LMFDB - Embedded newform 100.4.i.a.9.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(9,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("100.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.i (of order $10$, degree $4$, 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:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.8
Character	$\chi$	$=$	100.9
Dual form			100.4.i.a.89.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.21445 - 2.66904i) q^{3} +(-9.50227 - 5.89126i) q^{5} -24.1794i q^{7} +(38.5100 - 27.9792i) q^{9} +O(q^{10})$	\(q+(8.21445 - 2.66904i) q^{3} +(-9.50227 - 5.89126i) q^{5} -24.1794i q^{7} +(38.5100 - 27.9792i) q^{9} +(-18.1311 - 13.1730i) q^{11} +(29.0992 + 40.0516i) q^{13} +(-93.7799 - 23.0316i) q^{15} +(66.2212 + 21.5166i) q^{17} +(-40.4144 + 124.383i) q^{19} +(-64.5356 - 198.620i) q^{21} +(114.398 - 157.455i) q^{23} +(55.5861 + 111.961i) q^{25} +(104.588 - 143.952i) q^{27} +(20.0210 + 61.6182i) q^{29} +(47.6687 - 146.709i) q^{31} +(-184.097 - 59.8166i) q^{33} +(-142.447 + 229.759i) q^{35} +(43.7607 + 60.2314i) q^{37} +(345.934 + 251.335i) q^{39} +(-180.765 + 131.333i) q^{41} +401.934i q^{43} +(-530.765 + 38.9929i) q^{45} +(-257.702 + 83.7326i) q^{47} -241.641 q^{49} +601.400 q^{51} +(-336.899 + 109.465i) q^{53} +(94.6810 + 231.989i) q^{55} +1129.60i q^{57} +(557.152 - 404.795i) q^{59} +(-168.898 - 122.711i) q^{61} +(-676.519 - 931.148i) q^{63} +(-40.5538 - 552.012i) q^{65} +(587.013 + 190.732i) q^{67} +(519.462 - 1598.74i) q^{69} +(-79.6952 - 245.277i) q^{71} +(130.747 - 179.957i) q^{73} +(755.437 + 771.334i) q^{75} +(-318.515 + 438.399i) q^{77} +(246.022 + 757.177i) q^{79} +(77.7580 - 239.314i) q^{81} +(-961.201 - 312.313i) q^{83} +(-502.492 - 594.583i) q^{85} +(328.922 + 452.723i) q^{87} +(398.492 + 289.522i) q^{89} +(968.423 - 703.600i) q^{91} -1332.37i q^{93} +(1116.80 - 943.826i) q^{95} +(-1327.15 + 431.218i) q^{97} -1066.80 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) $ 32 * q + 6 * q^5 + 122 * q^9	$ 32 q + 6 q^{5} + 122 q^{9} + 20 q^{11} + 68 q^{15} - 160 q^{17} + 2 q^{19} - 108 q^{21} + 290 q^{23} + 654 q^{25} + 600 q^{27} + 62 q^{29} - 378 q^{31} - 1280 q^{33} - 278 q^{35} + 680 q^{37} + 592 q^{39} - 528 q^{41} - 1044 q^{45} - 1810 q^{47} - 2796 q^{49} + 1664 q^{51} - 510 q^{53} - 1350 q^{55} + 144 q^{59} - 1346 q^{61} + 1660 q^{63} + 1142 q^{65} + 1890 q^{67} + 956 q^{69} + 786 q^{71} + 3720 q^{73} - 78 q^{75} + 2160 q^{77} + 896 q^{79} + 348 q^{81} + 570 q^{83} + 224 q^{85} + 3240 q^{87} - 2512 q^{89} - 2212 q^{91} + 1536 q^{95} - 2250 q^{97} - 2540 q^{99}+O(q^{100}) $ 32 * q + 6 * q^5 + 122 * q^9 + 20 * q^11 + 68 * q^15 - 160 * q^17 + 2 * q^19 - 108 * q^21 + 290 * q^23 + 654 * q^25 + 600 * q^27 + 62 * q^29 - 378 * q^31 - 1280 * q^33 - 278 * q^35 + 680 * q^37 + 592 * q^39 - 528 * q^41 - 1044 * q^45 - 1810 * q^47 - 2796 * q^49 + 1664 * q^51 - 510 * q^53 - 1350 * q^55 + 144 * q^59 - 1346 * q^61 + 1660 * q^63 + 1142 * q^65 + 1890 * q^67 + 956 * q^69 + 786 * q^71 + 3720 * q^73 - 78 * q^75 + 2160 * q^77 + 896 * q^79 + 348 * q^81 + 570 * q^83 + 224 * q^85 + 3240 * q^87 - 2512 * q^89 - 2212 * q^91 + 1536 * q^95 - 2250 * q^97 - 2540 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	8.21445	−	2.66904i	1.58087	−	0.513657i	0.618591	−	0.785713i	$-0.287704\pi$
$3$	8.21445	−	2.66904i	1.58087	−	0.513657i	0.962281	+	0.272056i	$0.0877037\pi$
$4$		0			0
$5$	−9.50227	−	5.89126i	−0.849908	−	0.526930i
$5$	−9.50227	−	5.89126i	−0.849908	−	0.526930i
$6$		0			0
$7$		−	24.1794i		−	1.30556i	−0.757546	−	0.652781i	$-0.773602\pi$
$7$		−	24.1794i		−	1.30556i	0.757546	−	0.652781i	$-0.226398\pi$
$8$		0			0
$9$	38.5100	−	27.9792i	1.42630	−	1.03627i
$10$		0			0
$11$	−18.1311	−	13.1730i	−0.496976	−	0.361074i	0.310885	−	0.950448i	$-0.399375\pi$
$11$	−18.1311	−	13.1730i	−0.496976	−	0.361074i	−0.807861	+	0.589373i	$0.799375\pi$
$12$		0			0
$13$	29.0992	+	40.0516i	0.620821	+	0.854486i	0.997412	−	0.0718929i	$-0.0229040\pi$
$13$	29.0992	+	40.0516i	0.620821	+	0.854486i	−0.376592	+	0.926379i	$0.622904\pi$
$14$		0			0
$15$	−93.7799	−	23.0316i	−1.61426	−	0.396449i
$16$		0			0
$17$	66.2212	+	21.5166i	0.944765	+	0.306973i	0.740587	−	0.671961i	$-0.234548\pi$
$17$	66.2212	+	21.5166i	0.944765	+	0.306973i	0.204178	+	0.978934i	$0.434548\pi$
$18$		0			0
$19$	−40.4144	+	124.383i	−0.487984	+	1.50186i	0.339628	+	0.940560i	$0.389699\pi$
$19$	−40.4144	+	124.383i	−0.487984	+	1.50186i	−0.827612	+	0.561300i	$0.810301\pi$
$20$		0			0
$21$	−64.5356	−	198.620i	−0.670611	−	2.06393i
$22$		0			0
$23$	114.398	−	157.455i	1.03711	−	1.42746i	0.137641	−	0.990482i	$-0.456048\pi$
$23$	114.398	−	157.455i	1.03711	−	1.42746i	0.899471	−	0.436980i	$-0.143952\pi$
$24$		0			0
$25$	55.5861	+	111.961i	0.444689	+	0.895685i
$26$		0			0
$27$	104.588	−	143.952i	0.745477	−	1.02606i
$28$		0			0
$29$	20.0210	+	61.6182i	0.128200	+	0.394559i	0.994471	−	0.105016i	$-0.0334895\pi$
$29$	20.0210	+	61.6182i	0.128200	+	0.394559i	−0.866271	+	0.499575i	$0.833489\pi$
$30$		0			0
$31$	47.6687	−	146.709i	0.276179	−	0.849992i	−0.712726	−	0.701443i	$-0.752540\pi$
$31$	47.6687	−	146.709i	0.276179	−	0.849992i	0.988905	−	0.148549i	$-0.0474604\pi$
$32$		0			0
$33$	−184.097	−	59.8166i	−0.971124	−	0.315537i
$34$		0			0
$35$	−142.447	+	229.759i	−0.687941	+	1.10961i
$36$		0			0
$37$	43.7607	+	60.2314i	0.194438	+	0.267621i	0.895093	−	0.445879i	$-0.147109\pi$
$37$	43.7607	+	60.2314i	0.194438	+	0.267621i	−0.700655	+	0.713500i	$0.747109\pi$
$38$		0			0
$39$	345.934	+	251.335i	1.42035	+	1.03195i
$40$		0			0
$41$	−180.765	+	131.333i	−0.688553	+	0.500263i	−0.876184	−	0.481976i	$-0.839919\pi$
$41$	−180.765	+	131.333i	−0.688553	+	0.500263i	0.187631	+	0.982240i	$0.439919\pi$
$42$		0			0
$43$			401.934i			1.42545i	0.701443	+	0.712725i	$0.252539\pi$
$43$			401.934i			1.42545i	−0.701443	+	0.712725i	$0.747461\pi$
$44$		0			0
$45$	−530.765	+	38.9929i	−1.75826	+	0.129172i
$46$		0			0
$47$	−257.702	+	83.7326i	−0.799782	+	0.259865i	−0.680264	−	0.732967i	$-0.738135\pi$
$47$	−257.702	+	83.7326i	−0.799782	+	0.259865i	−0.119518	+	0.992832i	$0.538135\pi$
$48$		0			0
$49$	−241.641			−0.704494
$50$		0			0
$51$	601.400			1.65123
$52$		0			0
$53$	−336.899	+	109.465i	−0.873143	+	0.283701i	−0.711107	−	0.703083i	$-0.751806\pi$
$53$	−336.899	+	109.465i	−0.873143	+	0.283701i	−0.162036	+	0.986785i	$0.551806\pi$
$54$		0			0
$55$	94.6810	+	231.989i	0.232123	+	0.568752i
$56$		0			0
$57$			1129.60i			2.62491i
$58$		0			0
$59$	557.152	−	404.795i	1.22941	−	0.893217i	0.232562	−	0.972582i	$-0.425289\pi$
$59$	557.152	−	404.795i	1.22941	−	0.893217i	0.996846	+	0.0793647i	$0.0252892\pi$
$60$		0			0
$61$	−168.898	−	122.711i	−0.354511	−	0.257567i	0.396248	−	0.918143i	$-0.370312\pi$
$61$	−168.898	−	122.711i	−0.354511	−	0.257567i	−0.750759	+	0.660576i	$0.770312\pi$
$62$		0			0
$63$	−676.519	−	931.148i	−1.35291	−	1.86212i
$64$		0			0
$65$	−40.5538	−	552.012i	−0.0773859	−	1.05336i
$66$		0			0
$67$	587.013	+	190.732i	1.07037	+	0.347785i	0.790633	−	0.612290i	$-0.209752\pi$
$67$	587.013	+	190.732i	1.07037	+	0.347785i	0.279740	+	0.960076i	$0.409752\pi$
$68$		0			0
$69$	519.462	−	1598.74i	0.906317	−	2.78936i
$70$		0			0
$71$	−79.6952	−	245.277i	−0.133212	−	0.409986i	0.862095	−	0.506746i	$-0.169152\pi$
$71$	−79.6952	−	245.277i	−0.133212	−	0.409986i	−0.995308	+	0.0967605i	$0.969152\pi$
$72$		0			0
$73$	130.747	−	179.957i	0.209626	−	0.288526i	−0.691237	−	0.722628i	$-0.742934\pi$
$73$	130.747	−	179.957i	0.209626	−	0.288526i	0.900864	+	0.434102i	$0.142934\pi$
$74$		0			0
$75$	755.437	+	771.334i	1.16307	+	1.18755i
$76$		0			0
$77$	−318.515	+	438.399i	−0.471405	+	0.648834i
$78$		0			0
$79$	246.022	+	757.177i	0.350375	+	1.07834i	0.958643	+	0.284611i	$0.0918646\pi$
$79$	246.022	+	757.177i	0.350375	+	1.07834i	−0.608268	+	0.793732i	$0.708135\pi$
$80$		0			0
$81$	77.7580	−	239.314i	0.106664	−	0.328278i
$82$		0			0
$83$	−961.201	−	312.313i	−1.27115	−	0.413022i	−0.405696	−	0.914008i	$-0.632971\pi$
$83$	−961.201	−	312.313i	−1.27115	−	0.413022i	−0.865455	+	0.500986i	$0.832971\pi$
$84$		0			0
$85$	−502.492	−	594.583i	−0.641210	−	0.758724i
$86$		0			0
$87$	328.922	+	452.723i	0.405336	+	0.557896i
$88$		0			0
$89$	398.492	+	289.522i	0.474608	+	0.344823i	0.799234	−	0.601019i	$-0.205239\pi$
$89$	398.492	+	289.522i	0.474608	+	0.344823i	−0.324626	+	0.945842i	$0.605239\pi$
$90$		0			0
$91$	968.423	−	703.600i	1.11559	−	0.810520i
$92$		0			0
$93$		−	1332.37i		−	1.48559i
$94$		0			0
$95$	1116.80	−	943.826i	1.20612	−	1.01931i
$96$		0			0
$97$	−1327.15	+	431.218i	−1.38919	+	0.451377i	−0.905681	−	0.423960i	$-0.860640\pi$
$97$	−1327.15	+	431.218i	−1.38919	+	0.451377i	−0.483514	+	0.875337i	$0.660640\pi$
$98$		0			0
$99$	−1066.80			−1.08301
$100$		0			0
$101$	226.742			0.223383			0.111691	−	0.993743i	$-0.464373\pi$
$101$	226.742			0.223383			0.111691	+	0.993743i	$0.464373\pi$
$102$		0			0
$103$	−1130.82	+	367.426i	−1.08178	+	0.351491i	−0.795064	−	0.606525i	$-0.792563\pi$
$103$	−1130.82	+	367.426i	−1.08178	+	0.351491i	−0.286714	+	0.958016i	$0.592563\pi$
$104$		0			0
$105$	−556.889	+	2267.54i	−0.517589	+	2.10752i
$106$		0			0
$107$		−	1302.83i		−	1.17709i	−0.808463	−	0.588547i	$-0.799700\pi$
$107$		−	1302.83i		−	1.17709i	0.808463	−	0.588547i	$-0.200300\pi$
$108$		0			0
$109$	653.845	−	475.047i	0.574560	−	0.417442i	−0.262199	−	0.965014i	$-0.584448\pi$
$109$	653.845	−	475.047i	0.574560	−	0.417442i	0.836759	+	0.547572i	$0.184448\pi$
$110$		0			0
$111$	520.230	+	377.969i	0.444848	+	0.323201i
$112$		0			0
$113$	276.930	+	381.161i	0.230543	+	0.317315i	0.908579	−	0.417714i	$-0.137169\pi$
$113$	276.930	+	381.161i	0.230543	+	0.317315i	−0.678036	+	0.735029i	$0.737169\pi$
$114$		0			0
$115$	−2014.65	+	822.232i	−1.63362	+	0.666726i
$116$		0			0
$117$	2241.22	+	728.218i	1.77095	+	0.575417i
$118$		0			0
$119$	520.257	−	1601.19i	0.400772	−	1.23345i
$120$		0			0
$121$	−256.093	−	788.173i	−0.192406	−	0.592166i
$122$		0			0
$123$	−1134.35	+	1561.30i	−0.831551	+	1.14453i
$124$		0			0
$125$	131.396	−	1391.35i	0.0940190	−	0.995570i
$126$		0			0
$127$	1049.36	−	1444.33i	0.733197	−	1.00916i	−0.265785	−	0.964032i	$-0.585631\pi$
$127$	1049.36	−	1444.33i	0.733197	−	1.00916i	0.998981	−	0.0451261i	$-0.0143690\pi$
$128$		0			0
$129$	1072.78	+	3301.67i	0.732192	+	2.25346i
$130$		0			0
$131$	433.554	−	1334.34i	0.289159	−	0.889940i	−0.695962	−	0.718078i	$-0.745022\pi$
$131$	433.554	−	1334.34i	0.289159	−	0.889940i	0.985121	−	0.171861i	$-0.0549781\pi$
$132$		0			0
$133$	3007.49	+	977.194i	1.96077	+	0.637094i
$134$		0			0
$135$	−1841.88	+	751.721i	−1.17425	+	0.479244i
$136$		0			0
$137$	−795.744	−	1095.25i	−0.496241	−	0.683017i	0.485283	−	0.874357i	$-0.338717\pi$
$137$	−795.744	−	1095.25i	−0.496241	−	0.683017i	−0.981524	+	0.191340i	$0.938717\pi$
$138$		0			0
$139$	1462.44	+	1062.52i	0.892389	+	0.648359i	0.936500	−	0.350668i	$-0.114045\pi$
$139$	1462.44	+	1062.52i	0.892389	+	0.648359i	−0.0441105	+	0.999027i	$0.514045\pi$
$140$		0			0
$141$	−1893.40	+	1375.64i	−1.13087	+	0.821627i
$142$		0			0
$143$		−	1109.51i		−	0.648822i
$144$		0			0
$145$	172.764	−	703.461i	0.0989468	−	0.402891i
$146$		0			0
$147$	−1984.95	+	644.950i	−1.11371	+	0.361868i
$148$		0			0
$149$	−2232.80			−1.22764			−0.613818	−	0.789448i	$-0.710367\pi$
$149$	−2232.80			−1.22764			−0.613818	+	0.789448i	$0.710367\pi$
$150$		0			0
$151$	−2599.73			−1.40108			−0.700541	−	0.713612i	$-0.747058\pi$
$151$	−2599.73			−1.40108			−0.700541	+	0.713612i	$0.747058\pi$
$152$		0			0
$153$	3152.20	−	1024.21i	1.66562	−	0.541193i
$154$		0			0
$155$	−1317.26	+	1113.24i	−0.682614	+	0.576888i
$156$		0			0
$157$			3468.47i			1.76315i	0.472046	+	0.881574i	$0.343516\pi$
$157$			3468.47i			1.76315i	−0.472046	+	0.881574i	$0.656484\pi$
$158$		0			0
$159$	−2475.27	+	1798.39i	−1.23460	+	0.896991i
$160$		0			0
$161$	−3807.16	−	2766.06i	−1.86364	−	1.35401i
$162$		0			0
$163$	1562.58	+	2150.71i	0.750865	+	1.03348i	0.997919	+	0.0644758i	$0.0205375\pi$
$163$	1562.58	+	2150.71i	0.750865	+	1.03348i	−0.247054	+	0.969002i	$0.579462\pi$
$164$		0			0
$165$	1396.94	+	1652.95i	0.659101	+	0.779893i
$166$		0			0
$167$	895.967	+	291.117i	0.415162	+	0.134894i	0.509147	−	0.860679i	$-0.329961\pi$
$167$	895.967	+	291.117i	0.415162	+	0.134894i	−0.0939857	+	0.995574i	$0.529961\pi$
$168$		0			0
$169$	−78.4586	+	241.471i	−0.0357117	+	0.109909i
$170$		0			0
$171$	1923.77	+	5920.74i	0.860316	+	2.64778i
$172$		0			0
$173$	−6.14258	+	8.45453i	−0.00269949	+	0.00371553i	−0.810365	−	0.585926i	$-0.800731\pi$
$173$	−6.14258	+	8.45453i	−0.00269949	+	0.00371553i	0.807665	+	0.589641i	$0.200731\pi$
$174$		0			0
$175$	2707.14	−	1344.04i	1.16937	−	0.580569i
$176$		0			0
$177$	3496.29	−	4812.23i	1.48473	−	2.04356i
$178$		0			0
$179$	288.537	+	888.027i	0.120482	+	0.370806i	0.993051	−	0.117685i	$-0.0375475\pi$
$179$	288.537	+	888.027i	0.120482	+	0.370806i	−0.872569	+	0.488491i	$0.837547\pi$
$180$		0			0
$181$	552.751	−	1701.19i	0.226993	−	0.698612i	−0.771091	−	0.636726i	$-0.780288\pi$
$181$	552.751	−	1701.19i	0.226993	−	0.698612i	0.998083	−	0.0618861i	$-0.0197116\pi$
$182$		0			0
$183$	−1714.92	−	557.213i	−0.692737	−	0.225084i
$184$		0			0
$185$	−60.9867	−	830.141i	−0.0242369	−	0.329909i
$186$		0			0
$187$	−917.226	−	1262.45i	−0.358686	−	0.493688i
$188$		0			0
$189$	−3480.68	−	2528.86i	−1.33959	−	0.973267i
$190$		0			0
$191$	909.020	−	660.442i	0.344369	−	0.250198i	−0.402134	−	0.915581i	$-0.631731\pi$
$191$	909.020	−	660.442i	0.344369	−	0.250198i	0.746503	+	0.665382i	$0.231731\pi$
$192$		0			0
$193$			2419.61i			0.902420i	0.892418	+	0.451210i	$0.149007\pi$
$193$			2419.61i			0.902420i	−0.892418	+	0.451210i	$0.850993\pi$
$194$		0			0
$195$	−1806.47	−	4426.24i	−0.663405	−	1.62549i
$196$		0			0
$197$	−2975.82	+	966.903i	−1.07624	+	0.349690i	−0.792913	−	0.609334i	$-0.791437\pi$
$197$	−2975.82	+	966.903i	−1.07624	+	0.349690i	−0.283323	+	0.959025i	$0.591437\pi$
$198$		0			0
$199$	−594.057			−0.211616			−0.105808	−	0.994387i	$-0.533743\pi$
$199$	−594.057			−0.211616			−0.105808	+	0.994387i	$0.533743\pi$
$200$		0			0
$201$	5331.06			1.87077
$202$		0			0
$203$	1489.89	−	484.094i	0.515121	−	0.167373i
$204$		0			0
$205$	2491.39	−	183.031i	0.848811	−	0.0623583i
$206$		0			0
$207$		−	9264.35i		−	3.11071i
$208$		0			0
$209$	2371.25	−	1722.82i	0.784800	−	0.570190i
$210$		0			0
$211$	1298.23	+	943.221i	0.423574	+	0.307744i	0.779074	−	0.626932i	$-0.215690\pi$
$211$	1298.23	+	943.221i	0.423574	+	0.307744i	−0.355501	+	0.934676i	$0.615690\pi$
$212$		0			0
$213$	−1309.31	−	1802.10i	−0.421184	−	0.579710i
$214$		0			0
$215$	2367.90	−	3819.28i	0.751113	−	1.21150i
$216$		0			0
$217$	−3547.34	−	1152.60i	−1.10972	−	0.360569i
$218$		0			0
$219$	593.699	−	1827.22i	0.183189	−	0.563799i
$220$		0			0
$221$	1065.21	+	3278.38i	0.324226	+	0.997864i
$222$		0			0
$223$	290.704	−	400.120i	0.0872960	−	0.120153i	−0.763135	−	0.646239i	$-0.776341\pi$
$223$	290.704	−	400.120i	0.0872960	−	0.120153i	0.850431	+	0.526086i	$0.176341\pi$
$224$		0			0
$225$	5273.19	+	2756.36i	1.56243	+	0.816698i
$226$		0			0
$227$	−2018.56	+	2778.31i	−0.590205	+	0.812348i	−0.994768	−	0.102163i	$-0.967424\pi$
$227$	−2018.56	+	2778.31i	−0.590205	+	0.812348i	0.404563	+	0.914510i	$0.367424\pi$
$228$		0			0
$229$	−1685.39	−	5187.10i	−0.486349	−	1.49683i	−0.830018	−	0.557737i	$-0.811670\pi$
$229$	−1685.39	−	5187.10i	−0.486349	−	1.49683i	0.343669	−	0.939091i	$-0.388330\pi$
$230$		0			0
$231$	−1446.33	+	4451.34i	−0.411954	+	1.26786i
$232$		0			0
$233$	−1780.71	−	578.587i	−0.500678	−	0.162680i	0.0477804	−	0.998858i	$-0.484785\pi$
$233$	−1780.71	−	578.587i	−0.500678	−	0.162680i	−0.548459	+	0.836178i	$0.684785\pi$
$234$		0			0
$235$	2942.05	+	722.543i	0.816672	+	0.200568i
$236$		0			0
$237$	4041.87	+	5563.16i	1.10780	+	1.52475i
$238$		0			0
$239$	1008.72	+	732.881i	0.273008	+	0.198352i	0.715862	−	0.698242i	$-0.246034\pi$
$239$	1008.72	+	732.881i	0.273008	+	0.198352i	−0.442854	+	0.896594i	$0.646034\pi$
$240$		0			0
$241$	−3002.84	+	2181.69i	−0.802614	+	0.583133i	−0.911680	−	0.410901i	$-0.865214\pi$
$241$	−3002.84	+	2181.69i	−0.802614	+	0.583133i	0.109066	+	0.994035i	$0.465214\pi$
$242$		0			0
$243$			2630.87i			0.694528i
$244$		0			0
$245$	2296.14	+	1423.57i	0.598755	+	0.371219i
$246$		0			0
$247$	−6157.76	+	2000.78i	−1.58627	+	0.515410i
$248$		0			0
$249$	−8729.32			−2.22168
$250$		0			0
$251$	−2849.84			−0.716655			−0.358328	−	0.933596i	$-0.616653\pi$
$251$	−2849.84			−0.716655			−0.358328	+	0.933596i	$0.616653\pi$
$252$		0			0
$253$	−4148.32	+	1347.87i	−1.03084	+	0.334940i
$254$		0			0
$255$	−5714.66	−	3543.00i	−1.40340	−	0.870084i
$256$		0			0
$257$		−	4683.72i		−	1.13682i	−0.822746	−	0.568410i	$-0.807559\pi$
$257$		−	4683.72i		−	1.13682i	0.822746	−	0.568410i	$-0.192441\pi$
$258$		0			0
$259$	1456.36	−	1058.11i	0.349396	−	0.253851i
$260$		0			0
$261$	2495.03	+	1812.75i	0.591719	+	0.429909i
$262$		0			0
$263$	3371.64	+	4640.67i	0.790511	+	1.08805i	0.994044	+	0.108977i	$0.0347576\pi$
$263$	3371.64	+	4640.67i	0.790511	+	1.08805i	−0.203533	+	0.979068i	$0.565242\pi$
$264$		0			0
$265$	3846.19	+	944.592i	0.891583	+	0.218965i
$266$		0			0
$267$	4046.14	+	1314.67i	0.927415	+	0.301335i
$268$		0			0
$269$	−2654.59	+	8169.99i	−0.601685	+	1.85180i	−0.0835391	+	0.996504i	$0.526622\pi$
$269$	−2654.59	+	8169.99i	−0.601685	+	1.85180i	−0.518146	+	0.855292i	$0.673378\pi$
$270$		0			0
$271$	750.317	+	2309.24i	0.168186	+	0.517624i	0.999257	−	0.0385426i	$-0.0122715\pi$
$271$	750.317	+	2309.24i	0.168186	+	0.517624i	−0.831071	+	0.556167i	$0.812272\pi$
$272$		0			0
$273$	6077.13	−	8364.45i	1.34727	−	1.85436i
$274$		0			0
$275$	467.023	−	2762.21i	0.102409	−	0.605700i
$276$		0			0
$277$	−2758.76	+	3797.11i	−0.598404	+	0.823633i	−0.995561	−	0.0941182i	$-0.969997\pi$
$277$	−2758.76	+	3797.11i	−0.598404	+	0.823633i	0.397157	+	0.917751i	$0.369997\pi$
$278$		0			0
$279$	−2269.08	−	6983.51i	−0.486904	−	1.49854i
$280$		0			0
$281$	375.481	−	1155.61i	0.0797128	−	0.245331i	−0.903256	−	0.429101i	$-0.858830\pi$
$281$	375.481	−	1155.61i	0.0797128	−	0.245331i	0.982969	+	0.183770i	$0.0588303\pi$
$282$		0			0
$283$	1286.88	+	418.133i	0.270308	+	0.0878284i	0.441035	−	0.897490i	$-0.354612\pi$
$283$	1286.88	+	418.133i	0.270308	+	0.0878284i	−0.170727	+	0.985318i	$0.554612\pi$
$284$		0			0
$285$	6654.79	−	10733.8i	1.38314	−	2.23093i
$286$		0			0
$287$	3175.55	+	4370.77i	0.653125	+	0.898949i
$288$		0			0
$289$	−52.4154	−	38.0820i	−0.0106687	−	0.00775128i
$290$		0			0
$291$	−9750.89	+	7084.44i	−1.96429	+	1.42714i
$292$		0			0
$293$			4411.45i			0.879589i	0.898099	+	0.439794i	$0.144949\pi$
$293$			4411.45i			0.879589i	−0.898099	+	0.439794i	$0.855051\pi$
$294$		0			0
$295$	−7678.96	+	564.139i	−1.51555	+	0.111340i
$296$		0			0
$297$	−3792.58	+	1232.28i	−0.740969	+	0.240755i
$298$		0			0
$299$	9635.21			1.86361
$300$		0			0
$301$	9718.51			1.86102
$302$		0			0
$303$	1862.56	−	605.182i	0.353139	−	0.114742i
$304$		0			0
$305$	881.987	+	2161.06i	0.165582	+	0.405711i
$306$		0			0
$307$		−	4903.06i		−	0.911506i	−0.890106	−	0.455753i	$-0.849370\pi$
$307$		−	4903.06i		−	0.911506i	0.890106	−	0.455753i	$-0.150630\pi$
$308$		0			0
$309$	−8308.41	+	6036.41i	−1.52961	+	1.11133i
$310$		0			0
$311$	−3727.25	−	2708.00i	−0.679591	−	0.493752i	0.193631	−	0.981074i	$-0.437974\pi$
$311$	−3727.25	−	2708.00i	−0.679591	−	0.493752i	−0.873222	+	0.487323i	$0.837974\pi$
$312$		0			0
$313$	308.486	+	424.594i	0.0557082	+	0.0766757i	0.835962	−	0.548787i	$-0.184910\pi$
$313$	308.486	+	424.594i	0.0557082	+	0.0766757i	−0.780254	+	0.625463i	$0.784910\pi$
$314$		0			0
$315$	942.824	+	12833.6i	0.168642	+	2.29552i
$316$		0			0
$317$	−2164.72	−	703.361i	−0.383543	−	0.124621i	0.110898	−	0.993832i	$-0.464627\pi$
$317$	−2164.72	−	703.361i	−0.383543	−	0.124621i	−0.494441	+	0.869211i	$0.664627\pi$
$318$		0			0
$319$	448.696	−	1380.94i	0.0787528	−	0.242376i
$320$		0			0
$321$	−3477.29	−	10702.0i	−0.604622	−	1.86084i
$322$		0			0
$323$	−5352.58	+	7367.19i	−0.922060	+	1.26911i
$324$		0			0
$325$	−2866.69	+	5484.28i	−0.489279	+	0.936040i
$326$		0			0
$327$	4103.07	−	5647.39i	0.693884	−	0.955050i
$328$		0			0
$329$	2024.60	+	6231.08i	0.339270	+	1.04417i
$330$		0			0
$331$	1357.78	−	4178.82i	0.225469	−	0.693924i	−0.772774	−	0.634681i	$-0.781131\pi$
$331$	1357.78	−	4178.82i	0.225469	−	0.693924i	0.998244	−	0.0592425i	$-0.0188685\pi$
$332$		0			0
$333$	3370.45	+	1095.13i	0.554654	+	0.180218i
$334$		0			0
$335$	−4454.30	−	5270.63i	−0.726460	−	0.859598i
$336$		0			0
$337$	−886.002	−	1219.48i	−0.143216	−	0.197119i	0.731383	−	0.681967i	$-0.238875\pi$
$337$	−886.002	−	1219.48i	−0.143216	−	0.197119i	−0.874599	+	0.484847i	$0.838875\pi$
$338$		0			0
$339$	3292.16	+	2391.89i	0.527450	+	0.383215i
$340$		0			0
$341$	−2796.89	+	2032.06i	−0.444165	+	0.322705i
$342$		0			0
$343$		−	2450.79i		−	0.385802i
$344$		0			0
$345$	−14354.7	+	12131.4i	−2.24008	+	1.89313i
$346$		0			0
$347$	12037.3	−	3911.17i	1.86224	−	0.605079i	0.868181	−	0.496247i	$-0.165289\pi$
$347$	12037.3	−	3911.17i	1.86224	−	0.605079i	0.994060	−	0.108832i	$-0.0347109\pi$
$348$		0			0
$349$	8928.28			1.36940			0.684699	−	0.728826i	$-0.259934\pi$
$349$	8928.28			1.36940			0.684699	+	0.728826i	$0.259934\pi$
$350$		0			0
$351$	8808.94			1.33956
$352$		0			0
$353$	−1486.02	+	482.836i	−0.224058	+	0.0728010i	−0.418895	−	0.908035i	$-0.637582\pi$
$353$	−1486.02	+	482.836i	−0.224058	+	0.0728010i	0.194836	+	0.980836i	$0.437582\pi$
$354$		0			0
$355$	−687.704	+	2800.19i	−0.102816	+	0.418644i
$356$		0			0
$357$		−	14541.5i		−	2.15579i
$358$		0			0
$359$	−345.013	+	250.667i	−0.0507217	+	0.0368515i	−0.612857	−	0.790194i	$-0.709980\pi$
$359$	−345.013	+	250.667i	−0.0507217	+	0.0368515i	0.562136	+	0.827045i	$0.309980\pi$
$360$		0			0
$361$	−8288.68	−	6022.08i	−1.20844	−	0.877982i
$362$		0			0
$363$	−4207.33	−	5790.89i	−0.608340	−	0.837308i
$364$		0			0
$365$	−2302.56	+	939.739i	−0.330196	+	0.134762i
$366$		0			0
$367$	−4322.53	−	1404.48i	−0.614808	−	0.199763i	−0.0149741	−	0.999888i	$-0.504767\pi$
$367$	−4322.53	−	1404.48i	−0.614808	−	0.199763i	−0.599834	+	0.800125i	$0.704767\pi$
$368$		0			0
$369$	−3286.66	+	10115.3i	−0.463676	+	1.42705i
$370$		0			0
$371$	2646.79	+	8145.99i	0.370390	+	1.13994i
$372$		0			0
$373$	1045.34	−	1438.78i	0.145109	−	0.199725i	−0.730276	−	0.683153i	$-0.760608\pi$
$373$	1045.34	−	1438.78i	0.145109	−	0.199725i	0.875384	+	0.483428i	$0.160608\pi$
$374$		0			0
$375$	−2634.23	−	11779.9i	−0.362749	−	1.62216i
$376$		0			0
$377$	−1885.31	+	2594.91i	−0.257556	+	0.354495i
$378$		0			0
$379$	−1205.34	−	3709.64i	−0.163361	−	0.502775i	0.835550	−	0.549414i	$-0.185149\pi$
$379$	−1205.34	−	3709.64i	−0.163361	−	0.502775i	−0.998912	+	0.0466392i	$0.985149\pi$
$380$		0			0
$381$	4764.99	−	14665.1i	0.640729	−	1.97196i
$382$		0			0
$383$	6733.33	+	2187.79i	0.898322	+	0.291882i	0.721544	−	0.692368i	$-0.243433\pi$
$383$	6733.33	+	2187.79i	0.898322	+	0.291882i	0.176777	+	0.984251i	$0.443433\pi$
$384$		0			0
$385$	5609.34	−	2289.33i	0.742541	−	0.303051i
$386$		0			0
$387$	11245.8	+	15478.5i	1.47715	+	2.03312i
$388$		0			0
$389$	−11463.2	−	8328.54i	−1.49411	−	1.08554i	−0.972654	−	0.232260i	$-0.925388\pi$
$389$	−11463.2	−	8328.54i	−1.49411	−	1.08554i	−0.521459	−	0.853277i	$-0.674612\pi$
$390$		0			0
$391$	10963.4	−	7965.41i	1.41802	−	1.03025i
$392$		0			0
$393$		−	12118.1i		−	1.55541i
$394$		0			0
$395$	2122.96	−	8644.28i	0.270425	−	1.10112i
$396$		0			0
$397$	−9661.10	+	3139.08i	−1.22135	+	0.396841i	−0.847574	−	0.530677i	$-0.821938\pi$
$397$	−9661.10	+	3139.08i	−1.22135	+	0.396841i	−0.373778	+	0.927518i	$0.621938\pi$
$398$		0			0
$399$	27313.1			3.42698
$400$		0			0
$401$	−7255.06			−0.903493			−0.451746	−	0.892146i	$-0.649199\pi$
$401$	−7255.06			−0.903493			−0.451746	+	0.892146i	$0.649199\pi$
$402$		0			0
$403$	7263.07	−	2359.91i	0.897765	−	0.291701i
$404$		0			0
$405$	−2148.74	+	1815.94i	−0.263634	+	0.222802i
$406$		0			0
$407$		−	1668.52i		−	0.203208i
$408$		0			0
$409$	961.440	−	698.527i	0.116235	−	0.0844497i	−0.528149	−	0.849152i	$-0.677114\pi$
$409$	961.440	−	698.527i	0.116235	−	0.0844497i	0.644384	+	0.764702i	$0.277114\pi$
$410$		0			0
$411$	−9459.86	−	6872.99i	−1.13533	−	0.824865i
$412$		0			0
$413$	−9787.68	−	13471.6i	−1.16615	−	1.60507i
$414$		0			0
$415$	7293.67	+	8630.37i	0.862728	+	1.02084i
$416$		0			0
$417$	14849.0	+	4824.74i	1.74379	+	0.566591i
$418$		0			0
$419$	−2872.57	+	8840.87i	−0.334927	+	1.03080i	0.631831	+	0.775106i	$0.282304\pi$
$419$	−2872.57	+	8840.87i	−0.334927	+	1.03080i	−0.966758	+	0.255693i	$0.917696\pi$
$420$		0			0
$421$	−3376.71	−	10392.4i	−0.390904	−	1.20308i	−0.932106	−	0.362186i	$-0.882030\pi$
$421$	−3376.71	−	10392.4i	−0.390904	−	1.20308i	0.541202	−	0.840893i	$-0.317970\pi$
$422$		0			0
$423$	−7581.36	+	10434.8i	−0.871438	+	1.19943i
$424$		0			0
$425$	1271.97	+	8610.19i	0.145175	+	0.982719i
$426$		0			0
$427$	−2967.08	+	4083.84i	−0.336270	+	0.462836i
$428$		0			0
$429$	−2961.31	−	9113.99i	−0.333272	−	1.02570i
$430$		0			0
$431$	514.186	−	1582.50i	0.0574651	−	0.176859i	−0.918204	−	0.396108i	$-0.870361\pi$
$431$	514.186	−	1582.50i	0.0574651	−	0.176859i	0.975669	+	0.219249i	$0.0703606\pi$
$432$		0			0
$433$	7865.89	+	2555.78i	0.873004	+	0.283656i	0.711049	−	0.703142i	$-0.248220\pi$
$433$	7865.89	+	2555.78i	0.873004	+	0.283656i	0.161954	+	0.986798i	$0.448220\pi$
$434$		0			0
$435$	−458.400	−	6239.66i	−0.0505255	−	0.687745i
$436$		0			0
$437$	14961.4	+	20592.5i	1.63775	+	2.25418i
$438$		0			0
$439$	−10025.8	−	7284.16i	−1.08999	−	0.791923i	−0.110591	−	0.993866i	$-0.535274\pi$
$439$	−10025.8	−	7284.16i	−1.08999	−	0.791923i	−0.979397	+	0.201943i	$0.935274\pi$
$440$		0			0
$441$	−9305.62	+	6760.93i	−1.00482	+	0.730043i
$442$		0			0
$443$		−	2728.43i		−	0.292622i	−0.989239	−	0.146311i	$-0.953260\pi$
$443$		−	2728.43i		−	0.292622i	0.989239	−	0.146311i	$-0.0467400\pi$
$444$		0			0
$445$	−2080.93	−	5098.73i	−0.221676	−	0.543153i
$446$		0			0
$447$	−18341.2	+	5959.42i	−1.94074	+	0.630583i
$448$		0			0
$449$	13297.2			1.39762			0.698810	−	0.715307i	$-0.253713\pi$
$449$	13297.2			1.39762			0.698810	+	0.715307i	$0.253713\pi$
$450$		0			0
$451$	5007.52			0.522827
$452$		0			0
$453$	−21355.4	+	6938.79i	−2.21493	+	0.719675i
$454$		0			0
$455$	−13347.3	+	980.566i	−1.37523	+	0.101032i
$456$		0			0
$457$		−	2438.53i		−	0.249605i	−0.992182	−	0.124803i	$-0.960170\pi$
$457$		−	2438.53i		−	0.249605i	0.992182	−	0.124803i	$-0.0398297\pi$
$458$		0			0
$459$	10023.3	−	7282.34i	1.01927	−	0.740545i
$460$		0			0
$461$	11405.5	+	8286.56i	1.15229	+	0.837187i	0.988784	−	0.149355i	$-0.0477197\pi$
$461$	11405.5	+	8286.56i	1.15229	+	0.837187i	0.163506	+	0.986542i	$0.447720\pi$
$462$		0			0
$463$	1075.32	+	1480.05i	0.107936	+	0.148561i	0.859568	−	0.511022i	$-0.170733\pi$
$463$	1075.32	+	1480.05i	0.107936	+	0.148561i	−0.751632	+	0.659583i	$0.770733\pi$
$464$		0			0
$465$	−7849.32	+	12660.5i	−0.782803	+	1.26262i
$466$		0			0
$467$	−6417.64	−	2085.22i	−0.635916	−	0.206622i	−0.0267222	−	0.999643i	$-0.508507\pi$
$467$	−6417.64	−	2085.22i	−0.635916	−	0.206622i	−0.609194	+	0.793021i	$0.708507\pi$
$468$		0			0
$469$	4611.78	−	14193.6i	0.454055	−	1.39744i
$470$		0			0
$471$	9257.49	+	28491.6i	0.905653	+	2.78731i
$472$		0			0
$473$	5294.69	−	7287.52i	0.514694	−	0.708415i
$474$		0			0
$475$	−16172.4	+	2389.13i	−1.56219	+	0.230780i
$476$		0			0
$477$	−9911.24	+	13641.6i	−0.951372	+	1.30945i
$478$		0			0
$479$	2251.94	+	6930.76i	0.214810	+	0.661116i	0.999167	+	0.0408068i	$0.0129928\pi$
$479$	2251.94	+	6930.76i	0.214810	+	0.661116i	−0.784357	+	0.620309i	$0.787007\pi$
$480$		0			0
$481$	−1138.97	+	3505.38i	−0.107967	+	0.332290i
$482$		0			0
$483$	−38656.5	−	12560.3i	−3.64168	−	1.18325i
$484$		0			0
$485$	15151.4	+	3721.05i	1.41853	+	0.348380i
$486$		0			0
$487$	−387.811	−	533.776i	−0.0360850	−	0.0496667i	0.790593	−	0.612342i	$-0.209772\pi$
$487$	−387.811	−	533.776i	−0.0360850	−	0.0496667i	−0.826678	+	0.562675i	$0.809772\pi$
$488$		0			0
$489$	18576.1	+	13496.3i	1.71787	+	1.24811i
$490$		0			0
$491$	9613.86	−	6984.88i	0.883641	−	0.642002i	−0.0505715	−	0.998720i	$-0.516104\pi$
$491$	9613.86	−	6984.88i	0.883641	−	0.642002i	0.934212	+	0.356718i	$0.116104\pi$
$492$		0			0
$493$			4511.21i			0.412119i
$494$		0			0
$495$	10137.0	+	6284.80i	0.920455	+	0.570668i
$496$		0			0
$497$	−5930.63	+	1926.98i	−0.535262	+	0.173917i
$498$		0			0
$499$	−18980.7			−1.70279			−0.851396	−	0.524524i	$-0.824243\pi$
$499$	−18980.7			−1.70279			−0.851396	+	0.524524i	$0.824243\pi$
$500$		0			0
$501$	8136.88			0.725607
$502$		0			0
$503$	−6520.21	+	2118.55i	−0.577976	+	0.187796i	−0.583394	−	0.812190i	$-0.698275\pi$
$503$	−6520.21	+	2118.55i	−0.577976	+	0.187796i	0.00541766	+	0.999985i	$0.498275\pi$
$504$		0			0
$505$	−2154.56	−	1335.79i	−0.189855	−	0.117707i
$506$		0			0
$507$			2192.96i			0.192096i
$508$		0			0
$509$	3846.78	−	2794.85i	0.334981	−	0.243378i	−0.407560	−	0.913178i	$-0.633620\pi$
$509$	3846.78	−	2794.85i	0.334981	−	0.243378i	0.742541	+	0.669800i	$0.233620\pi$
$510$		0			0
$511$	−4351.25	−	3161.37i	−0.376689	−	0.273680i
$512$		0			0
$513$	13678.3	+	18826.6i	1.17722	+	1.62030i
$514$		0			0
$515$	12910.0	+	3170.58i	1.10462	+	0.271287i
$516$		0			0
$517$	5775.45	+	1876.56i	0.491303	+	0.159634i
$518$		0			0
$519$	−27.8924	+	85.8441i	−0.00235904	+	0.00726038i
$520$		0			0
$521$	1567.18	+	4823.28i	0.131784	+	0.405589i	0.995076	−	0.0991156i	$-0.0316014\pi$
$521$	1567.18	+	4823.28i	0.131784	+	0.405589i	−0.863292	+	0.504705i	$0.831601\pi$
$522$		0			0
$523$	−5711.32	+	7860.96i	−0.477512	+	0.657239i	−0.978024	−	0.208491i	$-0.933145\pi$
$523$	−5711.32	+	7860.96i	−0.477512	+	0.657239i	0.500513	+	0.865729i	$0.333145\pi$
$524$		0			0
$525$	18650.4	−	18266.0i	1.55042	−	1.51846i
$526$		0			0
$527$	6313.36	−	8689.59i	0.521849	−	0.718263i
$528$		0			0
$529$	−7945.42	−	24453.5i	−0.653030	−	2.00982i
$530$		0			0
$531$	10130.1	−	31177.3i	0.827891	−	2.54799i
$532$		0			0
$533$	−10520.2	−	3418.22i	−0.854936	−	0.277786i
$534$		0			0
$535$	−7675.29	+	12379.8i	−0.620246	+	1.00042i
$536$		0			0
$537$	4740.35	+	6524.54i	0.380934	+	0.524310i
$538$		0			0
$539$	4381.23	+	3183.15i	0.350117	+	0.254375i
$540$		0			0
$541$	6254.40	−	4544.08i	0.497038	−	0.361119i	−0.310847	−	0.950460i	$-0.600613\pi$
$541$	6254.40	−	4544.08i	0.497038	−	0.361119i	0.807884	+	0.589341i	$0.200613\pi$
$542$		0			0
$543$		−	15449.7i		−	1.22101i
$544$		0			0
$545$	−9011.64	+	662.044i	−0.708286	+	0.0520346i
$546$		0			0
$547$	2957.54	−	960.962i	0.231180	−	0.0751148i	−0.191136	−	0.981563i	$-0.561217\pi$
$547$	2957.54	−	960.962i	0.231180	−	0.0751148i	0.422316	+	0.906449i	$0.361217\pi$
$548$		0			0
$549$	−9937.63			−0.772546
$550$		0			0
$551$	−8473.37			−0.655132
$552$		0			0
$553$	18308.1	−	5948.65i	1.40784	−	0.457436i
$554$		0			0
$555$	−2716.65	−	6656.38i	−0.207775	−	0.509095i
$556$		0			0
$557$		−	191.340i		−	0.0145554i	−0.999974	−	0.00727768i	$-0.997683\pi$
$557$		−	191.340i		−	0.0145554i	0.999974	−	0.00727768i	$-0.00231658\pi$
$558$		0			0
$559$	−16098.1	+	11696.0i	−1.21803	+	0.884949i
$560$		0			0
$561$	−10904.0	−	7922.26i	−0.820623	−	0.596217i
$562$		0			0
$563$	−9292.77	−	12790.4i	−0.695637	−	0.957462i	−0.999988	−	0.00490235i	$-0.998440\pi$
$563$	−9292.77	−	12790.4i	−0.695637	−	0.957462i	0.304351	−	0.952560i	$-0.401560\pi$
$564$		0			0
$565$	−385.940	−	5253.35i	−0.0287374	−	0.391169i
$566$		0			0
$567$	−5786.47	−	1880.14i	−0.428587	−	0.139256i
$568$		0			0
$569$	−1701.66	+	5237.19i	−0.125373	+	0.385860i	−0.993969	−	0.109662i	$-0.965023\pi$
$569$	−1701.66	+	5237.19i	−0.125373	+	0.385860i	0.868595	+	0.495522i	$0.165023\pi$
$570$		0			0
$571$	3409.66	+	10493.8i	0.249894	+	0.769096i	0.994793	+	0.101918i	$0.0324979\pi$
$571$	3409.66	+	10493.8i	0.249894	+	0.769096i	−0.744899	+	0.667178i	$0.767502\pi$
$572$		0			0
$573$	5704.36	−	7851.38i	0.415887	−	0.572419i
$574$		0			0
$575$	23987.7	+	4055.74i	1.73975	+	0.294149i
$576$		0			0
$577$	5311.03	−	7310.01i	0.383191	−	0.527417i	−0.573236	−	0.819391i	$-0.694312\pi$
$577$	5311.03	−	7310.01i	0.383191	−	0.527417i	0.956426	+	0.291974i	$0.0943120\pi$
$578$		0			0
$579$	6458.02	+	19875.7i	0.463534	+	1.42661i
$580$		0			0
$581$	−7551.53	+	23241.2i	−0.539226	+	1.65957i
$582$		0			0
$583$	7550.34	+	2453.25i	0.536369	+	0.174277i
$584$		0			0
$585$	−17006.6	−	20123.4i	−1.20194	−	1.42222i
$586$		0			0
$587$	−4752.13	−	6540.74i	−0.334142	−	0.459907i	0.608577	−	0.793495i	$-0.291741\pi$
$587$	−4752.13	−	6540.74i	−0.334142	−	0.459907i	−0.942719	+	0.333588i	$0.891741\pi$
$588$		0			0
$589$	16321.6	+	11858.3i	1.14180	+	0.829565i
$590$		0			0
$591$	−21864.1	+	15885.2i	−1.52177	+	1.10563i
$592$		0			0
$593$			13770.5i			0.953606i	0.879010	+	0.476803i	$0.158204\pi$
$593$			13770.5i			0.953606i	−0.879010	+	0.476803i	$0.841796\pi$
$594$		0			0
$595$	−14376.6	+	12149.9i	−0.990562	+	0.837140i
$596$		0			0
$597$	−4879.86	+	1585.56i	−0.334538	+	0.108698i
$598$		0			0
$599$	−18239.1			−1.24412			−0.622061	−	0.782969i	$-0.713704\pi$
$599$	−18239.1			−1.24412			−0.622061	+	0.782969i	$0.713704\pi$
$600$		0			0
$601$	15294.4			1.03805			0.519027	−	0.854758i	$-0.326294\pi$
$601$	15294.4			1.03805			0.519027	+	0.854758i	$0.326294\pi$
$602$		0			0
$603$	27942.4	−	9079.04i	1.88707	−	0.613146i
$604$		0			0
$605$	−2209.87	+	8998.13i	−0.148502	+	0.604671i
$606$		0			0
$607$		−	6938.75i		−	0.463979i	−0.972718	−	0.231990i	$-0.925476\pi$
$607$		−	6938.75i		−	0.463979i	0.972718	−	0.231990i	$-0.0745235\pi$
$608$		0			0
$609$	10946.6	−	7953.13i	0.728369	−	0.529191i
$610$		0			0
$611$	−10852.6	−	7884.85i	−0.718572	−	0.522073i
$612$		0			0
$613$	8806.16	+	12120.6i	0.580224	+	0.798610i	0.993720	−	0.111896i	$-0.0356923\pi$
$613$	8806.16	+	12120.6i	0.580224	+	0.798610i	−0.413496	+	0.910506i	$0.635692\pi$
$614$		0			0
$615$	19976.9	−	8153.12i	1.30983	−	0.534578i
$616$		0			0
$617$	2780.24	+	903.355i	0.181407	+	0.0589428i	0.398312	−	0.917250i	$-0.369596\pi$
$617$	2780.24	+	903.355i	0.181407	+	0.0589428i	−0.216905	+	0.976193i	$0.569596\pi$
$618$		0			0
$619$	4794.78	−	14756.8i	0.311338	−	0.958200i	−0.665897	−	0.746043i	$-0.731951\pi$
$619$	4794.78	−	14756.8i	0.311338	−	0.958200i	0.977236	−	0.212157i	$-0.0680488\pi$
$620$		0			0
$621$	−10701.4	−	32935.7i	−0.691520	−	2.12828i
$622$		0			0
$623$	7000.45	−	9635.29i	0.450188	−	0.619630i
$624$		0			0
$625$	−9445.37	+	12446.9i	−0.604504	+	0.796602i
$626$		0			0
$627$	14880.3	−	20481.0i	0.947786	−	1.30452i
$628$		0			0
$629$	1601.91	+	4930.18i	0.101546	+	0.312526i
$630$		0			0
$631$	6213.88	−	19124.4i	0.392030	−	1.20654i	−0.539221	−	0.842164i	$-0.681281\pi$
$631$	6213.88	−	19124.4i	0.392030	−	1.20654i	0.931251	−	0.364379i	$-0.118719\pi$
$632$		0			0
$633$	13181.8	+	4283.02i	0.827691	+	0.268933i
$634$		0			0
$635$	−18480.2	+	7542.29i	−1.15491	+	0.471349i
$636$		0			0
$637$	−7031.57	−	9678.13i	−0.437364	−	0.601980i
$638$		0			0
$639$	−9931.71	−	7215.81i	−0.614855	−	0.446718i
$640$		0			0
$641$	−7645.65	+	5554.89i	−0.471115	+	0.342285i	−0.797876	−	0.602822i	$-0.794043\pi$
$641$	−7645.65	+	5554.89i	−0.471115	+	0.342285i	0.326760	+	0.945107i	$0.394043\pi$
$642$		0			0
$643$			21731.3i			1.33281i	0.745590	+	0.666405i	$0.232168\pi$
$643$			21731.3i			1.33281i	−0.745590	+	0.666405i	$0.767832\pi$
$644$		0			0
$645$	9257.18	−	37693.4i	0.565118	−	2.30105i
$646$		0			0
$647$	15163.4	−	4926.90i	0.921386	−	0.299376i	0.190350	−	0.981716i	$-0.439038\pi$
$647$	15163.4	−	4926.90i	0.921386	−	0.299376i	0.731035	+	0.682340i	$0.239038\pi$
$648$		0			0
$649$	−15434.2			−0.933504
$650$		0			0
$651$	−32215.8			−1.93953
$652$		0			0
$653$	−573.934	+	186.482i	−0.0343947	+	0.0111755i	−0.326164	−	0.945313i	$-0.605756\pi$
$653$	−573.934	+	186.482i	−0.0343947	+	0.0111755i	0.291769	+	0.956489i	$0.405756\pi$
$654$		0			0
$655$	−11980.7	+	10125.1i	−0.714695	+	0.604001i
$656$		0			0
$657$		−	10588.3i		−	0.628753i
$658$		0			0
$659$	14011.1	−	10179.7i	0.828220	−	0.601737i	−0.0908354	−	0.995866i	$-0.528954\pi$
$659$	14011.1	−	10179.7i	0.828220	−	0.601737i	0.919055	+	0.394129i	$0.128954\pi$
$660$		0			0
$661$	8182.81	+	5945.16i	0.481505	+	0.349834i	0.801908	−	0.597448i	$-0.203818\pi$
$661$	8182.81	+	5945.16i	0.481505	+	0.349834i	−0.320403	+	0.947281i	$0.603818\pi$
$662$		0			0
$663$	17500.3	+	24087.0i	1.02512	+	1.41095i
$664$		0			0
$665$	−22821.1	−	27003.5i	−1.33077	−	1.57466i
$666$		0			0
$667$	11992.4	+	3896.58i	0.696176	+	0.226201i
$668$		0			0
$669$	1320.04	−	4062.67i	0.0762866	−	0.234786i
$670$		0			0
$671$	1445.83	+	4449.79i	0.0831825	+	0.256009i
$672$		0			0
$673$	11222.2	−	15446.0i	0.642770	−	0.884698i	−0.355989	−	0.934490i	$-0.615856\pi$
$673$	11222.2	−	15446.0i	0.642770	−	0.884698i	0.998760	+	0.0497925i	$0.0158560\pi$
$674$		0			0
$675$	21930.6	+	3707.94i	1.25053	+	0.211435i
$676$		0			0
$677$	6213.38	−	8551.98i	0.352732	−	0.485494i	−0.595374	−	0.803449i	$-0.702996\pi$
$677$	6213.38	−	8551.98i	0.352732	−	0.485494i	0.948106	+	0.317955i	$0.102996\pi$
$678$		0			0
$679$	10426.6	+	32089.7i	0.589301	+	1.81368i
$680$		0			0
$681$	−9165.96	+	28209.9i	−0.515771	+	1.58738i
$682$		0			0
$683$	19449.7	+	6319.59i	1.08964	+	0.354044i	0.798106	−	0.602517i	$-0.205836\pi$
$683$	19449.7	+	6319.59i	1.08964	+	0.354044i	0.291530	+	0.956562i	$0.405836\pi$
$684$		0			0
$685$	1108.98	+	15095.3i	0.0618569	+	0.841986i
$686$		0			0
$687$	−27689.2	−	38110.8i	−1.53771	−	2.11648i
$688$		0			0
$689$	−14187.7	−	10308.0i	−0.784484	−	0.569961i
$690$		0			0
$691$	26519.9	−	19267.9i	1.46001	−	1.06076i	0.476649	−	0.879094i	$-0.341851\pi$
$691$	26519.9	−	19267.9i	1.46001	−	1.06076i	0.983360	−	0.181665i	$-0.0581487\pi$
$692$		0			0
$693$			25794.6i			1.41393i
$694$		0			0
$695$	−7636.86	−	18711.9i	−0.416809	−	1.02127i
$696$		0			0
$697$	−14796.3	+	4807.60i	−0.804088	+	0.261264i
$698$		0			0
$699$	−16171.8			−0.875071
$700$		0			0
$701$	13686.5			0.737419			0.368709	−	0.929545i	$-0.379800\pi$
$701$	13686.5			0.737419			0.368709	+	0.929545i	$0.379800\pi$
$702$		0			0
$703$	−9260.31	+	3008.86i	−0.496813	+	0.161424i
$704$		0			0
$705$	26095.8	−	1917.14i	1.39408	−	0.102417i
$706$		0			0
$707$		−	5482.47i		−	0.291640i
$708$		0			0
$709$	−15014.7	+	10908.8i	−0.795331	+	0.577842i	−0.909541	−	0.415615i	$-0.863566\pi$
$709$	−15014.7	+	10908.8i	−0.795331	+	0.577842i	0.114210	+	0.993457i	$0.463566\pi$
$710$		0			0
$711$	30659.5	+	22275.4i	1.61719	+	1.17496i
$712$		0			0
$713$	−17646.9	−	24288.9i	−0.926903	−	1.27577i
$714$		0			0
$715$	−6536.39	+	10542.8i	−0.341884	+	0.551439i
$716$		0			0
$717$	10242.2	+	3327.89i	0.533476	+	0.173337i
$718$		0			0
$719$	−6530.89	+	20100.0i	−0.338750	+	1.04257i	0.626095	+	0.779747i	$0.284652\pi$
$719$	−6530.89	+	20100.0i	−0.338750	+	1.04257i	−0.964845	+	0.262819i	$0.915348\pi$
$720$		0			0
$721$	8884.13	+	27342.6i	0.458894	+	1.41233i
$722$		0			0
$723$	−18843.7	+	25936.1i	−0.969301	+	1.33413i
$724$		0			0
$725$	−5785.92	+	5666.67i	−0.296391	+	0.290283i
$726$		0			0
$727$	−10015.2	+	13784.7i	−0.510926	+	0.703229i	−0.984075	−	0.177753i	$-0.943117\pi$
$727$	−10015.2	+	13784.7i	−0.510926	+	0.703229i	0.473149	+	0.880982i	$0.343117\pi$
$728$		0			0
$729$	9121.35	+	28072.6i	0.463413	+	1.42624i
$730$		0			0
$731$	−8648.25	+	26616.6i	−0.437574	+	1.34672i
$732$		0			0
$733$	25392.7	+	8250.59i	1.27954	+	0.415747i	0.868417	−	0.495834i	$-0.165138\pi$
$733$	25392.7	+	8250.59i	1.27954	+	0.415747i	0.411120	+	0.911581i	$0.365138\pi$
$734$		0			0
$735$	22661.1	+	5565.38i	1.13723	+	0.279296i
$736$		0			0
$737$	−8130.68	−	11190.9i	−0.406374	−	0.559325i
$738$		0			0
$739$	−20159.5	−	14646.7i	−1.00349	−	0.729077i	−0.0406555	−	0.999173i	$-0.512945\pi$
$739$	−20159.5	−	14646.7i	−1.00349	−	0.729077i	−0.962833	+	0.270096i	$0.912945\pi$
$740$		0			0
$741$	−45242.5	+	32870.6i	−2.24295	+	1.62960i
$742$		0			0
$743$		−	22140.3i		−	1.09320i	−0.837393	−	0.546602i	$-0.815921\pi$
$743$		−	22140.3i		−	1.09320i	0.837393	−	0.546602i	$-0.184079\pi$
$744$		0			0
$745$	21216.6	+	13154.0i	1.04338	+	0.646879i
$746$		0			0
$747$	−45754.2	+	14866.4i	−2.24104	+	0.728158i
$748$		0			0
$749$	−31501.5			−1.53677
$750$		0			0
$751$	−3300.45			−0.160366			−0.0801831	−	0.996780i	$-0.525551\pi$
$751$	−3300.45			−0.160366			−0.0801831	+	0.996780i	$0.525551\pi$
$752$		0			0
$753$	−23409.9	+	7606.34i	−1.13294	+	0.368115i
$754$		0			0
$755$	24703.4	+	15315.7i	1.19079	+	0.738273i
$756$		0			0
$757$			2357.32i			0.113181i	0.998397	+	0.0565906i	$0.0180230\pi$
$757$			2357.32i			0.113181i	−0.998397	+	0.0565906i	$0.981977\pi$
$758$		0			0
$759$	−30478.7	+	22144.0i	−1.45758	+	1.05900i
$760$		0			0
$761$	−9747.98	−	7082.32i	−0.464342	−	0.337364i	0.330890	−	0.943669i	$-0.392651\pi$
$761$	−9747.98	−	7082.32i	−0.464342	−	0.337364i	−0.795232	+	0.606305i	$0.792651\pi$
$762$		0			0
$763$	−11486.3	−	15809.6i	−0.544997	−	0.750124i
$764$		0			0
$765$	−35986.9	−	8838.09i	−1.70080	−	0.417702i
$766$		0			0
$767$	32425.4	+	10535.6i	1.52648	+	0.495985i
$768$		0			0
$769$	9207.51	−	28337.8i	0.431770	−	1.32885i	−0.464590	−	0.885526i	$-0.653798\pi$
$769$	9207.51	−	28337.8i	0.431770	−	1.32885i	0.896360	−	0.443326i	$-0.146202\pi$
$770$		0			0
$771$	−12501.0	−	38474.2i	−0.583935	−	1.79717i
$772$		0			0
$773$	−1481.89	+	2039.64i	−0.0689519	+	0.0949042i	−0.842100	−	0.539321i	$-0.818681\pi$
$773$	−1481.89	+	2039.64i	−0.0689519	+	0.0949042i	0.773148	+	0.634225i	$0.218681\pi$
$774$		0			0
$775$	19075.4	−	2817.97i	0.884139	−	0.130612i
$776$		0			0
$777$	9139.06	−	12578.8i	0.421959	−	0.580776i
$778$		0			0
$779$	−9030.08	−	27791.7i	−0.415322	−	1.27823i
$780$		0			0
$781$	−1786.07	+	5496.97i	−0.0818319	+	0.251853i
$782$		0			0
$783$	10964.0	+	3562.43i	0.500412	+	0.162594i
$784$		0			0
$785$	20433.7	−	32958.3i	0.929056	−	1.49851i
$786$		0			0
$787$	3274.06	+	4506.35i	0.148294	+	0.204109i	0.876701	−	0.481035i	$-0.159739\pi$
$787$	3274.06	+	4506.35i	0.148294	+	0.204109i	−0.728407	+	0.685144i	$0.759739\pi$
$788$		0			0
$789$	40082.3	+	29121.5i	1.80858	+	1.31401i
$790$		0			0
$791$	9216.22	−	6695.98i	0.414275	−	0.300988i
$792$		0			0
$793$		−	10335.4i		−	0.462827i
$794$		0			0
$795$	34115.5	−	2506.31i	1.52195	−	0.111811i
$796$		0			0
$797$	17805.2	−	5785.27i	0.791335	−	0.257120i	0.114662	−	0.993405i	$-0.463421\pi$
$797$	17805.2	−	5785.27i	0.791335	−	0.257120i	0.676672	+	0.736284i	$0.263421\pi$
$798$		0			0
$799$	−18867.0			−0.835377
$800$		0			0
$801$	23446.5			1.03426
$802$		0			0
$803$	−4741.16	+	1540.50i	−0.208359	+	0.0676999i
$804$		0			0
$805$	19881.0	+	48712.9i	0.870453	+	2.13280i
$806$		0			0
$807$			74197.2i			3.23651i
$808$		0			0
$809$	12034.0	−	8743.19i	0.522981	−	0.379968i	−0.294745	−	0.955576i	$-0.595235\pi$
$809$	12034.0	−	8743.19i	0.522981	−	0.379968i	0.817726	+	0.575608i	$0.195235\pi$
$810$		0			0
$811$	368.721	+	267.892i	0.0159649	+	0.0115992i	0.595739	−	0.803178i	$-0.296859\pi$
$811$	368.721	+	267.892i	0.0159649	+	0.0115992i	−0.579774	+	0.814777i	$0.696859\pi$
$812$		0			0
$813$	12326.9	+	16966.5i	0.531762	+	0.731908i
$814$		0			0
$815$	−2177.68	−	29642.2i	−0.0935961	−	1.27402i
$816$		0			0
$817$	−49993.6	−	16243.9i	−2.14083	−	0.695597i
$818$		0			0
$819$	17607.8	−	54191.4i	0.751243	−	2.31209i
$820$		0			0
$821$	3232.82	+	9949.59i	0.137425	+	0.422951i	0.995959	−	0.0898051i	$-0.0286244\pi$
$821$	3232.82	+	9949.59i	0.137425	+	0.422951i	−0.858534	+	0.512756i	$0.828624\pi$
$822$		0			0
$823$	18707.6	−	25748.9i	0.792354	−	1.09058i	−0.201457	−	0.979497i	$-0.564567\pi$
$823$	18707.6	−	25748.9i	0.792354	−	1.09058i	0.993811	−	0.111085i	$-0.0354325\pi$
$824$		0			0
$825$	−3536.10	−	23936.5i	−0.149226	−	1.01014i
$826$		0			0
$827$	8274.08	−	11388.3i	0.347906	−	0.478851i	−0.598824	−	0.800881i	$-0.704365\pi$
$827$	8274.08	−	11388.3i	0.347906	−	0.478851i	0.946730	+	0.322030i	$0.104365\pi$
$828$		0			0
$829$	−9540.34	−	29362.1i	−0.399698	−	1.23014i	−0.925242	−	0.379377i	$-0.876138\pi$
$829$	−9540.34	−	29362.1i	−0.399698	−	1.23014i	0.525544	−	0.850766i	$-0.323862\pi$
$830$		0			0
$831$	−12527.1	+	38554.4i	−0.522936	+	1.60943i
$832$		0			0
$833$	−16001.8	−	5199.29i	−0.665581	−	0.216260i
$834$		0			0
$835$	−6798.67	−	8044.65i	−0.281770	−	0.333409i
$836$		0			0
$837$	−16133.6	−	22206.0i	−0.666259	−	0.917027i
$838$		0			0
$839$	−8267.07	−	6006.38i	−0.340180	−	0.247155i	0.404558	−	0.914512i	$-0.367425\pi$
$839$	−8267.07	−	6006.38i	−0.340180	−	0.247155i	−0.744738	+	0.667357i	$0.767425\pi$
$840$		0			0
$841$	16335.2	−	11868.2i	0.669776	−	0.486620i
$842$		0			0
$843$		−	10494.9i		−	0.428782i
$844$		0			0
$845$	2168.10	−	1832.30i	0.0882663	−	0.0745953i
$846$		0			0
$847$	−19057.5	+	6192.16i	−0.773109	+	0.251198i
$848$		0			0
$849$	11687.0			0.472436
$850$		0			0
$851$	14489.9			0.583674
$852$		0			0
$853$	−36840.0	+	11970.0i	−1.47875	+	0.480476i	−0.933740	−	0.357952i	$-0.883475\pi$
$853$	−36840.0	+	11970.0i	−1.47875	+	0.480476i	−0.545013	+	0.838428i	$0.683475\pi$
$854$		0			0
$855$	16600.5	−	67593.9i	0.664006	−	2.70370i
$856$		0			0
$857$			16363.3i			0.652228i	0.945330	+	0.326114i	$0.105739\pi$
$857$			16363.3i			0.652228i	−0.945330	+	0.326114i	$0.894261\pi$
$858$		0			0
$859$	26520.2	−	19268.0i	1.05338	−	0.765328i	0.0805308	−	0.996752i	$-0.474338\pi$
$859$	26520.2	−	19268.0i	1.05338	−	0.765328i	0.972853	+	0.231424i	$0.0743385\pi$
$860$		0			0
$861$	37751.2	+	27427.8i	1.49426	+	1.08564i
$862$		0			0
$863$	−3689.12	−	5077.64i	−0.145515	−	0.200284i	0.730038	−	0.683407i	$-0.239502\pi$
$863$	−3689.12	−	5077.64i	−0.145515	−	0.200284i	−0.875553	+	0.483123i	$0.839502\pi$
$864$		0			0
$865$	108.176	−	44.1497i	0.00425214	−	0.00173542i
$866$		0			0
$867$	−532.206	−	172.924i	−0.0208474	−	0.00677372i
$868$		0			0
$869$	5513.67	−	16969.3i	0.215234	−	0.662422i
$870$		0			0
$871$	9442.48	+	29061.0i	0.367332	+	1.13053i
$872$		0			0
$873$	−39043.6	+	53738.9i	−1.51366	+	2.08337i
$874$		0			0
$875$	−33642.0	−	3177.06i	−1.29978	−	0.122748i
$876$		0			0
$877$	14019.1	−	19295.6i	0.539784	−	0.742949i	−0.448798	−	0.893633i	$-0.648148\pi$
$877$	14019.1	−	19295.6i	0.539784	−	0.742949i	0.988582	+	0.150684i	$0.0481477\pi$
$878$		0			0
$879$	11774.3	+	36237.6i	0.451807	+	1.39052i
$880$		0			0
$881$	9439.80	−	29052.7i	0.360993	−	1.11102i	−0.591459	−	0.806335i	$-0.701448\pi$
$881$	9439.80	−	29052.7i	0.360993	−	1.11102i	0.952452	−	0.304688i	$-0.0985521\pi$
$882$		0			0
$883$	13522.5	+	4393.71i	0.515365	+	0.167452i	0.555141	−	0.831756i	$-0.312664\pi$
$883$	13522.5	+	4393.71i	0.515365	+	0.167452i	−0.0397760	+	0.999209i	$0.512664\pi$
$884$		0			0
$885$	−61572.8	+	25129.5i	−2.33870	+	0.954486i
$886$		0			0
$887$	399.424	+	549.760i	0.0151199	+	0.0208108i	0.816510	−	0.577331i	$-0.195906\pi$
$887$	399.424	+	549.760i	0.0151199	+	0.0208108i	−0.801390	+	0.598142i	$0.795906\pi$
$888$		0			0
$889$	−34922.9	−	25372.9i	−1.31752	−	0.957234i
$890$		0			0
$891$	−4562.34	+	3314.73i	−0.171542	+	0.124633i
$892$		0			0
$893$		−	35437.7i		−	1.32797i
$894$		0			0
$895$	2489.84	−	10138.1i	0.0929901	−	0.378637i
$896$		0			0
$897$	79148.0	−	25716.8i	2.94613	−	0.957255i
$898$		0			0
$899$	9994.33			0.370778
$900$		0			0
$901$	−24665.1			−0.912003
$902$		0			0
$903$	79832.3	−	25939.1i	2.94203	−	0.955923i
$904$		0			0
$905$	−15274.6	+	12908.8i	−0.561043	+	0.474147i
$906$		0			0
$907$			22201.4i			0.812771i	0.913702	+	0.406386i	$0.133211\pi$
$907$			22201.4i			0.812771i	−0.913702	+	0.406386i	$0.866789\pi$
$908$		0			0
$909$	8731.83	−	6344.05i	0.318610	−	0.231484i
$910$		0			0
$911$	−22980.0	−	16695.9i	−0.835742	−	0.607202i	0.0854361	−	0.996344i	$-0.472772\pi$
$911$	−22980.0	−	16695.9i	−0.835742	−	0.607202i	−0.921178	+	0.389142i	$0.872772\pi$
$912$		0			0
$913$	13313.5	+	18324.5i	0.482600	+	0.664242i
$914$		0			0
$915$	13013.0	+	15397.9i	0.470160	+	0.556325i
$916$		0			0
$917$	−32263.6	−	10483.1i	−1.16187	−	0.377515i
$918$		0			0
$919$	6696.79	−	20610.6i	0.240377	−	0.739805i	−0.755985	−	0.654589i	$-0.772842\pi$
$919$	6696.79	−	20610.6i	0.240377	−	0.739805i	0.996362	−	0.0852165i	$-0.0271582\pi$
$920$		0			0
$921$	−13086.5	−	40276.0i	−0.468201	−	1.44098i
$922$		0			0
$923$	7504.66	−	10329.3i	0.267626	−	0.368356i
$924$		0			0
$925$	−4311.06	+	8247.51i	−0.153240	+	0.293164i
$926$		0			0
$927$	−33267.7	+	45789.1i	−1.17870	+	1.62234i
$928$		0			0
$929$	14671.9	+	45155.4i	0.518157	+	1.59472i	0.777463	+	0.628929i	$0.216506\pi$
$929$	14671.9	+	45155.4i	0.518157	+	1.59472i	−0.259305	+	0.965795i	$0.583494\pi$
$930$		0			0
$931$	9765.79	−	30056.0i	0.343782	−	1.05805i
$932$		0			0
$933$	−37845.1	−	12296.6i	−1.32797	−	0.431482i
$934$		0			0
$935$	1278.28	+	17399.8i	0.0447105	+	0.608592i
$936$		0			0
$937$	−13057.6	−	17972.2i	−0.455253	−	0.626601i	0.518263	−	0.855221i	$-0.326579\pi$
$937$	−13057.6	−	17972.2i	−0.455253	−	0.626601i	−0.973516	+	0.228620i	$0.926579\pi$
$938$		0			0
$939$	3667.30	+	2664.45i	0.127452	+	0.0925997i
$940$		0			0
$941$	−9225.97	+	6703.06i	−0.319615	+	0.232214i	−0.736011	−	0.676969i	$-0.763293\pi$
$941$	−9225.97	+	6703.06i	−0.319615	+	0.232214i	0.416396	+	0.909183i	$0.363293\pi$
$942$		0			0
$943$			43486.5i			1.50171i
$944$		0			0
$945$	18176.1	+	44535.5i	0.625683	+	1.53306i
$946$		0			0
$947$	28330.0	−	9204.98i	0.972124	−	0.315862i	0.220451	−	0.975398i	$-0.429247\pi$
$947$	28330.0	−	9204.98i	0.972124	−	0.315862i	0.751673	+	0.659536i	$0.229247\pi$
$948$		0			0
$949$	11012.2			0.376682
$950$		0			0
$951$	−19659.3			−0.670344
$952$		0			0
$953$	−50865.9	+	16527.3i	−1.72897	+	0.561777i	−0.993300	−	0.115563i	$-0.963133\pi$
$953$	−50865.9	+	16527.3i	−1.72897	+	0.561777i	−0.735670	+	0.677340i	$0.763133\pi$
$954$		0			0
$955$	−12528.6	+	920.419i	−0.424519	+	0.0311875i
$956$		0			0
$957$		−	12541.3i		−	0.423618i
$958$		0			0
$959$	−26482.4	+	19240.6i	−0.891722	+	0.647874i
$960$		0			0
$961$	4850.13	+	3523.83i	0.162805	+	0.118285i
$962$		0			0
$963$	−36452.0	−	50171.9i	−1.21978	−	1.67889i
$964$		0			0
$965$	14254.5	−	22991.7i	0.475513	−	0.766974i
$966$		0			0
$967$	1359.78	+	441.820i	0.0452199	+	0.0146928i	0.331540	−	0.943441i	$-0.392432\pi$
$967$	1359.78	+	441.820i	0.0452199	+	0.0146928i	−0.286320	+	0.958134i	$0.592432\pi$
$968$		0			0
$969$	−24305.2	+	74803.7i	−0.805774	+	2.47992i
$970$		0			0
$971$	−15411.8	−	47432.8i	−0.509361	−	1.56765i	−0.793313	−	0.608814i	$-0.791646\pi$
$971$	−15411.8	−	47432.8i	−0.509361	−	1.56765i	0.283952	−	0.958839i	$-0.408354\pi$
$972$		0			0
$973$	25691.1	−	35360.7i	0.846473	−	1.16507i
$974$		0			0
$975$	−8910.58	+	52701.7i	−0.292684	+	1.73108i
$976$		0			0
$977$	−100.924	+	138.909i	−0.00330484	+	0.00454873i	−0.810666	−	0.585509i	$-0.800895\pi$
$977$	−100.924	+	138.909i	−0.00330484	+	0.00454873i	0.807361	+	0.590057i	$0.200895\pi$
$978$		0			0
$979$	−3411.24	−	10498.7i	−0.111362	−	0.342738i
$980$		0			0
$981$	11888.2	−	36588.1i	0.386912	−	1.19079i
$982$		0			0
$983$	31587.3	+	10263.3i	1.02490	+	0.333010i	0.772772	−	0.634683i	$-0.218870\pi$
$983$	31587.3	+	10263.3i	1.02490	+	0.333010i	0.252128	+	0.967694i	$0.418870\pi$
$984$		0			0
$985$	33973.3	+	8343.57i	1.09896	+	0.269897i
$986$		0			0
$987$	33262.0	+	45781.2i	1.07269	+	1.47642i
$988$		0			0
$989$	63286.5	+	45980.4i	2.03478	+	1.47835i
$990$		0			0
$991$	33262.0	−	24166.3i	1.06620	−	0.774638i	0.0909729	−	0.995853i	$-0.471002\pi$
$991$	33262.0	−	24166.3i	1.06620	−	0.774638i	0.975225	+	0.221215i	$0.0710023\pi$
$992$		0			0
$993$		−	37950.7i		−	1.21282i
$994$		0			0
$995$	5644.89	+	3499.75i	0.179854	+	0.111507i
$996$		0			0
$997$	17735.3	−	5762.56i	0.563374	−	0.183051i	−0.0134649	−	0.999909i	$-0.504286\pi$
$997$	17735.3	−	5762.56i	0.563374	−	0.183051i	0.576839	+	0.816858i	$0.304286\pi$
$998$		0			0
$999$	13247.3			0.419545

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.i.a.9.8	✓	32
5.2	odd	4		500.4.g.b.201.2		64
5.3	odd	4		500.4.g.b.201.15		64
5.4	even	2		500.4.i.a.49.1		32
25.2	odd	20		500.4.g.b.301.2		64
25.8	odd	20		2500.4.a.g.1.30		32
25.11	even	5		500.4.i.a.449.1		32
25.14	even	10	inner	100.4.i.a.89.8	yes	32
25.17	odd	20		2500.4.a.g.1.3		32
25.23	odd	20		500.4.g.b.301.15		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.i.a.9.8	✓	32	1.1	even	1	trivial
100.4.i.a.89.8	yes	32	25.14	even	10	inner
500.4.g.b.201.2		64	5.2	odd	4
500.4.g.b.201.15		64	5.3	odd	4
500.4.g.b.301.2		64	25.2	odd	20
500.4.g.b.301.15		64	25.23	odd	20
500.4.i.a.49.1		32	5.4	even	2
500.4.i.a.449.1		32	25.11	even	5
2500.4.a.g.1.3		32	25.17	odd	20
2500.4.a.g.1.30		32	25.8	odd	20

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(8.21445 - 2.66904i) q^{3} +(-9.50227 - 5.89126i) q^{5} -24.1794i q^{7} +(38.5100 - 27.9792i) q^{9} +O(q^{10})\)	\(q+(8.21445 - 2.66904i) q^{3} +(-9.50227 - 5.89126i) q^{5} -24.1794i q^{7} +(38.5100 - 27.9792i) q^{9} +(-18.1311 - 13.1730i) q^{11} +(29.0992 + 40.0516i) q^{13} +(-93.7799 - 23.0316i) q^{15} +(66.2212 + 21.5166i) q^{17} +(-40.4144 + 124.383i) q^{19} +(-64.5356 - 198.620i) q^{21} +(114.398 - 157.455i) q^{23} +(55.5861 + 111.961i) q^{25} +(104.588 - 143.952i) q^{27} +(20.0210 + 61.6182i) q^{29} +(47.6687 - 146.709i) q^{31} +(-184.097 - 59.8166i) q^{33} +(-142.447 + 229.759i) q^{35} +(43.7607 + 60.2314i) q^{37} +(345.934 + 251.335i) q^{39} +(-180.765 + 131.333i) q^{41} +401.934i q^{43} +(-530.765 + 38.9929i) q^{45} +(-257.702 + 83.7326i) q^{47} -241.641 q^{49} +601.400 q^{51} +(-336.899 + 109.465i) q^{53} +(94.6810 + 231.989i) q^{55} +1129.60i q^{57} +(557.152 - 404.795i) q^{59} +(-168.898 - 122.711i) q^{61} +(-676.519 - 931.148i) q^{63} +(-40.5538 - 552.012i) q^{65} +(587.013 + 190.732i) q^{67} +(519.462 - 1598.74i) q^{69} +(-79.6952 - 245.277i) q^{71} +(130.747 - 179.957i) q^{73} +(755.437 + 771.334i) q^{75} +(-318.515 + 438.399i) q^{77} +(246.022 + 757.177i) q^{79} +(77.7580 - 239.314i) q^{81} +(-961.201 - 312.313i) q^{83} +(-502.492 - 594.583i) q^{85} +(328.922 + 452.723i) q^{87} +(398.492 + 289.522i) q^{89} +(968.423 - 703.600i) q^{91} -1332.37i q^{93} +(1116.80 - 943.826i) q^{95} +(-1327.15 + 431.218i) q^{97} -1066.80 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) \) 32 * q + 6 * q^5 + 122 * q^9	\( 32 q + 6 q^{5} + 122 q^{9} + 20 q^{11} + 68 q^{15} - 160 q^{17} + 2 q^{19} - 108 q^{21} + 290 q^{23} + 654 q^{25} + 600 q^{27} + 62 q^{29} - 378 q^{31} - 1280 q^{33} - 278 q^{35} + 680 q^{37} + 592 q^{39} - 528 q^{41} - 1044 q^{45} - 1810 q^{47} - 2796 q^{49} + 1664 q^{51} - 510 q^{53} - 1350 q^{55} + 144 q^{59} - 1346 q^{61} + 1660 q^{63} + 1142 q^{65} + 1890 q^{67} + 956 q^{69} + 786 q^{71} + 3720 q^{73} - 78 q^{75} + 2160 q^{77} + 896 q^{79} + 348 q^{81} + 570 q^{83} + 224 q^{85} + 3240 q^{87} - 2512 q^{89} - 2212 q^{91} + 1536 q^{95} - 2250 q^{97} - 2540 q^{99}+O(q^{100}) \) 32 * q + 6 * q^5 + 122 * q^9 + 20 * q^11 + 68 * q^15 - 160 * q^17 + 2 * q^19 - 108 * q^21 + 290 * q^23 + 654 * q^25 + 600 * q^27 + 62 * q^29 - 378 * q^31 - 1280 * q^33 - 278 * q^35 + 680 * q^37 + 592 * q^39 - 528 * q^41 - 1044 * q^45 - 1810 * q^47 - 2796 * q^49 + 1664 * q^51 - 510 * q^53 - 1350 * q^55 + 144 * q^59 - 1346 * q^61 + 1660 * q^63 + 1142 * q^65 + 1890 * q^67 + 956 * q^69 + 786 * q^71 + 3720 * q^73 - 78 * q^75 + 2160 * q^77 + 896 * q^79 + 348 * q^81 + 570 * q^83 + 224 * q^85 + 3240 * q^87 - 2512 * q^89 - 2212 * q^91 + 1536 * q^95 - 2250 * q^97 - 2540 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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