LMFDB - Embedded newform 2100.2.q.j.1801.1

Newspace parameters

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.q (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
Defining polynomial:	$x^{4} + 2 x^{2} + 4$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1801.1
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	2100.1801
Dual form			2100.2.q.j.1201.1

$q$-expansion

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-1.62132 + 2.09077i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(-1.62132 + 2.09077i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.12132 + 3.67423i) q^{11} -5.00000 q^{13} +(-2.12132 - 3.67423i) q^{17} +(-1.62132 + 2.80821i) q^{19} +(-2.62132 - 0.358719i) q^{21} +(3.00000 - 5.19615i) q^{23} -1.00000 q^{27} -8.48528 q^{29} +(2.00000 + 3.46410i) q^{31} +(-2.12132 + 3.67423i) q^{33} +(2.50000 - 4.33013i) q^{37} +(-2.50000 - 4.33013i) q^{39} -1.75736 q^{41} -4.48528 q^{43} +(0.878680 - 1.52192i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(2.12132 - 3.67423i) q^{51} +(-2.12132 - 3.67423i) q^{53} -3.24264 q^{57} +(-0.878680 - 1.52192i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-1.00000 - 2.44949i) q^{63} +(-6.86396 - 11.8887i) q^{67} +6.00000 q^{69} +8.48528 q^{71} +(6.74264 + 11.6786i) q^{73} +(-11.1213 - 1.52192i) q^{77} +(-0.378680 + 0.655892i) q^{79} +(-0.500000 - 0.866025i) q^{81} -10.2426 q^{83} +(-4.24264 - 7.34847i) q^{87} +(-8.12132 + 14.0665i) q^{89} +(8.10660 - 10.4539i) q^{91} +(-2.00000 + 3.46410i) q^{93} -15.9706 q^{97} -4.24264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4q + 2q^{3} + 2q^{7} - 2q^{9} + O(q^{10}) $	$ 4q + 2q^{3} + 2q^{7} - 2q^{9} - 20q^{13} + 2q^{19} - 2q^{21} + 12q^{23} - 4q^{27} + 8q^{31} + 10q^{37} - 10q^{39} - 24q^{41} + 16q^{43} + 12q^{47} + 10q^{49} + 4q^{57} - 12q^{59} + 2q^{61} - 4q^{63} - 2q^{67} + 24q^{69} + 10q^{73} - 36q^{77} - 10q^{79} - 2q^{81} - 24q^{83} - 24q^{89} - 10q^{91} - 8q^{93} + 4q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.12132	+	3.67423i	0.639602	+	1.10782i	0.985520	+	0.169559i	$0.0542342\pi$
$11$	2.12132	+	3.67423i	0.639602	+	1.10782i	−0.345918	+	0.938265i	$0.612432\pi$
$12$		0			0
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.12132	−	3.67423i	−0.514496	−	0.891133i	−0.999859	−	0.0168199i	$-0.994646\pi$
$17$	−2.12132	−	3.67423i	−0.514496	−	0.891133i	0.485363	−	0.874313i	$-0.338688\pi$
$18$		0			0
$19$	−1.62132	+	2.80821i	−0.371956	+	0.644247i	−0.989866	−	0.142001i	$-0.954646\pi$
$19$	−1.62132	+	2.80821i	−0.371956	+	0.644247i	0.617910	+	0.786249i	$0.287980\pi$
$20$		0			0
$21$	−2.62132	−	0.358719i	−0.572019	−	0.0782790i
$22$		0			0
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−8.48528			−1.57568			−0.787839	−	0.615882i	$-0.788800\pi$
$29$	−8.48528			−1.57568			−0.787839	+	0.615882i	$0.788800\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$	−2.12132	+	3.67423i	−0.369274	+	0.639602i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.50000	−	4.33013i	0.410997	−	0.711868i	−0.584002	−	0.811752i	$-0.698514\pi$
$37$	2.50000	−	4.33013i	0.410997	−	0.711868i	0.994999	+	0.0998840i	$0.0318472\pi$
$38$		0			0
$39$	−2.50000	−	4.33013i	−0.400320	−	0.693375i
$40$		0			0
$41$	−1.75736			−0.274453			−0.137227	−	0.990540i	$-0.543819\pi$
$41$	−1.75736			−0.274453			−0.137227	+	0.990540i	$0.543819\pi$
$42$		0			0
$43$	−4.48528			−0.683999			−0.341999	−	0.939700i	$-0.611104\pi$
$43$	−4.48528			−0.683999			−0.341999	+	0.939700i	$0.611104\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.878680	−	1.52192i	0.128169	−	0.221995i	−0.794798	−	0.606873i	$-0.792423\pi$
$47$	0.878680	−	1.52192i	0.128169	−	0.221995i	0.922967	+	0.384879i	$0.125757\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$		0			0
$51$	2.12132	−	3.67423i	0.297044	−	0.514496i
$52$		0			0
$53$	−2.12132	−	3.67423i	−0.291386	−	0.504695i	0.682752	−	0.730650i	$-0.260783\pi$
$53$	−2.12132	−	3.67423i	−0.291386	−	0.504695i	−0.974138	+	0.225955i	$0.927450\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.24264			−0.429498
$58$		0			0
$59$	−0.878680	−	1.52192i	−0.114394	−	0.198137i	0.803143	−	0.595786i	$-0.203159\pi$
$59$	−0.878680	−	1.52192i	−0.114394	−	0.198137i	−0.917537	+	0.397649i	$0.869826\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$	−1.00000	−	2.44949i	−0.125988	−	0.308607i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.86396	−	11.8887i	−0.838566	−	1.45244i	−0.891093	−	0.453820i	$-0.850061\pi$
$67$	−6.86396	−	11.8887i	−0.838566	−	1.45244i	0.0525271	−	0.998619i	$-0.483272\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$	8.48528			1.00702			0.503509	−	0.863990i	$-0.332042\pi$
$71$	8.48528			1.00702			0.503509	+	0.863990i	$0.332042\pi$
$72$		0			0
$73$	6.74264	+	11.6786i	0.789166	+	1.36688i	0.926478	+	0.376348i	$0.122820\pi$
$73$	6.74264	+	11.6786i	0.789166	+	1.36688i	−0.137312	+	0.990528i	$0.543846\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−11.1213	−	1.52192i	−1.26739	−	0.173439i
$78$		0			0
$79$	−0.378680	+	0.655892i	−0.0426048	+	0.0737937i	−0.886541	−	0.462649i	$-0.846899\pi$
$79$	−0.378680	+	0.655892i	−0.0426048	+	0.0737937i	0.843937	+	0.536443i	$0.180232\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−10.2426			−1.12428			−0.562138	−	0.827043i	$-0.690021\pi$
$83$	−10.2426			−1.12428			−0.562138	+	0.827043i	$0.690021\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.24264	−	7.34847i	−0.454859	−	0.787839i
$88$		0			0
$89$	−8.12132	+	14.0665i	−0.860858	+	1.49105i	0.0102435	+	0.999948i	$0.496739\pi$
$89$	−8.12132	+	14.0665i	−0.860858	+	1.49105i	−0.871102	+	0.491103i	$0.836594\pi$
$90$		0			0
$91$	8.10660	−	10.4539i	0.849803	−	1.09586i
$92$		0			0
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−15.9706			−1.62156			−0.810782	−	0.585348i	$-0.800958\pi$
$97$	−15.9706			−1.62156			−0.810782	+	0.585348i	$0.800958\pi$
$98$		0			0
$99$	−4.24264			−0.426401
$100$		0			0
$101$	9.36396	+	16.2189i	0.931749	+	1.61384i	0.780331	+	0.625367i	$0.215051\pi$
$101$	9.36396	+	16.2189i	0.931749	+	1.61384i	0.151418	+	0.988470i	$0.451616\pi$
$102$		0			0
$103$	4.62132	−	8.00436i	0.455352	−	0.788693i	−0.543356	−	0.839502i	$-0.682847\pi$
$103$	4.62132	−	8.00436i	0.455352	−	0.788693i	0.998708	+	0.0508091i	$0.0161800\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.36396	+	16.2189i	−0.905248	+	1.56794i	−0.0846647	+	0.996409i	$0.526982\pi$
$107$	−9.36396	+	16.2189i	−0.905248	+	1.56794i	−0.820584	+	0.571527i	$0.806351\pi$
$108$		0			0
$109$	−9.74264	−	16.8747i	−0.933176	−	1.61631i	−0.777855	−	0.628444i	$-0.783692\pi$
$109$	−9.74264	−	16.8747i	−0.933176	−	1.61631i	−0.155321	−	0.987864i	$-0.549641\pi$
$110$		0			0
$111$	5.00000			0.474579
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.50000	−	4.33013i	0.231125	−	0.400320i
$118$		0			0
$119$	11.1213	+	1.52192i	1.01949	+	0.139514i
$120$		0			0
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$		0			0
$123$	−0.878680	−	1.52192i	−0.0792279	−	0.137227i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−9.24264			−0.820152			−0.410076	−	0.912051i	$-0.634498\pi$
$127$	−9.24264			−0.820152			−0.410076	+	0.912051i	$0.634498\pi$
$128$		0			0
$129$	−2.24264	−	3.88437i	−0.197454	−	0.341999i
$130$		0			0
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		0			0
$133$	−3.24264	−	7.94282i	−0.281173	−	0.688729i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.24264	+	12.5446i	0.618781	+	1.07176i	0.989709	+	0.143098i	$0.0457063\pi$
$137$	7.24264	+	12.5446i	0.618781	+	1.07176i	−0.370928	+	0.928662i	$0.620960\pi$
$138$		0			0
$139$	−13.7279			−1.16439			−0.582194	−	0.813050i	$-0.697805\pi$
$139$	−13.7279			−1.16439			−0.582194	+	0.813050i	$0.697805\pi$
$140$		0			0
$141$	1.75736			0.147996
$142$		0			0
$143$	−10.6066	−	18.3712i	−0.886969	−	1.53627i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.00000	−	4.89898i	0.412393	−	0.404061i
$148$		0			0
$149$	6.87868	−	11.9142i	0.563523	−	0.976051i	−0.433662	−	0.901076i	$-0.642779\pi$
$149$	6.87868	−	11.9142i	0.563523	−	0.976051i	0.997185	−	0.0749755i	$-0.0238879\pi$
$150$		0			0
$151$	−5.86396	−	10.1567i	−0.477202	−	0.826539i	0.522456	−	0.852666i	$-0.325016\pi$
$151$	−5.86396	−	10.1567i	−0.477202	−	0.826539i	−0.999659	+	0.0261273i	$0.991682\pi$
$152$		0			0
$153$	4.24264			0.342997
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.742641	+	1.28629i	0.0592692	+	0.102657i	0.894138	−	0.447792i	$-0.147790\pi$
$157$	0.742641	+	1.28629i	0.0592692	+	0.102657i	−0.834868	+	0.550450i	$0.814456\pi$
$158$		0			0
$159$	2.12132	−	3.67423i	0.168232	−	0.291386i
$160$		0			0
$161$	6.00000	+	14.6969i	0.472866	+	1.15828i
$162$		0			0
$163$	−4.37868	+	7.58410i	−0.342965	+	0.594032i	−0.984982	−	0.172658i	$-0.944764\pi$
$163$	−4.37868	+	7.58410i	−0.342965	+	0.594032i	0.642017	+	0.766690i	$0.278098\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.75736			0.135989			0.0679943	−	0.997686i	$-0.478340\pi$
$167$	1.75736			0.135989			0.0679943	+	0.997686i	$0.478340\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−1.62132	−	2.80821i	−0.123985	−	0.214749i
$172$		0			0
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.878680	−	1.52192i	0.0660456	−	0.114394i
$178$		0			0
$179$	−1.75736	−	3.04384i	−0.131351	−	0.227507i	0.792846	−	0.609421i	$-0.208598\pi$
$179$	−1.75736	−	3.04384i	−0.131351	−	0.227507i	−0.924198	+	0.381914i	$0.875265\pi$
$180$		0			0
$181$	4.48528			0.333388			0.166694	−	0.986009i	$-0.446691\pi$
$181$	4.48528			0.333388			0.166694	+	0.986009i	$0.446691\pi$
$182$		0			0
$183$	1.00000			0.0739221
$184$		0			0
$185$		0			0
$186$		0			0
$187$	9.00000	−	15.5885i	0.658145	−	1.13994i
$188$		0			0
$189$	1.62132	−	2.09077i	0.117934	−	0.152081i
$190$		0			0
$191$	−8.12132	+	14.0665i	−0.587638	+	1.01782i	0.406903	+	0.913471i	$0.366609\pi$
$191$	−8.12132	+	14.0665i	−0.587638	+	1.01782i	−0.994541	+	0.104348i	$0.966725\pi$
$192$		0			0
$193$	2.24264	+	3.88437i	0.161429	+	0.279603i	0.935381	−	0.353641i	$-0.115056\pi$
$193$	2.24264	+	3.88437i	0.161429	+	0.279603i	−0.773953	+	0.633244i	$0.781723\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.48528			−0.604551			−0.302276	−	0.953221i	$-0.597746\pi$
$197$	−8.48528			−0.604551			−0.302276	+	0.953221i	$0.597746\pi$
$198$		0			0
$199$	8.62132	+	14.9326i	0.611149	+	1.05854i	0.991047	+	0.133513i	$0.0426258\pi$
$199$	8.62132	+	14.9326i	0.611149	+	1.05854i	−0.379898	+	0.925028i	$0.624041\pi$
$200$		0			0
$201$	6.86396	−	11.8887i	0.484146	−	0.838566i
$202$		0			0
$203$	13.7574	−	17.7408i	0.965577	−	1.24516i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$		0			0
$209$	−13.7574			−0.951616
$210$		0			0
$211$	12.7574			0.878253			0.439126	−	0.898425i	$-0.355288\pi$
$211$	12.7574			0.878253			0.439126	+	0.898425i	$0.355288\pi$
$212$		0			0
$213$	4.24264	+	7.34847i	0.290701	+	0.503509i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−10.4853	−	1.43488i	−0.711787	−	0.0974059i
$218$		0			0
$219$	−6.74264	+	11.6786i	−0.455625	+	0.789166i
$220$		0			0
$221$	10.6066	+	18.3712i	0.713477	+	1.23578i
$222$		0			0
$223$	−9.24264			−0.618933			−0.309466	−	0.950910i	$-0.600150\pi$
$223$	−9.24264			−0.618933			−0.309466	+	0.950910i	$0.600150\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.75736	−	3.04384i	−0.116640	−	0.202026i	0.801794	−	0.597600i	$-0.203879\pi$
$227$	−1.75736	−	3.04384i	−0.116640	−	0.202026i	−0.918434	+	0.395574i	$0.870546\pi$
$228$		0			0
$229$	2.98528	−	5.17066i	0.197273	−	0.341687i	−0.750370	−	0.661018i	$-0.770125\pi$
$229$	2.98528	−	5.17066i	0.197273	−	0.341687i	0.947643	+	0.319331i	$0.103458\pi$
$230$		0			0
$231$	−4.24264	−	10.3923i	−0.279145	−	0.683763i
$232$		0			0
$233$	−5.12132	+	8.87039i	−0.335509	+	0.581118i	−0.983582	−	0.180459i	$-0.942242\pi$
$233$	−5.12132	+	8.87039i	−0.335509	+	0.581118i	0.648074	+	0.761578i	$0.275575\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.757359			−0.0491958
$238$		0			0
$239$	28.9706			1.87395			0.936975	−	0.349397i	$-0.113613\pi$
$239$	28.9706			1.87395			0.936975	+	0.349397i	$0.113613\pi$
$240$		0			0
$241$	−13.9853	−	24.2232i	−0.900871	−	1.56035i	−0.826366	−	0.563134i	$-0.809595\pi$
$241$	−13.9853	−	24.2232i	−0.900871	−	1.56035i	−0.0745056	−	0.997221i	$-0.523738\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.10660	−	14.0410i	0.515811	−	0.893410i
$248$		0			0
$249$	−5.12132	−	8.87039i	−0.324550	−	0.562138i
$250$		0			0
$251$	−7.75736			−0.489640			−0.244820	−	0.969569i	$-0.578729\pi$
$251$	−7.75736			−0.489640			−0.244820	+	0.969569i	$0.578729\pi$
$252$		0			0
$253$	25.4558			1.60040
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.87868	+	11.9142i	−0.429080	+	0.743189i	−0.996792	−	0.0800388i	$-0.974496\pi$
$257$	−6.87868	+	11.9142i	−0.429080	+	0.743189i	0.567712	+	0.823228i	$0.307829\pi$
$258$		0			0
$259$	5.00000	+	12.2474i	0.310685	+	0.761019i
$260$		0			0
$261$	4.24264	−	7.34847i	0.262613	−	0.454859i
$262$		0			0
$263$	−2.48528	−	4.30463i	−0.153249	−	0.265435i	0.779171	−	0.626811i	$-0.215640\pi$
$263$	−2.48528	−	4.30463i	−0.153249	−	0.265435i	−0.932420	+	0.361376i	$0.882307\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−16.2426			−0.994033
$268$		0			0
$269$	−3.36396	−	5.82655i	−0.205104	−	0.355251i	0.745062	−	0.666996i	$-0.232420\pi$
$269$	−3.36396	−	5.82655i	−0.205104	−	0.355251i	−0.950166	+	0.311745i	$0.899087\pi$
$270$		0			0
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	−0.894799	−	0.446469i	$-0.852681\pi$
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	0.834053	+	0.551684i	$0.186015\pi$
$272$		0			0
$273$	13.1066	+	1.79360i	0.793248	+	0.108553i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	15.7426	+	27.2671i	0.945884	+	1.63832i	0.753972	+	0.656906i	$0.228135\pi$
$277$	15.7426	+	27.2671i	0.945884	+	1.63832i	0.191911	+	0.981412i	$0.438531\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−19.7574			−1.17863			−0.589313	−	0.807905i	$-0.700601\pi$
$281$	−19.7574			−1.17863			−0.589313	+	0.807905i	$0.700601\pi$
$282$		0			0
$283$	−5.62132	−	9.73641i	−0.334153	−	0.578770i	0.649169	−	0.760644i	$-0.275117\pi$
$283$	−5.62132	−	9.73641i	−0.334153	−	0.578770i	−0.983322	+	0.181875i	$0.941783\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.84924	−	3.67423i	0.168185	−	0.216883i
$288$		0			0
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$	−7.98528	−	13.8309i	−0.468105	−	0.810782i
$292$		0			0
$293$	−20.4853			−1.19676			−0.598381	−	0.801211i	$-0.704189\pi$
$293$	−20.4853			−1.19676			−0.598381	+	0.801211i	$0.704189\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.12132	−	3.67423i	−0.123091	−	0.213201i
$298$		0			0
$299$	−15.0000	+	25.9808i	−0.867472	+	1.50251i
$300$		0			0
$301$	7.27208	−	9.37769i	0.419156	−	0.540521i
$302$		0			0
$303$	−9.36396	+	16.2189i	−0.537946	+	0.931749i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	12.4853			0.712573			0.356286	−	0.934377i	$-0.384043\pi$
$307$	12.4853			0.712573			0.356286	+	0.934377i	$0.384043\pi$
$308$		0			0
$309$	9.24264			0.525795
$310$		0			0
$311$	1.24264	+	2.15232i	0.0704637	+	0.122047i	0.899105	−	0.437734i	$-0.144219\pi$
$311$	1.24264	+	2.15232i	0.0704637	+	0.122047i	−0.828641	+	0.559781i	$0.810885\pi$
$312$		0			0
$313$	−16.4853	+	28.5533i	−0.931803	+	1.61393i	−0.151566	+	0.988447i	$0.548431\pi$
$313$	−16.4853	+	28.5533i	−0.931803	+	1.61393i	−0.780238	+	0.625483i	$0.784902\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$		0			0
$319$	−18.0000	−	31.1769i	−1.00781	−	1.74557i
$320$		0			0
$321$	−18.7279			−1.04529
$322$		0			0
$323$	13.7574			0.765480
$324$		0			0
$325$		0			0
$326$		0			0
$327$	9.74264	−	16.8747i	0.538769	−	0.933176i
$328$		0			0
$329$	1.75736	+	4.30463i	0.0968864	+	0.237322i
$330$		0			0
$331$	4.37868	−	7.58410i	0.240674	−	0.416860i	−0.720232	−	0.693733i	$-0.755965\pi$
$331$	4.37868	−	7.58410i	0.240674	−	0.416860i	0.960906	+	0.276873i	$0.0892982\pi$
$332$		0			0
$333$	2.50000	+	4.33013i	0.136999	+	0.237289i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	8.97056			0.488658			0.244329	−	0.969692i	$-0.421432\pi$
$337$	8.97056			0.488658			0.244329	+	0.969692i	$0.421432\pi$
$338$		0			0
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$		0			0
$341$	−8.48528	+	14.6969i	−0.459504	+	0.795884i
$342$		0			0
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	15.3640	+	26.6112i	0.824781	+	1.42856i	0.902087	+	0.431555i	$0.142035\pi$
$347$	15.3640	+	26.6112i	0.824781	+	1.42856i	−0.0773062	+	0.997007i	$0.524632\pi$
$348$		0			0
$349$	8.00000			0.428230			0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000			0.428230			0.214115	+	0.976808i	$0.431313\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$		0			0
$353$	3.36396	+	5.82655i	0.179046	+	0.310116i	0.941554	−	0.336862i	$-0.109366\pi$
$353$	3.36396	+	5.82655i	0.179046	+	0.310116i	−0.762508	+	0.646978i	$0.776032\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	4.24264	+	10.3923i	0.224544	+	0.550019i
$358$		0			0
$359$	−15.3640	+	26.6112i	−0.810879	+	1.40448i	0.101371	+	0.994849i	$0.467677\pi$
$359$	−15.3640	+	26.6112i	−0.810879	+	1.40448i	−0.912250	+	0.409635i	$0.865656\pi$
$360$		0			0
$361$	4.24264	+	7.34847i	0.223297	+	0.386762i
$362$		0			0
$363$	−7.00000			−0.367405
$364$		0			0
$365$		0			0
$366$		0			0
$367$	7.00000	+	12.1244i	0.365397	+	0.632886i	0.988840	−	0.148983i	$-0.0475999\pi$
$367$	7.00000	+	12.1244i	0.365397	+	0.632886i	−0.623443	+	0.781869i	$0.714267\pi$
$368$		0			0
$369$	0.878680	−	1.52192i	0.0457422	−	0.0792279i
$370$		0			0
$371$	11.1213	+	1.52192i	0.577390	+	0.0790140i
$372$		0			0
$373$	−7.74264	+	13.4106i	−0.400899	+	0.694377i	−0.993835	−	0.110873i	$-0.964635\pi$
$373$	−7.74264	+	13.4106i	−0.400899	+	0.694377i	0.592936	+	0.805250i	$0.297969\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	42.4264			2.18507
$378$		0			0
$379$	11.7279			0.602423			0.301211	−	0.953557i	$-0.402609\pi$
$379$	11.7279			0.602423			0.301211	+	0.953557i	$0.402609\pi$
$380$		0			0
$381$	−4.62132	−	8.00436i	−0.236757	−	0.410076i
$382$		0			0
$383$	9.72792	−	16.8493i	0.497074	−	0.860957i	−0.502921	−	0.864333i	$-0.667741\pi$
$383$	9.72792	−	16.8493i	0.497074	−	0.860957i	0.999994	+	0.00337583i	$0.00107456\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.24264	−	3.88437i	0.114000	−	0.197454i
$388$		0			0
$389$	−2.63604	−	4.56575i	−0.133652	−	0.231493i	0.791429	−	0.611261i	$-0.209337\pi$
$389$	−2.63604	−	4.56575i	−0.133652	−	0.231493i	−0.925082	+	0.379768i	$0.876004\pi$
$390$		0			0
$391$	−25.4558			−1.28736
$392$		0			0
$393$	−6.00000			−0.302660
$394$		0			0
$395$		0			0
$396$		0			0
$397$	10.0000	−	17.3205i	0.501886	−	0.869291i	−0.498112	−	0.867113i	$-0.665973\pi$
$397$	10.0000	−	17.3205i	0.501886	−	0.869291i	0.999998	−	0.00217869i	$-0.000693499\pi$
$398$		0			0
$399$	5.25736	−	6.77962i	0.263197	−	0.339405i
$400$		0			0
$401$	−7.60660	+	13.1750i	−0.379856	+	0.657929i	−0.991041	−	0.133558i	$-0.957360\pi$
$401$	−7.60660	+	13.1750i	−0.379856	+	0.657929i	0.611185	+	0.791487i	$0.290693\pi$
$402$		0			0
$403$	−10.0000	−	17.3205i	−0.498135	−	0.862796i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.2132			1.05150
$408$		0			0
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	−0.766426	+	0.642333i	$0.777967\pi$
$410$		0			0
$411$	−7.24264	+	12.5446i	−0.357253	+	0.618781i
$412$		0			0
$413$	4.60660	+	0.630399i	0.226676	+	0.0310199i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−6.86396	−	11.8887i	−0.336130	−	0.582194i
$418$		0			0
$419$	12.7279			0.621800			0.310900	−	0.950443i	$-0.399370\pi$
$419$	12.7279			0.621800			0.310900	+	0.950443i	$0.399370\pi$
$420$		0			0
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$		0			0
$423$	0.878680	+	1.52192i	0.0427229	+	0.0739982i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.00000	+	2.44949i	0.0483934	+	0.118539i
$428$		0			0
$429$	10.6066	−	18.3712i	0.512092	−	0.886969i
$430$		0			0
$431$	−13.2426	−	22.9369i	−0.637876	−	1.10483i	−0.985898	−	0.167347i	$-0.946480\pi$
$431$	−13.2426	−	22.9369i	−0.637876	−	1.10483i	0.348023	−	0.937486i	$-0.386853\pi$
$432$		0			0
$433$	8.97056			0.431098			0.215549	−	0.976493i	$-0.430846\pi$
$433$	8.97056			0.431098			0.215549	+	0.976493i	$0.430846\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	9.72792	+	16.8493i	0.465350	+	0.806009i
$438$		0			0
$439$	−17.8640	+	30.9413i	−0.852600	+	1.47675i	0.0262531	+	0.999655i	$0.491642\pi$
$439$	−17.8640	+	30.9413i	−0.852600	+	1.47675i	−0.878853	+	0.477092i	$0.841691\pi$
$440$		0			0
$441$	6.74264	+	1.88064i	0.321078	+	0.0895542i
$442$		0			0
$443$	15.7279	−	27.2416i	0.747256	−	1.29429i	−0.201877	−	0.979411i	$-0.564704\pi$
$443$	15.7279	−	27.2416i	0.747256	−	1.29429i	0.949133	−	0.314875i	$-0.101963\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	13.7574			0.650701
$448$		0			0
$449$	36.7279			1.73330			0.866649	−	0.498919i	$-0.166269\pi$
$449$	36.7279			1.73330			0.866649	+	0.498919i	$0.166269\pi$
$450$		0			0
$451$	−3.72792	−	6.45695i	−0.175541	−	0.304046i
$452$		0			0
$453$	5.86396	−	10.1567i	0.275513	−	0.477202i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.74264	−	6.48244i	0.175073	−	0.303236i	−0.765113	−	0.643896i	$-0.777317\pi$
$457$	3.74264	−	6.48244i	0.175073	−	0.303236i	0.940187	+	0.340660i	$0.110650\pi$
$458$		0			0
$459$	2.12132	+	3.67423i	0.0990148	+	0.171499i
$460$		0			0
$461$	−26.4853			−1.23354			−0.616771	−	0.787142i	$-0.711560\pi$
$461$	−26.4853			−1.23354			−0.616771	+	0.787142i	$0.711560\pi$
$462$		0			0
$463$	2.75736			0.128145			0.0640727	−	0.997945i	$-0.479591\pi$
$463$	2.75736			0.128145			0.0640727	+	0.997945i	$0.479591\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15.7279	+	27.2416i	−0.727801	+	1.26059i	0.230009	+	0.973188i	$0.426124\pi$
$467$	−15.7279	+	27.2416i	−0.727801	+	1.26059i	−0.957810	+	0.287401i	$0.907209\pi$
$468$		0			0
$469$	35.9853	+	4.92447i	1.66165	+	0.227391i
$470$		0			0
$471$	−0.742641	+	1.28629i	−0.0342191	+	0.0592692i
$472$		0			0
$473$	−9.51472	−	16.4800i	−0.437487	−	0.757750i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	4.24264			0.194257
$478$		0			0
$479$	13.6066	+	23.5673i	0.621702	+	1.07682i	0.989169	+	0.146782i	$0.0468916\pi$
$479$	13.6066	+	23.5673i	0.621702	+	1.07682i	−0.367467	+	0.930036i	$0.619775\pi$
$480$		0			0
$481$	−12.5000	+	21.6506i	−0.569951	+	0.987184i
$482$		0			0
$483$	−9.72792	+	12.5446i	−0.442636	+	0.570800i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	5.75736	+	9.97204i	0.260891	+	0.451876i	0.966479	−	0.256746i	$-0.0826504\pi$
$487$	5.75736	+	9.97204i	0.260891	+	0.451876i	−0.705588	+	0.708622i	$0.749317\pi$
$488$		0			0
$489$	−8.75736			−0.396021
$490$		0			0
$491$	21.5147			0.970946			0.485473	−	0.874252i	$-0.338647\pi$
$491$	21.5147			0.970946			0.485473	+	0.874252i	$0.338647\pi$
$492$		0			0
$493$	18.0000	+	31.1769i	0.810679	+	1.40414i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−13.7574	+	17.7408i	−0.617102	+	0.795782i
$498$		0			0
$499$	2.62132	−	4.54026i	0.117346	−	0.203250i	−0.801369	−	0.598170i	$-0.795895\pi$
$499$	2.62132	−	4.54026i	0.117346	−	0.203250i	0.918715	+	0.394921i	$0.129228\pi$
$500$		0			0
$501$	0.878680	+	1.52192i	0.0392565	+	0.0679943i
$502$		0			0
$503$	25.4558			1.13502			0.567510	−	0.823367i	$-0.307907\pi$
$503$	25.4558			1.13502			0.567510	+	0.823367i	$0.307907\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$		0			0
$509$	−22.2426	+	38.5254i	−0.985888	+	1.70761i	−0.347964	+	0.937508i	$0.613127\pi$
$509$	−22.2426	+	38.5254i	−0.985888	+	1.70761i	−0.637923	+	0.770100i	$0.720206\pi$
$510$		0			0
$511$	−35.3492	−	4.83743i	−1.56376	−	0.213995i
$512$		0			0
$513$	1.62132	−	2.80821i	0.0715830	−	0.123985i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	7.45584			0.327908
$518$		0			0
$519$	−6.00000			−0.263371
$520$		0			0
$521$	21.7279	+	37.6339i	0.951918	+	1.64877i	0.741269	+	0.671208i	$0.234224\pi$
$521$	21.7279	+	37.6339i	0.951918	+	1.64877i	0.210648	+	0.977562i	$0.432443\pi$
$522$		0			0
$523$	−3.75736	+	6.50794i	−0.164298	+	0.284572i	−0.936406	−	0.350919i	$-0.885869\pi$
$523$	−3.75736	+	6.50794i	−0.164298	+	0.284572i	0.772108	+	0.635492i	$0.219202\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.48528	−	14.6969i	0.369625	−	0.640209i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	1.75736			0.0762629
$532$		0			0
$533$	8.78680			0.380598
$534$		0			0
$535$		0			0
$536$		0			0
$537$	1.75736	−	3.04384i	0.0758357	−	0.131351i
$538$		0			0
$539$	21.2132	−	20.7846i	0.913717	−	0.895257i
$540$		0			0
$541$	7.74264	−	13.4106i	0.332882	−	0.576569i	−0.650194	−	0.759769i	$-0.725312\pi$
$541$	7.74264	−	13.4106i	0.332882	−	0.576569i	0.983076	+	0.183200i	$0.0586455\pi$
$542$		0			0
$543$	2.24264	+	3.88437i	0.0962409	+	0.166694i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−26.0000			−1.11168			−0.555840	−	0.831289i	$-0.687603\pi$
$547$	−26.0000			−1.11168			−0.555840	+	0.831289i	$0.687603\pi$
$548$		0			0
$549$	0.500000	+	0.866025i	0.0213395	+	0.0369611i
$550$		0			0
$551$	13.7574	−	23.8284i	0.586083	−	1.01513i
$552$		0			0
$553$	−0.757359	−	1.85514i	−0.0322062	−	0.0788887i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	22.2426	+	38.5254i	0.942451	+	1.63237i	0.760776	+	0.649014i	$0.224818\pi$
$557$	22.2426	+	38.5254i	0.942451	+	1.63237i	0.181675	+	0.983359i	$0.441848\pi$
$558$		0			0
$559$	22.4264			0.948536
$560$		0			0
$561$	18.0000			0.759961
$562$		0			0
$563$	14.1213	+	24.4588i	0.595143	+	1.03082i	0.993527	+	0.113599i	$0.0362378\pi$
$563$	14.1213	+	24.4588i	0.595143	+	1.03082i	−0.398384	+	0.917219i	$0.630429\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.62132	+	0.358719i	0.110085	+	0.0150648i
$568$		0			0
$569$	−2.63604	+	4.56575i	−0.110509	+	0.191406i	−0.915975	−	0.401234i	$-0.868581\pi$
$569$	−2.63604	+	4.56575i	−0.110509	+	0.191406i	0.805467	+	0.592641i	$0.201915\pi$
$570$		0			0
$571$	−22.6213	−	39.1813i	−0.946673	−	1.63969i	−0.752367	−	0.658744i	$-0.771088\pi$
$571$	−22.6213	−	39.1813i	−0.946673	−	1.63969i	−0.194306	−	0.980941i	$-0.562245\pi$
$572$		0			0
$573$	−16.2426			−0.678546
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−7.48528	−	12.9649i	−0.311616	−	0.539735i	0.667096	−	0.744972i	$-0.267537\pi$
$577$	−7.48528	−	12.9649i	−0.311616	−	0.539735i	−0.978712	+	0.205236i	$0.934204\pi$
$578$		0			0
$579$	−2.24264	+	3.88437i	−0.0932010	+	0.161429i
$580$		0			0
$581$	16.6066	−	21.4150i	0.688958	−	0.888444i
$582$		0			0
$583$	9.00000	−	15.5885i	0.372742	−	0.645608i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.9706			−0.452804			−0.226402	−	0.974034i	$-0.572696\pi$
$587$	−10.9706			−0.452804			−0.226402	+	0.974034i	$0.572696\pi$
$588$		0			0
$589$	−12.9706			−0.534443
$590$		0			0
$591$	−4.24264	−	7.34847i	−0.174519	−	0.302276i
$592$		0			0
$593$	−17.4853	+	30.2854i	−0.718034	+	1.24367i	0.243743	+	0.969840i	$0.421625\pi$
$593$	−17.4853	+	30.2854i	−0.718034	+	1.24367i	−0.961777	+	0.273832i	$0.911709\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.62132	+	14.9326i	−0.352847	+	0.611149i
$598$		0			0
$599$	−17.8492	−	30.9158i	−0.729300	−	1.26319i	−0.957179	−	0.289496i	$-0.906512\pi$
$599$	−17.8492	−	30.9158i	−0.729300	−	1.26319i	0.227879	−	0.973689i	$-0.426821\pi$
$600$		0			0
$601$	7.48528			0.305331			0.152665	−	0.988278i	$-0.451214\pi$
$601$	7.48528			0.305331			0.152665	+	0.988278i	$0.451214\pi$
$602$		0			0
$603$	13.7279			0.559044
$604$		0			0
$605$		0			0
$606$		0			0
$607$	21.5919	−	37.3982i	0.876388	−	1.51795i	0.0211102	−	0.999777i	$-0.493280\pi$
$607$	21.5919	−	37.3982i	0.876388	−	1.51795i	0.855277	−	0.518171i	$-0.173387\pi$
$608$		0			0
$609$	22.2426	+	3.04384i	0.901317	+	0.123342i
$610$		0			0
$611$	−4.39340	+	7.60959i	−0.177738	+	0.307851i
$612$		0			0
$613$	−8.00000	−	13.8564i	−0.323117	−	0.559655i	0.658012	−	0.753007i	$-0.271397\pi$
$613$	−8.00000	−	13.8564i	−0.323117	−	0.559655i	−0.981129	+	0.193352i	$0.938064\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	37.4558			1.50792			0.753958	−	0.656923i	$-0.228142\pi$
$617$	37.4558			1.50792			0.753958	+	0.656923i	$0.228142\pi$
$618$		0			0
$619$	−8.24264	−	14.2767i	−0.331300	−	0.573828i	0.651467	−	0.758677i	$-0.274154\pi$
$619$	−8.24264	−	14.2767i	−0.331300	−	0.573828i	−0.982767	+	0.184849i	$0.940820\pi$
$620$		0			0
$621$	−3.00000	+	5.19615i	−0.120386	+	0.208514i
$622$		0			0
$623$	−16.2426	−	39.7862i	−0.650748	−	1.59400i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−6.87868	−	11.9142i	−0.274708	−	0.475808i
$628$		0			0
$629$	−21.2132			−0.845826
$630$		0			0
$631$	−16.2132			−0.645437			−0.322719	−	0.946495i	$-0.604597\pi$
$631$	−16.2132			−0.645437			−0.322719	+	0.946495i	$0.604597\pi$
$632$		0			0
$633$	6.37868	+	11.0482i	0.253530	+	0.439126i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	8.71320	+	33.8981i	0.345230	+	1.34309i
$638$		0			0
$639$	−4.24264	+	7.34847i	−0.167836	+	0.290701i
$640$		0			0
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	0.525584	−	0.850741i	$-0.323847\pi$
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	−0.999556	+	0.0297987i	$0.990513\pi$
$642$		0			0
$643$	−23.7279			−0.935738			−0.467869	−	0.883798i	$-0.654978\pi$
$643$	−23.7279			−0.935738			−0.467869	+	0.883798i	$0.654978\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−20.1213	−	34.8511i	−0.791051	−	1.37014i	−0.925317	−	0.379195i	$-0.876201\pi$
$647$	−20.1213	−	34.8511i	−0.791051	−	1.37014i	0.134266	−	0.990945i	$-0.457132\pi$
$648$		0			0
$649$	3.72792	−	6.45695i	0.146334	−	0.253457i
$650$		0			0
$651$	−4.00000	−	9.79796i	−0.156772	−	0.384012i
$652$		0			0
$653$	−11.1213	+	19.2627i	−0.435211	+	0.753807i	−0.997313	−	0.0732606i	$-0.976660\pi$
$653$	−11.1213	+	19.2627i	−0.435211	+	0.753807i	0.562102	+	0.827068i	$0.309993\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−13.4853			−0.526111
$658$		0			0
$659$	23.2721			0.906551			0.453276	−	0.891370i	$-0.350255\pi$
$659$	23.2721			0.906551			0.453276	+	0.891370i	$0.350255\pi$
$660$		0			0
$661$	−0.0147186	−	0.0254934i	−0.000572488	−	0.000991579i	0.865739	−	0.500496i	$-0.166849\pi$
$661$	−0.0147186	−	0.0254934i	−0.000572488	−	0.000991579i	−0.866312	+	0.499504i	$0.833516\pi$
$662$		0			0
$663$	−10.6066	+	18.3712i	−0.411926	+	0.713477i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−25.4558	+	44.0908i	−0.985654	+	1.70720i
$668$		0			0
$669$	−4.62132	−	8.00436i	−0.178671	−	0.309466i
$670$		0			0
$671$	4.24264			0.163785
$672$		0			0
$673$	21.4853			0.828197			0.414098	−	0.910232i	$-0.364097\pi$
$673$	21.4853			0.828197			0.414098	+	0.910232i	$0.364097\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.72792	−	16.8493i	0.373874	−	0.647569i	−0.616283	−	0.787524i	$-0.711362\pi$
$677$	9.72792	−	16.8493i	0.373874	−	0.647569i	0.990158	+	0.139955i	$0.0446958\pi$
$678$		0			0
$679$	25.8934	−	33.3908i	0.993697	−	1.28142i
$680$		0			0
$681$	1.75736	−	3.04384i	0.0673422	−	0.116640i
$682$		0			0
$683$	−12.3640	−	21.4150i	−0.473094	−	0.819423i	0.526432	−	0.850217i	$-0.323530\pi$
$683$	−12.3640	−	21.4150i	−0.473094	−	0.819423i	−0.999526	+	0.0307948i	$0.990196\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	5.97056			0.227791
$688$		0			0
$689$	10.6066	+	18.3712i	0.404079	+	0.699886i
$690$		0			0
$691$	15.3492	−	26.5857i	0.583913	−	1.01137i	−0.411097	−	0.911591i	$-0.634854\pi$
$691$	15.3492	−	26.5857i	0.583913	−	1.01137i	0.995010	−	0.0997750i	$-0.0318123\pi$
$692$		0			0
$693$	6.87868	−	8.87039i	0.261299	−	0.336958i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	3.72792	+	6.45695i	0.141205	+	0.244574i
$698$		0			0
$699$	−10.2426			−0.387412
$700$		0			0
$701$	−36.7279			−1.38719			−0.693597	−	0.720363i	$-0.743975\pi$
$701$	−36.7279			−1.38719			−0.693597	+	0.720363i	$0.743975\pi$
$702$		0			0
$703$	8.10660	+	14.0410i	0.305746	+	0.529568i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−49.0919	−	6.71807i	−1.84629	−	0.252659i
$708$		0			0
$709$	4.74264	−	8.21449i	0.178114	−	0.308502i	−0.763121	−	0.646256i	$-0.776334\pi$
$709$	4.74264	−	8.21449i	0.178114	−	0.308502i	0.941234	+	0.337754i	$0.109667\pi$
$710$		0			0
$711$	−0.378680	−	0.655892i	−0.0142016	−	0.0245979i
$712$		0			0
$713$	24.0000			0.898807
$714$		0			0
$715$		0			0
$716$		0			0
$717$	14.4853	+	25.0892i	0.540963	+	0.936975i
$718$		0			0
$719$	13.0919	−	22.6758i	0.488245	−	0.845665i	−0.511664	−	0.859186i	$-0.670971\pi$
$719$	13.0919	−	22.6758i	0.488245	−	0.845665i	0.999909	+	0.0135209i	$0.00430397\pi$
$720$		0			0
$721$	9.24264	+	22.6398i	0.344214	+	0.843148i
$722$		0			0
$723$	13.9853	−	24.2232i	0.520118	−	0.900871i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	47.2426			1.75213			0.876066	−	0.482191i	$-0.160159\pi$
$727$	47.2426			1.75213			0.876066	+	0.482191i	$0.160159\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	9.51472	+	16.4800i	0.351915	+	0.609534i
$732$		0			0
$733$	4.25736	−	7.37396i	0.157249	−	0.272364i	−0.776627	−	0.629961i	$-0.783071\pi$
$733$	4.25736	−	7.37396i	0.157249	−	0.272364i	0.933876	+	0.357598i	$0.116404\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	29.1213	−	50.4396i	1.07270	−	1.85797i
$738$		0			0
$739$	20.8345	+	36.0865i	0.766410	+	1.32746i	0.939498	+	0.342555i	$0.111292\pi$
$739$	20.8345	+	36.0865i	0.766410	+	1.32746i	−0.173087	+	0.984906i	$0.555374\pi$
$740$		0			0
$741$	16.2132			0.595607
$742$		0			0
$743$	22.9706			0.842708			0.421354	−	0.906896i	$-0.361555\pi$
$743$	22.9706			0.842708			0.421354	+	0.906896i	$0.361555\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.12132	−	8.87039i	0.187379	−	0.324550i
$748$		0			0
$749$	−18.7279	−	45.8739i	−0.684303	−	1.67619i
$750$		0			0
$751$	3.86396	−	6.69258i	0.140998	−	0.244216i	−0.786875	−	0.617113i	$-0.788302\pi$
$751$	3.86396	−	6.69258i	0.140998	−	0.244216i	0.927873	+	0.372897i	$0.121636\pi$
$752$		0			0
$753$	−3.87868	−	6.71807i	−0.141347	−	0.244820i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−36.4558			−1.32501			−0.662505	−	0.749057i	$-0.730507\pi$
$757$	−36.4558			−1.32501			−0.662505	+	0.749057i	$0.730507\pi$
$758$		0			0
$759$	12.7279	+	22.0454i	0.461994	+	0.800198i
$760$		0			0
$761$	−15.8787	+	27.5027i	−0.575602	+	0.996971i	0.420374	+	0.907351i	$0.361899\pi$
$761$	−15.8787	+	27.5027i	−0.575602	+	0.996971i	−0.995976	+	0.0896206i	$0.971435\pi$
$762$		0			0
$763$	51.0772	+	6.98975i	1.84912	+	0.253046i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.39340	+	7.60959i	0.158636	+	0.274766i
$768$		0			0
$769$	−48.4853			−1.74842			−0.874212	−	0.485544i	$-0.838621\pi$
$769$	−48.4853			−1.74842			−0.874212	+	0.485544i	$0.838621\pi$
$770$		0			0
$771$	−13.7574			−0.495459
$772$		0			0
$773$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$773$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−8.10660	+	10.4539i	−0.290823	+	0.375030i
$778$		0			0
$779$	2.84924	−	4.93503i	0.102085	−	0.176816i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$		0			0
$783$	8.48528			0.303239
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−3.86396	−	6.69258i	−0.137735	−	0.238565i	0.788904	−	0.614517i	$-0.210649\pi$
$787$	−3.86396	−	6.69258i	−0.137735	−	0.238565i	−0.926639	+	0.375952i	$0.877316\pi$
$788$		0			0
$789$	2.48528	−	4.30463i	0.0884784	−	0.153249i
$790$		0			0
$791$	−9.72792	+	12.5446i	−0.345885	+	0.446035i
$792$		0			0
$793$	−2.50000	+	4.33013i	−0.0887776	+	0.153767i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−36.4264			−1.29029			−0.645145	−	0.764060i	$-0.723203\pi$
$797$	−36.4264			−1.29029			−0.645145	+	0.764060i	$0.723203\pi$
$798$		0			0
$799$	−7.45584			−0.263769
$800$		0			0
$801$	−8.12132	−	14.0665i	−0.286953	−	0.497017i
$802$		0			0
$803$	−28.6066	+	49.5481i	−1.00951	+	1.74851i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.36396	−	5.82655i	0.118417	−	0.205104i
$808$		0			0
$809$	−2.27208	−	3.93535i	−0.0798820	−	0.138360i

Overview	Features
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.q (of order \(3\), degree \(2\), minimal)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about