662015	+	0.749490i	$0.269701\pi$
$809$			1212.68i			1.49898i	−0.662015	+	0.749490i	$0.730299\pi$
$810$		0			0
$811$	−971.089			−1.19740			−0.598699	−	0.800974i	$-0.704315\pi$
$811$	−971.089			−1.19740			−0.598699	+	0.800974i	$0.704315\pi$
$812$	−105.072	−	105.072i	−0.129400	−	0.129400i
$813$		0			0
$814$		−	1950.01i		−	2.39559i
$815$	−1243.44	−	695.651i	−1.52570	−	0.853559i
$816$		0			0
$817$	−195.458	−	195.458i	−0.239238	−	0.239238i
$818$	501.701	−	501.701i	0.613327	−	0.613327i
$819$		0			0
$820$	−110.531	+	31.2248i	−0.134794	+	0.0380790i
$821$	997.382			1.21484			0.607419	−	0.794382i	$-0.292205\pi$
$821$	997.382			1.21484			0.607419	+	0.794382i	$0.292205\pi$
$822$		0			0
$823$	475.439	−	475.439i	0.577690	−	0.577690i	−0.356576	−	0.934266i	$-0.616056\pi$
$823$	475.439	−	475.439i	0.577690	−	0.577690i	0.934266	+	0.356576i	$0.116056\pi$
$824$		−	561.096i		−	0.680942i
$825$		0			0
$826$	282.805			0.342379
$827$	302.620	+	302.620i	0.365925	+	0.365925i	0.865989	−	0.500064i	$-0.166690\pi$
$827$	302.620	+	302.620i	0.365925	+	0.365925i	−0.500064	+	0.865989i	$0.666690\pi$
$828$		0			0
$829$			317.984i			0.383576i	0.981436	+	0.191788i	$0.0614286\pi$
$829$			317.984i			0.383576i	−0.981436	+	0.191788i	$0.938571\pi$
$830$	−423.302	−	1498.42i	−0.510002	−	1.80533i
$831$		0			0
$832$	619.985	+	619.985i	0.745174	+	0.745174i
$833$	−21.3670	+	21.3670i	−0.0256507	+	0.0256507i
$834$		0			0
$835$	−143.216	+	255.992i	−0.171516	+	0.306577i
$836$	71.3549			0.0853528
$837$		0			0
$838$	−291.171	+	291.171i	−0.347460	+	0.347460i
$839$			755.271i			0.900204i	0.892977	+	0.450102i	$0.148612\pi$
$839$			755.271i			0.900204i	−0.892977	+	0.450102i	$0.851388\pi$
$840$		0			0
$841$	−1693.80			−2.01403
$842$	710.110	+	710.110i	0.843361	+	0.843361i
$843$		0			0
$844$		−	40.0943i		−	0.0475051i
$845$	1805.48	−	510.044i	2.13666	−	0.603603i
$846$		0			0
$847$	125.497	+	125.497i	0.148167	+	0.148167i
$848$	886.345	−	886.345i	1.04522	−	1.04522i
$849$		0			0
$850$	−127.716	−	208.008i	−0.150255	−	0.244715i
$851$	−410.465			−0.482332
$852$		0			0
$853$	672.027	−	672.027i	0.787840	−	0.787840i	−0.193300	−	0.981140i	$-0.561919\pi$
$853$	672.027	−	672.027i	0.787840	−	0.787840i	0.981140	+	0.193300i	$0.0619190\pi$
$854$			202.149i			0.236709i
$855$		0			0
$856$	484.719			0.566261
$857$	−101.904	−	101.904i	−0.118907	−	0.118907i	0.645149	−	0.764057i	$-0.276795\pi$
$857$	−101.904	−	101.904i	−0.118907	−	0.118907i	−0.764057	+	0.645149i	$0.776795\pi$
$858$		0			0
$859$			152.886i			0.177982i	0.996032	+	0.0889909i	$0.0283642\pi$
$859$			152.886i			0.177982i	−0.996032	+	0.0889909i	$0.971636\pi$
$860$	−161.394	+	288.485i	−0.187668	+	0.335447i
$861$		0			0
$862$	335.353	+	335.353i	0.389041	+	0.389041i
$863$	−181.809	+	181.809i	−0.210671	+	0.210671i	−0.804553	−	0.593881i	$-0.797595\pi$
$863$	−181.809	+	181.809i	−0.210671	+	0.210671i	0.593881	+	0.804553i	$0.297595\pi$
$864$		0			0
$865$	−802.351	−	448.880i	−0.927574	−	0.518937i
$866$	1897.22			2.19078
$867$		0			0
$868$	−23.0886	+	23.0886i	−0.0265997	+	0.0265997i
$869$		−	730.072i		−	0.840129i
$870$		0			0
$871$	2082.58			2.39102
$872$	178.701	+	178.701i	0.204932	+	0.204932i
$873$		0			0
$874$		−	68.8764i		−	0.0788059i
$875$	−13.4150	−	330.447i	−0.0153314	−	0.377653i
$876$		0			0
$877$	342.206	+	342.206i	0.390201	+	0.390201i	0.874759	−	0.484558i	$-0.161020\pi$
$877$	342.206	+	342.206i	0.390201	+	0.390201i	−0.484558	+	0.874759i	$0.661020\pi$
$878$	146.424	−	146.424i	0.166769	−	0.166769i
$879$		0			0
$880$	358.252	+	1268.15i	0.407104	+	1.44108i
$881$	−1421.22			−1.61318			−0.806592	−	0.591108i	$-0.798691\pi$
$881$	−1421.22			−1.61318			−0.806592	+	0.591108i	$0.798691\pi$
$882$		0			0
$883$	−1050.05	+	1050.05i	−1.18919	+	1.18919i	−0.211896	+	0.977292i	$0.567964\pi$
$883$	−1050.05	+	1050.05i	−1.18919	+	1.18919i	−0.977292	+	0.211896i	$0.932036\pi$
$884$		−	112.340i		−	0.127081i
$885$		0			0
$886$	−967.106			−1.09154
$887$	−798.714	−	798.714i	−0.900467	−	0.900467i	0.0950093	−	0.995476i	$-0.469712\pi$
$887$	−798.714	−	798.714i	−0.900467	−	0.900467i	−0.995476	+	0.0950093i	$0.969712\pi$
$888$		0			0
$889$		−	14.9278i		−	0.0167916i
$890$	1540.97	+	862.107i	1.73143	+	0.968660i
$891$		0			0
$892$	−257.032	−	257.032i	−0.288153	−	0.288153i
$893$	−95.2630	+	95.2630i	−0.106678	+	0.106678i
$894$		0			0
$895$	458.485	−	129.521i	0.512273	−	0.144717i
$896$	408.732			0.456174
$897$		0			0
$898$	−304.093	+	304.093i	−0.338634	+	0.338634i
$899$			556.995i			0.619572i
$900$		0			0
$901$	281.564			0.312501
$902$	451.654	+	451.654i	0.500725	+	0.500725i
$903$		0			0
$904$		−	373.947i		−	0.413658i
$905$	−257.326	−	910.893i	−0.284338	−	1.00651i
$906$		0			0
$907$	807.370	+	807.370i	0.890154	+	0.890154i	0.994537	−	0.104383i	$-0.0332867\pi$
$907$	807.370	+	807.370i	0.890154	+	0.890154i	−0.104383	+	0.994537i	$0.533287\pi$
$908$	110.993	−	110.993i	0.122239	−	0.122239i
$909$		0			0
$910$	340.792	−	609.150i	0.374497	−	0.669395i
$911$	1177.41			1.29244			0.646220	−	0.763151i	$-0.276349\pi$
$911$	1177.41			1.29244			0.646220	+	0.763151i	$0.276349\pi$
$912$		0			0
$913$	−1335.21	+	1335.21i	−1.46244	+	1.46244i
$914$		−	265.572i		−	0.290560i
$915$		0			0
$916$	13.7910			0.0150557
$917$	135.754	+	135.754i	0.148042	+	0.148042i
$918$		0			0
$919$			858.202i			0.933843i	0.884299	+	0.466922i	$0.154637\pi$
$919$			858.202i			0.933843i	−0.884299	+	0.466922i	$0.845363\pi$
$920$	204.958	−	57.9003i	0.222780	−	0.0629351i
$921$		0			0
$922$	−369.591	−	369.591i	−0.400857	−	0.400857i
$923$	−514.480	+	514.480i	−0.557399	+	0.557399i
$924$		0			0
$925$	1528.55	+	365.568i	1.65249	+	0.395209i
$926$	−1868.20			−2.01750
$927$		0			0
$928$	−618.380	+	618.380i	−0.666358	+	0.666358i
$929$			874.985i			0.941857i	0.882171	+	0.470929i	$0.156081\pi$
$929$			874.985i			0.941857i	−0.882171	+	0.470929i	$0.843919\pi$
$930$		0			0
$931$	32.6487			0.0350684
$932$	−239.375	−	239.375i	−0.256841	−	0.256841i
$933$		0			0
$934$			161.746i			0.173176i
$935$	−144.523	+	258.329i	−0.154570	+	0.276287i
$936$		0			0
$937$	−758.907	−	758.907i	−0.809932	−	0.809932i	0.174691	−	0.984623i	$-0.444107\pi$
$937$	−758.907	−	758.907i	−0.809932	−	0.809932i	−0.984623	+	0.174691i	$0.944107\pi$
$938$	377.738	−	377.738i	0.402706	−	0.402706i
$939$		0			0
$940$	140.603	+	78.6611i	0.149577	+	0.0836820i
$941$	−994.076			−1.05640			−0.528202	−	0.849119i	$-0.677134\pi$
$941$	−994.076			−1.05640			−0.528202	+	0.849119i	$0.677134\pi$
$942$		0			0
$943$	95.0702	−	95.0702i	0.100817	−	0.100817i
$944$		−	908.226i		−	0.962104i
$945$		0			0
$946$	1838.31			1.94324
$947$	402.372	+	402.372i	0.424891	+	0.424891i	0.886884	−	0.461993i	$-0.152865\pi$
$947$	402.372	+	402.372i	0.424891	+	0.424891i	−0.461993	+	0.886884i	$0.652865\pi$
$948$		0			0
$949$		−	630.069i		−	0.663930i
$950$	−61.3427	+	256.493i	−0.0645712	+	0.269993i
$951$		0			0
$952$	52.6872	+	52.6872i	0.0553437	+	0.0553437i
$953$	103.317	−	103.317i	0.108413	−	0.108413i	−0.650820	−	0.759232i	$-0.725575\pi$
$953$	103.317	−	103.317i	0.108413	−	0.108413i	0.759232	+	0.650820i	$0.225575\pi$
$954$		0			0
$955$	−441.476	−	1562.76i	−0.462279	−	1.63639i
$956$	−11.9038			−0.0124516
$957$		0			0
$958$	−766.089	+	766.089i	−0.799675	+	0.799675i
$959$		−	253.145i		−	0.263968i
$960$		0			0
$961$	−838.606			−0.872639
$962$	2345.52	+	2345.52i	2.43817	+	2.43817i
$963$		0			0
$964$		−	242.101i		−	0.251142i
$965$	−152.598	−	85.3719i	−0.158133	−	0.0884682i
$966$		0			0
$967$	−358.664	−	358.664i	−0.370904	−	0.370904i	0.496902	−	0.867806i	$-0.334471\pi$
$967$	−358.664	−	358.664i	−0.370904	−	0.370904i	−0.867806	+	0.496902i	$0.834471\pi$
$968$	309.454	−	309.454i	0.319684	−	0.319684i
$969$		0			0
$970$	1173.38	−	331.478i	1.20967	−	0.341729i
$971$	261.240			0.269042			0.134521	−	0.990911i	$-0.457050\pi$
$971$	261.240			0.269042			0.134521	+	0.990911i	$0.457050\pi$
$972$		0			0
$973$	−248.805	+	248.805i	−0.255709	+	0.255709i
$974$			1706.04i			1.75158i
$975$		0			0
$976$	649.201			0.665165
$977$	−510.551	−	510.551i	−0.522570	−	0.522570i	0.395777	−	0.918347i	$-0.370475\pi$
$977$	−510.551	−	510.551i	−0.522570	−	0.522570i	−0.918347	+	0.395777i	$0.870475\pi$
$978$		0			0
$979$		−	2141.33i		−	2.18726i
$980$	−10.6144	−	37.5732i	−0.0108310	−	0.0383400i
$981$		0			0
$982$	557.027	+	557.027i	0.567237	+	0.567237i
$983$	−920.586	+	920.586i	−0.936507	+	0.936507i	−0.998101	−	0.0615942i	$-0.980382\pi$
$983$	−920.586	+	920.586i	−0.936507	+	0.936507i	0.0615942	+	0.998101i	$0.480382\pi$
$984$		0			0
$985$	31.3788	−	56.0881i	0.0318567	−	0.0569422i
$986$	−491.561			−0.498541
$987$		0			0
$988$	−85.8275	+	85.8275i	−0.0868700	+	0.0868700i
$989$		−	386.952i		−	0.391255i
$990$		0			0
$991$	189.108			0.190825			0.0954126	−	0.995438i	$-0.469583\pi$
$991$	189.108			0.190825			0.0954126	+	0.995438i	$0.469583\pi$
$992$	135.883	+	135.883i	0.136978	+	0.136978i
$993$		0			0
$994$			186.633i			0.187759i
$995$	−573.513	+	162.016i	−0.576395	+	0.162831i
$996$		0			0
$997$	67.1053	+	67.1053i	0.0673072	+	0.0673072i	0.739959	−	0.672652i	$-0.234845\pi$
$997$	67.1053	+	67.1053i	0.0673072	+	0.0673072i	−0.672652	+	0.739959i	$0.734845\pi$
$998$	−1064.65	+	1064.65i	−1.06678	+	1.06678i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.o.b.127.11		24
3.2	odd	2		105.3.l.a.22.2	✓	24
5.3	odd	4	inner	315.3.o.b.253.11		24
15.2	even	4		525.3.l.e.43.11		24
15.8	even	4		105.3.l.a.43.2	yes	24
15.14	odd	2		525.3.l.e.232.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.2	✓	24	3.2	odd	2
105.3.l.a.43.2	yes	24	15.8	even	4
315.3.o.b.127.11		24	1.1	even	1	trivial
315.3.o.b.253.11		24	5.3	odd	4	inner
525.3.l.e.43.11		24	15.2	even	4
525.3.l.e.232.11		24	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.59930 + 1.59930i) q^{2} +1.11554i q^{4} +(1.35929 + 4.81169i) q^{5} +(1.87083 + 1.87083i) q^{7} +(4.61313 - 4.61313i) q^{8} +O(q^{10})\)	\(q+(1.59930 + 1.59930i) q^{2} +1.11554i q^{4} +(1.35929 + 4.81169i) q^{5} +(1.87083 + 1.87083i) q^{7} +(4.61313 - 4.61313i) q^{8} +(-5.52142 + 9.86926i) q^{10} +13.7143 q^{11} +(-16.4959 + 16.4959i) q^{13} +5.98404i q^{14} +19.2177 q^{16} +(3.05243 + 3.05243i) q^{17} -4.66410i q^{19} +(-5.36761 + 1.51634i) q^{20} +(21.9333 + 21.9333i) q^{22} +(4.61681 - 4.61681i) q^{23} +(-21.3046 + 13.0810i) q^{25} -52.7638 q^{26} +(-2.08698 + 2.08698i) q^{28} +50.3467i q^{29} +11.0632 q^{31} +(12.2824 + 12.2824i) q^{32} +9.76351i q^{34} +(-6.45883 + 11.5448i) q^{35} +(-44.4533 - 44.4533i) q^{37} +(7.45931 - 7.45931i) q^{38} +(28.4675 + 15.9263i) q^{40} +20.5922 q^{41} +(41.9068 - 41.9068i) q^{43} +15.2988i q^{44} +14.7673 q^{46} +(-20.4247 - 20.4247i) q^{47} +7.00000i q^{49} +(-54.9930 - 13.1521i) q^{50} +(-18.4017 - 18.4017i) q^{52} +(46.1212 - 46.1212i) q^{53} +(18.6417 + 65.9888i) q^{55} +17.2608 q^{56} +(-80.5197 + 80.5197i) q^{58} -47.2598i q^{59} +33.7814 q^{61} +(17.6934 + 17.6934i) q^{62} -37.5843i q^{64} +(-101.796 - 56.9502i) q^{65} +(-63.1243 - 63.1243i) q^{67} +(-3.40509 + 3.40509i) q^{68} +(-28.7933 + 8.13407i) q^{70} +31.1884 q^{71} +(-19.0978 + 19.0978i) q^{73} -142.189i q^{74} +5.20297 q^{76} +(25.6570 + 25.6570i) q^{77} -53.2345i q^{79} +(26.1225 + 92.4696i) q^{80} +(32.9332 + 32.9332i) q^{82} +(-97.3590 + 97.3590i) q^{83} +(-10.5382 + 18.8365i) q^{85} +134.043 q^{86} +(63.2657 - 63.2657i) q^{88} -156.139i q^{89} -61.7219 q^{91} +(5.15021 + 5.15021i) q^{92} -65.3306i q^{94} +(22.4422 - 6.33989i) q^{95} +(-76.2395 - 76.2395i) q^{97} +(-11.1951 + 11.1951i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) \) 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8	\( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) \) 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8 - 40 * q^10 + 64 * q^13 - 184 * q^16 - 24 * q^17 - 72 * q^20 + 8 * q^22 - 8 * q^23 - 136 * q^25 + 80 * q^26 + 96 * q^31 - 56 * q^32 + 8 * q^37 - 56 * q^38 + 232 * q^40 - 320 * q^41 - 112 * q^43 + 320 * q^46 - 64 * q^47 + 256 * q^50 + 96 * q^52 + 72 * q^53 - 80 * q^55 + 336 * q^56 - 512 * q^58 - 496 * q^61 + 776 * q^62 - 312 * q^65 - 192 * q^67 - 568 * q^68 + 112 * q^70 + 144 * q^71 + 224 * q^73 + 416 * q^76 - 112 * q^77 + 528 * q^80 + 352 * q^82 + 32 * q^83 + 24 * q^85 - 240 * q^86 + 216 * q^88 - 1304 * q^92 - 376 * q^95 - 816 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

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