Properties

 Label 2646.2.e.n.1549.1 Level $2646$ Weight $2$ Character 2646.1549 Analytic conductor $21.128$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$2646 = 2 \cdot 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2646.e (of order $$3$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$21.1284163748$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-11})$$ Defining polynomial: $$x^{4} - x^{3} - 2 x^{2} - 3 x + 9$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 126) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 1549.1 Root $$-1.18614 - 1.26217i$$ of defining polynomial Character $$\chi$$ $$=$$ 2646.1549 Dual form 2646.2.e.n.2125.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} +(-0.686141 - 1.18843i) q^{5} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} +(-0.686141 - 1.18843i) q^{5} +1.00000 q^{8} +(-0.686141 - 1.18843i) q^{10} +(2.18614 - 3.78651i) q^{11} +(-1.00000 + 1.73205i) q^{13} +1.00000 q^{16} +(-2.18614 - 3.78651i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-0.686141 - 1.18843i) q^{20} +(2.18614 - 3.78651i) q^{22} +(-3.68614 - 6.38458i) q^{23} +(1.55842 - 2.69927i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(1.37228 + 2.37686i) q^{29} +2.00000 q^{31} +1.00000 q^{32} +(-2.18614 - 3.78651i) q^{34} +(-1.00000 + 1.73205i) q^{37} +(-2.50000 + 4.33013i) q^{38} +(-0.686141 - 1.18843i) q^{40} +(5.18614 - 8.98266i) q^{41} +(-4.55842 - 7.89542i) q^{43} +(2.18614 - 3.78651i) q^{44} +(-3.68614 - 6.38458i) q^{46} +(1.55842 - 2.69927i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(1.37228 + 2.37686i) q^{53} -6.00000 q^{55} +(1.37228 + 2.37686i) q^{58} -7.11684 q^{59} -14.1168 q^{61} +2.00000 q^{62} +1.00000 q^{64} +2.74456 q^{65} +15.1168 q^{67} +(-2.18614 - 3.78651i) q^{68} -10.1168 q^{71} +(2.55842 + 4.43132i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-2.50000 + 4.33013i) q^{76} +12.1168 q^{79} +(-0.686141 - 1.18843i) q^{80} +(5.18614 - 8.98266i) q^{82} +(-2.74456 - 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-4.55842 - 7.89542i) q^{86} +(2.18614 - 3.78651i) q^{88} +(1.62772 - 2.81929i) q^{89} +(-3.68614 - 6.38458i) q^{92} +6.86141 q^{95} +(-4.55842 - 7.89542i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 4 q^{2} + 4 q^{4} + 3 q^{5} + 4 q^{8} + O(q^{10})$$ $$4 q + 4 q^{2} + 4 q^{4} + 3 q^{5} + 4 q^{8} + 3 q^{10} + 3 q^{11} - 4 q^{13} + 4 q^{16} - 3 q^{17} - 10 q^{19} + 3 q^{20} + 3 q^{22} - 9 q^{23} - 11 q^{25} - 4 q^{26} - 6 q^{29} + 8 q^{31} + 4 q^{32} - 3 q^{34} - 4 q^{37} - 10 q^{38} + 3 q^{40} + 15 q^{41} - q^{43} + 3 q^{44} - 9 q^{46} - 11 q^{50} - 4 q^{52} - 6 q^{53} - 24 q^{55} - 6 q^{58} + 6 q^{59} - 22 q^{61} + 8 q^{62} + 4 q^{64} - 12 q^{65} + 26 q^{67} - 3 q^{68} - 6 q^{71} - 7 q^{73} - 4 q^{74} - 10 q^{76} + 14 q^{79} + 3 q^{80} + 15 q^{82} + 12 q^{83} - 12 q^{85} - q^{86} + 3 q^{88} + 18 q^{89} - 9 q^{92} - 30 q^{95} - q^{97} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$1081$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$

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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ −0.686141 1.18843i −0.306851 0.531482i 0.670820 0.741620i $$-0.265942\pi$$
−0.977672 + 0.210138i $$0.932609\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ −0.686141 1.18843i −0.216977 0.375815i
$$11$$ 2.18614 3.78651i 0.659146 1.14167i −0.321691 0.946845i $$-0.604251\pi$$
0.980837 0.194830i $$-0.0624155\pi$$
$$12$$ 0 0
$$13$$ −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i $$-0.922790\pi$$
0.693375 + 0.720577i $$0.256123\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −2.18614 3.78651i −0.530217 0.918363i −0.999379 0.0352504i $$-0.988777\pi$$
0.469162 0.883112i $$-0.344556\pi$$
$$18$$ 0 0
$$19$$ −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i $$0.361097\pi$$
−0.996199 + 0.0871106i $$0.972237\pi$$
$$20$$ −0.686141 1.18843i −0.153426 0.265741i
$$21$$ 0 0
$$22$$ 2.18614 3.78651i 0.466087 0.807286i
$$23$$ −3.68614 6.38458i −0.768613 1.33128i −0.938315 0.345782i $$-0.887614\pi$$
0.169701 0.985496i $$-0.445720\pi$$
$$24$$ 0 0
$$25$$ 1.55842 2.69927i 0.311684 0.539853i
$$26$$ −1.00000 + 1.73205i −0.196116 + 0.339683i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 1.37228 + 2.37686i 0.254826 + 0.441372i 0.964848 0.262807i $$-0.0846484\pi$$
−0.710022 + 0.704179i $$0.751315\pi$$
$$30$$ 0 0
$$31$$ 2.00000 0.359211 0.179605 0.983739i $$-0.442518\pi$$
0.179605 + 0.983739i $$0.442518\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ −2.18614 3.78651i −0.374920 0.649381i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i $$-0.885902\pi$$
0.772043 + 0.635571i $$0.219235\pi$$
$$38$$ −2.50000 + 4.33013i −0.405554 + 0.702439i
$$39$$ 0 0
$$40$$ −0.686141 1.18843i −0.108488 0.187907i
$$41$$ 5.18614 8.98266i 0.809939 1.40286i −0.102966 0.994685i $$-0.532833\pi$$
0.912906 0.408171i $$-0.133833\pi$$
$$42$$ 0 0
$$43$$ −4.55842 7.89542i −0.695153 1.20404i −0.970129 0.242589i $$-0.922003\pi$$
0.274976 0.961451i $$-0.411330\pi$$
$$44$$ 2.18614 3.78651i 0.329573 0.570837i
$$45$$ 0 0
$$46$$ −3.68614 6.38458i −0.543492 0.941355i
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 1.55842 2.69927i 0.220394 0.381734i
$$51$$ 0 0
$$52$$ −1.00000 + 1.73205i −0.138675 + 0.240192i
$$53$$ 1.37228 + 2.37686i 0.188497 + 0.326487i 0.944749 0.327793i $$-0.106305\pi$$
−0.756252 + 0.654280i $$0.772972\pi$$
$$54$$ 0 0
$$55$$ −6.00000 −0.809040
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 1.37228 + 2.37686i 0.180189 + 0.312097i
$$59$$ −7.11684 −0.926534 −0.463267 0.886219i $$-0.653323\pi$$
−0.463267 + 0.886219i $$0.653323\pi$$
$$60$$ 0 0
$$61$$ −14.1168 −1.80748 −0.903738 0.428085i $$-0.859188\pi$$
−0.903738 + 0.428085i $$0.859188\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 2.74456 0.340421
$$66$$ 0 0
$$67$$ 15.1168 1.84682 0.923408 0.383819i $$-0.125391\pi$$
0.923408 + 0.383819i $$0.125391\pi$$
$$68$$ −2.18614 3.78651i −0.265108 0.459181i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −10.1168 −1.20065 −0.600324 0.799757i $$-0.704962\pi$$
−0.600324 + 0.799757i $$0.704962\pi$$
$$72$$ 0 0
$$73$$ 2.55842 + 4.43132i 0.299441 + 0.518646i 0.976008 0.217734i $$-0.0698666\pi$$
−0.676567 + 0.736381i $$0.736533\pi$$
$$74$$ −1.00000 + 1.73205i −0.116248 + 0.201347i
$$75$$ 0 0
$$76$$ −2.50000 + 4.33013i −0.286770 + 0.496700i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 12.1168 1.36325 0.681626 0.731701i $$-0.261273\pi$$
0.681626 + 0.731701i $$0.261273\pi$$
$$80$$ −0.686141 1.18843i −0.0767129 0.132871i
$$81$$ 0 0
$$82$$ 5.18614 8.98266i 0.572713 0.991969i
$$83$$ −2.74456 4.75372i −0.301255 0.521789i 0.675166 0.737666i $$-0.264072\pi$$
−0.976420 + 0.215877i $$0.930739\pi$$
$$84$$ 0 0
$$85$$ −3.00000 + 5.19615i −0.325396 + 0.563602i
$$86$$ −4.55842 7.89542i −0.491547 0.851385i
$$87$$ 0 0
$$88$$ 2.18614 3.78651i 0.233043 0.403643i
$$89$$ 1.62772 2.81929i 0.172538 0.298844i −0.766769 0.641924i $$-0.778137\pi$$
0.939306 + 0.343079i $$0.111470\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −3.68614 6.38458i −0.384307 0.665639i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 6.86141 0.703965
$$96$$ 0 0
$$97$$ −4.55842 7.89542i −0.462838 0.801658i 0.536263 0.844051i $$-0.319835\pi$$
−0.999101 + 0.0423924i $$0.986502\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 1.55842 2.69927i 0.155842 0.269927i
$$101$$ 3.68614 6.38458i 0.366785 0.635290i −0.622276 0.782798i $$-0.713792\pi$$
0.989061 + 0.147508i $$0.0471252\pi$$
$$102$$ 0 0
$$103$$ 5.00000 + 8.66025i 0.492665 + 0.853320i 0.999964 0.00844953i $$-0.00268960\pi$$
−0.507300 + 0.861770i $$0.669356\pi$$
$$104$$ −1.00000 + 1.73205i −0.0980581 + 0.169842i
$$105$$ 0 0
$$106$$ 1.37228 + 2.37686i 0.133288 + 0.230861i
$$107$$ −0.813859 + 1.40965i −0.0786788 + 0.136276i −0.902680 0.430312i $$-0.858403\pi$$
0.824001 + 0.566588i $$0.191737\pi$$
$$108$$ 0 0
$$109$$ −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i $$-0.932756\pi$$
0.307290 0.951616i $$-0.400578\pi$$
$$110$$ −6.00000 −0.572078
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0.686141 1.18843i 0.0645467 0.111798i −0.831946 0.554856i $$-0.812773\pi$$
0.896493 + 0.443058i $$0.146107\pi$$
$$114$$ 0 0
$$115$$ −5.05842 + 8.76144i −0.471700 + 0.817009i
$$116$$ 1.37228 + 2.37686i 0.127413 + 0.220686i
$$117$$ 0 0
$$118$$ −7.11684 −0.655159
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −4.05842 7.02939i −0.368947 0.639036i
$$122$$ −14.1168 −1.27808
$$123$$ 0 0
$$124$$ 2.00000 0.179605
$$125$$ −11.1386 −0.996266
$$126$$ 0 0
$$127$$ −14.1168 −1.25267 −0.626334 0.779555i $$-0.715445\pi$$
−0.626334 + 0.779555i $$0.715445\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 2.74456 0.240714
$$131$$ −3.68614 6.38458i −0.322060 0.557824i 0.658853 0.752271i $$-0.271042\pi$$
−0.980913 + 0.194448i $$0.937708\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 15.1168 1.30590
$$135$$ 0 0
$$136$$ −2.18614 3.78651i −0.187460 0.324690i
$$137$$ 8.18614 14.1788i 0.699389 1.21138i −0.269289 0.963059i $$-0.586789\pi$$
0.968678 0.248318i $$-0.0798779\pi$$
$$138$$ 0 0
$$139$$ 10.6168 18.3889i 0.900509 1.55973i 0.0736742 0.997282i $$-0.476528\pi$$
0.826835 0.562445i $$-0.190139\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −10.1168 −0.848987
$$143$$ 4.37228 + 7.57301i 0.365629 + 0.633287i
$$144$$ 0 0
$$145$$ 1.88316 3.26172i 0.156388 0.270871i
$$146$$ 2.55842 + 4.43132i 0.211737 + 0.366738i
$$147$$ 0 0
$$148$$ −1.00000 + 1.73205i −0.0821995 + 0.142374i
$$149$$ 7.37228 + 12.7692i 0.603961 + 1.04609i 0.992215 + 0.124538i $$0.0397450\pi$$
−0.388254 + 0.921552i $$0.626922\pi$$
$$150$$ 0 0
$$151$$ 4.05842 7.02939i 0.330270 0.572044i −0.652295 0.757965i $$-0.726194\pi$$
0.982565 + 0.185921i $$0.0595270\pi$$
$$152$$ −2.50000 + 4.33013i −0.202777 + 0.351220i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −1.37228 2.37686i −0.110224 0.190914i
$$156$$ 0 0
$$157$$ −8.11684 −0.647795 −0.323897 0.946092i $$-0.604993\pi$$
−0.323897 + 0.946092i $$0.604993\pi$$
$$158$$ 12.1168 0.963964
$$159$$ 0 0
$$160$$ −0.686141 1.18843i −0.0542442 0.0939537i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −8.11684 + 14.0588i −0.635760 + 1.10117i 0.350593 + 0.936528i $$0.385980\pi$$
−0.986354 + 0.164641i $$0.947353\pi$$
$$164$$ 5.18614 8.98266i 0.404970 0.701428i
$$165$$ 0 0
$$166$$ −2.74456 4.75372i −0.213019 0.368960i
$$167$$ 8.74456 15.1460i 0.676675 1.17203i −0.299302 0.954158i $$-0.596754\pi$$
0.975976 0.217876i $$-0.0699129\pi$$
$$168$$ 0 0
$$169$$ 4.50000 + 7.79423i 0.346154 + 0.599556i
$$170$$ −3.00000 + 5.19615i −0.230089 + 0.398527i
$$171$$ 0 0
$$172$$ −4.55842 7.89542i −0.347576 0.602020i
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 2.18614 3.78651i 0.164787 0.285419i
$$177$$ 0 0
$$178$$ 1.62772 2.81929i 0.122003 0.211315i
$$179$$ 7.37228 + 12.7692i 0.551030 + 0.954412i 0.998201 + 0.0599635i $$0.0190984\pi$$
−0.447170 + 0.894449i $$0.647568\pi$$
$$180$$ 0 0
$$181$$ 18.1168 1.34661 0.673307 0.739363i $$-0.264873\pi$$
0.673307 + 0.739363i $$0.264873\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −3.68614 6.38458i −0.271746 0.470678i
$$185$$ 2.74456 0.201784
$$186$$ 0 0
$$187$$ −19.1168 −1.39796
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 6.86141 0.497779
$$191$$ 1.88316 0.136260 0.0681302 0.997676i $$-0.478297\pi$$
0.0681302 + 0.997676i $$0.478297\pi$$
$$192$$ 0 0
$$193$$ −7.00000 −0.503871 −0.251936 0.967744i $$-0.581067\pi$$
−0.251936 + 0.967744i $$0.581067\pi$$
$$194$$ −4.55842 7.89542i −0.327276 0.566858i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i $$-0.0513380\pi$$
−0.632581 + 0.774494i $$0.718005\pi$$
$$200$$ 1.55842 2.69927i 0.110197 0.190867i
$$201$$ 0 0
$$202$$ 3.68614 6.38458i 0.259356 0.449218i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −14.2337 −0.994124
$$206$$ 5.00000 + 8.66025i 0.348367 + 0.603388i
$$207$$ 0 0
$$208$$ −1.00000 + 1.73205i −0.0693375 + 0.120096i
$$209$$ 10.9307 + 18.9325i 0.756093 + 1.30959i
$$210$$ 0 0
$$211$$ 8.00000 13.8564i 0.550743 0.953914i −0.447478 0.894295i $$-0.647678\pi$$
0.998221 0.0596196i $$-0.0189888\pi$$
$$212$$ 1.37228 + 2.37686i 0.0942487 + 0.163243i
$$213$$ 0 0
$$214$$ −0.813859 + 1.40965i −0.0556343 + 0.0963614i
$$215$$ −6.25544 + 10.8347i −0.426617 + 0.738923i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −7.00000 12.1244i −0.474100 0.821165i
$$219$$ 0 0
$$220$$ −6.00000 −0.404520
$$221$$ 8.74456 0.588223
$$222$$ 0 0
$$223$$ 2.00000 + 3.46410i 0.133930 + 0.231973i 0.925188 0.379509i $$-0.123907\pi$$
−0.791258 + 0.611482i $$0.790574\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0.686141 1.18843i 0.0456414 0.0790532i
$$227$$ −11.8723 + 20.5634i −0.787991 + 1.36484i 0.139205 + 0.990264i $$0.455545\pi$$
−0.927196 + 0.374577i $$0.877788\pi$$
$$228$$ 0 0
$$229$$ 10.0584 + 17.4217i 0.664679 + 1.15126i 0.979372 + 0.202065i $$0.0647651\pi$$
−0.314693 + 0.949194i $$0.601902\pi$$
$$230$$ −5.05842 + 8.76144i −0.333542 + 0.577713i
$$231$$ 0 0
$$232$$ 1.37228 + 2.37686i 0.0900947 + 0.156049i
$$233$$ −5.87228 + 10.1711i −0.384706 + 0.666330i −0.991728 0.128354i $$-0.959030\pi$$
0.607022 + 0.794685i $$0.292364\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −7.11684 −0.463267
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −9.43070 + 16.3345i −0.610021 + 1.05659i 0.381215 + 0.924487i $$0.375506\pi$$
−0.991236 + 0.132102i $$0.957827\pi$$
$$240$$ 0 0
$$241$$ −0.441578 + 0.764836i −0.0284445 + 0.0492674i −0.879897 0.475164i $$-0.842389\pi$$
0.851453 + 0.524431i $$0.175722\pi$$
$$242$$ −4.05842 7.02939i −0.260885 0.451867i
$$243$$ 0 0
$$244$$ −14.1168 −0.903738
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −5.00000 8.66025i −0.318142 0.551039i
$$248$$ 2.00000 0.127000
$$249$$ 0 0
$$250$$ −11.1386 −0.704467
$$251$$ 9.00000 0.568075 0.284037 0.958813i $$-0.408326\pi$$
0.284037 + 0.958813i $$0.408326\pi$$
$$252$$ 0 0
$$253$$ −32.2337 −2.02651
$$254$$ −14.1168 −0.885770
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 10.9307 + 18.9325i 0.681839 + 1.18098i 0.974419 + 0.224738i $$0.0721527\pi$$
−0.292581 + 0.956241i $$0.594514\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 2.74456 0.170211
$$261$$ 0 0
$$262$$ −3.68614 6.38458i −0.227731 0.394441i
$$263$$ 6.68614 11.5807i 0.412285 0.714099i −0.582854 0.812577i $$-0.698064\pi$$
0.995139 + 0.0984781i $$0.0313974\pi$$
$$264$$ 0 0
$$265$$ 1.88316 3.26172i 0.115681 0.200366i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 15.1168 0.923408
$$269$$ −3.68614 6.38458i −0.224748 0.389275i 0.731496 0.681846i $$-0.238823\pi$$
−0.956244 + 0.292571i $$0.905489\pi$$
$$270$$ 0 0
$$271$$ 9.11684 15.7908i 0.553809 0.959225i −0.444186 0.895934i $$-0.646507\pi$$
0.997995 0.0632906i $$-0.0201595\pi$$
$$272$$ −2.18614 3.78651i −0.132554 0.229591i
$$273$$ 0 0
$$274$$ 8.18614 14.1788i 0.494543 0.856573i
$$275$$ −6.81386 11.8020i −0.410891 0.711684i
$$276$$ 0 0
$$277$$ −11.1168 + 19.2549i −0.667946 + 1.15692i 0.310531 + 0.950563i $$0.399493\pi$$
−0.978477 + 0.206354i $$0.933840\pi$$
$$278$$ 10.6168 18.3889i 0.636756 1.10289i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 5.31386 + 9.20387i 0.316998 + 0.549057i 0.979860 0.199685i $$-0.0639917\pi$$
−0.662862 + 0.748742i $$0.730658\pi$$
$$282$$ 0 0
$$283$$ 9.88316 0.587493 0.293746 0.955883i $$-0.405098\pi$$
0.293746 + 0.955883i $$0.405098\pi$$
$$284$$ −10.1168 −0.600324
$$285$$ 0 0
$$286$$ 4.37228 + 7.57301i 0.258538 + 0.447802i
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −1.05842 + 1.83324i −0.0622601 + 0.107838i
$$290$$ 1.88316 3.26172i 0.110583 0.191535i
$$291$$ 0 0
$$292$$ 2.55842 + 4.43132i 0.149720 + 0.259323i
$$293$$ −2.31386 + 4.00772i −0.135177 + 0.234134i −0.925665 0.378344i $$-0.876494\pi$$
0.790488 + 0.612478i $$0.209827\pi$$
$$294$$ 0 0
$$295$$ 4.88316 + 8.45787i 0.284308 + 0.492436i
$$296$$ −1.00000 + 1.73205i −0.0581238 + 0.100673i
$$297$$ 0 0
$$298$$ 7.37228 + 12.7692i 0.427065 + 0.739698i
$$299$$ 14.7446 0.852700
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 4.05842 7.02939i 0.233536 0.404496i
$$303$$ 0 0
$$304$$ −2.50000 + 4.33013i −0.143385 + 0.248350i
$$305$$ 9.68614 + 16.7769i 0.554627 + 0.960642i
$$306$$ 0 0
$$307$$ −13.0000 −0.741949 −0.370975 0.928643i $$-0.620976\pi$$
−0.370975 + 0.928643i $$0.620976\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −1.37228 2.37686i −0.0779403 0.134997i
$$311$$ 26.2337 1.48758 0.743788 0.668416i $$-0.233027\pi$$
0.743788 + 0.668416i $$0.233027\pi$$
$$312$$ 0 0
$$313$$ −2.88316 −0.162966 −0.0814828 0.996675i $$-0.525966\pi$$
−0.0814828 + 0.996675i $$0.525966\pi$$
$$314$$ −8.11684 −0.458060
$$315$$ 0 0
$$316$$ 12.1168 0.681626
$$317$$ 6.00000 0.336994 0.168497 0.985702i $$-0.446109\pi$$
0.168497 + 0.985702i $$0.446109\pi$$
$$318$$ 0 0
$$319$$ 12.0000 0.671871
$$320$$ −0.686141 1.18843i −0.0383564 0.0664353i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 21.8614 1.21640
$$324$$ 0 0
$$325$$ 3.11684 + 5.39853i 0.172891 + 0.299457i
$$326$$ −8.11684 + 14.0588i −0.449550 + 0.778644i
$$327$$ 0 0
$$328$$ 5.18614 8.98266i 0.286357 0.495984i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −12.2337 −0.672424 −0.336212 0.941786i $$-0.609146\pi$$
−0.336212 + 0.941786i $$0.609146\pi$$
$$332$$ −2.74456 4.75372i −0.150627 0.260894i
$$333$$ 0 0
$$334$$ 8.74456 15.1460i 0.478481 0.828754i
$$335$$ −10.3723 17.9653i −0.566698 0.981550i
$$336$$ 0 0
$$337$$ −4.55842 + 7.89542i −0.248313 + 0.430091i −0.963058 0.269294i $$-0.913210\pi$$
0.714745 + 0.699385i $$0.246543\pi$$
$$338$$ 4.50000 + 7.79423i 0.244768 + 0.423950i
$$339$$ 0 0
$$340$$ −3.00000 + 5.19615i −0.162698 + 0.281801i
$$341$$ 4.37228 7.57301i 0.236772 0.410102i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −4.55842 7.89542i −0.245774 0.425692i
$$345$$ 0 0
$$346$$ 6.00000 0.322562
$$347$$ −7.11684 −0.382052 −0.191026 0.981585i $$-0.561182\pi$$
−0.191026 + 0.981585i $$0.561182\pi$$
$$348$$ 0 0
$$349$$ 11.0000 + 19.0526i 0.588817 + 1.01986i 0.994388 + 0.105797i $$0.0337393\pi$$
−0.405571 + 0.914063i $$0.632927\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 2.18614 3.78651i 0.116522 0.201821i
$$353$$ −3.81386 + 6.60580i −0.202991 + 0.351591i −0.949491 0.313795i $$-0.898400\pi$$
0.746500 + 0.665386i $$0.231733\pi$$
$$354$$ 0 0
$$355$$ 6.94158 + 12.0232i 0.368421 + 0.638123i
$$356$$ 1.62772 2.81929i 0.0862689 0.149422i
$$357$$ 0 0
$$358$$ 7.37228 + 12.7692i 0.389637 + 0.674871i
$$359$$ −3.43070 + 5.94215i −0.181066 + 0.313615i −0.942244 0.334928i $$-0.891288\pi$$
0.761178 + 0.648543i $$0.224621\pi$$
$$360$$ 0 0
$$361$$ −3.00000 5.19615i −0.157895 0.273482i
$$362$$ 18.1168 0.952200
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 3.51087 6.08101i 0.183768 0.318295i
$$366$$ 0 0
$$367$$ −11.1168 + 19.2549i −0.580295 + 1.00510i 0.415150 + 0.909753i $$0.363729\pi$$
−0.995444 + 0.0953465i $$0.969604\pi$$
$$368$$ −3.68614 6.38458i −0.192153 0.332819i
$$369$$ 0 0
$$370$$ 2.74456 0.142683
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i $$-0.0833099\pi$$
−0.707055 + 0.707159i $$0.749977\pi$$
$$374$$ −19.1168 −0.988508
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −5.48913 −0.282704
$$378$$ 0 0
$$379$$ 9.11684 0.468301 0.234150 0.972200i $$-0.424769\pi$$
0.234150 + 0.972200i $$0.424769\pi$$
$$380$$ 6.86141 0.351983
$$381$$ 0 0
$$382$$ 1.88316 0.0963506
$$383$$ −10.6277 18.4077i −0.543051 0.940592i −0.998727 0.0504462i $$-0.983936\pi$$
0.455676 0.890146i $$-0.349398\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −7.00000 −0.356291
$$387$$ 0 0
$$388$$ −4.55842 7.89542i −0.231419 0.400829i
$$389$$ −17.4891 + 30.2921i −0.886734 + 1.53587i −0.0430204 + 0.999074i $$0.513698\pi$$
−0.843713 + 0.536794i $$0.819635\pi$$
$$390$$ 0 0
$$391$$ −16.1168 + 27.9152i −0.815064 + 1.41173i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 6.00000 0.302276
$$395$$ −8.31386 14.4000i −0.418316 0.724544i
$$396$$ 0 0
$$397$$ 11.0000 19.0526i 0.552074 0.956221i −0.446051 0.895008i $$-0.647170\pi$$
0.998125 0.0612128i $$-0.0194968\pi$$
$$398$$ 5.00000 + 8.66025i 0.250627 + 0.434099i
$$399$$ 0 0
$$400$$ 1.55842 2.69927i 0.0779211 0.134963i
$$401$$ −0.127719 0.221215i −0.00637797 0.0110470i 0.862819 0.505513i $$-0.168697\pi$$
−0.869197 + 0.494466i $$0.835364\pi$$
$$402$$ 0 0
$$403$$ −2.00000 + 3.46410i −0.0996271 + 0.172559i
$$404$$ 3.68614 6.38458i 0.183392 0.317645i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 4.37228 + 7.57301i 0.216726 + 0.375380i
$$408$$ 0 0
$$409$$ 29.3505 1.45129 0.725645 0.688069i $$-0.241541\pi$$
0.725645 + 0.688069i $$0.241541\pi$$
$$410$$ −14.2337 −0.702952
$$411$$ 0 0
$$412$$ 5.00000 + 8.66025i 0.246332 + 0.426660i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −3.76631 + 6.52344i −0.184881 + 0.320223i
$$416$$ −1.00000 + 1.73205i −0.0490290 + 0.0849208i
$$417$$ 0 0
$$418$$ 10.9307 + 18.9325i 0.534638 + 0.926020i
$$419$$ 13.8030 23.9075i 0.674320 1.16796i −0.302347 0.953198i $$-0.597770\pi$$
0.976667 0.214759i $$-0.0688964\pi$$
$$420$$ 0 0
$$421$$ 0.116844 + 0.202380i 0.00569463 + 0.00986338i 0.868859 0.495060i $$-0.164854\pi$$
−0.863164 + 0.504924i $$0.831521\pi$$
$$422$$ 8.00000 13.8564i 0.389434 0.674519i
$$423$$ 0 0
$$424$$ 1.37228 + 2.37686i 0.0666439 + 0.115431i
$$425$$ −13.6277 −0.661041
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −0.813859 + 1.40965i −0.0393394 + 0.0681378i
$$429$$ 0 0
$$430$$ −6.25544 + 10.8347i −0.301664 + 0.522497i
$$431$$ −14.7446 25.5383i −0.710221 1.23014i −0.964774 0.263079i $$-0.915262\pi$$
0.254554 0.967059i $$-0.418071\pi$$
$$432$$ 0 0
$$433$$ −2.88316 −0.138556 −0.0692778 0.997597i $$-0.522069\pi$$
−0.0692778 + 0.997597i $$0.522069\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −7.00000 12.1244i −0.335239 0.580651i
$$437$$ 36.8614 1.76332
$$438$$ 0 0
$$439$$ 8.00000 0.381819 0.190910 0.981608i $$-0.438856\pi$$
0.190910 + 0.981608i $$0.438856\pi$$
$$440$$ −6.00000 −0.286039
$$441$$ 0 0
$$442$$ 8.74456 0.415936
$$443$$ 22.8832 1.08721 0.543606 0.839341i $$-0.317059\pi$$
0.543606 + 0.839341i $$0.317059\pi$$
$$444$$ 0 0
$$445$$ −4.46738 −0.211774
$$446$$ 2.00000 + 3.46410i 0.0947027 + 0.164030i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −33.0000 −1.55737 −0.778683 0.627417i $$-0.784112\pi$$
−0.778683 + 0.627417i $$0.784112\pi$$
$$450$$ 0 0
$$451$$ −22.6753 39.2747i −1.06774 1.84937i
$$452$$ 0.686141 1.18843i 0.0322733 0.0558991i
$$453$$ 0 0
$$454$$ −11.8723 + 20.5634i −0.557194 + 0.965088i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 33.4674 1.56554 0.782769 0.622312i $$-0.213807\pi$$
0.782769 + 0.622312i $$0.213807\pi$$
$$458$$ 10.0584 + 17.4217i 0.469999 + 0.814062i
$$459$$ 0 0
$$460$$ −5.05842 + 8.76144i −0.235850 + 0.408504i
$$461$$ 15.4307 + 26.7268i 0.718680 + 1.24479i 0.961523 + 0.274724i $$0.0885865\pi$$
−0.242844 + 0.970065i $$0.578080\pi$$
$$462$$ 0 0
$$463$$ 2.94158 5.09496i 0.136707 0.236783i −0.789541 0.613697i $$-0.789682\pi$$
0.926248 + 0.376914i $$0.123015\pi$$
$$464$$ 1.37228 + 2.37686i 0.0637066 + 0.110343i
$$465$$ 0 0
$$466$$ −5.87228 + 10.1711i −0.272028 + 0.471167i
$$467$$ −15.0475 + 26.0631i −0.696317 + 1.20606i 0.273417 + 0.961896i $$0.411846\pi$$
−0.969735 + 0.244162i $$0.921487\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −7.11684 −0.327579
$$473$$ −39.8614 −1.83283
$$474$$ 0 0
$$475$$ 7.79211 + 13.4963i 0.357527 + 0.619254i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −9.43070 + 16.3345i −0.431350 + 0.747121i
$$479$$ 10.6277 18.4077i 0.485593 0.841072i −0.514270 0.857628i $$-0.671937\pi$$
0.999863 + 0.0165568i $$0.00527043\pi$$
$$480$$ 0 0
$$481$$ −2.00000 3.46410i −0.0911922 0.157949i
$$482$$ −0.441578 + 0.764836i −0.0201133 + 0.0348373i
$$483$$ 0 0
$$484$$ −4.05842 7.02939i −0.184474 0.319518i
$$485$$ −6.25544 + 10.8347i −0.284045 + 0.491980i
$$486$$ 0 0
$$487$$ 8.17527 + 14.1600i 0.370457 + 0.641650i 0.989636 0.143600i $$-0.0458679\pi$$
−0.619179 + 0.785250i $$0.712535\pi$$
$$488$$ −14.1168 −0.639040
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −9.81386 + 16.9981i −0.442893 + 0.767114i −0.997903 0.0647303i $$-0.979381\pi$$
0.555010 + 0.831844i $$0.312715\pi$$
$$492$$ 0 0
$$493$$ 6.00000 10.3923i 0.270226 0.468046i
$$494$$ −5.00000 8.66025i −0.224961 0.389643i
$$495$$ 0 0
$$496$$ 2.00000 0.0898027
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −0.441578 0.764836i −0.0197677 0.0342387i 0.855972 0.517022i $$-0.172959\pi$$
−0.875740 + 0.482783i $$0.839626\pi$$
$$500$$ −11.1386 −0.498133
$$501$$ 0 0
$$502$$ 9.00000 0.401690
$$503$$ −2.23369 −0.0995952 −0.0497976 0.998759i $$-0.515858\pi$$
−0.0497976 + 0.998759i $$0.515858\pi$$
$$504$$ 0 0
$$505$$ −10.1168 −0.450194
$$506$$ −32.2337 −1.43296
$$507$$ 0 0
$$508$$ −14.1168 −0.626334
$$509$$ 8.48913 + 14.7036i 0.376274 + 0.651725i 0.990517 0.137392i $$-0.0438718\pi$$
−0.614243 + 0.789117i $$0.710539\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 10.9307 + 18.9325i 0.482133 + 0.835078i
$$515$$ 6.86141 11.8843i 0.302350 0.523685i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 2.74456 0.120357
$$521$$ 1.93070 + 3.34408i 0.0845856 + 0.146507i 0.905215 0.424955i $$-0.139710\pi$$
−0.820629 + 0.571461i $$0.806377\pi$$
$$522$$ 0 0
$$523$$ 8.94158 15.4873i 0.390988 0.677211i −0.601592 0.798803i $$-0.705467\pi$$
0.992580 + 0.121592i $$0.0388001\pi$$
$$524$$ −3.68614 6.38458i −0.161030 0.278912i
$$525$$ 0 0
$$526$$ 6.68614 11.5807i 0.291530 0.504944i
$$527$$ −4.37228 7.57301i −0.190460 0.329886i
$$528$$ 0 0
$$529$$ −15.6753 + 27.1504i −0.681533 + 1.18045i
$$530$$ 1.88316 3.26172i 0.0817991 0.141680i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 10.3723 + 17.9653i 0.449273 + 0.778164i
$$534$$ 0 0
$$535$$ 2.23369 0.0965708
$$536$$ 15.1168 0.652948
$$537$$ 0 0
$$538$$ −3.68614 6.38458i −0.158921 0.275259i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −14.1168 + 24.4511i −0.606931 + 1.05123i 0.384813 + 0.922995i $$0.374266\pi$$
−0.991743 + 0.128240i $$0.959067\pi$$
$$542$$ 9.11684 15.7908i 0.391602 0.678275i
$$543$$ 0 0
$$544$$ −2.18614 3.78651i −0.0937300 0.162345i
$$545$$ −9.60597 + 16.6380i −0.411475 + 0.712695i
$$546$$ 0 0
$$547$$ −0.441578 0.764836i −0.0188805 0.0327020i 0.856431 0.516262i $$-0.172677\pi$$
−0.875311 + 0.483560i $$0.839344\pi$$
$$548$$ 8.18614 14.1788i 0.349695 0.605689i
$$549$$ 0 0
$$550$$ −6.81386 11.8020i −0.290544 0.503237i
$$551$$ −13.7228 −0.584611
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −11.1168 + 19.2549i −0.472309 + 0.818064i
$$555$$ 0 0
$$556$$ 10.6168 18.3889i 0.450254 0.779864i
$$557$$ 3.25544 + 5.63858i 0.137937 + 0.238914i 0.926716 0.375763i $$-0.122619\pi$$
−0.788778 + 0.614678i $$0.789286\pi$$
$$558$$ 0 0
$$559$$ 18.2337 0.771203
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 5.31386 + 9.20387i 0.224152 + 0.388242i
$$563$$ −3.00000 −0.126435 −0.0632175 0.998000i $$-0.520136\pi$$
−0.0632175 + 0.998000i $$0.520136\pi$$
$$564$$ 0 0
$$565$$ −1.88316 −0.0792250
$$566$$ 9.88316 0.415420
$$567$$ 0 0
$$568$$ −10.1168 −0.424493
$$569$$ 1.11684 0.0468205 0.0234103 0.999726i $$-0.492548\pi$$
0.0234103 + 0.999726i $$0.492548\pi$$
$$570$$ 0 0
$$571$$ 29.3505 1.22828 0.614141 0.789197i $$-0.289503\pi$$
0.614141 + 0.789197i $$0.289503\pi$$
$$572$$ 4.37228 + 7.57301i 0.182814 + 0.316644i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −22.9783 −0.958259
$$576$$ 0 0
$$577$$ −13.5584 23.4839i −0.564444 0.977647i −0.997101 0.0760878i $$-0.975757\pi$$
0.432657 0.901559i $$-0.357576\pi$$
$$578$$ −1.05842 + 1.83324i −0.0440246 + 0.0762528i
$$579$$ 0 0
$$580$$ 1.88316 3.26172i 0.0781938 0.135436i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 12.0000 0.496989
$$584$$ 2.55842 + 4.43132i 0.105868 + 0.183369i
$$585$$ 0 0
$$586$$ −2.31386 + 4.00772i −0.0955846 + 0.165557i
$$587$$ −4.24456 7.35180i −0.175192 0.303441i 0.765036 0.643988i $$-0.222721\pi$$
−0.940228 + 0.340547i $$0.889388\pi$$
$$588$$ 0 0
$$589$$ −5.00000 + 8.66025i −0.206021 + 0.356840i
$$590$$ 4.88316 + 8.45787i 0.201036 + 0.348205i
$$591$$ 0 0
$$592$$ −1.00000 + 1.73205i −0.0410997 + 0.0711868i
$$593$$ 1.62772 2.81929i 0.0668424 0.115774i −0.830667 0.556769i $$-0.812041\pi$$
0.897510 + 0.440995i $$0.145374\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 7.37228 + 12.7692i 0.301980 + 0.523045i
$$597$$ 0 0
$$598$$ 14.7446 0.602950
$$599$$ −24.0000 −0.980613 −0.490307 0.871550i $$-0.663115\pi$$
−0.490307 + 0.871550i $$0.663115\pi$$
$$600$$ 0 0
$$601$$ −3.44158 5.96099i −0.140385 0.243154i 0.787257 0.616625i $$-0.211501\pi$$
−0.927642 + 0.373472i $$0.878167\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 4.05842 7.02939i 0.165135 0.286022i
$$605$$ −5.56930 + 9.64630i −0.226424 + 0.392178i
$$606$$ 0 0
$$607$$ 6.11684 + 10.5947i 0.248275 + 0.430025i 0.963047 0.269332i $$-0.0868030\pi$$
−0.714772 + 0.699357i $$0.753470\pi$$
$$608$$ −2.50000 + 4.33013i −0.101388 + 0.175610i
$$609$$ 0 0
$$610$$ 9.68614 + 16.7769i 0.392180 + 0.679276i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0.883156 + 1.52967i 0.0356703 + 0.0617828i 0.883309 0.468790i $$-0.155310\pi$$
−0.847639 + 0.530573i $$0.821977\pi$$
$$614$$ −13.0000 −0.524637
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −4.93070 + 8.54023i −0.198503 + 0.343817i −0.948043 0.318142i $$-0.896941\pi$$
0.749540 + 0.661959i $$0.230275\pi$$
$$618$$ 0 0
$$619$$ 11.7337 20.3233i 0.471617 0.816864i −0.527856 0.849334i $$-0.677004\pi$$
0.999473 + 0.0324697i $$0.0103373\pi$$
$$620$$ −1.37228 2.37686i −0.0551121 0.0954570i
$$621$$ 0 0
$$622$$ 26.2337 1.05188
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.149468 0.258886i −0.00597872 0.0103555i
$$626$$ −2.88316 −0.115234
$$627$$ 0 0
$$628$$ −8.11684 −0.323897
$$629$$ 8.74456 0.348669
$$630$$ 0 0
$$631$$ 14.3505 0.571286 0.285643 0.958336i $$-0.407793\pi$$
0.285643 + 0.958336i $$0.407793\pi$$
$$632$$ 12.1168 0.481982
$$633$$ 0 0
$$634$$ 6.00000 0.238290
$$635$$ 9.68614 + 16.7769i 0.384383 + 0.665770i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 12.0000 0.475085
$$639$$ 0 0
$$640$$ −0.686141 1.18843i −0.0271221 0.0469768i
$$641$$ −23.1060 + 40.0207i −0.912631 + 1.58072i −0.102298 + 0.994754i $$0.532619\pi$$
−0.810333 + 0.585969i $$0.800714\pi$$
$$642$$ 0 0
$$643$$ 12.6753 21.9542i 0.499864 0.865789i −0.500136 0.865947i $$-0.666717\pi$$
1.00000 0.000157386i $$5.00974e-5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 21.8614 0.860126
$$647$$ −8.74456 15.1460i −0.343784 0.595452i 0.641348 0.767250i $$-0.278376\pi$$
−0.985132 + 0.171798i $$0.945042\pi$$
$$648$$ 0 0
$$649$$ −15.5584 + 26.9480i −0.610721 + 1.05780i
$$650$$ 3.11684 + 5.39853i 0.122253 + 0.211748i
$$651$$ 0 0
$$652$$ −8.11684 + 14.0588i −0.317880 + 0.550585i
$$653$$ −7.62772 13.2116i −0.298496 0.517010i 0.677296 0.735710i $$-0.263152\pi$$
−0.975792 + 0.218701i $$0.929818\pi$$
$$654$$ 0 0
$$655$$ −5.05842 + 8.76144i −0.197649 + 0.342338i
$$656$$ 5.18614 8.98266i 0.202485 0.350714i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −4.62772 8.01544i −0.180270 0.312237i 0.761702 0.647927i $$-0.224364\pi$$
−0.941973 + 0.335690i $$0.891031\pi$$
$$660$$ 0 0
$$661$$ 9.88316 0.384410 0.192205 0.981355i $$-0.438436\pi$$
0.192205 + 0.981355i $$0.438436\pi$$
$$662$$ −12.2337 −0.475476
$$663$$ 0 0
$$664$$ −2.74456 4.75372i −0.106510 0.184480i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 10.1168 17.5229i 0.391726 0.678489i
$$668$$ 8.74456 15.1460i 0.338337 0.586017i
$$669$$ 0 0
$$670$$ −10.3723 17.9653i −0.400716 0.694061i
$$671$$ −30.8614 + 53.4535i −1.19139 + 2.06355i
$$672$$ 0 0
$$673$$ 10.0584 + 17.4217i 0.387724 + 0.671557i 0.992143 0.125109i $$-0.0399281\pi$$
−0.604419 + 0.796666i $$0.706595\pi$$
$$674$$ −4.55842 + 7.89542i −0.175584 + 0.304120i
$$675$$ 0 0
$$676$$ 4.50000 + 7.79423i 0.173077 + 0.299778i
$$677$$ 34.4674 1.32469 0.662344 0.749199i $$-0.269562\pi$$
0.662344 + 0.749199i $$0.269562\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −3.00000 + 5.19615i −0.115045 + 0.199263i
$$681$$ 0 0
$$682$$ 4.37228 7.57301i 0.167423 0.289986i
$$683$$ −22.4198 38.8323i −0.857871 1.48588i −0.873956 0.486005i $$-0.838454\pi$$
0.0160849 0.999871i $$-0.494880\pi$$
$$684$$ 0 0
$$685$$ −22.4674 −0.858434
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −4.55842 7.89542i −0.173788 0.301010i
$$689$$ −5.48913 −0.209119
$$690$$ 0 0
$$691$$ −5.88316 −0.223806 −0.111903 0.993719i $$-0.535695\pi$$
−0.111903 + 0.993719i $$0.535695\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ −7.11684 −0.270152
$$695$$ −29.1386 −1.10529
$$696$$ 0 0
$$697$$ −45.3505 −1.71777
$$698$$ 11.0000 + 19.0526i 0.416356 + 0.721150i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 3.76631 0.142252 0.0711258 0.997467i $$-0.477341\pi$$
0.0711258 + 0.997467i $$0.477341\pi$$
$$702$$ 0 0
$$703$$ −5.00000 8.66025i −0.188579 0.326628i
$$704$$ 2.18614 3.78651i 0.0823933 0.142709i
$$705$$ 0 0
$$706$$ −3.81386 + 6.60580i −0.143536 + 0.248612i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 44.0000 1.65245 0.826227 0.563337i $$-0.190483\pi$$
0.826227 + 0.563337i $$0.190483\pi$$
$$710$$ 6.94158 + 12.0232i 0.260513 + 0.451221i
$$711$$ 0 0
$$712$$ 1.62772 2.81929i 0.0610013 0.105657i
$$713$$ −7.37228 12.7692i −0.276094 0.478209i
$$714$$ 0 0
$$715$$ 6.00000 10.3923i 0.224387 0.388650i
$$716$$ 7.37228 + 12.7692i 0.275515 + 0.477206i
$$717$$ 0 0
$$718$$ −3.43070 + 5.94215i −0.128033 + 0.221759i
$$719$$ −4.37228 + 7.57301i −0.163059 + 0.282426i −0.935964 0.352095i $$-0.885469\pi$$
0.772906 + 0.634521i $$0.218803\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −3.00000 5.19615i −0.111648 0.193381i
$$723$$ 0 0
$$724$$ 18.1168 0.673307
$$725$$ 8.55437 0.317701
$$726$$ 0 0
$$727$$ 0.883156 + 1.52967i 0.0327544 + 0.0567324i 0.881938 0.471366i $$-0.156239\pi$$
−0.849183 + 0.528098i $$0.822905\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 3.51087 6.08101i 0.129943 0.225068i
$$731$$ −19.9307 + 34.5210i −0.737164 + 1.27680i
$$732$$ 0 0
$$733$$ 11.9416 + 20.6834i 0.441072 + 0.763960i 0.997769 0.0667560i $$-0.0212649\pi$$
−0.556697 + 0.830716i $$0.687932\pi$$
$$734$$ −11.1168 + 19.2549i −0.410330 + 0.710713i
$$735$$ 0 0
$$736$$ −3.68614 6.38458i −0.135873 0.235339i
$$737$$ 33.0475 57.2400i 1.21732 2.10846i
$$738$$ 0 0
$$739$$ −4.55842 7.89542i −0.167684 0.290438i 0.769921 0.638139i $$-0.220296\pi$$
−0.937605 + 0.347702i $$0.886962\pi$$
$$740$$ 2.74456 0.100892
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 21.8614 37.8651i 0.802017 1.38913i −0.116269 0.993218i $$-0.537094\pi$$
0.918286 0.395917i $$-0.129573\pi$$
$$744$$ 0 0
$$745$$ 10.1168 17.5229i 0.370652 0.641989i
$$746$$ 5.00000 + 8.66025i 0.183063 + 0.317074i
$$747$$ 0 0
$$748$$ −19.1168 −0.698981
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −0.0584220 0.101190i −0.00213185 0.00369247i 0.864958 0.501845i $$-0.167345\pi$$
−0.867089 + 0.498153i $$0.834012\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ −5.48913 −0.199902
$$755$$ −11.1386 −0.405375
$$756$$ 0 0
$$757$$ 11.7663 0.427654 0.213827 0.976872i $$-0.431407\pi$$
0.213827 + 0.976872i $$0.431407\pi$$
$$758$$ 9.11684 0.331139
$$759$$ 0 0
$$760$$ 6.86141 0.248889
$$761$$ 6.25544 + 10.8347i 0.226759 + 0.392759i 0.956846 0.290596i $$-0.0938536\pi$$
−0.730086 + 0.683355i $$0.760520\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 1.88316 0.0681302
$$765$$ 0 0
$$766$$ −10.6277 18.4077i −0.383995 0.665099i
$$767$$ 7.11684 12.3267i 0.256974 0.445093i
$$768$$ 0 0
$$769$$ 5.00000 8.66025i 0.180305 0.312297i −0.761680 0.647954i $$-0.775625\pi$$
0.941984 + 0.335657i $$0.108958\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −7.00000 −0.251936
$$773$$ −5.56930 9.64630i −0.200314 0.346953i 0.748316 0.663343i $$-0.230863\pi$$
−0.948629 + 0.316389i $$0.897529\pi$$
$$774$$ 0 0
$$775$$ 3.11684 5.39853i 0.111960 0.193921i
$$776$$ −4.55842 7.89542i −0.163638 0.283429i
$$777$$ 0 0
$$778$$ −17.4891 + 30.2921i −0.627016 + 1.08602i
$$779$$ 25.9307 + 44.9133i 0.929064 + 1.60919i
$$780$$ 0 0
$$781$$ −22.1168 + 38.3075i −0.791403 + 1.37075i
$$782$$ −16.1168 + 27.9152i −0.576337 + 0.998245i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 5.56930 + 9.64630i 0.198777 + 0.344291i
$$786$$ 0 0
$$787$$ −4.00000 −0.142585 −0.0712923 0.997455i $$-0.522712\pi$$
−0.0712923 + 0.997455i $$0.522712\pi$$
$$788$$ 6.00000 0.213741
$$789$$ 0 0
$$790$$ −8.31386 14.4000i −0.295794 0.512330i
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 14.1168 24.4511i 0.501304 0.868284i
$$794$$ 11.0000 19.0526i 0.390375 0.676150i