# Properties

 Label 1400.2.x.c.993.2 Level $1400$ Weight $2$ Character 1400.993 Analytic conductor $11.179$ Analytic rank $0$ Dimension $32$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1400 = 2^{3} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1400.x (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$11.1790562830$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$16$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 993.2 Character $$\chi$$ $$=$$ 1400.993 Dual form 1400.2.x.c.657.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.09284 + 2.09284i) q^{3} +(2.59595 + 0.510946i) q^{7} -5.75996i q^{9} +O(q^{10})$$ $$q+(-2.09284 + 2.09284i) q^{3} +(2.59595 + 0.510946i) q^{7} -5.75996i q^{9} -3.94864 q^{11} +(1.69798 - 1.69798i) q^{13} +(2.66927 + 2.66927i) q^{17} +5.36102 q^{19} +(-6.50223 + 4.36357i) q^{21} +(3.55527 + 3.55527i) q^{23} +(5.77616 + 5.77616i) q^{27} -7.24449i q^{29} -0.174160i q^{31} +(8.26386 - 8.26386i) q^{33} +(4.85737 - 4.85737i) q^{37} +7.10719i q^{39} -0.732583i q^{41} +(8.20187 + 8.20187i) q^{43} +(2.31716 + 2.31716i) q^{47} +(6.47787 + 2.65278i) q^{49} -11.1727 q^{51} +(-4.53449 - 4.53449i) q^{53} +(-11.2198 + 11.2198i) q^{57} -13.1904 q^{59} +13.3556i q^{61} +(2.94303 - 14.9525i) q^{63} +(-6.55658 + 6.55658i) q^{67} -14.8812 q^{69} +16.3312 q^{71} +(-7.02549 + 7.02549i) q^{73} +(-10.2504 - 2.01754i) q^{77} -6.63234i q^{79} -6.89727 q^{81} +(-10.4642 + 10.4642i) q^{83} +(15.1616 + 15.1616i) q^{87} +3.43554 q^{89} +(5.27543 - 3.54028i) q^{91} +(0.364490 + 0.364490i) q^{93} +(-1.40892 - 1.40892i) q^{97} +22.7440i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$32q + O(q^{10})$$ $$32q - 16q^{11} - 40q^{21} + 32q^{51} + 128q^{71} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$$.

 $$n$$ $$351$$ $$701$$ $$801$$ $$1177$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −2.09284 + 2.09284i −1.20830 + 1.20830i −0.236725 + 0.971577i $$0.576074\pi$$
−0.971577 + 0.236725i $$0.923926\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.59595 + 0.510946i 0.981175 + 0.193119i
$$8$$ 0 0
$$9$$ 5.75996i 1.91999i
$$10$$ 0 0
$$11$$ −3.94864 −1.19056 −0.595279 0.803519i $$-0.702959\pi$$
−0.595279 + 0.803519i $$0.702959\pi$$
$$12$$ 0 0
$$13$$ 1.69798 1.69798i 0.470934 0.470934i −0.431283 0.902217i $$-0.641939\pi$$
0.902217 + 0.431283i $$0.141939\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2.66927 + 2.66927i 0.647392 + 0.647392i 0.952362 0.304970i $$-0.0986464\pi$$
−0.304970 + 0.952362i $$0.598646\pi$$
$$18$$ 0 0
$$19$$ 5.36102 1.22990 0.614952 0.788565i $$-0.289176\pi$$
0.614952 + 0.788565i $$0.289176\pi$$
$$20$$ 0 0
$$21$$ −6.50223 + 4.36357i −1.41890 + 0.952209i
$$22$$ 0 0
$$23$$ 3.55527 + 3.55527i 0.741325 + 0.741325i 0.972833 0.231508i $$-0.0743660\pi$$
−0.231508 + 0.972833i $$0.574366\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 5.77616 + 5.77616i 1.11162 + 1.11162i
$$28$$ 0 0
$$29$$ 7.24449i 1.34527i −0.739975 0.672634i $$-0.765163\pi$$
0.739975 0.672634i $$-0.234837\pi$$
$$30$$ 0 0
$$31$$ 0.174160i 0.0312801i −0.999878 0.0156401i $$-0.995021\pi$$
0.999878 0.0156401i $$-0.00497859\pi$$
$$32$$ 0 0
$$33$$ 8.26386 8.26386i 1.43855 1.43855i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 4.85737 4.85737i 0.798547 0.798547i −0.184320 0.982866i $$-0.559008\pi$$
0.982866 + 0.184320i $$0.0590081\pi$$
$$38$$ 0 0
$$39$$ 7.10719i 1.13806i
$$40$$ 0 0
$$41$$ 0.732583i 0.114410i −0.998362 0.0572051i $$-0.981781\pi$$
0.998362 0.0572051i $$-0.0182189\pi$$
$$42$$ 0 0
$$43$$ 8.20187 + 8.20187i 1.25077 + 1.25077i 0.955374 + 0.295400i $$0.0954529\pi$$
0.295400 + 0.955374i $$0.404547\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 2.31716 + 2.31716i 0.337993 + 0.337993i 0.855612 0.517619i $$-0.173181\pi$$
−0.517619 + 0.855612i $$0.673181\pi$$
$$48$$ 0 0
$$49$$ 6.47787 + 2.65278i 0.925410 + 0.378968i
$$50$$ 0 0
$$51$$ −11.1727 −1.56449
$$52$$ 0 0
$$53$$ −4.53449 4.53449i −0.622860 0.622860i 0.323402 0.946262i $$-0.395173\pi$$
−0.946262 + 0.323402i $$0.895173\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −11.2198 + 11.2198i −1.48609 + 1.48609i
$$58$$ 0 0
$$59$$ −13.1904 −1.71724 −0.858620 0.512613i $$-0.828678\pi$$
−0.858620 + 0.512613i $$0.828678\pi$$
$$60$$ 0 0
$$61$$ 13.3556i 1.71001i 0.518622 + 0.855004i $$0.326445\pi$$
−0.518622 + 0.855004i $$0.673555\pi$$
$$62$$ 0 0
$$63$$ 2.94303 14.9525i 0.370787 1.88384i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −6.55658 + 6.55658i −0.801014 + 0.801014i −0.983254 0.182240i $$-0.941665\pi$$
0.182240 + 0.983254i $$0.441665\pi$$
$$68$$ 0 0
$$69$$ −14.8812 −1.79149
$$70$$ 0 0
$$71$$ 16.3312 1.93816 0.969081 0.246742i $$-0.0793599\pi$$
0.969081 + 0.246742i $$0.0793599\pi$$
$$72$$ 0 0
$$73$$ −7.02549 + 7.02549i −0.822271 + 0.822271i −0.986433 0.164162i $$-0.947508\pi$$
0.164162 + 0.986433i $$0.447508\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −10.2504 2.01754i −1.16815 0.229920i
$$78$$ 0 0
$$79$$ 6.63234i 0.746197i −0.927792 0.373098i $$-0.878295\pi$$
0.927792 0.373098i $$-0.121705\pi$$
$$80$$ 0 0
$$81$$ −6.89727 −0.766363
$$82$$ 0 0
$$83$$ −10.4642 + 10.4642i −1.14860 + 1.14860i −0.161766 + 0.986829i $$0.551719\pi$$
−0.986829 + 0.161766i $$0.948281\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 15.1616 + 15.1616i 1.62549 + 1.62549i
$$88$$ 0 0
$$89$$ 3.43554 0.364166 0.182083 0.983283i $$-0.441716\pi$$
0.182083 + 0.983283i $$0.441716\pi$$
$$90$$ 0 0
$$91$$ 5.27543 3.54028i 0.553015 0.371122i
$$92$$ 0 0
$$93$$ 0.364490 + 0.364490i 0.0377958 + 0.0377958i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −1.40892 1.40892i −0.143054 0.143054i 0.631953 0.775007i $$-0.282254\pi$$
−0.775007 + 0.631953i $$0.782254\pi$$
$$98$$ 0 0
$$99$$ 22.7440i 2.28586i
$$100$$ 0 0
$$101$$ 12.1783i 1.21178i 0.795547 + 0.605891i $$0.207183\pi$$
−0.795547 + 0.605891i $$0.792817\pi$$
$$102$$ 0 0
$$103$$ 9.52421 9.52421i 0.938449 0.938449i −0.0597638 0.998213i $$-0.519035\pi$$
0.998213 + 0.0597638i $$0.0190348\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −8.98949 + 8.98949i −0.869046 + 0.869046i −0.992367 0.123321i $$-0.960646\pi$$
0.123321 + 0.992367i $$0.460646\pi$$
$$108$$ 0 0
$$109$$ 3.86269i 0.369979i −0.982741 0.184989i $$-0.940775\pi$$
0.982741 0.184989i $$-0.0592251\pi$$
$$110$$ 0 0
$$111$$ 20.3314i 1.92977i
$$112$$ 0 0
$$113$$ 2.94525 + 2.94525i 0.277066 + 0.277066i 0.831937 0.554870i $$-0.187232\pi$$
−0.554870 + 0.831937i $$0.687232\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −9.78028 9.78028i −0.904187 0.904187i
$$118$$ 0 0
$$119$$ 5.56542 + 8.29312i 0.510181 + 0.760229i
$$120$$ 0 0
$$121$$ 4.59172 0.417429
$$122$$ 0 0
$$123$$ 1.53318 + 1.53318i 0.138242 + 0.138242i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −1.73709 + 1.73709i −0.154142 + 0.154142i −0.779965 0.625823i $$-0.784763\pi$$
0.625823 + 0.779965i $$0.284763\pi$$
$$128$$ 0 0
$$129$$ −34.3304 −3.02262
$$130$$ 0 0
$$131$$ 2.70296i 0.236158i 0.993004 + 0.118079i $$0.0376737\pi$$
−0.993004 + 0.118079i $$0.962326\pi$$
$$132$$ 0 0
$$133$$ 13.9169 + 2.73919i 1.20675 + 0.237518i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 3.26814 3.26814i 0.279216 0.279216i −0.553580 0.832796i $$-0.686739\pi$$
0.832796 + 0.553580i $$0.186739\pi$$
$$138$$ 0 0
$$139$$ 21.4638 1.82054 0.910269 0.414017i $$-0.135874\pi$$
0.910269 + 0.414017i $$0.135874\pi$$
$$140$$ 0 0
$$141$$ −9.69891 −0.816795
$$142$$ 0 0
$$143$$ −6.70469 + 6.70469i −0.560674 + 0.560674i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −19.1090 + 8.00531i −1.57608 + 0.660267i
$$148$$ 0 0
$$149$$ 2.09645i 0.171747i −0.996306 0.0858737i $$-0.972632\pi$$
0.996306 0.0858737i $$-0.0273682\pi$$
$$150$$ 0 0
$$151$$ 1.78039 0.144886 0.0724432 0.997373i $$-0.476920\pi$$
0.0724432 + 0.997373i $$0.476920\pi$$
$$152$$ 0 0
$$153$$ 15.3749 15.3749i 1.24298 1.24298i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 4.64528 + 4.64528i 0.370734 + 0.370734i 0.867744 0.497011i $$-0.165569\pi$$
−0.497011 + 0.867744i $$0.665569\pi$$
$$158$$ 0 0
$$159$$ 18.9799 1.50521
$$160$$ 0 0
$$161$$ 7.41274 + 11.0458i 0.584205 + 0.870534i
$$162$$ 0 0
$$163$$ 1.67419 + 1.67419i 0.131132 + 0.131132i 0.769627 0.638494i $$-0.220442\pi$$
−0.638494 + 0.769627i $$0.720442\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −1.65522 1.65522i −0.128084 0.128084i 0.640158 0.768243i $$-0.278869\pi$$
−0.768243 + 0.640158i $$0.778869\pi$$
$$168$$ 0 0
$$169$$ 7.23375i 0.556443i
$$170$$ 0 0
$$171$$ 30.8793i 2.36140i
$$172$$ 0 0
$$173$$ −0.949313 + 0.949313i −0.0721750 + 0.0721750i −0.742273 0.670098i $$-0.766252\pi$$
0.670098 + 0.742273i $$0.266252\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 27.6053 27.6053i 2.07494 2.07494i
$$178$$ 0 0
$$179$$ 16.6926i 1.24767i −0.781558 0.623833i $$-0.785575\pi$$
0.781558 0.623833i $$-0.214425\pi$$
$$180$$ 0 0
$$181$$ 18.6406i 1.38554i −0.721158 0.692771i $$-0.756390\pi$$
0.721158 0.692771i $$-0.243610\pi$$
$$182$$ 0 0
$$183$$ −27.9511 27.9511i −2.06621 2.06621i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −10.5400 10.5400i −0.770758 0.770758i
$$188$$ 0 0
$$189$$ 12.0433 + 17.9459i 0.876020 + 1.30537i
$$190$$ 0 0
$$191$$ −4.33648 −0.313777 −0.156888 0.987616i $$-0.550146\pi$$
−0.156888 + 0.987616i $$0.550146\pi$$
$$192$$ 0 0
$$193$$ 11.8884 + 11.8884i 0.855747 + 0.855747i 0.990834 0.135087i $$-0.0431313\pi$$
−0.135087 + 0.990834i $$0.543131\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2.85131 2.85131i 0.203148 0.203148i −0.598200 0.801347i $$-0.704117\pi$$
0.801347 + 0.598200i $$0.204117\pi$$
$$198$$ 0 0
$$199$$ −4.34228 −0.307816 −0.153908 0.988085i $$-0.549186\pi$$
−0.153908 + 0.988085i $$0.549186\pi$$
$$200$$ 0 0
$$201$$ 27.4438i 1.93573i
$$202$$ 0 0
$$203$$ 3.70154 18.8063i 0.259797 1.31994i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 20.4782 20.4782i 1.42333 1.42333i
$$208$$ 0 0
$$209$$ −21.1687 −1.46427
$$210$$ 0 0
$$211$$ −18.8362 −1.29674 −0.648369 0.761326i $$-0.724549\pi$$
−0.648369 + 0.761326i $$0.724549\pi$$
$$212$$ 0 0
$$213$$ −34.1787 + 34.1787i −2.34189 + 2.34189i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0.0889865 0.452111i 0.00604080 0.0306913i
$$218$$ 0 0
$$219$$ 29.4065i 1.98710i
$$220$$ 0 0
$$221$$ 9.06470 0.609758
$$222$$ 0 0
$$223$$ −13.9232 + 13.9232i −0.932366 + 0.932366i −0.997853 0.0654872i $$-0.979140\pi$$
0.0654872 + 0.997853i $$0.479140\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 6.91799 + 6.91799i 0.459163 + 0.459163i 0.898381 0.439218i $$-0.144744\pi$$
−0.439218 + 0.898381i $$0.644744\pi$$
$$228$$ 0 0
$$229$$ 1.64658 0.108809 0.0544047 0.998519i $$-0.482674\pi$$
0.0544047 + 0.998519i $$0.482674\pi$$
$$230$$ 0 0
$$231$$ 25.6749 17.2302i 1.68929 1.13366i
$$232$$ 0 0
$$233$$ 4.73081 + 4.73081i 0.309926 + 0.309926i 0.844881 0.534955i $$-0.179671\pi$$
−0.534955 + 0.844881i $$0.679671\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 13.8804 + 13.8804i 0.901631 + 0.901631i
$$238$$ 0 0
$$239$$ 5.18344i 0.335289i −0.985848 0.167644i $$-0.946384\pi$$
0.985848 0.167644i $$-0.0536160\pi$$
$$240$$ 0 0
$$241$$ 8.65109i 0.557265i 0.960398 + 0.278633i $$0.0898812\pi$$
−0.960398 + 0.278633i $$0.910119\pi$$
$$242$$ 0 0
$$243$$ −2.89359 + 2.89359i −0.185624 + 0.185624i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 9.10289 9.10289i 0.579203 0.579203i
$$248$$ 0 0
$$249$$ 43.7998i 2.77570i
$$250$$ 0 0
$$251$$ 11.0974i 0.700459i −0.936664 0.350230i $$-0.886104\pi$$
0.936664 0.350230i $$-0.113896\pi$$
$$252$$ 0 0
$$253$$ −14.0385 14.0385i −0.882591 0.882591i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 1.62391 + 1.62391i 0.101297 + 0.101297i 0.755939 0.654642i $$-0.227181\pi$$
−0.654642 + 0.755939i $$0.727181\pi$$
$$258$$ 0 0
$$259$$ 15.0913 10.1276i 0.937729 0.629300i
$$260$$ 0 0
$$261$$ −41.7280 −2.58290
$$262$$ 0 0
$$263$$ 20.7161 + 20.7161i 1.27741 + 1.27741i 0.942111 + 0.335301i $$0.108838\pi$$
0.335301 + 0.942111i $$0.391162\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −7.19003 + 7.19003i −0.440023 + 0.440023i
$$268$$ 0 0
$$269$$ 31.0977 1.89606 0.948031 0.318179i $$-0.103071\pi$$
0.948031 + 0.318179i $$0.103071\pi$$
$$270$$ 0 0
$$271$$ 9.24962i 0.561875i 0.959726 + 0.280937i $$0.0906453\pi$$
−0.959726 + 0.280937i $$0.909355\pi$$
$$272$$ 0 0
$$273$$ −3.63139 + 18.4499i −0.219782 + 1.11664i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 14.3476 14.3476i 0.862066 0.862066i −0.129512 0.991578i $$-0.541341\pi$$
0.991578 + 0.129512i $$0.0413410\pi$$
$$278$$ 0 0
$$279$$ −1.00316 −0.0600574
$$280$$ 0 0
$$281$$ 12.3108 0.734402 0.367201 0.930142i $$-0.380316\pi$$
0.367201 + 0.930142i $$0.380316\pi$$
$$282$$ 0 0
$$283$$ 7.14401 7.14401i 0.424667 0.424667i −0.462140 0.886807i $$-0.652918\pi$$
0.886807 + 0.462140i $$0.152918\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0.374310 1.90174i 0.0220948 0.112256i
$$288$$ 0 0
$$289$$ 2.75003i 0.161766i
$$290$$ 0 0
$$291$$ 5.89727 0.345704
$$292$$ 0 0
$$293$$ −10.8037 + 10.8037i −0.631156 + 0.631156i −0.948358 0.317202i $$-0.897257\pi$$
0.317202 + 0.948358i $$0.397257\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −22.8079 22.8079i −1.32345 1.32345i
$$298$$ 0 0
$$299$$ 12.0735 0.698230
$$300$$ 0 0
$$301$$ 17.1009 + 25.4823i 0.985680 + 1.46878i
$$302$$ 0 0
$$303$$ −25.4872 25.4872i −1.46420 1.46420i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −21.5142 21.5142i −1.22788 1.22788i −0.964765 0.263113i $$-0.915251\pi$$
−0.263113 0.964765i $$-0.584749\pi$$
$$308$$ 0 0
$$309$$ 39.8653i 2.26786i
$$310$$ 0 0
$$311$$ 15.8682i 0.899802i −0.893078 0.449901i $$-0.851459\pi$$
0.893078 0.449901i $$-0.148541\pi$$
$$312$$ 0 0
$$313$$ 16.6132 16.6132i 0.939036 0.939036i −0.0592093 0.998246i $$-0.518858\pi$$
0.998246 + 0.0592093i $$0.0188579\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 9.53714 9.53714i 0.535659 0.535659i −0.386592 0.922251i $$-0.626348\pi$$
0.922251 + 0.386592i $$0.126348\pi$$
$$318$$ 0 0
$$319$$ 28.6059i 1.60162i
$$320$$ 0 0
$$321$$ 37.6271i 2.10014i
$$322$$ 0 0
$$323$$ 14.3100 + 14.3100i 0.796230 + 0.796230i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 8.08400 + 8.08400i 0.447046 + 0.447046i
$$328$$ 0 0
$$329$$ 4.83129 + 7.19917i 0.266357 + 0.396903i
$$330$$ 0 0
$$331$$ 12.9177 0.710021 0.355011 0.934862i $$-0.384477\pi$$
0.355011 + 0.934862i $$0.384477\pi$$
$$332$$ 0 0
$$333$$ −27.9783 27.9783i −1.53320 1.53320i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 7.12871 7.12871i 0.388326 0.388326i −0.485764 0.874090i $$-0.661459\pi$$
0.874090 + 0.485764i $$0.161459\pi$$
$$338$$ 0 0
$$339$$ −12.3279 −0.669559
$$340$$ 0 0
$$341$$ 0.687696i 0.0372408i
$$342$$ 0 0
$$343$$ 15.4608 + 10.1963i 0.834803 + 0.550549i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.28294 1.28294i 0.0688717 0.0688717i −0.671832 0.740704i $$-0.734492\pi$$
0.740704 + 0.671832i $$0.234492\pi$$
$$348$$ 0 0
$$349$$ 14.4635 0.774213 0.387106 0.922035i $$-0.373475\pi$$
0.387106 + 0.922035i $$0.373475\pi$$
$$350$$ 0 0
$$351$$ 19.6156 1.04700
$$352$$ 0 0
$$353$$ −1.19731 + 1.19731i −0.0637263 + 0.0637263i −0.738252 0.674525i $$-0.764348\pi$$
0.674525 + 0.738252i $$0.264348\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −29.0037 5.70864i −1.53504 0.302133i
$$358$$ 0 0
$$359$$ 27.1832i 1.43467i −0.696726 0.717337i $$-0.745361\pi$$
0.696726 0.717337i $$-0.254639\pi$$
$$360$$ 0 0
$$361$$ 9.74058 0.512662
$$362$$ 0 0
$$363$$ −9.60974 + 9.60974i −0.504380 + 0.504380i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −18.0535 18.0535i −0.942383 0.942383i 0.0560450 0.998428i $$-0.482151\pi$$
−0.998428 + 0.0560450i $$0.982151\pi$$
$$368$$ 0 0
$$369$$ −4.21965 −0.219666
$$370$$ 0 0
$$371$$ −9.45441 14.0882i −0.490849 0.731421i
$$372$$ 0 0
$$373$$ 23.4769 + 23.4769i 1.21559 + 1.21559i 0.969161 + 0.246430i $$0.0792574\pi$$
0.246430 + 0.969161i $$0.420743\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −12.3010 12.3010i −0.633533 0.633533i
$$378$$ 0 0
$$379$$ 32.9476i 1.69241i 0.532861 + 0.846203i $$0.321117\pi$$
−0.532861 + 0.846203i $$0.678883\pi$$
$$380$$ 0 0
$$381$$ 7.27092i 0.372501i
$$382$$ 0 0
$$383$$ −12.6328 + 12.6328i −0.645506 + 0.645506i −0.951904 0.306398i $$-0.900876\pi$$
0.306398 + 0.951904i $$0.400876\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 47.2425 47.2425i 2.40147 2.40147i
$$388$$ 0 0
$$389$$ 3.77597i 0.191449i 0.995408 + 0.0957246i $$0.0305168\pi$$
−0.995408 + 0.0957246i $$0.969483\pi$$
$$390$$ 0 0
$$391$$ 18.9799i 0.959856i
$$392$$ 0 0
$$393$$ −5.65685 5.65685i −0.285351 0.285351i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −16.0271 16.0271i −0.804375 0.804375i 0.179401 0.983776i $$-0.442584\pi$$
−0.983776 + 0.179401i $$0.942584\pi$$
$$398$$ 0 0
$$399$$ −34.8586 + 23.3932i −1.74511 + 1.17113i
$$400$$ 0 0
$$401$$ 3.52985 0.176272 0.0881362 0.996108i $$-0.471909\pi$$
0.0881362 + 0.996108i $$0.471909\pi$$
$$402$$ 0 0
$$403$$ −0.295720 0.295720i −0.0147309 0.0147309i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −19.1800 + 19.1800i −0.950717 + 0.950717i
$$408$$ 0 0
$$409$$ 5.07318 0.250852 0.125426 0.992103i $$-0.459970\pi$$
0.125426 + 0.992103i $$0.459970\pi$$
$$410$$ 0 0
$$411$$ 13.6794i 0.674754i
$$412$$ 0 0
$$413$$ −34.2415 6.73957i −1.68491 0.331632i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −44.9204 + 44.9204i −2.19976 + 2.19976i
$$418$$ 0 0
$$419$$ −9.44663 −0.461498 −0.230749 0.973013i $$-0.574118\pi$$
−0.230749 + 0.973013i $$0.574118\pi$$
$$420$$ 0 0
$$421$$ 30.4827 1.48564 0.742818 0.669493i $$-0.233489\pi$$
0.742818 + 0.669493i $$0.233489\pi$$
$$422$$ 0 0
$$423$$ 13.3468 13.3468i 0.648942 0.648942i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −6.82398 + 34.6704i −0.330236 + 1.67782i
$$428$$ 0 0
$$429$$ 28.0637i 1.35493i
$$430$$ 0 0
$$431$$ −11.4845 −0.553191 −0.276595 0.960987i $$-0.589206\pi$$
−0.276595 + 0.960987i $$0.589206\pi$$
$$432$$ 0 0
$$433$$ 26.8641 26.8641i 1.29101 1.29101i 0.356845 0.934164i $$-0.383852\pi$$
0.934164 0.356845i $$-0.116148\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 19.0599 + 19.0599i 0.911758 + 0.911758i
$$438$$ 0 0
$$439$$ −13.5387 −0.646166 −0.323083 0.946371i $$-0.604719\pi$$
−0.323083 + 0.946371i $$0.604719\pi$$
$$440$$ 0 0
$$441$$ 15.2799 37.3123i 0.727614 1.77677i
$$442$$ 0 0
$$443$$ −7.27325 7.27325i −0.345563 0.345563i 0.512891 0.858454i $$-0.328574\pi$$
−0.858454 + 0.512891i $$0.828574\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 4.38752 + 4.38752i 0.207523 + 0.207523i
$$448$$ 0 0
$$449$$ 4.85641i 0.229188i 0.993412 + 0.114594i $$0.0365567\pi$$
−0.993412 + 0.114594i $$0.963443\pi$$
$$450$$ 0 0
$$451$$ 2.89270i 0.136212i
$$452$$ 0 0
$$453$$ −3.72608 + 3.72608i −0.175066 + 0.175066i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −14.5716 + 14.5716i −0.681629 + 0.681629i −0.960367 0.278738i $$-0.910084\pi$$
0.278738 + 0.960367i $$0.410084\pi$$
$$458$$ 0 0
$$459$$ 30.8362i 1.43931i
$$460$$ 0 0
$$461$$ 7.19256i 0.334991i 0.985873 + 0.167495i $$0.0535680\pi$$
−0.985873 + 0.167495i $$0.946432\pi$$
$$462$$ 0 0
$$463$$ 3.74846 + 3.74846i 0.174206 + 0.174206i 0.788824 0.614619i $$-0.210690\pi$$
−0.614619 + 0.788824i $$0.710690\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −17.4030 17.4030i −0.805314 0.805314i 0.178607 0.983921i $$-0.442841\pi$$
−0.983921 + 0.178607i $$0.942841\pi$$
$$468$$ 0 0
$$469$$ −20.3706 + 13.6705i −0.940626 + 0.631244i
$$470$$ 0 0
$$471$$ −19.4437 −0.895917
$$472$$ 0 0
$$473$$ −32.3862 32.3862i −1.48912 1.48912i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −26.1185 + 26.1185i −1.19588 + 1.19588i
$$478$$ 0 0
$$479$$ −29.8582 −1.36426 −0.682129 0.731232i $$-0.738946\pi$$
−0.682129 + 0.731232i $$0.738946\pi$$
$$480$$ 0 0
$$481$$ 16.4954i 0.752125i
$$482$$ 0 0
$$483$$ −38.6308 7.60350i −1.75776 0.345971i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 18.7577 18.7577i 0.849993 0.849993i −0.140139 0.990132i $$-0.544755\pi$$
0.990132 + 0.140139i $$0.0447550\pi$$
$$488$$ 0 0
$$489$$ −7.00761 −0.316895
$$490$$ 0 0
$$491$$ 20.7440 0.936163 0.468081 0.883685i $$-0.344945\pi$$
0.468081 + 0.883685i $$0.344945\pi$$
$$492$$ 0 0
$$493$$ 19.3375 19.3375i 0.870917 0.870917i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 42.3950 + 8.34438i 1.90168 + 0.374297i
$$498$$ 0 0
$$499$$ 1.19553i 0.0535192i −0.999642 0.0267596i $$-0.991481\pi$$
0.999642 0.0267596i $$-0.00851886\pi$$
$$500$$ 0 0
$$501$$ 6.92820 0.309529
$$502$$ 0 0
$$503$$ −12.8461 + 12.8461i −0.572779 + 0.572779i −0.932904 0.360125i $$-0.882734\pi$$
0.360125 + 0.932904i $$0.382734\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −15.1391 15.1391i −0.672351 0.672351i
$$508$$ 0 0
$$509$$ −18.4311 −0.816943 −0.408471 0.912771i $$-0.633938\pi$$
−0.408471 + 0.912771i $$0.633938\pi$$
$$510$$ 0 0
$$511$$ −21.8274 + 14.6481i −0.965589 + 0.647996i
$$512$$ 0 0
$$513$$ 30.9661 + 30.9661i 1.36719 + 1.36719i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −9.14963 9.14963i −0.402400 0.402400i
$$518$$ 0 0
$$519$$ 3.97352i 0.174418i
$$520$$ 0 0
$$521$$ 30.4435i 1.33375i 0.745168 + 0.666877i $$0.232369\pi$$
−0.745168 + 0.666877i $$0.767631\pi$$
$$522$$ 0 0
$$523$$ −12.5460 + 12.5460i −0.548599 + 0.548599i −0.926036 0.377436i $$-0.876806\pi$$
0.377436 + 0.926036i $$0.376806\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0.464880 0.464880i 0.0202505 0.0202505i
$$528$$ 0 0
$$529$$ 2.27988i 0.0991254i
$$530$$ 0 0
$$531$$ 75.9760i 3.29708i
$$532$$ 0 0
$$533$$ −1.24391 1.24391i −0.0538796 0.0538796i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 34.9350 + 34.9350i 1.50756 + 1.50756i
$$538$$ 0 0
$$539$$ −25.5787 10.4748i −1.10175 0.451183i
$$540$$ 0 0
$$541$$ −20.0700 −0.862875 −0.431438 0.902143i $$-0.641994\pi$$
−0.431438 + 0.902143i $$0.641994\pi$$
$$542$$ 0 0
$$543$$ 39.0117 + 39.0117i 1.67415 + 1.67415i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −12.3298 + 12.3298i −0.527185 + 0.527185i −0.919732 0.392547i $$-0.871594\pi$$
0.392547 + 0.919732i $$0.371594\pi$$
$$548$$ 0 0
$$549$$ 76.9277 3.28319
$$550$$ 0 0
$$551$$ 38.8379i 1.65455i
$$552$$ 0 0
$$553$$ 3.38877 17.2172i 0.144105 0.732150i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −10.8455 + 10.8455i −0.459541 + 0.459541i −0.898505 0.438964i $$-0.855346\pi$$
0.438964 + 0.898505i $$0.355346\pi$$
$$558$$ 0 0
$$559$$ 27.8532 1.17806
$$560$$ 0 0
$$561$$ 44.1169 1.86262
$$562$$ 0 0
$$563$$ 29.8745 29.8745i 1.25906 1.25906i 0.307517 0.951542i $$-0.400502\pi$$
0.951542 0.307517i $$-0.0994982\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −17.9049 3.52413i −0.751937 0.148000i
$$568$$ 0 0
$$569$$ 16.2736i 0.682225i −0.940023 0.341112i $$-0.889196\pi$$
0.940023 0.341112i $$-0.110804\pi$$
$$570$$ 0 0
$$571$$ −24.0495 −1.00644 −0.503221 0.864158i $$-0.667852\pi$$
−0.503221 + 0.864158i $$0.667852\pi$$
$$572$$ 0 0
$$573$$ 9.07557 9.07557i 0.379137 0.379137i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −11.1701 11.1701i −0.465017 0.465017i 0.435278 0.900296i $$-0.356650\pi$$
−0.900296 + 0.435278i $$0.856650\pi$$
$$578$$ 0 0
$$579$$ −49.7611 −2.06800
$$580$$ 0 0
$$581$$ −32.5111 + 21.8179i −1.34879 + 0.905157i
$$582$$ 0 0
$$583$$ 17.9050 + 17.9050i 0.741551 + 0.741551i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 15.4617 + 15.4617i 0.638171 + 0.638171i 0.950104 0.311933i $$-0.100977\pi$$
−0.311933 + 0.950104i $$0.600977\pi$$
$$588$$ 0 0
$$589$$ 0.933678i 0.0384715i
$$590$$ 0 0
$$591$$ 11.9347i 0.490928i
$$592$$ 0 0
$$593$$ −32.5438 + 32.5438i −1.33641 + 1.33641i −0.436904 + 0.899508i $$0.643925\pi$$
−0.899508 + 0.436904i $$0.856075\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 9.08770 9.08770i 0.371935 0.371935i
$$598$$ 0 0
$$599$$ 21.7804i 0.889923i 0.895550 + 0.444961i $$0.146783\pi$$
−0.895550 + 0.444961i $$0.853217\pi$$
$$600$$ 0 0
$$601$$ 19.8736i 0.810660i −0.914170 0.405330i $$-0.867157\pi$$
0.914170 0.405330i $$-0.132843\pi$$
$$602$$ 0 0
$$603$$ 37.7657 + 37.7657i 1.53794 + 1.53794i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −6.80167 6.80167i −0.276071 0.276071i 0.555467 0.831538i $$-0.312539\pi$$
−0.831538 + 0.555467i $$0.812539\pi$$
$$608$$ 0 0
$$609$$ 31.6119 + 47.1054i 1.28098 + 1.90881i
$$610$$ 0 0
$$611$$ 7.86898 0.318345
$$612$$ 0 0
$$613$$ −13.0751 13.0751i −0.528098 0.528098i 0.391907 0.920005i $$-0.371815\pi$$
−0.920005 + 0.391907i $$0.871815\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −21.6256 + 21.6256i −0.870614 + 0.870614i −0.992539 0.121925i $$-0.961093\pi$$
0.121925 + 0.992539i $$0.461093\pi$$
$$618$$ 0 0
$$619$$ 42.9528 1.72642 0.863210 0.504845i $$-0.168451\pi$$
0.863210 + 0.504845i $$0.168451\pi$$
$$620$$ 0 0
$$621$$ 41.0716i 1.64815i
$$622$$ 0 0
$$623$$ 8.91847 + 1.75537i 0.357311 + 0.0703276i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 44.3028 44.3028i 1.76928 1.76928i
$$628$$ 0 0
$$629$$ 25.9312 1.03395
$$630$$ 0 0
$$631$$ −22.7175 −0.904370 −0.452185 0.891924i $$-0.649355\pi$$
−0.452185 + 0.891924i $$0.649355\pi$$
$$632$$ 0 0
$$633$$ 39.4212 39.4212i 1.56685 1.56685i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 15.5036 6.49492i 0.614276 0.257338i
$$638$$ 0 0
$$639$$ 94.0674i 3.72125i
$$640$$ 0 0
$$641$$ −26.0435 −1.02866 −0.514328 0.857594i $$-0.671959\pi$$
−0.514328 + 0.857594i $$0.671959\pi$$
$$642$$ 0 0
$$643$$ 12.7907 12.7907i 0.504416 0.504416i −0.408391 0.912807i $$-0.633910\pi$$
0.912807 + 0.408391i $$0.133910\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.81311 + 1.81311i 0.0712805 + 0.0712805i 0.741848 0.670568i $$-0.233949\pi$$
−0.670568 + 0.741848i $$0.733949\pi$$
$$648$$ 0 0
$$649$$ 52.0840 2.04447
$$650$$ 0 0
$$651$$ 0.759961 + 1.13243i 0.0297852 + 0.0443834i
$$652$$ 0 0
$$653$$ −21.4676 21.4676i −0.840092 0.840092i 0.148778 0.988871i $$-0.452466\pi$$
−0.988871 + 0.148778i $$0.952466\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 40.4665 + 40.4665i 1.57875 + 1.57875i
$$658$$ 0 0
$$659$$ 27.6423i 1.07679i −0.842692 0.538396i $$-0.819031\pi$$
0.842692 0.538396i $$-0.180969\pi$$
$$660$$ 0 0
$$661$$ 7.38292i 0.287162i 0.989639 + 0.143581i $$0.0458618\pi$$
−0.989639 + 0.143581i $$0.954138\pi$$
$$662$$ 0 0
$$663$$ −18.9710 + 18.9710i −0.736772 + 0.736772i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 25.7561 25.7561i 0.997281 0.997281i
$$668$$ 0 0
$$669$$ 58.2781i 2.25316i
$$670$$ 0 0
$$671$$ 52.7363i 2.03586i
$$672$$ 0 0
$$673$$ 12.4963 + 12.4963i 0.481697 + 0.481697i 0.905673 0.423976i $$-0.139366\pi$$
−0.423976 + 0.905673i $$0.639366\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 27.0753 + 27.0753i 1.04059 + 1.04059i 0.999141 + 0.0414483i $$0.0131972\pi$$
0.0414483 + 0.999141i $$0.486803\pi$$
$$678$$ 0 0
$$679$$ −2.93759 4.37735i −0.112734 0.167987i
$$680$$ 0 0
$$681$$ −28.9565 −1.10962
$$682$$ 0 0
$$683$$ −17.7113 17.7113i −0.677704 0.677704i 0.281776 0.959480i $$-0.409076\pi$$
−0.959480 + 0.281776i $$0.909076\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −3.44604 + 3.44604i −0.131474 + 0.131474i
$$688$$ 0 0
$$689$$ −15.3989 −0.586652
$$690$$ 0 0
$$691$$ 2.75386i 0.104762i 0.998627 + 0.0523810i $$0.0166810\pi$$
−0.998627 + 0.0523810i $$0.983319\pi$$
$$692$$ 0 0
$$693$$ −11.6209 + 59.0422i −0.441443 + 2.24283i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 1.95546 1.95546i 0.0740683 0.0740683i
$$698$$ 0 0
$$699$$ −19.8017 −0.748968
$$700$$ 0 0
$$701$$ −1.66352 −0.0628301 −0.0314151 0.999506i $$-0.510001\pi$$
−0.0314151 + 0.999506i $$0.510001\pi$$
$$702$$ 0 0
$$703$$ 26.0405 26.0405i 0.982135 0.982135i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −6.22244 + 31.6141i −0.234019 + 1.18897i
$$708$$ 0 0
$$709$$ 28.7442i 1.07951i 0.841822 + 0.539756i $$0.181484\pi$$
−0.841822 + 0.539756i $$0.818516\pi$$
$$710$$ 0 0
$$711$$ −38.2020 −1.43269
$$712$$ 0 0
$$713$$ 0.619187 0.619187i 0.0231887 0.0231887i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 10.8481 + 10.8481i 0.405130 + 0.405130i
$$718$$ 0 0
$$719$$ −42.1059 −1.57029 −0.785143 0.619314i $$-0.787411\pi$$
−0.785143 + 0.619314i $$0.787411\pi$$
$$720$$ 0 0
$$721$$ 29.5907 19.8580i 1.10202 0.739550i
$$722$$ 0 0
$$723$$ −18.1053 18.1053i −0.673345 0.673345i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −15.6639 15.6639i −0.580943 0.580943i 0.354219 0.935162i $$-0.384747\pi$$
−0.935162 + 0.354219i $$0.884747\pi$$
$$728$$ 0 0
$$729$$ 32.8035i 1.21494i
$$730$$ 0 0
$$731$$ 43.7860i 1.61948i
$$732$$ 0 0
$$733$$ −3.73703 + 3.73703i −0.138031 + 0.138031i −0.772746 0.634715i $$-0.781117\pi$$
0.634715 + 0.772746i $$0.281117\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 25.8895 25.8895i 0.953654 0.953654i
$$738$$ 0 0
$$739$$ 14.2445i 0.523993i −0.965069 0.261997i $$-0.915619\pi$$
0.965069 0.261997i $$-0.0843809\pi$$
$$740$$ 0 0
$$741$$ 38.1018i 1.39970i
$$742$$ 0 0
$$743$$ −4.30083 4.30083i −0.157782 0.157782i 0.623801 0.781583i $$-0.285588\pi$$
−0.781583 + 0.623801i $$0.785588\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 60.2734 + 60.2734i 2.20529 + 2.20529i
$$748$$ 0 0
$$749$$ −27.9294 + 18.7431i −1.02052 + 0.684857i
$$750$$ 0 0
$$751$$ −28.2906 −1.03234 −0.516170 0.856486i $$-0.672643\pi$$
−0.516170 + 0.856486i $$0.672643\pi$$
$$752$$ 0 0
$$753$$ 23.2250 + 23.2250i 0.846366 + 0.846366i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 15.1132 15.1132i 0.549299 0.549299i −0.376939 0.926238i $$-0.623023\pi$$
0.926238 + 0.376939i $$0.123023\pi$$
$$758$$ 0 0
$$759$$ 58.7605 2.13287
$$760$$ 0 0
$$761$$ 23.7113i 0.859533i −0.902940 0.429766i $$-0.858596\pi$$
0.902940 0.429766i $$-0.141404\pi$$
$$762$$ 0 0
$$763$$ 1.97363 10.0273i 0.0714501 0.363014i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −22.3969 + 22.3969i −0.808706 + 0.808706i
$$768$$ 0 0
$$769$$ −27.3228 −0.985286 −0.492643 0.870232i $$-0.663969\pi$$
−0.492643 + 0.870232i $$0.663969\pi$$
$$770$$ 0 0
$$771$$ −6.79718 −0.244794
$$772$$ 0 0
$$773$$ −7.79374 + 7.79374i −0.280321 + 0.280321i −0.833237 0.552916i $$-0.813515\pi$$
0.552916 + 0.833237i $$0.313515\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −10.3882 + 52.7792i −0.372676 + 1.89344i
$$778$$ 0 0
$$779$$ 3.92739i 0.140713i
$$780$$ 0 0
$$781$$ −64.4861 −2.30750
$$782$$ 0 0
$$783$$ 41.8453 41.8453i 1.49543 1.49543i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 6.99375 + 6.99375i 0.249300 + 0.249300i 0.820683 0.571383i $$-0.193593\pi$$
−0.571383 + 0.820683i $$0.693593\pi$$
$$788$$ 0 0
$$789$$ −86.7112 −3.08700
$$790$$ 0 0
$$791$$ 6.14086 + 9.15059i 0.218344 + 0.325357i
$$792$$ 0 0
$$793$$ 22.6775 + 22.6775i 0.805300 + 0.805300i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −14.1365 14.1365i −0.500740 0.500740i 0.410928 0.911668i $$-0.365205\pi$$
−0.911668 + 0.410928i $$0.865205\pi$$
$$798$$ 0 0
$$799$$ 12.3703i 0.437628i
$$800$$ 0 0
$$801$$ 19.7886i 0.699195i
$$802$$ 0 0
$$803$$ 27.7411 27.7411i 0.978962 0.978962i
$$804$$ 0 0 <